LMFDB - Embedded newform 78.3.l.a.19.1

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			19.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.19
Dual form			78.3.l.a.37.1

$q$-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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$

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	−0.822441	−	0.568851i	$-0.807388\pi$
$5$	−1.26795	+	1.26795i	−0.253590	+	0.253590i	0.568851	+	0.822441i	$0.307388\pi$
$6$	−2.36603	−	0.633975i	−0.394338	−	0.105662i
$7$	−2.50000	+	9.33013i	−0.357143	+	1.33288i	0.520624	+	0.853786i	$0.325700\pi$
$7$	−2.50000	+	9.33013i	−0.357143	+	1.33288i	−0.877766	+	0.479089i	$0.840967\pi$
$8$	−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	0.222447	−	0.974945i	$-0.428596\pi$
$11$	9.92820	−	2.66025i	0.902564	−	0.241841i	0.680117	+	0.733104i	$0.261929\pi$
$12$		−	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	0.0667738	−	0.997768i	$-0.478729\pi$
$17$	16.3923	−	9.46410i	0.964253	−	0.556712i	0.897479	+	0.441056i	$0.145396\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$	31.9545	+	8.56218i	1.68181	+	0.450641i	0.968257	−	0.249956i	$-0.0804160\pi$
$19$	31.9545	+	8.56218i	1.68181	+	0.450641i	0.713558	+	0.700597i	$0.247083\pi$
$20$	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	0.419957	−	0.907544i	$-0.362045\pi$
$23$	−3.58846	−	2.07180i	−0.156020	−	0.0900781i	−0.575977	+	0.817466i	$0.695378\pi$
$24$	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	−0.677193	−	0.735805i	$-0.736804\pi$
$29$	8.66025	−	15.0000i	0.298629	−	0.517241i	0.975823	+	0.218564i	$0.0701372\pi$
$30$	3.80385	−	2.19615i	0.126795	−	0.0732051i
$31$	22.1699	−	22.1699i	0.715157	−	0.715157i	−0.252452	−	0.967609i	$-0.581237\pi$
$31$	22.1699	−	22.1699i	0.715157	−	0.715157i	0.967609	+	0.252452i	$0.0812370\pi$
$32$	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	−0.707325	−	0.706889i	$-0.750098\pi$
$37$	−35.7583	+	9.58142i	−0.966441	+	0.258957i	−0.259117	+	0.965846i	$0.583431\pi$
$38$			46.7846i			1.23117i
$39$		−	22.5167i		−	0.577350i
$40$	5.07180			0.126795
$41$	−6.67949	−	24.9282i	−0.162914	−	0.608005i	−0.998297	−	0.0583360i	$-0.981421\pi$
$41$	−6.67949	−	24.9282i	−0.162914	−	0.608005i	0.835383	−	0.549669i	$-0.185246\pi$
$42$	11.8301	−	20.4904i	0.281670	−	0.487866i
$43$	−13.2846	+	7.66987i	−0.308944	+	0.178369i	−0.646454	−	0.762953i	$-0.723749\pi$
$43$	−13.2846	+	7.66987i	−0.308944	+	0.178369i	0.337510	+	0.941322i	$0.390415\pi$
$44$	−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	0.777826	−	0.628480i	$-0.216323\pi$
$47$	7.01924	+	7.01924i	0.149345	+	0.149345i	−0.628480	+	0.777826i	$0.716323\pi$
$48$	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	0.655253	+	0.755409i	$0.272562\pi$
$59$	−17.1051	+	63.8372i	−0.289917	+	1.08199i	−0.945171	+	0.326577i	$0.894105\pi$
$60$	4.39230	+	4.39230i	0.0732051	+	0.0732051i
$61$	3.65064	+	6.32309i	0.0598465	+	0.103657i	0.894396	−	0.447275i	$-0.147606\pi$
$61$	3.65064	+	6.32309i	0.0598465	+	0.103657i	−0.834550	+	0.550932i	$0.814272\pi$
$62$	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	−0.999377	−	0.0352988i	$-0.988762\pi$
$67$	−10.1532	−	37.8923i	−0.151540	−	0.565557i	0.847836	−	0.530258i	$-0.177905\pi$
$68$	−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	0.900606	−	0.434636i	$-0.143123\pi$
$71$	103.890	+	27.8372i	1.46324	+	0.392073i	0.562630	+	0.826709i	$0.309790\pi$
$72$	−2.19615	+	8.19615i	−0.0305021	+	0.113835i
$73$	−67.4186	−	67.4186i	−0.923542	−	0.923542i	0.0737356	−	0.997278i	$-0.476508\pi$
$73$	−67.4186	−	67.4186i	−0.923542	−	0.923542i	−0.997278	+	0.0737356i	$0.976508\pi$
$74$	−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	0.439516	−	0.898235i	$-0.355150\pi$
$83$	111.033	−	111.033i	1.33775	−	1.33775i	0.898235	−	0.439516i	$-0.144850\pi$
$84$	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	0.824065	−	0.566496i	$-0.191701\pi$
$89$	162.067	−	43.4256i	1.82097	−	0.487928i	0.996909	+	0.0785673i	$0.0250346\pi$
$90$			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	0.929138	−	0.369733i	$-0.120551\pi$
$97$	150.246	+	40.2583i	1.54893	+	0.415034i	0.619791	+	0.784767i	$0.287217\pi$
$98$	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	−0.991122	−	0.132958i	$-0.957552\pi$
$101$	−161.785	−	93.4064i	−1.60183	−	0.924816i	−0.610706	−	0.791857i	$-0.709114\pi$
$102$	−44.7846	+	12.0000i	−0.439065	+	0.117647i
$103$		−	83.2628i		−	0.808377i	−0.914676	−	0.404188i	$-0.867554\pi$
$103$		−	83.2628i		−	0.808377i	0.914676	−	0.404188i	$-0.132446\pi$
$104$	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	−0.999709	−	0.0241269i	$-0.992319\pi$
$107$	−51.2487	+	88.7654i	−0.478960	+	0.829583i	0.520749	+	0.853710i	$0.325653\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	48.1891	−	48.1891i	0.442102	−	0.442102i	−0.450616	−	0.892718i	$-0.648796\pi$
$109$	48.1891	−	48.1891i	0.442102	−	0.442102i	0.892718	+	0.450616i	$0.148796\pi$
$110$	−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	0.948550	−	0.316627i	$-0.102550\pi$
$113$	22.6077	+	39.1577i	0.200068	+	0.346528i	−0.748482	+	0.663155i	$0.769217\pi$
$114$	−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	0.988169	+	0.153372i	$0.0490132\pi$
$127$	205.115	+	118.423i	1.61508	+	0.932465i	0.626908	+	0.779093i	$0.284320\pi$
$128$	−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	−0.770938	−	0.636911i	$-0.780212\pi$
$137$	29.4782	−	110.014i	0.215169	−	0.803023i	0.986107	−	0.166112i	$-0.0531213\pi$
$138$	7.17691	+	7.17691i	0.0520066	+	0.0520066i
$139$	47.8538	+	82.8853i	0.344272	+	0.596297i	0.985221	−	0.171287i	$-0.0547924\pi$
$139$	47.8538	+	82.8853i	0.344272	+	0.596297i	−0.640949	+	0.767583i	$0.721459\pi$
$140$	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	0.0697402	−	0.997565i	$-0.477783\pi$
$149$	−54.9282	−	14.7180i	−0.368646	−	0.0987783i	−0.438386	+	0.898787i	$0.644450\pi$
$150$	13.8109	−	51.5429i	0.0920726	−	0.343620i
$151$	−55.0385	−	55.0385i	−0.364493	−	0.364493i	0.500971	−	0.865464i	$-0.332976\pi$
$151$	−55.0385	−	55.0385i	−0.364493	−	0.364493i	−0.865464	+	0.500971i	$0.832976\pi$
$152$	−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	0.589659	+	0.807652i	$0.299262\pi$
$163$	−52.9468	+	197.600i	−0.324827	+	1.21227i	−0.914486	+	0.404618i	$0.867405\pi$
$164$	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	−0.694420	−	0.719570i	$-0.744339\pi$
$167$	−156.315	+	41.8846i	−0.936020	+	0.250806i	−0.241600	+	0.970376i	$0.577672\pi$
$168$			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	0.356511	−	0.934291i	$-0.383966\pi$
$173$	232.492	−	134.229i	1.34389	−	0.775893i	0.987375	+	0.158398i	$0.0506330\pi$
$174$	−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	−0.390167	−	0.920744i	$-0.627583\pi$
$179$	−247.492	−	142.890i	−1.38264	−	0.798267i	−0.992471	+	0.122477i	$0.960916\pi$
$180$	−10.3923	+	2.78461i	−0.0577350	+	0.0154701i
$181$		−	177.646i		−	0.981471i	−0.871309	−	0.490735i	$-0.836728\pi$
$181$		−	177.646i		−	0.981471i	0.871309	−	0.490735i	$-0.163272\pi$
$182$	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	−0.999815	−	0.0192120i	$-0.993884\pi$
$191$	−98.6603	−	170.885i	−0.516546	−	0.894684i	0.483270	−	0.875472i	$-0.339449\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	−20.2846	+	5.43524i	−0.105102	+	0.0281619i	−0.310987	−	0.950414i	$-0.600659\pi$
$193$	−20.2846	+	5.43524i	−0.105102	+	0.0281619i	0.205885	+	0.978576i	$0.433993\pi$
$194$			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	0.991271	+	0.131839i	$0.0420882\pi$
$197$	39.1487	+	146.105i	0.198725	+	0.741650i	−0.792547	+	0.609811i	$0.791245\pi$
$198$	21.8038	−	37.7654i	0.110120	−	0.190734i
$199$	19.2391	−	11.1077i	0.0966789	−	0.0558176i	−0.450881	−	0.892584i	$-0.648890\pi$
$199$	19.2391	−	11.1077i	0.0966789	−	0.0558176i	0.547560	+	0.836766i	$0.315557\pi$
$200$	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	−0.932012	−	0.362426i	$-0.881948\pi$
$211$	−32.1007	+	55.6000i	−0.152136	+	0.263507i	0.779877	+	0.625933i	$0.215282\pi$
$212$	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	−0.968841	−	0.247684i	$-0.920331\pi$
$223$	−56.5622	−	211.093i	−0.253642	−	0.946605i	0.715199	−	0.698921i	$-0.246336\pi$
$224$	−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	0.393725	−	0.919228i	$-0.371186\pi$
$227$	62.4449	+	16.7321i	0.275088	+	0.0737095i	−0.118638	+	0.992938i	$0.537853\pi$
$228$	29.6603	−	110.694i	0.130089	−	0.485498i
$229$	58.6846	+	58.6846i	0.256265	+	0.256265i	0.823533	−	0.567268i	$-0.192000\pi$
$229$	58.6846	+	58.6846i	0.256265	+	0.256265i	−0.567268	+	0.823533i	$0.692000\pi$
$230$	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	$-0.695698\pi$
$233$		−	380.669i		−	1.63377i	0.576798	−	0.816887i	$-0.304302\pi$
$234$	−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	−0.964265	−	0.264941i	$-0.914648\pi$
$239$	−167.138	+	167.138i	−0.699324	+	0.699324i	0.264941	+	0.964265i	$0.414648\pi$
$240$	−12.0000	−	3.21539i	−0.0500000	−	0.0133975i
$241$	0.796806	−	2.97372i	0.00330625	−	0.0123391i	−0.964253	−	0.264983i	$-0.914634\pi$
$241$	0.796806	−	2.97372i	0.00330625	−	0.0123391i	0.967559	+	0.252644i	$0.0813002\pi$
$242$	−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	−0.814791	−	0.579755i	$-0.803148\pi$
$251$	−180.746	+	104.354i	−0.720104	+	0.415752i	0.0946869	+	0.995507i	$0.469815\pi$
$252$	−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	0.619812	−	0.784750i	$-0.287209\pi$
$257$	64.2769	+	37.1103i	0.250105	+	0.144398i	−0.369708	+	0.929148i	$0.620542\pi$
$258$	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	−0.841936	−	0.539577i	$-0.818584\pi$
$263$	12.1821	−	21.1000i	0.0463197	−	0.0802280i	0.888256	+	0.459349i	$0.151917\pi$
$264$	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	0.981846	−	0.189679i	$-0.0607448\pi$
$269$	87.8705	+	152.196i	0.326656	+	0.565785i	−0.655190	+	0.755464i	$0.727411\pi$
$270$	−11.4115	−	6.58846i	−0.0422650	−	0.0244017i
$271$	269.169	−	72.1237i	0.993244	−	0.266139i	0.274632	−	0.961550i	$-0.411444\pi$
$271$	269.169	−	72.1237i	0.993244	−	0.266139i	0.718613	+	0.695411i	$0.244777\pi$
$272$		−	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	−0.994127	−	0.108216i	$-0.965486\pi$
$277$	−387.100	+	223.492i	−1.39747	+	0.806831i	−0.403345	+	0.915048i	$0.632153\pi$
$278$	−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	0.697172	−	0.716904i	$-0.254442\pi$
$281$	−5.54483	−	5.54483i	−0.0197325	−	0.0197325i	−0.716904	+	0.697172i	$0.754442\pi$
$282$	−12.1577	−	21.0577i	−0.0431123	−	0.0746727i
$283$	14.4160	+	8.32309i	0.0509400	+	0.0294102i	0.525254	−	0.850946i	$-0.323970\pi$
$283$	14.4160	+	8.32309i	0.0509400	+	0.0294102i	−0.474314	+	0.880356i	$0.657304\pi$
$284$	−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	−0.832487	−	0.554044i	$-0.813084\pi$
$293$	48.4885	−	180.962i	0.165490	−	0.617616i	0.997977	−	0.0635723i	$-0.0202493\pi$
$294$	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	0.967020	+	0.254702i	$0.0819774\pi$
$307$	375.069	+	375.069i	1.22172	+	1.22172i	0.254702	+	0.967020i	$0.418023\pi$
$308$	−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	$0.158011\pi$
$311$			296.238i			0.952535i	−0.879300	+	0.476268i	$0.841989\pi$
$312$	−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	−0.994088	−	0.108575i	$-0.965371\pi$
$317$	−280.708	+	280.708i	−0.885513	+	0.885513i	0.108575	+	0.994088i	$0.465371\pi$
$318$	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	0.0451334	−	0.998981i	$-0.485629\pi$
$331$	−137.454	−	36.8308i	−0.415270	−	0.111271i	−0.460404	+	0.887710i	$0.652295\pi$
$332$	−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	$-0.827573\pi$
$337$		−	347.508i		−	1.03118i	0.856835	−	0.515590i	$-0.172427\pi$
$338$	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	−0.987410	−	0.158183i	$-0.949436\pi$
$347$	−218.851	−	379.061i	−0.630695	−	1.09240i	0.356715	−	0.934213i	$-0.383897\pi$
$348$	−51.9615	−	30.0000i	−0.149315	−	0.0862069i
$349$	−432.889	+	115.992i	−1.24037	+	0.332356i	−0.818609	−	0.574351i	$-0.805254\pi$
$349$	−432.889	+	115.992i	−1.24037	+	0.332356i	−0.421761	+	0.906707i	$0.638588\pi$
$350$		−	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	−0.751951	−	0.659218i	$-0.770887\pi$
$353$	−151.914	−	566.951i	−0.430352	−	1.60609i	0.321600	−	0.946876i	$-0.395779\pi$
$354$	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	0.790939	−	0.611895i	$-0.209592\pi$
$359$	64.2769	+	64.2769i	0.179044	+	0.179044i	−0.611895	+	0.790939i	$0.709592\pi$
$360$	−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	−0.678672	−	0.734442i	$-0.737444\pi$
$367$	108.892	−	188.607i	0.296709	−	0.513916i	0.975381	+	0.220526i	$0.0707774\pi$
$368$	−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	0.974840	−	0.222905i	$-0.0715541\pi$
$373$	109.803	+	190.185i	0.294378	+	0.509878i	−0.680462	+	0.732784i	$0.738221\pi$
$374$	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	0.999995	−	0.00312126i	$-0.000993528\pi$
$379$	50.1846	+	187.292i	0.132413	+	0.494173i	−0.867582	+	0.497294i	$0.834327\pi$
$380$	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	0.495964	−	0.868343i	$-0.334815\pi$
$383$	188.172	+	50.4205i	0.491310	+	0.131646i	−0.00465401	+	0.999989i	$0.501481\pi$
$384$	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	$0.00726337\pi$
$389$			17.7513i			0.0456331i	−0.999740	+	0.0228166i	$0.992737\pi$
$390$	−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	0.764314	+	0.644844i	$0.223078\pi$
$397$	−87.3494	+	325.992i	−0.220024	+	0.821139i	−0.984337	+	0.176295i	$0.943589\pi$
$398$	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	−0.817686	−	0.575664i	$-0.804744\pi$
$401$	−496.435	+	133.019i	−1.23799	+	0.331719i	−0.420305	+	0.907383i	$0.638077\pi$
$402$			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	−0.506418	−	0.862288i	$-0.669031\pi$
$409$	−562.838	−	150.812i	−1.37613	−	0.368734i	−0.869715	+	0.493554i	$0.835697\pi$
$410$	−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	0.156479	−	0.987681i	$-0.449986\pi$
$419$	391.177	−	677.538i	0.933596	−	1.61704i	0.777118	−	0.629355i	$-0.216681\pi$
$420$	−51.9615	+	30.0000i	−0.123718	+	0.0714286i
$421$	−27.0352	+	27.0352i	−0.0642166	+	0.0642166i	−0.738486	−	0.674269i	$-0.764459\pi$
$421$	−27.0352	+	27.0352i	−0.0642166	+	0.0642166i	0.674269	+	0.738486i	$0.264459\pi$
$422$	−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	0.848645	+	0.528963i	$0.177419\pi$
$431$	162.995	+	608.305i	0.378178	+	1.41138i	−0.470467	+	0.882418i	$0.655914\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−205.928	+	118.892i	−0.475583	+	0.274578i	−0.718574	−	0.695451i	$-0.755205\pi$
$433$	−205.928	+	118.892i	−0.475583	+	0.274578i	0.242991	+	0.970029i	$0.421872\pi$
$434$	−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	0.989639	−	0.143576i	$-0.0458600\pi$
$439$	597.092	+	344.731i	1.36012	+	0.785265i	0.370480	+	0.928841i	$0.379193\pi$
$440$	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	0.834608	+	0.550844i	$0.185694\pi$
$449$	−73.4589	+	274.153i	−0.163606	+	0.610585i	−0.998214	+	0.0597407i	$0.980973\pi$
$450$	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	0.913280	−	0.407331i	$-0.133541\pi$
$457$	−37.1584	−	138.677i	−0.0813093	−	0.303451i	−0.994590	+	0.103881i	$0.966874\pi$
$458$	−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	0.815765	−	0.578383i	$-0.196316\pi$
$461$	568.435	+	152.312i	1.23305	+	0.330394i	0.417282	+	0.908777i	$0.362983\pi$
$462$	62.9423	−	234.904i	0.136239	−	0.508450i
$463$	−169.599	−	169.599i	−0.366305	−	0.366305i	0.499823	−	0.866128i	$-0.333399\pi$
$463$	−169.599	−	169.599i	−0.366305	−	0.366305i	−0.866128	+	0.499823i	$0.833399\pi$
$464$	−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	$-0.712961\pi$
$467$		−	732.649i		−	1.56884i	0.620230	−	0.784420i	$-0.287039\pi$
$468$	−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	−0.611588	−	0.791176i	$-0.709469\pi$
$479$	−357.167	+	95.7025i	−0.745651	+	0.199796i	−0.134063	+	0.990973i	$0.542802\pi$
$480$		−	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	0.445788	−	0.895139i	$-0.352924\pi$
$487$	187.145	+	50.1455i	0.384282	+	0.102968i	−0.0615056	+	0.998107i	$0.519590\pi$
$488$	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	0.467079	−	0.884215i	$-0.345306\pi$
$491$	−31.9808	−	18.4641i	−0.0651339	−	0.0376051i	−0.532213	+	0.846610i	$0.678640\pi$
$492$	−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	−0.0701438	−	0.997537i	$-0.522346\pi$
$499$	462.769	−	462.769i	0.927393	−	0.927393i	0.997537	+	0.0701438i	$0.0223458\pi$
$500$	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	0.987393	−	0.158286i	$-0.0505969\pi$
$503$	179.378	+	310.692i	0.356617	+	0.617678i	−0.630777	+	0.775965i	$0.717264\pi$
$504$	−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	−0.853067	−	0.521802i	$-0.825260\pi$
$509$	−190.972	−	712.717i	−0.375190	−	1.40023i	0.477876	−	0.878427i	$-0.341407\pi$
$510$	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	−0.885369	−	0.464888i	$-0.846094\pi$
$523$	−20.9615	+	36.3064i	−0.0400794	+	0.0694196i	0.845290	+	0.534308i	$0.179428\pi$
$524$	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	0.702989	−	0.711201i	$-0.251848\pi$
$541$	−4.44298	−	4.44298i	−0.00821253	−	0.00821253i	−0.711201	+	0.702989i	$0.751848\pi$
$542$	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	−0.779945	−	0.625848i	$-0.784753\pi$
$557$	−636.358	+	170.512i	−1.14247	+	0.306125i	−0.362528	+	0.931973i	$0.618086\pi$
$558$		−	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	−0.430205	−	0.902731i	$-0.641559\pi$
$563$	76.8385	−	44.3628i	0.136481	−	0.0787971i	0.566686	+	0.823934i	$0.308225\pi$
$564$	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	0.134223	−	0.990951i	$-0.457146\pi$
$569$	−373.750	−	215.785i	−0.656854	−	0.379235i	−0.791077	+	0.611716i	$0.790479\pi$
$570$	140.354	−	37.6077i	0.246235	−	0.0659784i
$571$			959.892i			1.68107i	0.541756	+	0.840536i	$0.317760\pi$
$571$			959.892i			1.68107i	−0.541756	+	0.840536i	$0.682240\pi$
$572$	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	−0.924588	−	0.380968i	$-0.875591\pi$
$577$	−313.669	+	313.669i	−0.543621	+	0.543621i	0.380968	+	0.924588i	$0.375591\pi$
$578$	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	0.897929	−	0.440141i	$-0.145071\pi$
$587$	−58.5654	−	218.569i	−0.0997708	−	0.372350i	−0.997700	+	0.0677912i	$0.978405\pi$
$588$	−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	0.930811	−	0.365500i	$-0.119102\pi$
$593$	335.229	+	335.229i	0.565311	+	0.565311i	−0.365500	+	0.930811i	$0.619102\pi$
$594$	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	−0.858625	−	0.512605i	$-0.828681\pi$
$601$	8.78461	−	15.2154i	0.0146167	−	0.0253168i	0.873241	+	0.487288i	$0.162014\pi$
$602$	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	−0.969939	−	0.243350i	$-0.921754\pi$
$607$	−422.300	−	731.445i	−0.695716	−	1.20502i	0.274222	−	0.961666i	$-0.411580\pi$
$608$	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	−0.961534	−	0.274685i	$-0.911426\pi$
$613$	−163.158	−	608.915i	−0.266164	−	0.993337i	0.695370	−	0.718651i	$-0.255240\pi$
$614$	−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	0.344495	−	0.938788i	$-0.388050\pi$
$617$	107.014	+	28.6743i	0.173443	+	0.0464738i	−0.171053	+	0.985262i	$0.554717\pi$
$618$	−52.7865	+	197.002i	−0.0854150	+	0.318773i
$619$	−111.970	−	111.970i	−0.180888	−	0.180888i	0.610854	−	0.791743i	$-0.290826\pi$
$619$	−111.970	−	111.970i	−0.180888	−	0.180888i	−0.791743	+	0.610854i	$0.790826\pi$
$620$	−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	−0.257450	−	0.966292i	$-0.582882\pi$
$631$	283.101	−	1056.55i	0.448654	−	1.67440i	0.706104	−	0.708108i	$-0.250451\pi$
$632$	−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	−0.749952	−	0.661493i	$-0.769923\pi$
$641$	−353.869	+	204.306i	−0.552058	+	0.318731i	0.197894	+	0.980223i	$0.436590\pi$
$642$	177.531	−	177.531i	0.276528	−	0.276528i
$643$	−432.661	−	115.931i	−0.672879	−	0.180297i	−0.0938279	−	0.995588i	$-0.529910\pi$
$643$	−432.661	−	115.931i	−0.672879	−	0.180297i	−0.579052	+	0.815291i	$0.696577\pi$
$644$	−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	0.268123	−	0.963385i	$-0.413597\pi$
$647$	−279.588	−	161.420i	−0.432131	−	0.249491i	−0.700254	+	0.713894i	$0.746930\pi$
$648$	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	−0.149314	−	0.988790i	$-0.547706\pi$
$653$	510.424	−	884.081i	0.781660	−	1.35388i	0.930974	−	0.365086i	$-0.118960\pi$
$654$	−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	0.766630	−	0.642089i	$-0.221932\pi$
$659$	−113.842	−	197.181i	−0.172750	−	0.299212i	−0.939380	+	0.342877i	$0.888599\pi$
$660$	55.2923	+	31.9230i	0.0837763	+	0.0483683i
$661$	146.181	−	39.1692i	0.221152	−	0.0592575i	−0.146542	−	0.989205i	$-0.546814\pi$
$661$	146.181	−	39.1692i	0.221152	−	0.0592575i	0.367693	+	0.929947i	$0.380148\pi$
$662$		−	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	−0.0302828	−	0.999541i	$-0.509641\pi$
$673$	−613.138	−	353.996i	−0.911052	−	0.525996i	−0.880770	+	0.473545i	$0.842974\pi$
$674$	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	−0.987804	−	0.155701i	$-0.950236\pi$
$683$	−37.2168	+	138.895i	−0.0544901	+	0.203360i	0.933314	+	0.359061i	$0.116903\pi$
$684$	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	0.989766	+	0.142697i	$0.0455774\pi$
$691$	140.931	+	525.961i	0.203952	+	0.761159i	−0.785815	+	0.618462i	$0.787756\pi$
$692$	−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	$0.132861\pi$
$701$			568.344i			0.810761i	−0.914148	+	0.405381i	$0.867139\pi$
$702$	−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	−0.866074	−	0.499916i	$-0.833364\pi$
$709$	94.9538	−	354.372i	0.133926	−	0.499820i	1.00000		9.64632e-5i	$3.07052e-5\pi$
$710$	−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	−0.332829	−	0.942987i	$-0.608003\pi$
$719$	228.215	−	131.760i	0.317407	−	0.183255i	0.650236	+	0.759732i	$0.274670\pi$
$720$	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	$0.206482\pi$
$727$			878.415i			1.20827i	−0.796880	+	0.604137i	$0.793518\pi$
$728$	−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	−0.800016	−	0.599979i	$-0.795176\pi$
$733$	−146.627	+	146.627i	−0.200037	+	0.200037i	0.599979	+	0.800016i	$0.295176\pi$
$734$	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	0.187694	−	0.982227i	$-0.439899\pi$
$739$	621.762	−	166.601i	0.841356	−	0.225441i	0.653662	+	0.756787i	$0.273232\pi$
$740$			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	0.963511	−	0.267670i	$-0.0862535\pi$
$743$	−3.52835	−	13.1680i	−0.00474879	−	0.0177227i	−0.968260	+	0.249947i	$0.919587\pi$
$744$	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	0.404855	−	0.914381i	$-0.367322\pi$
$751$	−138.631	−	80.0385i	−0.184595	−	0.106576i	−0.589450	+	0.807805i	$0.700655\pi$
$752$	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	0.271360	−	0.962478i	$-0.412527\pi$
$757$	733.692	−	1270.79i	0.969210	−	1.67872i	0.697850	−	0.716244i	$-0.254140\pi$
$758$	−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	−0.927811	−	0.373051i	$-0.878312\pi$
$761$	47.3514	−	176.718i	0.0622227	−	0.232218i	0.990033	+	0.140833i	$0.0449782\pi$
$762$	−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	−

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

L-functions

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