LMFDB - Embedded newform 78.3.l.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(7,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.l (of order $12$, degree $4$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.37
Dual form			78.3.l.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.19615 + 1.26795i) q^{10} +(9.92820 + 2.66025i) q^{11} +3.46410i q^{12} +(-11.2583 - 6.50000i) q^{13} -13.6603 q^{14} +(-0.803848 + 3.00000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(16.3923 + 9.46410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(31.9545 - 8.56218i) q^{19} +(0.928203 + 3.46410i) q^{20} +(-11.8301 + 11.8301i) q^{21} +(7.26795 - 12.5885i) q^{22} +(-3.58846 + 2.07180i) q^{23} +(4.73205 + 1.26795i) q^{24} -21.7846i q^{25} +(-13.0000 + 13.0000i) q^{26} +5.19615 q^{27} +(-5.00000 + 18.6603i) q^{28} +(8.66025 + 15.0000i) q^{29} +(3.80385 + 2.19615i) q^{30} +(22.1699 + 22.1699i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-4.60770 - 17.1962i) q^{33} +(18.9282 - 18.9282i) q^{34} +(-8.66025 + 15.0000i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-35.7583 - 9.58142i) q^{37} -46.7846i q^{38} +22.5167i q^{39} +5.07180 q^{40} +(-6.67949 + 24.9282i) q^{41} +(11.8301 + 20.4904i) q^{42} +(-13.2846 - 7.66987i) q^{43} +(-14.5359 - 14.5359i) q^{44} +(5.19615 - 1.39230i) q^{45} +(1.51666 + 5.66025i) q^{46} +(7.01924 - 7.01924i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-38.3660 + 22.1506i) q^{49} +(-29.7583 - 7.97372i) q^{50} -32.7846i q^{51} +(13.0000 + 22.5167i) q^{52} -61.6743 q^{53} +(1.90192 - 7.09808i) q^{54} +(-9.21539 - 15.9615i) q^{55} +(23.6603 + 13.6603i) q^{56} +(-40.5167 - 40.5167i) q^{57} +(23.6603 - 6.33975i) q^{58} +(-17.1051 - 63.8372i) q^{59} +(4.39230 - 4.39230i) q^{60} +(3.65064 - 6.32309i) q^{61} +(38.3993 - 22.1699i) q^{62} +(27.9904 + 7.50000i) q^{63} -8.00000i q^{64} +(6.03332 + 22.5167i) q^{65} -25.1769 q^{66} +(-10.1532 + 37.8923i) q^{67} +(-18.9282 - 32.7846i) q^{68} +(6.21539 + 3.58846i) q^{69} +(17.3205 + 17.3205i) q^{70} +(103.890 - 27.8372i) q^{71} +(-2.19615 - 8.19615i) q^{72} +(-67.4186 + 67.4186i) q^{73} +(-26.1769 + 45.3397i) q^{74} +(-32.6769 + 18.8660i) q^{75} +(-63.9090 - 17.1244i) q^{76} -99.2820i q^{77} +(30.7583 + 8.24167i) q^{78} +11.8756 q^{79} +(1.85641 - 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(31.6077 + 18.2487i) q^{82} +(111.033 + 111.033i) q^{83} +(32.3205 - 8.66025i) q^{84} +(-8.78461 - 32.7846i) q^{85} +(-15.3397 + 15.3397i) q^{86} +(15.0000 - 25.9808i) q^{87} +(-25.1769 + 14.5359i) q^{88} +(162.067 + 43.4256i) q^{89} -7.60770i q^{90} +(-32.5000 + 121.292i) q^{91} +8.28719 q^{92} +(14.0551 - 52.4545i) q^{93} +(-7.01924 - 12.1577i) q^{94} +(-51.3731 - 29.6603i) q^{95} +(-6.92820 - 6.92820i) q^{96} +(150.246 - 40.2583i) q^{97} +(16.2154 + 60.5167i) q^{98} +(-21.8038 + 21.8038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 + 12 * q^10 + 12 * q^11 - 20 * q^14 - 24 * q^15 + 8 * q^16 + 24 * q^17 + 12 * q^18 + 62 * q^19 - 24 * q^20 - 30 * q^21 + 36 * q^22 + 48 * q^23 + 12 * q^24 - 52 * q^26 - 20 * q^28 + 36 * q^30 + 106 * q^31 + 8 * q^32 - 60 * q^33 + 48 * q^34 - 98 * q^37 + 48 * q^40 - 96 * q^41 + 30 * q^42 + 30 * q^43 - 72 * q^44 - 84 * q^46 + 132 * q^47 - 150 * q^49 - 74 * q^50 + 52 * q^52 + 72 * q^53 + 18 * q^54 - 120 * q^55 + 60 * q^56 - 72 * q^57 + 60 * q^58 + 84 * q^59 - 24 * q^60 - 72 * q^61 - 30 * q^62 + 60 * q^63 - 156 * q^65 + 24 * q^66 - 148 * q^67 - 48 * q^68 + 108 * q^69 + 180 * q^71 + 12 * q^72 - 190 * q^73 + 20 * q^74 - 6 * q^75 - 124 * q^76 + 78 * q^78 + 96 * q^79 - 48 * q^80 - 18 * q^81 + 168 * q^82 + 264 * q^83 + 60 * q^84 + 48 * q^85 - 96 * q^86 + 60 * q^87 + 24 * q^88 + 288 * q^89 - 130 * q^91 + 144 * q^92 + 174 * q^93 - 132 * q^94 - 60 * q^95 + 310 * q^97 + 148 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	0.568851	−	0.822441i	$-0.307388\pi$
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	−0.822441	+	0.568851i	$0.807388\pi$
$6$	−2.36603	+	0.633975i	−0.394338	+	0.105662i
$7$	−2.50000	−	9.33013i	−0.357143	−	1.33288i	−0.877766	−	0.479089i	$-0.840967\pi$
$7$	−2.50000	−	9.33013i	−0.357143	−	1.33288i	0.520624	−	0.853786i	$-0.325700\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−2.19615	+	1.26795i	−0.219615	+	0.126795i
$11$	9.92820	+	2.66025i	0.902564	+	0.241841i	0.680117	−	0.733104i	$-0.261929\pi$
$11$	9.92820	+	2.66025i	0.902564	+	0.241841i	0.222447	+	0.974945i	$0.428596\pi$
$12$			3.46410i			0.288675i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$14$	−13.6603			−0.975732
$15$	−0.803848	+	3.00000i	−0.0535898	+	0.200000i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	16.3923	+	9.46410i	0.964253	+	0.556712i	0.897479	−	0.441056i	$-0.145396\pi$
$17$	16.3923	+	9.46410i	0.964253	+	0.556712i	0.0667738	+	0.997768i	$0.478729\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$	31.9545	−	8.56218i	1.68181	−	0.450641i	0.713558	−	0.700597i	$-0.247083\pi$
$19$	31.9545	−	8.56218i	1.68181	−	0.450641i	0.968257	+	0.249956i	$0.0804160\pi$
$20$	0.928203	+	3.46410i	0.0464102	+	0.173205i
$21$	−11.8301	+	11.8301i	−0.563339	+	0.563339i
$22$	7.26795	−	12.5885i	0.330361	−	0.572203i
$23$	−3.58846	+	2.07180i	−0.156020	+	0.0900781i	−0.575977	−	0.817466i	$-0.695378\pi$
$23$	−3.58846	+	2.07180i	−0.156020	+	0.0900781i	0.419957	+	0.907544i	$0.362045\pi$
$24$	4.73205	+	1.26795i	0.197169	+	0.0528312i
$25$		−	21.7846i		−	0.871384i
$26$	−13.0000	+	13.0000i	−0.500000	+	0.500000i
$27$	5.19615			0.192450
$28$	−5.00000	+	18.6603i	−0.178571	+	0.666438i
$29$	8.66025	+	15.0000i	0.298629	+	0.517241i	0.975823	−	0.218564i	$-0.0701372\pi$
$29$	8.66025	+	15.0000i	0.298629	+	0.517241i	−0.677193	+	0.735805i	$0.736804\pi$
$30$	3.80385	+	2.19615i	0.126795	+	0.0732051i
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	0.967609	−	0.252452i	$-0.0812370\pi$
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	−0.252452	+	0.967609i	$0.581237\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	−4.60770	−	17.1962i	−0.139627	−	0.521096i
$34$	18.9282	−	18.9282i	0.556712	−	0.556712i
$35$	−8.66025	+	15.0000i	−0.247436	+	0.428571i
$36$	5.19615	−	3.00000i	0.144338	−	0.0833333i
$37$	−35.7583	−	9.58142i	−0.966441	−	0.258957i	−0.259117	−	0.965846i	$-0.583431\pi$
$37$	−35.7583	−	9.58142i	−0.966441	−	0.258957i	−0.707325	+	0.706889i	$0.750098\pi$
$38$		−	46.7846i		−	1.23117i
$39$			22.5167i			0.577350i
$40$	5.07180			0.126795
$41$	−6.67949	+	24.9282i	−0.162914	+	0.608005i	0.835383	+	0.549669i	$0.185246\pi$
$41$	−6.67949	+	24.9282i	−0.162914	+	0.608005i	−0.998297	+	0.0583360i	$0.981421\pi$
$42$	11.8301	+	20.4904i	0.281670	+	0.487866i
$43$	−13.2846	−	7.66987i	−0.308944	−	0.178369i	0.337510	−	0.941322i	$-0.390415\pi$
$43$	−13.2846	−	7.66987i	−0.308944	−	0.178369i	−0.646454	+	0.762953i	$0.723749\pi$
$44$	−14.5359	−	14.5359i	−0.330361	−	0.330361i
$45$	5.19615	−	1.39230i	0.115470	−	0.0309401i
$46$	1.51666	+	5.66025i	0.0329709	+	0.123049i
$47$	7.01924	−	7.01924i	0.149345	−	0.149345i	−0.628480	−	0.777826i	$-0.716323\pi$
$47$	7.01924	−	7.01924i	0.149345	−	0.149345i	0.777826	+	0.628480i	$0.216323\pi$
$48$	3.46410	−	6.00000i	0.0721688	−	0.125000i
$49$	−38.3660	+	22.1506i	−0.782980	+	0.452054i
$50$	−29.7583	−	7.97372i	−0.595167	−	0.159474i
$51$		−	32.7846i		−	0.642835i
$52$	13.0000	+	22.5167i	0.250000	+	0.433013i
$53$	−61.6743			−1.16367			−0.581833	−	0.813308i	$-0.697664\pi$
$53$	−61.6743			−1.16367			−0.581833	+	0.813308i	$0.697664\pi$
$54$	1.90192	−	7.09808i	0.0352208	−	0.131446i
$55$	−9.21539	−	15.9615i	−0.167553	−	0.290210i
$56$	23.6603	+	13.6603i	0.422505	+	0.243933i
$57$	−40.5167	−	40.5167i	−0.710819	−	0.710819i
$58$	23.6603	−	6.33975i	0.407935	−	0.109306i
$59$	−17.1051	−	63.8372i	−0.289917	−	1.08199i	−0.945171	−	0.326577i	$-0.894105\pi$
$59$	−17.1051	−	63.8372i	−0.289917	−	1.08199i	0.655253	−	0.755409i	$-0.272562\pi$
$60$	4.39230	−	4.39230i	0.0732051	−	0.0732051i
$61$	3.65064	−	6.32309i	0.0598465	−	0.103657i	−0.834550	−	0.550932i	$-0.814272\pi$
$61$	3.65064	−	6.32309i	0.0598465	−	0.103657i	0.894396	+	0.447275i	$0.147606\pi$
$62$	38.3993	−	22.1699i	0.619344	−	0.357579i
$63$	27.9904	+	7.50000i	0.444292	+	0.119048i
$64$		−	8.00000i		−	0.125000i
$65$	6.03332	+	22.5167i	0.0928203	+	0.346410i
$66$	−25.1769			−0.381468
$67$	−10.1532	+	37.8923i	−0.151540	+	0.565557i	0.847836	+	0.530258i	$0.177905\pi$
$67$	−10.1532	+	37.8923i	−0.151540	+	0.565557i	−0.999377	+	0.0352988i	$0.988762\pi$
$68$	−18.9282	−	32.7846i	−0.278356	−	0.482127i
$69$	6.21539	+	3.58846i	0.0900781	+	0.0520066i
$70$	17.3205	+	17.3205i	0.247436	+	0.247436i
$71$	103.890	−	27.8372i	1.46324	−	0.392073i	0.562630	−	0.826709i	$-0.309790\pi$
$71$	103.890	−	27.8372i	1.46324	−	0.392073i	0.900606	+	0.434636i	$0.143123\pi$
$72$	−2.19615	−	8.19615i	−0.0305021	−	0.113835i
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	−0.997278	−	0.0737356i	$-0.976508\pi$
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	0.0737356	+	0.997278i	$0.476508\pi$
$74$	−26.1769	+	45.3397i	−0.353742	+	0.612699i
$75$	−32.6769	+	18.8660i	−0.435692	+	0.251547i
$76$	−63.9090	−	17.1244i	−0.840907	−	0.225320i
$77$		−	99.2820i		−	1.28938i
$78$	30.7583	+	8.24167i	0.394338	+	0.105662i
$79$	11.8756			0.150325			0.0751623	−	0.997171i	$-0.476053\pi$
$79$	11.8756			0.150325			0.0751623	+	0.997171i	$0.476053\pi$
$80$	1.85641	−	6.92820i	0.0232051	−	0.0866025i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	31.6077	+	18.2487i	0.385460	+	0.222545i
$83$	111.033	+	111.033i	1.33775	+	1.33775i	0.898235	+	0.439516i	$0.144850\pi$
$83$	111.033	+	111.033i	1.33775	+	1.33775i	0.439516	+	0.898235i	$0.355150\pi$
$84$	32.3205	−	8.66025i	0.384768	−	0.103098i
$85$	−8.78461	−	32.7846i	−0.103348	−	0.385701i
$86$	−15.3397	+	15.3397i	−0.178369	+	0.178369i
$87$	15.0000	−	25.9808i	0.172414	−	0.298629i
$88$	−25.1769	+	14.5359i	−0.286101	+	0.165181i
$89$	162.067	+	43.4256i	1.82097	+	0.487928i	0.996909	−	0.0785673i	$-0.0250346\pi$
$89$	162.067	+	43.4256i	1.82097	+	0.487928i	0.824065	+	0.566496i	$0.191701\pi$
$90$		−	7.60770i		−	0.0845299i
$91$	−32.5000	+	121.292i	−0.357143	+	1.33288i
$92$	8.28719			0.0900781
$93$	14.0551	−	52.4545i	0.151130	−	0.564027i
$94$	−7.01924	−	12.1577i	−0.0746727	−	0.129337i
$95$	−51.3731	−	29.6603i	−0.540769	−	0.312213i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	150.246	−	40.2583i	1.54893	−	0.415034i	0.619791	−	0.784767i	$-0.287217\pi$
$97$	150.246	−	40.2583i	1.54893	−	0.415034i	0.929138	+	0.369733i	$0.120551\pi$
$98$	16.2154	+	60.5167i	0.165463	+	0.617517i
$99$	−21.8038	+	21.8038i	−0.220241	+	0.220241i
$100$	−21.7846	+	37.7321i	−0.217846	+	0.377321i
$101$	−161.785	+	93.4064i	−1.60183	+	0.924816i	−0.610706	+	0.791857i	$0.709114\pi$
$101$	−161.785	+	93.4064i	−1.60183	+	0.924816i	−0.991122	+	0.132958i	$0.957552\pi$
$102$	−44.7846	−	12.0000i	−0.439065	−	0.117647i
$103$			83.2628i			0.808377i	0.914676	+	0.404188i	$0.132446\pi$
$103$			83.2628i			0.808377i	−0.914676	+	0.404188i	$0.867554\pi$
$104$	35.5167	−	9.51666i	0.341506	−	0.0915064i
$105$	30.0000			0.285714
$106$	−22.5744	+	84.2487i	−0.212966	+	0.794799i
$107$	−51.2487	−	88.7654i	−0.478960	−	0.829583i	0.520749	−	0.853710i	$-0.325653\pi$
$107$	−51.2487	−	88.7654i	−0.478960	−	0.829583i	−0.999709	+	0.0241269i	$0.992319\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	0.892718	−	0.450616i	$-0.148796\pi$
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	−0.450616	+	0.892718i	$0.648796\pi$
$110$	−25.1769	+	6.74613i	−0.228881	+	0.0613285i
$111$	16.5955	+	61.9352i	0.149509	+	0.557975i
$112$	27.3205	−	27.3205i	0.243933	−	0.243933i
$113$	22.6077	−	39.1577i	0.200068	−	0.346528i	−0.748482	−	0.663155i	$-0.769217\pi$
$113$	22.6077	−	39.1577i	0.200068	−	0.346528i	0.948550	+	0.316627i	$0.102550\pi$
$114$	−70.1769	+	40.5167i	−0.615587	+	0.355409i
$115$	7.17691	+	1.92305i	0.0624080	+	0.0167222i
$116$		−	34.6410i		−	0.298629i
$117$	33.7750	−	19.5000i	0.288675	−	0.166667i
$118$	−93.4641			−0.792069
$119$	47.3205	−	176.603i	0.397651	−	1.48405i
$120$	−4.39230	−	7.60770i	−0.0366025	−	0.0633975i
$121$	−13.2968	−	7.67691i	−0.109891	−	0.0634456i
$122$	−7.30127	−	7.30127i	−0.0598465	−	0.0598465i
$123$	43.1769	−	11.5692i	0.351032	−	0.0940587i
$124$	−16.2295	−	60.5692i	−0.130883	−	0.488461i
$125$	−59.3205	+	59.3205i	−0.474564	+	0.474564i
$126$	20.4904	−	35.4904i	0.162622	−	0.281670i
$127$	205.115	−	118.423i	1.61508	−	0.932465i	0.626908	−	0.779093i	$-0.284320\pi$
$127$	205.115	−	118.423i	1.61508	−	0.932465i	0.988169	−	0.153372i	$-0.0490132\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$			26.5692i			0.205963i
$130$	32.9667			0.253590
$131$	−209.636			−1.60027			−0.800137	−	0.599817i	$-0.795240\pi$
$131$	−209.636			−1.60027			−0.800137	+	0.599817i	$0.795240\pi$
$132$	−9.21539	+	34.3923i	−0.0698136	+	0.260548i
$133$	−159.772	−	276.734i	−1.20130	−	2.08071i
$134$	48.0455	+	27.7391i	0.358549	+	0.207008i
$135$	−6.58846	−	6.58846i	−0.0488034	−	0.0488034i
$136$	−51.7128	+	13.8564i	−0.380241	+	0.101885i
$137$	29.4782	+	110.014i	0.215169	+	0.803023i	0.986107	+	0.166112i	$0.0531213\pi$
$137$	29.4782	+	110.014i	0.215169	+	0.803023i	−0.770938	+	0.636911i	$0.780212\pi$
$138$	7.17691	−	7.17691i	0.0520066	−	0.0520066i
$139$	47.8538	−	82.8853i	0.344272	−	0.596297i	−0.640949	−	0.767583i	$-0.721459\pi$
$139$	47.8538	−	82.8853i	0.344272	−	0.596297i	0.985221	+	0.171287i	$0.0547924\pi$
$140$	30.0000	−	17.3205i	0.214286	−	0.123718i
$141$	−16.6077	−	4.45002i	−0.117785	−	0.0315604i
$142$		−	152.105i		−	1.07116i
$143$	−94.4833	−	94.4833i	−0.660723	−	0.660723i
$144$	−12.0000			−0.0833333
$145$	8.03848	−	30.0000i	0.0554378	−	0.206897i
$146$	67.4186	+	116.772i	0.461771	+	0.799811i
$147$	66.4519	+	38.3660i	0.452054	+	0.260993i
$148$	52.3538	+	52.3538i	0.353742	+	0.353742i
$149$	−54.9282	+	14.7180i	−0.368646	+	0.0987783i	−0.438386	−	0.898787i	$-0.644450\pi$
$149$	−54.9282	+	14.7180i	−0.368646	+	0.0987783i	0.0697402	+	0.997565i	$0.477783\pi$
$150$	13.8109	+	51.5429i	0.0920726	+	0.343620i
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	−0.865464	−	0.500971i	$-0.832976\pi$
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	0.500971	+	0.865464i	$0.332976\pi$
$152$	−46.7846	+	81.0333i	−0.307793	+	0.533114i
$153$	−49.1769	+	28.3923i	−0.321418	+	0.185571i
$154$	−135.622	−	36.3397i	−0.880661	−	0.235972i
$155$		−	56.2205i		−	0.362713i
$156$	22.5167	−	39.0000i	0.144338	−	0.250000i
$157$	55.4308			0.353062			0.176531	−	0.984295i	$-0.443512\pi$
$157$	55.4308			0.353062			0.176531	+	0.984295i	$0.443512\pi$
$158$	4.34679	−	16.2224i	0.0275113	−	0.102674i
$159$	53.4115	+	92.5115i	0.335922	+	0.581833i
$160$	−8.78461	−	5.07180i	−0.0549038	−	0.0316987i
$161$	28.3013	+	28.3013i	0.175784	+	0.175784i
$162$	−12.2942	+	3.29423i	−0.0758903	+	0.0203347i
$163$	−52.9468	−	197.600i	−0.324827	−	1.21227i	−0.914486	−	0.404618i	$-0.867405\pi$
$163$	−52.9468	−	197.600i	−0.324827	−	1.21227i	0.589659	−	0.807652i	$-0.299262\pi$
$164$	36.4974	−	36.4974i	0.222545	−	0.222545i
$165$	−15.9615	+	27.6462i	−0.0967365	+	0.167553i
$166$	192.315	−	111.033i	1.15853	−	0.668875i
$167$	−156.315	−	41.8846i	−0.936020	−	0.250806i	−0.241600	−	0.970376i	$-0.577672\pi$
$167$	−156.315	−	41.8846i	−0.936020	−	0.250806i	−0.694420	+	0.719570i	$0.744339\pi$
$168$		−	47.3205i		−	0.281670i
$169$	84.5000	+	146.358i	0.500000	+	0.866025i
$170$	−48.0000			−0.282353
$171$	−25.6865	+	95.8634i	−0.150214	+	0.560605i
$172$	15.3397	+	26.5692i	0.0891846	+	0.154472i
$173$	232.492	+	134.229i	1.34389	+	0.775893i	0.987375	−	0.158398i	$-0.0506330\pi$
$173$	232.492	+	134.229i	1.34389	+	0.775893i	0.356511	+	0.934291i	$0.383966\pi$
$174$	−30.0000	−	30.0000i	−0.172414	−	0.172414i
$175$	−203.253	+	54.4615i	−1.16145	+	0.311209i
$176$	10.6410	+	39.7128i	0.0604603	+	0.225641i
$177$	−80.9423	+	80.9423i	−0.457301	+	0.457301i
$178$	118.641	−	205.492i	0.666523	−	1.15445i
$179$	−247.492	+	142.890i	−1.38264	+	0.798267i	−0.992471	−	0.122477i	$-0.960916\pi$
$179$	−247.492	+	142.890i	−1.38264	+	0.798267i	−0.390167	+	0.920744i	$0.627583\pi$
$180$	−10.3923	−	2.78461i	−0.0577350	−	0.0154701i
$181$			177.646i			0.981471i	0.871309	+	0.490735i	$0.163272\pi$
$181$			177.646i			0.981471i	−0.871309	+	0.490735i	$0.836728\pi$
$182$	153.792	+	88.7917i	0.845009	+	0.487866i
$183$	−12.6462			−0.0691048
$184$	3.03332	−	11.3205i	0.0164854	−	0.0615245i
$185$	33.1910	+	57.4885i	0.179411	+	0.310749i
$186$	−66.5096	−	38.3993i	−0.357579	−	0.206448i
$187$	137.569	+	137.569i	0.735664	+	0.735664i
$188$	−19.1769	+	5.13844i	−0.102005	+	0.0273321i
$189$	−12.9904	−	48.4808i	−0.0687322	−	0.256512i
$190$	−59.3205	+	59.3205i	−0.312213	+	0.312213i
$191$	−98.6603	+	170.885i	−0.516546	+	0.894684i	0.483270	+	0.875472i	$0.339449\pi$
$191$	−98.6603	+	170.885i	−0.516546	+	0.894684i	−0.999815	+	0.0192120i	$0.993884\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−20.2846	−	5.43524i	−0.105102	−	0.0281619i	0.205885	−	0.978576i	$-0.433993\pi$
$193$	−20.2846	−	5.43524i	−0.105102	−	0.0281619i	−0.310987	+	0.950414i	$0.600659\pi$
$194$		−	219.976i		−	1.13389i
$195$	28.5500	−	28.5500i	0.146410	−	0.146410i
$196$	88.6025			0.452054
$197$	39.1487	−	146.105i	0.198725	−	0.741650i	−0.792547	−	0.609811i	$-0.791245\pi$
$197$	39.1487	−	146.105i	0.198725	−	0.741650i	0.991271	−	0.131839i	$-0.0420882\pi$
$198$	21.8038	+	37.7654i	0.110120	+	0.190734i
$199$	19.2391	+	11.1077i	0.0966789	+	0.0558176i	0.547560	−	0.836766i	$-0.315557\pi$
$199$	19.2391	+	11.1077i	0.0966789	+	0.0558176i	−0.450881	+	0.892584i	$0.648890\pi$
$200$	43.5692	+	43.5692i	0.217846	+	0.217846i
$201$	65.6314	−	17.5859i	0.326524	−	0.0874919i
$202$	68.3782	+	255.191i	0.338506	+	1.26332i
$203$	118.301	−	118.301i	0.582765	−	0.582765i
$204$	−32.7846	+	56.7846i	−0.160709	+	0.278356i
$205$	40.0770	−	23.1384i	0.195497	−	0.112870i
$206$	113.739	+	30.4763i	0.552132	+	0.147943i
$207$		−	12.4308i		−	0.0600521i
$208$		−	52.0000i		−	0.250000i
$209$	340.028			1.62693
$210$	10.9808	−	40.9808i	0.0522893	−	0.195146i
$211$	−32.1007	−	55.6000i	−0.152136	−	0.263507i	0.779877	−	0.625933i	$-0.215282\pi$
$211$	−32.1007	−	55.6000i	−0.152136	−	0.263507i	−0.932012	+	0.362426i	$0.881948\pi$
$212$	106.823	+	61.6743i	0.503882	+	0.290917i
$213$	−131.727	−	131.727i	−0.618436	−	0.618436i
$214$	−140.014	+	37.5167i	−0.654271	+	0.175311i
$215$	7.11920	+	26.5692i	0.0331126	+	0.123578i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	151.423	−	262.272i	0.697802	−	1.20863i
$218$	83.4660	−	48.1891i	0.382872	−	0.221051i
$219$	159.514	+	42.7417i	0.728375	+	0.195167i
$220$			36.8616i			0.167553i
$221$	−123.033	−	213.100i	−0.556712	−	0.964253i
$222$	90.6795			0.408466
$223$	−56.5622	+	211.093i	−0.253642	+	0.946605i	0.715199	+	0.698921i	$0.246336\pi$
$223$	−56.5622	+	211.093i	−0.253642	+	0.946605i	−0.968841	+	0.247684i	$0.920331\pi$
$224$	−27.3205	−	47.3205i	−0.121967	−	0.211252i
$225$	56.5981	+	32.6769i	0.251547	+	0.145231i
$226$	−45.2154	−	45.2154i	−0.200068	−	0.200068i
$227$	62.4449	−	16.7321i	0.275088	−	0.0737095i	−0.118638	−	0.992938i	$-0.537853\pi$
$227$	62.4449	−	16.7321i	0.275088	−	0.0737095i	0.393725	+	0.919228i	$0.371186\pi$
$228$	29.6603	+	110.694i	0.130089	+	0.485498i
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	−0.567268	−	0.823533i	$-0.692000\pi$
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	0.823533	+	0.567268i	$0.192000\pi$
$230$	5.25387	−	9.09996i	0.0228429	−	0.0395651i
$231$	−148.923	+	85.9808i	−0.644689	+	0.372211i
$232$	−47.3205	−	12.6795i	−0.203968	−	0.0546530i
$233$			380.669i			1.63377i	0.576798	+	0.816887i	$0.304302\pi$
$233$			380.669i			1.63377i	−0.576798	+	0.816887i	$0.695698\pi$
$234$	−14.2750	−	53.2750i	−0.0610042	−	0.227671i
$235$	−17.8001			−0.0757450
$236$	−34.2102	+	127.674i	−0.144959	+	0.540993i
$237$	−10.2846	−	17.8135i	−0.0433950	−	0.0751623i
$238$	−223.923	−	129.282i	−0.940853	−	0.543202i
$239$	−167.138	−	167.138i	−0.699324	−	0.699324i	0.264941	−	0.964265i	$-0.414648\pi$
$239$	−167.138	−	167.138i	−0.699324	−	0.699324i	−0.964265	+	0.264941i	$0.914648\pi$
$240$	−12.0000	+	3.21539i	−0.0500000	+	0.0133975i
$241$	0.796806	+	2.97372i	0.00330625	+	0.0123391i	0.967559	−	0.252644i	$-0.0813002\pi$
$241$	0.796806	+	2.97372i	0.00330625	+	0.0123391i	−0.964253	+	0.264983i	$0.914634\pi$
$242$	−15.3538	+	15.3538i	−0.0634456	+	0.0634456i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$	−12.6462	+	7.30127i	−0.0518286	+	0.0299232i
$245$	76.7321	+	20.5603i	0.313192	+	0.0839196i
$246$		−	63.2154i		−	0.256973i
$247$	−415.408	−	111.308i	−1.68181	−	0.450641i
$248$	−88.6795			−0.357579
$249$	70.3923	−	262.708i	0.282700	−	1.05505i
$250$	59.3205	+	102.746i	0.237282	+	0.410985i
$251$	−180.746	−	104.354i	−0.720104	−	0.415752i	0.0946869	−	0.995507i	$-0.469815\pi$
$251$	−180.746	−	104.354i	−0.720104	−	0.415752i	−0.814791	+	0.579755i	$0.803148\pi$
$252$	−40.9808	−	40.9808i	−0.162622	−	0.162622i
$253$	−41.1384	+	11.0230i	−0.162603	+	0.0435692i
$254$	−86.6917	−	323.538i	−0.341306	−	1.27377i
$255$	−41.5692	+	41.5692i	−0.163017	+	0.163017i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	64.2769	−	37.1103i	0.250105	−	0.144398i	−0.369708	−	0.929148i	$-0.620542\pi$
$257$	64.2769	−	37.1103i	0.250105	−	0.144398i	0.619812	+	0.784750i	$0.287209\pi$
$258$	36.2942	+	9.72501i	0.140675	+	0.0376938i
$259$			357.583i			1.38063i
$260$	12.0666	−	45.0333i	0.0464102	−	0.173205i
$261$	−51.9615			−0.199086
$262$	−76.7321	+	286.368i	−0.292870	+	1.09301i
$263$	12.1821	+	21.1000i	0.0463197	+	0.0802280i	0.888256	−	0.459349i	$-0.151917\pi$
$263$	12.1821	+	21.1000i	0.0463197	+	0.0802280i	−0.841936	+	0.539577i	$0.818584\pi$
$264$	43.6077	+	25.1769i	0.165181	+	0.0953671i
$265$	78.1999	+	78.1999i	0.295094	+	0.295094i
$266$	−436.506	+	116.962i	−1.64100	+	0.439705i
$267$	−75.2154	−	280.708i	−0.281706	−	1.05134i
$268$	55.4782	−	55.4782i	0.207008	−	0.207008i
$269$	87.8705	−	152.196i	0.326656	−	0.565785i	−0.655190	−	0.755464i	$-0.727411\pi$
$269$	87.8705	−	152.196i	0.326656	−	0.565785i	0.981846	+	0.189679i	$0.0607448\pi$
$270$	−11.4115	+	6.58846i	−0.0422650	+	0.0244017i
$271$	269.169	+	72.1237i	0.993244	+	0.266139i	0.718613	−	0.695411i	$-0.244777\pi$
$271$	269.169	+	72.1237i	0.993244	+	0.266139i	0.274632	+	0.961550i	$0.411444\pi$
$272$			75.7128i			0.278356i
$273$	210.083	−	56.2917i	0.769536	−	0.206197i
$274$	161.072			0.587853
$275$	57.9526	−	216.282i	0.210737	−	0.786480i
$276$	−7.17691	−	12.4308i	−0.0260033	−	0.0450391i
$277$	−387.100	−	223.492i	−1.39747	−	0.806831i	−0.403345	−	0.915048i	$-0.632153\pi$
$277$	−387.100	−	223.492i	−1.39747	−	0.806831i	−0.994127	+	0.108216i	$0.965486\pi$
$278$	−95.7077	−	95.7077i	−0.344272	−	0.344272i
$279$	−90.8538	+	24.3442i	−0.325641	+	0.0872552i
$280$	−12.6795	−	47.3205i	−0.0452839	−	0.169002i
$281$	−5.54483	+	5.54483i	−0.0197325	+	0.0197325i	−0.716904	−	0.697172i	$-0.754442\pi$
$281$	−5.54483	+	5.54483i	−0.0197325	+	0.0197325i	0.697172	+	0.716904i	$0.254442\pi$
$282$	−12.1577	+	21.0577i	−0.0431123	+	0.0746727i
$283$	14.4160	−	8.32309i	0.0509400	−	0.0294102i	−0.474314	−	0.880356i	$-0.657304\pi$
$283$	14.4160	−	8.32309i	0.0509400	−	0.0294102i	0.525254	+	0.850946i	$0.323970\pi$
$284$	−207.779	−	55.6743i	−0.731618	−	0.196036i
$285$			102.746i			0.360513i
$286$	−163.650	+	94.4833i	−0.572203	+	0.330361i
$287$	249.282			0.868579
$288$	−4.39230	+	16.3923i	−0.0152511	+	0.0569177i
$289$	34.6384	+	59.9955i	0.119856	+	0.207597i
$290$	−38.0385	−	21.9615i	−0.131167	−	0.0757294i
$291$	−190.504	−	190.504i	−0.654655	−	0.654655i
$292$	184.191	−	49.3538i	0.630791	−	0.169020i
$293$	48.4885	+	180.962i	0.165490	+	0.617616i	0.997977	+	0.0635723i	$0.0202493\pi$
$293$	48.4885	+	180.962i	0.165490	+	0.617616i	−0.832487	+	0.554044i	$0.813084\pi$
$294$	76.7321	−	76.7321i	0.260993	−	0.260993i
$295$	−59.2539	+	102.631i	−0.200861	+	0.347901i
$296$	90.6795	−	52.3538i	0.306350	−	0.176871i
$297$	51.5885	+	13.8231i	0.173699	+	0.0465424i
$298$			80.4205i			0.269867i
$299$	53.8667			0.180156
$300$	75.4641			0.251547
$301$	−38.3494	+	143.122i	−0.127407	+	0.475488i
$302$	55.0385	+	95.3294i	0.182247	+	0.315660i
$303$	280.219	+	161.785i	0.924816	+	0.533943i
$304$	93.5692	+	93.5692i	0.307793	+	0.307793i
$305$	−12.6462	+	3.38853i	−0.0414629	+	0.0111099i
$306$	20.7846	+	77.5692i	0.0679236	+	0.253494i
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.254702	−	0.967020i	$-0.418023\pi$
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.967020	−	0.254702i	$-0.0819774\pi$
$308$	−99.2820	+	171.962i	−0.322344	+	0.558317i
$309$	124.894	−	72.1077i	0.404188	−	0.233358i
$310$	−76.7987	−	20.5781i	−0.247738	−	0.0663811i
$311$		−	296.238i		−	0.952535i	−0.879300	−	0.476268i	$-0.841989\pi$
$311$		−	296.238i		−	0.952535i	0.879300	−	0.476268i	$-0.158011\pi$
$312$	−45.0333	−	45.0333i	−0.144338	−	0.144338i
$313$	118.286			0.377910			0.188955	−	0.981986i	$-0.439490\pi$
$313$	118.286			0.377910			0.188955	+	0.981986i	$0.439490\pi$
$314$	20.2891	−	75.7199i	0.0646149	−	0.241146i
$315$	−25.9808	−	45.0000i	−0.0824786	−	0.142857i
$316$	−20.5692	−	11.8756i	−0.0650925	−	0.0375812i
$317$	−280.708	−	280.708i	−0.885513	−	0.885513i	0.108575	−	0.994088i	$-0.465371\pi$
$317$	−280.708	−	280.708i	−0.885513	−	0.885513i	−0.994088	+	0.108575i	$0.965371\pi$
$318$	145.923	−	39.1000i	0.458878	−	0.122956i
$319$	46.0770	+	171.962i	0.144442	+	0.539064i
$320$	−10.1436	+	10.1436i	−0.0316987	+	0.0316987i
$321$	−88.7654	+	153.746i	−0.276528	+	0.478960i
$322$	49.0192	−	28.3013i	0.152234	−	0.0878921i
$323$	604.841	+	162.067i	1.87257	+	0.501754i
$324$			18.0000i			0.0555556i
$325$	−141.600	+	245.258i	−0.435692	+	0.754641i
$326$	−289.306			−0.887443
$327$	30.5507	−	114.017i	0.0934271	−	0.348675i
$328$	−36.4974	−	63.2154i	−0.111273	−	0.192730i
$329$	−83.0385	−	47.9423i	−0.252397	−	0.145721i
$330$	31.9230	+	31.9230i	0.0967365	+	0.0967365i
$331$	−137.454	+	36.8308i	−0.415270	+	0.111271i	−0.460404	−	0.887710i	$-0.652295\pi$
$331$	−137.454	+	36.8308i	−0.415270	+	0.111271i	0.0451334	+	0.998981i	$0.485629\pi$
$332$	−81.2820	−	303.349i	−0.244825	−	0.913701i
$333$	78.5307	−	78.5307i	0.235828	−	0.235828i
$334$	−114.431	+	198.200i	−0.342607	+	0.593413i
$335$	60.9193	−	35.1718i	0.181849	−	0.104990i
$336$	−64.6410	−	17.3205i	−0.192384	−	0.0515491i
$337$			347.508i			1.03118i	0.856835	+	0.515590i	$0.172427\pi$
$337$			347.508i			1.03118i	−0.856835	+	0.515590i	$0.827573\pi$
$338$	230.858	−	61.8583i	0.683013	−	0.183013i
$339$	−78.3154			−0.231019
$340$	−17.5692	+	65.5692i	−0.0516742	+	0.192851i
$341$	161.130	+	279.084i	0.472521	+	0.818430i
$342$	121.550	+	70.1769i	0.355409	+	0.205196i
$343$	−32.0929	−	32.0929i	−0.0935654	−	0.0935654i
$344$	41.9090	−	11.2295i	0.121828	−	0.0326438i
$345$	−3.33082	−	12.4308i	−0.00965454	−	0.0360312i
$346$	268.459	−	268.459i	0.775893	−	0.775893i
$347$	−218.851	+	379.061i	−0.630695	+	1.09240i	0.356715	+	0.934213i	$0.383897\pi$
$347$	−218.851	+	379.061i	−0.630695	+	1.09240i	−0.987410	+	0.158183i	$0.949436\pi$
$348$	−51.9615	+	30.0000i	−0.149315	+	0.0862069i
$349$	−432.889	−	115.992i	−1.24037	−	0.332356i	−0.421761	−	0.906707i	$-0.638588\pi$
$349$	−432.889	−	115.992i	−1.24037	−	0.332356i	−0.818609	+	0.574351i	$0.805254\pi$
$350$			297.583i			0.850238i
$351$	−58.5000	−	33.7750i	−0.166667	−	0.0962250i
$352$	58.1436			0.165181
$353$	−151.914	+	566.951i	−0.430352	+	1.60609i	0.321600	+	0.946876i	$0.395779\pi$
$353$	−151.914	+	566.951i	−0.430352	+	1.60609i	−0.751951	+	0.659218i	$0.770887\pi$
$354$	80.9423	+	140.196i	0.228651	+	0.396034i
$355$	−167.023	−	96.4308i	−0.470487	−	0.271636i
$356$	−237.282	−	237.282i	−0.666523	−	0.666523i
$357$	−305.885	+	81.9615i	−0.856820	+	0.229584i
$358$	104.603	+	390.382i	0.292186	+	1.09045i
$359$	64.2769	−	64.2769i	0.179044	−	0.179044i	−0.611895	−	0.790939i	$-0.709592\pi$
$359$	64.2769	−	64.2769i	0.179044	−	0.179044i	0.790939	+	0.611895i	$0.209592\pi$
$360$	−7.60770	+	13.1769i	−0.0211325	+	0.0366025i
$361$	635.143	−	366.700i	1.75940	−	1.01579i
$362$	242.669	+	65.0230i	0.670357	+	0.179622i
$363$			26.5936i			0.0732606i
$364$	177.583	−	177.583i	0.487866	−	0.487866i
$365$	170.967			0.468402
$366$	−4.62882	+	17.2750i	−0.0126470	+	0.0471994i
$367$	108.892	+	188.607i	0.296709	+	0.513916i	0.975381	−	0.220526i	$-0.0707774\pi$
$367$	108.892	+	188.607i	0.296709	+	0.513916i	−0.678672	+	0.734442i	$0.737444\pi$
$368$	−14.3538	−	8.28719i	−0.0390050	−	0.0225195i
$369$	−54.7461	−	54.7461i	−0.148364	−	0.148364i
$370$	90.6795	−	24.2975i	0.245080	−	0.0656689i
$371$	154.186	+	575.429i	0.415595	+	1.55102i
$372$	−76.7987	+	76.7987i	−0.206448	+	0.206448i
$373$	109.803	−	190.185i	0.294378	−	0.509878i	−0.680462	−	0.732784i	$-0.738221\pi$
$373$	109.803	−	190.185i	0.294378	−	0.509878i	0.974840	+	0.222905i	$0.0715541\pi$
$374$	238.277	−	137.569i	0.637104	−	0.367832i
$375$	140.354	+	37.6077i	0.374277	+	0.100287i
$376$			28.0770i			0.0746727i
$377$		−	225.167i		−	0.597259i
$378$	−70.9808			−0.187780
$379$	50.1846	−	187.292i	0.132413	−	0.494173i	−0.867582	−	0.497294i	$-0.834327\pi$
$379$	50.1846	−	187.292i	0.132413	−	0.494173i	0.999995	+	0.00312126i	$0.000993528\pi$
$380$	59.3205	+	102.746i	0.156107	+	0.270385i
$381$	−355.269	−	205.115i	−0.932465	−	0.538359i
$382$	197.321	+	197.321i	0.516546	+	0.516546i
$383$	188.172	−	50.4205i	0.491310	−	0.131646i	−0.00465401	−	0.999989i	$-0.501481\pi$
$383$	188.172	−	50.4205i	0.491310	−	0.131646i	0.495964	+	0.868343i	$0.334815\pi$
$384$	5.07180	+	18.9282i	0.0132078	+	0.0492922i
$385$	−125.885	+	125.885i	−0.326973	+	0.326973i
$386$	−14.8494	+	25.7199i	−0.0384699	+	0.0666317i
$387$	39.8538	−	23.0096i	0.102981	−	0.0594564i
$388$	−300.492	−	80.5167i	−0.774465	−	0.207517i
$389$		−	17.7513i		−	0.0456331i	−0.999740	−	0.0228166i	$-0.992737\pi$
$389$		−	17.7513i		−	0.0456331i	0.999740	−	0.0228166i	$-0.00726337\pi$
$390$	−28.5500	−	49.4500i	−0.0732051	−	0.126795i
$391$	−78.4308			−0.200590
$392$	32.4308	−	121.033i	0.0827316	−	0.308758i
$393$	181.550	+	314.454i	0.461959	+	0.800137i
$394$	−185.254	−	106.956i	−0.470187	−	0.271463i
$395$	−15.0577	−	15.0577i	−0.0381208	−	0.0381208i
$396$	59.5692	−	15.9615i	0.150427	−	0.0403069i
$397$	−87.3494	−	325.992i	−0.220024	−	0.821139i	−0.984337	−	0.176295i	$-0.943589\pi$
$397$	−87.3494	−	325.992i	−0.220024	−	0.821139i	0.764314	−	0.644844i	$-0.223078\pi$
$398$	22.2154	−	22.2154i	0.0558176	−	0.0558176i
$399$	−276.734	+	479.317i	−0.693569	+	1.20130i
$400$	75.4641	−	43.5692i	0.188660	−	0.108923i
$401$	−496.435	−	133.019i	−1.23799	−	0.331719i	−0.420305	−	0.907383i	$-0.638077\pi$
$401$	−496.435	−	133.019i	−1.23799	−	0.331719i	−0.817686	+	0.575664i	$0.804744\pi$
$402$		−	96.0910i		−	0.239032i
$403$	−105.492	−	393.700i	−0.261766	−	0.976923i
$404$	373.626			0.924816
$405$	−4.17691	+	15.5885i	−0.0103134	+	0.0384900i
$406$	−118.301	−	204.904i	−0.291382	−	0.504689i
$407$	−329.527	−	190.252i	−0.809649	−	0.467451i
$408$	65.5692	+	65.5692i	0.160709	+	0.160709i
$409$	−562.838	+	150.812i	−1.37613	+	0.368734i	−0.869715	−	0.493554i	$-0.835697\pi$
$409$	−562.838	+	150.812i	−1.37613	+	0.368734i	−0.506418	+	0.862288i	$0.669031\pi$
$410$	−16.9385	−	63.2154i	−0.0413134	−	0.154184i
$411$	139.492	−	139.492i	0.339397	−	0.339397i
$412$	83.2628	−	144.215i	0.202094	−	0.350037i
$413$	−552.846	+	319.186i	−1.33861	+	0.772847i
$414$	−16.9808	−	4.54998i	−0.0410163	−	0.0109903i
$415$		−	281.569i		−	0.678480i
$416$	−71.0333	−	19.0333i	−0.170753	−	0.0457532i
$417$	−165.771			−0.397531
$418$	124.459	−	464.487i	0.297749	−	1.11121i
$419$	391.177	+	677.538i	0.933596	+	1.61704i	0.777118	+	0.629355i	$0.216681\pi$
$419$	391.177	+	677.538i	0.933596	+	1.61704i	0.156479	+	0.987681i	$0.449986\pi$
$420$	−51.9615	−	30.0000i	−0.123718	−	0.0714286i
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	0.674269	−	0.738486i	$-0.264459\pi$
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	−0.738486	+	0.674269i	$0.764459\pi$
$422$	−87.7006	+	23.4993i	−0.207821	+	0.0556856i
$423$	7.70766	+	28.7654i	0.0182214	+	0.0680032i
$424$	123.349	−	123.349i	0.290917	−	0.290917i
$425$	206.172	−	357.100i	0.485110	−	0.840235i
$426$	−228.158	+	131.727i	−0.535581	+	0.309218i
$427$	−68.1218	−	18.2532i	−0.159536	−	0.0427475i
$428$			204.995i			0.478960i
$429$	−59.9000	+	223.550i	−0.139627	+	0.521096i
$430$	38.9000			0.0904652
$431$	162.995	−	608.305i	0.378178	−	1.41138i	−0.470467	−	0.882418i	$-0.655914\pi$
$431$	162.995	−	608.305i	0.378178	−	1.41138i	0.848645	−	0.528963i	$-0.177419\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	−205.928	−	118.892i	−0.475583	−	0.274578i	0.242991	−	0.970029i	$-0.421872\pi$
$433$	−205.928	−	118.892i	−0.475583	−	0.274578i	−0.718574	+	0.695451i	$0.755205\pi$
$434$	−302.846	−	302.846i	−0.697802	−	0.697802i
$435$	−51.9615	+	13.9230i	−0.119452	+	0.0320070i
$436$	−35.2769	−	131.655i	−0.0809103	−	0.301961i
$437$	−96.9282	+	96.9282i	−0.221804	+	0.221804i
$438$	116.772	−	202.256i	0.266604	−	0.461771i
$439$	597.092	−	344.731i	1.36012	−	0.785265i	0.370480	−	0.928841i	$-0.379193\pi$
$439$	597.092	−	344.731i	1.36012	−	0.785265i	0.989639	+	0.143576i	$0.0458600\pi$
$440$	50.3538	+	13.4923i	0.114441	+	0.0306642i
$441$		−	132.904i		−	0.301369i
$442$	−336.133	+	90.0666i	−0.760483	+	0.203771i
$443$	−304.028			−0.686294			−0.343147	−	0.939282i	$-0.611493\pi$
$443$	−304.028			−0.686294			−0.343147	+	0.939282i	$0.611493\pi$
$444$	33.1910	−	123.870i	0.0747545	−	0.278988i
$445$	−150.431	−	260.554i	−0.338047	−	0.585514i
$446$	267.655	+	154.531i	0.600124	+	0.346481i
$447$	69.6462	+	69.6462i	0.155808	+	0.155808i
$448$	−74.6410	+	20.0000i	−0.166609	+	0.0446429i
$449$	−73.4589	−	274.153i	−0.163606	−	0.610585i	−0.998214	−	0.0597407i	$-0.980973\pi$
$449$	−73.4589	−	274.153i	−0.163606	−	0.610585i	0.834608	−	0.550844i	$-0.185694\pi$
$450$	65.3538	−	65.3538i	0.145231	−	0.145231i
$451$	−132.631	+	229.723i	−0.294081	+	0.509364i
$452$	−78.3154	+	45.2154i	−0.173264	+	0.100034i
$453$	130.222	+	34.8930i	0.287467	+	0.0770265i
$454$		−	91.4256i		−	0.201378i
$455$	195.000	−	112.583i	0.428571	−	0.247436i
$456$	162.067			0.355409
$457$	−37.1584	+	138.677i	−0.0813093	+	0.303451i	−0.994590	−	0.103881i	$-0.966874\pi$
$457$	−37.1584	+	138.677i	−0.0813093	+	0.303451i	0.913280	+	0.407331i	$0.133541\pi$
$458$	−58.6846	−	101.645i	−0.128132	−	0.221932i
$459$	85.1769	+	49.1769i	0.185571	+	0.107139i
$460$	−10.5077	−	10.5077i	−0.0228429	−	0.0228429i
$461$	568.435	−	152.312i	1.23305	−	0.330394i	0.417282	−	0.908777i	$-0.362983\pi$
$461$	568.435	−	152.312i	1.23305	−	0.330394i	0.815765	+	0.578383i	$0.196316\pi$
$462$	62.9423	+	234.904i	0.136239	+	0.508450i
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	−0.866128	−	0.499823i	$-0.833399\pi$
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	0.499823	+	0.866128i	$0.333399\pi$
$464$	−34.6410	+	60.0000i	−0.0746574	+	0.129310i
$465$	−84.3308	+	48.6884i	−0.181357	+	0.104706i
$466$	520.004	+	139.335i	1.11589	+	0.299001i
$467$			732.649i			1.56884i	0.620230	+	0.784420i	$0.287039\pi$
$467$			732.649i			1.56884i	−0.620230	+	0.784420i	$0.712961\pi$
$468$	−78.0000			−0.166667
$469$	378.923			0.807938
$470$	−6.51528	+	24.3154i	−0.0138623	+	0.0517348i
$471$	−48.0045	−	83.1462i	−0.101920	−	0.176531i
$472$	161.885	+	93.4641i	0.342976	+	0.198017i
$473$	−111.488	−	111.488i	−0.235705	−	0.235705i
$474$	−28.0981	+	7.52886i	−0.0592786	+	0.0158837i
$475$	−186.524	−	696.116i	−0.392681	−	1.46551i
$476$	−258.564	+	258.564i	−0.543202	+	0.543202i
$477$	92.5115	−	160.235i	0.193944	−	0.335922i
$478$	−289.492	+	167.138i	−0.605632	+	0.349662i
$479$	−357.167	−	95.7025i	−0.745651	−	0.199796i	−0.134063	−	0.990973i	$-0.542802\pi$
$479$	−357.167	−	95.7025i	−0.745651	−	0.199796i	−0.611588	+	0.791176i	$0.709469\pi$
$480$			17.5692i			0.0366025i
$481$	340.300	+	340.300i	0.707484	+	0.707484i
$482$	4.35383			0.00903284
$483$	17.9423	−	66.9615i	0.0371476	−	0.138637i
$484$	15.3538	+	26.5936i	0.0317228	+	0.0549455i
$485$	−241.550	−	139.459i	−0.498041	−	0.287544i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	187.145	−	50.1455i	0.384282	−	0.102968i	−0.0615056	−	0.998107i	$-0.519590\pi$
$487$	187.145	−	50.1455i	0.384282	−	0.102968i	0.445788	+	0.895139i	$0.352924\pi$
$488$	5.34490	+	19.9474i	0.0109527	+	0.0408759i
$489$	−250.547	+	250.547i	−0.512365	+	0.512365i
$490$	56.1718	−	97.2923i	0.114636	−	0.198556i
$491$	−31.9808	+	18.4641i	−0.0651339	+	0.0376051i	−0.532213	−	0.846610i	$-0.678640\pi$
$491$	−31.9808	+	18.4641i	−0.0651339	+	0.0376051i	0.467079	+	0.884215i	$0.345306\pi$
$492$	−86.3538	−	23.1384i	−0.175516	−	0.0470293i
$493$			327.846i			0.665002i
$494$	−304.100	+	526.717i	−0.615587	+	1.06623i
$495$	55.2923			0.111702
$496$	−32.4589	+	121.138i	−0.0654414	+	0.244231i
$497$	−519.449	−	899.711i	−1.04517	−	1.81028i
$498$	−333.100	−	192.315i	−0.668875	−	0.386175i
$499$	462.769	+	462.769i	0.927393	+	0.927393i	0.997537	−	0.0701438i	$-0.0223458\pi$
$499$	462.769	+	462.769i	0.927393	+	0.927393i	−0.0701438	+	0.997537i	$0.522346\pi$
$500$	162.067	−	43.4256i	0.324133	−	0.0868513i
$501$	72.5462	+	270.746i	0.144803	+	0.540411i
$502$	−208.708	+	208.708i	−0.415752	+	0.415752i
$503$	179.378	−	310.692i	0.356617	−	0.617678i	−0.630777	−	0.775965i	$-0.717264\pi$
$503$	179.378	−	310.692i	0.356617	−	0.617678i	0.987393	+	0.158286i	$0.0505969\pi$
$504$	−70.9808	+	40.9808i	−0.140835	+	0.0813110i
$505$	323.569	+	86.7001i	0.640731	+	0.171683i
$506$			60.2309i			0.119033i
$507$	146.358	−	253.500i	0.288675	−	0.500000i
$508$	−473.692			−0.932465
$509$	−190.972	+	712.717i	−0.375190	+	1.40023i	0.477876	+	0.878427i	$0.341407\pi$
$509$	−190.972	+	712.717i	−0.375190	+	1.40023i	−0.853067	+	0.521802i	$0.825260\pi$
$510$	41.5692	+	72.0000i	0.0815083	+	0.141176i
$511$	797.570	+	460.477i	1.56080	+	0.901130i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	166.040	−	44.4904i	0.323665	−	0.0867259i
$514$	−27.1666	−	101.387i	−0.0528533	−	0.197251i
$515$	105.573	−	105.573i	0.204996	−	0.204996i
$516$	26.5692	−	46.0192i	0.0514907	−	0.0891846i
$517$	88.3614	−	51.0155i	0.170912	−	0.0986759i
$518$	488.468	+	130.885i	0.942988	+	0.252673i
$519$		−	464.985i		−	0.895924i
$520$	−57.1000	−	32.9667i	−0.109808	−	0.0633975i
$521$	156.049			0.299518			0.149759	−	0.988723i	$-0.452150\pi$
$521$	156.049			0.299518			0.149759	+	0.988723i	$0.452150\pi$
$522$	−19.0192	+	70.9808i	−0.0364353	+	0.135978i
$523$	−20.9615	−	36.3064i	−0.0400794	−	0.0694196i	0.845290	−	0.534308i	$-0.179428\pi$
$523$	−20.9615	−	36.3064i	−0.0400794	−	0.0694196i	−0.885369	+	0.464888i	$0.846094\pi$
$524$	363.100	+	209.636i	0.692939	+	0.400068i
$525$	257.715	+	257.715i	0.490885	+	0.490885i
$526$	33.2820	−	8.91789i	0.0632738	−	0.0169542i
$527$	153.597	+	573.233i	0.291456	+	1.08773i
$528$	50.3538	−	50.3538i	0.0953671	−	0.0953671i
$529$	−255.915	+	443.258i	−0.483772	+	0.837917i
$530$	135.446	−	78.1999i	0.255559	−	0.147547i
$531$	191.512	+	51.3154i	0.360662	+	0.0966391i
$532$			639.090i			1.20130i
$533$	237.233	−	237.233i	0.445091	−	0.445091i
$534$	−410.985			−0.769634
$535$	−47.5692	+	177.531i	−0.0889144	+	0.331833i
$536$	−55.4782	−	96.0910i	−0.103504	−	0.179274i
$537$	428.669	+	247.492i	0.798267	+	0.460879i
$538$	−175.741	−	175.741i	−0.326656	−	0.326656i
$539$	−439.832	+	117.853i	−0.816015	+	0.218651i
$540$	4.82309	+	18.0000i	0.00893164	+	0.0333333i
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	−0.711201	−	0.702989i	$-0.751848\pi$
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	0.702989	+	0.711201i	$0.251848\pi$
$542$	197.046	−	341.293i	0.363553	−	0.629692i
$543$	266.469	−	153.846i	0.490735	−	0.283326i
$544$	103.426	+	27.7128i	0.190121	+	0.0509427i
$545$		−	122.203i		−	0.224225i
$546$		−	307.583i		−	0.563339i
$547$	−101.508			−0.185572			−0.0927859	−	0.995686i	$-0.529577\pi$
$547$	−101.508			−0.185572			−0.0927859	+	0.995686i	$0.529577\pi$
$548$	58.9564	−	220.028i	0.107585	−	0.401511i
$549$	10.9519	+	18.9693i	0.0199488	+	0.0345524i
$550$	−274.235	−	158.329i	−0.498608	−	0.287872i
$551$	405.167	+	405.167i	0.735330	+	0.735330i
$552$	−19.6077	+	5.25387i	−0.0355212	+	0.00951787i
$553$	−29.6891	−	110.801i	−0.0536874	−	0.200364i
$554$	−446.985	+	446.985i	−0.806831	+	0.806831i
$555$	57.4885	−	99.5730i	0.103583	−	0.179411i
$556$	−165.771	+	95.7077i	−0.298148	+	0.172136i
$557$	−636.358	−	170.512i	−1.14247	−	0.306125i	−0.362528	−	0.931973i	$-0.618086\pi$
$557$	−636.358	−	170.512i	−1.14247	−	0.306125i	−0.779945	+	0.625848i	$0.784753\pi$
$558$			133.019i			0.238386i
$559$	99.7083	+	172.700i	0.178369	+	0.308944i
$560$	−69.2820			−0.123718
$561$	87.2154	−	325.492i	0.155464	−	0.580200i
$562$	5.54483	+	9.60392i	0.00986624	+	0.0170888i
$563$	76.8385	+	44.3628i	0.136481	+	0.0787971i	0.566686	−	0.823934i	$-0.308225\pi$
$563$	76.8385	+	44.3628i	0.136481	+	0.0787971i	−0.430205	+	0.902731i	$0.641559\pi$
$564$	24.3154	+	24.3154i	0.0431123	+	0.0431123i
$565$	−78.3154	+	20.9845i	−0.138611	+	0.0371408i
$566$	−6.09292	−	22.7391i	−0.0107649	−	0.0401751i
$567$	−61.4711	+	61.4711i	−0.108415	+	0.108415i
$568$	−152.105	+	263.454i	−0.267791	+	0.463827i
$569$	−373.750	+	215.785i	−0.656854	+	0.379235i	−0.791077	−	0.611716i	$-0.790479\pi$
$569$	−373.750	+	215.785i	−0.656854	+	0.379235i	0.134223	+	0.990951i	$0.457146\pi$
$570$	140.354	+	37.6077i	0.246235	+	0.0659784i
$571$		−	959.892i		−	1.68107i	−0.541756	−	0.840536i	$-0.682240\pi$
$571$		−	959.892i		−	1.68107i	0.541756	−	0.840536i	$-0.317760\pi$
$572$	69.1666	+	258.133i	0.120921	+	0.451282i
$573$	341.769			0.596456
$574$	91.2436	−	340.526i	0.158961	−	0.593250i
$575$	45.1333	+	78.1731i	0.0784927	+	0.135953i
$576$	20.7846	+	12.0000i	0.0360844	+	0.0208333i
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	0.380968	−	0.924588i	$-0.375591\pi$
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	−0.924588	+	0.380968i	$0.875591\pi$
$578$	94.6340	−	25.3571i	0.163727	−	0.0438704i
$579$	9.41412	+	35.1340i	0.0162593	+	0.0606804i
$580$	−43.9230	+	43.9230i	−0.0757294	+	0.0757294i
$581$	758.372	−	1313.54i	1.30529	−	2.26082i
$582$	−329.963	+	190.504i	−0.566947	+	0.327327i
$583$	−612.315	−	164.069i	−1.05028	−	0.281423i
$584$		−	269.674i		−	0.461771i
$585$	−67.5500	−	18.1000i	−0.115470	−	0.0309401i
$586$	264.946			0.452126
$587$	−58.5654	+	218.569i	−0.0997708	+	0.372350i	−0.997700	−	0.0677912i	$-0.978405\pi$
$587$	−58.5654	+	218.569i	−0.0997708	+	0.372350i	0.897929	+	0.440141i	$0.145071\pi$
$588$	−76.7321	−	132.904i	−0.130497	−	0.226027i
$589$	898.249	+	518.604i	1.52504	+	0.880483i
$590$	118.508	+	118.508i	0.200861	+	0.200861i
$591$	−253.061	+	67.8076i	−0.428192	+	0.114734i
$592$	−38.3257	−	143.033i	−0.0647393	−	0.241610i
$593$	335.229	−	335.229i	0.565311	−	0.565311i	−0.365500	−	0.930811i	$-0.619102\pi$
$593$	335.229	−	335.229i	0.565311	−	0.565311i	0.930811	+	0.365500i	$0.119102\pi$
$594$	37.7654	−	65.4115i	0.0635781	−	0.110120i
$595$	−283.923	+	163.923i	−0.477182	+	0.275501i
$596$	109.856	+	29.4359i	0.184323	+	0.0493892i
$597$		−	38.4782i		−	0.0644526i
$598$	19.7166	−	73.5833i	0.0329709	−	0.123049i
$599$	136.908			0.228560			0.114280	−	0.993449i	$-0.463544\pi$
$599$	136.908			0.228560			0.114280	+	0.993449i	$0.463544\pi$
$600$	27.6218	−	103.086i	0.0460363	−	0.171810i
$601$	8.78461	+	15.2154i	0.0146167	+	0.0253168i	0.873241	−	0.487288i	$-0.162014\pi$
$601$	8.78461	+	15.2154i	0.0146167	+	0.0253168i	−0.858625	+	0.512605i	$0.828681\pi$
$602$	181.471	+	104.772i	0.301447	+	0.174041i
$603$	−83.2173	−	83.2173i	−0.138005	−	0.138005i
$604$	150.368	−	40.2910i	0.248953	−	0.0667069i
$605$	7.12574	+	26.5936i	0.0117781	+	0.0439564i
$606$	323.569	−	323.569i	0.533943	−	0.533943i
$607$	−422.300	+	731.445i	−0.695716	+	1.20502i	0.274222	+	0.961666i	$0.411580\pi$
$607$	−422.300	+	731.445i	−0.695716	+	1.20502i	−0.969939	+	0.243350i	$0.921754\pi$
$608$	162.067	−	93.5692i	0.266557	−	0.153897i
$609$	−279.904	−	75.0000i	−0.459612	−	0.123153i
$610$			18.5153i			0.0303529i
$611$	−124.650	+	33.3999i	−0.204010	+	0.0546642i
$612$	113.569			0.185571
$613$	−163.158	+	608.915i	−0.266164	+	0.993337i	0.695370	+	0.718651i	$0.255240\pi$
$613$	−163.158	+	608.915i	−0.266164	+	0.993337i	−0.961534	+	0.274685i	$0.911426\pi$
$614$	−375.069	−	649.638i	−0.610861	−	1.05804i
$615$	−69.4153	−	40.0770i	−0.112870	−	0.0651658i
$616$	198.564	+	198.564i	0.322344	+	0.322344i
$617$	107.014	−	28.6743i	0.173443	−	0.0464738i	−0.171053	−	0.985262i	$-0.554717\pi$
$617$	107.014	−	28.6743i	0.173443	−	0.0464738i	0.344495	+	0.938788i	$0.388050\pi$
$618$	−52.7865	−	197.002i	−0.0854150	−	0.318773i
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	−0.791743	−	0.610854i	$-0.790826\pi$
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	0.610854	+	0.791743i	$0.290826\pi$
$620$	−56.2205	+	97.3768i	−0.0906783	+	0.157059i
$621$	−18.6462	+	10.7654i	−0.0300260	+	0.0173355i
$622$	−404.669	−	108.431i	−0.650594	−	0.174326i
$623$		−	1620.67i		−	2.60139i
$624$	−78.0000	+	45.0333i	−0.125000	+	0.0721688i
$625$	−394.184			−0.630695
$626$	43.2956	−	161.581i	0.0691623	−	0.258117i
$627$	−294.473	−	510.042i	−0.469654	−	0.813465i
$628$	−96.0089	−	55.4308i	−0.152880	−	0.0882656i
$629$	−495.482	−	495.482i	−0.787730	−	0.787730i
$630$	−70.9808	+	19.0192i	−0.112668	+	0.0301893i
$631$	283.101	+	1056.55i	0.448654	+	1.67440i	0.706104	+	0.708108i	$0.250451\pi$
$631$	283.101	+	1056.55i	0.448654	+	1.67440i	−0.257450	+	0.966292i	$0.582882\pi$
$632$	−23.7513	+	23.7513i	−0.0375812	+	0.0375812i
$633$	−55.6000	+	96.3020i	−0.0878356	+	0.152136i
$634$	−486.200	+	280.708i	−0.766877	+	0.442757i
$635$	−410.229	−	109.921i	−0.646031	−	0.173103i
$636$		−	213.646i		−	0.335922i
$637$	575.917			0.904108
$638$	251.769			0.394622
$639$	−83.5115	+	311.669i	−0.130691	+	0.487745i
$640$	10.1436	+	17.5692i	0.0158494	+	0.0274519i
$641$	−353.869	−	204.306i	−0.552058	−	0.318731i	0.197894	−	0.980223i	$-0.436590\pi$
$641$	−353.869	−	204.306i	−0.552058	−	0.318731i	−0.749952	+	0.661493i	$0.769923\pi$
$642$	177.531	+	177.531i	0.276528	+	0.276528i
$643$	−432.661	+	115.931i	−0.672879	+	0.180297i	−0.579052	−	0.815291i	$-0.696577\pi$
$643$	−432.661	+	115.931i	−0.672879	+	0.180297i	−0.0938279	+	0.995588i	$0.529910\pi$
$644$	−20.7180	−	77.3205i	−0.0321708	−	0.120063i
$645$	33.6884	−	33.6884i	0.0522301	−	0.0522301i
$646$	442.774	−	766.908i	0.685409	−	1.18716i
$647$	−279.588	+	161.420i	−0.432131	+	0.249491i	−0.700254	−	0.713894i	$-0.746930\pi$
$647$	−279.588	+	161.420i	−0.432131	+	0.249491i	0.268123	+	0.963385i	$0.413597\pi$
$648$	24.5885	+	6.58846i	0.0379452	+	0.0101674i
$649$		−	679.292i		−	1.04668i
$650$	283.200	+	283.200i	0.435692	+	0.435692i
$651$	−524.545			−0.805752
$652$	−105.894	+	395.200i	−0.162413	+	0.606135i
$653$	510.424	+	884.081i	0.781660	+	1.35388i	0.930974	+	0.365086i	$0.118960\pi$
$653$	510.424	+	884.081i	0.781660	+	1.35388i	−0.149314	+	0.988790i	$0.547706\pi$
$654$	−144.567	−	83.4660i	−0.221051	−	0.127624i
$655$	265.808	+	265.808i	0.405813	+	0.405813i
$656$	−99.7128	+	26.7180i	−0.152001	+	0.0407286i
$657$	−74.0307	−	276.286i	−0.112680	−	0.420527i
$658$	−95.8846	+	95.8846i	−0.145721	+	0.145721i
$659$	−113.842	+	197.181i	−0.172750	+	0.299212i	−0.939380	−	0.342877i	$-0.888599\pi$
$659$	−113.842	+	197.181i	−0.172750	+	0.299212i	0.766630	+	0.642089i	$0.221932\pi$
$660$	55.2923	−	31.9230i	0.0837763	−	0.0483683i
$661$	146.181	+	39.1692i	0.221152	+	0.0592575i	0.367693	−	0.929947i	$-0.380148\pi$
$661$	146.181	+	39.1692i	0.221152	+	0.0592575i	−0.146542	+	0.989205i	$0.546814\pi$
$662$			201.247i			0.303999i
$663$	−213.100	+	369.100i	−0.321418	+	0.556712i
$664$	−444.133			−0.668875
$665$	−148.301	+	553.468i	−0.223009	+	0.832283i
$666$	−78.5307	−	136.019i	−0.117914	−	0.204233i
$667$	−62.1539	−	35.8846i	−0.0931843	−	0.0538000i
$668$	228.862	+	228.862i	0.342607	+	0.342607i
$669$	365.624	−	97.9686i	0.546523	−	0.146440i
$670$	−25.7475	−	96.0910i	−0.0384291	−	0.143419i
$671$	53.0653	−	53.0653i	0.0790838	−	0.0790838i
$672$	−47.3205	+	81.9615i	−0.0704174	+	0.121967i
$673$	−613.138	+	353.996i	−0.911052	+	0.525996i	−0.880770	−	0.473545i	$-0.842974\pi$
$673$	−613.138	+	353.996i	−0.911052	+	0.525996i	−0.0302828	+	0.999541i	$0.509641\pi$
$674$	474.704	+	127.197i	0.704309	+	0.188719i
$675$		−	113.196i		−	0.167698i
$676$		−	338.000i		−	0.500000i
$677$	−754.592			−1.11461			−0.557306	−	0.830307i	$-0.688165\pi$
$677$	−754.592			−1.11461			−0.557306	+	0.830307i	$0.688165\pi$
$678$	−28.6654	+	106.981i	−0.0422794	+	0.157789i
$679$	−751.231	−	1301.17i	−1.10638	−	1.91630i
$680$	83.1384	+	48.0000i	0.122262	+	0.0705882i
$681$	−79.1769	−	79.1769i	−0.116266	−	0.116266i
$682$	440.214	−	117.955i	0.645475	−	0.172955i
$683$	−37.2168	−	138.895i	−0.0544901	−	0.203360i	0.933314	−	0.359061i	$-0.116903\pi$
$683$	−37.2168	−	138.895i	−0.0544901	−	0.203360i	−0.987804	+	0.155701i	$0.950236\pi$
$684$	140.354	−	140.354i	0.205196	−	0.205196i
$685$	102.115	−	176.869i	0.149074	−	0.258203i
$686$	−55.5866	+	32.0929i	−0.0810300	+	0.0467827i
$687$	−138.849	−	37.2046i	−0.202110	−	0.0541551i
$688$		−	61.3590i		−	0.0891846i
$689$	694.350	+	400.883i	1.00776	+	0.581833i
$690$	−18.1999			−0.0263767
$691$	140.931	−	525.961i	0.203952	−	0.761159i	−0.785815	−	0.618462i	$-0.787756\pi$
$691$	140.931	−	525.961i	0.203952	−	0.761159i	0.989766	−	0.142697i	$-0.0455774\pi$
$692$	−268.459	−	464.985i	−0.387946	−	0.671943i
$693$	257.942	+	148.923i	0.372211	+	0.214896i
$694$	437.703	+	437.703i	0.630695	+	0.630695i
$695$	−165.771	+	44.4181i	−0.238519	+	0.0639109i
$696$	21.9615	+	81.9615i	0.0315539	+	0.117761i
$697$	−345.415	+	345.415i	−0.495574	+	0.495574i
$698$	−316.897	+	548.881i	−0.454007	+	0.786363i
$699$	571.004	−	329.669i	0.816887	−	0.471630i
$700$	406.506	+	108.923i	0.580723	+	0.155604i
$701$		−	568.344i		−	0.810761i	−0.914148	−	0.405381i	$-0.867139\pi$
$701$		−	568.344i		−	0.810761i	0.914148	−	0.405381i	$-0.132861\pi$
$702$	−67.5500	+	67.5500i	−0.0962250	+	0.0962250i
$703$	−1224.68			−1.74207
$704$	21.2820	−	79.4256i	0.0302302	−	0.112820i
$705$	15.4153	+	26.7001i	0.0218657	+	0.0378725i
$706$	718.865	+	415.037i	1.01822	+	0.587871i
$707$	1275.95	+	1275.95i	1.80475	+	1.80475i
$708$	221.138	−	59.2539i	0.312342	−	0.0836919i
$709$	94.9538	+	354.372i	0.133926	+	0.499820i	1.00000		9.64632e-5i	$-3.07052e-5\pi$
$709$	94.9538	+	354.372i	0.133926	+	0.499820i	−0.866074	+	0.499916i	$0.833364\pi$
$710$	−192.862	+	192.862i	−0.271636	+	0.271636i
$711$	−17.8135	+	30.8538i	−0.0250541	+	0.0433950i
$712$	−410.985	+	237.282i	−0.577225	+	0.333261i
$713$	−125.487	−	33.6242i	−0.175999	−	0.0471587i
$714$			447.846i			0.627235i
$715$			239.600i			0.335105i
$716$	571.559			0.798267
$717$	−105.962	+	395.454i	−0.147785	+	0.551539i
$718$	−64.2769	−	111.331i	−0.0895221	−	0.155057i
$719$	228.215	+	131.760i	0.317407	+	0.183255i	0.650236	−	0.759732i	$-0.274670\pi$
$719$	228.215	+	131.760i	0.317407	+	0.183255i	−0.332829	+	0.942987i	$0.608003\pi$
$720$	15.2154	+	15.2154i	0.0211325	+	0.0211325i
$721$	776.852	−	208.157i	1.07747	−	0.288706i
$722$	−268.443	−	1001.84i	−0.371805	−	1.38759i
$723$	3.77053	−	3.77053i	0.00521511	−	0.00521511i
$724$	177.646	−	307.692i	0.245368	−	0.424989i
$725$	326.769	−	188.660i	0.450716	−	0.260221i
$726$	36.3275	+	9.73394i	0.0500379	+	0.0134076i
$727$		−	878.415i		−	1.20827i	−0.796880	−	0.604137i	$-0.793518\pi$
$727$		−	878.415i		−	1.20827i	0.796880	−	0.604137i	$-0.206482\pi$
$728$	−177.583	−	307.583i	−0.243933	−	0.422505i
$729$	27.0000			0.0370370
$730$	62.5781	−	233.545i	0.0857235	−	0.319924i
$731$	−145.177	−	251.454i	−0.198600	−	0.343986i
$732$	21.9038	+	12.6462i	0.0299232	+	0.0172762i
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	0.599979	−	0.800016i	$-0.295176\pi$
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	−0.800016	+	0.599979i	$0.795176\pi$
$734$	297.499	−	79.7147i	0.405312	−	0.108603i
$735$	−35.6115	−	132.904i	−0.0484510	−	0.180822i
$736$	−16.5744	+	16.5744i	−0.0225195	+	0.0225195i
$737$	−201.606	+	349.192i	−0.273550	+	0.473802i
$738$	−94.8231	+	54.7461i	−0.128487	+	0.0741818i
$739$	621.762	+	166.601i	0.841356	+	0.225441i	0.653662	−	0.756787i	$-0.273232\pi$
$739$	621.762	+	166.601i	0.841356	+	0.225441i	0.187694	+	0.982227i	$0.439899\pi$
$740$		−	132.764i		−	0.179411i
$741$	192.792	+	719.508i	0.260178	+	0.970996i
$742$	842.487			1.13543
$743$	−3.52835	+	13.1680i	−0.00474879	+	0.0177227i	−0.968260	−	0.249947i	$-0.919587\pi$
$743$	−3.52835	+	13.1680i	−0.00474879	+	0.0177227i	0.963511	+	0.267670i	$0.0862535\pi$
$744$	76.7987	+	133.019i	0.103224	+	0.178789i
$745$	88.3078	+	50.9845i	0.118534	+	0.0684356i
$746$	−219.606	−	219.606i	−0.294378	−	0.294378i
$747$	−455.023	+	121.923i	−0.609134	+	0.163217i
$748$	−100.708	−	375.846i	−0.134636	−	0.502468i
$749$	−700.070	+	700.070i	−0.934673	+	0.934673i
$750$	102.746	−	177.962i	0.136995	−	0.237282i
$751$	−138.631	+	80.0385i	−0.184595	+	0.106576i	−0.589450	−	0.807805i	$-0.700655\pi$
$751$	−138.631	+	80.0385i	−0.184595	+	0.106576i	0.404855	+	0.914381i	$0.367322\pi$
$752$	38.3538	+	10.2769i	0.0510024	+	0.0136661i
$753$			361.492i			0.480069i
$754$	−307.583	−	82.4167i	−0.407935	−	0.109306i
$755$	139.572			0.184864
$756$	−25.9808	+	96.9615i	−0.0343661	+	0.128256i
$757$	733.692	+	1270.79i	0.969210	+	1.67872i	0.697850	+	0.716244i	$0.254140\pi$
$757$	733.692	+	1270.79i	0.969210	+	1.67872i	0.271360	+	0.962478i	$0.412527\pi$
$758$	−237.476	−	137.107i	−0.313293	−	0.180880i
$759$	52.1615	+	52.1615i	0.0687239	+	0.0687239i
$760$	162.067	−	43.4256i	0.213246	−	0.0571390i
$761$	47.3514	+	176.718i	0.0622227	+	0.232218i	0.990033	−	0.140833i	$-0.0449782\pi$
$761$	47.3514	+	176.718i	0.0622227	+	0.232218i	−0.927811	+	0.373051i	$0.878312\pi$
$762$	−410.229	+	410.229i	−0.538359	+	0.538359i
$763$	329.138	−	570.083i	0.431373	−	0.747160i
$764$	341.769	−	197.321i	0.447342	−	0.258273i
$765$	98.3538	+	26.3538i	0.128567	+	0.0344494i
$766$		−	275.503i		−	0.359664i
$767$	−222.367	+	829.883i	−0.289917	+	1.08199i
$768$	27.7128			0.0360844
$769$	351.866	−	1313.18i	0.457563	−	1.70765i	−0.222879	−	0.974846i	$-0.571546\pi$
$769$	351.866	−	1313.18i	0.457563	−	1.70765i	0.680442	−	0.732802i	$-0.261788\pi$
$770$	125.885	+	218.038i	0.163486	+	0.283167i
$771$	−111.331	−	64.2769i	−0.144398	−	0.0833682i
$772$	29.6987	+	29.6987i	0.0384699	+	0.0384699i
$773$	945.606	−	253.374i	1.22329	−	0.327781i	0.411329	−	0.911487i	$-0.365065\pi$
$773$	945.606	−	253.374i	1.22329	−	0.327781i	0.811965	+	0.583706i	$0.198398\pi$
$774$	−16.8442	−	62.8634i	−0.0217625	−	0.0812189i
$775$	482.962	−	482.962i	0.623177	−	0.623177i
$776$	−219.976	+	381.009i	−0.283474	+	0.490991i
$777$	536.375	−	309.676i	0.690315	−	0.398554i
$778$	−24.2487	−	6.49742i	−0.0311680	−	0.00835144i
$779$			853.759i			1.09597i
$780$	−78.0000	+	20.9000i	−0.100000	+	0.0267949i
$781$	1105.49			1.41548
$782$	−28.7077	+	107.138i	−0.0367106	+	0.137006i
$783$	45.0000	+	77.9423i	0.0574713	+	0.0995431i
$784$	−153.464	−	88.6025i	−0.195745	−	0.113013i
$785$	−70.2834	−	70.2834i	−0.0895330	−	0.0895330i
$786$	496.004	−	132.904i	0.631048	−	0.169089i
$787$	30.5460	+	113.999i	0.0388132	+	0.144853i	0.982613	−	0.185664i	$-0.0594436\pi$
$787$	30.5460	+	113.999i	0.0388132	+	0.144853i	−0.943800	+	0.330517i	$0.892777\pi$
$788$	−213.913	+	213.913i	−0.271463	+	0.271463i
$789$	21.1000	−	36.5462i	0.0267427	−	0.0463197i
$790$	−26.0807	+	15.0577i	−0.0330136	+	0.0190604i
$791$	−421.865	−	113.038i	−0.533332	−	0.142906i
$792$		−	87.2154i		−	0.110120i
$793$	−82.2001	+	47.4583i	−0.103657	+	0.0598465i
$794$	−477.286			−0.601116
$795$	49.5768	−	185.023i	0.0623607	−	0.232733i
$796$	−22.2154	−	38.4782i	−0.0279088	−	0.0483394i
$797$	491.138	+	283.559i	0.616234	+	0.355783i	0.775401	−	0.631469i	$-0.217548\pi$
$797$	491.138	+	283.559i	0.616234	+	0.355783i	−0.159167	+	0.987252i	$0.550881\pi$
$798$	553.468	+	553.468i	0.693569	+	0.693569i
$799$	181.492	−	48.6307i	0.227149	−	0.0608645i
$800$	−31.8949	−	119.033i	−0.0398686	−	0.148792i
$801$	−355.923	+	355.923i	−0.444348	+	0.444348i
$802$	−363.415	+	629.454i	−0.453136	+	0.784855i
$803$	−848.696	+	489.995i	−1.05691	+	0.610205i
$804$	−131.263	−	35.1718i	−0.163262	−	0.0437460i
$805$		−	71.7691i		−	0.0891542i
$806$	−576.417			−0.715157
$807$	−304.392			−0.377190
$808$	136.756	−	510.382i	0.169253	−	0.631661i
$809$	−43.7231	−	75.7307i	−0.0540459	−	0.0936102i	0.837737	−	0.546074i	$-0.183878\pi$
$809$	−43.7231	−	75.7307i	−0.0540459	−	0.0936102i	−0.891783	+	0.452464i	$0.850545\pi$
$810$	19.7654	+	11.4115i	0.0244017	+	0.0140883i
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	0.310413	−	0.950602i	$-0.399533\pi$
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	−0.950602	+	0.310413i	$0.899533\pi$
$812$	−323.205	+	86.6025i	−0.398036	+	0.106653i
$813$	−124.922	−	466.215i	−0.153655	−	0.573450i
$814$	−380.505	+	380.505i	−0.467451	+	0.467451i
$815$	−183.413	+	317.681i	−0.225047	+	0.389792i
$816$	113.569	−	65.5692i	0.139178	−	0.0803544i
$817$	−490.174	−	131.342i	−0.599968	−	0.160761i
$818$			824.053i			1.00740i
$819$	−266.375	−	266.375i	−0.325244	−	0.325244i
$820$	−92.5538			−0.112870
$821$	148.881	−	555.631i	0.181341	−	0.676773i	−0.814044	−	0.580804i	$-0.802738\pi$
$821$	148.881	−	555.631i	0.181341	−	0.676773i	0.995384	−	0.0959692i	$-0.0305950\pi$
$822$	−139.492	−	241.608i	−0.169699	−	0.293927i
$823$	−285.069	−	164.585i	−0.346378	−	0.199981i	0.316711	−	0.948522i	$-0.397422\pi$
$823$	−285.069	−	164.585i	−0.346378	−	0.199981i	−0.663089	+	0.748541i	$0.730755\pi$
$824$	−166.526	−	166.526i	−0.202094	−	0.202094i
$825$	−374.611	+	100.377i	−0.454075	+	0.121669i
$826$	233.660	+	872.032i	0.282882	+	1.05573i
$827$	514.410	−	514.410i	0.622020	−	0.622020i	−0.324028	−	0.946048i	$-0.605037\pi$
$827$	514.410	−	514.410i	0.622020	−	0.622020i	0.946048	+	0.324028i	$0.105037\pi$
$828$	−12.4308	+	21.5307i	−0.0150130	+	0.0260033i
$829$	−816.742	+	471.546i	−0.985213	+	0.568813i	−0.903840	−	0.427871i	$-0.859264\pi$
$829$	−816.742	+	471.546i	−0.985213	+	0.568813i	−0.0813731	+	0.996684i	$0.525931\pi$
$830$	−384.631	−	103.061i	−0.463410	−	0.124170i
$831$			774.200i			0.931649i
$832$	−52.0000	+	90.0666i	−0.0625000	+	0.108253i
$833$	−838.543			−1.00665
$834$	−60.6762	+	226.447i	−0.0727533	+	0.271519i
$835$	145.092	+	251.307i	0.173763	+	0.300967i
$836$	−588.946	−	340.028i	−0.704481	−	0.406732i
$837$	115.198	+	115.198i	0.137632	+	0.137632i
$838$	1068.72	−	286.361i	1.27532	−	0.341720i
$839$	−203.536	−	759.606i	−0.242593	−	0.905371i	−0.974578	−	0.224050i	$-0.928072\pi$
$839$	−203.536	−	759.606i	−0.242593	−	0.905371i	0.731984	−	0.681321i	$-0.238594\pi$
$840$	−60.0000	+	60.0000i	−0.0714286	+	0.0714286i
$841$	270.500	−	468.520i	0.321641	−	0.557098i
$842$	−46.8264	+	27.0352i	−0.0556132	+	0.0321083i
$843$	13.1192	+	3.51528i	0.0155625	+	0.00416996i
$844$			128.403i			0.152136i
$845$	78.4332	−	292.717i	0.0928203	−	0.346410i
$846$	42.1154			0.0497818
$847$	−38.3846	+	143.253i	−0.0453183	+	0.169130i
$848$	−123.349	−	213.646i	−0.145458	−	0.251941i
$849$	−24.9693	−	14.4160i	−0.0294102	−	0.0169800i
$850$	−412.344	−	412.344i	−0.485110	−	0.485110i
$851$	148.168	−	39.7015i	0.174110	−	0.0466528i
$852$	96.4308	+	359.885i	0.113182	+	0.422400i
$853$	472.527	−	472.527i	0.553960	−	0.553960i	−0.373622	−	0.927581i	$-0.621884\pi$
$853$	472.527	−	472.527i	0.553960	−	0.553960i	0.927581	+	0.373622i	$0.121884\pi$
$854$	−49.8686	+	86.3750i	−0.0583941	+	0.101142i
$855$	154.119	−	88.9808i	0.180256	−	0.104071i
$856$	280.028	+	75.0333i	0.327136	+	0.0876557i
$857$		−	436.543i		−	0.509386i	−0.967022	−	0.254693i	$-0.918026\pi$
$857$		−	436.543i		−	0.509386i	0.967022	−	0.254693i	$-0.0819743\pi$
$858$	283.450	+	163.650i	0.330361	+	0.190734i
$859$	−1238.40			−1.44167			−0.720837	−	0.693104i	$-0.756243\pi$
$859$	−1238.40			−1.44167			−0.720837	+	0.693104i	$0.756243\pi$
$860$	14.2384	−	53.1384i	0.0165563	−	0.0617889i
$861$	−215.885	−	373.923i	−0.250737	−	0.434289i
$862$	−771.300	−	445.310i	−0.894779	−	0.516601i
$863$	729.373	+	729.373i	0.845160	+	0.845160i	0.989525	−	0.144365i	$-0.0461138\pi$
$863$	729.373	+	729.373i	0.845160	+	0.845160i	−0.144365	+	0.989525i	$0.546114\pi$
$864$	28.3923	−	7.60770i	0.0328615	−	0.00880520i
$865$	−124.592	−	464.985i	−0.144037	−	0.537554i
$866$	−237.785	+	237.785i	−0.274578	+	0.274578i
$867$	59.9955	−	103.915i	0.0691990	−	0.119856i
$868$	−524.545	+	302.846i	−0.604314	+	0.348901i
$869$	117.904	+	31.5922i	0.135678	+	0.0363547i
$870$			76.0770i			0.0874448i
$871$	360.608	−	360.608i	0.414016	−	0.414016i
$872$	−192.756			−0.221051
$873$	−120.775	+	450.738i	−0.138345	+	0.516310i
$874$	96.9282	+	167.885i	0.110902	+	0.192088i
$875$	701.769	+	405.167i	0.802022	+	0.463048i
$876$	−233.545	−	233.545i	−0.266604	−	0.266604i
$877$	1314.21	−	352.142i	1.49853	−	0.401530i	0.585923	−	0.810367i	$-0.300732\pi$
$877$	1314.21	−	352.142i	1.49853	−	0.401530i	0.912607	+	0.408837i	$0.134066\pi$
$878$	−252.361	−	941.824i	−0.287427	−	1.07269i
$879$	229.450	−	229.450i	0.261035	−	0.261035i
$880$	36.8616	−	63.8461i	0.0418881	−	0.0725524i
$881$	1354.17	−	781.832i	1.53709	−	0.887437i	0.538079	−	0.842895i	$-0.319150\pi$
$881$	1354.17	−	781.832i	1.53709	−	0.887437i	0.999007	−	0.0445423i	$-0.0141829\pi$
$882$	−181.550	−	48.6462i	−0.205839	−	0.0551544i
$883$		−	452.723i		−	0.512710i	−0.966583	−	0.256355i	$-0.917478\pi$
$883$		−	452.723i		−	0.512710i	0.966583	−	0.256355i	$-0.0825216\pi$
$884$			492.133i			0.556712i
$885$	205.261			0.231934
$886$	−111.282	+	415.310i	−0.125600	+	0.468747i
$887$	−455.469	−	788.896i	−0.513494	−	0.889398i	−0.999877	−	0.0156524i	$-0.995017\pi$
$887$	−455.469	−	788.896i	−0.513494	−	0.889398i	0.486383	−	0.873745i	$-0.338316\pi$
$888$	−157.061	−	90.6795i	−0.176871	−	0.102117i
$889$	−1617.69	−	1617.69i	−1.81967	−	1.81967i
$890$	−410.985	+	110.123i	−0.461780	+	0.123734i
$891$	−23.9423	−	89.3538i	−0.0268713	−	0.100285i
$892$	309.061	−	309.061i	0.346481	−	0.346481i
$893$	164.196	−	284.396i	0.183870	−	0.318473i
$894$	120.631	−	69.6462i	0.134934	−	0.0779040i
$895$	494.985	+	132.631i	0.553055	+	0.148191i
$896$			109.282i			0.121967i
$897$	−46.6499	−	80.8001i	−0.0520066	−	0.0900781i
$898$	−401.387			−0.446979
$899$	−140.551	+	524.545i	−0.156342	+	0.583476i
$900$	−65.3538	−	113.196i	−0.0726154	−	0.125774i
$901$	−1010.98	−	583.692i	−1.12207	−	0.647827i
$902$	265.261	+	265.261i	0.294081	+	0.294081i
$903$	247.894	−	66.4230i	0.274523	−	0.0735582i
$904$	33.1000	+	123.531i	0.0366150	+	0.136649i
$905$	225.246	−	225.246i	0.248891	−	0.248891i
$906$	95.3294	−	165.115i	0.105220	−	0.182247i
$907$	385.501	−	222.569i	0.425029	−	0.245391i	−0.272198	−	0.962241i	$-0.587750\pi$
$907$	385.501	−	222.569i	0.425029	−	0.245391i	0.697227	+	0.716851i	$0.254417\pi$
$908$	−124.890	−	33.4641i	−0.137544	−	0.0368547i
$909$		−	560.438i		−	0.616544i
$910$	−82.4167	−	307.583i	−0.0905678	−	0.338004i
$911$	717.233			0.787303			0.393652	−	0.919260i	$-0.371212\pi$
$911$	717.233			0.787303			0.393652	+	0.919260i	$0.371212\pi$
$912$	59.3205	−	221.387i	0.0650444	−	0.242749i
$913$	806.985	+	1397.74i	0.883882	+	1.53093i
$914$	175.835	+	101.519i	0.192380	+	0.111071i
$915$	16.0347	+	16.0347i	0.0175243	+	0.0175243i
$916$	−160.329	+	42.9601i	−0.175032	+	0.0468997i
$917$	524.090	+	1955.93i	0.571526	+	2.13297i
$918$	98.3538	−	98.3538i	0.107139	−	0.107139i
$919$	−371.569	+	643.577i	−0.404319	+	0.700301i	−0.994242	−	0.107158i	$-0.965825\pi$
$919$	−371.569	+	643.577i	−0.404319	+	0.700301i	0.589923	+	0.807460i	$0.299158\pi$
$920$	−18.1999	+	10.5077i	−0.0197825	+	0.0114214i
$921$	−887.422	−	237.784i	−0.963541	−	0.258180i
$922$		−	832.246i		−	0.902653i
$923$	−1350.57	−	361.883i	−1.46324	−	0.392073i
$924$	343.923			0.372211
$925$	−208.727	+	778.981i	−0.225651	+	0.842142i
$926$	169.599	+	293.755i	0.183153	+	0.317230i
$927$	−216.323	−	124.894i	−0.233358	−	0.134729i
$928$	69.2820	+	69.2820i	0.0746574	+	0.0746574i
$929$	1424.14	−	381.597i	1.53298	−	0.410761i	0.608992	−	0.793176i	$-0.291574\pi$
$929$	1424.14	−	381.597i	1.53298	−	0.410761i	0.923991	+	0.382415i	$0.124908\pi$
$930$	35.6424	+	133.019i	0.0383252	+	0.143031i
$931$	−1036.31	+	1036.31i	−1.11311	+	1.11311i
$932$	380.669	−	659.338i	0.408443	−	0.707445i
$933$	−444.358	+	256.550i	−0.476268	+	0.274973i
$934$	1000.82	+	268.168i	1.07154	+	0.287118i
$935$		−	348.862i		−	0.373114i
$936$	−28.5500	+	106.550i	−0.0305021	+	0.113835i
$937$	−172.477			−0.184073			−0.0920367	−	0.995756i	$-0.529338\pi$
$937$	−172.477			−0.184073			−0.0920367	+	0.995756i	$0.529338\pi$
$938$	138.695	−	517.619i	0.147863	−	0.551832i
$939$	−102.439	−	177.429i	−0.109093	−	0.188955i
$940$	30.8306	+	17.8001i	0.0327985	+	0.0189362i
$941$	145.055	+	145.055i	0.154150	+	0.154150i	0.779969	−	0.625819i	$-0.215235\pi$
$941$	145.055	+	145.055i	0.154150	+	0.154150i	−0.625819	+	0.779969i	$0.715235\pi$
$942$	−131.151	+	35.1417i	−0.139226	+	0.0373054i
$943$	−27.6771	−	103.292i	−0.0293501	−	0.109536i
$944$	186.928	−	186.928i	0.198017	−	0.198017i
$945$	−45.0000	+	77.9423i	−0.0476190	+	0.0824786i
$946$	−193.104	+	111.488i	−0.204127	+	0.117853i
$947$	−665.902	−	178.428i	−0.703170	−	0.188414i	−0.110520	−	0.993874i	$-0.535252\pi$
$947$	−665.902	−	178.428i	−0.703170	−	0.188414i	−0.592650	+	0.805460i	$0.701918\pi$
$948$			41.1384i			0.0433950i
$949$	1197.24	−	320.800i	1.26158	−	0.338040i
$950$	−1019.18			−1.07283
$951$	−177.962	+	664.161i	−0.187131	+	0.698382i
$952$	258.564	+	447.846i	0.271601	+	0.470427i
$953$	−1044.96	−	603.309i	−1.09650	−	0.633063i	−0.161198	−	0.986922i	$-0.551536\pi$
$953$	−1044.96	−	603.309i	−1.09650	−	0.633063i	−0.935299	+	0.353859i	$0.884869\pi$
$954$	−185.023	−	185.023i	−0.193944	−	0.193944i
$955$	341.769	−	91.5768i	0.357873	−	0.0958919i
$956$	122.354	+	456.631i	0.127985	+	0.477647i
$957$	218.038	−	218.038i	0.227835	−	0.227835i
$958$	−261.464	+	452.869i	−0.272927	+	0.472723i
$959$	952.750	−	550.070i	0.993483	−	0.573588i
$960$	24.0000	+	6.43078i	0.0250000	+	0.00669873i
$961$			22.0065i			0.0228996i
$962$	589.417	−	340.300i	0.612699	−	0.353742i
$963$	307.492			0.319307
$964$	1.59361	−	5.94744i	0.00165312	−	0.00616954i
$965$	18.8282	+	32.6115i	0.0195111	+	0.0337943i
$966$	−84.9038	−	49.0192i	−0.0878921	−	0.0507446i
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	0.613820	−	0.789446i	$-0.289632\pi$
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	−0.789446	+	0.613820i	$0.789632\pi$
$968$	41.9474	−	11.2398i	0.0433341	−	0.0116113i
$969$	−280.708	−	1047.62i	−0.289688	−	1.08113i
$970$	−278.918	+	278.918i	−0.287544	+	0.287544i
$971$	−373.850	+	647.527i	−0.385015	+	0.666866i	−0.991771	−	0.128022i	$-0.959137\pi$
$971$	−373.850	+	647.527i	−0.385015	+	0.666866i	0.606756	+	0.794888i	$0.292471\pi$
$972$	27.0000	−	15.5885i	0.0277778	−	0.0160375i
$973$	−892.965	−	239.269i	−0.917744	−	0.245909i
$974$		−	274.000i		−	0.281314i
$975$	490.517			0.503094
$976$	29.2051			0.0299232
$977$	−55.9897	+	208.956i	−0.0573078	+	0.213876i	−0.988642	−	0.150290i	$-0.951979\pi$
$977$	−55.9897	+	208.956i	−0.0573078	+	0.213876i	0.931334	+	0.364166i	$0.118646\pi$
$978$	250.547	+	433.960i	0.256183	+	0.443722i
$979$	1493.51	+	862.277i	1.52554	+	0.880773i
$980$	−112.344	−	112.344i	−0.114636	−	0.114636i
$981$	−197.483	+	52.9153i	−0.201307	+	0.0539402i
$982$	13.5167	+	50.4449i	0.0137644	+	0.0513695i
$983$	1367.93	−	1367.93i	1.39158	−	1.39158i	0.569801	−	0.821783i	$-0.307020\pi$
$983$	1367.93	−	1367.93i	1.39158	−	1.39158i	0.821783	−	0.569801i	$-0.192980\pi$
$984$	−63.2154	+	109.492i	−0.0642433	+	0.111273i
$985$	−234.892	+	135.615i	−0.238470	+	0.137680i
$986$	447.846	+	120.000i	0.454205	+	0.121704i
$987$			166.077i			0.168264i
$988$	608.200	+	608.200i	0.615587	+	0.615587i
$989$	63.5617			0.0642686
$990$	20.2384	−	75.5307i	0.0204428	−	0.0762937i
$991$	935.631	+	1620.56i	0.944128	+	1.63528i	0.757488	+	0.652849i	$0.226426\pi$
$991$	935.631	+	1620.56i	0.944128	+	1.63528i	0.186640	+	0.982428i	$0.440240\pi$
$992$	153.597	+	88.6795i	0.154836	+	0.0893946i
$993$	174.285	+	174.285i	0.175514	+	0.175514i
$994$	−1419.16	+	380.263i	−1.42773	+	0.382558i
$995$	−10.3102	−	38.4782i	−0.0103620	−	0.0386715i
$996$	−384.631	+	384.631i	−0.386175	+	0.386175i
$997$	−768.584	+	1331.23i	−0.770897	+	1.33523i	0.166175	+	0.986096i	$0.446858\pi$
$997$	−768.584	+	1331.23i	−0.770897	+	1.33523i	−0.937072	+	0.349137i	$0.886475\pi$
$998$	801.540	−	462.769i	0.803146	−	0.463697i
$999$	−185.806	−	49.7865i	−0.185992	−	0.0498363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.a.37.1	yes	4
3.2	odd	2		234.3.bb.c.37.1		4
13.2	odd	12		1014.3.f.e.577.2		4
13.3	even	3		1014.3.f.e.775.2		4
13.6	odd	12	inner	78.3.l.a.19.1	✓	4
13.10	even	6		1014.3.f.d.775.2		4
13.11	odd	12		1014.3.f.d.577.2		4
39.32	even	12		234.3.bb.c.19.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.19.1	✓	4	13.6	odd	12	inner
78.3.l.a.37.1	yes	4	1.1	even	1	trivial
234.3.bb.c.19.1		4	39.32	even	12
234.3.bb.c.37.1		4	3.2	odd	2
1014.3.f.d.577.2		4	13.11	odd	12
1014.3.f.d.775.2		4	13.10	even	6
1014.3.f.e.577.2		4	13.2	odd	12
1014.3.f.e.775.2		4	13.3	even	3

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.19615 + 1.26795i) q^{10} +(9.92820 + 2.66025i) q^{11} +3.46410i q^{12} +(-11.2583 - 6.50000i) q^{13} -13.6603 q^{14} +(-0.803848 + 3.00000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(16.3923 + 9.46410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(31.9545 - 8.56218i) q^{19} +(0.928203 + 3.46410i) q^{20} +(-11.8301 + 11.8301i) q^{21} +(7.26795 - 12.5885i) q^{22} +(-3.58846 + 2.07180i) q^{23} +(4.73205 + 1.26795i) q^{24} -21.7846i q^{25} +(-13.0000 + 13.0000i) q^{26} +5.19615 q^{27} +(-5.00000 + 18.6603i) q^{28} +(8.66025 + 15.0000i) q^{29} +(3.80385 + 2.19615i) q^{30} +(22.1699 + 22.1699i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-4.60770 - 17.1962i) q^{33} +(18.9282 - 18.9282i) q^{34} +(-8.66025 + 15.0000i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-35.7583 - 9.58142i) q^{37} -46.7846i q^{38} +22.5167i q^{39} +5.07180 q^{40} +(-6.67949 + 24.9282i) q^{41} +(11.8301 + 20.4904i) q^{42} +(-13.2846 - 7.66987i) q^{43} +(-14.5359 - 14.5359i) q^{44} +(5.19615 - 1.39230i) q^{45} +(1.51666 + 5.66025i) q^{46} +(7.01924 - 7.01924i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-38.3660 + 22.1506i) q^{49} +(-29.7583 - 7.97372i) q^{50} -32.7846i q^{51} +(13.0000 + 22.5167i) q^{52} -61.6743 q^{53} +(1.90192 - 7.09808i) q^{54} +(-9.21539 - 15.9615i) q^{55} +(23.6603 + 13.6603i) q^{56} +(-40.5167 - 40.5167i) q^{57} +(23.6603 - 6.33975i) q^{58} +(-17.1051 - 63.8372i) q^{59} +(4.39230 - 4.39230i) q^{60} +(3.65064 - 6.32309i) q^{61} +(38.3993 - 22.1699i) q^{62} +(27.9904 + 7.50000i) q^{63} -8.00000i q^{64} +(6.03332 + 22.5167i) q^{65} -25.1769 q^{66} +(-10.1532 + 37.8923i) q^{67} +(-18.9282 - 32.7846i) q^{68} +(6.21539 + 3.58846i) q^{69} +(17.3205 + 17.3205i) q^{70} +(103.890 - 27.8372i) q^{71} +(-2.19615 - 8.19615i) q^{72} +(-67.4186 + 67.4186i) q^{73} +(-26.1769 + 45.3397i) q^{74} +(-32.6769 + 18.8660i) q^{75} +(-63.9090 - 17.1244i) q^{76} -99.2820i q^{77} +(30.7583 + 8.24167i) q^{78} +11.8756 q^{79} +(1.85641 - 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(31.6077 + 18.2487i) q^{82} +(111.033 + 111.033i) q^{83} +(32.3205 - 8.66025i) q^{84} +(-8.78461 - 32.7846i) q^{85} +(-15.3397 + 15.3397i) q^{86} +(15.0000 - 25.9808i) q^{87} +(-25.1769 + 14.5359i) q^{88} +(162.067 + 43.4256i) q^{89} -7.60770i q^{90} +(-32.5000 + 121.292i) q^{91} +8.28719 q^{92} +(14.0551 - 52.4545i) q^{93} +(-7.01924 - 12.1577i) q^{94} +(-51.3731 - 29.6603i) q^{95} +(-6.92820 - 6.92820i) q^{96} +(150.246 - 40.2583i) q^{97} +(16.2154 + 60.5167i) q^{98} +(-21.8038 + 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 + 12 * q^10 + 12 * q^11 - 20 * q^14 - 24 * q^15 + 8 * q^16 + 24 * q^17 + 12 * q^18 + 62 * q^19 - 24 * q^20 - 30 * q^21 + 36 * q^22 + 48 * q^23 + 12 * q^24 - 52 * q^26 - 20 * q^28 + 36 * q^30 + 106 * q^31 + 8 * q^32 - 60 * q^33 + 48 * q^34 - 98 * q^37 + 48 * q^40 - 96 * q^41 + 30 * q^42 + 30 * q^43 - 72 * q^44 - 84 * q^46 + 132 * q^47 - 150 * q^49 - 74 * q^50 + 52 * q^52 + 72 * q^53 + 18 * q^54 - 120 * q^55 + 60 * q^56 - 72 * q^57 + 60 * q^58 + 84 * q^59 - 24 * q^60 - 72 * q^61 - 30 * q^62 + 60 * q^63 - 156 * q^65 + 24 * q^66 - 148 * q^67 - 48 * q^68 + 108 * q^69 + 180 * q^71 + 12 * q^72 - 190 * q^73 + 20 * q^74 - 6 * q^75 - 124 * q^76 + 78 * q^78 + 96 * q^79 - 48 * q^80 - 18 * q^81 + 168 * q^82 + 264 * q^83 + 60 * q^84 + 48 * q^85 - 96 * q^86 + 60 * q^87 + 24 * q^88 + 288 * q^89 - 130 * q^91 + 144 * q^92 + 174 * q^93 - 132 * q^94 - 60 * q^95 + 310 * q^97 + 148 * q^98 - 108 * q^99

Introduction

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