LMFDB - Embedded newform 78.3.l.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.633975 + 0.633975i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(3.26795 + 12.1962i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	0.633975	+	0.633975i	0.126795	+	0.126795i	0.767656	−	0.640862i	$-0.221423\pi$
$5$	0.633975	+	0.633975i	0.126795	+	0.126795i	−0.640862	+	0.767656i	$0.721423\pi$
$6$	−2.36603	+	0.633975i	−0.394338	+	0.105662i
$7$	3.26795	+	12.1962i	0.466850	+	1.74231i	0.650682	+	0.759350i	$0.274483\pi$
$7$	3.26795	+	12.1962i	0.466850	+	1.74231i	−0.183833	+	0.982958i	$0.558850\pi$
$8$	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	−0.658787	−	0.752330i	$-0.728930\pi$
$11$	−17.6603	−	4.73205i	−1.60548	−	0.430186i	−0.946691	+	0.322143i	$0.895597\pi$
$12$		−	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	0.875029	−	0.484071i	$-0.160842\pi$
$17$	15.1865	+	8.76795i	0.893325	+	0.515762i	0.0182967	+	0.999833i	$0.494176\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	16.1962	−	4.33975i	0.852429	−	0.228408i	0.193954	−	0.981011i	$-0.437869\pi$
$19$	16.1962	−	4.33975i	0.852429	−	0.228408i	0.658475	+	0.752603i	$0.271202\pi$
$20$	−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	−0.0381345	−	0.999273i	$-0.512142\pi$
$23$	18.5885	−	10.7321i	0.808194	−	0.466611i	0.846328	+	0.532662i	$0.178808\pi$
$24$	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	−0.978861	−	0.204527i	$-0.934434\pi$
$29$	−19.3301	−	33.4808i	−0.666556	−	1.15451i	0.312305	−	0.949982i	$-0.398899\pi$
$30$	−1.90192	−	1.09808i	−0.0633975	−	0.0366025i
$31$	25.4641	+	25.4641i	0.821423	+	0.821423i	0.986312	−	0.164889i	$-0.0527267\pi$
$31$	25.4641	+	25.4641i	0.821423	+	0.821423i	−0.164889	+	0.986312i	$0.552727\pi$
$32$	−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	0.298652	−	0.954362i	$-0.403463\pi$
$37$	2.96410	+	0.794229i	0.0801109	+	0.0214656i	−0.218541	+	0.975828i	$0.570130\pi$
$38$			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	−0.799605	−	0.600526i	$-0.794958\pi$
$41$	7.91858	−	29.5526i	0.193136	−	0.720794i	0.992741	−	0.120268i	$-0.0383754\pi$
$42$	−15.4641	−	26.7846i	−0.368193	−	0.637729i
$43$	−15.3731	−	8.87564i	−0.357513	−	0.206410i	0.310476	−	0.950581i	$-0.399512\pi$
$43$	−15.3731	−	8.87564i	−0.357513	−	0.206410i	−0.667989	+	0.744171i	$0.732845\pi$
$44$	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	−0.950135	−	0.311838i	$-0.899056\pi$
$47$	−30.0000	+	30.0000i	−0.638298	+	0.638298i	0.311838	+	0.950135i	$0.399056\pi$
$48$	−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	0.996751	−	0.0805505i	$-0.0256678\pi$
$59$	5.50258	+	20.5359i	0.0932640	+	0.348066i	−0.903487	+	0.428617i	$0.859001\pi$
$60$	2.19615	−	2.19615i	0.0366025	−	0.0366025i
$61$	21.1077	−	36.5596i	0.346028	−	0.599338i	−0.639512	−	0.768781i	$-0.720864\pi$
$61$	21.1077	−	36.5596i	0.346028	−	0.599338i	0.985540	+	0.169443i	$0.0541970\pi$
$62$	−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	−0.999892	−	0.0146863i	$-0.995325\pi$
$67$	−8.48334	+	31.6603i	−0.126617	+	0.472541i	0.873275	+	0.487227i	$0.161992\pi$
$68$	−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	−0.0178882	−	0.999840i	$-0.505694\pi$
$71$	33.1244	−	8.87564i	0.466540	−	0.125009i	0.484428	+	0.874831i	$0.339028\pi$
$72$	2.19615	+	8.19615i	0.0305021	+	0.113835i
$73$	−15.9212	+	15.9212i	−0.218098	+	0.218098i	−0.807697	−	0.589598i	$-0.799286\pi$
$73$	−15.9212	+	15.9212i	−0.218098	+	0.218098i	0.589598	+	0.807697i	$0.299286\pi$
$74$	−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	0.981296	+	0.192507i	$0.0616619\pi$
$83$	97.4256	+	97.4256i	1.17380	+	1.17380i	0.192507	+	0.981296i	$0.438338\pi$
$84$	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	0.265680	−	0.964061i	$-0.414404\pi$
$89$	1.22243	+	0.327550i	0.0137352	+	0.00368033i	−0.251945	+	0.967742i	$0.581070\pi$
$90$		−	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	−0.504140	−	0.863622i	$-0.668191\pi$
$97$	−49.3660	+	13.2276i	−0.508928	+	0.136367i	−0.00478762	+	0.999989i	$0.501524\pi$
$98$	−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	−0.343806	−	0.939041i	$-0.611716\pi$
$101$	30.0500	−	17.3494i	0.297525	−	0.171776i	0.641330	+	0.767265i	$0.278383\pi$
$102$	−41.4904	−	11.1173i	−0.406768	−	0.108993i
$103$		−	196.890i		−	1.91155i	−0.294098	−	0.955775i	$-0.595019\pi$
$103$		−	196.890i		−	1.91155i	0.294098	−	0.955775i	$-0.404981\pi$
$104$	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	0.769020	−	0.639225i	$-0.220745\pi$
$107$	−18.0910	−	31.3346i	−0.169075	−	0.292847i	−0.938095	+	0.346378i	$0.887411\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−127.497	−	127.497i	−1.16970	−	1.16970i	−0.982280	−	0.187422i	$-0.939987\pi$
$109$	−127.497	−	127.497i	−1.16970	−	1.16970i	−0.187422	−	0.982280i	$-0.560013\pi$
$110$	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	−0.986264	−	0.165177i	$-0.947181\pi$
$113$	−39.5596	+	68.5192i	−0.350085	+	0.606365i	0.636179	+	0.771541i	$0.280514\pi$
$114$	−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	−0.192200	−	0.981356i	$-0.561562\pi$
$127$	71.3205	−	41.1769i	0.561579	−	0.324228i	0.753779	+	0.657128i	$0.228229\pi$
$128$	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	0.913864	+	0.406020i	$0.133084\pi$
$137$	44.5859	+	166.397i	0.325444	+	1.21457i	−0.588420	+	0.808555i	$0.700250\pi$
$138$	−37.1769	+	37.1769i	−0.269398	+	0.269398i
$139$	−6.35383	+	11.0052i	−0.0457110	+	0.0791738i	−0.887976	−	0.459890i	$-0.847889\pi$
$139$	−6.35383	+	11.0052i	−0.0457110	+	0.0791738i	0.842265	+	0.539064i	$0.181222\pi$
$140$	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	0.137210	−	0.990542i	$-0.456187\pi$
$149$	111.945	−	29.9955i	0.751308	−	0.201312i	0.614098	+	0.789230i	$0.289520\pi$
$150$	15.3397	+	57.2487i	0.102265	+	0.381658i
$151$	−118.603	+	118.603i	−0.785447	+	0.785447i	−0.980744	−	0.195297i	$-0.937433\pi$
$151$	−118.603	+	118.603i	−0.785447	+	0.785447i	0.195297	+	0.980744i	$0.437433\pi$
$152$	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	−0.675211	−	0.737624i	$-0.735948\pi$
$163$	−74.8616	−	279.387i	−0.459273	−	1.71403i	0.215938	−	0.976407i	$-0.430719\pi$
$164$	−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	−0.634545	−	0.772886i	$-0.718813\pi$
$167$	−262.277	−	70.2769i	−1.57052	−	0.420820i	−0.935975	+	0.352066i	$0.885479\pi$
$168$			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	0.206179	−	0.978514i	$-0.433897\pi$
$173$	−93.1000	−	53.7513i	−0.538150	−	0.310701i	−0.744329	+	0.667813i	$0.767230\pi$
$174$	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	−0.765526	−	0.643405i	$-0.777521\pi$
$179$	−105.804	+	61.0859i	−0.591083	+	0.341262i	0.174443	+	0.984667i	$0.444188\pi$
$180$	5.19615	+	1.39230i	0.0288675	+	0.00773503i
$181$		−	65.2872i		−	0.360703i	−0.983602	−	0.180351i	$-0.942277\pi$
$181$		−	65.2872i		−	0.360703i	0.983602	−	0.180351i	$-0.0577235\pi$
$182$	−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	−0.823244	−	0.567688i	$-0.807838\pi$
$191$	15.2820	−	26.4693i	0.0800106	−	0.138582i	0.903254	+	0.429106i	$0.141171\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−45.8468	−	12.2846i	−0.237548	−	0.0636508i	0.138081	−	0.990421i	$-0.455907\pi$
$193$	−45.8468	−	12.2846i	−0.237548	−	0.0636508i	−0.375629	+	0.926770i	$0.622573\pi$
$194$		−	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	−0.646068	−	0.763280i	$-0.723588\pi$
$197$	58.1314	−	216.949i	0.295083	−	1.10127i	0.941151	−	0.337986i	$-0.109746\pi$
$198$	38.7846	+	67.1769i	0.195882	+	0.339277i
$199$	139.583	+	80.5885i	0.701424	+	0.404967i	0.807877	−	0.589351i	$-0.200616\pi$
$199$	139.583	+	80.5885i	0.701424	+	0.404967i	−0.106454	+	0.994318i	$0.533950\pi$
$200$	−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	0.988819	−	0.149119i	$-0.0476436\pi$
$211$	77.0718	+	133.492i	0.365269	+	0.632665i	−0.623550	+	0.781783i	$0.714310\pi$
$212$	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	−0.828166	−	0.560483i	$-0.810616\pi$
$223$	37.7513	−	140.890i	0.169288	−	0.631792i	0.997454	−	0.0713095i	$-0.0227178\pi$
$224$	−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	−0.926011	−	0.377496i	$-0.876785\pi$
$227$	−349.401	+	93.6218i	−1.53921	+	0.412431i	−0.613201	+	0.789927i	$0.710119\pi$
$228$	−15.0333	−	56.1051i	−0.0659356	−	0.246075i
$229$	52.5692	−	52.5692i	0.229560	−	0.229560i	−0.582949	−	0.812509i	$-0.698101\pi$
$229$	52.5692	−	52.5692i	0.229560	−	0.229560i	0.812509	+	0.582949i	$0.198101\pi$
$230$	−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	$0.168977\pi$
$233$			235.923i			1.01255i	−0.862373	+	0.506273i	$0.831023\pi$
$234$	−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	0.302297	−	0.953214i	$-0.402247\pi$
$239$	−155.569	−	155.569i	−0.650917	−	0.650917i	−0.953214	+	0.302297i	$0.902247\pi$
$240$	−6.00000	+	1.60770i	−0.0250000	+	0.00669873i
$241$	98.8820	+	369.033i	0.410299	+	1.53126i	0.794069	+	0.607827i	$0.207959\pi$
$241$	98.8820	+	369.033i	0.410299	+	1.53126i	−0.383771	+	0.923428i	$0.625375\pi$
$242$	−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	0.367828	−	0.929894i	$-0.380102\pi$
$251$	−63.6462	−	36.7461i	−0.253570	−	0.146399i	−0.621398	+	0.783495i	$0.713435\pi$
$252$	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	0.561624	−	0.827392i	$-0.310177\pi$
$257$	400.658	−	231.320i	1.55898	−	0.900077i	0.997355	−	0.0726847i	$-0.0231567\pi$
$258$	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	0.739069	+	0.673630i	$0.235266\pi$
$263$	250.617	+	434.081i	0.952915	+	1.65050i	0.213846	+	0.976867i	$0.431401\pi$
$264$	−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	−0.828038	−	0.560672i	$-0.810543\pi$
$269$	19.2436	−	33.3308i	0.0715374	−	0.123906i	0.899575	+	0.436766i	$0.143876\pi$
$270$	5.70577	−	3.29423i	0.0211325	−	0.0122008i
$271$	−192.028	−	51.4538i	−0.708591	−	0.189866i	−0.113516	−	0.993536i	$-0.536211\pi$
$271$	−192.028	−	51.4538i	−0.708591	−	0.189866i	−0.595075	+	0.803670i	$0.702878\pi$
$272$			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	0.413300	−	0.910595i	$-0.364376\pi$
$277$	−46.7154	−	26.9711i	−0.168648	−	0.0973687i	−0.581948	+	0.813226i	$0.697709\pi$
$278$	−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	−0.330959	−	0.943645i	$-0.607372\pi$
$281$	172.165	−	172.165i	0.612686	−	0.612686i	0.943645	+	0.330959i	$0.107372\pi$
$282$	51.9615	−	90.0000i	0.184261	−	0.319149i
$283$	−433.086	+	250.042i	−1.53034	+	0.883542i	−0.530993	+	0.847376i	$0.678181\pi$
$283$	−433.086	+	250.042i	−1.53034	+	0.883542i	−0.999346	+	0.0361653i	$0.988486\pi$
$284$	−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	0.999595	−	0.0284731i	$-0.00906449\pi$
$293$	35.0673	+	130.873i	0.119684	+	0.446666i	−0.879911	+	0.475139i	$0.842398\pi$
$294$	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	−0.557573	−	0.830128i	$-0.688267\pi$
$307$	83.6743	−	83.6743i	0.272555	−	0.272555i	0.830128	+	0.557573i	$0.188267\pi$
$308$	−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	$-0.907177\pi$
$311$		−	178.823i		−	0.574994i	0.957782	−	0.287497i	$-0.0928231\pi$
$312$	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	0.957348	−	0.288937i	$-0.0933017\pi$
$317$	211.886	+	211.886i	0.668412	+	0.668412i	−0.288937	+	0.957348i	$0.593302\pi$
$318$	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	−0.400429	−	0.916328i	$-0.631139\pi$
$331$	−95.6743	+	25.6359i	−0.289046	+	0.0774497i	0.111382	+	0.993778i	$0.464472\pi$
$332$	−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	$0.0250926\pi$
$337$			53.0770i			0.157498i	−0.996894	+	0.0787492i	$0.974907\pi$
$338$	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	0.286047	−	0.958216i	$-0.407659\pi$
$347$	337.583	−	584.711i	0.972863	−	1.68505i	0.686816	−	0.726832i	$-0.259008\pi$
$348$	−115.981	+	66.9615i	−0.333278	+	0.192418i
$349$	572.154	+	153.308i	1.63941	+	0.439279i	0.956621	−	0.291336i	$-0.0940997\pi$
$349$	572.154	+	153.308i	1.63941	+	0.439279i	0.682790	+	0.730615i	$0.260766\pi$
$350$			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	−0.908333	−	0.418247i	$-0.862645\pi$
$353$	30.8628	−	115.181i	0.0874299	−	0.326293i	0.995763	+	0.0919541i	$0.0293113\pi$
$354$	−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	−0.0468219	+	0.998903i	$0.514909\pi$
$359$	−375.415	+	375.415i	−1.04573	+	1.04573i	−0.998903	+	0.0468219i	$0.985091\pi$
$360$	−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	0.973428	−	0.228995i	$-0.0735438\pi$
$367$	105.842	+	183.324i	0.288399	+	0.499521i	−0.685029	+	0.728516i	$0.740210\pi$
$368$	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	−0.818053	−	0.575142i	$-0.804947\pi$
$373$	33.2199	−	57.5385i	0.0890613	−	0.154259i	0.907115	+	0.420884i	$0.138280\pi$
$374$	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	−0.892751	−	0.450551i	$-0.851228\pi$
$379$	40.0488	−	149.464i	0.105670	−	0.394364i	0.998420	+	0.0561867i	$0.0178942\pi$
$380$	−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	−0.716386	−	0.697704i	$-0.754205\pi$
$383$	−378.382	+	101.387i	−0.987943	+	0.264718i	−0.271556	+	0.962423i	$0.587538\pi$
$384$	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	$0.280220\pi$
$389$			599.802i			1.54191i	−0.636890	+	0.770954i	$0.719780\pi$
$390$	−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	−0.887682	−	0.460457i	$-0.847685\pi$
$397$	−138.615	−	517.317i	−0.349156	−	1.30307i	0.538526	−	0.842609i	$-0.318981\pi$
$398$	−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	−0.306117	−	0.951994i	$-0.599030\pi$
$401$	−419.935	−	112.521i	−1.04722	−	0.280601i	−0.741102	+	0.671393i	$0.765696\pi$
$402$		−	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	−0.952891	−	0.303312i	$-0.901908\pi$
$409$	−665.224	+	178.246i	−1.62646	+	0.435810i	−0.673572	+	0.739121i	$0.735241\pi$
$410$	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	0.985112	−	0.171913i	$-0.0549947\pi$
$419$	144.000	+	249.415i	0.343675	+	0.595263i	−0.641437	+	0.767176i	$0.721661\pi$
$420$	33.9615	+	19.6077i	0.0808608	+	0.0466850i
$421$	87.8930	+	87.8930i	0.208772	+	0.208772i	0.803745	−	0.594973i	$-0.202837\pi$
$421$	87.8930	+	87.8930i	0.208772	+	0.208772i	−0.594973	+	0.803745i	$0.702837\pi$
$422$	−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	−0.970612	−	0.240651i	$-0.922639\pi$
$431$	−4.18584	+	15.6218i	−0.00971193	+	0.0362454i	0.960900	+	0.276896i	$0.0893058\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	307.782	+	177.698i	0.710813	+	0.410388i	0.811362	−	0.584544i	$-0.198727\pi$
$433$	307.782	+	177.698i	0.710813	+	0.410388i	−0.100549	+	0.994932i	$0.532060\pi$
$434$	−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	−0.281541	−	0.959549i	$-0.590846\pi$
$439$	179.412	−	103.583i	0.408682	−	0.235953i	0.690223	+	0.723596i	$0.257512\pi$
$440$	−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	0.933075	+	0.359683i	$0.117115\pi$
$449$	136.878	+	510.834i	0.304850	+	1.13771i	−0.628225	+	0.778032i	$0.716218\pi$
$450$	−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	−0.936250	−	0.351336i	$-0.885728\pi$
$457$	22.9571	−	85.6769i	0.0502343	−	0.187477i	0.986484	+	0.163859i	$0.0523942\pi$
$458$	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	−0.175672	−	0.984449i	$-0.556210\pi$
$461$	75.7961	−	20.3095i	0.164417	−	0.0440553i	0.340088	+	0.940393i	$0.389543\pi$
$462$	146.354	+	546.200i	0.316783	+	1.18225i
$463$	−264.908	+	264.908i	−0.572155	+	0.572155i	−0.932730	−	0.360575i	$-0.882580\pi$
$463$	−264.908	+	264.908i	−0.572155	+	0.572155i	0.360575	+	0.932730i	$0.382580\pi$
$464$	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	$0.115896\pi$
$467$			332.603i			0.712211i	−0.934446	+	0.356106i	$0.884104\pi$
$468$	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	−0.501632	−	0.865081i	$-0.667267\pi$
$479$	−655.559	−	175.656i	−1.36860	−	0.366715i	−0.866967	+	0.498366i	$0.833934\pi$
$480$		−	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	0.337384	−	0.941367i	$-0.390458\pi$
$487$	535.822	−	143.573i	1.10025	−	0.294811i	0.762866	+	0.646556i	$0.223791\pi$
$488$	−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	−0.914430	−	0.404744i	$-0.867361\pi$
$491$	−501.373	+	289.468i	−1.02113	+	0.589548i	−0.106696	+	0.994292i	$0.534027\pi$
$492$	−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	0.746348	−	0.665556i	$-0.231805\pi$
$499$	40.3154	+	40.3154i	0.0807923	+	0.0807923i	−0.665556	+	0.746348i	$0.731805\pi$
$500$	−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	−0.624946	−	0.780668i	$-0.714879\pi$
$503$	182.894	−	316.781i	0.363605	−	0.629783i	0.988551	+	0.150885i	$0.0482123\pi$
$504$	−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	0.529675	+	0.848200i	$0.322314\pi$
$509$	−179.747	+	670.824i	−0.353137	+	1.31793i	−0.882813	+	0.469725i	$0.844353\pi$
$510$	−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	0.835219	−	0.549918i	$-0.185341\pi$
$523$	−30.6654	−	53.1140i	−0.0586337	−	0.101556i	−0.893852	+	0.448362i	$0.852008\pi$
$524$	−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	−0.945052	−	0.326920i	$-0.893989\pi$
$541$	−334.410	+	334.410i	−0.618132	+	0.618132i	0.326920	+	0.945052i	$0.393989\pi$
$542$	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	0.595796	−	0.803136i	$-0.296837\pi$
$557$	395.583	+	105.996i	0.710202	+	0.190298i	0.114406	+	0.993434i	$0.463503\pi$
$558$		−	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	0.526406	−	0.850233i	$-0.323539\pi$
$563$	30.0000	+	17.3205i	0.0532860	+	0.0307647i	−0.473120	+	0.880998i	$0.656872\pi$
$564$	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	−0.698320	−	0.715785i	$-0.746069\pi$
$569$	−243.300	+	140.469i	−0.427592	+	0.246870i	0.270728	+	0.962656i	$0.412736\pi$
$570$	−35.5692	−	9.53074i	−0.0624021	−	0.0167206i
$571$			978.823i			1.71423i	0.515128	+	0.857113i	$0.327744\pi$
$571$			978.823i			1.71423i	−0.515128	+	0.857113i	$0.672256\pi$
$572$	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	0.926410	−	0.376516i	$-0.122878\pi$
$577$	317.289	+	317.289i	0.549894	+	0.549894i	−0.376516	+	0.926410i	$0.622878\pi$
$578$	−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	−0.704484	−	0.709720i	$-0.748821\pi$
$587$	152.900	−	570.631i	0.260477	−	0.972114i	0.964961	−	0.262394i	$-0.0845119\pi$
$588$	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	−0.979346	−	0.202191i	$-0.935194\pi$
$593$	−460.853	+	460.853i	−0.777155	+	0.777155i	0.202191	+	0.979346i	$0.435194\pi$
$594$	−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	0.608429	−	0.793608i	$-0.291800\pi$
$601$	−230.225	−	398.761i	−0.383070	−	0.663497i	−0.991499	+	0.130111i	$0.958466\pi$
$602$	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	−0.849114	−	0.528209i	$-0.822864\pi$
$607$	19.9615	−	34.5744i	0.0328855	−	0.0569594i	0.882000	+	0.471250i	$0.156197\pi$
$608$	−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	−0.790186	−	0.612867i	$-0.790016\pi$
$613$	122.949	−	458.851i	0.200569	−	0.748533i	0.990755	−	0.135666i	$-0.0433173\pi$
$614$	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	0.256336	−	0.966588i	$-0.417485\pi$
$617$	593.322	−	158.980i	0.961624	−	0.257666i	0.705287	+	0.708921i	$0.250818\pi$
$618$	124.823	+	465.846i	0.201979	+	0.753796i
$619$	−417.520	+	417.520i	−0.674508	+	0.674508i	−0.958752	−	0.284244i	$-0.908257\pi$
$619$	−417.520	+	417.520i	−0.674508	+	0.674508i	0.284244	+	0.958752i	$0.408257\pi$
$620$	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	0.921387	−	0.388646i	$-0.127057\pi$
$631$	−44.7255	−	166.918i	−0.0708804	−	0.264529i	−0.992268	+	0.124117i	$0.960390\pi$
$632$	−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	0.192711	−	0.981256i	$-0.438272\pi$
$641$	−359.425	−	207.514i	−0.560725	−	0.323735i	−0.753437	+	0.657521i	$0.771605\pi$
$642$	62.6692	+	62.6692i	0.0976155	+	0.0976155i
$643$	−345.023	+	92.4486i	−0.536583	+	0.143777i	−0.516927	−	0.856030i	$-0.672924\pi$
$643$	−345.023	+	92.4486i	−0.536583	+	0.143777i	−0.0196567	+	0.999807i	$0.506257\pi$
$644$	−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	−0.836541	−	0.547905i	$-0.815426\pi$
$647$	−504.862	+	291.482i	−0.780312	+	0.450513i	0.0562291	+	0.998418i	$0.482092\pi$
$648$	−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	0.692154	−	0.721750i	$-0.256662\pi$
$653$	−182.172	−	315.531i	−0.278977	−	0.483202i	−0.971131	+	0.238548i	$0.923329\pi$
$654$	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	0.0308117	−	0.999525i	$-0.490191\pi$
$659$	580.592	−	1005.62i	0.881020	−	1.52597i	0.850208	−	0.526446i	$-0.176476\pi$
$660$	−49.1769	+	28.3923i	−0.0745105	+	0.0430186i
$661$	274.738	+	73.6159i	0.415641	+	0.111371i	0.460578	−	0.887619i	$-0.347642\pi$
$661$	274.738	+	73.6159i	0.415641	+	0.111371i	−0.0449374	+	0.998990i	$0.514309\pi$
$662$		−	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	−0.955162	−	0.296085i	$-0.904319\pi$
$673$	−791.667	+	457.069i	−1.17633	+	0.679152i	−0.221164	+	0.975237i	$0.570986\pi$
$674$	−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	−0.930309	−	0.366777i	$-0.880461\pi$
$683$	−210.382	−	785.156i	−0.308026	−	1.14957i	0.622282	−	0.782793i	$-0.286206\pi$
$684$	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	−0.997239	−	0.0742560i	$-0.976342\pi$
$691$	−66.6654	+	248.799i	−0.0964767	+	0.360056i	0.900762	+	0.434312i	$0.143008\pi$
$692$	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	$-0.683684\pi$
$701$		−	1174.97i		−	1.67614i	0.545563	−	0.838070i	$-0.316316\pi$
$702$	−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	0.967200	+	0.254014i	$0.0817510\pi$
$709$	181.920	+	678.936i	0.256587	+	0.957597i	−0.710613	+	0.703583i	$0.751582\pi$
$710$	−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	0.0143368	−	0.999897i	$-0.495436\pi$
$719$	−607.146	−	350.536i	−0.844431	−	0.487533i	−0.858768	+	0.512365i	$0.828770\pi$
$720$	−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	$-0.937265\pi$
$727$		−	284.715i		−	0.391630i	0.980641	−	0.195815i	$-0.0627353\pi$
$728$	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	0.992841	+	0.119447i	$0.0381122\pi$
$733$	815.307	+	815.307i	1.11229	+	1.11229i	0.119447	+	0.992841i	$0.461888\pi$
$734$	−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	−0.596745	−	0.802431i	$-0.703540\pi$
$739$	−1119.41	−	299.944i	−1.51476	−	0.405878i	−0.918012	+	0.396553i	$0.870206\pi$
$740$		−	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	−0.966701	−	0.255907i	$-0.917626\pi$
$743$	−1.15906	+	4.32566i	−0.00155997	+	0.00582189i	0.965141	+	0.261729i	$0.0842926\pi$
$744$	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	−0.00246040	−	0.999997i	$-0.500783\pi$
$751$	647.611	−	373.899i	0.862332	−	0.497868i	0.864793	+	0.502129i	$0.167450\pi$
$752$	−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	0.987223	+	0.159346i	$0.0509386\pi$
$757$	478.128	+	828.142i	0.631609	+	1.09398i	−0.355614	+	0.934633i	$0.615728\pi$
$758$	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	0.985511	+	0.169611i	$0.0542513\pi$
$761$	165.015	+	615.843i	0.216839	+	0.809255i	−0.768672	+	0.639643i	$0.779082\pi$
$762$	−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	−0.708184	−	0.706028i	$-0.750485\pi$
$769$	198.506	−	740.834i	0.258135	−	0.963373i	0.966319	−	0.257346i	$-0.0828479\pi$
$770$	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	−0.562131	−	0.827049i	$-0.690018\pi$
$773$	−491.184	+	131.612i	−0.635426	+	0.170262i	−0.0732950	+	0.997310i	$0.523351\pi$
$774$	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	0.957559	−	0.288239i	$-0.0930697\pi$
$787$	−12.4589	−	46.4974i	−0.0158309	−	0.0590819i	−0.973389	+	0.229157i	$0.926403\pi$
$788$	−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	0.950341	−	0.311212i	$-0.100735\pi$
$797$	921.327	+	531.928i	1.15599	+	0.667413i	0.205653	+	0.978625i	$0.434068\pi$
$798$	−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	0.999624	−	0.0274045i	$-0.00872423\pi$
$809$	385.148	+	667.096i	0.476079	+	0.824593i	−0.523545	+	0.851998i	$0.675391\pi$
$810$	9.88269	+	5.70577i	0.0122008	+	0.00704416i
$811$	448.420	+	448.420i	0.552923	+	0.552923i	0.927283	−	0.374360i	$-0.122138\pi$
$811$	448.420	+	448.420i	0.552923	+	0.552923i	−0.374360	+	0.927283i	$0.622138\pi$
$812$	−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	−0.862067	−	0.506794i	$-0.830831\pi$
$821$	113.217	−	422.533i	0.137902	−	0.514656i	0.999969	−	0.00786244i	$-0.00250272\pi$
$822$	−210.983	−	365.433i	−0.256670	−	0.444565i
$823$	856.361	+	494.420i	1.04054	+	0.600754i	0.919985	−	0.391953i	$-0.128200\pi$
$823$	856.361	+	494.420i	1.04054	+	0.600754i	0.120551	+	0.992707i	$0.461534\pi$
$824$	−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	−0.785469	−	0.618901i	$-0.787578\pi$
$827$	−137.751	+	137.751i	−0.166567	+	0.166567i	0.618901	+	0.785469i	$0.287578\pi$
$828$	64.3923	−	111.531i	0.0777685	−	0.134699i
$829$	−381.028	+	219.987i	−0.459624	+	0.265364i	−0.711886	−	0.702295i	$-0.752159\pi$
$829$	−381.028	+	219.987i	−0.459624	+	0.265364i	0.252262	+	0.967659i	$0.418825\pi$
$830$	−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	0.921805	−	0.387653i	$-0.126714\pi$
$839$	−59.0052	−	220.210i	−0.0703280	−	0.262468i	−0.992133	+	0.125185i	$0.960047\pi$
$840$	−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	−0.829441	−	0.558595i	$-0.811341\pi$
$853$	−231.031	+	231.031i	−0.270846	+	0.270846i	0.558595	+	0.829441i	$0.311341\pi$
$854$	−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	$0.0529428\pi$
$857$			283.768i			0.331118i	−0.986200	+	0.165559i	$0.947057\pi$
$858$	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	0.964554	−	0.263886i	$-0.0850042\pi$
$863$	604.677	+	604.677i	0.700668	+	0.700668i	−0.263886	+	0.964554i	$0.585004\pi$
$864$	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	−0.486084	−	0.873912i	$-0.661575\pi$
$877$	−412.267	+	110.467i	−0.470088	+	0.125960i	0.0159955	+	0.999872i	$0.494908\pi$
$878$	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	−0.586854	−	0.809693i	$-0.699634\pi$
$881$	−157.758	+	91.0814i	−0.179067	+	0.103384i	0.407787	+	0.913077i	$0.366300\pi$
$882$	452.533	+	121.256i	0.513076	+	0.137478i
$883$			1334.37i			1.51118i	0.655047	+	0.755588i	$0.272649\pi$
$883$			1334.37i			1.51118i	−0.655047	+	0.755588i	$0.727351\pi$
$884$	−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	0.574533	−	0.818481i	$-0.305184\pi$
$887$	−373.923	−	647.654i	−0.421559	−	0.730162i	−0.996092	+	0.0883194i	$0.971850\pi$
$888$	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	−0.0253838	−	0.999678i	$-0.508081\pi$
$907$	750.697	−	433.415i	0.827671	−	0.477856i	0.853054	+	0.521822i	$0.174747\pi$
$908$	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	−0.534038	−	0.845460i	$-0.679326\pi$
$919$	427.492	−	740.438i	0.465171	−	0.805700i	0.999209	+	0.0397604i	$0.0126595\pi$
$920$	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	−0.162346	−	0.986734i	$-0.551906\pi$
$929$	176.905	−	47.4014i	0.190425	−	0.0510241i	0.352771	+	0.935710i	$0.385239\pi$
$930$	−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	0.209465	−	0.977816i	$-0.432828\pi$
$941$	−723.018	−	723.018i	−0.768351	−	0.768351i	−0.977816	+	0.209465i	$0.932828\pi$
$942$	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	0.0794386	−	0.996840i	$-0.474687\pi$
$947$	−331.626	−	88.8588i	−0.350185	−	0.0938319i	−0.429624	+	0.903008i	$0.641354\pi$
$948$			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	0.987472	+	0.157795i	$0.0504385\pi$
$953$	1541.82	+	890.172i	1.61786	+	0.934073i	0.630390	+	0.776278i	$0.282895\pi$
$954$	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	0.426227	−	0.904616i	$-0.359843\pi$
$967$	−462.603	−	462.603i	−0.478389	−	0.478389i	−0.904616	+	0.426227i	$0.859843\pi$
$968$	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	−0.966697	−	0.255923i	$-0.917621\pi$
$971$	−254.123	+	440.154i	−0.261713	+	0.453300i	0.704984	+	0.709223i	$0.250954\pi$
$972$	−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	−0.251638	−	0.967821i	$-0.580969\pi$
$977$	439.843	−	1641.52i	0.450198	−	1.68016i	0.701836	−	0.712339i	$-0.252364\pi$
$978$	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	−0.0605783	−	0.998163i	$-0.519294\pi$
$983$	921.646	−	921.646i	0.937585	−	0.937585i	0.998163	+	0.0605783i	$0.0192945\pi$
$984$	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	−0.927575	−	0.373637i	$-0.878110\pi$
$991$	−780.281	−	1351.49i	−0.787367	−	1.36376i	0.140208	−	0.990122i	$-0.455223\pi$
$992$	−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	−0.987525	−	0.157463i	$-0.949668\pi$
$997$	−356.323	+	617.170i	−0.357395	+	0.619027i	0.630130	+	0.776490i	$0.283002\pi$
$998$	−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.37.1	yes	4
3.2	odd	2		234.3.bb.a.37.1		4
13.2	odd	12		1014.3.f.b.577.1		4
13.3	even	3		1014.3.f.b.775.1		4
13.6	odd	12	inner	78.3.l.b.19.1	✓	4
13.10	even	6		1014.3.f.g.775.1		4
13.11	odd	12		1014.3.f.g.577.1		4
39.32	even	12		234.3.bb.a.19.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.b.19.1	✓	4	13.6	odd	12	inner
78.3.l.b.37.1	yes	4	1.1	even	1	trivial
234.3.bb.a.19.1		4	39.32	even	12
234.3.bb.a.37.1		4	3.2	odd	2
1014.3.f.b.577.1		4	13.2	odd	12
1014.3.f.b.775.1		4	13.3	even	3
1014.3.f.g.577.1		4	13.11	odd	12
1014.3.f.g.775.1		4	13.10	even	6

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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