LMFDB - Embedded newform 57.3.g.b.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,3,Mod(31,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, 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("57.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	57.g (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:	$1.55313750685$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.2
Root			$0.500000 - 0.630453i$ of defining polynomial
Character	$\chi$	$=$	57.46
Dual form			57.3.g.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.204011 + 0.117786i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.97225 - 3.41604i) q^{4} +(2.88028 - 4.98878i) q^{5} +(-0.204011 - 0.353358i) q^{6} +1.94451 q^{7} -1.87150i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.204011 + 0.117786i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.97225 - 3.41604i) q^{4} +(2.88028 - 4.98878i) q^{5} +(-0.204011 - 0.353358i) q^{6} +1.94451 q^{7} -1.87150i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.17522 - 0.678513i) q^{10} +8.46561 q^{11} +6.83208i q^{12} +(-16.7415 + 9.66573i) q^{13} +(0.396701 + 0.229036i) q^{14} +(-8.64083 + 4.98878i) q^{15} +(-7.66857 + 13.2824i) q^{16} +(12.5365 - 21.7138i) q^{17} +0.706716i q^{18} +(17.8181 + 6.59651i) q^{19} -22.7225 q^{20} +(-2.91676 - 1.68399i) q^{21} +(1.72708 + 0.997131i) q^{22} +(15.6408 + 27.0907i) q^{23} +(-1.62077 + 2.80726i) q^{24} +(-4.09198 - 7.08751i) q^{25} -4.55395 q^{26} -5.19615i q^{27} +(-3.83506 - 6.64251i) q^{28} +(13.7071 - 7.91383i) q^{29} -2.35044 q^{30} +14.4237i q^{31} +(-9.61203 + 5.54951i) q^{32} +(-12.6984 - 7.33143i) q^{33} +(5.11517 - 2.95325i) q^{34} +(5.60071 - 9.70072i) q^{35} +(5.91676 - 10.2481i) q^{36} -41.6423i q^{37} +(2.85813 + 3.44449i) q^{38} +33.4831 q^{39} +(-9.33653 - 5.39045i) q^{40} +(1.53439 + 0.885881i) q^{41} +(-0.396701 - 0.687107i) q^{42} +(14.4358 - 25.0035i) q^{43} +(-16.6963 - 28.9189i) q^{44} +17.2817 q^{45} +7.36909i q^{46} +(1.70506 + 2.95325i) q^{47} +(23.0057 - 13.2824i) q^{48} -45.2189 q^{49} -1.92791i q^{50} +(-37.6094 + 21.7138i) q^{51} +(66.0371 + 38.1265i) q^{52} +(-80.0952 + 46.2430i) q^{53} +(0.612034 - 1.06007i) q^{54} +(24.3833 - 42.2331i) q^{55} -3.63915i q^{56} +(-21.0145 - 25.3257i) q^{57} +3.72855 q^{58} +(4.27292 + 2.46697i) q^{59} +(34.0838 + 19.6783i) q^{60} +(7.45989 + 12.9209i) q^{61} +(-1.69891 + 2.94259i) q^{62} +(2.91676 + 5.05197i) q^{63} +58.7340 q^{64} +111.360i q^{65} +(-1.72708 - 2.99139i) q^{66} +(-70.4113 + 40.6520i) q^{67} -98.9005 q^{68} -54.1814i q^{69} +(2.28522 - 1.31937i) q^{70} +(52.9948 + 30.5966i) q^{71} +(4.86231 - 2.80726i) q^{72} +(-38.8299 + 67.2553i) q^{73} +(4.90489 - 8.49551i) q^{74} +14.1750i q^{75} +(-12.6079 - 73.8775i) q^{76} +16.4614 q^{77} +(6.83093 + 3.94384i) q^{78} +(84.0207 + 48.5094i) q^{79} +(44.1752 + 76.5137i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.208689 + 0.361460i) q^{82} -102.323 q^{83} +13.2850i q^{84} +(-72.2171 - 125.084i) q^{85} +(5.89012 - 3.40067i) q^{86} -27.4143 q^{87} -15.8434i q^{88} +(103.596 - 59.8111i) q^{89} +(3.52566 + 2.03554i) q^{90} +(-32.5540 + 18.7951i) q^{91} +(61.6953 - 106.859i) q^{92} +(12.4913 - 21.6355i) q^{93} +0.803328i q^{94} +(84.2297 - 69.8911i) q^{95} +19.2241 q^{96} +(-42.1438 - 24.3318i) q^{97} +(-9.22517 - 5.32616i) q^{98} +(12.6984 + 21.9943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.204011	+	0.117786i	0.102006	+	0.0588930i	0.550135	−	0.835076i	$-0.314576\pi$
$2$	0.204011	+	0.117786i	0.102006	+	0.0588930i	−0.448129	+	0.893969i	$0.647910\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.97225	−	3.41604i	−0.493063	−	0.854011i
$5$	2.88028	−	4.98878i	0.576055	−	0.997757i	−0.419871	−	0.907584i	$-0.637925\pi$
$5$	2.88028	−	4.98878i	0.576055	−	0.997757i	0.995926	−	0.0901730i	$-0.0287420\pi$
$6$	−0.204011	−	0.353358i	−0.0340019	−	0.0588930i
$7$	1.94451			0.277787			0.138893	−	0.990307i	$-0.455646\pi$
$7$	1.94451			0.277787			0.138893	+	0.990307i	$0.455646\pi$
$8$		−	1.87150i		−	0.233938i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	1.17522	−	0.678513i	0.117522	−	0.0678513i
$11$	8.46561			0.769601			0.384800	−	0.923000i	$-0.374270\pi$
$11$	8.46561			0.769601			0.384800	+	0.923000i	$0.374270\pi$
$12$			6.83208i			0.569340i
$13$	−16.7415	+	9.66573i	−1.28781	+	0.743518i	−0.978263	−	0.207366i	$-0.933511\pi$
$13$	−16.7415	+	9.66573i	−1.28781	+	0.743518i	−0.309547	+	0.950884i	$0.600178\pi$
$14$	0.396701	+	0.229036i	0.0283358	+	0.0163597i
$15$	−8.64083	+	4.98878i	−0.576055	+	0.332586i
$16$	−7.66857	+	13.2824i	−0.479286	+	0.830148i
$17$	12.5365	−	21.7138i	0.737440	−	1.27728i	−0.216204	−	0.976348i	$-0.569368\pi$
$17$	12.5365	−	21.7138i	0.737440	−	1.27728i	0.953644	−	0.300936i	$-0.0972990\pi$
$18$			0.706716i			0.0392620i
$19$	17.8181	+	6.59651i	0.937797	+	0.347185i
$19$	17.8181	+	6.59651i	0.937797	+	0.347185i
$20$	−22.7225			−1.13613
$21$	−2.91676	−	1.68399i	−0.138893	−	0.0801901i
$22$	1.72708	+	0.997131i	0.0785037	+	0.0453241i
$23$	15.6408	+	27.0907i	0.680036	+	1.17786i	0.974969	+	0.222339i	$0.0713692\pi$
$23$	15.6408	+	27.0907i	0.680036	+	1.17786i	−0.294933	+	0.955518i	$0.595297\pi$
$24$	−1.62077	+	2.80726i	−0.0675321	+	0.116969i
$25$	−4.09198	−	7.08751i	−0.163679	−	0.283500i
$26$	−4.55395			−0.175152
$27$		−	5.19615i		−	0.192450i
$28$	−3.83506	−	6.64251i	−0.136966	−	0.237233i
$29$	13.7071	−	7.91383i	0.472660	−	0.272891i	−0.244692	−	0.969601i	$-0.578687\pi$
$29$	13.7071	−	7.91383i	0.472660	−	0.272891i	0.717353	+	0.696710i	$0.245354\pi$
$30$	−2.35044			−0.0783479
$31$			14.4237i			0.465280i	0.972563	+	0.232640i	$0.0747363\pi$
$31$			14.4237i			0.465280i	−0.972563	+	0.232640i	$0.925264\pi$
$32$	−9.61203	+	5.54951i	−0.300376	+	0.173422i
$33$	−12.6984	−	7.33143i	−0.384800	−	0.222165i
$34$	5.11517	−	2.95325i	0.150446	−	0.0868602i
$35$	5.60071	−	9.70072i	0.160020	−	0.277163i
$36$	5.91676	−	10.2481i	0.164354	−	0.284670i
$37$		−	41.6423i		−	1.12547i	−0.826638	−	0.562734i	$-0.809749\pi$
$37$		−	41.6423i		−	1.12547i	0.826638	−	0.562734i	$-0.190251\pi$
$38$	2.85813	+	3.44449i	0.0752139	+	0.0906445i
$39$	33.4831			0.858541
$40$	−9.33653	−	5.39045i	−0.233413	−	0.134761i
$41$	1.53439	+	0.885881i	0.0374242	+	0.0216069i	0.518595	−	0.855020i	$-0.326455\pi$
$41$	1.53439	+	0.885881i	0.0374242	+	0.0216069i	−0.481171	+	0.876627i	$0.659788\pi$
$42$	−0.396701	−	0.687107i	−0.00944527	−	0.0163597i
$43$	14.4358	−	25.0035i	0.335716	−	0.581476i	−0.647906	−	0.761720i	$-0.724355\pi$
$43$	14.4358	−	25.0035i	0.335716	−	0.581476i	0.983622	+	0.180243i	$0.0576886\pi$
$44$	−16.6963	−	28.9189i	−0.379462	−	0.657247i
$45$	17.2817			0.384037
$46$			7.36909i			0.160198i
$47$	1.70506	+	2.95325i	0.0362778	+	0.0628350i	0.883594	−	0.468253i	$-0.155117\pi$
$47$	1.70506	+	2.95325i	0.0362778	+	0.0628350i	−0.847316	+	0.531088i	$0.821783\pi$
$48$	23.0057	−	13.2824i	0.479286	−	0.276716i
$49$	−45.2189			−0.922835
$50$		−	1.92791i		−	0.0385582i
$51$	−37.6094	+	21.7138i	−0.737440	+	0.425761i
$52$	66.0371	+	38.1265i	1.26994	+	0.733203i
$53$	−80.0952	+	46.2430i	−1.51123	+	0.872510i	−0.511317	+	0.859392i	$0.670842\pi$
$53$	−80.0952	+	46.2430i	−1.51123	+	0.872510i	−0.999914	+	0.0131174i	$0.995824\pi$
$54$	0.612034	−	1.06007i	0.0113340	−	0.0196310i
$55$	24.3833	−	42.2331i	0.443333	−	0.767874i
$56$		−	3.63915i		−	0.0649848i
$57$	−21.0145	−	25.3257i	−0.368675	−	0.444311i
$58$	3.72855			0.0642854
$59$	4.27292	+	2.46697i	0.0724224	+	0.0418131i	0.535774	−	0.844361i	$-0.320020\pi$
$59$	4.27292	+	2.46697i	0.0724224	+	0.0418131i	−0.463352	+	0.886175i	$0.653353\pi$
$60$	34.0838	+	19.6783i	0.568063	+	0.327971i
$61$	7.45989	+	12.9209i	0.122293	+	0.211818i	0.920672	−	0.390338i	$-0.127642\pi$
$61$	7.45989	+	12.9209i	0.122293	+	0.211818i	−0.798378	+	0.602156i	$0.794309\pi$
$62$	−1.69891	+	2.94259i	−0.0274017	+	0.0474612i
$63$	2.91676	+	5.05197i	0.0462978	+	0.0801901i
$64$	58.7340			0.917718
$65$			111.360i			1.71323i
$66$	−1.72708	−	2.99139i	−0.0261679	−	0.0453241i
$67$	−70.4113	+	40.6520i	−1.05091	+	0.606746i	−0.922905	−	0.385027i	$-0.874192\pi$
$67$	−70.4113	+	40.6520i	−1.05091	+	0.606746i	−0.128009	+	0.991773i	$0.540859\pi$
$68$	−98.9005			−1.45442
$69$		−	54.1814i		−	0.785238i
$70$	2.28522	−	1.31937i	0.0326460	−	0.0188482i
$71$	52.9948	+	30.5966i	0.746406	+	0.430938i	0.824394	−	0.566017i	$-0.191516\pi$
$71$	52.9948	+	30.5966i	0.746406	+	0.430938i	−0.0779878	+	0.996954i	$0.524850\pi$
$72$	4.86231	−	2.80726i	0.0675321	−	0.0389897i
$73$	−38.8299	+	67.2553i	−0.531916	+	0.921306i	0.467390	+	0.884051i	$0.345195\pi$
$73$	−38.8299	+	67.2553i	−0.531916	+	0.921306i	−0.999306	+	0.0372545i	$0.988139\pi$
$74$	4.90489	−	8.49551i	0.0662822	−	0.114804i
$75$			14.1750i			0.189000i
$76$	−12.6079	−	73.8775i	−0.165894	−	0.972072i
$77$	16.4614			0.213785
$78$	6.83093	+	3.94384i	0.0875760	+	0.0505621i
$79$	84.0207	+	48.5094i	1.06355	+	0.614043i	0.926413	−	0.376509i	$-0.122875\pi$
$79$	84.0207	+	48.5094i	1.06355	+	0.614043i	0.137140	+	0.990552i	$0.456209\pi$
$80$	44.1752	+	76.5137i	0.552190	+	0.956422i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	0.208689	+	0.361460i	0.00254499	+	0.00440805i
$83$	−102.323			−1.23280			−0.616401	−	0.787432i	$-0.711410\pi$
$83$	−102.323			−1.23280			−0.616401	+	0.787432i	$0.711410\pi$
$84$			13.2850i			0.158155i
$85$	−72.2171	−	125.084i	−0.849612	−	1.47157i
$86$	5.89012	−	3.40067i	0.0684898	−	0.0395426i
$87$	−27.4143			−0.315107
$88$		−	15.8434i		−	0.180039i
$89$	103.596	−	59.8111i	1.16400	−	0.672034i	0.211739	−	0.977326i	$-0.432087\pi$
$89$	103.596	−	59.8111i	1.16400	−	0.672034i	0.952259	+	0.305292i	$0.0987540\pi$
$90$	3.52566	+	2.03554i	0.0391739	+	0.0226171i
$91$	−32.5540	+	18.7951i	−0.357737	+	0.206539i
$92$	61.6953	−	106.859i	0.670601	−	1.16152i
$93$	12.4913	−	21.6355i	0.134315	−	0.232640i
$94$			0.803328i			0.00854604i
$95$	84.2297	−	69.8911i	0.886629	−	0.735695i
$96$	19.2241			0.200251
$97$	−42.1438	−	24.3318i	−0.434473	−	0.250843i	0.266778	−	0.963758i	$-0.414041\pi$
$97$	−42.1438	−	24.3318i	−0.434473	−	0.250843i	−0.701250	+	0.712915i	$0.747374\pi$
$98$	−9.22517	−	5.32616i	−0.0941344	−	0.0543485i
$99$	12.6984	+	21.9943i	0.128267	+	0.222165i
$100$	−16.1408	+	27.9567i	−0.161408	+	0.279567i
$101$	−81.5540	−	141.256i	−0.807465	−	1.39857i	−0.914614	−	0.404327i	$-0.867506\pi$
$101$	−81.5540	−	141.256i	−0.807465	−	1.39857i	0.107149	−	0.994243i	$-0.465828\pi$
$102$	−10.2303			−0.100297
$103$			18.2732i			0.177410i	0.996058	+	0.0887050i	$0.0282728\pi$
$103$			18.2732i			0.177410i	−0.996058	+	0.0887050i	$0.971727\pi$
$104$	18.0895	+	31.3319i	0.173937	+	0.301268i
$105$	−16.8021	+	9.70072i	−0.160020	+	0.0923878i
$106$	−21.7871			−0.205539
$107$			55.4789i			0.518494i	0.965811	+	0.259247i	$0.0834744\pi$
$107$			55.4789i			0.518494i	−0.965811	+	0.259247i	$0.916526\pi$
$108$	−17.7503	+	10.2481i	−0.164354	+	0.0948901i
$109$	96.4369	+	55.6779i	0.884743	+	0.510806i	0.872219	−	0.489115i	$-0.162680\pi$
$109$	96.4369	+	55.6779i	0.884743	+	0.510806i	0.0125234	+	0.999922i	$0.496014\pi$
$110$	9.94894	−	5.74402i	0.0904449	−	0.0522184i
$111$	−36.0633	+	62.4635i	−0.324895	+	0.562734i
$112$	−14.9116	+	25.8276i	−0.133139	+	0.230604i
$113$		−	110.968i		−	0.982019i	−0.871154	−	0.491010i	$-0.836628\pi$
$113$		−	110.968i		−	0.982019i	0.871154	−	0.491010i	$-0.163372\pi$
$114$	−1.30417	−	7.64195i	−0.0114401	−	0.0670346i
$115$	180.200			1.56695
$116$	−54.0679	−	31.2161i	−0.466103	−	0.269105i
$117$	−50.2246	−	28.9972i	−0.429270	−	0.247839i
$118$	0.581150	+	1.00658i	0.00492500	+	0.00853034i
$119$	24.3773	−	42.2227i	0.204851	−	0.354812i
$120$	9.33653	+	16.1713i	0.0778044	+	0.134761i
$121$	−49.3335			−0.407715
$122$			3.51468i			0.0288089i
$123$	−1.53439	−	2.65764i	−0.0124747	−	0.0216069i
$124$	49.2719	−	28.4471i	0.397354	−	0.229412i
$125$	96.8697			0.774958
$126$			1.37421i			0.0109065i
$127$	−209.627	+	121.028i	−1.65061	+	0.952979i	−0.673785	+	0.738927i	$0.735333\pi$
$127$	−209.627	+	121.028i	−1.65061	+	0.952979i	−0.976822	+	0.214052i	$0.931334\pi$
$128$	50.4305	+	29.1161i	0.393989	+	0.227469i
$129$	−43.3073	+	25.0035i	−0.335716	+	0.193825i
$130$	−13.1166	+	22.7187i	−0.100897	+	0.174759i
$131$	78.7288	−	136.362i	0.600983	−	1.04093i	−0.391689	−	0.920098i	$-0.628109\pi$
$131$	78.7288	−	136.362i	0.600983	−	1.04093i	0.992672	−	0.120836i	$-0.0385575\pi$
$132$			57.8378i			0.438165i
$133$	34.6475	+	12.8270i	0.260507	+	0.0964433i
$134$	−19.1529			−0.142932
$135$	−25.9225	−	14.9664i	−0.192018	−	0.110862i
$136$	−40.6375	−	23.4621i	−0.298805	−	0.172515i
$137$	121.173	+	209.877i	0.884473	+	1.53195i	0.846317	+	0.532680i	$0.178815\pi$
$137$	121.173	+	209.877i	0.884473	+	1.53195i	0.0381558	+	0.999272i	$0.487852\pi$
$138$	6.38182	−	11.0536i	0.0462450	−	0.0800988i
$139$	−65.0431	−	112.658i	−0.467936	−	0.810489i	0.531392	−	0.847126i	$-0.321669\pi$
$139$	−65.0431	−	112.658i	−0.467936	−	0.810489i	−0.999329	+	0.0366365i	$0.988336\pi$
$140$	−44.1841			−0.315601
$141$		−	5.90649i		−	0.0418900i
$142$	7.20770	+	12.4841i	0.0507585	+	0.0879162i
$143$	−141.727	+	81.8263i	−0.991100	+	0.572212i
$144$	−46.0114			−0.319524
$145$		−	91.1760i		−	0.628800i
$146$	−15.8435	+	9.14724i	−0.108517	+	0.0626523i
$147$	67.8283	+	39.1607i	0.461417	+	0.266399i
$148$	−142.252	+	82.1292i	−0.961162	+	0.554927i
$149$	−102.368	+	177.306i	−0.687030	+	1.18997i	0.285764	+	0.958300i	$0.407753\pi$
$149$	−102.368	+	177.306i	−0.687030	+	1.18997i	−0.972794	+	0.231672i	$0.925581\pi$
$150$	−1.66962	+	2.89187i	−0.0111308	+	0.0192791i
$151$			234.305i			1.55169i	0.630924	+	0.775845i	$0.282676\pi$
$151$			234.305i			1.55169i	−0.630924	+	0.775845i	$0.717324\pi$
$152$	12.3454	−	33.3467i	0.0812197	−	0.219386i
$153$	75.2189			0.491627
$154$	3.35832	+	1.93893i	0.0218073	+	0.0125904i
$155$	71.9566	+	41.5441i	0.464236	+	0.268027i
$156$	−66.0371	−	114.380i	−0.423315	−	0.733203i
$157$	44.2955	−	76.7220i	0.282137	−	0.488675i	−0.689774	−	0.724025i	$-0.742290\pi$
$157$	44.2955	−	76.7220i	0.282137	−	0.488675i	0.971911	+	0.235349i	$0.0756234\pi$
$158$	11.4275	+	19.7929i	0.0723257	+	0.125272i
$159$	160.190			1.00749
$160$			63.9365i			0.399603i
$161$	30.4137	+	52.6780i	0.188905	+	0.327193i
$162$	−1.83610	+	1.06007i	−0.0113340	+	0.00654367i
$163$	115.918			0.711153			0.355576	−	0.934647i	$-0.384285\pi$
$163$	115.918			0.711153			0.355576	+	0.934647i	$0.384285\pi$
$164$		−	6.98873i		−	0.0426142i
$165$	−73.1499	+	42.2331i	−0.443333	+	0.255958i
$166$	−20.8750	−	12.0522i	−0.125753	−	0.0726035i
$167$	78.0426	−	45.0579i	0.467321	−	0.269808i	−0.247797	−	0.968812i	$-0.579707\pi$
$167$	78.0426	−	45.0579i	0.467321	−	0.269808i	0.715118	+	0.699004i	$0.246373\pi$
$168$	−3.15160	+	5.45873i	−0.0187595	+	0.0324924i
$169$	102.353	−	177.280i	0.605638	−	1.04900i
$170$		−	34.0247i		−	0.200145i
$171$	9.58896	+	56.1876i	0.0560758	+	0.328583i
$172$	−113.884			−0.662116
$173$	−38.5739	−	22.2707i	−0.222971	−	0.128732i	0.384354	−	0.923186i	$-0.374424\pi$
$173$	−38.5739	−	22.2707i	−0.222971	−	0.128732i	−0.607325	+	0.794454i	$0.707757\pi$
$174$	−5.59283	−	3.22902i	−0.0321427	−	0.0185576i
$175$	−7.95687	−	13.7817i	−0.0454678	−	0.0787526i
$176$	−64.9192	+	112.443i	−0.368859	+	0.638882i
$177$	−4.27292	−	7.40091i	−0.0241408	−	0.0418131i
$178$	28.1796			0.158313
$179$		−	229.632i		−	1.28286i	−0.767181	−	0.641431i	$-0.778341\pi$
$179$		−	229.632i		−	1.28286i	0.767181	−	0.641431i	$-0.221659\pi$
$180$	−34.0838	−	59.0349i	−0.189354	−	0.327971i
$181$	157.070	−	90.6845i	0.867791	−	0.501019i	0.00117734	−	0.999999i	$-0.499625\pi$
$181$	157.070	−	90.6845i	0.867791	−	0.501019i	0.866613	+	0.498980i	$0.166292\pi$
$182$	−8.85519			−0.0486549
$183$		−	25.8418i		−	0.141212i
$184$	50.7004	−	29.2719i	0.275545	−	0.159086i
$185$	−207.745	−	119.941i	−1.12294	−	0.648332i
$186$	5.09672	−	2.94259i	0.0274017	−	0.0158204i
$187$	106.129	−	183.821i	0.567535	−	0.982999i
$188$	6.72561	−	11.6491i	0.0357745	−	0.0619633i
$189$		−	10.1039i		−	0.0534600i
$190$	25.4160	−	4.33749i	0.133769	−	0.0228289i
$191$	−278.704			−1.45918			−0.729592	−	0.683882i	$-0.760290\pi$
$191$	−278.704			−1.45918			−0.729592	+	0.683882i	$0.760290\pi$
$192$	−88.1010	−	50.8651i	−0.458859	−	0.264922i
$193$	−167.512	−	96.7133i	−0.867939	−	0.501105i	−0.00127645	−	0.999999i	$-0.500406\pi$
$193$	−167.512	−	96.7133i	−0.867939	−	0.501105i	−0.866663	+	0.498894i	$0.833740\pi$
$194$	−5.73188	−	9.92791i	−0.0295458	−	0.0511748i
$195$	96.4405	−	167.040i	0.494567	−	0.856615i
$196$	89.1831	+	154.470i	0.455016	+	0.788111i
$197$	−96.9300			−0.492030			−0.246015	−	0.969266i	$-0.579121\pi$
$197$	−96.9300			−0.492030			−0.246015	+	0.969266i	$0.579121\pi$
$198$			5.98278i			0.0302161i
$199$	172.893	+	299.460i	0.868811	+	1.50482i	0.863213	+	0.504840i	$0.168449\pi$
$199$	172.893	+	299.460i	0.868811	+	1.50482i	0.00559823	+	0.999984i	$0.498218\pi$
$200$	−13.2643	+	7.65815i	−0.0663215	+	0.0382908i
$201$	140.823			0.700610
$202$		−	38.4237i		−	0.190216i
$203$	26.6536	−	15.3885i	0.131299	−	0.0758053i
$204$	148.351	+	85.6503i	0.727209	+	0.419854i
$205$	8.83894	−	5.10316i	0.0431168	−	0.0248935i
$206$	−2.15233	+	3.72795i	−0.0104482	+	0.0180968i
$207$	−46.9225	+	81.2721i	−0.226679	+	0.392619i
$208$		−	296.490i		−	1.42543i
$209$	150.841	+	55.8435i	0.721729	+	0.267194i
$210$	−4.57044			−0.0217640
$211$	−11.1758	−	6.45233i	−0.0529657	−	0.0305798i	0.473283	−	0.880910i	$-0.343069\pi$
$211$	−11.1758	−	6.45233i	−0.0529657	−	0.0305798i	−0.526249	+	0.850330i	$0.676402\pi$
$212$	315.936	+	182.406i	1.49026	+	0.860405i
$213$	−52.9948	−	91.7897i	−0.248802	−	0.430938i
$214$	−6.53464	+	11.3183i	−0.0305357	+	0.0528894i
$215$	−83.1580	−	144.034i	−0.386781	−	0.669925i
$216$	−9.72462			−0.0450214
$217$			28.0469i			0.129248i
$218$	13.1162	+	22.7179i	0.0601659	+	0.104210i
$219$	116.490	−	67.2553i	0.531916	−	0.307102i
$220$	−192.360			−0.874364
$221$			484.697i			2.19320i
$222$	−14.7147	+	8.49551i	−0.0662822	+	0.0382681i
$223$	−80.3821	−	46.4086i	−0.360458	−	0.208110i	0.308824	−	0.951119i	$-0.400065\pi$
$223$	−80.3821	−	46.4086i	−0.360458	−	0.208110i	−0.669282	+	0.743009i	$0.733398\pi$
$224$	−18.6907	+	10.7911i	−0.0834404	+	0.0481744i
$225$	12.2759	−	21.2625i	0.0545597	−	0.0945002i
$226$	13.0705	−	22.6388i	0.0578341	−	0.100172i
$227$		−	280.870i		−	1.23731i	−0.785662	−	0.618656i	$-0.787677\pi$
$227$		−	280.870i		−	1.23731i	0.785662	−	0.618656i	$-0.212323\pi$
$228$	−45.0679	+	121.735i	−0.197666	+	0.533926i
$229$	137.541			0.600615			0.300308	−	0.953842i	$-0.402911\pi$
$229$	137.541			0.600615			0.300308	+	0.953842i	$0.402911\pi$
$230$	36.7628	+	21.2250i	0.159838	+	0.0922826i
$231$	−24.6921	−	14.2560i	−0.106892	−	0.0617143i
$232$	−14.8108	−	25.6530i	−0.0638395	−	0.110573i
$233$	−183.683	+	318.148i	−0.788339	+	1.36544i	0.138645	+	0.990342i	$0.455725\pi$
$233$	−183.683	+	318.148i	−0.788339	+	1.36544i	−0.926984	+	0.375101i	$0.877608\pi$
$234$	−6.83093	−	11.8315i	−0.0291920	−	0.0505621i
$235$	19.6441			0.0835921
$236$		−	19.4620i		−	0.0824659i
$237$	−84.0207	−	145.528i	−0.354518	−	0.614043i
$238$	9.94648	−	5.74260i	0.0417919	−	0.0241286i
$239$	−196.388			−0.821707			−0.410854	−	0.911701i	$-0.634769\pi$
$239$	−196.388			−0.821707			−0.410854	+	0.911701i	$0.634769\pi$
$240$		−	153.027i		−	0.637614i
$241$	−118.225	+	68.2572i	−0.490560	+	0.283225i	−0.724807	−	0.688952i	$-0.758071\pi$
$241$	−118.225	+	68.2572i	−0.490560	+	0.283225i	0.234247	+	0.972177i	$0.424738\pi$
$242$	−10.0646	−	5.81079i	−0.0415892	−	0.0240115i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	29.4256	−	50.9666i	0.120597	−	0.208879i
$245$	−130.243	+	225.587i	−0.531604	+	0.920765i
$246$		−	0.722920i		−	0.00293870i
$247$	−362.063	+	61.7896i	−1.46584	+	0.250160i
$248$	26.9940			0.108847
$249$	153.484	+	88.6140i	0.616401	+	0.355879i
$250$	19.7625	+	11.4099i	0.0790501	+	0.0456396i
$251$	−23.3322	−	40.4126i	−0.0929571	−	0.161006i	0.815797	−	0.578338i	$-0.196299\pi$
$251$	−23.3322	−	40.4126i	−0.0929571	−	0.161006i	−0.908754	+	0.417332i	$0.862965\pi$
$252$	11.5052	−	19.9275i	0.0456554	−	0.0790775i
$253$	132.409	+	229.339i	0.523356	+	0.906480i
$254$	−57.0218			−0.224495
$255$			250.167i			0.981048i
$256$	−110.609	−	191.580i	−0.432066	−	0.748361i
$257$	4.73878	−	2.73593i	0.0184388	−	0.0106457i	−0.490752	−	0.871299i	$-0.663278\pi$
$257$	4.73878	−	2.73593i	0.0184388	−	0.0106457i	0.509191	+	0.860653i	$0.329945\pi$
$258$	−11.7802			−0.0456599
$259$		−	80.9737i		−	0.312640i
$260$	380.410	−	219.630i	1.46312	−	0.844730i
$261$	41.1214	+	23.7415i	0.157553	+	0.0909635i
$262$	32.1232	−	18.5463i	0.122607	−	0.0707874i
$263$	37.1071	−	64.2713i	0.141091	−	0.244378i	−0.786816	−	0.617187i	$-0.788272\pi$
$263$	37.1071	−	64.2713i	0.141091	−	0.244378i	0.927908	+	0.372809i	$0.121606\pi$
$264$	−13.7208	+	23.7651i	−0.0519727	+	0.0900194i
$265$			532.770i			2.01045i
$266$	5.55764	+	6.69784i	0.0208934	+	0.0251798i
$267$	−207.192			−0.775998
$268$	277.738	+	160.352i	1.03633	+	0.598328i
$269$	−64.2197	−	37.0772i	−0.238735	−	0.137834i	0.375860	−	0.926676i	$-0.377347\pi$
$269$	−64.2197	−	37.0772i	−0.238735	−	0.137834i	−0.614595	+	0.788843i	$0.710681\pi$
$270$	−3.52566	−	6.10661i	−0.0130580	−	0.0226171i
$271$	48.0380	−	83.2043i	0.177262	−	0.307027i	−0.763680	−	0.645595i	$-0.776609\pi$
$271$	48.0380	−	83.2043i	0.177262	−	0.307027i	0.940942	+	0.338568i	$0.109943\pi$
$272$	192.274	+	333.028i	0.706889	+	1.22437i
$273$	65.1080			0.238491
$274$			57.0898i			0.208357i
$275$	−34.6411	−	60.0001i	−0.125968	−	0.218182i
$276$	−185.086	+	106.859i	−0.670601	+	0.387172i
$277$	123.007			0.444068			0.222034	−	0.975039i	$-0.428730\pi$
$277$	123.007			0.444068			0.222034	+	0.975039i	$0.428730\pi$
$278$		−	30.6447i		−	0.110233i
$279$	−37.4738	+	21.6355i	−0.134315	+	0.0775466i
$280$	−18.1549	−	10.4818i	−0.0648391	−	0.0374348i
$281$	352.110	−	203.291i	1.25306	−	0.723454i	0.281344	−	0.959607i	$-0.409220\pi$
$281$	352.110	−	203.291i	1.25306	−	0.723454i	0.971716	+	0.236153i	$0.0758866\pi$
$282$	0.695702	−	1.20499i	0.00246703	−	0.00427302i
$283$	−92.7689	+	160.680i	−0.327805	+	0.567776i	−0.982076	−	0.188485i	$-0.939642\pi$
$283$	−92.7689	+	160.680i	−0.327805	+	0.567776i	0.654271	+	0.756260i	$0.272976\pi$
$284$		−	241.377i		−	0.849918i
$285$	−186.872	+	31.8915i	−0.655691	+	0.111900i
$286$	−38.5520			−0.134797
$287$	2.98363	+	1.72260i	0.0103959	+	0.00600209i
$288$	−28.8361	−	16.6485i	−0.100125	−	0.0578074i
$289$	−169.827	−	294.149i	−0.587636	−	1.01782i
$290$	10.7393	−	18.6009i	0.0370319	−	0.0641412i
$291$	42.1438	+	72.9953i	0.144824	+	0.250843i
$292$	306.329			1.04907
$293$		−	360.407i		−	1.23006i	−0.788505	−	0.615028i	$-0.789145\pi$
$293$		−	360.407i		−	1.23006i	0.788505	−	0.615028i	$-0.210855\pi$
$294$	9.22517	+	15.9785i	0.0313781	+	0.0543485i
$295$	24.6144	−	14.2111i	0.0834385	−	0.0481733i
$296$	−77.9338			−0.263290
$297$		−	43.9886i		−	0.148110i
$298$	−41.7683	+	24.1149i	−0.140162	+	0.0809226i
$299$	−523.703	−	302.360i	−1.75152	−	1.01124i
$300$	48.4225	−	27.9567i	0.161408	−	0.0931891i
$301$	28.0704	−	48.6194i	0.0932573	−	0.161526i
$302$	−27.5979	+	47.8009i	−0.0913837	+	0.158281i
$303$			282.511i			0.932380i
$304$	−224.257	+	186.081i	−0.737687	+	0.612109i
$305$	85.9461			0.281791
$306$	15.3455	+	8.85974i	0.0501487	+	0.0289534i
$307$	−233.152	−	134.610i	−0.759453	−	0.438470i	0.0696463	−	0.997572i	$-0.477813\pi$
$307$	−233.152	−	134.610i	−0.759453	−	0.438470i	−0.829099	+	0.559101i	$0.811146\pi$
$308$	−32.4661	−	56.2329i	−0.105409	−	0.182574i
$309$	15.8251	−	27.4098i	0.0512139	−	0.0887050i
$310$	9.78664	+	16.9510i	0.0315698	+	0.0546805i
$311$	53.4530			0.171874			0.0859372	−	0.996301i	$-0.472612\pi$
$311$	53.4530			0.171874			0.0859372	+	0.996301i	$0.472612\pi$
$312$		−	62.6637i		−	0.200845i
$313$	−119.760	−	207.430i	−0.382618	−	0.662715i	0.608817	−	0.793310i	$-0.291644\pi$
$313$	−119.760	−	207.430i	−0.382618	−	0.662715i	−0.991436	+	0.130596i	$0.958311\pi$
$314$	18.0736	−	10.4348i	0.0575592	−	0.0332318i
$315$	33.6043			0.106680
$316$		−	382.691i		−	1.21105i
$317$	391.754	−	226.179i	1.23582	−	0.713499i	0.267580	−	0.963536i	$-0.413776\pi$
$317$	391.754	−	226.179i	1.23582	−	0.713499i	0.968236	+	0.250036i	$0.0804426\pi$
$318$	32.6807	+	18.8682i	0.102769	+	0.0593340i
$319$	116.039	−	66.9954i	0.363760	−	0.210017i
$320$	169.170	−	293.011i	0.528656	−	0.915660i
$321$	48.0461	−	83.2184i	0.149676	−	0.259247i
$322$			14.3292i			0.0445007i
$323$	366.612	−	304.203i	1.13502	−	0.941805i
$324$	35.5006			0.109570
$325$	137.012	+	79.1039i	0.421575	+	0.243397i
$326$	23.6486	+	13.6535i	0.0725417	+	0.0418820i
$327$	−96.4369	−	167.034i	−0.294914	−	0.510806i
$328$	1.65793	−	2.87162i	0.00505467	−	0.00875494i
$329$	3.31549	+	5.74260i	0.0100775	+	0.0174547i
$330$	−19.8979			−0.0602966
$331$		−	95.4707i		−	0.288431i	−0.989546	−	0.144216i	$-0.953934\pi$
$331$		−	95.4707i		−	0.288431i	0.989546	−	0.144216i	$-0.0460659\pi$
$332$	201.806	+	349.538i	0.607850	+	1.05283i
$333$	108.190	−	62.4635i	0.324895	−	0.187578i
$334$	21.2288			0.0635592
$335$			468.356i			1.39808i
$336$	44.7348	−	25.8276i	0.133139	−	0.0768679i
$337$	−82.2367	−	47.4794i	−0.244026	−	0.140888i	0.373000	−	0.927831i	$-0.378329\pi$
$337$	−82.2367	−	47.4794i	−0.244026	−	0.140888i	−0.617026	+	0.786943i	$0.711663\pi$
$338$	41.7623	−	24.1115i	0.123557	−	0.0713357i
$339$	−96.1013	+	166.452i	−0.283485	+	0.491010i
$340$	−284.861	+	493.393i	−0.837825	+	1.45116i
$341$			122.105i			0.358080i
$342$	−4.66186	+	12.5924i	−0.0136312	+	0.0368198i
$343$	−183.209			−0.534138
$344$	−46.7941	−	27.0166i	−0.136029	−	0.0785366i
$345$	−270.299	−	156.057i	−0.783476	−	0.452340i
$346$	−5.24635	−	9.08694i	−0.0151628	−	0.0262628i
$347$	115.221	−	199.568i	0.332048	−	0.575124i	−0.650865	−	0.759193i	$-0.725594\pi$
$347$	115.221	−	199.568i	0.332048	−	0.575124i	0.982913	+	0.184069i	$0.0589270\pi$
$348$	54.0679	+	93.6484i	0.155368	+	0.269105i
$349$	−209.160			−0.599312			−0.299656	−	0.954047i	$-0.596872\pi$
$349$	−209.160			−0.599312			−0.299656	+	0.954047i	$0.596872\pi$
$350$		−	3.74884i		−	0.0107110i
$351$	50.2246	+	86.9916i	0.143090	+	0.247839i
$352$	−81.3717	+	46.9800i	−0.231170	+	0.133466i
$353$	326.125			0.923866			0.461933	−	0.886915i	$-0.347156\pi$
$353$	326.125			0.923866			0.461933	+	0.886915i	$0.347156\pi$
$354$		−	2.01316i		−	0.00568690i
$355$	305.279	−	176.253i	0.859942	−	0.496488i
$356$	−408.634	−	235.925i	−1.14785	−	0.662711i
$357$	−73.1318	+	42.2227i	−0.204851	+	0.118271i
$358$	27.0475	−	46.8476i	0.0755516	−	0.130859i
$359$	−268.735	+	465.463i	−0.748566	+	1.29655i	0.199945	+	0.979807i	$0.435924\pi$
$359$	−268.735	+	465.463i	−0.748566	+	1.29655i	−0.948510	+	0.316747i	$0.897410\pi$
$360$		−	32.3427i		−	0.0898408i
$361$	273.972	+	235.075i	0.758925	+	0.651178i
$362$	42.7255			0.118026
$363$	74.0002	+	42.7240i	0.203857	+	0.117697i
$364$	128.410	+	74.1373i	0.352773	+	0.203674i
$365$	223.682	+	387.428i	0.612826	+	1.06145i
$366$	3.04380	−	5.27202i	0.00831640	−	0.0144044i
$367$	−181.274	−	313.976i	−0.493935	−	0.855520i	0.506041	−	0.862509i	$-0.331108\pi$
$367$	−181.274	−	313.976i	−0.493935	−	0.855520i	−0.999976	+	0.00698970i	$0.997775\pi$
$368$	−479.771			−1.30373
$369$			5.31529i			0.0144046i
$370$	−28.2548	−	48.9388i	−0.0763644	−	0.132267i
$371$	−155.746	+	89.9198i	−0.419800	+	0.242371i
$372$	−98.5437			−0.264902
$373$			336.486i			0.902108i	0.892497	+	0.451054i	$0.148952\pi$
$373$			336.486i			0.902108i	−0.892497	+	0.451054i	$0.851048\pi$
$374$	43.3030	−	25.0010i	0.115784	−	0.0668477i
$375$	−145.305	−	83.8916i	−0.387479	−	0.223711i
$376$	5.52701	−	3.19102i	0.0146995	−	0.00848676i
$377$	−152.986	+	264.979i	−0.405798	+	0.702863i
$378$	1.19010	−	2.06132i	0.00314842	−	0.00545323i
$379$			336.744i			0.888507i	0.895901	+	0.444253i	$0.146531\pi$
$379$			336.744i			0.888507i	−0.895901	+	0.444253i	$0.853469\pi$
$380$	−404.873	−	149.889i	−1.06546	−	0.394446i
$381$	419.254			1.10041
$382$	−56.8589	−	32.8275i	−0.148845	−	0.0859358i
$383$	−193.755	−	111.865i	−0.505888	−	0.292075i	0.225254	−	0.974300i	$-0.427679\pi$
$383$	−193.755	−	111.865i	−0.505888	−	0.292075i	−0.731142	+	0.682226i	$0.761012\pi$
$384$	−50.4305	−	87.3483i	−0.131330	−	0.227469i
$385$	47.4134	−	82.1225i	0.123152	−	0.213305i
$386$	−22.7830	−	39.4612i	−0.0590232	−	0.102231i
$387$	86.6146			0.223810
$388$			191.954i			0.494726i
$389$	100.458	+	173.998i	0.258246	+	0.447295i	0.965772	−	0.259392i	$-0.0835221\pi$
$389$	100.458	+	173.998i	0.258246	+	0.447295i	−0.707526	+	0.706687i	$0.750189\pi$
$390$	39.3499	−	22.7187i	0.100897	−	0.0582531i
$391$	784.324			2.00594
$392$			84.6274i			0.215886i
$393$	−236.186	+	136.362i	−0.600983	+	0.346978i
$394$	−19.7748	−	11.4170i	−0.0501899	−	0.0289772i
$395$	484.006	−	279.441i	1.22533	−	0.707445i
$396$	50.0890	−	86.7566i	0.126487	−	0.219082i
$397$	−53.1506	+	92.0595i	−0.133880	+	0.231888i	−0.925169	−	0.379555i	$-0.876077\pi$
$397$	−53.1506	+	92.0595i	−0.133880	+	0.231888i	0.791289	+	0.611443i	$0.209410\pi$
$398$			81.4577i			0.204668i
$399$	−40.8627	−	49.2460i	−0.102413	−	0.123424i
$400$	125.519			0.313796
$401$	185.008	+	106.815i	0.461368	+	0.266371i	0.712619	−	0.701551i	$-0.247509\pi$
$401$	185.008	+	106.815i	0.461368	+	0.266371i	−0.251252	+	0.967922i	$0.580842\pi$
$402$	28.7294	+	16.5869i	0.0714662	+	0.0412610i
$403$	−139.415	−	241.474i	−0.345944	−	0.599192i
$404$	−321.690	+	557.184i	−0.796262	+	1.37917i
$405$	25.9225	+	44.8991i	0.0640061	+	0.110862i
$406$	7.25019			0.0178576
$407$		−	352.528i		−	0.866161i
$408$	40.6375	+	70.3862i	0.0996017	+	0.172515i
$409$	−46.6112	+	26.9110i	−0.113964	+	0.0657970i	−0.555898	−	0.831250i	$-0.687626\pi$
$409$	−46.6112	+	26.9110i	−0.113964	+	0.0657970i	0.441935	+	0.897047i	$0.354292\pi$
$410$	2.40433			0.00586421
$411$		−	419.755i		−	1.02130i
$412$	62.4221	−	36.0394i	0.151510	−	0.0874744i
$413$	8.30872	+	4.79704i	0.0201180	+	0.0116151i
$414$	−19.1454	+	11.0536i	−0.0462450	+	0.0266996i
$415$	−294.717	+	510.465i	−0.710162	+	1.23004i
$416$	107.280	−	185.815i	0.257885	−	0.446670i
$417$			225.316i			0.540326i
$418$	24.1958	+	29.1597i	0.0578846	+	0.0697601i
$419$	−808.890			−1.93052			−0.965262	−	0.261282i	$-0.915855\pi$
$419$	−808.890			−1.93052			−0.965262	+	0.261282i	$0.915855\pi$
$420$	66.2761	+	38.2645i	0.157800	+	0.0911061i
$421$	−309.086	−	178.451i	−0.734171	−	0.423874i	0.0857753	−	0.996315i	$-0.472663\pi$
$421$	−309.086	−	178.451i	−0.734171	−	0.423874i	−0.819946	+	0.572441i	$0.805997\pi$
$422$	−1.51999	−	2.63270i	−0.00360187	−	0.00623863i
$423$	−5.11517	+	8.85974i	−0.0120926	+	0.0209450i
$424$	86.5440	+	149.899i	0.204113	+	0.353534i
$425$	−205.196			−0.482814
$426$		−	24.9682i		−	0.0586108i
$427$	14.5058	+	25.1248i	0.0339714	+	0.0588402i
$428$	189.518	−	109.418i	0.442800	−	0.255651i
$429$	283.455			0.660733
$430$		−	39.1794i		−	0.0911149i
$431$	−36.3673	+	20.9967i	−0.0843789	+	0.0487162i	−0.541596	−	0.840639i	$-0.682180\pi$
$431$	−36.3673	+	20.9967i	−0.0843789	+	0.0487162i	0.457217	+	0.889355i	$0.348846\pi$
$432$	69.0172	+	39.8471i	0.159762	+	0.0922386i
$433$	533.602	−	308.075i	1.23234	−	0.711491i	0.264821	−	0.964298i	$-0.414687\pi$
$433$	533.602	−	308.075i	1.23234	−	0.711491i	0.967517	+	0.252807i	$0.0813538\pi$
$434$	−3.30353	+	5.72189i	−0.00761183	+	0.0131841i
$435$	−78.9607	+	136.764i	−0.181519	+	0.314400i
$436$		−	439.244i		−	1.00744i
$437$	99.9862	+	585.881i	0.228801	+	1.34069i
$438$	31.6870			0.0723447
$439$	−408.012	−	235.566i	−0.929413	−	0.536597i	−0.0427870	−	0.999084i	$-0.513624\pi$
$439$	−408.012	−	235.566i	−0.929413	−	0.536597i	−0.886626	+	0.462487i	$0.846957\pi$
$440$	−79.0394	−	45.6334i	−0.179635	−	0.103712i
$441$	−67.8283	−	117.482i	−0.153806	−	0.266399i
$442$	−57.0906	+	98.8838i	−0.129164	+	0.223719i
$443$	52.2697	+	90.5338i	0.117990	+	0.204365i	0.918971	−	0.394325i	$-0.129021\pi$
$443$	52.2697	+	90.5338i	0.117990	+	0.204365i	−0.800981	+	0.598690i	$0.795688\pi$
$444$	284.504			0.640774
$445$		−	689.089i		−	1.54852i
$446$	−10.9326	−	18.9358i	−0.0245125	−	0.0424569i
$447$	307.103	−	177.306i	0.687030	−	0.396657i
$448$	114.209			0.254930
$449$		−	713.259i		−	1.58855i	−0.607559	−	0.794275i	$-0.707851\pi$
$449$		−	713.259i		−	1.58855i	0.607559	−	0.794275i	$-0.292149\pi$
$450$	5.00886	−	2.89187i	0.0111308	−	0.00642637i
$451$	12.9896	+	7.49952i	0.0288017	+	0.0166287i
$452$	−379.072	+	218.857i	−0.838655	+	0.484198i
$453$	202.914	−	351.458i	0.447934	−	0.775845i
$454$	33.0826	−	57.3007i	0.0728691	−	0.126213i
$455$			216.540i			0.475912i
$456$	−47.3972	+	39.3286i	−0.103941	+	0.0862470i
$457$	−5.29457			−0.0115855			−0.00579275	−	0.999983i	$-0.501844\pi$
$457$	−5.29457			−0.0115855			−0.00579275	+	0.999983i	$0.501844\pi$
$458$	28.0599	+	16.2004i	0.0612662	+	0.0353721i
$459$	−112.828	−	65.1415i	−0.245813	−	0.141920i
$460$	−355.399	−	615.569i	−0.772607	−	1.33819i
$461$	−93.4120	+	161.794i	−0.202629	+	0.350964i	−0.949375	−	0.314146i	$-0.898282\pi$
$461$	−93.4120	+	161.794i	−0.202629	+	0.350964i	0.746746	+	0.665110i	$0.231615\pi$
$462$	−3.35832	−	5.81678i	−0.00726909	−	0.0125904i
$463$	718.582			1.55201			0.776007	−	0.630725i	$-0.217242\pi$
$463$	718.582			1.55201			0.776007	+	0.630725i	$0.217242\pi$
$464$			242.751i			0.523170i
$465$	−71.9566	−	124.632i	−0.154745	−	0.268027i
$466$	−74.9468	+	43.2706i	−0.160830	+	0.0928553i
$467$	864.548			1.85128			0.925641	−	0.378404i	$-0.123527\pi$
$467$	864.548			1.85128			0.925641	+	0.378404i	$0.123527\pi$
$468$			228.759i			0.488802i
$469$	−136.915	+	79.0480i	−0.291930	+	0.168546i
$470$	4.00763	+	2.31381i	0.00852687	+	0.00492299i
$471$	−132.886	+	76.7220i	−0.282137	+	0.162892i
$472$	4.61695	−	7.99679i	0.00978167	−	0.0169423i
$473$	122.208	−	211.670i	0.258367	−	0.447505i
$474$		−	39.5859i		−	0.0835145i
$475$	−26.1585	−	153.279i	−0.0550706	−	0.322693i
$476$	−192.313			−0.404018
$477$	−240.286	−	138.729i	−0.503744	−	0.290837i
$478$	−40.0654	−	23.1318i	−0.0838189	−	0.0483928i
$479$	63.1395	+	109.361i	0.131815	+	0.228311i	0.924376	−	0.381482i	$-0.124586\pi$
$479$	63.1395	+	109.361i	0.131815	+	0.228311i	−0.792561	+	0.609793i	$0.791253\pi$
$480$	55.3706	−	95.9047i	0.115355	−	0.199802i
$481$	402.504	+	697.157i	0.836806	+	1.44939i
$482$	−32.1590			−0.0667199
$483$		−	105.356i		−	0.218129i
$484$	97.2981	+	168.525i	0.201029	+	0.348193i
$485$	−242.772	+	140.164i	−0.500560	+	0.288999i
$486$	3.67221			0.00755598
$487$		−	12.1199i		−	0.0248868i	−0.999923	−	0.0124434i	$-0.996039\pi$
$487$		−	12.1199i		−	0.0248868i	0.999923	−	0.0124434i	$-0.00396097\pi$
$488$	24.1815	−	13.9612i	0.0495523	−	0.0286090i
$489$	−173.877	−	100.388i	−0.355576	−	0.205292i
$490$	−53.1421	+	30.6816i	−0.108453	+	0.0626155i
$491$	246.271	−	426.554i	0.501570	−	0.868745i	−0.498428	−	0.866931i	$-0.666089\pi$
$491$	246.271	−	426.554i	0.501570	−	0.868745i	0.999998	−	0.00181372i	$-0.000577326\pi$
$492$	−6.05241	+	10.4831i	−0.0123017	+	0.0213071i
$493$		−	396.846i		−	0.804962i
$494$	−81.1430	−	30.0402i	−0.164257	−	0.0608102i
$495$	146.300			0.295555
$496$	−191.580	−	110.609i	−0.386251	−	0.223002i
$497$	103.049	+	59.4952i	0.207342	+	0.119709i
$498$	20.8750	+	36.1565i	0.0419176	+	0.0726035i
$499$	173.134	−	299.877i	0.346962	−	0.600956i	−0.638746	−	0.769417i	$-0.720547\pi$
$499$	173.134	−	299.877i	0.346962	−	0.600956i	0.985708	+	0.168462i	$0.0538800\pi$
$500$	−191.052	−	330.911i	−0.382103	−	0.661822i
$501$	−156.085			−0.311547
$502$		−	10.9928i		−	0.0218981i
$503$	166.249	+	287.952i	0.330516	+	0.572470i	0.982613	−	0.185665i	$-0.0594441\pi$
$503$	166.249	+	287.952i	0.330516	+	0.572470i	−0.652098	+	0.758135i	$0.726111\pi$
$504$	9.45479	−	5.45873i	0.0187595	−	0.0108308i
$505$	−939.592			−1.86058
$506$			62.3838i			0.123288i
$507$	−307.058	+	177.280i	−0.605638	+	0.349665i
$508$	826.876	+	477.397i	1.62771	+	0.939758i
$509$	−461.493	+	266.443i	−0.906666	+	0.523464i	−0.879357	−	0.476163i	$-0.842027\pi$
$509$	−461.493	+	266.443i	−0.906666	+	0.523464i	−0.0273090	+	0.999627i	$0.508694\pi$
$510$	−29.4662	+	51.0370i	−0.0577769	+	0.100073i
$511$	−75.5049	+	130.778i	−0.147759	+	0.255926i
$512$		−	285.041i		−	0.556722i
$513$	34.2765	−	92.5858i	0.0668158	−	0.180479i
$514$	1.28902			0.00250782
$515$	91.1612	+	52.6319i	0.177012	+	0.102198i
$516$	170.826	+	98.6264i	0.331058	+	0.191136i
$517$	14.4343	+	25.0010i	0.0279194	+	0.0483579i
$518$	9.53758	−	16.5196i	0.0184123	−	0.0318911i
$519$	38.5739	+	66.8120i	0.0743235	+	0.128732i
$520$	208.411			0.400789
$521$			74.3056i			0.142621i	0.997454	+	0.0713106i	$0.0227181\pi$
$521$			74.3056i			0.142621i	−0.997454	+	0.0713106i	$0.977282\pi$
$522$	5.59283	+	9.68707i	0.0107142	+	0.0185576i
$523$	25.3191	−	14.6180i	0.0484113	−	0.0279503i	−0.475599	−	0.879662i	$-0.657769\pi$
$523$	25.3191	−	14.6180i	0.0484113	−	0.0279503i	0.524010	+	0.851712i	$0.324435\pi$
$524$	−621.092			−1.18529
$525$			27.5634i			0.0525017i
$526$	15.1405	−	8.74139i	0.0287843	−	0.0166186i
$527$	313.193	+	180.822i	0.594294	+	0.343116i
$528$	194.757	−	112.443i	0.368859	−	0.212961i
$529$	−224.771	+	389.315i	−0.424898	+	0.735945i
$530$	−62.7529	+	108.691i	−0.118402	+	0.205078i
$531$			14.8018i			0.0278754i
$532$	−24.5162	−	143.655i	−0.0460830	−	0.270029i
$533$	−34.2508			−0.0642603
$534$	−42.2695	−	24.4043i	−0.0791563	−	0.0457009i
$535$	276.772	+	159.795i	0.517331	+	0.298681i
$536$	76.0803	+	131.775i	0.141941	+	0.245849i
$537$	−198.867	+	344.448i	−0.370330	+	0.641431i
$538$	−8.73436	−	15.1284i	−0.0162349	−	0.0281196i
$539$	−382.805			−0.710214
$540$			118.070i			0.218648i
$541$	109.055	+	188.889i	0.201580	+	0.349147i	0.949038	−	0.315163i	$-0.102059\pi$
$541$	109.055	+	188.889i	0.201580	+	0.349147i	−0.747458	+	0.664310i	$0.768726\pi$
$542$	19.6006	−	11.3164i	0.0361635	−	0.0208790i
$543$	−314.140			−0.578527
$544$			278.285i			0.511554i
$545$	555.530	−	320.735i	1.01932	−	0.588505i
$546$	13.2828	+	7.66882i	0.0243274	+	0.0140455i
$547$	−465.237	+	268.605i	−0.850525	+	0.491051i	−0.860828	−	0.508896i	$-0.830054\pi$
$547$	−465.237	+	268.605i	−0.850525	+	0.491051i	0.0103027	+	0.999947i	$0.496721\pi$
$548$	477.967	−	827.863i	0.872202	−	1.51070i
$549$	−22.3797	+	38.7627i	−0.0407644	+	0.0706060i
$550$		−	16.3209i		−	0.0296744i
$551$	296.440	−	50.5903i	0.538003	−	0.0918154i
$552$	−101.401			−0.183697
$553$	163.379	+	94.3268i	0.295441	+	0.170573i
$554$	25.0948	+	14.4885i	0.0452975	+	0.0261525i
$555$	207.745	+	359.824i	0.374315	+	0.648332i
$556$	−256.563	+	444.380i	−0.461444	+	0.799245i
$557$	−158.164	−	273.947i	−0.283956	−	0.491826i	0.688399	−	0.725332i	$-0.258314\pi$
$557$	−158.164	−	273.947i	−0.283956	−	0.491826i	−0.972355	+	0.233505i	$0.924980\pi$
$558$	−10.1934			−0.0182678
$559$			558.129i			0.998442i
$560$	85.8990	+	148.781i	0.153391	+	0.265681i
$561$	−318.387	+	183.821i	−0.567535	+	0.327666i
$562$	95.7792			0.170426
$563$			595.272i			1.05732i	0.848833	+	0.528661i	$0.177306\pi$
$563$			595.272i			1.05732i	−0.848833	+	0.528661i	$0.822694\pi$
$564$	−20.1768	+	11.6491i	−0.0357745	+	0.0206544i
$565$	−553.596	−	319.619i	−0.979816	−	0.565697i
$566$	−37.8518	+	21.8538i	−0.0668760	+	0.0386109i
$567$	−8.75028	+	15.1559i	−0.0154326	+	0.0267300i
$568$	57.2616	−	99.1800i	0.100813	−	0.174613i
$569$		−	536.213i		−	0.942377i	−0.882032	−	0.471189i	$-0.843825\pi$
$569$		−	536.213i		−	0.942377i	0.882032	−	0.471189i	$-0.156175\pi$
$570$	−41.8804	−	15.5047i	−0.0734744	−	0.0272012i
$571$	−84.5912			−0.148146			−0.0740729	−	0.997253i	$-0.523600\pi$
$571$	−84.5912			−0.148146			−0.0740729	+	0.997253i	$0.523600\pi$
$572$	559.044	+	322.764i	0.977350	+	0.564273i
$573$	418.056	+	241.365i	0.729592	+	0.421230i
$574$	0.405797	+	0.702861i	0.000706963	+	0.00122450i
$575$	128.004	−	221.709i	0.222615	−	0.385581i
$576$	88.1010	+	152.595i	0.152953	+	0.264922i
$577$	−850.008			−1.47315			−0.736575	−	0.676356i	$-0.763558\pi$
$577$	−850.008			−1.47315			−0.736575	+	0.676356i	$0.763558\pi$
$578$		−	80.0129i		−	0.138431i
$579$	167.512	+	290.140i	0.289313	+	0.501105i
$580$	−311.461	+	179.822i	−0.537002	+	0.310038i
$581$	−198.967			−0.342456
$582$			19.8558i			0.0341165i
$583$	−678.055	+	391.475i	−1.16304	+	0.671484i
$584$	125.869	+	72.6703i	0.215528	+	0.124435i
$585$	−289.322	+	167.040i	−0.494567	+	0.285538i
$586$	42.4509	−	73.5271i	0.0724417	−	0.125473i
$587$	229.370	−	397.281i	0.390750	−	0.676798i	−0.601799	−	0.798648i	$-0.705549\pi$
$587$	229.370	−	397.281i	0.390750	−	0.676798i	0.992549	+	0.121849i	$0.0388825\pi$
$588$		−	308.939i		−	0.525407i
$589$	−95.1459	+	257.003i	−0.161538	+	0.436338i
$590$	6.69548			0.0113483
$591$	145.395	+	83.9438i	0.246015	+	0.142037i
$592$	553.108	+	319.337i	0.934305	+	0.539421i
$593$	−51.3293	−	88.9049i	−0.0865586	−	0.149924i	0.819496	−	0.573085i	$-0.194254\pi$
$593$	−51.3293	−	88.9049i	−0.0865586	−	0.149924i	−0.906054	+	0.423161i	$0.860920\pi$
$594$	5.18124	−	8.97418i	0.00872263	−	0.0151080i
$595$	−140.426	−	243.226i	−0.236011	−	0.408783i
$596$	807.579			1.35500
$597$		−	598.920i		−	1.00322i
$598$	−71.2276	−	123.370i	−0.119110	−	0.206304i
$599$	322.250	−	186.051i	0.537980	−	0.310603i	−0.206280	−	0.978493i	$-0.566136\pi$
$599$	322.250	−	186.051i	0.537980	−	0.310603i	0.744260	+	0.667890i	$0.232802\pi$
$600$	26.5286			0.0442144
$601$		−	850.837i		−	1.41570i	−0.706362	−	0.707851i	$-0.749665\pi$
$601$		−	850.837i		−	1.41570i	0.706362	−	0.707851i	$-0.250335\pi$
$602$	11.4534	−	6.61261i	0.0190256	−	0.0109844i
$603$	−211.234	−	121.956i	−0.350305	−	0.202249i
$604$	800.396	−	462.109i	1.32516	−	0.765081i
$605$	−142.094	+	246.114i	−0.234866	+	0.406800i
$606$	−33.2759	+	57.6355i	−0.0549107	+	0.0951081i
$607$			314.498i			0.518119i	0.965861	+	0.259060i	$0.0834126\pi$
$607$			314.498i			0.518119i	−0.965861	+	0.259060i	$0.916587\pi$
$608$	−207.876	+	35.4760i	−0.341901	+	0.0583488i
$609$	−53.3073			−0.0875324
$610$	17.5340	+	10.1233i	0.0287442	+	0.0165955i
$611$	−57.0906	−	32.9613i	−0.0934379	−	0.0539464i
$612$	−148.351	−	256.951i	−0.242403	−	0.419854i
$613$	146.198	−	253.222i	0.238495	−	0.413086i	−0.721787	−	0.692115i	$-0.756679\pi$
$613$	146.198	−	253.222i	0.238495	−	0.413086i	0.960283	+	0.279029i	$0.0900125\pi$
$614$	−31.7105	−	54.9241i	−0.0516457	−	0.0894530i
$615$	−17.6779			−0.0287445
$616$		−	30.8076i		−	0.0500124i
$617$	−438.183	−	758.955i	−0.710183	−	1.23007i	−0.964788	−	0.263028i	$-0.915279\pi$
$617$	−438.183	−	758.955i	−0.710183	−	1.23007i	0.254605	−	0.967045i	$-0.418055\pi$
$618$	6.45700	−	3.72795i	0.0104482	−	0.00603228i
$619$	−166.847			−0.269542			−0.134771	−	0.990877i	$-0.543030\pi$
$619$	−166.847			−0.269542			−0.134771	+	0.990877i	$0.543030\pi$
$620$		−	327.742i		−	0.528617i
$621$	140.767	−	81.2721i	0.226679	−	0.130873i
$622$	10.9050	+	6.29601i	0.0175322	+	0.0101222i
$623$	201.443	−	116.303i	0.323343	−	0.186682i
$624$	−256.767	+	444.734i	−0.411486	+	0.712715i
$625$	381.311	−	660.450i	0.610097	−	1.05672i
$626$		−	56.4240i		−	0.0901342i
$627$	−177.900	−	214.398i	−0.283732	−	0.341942i
$628$	−349.448			−0.556445
$629$	−904.214	−	522.048i	−1.43754	−	0.829965i
$630$	6.85566	+	3.95812i	0.0108820	+	0.00628272i
$631$	464.592	+	804.698i	0.736280	+	1.27527i	0.954160	+	0.299298i	$0.0967525\pi$
$631$	464.592	+	804.698i	0.736280	+	1.27527i	−0.217880	+	0.975976i	$0.569914\pi$
$632$	90.7855	−	157.245i	0.143648	−	0.248806i
$633$	11.1758	+	19.3570i	0.0176552	+	0.0305798i
$634$	106.563			0.168080
$635$			1394.38i			2.19587i
$636$	−315.936	−	547.217i	−0.496755	−	0.860405i
$637$	757.034	−	437.074i	1.18844	−	0.686144i
$638$	31.5645			0.0494741
$639$			183.579i			0.287292i
$640$	290.508	−	167.725i	0.453918	−	0.262070i
$641$	425.692	+	245.773i	0.664106	+	0.383422i	0.793840	−	0.608127i	$-0.208079\pi$
$641$	425.692	+	245.773i	0.664106	+	0.383422i	−0.129734	+	0.991549i	$0.541412\pi$
$642$	19.6039	−	11.3183i	0.0305357	−	0.0176298i
$643$	175.770	−	304.442i	0.273359	−	0.473472i	−0.696361	−	0.717692i	$-0.745199\pi$
$643$	175.770	−	304.442i	0.273359	−	0.473472i	0.969720	+	0.244220i	$0.0785319\pi$
$644$	119.967	−	207.789i	0.186284	−	0.322653i
$645$			288.068i			0.446617i
$646$	110.624	−	18.8790i	0.171245	−	0.0292245i
$647$	767.027			1.18551			0.592757	−	0.805381i	$-0.298039\pi$
$647$	767.027			1.18551			0.592757	+	0.805381i	$0.298039\pi$
$648$	14.5869	+	8.42177i	0.0225107	+	0.0129966i
$649$	36.1729	+	20.8844i	0.0557363	+	0.0321794i
$650$	18.6347	+	32.2762i	0.0286687	+	0.0496557i
$651$	24.2893	−	42.0704i	0.0373108	−	0.0646242i
$652$	−228.619	−	395.981i	−0.350643	−	0.607332i
$653$	−254.877			−0.390317			−0.195159	−	0.980772i	$-0.562522\pi$
$653$	−254.877			−0.390317			−0.195159	+	0.980772i	$0.562522\pi$
$654$		−	45.4357i		−	0.0694736i
$655$	−453.521	−	785.522i	−0.692399	−	1.19927i
$656$	−23.5332	+	13.5869i	−0.0358738	+	0.0207117i
$657$	−232.979			−0.354611
$658$			1.56208i			0.00237398i
$659$	−427.502	+	246.818i	−0.648713	+	0.374535i	−0.787963	−	0.615723i	$-0.788864\pi$
$659$	−427.502	+	246.818i	−0.648713	+	0.374535i	0.139250	+	0.990257i	$0.455531\pi$
$660$	288.540	+	166.589i	0.437182	+	0.252407i
$661$	−1110.75	+	641.292i	−1.68041	+	0.970185i	−0.719021	+	0.694988i	$0.755410\pi$
$661$	−1110.75	+	641.292i	−1.68041	+	0.970185i	−0.961388	+	0.275197i	$0.911257\pi$
$662$	11.2451	−	19.4771i	0.0169866	−	0.0294216i
$663$	419.760	−	727.046i	0.633122	−	1.09660i
$664$			191.497i			0.288399i
$665$	163.785	−	135.904i	0.246294	−	0.204366i
$666$	29.4293			0.0441882
$667$	428.782	+	247.558i	0.642852	+	0.371151i
$668$	−307.839	−	177.731i	−0.460837	−	0.266065i
$669$	80.3821	+	139.226i	0.120153	+	0.208110i
$670$	−55.1658	+	95.5499i	−0.0823370	+	0.142612i
$671$	63.1525	+	109.383i	0.0941169	+	0.163015i
$672$	37.3813			0.0556270
$673$			337.649i			0.501707i	0.968025	+	0.250853i	$0.0807112\pi$
$673$			337.649i			0.501707i	−0.968025	+	0.250853i	$0.919289\pi$
$674$	−11.1848	−	19.3727i	−0.0165947	−	0.0287428i
$675$	−36.8278	+	21.2625i	−0.0545597	+	0.0315001i
$676$	−807.462			−1.19447
$677$			394.197i			0.582270i	0.956682	+	0.291135i	$0.0940329\pi$
$677$			394.197i			0.582270i	−0.956682	+	0.291135i	$0.905967\pi$
$678$	−39.2115	+	22.6388i	−0.0578341	+	0.0333905i
$679$	−81.9489	−	47.3132i	−0.120691	−	0.0696808i
$680$	−234.094	+	135.155i	−0.344257	+	0.198757i
$681$	−243.240	+	421.305i	−0.357181	+	0.618656i
$682$	−14.3823	+	24.9108i	−0.0210884	+	0.0365262i
$683$			612.782i			0.897192i	0.893735	+	0.448596i	$0.148076\pi$
$683$			612.782i			0.897192i	−0.893735	+	0.448596i	$0.851924\pi$
$684$	173.028	−	143.573i	0.252964	−	0.209901i
$685$	1396.04			2.03802
$686$	−37.3768	−	21.5795i	−0.0544851	−	0.0314570i
$687$	−206.311	−	119.114i	−0.300308	−	0.173383i
$688$	221.404	+	383.482i	0.321807	+	0.557387i
$689$	893.945	−	1548.36i	1.29745	−	2.24725i
$690$	−36.7628	−	63.6750i	−0.0532794	−	0.0922826i
$691$	254.757			0.368678			0.184339	−	0.982863i	$-0.440986\pi$
$691$	254.757			0.368678			0.184339	+	0.982863i	$0.440986\pi$
$692$			175.693i			0.253892i
$693$	24.6921	+	42.7680i	0.0356308	+	0.0617143i
$694$	47.0127	−	27.1428i	0.0677417	−	0.0391107i
$695$	−749.369			−1.07823
$696$			51.3060i			0.0737155i
$697$	38.4717	−	22.2117i	0.0551962	−	0.0318675i
$698$	−42.6710	−	24.6361i	−0.0611333	−	0.0352953i
$699$	551.049	−	318.148i	0.788339	−	0.455148i
$700$	−31.3859	+	54.3620i	−0.0448370	+	0.0776600i
$701$	−3.62864	+	6.28499i	−0.00517638	+	0.00896576i	−0.868602	−	0.495510i	$-0.834981\pi$
$701$	−3.62864	+	6.28499i	−0.00517638	+	0.00896576i	0.863426	+	0.504476i	$0.168314\pi$
$702$			23.6630i			0.0337080i
$703$	274.694	−	741.989i	0.390746	−	1.05546i
$704$	497.219			0.706277
$705$	−29.4662	−	17.0123i	−0.0417960	−	0.0241310i
$706$	66.5332	+	38.4130i	0.0942396	+	0.0544093i
$707$	−158.582	−	274.672i	−0.224303	−	0.388504i
$708$	−16.8546	+	29.1929i	−0.0238059	+	0.0412330i
$709$	−522.280	−	904.615i	−0.736643	−	1.27590i	−0.953999	−	0.299810i	$-0.903077\pi$
$709$	−522.280	−	904.615i	−0.736643	−	1.27590i	0.217356	−	0.976092i	$-0.430257\pi$
$710$	83.0407			0.116959
$711$			291.056i			0.409362i
$712$	−111.937	−	193.880i	−0.157214	−	0.272303i
$713$	−390.747	+	225.598i	−0.548033	+	0.316407i
$714$	−19.8930			−0.0278613
$715$			942.729i			1.31850i
$716$	−784.433	+	452.893i	−1.09558	+	0.632532i
$717$	294.582	+	170.077i	0.410854	+	0.237207i
$718$	−109.650	+	63.3065i	−0.152716	+	0.0881706i
$719$	−658.810	+	1141.09i	−0.916286	+	1.58705i	−0.111279	+	0.993789i	$0.535495\pi$
$719$	−658.810	+	1141.09i	−0.916286	+	1.58705i	−0.805007	+	0.593265i	$0.797839\pi$
$720$	−132.526	+	229.541i	−0.184063	+	0.318807i
$721$			35.5324i			0.0492821i
$722$	28.2049	+	80.2281i	0.0390649	+	0.111119i
$723$	236.450			0.327040
$724$	−619.564	−	357.705i	−0.855751	−	0.494068i
$725$	−112.179	−	64.7664i	−0.154729	−	0.0893330i
$726$	10.0646	+	17.4324i	0.0138631	+	0.0240115i
$727$	−88.8280	+	153.855i	−0.122184	+	0.211630i	−0.920629	−	0.390439i	$-0.872323\pi$
$727$	−88.8280	+	153.855i	−0.122184	+	0.211630i	0.798444	+	0.602068i	$0.205657\pi$
$728$	35.1751	+	60.9250i	0.0483174	+	0.0836882i
$729$	−27.0000			−0.0370370
$730$			105.386i			0.144365i
$731$	−361.948	−	626.912i	−0.495140	−	0.857608i
$732$	−88.2767	+	50.9666i	−0.120597	+	0.0696265i
$733$	321.795			0.439011			0.219505	−	0.975611i	$-0.429556\pi$
$733$	321.795			0.439011			0.219505	+	0.975611i	$0.429556\pi$
$734$		−	85.4062i		−	0.116357i
$735$	390.729	−	225.587i	0.531604	−	0.306922i
$736$	−300.680	−	173.598i	−0.408533	−	0.235867i
$737$	−596.074	+	344.144i	−0.808785	+	0.466952i
$738$	−0.626067	+	1.08438i	−0.000848329	+	0.00146935i
$739$	85.7034	−	148.443i	0.115972	−	0.200870i	−0.802196	−	0.597061i	$-0.796335\pi$
$739$	85.7034	−	148.443i	0.115972	−	0.200870i	0.918168	+	0.396191i	$0.129668\pi$
$740$			946.219i			1.27867i
$741$	596.606	+	220.872i	0.805136	+	0.298072i
$742$	−42.3652			−0.0570960
$743$	−257.044	−	148.405i	−0.345955	−	0.199737i	0.316947	−	0.948443i	$-0.397342\pi$
$743$	−257.044	−	148.405i	−0.345955	−	0.199737i	−0.662902	+	0.748706i	$0.730675\pi$
$744$	−40.4909	−	23.3775i	−0.0544233	−	0.0314213i
$745$	589.693	+	1021.38i	0.791535	+	1.37098i
$746$	−39.6334	+	68.6471i	−0.0531279	+	0.0920202i
$747$	−153.484	−	265.842i	−0.205467	−	0.355879i
$748$	−837.253			−1.11932
$749$			107.879i			0.144031i
$750$	−19.7625	−	34.2297i	−0.0263500	−	0.0456396i
$751$	−117.403	+	67.7829i	−0.156329	+	0.0902568i	−0.576124	−	0.817362i	$-0.695435\pi$
$751$	−117.403	+	67.7829i	−0.156329	+	0.0902568i	0.419795	+	0.907619i	$0.362102\pi$
$752$	−52.3014			−0.0695498
$753$			80.8252i			0.107338i
$754$	−62.4217	+	36.0392i	−0.0827874	+	0.0477974i
$755$	1168.90	+	674.864i	1.54821	+	0.893859i
$756$	−34.5155	+	19.9275i	−0.0456554	+	0.0263592i
$757$	4.71078	−	8.15931i	0.00622296	−	0.0107785i	−0.862897	−	0.505380i	$-0.831352\pi$
$757$	4.71078	−	8.15931i	0.00622296	−	0.0107785i	0.869120	+	0.494601i	$0.164686\pi$
$758$	−39.6637	+	68.6996i	−0.0523268	+	0.0906327i
$759$		−	458.679i		−	0.604320i
$760$	−130.801	−	157.636i	−0.172107	−	0.207416i
$761$	−501.946			−0.659587			−0.329794	−	0.944053i	$-0.606979\pi$
$761$	−501.946			−0.659587			−0.329794	+	0.944053i	$0.606979\pi$
$762$	85.5327	+	49.3823i	0.112248	+	0.0648062i
$763$	187.522	+	108.266i	0.245770	+	0.141895i
$764$	549.675	+	952.066i	0.719470	+	1.24616i
$765$	216.651	−	375.251i	0.283204	−	0.490524i
$766$	−26.3522	−	45.6433i	−0.0344023	−	0.0595866i
$767$	−95.3803			−0.124355
$768$			383.161i			0.498907i
$769$	722.257	+	1250.99i	0.939216	+	1.62677i	0.766937	+	0.641722i	$0.221780\pi$
$769$	722.257	+	1250.99i	0.939216	+	1.62677i	0.172279	+	0.985048i	$0.444887\pi$
$770$	19.3458	−	11.1693i	0.0251244	−	0.0145056i
$771$	−9.47756			−0.0122926
$772$			762.972i			0.988306i
$773$	−572.771	+	330.690i	−0.740972	+	0.427800i	−0.822423	−	0.568877i	$-0.807378\pi$
$773$	−572.771	+	330.690i	−0.740972	+	0.427800i	0.0814506	+	0.996677i	$0.474045\pi$
$774$	17.6704	+	10.2020i	0.0228299	+	0.0131809i
$775$	102.228	−	59.0213i	0.131907	−	0.0761565i
$776$	−45.5370	+	78.8724i	−0.0586817	+	0.101640i
$777$	−70.1253	+	121.461i	−0.0902514	+	0.156320i
$778$			47.3301i			0.0608356i
$779$	21.4963	+	25.9064i	0.0275947	+	0.0332559i
$780$	−760.820			−0.975411
$781$	448.633	+	259.019i	0.574435	+	0.331650i
$782$	160.011	+	92.3824i	0.204618	+	0.118136i
$783$	−41.1214	−	71.2244i	−0.0525178	−	0.0909635i
$784$	346.764	−	600.614i	0.442302	−	0.766089i
$785$	−255.166	−	441.961i	−0.325053	−	0.563008i
$786$	−64.2463			−0.0817383
$787$		−	1319.00i		−	1.67598i	−0.545686	−	0.837990i	$-0.683731\pi$
$787$		−	1319.00i		−	1.67598i	0.545686	−	0.837990i	$-0.316269\pi$
$788$	191.170	+	331.117i	0.242602	+	0.420199i
$789$	−111.321	+	64.2713i	−0.141091	+	0.0814592i
$790$	131.657			0.166654
$791$		−	215.778i		−	0.272792i
$792$	41.1624	−	23.7651i	0.0519727	−	0.0300065i
$793$	−249.780	−	144.211i	−0.314981	−	0.181854i
$794$	−21.6866	+	12.5208i	−0.0273132	+	0.0157693i
$795$	461.393	−	799.156i	0.580368	−	1.00523i
$796$	681.979	−	1181.22i	0.856757	−	1.48395i
$797$		−	512.600i		−	0.643162i	−0.946882	−	0.321581i	$-0.895786\pi$
$797$		−	512.600i		−	0.643162i	0.946882	−	0.321581i	$-0.104214\pi$
$798$	−2.53597	−	14.8598i	−0.00317791	−	0.0186213i
$799$	85.5017			0.107011
$800$	78.6644	+	45.4169i	0.0983306	+	0.0567712i
$801$	310.787	+	179.433i	0.387999	+	0.224011i
$802$	25.1626	+	43.5828i	0.0313748	+	0.0543427i
$803$	−328.719	+	569.357i	−0.409363	+	0.709038i
$804$	−277.738	−	481.056i	−0.345445	−	0.598328i
$805$	350.399			0.435278
$806$		−	65.6847i		−	0.0814947i
$807$	64.2197	+	111.232i	0.0795783	+	0.137834i
$808$	−264.360	+	152.629i	−0.327179	+	0.188897i
$809$	368.489			0.455487			0.227743	−	0.973721i	$-0.426865\pi$
$809$	368.489			0.455487			0.227743	+	0.973721i	$0.426865\pi$
$810$			12.2132i			0.0150781i
$811$	−5.72688	+	3.30642i	−0.00706150	+	0.00407696i	−0.503527	−	0.863980i	$-0.667964\pi$
$811$	−5.72688	+	3.30642i	−0.00706150	+	0.00407696i	0.496465	+	0.868057i	$0.334631\pi$
$812$	−105.135	−	60.7000i	−0.129477	−	0.0747536i
$813$	−144.114	+	83.2043i	−0.177262	+	0.102342i
$814$	41.5228	−	71.9197i	0.0510109	−	0.0883534i
$815$	333.876	−	578.290i	0.409663	−	0.709558i
$816$		−	666.056i		−	0.816246i
$817$	422.154	−	350.290i	0.516713	−	0.428751i
$818$	−12.6789			−0.0154999
$819$	−97.6621	−	56.3852i	−0.119246	−	0.0688464i
$820$	−34.8652	−	20.1295i	−0.0425186	−	0.0245481i
$821$	−541.742	−	938.324i	−0.659856	−	1.14290i	−0.980653	−	0.195756i	$-0.937284\pi$
$821$	−541.742	−	938.324i	−0.659856	−	1.14290i	0.320796	−	0.947148i	$-0.396049\pi$
$822$	49.4413	−	85.6348i	0.0601475	−	0.104179i
$823$	−160.542	−	278.067i	−0.195069	−	0.337869i	0.751854	−	0.659329i	$-0.229160\pi$
$823$	−160.542	−	278.067i	−0.195069	−	0.337869i	−0.946923	+	0.321460i	$0.895826\pi$
$824$	34.1984			0.0415029
$825$			120.000i			0.145455i
$826$	1.13005	+	1.95730i	0.00136810	+	0.00236961i
$827$	−710.535	+	410.228i	−0.859172	+	0.496043i	−0.863735	−	0.503946i	$-0.831881\pi$
$827$	−710.535	+	410.228i	−0.859172	+	0.496043i	0.00456293	+	0.999990i	$0.498548\pi$
$828$	370.172			0.447068
$829$		−	1041.55i		−	1.25640i	−0.778053	−	0.628199i	$-0.783792\pi$
$829$		−	1041.55i		−	1.25640i	0.778053	−	0.628199i	$-0.216208\pi$
$830$	−120.251	+	69.4272i	−0.144881	+	0.0836472i
$831$	−184.510	−	106.527i	−0.222034	−	0.128191i
$832$	−983.297	+	567.707i	−1.18185	+	0.682340i
$833$	−566.886	+	981.875i	−0.680535	+	1.17872i
$834$	−26.5391	+	45.9670i	−0.0318214	+	0.0551164i
$835$		−	519.117i		−	0.621697i
$836$	−106.734	−	625.418i	−0.127672	−	0.748108i
$837$	74.9476			0.0895431
$838$	−165.023	−	95.2760i	−0.196925	−	0.113694i
$839$	791.650	+	457.059i	0.943564	+	0.544767i	0.891076	−	0.453855i	$-0.149952\pi$
$839$	791.650	+	457.059i	0.943564	+	0.544767i	0.0524880	+	0.998622i	$0.483285\pi$
$840$	18.1549	+	31.4453i	0.0216130	+	0.0374348i
$841$	−295.243	+	511.375i	−0.351061	+	0.608056i
$842$	−42.0380	−	72.8120i	−0.0499264	−	0.0864751i
$843$	−704.219			−0.835373
$844$			50.9025i			0.0603111i
$845$	−589.608	−	1021.23i	−0.697761	−	1.20856i
$846$	−2.08711	+	1.20499i	−0.00246703	+	0.00142434i
$847$	−95.9292			−0.113258
$848$		−	1418.47i		−	1.67273i
$849$	278.307	−	160.680i	0.327805	−	0.189259i
$850$	−41.8623	−	24.1692i	−0.0492498	−	0.0284344i
$851$	1128.12	−	651.320i	1.32564	−	0.765359i
$852$	−209.038	+	362.065i	−0.245350	+	0.424959i
$853$	−3.45117	+	5.97759i	−0.00404592	+	0.00700773i	−0.868041	−	0.496492i	$-0.834621\pi$
$853$	−3.45117	+	5.97759i	−0.00404592	+	0.00700773i	0.863995	+	0.503500i	$0.167955\pi$
$854$			6.83432i			0.00800272i
$855$	307.927	+	113.999i	0.360148	+	0.133332i
$856$	103.829			0.121296
$857$	543.649	+	313.876i	0.634363	+	0.366250i	0.782440	−	0.622726i	$-0.213975\pi$
$857$	543.649	+	313.876i	0.634363	+	0.366250i	−0.148077	+	0.988976i	$0.547308\pi$
$858$	57.8280	+	33.3870i	0.0673986	+	0.0389126i
$859$	347.688	+	602.214i	0.404759	+	0.701064i	0.994293	−	0.106680i	$-0.0340220\pi$
$859$	347.688	+	602.214i	0.404759	+	0.701064i	−0.589534	+	0.807743i	$0.700689\pi$
$860$	−328.017	+	568.142i	−0.381415	+	0.660631i
$861$	−2.98363	−	5.16780i	−0.00346531	−	0.00600209i
$862$	−9.89246			−0.0114762
$863$		−	636.029i		−	0.736998i	−0.929628	−	0.368499i	$-0.879872\pi$
$863$		−	636.029i		−	0.736998i	0.929628	−	0.368499i	$-0.120128\pi$
$864$	28.8361	+	49.9456i	0.0333751	+	0.0578074i
$865$	−222.207	+	128.291i	−0.256887	+	0.148314i
$866$	145.148			0.167607
$867$			588.297i			0.678544i
$868$	95.8094	−	55.3156i	0.110380	−	0.0637276i
$869$	711.287	+	410.662i	0.818512	+	0.472568i
$870$	−32.2178	+	18.6009i	−0.0370319	+	0.0213804i
$871$	785.862	−	1361.15i	0.902253	−	1.56275i
$872$	104.201	−	180.482i	0.119497	−	0.206975i
$873$		−	145.991i		−	0.167229i
$874$	−48.6103	+	131.303i	−0.0556182	+	0.150233i
$875$	188.364			0.215273
$876$	−459.494	−	265.289i	−0.524537	−	0.302841i
$877$	−710.586	−	410.257i	−0.810246	−	0.467796i	0.0367954	−	0.999323i	$-0.488285\pi$
$877$	−710.586	−	410.257i	−0.810246	−	0.467796i	−0.847041	+	0.531527i	$0.821618\pi$
$878$	−55.4928	−	96.1163i	−0.0632036	−	0.109472i
$879$	−312.121	+	540.610i	−0.355087	+	0.615028i
$880$	373.970	+	647.735i	0.424966	+	0.736063i
$881$	1473.56			1.67260			0.836301	−	0.548271i	$-0.184714\pi$
$881$	1473.56			1.67260			0.836301	+	0.548271i	$0.184714\pi$
$882$		−	31.9569i		−	0.0362324i
$883$	204.732	+	354.606i	0.231859	+	0.401592i	0.958355	−	0.285578i	$-0.0921857\pi$
$883$	204.732	+	354.606i	0.231859	+	0.401592i	−0.726496	+	0.687171i	$0.758852\pi$
$884$	1655.75	−	955.945i	1.87302	−	1.08139i
$885$	−49.2287			−0.0556257
$886$			24.6266i			0.0277952i
$887$	−1177.32	+	679.728i	−1.32731	+	0.766322i	−0.984883	−	0.173223i	$-0.944582\pi$
$887$	−1177.32	+	679.728i	−1.32731	+	0.766322i	−0.342426	+	0.939545i	$0.611249\pi$
$888$	116.901	+	67.4926i	0.131645	+	0.0760052i
$889$	−407.621	+	235.340i	−0.458517	+	0.264725i
$890$	81.1651	−	140.582i	0.0911968	−	0.157957i
$891$	−38.0952	+	65.9829i	−0.0427556	+	0.0740549i
$892$			366.118i			0.410446i
$893$	10.8998	+	63.8688i	0.0122058	+	0.0715216i
$894$	83.5366			0.0934414
$895$	−1145.59	−	661.404i	−1.27998	−	0.738999i
$896$	98.0625	+	56.6164i	0.109445	+	0.0631879i
$897$	523.703	+	907.080i	0.583838	+	1.01124i
$898$	84.0119	−	145.513i	0.0935545	−	0.162041i
$899$	114.146	+	197.707i	0.126970	+	0.219919i
$900$	−96.8450			−0.107606
$901$			2318.90i			2.57369i
$902$	1.76668	+	3.05998i	0.00195862	+	0.00339244i
$903$	−84.2113	+	48.6194i	−0.0932573	+	0.0538421i
$904$	−207.677			−0.229732
$905$		−	1044.79i		−	1.15446i
$906$	82.7937	−	47.8009i	0.0913837	−	0.0527604i
$907$	1396.68	+	806.372i	1.53989	+	0.889054i	0.998845	+	0.0480579i	$0.0153032\pi$
$907$	1396.68	+	806.372i	1.53989	+	0.889054i	0.541042	+	0.840996i	$0.318030\pi$
$908$	−959.463	+	553.946i	−1.05668	+	0.610073i
$909$	244.662	−	423.767i	0.269155	−	0.466190i
$910$	−25.5054	+	44.1766i	−0.0280279	+	0.0485458i
$911$		−	5.81037i		−	0.00637801i	−0.999995	−	0.00318901i	$-0.998985\pi$
$911$		−	5.81037i		−	0.00637801i	0.999995	−	0.00318901i	$-0.00101509\pi$
$912$	497.536	−	84.9094i	0.545544	−	0.0931024i
$913$	−866.223			−0.948766
$914$	−1.08015	−	0.623627i	−0.00118179	−	0.000682305i
$915$	−128.919	−	74.4315i	−0.140895	−	0.0813459i
$916$	−271.265	−	469.846i	−0.296141	−	0.512932i
$917$	153.089	−	265.157i	0.166945	−	0.289157i
$918$	−15.3455	−	26.5792i	−0.0167162	−	0.0289534i
$919$	−223.733			−0.243452			−0.121726	−	0.992564i	$-0.538843\pi$
$919$	−223.733			−0.243452			−0.121726	+	0.992564i	$0.538843\pi$
$920$		−	337.244i		−	0.366570i
$921$	233.152	+	403.831i	0.253151	+	0.438470i
$922$	−38.1142	+	22.0053i	−0.0413386	+	0.0238669i
$923$	−1182.95			−1.28164
$924$			112.466i			0.121716i
$925$	−295.140	+	170.399i	−0.319071	+	0.184216i
$926$	146.599	+	84.6390i	0.158314	+	0.0914028i
$927$	−47.4752	+	27.4098i	−0.0512139	+	0.0295683i
$928$	−87.8357	+	152.136i	−0.0946506	+	0.163940i
$929$	−87.0368	+	150.752i	−0.0936887	+	0.162274i	−0.909061	−	0.416664i	$-0.863199\pi$
$929$	−87.0368	+	150.752i	−0.0936887	+	0.162274i	0.815372	+	0.578938i	$0.196533\pi$
$930$		−	33.9019i		−	0.0364537i
$931$	−805.717	−	298.287i	−0.865431	−	0.320394i
$932$	1449.08			1.55480
$933$	−80.1794	−	46.2916i	−0.0859372	−	0.0496159i
$934$	176.378	+	101.832i	0.188841	+	0.109028i
$935$	−611.361	−	1058.91i	−0.653862	−	1.13252i
$936$	−54.2684	+	93.9956i	−0.0579790	+	0.100423i
$937$	71.6605	+	124.120i	0.0764786	+	0.132465i	0.901728	−	0.432303i	$-0.142299\pi$
$937$	71.6605	+	124.120i	0.0764786	+	0.132465i	−0.825250	+	0.564768i	$0.808966\pi$
$938$	−37.2430			−0.0397047
$939$			414.859i			0.441810i
$940$	−38.7432	−	67.1052i	−0.0412162	−	0.0713885i
$941$	−133.495	+	77.0732i	−0.141865	+	0.0819057i	−0.569252	−	0.822163i	$-0.692767\pi$
$941$	−133.495	+	77.0732i	−0.141865	+	0.0819057i	0.427388	+	0.904068i	$0.359434\pi$
$942$	−36.1472			−0.0383728
$943$			55.4237i			0.0587738i
$944$	−65.5344	+	37.8363i	−0.0694220	+	0.0400808i
$945$	−50.4064	−	29.1022i	−0.0533401	−	0.0307959i
$946$	49.8635	−	28.7887i	0.0527098	−	0.0304320i
$947$	−79.3787	+	137.488i	−0.0838213	+	0.145183i	−0.904888	−	0.425649i	$-0.860046\pi$
$947$	−79.3787	+	137.488i	−0.0838213	+	0.145183i	0.821067	+	0.570832i	$0.193379\pi$
$948$	−331.420	+	574.037i	−0.349599	+	0.605524i
$949$		−	1501.28i		−	1.58196i
$950$	12.7175	−	34.3518i	0.0133868	−	0.0361598i
$951$	−783.508			−0.823878
$952$	−79.0199	−	45.6221i	−0.0830041	−	0.0479224i
$953$	191.938	+	110.815i	0.201404	+	0.116280i	0.597310	−	0.802010i	$-0.296236\pi$
$953$	191.938	+	110.815i	0.201404	+	0.116280i	−0.395906	+	0.918291i	$0.629570\pi$
$954$	−32.6807	−	56.6046i	−0.0342565	−	0.0593340i
$955$	−802.745	+	1390.40i	−0.840571	+	1.45591i
$956$	387.327	+	670.870i	0.405154	+	0.701747i
$957$	−232.079			−0.242507
$958$			29.7478i			0.0310520i
$959$	235.621	+	408.108i	0.245695	+	0.425556i
$960$	−507.510	+	293.011i	−0.528656	+	0.305220i
$961$	752.958			0.783515
$962$			189.637i			0.197128i
$963$	−144.138	+	83.2184i	−0.149676	+	0.0864157i
$964$	466.339	+	269.241i	0.483754	+	0.279295i
$965$	−964.963	+	557.122i	−0.999962	+	0.577328i
$966$	12.4095	−	21.4938i	0.0128462	−	0.0222504i
$967$	−252.311	+	437.015i	−0.260921	+	0.451929i	−0.966487	−	0.256716i	$-0.917360\pi$
$967$	−252.311	+	437.015i	−0.260921	+	0.451929i	0.705566	+	0.708645i	$0.250693\pi$
$968$			92.3278i			0.0953799i
$969$	−813.366	+	138.809i	−0.839387	+	0.143249i
$970$	−66.0376			−0.0680800
$971$	−1145.39	−	661.292i	−1.17960	−	0.681042i	−0.223678	−	0.974663i	$-0.571806\pi$
$971$	−1145.39	−	661.292i	−1.17960	−	0.681042i	−0.955922	+	0.293621i	$0.905140\pi$
$972$	−53.2508	−	30.7444i	−0.0547848	−	0.0316300i
$973$	−126.477	−	219.064i	−0.129986	−	0.225143i
$974$	1.42755	−	2.47260i	0.00146566	−	0.00253860i
$975$	−137.012	−	237.312i	−0.140525	−	0.243397i
$976$	−228.827			−0.234454
$977$		−	1211.93i		−	1.24046i	−0.784419	−	0.620231i	$-0.787039\pi$
$977$		−	1211.93i		−	1.24046i	0.784419	−	0.620231i	$-0.212961\pi$
$978$	−23.6486	−	40.9605i	−0.0241806	−	0.0418820i
$979$	877.001	−	506.337i	0.895814	−	0.517198i
$980$	1027.49			1.04846
$981$			334.067i			0.340538i
$982$	100.484	−	58.0145i	0.102326	−	0.0590779i
$983$	924.023	+	533.485i	0.940003	+	0.542711i	0.889961	−	0.456036i	$-0.150731\pi$
$983$	924.023	+	533.485i	0.940003	+	0.542711i	0.0500419	+	0.998747i	$0.484065\pi$
$984$	−4.97379	+	2.87162i	−0.00505467	+	0.00291831i
$985$	−279.185	+	483.563i	−0.283437	+	0.490927i
$986$	46.7430	−	80.9612i	0.0474066	−	0.0821107i
$987$		−	11.4852i		−	0.0116365i
$988$	925.156	+	1114.96i	0.936393	+	1.12850i
$989$	903.150			0.913195
$990$	29.8468	+	17.2321i	0.0301483	+	0.0174061i
$991$	−225.943	−	130.448i	−0.227995	−	0.131633i	0.381652	−	0.924306i	$-0.375355\pi$
$991$	−225.943	−	130.448i	−0.227995	−	0.131633i	−0.609647	+	0.792673i	$0.708689\pi$
$992$	−80.0443	−	138.641i	−0.0806898	−	0.139759i
$993$	−82.6800	+	143.206i	−0.0832629	+	0.144216i
$994$	14.0154	+	24.2754i	0.0141000	+	0.0244219i
$995$	1991.92			2.00193
$996$		−	699.077i		−	0.701884i
$997$	361.653	+	626.401i	0.362741	+	0.628286i	0.988411	−	0.151802i	$-0.0485076\pi$
$997$	361.653	+	626.401i	0.362741	+	0.628286i	−0.625670	+	0.780088i	$0.715174\pi$
$998$	70.6426	−	40.7855i	0.0707842	−	0.0408673i
$999$	−216.380			−0.216596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.3.g.b.46.2	yes	6
3.2	odd	2		171.3.p.c.46.2		6
4.3	odd	2		912.3.be.f.673.3		6
19.12	odd	6	inner	57.3.g.b.31.2	✓	6
57.50	even	6		171.3.p.c.145.2		6
76.31	even	6		912.3.be.f.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.2	✓	6	19.12	odd	6	inner
57.3.g.b.46.2	yes	6	1.1	even	1	trivial
171.3.p.c.46.2		6	3.2	odd	2
171.3.p.c.145.2		6	57.50	even	6
912.3.be.f.145.3		6	76.31	even	6
912.3.be.f.673.3		6	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	57.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.204011 + 0.117786i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.97225 - 3.41604i) q^{4} +(2.88028 - 4.98878i) q^{5} +(-0.204011 - 0.353358i) q^{6} +1.94451 q^{7} -1.87150i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.204011 + 0.117786i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.97225 - 3.41604i) q^{4} +(2.88028 - 4.98878i) q^{5} +(-0.204011 - 0.353358i) q^{6} +1.94451 q^{7} -1.87150i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.17522 - 0.678513i) q^{10} +8.46561 q^{11} +6.83208i q^{12} +(-16.7415 + 9.66573i) q^{13} +(0.396701 + 0.229036i) q^{14} +(-8.64083 + 4.98878i) q^{15} +(-7.66857 + 13.2824i) q^{16} +(12.5365 - 21.7138i) q^{17} +0.706716i q^{18} +(17.8181 + 6.59651i) q^{19} -22.7225 q^{20} +(-2.91676 - 1.68399i) q^{21} +(1.72708 + 0.997131i) q^{22} +(15.6408 + 27.0907i) q^{23} +(-1.62077 + 2.80726i) q^{24} +(-4.09198 - 7.08751i) q^{25} -4.55395 q^{26} -5.19615i q^{27} +(-3.83506 - 6.64251i) q^{28} +(13.7071 - 7.91383i) q^{29} -2.35044 q^{30} +14.4237i q^{31} +(-9.61203 + 5.54951i) q^{32} +(-12.6984 - 7.33143i) q^{33} +(5.11517 - 2.95325i) q^{34} +(5.60071 - 9.70072i) q^{35} +(5.91676 - 10.2481i) q^{36} -41.6423i q^{37} +(2.85813 + 3.44449i) q^{38} +33.4831 q^{39} +(-9.33653 - 5.39045i) q^{40} +(1.53439 + 0.885881i) q^{41} +(-0.396701 - 0.687107i) q^{42} +(14.4358 - 25.0035i) q^{43} +(-16.6963 - 28.9189i) q^{44} +17.2817 q^{45} +7.36909i q^{46} +(1.70506 + 2.95325i) q^{47} +(23.0057 - 13.2824i) q^{48} -45.2189 q^{49} -1.92791i q^{50} +(-37.6094 + 21.7138i) q^{51} +(66.0371 + 38.1265i) q^{52} +(-80.0952 + 46.2430i) q^{53} +(0.612034 - 1.06007i) q^{54} +(24.3833 - 42.2331i) q^{55} -3.63915i q^{56} +(-21.0145 - 25.3257i) q^{57} +3.72855 q^{58} +(4.27292 + 2.46697i) q^{59} +(34.0838 + 19.6783i) q^{60} +(7.45989 + 12.9209i) q^{61} +(-1.69891 + 2.94259i) q^{62} +(2.91676 + 5.05197i) q^{63} +58.7340 q^{64} +111.360i q^{65} +(-1.72708 - 2.99139i) q^{66} +(-70.4113 + 40.6520i) q^{67} -98.9005 q^{68} -54.1814i q^{69} +(2.28522 - 1.31937i) q^{70} +(52.9948 + 30.5966i) q^{71} +(4.86231 - 2.80726i) q^{72} +(-38.8299 + 67.2553i) q^{73} +(4.90489 - 8.49551i) q^{74} +14.1750i q^{75} +(-12.6079 - 73.8775i) q^{76} +16.4614 q^{77} +(6.83093 + 3.94384i) q^{78} +(84.0207 + 48.5094i) q^{79} +(44.1752 + 76.5137i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.208689 + 0.361460i) q^{82} -102.323 q^{83} +13.2850i q^{84} +(-72.2171 - 125.084i) q^{85} +(5.89012 - 3.40067i) q^{86} -27.4143 q^{87} -15.8434i q^{88} +(103.596 - 59.8111i) q^{89} +(3.52566 + 2.03554i) q^{90} +(-32.5540 + 18.7951i) q^{91} +(61.6953 - 106.859i) q^{92} +(12.4913 - 21.6355i) q^{93} +0.803328i q^{94} +(84.2297 - 69.8911i) q^{95} +19.2241 q^{96} +(-42.1438 - 24.3318i) q^{97} +(-9.22517 - 5.32616i) q^{98} +(12.6984 + 21.9943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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