LMFDB - Embedded newform 78.3.l.b.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.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.09808 - 0.633975i) q^{10} +(-17.6603 + 4.73205i) q^{11} +3.46410i q^{12} +(11.2583 + 6.50000i) q^{13} -17.8564 q^{14} +(-0.401924 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(15.1865 - 8.76795i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(16.1962 + 4.33975i) q^{19} +(-0.464102 + 1.73205i) q^{20} +(-15.4641 - 15.4641i) q^{21} +(12.9282 + 22.3923i) q^{22} +(18.5885 + 10.7321i) q^{23} +(4.73205 - 1.26795i) q^{24} +24.1962i q^{25} +(4.75833 - 17.7583i) q^{26} -5.19615 q^{27} +(6.53590 + 24.3923i) q^{28} +(-19.3301 + 33.4808i) q^{29} +(-1.90192 + 1.09808i) q^{30} +(25.4641 - 25.4641i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-8.19615 + 30.5885i) q^{33} +(-17.5359 - 17.5359i) q^{34} +(-5.66025 - 9.80385i) q^{35} +(5.19615 + 3.00000i) q^{36} +(2.96410 - 0.794229i) q^{37} -23.7128i q^{38} +(19.5000 - 11.2583i) q^{39} +2.53590 q^{40} +(7.91858 + 29.5526i) q^{41} +(-15.4641 + 26.7846i) q^{42} +(-15.3731 + 8.87564i) q^{43} +(25.8564 - 25.8564i) q^{44} +(-2.59808 - 0.696152i) q^{45} +(7.85641 - 29.3205i) q^{46} +(-30.0000 - 30.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-95.6314 - 55.2128i) q^{49} +(33.0526 - 8.85641i) q^{50} -30.3731i q^{51} -26.0000 q^{52} -23.1051 q^{53} +(1.90192 + 7.09808i) q^{54} +(-8.19615 + 14.1962i) q^{55} +(30.9282 - 17.8564i) q^{56} +(20.5359 - 20.5359i) q^{57} +(52.8109 + 14.1506i) q^{58} +(5.50258 - 20.5359i) q^{59} +(2.19615 + 2.19615i) q^{60} +(21.1077 + 36.5596i) q^{61} +(-44.1051 - 25.4641i) q^{62} +(-36.5885 + 9.80385i) q^{63} +8.00000i q^{64} +(11.2583 - 3.01666i) q^{65} +44.7846 q^{66} +(-8.48334 - 31.6603i) q^{67} +(-17.5359 + 30.3731i) q^{68} +(32.1962 - 18.5885i) q^{69} +(-11.3205 + 11.3205i) q^{70} +(33.1244 + 8.87564i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-15.9212 - 15.9212i) q^{73} +(-2.16987 - 3.75833i) q^{74} +(36.2942 + 20.9545i) q^{75} +(-32.3923 + 8.67949i) q^{76} +230.851i q^{77} +(-22.5167 - 22.5167i) q^{78} -89.5692 q^{79} +(-0.928203 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(37.4711 - 21.6340i) q^{82} +(97.4256 - 97.4256i) q^{83} +(42.2487 + 11.3205i) q^{84} +(4.06922 - 15.1865i) q^{85} +(17.7513 + 17.7513i) q^{86} +(33.4808 + 57.9904i) q^{87} +(-44.7846 - 25.8564i) q^{88} +(1.22243 - 0.327550i) q^{89} +3.80385i q^{90} +(116.067 - 116.067i) q^{91} -42.9282 q^{92} +(-16.1436 - 60.2487i) q^{93} +(-30.0000 + 51.9615i) q^{94} +(13.0192 - 7.51666i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-49.3660 - 13.2276i) q^{97} +(-40.4186 + 150.844i) q^{98} +(38.7846 + 38.7846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9} + 6 q^{10} - 36 q^{11} - 16 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} - 12 q^{18} + 44 q^{19} + 12 q^{20} - 48 q^{21} + 24 q^{22} + 12 q^{23} + 12 q^{24} - 26 q^{26} + 40 q^{28} - 60 q^{29} - 18 q^{30} + 88 q^{31} - 8 q^{32} - 12 q^{33} - 84 q^{34} + 12 q^{35} - 2 q^{37} + 78 q^{39} + 24 q^{40} - 48 q^{41} - 48 q^{42} + 84 q^{43} + 48 q^{44} - 24 q^{46} - 120 q^{47} - 192 q^{49} + 56 q^{50} - 104 q^{52} + 60 q^{53} + 18 q^{54} - 12 q^{55} + 96 q^{56} + 96 q^{57} + 90 q^{58} + 216 q^{59} - 12 q^{60} + 126 q^{61} - 24 q^{62} - 84 q^{63} + 96 q^{66} - 124 q^{67} - 84 q^{68} + 108 q^{69} + 24 q^{70} + 84 q^{71} - 12 q^{72} - 178 q^{73} - 26 q^{74} + 114 q^{75} - 88 q^{76} - 192 q^{79} + 24 q^{80} - 18 q^{81} - 6 q^{82} + 168 q^{83} + 72 q^{84} - 150 q^{85} + 168 q^{86} + 30 q^{87} - 96 q^{88} - 54 q^{89} + 104 q^{91} - 144 q^{92} - 120 q^{93} - 120 q^{94} + 156 q^{95} - 194 q^{97} - 82 q^{98} + 72 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 + 6 * q^10 - 36 * q^11 - 16 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 - 12 * q^18 + 44 * q^19 + 12 * q^20 - 48 * q^21 + 24 * q^22 + 12 * q^23 + 12 * q^24 - 26 * q^26 + 40 * q^28 - 60 * q^29 - 18 * q^30 + 88 * q^31 - 8 * q^32 - 12 * q^33 - 84 * q^34 + 12 * q^35 - 2 * q^37 + 78 * q^39 + 24 * q^40 - 48 * q^41 - 48 * q^42 + 84 * q^43 + 48 * q^44 - 24 * q^46 - 120 * q^47 - 192 * q^49 + 56 * q^50 - 104 * q^52 + 60 * q^53 + 18 * q^54 - 12 * q^55 + 96 * q^56 + 96 * q^57 + 90 * q^58 + 216 * q^59 - 12 * q^60 + 126 * q^61 - 24 * q^62 - 84 * q^63 + 96 * q^66 - 124 * q^67 - 84 * q^68 + 108 * q^69 + 24 * q^70 + 84 * q^71 - 12 * q^72 - 178 * q^73 - 26 * q^74 + 114 * q^75 - 88 * q^76 - 192 * q^79 + 24 * q^80 - 18 * q^81 - 6 * q^82 + 168 * q^83 + 72 * q^84 - 150 * q^85 + 168 * q^86 + 30 * q^87 - 96 * q^88 - 54 * q^89 + 104 * q^91 - 144 * q^92 - 120 * q^93 - 120 * q^94 + 156 * q^95 - 194 * q^97 - 82 * q^98 + 72 * 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
$5$	0.633975	−	0.633975i	0.126795	−	0.126795i	−0.640862	−	0.767656i	$-0.721423\pi$
$5$	0.633975	−	0.633975i	0.126795	−	0.126795i	0.767656	+	0.640862i	$0.221423\pi$
$6$	−2.36603	−	0.633975i	−0.394338	−	0.105662i
$7$	3.26795	−	12.1962i	0.466850	−	1.74231i	−0.183833	−	0.982958i	$-0.558850\pi$
$7$	3.26795	−	12.1962i	0.466850	−	1.74231i	0.650682	−	0.759350i	$-0.274483\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	−1.09808	−	0.633975i	−0.109808	−	0.0633975i
$11$	−17.6603	+	4.73205i	−1.60548	+	0.430186i	−0.946691	−	0.322143i	$-0.895597\pi$
$11$	−17.6603	+	4.73205i	−1.60548	+	0.430186i	−0.658787	+	0.752330i	$0.728930\pi$
$12$			3.46410i			0.288675i
$13$	11.2583	+	6.50000i	0.866025	+	0.500000i
$13$	11.2583	+	6.50000i	0.866025	+	0.500000i
$14$	−17.8564			−1.27546
$15$	−0.401924	−	1.50000i	−0.0267949	−	0.100000i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	15.1865	−	8.76795i	0.893325	−	0.515762i	0.0182967	−	0.999833i	$-0.494176\pi$
$17$	15.1865	−	8.76795i	0.893325	−	0.515762i	0.875029	+	0.484071i	$0.160842\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	16.1962	+	4.33975i	0.852429	+	0.228408i	0.658475	−	0.752603i	$-0.271202\pi$
$19$	16.1962	+	4.33975i	0.852429	+	0.228408i	0.193954	+	0.981011i	$0.437869\pi$
$20$	−0.464102	+	1.73205i	−0.0232051	+	0.0866025i
$21$	−15.4641	−	15.4641i	−0.736386	−	0.736386i
$22$	12.9282	+	22.3923i	0.587646	+	1.01783i
$23$	18.5885	+	10.7321i	0.808194	+	0.466611i	0.846328	−	0.532662i	$-0.178808\pi$
$23$	18.5885	+	10.7321i	0.808194	+	0.466611i	−0.0381345	+	0.999273i	$0.512142\pi$
$24$	4.73205	−	1.26795i	0.197169	−	0.0528312i
$25$			24.1962i			0.967846i
$26$	4.75833	−	17.7583i	0.183013	−	0.683013i
$27$	−5.19615			−0.192450
$28$	6.53590	+	24.3923i	0.233425	+	0.871154i
$29$	−19.3301	+	33.4808i	−0.666556	+	1.15451i	0.312305	+	0.949982i	$0.398899\pi$
$29$	−19.3301	+	33.4808i	−0.666556	+	1.15451i	−0.978861	+	0.204527i	$0.934434\pi$
$30$	−1.90192	+	1.09808i	−0.0633975	+	0.0366025i
$31$	25.4641	−	25.4641i	0.821423	−	0.821423i	−0.164889	−	0.986312i	$-0.552727\pi$
$31$	25.4641	−	25.4641i	0.821423	−	0.821423i	0.986312	+	0.164889i	$0.0527267\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	−8.19615	+	30.5885i	−0.248368	+	0.926923i
$34$	−17.5359	−	17.5359i	−0.515762	−	0.515762i
$35$	−5.66025	−	9.80385i	−0.161722	−	0.280110i
$36$	5.19615	+	3.00000i	0.144338	+	0.0833333i
$37$	2.96410	−	0.794229i	0.0801109	−	0.0214656i	−0.218541	−	0.975828i	$-0.570130\pi$
$37$	2.96410	−	0.794229i	0.0801109	−	0.0214656i	0.298652	+	0.954362i	$0.403463\pi$
$38$		−	23.7128i		−	0.624021i
$39$	19.5000	−	11.2583i	0.500000	−	0.288675i
$40$	2.53590			0.0633975
$41$	7.91858	+	29.5526i	0.193136	+	0.720794i	0.992741	+	0.120268i	$0.0383754\pi$
$41$	7.91858	+	29.5526i	0.193136	+	0.720794i	−0.799605	+	0.600526i	$0.794958\pi$
$42$	−15.4641	+	26.7846i	−0.368193	+	0.637729i
$43$	−15.3731	+	8.87564i	−0.357513	+	0.206410i	−0.667989	−	0.744171i	$-0.732845\pi$
$43$	−15.3731	+	8.87564i	−0.357513	+	0.206410i	0.310476	+	0.950581i	$0.399512\pi$
$44$	25.8564	−	25.8564i	0.587646	−	0.587646i
$45$	−2.59808	−	0.696152i	−0.0577350	−	0.0154701i
$46$	7.85641	−	29.3205i	0.170791	−	0.637402i
$47$	−30.0000	−	30.0000i	−0.638298	−	0.638298i	0.311838	−	0.950135i	$-0.399056\pi$
$47$	−30.0000	−	30.0000i	−0.638298	−	0.638298i	−0.950135	+	0.311838i	$0.899056\pi$
$48$	−3.46410	−	6.00000i	−0.0721688	−	0.125000i
$49$	−95.6314	−	55.2128i	−1.95166	−	1.12679i
$50$	33.0526	−	8.85641i	0.661051	−	0.177128i
$51$		−	30.3731i		−	0.595550i
$52$	−26.0000			−0.500000
$53$	−23.1051			−0.435946			−0.217973	−	0.975955i	$-0.569944\pi$
$53$	−23.1051			−0.435946			−0.217973	+	0.975955i	$0.569944\pi$
$54$	1.90192	+	7.09808i	0.0352208	+	0.131446i
$55$	−8.19615	+	14.1962i	−0.149021	+	0.258112i
$56$	30.9282	−	17.8564i	0.552289	−	0.318864i
$57$	20.5359	−	20.5359i	0.360279	−	0.360279i
$58$	52.8109	+	14.1506i	0.910533	+	0.243976i
$59$	5.50258	−	20.5359i	0.0932640	−	0.348066i	−0.903487	−	0.428617i	$-0.859001\pi$
$59$	5.50258	−	20.5359i	0.0932640	−	0.348066i	0.996751	+	0.0805505i	$0.0256678\pi$
$60$	2.19615	+	2.19615i	0.0366025	+	0.0366025i
$61$	21.1077	+	36.5596i	0.346028	+	0.599338i	0.985540	−	0.169443i	$-0.0541970\pi$
$61$	21.1077	+	36.5596i	0.346028	+	0.599338i	−0.639512	+	0.768781i	$0.720864\pi$
$62$	−44.1051	−	25.4641i	−0.711373	−	0.410711i
$63$	−36.5885	+	9.80385i	−0.580769	+	0.155617i
$64$			8.00000i			0.125000i
$65$	11.2583	−	3.01666i	0.173205	−	0.0464102i
$66$	44.7846			0.678555
$67$	−8.48334	−	31.6603i	−0.126617	−	0.472541i	0.873275	−	0.487227i	$-0.161992\pi$
$67$	−8.48334	−	31.6603i	−0.126617	−	0.472541i	−0.999892	+	0.0146863i	$0.995325\pi$
$68$	−17.5359	+	30.3731i	−0.257881	+	0.446663i
$69$	32.1962	−	18.5885i	0.466611	−	0.269398i
$70$	−11.3205	+	11.3205i	−0.161722	+	0.161722i
$71$	33.1244	+	8.87564i	0.466540	+	0.125009i	0.484428	−	0.874831i	$-0.339028\pi$
$71$	33.1244	+	8.87564i	0.466540	+	0.125009i	−0.0178882	+	0.999840i	$0.505694\pi$
$72$	2.19615	−	8.19615i	0.0305021	−	0.113835i
$73$	−15.9212	−	15.9212i	−0.218098	−	0.218098i	0.589598	−	0.807697i	$-0.299286\pi$
$73$	−15.9212	−	15.9212i	−0.218098	−	0.218098i	−0.807697	+	0.589598i	$0.799286\pi$
$74$	−2.16987	−	3.75833i	−0.0293226	−	0.0507882i
$75$	36.2942	+	20.9545i	0.483923	+	0.279393i
$76$	−32.3923	+	8.67949i	−0.426215	+	0.114204i
$77$			230.851i			2.99807i
$78$	−22.5167	−	22.5167i	−0.288675	−	0.288675i
$79$	−89.5692			−1.13379			−0.566894	−	0.823791i	$-0.691855\pi$
$79$	−89.5692			−1.13379			−0.566894	+	0.823791i	$0.691855\pi$
$80$	−0.928203	−	3.46410i	−0.0116025	−	0.0433013i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	37.4711	−	21.6340i	0.456965	−	0.263829i
$83$	97.4256	−	97.4256i	1.17380	−	1.17380i	0.192507	−	0.981296i	$-0.438338\pi$
$83$	97.4256	−	97.4256i	1.17380	−	1.17380i	0.981296	−	0.192507i	$-0.0616619\pi$
$84$	42.2487	+	11.3205i	0.502961	+	0.134768i
$85$	4.06922	−	15.1865i	0.0478732	−	0.178665i
$86$	17.7513	+	17.7513i	0.206410	+	0.206410i
$87$	33.4808	+	57.9904i	0.384836	+	0.666556i
$88$	−44.7846	−	25.8564i	−0.508916	−	0.293823i
$89$	1.22243	−	0.327550i	0.0137352	−	0.00368033i	−0.251945	−	0.967742i	$-0.581070\pi$
$89$	1.22243	−	0.327550i	0.0137352	−	0.00368033i	0.265680	+	0.964061i	$0.414404\pi$
$90$			3.80385i			0.0422650i
$91$	116.067	−	116.067i	1.27546	−	1.27546i
$92$	−42.9282			−0.466611
$93$	−16.1436	−	60.2487i	−0.173587	−	0.647836i
$94$	−30.0000	+	51.9615i	−0.319149	+	0.552782i
$95$	13.0192	−	7.51666i	0.137045	−	0.0791227i
$96$	−6.92820	+	6.92820i	−0.0721688	+	0.0721688i
$97$	−49.3660	−	13.2276i	−0.508928	−	0.136367i	−0.00478762	−	0.999989i	$-0.501524\pi$
$97$	−49.3660	−	13.2276i	−0.508928	−	0.136367i	−0.504140	+	0.863622i	$0.668191\pi$
$98$	−40.4186	+	150.844i	−0.412435	+	1.53923i
$99$	38.7846	+	38.7846i	0.391764	+	0.391764i
$100$	−24.1962	−	41.9090i	−0.241962	−	0.419090i
$101$	30.0500	+	17.3494i	0.297525	+	0.171776i	0.641330	−	0.767265i	$-0.278383\pi$
$101$	30.0500	+	17.3494i	0.297525	+	0.171776i	−0.343806	+	0.939041i	$0.611716\pi$
$102$	−41.4904	+	11.1173i	−0.406768	+	0.108993i
$103$			196.890i			1.91155i	0.294098	+	0.955775i	$0.404981\pi$
$103$			196.890i			1.91155i	−0.294098	+	0.955775i	$0.595019\pi$
$104$	9.51666	+	35.5167i	0.0915064	+	0.341506i
$105$	−19.6077			−0.186740
$106$	8.45706	+	31.5622i	0.0797836	+	0.297756i
$107$	−18.0910	+	31.3346i	−0.169075	+	0.292847i	−0.938095	−	0.346378i	$-0.887411\pi$
$107$	−18.0910	+	31.3346i	−0.169075	+	0.292847i	0.769020	+	0.639225i	$0.220745\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−127.497	+	127.497i	−1.16970	+	1.16970i	−0.187422	+	0.982280i	$0.560013\pi$
$109$	−127.497	+	127.497i	−1.16970	+	1.16970i	−0.982280	+	0.187422i	$0.939987\pi$
$110$	22.3923	+	6.00000i	0.203566	+	0.0545455i
$111$	1.37564	−	5.13397i	0.0123932	−	0.0462520i
$112$	−35.7128	−	35.7128i	−0.318864	−	0.318864i
$113$	−39.5596	−	68.5192i	−0.350085	−	0.606365i	0.636179	−	0.771541i	$-0.280514\pi$
$113$	−39.5596	−	68.5192i	−0.350085	−	0.606365i	−0.986264	+	0.165177i	$0.947181\pi$
$114$	−35.5692	−	20.5359i	−0.312011	−	0.180139i
$115$	18.5885	−	4.98076i	0.161639	−	0.0433110i
$116$		−	77.3205i		−	0.666556i
$117$		−	39.0000i		−	0.333333i
$118$	−30.0666			−0.254802
$119$	−57.3064	−	213.870i	−0.481567	−	1.79723i
$120$	2.19615	−	3.80385i	0.0183013	−	0.0316987i
$121$	184.703	−	106.638i	1.52647	−	0.881309i
$122$	42.2154	−	42.2154i	0.346028	−	0.346028i
$123$	51.1865	+	13.7154i	0.416151	+	0.111507i
$124$	−18.6410	+	69.5692i	−0.150331	+	0.561042i
$125$	31.1891	+	31.1891i	0.249513	+	0.249513i
$126$	26.7846	+	46.3923i	0.212576	+	0.368193i
$127$	71.3205	+	41.1769i	0.561579	+	0.324228i	0.753779	−	0.657128i	$-0.228229\pi$
$127$	71.3205	+	41.1769i	0.561579	+	0.324228i	−0.192200	+	0.981356i	$0.561562\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$			30.7461i			0.238342i
$130$	−8.24167	−	14.2750i	−0.0633975	−	0.109808i
$131$	5.93336			0.0452928			0.0226464	−	0.999744i	$-0.492791\pi$
$131$	5.93336			0.0452928			0.0226464	+	0.999744i	$0.492791\pi$
$132$	−16.3923	−	61.1769i	−0.124184	−	0.463461i
$133$	105.856	−	183.349i	0.795913	−	1.37856i
$134$	−40.1436	+	23.1769i	−0.299579	+	0.172962i
$135$	−3.29423	+	3.29423i	−0.0244017	+	0.0244017i
$136$	47.9090	+	12.8372i	0.352272	+	0.0943909i
$137$	44.5859	−	166.397i	0.325444	−	1.21457i	−0.588420	−	0.808555i	$-0.700250\pi$
$137$	44.5859	−	166.397i	0.325444	−	1.21457i	0.913864	−	0.406020i	$-0.133084\pi$
$138$	−37.1769	−	37.1769i	−0.269398	−	0.269398i
$139$	−6.35383	−	11.0052i	−0.0457110	−	0.0791738i	0.842265	−	0.539064i	$-0.181222\pi$
$139$	−6.35383	−	11.0052i	−0.0457110	−	0.0791738i	−0.887976	+	0.459890i	$0.847889\pi$
$140$	19.6077	+	11.3205i	0.140055	+	0.0808608i
$141$	−70.9808	+	19.0192i	−0.503410	+	0.134888i
$142$		−	48.4974i		−	0.341531i
$143$	−229.583	−	61.5167i	−1.60548	−	0.430186i
$144$	−12.0000			−0.0833333
$145$	8.97114	+	33.4808i	0.0618700	+	0.230902i
$146$	−15.9212	+	27.5763i	−0.109049	+	0.188878i
$147$	−165.638	+	95.6314i	−1.12679	+	0.650554i
$148$	−4.33975	+	4.33975i	−0.0293226	+	0.0293226i
$149$	111.945	+	29.9955i	0.751308	+	0.201312i	0.614098	−	0.789230i	$-0.289520\pi$
$149$	111.945	+	29.9955i	0.751308	+	0.201312i	0.137210	+	0.990542i	$0.456187\pi$
$150$	15.3397	−	57.2487i	0.102265	−	0.381658i
$151$	−118.603	−	118.603i	−0.785447	−	0.785447i	0.195297	−	0.980744i	$-0.437433\pi$
$151$	−118.603	−	118.603i	−0.785447	−	0.785447i	−0.980744	+	0.195297i	$0.937433\pi$
$152$	23.7128	+	41.0718i	0.156005	+	0.270209i
$153$	−45.5596	−	26.3038i	−0.297775	−	0.171921i
$154$	315.349	−	84.4974i	2.04772	−	0.548685i
$155$		−	32.2872i		−	0.208304i
$156$	−22.5167	+	39.0000i	−0.144338	+	0.250000i
$157$	−16.2961			−0.103797			−0.0518985	−	0.998652i	$-0.516527\pi$
$157$	−16.2961			−0.103797			−0.0518985	+	0.998652i	$0.516527\pi$
$158$	32.7846	+	122.354i	0.207498	+	0.774391i
$159$	−20.0096	+	34.6577i	−0.125847	+	0.217973i
$160$	−4.39230	+	2.53590i	−0.0274519	+	0.0158494i
$161$	191.636	−	191.636i	1.19028	−	1.19028i
$162$	12.2942	+	3.29423i	0.0758903	+	0.0203347i
$163$	−74.8616	+	279.387i	−0.459273	+	1.71403i	0.215938	+	0.976407i	$0.430719\pi$
$163$	−74.8616	+	279.387i	−0.459273	+	1.71403i	−0.675211	+	0.737624i	$0.735948\pi$
$164$	−43.2679	−	43.2679i	−0.263829	−	0.263829i
$165$	14.1962	+	24.5885i	0.0860373	+	0.149021i
$166$	−168.746	−	97.4256i	−1.01654	−	0.586901i
$167$	−262.277	+	70.2769i	−1.57052	+	0.420820i	−0.935975	−	0.352066i	$-0.885479\pi$
$167$	−262.277	+	70.2769i	−1.57052	+	0.420820i	−0.634545	+	0.772886i	$0.718813\pi$
$168$		−	61.8564i		−	0.368193i
$169$	84.5000	+	146.358i	0.500000	+	0.866025i
$170$	−22.2346			−0.130792
$171$	−13.0192	−	48.5885i	−0.0761359	−	0.284143i
$172$	17.7513	−	30.7461i	0.103205	−	0.178757i
$173$	−93.1000	+	53.7513i	−0.538150	+	0.310701i	−0.744329	−	0.667813i	$-0.767230\pi$
$173$	−93.1000	+	53.7513i	−0.538150	+	0.310701i	0.206179	+	0.978514i	$0.433897\pi$
$174$	66.9615	−	66.9615i	0.384836	−	0.384836i
$175$	295.100	+	79.0718i	1.68629	+	0.451839i
$176$	−18.9282	+	70.6410i	−0.107547	+	0.401369i
$177$	−26.0385	−	26.0385i	−0.147110	−	0.147110i
$178$	−0.894882	−	1.54998i	−0.00502743	−	0.00870776i
$179$	−105.804	−	61.0859i	−0.591083	−	0.341262i	0.174443	−	0.984667i	$-0.444188\pi$
$179$	−105.804	−	61.0859i	−0.591083	−	0.341262i	−0.765526	+	0.643405i	$0.777521\pi$
$180$	5.19615	−	1.39230i	0.0288675	−	0.00773503i
$181$			65.2872i			0.360703i	0.983602	+	0.180351i	$0.0577235\pi$
$181$			65.2872i			0.360703i	−0.983602	+	0.180351i	$0.942277\pi$
$182$	−201.033	−	116.067i	−1.10458	−	0.637729i
$183$	73.1192			0.399558
$184$	15.7128	+	58.6410i	0.0853957	+	0.318701i
$185$	1.37564	−	2.38269i	0.00743592	−	0.0128794i
$186$	−76.3923	+	44.1051i	−0.410711	+	0.237124i
$187$	−226.708	+	226.708i	−1.21234	+	1.21234i
$188$	81.9615	+	21.9615i	0.435966	+	0.116817i
$189$	−16.9808	+	63.3731i	−0.0898453	+	0.335307i
$190$	−15.0333	−	15.0333i	−0.0791227	−	0.0791227i
$191$	15.2820	+	26.4693i	0.0800106	+	0.138582i	0.903254	−	0.429106i	$-0.141171\pi$
$191$	15.2820	+	26.4693i	0.0800106	+	0.138582i	−0.823244	+	0.567688i	$0.807838\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−45.8468	+	12.2846i	−0.237548	+	0.0636508i	−0.375629	−	0.926770i	$-0.622573\pi$
$193$	−45.8468	+	12.2846i	−0.237548	+	0.0636508i	0.138081	+	0.990421i	$0.455907\pi$
$194$			72.2769i			0.372561i
$195$	5.22501	−	19.5000i	0.0267949	−	0.100000i
$196$	220.851			1.12679
$197$	58.1314	+	216.949i	0.295083	+	1.10127i	0.941151	+	0.337986i	$0.109746\pi$
$197$	58.1314	+	216.949i	0.295083	+	1.10127i	−0.646068	+	0.763280i	$0.723588\pi$
$198$	38.7846	−	67.1769i	0.195882	−	0.339277i
$199$	139.583	−	80.5885i	0.701424	−	0.404967i	−0.106454	−	0.994318i	$-0.533950\pi$
$199$	139.583	−	80.5885i	0.701424	−	0.404967i	0.807877	+	0.589351i	$0.200616\pi$
$200$	−48.3923	+	48.3923i	−0.241962	+	0.241962i
$201$	−54.8372	−	14.6936i	−0.272822	−	0.0731024i
$202$	12.7006	−	47.3993i	0.0628743	−	0.234650i
$203$	345.167	+	345.167i	1.70033	+	1.70033i
$204$	30.3731	+	52.6077i	0.148888	+	0.257881i
$205$	23.7558	+	13.7154i	0.115882	+	0.0669043i
$206$	268.956	−	72.0666i	1.30561	−	0.349838i
$207$		−	64.3923i		−	0.311074i
$208$	45.0333	−	26.0000i	0.216506	−	0.125000i
$209$	−306.564			−1.46681
$210$	7.17691	+	26.7846i	0.0341758	+	0.127546i
$211$	77.0718	−	133.492i	0.365269	−	0.632665i	−0.623550	−	0.781783i	$-0.714310\pi$
$211$	77.0718	−	133.492i	0.365269	−	0.632665i	0.988819	+	0.149119i	$0.0476436\pi$
$212$	40.0192	−	23.1051i	0.188770	−	0.108986i
$213$	42.0000	−	42.0000i	0.197183	−	0.197183i
$214$	49.4256	+	13.2436i	0.230961	+	0.0618858i
$215$	−4.11920	+	15.3731i	−0.0191591	+	0.0715026i
$216$	−10.3923	−	10.3923i	−0.0481125	−	0.0481125i
$217$	−227.349	−	393.779i	−1.04769	−	1.81465i
$218$	220.832	+	127.497i	1.01299	+	0.584851i
$219$	−37.6699	+	10.0936i	−0.172009	+	0.0460896i
$220$		−	32.7846i		−	0.149021i
$221$	227.967			1.03152
$222$	−7.51666			−0.0338588
$223$	37.7513	+	140.890i	0.169288	+	0.631792i	0.997454	+	0.0713095i	$0.0227178\pi$
$223$	37.7513	+	140.890i	0.169288	+	0.631792i	−0.828166	+	0.560483i	$0.810616\pi$
$224$	−35.7128	+	61.8564i	−0.159432	+	0.276145i
$225$	62.8634	−	36.2942i	0.279393	−	0.161308i
$226$	−79.1192	+	79.1192i	−0.350085	+	0.350085i
$227$	−349.401	−	93.6218i	−1.53921	−	0.412431i	−0.613201	−	0.789927i	$-0.710119\pi$
$227$	−349.401	−	93.6218i	−1.53921	−	0.412431i	−0.926011	+	0.377496i	$0.876785\pi$
$228$	−15.0333	+	56.1051i	−0.0659356	+	0.246075i
$229$	52.5692	+	52.5692i	0.229560	+	0.229560i	0.812509	−	0.582949i	$-0.198101\pi$
$229$	52.5692	+	52.5692i	0.229560	+	0.229560i	−0.582949	+	0.812509i	$0.698101\pi$
$230$	−13.6077	−	23.5692i	−0.0591639	−	0.102475i
$231$	346.277	+	199.923i	1.49903	+	0.865468i
$232$	−105.622	+	28.3013i	−0.455266	+	0.121988i
$233$		−	235.923i		−	1.01255i	−0.862373	−	0.506273i	$-0.831023\pi$
$233$		−	235.923i		−	1.01255i	0.862373	−	0.506273i	$-0.168977\pi$
$234$	−53.2750	+	14.2750i	−0.227671	+	0.0610042i
$235$	−38.0385			−0.161866
$236$	11.0052	+	41.0718i	0.0466320	+	0.174033i
$237$	−77.5692	+	134.354i	−0.327296	+	0.566894i
$238$	−271.177	+	156.564i	−1.13940	+	0.657832i
$239$	−155.569	+	155.569i	−0.650917	+	0.650917i	−0.953214	−	0.302297i	$-0.902247\pi$
$239$	−155.569	+	155.569i	−0.650917	+	0.650917i	0.302297	+	0.953214i	$0.402247\pi$
$240$	−6.00000	−	1.60770i	−0.0250000	−	0.00669873i
$241$	98.8820	−	369.033i	0.410299	−	1.53126i	−0.383771	−	0.923428i	$-0.625375\pi$
$241$	98.8820	−	369.033i	0.410299	−	1.53126i	0.794069	−	0.607827i	$-0.207959\pi$
$242$	−213.277	−	213.277i	−0.881309	−	0.881309i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$	−73.1192	−	42.2154i	−0.299669	−	0.173014i
$245$	−95.6314	+	25.6244i	−0.390332	+	0.104589i
$246$		−	74.9423i		−	0.304643i
$247$	154.133	+	154.133i	0.624021	+	0.624021i
$248$	101.856			0.410711
$249$	−61.7654	−	230.512i	−0.248054	−	0.925749i
$250$	31.1891	−	54.0211i	0.124756	−	0.216084i
$251$	−63.6462	+	36.7461i	−0.253570	+	0.146399i	−0.621398	−	0.783495i	$-0.713435\pi$
$251$	−63.6462	+	36.7461i	−0.253570	+	0.146399i	0.367828	+	0.929894i	$0.380102\pi$
$252$	53.5692	−	53.5692i	0.212576	−	0.212576i
$253$	−379.061	−	101.569i	−1.49827	−	0.401459i
$254$	30.1436	−	112.497i	0.118676	−	0.442903i
$255$	−19.2558	−	19.2558i	−0.0755128	−	0.0755128i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	400.658	+	231.320i	1.55898	+	0.900077i	0.997355	+	0.0726847i	$0.0231567\pi$
$257$	400.658	+	231.320i	1.55898	+	0.900077i	0.561624	+	0.827392i	$0.310177\pi$
$258$	42.0000	−	11.2539i	0.162791	−	0.0436196i
$259$		−	38.7461i		−	0.149599i
$260$	−16.4833	+	16.4833i	−0.0633975	+	0.0633975i
$261$	115.981			0.444371
$262$	−2.17176	−	8.10512i	−0.00828916	−	0.0309356i
$263$	250.617	−	434.081i	0.952915	−	1.65050i	0.213846	−	0.976867i	$-0.431401\pi$
$263$	250.617	−	434.081i	0.952915	−	1.65050i	0.739069	−	0.673630i	$-0.235266\pi$
$264$	−77.5692	+	44.7846i	−0.293823	+	0.169639i
$265$	−14.6481	+	14.6481i	−0.0552757	+	0.0552757i
$266$	−289.205	−	77.4923i	−1.08724	−	0.291324i
$267$	0.567333	−	2.11731i	0.00212484	−	0.00793002i
$268$	46.3538	+	46.3538i	0.172962	+	0.172962i
$269$	19.2436	+	33.3308i	0.0715374	+	0.123906i	0.899575	−	0.436766i	$-0.143876\pi$
$269$	19.2436	+	33.3308i	0.0715374	+	0.123906i	−0.828038	+	0.560672i	$0.810543\pi$
$270$	5.70577	+	3.29423i	0.0211325	+	0.0122008i
$271$	−192.028	+	51.4538i	−0.708591	+	0.189866i	−0.595075	−	0.803670i	$-0.702878\pi$
$271$	−192.028	+	51.4538i	−0.708591	+	0.189866i	−0.113516	+	0.993536i	$0.536211\pi$
$272$		−	70.1436i		−	0.257881i
$273$	−73.5833	−	274.617i	−0.269536	−	1.00592i
$274$	−243.622			−0.889131
$275$	−114.497	−	427.310i	−0.416354	−	1.55386i
$276$	−37.1769	+	64.3923i	−0.134699	+	0.233305i
$277$	−46.7154	+	26.9711i	−0.168648	+	0.0973687i	−0.581948	−	0.813226i	$-0.697709\pi$
$277$	−46.7154	+	26.9711i	−0.168648	+	0.0973687i	0.413300	+	0.910595i	$0.364376\pi$
$278$	−12.7077	+	12.7077i	−0.0457110	+	0.0457110i
$279$	−104.354	−	27.9615i	−0.374028	−	0.100221i
$280$	8.28719	−	30.9282i	0.0295971	−	0.110458i
$281$	172.165	+	172.165i	0.612686	+	0.612686i	0.943645	−	0.330959i	$-0.107372\pi$
$281$	172.165	+	172.165i	0.612686	+	0.612686i	−0.330959	+	0.943645i	$0.607372\pi$
$282$	51.9615	+	90.0000i	0.184261	+	0.319149i
$283$	−433.086	−	250.042i	−1.53034	−	0.883542i	−0.999346	−	0.0361653i	$-0.988486\pi$
$283$	−433.086	−	250.042i	−1.53034	−	0.883542i	−0.530993	−	0.847376i	$-0.678181\pi$
$284$	−66.2487	+	17.7513i	−0.233270	+	0.0625045i
$285$		−	26.0385i		−	0.0913631i
$286$			336.133i			1.17529i
$287$	386.305			1.34601
$288$	4.39230	+	16.3923i	0.0152511	+	0.0569177i
$289$	9.25387	−	16.0282i	0.0320203	−	0.0554608i
$290$	42.4519	−	24.5096i	0.146386	−	0.0845159i
$291$	−62.5936	+	62.5936i	−0.215098	+	0.215098i
$292$	43.4974	+	11.6551i	0.148964	+	0.0399147i
$293$	35.0673	−	130.873i	0.119684	−	0.446666i	−0.879911	−	0.475139i	$-0.842398\pi$
$293$	35.0673	−	130.873i	0.119684	−	0.446666i	0.999595	+	0.0284731i	$0.00906449\pi$
$294$	191.263	+	191.263i	0.650554	+	0.650554i
$295$	−9.53074	−	16.5077i	−0.0323076	−	0.0559584i
$296$	7.51666	+	4.33975i	0.0253941	+	0.0146613i
$297$	91.7654	−	24.5885i	0.308974	−	0.0827894i
$298$		−	163.899i		−	0.549995i
$299$	139.517	+	241.650i	0.466611	+	0.808194i
$300$	−83.8179			−0.279393
$301$	58.0103	+	216.497i	0.192725	+	0.719261i
$302$	−118.603	+	205.426i	−0.392724	+	0.680217i
$303$	52.0481	−	30.0500i	0.171776	−	0.0991749i
$304$	47.4256	−	47.4256i	0.156005	−	0.156005i
$305$	36.5596	+	9.79612i	0.119868	+	0.0321184i
$306$	−19.2558	+	71.8634i	−0.0629273	+	0.234848i
$307$	83.6743	+	83.6743i	0.272555	+	0.272555i	0.830128	−	0.557573i	$-0.188267\pi$
$307$	83.6743	+	83.6743i	0.272555	+	0.272555i	−0.557573	+	0.830128i	$0.688267\pi$
$308$	−230.851	−	399.846i	−0.749517	−	1.29820i
$309$	295.335	+	170.512i	0.955775	+	0.551817i
$310$	−44.1051	+	11.8179i	−0.142275	+	0.0381224i
$311$			178.823i			0.574994i	0.957782	+	0.287497i	$0.0928231\pi$
$311$			178.823i			0.574994i	−0.957782	+	0.287497i	$0.907177\pi$
$312$	61.5167	+	16.4833i	0.197169	+	0.0528312i
$313$	230.123			0.735217			0.367609	−	0.929981i	$-0.380177\pi$
$313$	230.123			0.735217			0.367609	+	0.929981i	$0.380177\pi$
$314$	5.96479	+	22.2609i	0.0189962	+	0.0708946i
$315$	−16.9808	+	29.4115i	−0.0539072	+	0.0933700i
$316$	155.138	−	89.5692i	0.490944	−	0.283447i
$317$	211.886	−	211.886i	0.668412	−	0.668412i	−0.288937	−	0.957348i	$-0.593302\pi$
$317$	211.886	−	211.886i	0.668412	−	0.668412i	0.957348	+	0.288937i	$0.0933017\pi$
$318$	54.6673	+	14.6481i	0.171910	+	0.0460631i
$319$	182.942	−	682.750i	0.573487	−	2.14028i
$320$	5.07180	+	5.07180i	0.0158494	+	0.0158494i
$321$	31.3346	+	54.2731i	0.0976155	+	0.169075i
$322$	−331.923	−	191.636i	−1.03082	−	0.595142i
$323$	284.014	−	76.1013i	0.879301	−	0.235608i
$324$		−	18.0000i		−	0.0555556i
$325$	−157.275	+	272.408i	−0.483923	+	0.838179i
$326$	409.051			1.25476
$327$	80.8301	+	301.662i	0.247187	+	0.922514i
$328$	−43.2679	+	74.9423i	−0.131914	+	0.228483i
$329$	−463.923	+	267.846i	−1.41010	+	0.814122i
$330$	28.3923	−	28.3923i	0.0860373	−	0.0860373i
$331$	−95.6743	−	25.6359i	−0.289046	−	0.0774497i	0.111382	−	0.993778i	$-0.464472\pi$
$331$	−95.6743	−	25.6359i	−0.289046	−	0.0774497i	−0.400429	+	0.916328i	$0.631139\pi$
$332$	−71.3205	+	266.172i	−0.214821	+	0.801722i
$333$	−6.50962	−	6.50962i	−0.0195484	−	0.0195484i
$334$	192.000	+	332.554i	0.574850	+	0.995670i
$335$	−25.4500	−	14.6936i	−0.0759702	−	0.0438614i
$336$	−84.4974	+	22.6410i	−0.251480	+	0.0673840i
$337$		−	53.0770i		−	0.157498i	−0.996894	−	0.0787492i	$-0.974907\pi$
$337$		−	53.0770i		−	0.157498i	0.996894	−	0.0787492i	$-0.0250926\pi$
$338$	169.000	−	169.000i	0.500000	−	0.500000i
$339$	−137.038			−0.404243
$340$	8.13844	+	30.3731i	0.0239366	+	0.0893325i
$341$	−329.205	+	570.200i	−0.965411	+	1.67214i
$342$	−61.6077	+	35.5692i	−0.180139	+	0.104004i
$343$	−548.420	+	548.420i	−1.59889	+	1.59889i
$344$	−48.4974	−	12.9948i	−0.140981	−	0.0377757i
$345$	8.62693	−	32.1962i	0.0250056	−	0.0933222i
$346$	107.503	+	107.503i	0.310701	+	0.310701i
$347$	337.583	+	584.711i	0.972863	+	1.68505i	0.686816	+	0.726832i	$0.259008\pi$
$347$	337.583	+	584.711i	0.972863	+	1.68505i	0.286047	+	0.958216i	$0.407659\pi$
$348$	−115.981	−	66.9615i	−0.333278	−	0.192418i
$349$	572.154	−	153.308i	1.63941	−	0.439279i	0.682790	−	0.730615i	$-0.260766\pi$
$349$	572.154	−	153.308i	1.63941	−	0.439279i	0.956621	+	0.291336i	$0.0940997\pi$
$350$		−	432.056i		−	1.23445i
$351$	−58.5000	−	33.7750i	−0.166667	−	0.0962250i
$352$	103.426			0.293823
$353$	30.8628	+	115.181i	0.0874299	+	0.326293i	0.995763	−	0.0919541i	$-0.0293113\pi$
$353$	30.8628	+	115.181i	0.0874299	+	0.326293i	−0.908333	+	0.418247i	$0.862645\pi$
$354$	−26.0385	+	45.1000i	−0.0735550	+	0.127401i
$355$	26.6269	−	15.3731i	0.0750054	−	0.0433044i
$356$	−1.78976	+	1.78976i	−0.00502743	+	0.00502743i
$357$	−370.435	−	99.2576i	−1.03763	−	0.278033i
$358$	−44.7180	+	166.890i	−0.124911	+	0.466172i
$359$	−375.415	−	375.415i	−1.04573	−	1.04573i	−0.998903	−	0.0468219i	$-0.985091\pi$
$359$	−375.415	−	375.415i	−1.04573	−	1.04573i	−0.0468219	−	0.998903i	$-0.514909\pi$
$360$	−3.80385	−	6.58846i	−0.0105662	−	0.0183013i
$361$	−69.1532	−	39.9256i	−0.191560	−	0.110597i
$362$	89.1840	−	23.8968i	0.246365	−	0.0660132i
$363$		−	369.406i		−	1.01765i
$364$	−84.9667	+	317.100i	−0.233425	+	0.871154i
$365$	−20.1872			−0.0553075
$366$	−26.7635	−	99.8827i	−0.0731243	−	0.272904i
$367$	105.842	−	183.324i	0.288399	−	0.499521i	−0.685029	−	0.728516i	$-0.740210\pi$
$367$	105.842	−	183.324i	0.288399	−	0.499521i	0.973428	+	0.228995i	$0.0735438\pi$
$368$	74.3538	−	42.9282i	0.202048	−	0.116653i
$369$	64.9019	−	64.9019i	0.175886	−	0.175886i
$370$	−3.75833	−	1.00704i	−0.0101576	−	0.00272173i
$371$	−75.5064	+	281.794i	−0.203521	+	0.759551i
$372$	88.2102	+	88.2102i	0.237124	+	0.237124i
$373$	33.2199	+	57.5385i	0.0890613	+	0.154259i	0.907115	−	0.420884i	$-0.138280\pi$
$373$	33.2199	+	57.5385i	0.0890613	+	0.154259i	−0.818053	+	0.575142i	$0.804947\pi$
$374$	392.669	+	226.708i	1.04992	+	0.606170i
$375$	73.7942	−	19.7731i	0.196785	−	0.0527283i
$376$		−	120.000i		−	0.319149i
$377$	−435.250	+	251.292i	−1.15451	+	0.666556i
$378$	92.7846			0.245462
$379$	40.0488	+	149.464i	0.105670	+	0.394364i	0.998420	−	0.0561867i	$-0.0178942\pi$
$379$	40.0488	+	149.464i	0.105670	+	0.394364i	−0.892751	+	0.450551i	$0.851228\pi$
$380$	−15.0333	+	26.0385i	−0.0395614	+	0.0685223i
$381$	123.531	−	71.3205i	0.324228	−	0.187193i
$382$	30.5641	−	30.5641i	0.0800106	−	0.0800106i
$383$	−378.382	−	101.387i	−0.987943	−	0.264718i	−0.271556	−	0.962423i	$-0.587538\pi$
$383$	−378.382	−	101.387i	−0.987943	−	0.264718i	−0.716386	+	0.697704i	$0.754205\pi$
$384$	5.07180	−	18.9282i	0.0132078	−	0.0492922i
$385$	146.354	+	146.354i	0.380140	+	0.380140i
$386$	33.5622	+	58.1314i	0.0869486	+	0.150599i
$387$	46.1192	+	26.6269i	0.119171	+	0.0688034i
$388$	98.7321	−	26.4552i	0.254464	−	0.0681834i
$389$		−	599.802i		−	1.54191i	−0.636890	−	0.770954i	$-0.719780\pi$
$389$		−	599.802i		−	1.54191i	0.636890	−	0.770954i	$-0.280220\pi$
$390$	−28.5500			−0.0732051
$391$	376.392			0.962640
$392$	−80.8372	−	301.688i	−0.206217	−	0.769613i
$393$	5.13844	−	8.90004i	0.0130749	−	0.0226464i
$394$	275.081	−	158.818i	0.698174	−	0.403091i
$395$	−56.7846	+	56.7846i	−0.143759	+	0.143759i
$396$	−105.962	−	28.3923i	−0.267580	−	0.0716977i
$397$	−138.615	+	517.317i	−0.349156	+	1.30307i	0.538526	+	0.842609i	$0.318981\pi$
$397$	−138.615	+	517.317i	−0.349156	+	1.30307i	−0.887682	+	0.460457i	$0.847685\pi$
$398$	−161.177	−	161.177i	−0.404967	−	0.404967i
$399$	−183.349	−	317.569i	−0.459520	−	0.795913i
$400$	83.8179	+	48.3923i	0.209545	+	0.120981i
$401$	−419.935	+	112.521i	−1.04722	+	0.280601i	−0.741102	−	0.671393i	$-0.765696\pi$
$401$	−419.935	+	112.521i	−1.04722	+	0.280601i	−0.306117	+	0.951994i	$0.599030\pi$
$402$			80.2872i			0.199719i
$403$	452.200	−	121.167i	1.12208	−	0.300662i
$404$	−69.3975			−0.171776
$405$	2.08846	+	7.79423i	0.00515668	+	0.0192450i
$406$	345.167	−	597.846i	0.850164	−	1.47253i
$407$	−48.5885	+	28.0526i	−0.119382	+	0.0689252i
$408$	60.7461	−	60.7461i	0.148888	−	0.148888i
$409$	−665.224	−	178.246i	−1.62646	−	0.435810i	−0.673572	−	0.739121i	$-0.735241\pi$
$409$	−665.224	−	178.246i	−1.62646	−	0.435810i	−0.952891	+	0.303312i	$0.901908\pi$
$410$	10.0404	−	37.4711i	0.0244887	−	0.0913930i
$411$	−210.983	−	210.983i	−0.513340	−	0.513340i
$412$	−196.890	−	341.023i	−0.477888	−	0.827726i
$413$	−232.477	−	134.221i	−0.562898	−	0.324989i
$414$	−87.9615	+	23.5692i	−0.212467	+	0.0569305i
$415$		−	123.531i		−	0.297664i
$416$	−52.0000	−	52.0000i	−0.125000	−	0.125000i
$417$	−22.0103			−0.0527825
$418$	112.210	+	418.774i	0.268446	+	1.00185i
$419$	144.000	−	249.415i	0.343675	−	0.595263i	−0.641437	−	0.767176i	$-0.721661\pi$
$419$	144.000	−	249.415i	0.343675	−	0.595263i	0.985112	+	0.171913i	$0.0549947\pi$
$420$	33.9615	−	19.6077i	0.0808608	−	0.0466850i
$421$	87.8930	−	87.8930i	0.208772	−	0.208772i	−0.594973	−	0.803745i	$-0.702837\pi$
$421$	87.8930	−	87.8930i	0.208772	−	0.208772i	0.803745	+	0.594973i	$0.202837\pi$
$422$	−210.564	−	56.4205i	−0.498967	−	0.133698i
$423$	−32.9423	+	122.942i	−0.0778777	+	0.290644i
$424$	−46.2102	−	46.2102i	−0.108986	−	0.108986i
$425$	212.151	+	367.456i	0.499178	+	0.864602i
$426$	−72.7461	−	42.0000i	−0.170766	−	0.0985915i
$427$	514.865	−	137.958i	1.20577	−	0.323086i
$428$		−	72.3641i		−	0.169075i
$429$	−291.100	+	291.100i	−0.678555	+	0.678555i
$430$	22.5077			0.0523436
$431$	−4.18584	−	15.6218i	−0.00971193	−	0.0362454i	0.960900	−	0.276896i	$-0.0893058\pi$
$431$	−4.18584	−	15.6218i	−0.00971193	−	0.0362454i	−0.970612	+	0.240651i	$0.922639\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	307.782	−	177.698i	0.710813	−	0.410388i	−0.100549	−	0.994932i	$-0.532060\pi$
$433$	307.782	−	177.698i	0.710813	−	0.410388i	0.811362	+	0.584544i	$0.198727\pi$
$434$	−454.697	+	454.697i	−1.04769	+	1.04769i
$435$	57.9904	+	15.5385i	0.133311	+	0.0357206i
$436$	93.3346	−	348.329i	0.214070	−	0.798921i
$437$	254.487	+	254.487i	0.582350	+	0.582350i
$438$	27.5763	+	47.7635i	0.0629595	+	0.109049i
$439$	179.412	+	103.583i	0.408682	+	0.235953i	0.690223	−	0.723596i	$-0.257512\pi$
$439$	179.412	+	103.583i	0.408682	+	0.235953i	−0.281541	+	0.959549i	$0.590846\pi$
$440$	−44.7846	+	12.0000i	−0.101783	+	0.0272727i
$441$			331.277i			0.751195i
$442$	−83.4416	−	311.408i	−0.188782	−	0.704544i
$443$	394.641			0.890838			0.445419	−	0.895322i	$-0.353055\pi$
$443$	394.641			0.890838			0.445419	+	0.895322i	$0.353055\pi$
$444$	2.75129	+	10.2679i	0.00619660	+	0.0231260i
$445$	0.567333	−	0.982649i	0.00127490	−	0.00220820i
$446$	178.641	−	103.138i	0.400540	−	0.231252i
$447$	141.940	−	141.940i	0.317540	−	0.317540i
$448$	97.5692	+	26.1436i	0.217788	+	0.0583562i
$449$	136.878	−	510.834i	0.304850	−	1.13771i	−0.628225	−	0.778032i	$-0.716218\pi$
$449$	136.878	−	510.834i	0.304850	−	1.13771i	0.933075	−	0.359683i	$-0.117115\pi$
$450$	−72.5885	−	72.5885i	−0.161308	−	0.161308i
$451$	−279.688	−	484.435i	−0.620152	−	1.07413i
$452$	137.038	+	79.1192i	0.303182	+	0.175042i
$453$	−280.617	+	75.1910i	−0.619463	+	0.165985i
$454$			511.559i			1.12678i
$455$		−	147.167i		−	0.323443i
$456$	82.1436			0.180139
$457$	22.9571	+	85.6769i	0.0502343	+	0.187477i	0.986484	−	0.163859i	$-0.0523942\pi$
$457$	22.9571	+	85.6769i	0.0502343	+	0.187477i	−0.936250	+	0.351336i	$0.885728\pi$
$458$	52.5692	−	91.0526i	0.114780	−	0.198805i
$459$	−78.9115	+	45.5596i	−0.171921	+	0.0992584i
$460$	−27.2154	+	27.2154i	−0.0591639	+	0.0591639i
$461$	75.7961	+	20.3095i	0.164417	+	0.0440553i	0.340088	−	0.940393i	$-0.389543\pi$
$461$	75.7961	+	20.3095i	0.164417	+	0.0440553i	−0.175672	+	0.984449i	$0.556210\pi$
$462$	146.354	−	546.200i	0.316783	−	1.18225i
$463$	−264.908	−	264.908i	−0.572155	−	0.572155i	0.360575	−	0.932730i	$-0.382580\pi$
$463$	−264.908	−	264.908i	−0.572155	−	0.572155i	−0.932730	+	0.360575i	$0.882580\pi$
$464$	77.3205	+	133.923i	0.166639	+	0.288627i
$465$	−48.4308	−	27.9615i	−0.104152	−	0.0601323i
$466$	−322.277	+	86.3538i	−0.691581	+	0.185309i
$467$		−	332.603i		−	0.712211i	−0.934446	−	0.356106i	$-0.884104\pi$
$467$		−	332.603i		−	0.712211i	0.934446	−	0.356106i	$-0.115896\pi$
$468$	39.0000	+	67.5500i	0.0833333	+	0.144338i
$469$	−413.856			−0.882423
$470$	13.9230	+	51.9615i	0.0296235	+	0.110556i
$471$	−14.1128	+	24.4442i	−0.0299636	+	0.0518985i
$472$	52.0770	−	30.0666i	0.110333	−	0.0637005i
$473$	229.492	−	229.492i	0.485184	−	0.485184i
$474$	211.923	+	56.7846i	0.447095	+	0.119799i
$475$	−105.005	+	391.885i	−0.221063	+	0.825020i
$476$	313.128	+	313.128i	0.657832	+	0.657832i
$477$	34.6577	+	60.0289i	0.0726576	+	0.125847i
$478$	269.454	+	155.569i	0.563711	+	0.325459i
$479$	−655.559	+	175.656i	−1.36860	+	0.366715i	−0.866967	−	0.498366i	$-0.833934\pi$
$479$	−655.559	+	175.656i	−1.36860	+	0.366715i	−0.501632	+	0.865081i	$0.667267\pi$
$480$			8.78461i			0.0183013i
$481$	38.5333	+	10.3250i	0.0801109	+	0.0214656i
$482$	−540.301			−1.12096
$483$	−121.492	−	453.415i	−0.251537	−	0.938748i
$484$	−213.277	+	369.406i	−0.440655	+	0.763236i
$485$	−39.6828	+	22.9109i	−0.0818201	+	0.0472389i
$486$	15.5885	−	15.5885i	0.0320750	−	0.0320750i
$487$	535.822	+	143.573i	1.10025	+	0.294811i	0.762866	−	0.646556i	$-0.223791\pi$
$487$	535.822	+	143.573i	1.10025	+	0.294811i	0.337384	+	0.941367i	$0.390458\pi$
$488$	−30.9038	+	115.335i	−0.0633275	+	0.236341i
$489$	354.249	+	354.249i	0.724435	+	0.724435i
$490$	70.0070	+	121.256i	0.142872	+	0.247461i
$491$	−501.373	−	289.468i	−1.02113	−	0.589548i	−0.106696	−	0.994292i	$-0.534027\pi$
$491$	−501.373	−	289.468i	−1.02113	−	0.589548i	−0.914430	+	0.404744i	$0.867361\pi$
$492$	−102.373	+	27.4308i	−0.208075	+	0.0557536i
$493$			677.942i			1.37514i
$494$	154.133	−	266.967i	0.312011	−	0.540418i
$495$	49.1769			0.0993473
$496$	−37.2820	−	139.138i	−0.0751654	−	0.280521i
$497$	216.497	−	374.985i	0.435608	−	0.754496i
$498$	−292.277	+	168.746i	−0.586901	+	0.338848i
$499$	40.3154	−	40.3154i	0.0807923	−	0.0807923i	−0.665556	−	0.746348i	$-0.731805\pi$
$499$	40.3154	−	40.3154i	0.0807923	−	0.0807923i	0.746348	+	0.665556i	$0.231805\pi$
$500$	−85.2102	−	22.8320i	−0.170420	−	0.0456640i
$501$	−121.723	+	454.277i	−0.242960	+	0.906740i
$502$	73.4923	+	73.4923i	0.146399	+	0.146399i
$503$	182.894	+	316.781i	0.363605	+	0.629783i	0.988551	−	0.150885i	$-0.0482123\pi$
$503$	182.894	+	316.781i	0.363605	+	0.629783i	−0.624946	+	0.780668i	$0.714879\pi$
$504$	−92.7846	−	53.5692i	−0.184096	−	0.106288i
$505$	30.0500	−	8.05187i	0.0595049	−	0.0159443i
$506$			554.985i			1.09681i
$507$	292.717			0.577350
$508$	−164.708			−0.324228
$509$	−179.747	−	670.824i	−0.353137	−	1.31793i	−0.882813	−	0.469725i	$-0.844353\pi$
$509$	−179.747	−	670.824i	−0.353137	−	1.31793i	0.529675	−	0.848200i	$-0.322314\pi$
$510$	−19.2558	+	33.3519i	−0.0377564	+	0.0653960i
$511$	−246.206	+	142.147i	−0.481813	+	0.278175i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−84.1577	−	22.5500i	−0.164050	−	0.0439571i
$514$	169.338	−	631.977i	0.329451	−	1.22953i
$515$	124.823	+	124.823i	0.242375	+	0.242375i
$516$	−30.7461	−	53.2539i	−0.0595855	−	0.103205i
$517$	671.769	+	387.846i	1.29936	+	0.750186i
$518$	−52.9282	+	14.1821i	−0.102178	+	0.0273785i
$519$			186.200i			0.358767i
$520$	28.5500	+	16.4833i	0.0549038	+	0.0316987i
$521$	49.0526			0.0941508			0.0470754	−	0.998891i	$-0.485010\pi$
$521$	49.0526			0.0941508			0.0470754	+	0.998891i	$0.485010\pi$
$522$	−42.4519	−	158.433i	−0.0813255	−	0.303511i
$523$	−30.6654	+	53.1140i	−0.0586337	+	0.101556i	−0.893852	−	0.448362i	$-0.852008\pi$
$523$	−30.6654	+	53.1140i	−0.0586337	+	0.101556i	0.835219	+	0.549918i	$0.185341\pi$
$524$	−10.2769	+	5.93336i	−0.0196124	+	0.0113232i
$525$	374.172	−	374.172i	0.712708	−	0.712708i
$526$	−684.697	−	183.464i	−1.30171	−	0.348791i
$527$	163.443	−	609.979i	0.310139	−	1.15746i
$528$	89.5692	+	89.5692i	0.169639	+	0.169639i
$529$	−34.1462	−	59.1429i	−0.0645485	−	0.111801i
$530$	25.3712	+	14.6481i	0.0478702	+	0.0276378i
$531$	−61.6077	+	16.5077i	−0.116022	+	0.0310880i
$532$			423.426i			0.795913i
$533$	−102.942	+	384.183i	−0.193136	+	0.720794i
$534$	−3.09996			−0.00580517
$535$	8.39608	+	31.3346i	0.0156936	+	0.0585693i
$536$	46.3538	−	80.2872i	0.0864810	−	0.149790i
$537$	−183.258	+	105.804i	−0.341262	+	0.197028i
$538$	38.4871	−	38.4871i	0.0715374	−	0.0715374i
$539$	1950.14	+	522.540i	3.61808	+	0.969461i
$540$	2.41154	−	9.00000i	0.00446582	−	0.0166667i
$541$	−334.410	−	334.410i	−0.618132	−	0.618132i	0.326920	−	0.945052i	$-0.393989\pi$
$541$	−334.410	−	334.410i	−0.618132	−	0.618132i	−0.945052	+	0.326920i	$0.893989\pi$
$542$	140.574	+	243.482i	0.259362	+	0.449229i
$543$	97.9308	+	56.5404i	0.180351	+	0.104126i
$544$	−95.8179	+	25.6743i	−0.176136	+	0.0471955i
$545$			161.660i			0.296624i
$546$	−348.200	+	201.033i	−0.637729	+	0.368193i
$547$	−567.854			−1.03812			−0.519062	−	0.854737i	$-0.673719\pi$
$547$	−567.854			−1.03812			−0.519062	+	0.854737i	$0.673719\pi$
$548$	89.1718	+	332.794i	0.162722	+	0.607287i
$549$	63.3231	−	109.679i	0.115343	−	0.199779i
$550$	−541.808	+	312.813i	−0.985105	+	0.568751i
$551$	−458.372	+	458.372i	−0.831891	+	0.831891i
$552$	101.569	+	27.2154i	0.184002	+	0.0493032i
$553$	−292.708	+	1092.40i	−0.529309	+	1.97541i
$554$	53.9423	+	53.9423i	0.0973687	+	0.0973687i
$555$	−2.38269	−	4.12693i	−0.00429313	−	0.00743592i
$556$	22.0103	+	12.7077i	0.0395869	+	0.0228555i
$557$	395.583	−	105.996i	0.710202	−	0.190298i	0.114406	−	0.993434i	$-0.463503\pi$
$557$	395.583	−	105.996i	0.710202	−	0.190298i	0.595796	+	0.803136i	$0.296837\pi$
$558$			152.785i			0.273808i
$559$	−230.767			−0.412821
$560$	−45.2820			−0.0808608
$561$	143.727	+	536.396i	0.256198	+	0.956143i
$562$	172.165	−	298.198i	0.306343	−	0.530601i
$563$	30.0000	−	17.3205i	0.0532860	−	0.0307647i	−0.473120	−	0.880998i	$-0.656872\pi$
$563$	30.0000	−	17.3205i	0.0532860	−	0.0307647i	0.526406	+	0.850233i	$0.323539\pi$
$564$	103.923	−	103.923i	0.184261	−	0.184261i
$565$	−68.5192	−	18.3597i	−0.121273	−	0.0324950i
$566$	−183.044	+	683.128i	−0.323399	+	1.20694i
$567$	80.3538	+	80.3538i	0.141718	+	0.141718i
$568$	48.4974	+	84.0000i	0.0853828	+	0.147887i
$569$	−243.300	−	140.469i	−0.427592	−	0.246870i	0.270728	−	0.962656i	$-0.412736\pi$
$569$	−243.300	−	140.469i	−0.427592	−	0.246870i	−0.698320	+	0.715785i	$0.746069\pi$
$570$	−35.5692	+	9.53074i	−0.0624021	+	0.0167206i
$571$		−	978.823i		−	1.71423i	−0.515128	−	0.857113i	$-0.672256\pi$
$571$		−	978.823i		−	1.71423i	0.515128	−	0.857113i	$-0.327744\pi$
$572$	459.167	−	123.033i	0.802739	−	0.215093i
$573$	52.9385			0.0923883
$574$	−141.397	−	527.703i	−0.246337	−	0.919342i
$575$	−259.674	+	449.769i	−0.451608	+	0.782207i
$576$	20.7846	−	12.0000i	0.0360844	−	0.0208333i
$577$	317.289	−	317.289i	0.549894	−	0.549894i	−0.376516	−	0.926410i	$-0.622878\pi$
$577$	317.289	−	317.289i	0.549894	−	0.549894i	0.926410	+	0.376516i	$0.122878\pi$
$578$	−25.2820	−	6.77430i	−0.0437405	−	0.0117202i
$579$	−21.2776	+	79.4090i	−0.0367488	+	0.137148i
$580$	−49.0192	−	49.0192i	−0.0845159	−	0.0845159i
$581$	−869.836	−	1506.60i	−1.49714	−	2.59311i
$582$	108.415	+	62.5936i	0.186281	+	0.107549i
$583$	408.042	−	109.335i	0.699901	−	0.187538i
$584$		−	63.6846i		−	0.109049i
$585$	−24.7250	−	24.7250i	−0.0422650	−	0.0422650i
$586$	−191.611			−0.326982
$587$	152.900	+	570.631i	0.260477	+	0.972114i	0.964961	+	0.262394i	$0.0845119\pi$
$587$	152.900	+	570.631i	0.260477	+	0.972114i	−0.704484	+	0.709720i	$0.748821\pi$
$588$	191.263	−	331.277i	0.325277	−	0.563396i
$589$	522.928	−	301.913i	0.887824	−	0.512585i
$590$	−19.0615	+	19.0615i	−0.0323076	+	0.0323076i
$591$	375.767	+	100.687i	0.635816	+	0.170366i
$592$	3.17691	−	11.8564i	0.00536641	−	0.0200277i
$593$	−460.853	−	460.853i	−0.777155	−	0.777155i	0.202191	−	0.979346i	$-0.435194\pi$
$593$	−460.853	−	460.853i	−0.777155	−	0.777155i	−0.979346	+	0.202191i	$0.935194\pi$
$594$	−67.1769	−	116.354i	−0.113092	−	0.195882i
$595$	−171.919	−	99.2576i	−0.288940	−	0.166820i
$596$	−223.890	+	59.9911i	−0.375654	+	0.100656i
$597$		−	279.167i		−	0.467616i
$598$	279.033	−	279.033i	0.466611	−	0.466611i
$599$	967.923			1.61590			0.807949	−	0.589252i	$-0.200578\pi$
$599$	967.923			1.61590			0.807949	+	0.589252i	$0.200578\pi$
$600$	30.6795	+	114.497i	0.0511325	+	0.190829i
$601$	−230.225	+	398.761i	−0.383070	+	0.663497i	−0.991499	−	0.130111i	$-0.958466\pi$
$601$	−230.225	+	398.761i	−0.383070	+	0.663497i	0.608429	+	0.793608i	$0.291800\pi$
$602$	274.508	−	158.487i	0.455993	−	0.263268i
$603$	−69.5307	+	69.5307i	−0.115308	+	0.115308i
$604$	324.028	+	86.8231i	0.536470	+	0.143747i
$605$	49.4911	−	184.703i	0.0818034	−	0.305295i
$606$	−60.1000	−	60.1000i	−0.0991749	−	0.0991749i
$607$	19.9615	+	34.5744i	0.0328855	+	0.0569594i	0.882000	−	0.471250i	$-0.156197\pi$
$607$	19.9615	+	34.5744i	0.0328855	+	0.0569594i	−0.849114	+	0.528209i	$0.822864\pi$
$608$	−82.1436	−	47.4256i	−0.135105	−	0.0780027i
$609$	816.673	−	218.827i	1.34101	−	0.359322i
$610$		−	53.5270i		−	0.0877491i
$611$	−142.750	−	532.750i	−0.233633	−	0.871931i
$612$	105.215			0.171921
$613$	122.949	+	458.851i	0.200569	+	0.748533i	0.990755	+	0.135666i	$0.0433173\pi$
$613$	122.949	+	458.851i	0.200569	+	0.748533i	−0.790186	+	0.612867i	$0.790016\pi$
$614$	83.6743	−	144.928i	0.136277	−	0.236039i
$615$	41.1462	−	23.7558i	0.0669043	−	0.0386272i
$616$	−461.703	+	461.703i	−0.749517	+	0.749517i
$617$	593.322	+	158.980i	0.961624	+	0.257666i	0.705287	−	0.708921i	$-0.250818\pi$
$617$	593.322	+	158.980i	0.961624	+	0.257666i	0.256336	+	0.966588i	$0.417485\pi$
$618$	124.823	−	465.846i	0.201979	−	0.753796i
$619$	−417.520	−	417.520i	−0.674508	−	0.674508i	0.284244	−	0.958752i	$-0.408257\pi$
$619$	−417.520	−	417.520i	−0.674508	−	0.674508i	−0.958752	+	0.284244i	$0.908257\pi$
$620$	32.2872	+	55.9230i	0.0520761	+	0.0901985i
$621$	−96.5885	−	55.7654i	−0.155537	−	0.0897993i
$622$	244.277	−	65.4538i	0.392728	−	0.105231i
$623$		−	15.9794i		−	0.0256491i
$624$		−	90.0666i		−	0.144338i
$625$	−565.358			−0.904572
$626$	−84.2309	−	314.354i	−0.134554	−	0.502163i
$627$	−265.492	+	459.846i	−0.423433	+	0.733407i
$628$	28.2257	−	16.2961i	0.0449454	−	0.0259492i
$629$	38.0507	−	38.0507i	0.0604939	−	0.0604939i
$630$	46.3923	+	12.4308i	0.0736386	+	0.0197314i
$631$	−44.7255	+	166.918i	−0.0708804	+	0.264529i	−0.992268	−	0.124117i	$-0.960390\pi$
$631$	−44.7255	+	166.918i	−0.0708804	+	0.264529i	0.921387	+	0.388646i	$0.127057\pi$
$632$	−179.138	−	179.138i	−0.283447	−	0.283447i
$633$	−133.492	−	231.215i	−0.210888	−	0.365269i
$634$	−366.998	−	211.886i	−0.578861	−	0.334206i
$635$	71.3205	−	19.1103i	0.112316	−	0.0300949i
$636$		−	80.0385i		−	0.125847i
$637$	−717.767	−	1243.21i	−1.12679	−	1.95166i
$638$	−999.615			−1.56680
$639$	−26.6269	−	99.3731i	−0.0416697	−	0.155513i
$640$	5.07180	−	8.78461i	0.00792468	−	0.0137260i
$641$	−359.425	+	207.514i	−0.560725	+	0.323735i	−0.753437	−	0.657521i	$-0.771605\pi$
$641$	−359.425	+	207.514i	−0.560725	+	0.323735i	0.192711	+	0.981256i	$0.438272\pi$
$642$	62.6692	−	62.6692i	0.0976155	−	0.0976155i
$643$	−345.023	−	92.4486i	−0.536583	−	0.143777i	−0.0196567	−	0.999807i	$-0.506257\pi$
$643$	−345.023	−	92.4486i	−0.536583	−	0.143777i	−0.516927	+	0.856030i	$0.672924\pi$
$644$	−140.287	+	523.559i	−0.217837	+	0.812980i
$645$	19.4923	+	19.4923i	0.0302206	+	0.0302206i
$646$	−207.913	−	360.115i	−0.321846	−	0.557454i
$647$	−504.862	−	291.482i	−0.780312	−	0.450513i	0.0562291	−	0.998418i	$-0.482092\pi$
$647$	−504.862	−	291.482i	−0.780312	−	0.450513i	−0.836541	+	0.547905i	$0.815426\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$			388.708i			0.598933i
$650$	429.683	+	115.133i	0.661051	+	0.177128i
$651$	−787.559			−1.20977
$652$	−149.723	−	558.774i	−0.229637	−	0.857016i
$653$	−182.172	+	315.531i	−0.278977	+	0.483202i	−0.971131	−	0.238548i	$-0.923329\pi$
$653$	−182.172	+	315.531i	−0.278977	+	0.483202i	0.692154	+	0.721750i	$0.256662\pi$
$654$	382.492	−	220.832i	0.584851	−	0.337664i
$655$	3.76160	−	3.76160i	0.00574290	−	0.00574290i
$656$	118.210	+	31.6743i	0.180199	+	0.0482841i
$657$	−17.4826	+	65.2461i	−0.0266098	+	0.0993092i
$658$	535.692	+	535.692i	0.814122	+	0.814122i
$659$	580.592	+	1005.62i	0.881020	+	1.52597i	0.850208	+	0.526446i	$0.176476\pi$
$659$	580.592	+	1005.62i	0.881020	+	1.52597i	0.0308117	+	0.999525i	$0.490191\pi$
$660$	−49.1769	−	28.3923i	−0.0745105	−	0.0430186i
$661$	274.738	−	73.6159i	0.415641	−	0.111371i	−0.0449374	−	0.998990i	$-0.514309\pi$
$661$	274.738	−	73.6159i	0.415641	−	0.111371i	0.460578	+	0.887619i	$0.347642\pi$
$662$			140.077i			0.211597i
$663$	197.425	−	341.950i	0.297775	−	0.515762i
$664$	389.703			0.586901
$665$	−49.1281	−	183.349i	−0.0738769	−	0.275712i
$666$	−6.50962	+	11.2750i	−0.00977420	+	0.0169294i
$667$	−718.634	+	414.904i	−1.07741	+	0.622045i
$668$	384.000	−	384.000i	0.574850	−	0.574850i
$669$	244.028	+	65.3872i	0.364766	+	0.0977386i
$670$	−10.7564	+	40.1436i	−0.0160544	+	0.0599158i
$671$	−545.769	−	545.769i	−0.813367	−	0.813367i
$672$	61.8564	+	107.138i	0.0920482	+	0.159432i
$673$	−791.667	−	457.069i	−1.17633	−	0.679152i	−0.221164	−	0.975237i	$-0.570986\pi$
$673$	−791.667	−	457.069i	−1.17633	−	0.679152i	−0.955162	+	0.296085i	$0.904319\pi$
$674$	−72.5045	+	19.4275i	−0.107573	+	0.0288242i
$675$		−	125.727i		−	0.186262i
$676$	−292.717	−	169.000i	−0.433013	−	0.250000i
$677$	−148.677			−0.219611			−0.109806	−	0.993953i	$-0.535023\pi$
$677$	−148.677			−0.219611			−0.109806	+	0.993953i	$0.535023\pi$
$678$	50.1596	+	187.198i	0.0739817	+	0.276103i
$679$	−322.651	+	558.848i	−0.475186	+	0.823046i
$680$	38.5115	−	22.2346i	0.0566346	−	0.0326980i
$681$	−443.023	+	443.023i	−0.650548	+	0.650548i
$682$	899.405	+	240.995i	1.31878	+	0.353365i
$683$	−210.382	+	785.156i	−0.308026	+	1.14957i	0.622282	+	0.782793i	$0.286206\pi$
$683$	−210.382	+	785.156i	−0.308026	+	1.14957i	−0.930309	+	0.366777i	$0.880461\pi$
$684$	71.1384	+	71.1384i	0.104004	+	0.104004i
$685$	−77.2250	−	133.758i	−0.112737	−	0.195267i
$686$	949.892	+	548.420i	1.38468	+	0.799447i
$687$	124.380	−	33.3275i	0.181048	−	0.0485117i
$688$			71.0052i			0.103205i
$689$	−260.125	−	150.183i	−0.377540	−	0.217973i
$690$	−47.1384			−0.0683166
$691$	−66.6654	−	248.799i	−0.0964767	−	0.360056i	0.900762	−	0.434312i	$-0.143008\pi$
$691$	−66.6654	−	248.799i	−0.0964767	−	0.360056i	−0.997239	+	0.0742560i	$0.976342\pi$
$692$	107.503	−	186.200i	0.155351	−	0.269075i
$693$	599.769	−	346.277i	0.865468	−	0.499678i
$694$	675.167	−	675.167i	0.972863	−	0.972863i
$695$	−11.0052	−	2.94882i	−0.0158348	−	0.00424291i
$696$	−49.0192	+	182.942i	−0.0704299	+	0.262848i
$697$	379.371	+	379.371i	0.544292	+	0.544292i
$698$	−418.846	−	725.463i	−0.600066	−	1.03934i
$699$	−353.885	−	204.315i	−0.506273	−	0.292297i
$700$	−590.200	+	158.144i	−0.843143	+	0.225919i
$701$			1174.97i			1.67614i	0.545563	+	0.838070i	$0.316316\pi$
$701$			1174.97i			1.67614i	−0.545563	+	0.838070i	$0.683684\pi$
$702$	−24.7250	+	92.2750i	−0.0352208	+	0.131446i
$703$	51.4538			0.0731917
$704$	−37.8564	−	141.282i	−0.0537733	−	0.200685i
$705$	−32.9423	+	57.0577i	−0.0467266	+	0.0809329i
$706$	146.044	−	84.3186i	0.206861	−	0.119431i
$707$	309.797	−	309.797i	0.438186	−	0.438186i
$708$	71.1384	+	19.0615i	0.100478	+	0.0269230i
$709$	181.920	−	678.936i	0.256587	−	0.957597i	−0.710613	−	0.703583i	$-0.751582\pi$
$709$	181.920	−	678.936i	0.256587	−	0.957597i	0.967200	−	0.254014i	$-0.0817510\pi$
$710$	−30.7461	−	30.7461i	−0.0433044	−	0.0433044i
$711$	134.354	+	232.708i	0.188965	+	0.327296i
$712$	3.09996	+	1.78976i	0.00435388	+	0.00251371i
$713$	746.620	−	200.056i	1.04715	−	0.280584i
$714$			542.354i			0.759599i
$715$	−184.550	+	106.550i	−0.258112	+	0.149021i
$716$	244.344			0.341262
$717$	98.6269	+	368.081i	0.137555	+	0.513362i
$718$	−375.415	+	650.238i	−0.522863	+	0.905625i
$719$	−607.146	+	350.536i	−0.844431	+	0.487533i	−0.858768	−	0.512365i	$-0.828770\pi$
$719$	−607.146	+	350.536i	−0.844431	+	0.487533i	0.0143368	+	0.999897i	$0.495436\pi$
$720$	−7.60770	+	7.60770i	−0.0105662	+	0.0105662i
$721$	2401.30	+	643.426i	3.33051	+	0.892407i
$722$	−29.2276	+	109.079i	−0.0404814	+	0.151079i
$723$	−467.915	−	467.915i	−0.647185	−	0.647185i
$724$	−65.2872	−	113.081i	−0.0901757	−	0.156189i
$725$	−810.106	−	467.715i	−1.11739	−	0.645124i
$726$	−504.619	+	135.212i	−0.695067	+	0.186243i
$727$			284.715i			0.391630i	0.980641	+	0.195815i	$0.0627353\pi$
$727$			284.715i			0.391630i	−0.980641	+	0.195815i	$0.937265\pi$
$728$	464.267			0.637729
$729$	27.0000			0.0370370
$730$	7.38904	+	27.5763i	0.0101220	+	0.0377757i
$731$	−155.642	+	269.581i	−0.212917	+	0.368783i
$732$	−126.646	+	73.1192i	−0.173014	+	0.0998896i
$733$	815.307	−	815.307i	1.11229	−	1.11229i	0.119447	−	0.992841i	$-0.461888\pi$
$733$	815.307	−	815.307i	1.11229	−	1.11229i	0.992841	−	0.119447i	$-0.0381122\pi$
$734$	−289.167	−	77.4820i	−0.393960	−	0.105561i
$735$	−44.3827	+	165.638i	−0.0603846	+	0.225358i
$736$	−85.8564	−	85.8564i	−0.116653	−	0.116653i
$737$	299.636	+	518.985i	0.406562	+	0.704185i
$738$	−112.413	−	64.9019i	−0.152322	−	0.0879430i
$739$	−1119.41	+	299.944i	−1.51476	+	0.405878i	−0.918012	−	0.396553i	$-0.870206\pi$
$739$	−1119.41	+	299.944i	−1.51476	+	0.405878i	−0.596745	+	0.802431i	$0.703540\pi$
$740$			5.50258i			0.00743592i
$741$	364.683	−	97.7166i	0.492150	−	0.131871i
$742$	412.574			0.556030
$743$	−1.15906	−	4.32566i	−0.00155997	−	0.00582189i	0.965141	−	0.261729i	$-0.0842926\pi$
$743$	−1.15906	−	4.32566i	−0.00155997	−	0.00582189i	−0.966701	+	0.255907i	$0.917626\pi$
$744$	88.2102	−	152.785i	0.118562	−	0.205356i
$745$	89.9866	−	51.9538i	0.120787	−	0.0697366i
$746$	66.4397	−	66.4397i	0.0890613	−	0.0890613i
$747$	−399.258	−	106.981i	−0.534481	−	0.143214i
$748$	165.962	−	619.377i	0.221874	−	0.828044i
$749$	323.041	+	323.041i	0.431296	+	0.431296i
$750$	−54.0211	−	93.5673i	−0.0720282	−	0.124756i
$751$	647.611	+	373.899i	0.862332	+	0.497868i	0.864793	−	0.502129i	$-0.167450\pi$
$751$	647.611	+	373.899i	0.862332	+	0.497868i	−0.00246040	+	0.999997i	$0.500783\pi$
$752$	−163.923	+	43.9230i	−0.217983	+	0.0584083i
$753$			127.292i			0.169047i
$754$	502.583	+	502.583i	0.666556	+	0.666556i
$755$	−150.382			−0.199181
$756$	−33.9615	−	126.746i	−0.0449227	−	0.167654i
$757$	478.128	−	828.142i	0.631609	−	1.09398i	−0.355614	−	0.934633i	$-0.615728\pi$
$757$	478.128	−	828.142i	0.631609	−	1.09398i	0.987223	−	0.159346i	$-0.0509386\pi$
$758$	189.513	−	109.415i	0.250017	−	0.144347i
$759$	−480.631	+	480.631i	−0.633242	+	0.633242i
$760$	41.0718	+	11.0052i	0.0540418	+	0.0144805i
$761$	165.015	−	615.843i	0.216839	−	0.809255i	−0.768672	−	0.639643i	$-0.779082\pi$
$761$	165.015	−	615.843i	0.216839	−	0.809255i	0.985511	−	0.169611i	$-0.0542513\pi$
$762$	−142.641	−	142.641i	−0.187193	−	0.187193i
$763$	1138.32	+	1971.63i	1.49190	+	2.58405i
$764$	−52.9385	−	30.5641i	−0.0692912	−	0.0400053i
$765$	−45.5596	+	12.2077i	−0.0595550	+	0.0159577i
$766$			553.990i			0.723224i
$767$	195.433	−	195.433i	0.254802	−	0.254802i
$768$	−27.7128			−0.0360844
$769$	198.506	+	740.834i	0.258135	+	0.963373i	0.966319	+	0.257346i	$0.0828479\pi$
$769$	198.506	+	740.834i	0.258135	+	0.963373i	−0.708184	+	0.706028i	$0.750485\pi$
$770$	146.354	−	253.492i	0.190070	−	0.329211i
$771$	693.959	−	400.658i	0.900077	−	0.519660i
$772$	67.1244	−	67.1244i	0.0869486	−	0.0869486i
$773$	−491.184	−	131.612i	−0.635426	−	0.170262i	−0.0732950	−	0.997310i	$-0.523351\pi$
$773$	−491.184	−	131.612i	−0.635426	−	0.170262i	−0.562131	+	0.827049i	$0.690018\pi$
$774$	19.4923	−	72.7461i	0.0251838	−	0.0939873i
$775$	616.133	+	616.133i	0.795011	+	0.795011i
$776$	−72.2769	−	125.187i	−0.0931403	−	0.161324i
$777$	−58.1192	−	33.5551i	−0.0747995	−	0.0431855i
$778$	−819.345	+	219.543i	−1.05314	+	0.282189i
$779$			513.002i			0.658540i
$780$	10.4500	+	39.0000i	0.0133975	+	0.0500000i
$781$	−626.985			−0.802797
$782$	−137.769	−	514.161i	−0.176175	−	0.657495i
$783$	100.442	−	173.971i	0.128279	−	0.222185i
$784$	−382.526	+	220.851i	−0.487915	+	0.281698i
$785$	−10.3313	+	10.3313i	−0.0131609	+	0.0131609i
$786$	−14.0385	−	3.76160i	−0.0178607	−	0.00478575i
$787$	−12.4589	+	46.4974i	−0.0158309	+	0.0590819i	−0.973389	−	0.229157i	$-0.926403\pi$
$787$	−12.4589	+	46.4974i	−0.0158309	+	0.0590819i	0.957559	+	0.288239i	$0.0930697\pi$
$788$	−317.636	−	317.636i	−0.403091	−	0.403091i
$789$	−434.081	−	751.850i	−0.550166	−	0.952915i
$790$	98.3538	+	56.7846i	0.124499	+	0.0718793i
$791$	−964.950	+	258.558i	−1.21991	+	0.326874i
$792$			155.138i			0.195882i
$793$			548.800i			0.692056i
$794$	757.405			0.953911
$795$	9.28650	+	34.6577i	0.0116811	+	0.0435946i
$796$	−161.177	+	279.167i	−0.202484	+	0.350712i
$797$	921.327	−	531.928i	1.15599	−	0.667413i	0.205653	−	0.978625i	$-0.434068\pi$
$797$	921.327	−	531.928i	1.15599	−	0.667413i	0.950341	+	0.311212i	$0.100735\pi$
$798$	−366.697	+	366.697i	−0.459520	+	0.459520i
$799$	−718.634	−	192.558i	−0.899417	−	0.240998i
$800$	35.4256	−	132.210i	0.0442820	−	0.165263i
$801$	−2.68465	−	2.68465i	−0.00335162	−	0.00335162i
$802$	307.413	+	532.456i	0.383309	+	0.663910i
$803$	356.512	+	205.832i	0.443974	+	0.256329i
$804$	109.674	−	29.3872i	0.136411	−	0.0365512i
$805$		−	242.985i		−	0.301844i
$806$	−331.033	−	573.367i	−0.410711	−	0.711373i
$807$	66.6616			0.0826043
$808$	25.4012	+	94.7987i	0.0314372	+	0.117325i
$809$	385.148	−	667.096i	0.476079	−	0.824593i	−0.523545	−	0.851998i	$-0.675391\pi$
$809$	385.148	−	667.096i	0.476079	−	0.824593i	0.999624	+	0.0274045i	$0.00872423\pi$
$810$	9.88269	−	5.70577i	0.0122008	−	0.00704416i
$811$	448.420	−	448.420i	0.552923	−	0.552923i	−0.374360	−	0.927283i	$-0.622138\pi$
$811$	448.420	−	448.420i	0.552923	−	0.552923i	0.927283	+	0.374360i	$0.122138\pi$
$812$	−943.013	−	252.679i	−1.16135	−	0.311182i
$813$	−89.1206	+	332.603i	−0.109619	+	0.409105i
$814$	56.1051	+	56.1051i	0.0689252	+	0.0689252i
$815$	129.664	+	224.585i	0.159097	+	0.275564i
$816$	−105.215	−	60.7461i	−0.128940	−	0.0744438i
$817$	−287.503	+	77.0361i	−0.351900	+	0.0942914i
$818$			973.955i			1.19065i
$819$	−475.650	−	127.450i	−0.580769	−	0.155617i
$820$	−54.8616			−0.0669043
$821$	113.217	+	422.533i	0.137902	+	0.514656i	0.999969	+	0.00786244i	$0.00250272\pi$
$821$	113.217	+	422.533i	0.137902	+	0.514656i	−0.862067	+	0.506794i	$0.830831\pi$
$822$	−210.983	+	365.433i	−0.256670	+	0.444565i
$823$	856.361	−	494.420i	1.04054	−	0.600754i	0.120551	−	0.992707i	$-0.461534\pi$
$823$	856.361	−	494.420i	1.04054	−	0.600754i	0.919985	+	0.391953i	$0.128200\pi$
$824$	−393.779	+	393.779i	−0.477888	+	0.477888i
$825$	−740.123	−	198.315i	−0.897119	−	0.240382i
$826$	−98.2563	+	366.697i	−0.118954	+	0.443944i
$827$	−137.751	−	137.751i	−0.166567	−	0.166567i	0.618901	−	0.785469i	$-0.287578\pi$
$827$	−137.751	−	137.751i	−0.166567	−	0.166567i	−0.785469	+	0.618901i	$0.787578\pi$
$828$	64.3923	+	111.531i	0.0777685	+	0.134699i
$829$	−381.028	−	219.987i	−0.459624	−	0.265364i	0.252262	−	0.967659i	$-0.418825\pi$
$829$	−381.028	−	219.987i	−0.459624	−	0.265364i	−0.711886	+	0.702295i	$0.752159\pi$
$830$	−168.746	+	45.2154i	−0.203309	+	0.0544764i
$831$			93.4308i			0.112432i
$832$	−52.0000	+	90.0666i	−0.0625000	+	0.108253i
$833$	−1936.41			−2.32462
$834$	8.05633	+	30.0666i	0.00965987	+	0.0360511i
$835$	−121.723	+	210.831i	−0.145776	+	0.252492i
$836$	530.985	−	306.564i	0.635149	−	0.366703i
$837$	−132.315	+	132.315i	−0.158083	+	0.158083i
$838$	−393.415	−	105.415i	−0.469469	−	0.125794i
$839$	−59.0052	+	220.210i	−0.0703280	+	0.262468i	−0.992133	−	0.125185i	$-0.960047\pi$
$839$	−59.0052	+	220.210i	−0.0703280	+	0.262468i	0.921805	+	0.387653i	$0.126714\pi$
$840$	−39.2154	−	39.2154i	−0.0466850	−	0.0466850i
$841$	−326.808	−	566.047i	−0.388594	−	0.673065i
$842$	−152.235	−	87.8930i	−0.180802	−	0.104386i
$843$	407.346	−	109.148i	0.483210	−	0.129476i
$844$			308.287i			0.365269i
$845$	146.358	+	39.2166i	0.173205	+	0.0464102i
$846$	180.000			0.212766
$847$	−696.978	−	2601.16i	−0.822878	−	3.07102i
$848$	−46.2102	+	80.0385i	−0.0544932	+	0.0943850i
$849$	−750.127	+	433.086i	−0.883542	+	0.510113i
$850$	424.301	−	424.301i	0.499178	−	0.499178i
$851$	63.6218	+	17.0474i	0.0747612	+	0.0200322i
$852$	−30.7461	+	114.746i	−0.0360870	+	0.134679i
$853$	−231.031	−	231.031i	−0.270846	−	0.270846i	0.558595	−	0.829441i	$-0.311341\pi$
$853$	−231.031	−	231.031i	−0.270846	−	0.270846i	−0.829441	+	0.558595i	$0.811341\pi$
$854$	−376.908	−	652.823i	−0.441344	−	0.764430i
$855$	−39.0577	−	22.5500i	−0.0456815	−	0.0263742i
$856$	−98.8513	+	26.4871i	−0.115480	+	0.0309429i
$857$		−	283.768i		−	0.331118i	−0.986200	−	0.165559i	$-0.947057\pi$
$857$		−	283.768i		−	0.331118i	0.986200	−	0.165559i	$-0.0529428\pi$
$858$	504.200	+	291.100i	0.587646	+	0.339277i
$859$	1436.54			1.67234			0.836170	−	0.548470i	$-0.184789\pi$
$859$	1436.54			1.67234			0.836170	+	0.548470i	$0.184789\pi$
$860$	−8.23840	−	30.7461i	−0.00957954	−	0.0357513i
$861$	334.550	−	579.458i	0.388560	−	0.673005i
$862$	−19.8076	+	11.4359i	−0.0229787	+	0.0132667i
$863$	604.677	−	604.677i	0.700668	−	0.700668i	−0.263886	−	0.964554i	$-0.585004\pi$
$863$	604.677	−	604.677i	0.700668	−	0.700668i	0.964554	+	0.263886i	$0.0850042\pi$
$864$	28.3923	+	7.60770i	0.0328615	+	0.00880520i
$865$	−24.9461	+	93.1000i	−0.0288394	+	0.107630i
$866$	−355.396	−	355.396i	−0.410388	−	0.410388i
$867$	−16.0282	−	27.7616i	−0.0184869	−	0.0320203i
$868$	787.559	+	454.697i	0.907326	+	0.523845i
$869$	1581.82	−	423.846i	1.82027	−	0.487740i
$870$		−	84.9038i		−	0.0975906i
$871$	110.283	−	411.583i	0.126617	−	0.472541i
$872$	−509.990			−0.584851
$873$	39.6828	+	148.098i	0.0454556	+	0.169643i
$874$	254.487	−	440.785i	0.291175	−	0.504330i
$875$	482.312	−	278.463i	0.551213	−	0.318243i
$876$	55.1525	−	55.1525i	0.0629595	−	0.0629595i
$877$	−412.267	−	110.467i	−0.470088	−	0.125960i	0.0159955	−	0.999872i	$-0.494908\pi$
$877$	−412.267	−	110.467i	−0.470088	−	0.125960i	−0.486084	+	0.873912i	$0.661575\pi$
$878$	75.8282	−	282.995i	0.0863647	−	0.322318i
$879$	−165.940	−	165.940i	−0.188783	−	0.188783i
$880$	32.7846	+	56.7846i	0.0372552	+	0.0645280i
$881$	−157.758	−	91.0814i	−0.179067	−	0.103384i	0.407787	−	0.913077i	$-0.366300\pi$
$881$	−157.758	−	91.0814i	−0.179067	−	0.103384i	−0.586854	+	0.809693i	$0.699634\pi$
$882$	452.533	−	121.256i	0.513076	−	0.137478i
$883$		−	1334.37i		−	1.51118i	−0.655047	−	0.755588i	$-0.727351\pi$
$883$		−	1334.37i		−	1.51118i	0.655047	−	0.755588i	$-0.272649\pi$
$884$	−394.850	+	227.967i	−0.446663	+	0.257881i
$885$	−33.0155			−0.0373056
$886$	−144.449	−	539.090i	−0.163035	−	0.608453i
$887$	−373.923	+	647.654i	−0.421559	+	0.730162i	−0.996092	−	0.0883194i	$-0.971850\pi$
$887$	−373.923	+	647.654i	−0.421559	+	0.730162i	0.574533	+	0.818481i	$0.305184\pi$
$888$	13.0192	−	7.51666i	0.0146613	−	0.00846471i
$889$	735.272	−	735.272i	0.827077	−	0.827077i
$890$	−1.54998	−	0.415316i	−0.00174155	−	0.000466648i
$891$	42.5885	−	158.942i	0.0477985	−	0.178386i
$892$	−206.277	−	206.277i	−0.231252	−	0.231252i
$893$	−355.692	−	616.077i	−0.398312	−	0.689896i
$894$	−245.848	−	141.940i	−0.274998	−	0.158770i
$895$	−105.804	+	28.3501i	−0.118217	+	0.0316760i
$896$		−	142.851i		−	0.159432i
$897$	483.300			0.538796
$898$	−747.913			−0.832865
$899$	360.333	+	1344.78i	0.400816	+	1.49586i
$900$	−72.5885	+	125.727i	−0.0806538	+	0.139697i
$901$	−350.887	+	202.584i	−0.389441	+	0.224844i
$902$	−559.377	+	559.377i	−0.620152	+	0.620152i
$903$	374.985	+	100.477i	0.415265	+	0.111270i
$904$	57.9193	−	216.158i	0.0640700	−	0.239112i
$905$	41.3904	+	41.3904i	0.0457353	+	0.0457353i
$906$	205.426	+	355.808i	0.226739	+	0.392724i
$907$	750.697	+	433.415i	0.827671	+	0.477856i	0.853054	−	0.521822i	$-0.174747\pi$
$907$	750.697	+	433.415i	0.827671	+	0.477856i	−0.0253838	+	0.999678i	$0.508081\pi$
$908$	698.802	−	187.244i	0.769606	−	0.206215i
$909$		−	104.096i		−	0.114517i
$910$	−201.033	+	53.8667i	−0.220916	+	0.0591942i
$911$	92.5180			0.101557			0.0507783	−	0.998710i	$-0.483830\pi$
$911$	92.5180			0.101557			0.0507783	+	0.998710i	$0.483830\pi$
$912$	−30.0666	−	112.210i	−0.0329678	−	0.123038i
$913$	−1259.54	+	2181.58i	−1.37956	+	2.38947i
$914$	108.634	−	62.7199i	0.118856	−	0.0686213i
$915$	46.3557	−	46.3557i	0.0506620	−	0.0506620i
$916$	−143.622	−	38.4833i	−0.156792	−	0.0420124i
$917$	19.3899	−	72.3641i	0.0211449	−	0.0789140i
$918$	91.1192	+	91.1192i	0.0992584	+	0.0992584i
$919$	427.492	+	740.438i	0.465171	+	0.805700i	0.999209	−	0.0397604i	$-0.0126595\pi$
$919$	427.492	+	740.438i	0.465171	+	0.805700i	−0.534038	+	0.845460i	$0.679326\pi$
$920$	47.1384	+	27.2154i	0.0512374	+	0.0295819i
$921$	197.976	−	53.0474i	0.214957	−	0.0575976i
$922$		−	110.973i		−	0.120361i
$923$	315.233	+	315.233i	0.341531	+	0.341531i
$924$	−799.692			−0.865468
$925$	19.2173	+	71.7199i	0.0207754	+	0.0775350i
$926$	−264.908	+	458.833i	−0.286077	+	0.495500i
$927$	511.535	−	295.335i	0.551817	−	0.318592i
$928$	154.641	−	154.641i	0.166639	−	0.166639i
$929$	176.905	+	47.4014i	0.190425	+	0.0510241i	0.352771	−	0.935710i	$-0.385239\pi$
$929$	176.905	+	47.4014i	0.190425	+	0.0510241i	−0.162346	+	0.986734i	$0.551906\pi$
$930$	−20.4693	+	76.3923i	−0.0220100	+	0.0821423i
$931$	−1309.25	−	1309.25i	−1.40628	−	1.40628i
$932$	235.923	+	408.631i	0.253136	+	0.438445i
$933$	268.235	+	154.865i	0.287497	+	0.165986i
$934$	−454.344	+	121.741i	−0.486449	+	0.130344i
$935$			287.454i			0.307437i
$936$	78.0000	−	78.0000i	0.0833333	−	0.0833333i
$937$	1453.78			1.55153			0.775763	−	0.631025i	$-0.217365\pi$
$937$	1453.78			1.55153			0.775763	+	0.631025i	$0.217365\pi$
$938$	151.482	+	565.338i	0.161495	+	0.602706i
$939$	199.292	−	345.184i	0.212239	−	0.367609i
$940$	65.8846	−	38.0385i	0.0700900	−	0.0404665i
$941$	−723.018	+	723.018i	−0.768351	+	0.768351i	−0.977816	−	0.209465i	$-0.932828\pi$
$941$	−723.018	+	723.018i	−0.768351	+	0.768351i	0.209465	+	0.977816i	$0.432828\pi$
$942$	38.5570	+	10.3313i	0.0409310	+	0.0109674i
$943$	−169.965	+	634.319i	−0.180239	+	0.672661i
$944$	−60.1333	−	60.1333i	−0.0637005	−	0.0637005i
$945$	29.4115	+	50.9423i	0.0311233	+	0.0539072i
$946$	−397.492	−	229.492i	−0.420182	−	0.242592i
$947$	−331.626	+	88.8588i	−0.350185	+	0.0938319i	−0.429624	−	0.903008i	$-0.641354\pi$
$947$	−331.626	+	88.8588i	−0.350185	+	0.0938319i	0.0794386	+	0.996840i	$0.474687\pi$
$948$		−	310.277i		−	0.327296i
$949$	−75.7581	−	282.733i	−0.0798294	−	0.297928i
$950$	573.759			0.603957
$951$	−134.331	−	501.329i	−0.141252	−	0.527160i
$952$	313.128	−	542.354i	0.328916	−	0.569699i
$953$	1541.82	−	890.172i	1.61786	−	0.934073i	0.630390	−	0.776278i	$-0.282895\pi$
$953$	1541.82	−	890.172i	1.61786	−	0.934073i	0.987472	−	0.157795i	$-0.0504385\pi$
$954$	69.3154	−	69.3154i	0.0726576	−	0.0726576i
$955$	26.4693	+	7.09242i	0.0277165	+	0.00742661i
$956$	113.885	−	425.023i	0.119126	−	0.444585i
$957$	−865.692	−	865.692i	−0.904590	−	0.904590i
$958$	479.902	+	831.215i	0.500942	+	0.867657i
$959$	−1883.70	−	1087.55i	−1.96423	−	1.13405i
$960$	12.0000	−	3.21539i	0.0125000	−	0.00334936i
$961$		−	335.841i		−	0.349470i
$962$		−	56.4167i		−	0.0586452i
$963$	108.546			0.112717
$964$	197.764	+	738.065i	0.205149	+	0.765628i
$965$	−21.2776	+	36.8538i	−0.0220493	+	0.0381905i
$966$	−574.908	+	331.923i	−0.595142	+	0.343606i
$967$	−462.603	+	462.603i	−0.478389	+	0.478389i	−0.904616	−	0.426227i	$-0.859843\pi$
$967$	−462.603	+	462.603i	−0.478389	+	0.478389i	0.426227	+	0.904616i	$0.359843\pi$
$968$	582.683	+	156.130i	0.601946	+	0.161291i
$969$	131.811	−	491.927i	0.136028	−	0.507664i
$970$	45.8217	+	45.8217i	0.0472389	+	0.0472389i
$971$	−254.123	−	440.154i	−0.261713	−	0.453300i	0.704984	−	0.709223i	$-0.250954\pi$
$971$	−254.123	−	440.154i	−0.261713	−	0.453300i	−0.966697	+	0.255923i	$0.917621\pi$
$972$	−27.0000	−	15.5885i	−0.0277778	−	0.0160375i
$973$	−154.985	+	41.5280i	−0.159285	+	0.0426804i
$974$		−	784.497i		−	0.805439i
$975$	272.408	+	471.825i	0.279393	+	0.483923i
$976$	168.862			0.173014
$977$	439.843	+	1641.52i	0.450198	+	1.68016i	0.701836	+	0.712339i	$0.252364\pi$
$977$	439.843	+	1641.52i	0.450198	+	1.68016i	−0.251638	+	0.967821i	$0.580969\pi$
$978$	354.249	−	613.577i	0.362217	−	0.627379i
$979$	−20.0385	+	11.5692i	−0.0204683	+	0.0118174i
$980$	140.014	−	140.014i	0.142872	−	0.142872i
$981$	522.494	+	140.002i	0.532614	+	0.142713i
$982$	−211.905	+	790.841i	−0.215789	+	0.805337i
$983$	921.646	+	921.646i	0.937585	+	0.937585i	0.998163	−	0.0605783i	$-0.0192945\pi$
$983$	921.646	+	921.646i	0.937585	+	0.937585i	−0.0605783	+	0.998163i	$0.519294\pi$
$984$	74.9423	+	129.804i	0.0761609	+	0.131914i
$985$	174.394	+	100.687i	0.177050	+	0.102220i
$986$	926.086	−	248.144i	0.939236	−	0.251667i
$987$			927.846i			0.940067i
$988$	−421.100	−	112.833i	−0.426215	−	0.114204i
$989$	−381.015			−0.385253
$990$	−18.0000	−	67.1769i	−0.0181818	−	0.0678555i
$991$	−780.281	+	1351.49i	−0.787367	+	1.36376i	0.140208	+	0.990122i	$0.455223\pi$
$991$	−780.281	+	1351.49i	−0.787367	+	1.36376i	−0.927575	+	0.373637i	$0.878110\pi$
$992$	−176.420	+	101.856i	−0.177843	+	0.102678i
$993$	−121.310	+	121.310i	−0.122165	+	0.122165i
$994$	−591.482	−	158.487i	−0.595052	−	0.159444i
$995$	37.4012	−	139.583i	0.0375892	−	0.140285i
$996$	337.492	+	337.492i	0.338848	+	0.338848i
$997$	−356.323	−	617.170i	−0.357395	−	0.619027i	0.630130	−	0.776490i	$-0.283002\pi$
$997$	−356.323	−	617.170i	−0.357395	−	0.619027i	−0.987525	+	0.157463i	$0.949668\pi$
$998$	−69.8282	−	40.3154i	−0.0699682	−	0.0403961i
$999$	−15.4019	+	4.12693i	−0.0154173	+	0.00413106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.b.19.1	✓	4
3.2	odd	2		234.3.bb.a.19.1		4
13.4	even	6		1014.3.f.g.577.1		4
13.6	odd	12		1014.3.f.g.775.1		4
13.7	odd	12		1014.3.f.b.775.1		4
13.9	even	3		1014.3.f.b.577.1		4
13.11	odd	12	inner	78.3.l.b.37.1	yes	4
39.11	even	12		234.3.bb.a.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.b.19.1	✓	4	1.1	even	1	trivial
78.3.l.b.37.1	yes	4	13.11	odd	12	inner
234.3.bb.a.19.1		4	3.2	odd	2
234.3.bb.a.37.1		4	39.11	even	12
1014.3.f.b.577.1		4	13.9	even	3
1014.3.f.b.775.1		4	13.7	odd	12
1014.3.f.g.577.1		4	13.4	even	6
1014.3.f.g.775.1		4	13.6	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.09808 - 0.633975i) q^{10} +(-17.6603 + 4.73205i) q^{11} +3.46410i q^{12} +(11.2583 + 6.50000i) q^{13} -17.8564 q^{14} +(-0.401924 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(15.1865 - 8.76795i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(16.1962 + 4.33975i) q^{19} +(-0.464102 + 1.73205i) q^{20} +(-15.4641 - 15.4641i) q^{21} +(12.9282 + 22.3923i) q^{22} +(18.5885 + 10.7321i) q^{23} +(4.73205 - 1.26795i) q^{24} +24.1962i q^{25} +(4.75833 - 17.7583i) q^{26} -5.19615 q^{27} +(6.53590 + 24.3923i) q^{28} +(-19.3301 + 33.4808i) q^{29} +(-1.90192 + 1.09808i) q^{30} +(25.4641 - 25.4641i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-8.19615 + 30.5885i) q^{33} +(-17.5359 - 17.5359i) q^{34} +(-5.66025 - 9.80385i) q^{35} +(5.19615 + 3.00000i) q^{36} +(2.96410 - 0.794229i) q^{37} -23.7128i q^{38} +(19.5000 - 11.2583i) q^{39} +2.53590 q^{40} +(7.91858 + 29.5526i) q^{41} +(-15.4641 + 26.7846i) q^{42} +(-15.3731 + 8.87564i) q^{43} +(25.8564 - 25.8564i) q^{44} +(-2.59808 - 0.696152i) q^{45} +(7.85641 - 29.3205i) q^{46} +(-30.0000 - 30.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-95.6314 - 55.2128i) q^{49} +(33.0526 - 8.85641i) q^{50} -30.3731i q^{51} -26.0000 q^{52} -23.1051 q^{53} +(1.90192 + 7.09808i) q^{54} +(-8.19615 + 14.1962i) q^{55} +(30.9282 - 17.8564i) q^{56} +(20.5359 - 20.5359i) q^{57} +(52.8109 + 14.1506i) q^{58} +(5.50258 - 20.5359i) q^{59} +(2.19615 + 2.19615i) q^{60} +(21.1077 + 36.5596i) q^{61} +(-44.1051 - 25.4641i) q^{62} +(-36.5885 + 9.80385i) q^{63} +8.00000i q^{64} +(11.2583 - 3.01666i) q^{65} +44.7846 q^{66} +(-8.48334 - 31.6603i) q^{67} +(-17.5359 + 30.3731i) q^{68} +(32.1962 - 18.5885i) q^{69} +(-11.3205 + 11.3205i) q^{70} +(33.1244 + 8.87564i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-15.9212 - 15.9212i) q^{73} +(-2.16987 - 3.75833i) q^{74} +(36.2942 + 20.9545i) q^{75} +(-32.3923 + 8.67949i) q^{76} +230.851i q^{77} +(-22.5167 - 22.5167i) q^{78} -89.5692 q^{79} +(-0.928203 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(37.4711 - 21.6340i) q^{82} +(97.4256 - 97.4256i) q^{83} +(42.2487 + 11.3205i) q^{84} +(4.06922 - 15.1865i) q^{85} +(17.7513 + 17.7513i) q^{86} +(33.4808 + 57.9904i) q^{87} +(-44.7846 - 25.8564i) q^{88} +(1.22243 - 0.327550i) q^{89} +3.80385i q^{90} +(116.067 - 116.067i) q^{91} -42.9282 q^{92} +(-16.1436 - 60.2487i) q^{93} +(-30.0000 + 51.9615i) q^{94} +(13.0192 - 7.51666i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-49.3660 - 13.2276i) q^{97} +(-40.4186 + 150.844i) q^{98} +(38.7846 + 38.7846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9} + 6 q^{10} - 36 q^{11} - 16 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} - 12 q^{18} + 44 q^{19} + 12 q^{20} - 48 q^{21} + 24 q^{22} + 12 q^{23} + 12 q^{24} - 26 q^{26} + 40 q^{28} - 60 q^{29} - 18 q^{30} + 88 q^{31} - 8 q^{32} - 12 q^{33} - 84 q^{34} + 12 q^{35} - 2 q^{37} + 78 q^{39} + 24 q^{40} - 48 q^{41} - 48 q^{42} + 84 q^{43} + 48 q^{44} - 24 q^{46} - 120 q^{47} - 192 q^{49} + 56 q^{50} - 104 q^{52} + 60 q^{53} + 18 q^{54} - 12 q^{55} + 96 q^{56} + 96 q^{57} + 90 q^{58} + 216 q^{59} - 12 q^{60} + 126 q^{61} - 24 q^{62} - 84 q^{63} + 96 q^{66} - 124 q^{67} - 84 q^{68} + 108 q^{69} + 24 q^{70} + 84 q^{71} - 12 q^{72} - 178 q^{73} - 26 q^{74} + 114 q^{75} - 88 q^{76} - 192 q^{79} + 24 q^{80} - 18 q^{81} - 6 q^{82} + 168 q^{83} + 72 q^{84} - 150 q^{85} + 168 q^{86} + 30 q^{87} - 96 q^{88} - 54 q^{89} + 104 q^{91} - 144 q^{92} - 120 q^{93} - 120 q^{94} + 156 q^{95} - 194 q^{97} - 82 q^{98} + 72 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 + 6 * q^10 - 36 * q^11 - 16 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 - 12 * q^18 + 44 * q^19 + 12 * q^20 - 48 * q^21 + 24 * q^22 + 12 * q^23 + 12 * q^24 - 26 * q^26 + 40 * q^28 - 60 * q^29 - 18 * q^30 + 88 * q^31 - 8 * q^32 - 12 * q^33 - 84 * q^34 + 12 * q^35 - 2 * q^37 + 78 * q^39 + 24 * q^40 - 48 * q^41 - 48 * q^42 + 84 * q^43 + 48 * q^44 - 24 * q^46 - 120 * q^47 - 192 * q^49 + 56 * q^50 - 104 * q^52 + 60 * q^53 + 18 * q^54 - 12 * q^55 + 96 * q^56 + 96 * q^57 + 90 * q^58 + 216 * q^59 - 12 * q^60 + 126 * q^61 - 24 * q^62 - 84 * q^63 + 96 * q^66 - 124 * q^67 - 84 * q^68 + 108 * q^69 + 24 * q^70 + 84 * q^71 - 12 * q^72 - 178 * q^73 - 26 * q^74 + 114 * q^75 - 88 * q^76 - 192 * q^79 + 24 * q^80 - 18 * q^81 - 6 * q^82 + 168 * q^83 + 72 * q^84 - 150 * q^85 + 168 * q^86 + 30 * q^87 - 96 * q^88 - 54 * q^89 + 104 * q^91 - 144 * q^92 - 120 * q^93 - 120 * q^94 + 156 * q^95 - 194 * q^97 - 82 * q^98 + 72 * q^99

Introduction

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