LMFDB - Embedded newform 78.3.j.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(17,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("78.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2 x^{18} - 12 x^{17} - 51 x^{16} - 180 x^{15} + 1136 x^{14} + 144 x^{13} + 6481 x^{12} + \cdots + 3486784401 $ x^20 + 2x^18 - 12x^17 - 51x^16 - 180x^15 + 1136x^14 + 144x^13 + 6481x^12 - 16152x^11 - 55134x^10 - 145368x^9 + 524961x^8 + 104976x^7 + 7453296x^6 - 10628820x^5 - 27103491x^4 - 57395628x^3 + 86093442*x^2 + 3486784401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$0.410263 - 2.97181i$ of defining polynomial
Character	$\chi$	$=$	78.17
Dual form			78.3.j.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-0.410263 + 2.97181i) q^{3} +(-1.00000 - 1.73205i) q^{4} -9.12568 q^{5} +(-3.34962 - 2.60386i) q^{6} +(3.75604 - 2.16855i) q^{7} +2.82843 q^{8} +(-8.66337 - 2.43845i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.410263 + 2.97181i) q^{3} +(-1.00000 - 1.73205i) q^{4} -9.12568 q^{5} +(-3.34962 - 2.60386i) q^{6} +(3.75604 - 2.16855i) q^{7} +2.82843 q^{8} +(-8.66337 - 2.43845i) q^{9} +(6.45283 - 11.1766i) q^{10} +(-1.95827 + 3.39183i) q^{11} +(5.55760 - 2.26122i) q^{12} +(-1.61415 + 12.8994i) q^{13} +6.13359i q^{14} +(3.74393 - 27.1198i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-6.72177 + 3.88082i) q^{17} +(9.11241 - 8.88617i) q^{18} +(-30.6949 + 17.7217i) q^{19} +(9.12568 + 15.8061i) q^{20} +(4.90357 + 12.0519i) q^{21} +(-2.76942 - 4.79677i) q^{22} +(16.6520 + 9.61401i) q^{23} +(-1.16040 + 8.40556i) q^{24} +58.2780 q^{25} +(-14.6571 - 11.0982i) q^{26} +(10.8009 - 24.7455i) q^{27} +(-7.51208 - 4.33710i) q^{28} +(32.4049 + 18.7090i) q^{29} +(30.5675 + 23.7620i) q^{30} +1.27633i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.27648 - 7.21117i) q^{33} -10.9766i q^{34} +(-34.2764 + 19.7895i) q^{35} +(4.43985 + 17.4438i) q^{36} +(-15.0241 - 8.67414i) q^{37} -50.1245i q^{38} +(-37.6724 - 10.0891i) q^{39} -25.8113 q^{40} +(9.91090 - 17.1662i) q^{41} +(-18.2279 - 2.51638i) q^{42} +(-14.5164 - 25.1432i) q^{43} +7.83309 q^{44} +(79.0591 + 22.2525i) q^{45} +(-23.5494 + 13.5963i) q^{46} -18.7295 q^{47} +(-9.47414 - 7.36482i) q^{48} +(-15.0948 + 26.1449i) q^{49} +(-41.2088 + 71.3757i) q^{50} +(-8.77537 - 21.5680i) q^{51} +(23.9566 - 10.1036i) q^{52} +14.7174i q^{53} +(22.6696 + 30.7261i) q^{54} +(17.8706 - 30.9527i) q^{55} +(10.6237 - 6.13359i) q^{56} +(-40.0726 - 98.4901i) q^{57} +(-45.8274 + 26.4585i) q^{58} +(-34.9033 - 60.4543i) q^{59} +(-50.7168 + 20.6352i) q^{60} +(30.4453 + 52.7328i) q^{61} +(-1.56318 - 0.902503i) q^{62} +(-37.8279 + 9.62803i) q^{63} +8.00000 q^{64} +(14.7302 - 117.716i) q^{65} +(15.3913 - 6.26225i) q^{66} +(43.7994 + 25.2876i) q^{67} +(13.4435 + 7.76163i) q^{68} +(-35.4027 + 45.5422i) q^{69} -55.9731i q^{70} +(25.3645 + 43.9326i) q^{71} +(-24.5037 - 6.89698i) q^{72} -80.0631i q^{73} +(21.2472 - 12.2671i) q^{74} +(-23.9093 + 173.191i) q^{75} +(61.3898 + 35.4434i) q^{76} +16.9865i q^{77} +(38.9950 - 39.0050i) q^{78} -33.1864 q^{79} +(18.2514 - 31.6123i) q^{80} +(69.1079 + 42.2504i) q^{81} +(14.0161 + 24.2767i) q^{82} -7.74819 q^{83} +(15.9710 - 20.5452i) q^{84} +(61.3407 - 35.4151i) q^{85} +41.0587 q^{86} +(-68.8942 + 88.6258i) q^{87} +(-5.53883 + 9.59354i) q^{88} +(-41.9399 + 72.6421i) q^{89} +(-83.1569 + 81.0923i) q^{90} +(21.9102 + 51.9510i) q^{91} -38.4560i q^{92} +(-3.79302 - 0.523632i) q^{93} +(13.2438 - 22.9389i) q^{94} +(280.112 - 161.723i) q^{95} +(15.7193 - 6.39569i) q^{96} +(-59.8223 + 34.5384i) q^{97} +(-21.3472 - 36.9745i) q^{98} +(25.2360 - 24.6095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	−0.410263	+	2.97181i	−0.136754	+	0.990605i
$3$	−0.410263	+	2.97181i	−0.136754	+	0.990605i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−9.12568			−1.82514			−0.912568	−	0.408925i	$-0.865904\pi$
$5$	−9.12568			−1.82514			−0.912568	+	0.408925i	$0.865904\pi$
$6$	−3.34962	−	2.60386i	−0.558269	−	0.433976i
$7$	3.75604	−	2.16855i	0.536577	−	0.309793i	−0.207113	−	0.978317i	$-0.566407\pi$
$7$	3.75604	−	2.16855i	0.536577	−	0.309793i	0.743691	+	0.668524i	$0.233074\pi$
$8$	2.82843			0.353553
$9$	−8.66337	−	2.43845i	−0.962596	−	0.270939i
$10$	6.45283	−	11.1766i	0.645283	−	1.11766i
$11$	−1.95827	+	3.39183i	−0.178025	+	0.308348i	−0.941204	−	0.337839i	$-0.890304\pi$
$11$	−1.95827	+	3.39183i	−0.178025	+	0.308348i	0.763179	+	0.646187i	$0.223637\pi$
$12$	5.55760	−	2.26122i	0.463133	−	0.188435i
$13$	−1.61415	+	12.8994i	−0.124166	+	0.992262i
$13$	−1.61415	+	12.8994i	−0.124166	+	0.992262i
$14$			6.13359i			0.438113i
$15$	3.74393	−	27.1198i	0.249595	−	1.80799i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−6.72177	+	3.88082i	−0.395398	+	0.228283i	−0.684497	−	0.729016i	$-0.739978\pi$
$17$	−6.72177	+	3.88082i	−0.395398	+	0.228283i	0.289098	+	0.957299i	$0.406645\pi$
$18$	9.11241	−	8.88617i	0.506245	−	0.493676i
$19$	−30.6949	+	17.7217i	−1.61552	+	0.932721i	−0.627461	+	0.778648i	$0.715906\pi$
$19$	−30.6949	+	17.7217i	−1.61552	+	0.932721i	−0.988060	+	0.154073i	$0.950761\pi$
$20$	9.12568	+	15.8061i	0.456284	+	0.790307i
$21$	4.90357	+	12.0519i	0.233503	+	0.573901i
$22$	−2.76942	−	4.79677i	−0.125883	−	0.218035i
$23$	16.6520	+	9.61401i	0.723998	+	0.418000i	0.816222	−	0.577738i	$-0.196064\pi$
$23$	16.6520	+	9.61401i	0.723998	+	0.418000i	−0.0922244	+	0.995738i	$0.529398\pi$
$24$	−1.16040	+	8.40556i	−0.0483500	+	0.350232i
$25$	58.2780			2.33112
$26$	−14.6571	−	11.0982i	−0.563734	−	0.426853i
$27$	10.8009	−	24.7455i	0.400033	−	0.916501i
$28$	−7.51208	−	4.33710i	−0.268289	−	0.154896i
$29$	32.4049	+	18.7090i	1.11741	+	0.645137i	0.940739	−	0.339133i	$-0.110134\pi$
$29$	32.4049	+	18.7090i	1.11741	+	0.645137i	0.176672	+	0.984270i	$0.443467\pi$
$30$	30.5675	+	23.7620i	1.01892	+	0.792066i
$31$			1.27633i			0.0411720i	0.999788	+	0.0205860i	$0.00655319\pi$
$31$			1.27633i			0.0411720i	−0.999788	+	0.0205860i	$0.993447\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−9.27648	−	7.21117i	−0.281105	−	0.218520i
$34$		−	10.9766i		−	0.322841i
$35$	−34.2764	+	19.7895i	−0.979326	+	0.565414i
$36$	4.43985	+	17.4438i	0.123329	+	0.484551i
$37$	−15.0241	−	8.67414i	−0.406056	−	0.234436i	0.283038	−	0.959109i	$-0.408658\pi$
$37$	−15.0241	−	8.67414i	−0.406056	−	0.234436i	−0.689094	+	0.724672i	$0.741991\pi$
$38$		−	50.1245i		−	1.31907i
$39$	−37.6724	−	10.0891i	−0.965959	−	0.258695i
$40$	−25.8113			−0.645283
$41$	9.91090	−	17.1662i	0.241729	−	0.418687i	−0.719478	−	0.694516i	$-0.755619\pi$
$41$	9.91090	−	17.1662i	0.241729	−	0.418687i	0.961207	+	0.275828i	$0.0889521\pi$
$42$	−18.2279	−	2.51638i	−0.433997	−	0.0599139i
$43$	−14.5164	−	25.1432i	−0.337592	−	0.584726i	0.646387	−	0.763009i	$-0.276279\pi$
$43$	−14.5164	−	25.1432i	−0.337592	−	0.584726i	−0.983979	+	0.178283i	$0.942946\pi$
$44$	7.83309			0.178025
$45$	79.0591	+	22.2525i	1.75687	+	0.494501i
$46$	−23.5494	+	13.5963i	−0.511944	+	0.295571i
$47$	−18.7295			−0.398500			−0.199250	−	0.979949i	$-0.563851\pi$
$47$	−18.7295			−0.398500			−0.199250	+	0.979949i	$0.563851\pi$
$48$	−9.47414	−	7.36482i	−0.197378	−	0.153434i
$49$	−15.0948	+	26.1449i	−0.308057	+	0.533570i
$50$	−41.2088	+	71.3757i	−0.824175	+	1.42751i
$51$	−8.77537	−	21.5680i	−0.172066	−	0.422902i
$52$	23.9566	−	10.1036i	0.460703	−	0.194300i
$53$			14.7174i			0.277686i	0.990314	+	0.138843i	$0.0443384\pi$
$53$			14.7174i			0.277686i	−0.990314	+	0.138843i	$0.955662\pi$
$54$	22.6696	+	30.7261i	0.419807	+	0.569001i
$55$	17.8706	−	30.9527i	0.324919	−	0.562777i
$56$	10.6237	−	6.13359i	0.189709	−	0.109528i
$57$	−40.0726	−	98.4901i	−0.703029	−	1.72790i
$58$	−45.8274	+	26.4585i	−0.790128	+	0.456181i
$59$	−34.9033	−	60.4543i	−0.591581	−	1.02465i	−0.994020	−	0.109202i	$-0.965170\pi$
$59$	−34.9033	−	60.4543i	−0.591581	−	1.02465i	0.402438	−	0.915447i	$-0.368163\pi$
$60$	−50.7168	+	20.6352i	−0.845281	+	0.343919i
$61$	30.4453	+	52.7328i	0.499103	+	0.864472i	0.999999	−	0.00103559i	$-0.000329638\pi$
$61$	30.4453	+	52.7328i	0.499103	+	0.864472i	−0.500897	+	0.865507i	$0.666996\pi$
$62$	−1.56318	−	0.902503i	−0.0252126	−	0.0145565i
$63$	−37.8279	+	9.62803i	−0.600442	+	0.152826i
$64$	8.00000			0.125000
$65$	14.7302	−	117.716i	0.226619	−	1.81101i
$66$	15.3913	−	6.26225i	0.233201	−	0.0948826i
$67$	43.7994	+	25.2876i	0.653722	+	0.377426i	0.789881	−	0.613261i	$-0.210142\pi$
$67$	43.7994	+	25.2876i	0.653722	+	0.377426i	−0.136159	+	0.990687i	$0.543476\pi$
$68$	13.4435	+	7.76163i	0.197699	+	0.114142i
$69$	−35.4027	+	45.5422i	−0.513083	+	0.660033i
$70$		−	55.9731i		−	0.799616i
$71$	25.3645	+	43.9326i	0.357247	+	0.618769i	0.987500	−	0.157620i	$-0.0503822\pi$
$71$	25.3645	+	43.9326i	0.357247	+	0.618769i	−0.630253	+	0.776390i	$0.717049\pi$
$72$	−24.5037	−	6.89698i	−0.340329	−	0.0957914i
$73$		−	80.0631i		−	1.09675i	−0.836231	−	0.548377i	$-0.815246\pi$
$73$		−	80.0631i		−	1.09675i	0.836231	−	0.548377i	$-0.184754\pi$
$74$	21.2472	−	12.2671i	0.287125	−	0.165772i
$75$	−23.9093	+	173.191i	−0.318791	+	2.30922i
$76$	61.3898	+	35.4434i	0.807760	+	0.466360i
$77$			16.9865i			0.220603i
$78$	38.9950	−	39.0050i	0.499936	−	0.500064i
$79$	−33.1864			−0.420082			−0.210041	−	0.977693i	$-0.567360\pi$
$79$	−33.1864			−0.420082			−0.210041	+	0.977693i	$0.567360\pi$
$80$	18.2514	−	31.6123i	0.228142	−	0.395153i
$81$	69.1079	+	42.2504i	0.853184	+	0.521610i
$82$	14.0161	+	24.2767i	0.170928	+	0.296057i
$83$	−7.74819			−0.0933517			−0.0466759	−	0.998910i	$-0.514863\pi$
$83$	−7.74819			−0.0933517			−0.0466759	+	0.998910i	$0.514863\pi$
$84$	15.9710	−	20.5452i	0.190131	−	0.244585i
$85$	61.3407	−	35.4151i	0.721655	−	0.416648i
$86$	41.0587			0.477427
$87$	−68.8942	+	88.6258i	−0.791887	+	1.01869i
$88$	−5.53883	+	9.59354i	−0.0629413	+	0.109017i
$89$	−41.9399	+	72.6421i	−0.471235	+	0.816203i	−0.999459	−	0.0329024i	$-0.989525\pi$
$89$	−41.9399	+	72.6421i	−0.471235	+	0.816203i	0.528224	+	0.849105i	$0.322858\pi$
$90$	−83.1569	+	81.0923i	−0.923966	+	0.901026i
$91$	21.9102	+	51.9510i	0.240771	+	0.570890i
$92$		−	38.4560i		−	0.418000i
$93$	−3.79302	−	0.523632i	−0.0407852	−	0.00563045i
$94$	13.2438	−	22.9389i	0.140891	−	0.244031i
$95$	280.112	−	161.723i	2.94854	−	1.70234i
$96$	15.7193	−	6.39569i	0.163742	−	0.0666218i
$97$	−59.8223	+	34.5384i	−0.616724	+	0.356066i	−0.775593	−	0.631234i	$-0.782549\pi$
$97$	−59.8223	+	34.5384i	−0.616724	+	0.356066i	0.158868	+	0.987300i	$0.449215\pi$
$98$	−21.3472	−	36.9745i	−0.217829	−	0.377291i
$99$	25.2360	−	24.6095i	0.254910	−	0.248581i
$100$	−58.2780	−	100.940i	−0.582780	−	1.00940i
$101$	106.006	+	61.2024i	1.04956	+	0.605964i	0.922526	−	0.385934i	$-0.126121\pi$
$101$	106.006	+	61.2024i	1.04956	+	0.605964i	0.127035	+	0.991898i	$0.459454\pi$
$102$	32.6204	+	4.50330i	0.319808	+	0.0441500i
$103$	−7.22499			−0.0701456			−0.0350728	−	0.999385i	$-0.511166\pi$
$103$	−7.22499			−0.0701456			−0.0350728	+	0.999385i	$0.511166\pi$
$104$	−4.56551	+	36.4850i	−0.0438991	+	0.350817i
$105$	−44.7484	−	109.982i	−0.426175	−	1.04745i
$106$	−18.0250	−	10.4068i	−0.170047	−	0.0981769i
$107$	−157.176	−	90.7456i	−1.46893	−	0.848090i	−0.469541	−	0.882911i	$-0.655581\pi$
$107$	−157.176	−	90.7456i	−1.46893	−	0.848090i	−0.999394	+	0.0348206i	$0.988914\pi$
$108$	−53.6614	+	6.03783i	−0.496865	+	0.0559059i
$109$			148.459i			1.36201i	0.732280	+	0.681003i	$0.238456\pi$
$109$			148.459i			1.36201i	−0.732280	+	0.681003i	$0.761544\pi$
$110$	25.2728	+	43.7738i	0.229753	+	0.397943i
$111$	31.9418	−	41.0900i	0.287764	−	0.370181i
$112$			17.3484i			0.154896i
$113$	−31.1656	+	17.9934i	−0.275801	+	0.159234i	−0.631521	−	0.775359i	$-0.717569\pi$
$113$	−31.1656	+	17.9934i	−0.275801	+	0.159234i	0.355720	+	0.934593i	$0.384236\pi$
$114$	148.961	+	20.5642i	1.30667	+	0.180388i
$115$	−151.960	−	87.7344i	−1.32139	−	0.762907i
$116$		−	74.8359i		−	0.645137i
$117$	45.4386	−	107.816i	0.388364	−	0.921506i
$118$	98.7215			0.836623
$119$	−16.8315	+	29.1530i	−0.141441	+	0.244983i
$120$	10.5894	−	76.7065i	0.0882452	−	0.639220i
$121$	52.8303	+	91.5048i	0.436614	+	0.756238i
$122$	−86.1122			−0.705838
$123$	46.9487	+	36.4960i	0.381696	+	0.296716i
$124$	2.21067	−	1.27633i	0.0178280	−	0.0102930i
$125$	−303.684			−2.42947
$126$	14.9565	−	53.1375i	0.118702	−	0.421726i
$127$	63.2634	−	109.575i	0.498137	−	0.862798i	−0.501861	−	0.864948i	$-0.667351\pi$
$127$	63.2634	−	109.575i	0.498137	−	0.862798i	0.999998	+	0.00215029i	$0.000684458\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	80.6766	−	32.8249i	0.625400	−	0.254456i
$130$	133.756	+	101.278i	1.02889	+	0.779065i
$131$			158.096i			1.20684i	0.797425	+	0.603418i	$0.206195\pi$
$131$			158.096i			1.20684i	−0.797425	+	0.603418i	$0.793805\pi$
$132$	−3.21363	+	23.2785i	−0.0243457	+	0.176352i
$133$	−76.8608	+	133.127i	−0.577901	+	1.00095i
$134$	−61.9416	+	35.7620i	−0.462251	+	0.266881i
$135$	−98.5654	+	225.820i	−0.730114	+	1.67274i
$136$	−19.0120	+	10.9766i	−0.139794	+	0.0807103i
$137$	121.803	+	210.970i	0.889076	+	1.53992i	0.840970	+	0.541082i	$0.181985\pi$
$137$	121.803	+	210.970i	0.889076	+	1.53992i	0.0481058	+	0.998842i	$0.484682\pi$
$138$	−30.7441	−	75.5626i	−0.222783	−	0.547555i
$139$	−54.6258	−	94.6146i	−0.392991	−	0.680681i	0.599851	−	0.800111i	$-0.295226\pi$
$139$	−54.6258	−	94.6146i	−0.392991	−	0.680681i	−0.992843	+	0.119431i	$0.961893\pi$
$140$	68.5528	+	39.5790i	0.489663	+	0.282707i
$141$	7.68403	−	55.6606i	0.0544966	−	0.394756i
$142$	−71.7417			−0.505223
$143$	−40.5916	−	30.7355i	−0.283857	−	0.214933i
$144$	25.7738	−	25.1339i	0.178985	−	0.174541i
$145$	−295.717	−	170.732i	−2.03943	−	1.17746i
$146$	98.0568	+	56.6131i	0.671622	+	0.387761i
$147$	−71.5050	−	55.5852i	−0.486429	−	0.378131i
$148$			34.6966i			0.234436i
$149$	−89.7559	−	155.462i	−0.602389	−	1.04337i	−0.992458	−	0.122583i	$-0.960882\pi$
$149$	−89.7559	−	155.462i	−0.602389	−	1.04337i	0.390069	−	0.920785i	$-0.372451\pi$
$150$	−195.209	−	151.748i	−1.30139	−	1.01165i
$151$		−	49.4644i		−	0.327579i	−0.986495	−	0.163789i	$-0.947628\pi$
$151$		−	49.4644i		−	0.327579i	0.986495	−	0.163789i	$-0.0523718\pi$
$152$	−86.8182	+	50.1245i	−0.571173	+	0.329767i
$153$	67.6964	−	17.2302i	0.442460	−	0.112616i
$154$	−20.8041	−	12.0112i	−0.135091	−	0.0779950i
$155$		−	11.6474i		−	0.0751445i
$156$	20.1976	+	75.3396i	0.129471	+	0.482946i
$157$	124.230			0.791273			0.395637	−	0.918407i	$-0.370524\pi$
$157$	124.230			0.791273			0.395637	+	0.918407i	$0.370524\pi$
$158$	23.4664	−	40.6449i	0.148521	−	0.257246i
$159$	−43.7373	−	6.03799i	−0.275077	−	0.0379748i
$160$	25.8113	+	44.7065i	0.161321	+	0.279416i
$161$	83.3939			0.517974
$162$	−100.613	+	54.7640i	−0.621066	+	0.338049i
$163$	235.561	−	136.001i	1.44516	−	0.834363i	0.446972	−	0.894548i	$-0.352502\pi$
$163$	235.561	−	136.001i	1.44516	−	0.834363i	0.998187	+	0.0601847i	$0.0191690\pi$
$164$	−39.6436			−0.241729
$165$	84.6541	+	65.8068i	0.513055	+	0.398829i
$166$	5.47880	−	9.48956i	0.0330048	−	0.0571660i
$167$	−93.0441	+	161.157i	−0.557150	+	0.965013i	0.440582	+	0.897712i	$0.354772\pi$
$167$	−93.0441	+	161.157i	−0.557150	+	0.965013i	−0.997733	+	0.0673007i	$0.978561\pi$
$168$	13.8694	+	34.0880i	0.0825558	+	0.202905i
$169$	−163.789	−	41.6432i	−0.969166	−	0.246409i
$170$			100.169i			0.589229i
$171$	309.135	−	78.6816i	1.80780	−	0.460126i
$172$	−29.0329	+	50.2864i	−0.168796	+	0.292363i
$173$	67.8686	−	39.1839i	0.392304	−	0.226497i	−0.290854	−	0.956767i	$-0.593939\pi$
$173$	67.8686	−	39.1839i	0.392304	−	0.226497i	0.683158	+	0.730271i	$0.260606\pi$
$174$	−59.8284	−	147.046i	−0.343842	−	0.845090i
$175$	218.894	−	126.379i	1.25083	−	0.722164i
$176$	−7.83309	−	13.5673i	−0.0445062	−	0.0770870i
$177$	193.979	−	78.9240i	1.09592	−	0.445898i
$178$	−59.3120	−	102.731i	−0.333213	−	0.577143i
$179$	−117.717	−	67.9639i	−0.657636	−	0.379687i	0.133739	−	0.991017i	$-0.457302\pi$
$179$	−117.717	−	67.9639i	−0.657636	−	0.379687i	−0.791376	+	0.611330i	$0.790635\pi$
$180$	−40.5166	−	159.187i	−0.225092	−	0.884372i
$181$	46.5269			0.257055			0.128527	−	0.991706i	$-0.458975\pi$
$181$	46.5269			0.257055			0.128527	+	0.991706i	$0.458975\pi$
$182$	−79.1196	−	9.90054i	−0.434723	−	0.0543986i
$183$	−169.203	+	68.8434i	−0.924604	+	0.376194i
$184$	47.0988	+	27.1925i	0.255972	+	0.147785i
$185$	137.105	+	79.1574i	0.741107	+	0.427878i
$186$	3.32339	−	4.27522i	0.0178677	−	0.0229851i
$187$		−	30.3988i		−	0.162560i
$188$	18.7295	+	32.4405i	0.0996251	+	0.172556i
$189$	−13.0933	−	116.367i	−0.0692770	−	0.615701i
$190$			457.420i			2.40748i
$191$	96.9924	−	55.9986i	0.507814	−	0.293186i	−0.224121	−	0.974561i	$-0.571951\pi$
$191$	96.9924	−	55.9986i	0.507814	−	0.293186i	0.731935	+	0.681375i	$0.238618\pi$
$192$	−3.28210	+	23.7745i	−0.0170943	+	0.123826i
$193$	−58.8962	−	34.0037i	−0.305162	−	0.176185i	0.339598	−	0.940571i	$-0.389709\pi$
$193$	−58.8962	−	34.0037i	−0.305162	−	0.176185i	−0.644759	+	0.764386i	$0.723042\pi$
$194$		−	97.6893i		−	0.503553i
$195$	343.786	+	92.0700i	1.76301	+	0.472154i
$196$	60.3791			0.308057
$197$	−88.3945	+	153.104i	−0.448703	+	0.777177i	−0.998302	−	0.0582521i	$-0.981447\pi$
$197$	−88.3945	+	153.104i	−0.448703	+	0.777177i	0.549599	+	0.835429i	$0.314781\pi$
$198$	12.2958	+	48.3093i	0.0620999	+	0.243986i
$199$	−7.01166	−	12.1445i	−0.0352345	−	0.0610279i	0.847870	−	0.530203i	$-0.177884\pi$
$199$	−7.01166	−	12.1445i	−0.0352345	−	0.0610279i	−0.883105	+	0.469176i	$0.844551\pi$
$200$	164.835			0.824175
$201$	−93.1192	+	119.789i	−0.463280	+	0.595965i
$202$	−149.915	+	86.5533i	−0.742152	+	0.428481i
$203$	162.285			0.799436
$204$	−28.5815	+	36.7674i	−0.140106	+	0.180232i
$205$	−90.4437	+	156.653i	−0.441189	+	0.764161i
$206$	5.10884	−	8.84878i	0.0248002	−	0.0429552i
$207$	−120.819	−	123.895i	−0.583665	−	0.598525i
$208$	−41.4565	−	31.3904i	−0.199310	−	0.150915i
$209$		−	138.816i		−	0.664190i
$210$	166.342	+	22.9637i	0.792104	+	0.109351i
$211$	−133.023	+	230.402i	−0.630440	+	1.09195i	0.357022	+	0.934096i	$0.383792\pi$
$211$	−133.023	+	230.402i	−0.630440	+	1.09195i	−0.987462	+	0.157857i	$0.949541\pi$
$212$	25.4912	−	14.7174i	0.120242	−	0.0694215i
$213$	−140.966	+	57.3547i	−0.661811	+	0.269271i
$214$	222.280	−	128.334i	1.03869	−	0.599690i
$215$	132.472	+	229.449i	0.616151	+	1.06720i
$216$	30.5495	−	69.9909i	0.141433	−	0.324032i
$217$	2.76779	+	4.79395i	0.0127548	+	0.0220920i
$218$	−181.824	−	104.976i	−0.834055	−	0.481542i
$219$	237.933	+	32.8469i	1.08645	+	0.149986i
$220$	−71.4823			−0.324919
$221$	−39.2102	−	92.9710i	−0.177422	−	0.420683i
$222$	27.7386	+	68.1756i	0.124949	+	0.307097i
$223$	342.759	+	197.892i	1.53704	+	0.887409i	0.999010	+	0.0444817i	$0.0141636\pi$
$223$	342.759	+	197.892i	1.53704	+	0.887409i	0.538027	+	0.842927i	$0.319170\pi$
$224$	−21.2474	−	12.2672i	−0.0948543	−	0.0547642i
$225$	−504.884	−	142.108i	−2.24393	−	0.631592i
$226$		−	50.8931i		−	0.225191i
$227$	91.0736	+	157.744i	0.401205	+	0.694908i	0.993872	−	0.110540i	$-0.0352580\pi$
$227$	91.0736	+	157.744i	0.401205	+	0.694908i	−0.592666	+	0.805448i	$0.701925\pi$
$228$	−130.517	+	167.898i	−0.572444	+	0.736394i
$229$		−	28.4940i		−	0.124428i	−0.998063	−	0.0622141i	$-0.980184\pi$
$229$		−	28.4940i		−	0.124428i	0.998063	−	0.0622141i	$-0.0198162\pi$
$230$	214.904	−	124.075i	0.934367	−	0.539457i
$231$	−50.4806	−	6.96891i	−0.218531	−	0.0301685i
$232$	91.6549	+	52.9170i	0.395064	+	0.228090i
$233$		−	258.873i		−	1.11104i	−0.831502	−	0.555522i	$-0.812518\pi$
$233$		−	258.873i		−	1.11104i	0.831502	−	0.555522i	$-0.187482\pi$
$234$	99.9174	+	131.888i	0.426998	+	0.563625i
$235$	170.919			0.727317
$236$	−69.8066	+	120.909i	−0.295791	+	0.512325i
$237$	13.6152	−	98.6240i	0.0574480	−	0.416135i
$238$	−23.8033	−	41.2286i	−0.100014	−	0.173229i
$239$	10.1786			0.0425882			0.0212941	−	0.999773i	$-0.493221\pi$
$239$	10.1786			0.0425882			0.0212941	+	0.999773i	$0.493221\pi$
$240$	86.4580	+	67.2090i	0.360242	+	0.280038i
$241$	−69.5256	+	40.1406i	−0.288488	+	0.166559i	−0.637260	−	0.770649i	$-0.719932\pi$
$241$	−69.5256	+	40.1406i	−0.288488	+	0.166559i	0.348772	+	0.937208i	$0.386599\pi$
$242$	−149.427			−0.617466
$243$	−153.913	+	188.042i	−0.633386	+	0.773836i
$244$	60.8906	−	105.466i	0.249551	−	0.432236i
$245$	137.750	−	238.590i	0.562245	−	0.973837i
$246$	−77.8960	+	31.6935i	−0.316650	+	0.128836i
$247$	−179.053	−	424.551i	−0.724911	−	1.71883i
$248$			3.61001i			0.0145565i
$249$	3.17880	−	23.0262i	0.0127663	−	0.0924747i
$250$	214.737	−	371.936i	0.858949	−	1.48774i
$251$	−81.0109	+	46.7717i	−0.322753	+	0.186341i	−0.652619	−	0.757686i	$-0.726330\pi$
$251$	−81.0109	+	46.7717i	−0.322753	+	0.186341i	0.329866	+	0.944028i	$0.392996\pi$
$252$	54.5041	+	55.8917i	0.216286	+	0.221793i
$253$	−65.2181	+	37.6537i	−0.257779	+	0.148829i
$254$	89.4679	+	154.963i	0.352236	+	0.610090i
$255$	80.0812	+	196.823i	0.314044	+	0.771854i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−248.104	−	143.243i	−0.965384	−	0.557365i	−0.0675581	−	0.997715i	$-0.521521\pi$
$257$	−248.104	−	143.243i	−0.965384	−	0.557365i	−0.897826	+	0.440351i	$0.854854\pi$
$258$	−16.8449	+	122.019i	−0.0652902	+	0.472941i
$259$	−75.2413			−0.290507
$260$	−218.620	+	92.2023i	−0.840846	+	0.354624i
$261$	−235.115	−	241.101i	−0.900822	−	0.923757i
$262$	−193.627	−	111.790i	−0.739033	−	0.426681i
$263$	−317.283	−	183.183i	−1.20640	−	0.696515i	−0.244428	−	0.969667i	$-0.578600\pi$
$263$	−317.283	−	183.183i	−1.20640	−	0.696515i	−0.961971	+	0.273153i	$0.911934\pi$
$264$	−26.2378	−	20.3963i	−0.0993858	−	0.0772585i
$265$		−	134.306i		−	0.506815i
$266$	−108.698	−	188.270i	−0.408638	−	0.707781i
$267$	−198.672	−	154.440i	−0.744091	−	0.578427i
$268$		−	101.150i		−	0.377426i
$269$	−119.794	+	69.1631i	−0.445331	+	0.257112i	−0.705856	−	0.708355i	$-0.749438\pi$
$269$	−119.794	+	69.1631i	−0.445331	+	0.257112i	0.260525	+	0.965467i	$0.416104\pi$
$270$	−206.875	−	280.396i	−0.766204	−	1.03850i
$271$	−45.0963	−	26.0364i	−0.166407	−	0.0960752i	0.414483	−	0.910057i	$-0.363962\pi$
$271$	−45.0963	−	26.0364i	−0.166407	−	0.0960752i	−0.580891	+	0.813982i	$0.697296\pi$
$272$		−	31.0465i		−	0.114142i
$273$	−163.378	+	43.7994i	−0.598453	+	0.160437i
$274$	−344.512			−1.25734
$275$	−114.124	+	197.669i	−0.414997	+	0.718796i
$276$	114.284	+	15.7771i	0.414073	+	0.0571634i
$277$	61.3441	+	106.251i	0.221459	+	0.383578i	0.955251	−	0.295796i	$-0.0955848\pi$
$277$	61.3441	+	106.251i	0.221459	+	0.383578i	−0.733792	+	0.679374i	$0.762251\pi$
$278$	154.505			0.555773
$279$	3.11228	−	11.0573i	0.0111551	−	0.0396320i
$280$	−96.9483	+	55.9731i	−0.346244	+	0.199904i
$281$	461.303			1.64165			0.820824	−	0.571182i	$-0.193515\pi$
$281$	461.303			1.64165			0.820824	+	0.571182i	$0.193515\pi$
$282$	62.7367	+	48.7690i	0.222470	+	0.172940i
$283$	14.6169	−	25.3172i	0.0516498	−	0.0894600i	−0.839045	−	0.544063i	$-0.816885\pi$
$283$	14.6169	−	25.3172i	0.0516498	−	0.0894600i	0.890694	+	0.454603i	$0.150219\pi$
$284$	50.7290	−	87.8653i	0.178623	−	0.309385i
$285$	365.690	+	898.789i	1.28312	+	3.15364i
$286$	66.3457	−	27.9811i	0.231978	−	0.0978360i
$287$		−	85.9692i		−	0.299544i
$288$	12.5578	+	49.3386i	0.0436034	+	0.171315i
$289$	−114.379	+	198.109i	−0.395773	+	0.685500i
$290$	418.207	−	241.452i	1.44209	−	0.832592i
$291$	−78.0989	−	191.950i	−0.268381	−	0.659624i
$292$	−138.673	+	80.0631i	−0.474908	+	0.274189i
$293$	96.8731	+	167.789i	0.330625	+	0.572659i	0.982635	−	0.185551i	$-0.0594071\pi$
$293$	96.8731	+	167.789i	0.330625	+	0.572659i	−0.652010	+	0.758211i	$0.726074\pi$
$294$	118.639	−	48.2708i	0.403535	−	0.164186i
$295$	318.516	+	551.686i	1.07972	+	1.87012i
$296$	−42.4945	−	24.5342i	−0.143562	−	0.0828858i
$297$	62.7815	+	85.0932i	0.211385	+	0.286509i
$298$	253.868			0.851906
$299$	−150.894	+	199.282i	−0.504661	+	0.666494i
$300$	323.886	−	131.779i	1.07962	−	0.439264i
$301$	−109.049	−	62.9593i	−0.362288	−	0.209167i
$302$	60.5813	+	34.9766i	0.200600	+	0.115817i
$303$	−225.372	+	289.920i	−0.743803	+	0.956832i
$304$		−	141.774i		−	0.466360i
$305$	−277.834	−	481.222i	−0.910930	−	1.57778i
$306$	−26.7659	+	95.0944i	−0.0874703	+	0.310766i
$307$		−	174.622i		−	0.568802i	−0.958705	−	0.284401i	$-0.908205\pi$
$307$		−	174.622i		−	0.568802i	0.958705	−	0.284401i	$-0.0917947\pi$
$308$	29.4214	−	16.9865i	0.0955240	−	0.0551508i
$309$	2.96415	−	21.4713i	0.00959271	−	0.0694866i
$310$	14.2651	+	8.23595i	0.0460164	+	0.0265676i
$311$		−	46.1693i		−	0.148454i	−0.997241	−	0.0742272i	$-0.976351\pi$
$311$		−	46.1693i		−	0.148454i	0.997241	−	0.0742272i	$-0.0236490\pi$
$312$	−106.554	−	28.5363i	−0.341518	−	0.0914625i
$313$	−97.2890			−0.310827			−0.155414	−	0.987849i	$-0.549671\pi$
$313$	−97.2890			−0.310827			−0.155414	+	0.987849i	$0.549671\pi$
$314$	−87.8438	+	152.150i	−0.279757	+	0.484554i
$315$	345.205	−	87.8623i	1.09589	−	0.278928i
$316$	33.1864	+	57.4806i	0.105020	+	0.181901i
$317$	383.897			1.21103			0.605516	−	0.795833i	$-0.292967\pi$
$317$	383.897			1.21103			0.605516	+	0.795833i	$0.292967\pi$
$318$	38.3219	−	49.2975i	0.120509	−	0.155024i
$319$	−126.915	+	73.2746i	−0.397853	+	0.229701i
$320$	−73.0054			−0.228142
$321$	334.163	−	429.868i	1.04101	−	1.33915i
$322$	−58.9684	+	102.136i	−0.183132	+	0.317193i
$323$	137.549	−	238.242i	0.425849	−	0.737593i
$324$	4.07196	−	161.949i	0.0125678	−	0.499842i
$325$	−94.0695	+	751.751i	−0.289445	+	2.31308i
$326$			384.669i			1.17997i
$327$	−441.192	−	60.9071i	−1.34921	−	0.186260i
$328$	28.0323	−	48.5533i	0.0854642	−	0.148028i
$329$	−70.3488	+	40.6159i	−0.213826	+	0.123453i
$330$	−140.456	+	57.1473i	−0.425624	+	0.173174i
$331$	−83.1204	+	47.9896i	−0.251119	+	0.144984i	−0.620277	−	0.784383i	$-0.712980\pi$
$331$	−83.1204	+	47.9896i	−0.251119	+	0.144984i	0.369157	+	0.929367i	$0.379646\pi$
$332$	7.74819	+	13.4203i	0.0233379	+	0.0404225i
$333$	109.007	+	111.783i	0.327350	+	0.335684i
$334$	−131.584	−	227.911i	−0.393965	−	0.682367i
$335$	−399.699	−	230.766i	−1.19313	−	0.688854i
$336$	−51.5562	−	7.11741i	−0.153441	−	0.0211828i
$337$	−2.41052			−0.00715289			−0.00357645	−	0.999994i	$-0.501138\pi$
$337$	−2.41052			−0.00715289			−0.00357645	+	0.999994i	$0.501138\pi$
$338$	166.819	−	171.154i	0.493546	−	0.506372i
$339$	−40.6871	−	100.000i	−0.120021	−	0.294986i
$340$	−122.681	−	70.8302i	−0.360828	−	0.208324i
$341$	−4.32910	−	2.49941i	−0.0126953	−	0.00732964i
$342$	−122.226	+	434.247i	−0.357387	+	1.26973i
$343$			343.453i			1.00132i
$344$	−41.0587	−	71.1158i	−0.119357	−	0.206732i
$345$	323.074	−	415.604i	0.936446	−	1.20465i
$346$			110.829i			0.320315i
$347$	537.450	−	310.297i	1.54885	−	0.894227i	0.550616	−	0.834758i	$-0.314393\pi$
$347$	537.450	−	310.297i	1.54885	−	0.894227i	0.998230	−	0.0594686i	$-0.0189406\pi$
$348$	222.398	+	30.7024i	0.639076	+	0.0882253i
$349$	453.549	+	261.857i	1.29957	+	0.750305i	0.980329	−	0.197369i	$-0.0632398\pi$
$349$	453.549	+	261.857i	1.29957	+	0.750305i	0.319238	+	0.947675i	$0.396573\pi$
$350$			357.453i			1.02129i
$351$	301.768	+	179.268i	0.859738	+	0.510735i
$352$	22.1553			0.0629413
$353$	226.459	−	392.239i	0.641527	−	1.11116i	−0.343564	−	0.939129i	$-0.611634\pi$
$353$	226.459	−	392.239i	0.641527	−	1.11116i	0.985092	−	0.172029i	$-0.0550323\pi$
$354$	−40.5018	+	293.382i	−0.114412	+	0.828763i
$355$	−231.468	−	400.915i	−0.652024	−	1.12934i
$356$	167.760			0.471235
$357$	−79.7320	−	61.9805i	−0.223339	−	0.173615i
$358$	166.477	−	96.1155i	0.465019	−	0.268479i
$359$	70.0901			0.195237			0.0976185	−	0.995224i	$-0.468877\pi$
$359$	70.0901			0.195237			0.0976185	+	0.995224i	$0.468877\pi$
$360$	223.613	+	62.9397i	0.621147	+	0.174832i
$361$	447.617	−	775.296i	1.23994	−	2.14763i
$362$	−32.8995	+	56.9836i	−0.0908827	+	0.157413i
$363$	−293.610	+	119.461i	−0.808842	+	0.329093i
$364$	68.0716	−	89.9006i	0.187010	−	0.246980i
$365$			730.630i			2.00172i
$366$	35.3287	−	255.910i	0.0965264	−	0.699207i
$367$	217.354	−	376.469i	0.592246	−	1.02580i	−0.401683	−	0.915779i	$-0.631575\pi$
$367$	217.354	−	376.469i	0.592246	−	1.02580i	0.993929	−	0.110022i	$-0.0350920\pi$
$368$	−66.6078	+	38.4560i	−0.180999	+	0.104500i
$369$	−127.721	+	124.550i	−0.346127	+	0.337533i
$370$	−193.895	+	111.946i	−0.524041	+	0.302555i
$371$	31.9154	+	55.2790i	0.0860252	+	0.149000i
$372$	2.88607	+	7.09334i	0.00775824	+	0.0190681i
$373$	87.9603	+	152.352i	0.235818	+	0.408450i	0.959510	−	0.281674i	$-0.0908896\pi$
$373$	87.9603	+	152.352i	0.235818	+	0.408450i	−0.723692	+	0.690123i	$0.757556\pi$
$374$	37.2308	+	21.4952i	0.0995475	+	0.0574738i
$375$	124.590	−	902.493i	0.332241	−	2.40665i
$376$	−52.9751			−0.140891
$377$	−293.641	+	387.805i	−0.778889	+	1.02866i
$378$	151.779	+	66.2482i	0.401531	+	0.175260i
$379$	−184.066	−	106.271i	−0.485662	−	0.280397i	0.237111	−	0.971483i	$-0.423800\pi$
$379$	−184.066	−	106.271i	−0.485662	−	0.280397i	−0.722773	+	0.691085i	$0.757133\pi$
$380$	−560.223	−	323.445i	−1.47427	−	0.851171i
$381$	299.683	+	232.962i	0.786570	+	0.611448i
$382$			158.388i			0.414628i
$383$	99.6706	+	172.635i	0.260237	+	0.450743i	0.966305	−	0.257401i	$-0.0828661\pi$
$383$	99.6706	+	172.635i	0.260237	+	0.450743i	−0.706068	+	0.708144i	$0.749533\pi$
$384$	−26.7969	−	20.8309i	−0.0697837	−	0.0542470i
$385$		−	155.013i		−	0.402631i
$386$	83.2918	−	48.0885i	0.215782	−	0.124582i
$387$	64.4508	+	253.223i	0.166539	+	0.654322i
$388$	119.645	+	69.0768i	0.308362	+	0.178033i
$389$			542.778i			1.39532i	0.716431	+	0.697658i	$0.245774\pi$
$389$			542.778i			1.39532i	−0.716431	+	0.697658i	$0.754226\pi$
$390$	−355.856	+	355.947i	−0.912451	+	0.912685i
$391$	−149.241			−0.381690
$392$	−42.6945	+	73.9490i	−0.108914	+	0.188645i
$393$	−469.831	−	64.8608i	−1.19550	−	0.165040i
$394$	−125.009	−	216.521i	−0.317281	−	0.549547i
$395$	302.849			0.766706
$396$	−67.8609	−	19.1006i	−0.171366	−	0.0482339i
$397$	351.364	−	202.860i	0.885049	−	0.510983i	0.0127291	−	0.999919i	$-0.495948\pi$
$397$	351.364	−	202.860i	0.885049	−	0.510983i	0.872320	+	0.488936i	$0.162615\pi$
$398$	19.8320			0.0498291
$399$	−364.095	−	283.033i	−0.912519	−	0.709356i
$400$	−116.556	+	201.881i	−0.291390	+	0.504702i
$401$	−196.784	+	340.840i	−0.490734	+	0.849975i	−0.999943	−	0.0106671i	$-0.996604\pi$
$401$	−196.784	+	340.840i	−0.490734	+	0.849975i	0.509210	+	0.860643i	$0.329938\pi$
$402$	−80.8658	−	198.751i	−0.201159	−	0.494405i
$403$	−16.4639	−	2.06019i	−0.0408534	−	0.00511215i
$404$		−	244.810i		−	0.605964i
$405$	−630.656	−	385.564i	−1.55718	−	0.952009i
$406$	−114.753	+	198.758i	−0.282643	+	0.489552i
$407$	58.8424	−	33.9727i	0.144576	−	0.0834710i
$408$	−24.8205	−	61.0036i	−0.0608346	−	0.149519i
$409$	−93.6100	+	54.0458i	−0.228875	+	0.132141i	−0.610053	−	0.792361i	$-0.708852\pi$
$409$	−93.6100	+	54.0458i	−0.228875	+	0.132141i	0.381178	+	0.924502i	$0.375519\pi$
$410$	−127.907	−	221.541i	−0.311968	−	0.540344i
$411$	−676.934	+	275.424i	−1.64704	+	0.670131i
$412$	7.22499	+	12.5141i	0.0175364	+	0.0303739i
$413$	−262.196	−	151.379i	−0.634858	−	0.366536i
$414$	237.171	−	60.3653i	0.572877	−	0.145810i
$415$	70.7075			0.170380
$416$	67.7594	−	28.5773i	0.162883	−	0.0686955i
$417$	303.588	−	123.521i	0.728029	−	0.296213i
$418$	170.014	+	98.1575i	0.406732	+	0.234827i
$419$	203.633	+	117.567i	0.485997	+	0.280591i	0.722912	−	0.690940i	$-0.242803\pi$
$419$	203.633	+	117.567i	0.485997	+	0.280591i	−0.236915	+	0.971530i	$0.576136\pi$
$420$	−145.746	+	187.488i	−0.347015	+	0.446401i
$421$		−	460.455i		−	1.09372i	−0.837225	−	0.546859i	$-0.815823\pi$
$421$		−	460.455i		−	1.09372i	0.837225	−	0.546859i	$-0.184177\pi$
$422$	−188.123	−	325.838i	−0.445788	−	0.772128i
$423$	162.261	+	45.6710i	0.383595	+	0.107969i
$424$			41.6270i			0.0981769i
$425$	−391.731	+	226.166i	−0.921721	+	0.532156i
$426$	29.4330	−	213.203i	0.0690915	−	0.500477i
$427$	228.707	+	132.044i	0.535614	+	0.309237i
$428$			362.982i			0.848090i
$429$	107.993	−	108.021i	0.251733	−	0.251797i
$430$	−374.688			−0.871369
$431$	−308.611	+	534.529i	−0.716034	+	1.24021i	0.246525	+	0.969136i	$0.420711\pi$
$431$	−308.611	+	534.529i	−0.716034	+	1.24021i	−0.962559	+	0.271071i	$0.912622\pi$
$432$	64.1192	+	86.9064i	0.148424	+	0.201172i
$433$	179.660	+	311.180i	0.414919	+	0.718660i	0.995420	−	0.0955992i	$-0.0304767\pi$
$433$	179.660	+	311.180i	0.414919	+	0.718660i	−0.580501	+	0.814259i	$0.697143\pi$
$434$	−7.82850			−0.0180380
$435$	628.706	−	808.770i	1.44530	−	1.85924i
$436$	257.138	−	148.459i	0.589766	−	0.340502i
$437$	−681.506			−1.55951
$438$	−208.473	+	268.180i	−0.475965	+	0.612284i
$439$	−399.864	+	692.586i	−0.910853	+	1.57764i	−0.0979911	+	0.995187i	$0.531242\pi$
$439$	−399.864	+	692.586i	−0.910853	+	1.57764i	−0.812862	+	0.582456i	$0.802092\pi$
$440$	50.5456	−	87.5475i	0.114876	−	0.198972i
$441$	194.525	−	189.695i	0.441099	−	0.430148i
$442$	141.592	+	17.7179i	0.320343	+	0.0400858i
$443$		−	221.111i		−	0.499121i	−0.968359	−	0.249561i	$-0.919714\pi$
$443$		−	221.111i		−	0.499121i	0.968359	−	0.249561i	$-0.0802861\pi$
$444$	−103.112	−	14.2347i	−0.232234	−	0.0320602i
$445$	382.730	−	662.908i	0.860068	−	1.48968i
$446$	−484.735	+	279.862i	−1.08685	+	0.627493i
$447$	498.827	−	202.958i	1.11594	−	0.454044i
$448$	30.0483	−	17.3484i	0.0670721	−	0.0387241i
$449$	302.552	+	524.035i	0.673834	+	1.16712i	0.976808	+	0.214116i	$0.0686871\pi$
$449$	302.552	+	524.035i	0.673834	+	1.16712i	−0.302974	+	0.952999i	$0.597980\pi$
$450$	531.053	−	517.868i	1.18012	−	1.15082i
$451$	38.8165	+	67.2321i	0.0860676	+	0.149073i
$452$	62.3311	+	35.9869i	0.137901	+	0.0796170i
$453$	146.999	+	20.2934i	0.324501	+	0.0447978i
$454$	−257.595			−0.567390
$455$	−199.945	−	474.088i	−0.439440	−	1.04195i
$456$	−113.343	−	278.572i	−0.248558	−	0.610903i
$457$	447.804	+	258.539i	0.979876	+	0.565732i	0.902233	−	0.431249i	$-0.141927\pi$
$457$	447.804	+	258.539i	0.979876	+	0.565732i	0.0776436	+	0.996981i	$0.475260\pi$
$458$	34.8979	+	20.1483i	0.0761964	+	0.0439920i
$459$	23.4317	+	208.250i	0.0510495	+	0.453704i
$460$			350.937i			0.762907i
$461$	−125.647	−	217.626i	−0.272552	−	0.472074i	0.696963	−	0.717108i	$-0.254534\pi$
$461$	−125.647	−	217.626i	−0.272552	−	0.472074i	−0.969515	+	0.245033i	$0.921201\pi$
$462$	44.2303	−	56.8981i	0.0957366	−	0.123156i
$463$		−	696.572i		−	1.50448i	−0.658892	−	0.752238i	$-0.728974\pi$
$463$		−	696.572i		−	1.50448i	0.658892	−	0.752238i	$-0.271026\pi$
$464$	−129.620	+	74.8359i	−0.279353	+	0.161284i
$465$	34.6139	+	4.77850i	0.0744385	+	0.0102763i
$466$	317.054	+	183.051i	0.680373	+	0.392814i
$467$		−	390.977i		−	0.837210i	−0.908168	−	0.418605i	$-0.862519\pi$
$467$		−	390.977i		−	0.837210i	0.908168	−	0.418605i	$-0.137481\pi$
$468$	−232.182	+	29.1143i	−0.496115	+	0.0622101i
$469$	219.349			0.467696
$470$	−120.858	+	209.333i	−0.257145	+	0.445389i
$471$	−50.9669	+	369.188i	−0.108210	+	0.783839i
$472$	−98.7215	−	170.991i	−0.209156	−	0.362268i
$473$	113.709			0.240399
$474$	111.162	+	86.4128i	0.234519	+	0.182305i
$475$	−1788.84	+	1032.79i	−3.76597	+	2.17428i
$476$	67.3260			0.141441
$477$	35.8876	−	127.502i	0.0752360	−	0.267300i
$478$	−7.19735	+	12.4662i	−0.0150572	+	0.0260799i
$479$	−36.4399	+	63.1157i	−0.0760749	+	0.131766i	−0.901553	−	0.432668i	$-0.857572\pi$
$479$	−36.4399	+	63.1157i	−0.0760749	+	0.131766i	0.825478	+	0.564434i	$0.190905\pi$
$480$	−143.449	+	58.3650i	−0.298852	+	0.121594i
$481$	136.142	−	179.800i	0.283040	−	0.373804i
$482$		−	113.535i		−	0.235549i
$483$	−34.2134	+	247.831i	−0.0708352	+	0.513108i
$484$	105.661	−	183.010i	0.218307	−	0.378119i
$485$	545.919	−	315.186i	1.12561	−	0.649869i
$486$	−121.471	−	321.470i	−0.249940	−	0.661461i
$487$	−73.3380	+	42.3417i	−0.150591	+	0.0869439i	−0.573402	−	0.819274i	$-0.694377\pi$
$487$	−73.3380	+	42.3417i	−0.150591	+	0.0869439i	0.422811	+	0.906218i	$0.361043\pi$
$488$	86.1122	+	149.151i	0.176460	+	0.305637i
$489$	307.528	+	755.840i	0.628892	+	1.54568i
$490$	194.808	+	337.417i	0.397567	+	0.688607i
$491$	−261.994	−	151.262i	−0.533593	−	0.308070i	0.208886	−	0.977940i	$-0.433016\pi$
$491$	−261.994	−	151.262i	−0.533593	−	0.308070i	−0.742478	+	0.669870i	$0.766350\pi$
$492$	16.2643	−	117.813i	0.0330575	−	0.239458i
$493$	−290.424			−0.589096
$494$	646.576	+	80.9086i	1.30886	+	0.163783i
$495$	−230.296	+	224.578i	−0.465244	+	0.453694i
$496$	−4.42135	−	2.55266i	−0.00891400	−	0.00514650i
$497$	190.540	+	110.008i	0.383381	+	0.221345i
$498$	25.9535	+	20.1752i	0.0521154	+	0.0405124i
$499$		−	59.5961i		−	0.119431i	−0.998215	−	0.0597155i	$-0.980981\pi$
$499$		−	59.5961i		−	0.119431i	0.998215	−	0.0597155i	$-0.0190193\pi$
$500$	303.684	+	525.997i	0.607369	+	1.05199i
$501$	−440.757	−	342.627i	−0.879754	−	0.683886i
$502$		−	132.290i		−	0.263526i
$503$	217.501	−	125.574i	0.432408	−	0.249651i	−0.267964	−	0.963429i	$-0.586351\pi$
$503$	217.501	−	125.574i	0.432408	−	0.249651i	0.700372	+	0.713778i	$0.253018\pi$
$504$	−106.993	+	27.2322i	−0.212288	+	0.0540321i
$505$	−967.373	−	558.513i	−1.91559	−	1.10597i
$506$		−	106.501i		−	0.210476i
$507$	190.952	−	469.666i	0.376632	−	0.926363i
$508$	−253.053			−0.498137
$509$	257.978	−	446.830i	0.506832	−	0.877859i	−0.493137	−	0.869952i	$-0.664150\pi$
$509$	257.978	−	446.830i	0.506832	−	0.877859i	0.999969	−	0.00790722i	$-0.00251697\pi$
$510$	−297.684	−	41.0956i	−0.583693	−	0.0805797i
$511$	−173.621	−	300.720i	−0.339767	−	0.588493i
$512$	22.6274			0.0441942
$513$	107.001	+	950.971i	0.208578	+	1.85374i
$514$	350.872	−	202.576i	0.682630	−	0.394116i
$515$	65.9330			0.128025
$516$	−137.531	−	106.911i	−0.266533	−	0.207192i
$517$	36.6775	−	63.5273i	0.0709429	−	0.122877i
$518$	53.2036	−	92.1514i	0.102710	−	0.177898i
$519$	88.6034	+	217.769i	0.170720	+	0.419593i
$520$	41.6634	−	332.950i	0.0801219	−	0.640289i
$521$			745.682i			1.43125i	0.698484	+	0.715626i	$0.253858\pi$
$521$			745.682i			1.43125i	−0.698484	+	0.715626i	$0.746142\pi$
$522$	461.538	−	117.472i	0.884172	−	0.225041i
$523$	−61.9466	+	107.295i	−0.118445	+	0.205152i	−0.919152	−	0.393904i	$-0.871124\pi$
$523$	−61.9466	+	107.295i	−0.118445	+	0.205152i	0.800707	+	0.599056i	$0.204458\pi$
$524$	273.830	−	158.096i	0.522575	−	0.301709i
$525$	285.770	+	702.362i	0.544324	+	1.33783i
$526$	448.706	−	259.060i	0.853053	−	0.492510i
$527$	−4.95321	−	8.57921i	−0.00939888	−	0.0162793i
$528$	43.5332	−	17.7123i	0.0824492	−	0.0335461i
$529$	−79.6416	−	137.943i	−0.150551	−	0.260763i
$530$	164.491	+	94.9686i	0.310359	+	0.179186i
$531$	154.965	+	608.848i	0.291837	+	1.14661i
$532$	307.443			0.577901
$533$	205.436	+	155.554i	0.385433	+	0.291845i
$534$	329.632	−	134.117i	0.617289	−	0.251156i
$535$	1434.34	+	828.115i	2.68101	+	1.54788i
$536$	123.883	+	71.5241i	0.231126	+	0.133440i
$537$	250.271	−	321.950i	0.466054	−	0.599534i
$538$		−	195.623i		−	0.363611i
$539$	−59.1194	−	102.398i	−0.109683	−	0.189977i
$540$	489.697	−	55.0993i	0.906845	−	0.102036i
$541$			121.850i			0.225230i	0.993639	+	0.112615i	$0.0359227\pi$
$541$			121.850i			0.225230i	−0.993639	+	0.112615i	$0.964077\pi$
$542$	63.7758	−	36.8210i	0.117668	−	0.0679354i
$543$	−19.0883	+	138.269i	−0.0351534	+	0.254640i
$544$	38.0241	+	21.9532i	0.0698972	+	0.0403552i
$545$		−	1354.79i		−	2.48585i
$546$	61.8824	−	231.067i	0.113338	−	0.423200i
$547$	−185.017			−0.338239			−0.169120	−	0.985596i	$-0.554092\pi$
$547$	−185.017			−0.338239			−0.169120	+	0.985596i	$0.554092\pi$
$548$	243.607	−	421.939i	0.444538	−	0.769962i
$549$	−135.172	−	531.083i	−0.246216	−	0.967364i
$550$	−161.396	−	279.546i	−0.293447	−	0.508266i
$551$	−1326.22			−2.40693
$552$	−100.134	+	128.813i	−0.181402	+	0.233357i
$553$	−124.650	+	71.9665i	−0.225406	+	0.130138i
$554$	−173.507			−0.313190
$555$	−291.490	+	374.974i	−0.525208	+	0.675630i
$556$	−109.252	+	189.229i	−0.196496	+	0.340340i
$557$	154.231	−	267.135i	0.276895	−	0.479597i	−0.693716	−	0.720248i	$-0.744028\pi$
$557$	154.231	−	267.135i	0.276895	−	0.479597i	0.970612	+	0.240652i	$0.0773612\pi$
$558$	11.3417	+	11.6305i	0.0203256	+	0.0208431i
$559$	347.764	−	146.668i	0.622118	−	0.262376i
$560$		−	158.316i		−	0.282707i
$561$	90.3396	+	12.4715i	0.161033	+	0.0222308i
$562$	−326.190	+	564.978i	−0.580410	+	1.00530i
$563$	406.743	−	234.833i	0.722457	−	0.417111i	−0.0931994	−	0.995647i	$-0.529709\pi$
$563$	406.743	−	234.833i	0.722457	−	0.417111i	0.815656	+	0.578537i	$0.196376\pi$
$564$	−104.091	+	42.3515i	−0.184559	+	0.0750913i
$565$	284.407	−	164.202i	0.503375	−	0.290624i
$566$	20.6714	+	35.8039i	0.0365219	+	0.0632578i
$567$	351.194	+	8.83026i	0.619390	+	0.0155736i
$568$	71.7417	+	124.260i	0.126306	+	0.218768i
$569$	301.901	+	174.302i	0.530581	+	0.306331i	0.741253	−	0.671226i	$-0.234232\pi$
$569$	301.901	+	174.302i	0.530581	+	0.306331i	−0.210672	+	0.977557i	$0.567565\pi$
$570$	−1359.37	−	187.663i	−2.38486	−	0.329233i
$571$	−918.293			−1.60822			−0.804110	−	0.594481i	$-0.797358\pi$
$571$	−918.293			−1.60822			−0.804110	+	0.594481i	$0.797358\pi$
$572$	−12.6438	+	101.042i	−0.0221045	+	0.176647i
$573$	126.625	+	311.218i	0.220986	+	0.543137i
$574$	105.290	+	60.7894i	0.183433	+	0.105905i
$575$	970.442	+	560.285i	1.68773	+	0.974409i
$576$	−69.3069	−	19.5076i	−0.120325	−	0.0338674i
$577$			365.118i			0.632787i	0.948628	+	0.316394i	$0.102472\pi$
$577$			365.118i			0.632787i	−0.948628	+	0.316394i	$0.897528\pi$
$578$	−161.756	−	280.169i	−0.279854	−	0.484722i
$579$	125.216	−	161.078i	0.216262	−	0.278201i
$580$			682.928i			1.17746i
$581$	−29.1025	+	16.8023i	−0.0500904	+	0.0289197i
$582$	290.315	+	40.0783i	0.498822	+	0.0688631i
$583$	−49.9188	−	28.8206i	−0.0856240	−	0.0494350i
$584$		−	226.453i		−	0.387761i
$585$	−414.658	+	983.896i	−0.708817	+	1.68187i
$586$	−273.999			−0.467574
$587$	−353.378	+	612.069i	−0.602008	+	1.04271i	0.390509	+	0.920599i	$0.372299\pi$
$587$	−353.378	+	612.069i	−0.602008	+	1.04271i	−0.992517	+	0.122109i	$0.961034\pi$
$588$	−24.7713	+	179.436i	−0.0421281	+	0.305162i
$589$	−22.6188	−	39.1769i	−0.0384020	−	0.0665142i
$590$	−900.900			−1.52695
$591$	−418.731	−	325.505i	−0.708513	−	0.550770i
$592$	60.0962	−	34.6966i	0.101514	−	0.0586091i
$593$	511.072			0.861842			0.430921	−	0.902390i	$-0.358189\pi$
$593$	511.072			0.861842			0.430921	+	0.902390i	$0.358189\pi$
$594$	−148.611	+	16.7213i	−0.250186	+	0.0281503i
$595$	153.599	−	266.041i	0.258149	−	0.447127i
$596$	−179.512	+	310.924i	−0.301194	+	0.521684i
$597$	38.9680	−	15.8549i	0.0652730	−	0.0265576i
$598$	−137.371	−	325.720i	−0.229718	−	0.544682i
$599$		−	942.848i		−	1.57404i	−0.616930	−	0.787018i	$-0.711624\pi$
$599$		−	942.848i		−	1.57404i	0.616930	−	0.787018i	$-0.288376\pi$
$600$	−67.6257	+	489.859i	−0.112710	+	0.816432i
$601$	−218.045	+	377.666i	−0.362804	+	0.628396i	−0.988421	−	0.151735i	$-0.951514\pi$
$601$	−218.045	+	377.666i	−0.362804	+	0.628396i	0.625617	+	0.780131i	$0.284847\pi$
$602$	154.218	−	89.0379i	0.256176	−	0.147903i
$603$	−317.787	−	325.878i	−0.527011	−	0.540428i
$604$	−85.6749	+	49.4644i	−0.141846	+	0.0818947i
$605$	−482.113	−	835.044i	−0.796880	−	1.38024i
$606$	−195.716	−	481.028i	−0.322963	−	0.793776i
$607$	−54.5495	−	94.4824i	−0.0898673	−	0.155655i	0.817588	−	0.575804i	$-0.195311\pi$
$607$	−54.5495	−	94.4824i	−0.0898673	−	0.155655i	−0.907455	+	0.420149i	$0.861978\pi$
$608$	173.636	+	100.249i	0.285586	+	0.164883i
$609$	−66.5797	+	482.282i	−0.109326	+	0.791925i
$610$	785.833			1.28825
$611$	30.2323	−	241.599i	0.0494800	−	0.395416i
$612$	−97.5400	−	100.023i	−0.159379	−	0.163437i
$613$	−713.570	−	411.980i	−1.16406	−	0.672071i	−0.211788	−	0.977316i	$-0.567928\pi$
$613$	−713.570	−	411.980i	−1.16406	−	0.672071i	−0.952274	+	0.305244i	$0.901262\pi$
$614$	213.868	+	123.477i	0.348319	+	0.201102i
$615$	−428.438	−	333.051i	−0.696648	−	0.541546i
$616$			48.0449i			0.0779950i
$617$	367.020	+	635.698i	0.594846	+	1.03030i	0.993569	+	0.113232i	$0.0361205\pi$
$617$	367.020	+	635.698i	0.594846	+	1.03030i	−0.398722	+	0.917072i	$0.630546\pi$
$618$	24.2010	+	18.8129i	0.0391601	+	0.0304415i
$619$			467.085i			0.754580i	0.926095	+	0.377290i	$0.123144\pi$
$619$			467.085i			0.754580i	−0.926095	+	0.377290i	$0.876856\pi$
$620$	−20.1739	+	11.6474i	−0.0325385	+	0.0187861i
$621$	417.760	−	308.221i	0.672721	−	0.496331i
$622$	56.5457	+	32.6467i	0.0909094	+	0.0524866i
$623$			363.795i			0.583941i
$624$	110.295	−	110.323i	0.176754	−	0.176799i
$625$	1314.37			2.10300
$626$	68.7937	−	119.154i	0.109894	−	0.190342i
$627$	412.534	+	56.9509i	0.657950	+	0.0908309i
$628$	−124.230	−	215.172i	−0.197818	−	0.342631i
$629$	134.651			0.214072
$630$	−136.488	+	484.916i	−0.216647	+	0.769708i
$631$	535.730	−	309.304i	0.849017	−	0.490180i	−0.0113018	−	0.999936i	$-0.503598\pi$
$631$	535.730	−	309.304i	0.849017	−	0.490180i	0.860319	+	0.509756i	$0.170264\pi$
$632$	−93.8654			−0.148521
$633$	−630.138	−	489.844i	−0.995479	−	0.773846i
$634$	−271.456	+	470.176i	−0.428164	+	0.741602i
$635$	−577.321	+	999.949i	−0.909167	+	1.57472i
$636$	33.2792	+	81.7932i	0.0523258	+	0.128606i
$637$	−312.889	−	236.915i	−0.491191	−	0.371924i
$638$		−	207.252i		−	0.324846i
$639$	−112.615	−	442.455i	−0.176236	−	0.692417i
$640$	51.6226	−	89.4130i	0.0806604	−	0.139708i
$641$	−1099.69	+	634.906i	−1.71558	+	0.990493i	−0.789009	+	0.614382i	$0.789405\pi$
$641$	−1099.69	+	634.906i	−1.71558	+	0.990493i	−0.926575	+	0.376111i	$0.877261\pi$
$642$	290.191	+	713.227i	0.452010	+	1.11095i
$643$	−172.911	+	99.8301i	−0.268913	+	0.155257i	−0.628393	−	0.777896i	$-0.716287\pi$
$643$	−172.911	+	99.8301i	−0.268913	+	0.155257i	0.359481	+	0.933153i	$0.382954\pi$
$644$	−83.3939	−	144.442i	−0.129494	−	0.224289i
$645$	−736.228	+	299.549i	−1.14144	+	0.464417i
$646$	194.524	+	336.926i	0.301121	+	0.521557i
$647$	696.360	+	402.043i	1.07629	+	0.621396i	0.929893	−	0.367830i	$-0.119899\pi$
$647$	696.360	+	402.043i	1.07629	+	0.621396i	0.146397	+	0.989226i	$0.453232\pi$
$648$	195.467	+	119.502i	0.301646	+	0.184417i
$649$	273.401			0.421265
$650$	−854.186	−	646.780i	−1.31413	−	0.995045i
$651$	−15.3823	+	6.25858i	−0.0236287	+	0.00961379i
$652$	−471.122	−	272.002i	−0.722580	−	0.417182i
$653$	−1099.32	−	634.691i	−1.68349	−	0.971961i	−0.959314	−	0.282342i	$-0.908889\pi$
$653$	−1099.32	−	634.691i	−1.68349	−	0.971961i	−0.724172	−	0.689619i	$-0.757778\pi$
$654$	386.565	−	497.280i	0.591079	−	0.760366i
$655$		−	1442.73i		−	2.20264i
$656$	39.6436	+	68.6647i	0.0604323	+	0.104672i
$657$	−195.230	+	693.616i	−0.297154	+	1.05573i
$658$		−	114.879i		−	0.174588i
$659$	352.776	−	203.675i	0.535320	−	0.309067i	−0.207860	−	0.978159i	$-0.566650\pi$
$659$	352.776	−	203.675i	0.535320	−	0.309067i	0.743180	+	0.669091i	$0.233316\pi$
$660$	29.3265	−	212.432i	0.0444341	−	0.321867i
$661$	−573.089	−	330.873i	−0.867004	−	0.500565i	−0.000652274	−	1.00000i	$-0.500208\pi$
$661$	−573.089	−	330.873i	−0.867004	−	0.500565i	−0.866351	+	0.499435i	$0.833541\pi$
$662$		−	135.735i		−	0.205038i
$663$	292.379	−	78.3830i	0.440994	−	0.118225i
$664$	−21.9152			−0.0330048
$665$	701.407	−	1214.87i	1.05475	−	1.82688i
$666$	−213.985	+	54.4640i	−0.321299	+	0.0817778i
$667$	359.737	+	623.082i	0.539335	+	0.934156i
$668$	372.177			0.557150
$669$	−728.721	+	937.430i	−1.08927	+	1.40124i
$670$	565.259	−	326.353i	0.843671	−	0.487094i
$671$	−238.481			−0.355411
$672$	45.1728	−	58.1105i	0.0672214	−	0.0864739i
$673$	162.502	−	281.461i	0.241458	−	0.418218i	−0.719671	−	0.694315i	$-0.755708\pi$
$673$	162.502	−	281.461i	0.241458	−	0.418218i	0.961130	+	0.276096i	$0.0890409\pi$
$674$	1.70450	−	2.95228i	0.00252893	−	0.00438023i
$675$	629.454	−	1442.12i	0.932525	−	2.13647i
$676$	91.6609	+	325.334i	0.135593	+	0.481263i
$677$		−	556.246i		−	0.821634i	−0.911718	−	0.410817i	$-0.865244\pi$
$677$		−	556.246i		−	0.821634i	0.911718	−	0.410817i	$-0.134756\pi$
$678$	151.245	+	20.8796i	0.223075	+	0.0307958i
$679$	−149.797	+	259.455i	−0.220613	+	0.382114i
$680$	173.498	−	100.169i	0.255144	−	0.147307i
$681$	−506.151	+	205.937i	−0.743246	+	0.302404i
$682$	6.12227	−	3.53469i	0.00897694	−	0.00518284i
$683$	−505.184	−	875.004i	−0.739654	−	1.28112i	−0.952651	−	0.304065i	$-0.901656\pi$
$683$	−505.184	−	875.004i	−0.739654	−	1.28112i	0.212997	−	0.977053i	$-0.431677\pi$
$684$	−445.415	−	456.755i	−0.651192	−	0.667771i
$685$	−1111.54	−	1925.24i	−1.62268	−	2.81057i
$686$	−420.642	−	242.858i	−0.613181	−	0.354020i
$687$	84.6790	+	11.6901i	0.123259	+	0.0170161i
$688$	116.132			0.168796
$689$	−189.845	−	23.7561i	−0.275537	−	0.0344791i
$690$	280.561	+	689.560i	0.406610	+	0.999362i
$691$	377.138	+	217.740i	0.545785	+	0.315109i	0.747420	−	0.664351i	$-0.231292\pi$
$691$	377.138	+	217.740i	0.545785	+	0.315109i	−0.201635	+	0.979461i	$0.564626\pi$
$692$	−135.737	−	78.3679i	−0.196152	−	0.113248i
$693$	41.4206	−	147.160i	0.0597701	−	0.212352i
$694$			877.652i			1.26463i
$695$	498.497	+	863.423i	0.717262	+	1.24233i
$696$	−194.862	+	250.672i	−0.279974	+	0.360160i
$697$			153.850i			0.220731i
$698$	−641.415	+	370.321i	−0.918933	+	0.530546i
$699$	769.324	+	106.206i	1.10061	+	0.151940i
$700$	−437.789	−	252.758i	−0.625413	−	0.361082i
$701$			503.999i			0.718971i	0.933151	+	0.359486i	$0.117048\pi$
$701$			503.999i			0.718971i	−0.933151	+	0.359486i	$0.882952\pi$
$702$	−432.940	+	242.827i	−0.616723	+	0.345908i
$703$	614.882			0.874655
$704$	−15.6662	+	27.1346i	−0.0222531	+	0.0385435i
$705$	−70.1220	+	507.941i	−0.0994638	+	0.720484i
$706$	320.262	+	554.709i	0.453628	+	0.785707i
$707$	530.882			0.750894
$708$	−330.679	−	257.057i	−0.467061	−	0.363074i
$709$	865.253	−	499.554i	1.22038	−	0.704590i	0.255385	−	0.966839i	$-0.417798\pi$
$709$	865.253	−	499.554i	1.22038	−	0.704590i	0.965000	+	0.262250i	$0.0844645\pi$
$710$	654.692			0.922101
$711$	287.506	+	80.9236i	0.404369	+	0.113817i
$712$	−118.624	+	205.463i	−0.166607	+	0.288571i
$713$	−12.2707	+	21.2534i	−0.0172099	+	0.0298085i
$714$	132.289	−	53.8245i	0.185279	−	0.0753845i
$715$	370.426	+	280.482i	0.518078	+	0.392282i
$716$			271.856i			0.379687i
$717$	−4.17590	+	30.2489i	−0.00582413	+	0.0421881i
$718$	−49.5612	+	85.8425i	−0.0690267	+	0.119558i
$719$	−213.308	+	123.153i	−0.296673	+	0.171284i	−0.640947	−	0.767585i	$-0.721458\pi$
$719$	−213.308	+	123.153i	−0.296673	+	0.171284i	0.344274	+	0.938869i	$0.388125\pi$
$720$	−235.203	+	229.364i	−0.326671	+	0.318561i
$721$	−27.1374	+	15.6678i	−0.0376385	+	0.0217306i
$722$	633.026	+	1096.43i	0.876768	+	1.51861i
$723$	−90.7667	−	223.085i	−0.125542	−	0.308555i
$724$	−46.5269	−	80.5870i	−0.0642637	−	0.111308i
$725$	1888.49	+	1090.32i	2.60482	+	1.50389i
$726$	61.3043	−	444.069i	0.0844412	−	0.611665i
$727$	−166.980			−0.229684			−0.114842	−	0.993384i	$-0.536636\pi$
$727$	−166.980			−0.229684			−0.114842	+	0.993384i	$0.536636\pi$
$728$	61.9713	+	146.940i	0.0851255	+	0.201840i
$729$	−495.682	−	534.547i	−0.679947	−	0.733261i
$730$	−894.835	−	516.633i	−1.22580	−	0.707717i
$731$	195.152	+	112.671i	0.266966	+	0.154133i
$732$	288.443	+	224.224i	0.394048	+	0.306317i
$733$			601.051i			0.819988i	0.912088	+	0.409994i	$0.134469\pi$
$733$			601.051i			0.819988i	−0.912088	+	0.409994i	$0.865531\pi$
$734$	307.385	+	532.407i	0.418781	+	0.725350i
$735$	652.532	+	507.252i	0.887799	+	0.690139i
$736$		−	108.770i		−	0.147785i
$737$	−171.542	+	99.0399i	−0.232757	+	0.134383i
$738$	−62.2295	−	244.495i	−0.0843218	−	0.331294i
$739$	313.252	+	180.856i	0.423886	+	0.244731i	0.696739	−	0.717325i	$-0.254634\pi$
$739$	313.252	+	180.856i	0.423886	+	0.244731i	−0.272853	+	0.962056i	$0.587967\pi$
$740$		−	316.630i		−	0.427878i
$741$	1335.15	−	357.935i	1.80182	−	0.483043i
$742$	−90.2702			−0.121658
$743$	178.035	−	308.365i	0.239616	−	0.415027i	−0.720988	−	0.692948i	$-0.756312\pi$
$743$	178.035	−	308.365i	0.239616	−	0.415027i	0.960604	+	0.277920i	$0.0896451\pi$
$744$	−10.7283	−	1.48106i	−0.0144197	−	0.00199067i
$745$	819.084	+	1418.69i	1.09944	+	1.90429i
$746$	−248.789			−0.333498
$747$	67.1255	+	18.8936i	0.0898600	+	0.0252926i
$748$	−52.6522	+	30.3988i	−0.0703907	+	0.0406401i
$749$	−787.146			−1.05093
$750$	1017.23	+	790.751i	1.35630	+	1.05433i
$751$	−249.444	+	432.050i	−0.332149	+	0.575300i	−0.982933	−	0.183964i	$-0.941107\pi$
$751$	−249.444	+	432.050i	−0.332149	+	0.575300i	0.650784	+	0.759263i	$0.274440\pi$
$752$	37.4590	−	64.8809i	0.0498125	−	0.0862778i
$753$	−105.761	−	259.938i	−0.140453	−	0.345203i
$754$	−267.326	−	633.855i	−0.354544	−	0.840656i
$755$			451.396i			0.597876i
$756$	−188.461	+	139.046i	−0.249287	+	0.183923i
$757$	−628.865	+	1089.23i	−0.830734	+	1.43887i	0.0667237	+	0.997771i	$0.478745\pi$
$757$	−628.865	+	1089.23i	−0.830734	+	1.43887i	−0.897457	+	0.441101i	$0.854588\pi$
$758$	260.309	−	150.289i	0.343415	−	0.198271i
$759$	−85.1432	−	209.264i	−0.112178	−	0.275710i
$760$	792.275	−	457.420i	1.04247	−	0.601869i
$761$	−189.445	−	328.128i	−0.248942	−	0.431180i	0.714291	−	0.699849i	$-0.246749\pi$
$761$	−189.445	−	328.128i	−0.248942	−	0.431180i	−0.963232	+	0.268669i	$0.913416\pi$
$762$	−497.227	+	202.306i	−0.652528	+	0.265494i
$763$	321.940	+	557.617i	0.421940	+	0.730821i
$764$	−193.985	−	111.997i	−0.253907	−	0.146593i
$765$	−617.775	+	157.237i	−0.807549	+	0.205539i
$766$	−281.911			−0.368030
$767$	836.163	−	352.649i	1.09017	−	0.459777i
$768$	44.4608	−	18.0897i	0.0578916	−	0.0235544i
$769$	−444.886	−	256.855i	−0.578525	−	0.334012i	0.182022	−	0.983295i	$-0.441736\pi$
$769$	−444.886	−	256.855i	−0.578525	−	0.334012i	−0.760547	+	0.649283i	$0.775069\pi$
$770$	189.851	+	109.611i	0.246560	+	0.142352i
$771$	527.479	−	678.551i	0.684149	−	0.880092i
$772$			136.015i			0.176185i
$773$	−141.979	−	245.914i	−0.183672	−	0.318130i	0.759456	−	0.650559i	$-0.225465\pi$
$773$	−141.979	−	245.914i	−0.183672	−	0.318130i	−0.943128	+	0.332429i	$0.892132\pi$
$774$	−355.707	−	100.120i	−0.459569	−	0.129354i
$775$			74.3821i			0.0959769i
$776$	−169.203	+	97.6893i	−0.218045	+	0.125888i
$777$	30.8687	−	223.603i	0.0397281	−	0.287778i
$778$	−664.764	−	383.802i	−0.854453	−	0.493319i
$779$			702.552i			0.901864i
$780$	−184.316	−	687.525i	−0.236303	−	0.881442i
$781$	−198.683			−0.254395
$782$	105.529	−	182.782i	0.134948	−	0.233736i
$783$	812.965	−	599.803i	1.03827	−	0.766031i
$784$	−60.3791	−	104.580i	−0.0770142	−	0.133392i
$785$	−1133.68			−1.44418
$786$	411.658	−	529.559i	0.523738	−	0.673740i
$787$	−1004.70	+	580.062i	−1.27662	+	0.737055i	−0.976225	−	0.216761i	$-0.930451\pi$
$787$	−1004.70	+	580.062i	−1.27662	+	0.737055i	−0.300391	+	0.953816i	$0.597117\pi$
$788$	353.578			0.448703
$789$	674.557	−	867.753i	0.854951	−	1.09981i
$790$	−214.146	+	370.913i	−0.271071	+	0.469510i
$791$	−78.0394	+	135.168i	−0.0986591	+	0.170883i
$792$	71.3783	−	69.6062i	0.0901241	−	0.0878866i
$793$	−729.364	+	307.607i	−0.919753	+	0.387903i
$794$			573.776i			0.722639i
$795$	399.132	+	55.1008i	0.502053	+	0.0693091i
$796$	−14.0233	+	24.2891i	−0.0176172	+	0.0305139i
$797$	470.911	−	271.880i	0.590854	−	0.341130i	−0.174581	−	0.984643i	$-0.555857\pi$
$797$	470.911	−	271.880i	0.590854	−	0.341130i	0.765435	+	0.643513i	$0.222524\pi$
$798$	604.097	−	245.789i	0.757014	−	0.308006i
$799$	125.895	−	72.6858i	0.157566	−	0.0909710i
$800$	−164.835	−	285.503i	−0.206044	−	0.356878i
$801$	540.475	−	527.056i	0.674750	−	0.657998i
$802$	−278.295	−	482.021i	−0.347001	−	0.601023i
$803$	271.560	+	156.785i	0.338182	+	0.195249i
$804$	300.600	+	41.4982i	0.373880	+	0.0516147i
$805$	−761.025			−0.945373
$806$	14.1650	−	18.7073i	0.0175744	−	0.0232101i
$807$	−156.393	−	384.381i	−0.193795	−	0.476308i
$808$	299.829	+	173.107i	0.371076	+	0.214241i
$809$	−152.339	−	87.9532i	−0.188306	−	0.108718i	0.402883	−	0.915251i	$-0.368008\pi$
$809$	−152.339	−	87.9532i	−0.188306	−	0.108718i	−0.591189	+	0.806533i	$0.701341\pi$
$810$	918.159	−	499.759i	1.13353	−	0.616986i
$811$		−	1242.17i		−	1.53166i	−0.643046	−	0.765828i	$-0.722329\pi$
$811$		−	1242.17i		−	1.53166i	0.643046	−	0.765828i	$-0.277671\pi$
$812$	−162.285	−	281.087i	−0.199859	−	0.346166i
$813$	95.8767	−	123.336i	0.117929	−	0.151705i
$814$			96.0892i			0.118046i
$815$	−2149.65	+	1241.10i	−2.63761	+	1.52283i
$816$	92.2645	+	12.7372i	0.113069	+	0.0156094i
$817$	891.161	+	514.512i	1.09077	+	0.629758i
$818$		−	152.865i		−	0.186876i
$819$	−63.1359	−	503.498i	−0.0770890	−	0.614771i
$820$	361.775			0.441189
$821$	−394.410	+	683.138i	−0.480402	+	0.832081i	−0.999747	−	0.0224838i	$-0.992843\pi$
$821$	−394.410	+	683.138i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$822$	141.341	−	1023.83i	0.171947	−	1.24553i
$823$	70.0300	+	121.296i	0.0850911	+	0.147382i	0.905430	−	0.424495i	$-0.139549\pi$
$823$	70.0300	+	121.296i	0.0850911	+	0.147382i	−0.820339	+	0.571878i	$0.806215\pi$
$824$	−20.4354			−0.0248002
$825$	−540.614	−	420.252i	−0.655290	−	0.509397i
$826$	370.802	−	214.082i	0.448912	−	0.259180i
$827$	−292.003			−0.353087			−0.176544	−	0.984293i	$-0.556492\pi$
$827$	−292.003			−0.353087			−0.176544	+	0.984293i	$0.556492\pi$
$828$	−93.7732	+	333.159i	−0.113253	+	0.402366i
$829$	27.8715	−	48.2748i	0.0336206	−	0.0582326i	−0.848726	−	0.528834i	$-0.822630\pi$
$829$	27.8715	−	48.2748i	0.0336206	−	0.0582326i	0.882346	+	0.470601i	$0.155963\pi$
$830$	−49.9978	+	86.5987i	−0.0602383	+	0.104336i
$831$	−340.926	+	138.712i	−0.410260	+	0.166922i
$832$	−12.9132	+	103.195i	−0.0155207	+	0.124033i
$833$		−	234.320i		−	0.281297i
$834$	−63.3877	+	459.160i	−0.0760044	+	0.550552i
$835$	849.091	−	1470.67i	1.01688	−	1.76128i
$836$	−240.436	+	138.816i	−0.287603	+	0.166047i
$837$	31.5835	+	13.7855i	0.0377342	+	0.0164702i
$838$	−287.980	+	166.265i	−0.343652	+	0.198407i
$839$	−719.294	−	1245.85i	−0.857322	−	1.48493i	−0.874474	−	0.485073i	$-0.838793\pi$
$839$	−719.294	−	1245.85i	−0.857322	−	1.48493i	0.0171511	−	0.999853i	$-0.494540\pi$
$840$	−126.567	−	311.076i	−0.150676	−	0.370329i
$841$	279.552	+	484.198i	0.332404	+	0.575740i
$842$	563.940	+	325.591i	0.669763	+	0.386688i
$843$	−189.256	+	1370.91i	−0.224502	+	1.62622i
$844$	532.091			0.630440
$845$	1494.69	+	380.022i	1.76886	+	0.449731i
$846$	−170.671	+	166.434i	−0.201739	+	0.196730i
$847$	396.866	+	229.130i	0.468555	+	0.270520i
$848$	−50.9825	−	29.4347i	−0.0601208	−	0.0347108i
$849$	69.2412	+	53.8254i	0.0815562	+	0.0633986i
$850$		−	639.695i		−	0.752582i
$851$	−166.787	−	288.883i	−0.195989	−	0.339463i
$852$	240.307	+	186.805i	0.282051	+	0.219255i
$853$		−	454.837i		−	0.533220i	−0.963804	−	0.266610i	$-0.914096\pi$
$853$		−	454.837i		−	0.533220i	0.963804	−	0.266610i	$-0.0859036\pi$
$854$	−323.441	+	186.739i	−0.378737	+	0.218664i
$855$	−2821.06	+	718.023i	−3.29949	+	0.839793i
$856$	−444.561	−	256.667i	−0.519347	−	0.299845i
$857$			489.997i			0.571759i	0.958266	+	0.285879i	$0.0922856\pi$
$857$			489.997i			0.571759i	−0.958266	+	0.285879i	$0.907714\pi$
$858$	55.9354	+	208.647i	0.0651928	+	0.243178i
$859$	−731.949			−0.852094			−0.426047	−	0.904701i	$-0.640094\pi$
$859$	−731.949			−0.852094			−0.426047	+	0.904701i	$0.640094\pi$
$860$	264.945	−	458.898i	0.308075	−	0.533602i
$861$	255.484	+	35.2700i	0.296730	+	0.0409640i
$862$	−436.441	−	755.939i	−0.506313	−	0.876959i
$863$	1132.22			1.31196			0.655980	−	0.754779i	$-0.272256\pi$
$863$	1132.22			1.31196			0.655980	+	0.754779i	$0.272256\pi$
$864$	−151.777	+	17.0776i	−0.175668	+	0.0197657i
$865$	−619.347	+	357.580i	−0.716008	+	0.413387i
$866$	−508.155			−0.586783
$867$	−541.819	−	421.189i	−0.624936	−	0.485800i
$868$	5.53558	−	9.58791i	0.00637740	−	0.0110460i
$869$	64.9881	−	112.563i	0.0747849	−	0.129531i
$870$	545.975	+	1341.89i	0.627557	+	1.54240i
$871$	−396.893	+	524.167i	−0.455675	+	0.601800i
$872$			419.905i			0.481542i
$873$	602.482	−	153.345i	0.690129	−	0.175653i
$874$	481.898	−	834.671i	0.551370	−	0.955002i
$875$	−1140.65	+	658.555i	−1.30360	+	0.752634i
$876$	−181.040	−	444.958i	−0.206667	−	0.507943i
$877$	307.720	−	177.662i	0.350878	−	0.202580i	−0.314194	−	0.949359i	$-0.601734\pi$
$877$	307.720	−	177.662i	0.350878	−	0.202580i	0.665072	+	0.746779i	$0.268401\pi$
$878$	−565.494	−	979.464i	−0.644070	−	1.11556i
$879$	−538.382	+	219.051i	−0.612494	+	0.249205i
$880$	71.4823	+	123.811i	0.0812298	+	0.140694i
$881$	−192.762	−	111.291i	−0.218799	−	0.126324i	0.386595	−	0.922250i	$-0.373651\pi$
$881$	−192.762	−	111.291i	−0.218799	−	0.126324i	−0.605394	+	0.795926i	$0.706984\pi$
$882$	94.7785	+	372.378i	0.107459	+	0.422197i
$883$	−68.1448			−0.0771741			−0.0385871	−	0.999255i	$-0.512286\pi$
$883$	−68.1448			−0.0771741			−0.0385871	+	0.999255i	$0.512286\pi$
$884$	−121.820	+	160.885i	−0.137806	+	0.181997i
$885$	−1770.19	+	720.235i	−2.00021	+	0.813825i
$886$	270.804	+	156.349i	0.305648	+	0.176466i
$887$	−700.425	−	404.390i	−0.789656	−	0.455908i	0.0501854	−	0.998740i	$-0.484019\pi$
$887$	−700.425	−	404.390i	−0.789656	−	0.455908i	−0.839841	+	0.542832i	$0.817352\pi$
$888$	90.3450	−	116.220i	0.101740	−	0.130879i
$889$		−	548.759i		−	0.617277i
$890$	541.262	+	937.494i	0.608160	+	1.05336i
$891$	−278.638	+	151.664i	−0.312725	+	0.170218i
$892$		−	791.569i		−	0.887409i
$893$	574.900	−	331.919i	0.643785	−	0.371690i
$894$	−104.153	+	754.449i	−0.116502	+	0.843903i
$895$	1074.25	+	620.217i	1.20028	+	0.692979i
$896$			49.0687i			0.0547642i
$897$	−530.322	−	530.186i	−0.591218	−	0.591066i
$898$	−855.745			−0.952946
$899$	−23.8789	+	41.3594i	−0.0265616	+	0.0460060i
$900$	258.745	+	1016.59i	0.287495	+	1.12955i
$901$	−57.1154	−	98.9268i	−0.0633911	−	0.109797i
$902$	−109.790			−0.121718
$903$	231.842	−	298.243i	0.256746	−	0.330280i
$904$	−88.1495	+	50.8931i	−0.0975105	+	0.0562977i
$905$	−424.590			−0.469160
$906$	−128.798	+	165.687i	−0.142162	+	0.182877i
$907$	−565.453	+	979.393i	−0.623432	+	1.07982i	0.365410	+	0.930847i	$0.380929\pi$
$907$	−565.453	+	979.393i	−0.623432	+	1.07982i	−0.988842	+	0.148969i	$0.952404\pi$
$908$	182.147	−	315.488i	0.200603	−	0.347454i
$909$	−769.127	−	788.709i	−0.846124	−	0.867666i
$910$	722.020	+	90.3492i	0.793428	+	0.0992848i
$911$		−	713.293i		−	0.782978i	−0.920183	−	0.391489i	$-0.871960\pi$
$911$		−	713.293i		−	0.782978i	0.920183	−	0.391489i	$-0.128040\pi$
$912$	421.325	+	58.1645i	0.461979	+	0.0637768i
$913$	15.1731	−	26.2805i	0.0166189	−	0.0287848i
$914$	−633.290	+	365.630i	−0.692877	+	0.400033i
$915$	1544.09	−	628.243i	1.68753	−	0.686604i
$916$	−49.3531	+	28.4940i	−0.0538790	+	0.0311070i
$917$	342.838	+	593.813i	0.373869	+	0.647561i
$918$	−271.622	−	118.557i	−0.295884	−	0.129147i
$919$	721.103	+	1248.99i	0.784661	+	1.35907i	0.929201	+	0.369574i	$0.120496\pi$
$919$	721.103	+	1248.99i	0.784661	+	1.35907i	−0.144540	+	0.989499i	$0.546170\pi$
$920$	−429.809	−	248.150i	−0.467183	−	0.269729i
$921$	518.945	+	71.6411i	0.563458	+	0.0777862i
$922$	355.382			0.385447
$923$	−607.647	+	256.273i	−0.658339	+	0.277652i
$924$	38.4101	+	94.4039i	0.0415693	+	0.102169i
$925$	−875.572	−	505.512i	−0.946564	−	0.546499i
$926$	853.123	+	492.551i	0.921300	+	0.531913i
$927$	62.5928	+	17.6178i	0.0675219	+	0.0190052i
$928$		−	211.668i		−	0.228090i
$929$	−189.614	−	328.420i	−0.204105	−	0.353520i	0.745742	−	0.666235i	$-0.232095\pi$
$929$	−189.614	−	328.420i	−0.204105	−	0.353520i	−0.949847	+	0.312714i	$0.898762\pi$
$930$	−30.3282	+	39.0143i	−0.0326109	+	0.0419509i
$931$		−	1070.02i		−	1.14932i
$932$	−448.382	+	258.873i	−0.481096	+	0.277761i
$933$	137.207	+	18.9416i	0.147060	+	0.0203018i
$934$	478.847	+	276.463i	0.512684	+	0.295998i
$935$			277.410i			0.296695i
$936$	128.520	−	304.950i	0.137307	−	0.325802i
$937$	1245.12			1.32884			0.664418	−	0.747361i	$-0.268679\pi$
$937$	1245.12			1.32884			0.664418	+	0.747361i	$0.268679\pi$
$938$	−155.104	+	268.647i	−0.165356	+	0.286404i
$939$	39.9141	−	289.125i	0.0425070	−	0.307907i
$940$	−170.919	−	296.041i	−0.181829	−	0.314937i
$941$	−598.925			−0.636477			−0.318238	−	0.948011i	$-0.603091\pi$
$941$	−598.925			−0.636477			−0.318238	+	0.948011i	$0.603091\pi$
$942$	−416.122	−	323.477i	−0.441743	−	0.343394i
$943$	330.072	−	190.567i	0.350023	−	0.202086i
$944$	279.226			0.295791
$945$	119.486	+	1061.93i	0.126440	+	1.12374i
$946$	−80.4041	+	139.264i	−0.0849938	+	0.147214i
$947$	609.301	−	1055.34i	0.643401	−	1.11440i	−0.341267	−	0.939966i	$-0.610856\pi$
$947$	609.301	−	1055.34i	0.643401	−	1.11440i	0.984668	−	0.174437i	$-0.0558105\pi$
$948$	−184.437	+	75.0418i	−0.194554	+	0.0791580i
$949$	1032.77	+	129.234i	1.08827	+	0.136179i
$950$		−	2921.16i		−	3.07490i
$951$	−157.499	+	1140.87i	−0.165614	+	1.19965i
$952$	−47.6066	+	82.4571i	−0.0500070	+	0.0866146i
$953$	−111.090	+	64.1380i	−0.116569	+	0.0673012i	−0.557151	−	0.830411i	$-0.688105\pi$
$953$	−111.090	+	64.1380i	−0.116569	+	0.0673012i	0.440582	+	0.897712i	$0.354772\pi$
$954$	130.781	+	134.111i	0.137087	+	0.140577i
$955$	−885.122	+	511.025i	−0.926829	+	0.535105i
$956$	−10.1786	−	17.6298i	−0.0106471	−	0.0184413i
$957$	−165.690	−	407.230i	−0.173135	−	0.425528i
$958$	−51.5338	−	89.2591i	−0.0537931	−	0.0931723i
$959$	914.997	+	528.273i	0.954115	+	0.550859i
$960$	29.9514	−	216.959i	0.0311994	−	0.225999i
$961$	959.371			0.998305
$962$	123.942	+	293.877i	0.128838	+	0.305486i
$963$	1140.39	+	1169.43i	1.18421	+	1.21436i
$964$	139.051	+	80.2812i	0.144244	+	0.0832793i
$965$	537.468	+	310.307i	0.556961	+	0.321562i
$966$	−279.337	−	217.146i	−0.289169	−	0.224789i
$967$			1184.70i			1.22513i	0.790420	+	0.612566i	$0.209863\pi$
$967$			1184.70i			1.22513i	−0.790420	+	0.612566i	$0.790137\pi$
$968$	149.427	+	258.815i	0.154366	+	0.267371i
$969$	651.581	+	506.513i	0.672426	+	0.522717i
$970$			891.481i			0.919053i
$971$	1187.92	−	685.845i	1.22340	−	0.706329i	0.257757	−	0.966210i	$-0.417017\pi$
$971$	1187.92	−	685.845i	1.22340	−	0.706329i	0.965641	+	0.259881i	$0.0836833\pi$
$972$	479.611	+	78.5427i	0.493427	+	0.0808053i
$973$	−410.353	−	236.918i	−0.421740	−	0.243492i
$974$		−	119.760i		−	0.122957i
$975$	−2195.47	−	587.973i	−2.25177	−	0.603049i
$976$	−243.562			−0.249551
$977$	−864.817	+	1497.91i	−0.885177	+	1.53317i	−0.0396654	+	0.999213i	$0.512629\pi$
$977$	−864.817	+	1497.91i	−0.885177	+	1.53317i	−0.845511	+	0.533958i	$0.820704\pi$
$978$	−1143.17	−	157.816i	−1.16888	−	0.161366i
$979$	−164.260	−	284.506i	−0.167783	−	0.290609i
$980$	−551.000			−0.562245
$981$	362.009	−	1286.15i	0.369021	−	1.31106i
$982$	370.515	−	213.917i	0.377307	−	0.217838i
$983$	1313.03			1.33573			0.667867	−	0.744281i	$-0.267208\pi$
$983$	1313.03			1.33573			0.667867	+	0.744281i	$0.267208\pi$
$984$	132.791	+	103.226i	0.134950	+	0.104905i
$985$	806.660	−	1397.18i	0.818944	−	1.41845i
$986$	205.361	−	355.696i	0.208277	−	0.360746i
$987$	−91.8414	−	225.727i	−0.0930511	−	0.228700i
$988$	−556.291	+	734.680i	−0.563048	+	0.743603i
$989$		−	558.245i		−	0.564454i
$990$	−112.207	−	440.855i	−0.113341	−	0.445308i
$991$	−114.792	+	198.825i	−0.115834	+	0.200631i	−0.918113	−	0.396319i	$-0.870288\pi$
$991$	−114.792	+	198.825i	−0.115834	+	0.200631i	0.802279	+	0.596950i	$0.203621\pi$
$992$	6.25273	−	3.61001i	0.00630315	−	0.00363913i
$993$	−108.515	−	266.707i	−0.109280	−	0.268587i
$994$	−269.465	+	155.575i	−0.271091	+	0.156515i
$995$	63.9861	+	110.827i	0.0643077	+	0.111384i
$996$	−43.0613	+	17.5204i	−0.0432343	+	0.0175907i
$997$	−280.671	−	486.136i	−0.281515	−	0.487599i	0.690243	−	0.723578i	$-0.257504\pi$
$997$	−280.671	−	486.136i	−0.281515	−	0.487599i	−0.971758	+	0.235979i	$0.924170\pi$
$998$	72.9900	+	42.1408i	0.0731362	+	0.0422252i
$999$	−376.919	+	278.090i	−0.377297	+	0.278368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.j.a.17.3	✓	20
3.2	odd	2	inner	78.3.j.a.17.7	yes	20
13.10	even	6	inner	78.3.j.a.23.7	yes	20
39.23	odd	6	inner	78.3.j.a.23.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.j.a.17.3	✓	20	1.1	even	1	trivial
78.3.j.a.17.7	yes	20	3.2	odd	2	inner
78.3.j.a.23.3	yes	20	39.23	odd	6	inner
78.3.j.a.23.7	yes	20	13.10	even	6	inner

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.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.410263 + 2.97181i) q^{3} +(-1.00000 - 1.73205i) q^{4} -9.12568 q^{5} +(-3.34962 - 2.60386i) q^{6} +(3.75604 - 2.16855i) q^{7} +2.82843 q^{8} +(-8.66337 - 2.43845i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.410263 + 2.97181i) q^{3} +(-1.00000 - 1.73205i) q^{4} -9.12568 q^{5} +(-3.34962 - 2.60386i) q^{6} +(3.75604 - 2.16855i) q^{7} +2.82843 q^{8} +(-8.66337 - 2.43845i) q^{9} +(6.45283 - 11.1766i) q^{10} +(-1.95827 + 3.39183i) q^{11} +(5.55760 - 2.26122i) q^{12} +(-1.61415 + 12.8994i) q^{13} +6.13359i q^{14} +(3.74393 - 27.1198i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-6.72177 + 3.88082i) q^{17} +(9.11241 - 8.88617i) q^{18} +(-30.6949 + 17.7217i) q^{19} +(9.12568 + 15.8061i) q^{20} +(4.90357 + 12.0519i) q^{21} +(-2.76942 - 4.79677i) q^{22} +(16.6520 + 9.61401i) q^{23} +(-1.16040 + 8.40556i) q^{24} +58.2780 q^{25} +(-14.6571 - 11.0982i) q^{26} +(10.8009 - 24.7455i) q^{27} +(-7.51208 - 4.33710i) q^{28} +(32.4049 + 18.7090i) q^{29} +(30.5675 + 23.7620i) q^{30} +1.27633i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.27648 - 7.21117i) q^{33} -10.9766i q^{34} +(-34.2764 + 19.7895i) q^{35} +(4.43985 + 17.4438i) q^{36} +(-15.0241 - 8.67414i) q^{37} -50.1245i q^{38} +(-37.6724 - 10.0891i) q^{39} -25.8113 q^{40} +(9.91090 - 17.1662i) q^{41} +(-18.2279 - 2.51638i) q^{42} +(-14.5164 - 25.1432i) q^{43} +7.83309 q^{44} +(79.0591 + 22.2525i) q^{45} +(-23.5494 + 13.5963i) q^{46} -18.7295 q^{47} +(-9.47414 - 7.36482i) q^{48} +(-15.0948 + 26.1449i) q^{49} +(-41.2088 + 71.3757i) q^{50} +(-8.77537 - 21.5680i) q^{51} +(23.9566 - 10.1036i) q^{52} +14.7174i q^{53} +(22.6696 + 30.7261i) q^{54} +(17.8706 - 30.9527i) q^{55} +(10.6237 - 6.13359i) q^{56} +(-40.0726 - 98.4901i) q^{57} +(-45.8274 + 26.4585i) q^{58} +(-34.9033 - 60.4543i) q^{59} +(-50.7168 + 20.6352i) q^{60} +(30.4453 + 52.7328i) q^{61} +(-1.56318 - 0.902503i) q^{62} +(-37.8279 + 9.62803i) q^{63} +8.00000 q^{64} +(14.7302 - 117.716i) q^{65} +(15.3913 - 6.26225i) q^{66} +(43.7994 + 25.2876i) q^{67} +(13.4435 + 7.76163i) q^{68} +(-35.4027 + 45.5422i) q^{69} -55.9731i q^{70} +(25.3645 + 43.9326i) q^{71} +(-24.5037 - 6.89698i) q^{72} -80.0631i q^{73} +(21.2472 - 12.2671i) q^{74} +(-23.9093 + 173.191i) q^{75} +(61.3898 + 35.4434i) q^{76} +16.9865i q^{77} +(38.9950 - 39.0050i) q^{78} -33.1864 q^{79} +(18.2514 - 31.6123i) q^{80} +(69.1079 + 42.2504i) q^{81} +(14.0161 + 24.2767i) q^{82} -7.74819 q^{83} +(15.9710 - 20.5452i) q^{84} +(61.3407 - 35.4151i) q^{85} +41.0587 q^{86} +(-68.8942 + 88.6258i) q^{87} +(-5.53883 + 9.59354i) q^{88} +(-41.9399 + 72.6421i) q^{89} +(-83.1569 + 81.0923i) q^{90} +(21.9102 + 51.9510i) q^{91} -38.4560i q^{92} +(-3.79302 - 0.523632i) q^{93} +(13.2438 - 22.9389i) q^{94} +(280.112 - 161.723i) q^{95} +(15.7193 - 6.39569i) q^{96} +(-59.8223 + 34.5384i) q^{97} +(-21.3472 - 36.9745i) q^{98} +(25.2360 - 24.6095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

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