LMFDB - Embedded newform 315.2.bh.c.169.18

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			169.18
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.101400 + 0.0585435i) q^{2} +(1.22623 + 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-0.669567 - 2.13347i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(-0.866025 - 0.500000i) q^{7} -0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +O(q^{10})$	\(q+(0.101400 + 0.0585435i) q^{2} +(1.22623 + 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-0.669567 - 2.13347i) 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} +(1.78873 - 3.43518i) q^{15} +(-1.95897 + 3.39303i) q^{16} -0.511102i q^{17} +(-0.174891 + 0.304627i) q^{18} -3.30298 q^{19} +(-3.00497 + 3.27062i) 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} +(-4.10336 + 2.85700i) q^{25} +0.695922 q^{26} +(-3.66082 + 3.68760i) q^{27} +1.98629i q^{28} +(1.11642 - 1.93369i) q^{29} +(0.382485 - 0.243609i) 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} +(-0.995780 + 0.312515i) q^{40} +(-3.96117 - 6.86095i) q^{41} +(0.0522506 - 0.195954i) q^{42} +(3.06708 + 1.77078i) q^{43} -9.62308 q^{44} +(6.39550 - 2.02425i) q^{45} +0.322013 q^{46} +(-0.717764 - 0.414401i) q^{47} +(-6.55269 + 1.76432i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.583340 + 0.0494752i) 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} +(-7.68559 + 0.334692i) q^{60} +(-4.33664 + 7.51128i) q^{61} +0.545065i q^{62} +(1.49368 - 2.60171i) q^{63} +7.67285 q^{64} +(-9.78676 - 8.99184i) 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} +(-0.177135 + 0.192795i) q^{70} +8.45574 q^{71} +(1.40022 - 0.00340254i) q^{72} +9.31511i q^{73} +(-0.630762 + 1.09251i) q^{74} +(-8.52651 - 1.51612i) 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} +(-1.09042 + 0.342217i) q^{85} +(0.207335 + 0.359114i) q^{86} +(3.73439 - 1.00549i) q^{87} +(-1.95830 - 1.13062i) q^{88} -15.5602 q^{89} +(0.767012 + 0.169156i) q^{90} -5.94363 q^{91} +(-4.73085 - 2.73136i) q^{92} +(-2.07741 + 7.79086i) q^{93} +(-0.0485210 - 0.0840408i) q^{94} +(2.21157 + 7.04681i) 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	0.535422	−	0.844585i	$-0.320153\pi$
$2$	0.101400	+	0.0585435i	0.0717008	+	0.0413965i	−0.463721	+	0.885981i	$0.653486\pi$
$3$	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
$5$	−0.669567	−	2.13347i	−0.299439	−	0.954115i
$5$	−0.669567	−	2.13347i	−0.299439	−	0.954115i
$6$	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	0.430682	−	0.902504i	$-0.358273\pi$
$13$	5.14734	−	2.97182i	1.42761	−	0.824234i	0.996932	+	0.0782699i	$0.0249396\pi$
$14$	−0.0585435	−	0.101400i	−0.0156464	−	0.0271004i
$15$	1.78873	−	3.43518i	0.461849	−	0.886959i
$16$	−1.95897	+	3.39303i	−0.489741	+	0.848257i
$17$		−	0.511102i		−	0.123961i	−0.998077	−	0.0619803i	$-0.980258\pi$
$17$		−	0.511102i		−	0.123961i	0.998077	−	0.0619803i	$-0.0197416\pi$
$18$	−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	$0.623690\pi$
$20$	−3.00497	+	3.27062i	−0.671931	+	0.731332i
$21$	−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	−0.230691	−	0.973027i	$-0.574099\pi$
$23$	2.38175	−	1.37510i	0.496629	−	0.286729i	0.727320	+	0.686298i	$0.240765\pi$
$24$	0.570945	−	0.572335i	0.116544	−	0.116827i
$25$	−4.10336	+	2.85700i	−0.820672	+	0.571399i
$26$	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	$0.100195\pi$
$30$	0.382485	−	0.243609i	0.0698319	−	0.0444767i
$31$	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	$0.346279\pi$
$37$			10.7743i			1.77128i	−0.464375	+	0.885639i	$0.653721\pi$
$38$	−0.334923	−	0.193368i	−0.0543317	−	0.0313684i
$39$	9.94712	+	2.65237i	1.59281	+	0.424720i
$40$	−0.995780	+	0.312515i	−0.157447	+	0.0494130i
$41$	−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	0.715287	−	0.698831i	$-0.246296\pi$
$43$	3.06708	+	1.77078i	0.467725	+	0.270041i	−0.247562	+	0.968872i	$0.579629\pi$
$44$	−9.62308			−1.45073
$45$	6.39550	−	2.02425i	0.953385	−	0.301757i
$46$	0.322013			0.0474783
$47$	−0.717764	−	0.414401i	−0.104697	−	0.0604466i	0.446737	−	0.894665i	$-0.352586\pi$
$47$	−0.717764	−	0.414401i	−0.104697	−	0.0604466i	−0.551434	+	0.834218i	$0.685919\pi$
$48$	−6.55269	+	1.76432i	−0.945799	+	0.254658i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−0.583340	+	0.0494752i	−0.0824968	+	0.00699684i
$51$	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	$0.180033\pi$
$53$			7.80304i			1.07183i	−0.844272	+	0.535915i	$0.819967\pi$
$54$	−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	$0.945593\pi$
$60$	−7.68559	+	0.334692i	−0.992205	+	0.0432086i
$61$	−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
$65$	−9.78676	−	8.99184i	−1.21390	−	1.11530i
$66$	0.949347	+	0.253141i	0.116857	+	0.0311595i
$67$	10.1339	−	5.85079i	1.23805	−	0.714788i	0.269354	−	0.963041i	$-0.413190\pi$
$67$	10.1339	−	5.85079i	1.23805	−	0.714788i	0.968695	+	0.248253i	$0.0798564\pi$
$68$	−0.879187	+	0.507599i	−0.106617	+	0.0615554i
$69$	4.60268	+	1.22729i	0.554098	+	0.147749i
$70$	−0.177135	+	0.192795i	−0.0211717	+	0.0230434i
$71$	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	$0.183518\pi$
$73$			9.31511i			1.09025i	−0.838355	+	0.545125i	$0.816482\pi$
$74$	−0.630762	+	1.09251i	−0.0733246	+	0.127002i
$75$	−8.52651	−	1.51612i	−0.984557	−	0.175067i
$76$	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	$0.00861673\pi$
$83$	13.8742	+	8.01027i	1.52289	+	0.879242i	0.523257	+	0.852175i	$0.324717\pi$
$84$	−2.42974	+	2.43565i	−0.265107	+	0.265752i
$85$	−1.09042	+	0.342217i	−0.118273	+	0.0371186i
$86$	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	$0.808651\pi$
$90$	0.767012	+	0.169156i	0.0808501	+	0.0178306i
$91$	−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
$95$	2.21157	+	7.04681i	0.226902	+	0.722987i
$96$	−2.32999	−	0.621286i	−0.237804	−	0.0634098i
$97$	−1.49523	−	0.863270i	−0.151817	−	0.0876517i	0.422167	−	0.906518i	$-0.361270\pi$
$97$	−1.49523	−	0.863270i	−0.151817	−	0.0876517i	−0.573984	+	0.818866i	$0.694603\pi$
$98$			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	−0.821724	−	0.569886i	$-0.806987\pi$
$103$	−7.50054	+	4.33044i	−0.739050	+	0.426691i	0.0826739	+	0.996577i	$0.473654\pi$
$104$	−1.38707	−	2.40248i	−0.136014	−	0.235583i
$105$	−3.26668	+	2.08058i	−0.318795	+	0.203044i
$106$	−0.456817	+	0.791230i	−0.0443700	+	0.0768511i
$107$		−	15.4399i		−	1.49263i	−0.665594	−	0.746314i	$-0.731822\pi$
$107$		−	15.4399i		−	1.49263i	0.665594	−	0.746314i	$-0.268178\pi$
$108$	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	$0.336944\pi$
$110$	−0.934042	−	0.858176i	−0.0890574	−	0.0818238i
$111$	−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	−0.697474	−	0.716611i	$-0.745693\pi$
$113$	−4.52427	+	2.61209i	−0.425607	+	0.245725i	0.271866	+	0.962335i	$0.412359\pi$
$114$	−0.174155	−	0.646811i	−0.0163111	−	0.0605794i
$115$	−4.52848	−	4.16066i	−0.422283	−	0.387984i
$116$	−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
$120$	−1.60334	−	0.834877i	−0.146365	−	0.0762135i
$121$	−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	$0.0287818\pi$
$127$			2.03520i			0.180595i	−0.995915	+	0.0902975i	$0.971218\pi$
$128$	3.18943	+	1.84142i	0.281909	+	0.162760i
$129$	1.59483	+	5.92320i	0.140417	+	0.521509i
$130$	−0.465966	−	1.48473i	−0.0408679	−	0.130219i
$131$	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
$135$	10.3185	+	5.34114i	0.888078	+	0.459692i
$136$	−0.238553			−0.0204558
$137$	14.5369	+	8.39290i	1.24197	+	0.717054i	0.969496	−	0.245108i	$-0.0788235\pi$
$137$	14.5369	+	8.39290i	1.24197	+	0.717054i	0.272478	+	0.962162i	$0.412157\pi$
$138$	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	$-0.406752\pi$
$140$	4.23769	−	1.32995i	0.358150	−	0.112402i
$141$	−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	$0.839374\pi$
$150$	−0.775831	−	0.652906i	−0.0633464	−	0.0533096i
$151$	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
$155$	7.04266	−	7.66526i	0.565680	−	0.615689i
$156$	−5.31638	−	19.7450i	−0.425651	−	1.58087i
$157$	−9.61990	+	5.55405i	−0.767752	+	0.443262i	−0.832072	−	0.554668i	$-0.812845\pi$
$157$	−9.61990	+	5.55405i	−0.767752	+	0.443262i	0.0643202	+	0.997929i	$0.479512\pi$
$158$	0.0751887	−	0.0434102i	0.00598169	−	0.00345353i
$159$	−9.54512	+	9.56834i	−0.756977	+	0.758819i
$160$	2.29243	+	2.10623i	0.181232	+	0.166512i
$161$	−2.75021			−0.216747
$162$	−0.915152	−	0.522450i	−0.0719011	−	0.0410475i
$163$		−	11.7484i		−	0.920206i	−0.887866	−	0.460103i	$-0.847813\pi$
$163$		−	11.7484i		−	0.920206i	0.887866	−	0.460103i	$-0.152187\pi$
$164$	−7.86804	+	13.6278i	−0.614391	+	1.06416i
$165$	−10.0799	−	15.8262i	−0.784720	−	1.23207i
$166$	0.937898	+	1.62449i	0.0727950	+	0.126085i
$167$	−6.01692	+	3.47387i	−0.465603	+	0.268816i	−0.714397	−	0.699740i	$-0.753299\pi$
$167$	−6.01692	+	3.47387i	−0.465603	+	0.268816i	0.248794	+	0.968556i	$0.419966\pi$
$168$	−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	0.423187	−	0.906043i	$-0.360911\pi$
$173$	−1.97131	−	1.13814i	−0.149876	−	0.0865308i	−0.573062	+	0.819512i	$0.694245\pi$
$174$	0.437533	+	0.116667i	0.0331693	+	0.00884450i
$175$	4.98211	−	0.422551i	0.376612	−	0.0319418i
$176$	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	$0.348051\pi$
$180$	−9.83373	−	8.99103i	−0.732963	−	0.670152i
$181$	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
$185$	22.9865	−	7.21408i	1.69000	−	0.530390i
$186$	−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	−0.256473	−	0.966551i	$-0.582561\pi$
$193$	6.28422	−	3.62820i	0.452348	−	0.261163i	0.708821	+	0.705388i	$0.249227\pi$
$194$	−0.101078	−	0.175071i	−0.00725695	−	0.0125694i
$195$	−1.00151	−	22.9978i	−0.0717195	−	1.64691i
$196$	0.993145	−	1.72018i	0.0709390	−	0.122870i
$197$			14.2592i			1.01592i	0.861380	+	0.507962i	$0.169601\pi$
$197$			14.2592i			1.01592i	−0.861380	+	0.507962i	$0.830399\pi$
$198$	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	$0.511324\pi$
$200$	1.33348	+	1.91521i	0.0942914	+	0.135426i
$201$	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
$205$	−11.9853	+	13.0449i	−0.837093	+	0.911095i
$206$	−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
$210$	−0.453046	+	0.0197293i	−0.0312632	+	0.00136145i
$211$	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
$220$	6.44329	+	20.5305i	0.434407	+	1.38417i
$221$	−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	0.386601	−	0.922247i	$-0.373649\pi$
$223$	−3.26720	−	1.88632i	−0.218788	−	0.126317i	−0.605389	+	0.795930i	$0.706982\pi$
$224$	1.39222			0.0930218
$225$	−8.60088	−	12.2892i	−0.573392	−	0.819281i
$226$	−0.611682			−0.0406885
$227$	−10.8866	−	6.28539i	−0.722570	−	0.417176i	0.0931278	−	0.995654i	$-0.470313\pi$
$227$	−10.8866	−	6.28539i	−0.722570	−	0.417176i	−0.815698	+	0.578478i	$0.803647\pi$
$228$	−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	$0.878611\pi$
$230$	−0.215609	−	0.687005i	−0.0142169	−	0.0452998i
$231$	−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	$0.151397\pi$
$233$			13.9790i			0.915793i	−0.889005	+	0.457897i	$0.848603\pi$
$234$	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	$0.886947\pi$
$240$	8.15159	+	12.7986i	0.526183	+	0.826147i
$241$	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
$245$	1.51285	−	1.64660i	0.0966526	−	0.105197i
$246$	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
$250$	0.496139	+	1.21141i	0.0313786	+	0.0766163i
$251$	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
$255$	−1.75573	−	0.914225i	−0.109948	−	0.0572510i
$256$	−7.45725	−	12.9163i	−0.466078	−	0.807271i
$257$	−0.960275	+	0.554415i	−0.0599003	+	0.0345835i	−0.529651	−	0.848216i	$-0.677677\pi$
$257$	−0.960275	+	0.554415i	−0.0599003	+	0.0345835i	0.469751	+	0.882799i	$0.344344\pi$
$258$	−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	−0.293475	−	0.955967i	$-0.594812\pi$
$263$	−20.5652	−	11.8733i	−1.26810	−	0.732140i	−0.974629	+	0.223826i	$0.928145\pi$
$264$	−1.01829	−	3.78191i	−0.0626712	−	0.232760i
$265$	16.6475	−	5.22466i	1.02265	−	0.320948i
$266$	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	$0.677989\pi$
$270$	0.733614	+	1.14568i	0.0446463	+	0.0697236i
$271$	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
$275$	2.04715	+	24.1371i	0.123448	+	1.45552i
$276$	−2.45997	−	9.13631i	−0.148073	−	0.549941i
$277$	16.8571	+	9.73245i	1.01284	+	0.584766i	0.912023	−	0.410138i	$-0.134520\pi$
$277$	16.8571	+	9.73245i	1.01284	+	0.584766i	0.100821	+	0.994905i	$0.467853\pi$
$278$		−	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	−0.913355	−	0.407165i	$-0.866517\pi$
$283$	−17.1156	+	9.88170i	−1.01742	+	0.587406i	−0.104062	+	0.994571i	$0.533184\pi$
$284$	−8.39778	−	14.5454i	−0.498316	−	0.863109i
$285$	−5.90815	+	11.3463i	−0.349969	+	0.672099i
$286$	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
$290$	−0.430479	−	0.395514i	−0.0252786	−	0.0232254i
$291$	−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	−0.873088	−	0.487562i	$-0.837886\pi$
$293$	−15.1897	+	8.76977i	−0.887391	+	0.512336i	−0.0143029	+	0.999898i	$0.504553\pi$
$294$	−0.143227	+	0.143576i	−0.00835318	+	0.00837351i
$295$	−8.02760	+	8.73727i	−0.467385	+	0.508703i
$296$	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
$300$	5.86007	+	16.1728i	0.338331	+	0.933740i
$301$	−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	$0.0841953\pi$
$307$			9.16137i			0.522867i	−0.965221	+	0.261434i	$0.915805\pi$
$308$	8.33383	+	4.81154i	0.474864	+	0.274163i
$309$	−14.4946	−	3.86496i	−0.824571	−	0.219870i
$310$	1.16288	−	0.364958i	0.0660471	−	0.0207282i
$311$	−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	−0.227073	−	0.973878i	$-0.572916\pi$
$313$	−20.9473	−	12.0939i	−1.18401	−	0.683590i	−0.956939	+	0.290288i	$0.906249\pi$
$314$	−1.30061			−0.0733979
$315$	−6.55079	−	1.44470i	−0.369095	−	0.0813997i
$316$	−1.47284			−0.0828538
$317$	15.2473	+	8.80302i	0.856372	+	0.494427i	0.862796	−	0.505552i	$-0.168711\pi$
$317$	15.2473	+	8.80302i	0.856372	+	0.494427i	−0.00642336	+	0.999979i	$0.502045\pi$
$318$	−1.52804	+	0.411428i	−0.0856883	+	0.0230717i
$319$	−5.40876	−	9.36825i	−0.302832	−	0.524521i
$320$	−5.13749	−	16.3698i	−0.287194	−	0.915098i
$321$	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
$330$	−0.0955833	−	2.19489i	−0.00526169	−	0.120825i
$331$	−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
$335$	−19.2678	−	17.7028i	−1.05271	−	0.967207i
$336$	6.55696	+	1.74840i	0.357711	+	0.0953828i
$337$	1.28622	−	0.742599i	0.0700648	−	0.0404519i	−0.464558	−	0.885543i	$-0.653787\pi$
$337$	1.28622	−	0.742599i	0.0700648	−	0.0404519i	0.534623	+	0.845091i	$0.320454\pi$
$338$	2.26394	−	1.30709i	0.123142	−	0.0710962i
$339$	−8.74305	−	2.33131i	−0.474857	−	0.126620i
$340$	1.67162	+	1.53585i	0.0906563	+	0.0832929i
$341$	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
$345$	−0.463413	−	10.6414i	−0.0249493	−	0.572915i
$346$	−0.133261	−	0.230814i	−0.00716414	−	0.0124087i
$347$	−26.8564	+	15.5055i	−1.44173	+	0.832381i	−0.997965	−	0.0637641i	$-0.979689\pi$
$347$	−26.8564	+	15.5055i	−1.44173	+	0.832381i	−0.443761	+	0.896145i	$0.646356\pi$
$348$	−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	0.0376054	−	0.999293i	$-0.488027\pi$
$353$	−15.1998	−	8.77562i	−0.809005	−	0.467079i	−0.846610	+	0.532214i	$0.821360\pi$
$354$	0.760002	−	0.761851i	0.0403936	−	0.0404919i
$355$	−5.66168	−	18.0400i	−0.300491	−	0.957466i
$356$	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	$0.454607\pi$
$360$	−0.944802	−	2.98505i	−0.0497954	−	0.157326i
$361$	−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
$365$	19.8735	−	6.23708i	1.04023	−	0.326464i
$366$	−1.69956	−	0.453184i	−0.0888375	−	0.0236883i
$367$	−9.20085	−	5.31211i	−0.480281	−	0.277290i	0.240253	−	0.970710i	$-0.422770\pi$
$367$	−9.20085	−	5.31211i	−0.480281	−	0.277290i	−0.720533	+	0.693420i	$0.756103\pi$
$368$			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	−0.954163	−	0.299286i	$-0.903251\pi$
$373$	−22.6362	+	13.0690i	−1.17206	+	0.676687i	−0.217892	+	0.975973i	$0.569918\pi$
$374$	−0.144963	−	0.251083i	−0.00749586	−	0.0129832i
$375$	2.47447	+	19.2062i	0.127781	+	0.991802i
$376$	−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	$0.794532\pi$
$380$	9.92535	−	10.8028i	0.509160	−	0.554172i
$381$	−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	$-0.320909\pi$
$383$	29.9946	−	17.3174i	1.53265	−	0.884876i	0.999238	−	0.0390213i	$-0.0124240\pi$
$384$	1.65846	+	6.15950i	0.0846327	+	0.314326i
$385$	7.97734	+	7.32939i	0.406563	+	0.373540i
$386$	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	$0.859880\pi$
$390$	1.24482	−	2.39061i	0.0630338	−	0.121053i
$391$	−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	$-0.854157\pi$
$397$		−	17.6262i		−	0.884632i	0.896859	−	0.442316i	$-0.145843\pi$
$398$	−0.101754	−	0.0587475i	−0.00510045	−	0.00294475i
$399$	1.48740	+	5.52420i	0.0744631	+	0.276556i
$400$	−1.65553	−	19.5196i	−0.0827763	−	0.975979i
$401$	−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
$405$	6.11935	+	19.1717i	0.304073	+	0.952649i
$406$	−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	$0.597971\pi$
$410$	−1.97901	+	0.621092i	−0.0977364	+	0.0306735i
$411$	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	$0.952101\pi$
$420$	6.82326	+	3.55294i	0.332941	+	0.173366i
$421$	−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
$425$	1.46022	+	2.09724i	0.0708309	+	0.101731i
$426$	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
$430$	0.627334	−	0.682793i	0.0302527	−	0.0329272i
$431$	−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	$-0.983372\pi$
$433$		−	2.17297i		−	0.104426i	0.998636	−	0.0522131i	$-0.0166275\pi$
$434$	0.272533	−	0.472040i	0.0130820	−	0.0226587i
$435$	−4.64560	−	7.29395i	−0.222740	−	0.349718i
$436$	−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	0.0667792	−	0.997768i	$-0.478728\pi$
$443$	−16.0787	−	9.28306i	−0.763924	−	0.441051i	−0.830703	+	0.556716i	$0.812061\pi$
$444$	35.8159	+	9.55021i	1.69975	+	0.453233i
$445$	10.4186	+	33.1973i	0.493890	+	1.57370i
$446$	−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	$0.742089\pi$
$450$	−0.152678	−	1.74965i	−0.00719729	−	0.0824795i
$451$	−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
$455$	3.97966	+	12.6805i	0.186569	+	0.594473i
$456$	−1.88582	+	1.89041i	−0.0883118	+	0.0885266i
$457$	17.0409	+	9.83857i	0.797140	+	0.460229i	0.842470	−	0.538743i	$-0.181101\pi$
$457$	17.0409	+	9.83857i	0.797140	+	0.460229i	−0.0453300	+	0.998972i	$0.514434\pi$
$458$		−	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	0.286139	−	0.958188i	$-0.407628\pi$
$463$	27.0910	−	15.6410i	1.25902	−	0.726898i	0.972885	+	0.231290i	$0.0742946\pi$
$464$	4.37405	+	7.57607i	0.203060	+	0.351710i
$465$	18.0125	−	0.784410i	0.835311	−	0.0363761i
$466$	−0.818378	+	1.41747i	−0.0379106	+	0.0656631i
$467$		−	32.3796i		−	1.49835i	−0.662372	−	0.749175i	$-0.730450\pi$
$467$		−	32.3796i		−	1.49835i	0.662372	−	0.749175i	$-0.269550\pi$
$468$	17.6341	−	30.7153i	0.815136	−	1.41981i
$469$	−11.7016			−0.540329
$470$	−0.146810	+	0.159789i	−0.00677185	+	0.00737051i
$471$	−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
$475$	13.5533	−	9.43661i	0.621870	−	0.432981i
$476$	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	$-0.0977246\pi$
$480$	0.234591	+	5.38695i	0.0107076	+	0.245880i
$481$	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	$-0.969439\pi$
$487$		−	4.23105i		−	0.191727i	0.995394	−	0.0958635i	$-0.0305612\pi$
$488$	3.50583	+	2.02409i	0.158702	+	0.0916264i
$489$	14.3713	−	14.4063i	0.649893	−	0.651474i
$490$	0.249801	−	0.0783975i	0.0112849	−	0.00354164i
$491$	−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
$495$	6.99921	−	31.7369i	0.314591	−	1.42647i
$496$	−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	$0.870272\pi$
$500$	2.98632	−	22.0057i	0.133552	−	0.984125i
$501$	−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	$0.0858026\pi$
$503$			11.9452i			0.532609i	−0.963889	+	0.266304i	$0.914197\pi$
$504$	−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	$0.855618\pi$
$510$	−0.124509	−	0.195489i	−0.00551336	−	0.00865640i
$511$	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
$515$	14.2610	+	13.1026i	0.628413	+	0.577371i
$516$	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
$520$	−4.19688	+	4.56790i	−0.184045	+	0.200315i
$521$	−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	$-0.848045\pi$
$523$		−	21.0147i		−	0.918907i	0.888202	−	0.459454i	$-0.151955\pi$
$524$	13.5286	−	23.4323i	0.591001	−	1.02364i
$525$	6.62611	+	5.57625i	0.289187	+	0.243368i
$526$	−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
$535$	−32.9404	+	10.3380i	−1.42414	+	0.446952i
$536$	−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
$540$	−1.06010	−	23.0543i	−0.0456195	−	0.992097i
$541$	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
$545$	−6.85268	−	21.8350i	−0.293537	−	0.935308i
$546$	−0.313388	−	1.16392i	−0.0134117	−	0.0498112i
$547$	15.8515	+	9.15186i	0.677761	+	0.391305i	0.799011	−	0.601317i	$-0.205357\pi$
$547$	15.8515	+	9.15186i	0.677761	+	0.391305i	−0.121250	+	0.992622i	$0.538690\pi$
$548$		−	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
$555$	37.0115	+	19.2723i	1.57105	+	0.818062i
$556$	−16.0353	+	27.7740i	−0.680049	+	1.17788i
$557$			6.84812i			0.290164i	0.989420	+	0.145082i	$0.0463446\pi$
$557$			6.84812i			0.290164i	−0.989420	+	0.145082i	$0.953655\pi$
$558$	−1.63519	+	0.00397351i	−0.0692232	+	0.000168212i
$559$	21.0497			0.890307
$560$	−6.45125	−	5.92726i	−0.272615	−	0.250472i
$561$	−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	−0.286843	−	0.957978i	$-0.592606\pi$
$563$	9.47605	−	5.47100i	0.399368	−	0.230575i	0.686211	+	0.727402i	$0.259273\pi$
$564$	−2.01378	+	2.01868i	−0.0847953	+	0.0850016i
$565$	8.60210	+	7.90341i	0.361893	+	0.332499i
$566$	−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	$0.109493\pi$
$570$	−1.26334	+	0.804637i	−0.0529156	+	0.0337025i
$571$	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	$-0.993440\pi$
$577$		−	0.990001i		−	0.0412143i	0.999788	−	0.0206071i	$-0.00655992\pi$
$578$	1.69732	+	0.979946i	0.0705990	+	0.0407604i
$579$	12.1441	+	3.23820i	0.504693	+	0.134575i
$580$	2.96957	+	9.46205i	0.123305	+	0.392890i
$581$	−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
$585$	26.9041	−	29.4257i	1.11235	−	1.21660i
$586$	−2.05365			−0.0848355
$587$	14.0831	+	8.13090i	0.581273	+	0.335598i	0.761639	−	0.648001i	$-0.224395\pi$
$587$	14.0831	+	8.13090i	0.581273	+	0.335598i	−0.180366	+	0.983600i	$0.557728\pi$
$588$	3.32204	−	0.894467i	0.136999	−	0.0368872i
$589$	−7.68806	−	13.3161i	−0.316781	−	0.548681i
$590$	−1.32551	+	0.415998i	−0.0545704	+	0.0171264i
$591$	−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	$0.250120\pi$
$593$			34.4513i			1.41475i	−0.706840	+	0.707373i	$0.749880\pi$
$594$	−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	$0.787378\pi$
$600$	−0.707638	+	3.97968i	−0.0288892	+	0.162470i
$601$	−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
$605$	−18.8677	+	20.5356i	−0.767080	+	0.834892i
$606$	1.28188	+	0.341811i	0.0520729	+	0.0138851i
$607$	−17.7810	+	10.2659i	−0.721708	+	0.416679i	−0.815381	−	0.578925i	$-0.803473\pi$
$607$	−17.7810	+	10.2659i	−0.721708	+	0.416679i	0.0936728	+	0.995603i	$0.470139\pi$
$608$	3.98241	−	2.29925i	0.161508	−	0.0932467i
$609$	−3.73682	−	0.996413i	−0.151424	−	0.0403767i
$610$	1.67216	+	1.53634i	0.0677039	+	0.0622047i
$611$	−4.92610			−0.199289
$612$	−1.52920	−	2.63385i	−0.0618143	−	0.106467i
$613$		−	13.4401i		−	0.542839i	−0.962461	−	0.271419i	$-0.912507\pi$
$613$		−	13.4401i		−	0.542839i	0.962461	−	0.271419i	$-0.0874930\pi$
$614$	−0.536339	+	0.928966i	−0.0216449	+	0.0374900i
$615$	−30.6541	+	1.33492i	−1.23609	+	0.0538293i
$616$	1.13062	+	1.95830i	0.0455542	+	0.0789021i
$617$	−17.5021	+	10.1049i	−0.704610	+	0.406807i	−0.809062	−	0.587723i	$-0.800024\pi$
$617$	−17.5021	+	10.1049i	−0.704610	+	0.406807i	0.104452	+	0.994530i	$0.466691\pi$
$618$	−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
$625$	8.67515	−	23.4466i	0.347006	−	0.937863i
$626$	−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
$630$	−0.579674	−	0.529999i	−0.0230948	−	0.0211157i
$631$	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
$635$	4.34204	−	1.36270i	0.172308	−	0.0540772i
$636$	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	−0.998227	−	0.0595271i	$-0.981041\pi$
$643$	−36.6615	+	21.1665i	−1.44579	+	0.834726i	−0.447561	+	0.894253i	$0.647707\pi$
$644$	2.73136	+	4.73085i	0.107631	+	0.186422i
$645$	11.5691	−	7.36850i	0.455533	−	0.290134i
$646$	−0.0988309	+	0.171180i	−0.00388845	+	0.00673499i
$647$			27.5498i			1.08309i	0.840671	+	0.541547i	$0.182161\pi$
$647$			27.5498i			1.08309i	−0.840671	+	0.541547i	$0.817839\pi$
$648$	0.0204152	+	4.20063i	0.000801983	+	0.165016i
$649$	−25.7075			−1.00911
$650$	−2.85562	+	1.98825i	−0.112007	+	0.0779854i
$651$	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	−0.374109	−	0.927385i	$-0.622051\pi$
$653$	6.18342	−	3.57000i	0.241976	−	0.139705i	0.616085	+	0.787680i	$0.288718\pi$
$654$	0.539631	+	2.00419i	0.0211012	+	0.0783699i
$655$	20.6081	−	22.4299i	0.805224	−	0.876409i
$656$	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	$0.291136\pi$
$660$	−17.2131	+	33.0570i	−0.670019	+	1.28674i
$661$	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
$670$	−0.917375	−	2.92307i	−0.0354413	−	0.112928i
$671$	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	0.996143	−	0.0877496i	$-0.0279675\pi$
$673$	36.7918	+	21.2418i	1.41822	+	0.818810i	0.422078	+	0.906560i	$0.361301\pi$
$674$	0.173897			0.00669827
$675$	4.48619	−	25.5905i	0.172674	−	0.984979i
$676$	−44.3475			−1.70567
$677$	2.66200	+	1.53691i	0.102309	+	0.0590681i	0.550281	−	0.834979i	$-0.314520\pi$
$677$	2.66200	+	1.53691i	0.102309	+	0.0590681i	−0.447972	+	0.894047i	$0.647854\pi$
$678$	−0.750065	−	0.748244i	−0.0288061	−	0.0287361i
$679$	0.863270	+	1.49523i	0.0331292	+	0.0573815i
$680$	0.159727	+	0.508945i	0.00612526	+	0.0195172i
$681$	−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	$0.0745493\pi$
$683$			12.1299i			0.464137i	−0.972699	+	0.232068i	$0.925451\pi$
$684$	−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
$690$	0.575996	−	1.10617i	0.0219278	−	0.0421113i
$691$	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
$695$	−24.4265	+	26.5859i	−0.926550	+	1.00846i
$696$	−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
$700$	−5.67482	−	8.15047i	−0.214488	−	0.308059i
$701$	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
$705$	−2.70743	+	1.72439i	−0.101968	+	0.0649444i
$706$	−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
$715$	−61.4340	+	19.2804i	−2.29750	+	0.721048i
$716$	−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	$0.300567\pi$
$720$	−5.66024	+	25.6655i	−0.210945	+	0.956498i
$721$	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
$725$	0.943486	+	11.1242i	0.0350402	+	0.413144i
$726$	1.78627	−	1.79062i	0.0662947	−	0.0664560i
$727$	12.7626	+	7.36848i	0.473338	+	0.273282i	0.717636	−	0.696418i	$-0.245224\pi$
$727$	12.7626	+	7.36848i	0.473338	+	0.273282i	−0.244298	+	0.969700i	$0.578558\pi$
$728$			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	−0.997693	−	0.0678807i	$-0.978376\pi$
$733$	−38.9257	+	22.4738i	−1.43775	+	0.830088i	−0.440060	+	0.897968i	$0.645043\pi$
$734$	−0.621979	−	1.07730i	−0.0229577	−	0.0397638i
$735$	3.86932	−	0.168501i	0.142722	−	0.00621526i
$736$	−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	$0.661884\pi$
$740$	−35.2385	−	32.3763i	−1.29539	−	1.19018i
$741$	−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	−0.200271	−	0.979741i	$-0.564182\pi$
$743$	14.9394	−	8.62527i	0.548074	−	0.316430i	0.748345	+	0.663310i	$0.230849\pi$
$744$	3.63633	+	0.969617i	0.133314	+	0.0355479i
$745$	−0.700817	+	0.762771i	−0.0256759	+	0.0279458i
$746$	−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
$750$	−0.873483	+	2.09237i	−0.0318951	+	0.0764027i
$751$	−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	$-0.942866\pi$
$757$		−	9.82398i		−	0.357059i	0.983935	−	0.178529i	$-0.0571339\pi$
$758$	−3.15375	−	1.82082i	−0.114549	−	0.0661351i
$759$	16.2987	−	16.3384i	0.591607	−	0.593046i
$760$	3.28904	−	1.03223i	0.119306	−	0.0374430i
$761$	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
$765$	−1.03460	−	3.26875i	−0.0374059	−	0.118182i
$766$	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	$0.965545\pi$
$770$	0.379816	+	1.21022i	0.0136876	+	0.0436134i
$771$	−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	$0.0979702\pi$
$773$			16.8456i			0.605892i	−0.953008	+	0.302946i	$0.902030\pi$
$774$	−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
$780$	−38.5657	+	24.5629i	−1.38087	+	0.879494i
$781$	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
$785$	18.2906	+	16.8049i	0.652818	+	0.599794i
$786$	−1.95104	+	1.95579i	−0.0695913	+	0.0697607i
$787$	3.57799	−	2.06575i	0.127541	−	0.0736361i	−0.434872	−	0.900492i	$-0.643206\pi$
$787$	3.57799	−	2.06575i	0.127541	−	0.0736361i	0.562413	+	0.826856i	$0.309873\pi$
$788$	24.5283	−	14.1614i	0.873784	−	0.504480i
$789$	−10.6936	−	39.7159i	−0.380702	−	1.41392i
$790$	−0.142958	−	0.131346i	−0.00508622	−	0.00467310i
$791$	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
$795$	26.8048	+	13.9576i	0.950669	+	0.495023i
$796$	0.996607	+	1.72617i	0.0353238	+	0.0611826i
$797$	8.24281	−	4.75899i	0.291975	−	0.168572i	−0.346857	−	0.937918i	$-0.612751\pi$
$797$	8.24281	−	4.75899i	0.291975	−	0.168572i	0.638832	+	0.769346i	$0.279418\pi$
$798$	−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
$805$	1.84145	+	5.86748i	0.0649025	+	0.206801i
$806$	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	$0.403380\pi$
$810$	−0.501874	+	2.30226i	−0.0176340	+	0.0808932i
$811$	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
$815$	−25.0648	+	7.86634i	−0.877982	+	0.275546i
$816$	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	0.130563	−	0.991440i	$-0.458322\pi$
$823$	30.2502	−	17.4650i	1.05446	−	0.608791i	0.923894	+	0.382650i	$0.124988\pi$
$824$	2.02120	+	3.50082i	0.0704118	+	0.121957i
$825$	−27.0155	+	32.1018i	−0.940560	+	1.11764i
$826$	−0.310647	+	0.538056i	−0.0108088	+	0.0187214i
$827$		−	11.8658i		−	0.412614i	−0.978487	−	0.206307i	$-0.933855\pi$
$827$		−	11.8658i		−	0.412614i	0.978487	−	0.206307i	$-0.0661445\pi$
$828$	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	$0.514721\pi$
$830$	2.83780	−	3.08868i	0.0985016	−	0.107210i
$831$	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
$835$	11.4401	+	10.5109i	0.395901	+	0.363745i
$836$	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	$0.931048\pi$
$840$	0.971097	+	1.52470i	0.0335060	+	0.0526070i
$841$	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
$850$	0.0252869	+	0.298147i	0.000867332	+	0.0102263i
$851$	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	0.561723	−	0.827326i	$-0.310139\pi$
$853$	3.68287	+	2.12630i	0.126099	+	0.0728033i	−0.435624	+	0.900129i	$0.643472\pi$
$854$	1.01553			0.0347506
$855$	−21.1242	+	6.68605i	−0.722434	+	0.228658i
$856$	−7.20644			−0.246311
$857$	33.5963	+	19.3968i	1.14763	+	0.662583i	0.948308	−	0.317352i	$-0.102794\pi$
$857$	33.5963	+	19.3968i	1.14763	+	0.662583i	0.199319	+	0.979935i	$0.436127\pi$
$858$	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	$0.589063\pi$
$860$	−15.0080	+	4.71010i	−0.511768	+	0.160613i
$861$	−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	$0.365618\pi$
$863$			53.5952i			1.82440i	−0.409745	+	0.912200i	$0.634382\pi$
$864$	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
$870$	−0.0440522	−	1.01158i	−0.00149351	−	0.0342957i
$871$	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
$875$	−4.23735	−	10.3462i	−0.143249	−	0.349767i
$876$	30.9654	+	8.25683i	1.04622	+	0.278972i
$877$	4.34299	−	2.50743i	0.146652	−	0.0846698i	−0.424878	−	0.905250i	$-0.639683\pi$
$877$	4.34299	−	2.50743i	0.146652	−	0.0846698i	0.571531	+	0.820581i	$0.306350\pi$
$878$	1.46624	−	0.846535i	0.0494833	−	0.0285692i
$879$	−29.3538	−	7.82710i	−0.990078	−	0.264002i
$880$	28.7161	−	31.2547i	0.968018	−	1.05359i
$881$	−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	$-0.845415\pi$
$883$		−	27.7408i		−	0.933553i	0.884375	−	0.466776i	$-0.154585\pi$
$884$	−3.01698	+	5.22557i	−0.101472	+	0.175755i
$885$	−20.5316	+	0.894111i	−0.690163	+	0.0300552i
$886$	−1.08692	−	1.88261i	−0.0365159	−	0.0632475i
$887$	1.48760	−	0.858868i	0.0499488	−	0.0288380i	−0.474818	−	0.880084i	$-0.657486\pi$
$887$	1.48760	−	0.858868i	0.0499488	−	0.0288380i	0.524766	+	0.851246i	$0.324153\pi$
$888$	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
$895$	−8.23146	−	26.2282i	−0.275147	−	0.876713i
$896$	−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
$900$	−12.5977	+	27.0000i	−0.419924	+	0.900001i
$901$	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
$905$	−1.43754	−	4.58050i	−0.0477855	−	0.152261i
$906$	0.275290	+	0.0734052i	0.00914588	+	0.00243873i
$907$	−0.457757	−	0.264286i	−0.0151996	−	0.00877548i	0.492381	−	0.870380i	$-0.336127\pi$
$907$	−0.457757	−	0.264286i	−0.0151996	−	0.00877548i	−0.507581	+	0.861604i	$0.669460\pi$
$908$			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
$915$	18.0455	+	28.3328i	0.596565	+	0.936653i
$916$	−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	$0.357856\pi$
$920$	−1.94196	+	2.11363i	−0.0640244	+	0.0696844i
$921$	−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
$925$	−30.7820	−	44.2107i	−1.01211	−	1.45364i
$926$	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	$0.121512\pi$
$930$	1.87240	+	0.974976i	0.0613983	+	0.0319707i
$931$	−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	$-0.595297\pi$
$937$		−	58.4977i		−	1.91104i	0.294933	−	0.955518i	$-0.404703\pi$
$938$	−1.18654	−	0.685051i	−0.0387420	−	0.0223677i
$939$	−10.8923	−	40.4539i	−0.355456	−	1.32016i
$940$	3.51220	−	1.10227i	0.114555	−	0.0359521i
$941$	−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
$945$	−6.26555	−	9.78483i	−0.203818	−	0.318301i
$946$	2.00897			0.0653172
$947$	8.02904	+	4.63557i	0.260909	+	0.150636i	0.624749	−	0.780826i	$-0.285201\pi$
$947$	8.02904	+	4.63557i	0.260909	+	0.150636i	−0.363840	+	0.931461i	$0.618535\pi$
$948$	−1.80605	−	1.80166i	−0.0586576	−	0.0585153i
$949$	27.6828	+	47.9480i	0.898621	+	1.55646i
$950$	1.92676	−	0.163416i	0.0625125	−	0.00530190i
$951$	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	$-0.674023\pi$
$953$		−	52.7420i		−	1.70848i	0.519879	−	0.854240i	$-0.325977\pi$
$954$	−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
$960$	13.7247	−	26.3576i	0.442962	−	0.850688i
$961$	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
$965$	−11.9483	−	10.9779i	−0.384631	−	0.353390i
$966$	−0.145009	−	0.538563i	−0.00466559	−	0.0173280i
$967$	−17.3499	+	10.0170i	−0.557935	+	0.322124i	−0.752316	−	0.658802i	$-0.771063\pi$
$967$	−17.3499	+	10.0170i	−0.557935	+	0.322124i	0.194381	+	0.980926i	$0.437730\pi$
$968$	−5.04115	+	2.91051i	−0.162029	+	0.0935472i
$969$	−2.06505	+	2.07008i	−0.0663391	+	0.0665005i
$970$	−0.305831	+	0.332868i	−0.00981964	+	0.0106877i
$971$	−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
$975$	−48.3945	+	17.5352i	−1.54986	+	0.561577i
$976$	−16.9907	−	29.4287i	−0.543857	−	0.941989i
$977$	2.46175	−	1.42129i	0.0787583	−	0.0454711i	−0.460104	−	0.887865i	$-0.652188\pi$
$977$	2.46175	−	1.42129i	0.0787583	−	0.0454711i	0.538862	+	0.842394i	$0.318854\pi$
$978$	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	−0.317684	−	0.948197i	$-0.602905\pi$
$983$	−40.6862	−	23.4902i	−1.29769	−	0.749220i	−0.980004	+	0.198976i	$0.936238\pi$
$984$	−6.18837	−	1.65011i	−0.197278	−	0.0526037i
$985$	30.4214	−	9.54746i	0.969308	−	0.304207i
$986$	−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
$990$	2.56771	−	2.80837i	0.0816072	−	0.0892560i
$991$	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
$995$	0.671900	+	2.14090i	0.0213007	+	0.0678712i
$996$	38.9258	−	39.0205i	1.23341	−	1.23641i
$997$	3.91768	+	2.26187i	0.124074	+	0.0716342i	0.560753	−	0.827983i	$-0.310512\pi$
$997$	3.91768	+	2.26187i	0.124074	+	0.0716342i	−0.436678	+	0.899618i	$0.643845\pi$
$998$		−	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.169.18	yes	64
3.2	odd	2		945.2.bh.c.694.15		64
5.4	even	2	inner	315.2.bh.c.169.15	✓	64
9.4	even	3	inner	315.2.bh.c.274.15	yes	64
9.5	odd	6		945.2.bh.c.64.18		64
15.14	odd	2		945.2.bh.c.694.18		64
45.4	even	6	inner	315.2.bh.c.274.18	yes	64
45.14	odd	6		945.2.bh.c.64.15		64

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

\(f(q)\)	\(=\)	\(q+(0.101400 + 0.0585435i) q^{2} +(1.22623 + 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-0.669567 - 2.13347i) q^{5} +(0.0527266 + 0.195826i) q^{6} +(-0.866025 - 0.500000i) q^{7} -0.466742i q^{8} +(0.00728996 + 2.99999i) q^{9} +O(q^{10})\)	\(q+(0.101400 + 0.0585435i) q^{2} +(1.22623 + 1.22326i) q^{3} +(-0.993145 - 1.72018i) q^{4} +(-0.669567 - 2.13347i) 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} +(1.78873 - 3.43518i) q^{15} +(-1.95897 + 3.39303i) q^{16} -0.511102i q^{17} +(-0.174891 + 0.304627i) q^{18} -3.30298 q^{19} +(-3.00497 + 3.27062i) 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} +(-4.10336 + 2.85700i) q^{25} +0.695922 q^{26} +(-3.66082 + 3.68760i) q^{27} +1.98629i q^{28} +(1.11642 - 1.93369i) q^{29} +(0.382485 - 0.243609i) 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} +(-0.995780 + 0.312515i) q^{40} +(-3.96117 - 6.86095i) q^{41} +(0.0522506 - 0.195954i) q^{42} +(3.06708 + 1.77078i) q^{43} -9.62308 q^{44} +(6.39550 - 2.02425i) q^{45} +0.322013 q^{46} +(-0.717764 - 0.414401i) q^{47} +(-6.55269 + 1.76432i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.583340 + 0.0494752i) 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} +(-7.68559 + 0.334692i) q^{60} +(-4.33664 + 7.51128i) q^{61} +0.545065i q^{62} +(1.49368 - 2.60171i) q^{63} +7.67285 q^{64} +(-9.78676 - 8.99184i) 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} +(-0.177135 + 0.192795i) q^{70} +8.45574 q^{71} +(1.40022 - 0.00340254i) q^{72} +9.31511i q^{73} +(-0.630762 + 1.09251i) q^{74} +(-8.52651 - 1.51612i) 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} +(-1.09042 + 0.342217i) q^{85} +(0.207335 + 0.359114i) q^{86} +(3.73439 - 1.00549i) q^{87} +(-1.95830 - 1.13062i) q^{88} -15.5602 q^{89} +(0.767012 + 0.169156i) q^{90} -5.94363 q^{91} +(-4.73085 - 2.73136i) q^{92} +(-2.07741 + 7.79086i) q^{93} +(-0.0485210 - 0.0840408i) q^{94} +(2.21157 + 7.04681i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more