LMFDB - Embedded newform 315.2.bh.c.169.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.15
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.101400 - 0.0585435i) q^{2} +(-1.22623 - 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-1.51285 - 1.64660i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +O(q^{10})$	\(q+(-0.101400 - 0.0585435i) q^{2} +(-1.22623 - 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-1.51285 - 1.64660i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +(0.0570063 + 0.255533i) q^{10} +(2.42237 - 4.19567i) q^{11} +(-0.886391 + 3.32421i) q^{12} +(-5.14734 + 2.97182i) q^{13} +(-0.0585435 - 0.101400i) q^{14} +(-0.159098 + 3.86971i) q^{15} +(-1.95897 + 3.39303i) q^{16} +0.511102i q^{17} +(0.174891 - 0.304627i) q^{18} -3.30298 q^{19} +(-1.32995 + 4.23769i) q^{20} +(-0.450320 - 1.67249i) q^{21} +(-0.491259 + 0.283628i) q^{22} +(-2.38175 + 1.37510i) q^{23} +(0.570945 - 0.572335i) q^{24} +(-0.422551 + 4.98211i) q^{25} +0.695922 q^{26} +(3.66082 - 3.68760i) q^{27} -1.98629i q^{28} +(1.11642 - 1.93369i) q^{29} +(0.242679 - 0.383076i) q^{30} +(2.32761 + 4.03154i) q^{31} +(1.20570 - 0.696112i) q^{32} +(-8.10278 + 2.18169i) q^{33} +(0.0299217 - 0.0518259i) q^{34} +(-0.486872 - 2.18242i) q^{35} +(5.15328 - 2.99197i) q^{36} -10.7743i q^{37} +(0.334923 + 0.193368i) q^{38} +(9.94712 + 2.65237i) q^{39} +(0.768536 - 0.706113i) q^{40} +(-3.96117 - 6.86095i) q^{41} +(-0.0522506 + 0.195954i) q^{42} +(-3.06708 - 1.77078i) q^{43} -9.62308 q^{44} +(4.92874 - 4.55055i) q^{45} +0.322013 q^{46} +(0.717764 + 0.414401i) q^{47} +(6.55269 - 1.76432i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.334517 - 0.480450i) q^{50} +(0.625209 - 0.626730i) q^{51} +(10.2241 + 5.90289i) q^{52} -7.80304i q^{53} +(-0.587093 + 0.159607i) q^{54} +(-10.5733 + 2.35877i) q^{55} +(-0.233371 + 0.404211i) q^{56} +(4.05022 + 4.04039i) q^{57} +(-0.226410 + 0.130718i) q^{58} +(-2.65313 - 4.59536i) q^{59} +(6.81461 - 3.56951i) q^{60} +(-4.33664 + 7.51128i) q^{61} -0.545065i q^{62} +(-1.49368 + 2.60171i) q^{63} +7.67285 q^{64} +(12.6805 + 3.97966i) q^{65} +(0.949347 + 0.253141i) q^{66} +(-10.1339 + 5.85079i) q^{67} +(0.879187 - 0.507599i) q^{68} +(4.60268 + 1.22729i) q^{69} +(-0.0783975 + 0.249801i) q^{70} +8.45574 q^{71} +(-1.40022 + 0.00340254i) q^{72} -9.31511i q^{73} +(-0.630762 + 1.09251i) q^{74} +(6.61254 - 5.59234i) q^{75} +(3.28034 + 5.68172i) q^{76} +(4.19567 - 2.42237i) q^{77} +(-0.853361 - 0.851290i) q^{78} +(0.370752 - 0.642161i) q^{79} +(8.55057 - 1.90753i) q^{80} +(-8.99989 + 0.0437397i) q^{81} +0.927603i q^{82} +(-13.8742 - 8.01027i) q^{83} +(-2.42974 + 2.43565i) q^{84} +(0.841579 - 0.773223i) q^{85} +(0.207335 + 0.359114i) q^{86} +(-3.73439 + 1.00549i) q^{87} +(1.95830 + 1.13062i) q^{88} -15.5602 q^{89} +(-0.766181 + 0.172881i) q^{90} -5.94363 q^{91} +(4.73085 + 2.73136i) q^{92} +(2.07741 - 7.79086i) q^{93} +(-0.0485210 - 0.0840408i) q^{94} +(4.99693 + 5.43868i) q^{95} +(-2.32999 - 0.621286i) q^{96} +(1.49523 + 0.863270i) q^{97} -0.117087i q^{98} +(12.6046 + 7.23651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.101400	−	0.0585435i	−0.0717008	−	0.0413965i	0.463721	−	0.885981i	$-0.346514\pi$
$2$	−0.101400	−	0.0585435i	−0.0717008	−	0.0413965i	−0.535422	+	0.844585i	$0.679847\pi$
$3$	−1.22623	−	1.22326i	−0.707965	−	0.706247i
$3$	−1.22623	−	1.22326i	−0.707965	−	0.706247i
$4$	−0.993145	−	1.72018i	−0.496573	−	0.860089i
$5$	−1.51285	−	1.64660i	−0.676568	−	0.736380i
$5$	−1.51285	−	1.64660i	−0.676568	−	0.736380i
$6$	0.0527266	+	0.195826i	0.0215255	+	0.0799458i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			0.466742i			0.165018i
$9$	0.00728996	+	2.99999i	0.00242999	+	0.999997i
$10$	0.0570063	+	0.255533i	0.0180270	+	0.0808066i
$11$	2.42237	−	4.19567i	0.730373	−	1.26504i	−0.226351	−	0.974046i	$-0.572680\pi$
$11$	2.42237	−	4.19567i	0.730373	−	1.26504i	0.956724	−	0.290997i	$-0.0939871\pi$
$12$	−0.886391	+	3.32421i	−0.255879	+	0.959616i
$13$	−5.14734	+	2.97182i	−1.42761	+	0.824234i	−0.996932	−	0.0782699i	$-0.975060\pi$
$13$	−5.14734	+	2.97182i	−1.42761	+	0.824234i	−0.430682	+	0.902504i	$0.641727\pi$
$14$	−0.0585435	−	0.101400i	−0.0156464	−	0.0271004i
$15$	−0.159098	+	3.86971i	−0.0410790	+	0.999156i
$16$	−1.95897	+	3.39303i	−0.489741	+	0.848257i
$17$			0.511102i			0.123961i	0.998077	+	0.0619803i	$0.0197416\pi$
$17$			0.511102i			0.123961i	−0.998077	+	0.0619803i	$0.980258\pi$
$18$	0.174891	−	0.304627i	0.0412221	−	0.0718012i
$19$	−3.30298			−0.757756			−0.378878	−	0.925447i	$-0.623690\pi$
$19$	−3.30298			−0.757756			−0.378878	+	0.925447i	$0.623690\pi$
$20$	−1.32995	+	4.23769i	−0.297387	+	0.947575i
$21$	−0.450320	−	1.67249i	−0.0982679	−	0.364967i
$22$	−0.491259	+	0.283628i	−0.104737	+	0.0604697i
$23$	−2.38175	+	1.37510i	−0.496629	+	0.286729i	−0.727320	−	0.686298i	$-0.759235\pi$
$23$	−2.38175	+	1.37510i	−0.496629	+	0.286729i	0.230691	+	0.973027i	$0.425901\pi$
$24$	0.570945	−	0.572335i	0.116544	−	0.116827i
$25$	−0.422551	+	4.98211i	−0.0845101	+	0.996423i
$26$	0.695922			0.136481
$27$	3.66082	−	3.68760i	0.704525	−	0.709679i
$28$		−	1.98629i		−	0.375374i
$29$	1.11642	−	1.93369i	0.207314	−	0.359078i	−0.743554	−	0.668676i	$-0.766861\pi$
$29$	1.11642	−	1.93369i	0.207314	−	0.359078i	0.950867	+	0.309598i	$0.100195\pi$
$30$	0.242679	−	0.383076i	0.0443069	−	0.0699397i
$31$	2.32761	+	4.03154i	0.418051	+	0.724086i	0.995743	−	0.0921689i	$-0.0293800\pi$
$31$	2.32761	+	4.03154i	0.418051	+	0.724086i	−0.577692	+	0.816255i	$0.696047\pi$
$32$	1.20570	−	0.696112i	0.213140	−	0.123056i
$33$	−8.10278	+	2.18169i	−1.41051	+	0.379783i
$34$	0.0299217	−	0.0518259i	0.00513153	−	0.00888807i
$35$	−0.486872	−	2.18242i	−0.0822963	−	0.368896i
$36$	5.15328	−	2.99197i	0.858880	−	0.498661i
$37$		−	10.7743i		−	1.77128i	−0.464375	−	0.885639i	$-0.653721\pi$
$37$		−	10.7743i		−	1.77128i	0.464375	−	0.885639i	$-0.346279\pi$
$38$	0.334923	+	0.193368i	0.0543317	+	0.0313684i
$39$	9.94712	+	2.65237i	1.59281	+	0.424720i
$40$	0.768536	−	0.706113i	0.121516	−	0.111646i
$41$	−3.96117	−	6.86095i	−0.618631	−	1.07150i	−0.989736	−	0.142910i	$-0.954354\pi$
$41$	−3.96117	−	6.86095i	−0.618631	−	1.07150i	0.371104	−	0.928591i	$-0.378979\pi$
$42$	−0.0522506	+	0.195954i	−0.00806244	+	0.0302363i
$43$	−3.06708	−	1.77078i	−0.467725	−	0.270041i	0.247562	−	0.968872i	$-0.420371\pi$
$43$	−3.06708	−	1.77078i	−0.467725	−	0.270041i	−0.715287	+	0.698831i	$0.753704\pi$
$44$	−9.62308			−1.45073
$45$	4.92874	−	4.55055i	0.734733	−	0.678356i
$46$	0.322013			0.0474783
$47$	0.717764	+	0.414401i	0.104697	+	0.0604466i	0.551434	−	0.834218i	$-0.314081\pi$
$47$	0.717764	+	0.414401i	0.104697	+	0.0604466i	−0.446737	+	0.894665i	$0.647414\pi$
$48$	6.55269	−	1.76432i	0.945799	−	0.254658i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.334517	−	0.480450i	0.0473078	−	0.0679459i
$51$	0.625209	−	0.626730i	0.0875468	−	0.0877598i
$52$	10.2241	+	5.90289i	1.41783	+	0.818584i
$53$		−	7.80304i		−	1.07183i	−0.844272	−	0.535915i	$-0.819967\pi$
$53$		−	7.80304i		−	1.07183i	0.844272	−	0.535915i	$-0.180033\pi$
$54$	−0.587093	+	0.159607i	−0.0798932	+	0.0217197i
$55$	−10.5733	+	2.35877i	−1.42570	+	0.318057i
$56$	−0.233371	+	0.404211i	−0.0311855	+	0.0540149i
$57$	4.05022	+	4.04039i	0.536465	+	0.535163i
$58$	−0.226410	+	0.130718i	−0.0297291	+	0.0171641i
$59$	−2.65313	−	4.59536i	−0.345408	−	0.598265i	0.640020	−	0.768359i	$-0.278926\pi$
$59$	−2.65313	−	4.59536i	−0.345408	−	0.598265i	−0.985428	+	0.170094i	$0.945593\pi$
$60$	6.81461	−	3.56951i	0.879762	−	0.460822i
$61$	−4.33664	+	7.51128i	−0.555250	+	0.961720i	0.442635	+	0.896702i	$0.354044\pi$
$61$	−4.33664	+	7.51128i	−0.555250	+	0.961720i	−0.997884	+	0.0650183i	$0.979289\pi$
$62$		−	0.545065i		−	0.0692234i
$63$	−1.49368	+	2.60171i	−0.188186	+	0.327785i
$64$	7.67285			0.959107
$65$	12.6805	+	3.97966i	1.57283	+	0.493616i
$66$	0.949347	+	0.253141i	0.116857	+	0.0311595i
$67$	−10.1339	+	5.85079i	−1.23805	+	0.714788i	−0.968695	−	0.248253i	$-0.920144\pi$
$67$	−10.1339	+	5.85079i	−1.23805	+	0.714788i	−0.269354	+	0.963041i	$0.586810\pi$
$68$	0.879187	−	0.507599i	0.106617	−	0.0615554i
$69$	4.60268	+	1.22729i	0.554098	+	0.147749i
$70$	−0.0783975	+	0.249801i	−0.00937029	+	0.0298569i
$71$	8.45574			1.00351			0.501756	−	0.865009i	$-0.332688\pi$
$71$	8.45574			1.00351			0.501756	+	0.865009i	$0.332688\pi$
$72$	−1.40022	+	0.00340254i	−0.165018	+	0.000400993i
$73$		−	9.31511i		−	1.09025i	−0.838355	−	0.545125i	$-0.816482\pi$
$73$		−	9.31511i		−	1.09025i	0.838355	−	0.545125i	$-0.183518\pi$
$74$	−0.630762	+	1.09251i	−0.0733246	+	0.127002i
$75$	6.61254	−	5.59234i	0.763551	−	0.645748i
$76$	3.28034	+	5.68172i	0.376281	+	0.651738i
$77$	4.19567	−	2.42237i	0.478141	−	0.276055i
$78$	−0.853361	−	0.851290i	−0.0966242	−	0.0963896i
$79$	0.370752	−	0.642161i	0.0417128	−	0.0722488i	−0.844415	−	0.535689i	$-0.820052\pi$
$79$	0.370752	−	0.642161i	0.0417128	−	0.0722488i	0.886128	+	0.463440i	$0.153385\pi$
$80$	8.55057	−	1.90753i	0.955983	−	0.213268i
$81$	−8.99989	+	0.0437397i	−0.999988	+	0.00485996i
$82$			0.927603i			0.102437i
$83$	−13.8742	−	8.01027i	−1.52289	−	0.879242i	−0.999634	−	0.0270669i	$-0.991383\pi$
$83$	−13.8742	−	8.01027i	−1.52289	−	0.879242i	−0.523257	−	0.852175i	$-0.675283\pi$
$84$	−2.42974	+	2.43565i	−0.265107	+	0.265752i
$85$	0.841579	−	0.773223i	0.0912820	−	0.0838678i
$86$	0.207335	+	0.359114i	0.0223575	+	0.0387243i
$87$	−3.73439	+	1.00549i	−0.400368	+	0.107800i
$88$	1.95830	+	1.13062i	0.208755	+	0.120525i
$89$	−15.5602			−1.64938			−0.824691	−	0.565583i	$-0.808651\pi$
$89$	−15.5602			−1.64938			−0.824691	+	0.565583i	$0.808651\pi$
$90$	−0.766181	+	0.172881i	−0.0807625	+	0.0182233i
$91$	−5.94363			−0.623062
$92$	4.73085	+	2.73136i	0.493225	+	0.284764i
$93$	2.07741	−	7.79086i	0.215418	−	0.807875i
$94$	−0.0485210	−	0.0840408i	−0.00500456	−	0.00866815i
$95$	4.99693	+	5.43868i	0.512674	+	0.557996i
$96$	−2.32999	−	0.621286i	−0.237804	−	0.0634098i
$97$	1.49523	+	0.863270i	0.151817	+	0.0876517i	0.573984	−	0.818866i	$-0.305397\pi$
$97$	1.49523	+	0.863270i	0.151817	+	0.0876517i	−0.422167	+	0.906518i	$0.638730\pi$
$98$		−	0.117087i		−	0.0118276i
$99$	12.6046	+	7.23651i	1.26681	+	0.727297i
$100$	8.98978	−	4.22110i	0.898978	−	0.422110i
$101$	3.27088	−	5.66533i	0.325465	−	0.563721i	−0.656142	−	0.754638i	$-0.727813\pi$
$101$	3.27088	−	5.66533i	0.325465	−	0.563721i	0.981606	+	0.190916i	$0.0611459\pi$
$102$	−0.100087	+	0.0269487i	−0.00991012	+	0.00266832i
$103$	7.50054	−	4.33044i	0.739050	−	0.426691i	−0.0826739	−	0.996577i	$-0.526346\pi$
$103$	7.50054	−	4.33044i	0.739050	−	0.426691i	0.821724	+	0.569886i	$0.193013\pi$
$104$	−1.38707	−	2.40248i	−0.136014	−	0.235583i
$105$	−2.07264	+	3.27172i	−0.202269	+	0.319287i
$106$	−0.456817	+	0.791230i	−0.0443700	+	0.0768511i
$107$			15.4399i			1.49263i	0.665594	+	0.746314i	$0.268178\pi$
$107$			15.4399i			1.49263i	−0.665594	+	0.746314i	$0.731822\pi$
$108$	−9.97906	−	2.63493i	−0.960235	−	0.253547i
$109$	10.2345			0.980288			0.490144	−	0.871641i	$-0.336944\pi$
$109$	10.2345			0.980288			0.490144	+	0.871641i	$0.336944\pi$
$110$	1.21022	+	0.379816i	0.115390	+	0.0362140i
$111$	−13.1797	+	13.2117i	−1.25096	+	1.25400i
$112$	−3.39303	+	1.95897i	−0.320611	+	0.185105i
$113$	4.52427	−	2.61209i	0.425607	−	0.245725i	−0.271866	−	0.962335i	$-0.587641\pi$
$113$	4.52427	−	2.61209i	0.425607	−	0.245725i	0.697474	+	0.716611i	$0.254307\pi$
$114$	−0.174155	−	0.646811i	−0.0163111	−	0.0605794i
$115$	5.86748	+	1.84145i	0.547145	+	0.171716i
$116$	−4.43506			−0.411785
$117$	−8.95295	−	15.4203i	−0.827700	−	1.42561i
$118$			0.621294i			0.0571947i
$119$	−0.255551	+	0.442628i	−0.0234263	+	0.0405756i
$120$	−1.80616	−	0.0742579i	−0.164879	−	0.00677879i
$121$	−6.23579	−	10.8007i	−0.566890	−	0.981882i
$122$	0.879472	−	0.507764i	0.0796237	−	0.0459707i
$123$	−3.53538	+	13.2586i	−0.318775	+	1.19549i
$124$	4.62331	−	8.00781i	0.415186	−	0.719122i
$125$	8.84278	−	6.84144i	0.790922	−	0.611917i
$126$	0.303773	−	0.176369i	0.0270623	−	0.0157122i
$127$		−	2.03520i		−	0.180595i	−0.995915	−	0.0902975i	$-0.971218\pi$
$127$		−	2.03520i		−	0.180595i	0.995915	−	0.0902975i	$-0.0287818\pi$
$128$	−3.18943	−	1.84142i	−0.281909	−	0.162760i
$129$	1.59483	+	5.92320i	0.140417	+	0.521509i
$130$	−1.05283	−	1.14590i	−0.0923391	−	0.100502i
$131$	6.81100	+	11.7970i	0.595080	+	1.03071i	0.993536	+	0.113521i	$0.0362129\pi$
$131$	6.81100	+	11.7970i	0.595080	+	1.03071i	−0.398456	+	0.917188i	$0.630454\pi$
$132$	11.8001	+	11.7715i	1.02707	+	1.02458i
$133$	−2.86047	−	1.65149i	−0.248034	−	0.143203i
$134$	1.37010			0.118359
$135$	−11.6103	−	0.449083i	−0.999253	−	0.0386509i
$136$	−0.238553			−0.0204558
$137$	−14.5369	−	8.39290i	−1.24197	−	0.717054i	−0.272478	−	0.962162i	$-0.587843\pi$
$137$	−14.5369	−	8.39290i	−1.24197	−	0.717054i	−0.969496	+	0.245108i	$0.921177\pi$
$138$	−0.394863	−	0.393905i	−0.0336130	−	0.0335314i
$139$	−8.07299	−	13.9828i	−0.684742	−	1.18601i	−0.973518	−	0.228611i	$-0.926581\pi$
$139$	−8.07299	−	13.9828i	−0.684742	−	1.18601i	0.288776	−	0.957397i	$-0.406752\pi$
$140$	−3.27062	+	3.00497i	−0.276418	+	0.253966i
$141$	−0.373227	−	1.38616i	−0.0314313	−	0.116736i
$142$	−0.857414	−	0.495028i	−0.0719526	−	0.0415418i
$143$			28.7954i			2.40799i
$144$	−10.1933	−	5.85215i	−0.849445	−	0.487679i
$145$	−4.87298	+	1.08710i	−0.404679	+	0.0902791i
$146$	−0.545339	+	0.944554i	−0.0451325	+	0.0781718i
$147$	0.446255	−	1.67358i	0.0368065	−	0.138034i
$148$	−18.5336	+	10.7004i	−1.52346	+	0.879568i
$149$	−0.231621	−	0.401179i	−0.0189751	−	0.0328659i	0.856382	−	0.516343i	$-0.172707\pi$
$149$	−0.231621	−	0.401179i	−0.0189751	−	0.0328659i	−0.875357	+	0.483477i	$0.839374\pi$
$150$	−0.997908	+	0.179943i	−0.0814789	+	0.0146923i
$151$	0.702435	−	1.21665i	0.0571633	−	0.0990098i	−0.836028	−	0.548687i	$-0.815128\pi$
$151$	0.702435	−	1.21665i	0.0571633	−	0.0990098i	0.893191	+	0.449678i	$0.148461\pi$
$152$		−	1.54164i		−	0.125044i
$153$	−1.53330	+	0.00372592i	−0.123960	+	0.000301223i
$154$	−0.567256			−0.0457108
$155$	3.11698	−	9.93176i	0.250362	−	0.797738i
$156$	−5.31638	−	19.7450i	−0.425651	−	1.58087i
$157$	9.61990	−	5.55405i	0.767752	−	0.443262i	−0.0643202	−	0.997929i	$-0.520488\pi$
$157$	9.61990	−	5.55405i	0.767752	−	0.443262i	0.832072	+	0.554668i	$0.187155\pi$
$158$	−0.0751887	+	0.0434102i	−0.00598169	+	0.00345353i
$159$	−9.54512	+	9.56834i	−0.756977	+	0.758819i
$160$	−2.97026	−	0.932186i	−0.234820	−	0.0736958i
$161$	−2.75021			−0.216747
$162$	0.915152	+	0.522450i	0.0719011	+	0.0410475i
$163$			11.7484i			0.920206i	0.887866	+	0.460103i	$0.152187\pi$
$163$			11.7484i			0.920206i	−0.887866	+	0.460103i	$0.847813\pi$
$164$	−7.86804	+	13.6278i	−0.614391	+	1.06416i
$165$	15.8507	+	10.0414i	1.23397	+	0.781723i
$166$	0.937898	+	1.62449i	0.0727950	+	0.126085i
$167$	6.01692	−	3.47387i	0.465603	−	0.268816i	−0.248794	−	0.968556i	$-0.580034\pi$
$167$	6.01692	−	3.47387i	0.465603	−	0.268816i	0.714397	+	0.699740i	$0.246701\pi$
$168$	0.780621	−	0.210184i	0.0602262	−	0.0162160i
$169$	11.1634	−	19.3356i	0.858722	−	1.48735i
$170$	−0.130603	+	0.0291361i	−0.0100168	+	0.00223463i
$171$	−0.0240786	−	9.90892i	−0.00184134	−	0.757754i
$172$			7.03456i			0.536380i
$173$	1.97131	+	1.13814i	0.149876	+	0.0865308i	0.573062	−	0.819512i	$-0.305755\pi$
$173$	1.97131	+	1.13814i	0.149876	+	0.0865308i	−0.423187	+	0.906043i	$0.639089\pi$
$174$	0.437533	+	0.116667i	0.0331693	+	0.00884450i
$175$	−2.85700	+	4.10336i	−0.215969	+	0.310185i
$176$	9.49069	+	16.4384i	0.715388	+	1.23909i
$177$	−2.36794	+	8.88044i	−0.177986	+	0.667494i
$178$	1.57781	+	0.910950i	0.118262	+	0.0682786i
$179$	12.2937			0.918875			0.459438	−	0.888210i	$-0.348051\pi$
$179$	12.2937			0.918875			0.459438	+	0.888210i	$0.348051\pi$
$180$	−12.7227	−	3.95896i	−0.948295	−	0.295083i
$181$	2.14697			0.159583			0.0797917	−	0.996812i	$-0.474574\pi$
$181$	2.14697			0.159583			0.0797917	+	0.996812i	$0.474574\pi$
$182$	0.602686	+	0.347961i	0.0446740	+	0.0257926i
$183$	14.5059	−	3.90575i	1.07231	−	0.288721i
$184$	−0.641819	−	1.11166i	−0.0473156	−	0.0819529i
$185$	−17.7408	+	16.2999i	−1.30433	+	1.19839i
$186$	−0.666754	+	0.668377i	−0.0488888	+	0.0490077i
$187$	2.14442	+	1.23808i	0.156815	+	0.0905374i
$188$		−	1.64624i		−	0.120065i
$189$	5.01416	−	1.36315i	0.364727	−	0.0991545i
$190$	−0.188291	−	0.844021i	−0.0136601	−	0.0612317i
$191$	−2.10430	+	3.64476i	−0.152262	+	0.263726i	−0.932059	−	0.362307i	$-0.881989\pi$
$191$	−2.10430	+	3.64476i	−0.152262	+	0.263726i	0.779797	+	0.626033i	$0.215322\pi$
$192$	−9.40870	−	9.38586i	−0.679014	−	0.677366i
$193$	−6.28422	+	3.62820i	−0.452348	+	0.261163i	−0.708821	−	0.705388i	$-0.750773\pi$
$193$	−6.28422	+	3.62820i	−0.452348	+	0.261163i	0.256473	+	0.966551i	$0.417439\pi$
$194$	−0.101078	−	0.175071i	−0.00725695	−	0.0125694i
$195$	−10.6811	−	20.3915i	−0.764893	−	1.46027i
$196$	0.993145	−	1.72018i	0.0709390	−	0.122870i
$197$		−	14.2592i		−	1.01592i	−0.861380	−	0.507962i	$-0.830399\pi$
$197$		−	14.2592i		−	1.01592i	0.861380	−	0.507962i	$-0.169601\pi$
$198$	−0.854463	−	1.47170i	−0.0607241	−	0.104589i
$199$	−1.00349			−0.0711352			−0.0355676	−	0.999367i	$-0.511324\pi$
$199$	−1.00349			−0.0711352			−0.0355676	+	0.999367i	$0.511324\pi$
$200$	−2.32536	−	0.197222i	−0.164428	−	0.0139457i
$201$	19.5835	+	5.22189i	1.38131	+	0.368324i
$202$	−0.663336	+	0.382977i	−0.0466722	+	0.0269462i
$203$	1.93369	−	1.11642i	0.135719	−	0.0783572i
$204$	−1.69901	−	0.453037i	−0.118955	−	0.0317189i
$205$	−5.30454	+	16.9021i	−0.370485	+	1.18049i
$206$	−1.01407			−0.0706540
$207$	−4.14266	−	7.13520i	−0.287935	−	0.495931i
$208$		−	23.2868i		−	1.61465i
$209$	−8.00106	+	13.8582i	−0.553445	+	0.958595i
$210$	0.401704	−	0.210414i	0.0277202	−	0.0145199i
$211$	0.999224	+	1.73071i	0.0687894	+	0.119147i	0.898369	−	0.439242i	$-0.144753\pi$
$211$	0.999224	+	1.73071i	0.0687894	+	0.119147i	−0.829579	+	0.558389i	$0.811420\pi$
$212$	−13.4226	+	7.74955i	−0.921870	+	0.532242i
$213$	−10.3687	−	10.3435i	−0.710452	−	0.708727i
$214$	0.903903	−	1.56561i	0.0617895	−	0.107023i
$215$	1.72428	+	7.72916i	0.117595	+	0.527124i
$216$	1.72116	+	1.70866i	0.117110	+	0.116260i
$217$			4.65522i			0.316017i
$218$	−1.03778	−	0.599163i	−0.0702874	−	0.0405805i
$219$	−11.3948	+	11.4225i	−0.769986	+	0.771860i
$220$	14.5583	+	15.8453i	0.981520	+	1.06829i
$221$	−1.51890	−	2.63082i	−0.102172	−	0.176968i
$222$	2.10988	−	0.568090i	0.141606	−	0.0381277i
$223$	3.26720	+	1.88632i	0.218788	+	0.126317i	0.605389	−	0.795930i	$-0.293018\pi$
$223$	3.26720	+	1.88632i	0.218788	+	0.126317i	−0.386601	+	0.922247i	$0.626351\pi$
$224$	1.39222			0.0930218
$225$	−14.9494	−	1.23133i	−0.996625	−	0.0820886i
$226$	−0.611682			−0.0406885
$227$	10.8866	+	6.28539i	0.722570	+	0.417176i	0.815698	−	0.578478i	$-0.196353\pi$
$227$	10.8866	+	6.28539i	0.722570	+	0.417176i	−0.0931278	+	0.995654i	$0.529687\pi$
$228$	2.92774	−	10.9798i	0.193894	−	0.727155i
$229$	−2.14528	−	3.71573i	−0.141764	−	0.245543i	0.786397	−	0.617722i	$-0.211944\pi$
$229$	−2.14528	−	3.71573i	−0.141764	−	0.245543i	−0.928161	+	0.372179i	$0.878611\pi$
$230$	−0.487159	−	0.530226i	−0.0321223	−	0.0349620i
$231$	−8.10805	−	2.16199i	−0.533471	−	0.142249i
$232$	0.902536	+	0.521079i	0.0592544	+	0.0342105i
$233$		−	13.9790i		−	0.915793i	−0.889005	−	0.457897i	$-0.848603\pi$
$233$		−	13.9790i		−	0.915793i	0.889005	−	0.457897i	$-0.151397\pi$
$234$	0.00507324	+	2.08776i	0.000331648	+	0.136481i
$235$	−0.403521	−	1.80880i	−0.0263228	−	0.117993i
$236$	−5.26989	+	9.12772i	−0.343041	+	0.594164i
$237$	−1.24016	+	0.333914i	−0.0805567	+	0.0216900i
$238$	0.0518259	−	0.0299217i	0.00335937	−	0.00193954i
$239$	−2.59160	−	4.48879i	−0.167637	−	0.290356i	0.769952	−	0.638102i	$-0.220280\pi$
$239$	−2.59160	−	4.48879i	−0.167637	−	0.290356i	−0.937589	+	0.347747i	$0.886947\pi$
$240$	−12.8184	−	8.12046i	−0.827423	−	0.524174i
$241$	8.58187	−	14.8642i	0.552807	−	0.957490i	−0.445264	−	0.895399i	$-0.646890\pi$
$241$	8.58187	−	14.8642i	0.552807	−	0.957490i	0.998071	−	0.0620901i	$-0.0197766\pi$
$242$			1.46026i			0.0938690i
$243$	11.0895	+	10.9555i	0.711389	+	0.702798i
$244$	17.2276			1.10289
$245$	0.669567	−	2.13347i	0.0427770	−	0.136302i
$246$	1.13470	−	1.13746i	0.0723456	−	0.0725216i
$247$	17.0016	−	9.81586i	1.08178	−	0.624568i
$248$	−1.88169	+	1.08639i	−0.119487	+	0.0689861i
$249$	7.21437	+	26.7941i	0.457192	+	1.69801i
$250$	−1.29718	+	0.176036i	−0.0820409	+	0.0111335i
$251$	4.39653			0.277506			0.138753	−	0.990327i	$-0.455691\pi$
$251$	4.39653			0.277506			0.138753	+	0.990327i	$0.455691\pi$
$252$	5.95885	−	0.0144800i	0.375373	−	0.000912153i
$253$			13.3241i			0.837677i
$254$	−0.119148	+	0.206370i	−0.00747600	+	0.0129488i
$255$	−1.97782	−	0.0813155i	−0.123856	−	0.00509217i
$256$	−7.45725	−	12.9163i	−0.466078	−	0.807271i
$257$	0.960275	−	0.554415i	0.0599003	−	0.0345835i	−0.469751	−	0.882799i	$-0.655656\pi$
$257$	0.960275	−	0.554415i	0.0599003	−	0.0345835i	0.529651	+	0.848216i	$0.322323\pi$
$258$	0.185048	−	0.693981i	0.0115206	−	0.0432054i
$259$	5.38713	−	9.33078i	0.334740	−	0.579787i
$260$	−5.74790	−	25.7652i	−0.356470	−	1.59789i
$261$	5.80920	+	3.33515i	0.359580	+	0.206440i
$262$		−	1.59496i		−	0.0985368i
$263$	20.5652	+	11.8733i	1.26810	+	0.732140i	0.974629	−	0.223826i	$-0.0718549\pi$
$263$	20.5652	+	11.8733i	1.26810	+	0.732140i	0.293475	+	0.955967i	$0.405188\pi$
$264$	−1.01829	−	3.78191i	−0.0626712	−	0.232760i
$265$	−12.8485	+	11.8049i	−0.789274	+	0.725167i
$266$	0.193368	+	0.334923i	0.0118562	+	0.0205355i
$267$	19.0805	+	19.0342i	1.16771	+	1.16487i
$268$	20.1288	+	11.6214i	1.22956	+	0.709889i
$269$	−17.4011			−1.06097			−0.530483	−	0.847695i	$-0.677989\pi$
$269$	−17.4011			−1.06097			−0.530483	+	0.847695i	$0.677989\pi$
$270$	1.15099	+	0.725242i	0.0700472	+	0.0441368i
$271$	13.9423			0.846932			0.423466	−	0.905912i	$-0.360813\pi$
$271$	13.9423			0.846932			0.423466	+	0.905912i	$0.360813\pi$
$272$	−1.73418	−	1.00123i	−0.105150	−	0.0607086i
$273$	7.28827	+	7.27058i	0.441106	+	0.440036i
$274$	0.982699	+	1.70208i	0.0593670	+	0.102827i
$275$	19.8797	+	13.8414i	1.19879	+	0.834669i
$276$	−2.45997	−	9.13631i	−0.148073	−	0.549941i
$277$	−16.8571	−	9.73245i	−1.01284	−	0.584766i	−0.100821	−	0.994905i	$-0.532147\pi$
$277$	−16.8571	−	9.73245i	−1.01284	−	0.584766i	−0.912023	+	0.410138i	$0.865480\pi$
$278$			1.89048i			0.113384i
$279$	−12.0776	+	7.01220i	−0.723068	+	0.419809i
$280$	1.01863	−	0.227244i	0.0608747	−	0.0135804i
$281$	−3.44502	+	5.96695i	−0.205513	+	0.355959i	−0.950296	−	0.311348i	$-0.899220\pi$
$281$	−3.44502	+	5.96695i	−0.205513	+	0.355959i	0.744783	+	0.667307i	$0.232553\pi$
$282$	−0.0433054	+	0.162407i	−0.00257880	+	0.00967120i
$283$	17.1156	−	9.88170i	1.01742	−	0.587406i	0.104062	−	0.994571i	$-0.466816\pi$
$283$	17.1156	−	9.88170i	1.01742	−	0.587406i	0.913355	+	0.407165i	$0.133483\pi$
$284$	−8.39778	−	14.5454i	−0.498316	−	0.863109i
$285$	0.525499	−	12.7816i	0.0311279	−	0.757117i
$286$	1.68578	−	2.91986i	0.0996824	−	0.172655i
$287$		−	7.92235i		−	0.467641i
$288$	2.09712	+	3.61202i	0.123574	+	0.212840i
$289$	16.7388			0.984634
$290$	0.557765	+	0.175049i	0.0327531	+	0.0102792i
$291$	−0.777495	−	2.88761i	−0.0455776	−	0.169275i
$292$	−16.0236	+	9.25125i	−0.937713	+	0.541389i
$293$	15.1897	−	8.76977i	0.887391	−	0.512336i	0.0143029	−	0.999898i	$-0.495447\pi$
$293$	15.1897	−	8.76977i	0.887391	−	0.512336i	0.873088	+	0.487562i	$0.162114\pi$
$294$	−0.143227	+	0.143576i	−0.00835318	+	0.00837351i
$295$	−3.55290	+	11.3207i	−0.206858	+	0.659119i
$296$	5.02880			0.292293
$297$	−6.60411	−	24.2923i	−0.383209	−	1.40959i
$298$			0.0542395i			0.00314201i
$299$	8.17311	−	14.1562i	0.472663	−	0.818677i
$300$	−16.1870	−	5.82075i	−0.934559	−	0.336061i
$301$	−1.77078	−	3.06708i	−0.102066	−	0.176783i
$302$	−0.142454	+	0.0822459i	−0.00819731	+	0.00473272i
$303$	−10.9410	+	2.94589i	−0.628544	+	0.169237i
$304$	6.47043	−	11.2071i	0.371105	−	0.642772i
$305$	18.9287	−	4.22277i	1.08386	−	0.241795i
$306$	0.155695	+	0.0893870i	0.00890051	+	0.00510992i
$307$		−	9.16137i		−	0.522867i	−0.965221	−	0.261434i	$-0.915805\pi$
$307$		−	9.16137i		−	0.522867i	0.965221	−	0.261434i	$-0.0841953\pi$
$308$	−8.33383	−	4.81154i	−0.474864	−	0.274163i
$309$	−14.4946	−	3.86496i	−0.824571	−	0.219870i
$310$	−0.897502	+	0.824604i	−0.0509747	+	0.0468344i
$311$	−3.17592	−	5.50085i	−0.180090	−	0.311925i	0.761821	−	0.647787i	$-0.224305\pi$
$311$	−3.17592	−	5.50085i	−0.180090	−	0.311925i	−0.941911	+	0.335863i	$0.890972\pi$
$312$	−1.23798	+	4.64274i	−0.0700866	+	0.262844i
$313$	20.9473	+	12.0939i	1.18401	+	0.683590i	0.956939	−	0.290288i	$-0.0937510\pi$
$313$	20.9473	+	12.0939i	1.18401	+	0.683590i	0.227073	+	0.973878i	$0.427084\pi$
$314$	−1.30061			−0.0733979
$315$	6.54369	−	1.47652i	0.368695	−	0.0831925i
$316$	−1.47284			−0.0828538
$317$	−15.2473	−	8.80302i	−0.856372	−	0.494427i	0.00642336	−	0.999979i	$-0.497955\pi$
$317$	−15.2473	−	8.80302i	−0.856372	−	0.494427i	−0.862796	+	0.505552i	$0.831289\pi$
$318$	1.52804	−	0.411428i	0.0856883	−	0.0230717i
$319$	−5.40876	−	9.36825i	−0.302832	−	0.524521i
$320$	−11.6079	−	12.6341i	−0.648901	−	0.706267i
$321$	18.8869	−	18.9329i	1.05416	−	1.05673i
$322$	0.278872	+	0.161007i	0.0155409	+	0.00897255i
$323$		−	1.68816i		−	0.0939319i
$324$	9.01344	+	15.4380i	0.500747	+	0.857666i
$325$	−12.6309	−	26.9004i	−0.700637	−	1.49216i
$326$	0.687792	−	1.19129i	0.0380933	−	0.0659795i
$327$	−12.5499	−	12.5194i	−0.694010	−	0.692326i
$328$	3.20230	−	1.84885i	0.176817	−	0.102086i
$329$	0.414401	+	0.717764i	0.0228467	+	0.0395716i
$330$	−1.01940	−	1.94615i	−0.0561162	−	0.107132i
$331$	−10.7758	+	18.6642i	−0.592289	+	1.02587i	0.401634	+	0.915800i	$0.368442\pi$
$331$	−10.7758	+	18.6642i	−0.592289	+	1.02587i	−0.993923	+	0.110075i	$0.964891\pi$
$332$			31.8215i			1.74643i
$333$	32.3227	−	0.0785440i	1.77127	−	0.00430418i
$334$	−0.813489			−0.0445121
$335$	24.9650	+	7.83499i	1.36398	+	0.428071i
$336$	6.55696	+	1.74840i	0.357711	+	0.0953828i
$337$	−1.28622	+	0.742599i	−0.0700648	+	0.0404519i	−0.534623	−	0.845091i	$-0.679546\pi$
$337$	−1.28622	+	0.742599i	−0.0700648	+	0.0404519i	0.464558	+	0.885543i	$0.346213\pi$
$338$	−2.26394	+	1.30709i	−0.123142	+	0.0710962i
$339$	−8.74305	−	2.33131i	−0.474857	−	0.126620i
$340$	−2.16589	−	0.679742i	−0.117462	−	0.0368642i
$341$	22.5534			1.22133
$342$	−0.577661	+	1.00618i	−0.0312363	+	0.0544078i
$343$			1.00000i			0.0539949i
$344$	0.826497	−	1.43153i	0.0445617	−	0.0771832i
$345$	−4.94233	−	9.43547i	−0.266086	−	0.507989i
$346$	−0.133261	−	0.230814i	−0.00716414	−	0.0124087i
$347$	26.8564	−	15.5055i	1.44173	−	0.832381i	0.443761	−	0.896145i	$-0.353644\pi$
$347$	26.8564	−	15.5055i	1.44173	−	0.832381i	0.997965	+	0.0637641i	$0.0203105\pi$
$348$	5.43841	+	5.42521i	0.291529	+	0.290822i
$349$	−6.22134	+	10.7757i	−0.333021	+	0.576809i	−0.983103	−	0.183055i	$-0.941401\pi$
$349$	−6.22134	+	10.7757i	−0.333021	+	0.576809i	0.650082	+	0.759864i	$0.274735\pi$
$350$	0.529925	−	0.248823i	0.0283257	−	0.0133002i
$351$	−7.88459	+	29.8606i	−0.420848	+	1.59384i
$352$		−	6.74497i		−	0.359508i
$353$	15.1998	+	8.77562i	0.809005	+	0.467079i	0.846610	−	0.532214i	$-0.178640\pi$
$353$	15.1998	+	8.77562i	0.809005	+	0.467079i	−0.0376054	+	0.999293i	$0.511973\pi$
$354$	0.760002	−	0.761851i	0.0403936	−	0.0404919i
$355$	−12.7923	−	13.9232i	−0.678944	−	0.738966i
$356$	15.4536	+	26.7664i	0.819038	+	1.41862i
$357$	0.854812	−	0.230160i	0.0452414	−	0.0121813i
$358$	−1.24659	−	0.719716i	−0.0658841	−	0.0380382i
$359$	5.38576			0.284249			0.142125	−	0.989849i	$-0.454607\pi$
$359$	5.38576			0.284249			0.142125	+	0.989849i	$0.454607\pi$
$360$	2.12393	+	2.30045i	0.111941	+	0.121245i
$361$	−8.09030			−0.425805
$362$	−0.217704	−	0.125691i	−0.0114423	−	0.00660619i
$363$	−5.56550	+	20.8721i	−0.292113	+	1.09550i
$364$	5.90289	+	10.2241i	0.309396	+	0.535889i
$365$	−15.3382	+	14.0924i	−0.802839	+	0.737629i
$366$	−1.69956	−	0.453184i	−0.0888375	−	0.0236883i
$367$	9.20085	+	5.31211i	0.480281	+	0.277290i	0.720533	−	0.693420i	$-0.243897\pi$
$367$	9.20085	+	5.31211i	0.480281	+	0.277290i	−0.240253	+	0.970710i	$0.577230\pi$
$368$		−	10.7751i		−	0.561692i
$369$	20.5539	−	11.9335i	1.06999	−	0.621233i
$370$	2.75318	−	0.614201i	0.143131	−	0.0319308i
$371$	3.90152	−	6.75763i	0.202557	−	0.350839i
$372$	−15.4648	+	4.16394i	−0.801815	+	0.215890i
$373$	22.6362	−	13.0690i	1.17206	−	0.676687i	0.217892	−	0.975973i	$-0.430082\pi$
$373$	22.6362	−	13.0690i	1.17206	−	0.676687i	0.954163	+	0.299286i	$0.0967485\pi$
$374$	−0.144963	−	0.251083i	−0.00749586	−	0.0129832i
$375$	−19.2121	−	2.42780i	−0.992110	−	0.125371i
$376$	−0.193419	+	0.335011i	−0.00997481	+	0.0172769i
$377$			13.2712i			0.683499i
$378$	−0.588241	−	0.155323i	−0.0302558	−	0.00798894i
$379$	−31.1020			−1.59760			−0.798802	−	0.601594i	$-0.794532\pi$
$379$	−31.1020			−1.59760			−0.798802	+	0.601594i	$0.794532\pi$
$380$	4.39282	−	13.9970i	0.225347	−	0.718031i
$381$	−2.48957	+	2.49563i	−0.127545	+	0.127855i
$382$	0.426754	−	0.246387i	0.0218346	−	0.0126062i
$383$	−29.9946	+	17.3174i	−1.53265	+	0.884876i	−0.533413	+	0.845855i	$0.679091\pi$
$383$	−29.9946	+	17.3174i	−1.53265	+	0.884876i	−0.999238	+	0.0390213i	$0.987576\pi$
$384$	1.65846	+	6.15950i	0.0846327	+	0.314326i
$385$	−10.3361	−	3.24388i	−0.526777	−	0.165323i
$386$	0.849628			0.0432449
$387$	5.28996	−	9.21411i	0.268904	−	0.468380i
$388$		−	3.42941i		−	0.174102i
$389$	−16.1998	+	28.0589i	−0.821364	+	1.42264i	0.0833030	+	0.996524i	$0.473453\pi$
$389$	−16.1998	+	28.0589i	−0.821364	+	1.42264i	−0.904667	+	0.426120i	$0.859880\pi$
$390$	−0.110720	+	2.69302i	−0.00560652	+	0.136366i
$391$	−0.702819	−	1.21732i	−0.0355431	−	0.0615624i
$392$	−0.404211	+	0.233371i	−0.0204157	+	0.0117870i
$393$	6.07888	−	22.7974i	0.306639	−	1.14998i
$394$	−0.834781	+	1.44588i	−0.0420556	+	0.0728425i
$395$	−1.61827	+	0.361017i	−0.0814241	+	0.0181647i
$396$	−0.0701519	−	28.8691i	−0.00352526	−	1.45073i
$397$			17.6262i			0.884632i	0.896859	+	0.442316i	$0.145843\pi$
$397$			17.6262i			0.884632i	−0.896859	+	0.442316i	$0.854157\pi$
$398$	0.101754	+	0.0587475i	0.00510045	+	0.00294475i
$399$	1.48740	+	5.52420i	0.0744631	+	0.276556i
$400$	−16.0767	−	11.1935i	−0.803834	−	0.559676i
$401$	−17.5616	−	30.4176i	−0.876985	−	1.51898i	−0.854634	−	0.519232i	$-0.826218\pi$
$401$	−17.5616	−	30.4176i	−0.876985	−	1.51898i	−0.0223510	−	0.999750i	$-0.507115\pi$
$402$	−1.68006	−	1.67599i	−0.0837940	−	0.0835906i
$403$	−23.9620	−	13.8345i	−1.19363	−	0.689144i
$404$	−12.9938			−0.646468
$405$	13.6875	+	14.7530i	0.680139	+	0.733083i
$406$	−0.261436			−0.0129748
$407$	−45.2053	−	26.0993i	−2.24074	−	1.29369i
$408$	0.292521	+	0.291812i	0.0144820	+	0.0144468i
$409$	13.6279	+	23.6041i	0.673854	+	1.16715i	0.976802	+	0.214142i	$0.0686957\pi$
$409$	13.6279	+	23.6041i	0.673854	+	1.16715i	−0.302948	+	0.953007i	$0.597971\pi$
$410$	1.52739	−	1.40333i	0.0754323	−	0.0693054i
$411$	7.55898	+	28.0740i	0.372857	+	1.38479i
$412$	−14.8982	−	8.60151i	−0.733984	−	0.423766i
$413$		−	5.30626i		−	0.261104i
$414$	0.00234747	+	0.966037i	0.000115372	+	0.0474781i
$415$	7.79995	+	34.9636i	0.382884	+	1.71629i
$416$	−4.13743	+	7.16624i	−0.202854	+	0.351354i
$417$	−7.20522	+	27.0215i	−0.352841	+	1.32325i
$418$	1.62262	−	0.936820i	0.0793649	−	0.0458213i
$419$	−7.46158	−	12.9238i	−0.364522	−	0.631371i	0.624177	−	0.781283i	$-0.285434\pi$
$419$	−7.46158	−	12.9238i	−0.364522	−	0.631371i	−0.988699	+	0.149912i	$0.952101\pi$
$420$	7.68638	+	0.316015i	0.375057	+	0.0154200i
$421$	−7.21394	+	12.4949i	−0.351586	+	0.608965i	−0.986528	−	0.163595i	$-0.947691\pi$
$421$	−7.21394	+	12.4949i	−0.351586	+	0.608965i	0.634941	+	0.772560i	$0.281024\pi$
$422$		−	0.233992i		−	0.0113906i
$423$	−1.23797	+	2.15631i	−0.0601921	+	0.104843i
$424$	3.64201			0.176872
$425$	−2.54637	−	0.215967i	−0.123517	−	0.0104759i
$426$	0.445842	+	1.65586i	0.0216011	+	0.0802265i
$427$	−7.51128	+	4.33664i	−0.363496	+	0.209865i
$428$	26.5593	−	15.3340i	1.28379	−	0.741198i
$429$	35.2241	−	35.3098i	1.70064	−	1.70478i
$430$	0.277649	−	0.884684i	0.0133894	−	0.0426632i
$431$	−12.1826			−0.586817			−0.293408	−	0.955987i	$-0.594790\pi$
$431$	−12.1826			−0.586817			−0.293408	+	0.955987i	$0.594790\pi$
$432$	5.34072	+	19.6451i	0.256956	+	0.945178i
$433$			2.17297i			0.104426i	0.998636	+	0.0522131i	$0.0166275\pi$
$433$			2.17297i			0.104426i	−0.998636	+	0.0522131i	$0.983372\pi$
$434$	0.272533	−	0.472040i	0.0130820	−	0.0226587i
$435$	7.30522	+	4.62786i	0.350258	+	0.221889i
$436$	−10.1644	−	17.6052i	−0.486784	−	0.843135i
$437$	7.86688	−	4.54195i	0.376324	−	0.217271i
$438$	1.82414	−	0.491154i	0.0871609	−	0.0234682i
$439$	7.22997	−	12.5227i	0.345068	−	0.597675i	−0.640298	−	0.768126i	$-0.721189\pi$
$439$	7.22997	−	12.5227i	0.345068	−	0.597675i	0.985366	+	0.170451i	$0.0545226\pi$
$440$	−1.10094	−	4.93499i	−0.0524852	−	0.235267i
$441$	−2.59442	+	1.50631i	−0.123544	+	0.0717290i
$442$			0.355687i			0.0169183i
$443$	16.0787	+	9.28306i	0.763924	+	0.441051i	0.830703	−	0.556716i	$-0.187939\pi$
$443$	16.0787	+	9.28306i	0.763924	+	0.441051i	−0.0667792	+	0.997768i	$0.521272\pi$
$444$	35.8159	+	9.55021i	1.69975	+	0.453233i
$445$	23.5404	+	25.6214i	1.11592	+	1.21457i
$446$	−0.220863	−	0.382547i	−0.0104582	−	0.0181141i
$447$	−0.206724	+	0.775270i	−0.00977770	+	0.0366690i
$448$	6.64489	+	3.83643i	0.313941	+	0.181254i
$449$	−29.2127			−1.37863			−0.689316	−	0.724460i	$-0.742089\pi$
$449$	−29.2127			−1.37863			−0.689316	+	0.724460i	$0.742089\pi$
$450$	1.44378	+	1.00005i	0.0680606	+	0.0471426i
$451$	−38.3818			−1.80733
$452$	−8.98651	−	5.18836i	−0.422690	−	0.244040i
$453$	−2.34963	+	0.632641i	−0.110395	+	0.0297241i
$454$	−0.735937	−	1.27468i	−0.0345392	−	0.0598237i
$455$	8.99184	+	9.78676i	0.421544	+	0.458810i
$456$	−1.88582	+	1.89041i	−0.0883118	+	0.0885266i
$457$	−17.0409	−	9.83857i	−0.797140	−	0.460229i	0.0453300	−	0.998972i	$-0.485566\pi$
$457$	−17.0409	−	9.83857i	−0.797140	−	0.460229i	−0.842470	+	0.538743i	$0.818899\pi$
$458$			0.502368i			0.0234741i
$459$	1.88474	+	1.87105i	0.0879722	+	0.0873332i
$460$	−2.65964	−	11.9219i	−0.124006	−	0.555863i
$461$	10.1713	−	17.6172i	0.473723	−	0.820513i	−0.525824	−	0.850593i	$-0.676243\pi$
$461$	10.1713	−	17.6172i	0.473723	−	0.820513i	0.999547	+	0.0300804i	$0.00957632\pi$
$462$	0.695588	+	0.693900i	0.0323617	+	0.0322831i
$463$	−27.0910	+	15.6410i	−1.25902	+	0.726898i	−0.972885	−	0.231290i	$-0.925705\pi$
$463$	−27.0910	+	15.6410i	−1.25902	+	0.726898i	−0.286139	+	0.958188i	$0.592372\pi$
$464$	4.37405	+	7.57607i	0.203060	+	0.351710i
$465$	−15.9712	+	8.36578i	−0.740648	+	0.387954i
$466$	−0.818378	+	1.41747i	−0.0379106	+	0.0656631i
$467$			32.3796i			1.49835i	0.662372	+	0.749175i	$0.269550\pi$
$467$			32.3796i			1.49835i	−0.662372	+	0.749175i	$0.730450\pi$
$468$	−17.6341	+	30.7153i	−0.815136	+	1.41981i
$469$	−11.7016			−0.540329
$470$	−0.0649760	+	0.207036i	−0.00299712	+	0.00954985i
$471$	−18.5903	−	4.95704i	−0.856594	−	0.228409i
$472$	2.14485	−	1.23833i	0.0987247	−	0.0569987i
$473$	−14.8592	+	8.57897i	−0.683227	+	0.394461i
$474$	0.145301	+	0.0387440i	0.00667387	+	0.00177957i
$475$	1.39568	−	16.4558i	0.0640381	−	0.755046i
$476$	1.01520			0.0465315
$477$	23.4091	−	0.0568839i	1.07183	−	0.00260453i
$478$			0.606886i			0.0277583i
$479$	16.1594	−	27.9889i	0.738343	−	1.27885i	−0.214898	−	0.976636i	$-0.568942\pi$
$479$	16.1594	−	27.9889i	0.738343	−	1.27885i	0.953241	−	0.302211i	$-0.0977246\pi$
$480$	2.50193	+	4.77647i	0.114197	+	0.218015i
$481$	32.0191	+	55.4588i	1.45995	+	2.52870i
$482$	−1.74041	+	1.00482i	−0.0792734	+	0.0457685i
$483$	3.37239	+	3.36421i	0.153449	+	0.153077i
$484$	−12.3861	+	21.4533i	−0.563004	+	0.975151i
$485$	−0.840603	−	3.76803i	−0.0381698	−	0.171098i
$486$	−0.483099	−	1.76011i	−0.0219138	−	0.0798402i
$487$			4.23105i			0.191727i	0.995394	+	0.0958635i	$0.0305612\pi$
$487$			4.23105i			0.191727i	−0.995394	+	0.0958635i	$0.969439\pi$
$488$	−3.50583	−	2.02409i	−0.158702	−	0.0916264i
$489$	14.3713	−	14.4063i	0.649893	−	0.651474i
$490$	−0.192795	+	0.177135i	−0.00870958	+	0.00800216i
$491$	−15.8378	−	27.4319i	−0.714751	−	1.23798i	−0.963056	−	0.269303i	$-0.913207\pi$
$491$	−15.8378	−	27.4319i	−0.714751	−	1.23798i	0.248305	−	0.968682i	$-0.420127\pi$
$492$	26.3184	−	7.08627i	1.18652	−	0.319474i
$493$	0.988314	+	0.570604i	0.0445114	+	0.0256987i
$494$	−2.29862			−0.103420
$495$	−7.15337	−	31.7025i	−0.321520	−	1.42492i
$496$	−18.2388			−0.818948
$497$	7.32289	+	4.22787i	0.328476	+	0.189646i
$498$	0.837083	−	3.13929i	0.0375106	−	0.140675i
$499$	−2.58647	−	4.47990i	−0.115786	−	0.200548i	0.802307	−	0.596911i	$-0.203605\pi$
$499$	−2.58647	−	4.47990i	−0.115786	−	0.200548i	−0.918094	+	0.396363i	$0.870272\pi$
$500$	−20.5507	−	8.41662i	−0.919053	−	0.376403i
$501$	−11.6276	−	3.10046i	−0.519481	−	0.138518i
$502$	−0.445809	−	0.257388i	−0.0198974	−	0.0114878i
$503$		−	11.9452i		−	0.532609i	−0.963889	−	0.266304i	$-0.914197\pi$
$503$		−	11.9452i		−	0.532609i	0.963889	−	0.266304i	$-0.0858026\pi$
$504$	−1.21433	−	0.697165i	−0.0540906	−	0.0310542i
$505$	−14.2769	+	3.18500i	−0.635312	+	0.141731i
$506$	0.780037	−	1.35106i	0.0346769	−	0.0600621i
$507$	−37.3412	+	10.0542i	−1.65838	+	0.446523i
$508$	−3.50091	+	2.02125i	−0.155328	+	0.0896785i
$509$	−1.57817	−	2.73348i	−0.0699513	−	0.121159i	0.828928	−	0.559355i	$-0.188951\pi$
$509$	−1.57817	−	2.73348i	−0.0699513	−	0.121159i	−0.898880	+	0.438196i	$0.855618\pi$
$510$	0.195791	+	0.124034i	0.00866977	+	0.00549231i
$511$	4.65755	−	8.06712i	0.206038	−	0.356868i
$512$			9.11197i			0.402696i
$513$	−12.0916	+	12.1801i	−0.533858	+	0.537764i
$514$	−0.129830			−0.00572653
$515$	−18.4777	−	5.79903i	−0.814224	−	0.255536i
$516$	8.60506	−	8.62600i	0.378817	−	0.379738i
$517$	3.47739	−	2.00767i	0.152935	−	0.0882972i
$518$	−1.09251	+	0.630762i	−0.0480022	+	0.0277141i
$519$	−1.02505	−	3.80703i	−0.0449947	−	0.167110i
$520$	−1.85748	+	5.91855i	−0.0814557	+	0.259546i
$521$	−31.3407			−1.37306			−0.686531	−	0.727101i	$-0.740867\pi$
$521$	−31.3407			−1.37306			−0.686531	+	0.727101i	$0.740867\pi$
$522$	−0.393803	−	0.678275i	−0.0172363	−	0.0296873i
$523$			21.0147i			0.918907i	0.888202	+	0.459454i	$0.151955\pi$
$523$			21.0147i			0.918907i	−0.888202	+	0.459454i	$0.848045\pi$
$524$	13.5286	−	23.4323i	0.591001	−	1.02364i
$525$	8.52280	−	1.53684i	0.371966	−	0.0670730i
$526$	−1.39021	−	2.40792i	−0.0606161	−	0.104990i
$527$	−2.06053	+	1.18965i	−0.0897580	+	0.0518218i
$528$	8.47053	−	31.7668i	0.368633	−	1.38247i
$529$	−7.71818	+	13.3683i	−0.335573	+	0.581229i
$530$	1.99393	−	0.444823i	0.0866109	−	0.0193219i
$531$	13.7667	−	7.99287i	0.597424	−	0.346861i
$532$			6.56069i			0.284442i
$533$	40.7790	+	23.5438i	1.76633	+	1.01979i
$534$	−0.820439	−	3.04711i	−0.0355039	−	0.131861i
$535$	25.4232	−	23.3583i	1.09914	−	1.00987i
$536$	−2.73081	−	4.72991i	−0.117953	−	0.204301i
$537$	−15.0749	−	15.0384i	−0.650532	−	0.648953i
$538$	1.76448	+	1.01872i	0.0760721	+	0.0439203i
$539$	4.84475			0.208678
$540$	10.7582	+	20.4177i	0.462958	+	0.878639i
$541$	44.9830			1.93397			0.966985	−	0.254833i	$-0.0820204\pi$
$541$	44.9830			1.93397			0.966985	+	0.254833i	$0.0820204\pi$
$542$	−1.41375	−	0.816228i	−0.0607257	−	0.0350600i
$543$	−2.63269	−	2.62630i	−0.112979	−	0.112705i
$544$	0.355784	+	0.616236i	0.0152541	+	0.0264209i
$545$	−15.4833	−	16.8521i	−0.663232	−	0.721864i
$546$	−0.313388	−	1.16392i	−0.0134117	−	0.0498112i
$547$	−15.8515	−	9.15186i	−0.677761	−	0.391305i	0.121250	−	0.992622i	$-0.461310\pi$
$547$	−15.8515	−	9.15186i	−0.677761	−	0.391305i	−0.799011	+	0.601317i	$0.794643\pi$
$548$			33.3415i			1.42428i
$549$	−22.5654	−	12.9551i	−0.963067	−	0.552911i
$550$	−1.20549	−	2.56735i	−0.0514021	−	0.109472i
$551$	−3.68751	+	6.38695i	−0.157093	+	0.272093i
$552$	−0.572830	+	2.14827i	−0.0243813	+	0.0914363i
$553$	0.642161	−	0.370752i	0.0273075	−	0.0157660i
$554$	1.13954	+	1.97375i	0.0484145	+	0.0838564i
$555$	41.6933	+	1.71417i	1.76978	+	0.0727623i
$556$	−16.0353	+	27.7740i	−0.680049	+	1.17788i
$557$		−	6.84812i		−	0.290164i	−0.989420	−	0.145082i	$-0.953655\pi$
$557$		−	6.84812i		−	0.290164i	0.989420	−	0.145082i	$-0.0463446\pi$
$558$	1.63519	−	0.00397351i	0.0692232	−	0.000168212i
$559$	21.0497			0.890307
$560$	8.35878	+	2.62332i	0.353223	+	0.110855i
$561$	−1.11507	−	4.14135i	−0.0470781	−	0.174848i
$562$	0.698652	−	0.403367i	0.0294709	−	0.0170150i
$563$	−9.47605	+	5.47100i	−0.399368	+	0.230575i	−0.686211	−	0.727402i	$-0.740727\pi$
$563$	−9.47605	+	5.47100i	−0.399368	+	0.230575i	0.286843	+	0.957978i	$0.407394\pi$
$564$	−2.01378	+	2.01868i	−0.0847953	+	0.0850016i
$565$	−11.1456	−	3.49793i	−0.468899	−	0.147159i
$566$	−2.31403			−0.0972661
$567$	−7.81601	−	4.46207i	−0.328241	−	0.187389i
$568$			3.94665i			0.165598i
$569$	4.26152	−	7.38117i	0.178652	−	0.309435i	−0.762767	−	0.646674i	$-0.776160\pi$
$569$	4.26152	−	7.38117i	0.178652	−	0.309435i	0.941419	+	0.337239i	$0.109493\pi$
$570$	−0.801565	+	1.26529i	−0.0335739	+	0.0529973i
$571$	0.894713	+	1.54969i	0.0374426	+	0.0648524i	0.884139	−	0.467223i	$-0.154746\pi$
$571$	0.894713	+	1.54969i	0.0374426	+	0.0648524i	−0.846697	+	0.532076i	$0.821412\pi$
$572$	49.5332	−	28.5980i	2.07109	−	1.19574i
$573$	7.03884	−	1.89522i	0.294052	−	0.0791740i
$574$	−0.463802	+	0.803328i	−0.0193587	+	0.0335303i
$575$	−5.84451	−	12.4472i	−0.243733	−	0.519084i
$576$	0.0559348	+	23.0185i	0.00233062	+	0.959104i
$577$			0.990001i			0.0412143i	0.999788	+	0.0206071i	$0.00655992\pi$
$577$			0.990001i			0.0412143i	−0.999788	+	0.0206071i	$0.993440\pi$
$578$	−1.69732	−	0.979946i	−0.0705990	−	0.0407604i
$579$	12.1441	+	3.23820i	0.504693	+	0.134575i
$580$	6.70959	+	7.30275i	0.278601	+	0.303230i
$581$	−8.01027	−	13.8742i	−0.332322	−	0.575599i
$582$	−0.0902127	+	0.338322i	−0.00373944	+	0.0140239i
$583$	−32.7390	−	18.9019i	−1.35591	−	0.782836i
$584$	4.34776			0.179911
$585$	−11.8465	+	38.0705i	−0.489792	+	1.57402i
$586$	−2.05365			−0.0848355
$587$	−14.0831	−	8.13090i	−0.581273	−	0.335598i	0.180366	−	0.983600i	$-0.442272\pi$
$587$	−14.0831	−	8.13090i	−0.581273	−	0.335598i	−0.761639	+	0.648001i	$0.775605\pi$
$588$	−3.32204	+	0.894467i	−0.136999	+	0.0368872i
$589$	−7.68806	−	13.3161i	−0.316781	−	0.548681i
$590$	1.02302	−	0.939927i	0.0421171	−	0.0386962i
$591$	−17.4426	+	17.4850i	−0.717493	+	0.719238i
$592$	36.5574	+	21.1064i	1.50250	+	0.867468i
$593$		−	34.4513i		−	1.41475i	−0.706840	−	0.707373i	$-0.749880\pi$
$593$		−	34.4513i		−	1.41475i	0.706840	−	0.707373i	$-0.250120\pi$
$594$	−0.752500	+	2.84988i	−0.0308754	+	0.116932i
$595$	1.11544	−	0.248841i	0.0457286	−	0.0102015i
$596$	−0.460066	+	0.796858i	−0.0188451	+	0.0326406i
$597$	1.23051	+	1.22752i	0.0503613	+	0.0502390i
$598$	−1.65751	+	0.956965i	−0.0677807	+	0.0391332i
$599$	3.52117	+	6.09884i	0.143871	+	0.249192i	0.928951	−	0.370202i	$-0.120712\pi$
$599$	3.52117	+	6.09884i	0.143871	+	0.249192i	−0.785080	+	0.619394i	$0.787378\pi$
$600$	2.61018	+	3.08636i	0.106560	+	0.126000i
$601$	−7.66510	+	13.2763i	−0.312666	+	0.541553i	−0.978939	−	0.204155i	$-0.934555\pi$
$601$	−7.66510	+	13.2763i	−0.312666	+	0.541553i	0.666273	+	0.745708i	$0.267889\pi$
$602$			0.414670i			0.0169007i
$603$	−17.6262	−	30.3589i	−0.717795	−	1.23631i
$604$	−2.79048			−0.113543
$605$	−8.35055	+	26.6077i	−0.339498	+	1.08176i
$606$	1.28188	+	0.341811i	0.0520729	+	0.0138851i
$607$	17.7810	−	10.2659i	0.721708	−	0.416679i	−0.0936728	−	0.995603i	$-0.529861\pi$
$607$	17.7810	−	10.2659i	0.721708	−	0.416679i	0.815381	+	0.578925i	$0.196527\pi$
$608$	−3.98241	+	2.29925i	−0.161508	+	0.0932467i
$609$	−3.73682	−	0.996413i	−0.151424	−	0.0403767i
$610$	−2.16659	−	0.679963i	−0.0877228	−	0.0275309i
$611$	−4.92610			−0.199289
$612$	1.52920	+	2.63385i	0.0618143	+	0.106467i
$613$			13.4401i			0.542839i	0.962461	+	0.271419i	$0.0874930\pi$
$613$			13.4401i			0.542839i	−0.962461	+	0.271419i	$0.912507\pi$
$614$	−0.536339	+	0.928966i	−0.0216449	+	0.0374900i
$615$	27.1801	−	14.2370i	1.09601	−	0.574093i
$616$	1.13062	+	1.95830i	0.0455542	+	0.0789021i
$617$	17.5021	−	10.1049i	0.704610	−	0.406807i	−0.104452	−	0.994530i	$-0.533309\pi$
$617$	17.5021	−	10.1049i	0.704610	−	0.406807i	0.809062	+	0.587723i	$0.199976\pi$
$618$	1.24349	+	1.24047i	0.0500206	+	0.0498991i
$619$	2.78844	−	4.82972i	0.112077	−	0.194123i	−0.804531	−	0.593911i	$-0.797583\pi$
$619$	2.78844	−	4.82972i	0.112077	−	0.194123i	0.916608	+	0.399788i	$0.130916\pi$
$620$	−20.1800	+	4.50192i	−0.810449	+	0.180801i
$621$	−3.64832	+	13.8170i	−0.146402	+	0.554455i
$622$			0.743717i			0.0298203i
$623$	−13.4756	−	7.78012i	−0.539887	−	0.311704i
$624$	−28.4857	+	28.5550i	−1.14034	+	1.14311i
$625$	−24.6429	−	4.21039i	−0.985716	−	0.168416i
$626$	−1.41604	−	2.45266i	−0.0565964	−	0.0980279i
$627$	26.7633	−	7.20608i	1.06882	−	0.287783i
$628$	−19.1079	−	11.0320i	−0.762489	−	0.440223i
$629$	5.50675			0.219568
$630$	−0.749972	−	0.233371i	−0.0298796	−	0.00929771i
$631$	35.0504			1.39533			0.697667	−	0.716422i	$-0.254221\pi$
$631$	35.0504			1.39533			0.697667	+	0.716422i	$0.254221\pi$
$632$	0.299724	+	0.173046i	0.0119224	+	0.00688339i
$633$	0.891816	−	3.34455i	0.0354465	−	0.132934i
$634$	1.03072	+	1.78526i	0.0409351	+	0.0709016i
$635$	−3.35115	+	3.07896i	−0.132986	+	0.122185i
$636$	25.9389	+	6.91655i	1.02855	+	0.274259i
$637$	−5.14734	−	2.97182i	−0.203945	−	0.117748i
$638$			1.26659i			0.0501448i
$639$	0.0616420	+	25.3671i	0.00243852	+	1.00351i
$640$	1.79307	+	8.03750i	0.0708773	+	0.317710i
$641$	12.3059	−	21.3145i	0.486055	−	0.841872i	−0.513816	−	0.857900i	$-0.671769\pi$
$641$	12.3059	−	21.3145i	0.486055	−	0.841872i	0.999872	+	0.0160280i	$0.00510208\pi$
$642$	−3.02353	+	0.814092i	−0.119329	+	0.0321296i
$643$	36.6615	−	21.1665i	1.44579	−	0.834726i	0.447561	−	0.894253i	$-0.352293\pi$
$643$	36.6615	−	21.1665i	1.44579	−	0.834726i	0.998227	+	0.0595271i	$0.0189593\pi$
$644$	2.73136	+	4.73085i	0.107631	+	0.186422i
$645$	7.34037	−	11.5870i	0.289027	−	0.456237i
$646$	−0.0988309	+	0.171180i	−0.00388845	+	0.00673499i
$647$		−	27.5498i		−	1.08309i	−0.840671	−	0.541547i	$-0.817839\pi$
$647$		−	27.5498i		−	1.08309i	0.840671	−	0.541547i	$-0.182161\pi$
$648$	−0.0204152	−	4.20063i	−0.000801983	−	0.165016i
$649$	−25.7075			−1.00911
$650$	−0.294062	+	3.46716i	−0.0115341	+	0.135993i
$651$	5.69453	−	5.70838i	0.223186	−	0.223729i
$652$	20.2093	−	11.6679i	0.791459	−	0.456949i
$653$	−6.18342	+	3.57000i	−0.241976	+	0.139705i	−0.616085	−	0.787680i	$-0.711282\pi$
$653$	−6.18342	+	3.57000i	−0.241976	+	0.139705i	0.374109	+	0.927385i	$0.377949\pi$
$654$	0.539631	+	2.00419i	0.0211012	+	0.0783699i
$655$	9.12083	−	29.0621i	0.356381	−	1.13555i
$656$	31.0392			1.21188
$657$	27.9452	−	0.0679068i	1.09025	−	0.00264930i
$658$		−	0.0970419i		−	0.00378309i
$659$	−9.78428	+	16.9469i	−0.381141	+	0.660156i	−0.991226	−	0.132180i	$-0.957802\pi$
$659$	−9.78428	+	16.9469i	−0.381141	+	0.660156i	0.610084	+	0.792336i	$0.291136\pi$
$660$	1.53101	−	37.2386i	0.0595946	−	1.44951i
$661$	8.02613	+	13.9017i	0.312180	+	0.540712i	0.978834	−	0.204655i	$-0.0656074\pi$
$661$	8.02613	+	13.9017i	0.312180	+	0.540712i	−0.666654	+	0.745368i	$0.732274\pi$
$662$	2.18533	−	1.26170i	0.0849352	−	0.0490374i
$663$	−1.35563	+	5.08400i	−0.0526485	+	0.197446i
$664$	3.73873	−	6.47568i	0.145091	−	0.251305i
$665$	1.60813	+	7.20850i	0.0623606	+	0.279534i
$666$	−3.28213	−	1.88432i	−0.127180	−	0.0730158i
$667$			6.14076i			0.237771i
$668$	−11.9513	−	6.90011i	−0.462412	−	0.266973i
$669$	−1.69890	−	6.30969i	−0.0656831	−	0.243947i
$670$	−2.07276	−	2.25600i	−0.0800779	−	0.0871571i
$671$	21.0099	+	36.3902i	0.811079	+	1.40483i
$672$	−1.70719	−	1.70305i	−0.0658562	−	0.0656964i
$673$	−36.7918	−	21.2418i	−1.41822	−	0.818810i	−0.422078	−	0.906560i	$-0.638699\pi$
$673$	−36.7918	−	21.2418i	−1.41822	−	0.818810i	−0.996143	+	0.0877496i	$0.972032\pi$
$674$	0.173897			0.00669827
$675$	16.8252	+	19.7968i	0.647601	+	0.761979i
$676$	−44.3475			−1.70567
$677$	−2.66200	−	1.53691i	−0.102309	−	0.0590681i	0.447972	−	0.894047i	$-0.352146\pi$
$677$	−2.66200	−	1.53691i	−0.102309	−	0.0590681i	−0.550281	+	0.834979i	$0.685480\pi$
$678$	0.750065	+	0.748244i	0.0288061	+	0.0287361i
$679$	0.863270	+	1.49523i	0.0331292	+	0.0573815i
$680$	0.360896	+	0.392800i	0.0138397	+	0.0150632i
$681$	−5.66088	−	21.0245i	−0.216925	−	0.805659i
$682$	−2.28692	−	1.32035i	−0.0875706	−	0.0505589i
$683$		−	12.1299i		−	0.464137i	−0.972699	−	0.232068i	$-0.925451\pi$
$683$		−	12.1299i		−	0.464137i	0.972699	−	0.232068i	$-0.0745493\pi$
$684$	−17.0212	+	9.88242i	−0.650822	+	0.377864i
$685$	8.17253	+	36.6337i	0.312256	+	1.39970i
$686$	0.0585435	−	0.101400i	0.00223520	−	0.00387148i
$687$	−1.91468	+	7.18058i	−0.0730497	+	0.273956i
$688$	12.0166	−	6.93778i	0.458128	−	0.264501i
$689$	23.1892	+	40.1649i	0.883439	+	1.53016i
$690$	−0.0512317	+	1.24610i	−0.00195036	+	0.0474382i
$691$	15.4657	−	26.7874i	0.588344	−	1.01904i	−0.406105	−	0.913826i	$-0.633113\pi$
$691$	15.4657	−	26.7874i	0.588344	−	1.01904i	0.994449	−	0.105216i	$-0.0335533\pi$
$692$		−	4.52134i		−	0.171875i
$693$	7.29769	+	12.5693i	0.277216	+	0.477469i
$694$	−3.63099			−0.137831
$695$	−10.8108	+	34.4469i	−0.410077	+	1.30665i
$696$	−0.469305	−	1.74300i	−0.0177890	−	0.0660681i
$697$	3.50665	−	2.02456i	0.132824	−	0.0766859i
$698$	1.26169	−	0.728438i	0.0477557	−	0.0275718i
$699$	−17.0999	+	17.1415i	−0.646776	+	0.648350i
$700$	9.89592	+	0.839309i	0.374031	+	0.0317229i
$701$	21.1191			0.797657			0.398828	−	0.917026i	$-0.369417\pi$
$701$	21.1191			0.797657			0.398828	+	0.917026i	$0.369417\pi$
$702$	2.54764	−	2.56628i	0.0961546	−	0.0968581i
$703$			35.5872i			1.34220i
$704$	18.5865	−	32.1928i	0.700506	−	1.21331i
$705$	−1.71781	+	2.71161i	−0.0646965	+	0.102125i
$706$	−1.02751	−	1.77970i	−0.0386709	−	0.0669799i
$707$	5.66533	−	3.27088i	0.213067	−	0.123014i
$708$	17.6276	−	4.74628i	0.662487	−	0.178376i
$709$	−9.91042	+	17.1654i	−0.372194	+	0.644658i	−0.989903	−	0.141748i	$-0.954728\pi$
$709$	−9.91042	+	17.1654i	−0.372194	+	0.644658i	0.617709	+	0.786407i	$0.288061\pi$
$710$	0.482030	+	2.16072i	0.0180903	+	0.0810903i
$711$	1.92918	+	1.10757i	0.0723499	+	0.0415372i
$712$		−	7.26263i		−	0.272178i
$713$	−11.0876	−	6.40141i	−0.415233	−	0.239735i
$714$	−0.100152	−	0.0267054i	−0.00374811	−	0.000999424i
$715$	47.4144	−	43.5632i	1.77320	−	1.62917i
$716$	−12.2094	−	21.1474i	−0.456288	−	0.790315i
$717$	−2.31303	+	8.67449i	−0.0863817	+	0.323955i
$718$	−0.546117	−	0.315301i	−0.0203809	−	0.0117669i
$719$	31.4447			1.17269			0.586344	−	0.810062i	$-0.300567\pi$
$719$	31.4447			1.17269			0.586344	+	0.810062i	$0.300567\pi$
$720$	5.78491	+	25.6377i	0.215591	+	0.955462i
$721$	8.66087			0.322548
$722$	0.820358	+	0.473634i	0.0305306	+	0.0176268i
$723$	−28.7061	+	7.72918i	−1.06759	+	0.287451i
$724$	−2.13226	−	3.69318i	−0.0792447	−	0.137256i
$725$	9.16213	+	6.37920i	0.340273	+	0.236918i
$726$	1.78627	−	1.79062i	0.0662947	−	0.0664560i
$727$	−12.7626	−	7.36848i	−0.473338	−	0.273282i	0.244298	−	0.969700i	$-0.421442\pi$
$727$	−12.7626	−	7.36848i	−0.473338	−	0.273282i	−0.717636	+	0.696418i	$0.754776\pi$
$728$		−	2.77415i		−	0.102817i
$729$	−0.196827	−	26.9993i	−0.00728991	−	0.999973i
$730$	2.38032	−	0.531020i	0.0880994	−	0.0196539i
$731$	0.905048	−	1.56759i	0.0334744	−	0.0579794i
$732$	−21.1251	−	21.0738i	−0.780806	−	0.778911i
$733$	38.9257	−	22.4738i	1.43775	−	0.830088i	0.440060	−	0.897968i	$-0.354957\pi$
$733$	38.9257	−	22.4738i	1.43775	−	0.830088i	0.997693	+	0.0678807i	$0.0216237\pi$
$734$	−0.621979	−	1.07730i	−0.0229577	−	0.0397638i
$735$	−3.43082	+	1.79707i	−0.126548	+	0.0662861i
$736$	−1.91445	+	3.31593i	−0.0705676	+	0.122227i
$737$			56.6912i			2.08825i
$738$	−2.78280	+	0.00676219i	−0.102436	+	0.000248920i
$739$	−26.4740			−0.973863			−0.486932	−	0.873440i	$-0.661884\pi$
$739$	−26.4740			−0.973863			−0.486932	+	0.873440i	$0.661884\pi$
$740$	45.6579	+	14.3293i	1.67842	+	0.526754i
$741$	−32.8552	−	8.76075i	−1.20697	−	0.321834i
$742$	−0.791230	+	0.456817i	−0.0290470	+	0.0167703i
$743$	−14.9394	+	8.62527i	−0.548074	+	0.316430i	−0.748345	−	0.663310i	$-0.769151\pi$
$743$	−14.9394	+	8.62527i	−0.548074	+	0.316430i	0.200271	+	0.979741i	$0.435818\pi$
$744$	3.63633	+	0.969617i	0.133314	+	0.0355479i
$745$	−0.310171	+	0.988311i	−0.0113638	+	0.0362089i
$746$	−3.06042			−0.112050
$747$	23.9296	−	41.6809i	0.875538	−	1.52502i
$748$		−	4.91838i		−	0.179834i
$749$	−7.71993	+	13.3713i	−0.282080	+	0.488577i
$750$	1.80598	+	1.37092i	0.0659452	+	0.0500590i
$751$	−14.9965	−	25.9748i	−0.547232	−	0.947833i	−0.998463	−	0.0554258i	$-0.982348\pi$
$751$	−14.9965	−	25.9748i	−0.547232	−	0.947833i	0.451231	−	0.892407i	$-0.350985\pi$
$752$	−2.81215	+	1.62360i	−0.102549	+	0.0592065i
$753$	−5.39116	−	5.37808i	−0.196465	−	0.195988i
$754$	0.776939	−	1.34570i	0.0282945	−	0.0490074i
$755$	−3.06601	+	0.683991i	−0.111584	+	0.0248930i
$756$	−7.32465	−	7.27145i	−0.266395	−	0.264460i
$757$			9.82398i			0.357059i	0.983935	+	0.178529i	$0.0571339\pi$
$757$			9.82398i			0.357059i	−0.983935	+	0.178529i	$0.942866\pi$
$758$	3.15375	+	1.82082i	0.114549	+	0.0661351i
$759$	16.2987	−	16.3384i	0.591607	−	0.593046i
$760$	−2.53846	+	2.33228i	−0.0920797	+	0.0846007i
$761$	2.50018	+	4.33044i	0.0906316	+	0.156978i	0.907777	−	0.419453i	$-0.137778\pi$
$761$	2.50018	+	4.33044i	0.0906316	+	0.156978i	−0.817145	+	0.576431i	$0.804445\pi$
$762$	0.398546	−	0.107309i	0.0144378	−	0.00388741i
$763$	8.86334	+	5.11725i	0.320875	+	0.185257i
$764$	8.35952			0.302437
$765$	2.32580	+	2.51909i	0.0840893	+	0.0910779i
$766$	4.05528			0.146523
$767$	27.3131	+	15.7692i	0.986220	+	0.569394i
$768$	−6.65566	+	24.9605i	−0.240166	+	0.900686i
$769$	−11.1898	−	19.3813i	−0.403514	−	0.698906i	0.590634	−	0.806940i	$-0.298878\pi$
$769$	−11.1898	−	19.3813i	−0.403514	−	0.698906i	−0.994147	+	0.108034i	$0.965545\pi$
$770$	0.858176	+	0.934042i	0.0309265	+	0.0336605i
$771$	−1.85571	−	0.494821i	−0.0668318	−	0.0178205i
$772$	12.4823	+	7.20665i	0.449247	+	0.259373i
$773$		−	16.8456i		−	0.605892i	−0.953008	−	0.302946i	$-0.902030\pi$
$773$		−	16.8456i		−	0.605892i	0.953008	−	0.302946i	$-0.0979702\pi$
$774$	−1.07583	+	0.624621i	−0.0386699	+	0.0224515i
$775$	−21.0691	+	9.89289i	−0.756825	+	0.355363i
$776$	−0.402925	+	0.697886i	−0.0144641	+	0.0250526i
$777$	−18.0198	+	4.85187i	−0.646457	+	0.174060i
$778$	3.28533	−	1.89679i	0.117785	−	0.0680031i
$779$	13.0837	+	22.6616i	0.468772	+	0.811937i
$780$	−24.4691	+	38.6252i	−0.876136	+	1.38301i
$781$	20.4830	−	35.4775i	0.732938	−	1.26949i
$782$			0.164582i			0.00588543i
$783$	−3.04369	−	11.1958i	−0.108772	−	0.400105i
$784$	−3.91793			−0.139926
$785$	−23.6988	−	7.43762i	−0.845846	−	0.265460i
$786$	−1.95104	+	1.95579i	−0.0695913	+	0.0697607i
$787$	−3.57799	+	2.06575i	−0.127541	+	0.0736361i	−0.562413	−	0.826856i	$-0.690127\pi$
$787$	−3.57799	+	2.06575i	−0.127541	+	0.0736361i	0.434872	+	0.900492i	$0.356794\pi$
$788$	−24.5283	+	14.1614i	−0.873784	+	0.504480i
$789$	−10.6936	−	39.7159i	−0.380702	−	1.41392i
$790$	0.185228	+	0.0581320i	0.00659013	+	0.00206824i
$791$	5.22417			0.185750
$792$	−3.37759	+	5.88312i	−0.120017	+	0.209048i
$793$		−	51.5508i		−	1.83062i
$794$	1.03190	−	1.78730i	0.0366206	−	0.0634288i
$795$	30.1955	+	1.24145i	1.07093	+	0.0440297i
$796$	0.996607	+	1.72617i	0.0353238	+	0.0611826i
$797$	−8.24281	+	4.75899i	−0.291975	+	0.168572i	−0.638832	−	0.769346i	$-0.720582\pi$
$797$	−8.24281	+	4.75899i	−0.291975	+	0.168572i	0.346857	+	0.937918i	$0.387249\pi$
$798$	0.172583	−	0.647232i	0.00610937	−	0.0229118i
$799$	−0.211801	+	0.366851i	−0.00749300	+	0.0129783i
$800$	2.95864	+	6.30108i	0.104604	+	0.222777i
$801$	−0.113434	−	46.6806i	−0.00400798	−	1.64938i
$802$			4.11247i			0.145216i
$803$	−39.0832	−	22.5647i	−1.37921	−	0.796290i
$804$	−10.4667	−	38.8732i	−0.369131	−	1.37095i
$805$	4.16066	+	4.52848i	0.146644	+	0.159608i
$806$	1.61983	+	2.80564i	0.0570562	+	0.0988243i
$807$	21.3378	+	21.2860i	0.751127	+	0.749304i
$808$	2.64425	+	1.52666i	0.0930244	+	0.0537077i
$809$	17.0032			0.597800			0.298900	−	0.954284i	$-0.403380\pi$
$809$	17.0032			0.597800			0.298900	+	0.954284i	$0.403380\pi$
$810$	−0.524228	−	2.29727i	−0.0184195	−	0.0807180i
$811$	39.4445			1.38508			0.692542	−	0.721377i	$-0.256491\pi$
$811$	39.4445			1.38508			0.692542	+	0.721377i	$0.256491\pi$
$812$	−3.84087	−	2.21753i	−0.134788	−	0.0778200i
$813$	−17.0964	−	17.0550i	−0.599599	−	0.598143i
$814$	3.05588	+	5.29295i	0.107109	+	0.185518i
$815$	19.3449	−	17.7736i	0.677621	−	0.622582i
$816$	0.901750	+	3.34909i	0.0315676	+	0.117242i
$817$	10.1305	+	5.84885i	0.354421	+	0.204625i
$818$		−	3.19129i		−	0.111581i
$819$	−0.0433289	−	17.8308i	−0.00151403	−	0.623060i
$820$	34.3427	−	7.66145i	1.19930	−	0.267550i
$821$	−5.19943	+	9.00567i	−0.181461	+	0.314300i	−0.942378	−	0.334549i	$-0.891416\pi$
$821$	−5.19943	+	9.00567i	−0.181461	+	0.314300i	0.760917	+	0.648849i	$0.224749\pi$
$822$	0.877068	−	3.28924i	0.0305913	−	0.114725i
$823$	−30.2502	+	17.4650i	−1.05446	+	0.608791i	−0.923894	−	0.382650i	$-0.875012\pi$
$823$	−30.2502	+	17.4650i	−1.05446	+	0.608791i	−0.130563	+	0.991440i	$0.541678\pi$
$824$	2.02120	+	3.50082i	0.0704118	+	0.121957i
$825$	−7.44558	−	41.2908i	−0.259222	−	1.43756i
$826$	−0.310647	+	0.538056i	−0.0108088	+	0.0187214i
$827$			11.8658i			0.412614i	0.978487	+	0.206307i	$0.0661445\pi$
$827$			11.8658i			0.412614i	−0.978487	+	0.206307i	$0.933855\pi$
$828$	−8.15956	+	14.2124i	−0.283564	+	0.493915i
$829$	−2.66214			−0.0924601			−0.0462301	−	0.998931i	$-0.514721\pi$
$829$	−2.66214			−0.0924601			−0.0462301	+	0.998931i	$0.514721\pi$
$830$	1.25597	−	4.00195i	0.0435954	−	0.138910i
$831$	8.76544	+	32.5548i	0.304070	+	1.12931i
$832$	−39.4948	+	22.8023i	−1.36923	+	0.790528i
$833$	−0.442628	+	0.255551i	−0.0153361	+	0.00885432i
$834$	2.31254	−	2.31817i	0.0800769	−	0.0802717i
$835$	−14.8228	−	4.65197i	−0.512963	−	0.160988i
$836$	31.7849			1.09930
$837$	23.3877	+	6.17543i	0.808396	+	0.213454i
$838$			1.74731i			0.0603597i
$839$	−19.5357	+	33.8369i	−0.674448	+	1.16818i	0.302182	+	0.953250i	$0.402285\pi$
$839$	−19.5357	+	33.8369i	−0.674448	+	1.16818i	−0.976630	+	0.214928i	$0.931048\pi$
$840$	−1.52705	−	0.967389i	−0.0526883	−	0.0333781i
$841$	12.0072	+	20.7971i	0.414042	+	0.717142i
$842$	1.46299	−	0.844658i	0.0504180	−	0.0291089i
$843$	11.5235	−	3.10273i	0.396891	−	0.106864i
$844$	1.98475	−	3.43769i	0.0683179	−	0.118330i
$845$	−48.7264	+	10.8703i	−1.67624	+	0.373949i
$846$	0.251768	−	0.146175i	0.00865596	−	0.00502561i
$847$		−	12.4716i		−	0.428528i
$848$	26.4759	+	15.2859i	0.909188	+	0.524920i
$849$	−33.0755	−	8.81951i	−1.13515	−	0.302685i
$850$	0.245559	+	0.170972i	0.00842261	+	0.00586430i
$851$	14.8157	+	25.6616i	0.507877	+	0.879668i
$852$	−7.49510	+	28.1086i	−0.256778	+	0.962986i
$853$	−3.68287	−	2.12630i	−0.126099	−	0.0728033i	0.435624	−	0.900129i	$-0.356528\pi$
$853$	−3.68287	−	2.12630i	−0.126099	−	0.0728033i	−0.561723	+	0.827326i	$0.689861\pi$
$854$	1.01553			0.0347506
$855$	−16.2796	+	15.0304i	−0.556749	+	0.514029i
$856$	−7.20644			−0.246311
$857$	−33.5963	−	19.3968i	−1.14763	−	0.662583i	−0.199319	−	0.979935i	$-0.563873\pi$
$857$	−33.5963	−	19.3968i	−1.14763	−	0.662583i	−0.948308	+	0.317352i	$0.897206\pi$
$858$	−5.63890	+	1.51828i	−0.192509	+	0.0518333i
$859$	20.3480	+	35.2438i	0.694265	+	1.20250i	0.970428	+	0.241391i	$0.0776036\pi$
$859$	20.3480	+	35.2438i	0.694265	+	1.20250i	−0.276163	+	0.961111i	$0.589063\pi$
$860$	11.5831	−	10.6423i	0.394979	−	0.362898i
$861$	−9.69106	+	9.71464i	−0.330270	+	0.331074i
$862$	1.23532	+	0.713213i	0.0420752	+	0.0242921i
$863$		−	53.5952i		−	1.82440i	−0.409745	−	0.912200i	$-0.634382\pi$
$863$		−	53.5952i		−	1.82440i	0.409745	−	0.912200i	$-0.365618\pi$
$864$	1.84687	−	6.99448i	0.0628317	−	0.237957i
$865$	−1.10825	−	4.96778i	−0.0376817	−	0.168910i
$866$	0.127213	−	0.220339i	0.00432288	−	0.00748744i
$867$	−20.5256	−	20.4758i	−0.697087	−	0.695395i
$868$	8.00781	−	4.62331i	0.271803	−	0.156925i
$869$	−1.79620	−	3.11111i	−0.0609319	−	0.105537i
$870$	−0.469819	−	0.896939i	−0.0159284	−	0.0304091i
$871$	34.7750	−	60.2320i	1.17831	−	2.04088i
$872$			4.77688i			0.161766i
$873$	−2.57890	+	4.49196i	−0.0872826	+	0.152030i
$874$	−1.06360			−0.0359770
$875$	11.0788	−	1.50347i	0.374531	−	0.0508265i
$876$	30.9654	+	8.25683i	1.04622	+	0.278972i
$877$	−4.34299	+	2.50743i	−0.146652	+	0.0846698i	−0.571531	−	0.820581i	$-0.693650\pi$
$877$	−4.34299	+	2.50743i	−0.146652	+	0.0846698i	0.424878	+	0.905250i	$0.360317\pi$
$878$	−1.46624	+	0.846535i	−0.0494833	+	0.0285692i
$879$	−29.3538	−	7.82710i	−0.990078	−	0.264002i
$880$	12.7093	−	40.4962i	0.428431	−	1.36513i
$881$	−49.2275			−1.65852			−0.829259	−	0.558865i	$-0.811237\pi$
$881$	−49.2275			−1.65852			−0.829259	+	0.558865i	$0.811237\pi$
$882$	0.351260		0.000853559i	0.0118275		2.87408e-5i
$883$			27.7408i			0.933553i	0.884375	+	0.466776i	$0.154585\pi$
$883$			27.7408i			0.933553i	−0.884375	+	0.466776i	$0.845415\pi$
$884$	−3.01698	+	5.22557i	−0.101472	+	0.175755i
$885$	18.2048	−	9.53575i	0.611949	−	0.320541i
$886$	−1.08692	−	1.88261i	−0.0365159	−	0.0632475i
$887$	−1.48760	+	0.858868i	−0.0499488	+	0.0288380i	−0.524766	−	0.851246i	$-0.675847\pi$
$887$	−1.48760	+	0.858868i	−0.0499488	+	0.0288380i	0.474818	+	0.880084i	$0.342514\pi$
$888$	−6.16648	−	6.15151i	−0.206934	−	0.206431i
$889$	1.01760	−	1.76254i	0.0341292	−	0.0591136i
$890$	−0.887032	−	3.97615i	−0.0297334	−	0.133281i
$891$	−21.6176	+	37.8666i	−0.724216	+	1.26858i
$892$		−	7.49356i		−	0.250903i
$893$	−2.37076	−	1.36876i	−0.0793346	−	0.0458038i
$894$	0.0663488	−	0.0665103i	0.00221904	−	0.00222444i
$895$	−18.5986	−	20.2428i	−0.621682	−	0.676641i
$896$	−1.84142	−	3.18943i	−0.0615175	−	0.106551i
$897$	−27.3388	+	7.36104i	−0.912818	+	0.245778i
$898$	2.96218	+	1.71021i	0.0988491	+	0.0570705i
$899$	10.3943			0.346671
$900$	12.7288	+	26.9385i	0.424293	+	0.897949i
$901$	3.98815			0.132865
$902$	3.89192	+	2.24700i	0.129587	+	0.0748170i
$903$	−1.58044	+	5.92706i	−0.0525936	+	0.197240i
$904$	1.21917	+	2.11167i	0.0405491	+	0.0702330i
$905$	−3.24806	−	3.53520i	−0.107969	−	0.117514i
$906$	0.275290	+	0.0734052i	0.00914588	+	0.00243873i
$907$	0.457757	+	0.264286i	0.0151996	+	0.00877548i	0.507581	−	0.861604i	$-0.330540\pi$
$907$	0.457757	+	0.264286i	0.0151996	+	0.00877548i	−0.492381	+	0.870380i	$0.663873\pi$
$908$		−	24.9692i		−	0.828633i
$909$	17.0198	+	9.77131i	0.564511	+	0.324094i
$910$	−0.338825	−	1.51879i	−0.0112319	−	0.0503475i
$911$	−12.7747	+	22.1265i	−0.423246	+	0.733084i	−0.996255	−	0.0864654i	$-0.972443\pi$
$911$	−12.7747	+	22.1265i	−0.423246	+	0.733084i	0.573009	+	0.819549i	$0.305776\pi$
$912$	−21.6434	+	5.82753i	−0.716685	+	0.192969i
$913$	−67.2170	+	38.8077i	−2.22456	+	1.28435i
$914$	1.15197	+	1.99527i	0.0381037	+	0.0659976i
$915$	−28.3765	−	17.9766i	−0.938100	−	0.594287i
$916$	−4.26115	+	7.38053i	−0.140792	+	0.243859i
$917$			13.6220i			0.449838i
$918$	−0.0815754	−	0.300064i	−0.00269239	−	0.00990360i
$919$	26.1839			0.863726			0.431863	−	0.901939i	$-0.357856\pi$
$919$	26.1839			0.863726			0.431863	+	0.901939i	$0.357856\pi$
$920$	−0.859482	+	2.73860i	−0.0283363	+	0.0902890i
$921$	−11.2067	+	11.2340i	−0.369274	+	0.370172i
$922$	−2.06274	+	1.19092i	−0.0679327	+	0.0392210i
$923$	−43.5245	+	25.1289i	−1.43263	+	0.827128i
$924$	4.33346	+	16.0945i	0.142561	+	0.529469i
$925$	53.6786	+	4.55267i	1.76494	+	0.149691i
$926$	3.66271			0.120364
$927$	13.0460	+	22.4700i	0.428485	+	0.738011i
$928$		−	3.10861i		−	0.102045i
$929$	4.30929	−	7.46390i	0.141383	−	0.244883i	−0.786635	−	0.617419i	$-0.788178\pi$
$929$	4.30929	−	7.46390i	0.141383	−	0.244883i	0.928018	+	0.372536i	$0.121512\pi$
$930$	2.10925	+	0.0867189i	0.0691649	+	0.00284363i
$931$	−1.65149	−	2.86047i	−0.0541255	−	0.0937481i
$932$	−24.0463	+	13.8832i	−0.787664	+	0.454758i
$933$	−2.83454	+	10.6303i	−0.0927985	+	0.348020i
$934$	1.89562	−	3.28330i	0.0620264	−	0.107433i
$935$	−1.20557	−	5.40402i	−0.0394265	−	0.176730i
$936$	7.19731	−	4.17872i	0.235251	−	0.136586i
$937$			58.4977i			1.91104i	0.294933	+	0.955518i	$0.404703\pi$
$937$			58.4977i			1.91104i	−0.294933	+	0.955518i	$0.595297\pi$
$938$	1.18654	+	0.685051i	0.0387420	+	0.0223677i
$939$	−10.8923	−	40.4539i	−0.355456	−	1.32016i
$940$	−2.71070	+	2.49052i	−0.0884131	+	0.0812319i
$941$	−10.1778	−	17.6284i	−0.331786	−	0.574670i	0.651076	−	0.759013i	$-0.274318\pi$
$941$	−10.1778	−	17.6284i	−0.331786	−	0.574670i	−0.982862	+	0.184342i	$0.940985\pi$
$942$	1.59485	+	1.59098i	0.0519632	+	0.0518370i
$943$	18.8690	+	10.8940i	0.614461	+	0.354759i
$944$	20.7896			0.676643
$945$	−9.83025	−	6.19405i	−0.319778	−	0.201493i
$946$	2.00897			0.0653172
$947$	−8.02904	−	4.63557i	−0.260909	−	0.150636i	0.363840	−	0.931461i	$-0.381465\pi$
$947$	−8.02904	−	4.63557i	−0.260909	−	0.150636i	−0.624749	+	0.780826i	$0.714799\pi$
$948$	1.80605	+	1.80166i	0.0586576	+	0.0585153i
$949$	27.6828	+	47.9480i	0.898621	+	1.55646i
$950$	−1.10490	+	1.58692i	−0.0358478	+	0.0514864i
$951$	7.92835	+	29.4459i	0.257095	+	0.954848i
$952$	−0.206593	−	0.119277i	−0.00669572	−	0.00386578i
$953$			52.7420i			1.70848i	0.519879	+	0.854240i	$0.325977\pi$
$953$			52.7420i			1.70848i	−0.519879	+	0.854240i	$0.674023\pi$
$954$	−2.37701	−	1.36468i	−0.0769587	−	0.0441831i
$955$	9.18495	−	2.04905i	0.297218	−	0.0663058i
$956$	−5.14768	+	8.91604i	−0.166488	+	0.288365i
$957$	−4.82737	+	18.1039i	−0.156047	+	0.585217i
$958$	−3.27714	+	1.89206i	−0.105880	+	0.0611296i
$959$	−8.39290	−	14.5369i	−0.271021	−	0.469422i
$960$	−1.22074	+	29.6917i	−0.0393991	+	0.958297i
$961$	4.66446	−	8.07909i	0.150467	−	0.260616i
$962$		−	7.49804i		−	0.241747i
$963$	−46.3195	+	0.112556i	−1.49262	+	0.00362707i
$964$	−34.0922			−1.09804
$965$	15.4813	+	4.85864i	0.498360	+	0.156405i
$966$	−0.145009	−	0.538563i	−0.00466559	−	0.0173280i
$967$	17.3499	−	10.0170i	0.557935	−	0.322124i	−0.194381	−	0.980926i	$-0.562270\pi$
$967$	17.3499	−	10.0170i	0.557935	−	0.322124i	0.752316	+	0.658802i	$0.228937\pi$
$968$	5.04115	−	2.91051i	0.162029	−	0.0935472i
$969$	−2.06505	+	2.07008i	−0.0663391	+	0.0665005i
$970$	−0.135356	+	0.431291i	−0.00434603	+	0.0138479i
$971$	−35.8203			−1.14953			−0.574763	−	0.818320i	$-0.694906\pi$
$971$	−35.8203			−1.14953			−0.574763	+	0.818320i	$0.694906\pi$
$972$	7.83203	−	29.9563i	0.251212	−	0.960849i
$973$		−	16.1460i		−	0.517616i
$974$	0.247700	−	0.429029i	0.00793682	−	0.0137470i
$975$	−17.4176	+	48.4369i	−0.557809	+	1.55122i
$976$	−16.9907	−	29.4287i	−0.543857	−	0.941989i
$977$	−2.46175	+	1.42129i	−0.0787583	+	0.0454711i	−0.538862	−	0.842394i	$-0.681146\pi$
$977$	−2.46175	+	1.42129i	−0.0787583	+	0.0454711i	0.460104	+	0.887865i	$0.347812\pi$
$978$	−2.30065	+	0.619453i	−0.0735665	+	0.0198079i
$979$	−37.6927	+	65.2857i	−1.20466	+	2.08654i
$980$	−4.33492	+	0.967069i	−0.138474	+	0.0308919i
$981$	0.0746092	+	30.7034i	0.00238209	+	0.980285i
$982$			3.70880i			0.118353i
$983$	40.6862	+	23.4902i	1.29769	+	0.749220i	0.980004	−	0.198976i	$-0.0637617\pi$
$983$	40.6862	+	23.4902i	1.29769	+	0.749220i	0.317684	+	0.948197i	$0.397095\pi$
$984$	−6.18837	−	1.65011i	−0.197278	−	0.0526037i
$985$	−23.4791	+	21.5720i	−0.748105	+	0.687342i
$986$	−0.0668102	−	0.115719i	−0.00212767	−	0.00368523i
$987$	0.369857	−	1.38706i	0.0117727	−	0.0441507i
$988$	−33.7701	−	19.4972i	−1.07437	−	0.620287i
$989$	9.74001			0.309714
$990$	−1.13062	+	3.63343i	−0.0359335	+	0.115478i
$991$	23.2925			0.739911			0.369956	−	0.929049i	$-0.379373\pi$
$991$	23.2925			0.739911			0.369956	+	0.929049i	$0.379373\pi$
$992$	5.61280	+	3.24055i	0.178207	+	0.102888i
$993$	36.0446	−	9.70508i	1.14384	−	0.307981i
$994$	−0.495028	−	0.857414i	−0.0157013	−	0.0271955i
$995$	1.51813	+	1.65233i	0.0481278	+	0.0523825i
$996$	38.9258	−	39.0205i	1.23341	−	1.23641i
$997$	−3.91768	−	2.26187i	−0.124074	−	0.0716342i	0.436678	−	0.899618i	$-0.356155\pi$
$997$	−3.91768	−	2.26187i	−0.124074	−	0.0716342i	−0.560753	+	0.827983i	$0.689488\pi$
$998$			0.605684i			0.0191726i
$999$	−39.7312	−	39.4426i	−1.25704	−	1.24791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.15	✓	64
3.2	odd	2		945.2.bh.c.694.18		64
5.4	even	2	inner	315.2.bh.c.169.18	yes	64
9.4	even	3	inner	315.2.bh.c.274.18	yes	64
9.5	odd	6		945.2.bh.c.64.15		64
15.14	odd	2		945.2.bh.c.694.15		64
45.4	even	6	inner	315.2.bh.c.274.15	yes	64
45.14	odd	6		945.2.bh.c.64.18		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.15	✓	64	1.1	even	1	trivial
315.2.bh.c.169.18	yes	64	5.4	even	2	inner
315.2.bh.c.274.15	yes	64	45.4	even	6	inner
315.2.bh.c.274.18	yes	64	9.4	even	3	inner
945.2.bh.c.64.15		64	9.5	odd	6
945.2.bh.c.64.18		64	45.14	odd	6
945.2.bh.c.694.15		64	15.14	odd	2
945.2.bh.c.694.18		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.101400 - 0.0585435i) q^{2} +(-1.22623 - 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-1.51285 - 1.64660i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +O(q^{10})\)	\(q+(-0.101400 - 0.0585435i) q^{2} +(-1.22623 - 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-1.51285 - 1.64660i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +(0.0570063 + 0.255533i) q^{10} +(2.42237 - 4.19567i) q^{11} +(-0.886391 + 3.32421i) q^{12} +(-5.14734 + 2.97182i) q^{13} +(-0.0585435 - 0.101400i) q^{14} +(-0.159098 + 3.86971i) q^{15} +(-1.95897 + 3.39303i) q^{16} +0.511102i q^{17} +(0.174891 - 0.304627i) q^{18} -3.30298 q^{19} +(-1.32995 + 4.23769i) q^{20} +(-0.450320 - 1.67249i) q^{21} +(-0.491259 + 0.283628i) q^{22} +(-2.38175 + 1.37510i) q^{23} +(0.570945 - 0.572335i) q^{24} +(-0.422551 + 4.98211i) q^{25} +0.695922 q^{26} +(3.66082 - 3.68760i) q^{27} -1.98629i q^{28} +(1.11642 - 1.93369i) q^{29} +(0.242679 - 0.383076i) q^{30} +(2.32761 + 4.03154i) q^{31} +(1.20570 - 0.696112i) q^{32} +(-8.10278 + 2.18169i) q^{33} +(0.0299217 - 0.0518259i) q^{34} +(-0.486872 - 2.18242i) q^{35} +(5.15328 - 2.99197i) q^{36} -10.7743i q^{37} +(0.334923 + 0.193368i) q^{38} +(9.94712 + 2.65237i) q^{39} +(0.768536 - 0.706113i) q^{40} +(-3.96117 - 6.86095i) q^{41} +(-0.0522506 + 0.195954i) q^{42} +(-3.06708 - 1.77078i) q^{43} -9.62308 q^{44} +(4.92874 - 4.55055i) q^{45} +0.322013 q^{46} +(0.717764 + 0.414401i) q^{47} +(6.55269 - 1.76432i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.334517 - 0.480450i) q^{50} +(0.625209 - 0.626730i) q^{51} +(10.2241 + 5.90289i) q^{52} -7.80304i q^{53} +(-0.587093 + 0.159607i) q^{54} +(-10.5733 + 2.35877i) q^{55} +(-0.233371 + 0.404211i) q^{56} +(4.05022 + 4.04039i) q^{57} +(-0.226410 + 0.130718i) q^{58} +(-2.65313 - 4.59536i) q^{59} +(6.81461 - 3.56951i) q^{60} +(-4.33664 + 7.51128i) q^{61} -0.545065i q^{62} +(-1.49368 + 2.60171i) q^{63} +7.67285 q^{64} +(12.6805 + 3.97966i) q^{65} +(0.949347 + 0.253141i) q^{66} +(-10.1339 + 5.85079i) q^{67} +(0.879187 - 0.507599i) q^{68} +(4.60268 + 1.22729i) q^{69} +(-0.0783975 + 0.249801i) q^{70} +8.45574 q^{71} +(-1.40022 + 0.00340254i) q^{72} -9.31511i q^{73} +(-0.630762 + 1.09251i) q^{74} +(6.61254 - 5.59234i) q^{75} +(3.28034 + 5.68172i) q^{76} +(4.19567 - 2.42237i) q^{77} +(-0.853361 - 0.851290i) q^{78} +(0.370752 - 0.642161i) q^{79} +(8.55057 - 1.90753i) q^{80} +(-8.99989 + 0.0437397i) q^{81} +0.927603i q^{82} +(-13.8742 - 8.01027i) q^{83} +(-2.42974 + 2.43565i) q^{84} +(0.841579 - 0.773223i) q^{85} +(0.207335 + 0.359114i) q^{86} +(-3.73439 + 1.00549i) q^{87} +(1.95830 + 1.13062i) q^{88} -15.5602 q^{89} +(-0.766181 + 0.172881i) q^{90} -5.94363 q^{91} +(4.73085 + 2.73136i) q^{92} +(2.07741 - 7.79086i) q^{93} +(-0.0485210 - 0.0840408i) q^{94} +(4.99693 + 5.43868i) q^{95} +(-2.32999 - 0.621286i) q^{96} +(1.49523 + 0.863270i) q^{97} -0.117087i q^{98} +(12.6046 + 7.23651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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