LMFDB - Embedded newform 312.2.bt.c.19.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	312.19
Dual form			312.2.bt.c.115.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16911 + 0.795730i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.733627 + 1.86059i) q^{4} +(2.47909 + 2.47909i) q^{5} +(-1.27368 + 0.614612i) q^{6} +(-3.75755 - 1.00683i) q^{7} +(-0.622837 + 2.75900i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.925639 + 4.87102i) q^{10} +(0.509830 - 0.136608i) q^{11} +(-1.97813 - 0.294955i) q^{12} +(-0.521969 - 3.56757i) q^{13} +(-3.59181 - 4.16709i) q^{14} +(-3.38651 + 0.907411i) q^{15} +(-2.92358 + 2.72996i) q^{16} +(5.38161 - 3.10707i) q^{17} +(0.104568 - 1.41034i) q^{18} +(3.55975 + 0.953832i) q^{19} +(-2.79384 + 6.43131i) q^{20} +(2.75071 - 2.75071i) q^{21} +(0.704749 + 0.245977i) q^{22} +(-1.37494 + 2.38147i) q^{23} +(-2.07794 - 1.91889i) q^{24} +7.29182i q^{25} +(2.22858 - 4.58622i) q^{26} +1.00000 q^{27} +(-0.883339 - 7.72989i) q^{28} +(-0.839483 - 0.484676i) q^{29} +(-4.68125 - 1.63388i) q^{30} +(0.348039 + 0.348039i) q^{31} +(-5.59029 + 0.865233i) q^{32} +(-0.136608 + 0.509830i) q^{33} +(8.76407 + 0.649803i) q^{34} +(-6.81928 - 11.8113i) q^{35} +(1.24450 - 1.56563i) q^{36} +(1.50405 + 5.61319i) q^{37} +(3.40274 + 3.94773i) q^{38} +(3.35059 + 1.33175i) q^{39} +(-8.38389 + 5.29575i) q^{40} +(1.71600 + 6.40421i) q^{41} +(5.40471 - 1.02706i) q^{42} +(7.50871 - 4.33516i) q^{43} +(0.628197 + 0.848364i) q^{44} +(0.907411 - 3.38651i) q^{45} +(-3.50247 + 1.69011i) q^{46} +(-1.54875 + 1.54875i) q^{47} +(-0.902421 - 3.89688i) q^{48} +(7.04327 + 4.06643i) q^{49} +(-5.80232 + 8.52492i) q^{50} +6.21414i q^{51} +(6.25485 - 3.58844i) q^{52} -14.2470i q^{53} +(1.16911 + 0.795730i) q^{54} +(1.60258 + 0.925250i) q^{55} +(5.11819 - 9.73997i) q^{56} +(-2.60592 + 2.60592i) q^{57} +(-0.595775 - 1.23464i) q^{58} +(3.44998 - 12.8755i) q^{59} +(-4.17275 - 5.63519i) q^{60} +(-5.42370 + 3.13137i) q^{61} +(0.129950 + 0.683840i) q^{62} +(1.00683 + 3.75755i) q^{63} +(-7.22415 - 3.43681i) q^{64} +(7.55033 - 10.1383i) q^{65} +(-0.565397 + 0.487342i) q^{66} +(-1.76589 - 6.59040i) q^{67} +(9.72908 + 7.73352i) q^{68} +(-1.37494 - 2.38147i) q^{69} +(1.42616 - 19.2350i) q^{70} +(2.98604 - 11.1440i) q^{71} +(2.70078 - 0.840107i) q^{72} +(-5.69573 - 5.69573i) q^{73} +(-2.70819 + 7.75924i) q^{74} +(-6.31490 - 3.64591i) q^{75} +(0.836840 + 7.32298i) q^{76} -2.05325 q^{77} +(2.85749 + 4.22312i) q^{78} +4.82868i q^{79} +(-14.0157 - 0.480014i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.08983 + 8.85268i) q^{82} +(-10.2669 + 10.2669i) q^{83} +(7.13595 + 3.09995i) q^{84} +(21.0442 + 5.63879i) q^{85} +(12.2281 + 0.906642i) q^{86} +(0.839483 - 0.484676i) q^{87} +(0.0593617 + 1.49170i) q^{88} +(-7.12395 + 1.90886i) q^{89} +(3.75561 - 3.23714i) q^{90} +(-1.63062 + 13.9308i) q^{91} +(-5.43964 - 0.811092i) q^{92} +(-0.475430 + 0.127391i) q^{93} +(-3.04304 + 0.578269i) q^{94} +(6.46031 + 11.1896i) q^{95} +(2.04583 - 5.27395i) q^{96} +(-3.76138 - 1.00786i) q^{97} +(4.99856 + 10.3586i) q^{98} +(-0.373221 - 0.373221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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 $

$2$	1.16911	+	0.795730i	0.826684	+	0.562666i
$2$	1.16911	+	0.795730i	0.826684	+	0.562666i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.733627	+	1.86059i	0.366814	+	0.930294i
$5$	2.47909	+	2.47909i	1.10868	+	1.10868i	0.993324	+	0.115361i	$0.0368025\pi$
$5$	2.47909	+	2.47909i	1.10868	+	1.10868i	0.115361	+	0.993324i	$0.463198\pi$
$6$	−1.27368	+	0.614612i	−0.519976	+	0.250914i
$7$	−3.75755	−	1.00683i	−1.42022	−	0.380547i	−0.534658	−	0.845069i	$-0.679559\pi$
$7$	−3.75755	−	1.00683i	−1.42022	−	0.380547i	−0.885561	+	0.464522i	$0.846226\pi$
$8$	−0.622837	+	2.75900i	−0.220206	+	0.975453i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.925639	+	4.87102i	0.292713	+	1.54035i
$11$	0.509830	−	0.136608i	0.153719	−	0.0411890i	−0.181139	−	0.983458i	$-0.557978\pi$
$11$	0.509830	−	0.136608i	0.153719	−	0.0411890i	0.334858	+	0.942269i	$0.391312\pi$
$12$	−1.97813	−	0.294955i	−0.571037	−	0.0851461i
$13$	−0.521969	−	3.56757i	−0.144768	−	0.989466i
$13$	−0.521969	−	3.56757i	−0.144768	−	0.989466i
$14$	−3.59181	−	4.16709i	−0.959952	−	1.11370i
$15$	−3.38651	+	0.907411i	−0.874392	+	0.234293i
$16$	−2.92358	+	2.72996i	−0.730896	+	0.682489i
$17$	5.38161	−	3.10707i	1.30523	−	0.753576i	0.323935	−	0.946079i	$-0.394994\pi$
$17$	5.38161	−	3.10707i	1.30523	−	0.753576i	0.981296	+	0.192504i	$0.0616607\pi$
$18$	0.104568	−	1.41034i	0.0246470	−	0.332421i
$19$	3.55975	+	0.953832i	0.816662	+	0.218824i	0.642887	−	0.765961i	$-0.277737\pi$
$19$	3.55975	+	0.953832i	0.816662	+	0.218824i	0.173775	+	0.984785i	$0.444403\pi$
$20$	−2.79384	+	6.43131i	−0.624723	+	1.43808i
$21$	2.75071	−	2.75071i	0.600255	−	0.600255i
$22$	0.704749	+	0.245977i	0.150253	+	0.0524424i
$23$	−1.37494	+	2.38147i	−0.286696	+	0.496571i	−0.973019	−	0.230725i	$-0.925890\pi$
$23$	−1.37494	+	2.38147i	−0.286696	+	0.496571i	0.686323	+	0.727296i	$0.259223\pi$
$24$	−2.07794	−	1.91889i	−0.424159	−	0.391692i
$25$			7.29182i			1.45836i
$26$	2.22858	−	4.58622i	0.437061	−	0.899432i
$27$	1.00000			0.192450
$28$	−0.883339	−	7.72989i	−0.166935	−	1.46081i
$29$	−0.839483	−	0.484676i	−0.155888	−	0.0900020i	0.420027	−	0.907512i	$-0.362021\pi$
$29$	−0.839483	−	0.484676i	−0.155888	−	0.0900020i	−0.575915	+	0.817510i	$0.695354\pi$
$30$	−4.68125	−	1.63388i	−0.854675	−	0.298305i
$31$	0.348039	+	0.348039i	0.0625097	+	0.0625097i	0.737671	−	0.675161i	$-0.235926\pi$
$31$	0.348039	+	0.348039i	0.0625097	+	0.0625097i	−0.675161	+	0.737671i	$0.735926\pi$
$32$	−5.59029	+	0.865233i	−0.988233	+	0.152953i
$33$	−0.136608	+	0.509830i	−0.0237805	+	0.0887499i
$34$	8.76407	+	0.649803i	1.50303	+	0.111440i
$35$	−6.81928	−	11.8113i	−1.15267	−	1.99648i
$36$	1.24450	−	1.56563i	0.207417	−	0.260939i
$37$	1.50405	+	5.61319i	0.247264	+	0.922802i	0.972232	+	0.234019i	$0.0751879\pi$
$37$	1.50405	+	5.61319i	0.247264	+	0.922802i	−0.724968	+	0.688783i	$0.758145\pi$
$38$	3.40274	+	3.94773i	0.551997	+	0.640406i
$39$	3.35059	+	1.33175i	0.536524	+	0.213250i
$40$	−8.38389	+	5.29575i	−1.32561	+	0.837331i
$41$	1.71600	+	6.40421i	0.267994	+	1.00017i	0.960392	+	0.278653i	$0.0898878\pi$
$41$	1.71600	+	6.40421i	0.267994	+	1.00017i	−0.692398	+	0.721516i	$0.743446\pi$
$42$	5.40471	−	1.02706i	0.833965	−	0.158478i
$43$	7.50871	−	4.33516i	1.14507	−	0.661105i	0.197388	−	0.980326i	$-0.436754\pi$
$43$	7.50871	−	4.33516i	1.14507	−	0.661105i	0.947681	+	0.319220i	$0.103421\pi$
$44$	0.628197	+	0.848364i	0.0947043	+	0.127896i
$45$	0.907411	−	3.38651i	0.135269	−	0.504830i
$46$	−3.50247	+	1.69011i	−0.516411	+	0.249194i
$47$	−1.54875	+	1.54875i	−0.225908	+	0.225908i	−0.810981	−	0.585073i	$-0.801066\pi$
$47$	−1.54875	+	1.54875i	−0.225908	+	0.225908i	0.585073	+	0.810981i	$0.301066\pi$
$48$	−0.902421	−	3.89688i	−0.130253	−	0.562465i
$49$	7.04327	+	4.06643i	1.00618	+	0.580919i
$50$	−5.80232	+	8.52492i	−0.820572	+	1.20561i
$51$			6.21414i			0.870154i
$52$	6.25485	−	3.58844i	0.867391	−	0.497626i
$53$		−	14.2470i		−	1.95698i	−0.206300	−	0.978489i	$-0.566142\pi$
$53$		−	14.2470i		−	1.95698i	0.206300	−	0.978489i	$-0.433858\pi$
$54$	1.16911	+	0.795730i	0.159095	+	0.108285i
$55$	1.60258	+	0.925250i	0.216092	+	0.124761i
$56$	5.11819	−	9.73997i	0.683946	−	1.30156i
$57$	−2.60592	+	2.60592i	−0.345162	+	0.345162i
$58$	−0.595775	−	1.23464i	−0.0782291	−	0.162116i
$59$	3.44998	−	12.8755i	0.449149	−	1.67625i	−0.255594	−	0.966784i	$-0.582271\pi$
$59$	3.44998	−	12.8755i	0.449149	−	1.67625i	0.704743	−	0.709463i	$-0.251062\pi$
$60$	−4.17275	−	5.63519i	−0.538700	−	0.727500i
$61$	−5.42370	+	3.13137i	−0.694434	+	0.400931i	−0.805271	−	0.592907i	$-0.797980\pi$
$61$	−5.42370	+	3.13137i	−0.694434	+	0.400931i	0.110837	+	0.993839i	$0.464647\pi$
$62$	0.129950	+	0.683840i	0.0165037	+	0.0868478i
$63$	1.00683	+	3.75755i	0.126849	+	0.473406i
$64$	−7.22415	−	3.43681i	−0.903019	−	0.429602i
$65$	7.55033	−	10.1383i	0.936503	−	1.25751i
$66$	−0.565397	+	0.487342i	−0.0695955	+	0.0599877i
$67$	−1.76589	−	6.59040i	−0.215738	−	0.805146i	−0.985905	−	0.167304i	$-0.946494\pi$
$67$	−1.76589	−	6.59040i	−0.215738	−	0.805146i	0.770167	−	0.637842i	$-0.220173\pi$
$68$	9.72908	+	7.73352i	1.17982	+	0.937828i
$69$	−1.37494	−	2.38147i	−0.165524	−	0.286696i
$70$	1.42616	−	19.2350i	0.170459	−	2.29903i
$71$	2.98604	−	11.1440i	0.354377	−	1.32255i	−0.526889	−	0.849934i	$-0.676642\pi$
$71$	2.98604	−	11.1440i	0.354377	−	1.32255i	0.881266	−	0.472620i	$-0.156692\pi$
$72$	2.70078	−	0.840107i	0.318290	−	0.0990075i
$73$	−5.69573	−	5.69573i	−0.666634	−	0.666634i	0.290301	−	0.956935i	$-0.406245\pi$
$73$	−5.69573	−	5.69573i	−0.666634	−	0.666634i	−0.956935	+	0.290301i	$0.906245\pi$
$74$	−2.70819	+	7.75924i	−0.314820	+	0.901993i
$75$	−6.31490	−	3.64591i	−0.729182	−	0.420993i
$76$	0.836840	+	7.32298i	0.0959921	+	0.840004i
$77$	−2.05325			−0.233990
$78$	2.85749	+	4.22312i	0.323547	+	0.478174i
$79$			4.82868i			0.543269i	0.962400	+	0.271635i	$0.0875643\pi$
$79$			4.82868i			0.543269i	−0.962400	+	0.271635i	$0.912436\pi$
$80$	−14.0157	−	0.480014i	−1.56700	−	0.0536672i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.08983	+	8.85268i	−0.341214	+	0.977615i
$83$	−10.2669	+	10.2669i	−1.12693	+	1.12693i	−0.136261	+	0.990673i	$0.543509\pi$
$83$	−10.2669	+	10.2669i	−1.12693	+	1.12693i	−0.990673	+	0.136261i	$0.956491\pi$
$84$	7.13595	+	3.09995i	0.778596	+	0.338232i
$85$	21.0442	+	5.63879i	2.28257	+	0.611612i
$86$	12.2281	+	0.906642i	1.31859	+	0.0977657i
$87$	0.839483	−	0.484676i	0.0900020	−	0.0519627i
$88$	0.0593617	+	1.49170i	0.00632798	+	0.159016i
$89$	−7.12395	+	1.90886i	−0.755137	+	0.202338i	−0.615796	−	0.787906i	$-0.711165\pi$
$89$	−7.12395	+	1.90886i	−0.755137	+	0.202338i	−0.139342	+	0.990244i	$0.544499\pi$
$90$	3.75561	−	3.23714i	0.395876	−	0.341224i
$91$	−1.63062	+	13.9308i	−0.170935	+	1.46035i
$92$	−5.43964	−	0.811092i	−0.567121	−	0.0845622i
$93$	−0.475430	+	0.127391i	−0.0492998	+	0.0132098i
$94$	−3.04304	+	0.578269i	−0.313866	+	0.0596439i
$95$	6.46031	+	11.1896i	0.662814	+	1.14803i
$96$	2.04583	−	5.27395i	0.208802	−	0.538270i
$97$	−3.76138	−	1.00786i	−0.381911	−	0.102333i	0.0627557	−	0.998029i	$-0.480011\pi$
$97$	−3.76138	−	1.00786i	−0.381911	−	0.102333i	−0.444666	+	0.895696i	$0.646678\pi$
$98$	4.99856	+	10.3586i	0.504931	+	1.04638i
$99$	−0.373221	−	0.373221i	−0.0375101	−	0.0375101i
$100$	−13.5671	+	5.34948i	−1.35671	+	0.534948i
$101$	2.06215	−	3.57175i	0.205192	−	0.355402i	−0.745002	−	0.667062i	$-0.767552\pi$
$101$	2.06215	−	3.57175i	0.205192	−	0.355402i	0.950194	+	0.311660i	$0.100885\pi$
$102$	−4.94478	+	7.26501i	−0.489606	+	0.719343i
$103$	−9.66630			−0.952449			−0.476224	−	0.879324i	$-0.657995\pi$
$103$	−9.66630			−0.952449			−0.476224	+	0.879324i	$0.657995\pi$
$104$	10.1680	+	0.781903i	0.997056	+	0.0766719i
$105$	13.6386			1.33099
$106$	11.3368	−	16.6563i	1.10113	−	1.61780i
$107$	−1.07455	+	1.86118i	−0.103881	+	0.179927i	−0.913280	−	0.407331i	$-0.866459\pi$
$107$	−1.07455	+	1.86118i	−0.103881	+	0.179927i	0.809400	+	0.587258i	$0.199793\pi$
$108$	0.733627	+	1.86059i	0.0705933	+	0.179035i
$109$	8.97204	+	8.97204i	0.859365	+	0.859365i	0.991263	−	0.131898i	$-0.0421071\pi$
$109$	8.97204	+	8.97204i	0.859365	+	0.859365i	−0.131898	+	0.991263i	$0.542107\pi$
$110$	1.13734	+	2.35694i	0.108441	+	0.224725i
$111$	−5.61319	−	1.50405i	−0.532780	−	0.142758i
$112$	13.7341	−	7.31439i	1.29775	−	0.691145i
$113$	−5.34490	−	9.25763i	−0.502806	−	0.870885i	−0.999995	−	0.00324259i	$-0.998968\pi$
$113$	−5.34490	−	9.25763i	−0.502806	−	0.870885i	0.497189	−	0.867642i	$-0.334365\pi$
$114$	−5.12020	+	0.972992i	−0.479551	+	0.0911290i
$115$	−9.31251	+	2.49528i	−0.868396	+	0.232686i
$116$	0.285915	−	1.91750i	0.0265465	−	0.178036i
$117$	−2.82862	+	2.23582i	−0.261506	+	0.206702i
$118$	14.2788	−	12.3076i	1.31447	−	1.13301i
$119$	−23.3499	+	6.25660i	−2.14048	+	0.573541i
$120$	−0.394306	−	9.90853i	−0.0359950	−	0.904521i
$121$	−9.28502	+	5.36071i	−0.844092	+	0.487337i
$122$	−8.83262	−	0.654886i	−0.799668	−	0.0592906i
$123$	−6.40421	−	1.71600i	−0.577448	−	0.154727i
$124$	−0.392227	+	0.902889i	−0.0352230	+	0.0810818i
$125$	−5.68163	+	5.68163i	−0.508180	+	0.508180i
$126$	−1.81290	+	5.19414i	−0.161506	+	0.462731i
$127$	2.10087	−	3.63881i	0.186422	−	0.322892i	−0.757633	−	0.652681i	$-0.773644\pi$
$127$	2.10087	−	3.63881i	0.186422	−	0.322892i	0.944055	+	0.329789i	$0.106978\pi$
$128$	−5.71103	−	9.76648i	−0.504789	−	0.863243i
$129$			8.67032i			0.763379i
$130$	16.8945	−	5.84480i	1.48175	−	0.512623i
$131$	−1.54383			−0.134885			−0.0674425	−	0.997723i	$-0.521484\pi$
$131$	−1.54383			−0.134885			−0.0674425	+	0.997723i	$0.521484\pi$
$132$	−1.04880	+	0.119853i	−0.0912866	+	0.0104318i
$133$	−12.4156	−	7.16813i	−1.07657	−	0.621556i
$134$	3.17966	−	9.11007i	0.274681	−	0.786990i
$135$	2.47909	+	2.47909i	0.213366	+	0.213366i
$136$	5.22054	+	16.7830i	0.447658	+	1.43913i
$137$	−0.469582	+	1.75250i	−0.0401191	+	0.149726i	−0.983080	−	0.183177i	$-0.941362\pi$
$137$	−0.469582	+	1.75250i	−0.0401191	+	0.149726i	0.942961	+	0.332904i	$0.108028\pi$
$138$	0.287551	−	3.87828i	0.0244780	−	0.330141i
$139$	8.71429	+	15.0936i	0.739137	+	1.28022i	0.952885	+	0.303333i	$0.0980996\pi$
$139$	8.71429	+	15.0936i	0.739137	+	1.28022i	−0.213748	+	0.976889i	$0.568567\pi$
$140$	16.9732	−	21.3530i	1.43450	−	1.80466i
$141$	−0.566882	−	2.11563i	−0.0477401	−	0.178168i
$142$	12.3586	−	10.6525i	1.03711	−	0.893939i
$143$	−0.753475	−	1.74755i	−0.0630088	−	0.146137i
$144$	3.82600	+	1.16692i	0.318834	+	0.0972431i
$145$	−0.879600	−	3.28271i	−0.0730468	−	0.272615i
$146$	−2.12666	−	11.1912i	−0.176003	−	0.926188i
$147$	−7.04327	+	4.06643i	−0.580919	+	0.335394i
$148$	−9.34042	+	6.91640i	−0.767778	+	0.568525i
$149$	−2.21517	+	8.26714i	−0.181474	+	0.677271i	0.813884	+	0.581028i	$0.197349\pi$
$149$	−2.21517	+	8.26714i	−0.181474	+	0.677271i	−0.995358	+	0.0962430i	$0.969317\pi$
$150$	−4.48164	−	9.28742i	−0.365924	−	0.758314i
$151$	6.97806	−	6.97806i	0.567867	−	0.567867i	−0.363664	−	0.931530i	$-0.618474\pi$
$151$	6.97806	−	6.97806i	0.567867	−	0.567867i	0.931530	+	0.363664i	$0.118474\pi$
$152$	−4.84876	+	9.22726i	−0.393287	+	0.748429i
$153$	−5.38161	−	3.10707i	−0.435077	−	0.251192i
$154$	−2.40047	−	1.63383i	−0.193435	−	0.131658i
$155$			1.72564i			0.138607i
$156$	−0.0197482	+	7.21108i	−0.00158113	+	0.577348i
$157$		−	9.18347i		−	0.732921i	−0.930434	−	0.366460i	$-0.880570\pi$
$157$		−	9.18347i		−	0.732921i	0.930434	−	0.366460i	$-0.119430\pi$
$158$	−3.84233	+	5.64525i	−0.305679	+	0.449112i
$159$	12.3383	+	7.12351i	0.978489	+	0.564931i
$160$	−16.0039	−	11.7139i	−1.26522	−	0.926063i
$161$	7.56415	−	7.56415i	0.596139	−	0.596139i
$162$	−1.27368	+	0.614612i	−0.100069	+	0.0482885i
$163$	1.76943	−	6.60358i	0.138592	−	0.517233i	−0.861365	−	0.507986i	$-0.830390\pi$
$163$	1.76943	−	6.60358i	0.138592	−	0.517233i	0.999957	−	0.00924642i	$-0.00294327\pi$
$164$	−10.6567	+	7.89107i	−0.832147	+	0.616189i
$165$	−1.60258	+	0.925250i	−0.124761	+	0.0720307i
$166$	−20.1727	+	3.83342i	−1.56571	+	0.297531i
$167$	3.72987	+	13.9201i	0.288626	+	1.07717i	0.946149	+	0.323733i	$0.104938\pi$
$167$	3.72987	+	13.9201i	0.288626	+	1.07717i	−0.657522	+	0.753435i	$0.728395\pi$
$168$	5.87597	+	9.30247i	0.453341	+	0.717701i
$169$	−12.4551	+	3.72432i	−0.958084	+	0.286486i
$170$	20.1160	+	23.3379i	1.54283	+	1.78993i
$171$	−0.953832	−	3.55975i	−0.0729413	−	0.272221i
$172$	13.5745	+	10.7902i	1.03505	+	0.822748i
$173$	−5.54697	−	9.60764i	−0.421728	−	0.730455i	0.574380	−	0.818589i	$-0.305243\pi$
$173$	−5.54697	−	9.60764i	−0.421728	−	0.730455i	−0.996109	+	0.0881335i	$0.971910\pi$
$174$	1.36712	+	0.101364i	0.103641	+	0.00768435i
$175$	7.34163	−	27.3993i	0.554975	−	2.07120i
$176$	−1.11759	+	1.79120i	−0.0842418	+	0.135017i
$177$	9.42552	+	9.42552i	0.708465	+	0.708465i
$178$	−9.84760	−	3.43708i	−0.738109	−	0.257620i
$179$	8.53378	+	4.92698i	0.637844	+	0.368260i	0.783784	−	0.621034i	$-0.213287\pi$
$179$	8.53378	+	4.92698i	0.637844	+	0.368260i	−0.145939	+	0.989294i	$0.546620\pi$
$180$	6.96660	−	0.796113i	0.519259	−	0.0593388i
$181$	−3.48599			−0.259112			−0.129556	−	0.991572i	$-0.541355\pi$
$181$	−3.48599			−0.259112			−0.129556	+	0.991572i	$0.541355\pi$
$182$	−12.9916	+	14.9891i	−0.962998	+	1.11107i
$183$		−	6.26275i		−	0.462956i
$184$	−5.71411	−	5.27674i	−0.421250	−	0.389006i
$185$	−10.1869	+	17.6443i	−0.748959	+	1.29723i
$186$	−0.657198	−	0.229380i	−0.0481881	−	0.0168190i
$187$	2.31925	−	2.31925i	0.169600	−	0.169600i
$188$	−4.01779	−	1.74538i	−0.293028	−	0.127295i
$189$	−3.75755	−	1.00683i	−0.273321	−	0.0732362i
$190$	−1.35109	+	18.2225i	−0.0980183	+	1.32200i
$191$	−4.19758	+	2.42347i	−0.303726	+	0.175356i	−0.644116	−	0.764928i	$-0.722774\pi$
$191$	−4.19758	+	2.42347i	−0.303726	+	0.175356i	0.340390	+	0.940285i	$0.389441\pi$
$192$	6.58844	−	4.53789i	0.475480	−	0.327494i
$193$	−25.8461	+	6.92544i	−1.86044	+	0.498504i	−0.999940	−	0.0109406i	$-0.996517\pi$
$193$	−25.8461	+	6.92544i	−1.86044	+	0.498504i	−0.860503	+	0.509445i	$0.829851\pi$
$194$	−3.59548	−	4.17134i	−0.258140	−	0.299485i
$195$	5.00490	+	11.6080i	0.358409	+	0.831263i
$196$	−2.39883	+	16.0879i	−0.171345	+	1.14913i
$197$	25.6972	−	6.88555i	1.83085	−	0.490575i	0.832835	−	0.553522i	$-0.186716\pi$
$197$	25.6972	−	6.88555i	1.83085	−	0.490575i	0.998017	+	0.0629464i	$0.0200497\pi$
$198$	−0.139353	−	0.733319i	−0.00990336	−	0.0521147i
$199$	−10.0881	−	17.4731i	−0.715127	−	1.23864i	−0.962910	−	0.269821i	$-0.913035\pi$
$199$	−10.0881	−	17.4731i	−0.715127	−	1.23864i	0.247783	−	0.968816i	$-0.420298\pi$
$200$	−20.1181	−	4.54161i	−1.42257	−	0.321141i
$201$	6.59040	+	1.76589i	0.464851	+	0.124557i
$202$	5.25303	−	2.53485i	0.369602	−	0.178351i
$203$	2.66641	+	2.66641i	0.187145	+	0.187145i
$204$	−11.5620	+	4.55887i	−0.809500	+	0.319184i
$205$	−11.6225	+	20.1308i	−0.811751	+	1.40599i
$206$	−11.3009	−	7.69177i	−0.787374	−	0.535911i
$207$	2.74989			0.191130
$208$	11.2653	+	9.00513i	0.781110	+	0.624393i
$209$	1.94517			0.134550
$210$	15.9450	+	10.8526i	1.10031	+	0.748902i
$211$	7.10800	−	12.3114i	0.489335	−	0.847553i	−0.510590	−	0.859824i	$-0.670573\pi$
$211$	7.10800	−	12.3114i	0.489335	−	0.847553i	0.999925	+	0.0122714i	$0.00390622\pi$
$212$	26.5078	−	10.4520i	1.82057	−	0.717846i
$213$	8.15801	+	8.15801i	0.558977	+	0.558977i
$214$	−2.73726	+	1.32087i	−0.187115	+	0.0902925i
$215$	29.3621	+	7.86755i	2.00248	+	0.536562i
$216$	−0.622837	+	2.75900i	−0.0423787	+	0.187726i
$217$	−0.957356	−	1.65819i	−0.0649896	−	0.112565i
$218$	3.34996	+	17.6286i	0.226888	+	1.19396i
$219$	7.78051	−	2.08478i	0.525758	−	0.140876i
$220$	−0.545814	+	3.66053i	−0.0367988	+	0.246793i
$221$	−13.8937	−	17.5775i	−0.934593	−	1.18239i
$222$	−5.36560	−	6.22498i	−0.360116	−	0.417793i
$223$	−12.9267	+	3.46369i	−0.865634	+	0.231946i	−0.664199	−	0.747556i	$-0.731227\pi$
$223$	−12.9267	+	3.46369i	−0.865634	+	0.231946i	−0.201435	+	0.979502i	$0.564560\pi$
$224$	21.8769	+	2.37733i	1.46171	+	0.158842i
$225$	6.31490	−	3.64591i	0.420993	−	0.243061i
$226$	1.11781	−	15.0763i	0.0743559	−	1.00286i
$227$	15.1048	+	4.04732i	1.00254	+	0.268630i	0.722509	−	0.691361i	$-0.242989\pi$
$227$	15.1048	+	4.04732i	1.00254	+	0.268630i	0.280031	+	0.959991i	$0.409655\pi$
$228$	−6.76031	−	2.93677i	−0.447712	−	0.194492i
$229$	−10.5268	+	10.5268i	−0.695632	+	0.695632i	−0.963465	−	0.267833i	$-0.913692\pi$
$229$	−10.5268	+	10.5268i	−0.695632	+	0.695632i	0.267833	+	0.963465i	$0.413692\pi$
$230$	−12.8729	−	4.49299i	−0.848814	−	0.296259i
$231$	1.02662	−	1.77817i	0.0675470	−	0.116995i
$232$	1.86008	−	2.01426i	0.122120	−	0.132243i
$233$		−	23.2702i		−	1.52448i	−0.647293	−	0.762241i	$-0.724099\pi$
$233$		−	23.2702i		−	1.52448i	0.647293	−	0.762241i	$-0.275901\pi$
$234$	−5.08607	+	0.363100i	−0.332487	+	0.0237366i
$235$	−7.67899			−0.500922
$236$	26.4870	−	3.02682i	1.72416	−	0.197029i
$237$	−4.18176	−	2.41434i	−0.271635	−	0.156828i
$238$	−32.2772	−	11.2656i	−2.09222	−	0.730241i
$239$	5.96683	+	5.96683i	0.385962	+	0.385962i	0.873244	−	0.487282i	$-0.162012\pi$
$239$	5.96683	+	5.96683i	0.385962	+	0.385962i	−0.487282	+	0.873244i	$0.662012\pi$
$240$	7.42353	−	11.8979i	0.479187	−	0.768007i
$241$	−8.00014	+	29.8569i	−0.515334	+	1.92325i	−0.166641	+	0.986018i	$0.553292\pi$
$241$	−8.00014	+	29.8569i	−0.515334	+	1.92325i	−0.348694	+	0.937237i	$0.613375\pi$
$242$	−15.1209	−	1.12112i	−0.972006	−	0.0720684i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−9.80518	−	7.79401i	−0.627712	−	0.498961i
$245$	7.37985	+	27.5420i	0.471482	+	1.75959i
$246$	−6.12173	−	7.10221i	−0.390307	−	0.452820i
$247$	1.54478	−	13.1975i	0.0982922	−	0.839738i
$248$	−1.17701	+	0.743468i	−0.0747403	+	0.0472102i
$249$	−3.75793	−	14.0248i	−0.238149	−	0.888785i
$250$	−11.1635	+	2.12140i	−0.706041	+	0.134169i
$251$	−11.3156	+	6.53307i	−0.714235	+	0.412364i	−0.812627	−	0.582784i	$-0.801963\pi$
$251$	−11.3156	+	6.53307i	−0.714235	+	0.412364i	0.0983923	+	0.995148i	$0.468630\pi$
$252$	−6.25261	+	4.62994i	−0.393877	+	0.291659i
$253$	−0.375658	+	1.40197i	−0.0236174	+	0.0881413i
$254$	5.35165	−	2.58244i	0.335792	−	0.162036i
$255$	−15.4054	+	15.4054i	−0.964727	+	0.964727i
$256$	1.09466	−	15.9625i	0.0684165	−	0.997657i
$257$	13.8556	+	7.99953i	0.864288	+	0.498997i	0.865446	−	0.501002i	$-0.167035\pi$
$257$	13.8556	+	7.99953i	0.864288	+	0.498997i	−0.00115787	+	0.999999i	$0.500369\pi$
$258$	−6.89923	+	10.1365i	−0.429527	+	0.631073i
$259$		−	22.6061i		−	1.40468i
$260$	24.4024	+	6.61029i	1.51337	+	0.409953i
$261$			0.969351i			0.0600013i
$262$	−1.80490	−	1.22847i	−0.111507	−	0.0758952i
$263$	−5.61079	−	3.23939i	−0.345976	−	0.199749i	0.316935	−	0.948447i	$-0.397346\pi$
$263$	−5.61079	−	3.23939i	−0.345976	−	0.199749i	−0.662912	+	0.748698i	$0.730680\pi$
$264$	−1.32153	−	0.694443i	−0.0813348	−	0.0427400i
$265$	35.3197	−	35.3197i	2.16967	−	2.16967i
$266$	−8.81124	−	18.2598i	−0.540252	−	1.11958i
$267$	1.90886	−	7.12395i	0.116820	−	0.435979i
$268$	10.9665	−	8.12050i	0.669887	−	0.496039i
$269$	−9.43060	+	5.44476i	−0.574994	+	0.331973i	−0.759141	−	0.650926i	$-0.774381\pi$
$269$	−9.43060	+	5.44476i	−0.574994	+	0.331973i	0.184147	+	0.982899i	$0.441048\pi$
$270$	0.925639	+	4.87102i	0.0563326	+	0.296441i
$271$	6.52629	+	24.3564i	0.396444	+	1.47955i	0.819307	+	0.573355i	$0.194358\pi$
$271$	6.52629	+	24.3564i	0.396444	+	1.47955i	−0.422863	+	0.906193i	$0.638975\pi$
$272$	−7.25139	+	23.7753i	−0.439680	+	1.44159i
$273$	−11.2492	−	8.37758i	−0.680830	−	0.507034i
$274$	−1.94351	+	1.67521i	−0.117412	+	0.101203i
$275$	0.996124	+	3.71758i	0.0600685	+	0.224179i
$276$	3.42224	−	4.30532i	0.205995	−	0.259150i
$277$	8.00895	+	13.8719i	0.481211	+	0.833482i	0.999768	−	0.0215614i	$-0.00686374\pi$
$277$	8.00895	+	13.8719i	0.481211	+	0.833482i	−0.518556	+	0.855043i	$0.673530\pi$
$278$	−1.82248	+	24.5803i	−0.109305	+	1.47423i
$279$	0.127391	−	0.475430i	0.00762671	−	0.0284633i
$280$	36.8348	−	11.4578i	2.20130	−	0.684737i
$281$	6.67944	+	6.67944i	0.398462	+	0.398462i	0.877690	−	0.479228i	$-0.159083\pi$
$281$	6.67944	+	6.67944i	0.398462	+	0.398462i	−0.479228	+	0.877690i	$0.659083\pi$
$282$	1.02073	−	2.92449i	0.0607833	−	0.174151i
$283$	−0.711449	−	0.410755i	−0.0422913	−	0.0244169i	0.478705	−	0.877976i	$-0.341106\pi$
$283$	−0.711449	−	0.410755i	−0.0422913	−	0.0244169i	−0.520997	+	0.853559i	$0.674440\pi$
$284$	22.9251	−	2.61979i	1.36036	−	0.155456i
$285$	−12.9206			−0.765352
$286$	0.509682	−	2.64263i	0.0301381	−	0.156262i
$287$		−	25.7918i		−	1.52244i
$288$	3.54446	+	4.40872i	0.208859	+	0.259786i
$289$	10.8078	−	18.7196i	0.635753	−	1.10116i
$290$	1.58381	−	4.53777i	0.0930043	−	0.266467i
$291$	2.75352	−	2.75352i	0.161414	−	0.161414i
$292$	6.41886	−	14.7759i	0.375636	−	0.864697i
$293$	−3.12030	−	0.836083i	−0.182290	−	0.0488445i	0.166519	−	0.986038i	$-0.446747\pi$
$293$	−3.12030	−	0.836083i	−0.182290	−	0.0488445i	−0.348809	+	0.937194i	$0.613414\pi$
$294$	−11.4701	−	0.850441i	−0.668951	−	0.0495987i
$295$	40.4724	−	23.3668i	2.35639	−	1.36046i
$296$	−16.4236	+	0.653568i	−0.954600	+	0.0379879i
$297$	0.509830	−	0.136608i	0.0295833	−	0.00792683i
$298$	−9.16819	+	7.90250i	−0.531099	+	0.457780i
$299$	9.21374	+	3.66215i	0.532845	+	0.211788i
$300$	2.15075	−	14.4242i	0.124174	−	0.832780i
$301$	−32.5791	+	8.72955i	−1.87783	+	0.503163i
$302$	13.7108	−	2.60545i	0.788966	−	0.149927i
$303$	2.06215	+	3.57175i	0.118467	+	0.205192i
$304$	−13.0111	+	6.92936i	−0.746240	+	0.397426i
$305$	−21.2088	−	5.68289i	−1.21441	−	0.325401i
$306$	−3.81929	−	7.91481i	−0.218334	−	0.452460i
$307$	13.6272	+	13.6272i	0.777747	+	0.777747i	0.979447	−	0.201700i	$-0.0646467\pi$
$307$	13.6272	+	13.6272i	0.777747	+	0.777747i	−0.201700	+	0.979447i	$0.564647\pi$
$308$	−1.50632	−	3.82025i	−0.0858306	−	0.217679i
$309$	4.83315	−	8.37126i	0.274948	−	0.476224i
$310$	−1.37315	+	2.01746i	−0.0779895	+	0.114584i
$311$	−4.76959			−0.270458			−0.135229	−	0.990814i	$-0.543177\pi$
$311$	−4.76959			−0.270458			−0.135229	+	0.990814i	$0.543177\pi$
$312$	−5.76116	+	8.41481i	−0.326161	+	0.476395i
$313$	−17.9440			−1.01426			−0.507128	−	0.861871i	$-0.669293\pi$
$313$	−17.9440			−1.01426			−0.507128	+	0.861871i	$0.669293\pi$
$314$	7.30756	−	10.7365i	0.412390	−	0.605894i
$315$	−6.81928	+	11.8113i	−0.384223	+	0.665494i
$316$	−8.98420	+	3.54245i	−0.505401	+	0.199279i
$317$	4.79191	+	4.79191i	0.269141	+	0.269141i	0.828754	−	0.559613i	$-0.189050\pi$
$317$	4.79191	+	4.79191i	0.269141	+	0.269141i	−0.559613	+	0.828754i	$0.689050\pi$
$318$	8.75639	+	18.1461i	0.491034	+	1.01758i
$319$	−0.494204	−	0.132422i	−0.0276701	−	0.00741418i
$320$	−9.38916	−	26.4295i	−0.524870	−	1.47746i
$321$	−1.07455	−	1.86118i	−0.0599756	−	0.103881i
$322$	14.8623	−	2.82429i	0.828246	−	0.157391i
$323$	22.1208	−	5.92725i	1.23083	−	0.329801i
$324$	−1.97813	−	0.294955i	−0.109896	−	0.0163864i
$325$	26.0141	−	3.80610i	1.44300	−	0.211125i
$326$	7.32332	−	6.31232i	0.405601	−	0.349607i
$327$	−12.2560	+	3.28399i	−0.677760	+	0.181605i
$328$	−18.7380	+	0.745670i	−1.03463	+	0.0411727i
$329$	7.37883	−	4.26017i	0.406808	−	0.234871i
$330$	−2.60984	−	0.193504i	−0.143667	−	0.0106520i
$331$	−15.9635	−	4.27741i	−0.877435	−	0.235108i	−0.208135	−	0.978100i	$-0.566739\pi$
$331$	−15.9635	−	4.27741i	−0.877435	−	0.235108i	−0.669300	+	0.742992i	$0.733406\pi$
$332$	−26.6344	−	11.5704i	−1.46175	−	0.635006i
$333$	4.10914	−	4.10914i	0.225179	−	0.225179i
$334$	−6.71600	+	19.2420i	−0.367483	+	1.05288i
$335$	11.9604	−	20.7160i	0.653467	−	1.13184i
$336$	−0.532606	+	15.5513i	−0.0290560	+	0.848392i
$337$		−	22.1566i		−	1.20695i	−0.797382	−	0.603475i	$-0.793782\pi$
$337$		−	22.1566i		−	1.20695i	0.797382	−	0.603475i	$-0.206218\pi$
$338$	−17.5249	−	5.55676i	−0.953229	−	0.302248i
$339$	10.6898			0.580590
$340$	4.94716	+	43.2914i	0.268298	+	2.34781i
$341$	0.224986	+	0.129896i	0.0121837	+	0.00703424i
$342$	1.71747	−	4.92072i	0.0928699	−	0.266082i
$343$	−3.11618	−	3.11618i	−0.168258	−	0.168258i
$344$	7.28399	+	23.4166i	0.392726	+	1.26254i
$345$	2.49528	−	9.31251i	0.134341	−	0.501369i
$346$	1.16008	−	15.6463i	0.0623661	−	0.841148i
$347$	−15.3076	−	26.5135i	−0.821754	−	1.42332i	−0.904375	−	0.426738i	$-0.859663\pi$
$347$	−15.3076	−	26.5135i	−0.821754	−	1.42332i	0.0826215	−	0.996581i	$-0.473671\pi$
$348$	1.51765	+	1.20636i	0.0813546	+	0.0646677i
$349$	−3.87693	−	14.4689i	−0.207527	−	0.774502i	−0.988664	−	0.150143i	$-0.952027\pi$
$349$	−3.87693	−	14.4689i	−0.207527	−	0.774502i	0.781137	−	0.624359i	$-0.214640\pi$
$350$	30.3856	−	26.1908i	1.62418	−	1.39996i
$351$	−0.521969	−	3.56757i	−0.0278606	−	0.190423i
$352$	−2.73190	+	1.20480i	−0.145611	+	0.0642162i
$353$	−0.900492	−	3.36068i	−0.0479284	−	0.178871i	0.937812	−	0.347143i	$-0.112848\pi$
$353$	−0.900492	−	3.36068i	−0.0479284	−	0.178871i	−0.985741	+	0.168272i	$0.946181\pi$
$354$	3.51928	+	18.5196i	0.187048	+	0.984307i
$355$	35.0298	−	20.2245i	1.85919	−	1.07340i
$356$	−8.77792	−	11.8544i	−0.465229	−	0.628279i
$357$	6.25660	−	23.3499i	0.331134	−	1.23581i
$358$	6.05636	+	12.5508i	0.320089	+	0.663328i
$359$	−5.96490	+	5.96490i	−0.314815	+	0.314815i	−0.846772	−	0.531956i	$-0.821457\pi$
$359$	−5.96490	+	5.96490i	−0.314815	+	0.314815i	0.531956	+	0.846772i	$0.321457\pi$
$360$	8.77820	+	4.61279i	0.462652	+	0.243115i
$361$	−4.69247	−	2.70920i	−0.246972	−	0.142590i
$362$	−4.07550	−	2.77391i	−0.214204	−	0.145793i
$363$		−	10.7214i		−	0.562728i
$364$	−27.1158	+	7.18613i	−1.42126	+	0.376656i
$365$		−	28.2405i		−	1.47817i
$366$	4.98346	−	7.32183i	0.260490	−	0.382718i
$367$	18.8420	+	10.8784i	0.983545	+	0.567850i	0.903339	−	0.428928i	$-0.141109\pi$
$367$	18.8420	+	10.8784i	0.983545	+	0.567850i	0.0802066	+	0.996778i	$0.474442\pi$
$368$	−2.48156	−	10.7160i	−0.129360	−	0.558608i
$369$	4.68820	−	4.68820i	0.244058	−	0.244058i
$370$	−25.9497	+	12.5220i	−1.34906	+	0.650990i
$371$	−14.3443	+	53.5338i	−0.744721	+	2.77934i
$372$	−0.585811	−	0.791123i	−0.0303729	−	0.0410178i
$373$	27.8295	−	16.0674i	1.44096	−	0.831938i	0.443045	−	0.896499i	$-0.353898\pi$
$373$	27.8295	−	16.0674i	1.44096	−	0.831938i	0.997914	+	0.0645612i	$0.0205648\pi$
$374$	4.55695	−	0.865957i	0.235634	−	0.0447776i
$375$	−2.07962	−	7.76125i	−0.107391	−	0.400789i
$376$	−3.30838	−	5.23762i	−0.170617	−	0.270109i
$377$	−1.29093	+	3.24790i	−0.0664863	+	0.167275i
$378$	−3.59181	−	4.16709i	−0.184743	−	0.214332i
$379$	8.60355	+	32.1089i	0.441935	+	1.64932i	0.723905	+	0.689899i	$0.242345\pi$
$379$	8.60355	+	32.1089i	0.441935	+	1.64932i	−0.281971	+	0.959423i	$0.590988\pi$
$380$	−16.0798	+	20.2290i	−0.824874	+	1.03772i
$381$	2.10087	+	3.63881i	0.107631	+	0.186422i
$382$	−6.83585	−	0.506837i	−0.349753	−	0.0259321i
$383$	3.22968	−	12.0533i	0.165029	−	0.615896i	−0.833008	−	0.553261i	$-0.813383\pi$
$383$	3.22968	−	12.0533i	0.165029	−	0.615896i	0.998037	−	0.0626344i	$-0.0199502\pi$
$384$	11.3135	−	0.0626616i	0.577341	−	0.00319769i
$385$	−5.09020	−	5.09020i	−0.259421	−	0.259421i
$386$	−35.7277	−	12.4699i	−1.81849	−	0.634703i
$387$	−7.50871	−	4.33516i	−0.381689	−	0.220368i
$388$	−0.884241	−	7.73778i	−0.0448905	−	0.392826i
$389$	−12.9747			−0.657845			−0.328922	−	0.944357i	$-0.606685\pi$
$389$	−12.9747			−0.657845			−0.328922	+	0.944357i	$0.606685\pi$
$390$	−3.38552	+	17.5535i	−0.171433	+	0.888856i
$391$			17.0882i			0.864187i
$392$	−15.6061	+	16.8996i	−0.788226	+	0.853561i
$393$	0.771915	−	1.33700i	0.0389379	−	0.0674425i
$394$	35.5219	+	12.3981i	1.78957	+	0.624607i
$395$	−11.9708	+	11.9708i	−0.602315	+	0.602315i
$396$	0.420606	−	0.968216i	0.0211362	−	0.0486547i
$397$	−3.20096	−	0.857695i	−0.160652	−	0.0430465i	0.177597	−	0.984103i	$-0.443168\pi$
$397$	−3.20096	−	0.857695i	−0.160652	−	0.0430465i	−0.338248	+	0.941057i	$0.609834\pi$
$398$	2.10980	−	28.4554i	0.105755	−	1.42634i
$399$	12.4156	−	7.16813i	0.621556	−	0.358855i
$400$	−19.9063	−	21.3182i	−0.995317	−	1.06591i
$401$	12.1931	−	3.26714i	0.608896	−	0.163153i	0.0588209	−	0.998269i	$-0.481266\pi$
$401$	12.1931	−	3.26714i	0.608896	−	0.163153i	0.550075	+	0.835115i	$0.314599\pi$
$402$	6.29972	+	7.30870i	0.314201	+	0.364525i
$403$	1.05999	−	1.42332i	0.0528018	−	0.0709006i
$404$	8.15841	+	1.21648i	0.405896	+	0.0605222i
$405$	−3.38651	+	0.907411i	−0.168277	+	0.0450896i
$406$	0.995578	+	5.23906i	0.0494097	+	0.260010i
$407$	1.53362	+	2.65630i	0.0760186	+	0.131668i
$408$	−17.1448	−	3.87040i	−0.848795	−	0.191613i
$409$	26.0526	+	6.98078i	1.28822	+	0.345177i	0.836984	−	0.547228i	$-0.184317\pi$
$409$	26.0526	+	6.98078i	1.28822	+	0.345177i	0.451236	+	0.892405i	$0.350983\pi$
$410$	−29.6066	+	14.2867i	−1.46217	+	0.705568i
$411$	−1.28292	−	1.28292i	−0.0632819	−	0.0632819i
$412$	−7.09146	−	17.9850i	−0.349371	−	0.886058i
$413$	−25.9269	+	44.9067i	−1.27578	+	2.20972i
$414$	3.21492	+	2.18817i	0.158004	+	0.107543i
$415$	−50.9050			−2.49883
$416$	6.00474	+	19.4921i	0.294406	+	0.955680i
$417$	−17.4286			−0.853481
$418$	2.27411	+	1.54783i	0.111230	+	0.0757067i
$419$	4.72463	−	8.18330i	0.230813	−	0.399780i	−0.727234	−	0.686389i	$-0.759195\pi$
$419$	4.72463	−	8.18330i	0.230813	−	0.399780i	0.958048	+	0.286609i	$0.0925280\pi$
$420$	10.0056	+	25.3758i	0.488224	+	1.23821i
$421$	8.64486	+	8.64486i	0.421325	+	0.421325i	0.885660	−	0.464335i	$-0.153707\pi$
$421$	8.64486	+	8.64486i	0.421325	+	0.421325i	−0.464335	+	0.885660i	$0.653707\pi$
$422$	18.1066	−	8.73733i	0.881415	−	0.425327i
$423$	2.11563	+	0.566882i	0.102866	+	0.0275627i
$424$	39.3075	+	8.87357i	1.90894	+	0.430939i
$425$	22.6562	+	39.2417i	1.09899	+	1.90350i
$426$	3.04602	+	16.0292i	0.147580	+	0.776615i
$427$	23.5326	−	6.30553i	1.13882	−	0.305146i
$428$	−4.25121	−	0.633888i	−0.205490	−	0.0306401i
$429$	1.89016	+	0.221245i	0.0912577	+	0.0106818i
$430$	28.0670	+	32.5623i	1.35351	+	1.57029i
$431$	31.0269	−	8.31363i	1.49451	−	0.400454i	0.583255	−	0.812289i	$-0.301779\pi$
$431$	31.0269	−	8.31363i	1.49451	−	0.400454i	0.911258	+	0.411836i	$0.135112\pi$
$432$	−2.92358	+	2.72996i	−0.140661	+	0.131345i
$433$	−23.0742	+	13.3219i	−1.10887	+	0.640209i	−0.938538	−	0.345177i	$-0.887819\pi$
$433$	−23.0742	+	13.3219i	−1.10887	+	0.640209i	−0.170337	+	0.985386i	$0.554486\pi$
$434$	0.200218	−	2.70040i	0.00961079	−	0.129623i
$435$	3.28271	+	0.879600i	0.157394	+	0.0421736i
$436$	−10.1111	+	23.2754i	−0.484236	+	1.11469i
$437$	−7.16598	+	7.16598i	−0.342795	+	0.342795i
$438$	10.7552	+	3.75385i	0.513902	+	0.179366i
$439$	−0.948699	+	1.64319i	−0.0452789	+	0.0784254i	−0.887777	−	0.460274i	$-0.847751\pi$
$439$	−0.948699	+	1.64319i	−0.0452789	+	0.0784254i	0.842498	+	0.538700i	$0.181084\pi$
$440$	−3.55091	+	3.84524i	−0.169283	+	0.183315i
$441$		−	8.13286i		−	0.387279i
$442$	−2.25635	−	31.6056i	−0.107324	−	1.50333i
$443$	−15.2346			−0.723819			−0.361909	−	0.932213i	$-0.617875\pi$
$443$	−15.2346			−0.723819			−0.361909	+	0.932213i	$0.617875\pi$
$444$	−1.31957	−	11.5472i	−0.0626240	−	0.548008i
$445$	−22.3932	−	12.9287i	−1.06154	−	0.612879i
$446$	−17.8688	−	6.23671i	−0.846114	−	0.295317i
$447$	−6.05197	−	6.05197i	−0.286248	−	0.286248i
$448$	23.6848	+	20.1875i	1.11900	+	0.953769i
$449$	−1.46136	+	5.45387i	−0.0689658	+	0.257384i	−0.991797	−	0.127820i	$-0.959202\pi$
$449$	−1.46136	+	5.45387i	−0.0689658	+	0.257384i	0.922832	+	0.385204i	$0.125869\pi$
$450$	10.2840	+	0.762494i	0.484790	+	0.0359443i
$451$	1.74974	+	3.03063i	0.0823919	+	0.142707i
$452$	13.3035	−	16.7363i	0.625743	−	0.787210i
$453$	2.55415	+	9.53221i	0.120004	+	0.447862i
$454$	14.4386	+	16.7511i	0.677635	+	0.786168i
$455$	−38.5783	+	30.4934i	−1.80858	+	1.42955i
$456$	−5.56666	−	8.81278i	−0.260683	−	0.412696i
$457$	−0.148909	−	0.555736i	−0.00696567	−	0.0259962i	0.962356	−	0.271794i	$-0.0876168\pi$
$457$	−0.148909	−	0.555736i	−0.00696567	−	0.0259962i	−0.969321	+	0.245797i	$0.920950\pi$
$458$	−20.6835	+	3.93048i	−0.966477	+	0.183659i
$459$	5.38161	−	3.10707i	0.251192	−	0.145026i
$460$	−11.4746	−	15.4961i	−0.535006	−	0.722511i
$461$	−0.184854	+	0.689883i	−0.00860949	+	0.0321311i	−0.970097	−	0.242718i	$-0.921961\pi$
$461$	−0.184854	+	0.689883i	−0.00860949	+	0.0321311i	0.961487	+	0.274849i	$0.0886278\pi$
$462$	2.61518	−	1.26195i	0.121669	−	0.0587113i
$463$	−6.31342	+	6.31342i	−0.293410	+	0.293410i	−0.838426	−	0.545016i	$-0.816524\pi$
$463$	−6.31342	+	6.31342i	−0.293410	+	0.293410i	0.545016	+	0.838426i	$0.316524\pi$
$464$	3.77744	−	0.874763i	0.175363	−	0.0406099i
$465$	−1.49445	−	0.862822i	−0.0693035	−	0.0400124i
$466$	18.5168	−	27.2054i	0.857774	−	1.26027i
$467$			6.14918i			0.284550i	0.989827	+	0.142275i	$0.0454418\pi$
$467$			6.14918i			0.284550i	−0.989827	+	0.142275i	$0.954558\pi$
$468$	−6.23510	−	3.62264i	−0.288218	−	0.167457i
$469$			26.5417i			1.22558i
$470$	−8.97757	−	6.11041i	−0.414105	−	0.281852i
$471$	7.95312	+	4.59173i	0.366460	+	0.211576i
$472$	33.3747	+	17.5378i	1.53620	+	0.807244i
$473$	3.23595	−	3.23595i	0.148789	−	0.148789i
$474$	−2.96777	−	6.15018i	−0.136314	−	0.282487i
$475$	−6.95516	+	25.9570i	−0.319125	+	1.19099i
$476$	−28.7711	−	38.8546i	−1.31872	−	1.78090i
$477$	−12.3383	+	7.12351i	−0.564931	+	0.326163i
$478$	2.22788	+	11.7239i	0.101901	+	0.536237i
$479$	0.518005	+	1.93322i	0.0236683	+	0.0883311i	0.976750	−	0.214383i	$-0.0687740\pi$
$479$	0.518005	+	1.93322i	0.0236683	+	0.0883311i	−0.953081	+	0.302714i	$0.902107\pi$
$480$	18.1464	−	8.00281i	0.828268	−	0.365277i
$481$	19.2404	−	8.29571i	0.877285	−	0.378252i
$482$	−33.1111	+	28.5400i	−1.50817	+	1.29996i
$483$	2.76867	+	10.3328i	0.125979	+	0.470160i
$484$	−16.7858	−	13.3428i	−0.762991	−	0.606493i
$485$	−6.82625	−	11.8234i	−0.309964	−	0.536873i
$486$	0.104568	−	1.41034i	0.00474332	−	0.0639744i
$487$	−7.65344	+	28.5630i	−0.346811	+	1.29432i	0.543672	+	0.839298i	$0.317034\pi$
$487$	−7.65344	+	28.5630i	−0.346811	+	1.29432i	−0.890483	+	0.455017i	$0.849633\pi$
$488$	−5.26138	−	16.9143i	−0.238171	−	0.765675i
$489$	4.83416	+	4.83416i	0.218608	+	0.218608i
$490$	−13.2881	+	38.0719i	−0.600297	+	1.71991i
$491$	−7.25472	−	4.18851i	−0.327401	−	0.189025i	0.327286	−	0.944925i	$-0.393866\pi$
$491$	−7.25472	−	4.18851i	−0.327401	−	0.189025i	−0.654687	+	0.755900i	$0.727199\pi$
$492$	−1.50553	−	13.1745i	−0.0678744	−	0.593952i
$493$	−6.02369			−0.271293
$494$	12.3077	−	14.2001i	0.553749	−	0.638892i
$495$		−	1.85050i		−	0.0831738i
$496$	−1.96765	−	0.0673889i	−0.0883502	−	0.00302585i
$497$	−22.4403	+	38.8678i	−1.00659	+	1.74346i
$498$	6.76652	−	19.3868i	0.303215	−	0.868743i
$499$	−12.4133	+	12.4133i	−0.555697	+	0.555697i	−0.928079	−	0.372383i	$-0.878541\pi$
$499$	−12.4133	+	12.4133i	−0.555697	+	0.555697i	0.372383	+	0.928079i	$0.378541\pi$
$500$	−14.7394	−	6.40298i	−0.659165	−	0.286350i
$501$	−13.9201	−	3.72987i	−0.621903	−	0.166638i
$502$	−18.4277	−	1.36631i	−0.822470	−	0.0609812i
$503$	6.14015	−	3.54502i	0.273776	−	0.158065i	−0.356826	−	0.934171i	$-0.616141\pi$
$503$	6.14015	−	3.54502i	0.273776	−	0.158065i	0.630602	+	0.776106i	$0.282808\pi$
$504$	−10.9942	+	0.437508i	−0.489719	+	0.0194881i
$505$	13.9670	−	3.74244i	0.621522	−	0.166536i
$506$	−1.55478	+	1.34014i	−0.0691183	+	0.0595763i
$507$	3.00219	−	12.6486i	0.133332	−	0.561744i
$508$	8.31158	+	1.23932i	0.368767	+	0.0549859i
$509$	17.5776	−	4.70990i	0.779112	−	0.208762i	0.152719	−	0.988270i	$-0.451197\pi$
$509$	17.5776	−	4.70990i	0.779112	−	0.208762i	0.626393	+	0.779507i	$0.284530\pi$
$510$	−30.2692	+	5.75206i	−1.34034	+	0.254705i
$511$	15.6673	+	27.1366i	0.693081	+	1.20045i
$512$	13.9816	−	17.7908i	0.617907	−	0.786252i
$513$	3.55975	+	0.953832i	0.157167	+	0.0421127i
$514$	9.83322	+	20.3776i	0.433725	+	0.898818i
$515$	−23.9637	−	23.9637i	−1.05597	−	1.05597i
$516$	−16.1319	+	6.36078i	−0.710167	+	0.280018i
$517$	−0.578026	+	1.00117i	−0.0254216	+	0.0440314i
$518$	17.9884	−	26.4290i	0.790364	−	1.16122i
$519$	11.0939			0.486970
$520$	23.2691	+	27.1459i	1.02042	+	1.19043i
$521$	−3.28873			−0.144082			−0.0720410	−	0.997402i	$-0.522951\pi$
$521$	−3.28873			−0.144082			−0.0720410	+	0.997402i	$0.522951\pi$
$522$	−0.771342	+	1.13328i	−0.0337607	+	0.0496022i
$523$	15.1538	−	26.2472i	0.662630	−	1.14771i	−0.317292	−	0.948328i	$-0.602773\pi$
$523$	15.1538	−	26.2472i	0.662630	−	1.14771i	0.979922	−	0.199381i	$-0.0638933\pi$
$524$	−1.13260	−	2.87243i	−0.0494777	−	0.125483i
$525$	20.0577	+	20.0577i	0.875390	+	0.875390i
$526$	−3.98194	−	8.25188i	−0.173621	−	0.359799i
$527$	2.95439	+	0.791627i	0.128695	+	0.0344838i
$528$	−0.992427	−	1.86346i	−0.0431898	−	0.0810969i
$529$	7.71906	+	13.3698i	0.335611	+	0.581296i
$530$	69.3975	−	13.1876i	3.01443	−	0.572832i
$531$	−12.8755	+	3.44998i	−0.558749	+	0.149716i
$532$	4.22855	−	28.3590i	0.183331	−	1.22952i
$533$	21.9517	−	9.46475i	0.950836	−	0.409964i
$534$	7.90040	−	6.80973i	0.341884	−	0.294686i
$535$	−7.27795	+	1.95012i	−0.314653	+	0.0843111i
$536$	19.2828	−	0.767350i	0.832889	−	0.0331445i
$537$	−8.53378	+	4.92698i	−0.368260	+	0.212615i
$538$	−15.3580	−	1.13870i	−0.662128	−	0.0490929i
$539$	4.14637	+	1.11102i	0.178597	+	0.0478549i
$540$	−2.79384	+	6.43131i	−0.120228	+	0.276759i
$541$	6.90597	−	6.90597i	0.296911	−	0.296911i	−0.542892	−	0.839803i	$-0.682671\pi$
$541$	6.90597	−	6.90597i	0.296911	−	0.296911i	0.839803	+	0.542892i	$0.182671\pi$
$542$	−11.7512	+	33.6685i	−0.504758	+	1.44618i
$543$	1.74300	−	3.01896i	0.0747991	−	0.129556i
$544$	−27.3964	+	22.0258i	−1.17461	+	0.944348i
$545$			44.4851i			1.90553i
$546$	−6.48518	−	18.7456i	−0.277540	−	0.802237i
$547$	−13.8102			−0.590482			−0.295241	−	0.955423i	$-0.595400\pi$
$547$	−13.8102			−0.590482			−0.295241	+	0.955423i	$0.595400\pi$
$548$	−3.60519	+	0.411985i	−0.154006	+	0.0175991i
$549$	5.42370	+	3.13137i	0.231478	+	0.133644i
$550$	−1.79362	+	5.13890i	−0.0764801	+	0.219124i
$551$	−2.52605	−	2.52605i	−0.107613	−	0.107613i
$552$	7.42684	−	2.31020i	0.316107	−	0.0983286i
$553$	4.86167	−	18.1440i	0.206739	−	0.771562i
$554$	−1.67497	+	22.5907i	−0.0711625	+	0.959788i
$555$	−10.1869	−	17.6443i	−0.432412	−	0.748959i
$556$	−21.6899	+	27.2868i	−0.919858	+	1.15722i
$557$	−2.82150	−	10.5300i	−0.119551	−	0.446170i	0.880036	−	0.474907i	$-0.157518\pi$
$557$	−2.82150	−	10.5300i	−0.119551	−	0.446170i	−0.999587	+	0.0287368i	$0.990852\pi$
$558$	0.527248	−	0.454460i	0.0223202	−	0.0192388i
$559$	−19.3853	−	24.5250i	−0.819911	−	1.03730i
$560$	52.1812	+	15.9151i	2.20506	+	0.672535i
$561$	0.848904	+	3.16815i	0.0358408	+	0.133760i
$562$	2.49396	+	13.1240i	0.105201	+	0.553603i
$563$	−1.69071	+	0.976130i	−0.0712548	+	0.0411390i	−0.535204	−	0.844723i	$-0.679765\pi$
$563$	−1.69071	+	0.976130i	−0.0712548	+	0.0411390i	0.463949	+	0.885862i	$0.346432\pi$
$564$	3.52044	−	2.60682i	0.148237	−	0.109767i
$565$	9.70004	−	36.2010i	0.408084	−	1.52299i
$566$	−0.504911	−	1.04634i	−0.0212230	−	0.0439809i
$567$	2.75071	−	2.75071i	0.115519	−	0.115519i
$568$	28.8866	+	15.1794i	1.21205	+	0.636913i
$569$	−6.96741	−	4.02264i	−0.292089	−	0.168638i	0.346794	−	0.937941i	$-0.387270\pi$
$569$	−6.96741	−	4.02264i	−0.292089	−	0.168638i	−0.638884	+	0.769303i	$0.720603\pi$
$570$	−15.1056	−	10.2813i	−0.632704	−	0.430637i
$571$			30.0799i			1.25881i	0.777079	+	0.629403i	$0.216701\pi$
$571$			30.0799i			1.25881i	−0.777079	+	0.629403i	$0.783299\pi$
$572$	2.69870	−	2.68396i	0.112838	−	0.112222i
$573$		−	4.84694i		−	0.202484i
$574$	20.5233	−	30.1534i	0.856627	−	1.25858i
$575$	−17.3653	−	10.0258i	−0.724181	−	0.418106i
$576$	0.635707	+	7.97470i	0.0264878	+	0.332279i
$577$	−13.3448	+	13.3448i	−0.555551	+	0.555551i	−0.928038	−	0.372487i	$-0.878505\pi$
$577$	−13.3448	+	13.3448i	−0.555551	+	0.555551i	0.372487	+	0.928038i	$0.378505\pi$
$578$	27.5313	−	13.2852i	1.14515	−	0.552592i
$579$	6.92544	−	25.8461i	0.287812	−	1.07413i
$580$	5.46248	−	4.04486i	0.226817	−	0.167954i
$581$	48.9152	−	28.2412i	2.02934	−	1.17164i
$582$	5.41023	−	1.02811i	0.224261	−	0.0426163i
$583$	−1.94626	−	7.26355i	−0.0806059	−	0.300825i
$584$	19.2620	−	12.1670i	0.797068	−	0.503474i
$585$	−12.5552	−	1.46960i	−0.519095	−	0.0607606i
$586$	−2.98268	−	3.46039i	−0.123213	−	0.142947i
$587$	2.15095	+	8.02746i	0.0887793	+	0.331329i	0.996003	−	0.0893197i	$-0.0284693\pi$
$587$	2.15095	+	8.02746i	0.0887793	+	0.331329i	−0.907224	+	0.420648i	$0.861803\pi$
$588$	−12.7331	−	10.1214i	−0.525104	−	0.417399i
$589$	0.906961	+	1.57090i	0.0373707	+	0.0647279i
$590$	65.9102	+	4.88685i	2.71348	+	0.201188i
$591$	−6.88555	+	25.6972i	−0.283234	+	1.05704i
$592$	−19.7210	−	12.3046i	−0.810527	−	0.505717i
$593$	−19.6649	−	19.6649i	−0.807540	−	0.807540i	0.176721	−	0.984261i	$-0.443451\pi$
$593$	−19.6649	−	19.6649i	−0.807540	−	0.807540i	−0.984261	+	0.176721i	$0.943451\pi$
$594$	0.704749	+	0.245977i	0.0289162	+	0.0100925i
$595$	−73.3974	−	42.3760i	−3.00900	−	1.73725i
$596$	−17.0069	+	1.94347i	−0.696628	+	0.0796077i
$597$	20.1762			0.825758
$598$	7.85778	+	11.6131i	0.321328	+	0.474895i
$599$		−	45.6842i		−	1.86661i	−0.359088	−	0.933304i	$-0.616912\pi$
$599$		−	45.6842i		−	1.86661i	0.359088	−	0.933304i	$-0.383088\pi$
$600$	13.9922	−	15.1520i	0.571230	−	0.618577i
$601$	−8.81170	+	15.2623i	−0.359437	+	0.622562i	−0.987867	−	0.155304i	$-0.950364\pi$
$601$	−8.81170	+	15.2623i	−0.359437	+	0.622562i	0.628430	+	0.777866i	$0.283698\pi$
$602$	−45.0349	−	15.7184i	−1.83548	−	0.640634i
$603$	−4.82451	+	4.82451i	−0.196469	+	0.196469i
$604$	18.1026	+	7.86401i	0.736584	+	0.319982i
$605$	−36.3081	−	9.72873i	−1.47614	−	0.395529i
$606$	−0.431272	+	5.81668i	−0.0175192	+	0.236286i
$607$	−24.5125	+	14.1523i	−0.994932	+	0.574424i	−0.906745	−	0.421680i	$-0.861441\pi$
$607$	−24.5125	+	14.1523i	−0.994932	+	0.574424i	−0.0881869	+	0.996104i	$0.528107\pi$
$608$	−20.7253	−	2.25219i	−0.840523	−	0.0913382i
$609$	−3.64238	+	0.975973i	−0.147597	+	0.0395484i
$610$	−20.2734	−	23.5204i	−0.820845	−	0.952314i
$611$	6.33367	+	4.71687i	0.256233	+	0.190824i
$612$	1.83289	−	12.2924i	0.0740902	−	0.496890i
$613$	−7.36770	+	1.97417i	−0.297579	+	0.0797360i	−0.404519	−	0.914529i	$-0.632561\pi$
$613$	−7.36770	+	1.97417i	−0.297579	+	0.0797360i	0.106941	+	0.994265i	$0.465894\pi$
$614$	5.08811	+	26.7753i	0.205339	+	1.08056i
$615$	−11.6225	−	20.1308i	−0.468664	−	0.811751i
$616$	1.27884	−	5.66491i	0.0515259	−	0.228246i
$617$	−2.20669	−	0.591281i	−0.0888381	−	0.0238041i	0.214126	−	0.976806i	$-0.431310\pi$
$617$	−2.20669	−	0.591281i	−0.0888381	−	0.0238041i	−0.302964	+	0.953002i	$0.597976\pi$
$618$	12.3117	−	5.94103i	0.495251	−	0.238983i
$619$	−16.7902	−	16.7902i	−0.674854	−	0.674854i	0.283977	−	0.958831i	$-0.408346\pi$
$619$	−16.7902	−	16.7902i	−0.674854	−	0.674854i	−0.958831	+	0.283977i	$0.908346\pi$
$620$	−3.21071	+	1.26598i	−0.128945	+	0.0508429i
$621$	−1.37494	+	2.38147i	−0.0551746	+	0.0955652i
$622$	−5.57616	−	3.79530i	−0.223584	−	0.152178i
$623$	28.6905			1.14946
$624$	−13.4313	+	5.25350i	−0.537684	+	0.210308i
$625$	8.28849			0.331540
$626$	−20.9785	−	14.2786i	−0.838470	−	0.570688i
$627$	−0.972583	+	1.68456i	−0.0388412	+	0.0672750i
$628$	17.0867	−	6.73724i	0.681832	−	0.268845i
$629$	25.5348	+	25.5348i	1.01814	+	1.01814i
$630$	−17.3711	+	8.38243i	−0.692082	+	0.333964i
$631$	23.0380	+	6.17302i	0.917130	+	0.245744i	0.686358	−	0.727264i	$-0.259208\pi$
$631$	23.0380	+	6.17302i	0.917130	+	0.245744i	0.230772	+	0.973008i	$0.425875\pi$
$632$	−13.3223	−	3.00748i	−0.529934	−	0.119631i
$633$	7.10800	+	12.3114i	0.282518	+	0.489335i
$634$	1.78919	+	9.41533i	0.0710580	+	0.373931i
$635$	14.2292	−	3.81270i	0.564668	−	0.151302i
$636$	−4.20222	+	28.1825i	−0.166629	+	1.11751i
$637$	10.8309	−	27.2499i	0.429136	−	1.07968i
$638$	−0.472406	−	0.548068i	−0.0187027	−	0.0216982i
$639$	−11.1440	+	2.98604i	−0.440852	+	0.118126i
$640$	10.0538	−	38.3702i	0.397412	−	1.51672i
$641$	−2.89971	+	1.67415i	−0.114532	+	0.0661248i	−0.556171	−	0.831068i	$-0.687730\pi$
$641$	−2.89971	+	1.67415i	−0.114532	+	0.0661248i	0.441640	+	0.897192i	$0.354397\pi$
$642$	0.224728	−	3.03097i	0.00886932	−	0.119623i
$643$	−24.0364	−	6.44054i	−0.947905	−	0.253990i	−0.248432	−	0.968649i	$-0.579915\pi$
$643$	−24.0364	−	6.44054i	−0.947905	−	0.253990i	−0.699473	+	0.714659i	$0.746582\pi$
$644$	19.6231	+	8.52451i	0.773257	+	0.335913i
$645$	−21.4945	+	21.4945i	−0.846346	+	0.846346i
$646$	30.5781	+	10.6726i	1.20308	+	0.419907i
$647$	−11.3489	+	19.6569i	−0.446172	+	0.772793i	−0.998133	−	0.0610768i	$-0.980547\pi$
$647$	−11.3489	+	19.6569i	−0.446172	+	0.772793i	0.551961	+	0.833870i	$0.313880\pi$
$648$	−2.07794	−	1.91889i	−0.0816294	−	0.0753812i
$649$		−	7.03561i		−	0.276172i
$650$	33.4419	+	16.2504i	1.31170	+	0.637394i
$651$	1.91471			0.0750435
$652$	13.5847	−	1.55240i	0.532016	−	0.0607966i
$653$	26.2663	+	15.1649i	1.02788	+	0.593447i	0.916377	−	0.400317i	$-0.131100\pi$
$653$	26.2663	+	15.1649i	1.02788	+	0.593447i	0.111503	+	0.993764i	$0.464433\pi$
$654$	−16.9418	−	5.91315i	−0.662477	−	0.231222i
$655$	−3.82730	−	3.82730i	−0.149545	−	0.149545i
$656$	−22.5001	−	14.0386i	−0.878481	−	0.548116i
$657$	−2.08478	+	7.78051i	−0.0813350	+	0.303546i
$658$	12.0166	+	0.890958i	0.468456	+	0.0347332i
$659$	−3.59371	−	6.22449i	−0.139991	−	0.242472i	0.787502	−	0.616312i	$-0.211374\pi$
$659$	−3.59371	−	6.22449i	−0.139991	−	0.242472i	−0.927493	+	0.373841i	$0.878041\pi$
$660$	−2.89721	−	2.30296i	−0.112774	−	0.0896424i
$661$	−8.58726	−	32.0481i	−0.334006	−	1.24653i	−0.904943	−	0.425533i	$-0.860087\pi$
$661$	−8.58726	−	32.0481i	−0.334006	−	1.24653i	0.570937	−	0.820994i	$-0.306580\pi$
$662$	−15.2594	−	17.7034i	−0.593074	−	0.688063i
$663$	22.1694	−	3.24359i	0.860988	−	0.125971i
$664$	−21.9317	−	34.7208i	−0.851114	−	1.34743i
$665$	−13.0089	−	48.5498i	−0.504463	−	1.88268i
$666$	8.07379	−	1.53426i	0.312853	−	0.0594514i
$667$	2.30848	−	1.33280i	0.0893848	−	0.0516063i
$668$	−23.1632	+	17.1519i	−0.896211	+	0.663627i
$669$	3.46369	−	12.9267i	0.133914	−	0.499774i
$670$	30.4674	−	14.7020i	1.17706	−	0.567989i
$671$	−2.33739	+	2.33739i	−0.0902340	+	0.0902340i
$672$	−12.9973	+	17.7573i	−0.501381	+	0.685003i
$673$	11.8971	+	6.86881i	0.458601	+	0.264773i	0.711456	−	0.702731i	$-0.248036\pi$
$673$	11.8971	+	6.86881i	0.458601	+	0.264773i	−0.252855	+	0.967504i	$0.581370\pi$
$674$	17.6307	−	25.9035i	0.679109	−	0.997766i
$675$			7.29182i			0.280662i
$676$	−16.0668	−	20.4416i	−0.617955	−	0.786214i
$677$			4.56622i			0.175494i	0.996143	+	0.0877470i	$0.0279667\pi$
$677$			4.56622i			0.175494i	−0.996143	+	0.0877470i	$0.972033\pi$
$678$	12.4975	+	8.50619i	0.479964	+	0.326678i
$679$	13.1188	+	7.57416i	0.503454	+	0.290670i
$680$	−28.6645	+	54.5490i	−1.09923	+	2.09186i
$681$	−11.0575	+	11.0575i	−0.423723	+	0.423723i
$682$	0.159671	+	0.330890i	0.00611411	+	0.0126704i
$683$	4.87878	−	18.2078i	0.186681	−	0.696704i	−0.807583	−	0.589754i	$-0.799225\pi$
$683$	4.87878	−	18.2078i	0.186681	−	0.696704i	0.994264	−	0.106950i	$-0.0341085\pi$
$684$	5.92347	−	4.38622i	0.226490	−	0.167711i
$685$	−5.50876	+	3.18048i	−0.210479	+	0.121520i
$686$	−1.16351	−	6.12279i	−0.0444232	−	0.233769i
$687$	−3.85308	−	14.3799i	−0.147004	−	0.548628i
$688$	−10.1175	+	33.1727i	−0.385728	+	1.26470i
$689$	−50.8272	+	7.43650i	−1.93636	+	0.283308i
$690$	10.3275	−	8.90176i	0.393161	−	0.338884i
$691$	6.39032	+	23.8490i	0.243099	+	0.907258i	0.974329	+	0.225128i	$0.0722799\pi$
$691$	6.39032	+	23.8490i	0.243099	+	0.907258i	−0.731230	+	0.682131i	$0.761053\pi$
$692$	13.8065	−	17.3691i	0.524843	−	0.660273i
$693$	1.02662	+	1.77817i	0.0389983	+	0.0675470i
$694$	3.20138	−	43.1778i	0.121523	−	1.63901i
$695$	−15.8149	+	59.0220i	−0.599893	+	2.23883i
$696$	0.814358	+	2.61801i	0.0308682	+	0.0992353i
$697$	29.1332	+	29.1332i	1.10350	+	1.10350i
$698$	6.98078	−	20.0007i	0.264227	−	0.757037i
$699$	20.1526	+	11.6351i	0.762241	+	0.440080i
$700$	56.3649	−	6.44115i	2.13039	−	0.243452i
$701$	1.74269			0.0658204			0.0329102	−	0.999458i	$-0.489522\pi$
$701$	1.74269			0.0658204			0.0329102	+	0.999458i	$0.489522\pi$
$702$	2.22858	−	4.58622i	0.0841125	−	0.173096i
$703$			21.4161i			0.807725i
$704$	−4.15258	−	0.765310i	−0.156506	−	0.0288437i
$705$	3.83950	−	6.65020i	0.144604	−	0.250461i
$706$	1.62142	−	4.64555i	0.0610231	−	0.174838i
$707$	−11.3448	+	11.3448i	−0.426664	+	0.426664i
$708$	−10.6222	+	24.4518i	−0.399207	+	0.918956i
$709$	6.85982	+	1.83808i	0.257626	+	0.0690307i	0.385320	−	0.922783i	$-0.374091\pi$
$709$	6.85982	+	1.83808i	0.257626	+	0.0690307i	−0.127694	+	0.991814i	$0.540758\pi$
$710$	57.0468	+	4.22968i	2.14093	+	0.158737i
$711$	4.18176	−	2.41434i	0.156828	−	0.0905449i
$712$	−0.829473	−	20.8439i	−0.0310858	−	0.781157i
$713$	−1.30738	+	0.350311i	−0.0489617	+	0.0131193i
$714$	25.8949	−	22.3200i	0.969092	−	0.835306i
$715$	2.46440	−	6.20027i	0.0921632	−	0.231877i
$716$	−2.90647	+	19.4924i	−0.108620	+	0.728466i
$717$	−8.15084	+	2.18401i	−0.304399	+	0.0815634i
$718$	−11.7201	+	2.22716i	−0.437389	+	0.0831170i
$719$	4.63097	+	8.02108i	0.172706	+	0.299136i	0.939365	−	0.342919i	$-0.111416\pi$
$719$	4.63097	+	8.02108i	0.172706	+	0.299136i	−0.766659	+	0.642055i	$0.778082\pi$
$720$	6.59212	+	12.3779i	0.245674	+	0.461298i
$721$	36.3216	+	9.73233i	1.35269	+	0.362451i
$722$	−3.33022	−	6.90129i	−0.123938	−	0.256839i
$723$	−21.8568	−	21.8568i	−0.812863	−	0.812863i
$724$	−2.55742	−	6.48600i	−0.0950457	−	0.241050i
$725$	3.53417	−	6.12136i	0.131256	−	0.227341i
$726$	8.53135	−	12.5345i	0.316628	−	0.465199i
$727$	−9.77196			−0.362422			−0.181211	−	0.983444i	$-0.558002\pi$
$727$	−9.77196			−0.362422			−0.181211	+	0.983444i	$0.558002\pi$
$728$	−37.4196	−	13.1755i	−1.38686	−	0.488317i
$729$	1.00000			0.0370370
$730$	22.4718	−	33.0162i	0.831719	−	1.22198i
$731$	26.9393	−	46.6602i	0.996386	−	1.72579i
$732$	11.6524	−	4.59452i	0.430685	−	0.169818i
$733$	9.27968	+	9.27968i	0.342753	+	0.342753i	0.857401	−	0.514648i	$-0.172078\pi$
$733$	9.27968	+	9.27968i	0.342753	+	0.342753i	−0.514648	+	0.857401i	$0.672078\pi$
$734$	13.3720	+	27.7112i	0.493571	+	1.02284i
$735$	−27.5420	−	7.37985i	−1.01590	−	0.272210i
$736$	5.62581	−	14.5028i	0.207370	−	0.534579i
$737$	−1.80061	−	3.11875i	−0.0663263	−	0.114881i
$738$	9.21156	−	1.75047i	0.339082	−	0.0644358i
$739$	−2.98398	+	0.799556i	−0.109768	+	0.0294121i	−0.313285	−	0.949659i	$-0.601429\pi$
$739$	−2.98398	+	0.799556i	−0.109768	+	0.0294121i	0.203517	+	0.979071i	$0.434763\pi$
$740$	−40.3022	−	6.00937i	−1.48154	−	0.220909i
$741$	10.6570	+	7.93658i	0.391494	+	0.291558i
$742$	−59.3685	+	51.1726i	−2.17949	+	1.87860i
$743$	−30.5693	+	8.19102i	−1.12148	+	0.300499i	−0.771482	−	0.636251i	$-0.780484\pi$
$743$	−30.5693	+	8.19102i	−1.12148	+	0.300499i	−0.349997	+	0.936751i	$0.613818\pi$
$744$	−0.0553565	−	1.39106i	−0.00202947	−	0.0509986i
$745$	−25.9867	+	15.0034i	−0.952077	+	0.549682i
$746$	45.3210	+	3.36028i	1.65932	+	0.123029i
$747$	14.0248	+	3.75793i	0.513140	+	0.137495i
$748$	6.01664	+	2.61371i	0.219990	+	0.0955666i
$749$	5.91157	−	5.91157i	0.216004	−	0.216004i
$750$	3.74456	−	10.7286i	0.136732	−	0.391752i
$751$	17.0232	−	29.4850i	0.621185	−	1.07592i	−0.368080	−	0.929794i	$-0.619985\pi$
$751$	17.0232	−	29.4850i	0.621185	−	1.07592i	0.989265	−	0.146130i	$-0.0466818\pi$
$752$	0.299876	−	8.75592i	0.0109354	−	0.319295i
$753$		−	13.0661i		−	0.476156i
$754$	−4.09369	+	2.76991i	−0.149083	+	0.100874i
$755$	34.5985			1.25917
$756$	−0.883339	−	7.72989i	−0.0321267	−	0.281133i
$757$	7.91251	+	4.56829i	0.287585	+	0.166037i	0.636852	−	0.770986i	$-0.280236\pi$
$757$	7.91251	+	4.56829i	0.287585	+	0.166037i	−0.349267	+	0.937023i	$0.613569\pi$
$758$	−15.4915	+	44.3849i	−0.562677	+	1.61213i
$759$	−1.02632	−	1.02632i	−0.0372529	−	0.0372529i
$760$	−34.8958	+	10.8547i	−1.26580	+	0.393741i
$761$	10.4819	−	39.1189i	0.379968	−	1.41806i	−0.465980	−	0.884795i	$-0.654298\pi$
$761$	10.4819	−	39.1189i	0.379968	−	1.41806i	0.845948	−	0.533265i	$-0.179035\pi$
$762$	−0.439369	+	5.92588i	−0.0159166	+	0.214672i
$763$	−24.6795	−	42.7462i	−0.893458	−	1.54752i
$764$	−7.58854	−	6.03204i	−0.274544	−	0.218232i
$765$	−5.63879	−	21.0442i	−0.203871	−	0.760856i
$766$	13.3670	−	11.5217i	0.482970	−	0.416295i
$767$	−47.7350	−	5.58743i	−1.72361	−	0.201750i
$768$	13.2766	+	8.92926i	0.479078	+	0.322207i
$769$	−0.306215	−	1.14281i	−0.0110424	−	0.0412107i	0.960185	−	0.279366i	$-0.0901241\pi$
$769$	−0.306215	−	1.14281i	−0.0110424	−	0.0412107i	−0.971227	+	0.238155i	$0.923457\pi$
$770$	−1.90057	−	10.0014i	−0.0684917	−	0.360426i
$771$	−13.8556	+	7.99953i	−0.498997	+	0.288096i
$772$	−31.8468	−	43.0083i	−1.14619	−	1.54790i
$773$	−8.66967	+	32.3556i	−0.311826	+	1.16375i	0.615082	+	0.788463i	$0.289123\pi$
$773$	−8.66967	+	32.3556i	−0.311826	+	1.16375i	−0.926908	+	0.375288i	$0.877544\pi$
$774$	−5.32888	−	11.0432i	−0.191543	−	0.396939i
$775$	−2.53784	+	2.53784i	−0.0911618	+	0.0911618i
$776$	5.12341	−	9.74992i	0.183920	−	0.350002i
$777$	19.5775	+	11.3031i	0.702338	+	0.405495i
$778$	−15.1689	−	10.3244i	−0.543830	−	0.370147i
$779$			24.4341i			0.875444i
$780$	−17.9259	+	17.8280i	−0.641850	+	0.638344i
$781$		−	6.08948i		−	0.217899i
$782$	−13.5976	+	19.9779i	−0.486249	+	0.714410i
$783$	−0.839483	−	0.484676i	−0.0300007	−	0.0173209i
$784$	−31.6928	+	7.33927i	−1.13188	+	0.262117i
$785$	22.7667	−	22.7667i	0.812578	−	0.812578i
$786$	1.96634	−	0.948856i	0.0701370	−	0.0338446i
$787$	10.1171	−	37.7577i	0.360637	−	1.34592i	−0.512603	−	0.858626i	$-0.671319\pi$
$787$	10.1171	−	37.7577i	0.360637	−	1.34592i	0.873240	−	0.487290i	$-0.162015\pi$
$788$	31.6634	+	42.7605i	1.12796	+	1.52328i
$789$	5.61079	−	3.23939i	0.199749	−	0.115325i
$790$	−23.5206	+	4.46962i	−0.836826	+	0.159022i
$791$	10.7628	+	40.1674i	0.382682	+	1.42819i
$792$	1.26217	−	0.797261i	0.0448494	−	0.0283294i
$793$	14.0024	+	17.7149i	0.497240	+	0.629076i
$794$	−3.05978	−	3.54984i	−0.108587	−	0.125979i
$795$	12.9279	+	48.2476i	0.458505	+	1.71117i
$796$	25.1094	−	31.5886i	0.889978	−	1.11963i
$797$	9.38012	+	16.2468i	0.332261	+	0.575493i	0.982955	−	0.183847i	$-0.0588552\pi$
$797$	9.38012	+	16.2468i	0.332261	+	0.575493i	−0.650694	+	0.759340i	$0.725522\pi$
$798$	20.2190	+	1.49912i	0.715746	+	0.0530683i
$799$	−3.52268	+	13.1468i	−0.124624	+	0.465102i
$800$	−6.30912	−	40.7634i	−0.223061	−	1.44120i
$801$	5.21509	+	5.21509i	0.184266	+	0.184266i
$802$	16.8548	+	5.88280i	0.595165	+	0.207729i
$803$	−3.68193	−	2.12577i	−0.129933	−	0.0750166i
$804$	1.54930	+	13.5575i	0.0546395	+	0.478138i
$805$	37.5045			1.32186
$806$	2.37182	−	0.820549i	0.0835437	−	0.0289026i
$807$		−	10.8895i		−	0.383329i
$808$	8.57007	+	7.91409i	0.301494	+	0.278417i
$809$	−2.93058	+	5.07591i	−0.103034	+	0.178459i	−0.912933	−	0.408109i	$-0.866188\pi$
$809$	−2.93058	+	5.07591i	−0.103034	+	0.178459i	0.809900	+	0.586569i	$0.199522\pi$
$810$	−4.68125	−	1.63388i	−0.164482	−	0.0574088i
$811$	−16.1926	+	16.1926i	−0.568599	+	0.568599i	−0.931736	−	0.363137i	$-0.881706\pi$
$811$	−16.1926	+	16.1926i	−0.568599	+	0.568599i	0.363137	+	0.931736i	$0.381706\pi$
$812$	−3.00494	+	6.91724i	−0.105453	+	0.242748i
$813$	−24.3564	−	6.52629i	−0.854218	−	0.228887i
$814$	−0.320736	+	4.32585i	−0.0112418	+	0.151621i
$815$	20.7575	−	11.9843i	0.727103	−	0.419793i
$816$	−16.9643	−	18.1676i	−0.593871	−	0.635992i
$817$	30.8641	−	8.27002i	1.07980	−	0.289331i
$818$	24.9035	+	28.8921i	0.870731	+	1.01019i
$819$	12.8798	−	5.55326i	0.450056	−	0.194047i
$820$	−45.9816	−	6.85622i	−1.60575	−	0.239430i
$821$	44.8952	−	12.0296i	1.56685	−	0.419837i	0.632027	−	0.774946i	$-0.282223\pi$
$821$	44.8952	−	12.0296i	1.56685	−	0.419837i	0.934825	+	0.355109i	$0.115556\pi$
$822$	−0.479015	−	2.52073i	−0.0167076	−	0.0879207i
$823$	20.7612	+	35.9595i	0.723691	+	1.25347i	0.959511	+	0.281673i	$0.0908893\pi$
$823$	20.7612	+	35.9595i	0.723691	+	1.25347i	−0.235819	+	0.971797i	$0.575777\pi$
$824$	6.02053	−	26.6693i	0.209735	−	0.929069i
$825$	−3.71758	−	0.996124i	−0.129430	−	0.0346806i
$826$	−66.0450	+	31.8700i	−2.29800	+	1.10890i
$827$	33.7239	+	33.7239i	1.17270	+	1.17270i	0.981564	+	0.191132i	$0.0612158\pi$
$827$	33.7239	+	33.7239i	1.17270	+	1.17270i	0.191132	+	0.981564i	$0.438784\pi$
$828$	2.01739	+	5.11641i	0.0701092	+	0.177808i
$829$	5.05148	−	8.74942i	0.175445	−	0.303880i	−0.764870	−	0.644184i	$-0.777197\pi$
$829$	5.05148	−	8.74942i	0.175445	−	0.303880i	0.940315	+	0.340305i	$0.110530\pi$
$830$	−59.5135	−	40.5066i	−2.06574	−	1.40601i
$831$	−16.0179			−0.555655
$832$	−8.49029	+	27.5666i	−0.294348	+	0.955698i
$833$	50.5388			1.75106
$834$	−20.3759	−	13.8684i	−0.705560	−	0.480225i
$835$	−25.2625	+	43.7559i	−0.874244	+	1.51423i
$836$	1.42703	+	3.61915i	0.0493548	+	0.125171i
$837$	0.348039	+	0.348039i	0.0120300	+	0.0120300i
$838$	12.0353	−	5.80763i	0.415753	−	0.200621i
$839$	12.0121	+	3.21863i	0.414704	+	0.111119i	0.460137	−	0.887848i	$-0.347800\pi$
$839$	12.0121	+	3.21863i	0.414704	+	0.111119i	−0.0454336	+	0.998967i	$0.514467\pi$
$840$	−8.49460	+	37.6288i	−0.293092	+	1.29832i
$841$	−14.0302	−	24.3010i	−0.483799	−	0.837965i
$842$	3.22780	+	16.9858i	0.111237	+	0.585368i
$843$	−9.12428	+	2.44484i	−0.314257	+	0.0842049i
$844$	28.1211	+	4.19308i	0.967969	+	0.144332i
$845$	−40.1103	−	21.6444i	−1.37984	−	0.744591i
$846$	2.02232	+	2.34622i	0.0695287	+	0.0806646i
$847$	40.2862	−	10.7947i	1.38425	−	0.370909i
$848$	38.8937	+	41.6523i	1.33562	+	1.43035i
$849$	0.711449	−	0.410755i	0.0244169	−	0.0140971i
$850$	−4.73825	+	63.9060i	−0.162521	+	2.19196i
$851$	−15.4356	−	4.13596i	−0.529127	−	0.141779i
$852$	−9.19376	+	21.1636i	−0.314973	+	0.725054i
$853$	−7.43990	+	7.43990i	−0.254737	+	0.254737i	−0.822910	−	0.568172i	$-0.807651\pi$
$853$	−7.43990	+	7.43990i	−0.254737	+	0.254737i	0.568172	+	0.822910i	$0.307651\pi$
$854$	32.5296	+	11.3537i	1.11314	+	0.388516i
$855$	6.46031	−	11.1896i	0.220938	−	0.382676i
$856$	−4.46572	−	4.12390i	−0.152635	−	0.140952i
$857$		−	4.01848i		−	0.137269i	−0.997642	−	0.0686343i	$-0.978136\pi$
$857$		−	4.01848i		−	0.137269i	0.997642	−	0.0686343i	$-0.0218642\pi$
$858$	2.03375	+	1.76271i	0.0694310	+	0.0601781i
$859$	13.7027			0.467530			0.233765	−	0.972293i	$-0.424895\pi$
$859$	13.7027			0.467530			0.233765	+	0.972293i	$0.424895\pi$
$860$	6.90255	+	60.4026i	0.235375	+	2.05971i
$861$	22.3364	+	12.8959i	0.761222	+	0.439491i
$862$	42.8892	+	14.9695i	1.46081	+	0.509863i
$863$	−19.2109	−	19.2109i	−0.653945	−	0.653945i	0.299996	−	0.953941i	$-0.403015\pi$
$863$	−19.2109	−	19.2109i	−0.653945	−	0.653945i	−0.953941	+	0.299996i	$0.903015\pi$
$864$	−5.59029	+	0.865233i	−0.190186	+	0.0294358i
$865$	10.0668	−	37.5697i	0.342281	−	1.27741i
$866$	−37.5768	−	2.78610i	−1.27691	−	0.0946754i
$867$	10.8078	+	18.7196i	0.367052	+	0.635753i
$868$	2.38287	−	2.99774i	0.0808798	−	0.101750i
$869$	0.659639	+	2.46181i	0.0223767	+	0.0835111i
$870$	3.13792	+	3.64050i	0.106386	+	0.123425i
$871$	−22.5900	+	9.73993i	−0.765432	+	0.330025i
$872$	−30.3420	+	19.1657i	−1.02751	+	0.649033i
$873$	1.00786	+	3.76138i	0.0341109	+	0.127304i
$874$	−14.0800	+	2.67562i	−0.476262	+	0.0905041i
$875$	27.0694	−	15.6285i	0.915114	−	0.528341i
$876$	9.58691	+	12.9469i	0.323912	+	0.437434i
$877$	−9.02153	+	33.6688i	−0.304635	+	1.13691i	0.628623	+	0.777710i	$0.283619\pi$
$877$	−9.02153	+	33.6688i	−0.304635	+	1.13691i	−0.933259	+	0.359205i	$0.883048\pi$
$878$	−2.41667	+	1.16616i	−0.0815587	+	0.0393561i
$879$	2.28422	−	2.28422i	0.0770448	−	0.0770448i
$880$	−7.21117	+	1.66993i	−0.243089	+	0.0562934i
$881$	35.2176	+	20.3329i	1.18651	+	0.685033i	0.957512	−	0.288393i	$-0.0931210\pi$
$881$	35.2176	+	20.3329i	1.18651	+	0.685033i	0.229000	+	0.973426i	$0.426454\pi$
$882$	6.47156	−	9.50820i	0.217909	−	0.320158i
$883$			42.7286i			1.43793i	0.695045	+	0.718967i	$0.255385\pi$
$883$			42.7286i			1.43793i	−0.695045	+	0.718967i	$0.744615\pi$
$884$	22.5116	−	38.7458i	0.757147	−	1.30316i
$885$			46.7335i			1.57093i
$886$	−17.8109	−	12.1226i	−0.598370	−	0.407268i
$887$	−32.4061	−	18.7097i	−1.08809	−	0.628209i	−0.155022	−	0.987911i	$-0.549545\pi$
$887$	−32.4061	−	18.7097i	−1.08809	−	0.628209i	−0.933067	+	0.359702i	$0.882878\pi$
$888$	7.64577	−	14.5500i	0.256575	−	0.488266i
$889$	−11.5578	+	11.5578i	−0.387635	+	0.387635i
$890$	−15.8923	−	32.9340i	−0.532710	−	1.10395i
$891$	−0.136608	+	0.509830i	−0.00457655	+	0.0170799i
$892$	−15.9279	−	21.5102i	−0.533304	−	0.720213i
$893$	−6.99040	+	4.03591i	−0.233925	+	0.135057i
$894$	−2.25967	−	11.8911i	−0.0755747	−	0.397699i
$895$	8.94159	+	33.3705i	0.298884	+	1.11545i
$896$	11.6263	+	42.4480i	0.388407	+	1.41809i
$897$	−7.77839	+	6.14826i	−0.259713	+	0.205284i
$898$	−6.04829	+	5.21331i	−0.201834	+	0.173970i
$899$	−0.123487	−	0.460859i	−0.00411851	−	0.0153705i
$900$	11.4163	+	9.07469i	0.380544	+	0.302490i
$901$	−44.2665	−	76.6718i	−1.47473	−	2.55431i
$902$	−0.365935	+	4.93546i	−0.0121843	+	0.164333i
$903$	8.72955	−	32.5791i	0.290501	−	1.08417i
$904$	28.8708	−	8.98057i	0.960228	−	0.298689i
$905$	−8.64210	−	8.64210i	−0.287273	−	0.287273i
$906$	−4.59899	+	13.1766i	−0.152791	+	0.437763i
$907$	−5.92338	−	3.41986i	−0.196683	−	0.113555i	0.398425	−	0.917201i	$-0.369557\pi$
$907$	−5.92338	−	3.41986i	−0.196683	−	0.113555i	−0.595107	+	0.803646i	$0.702890\pi$
$908$	3.55089	+	31.0730i	0.117841	+	1.03119i
$909$	−4.12430			−0.136794
$910$	−69.3667	+	4.95216i	−2.29949	+	0.164162i
$911$		−	42.0719i		−	1.39390i	−0.717118	−	0.696952i	$-0.754539\pi$
$911$		−	42.0719i		−	1.39390i	0.717118	−	0.696952i	$-0.245461\pi$
$912$	0.504570	−	14.7327i	0.0167080	−	0.487847i
$913$	−3.83181	+	6.63689i	−0.126814	+	0.219649i
$914$	0.268125	−	0.768207i	0.00886879	−	0.0254100i
$915$	15.5259	−	15.5259i	0.513272	−	0.513272i
$916$	−27.3089	−	11.8633i	−0.902310	−	0.391975i
$917$	5.80101	+	1.55438i	0.191566	+	0.0513300i
$918$	8.76407	+	0.649803i	0.289257	+	0.0214467i
$919$	41.6791	−	24.0634i	1.37487	−	0.793780i	0.383331	−	0.923611i	$-0.374777\pi$
$919$	41.6791	−	24.0634i	1.37487	−	0.793780i	0.991536	+	0.129831i	$0.0414436\pi$
$920$	−1.08430	−	27.2474i	−0.0357482	−	0.898319i
$921$	−18.6151	+	4.98791i	−0.613390	+	0.164357i
$922$	−0.765075	+	0.659455i	−0.0251964	+	0.0217180i
$923$	−41.3158	−	4.83605i	−1.35992	−	0.159181i
$924$	4.06160	+	0.605616i	0.133617	+	0.0199233i
$925$	−40.9303	+	10.9672i	−1.34578	+	0.360601i
$926$	−12.4049	+	2.35729i	−0.407649	+	0.0774655i
$927$	4.83315	+	8.37126i	0.158741	+	0.274948i
$928$	5.11231	+	1.98313i	0.167820	+	0.0650994i
$929$	−13.2391	−	3.54740i	−0.434360	−	0.116387i	0.0350119	−	0.999387i	$-0.488853\pi$
$929$	−13.2391	−	3.54740i	−0.434360	−	0.116387i	−0.469372	+	0.883000i	$0.655520\pi$
$930$	−1.06060	−	2.19791i	−0.0347785	−	0.0720723i
$931$	21.1936	+	21.1936i	0.694591	+	0.694591i
$932$	43.2963	−	17.0717i	1.41822	−	0.559201i
$933$	2.38479	−	4.13058i	0.0780746	−	0.135229i
$934$	−4.89309	+	7.18906i	−0.160107	+	0.235233i
$935$	11.4993			0.376067
$936$	−4.40686	−	9.19671i	−0.144043	−	0.300604i
$937$	−39.4855			−1.28993			−0.644967	−	0.764211i	$-0.723129\pi$
$937$	−39.4855			−1.28993			−0.644967	+	0.764211i	$0.723129\pi$
$938$	−21.1200	+	31.0301i	−0.689593	+	1.01317i
$939$	8.97201	−	15.5400i	0.292791	−	0.507128i
$940$	−5.63352	−	14.2874i	−0.183745	−	0.466005i
$941$	−14.7244	−	14.7244i	−0.480002	−	0.480002i	0.425130	−	0.905132i	$-0.360228\pi$
$941$	−14.7244	−	14.7244i	−0.480002	−	0.480002i	−0.905132	+	0.425130i	$0.860228\pi$
$942$	5.64427	+	11.6968i	0.183900	+	0.381101i
$943$	−17.6108	−	4.71881i	−0.573488	−	0.153666i
$944$	25.0633	+	47.0609i	0.815740	+	1.53170i
$945$	−6.81928	−	11.8113i	−0.221831	−	0.384223i
$946$	6.35811	−	1.20823i	0.206720	−	0.0392830i
$947$	1.37814	−	0.369272i	0.0447836	−	0.0119997i	−0.236358	−	0.971666i	$-0.575954\pi$
$947$	1.37814	−	0.369272i	0.0447836	−	0.0119997i	0.281141	+	0.959666i	$0.409287\pi$
$948$	1.42424	−	9.55177i	0.0462573	−	0.310227i
$949$	−17.3469	+	23.2929i	−0.563104	+	0.756119i
$950$	−28.7861	+	24.8121i	−0.933945	+	0.805012i
$951$	−6.54588	+	1.75396i	−0.212265	+	0.0568761i
$952$	−2.71874	−	68.3193i	−0.0881148	−	2.21424i
$953$	25.2670	−	14.5879i	0.818477	−	0.472548i	−0.0314138	−	0.999506i	$-0.510001\pi$
$953$	25.2670	−	14.5879i	0.818477	−	0.472548i	0.849891	+	0.526958i	$0.176668\pi$
$954$	−20.0932	−	1.48979i	−0.650540	−	0.0482337i
$955$	−16.4142	−	4.39817i	−0.531151	−	0.142322i
$956$	−6.72439	+	15.4792i	−0.217482	+	0.500635i
$957$	0.361782	−	0.361782i	0.0116948	−	0.0116948i
$958$	−0.932718	+	2.67234i	−0.0301348	+	0.0863393i
$959$	3.52895	−	6.11232i	0.113956	−	0.197377i
$960$	27.5832	+	5.08351i	0.890245	+	0.164070i
$961$		−	30.7577i		−	0.992185i
$962$	29.0952	+	5.61156i	0.938067	+	0.180924i
$963$	2.14910			0.0692539
$964$	−61.4206	+	7.01889i	−1.97822	+	0.226063i
$965$	−81.2438	−	46.9061i	−2.61533	−	1.50996i
$966$	−4.98526	+	14.2833i	−0.160398	+	0.459558i
$967$	−13.3289	−	13.3289i	−0.428629	−	0.428629i	0.459532	−	0.888161i	$-0.348017\pi$
$967$	−13.3289	−	13.3289i	−0.428629	−	0.428629i	−0.888161	+	0.459532i	$0.848017\pi$
$968$	−9.00713	−	28.9562i	−0.289500	−	0.930687i
$969$	−5.92725	+	22.1208i	−0.190411	+	0.710622i
$970$	1.42762	−	19.2547i	0.0458381	−	0.618231i
$971$	19.8887	+	34.4483i	0.638259	+	1.10550i	0.985815	+	0.167838i	$0.0536786\pi$
$971$	19.8887	+	34.4483i	0.638259	+	1.10550i	−0.347555	+	0.937660i	$0.612988\pi$
$972$	1.24450	−	1.56563i	0.0399175	−	0.0502177i
$973$	−17.5476	−	65.4887i	−0.562552	−	2.09947i
$974$	−31.6762	+	27.3032i	−1.01497	+	0.874851i
$975$	−9.71085	+	24.4319i	−0.310996	+	0.782447i
$976$	7.30811	−	23.9613i	0.233927	−	0.766983i
$977$	−1.44178	−	5.38081i	−0.0461268	−	0.172147i	0.939020	−	0.343863i	$-0.111736\pi$
$977$	−1.44178	−	5.38081i	−0.0461268	−	0.172147i	−0.985147	+	0.171716i	$0.945069\pi$
$978$	1.80497	+	9.49834i	0.0577165	+	0.303723i
$979$	−3.37123	+	1.94638i	−0.107745	+	0.0622067i
$980$	−45.8303	+	33.9364i	−1.46399	+	1.08406i
$981$	3.28399	−	12.2560i	0.104850	−	0.391305i
$982$	−5.14862	−	10.6696i	−0.164299	−	0.340481i
$983$	18.3025	−	18.3025i	0.583758	−	0.583758i	−0.352176	−	0.935934i	$-0.614558\pi$
$983$	18.3025	−	18.3025i	0.583758	−	0.583758i	0.935934	+	0.352176i	$0.114558\pi$
$984$	8.72322	−	16.6004i	0.278086	−	0.529202i
$985$	80.7758	+	46.6359i	2.57373	+	1.48594i
$986$	−7.04234	−	4.79323i	−0.224274	−	0.152648i
$987$			8.52034i			0.271205i
$988$	25.6884	−	6.80785i	0.817258	−	0.216587i
$989$			23.8424i			0.758144i
$990$	1.47250	−	2.16344i	0.0467991	−	0.0687585i
$991$	2.57728	+	1.48799i	0.0818698	+	0.0472676i	0.540376	−	0.841424i	$-0.318282\pi$
$991$	2.57728	+	1.48799i	0.0818698	+	0.0472676i	−0.458506	+	0.888691i	$0.651615\pi$
$992$	−2.24678	−	1.64451i	−0.0713352	−	0.0522131i
$993$	11.6861	−	11.6861i	0.370848	−	0.370848i
$994$	−57.1635	+	27.5842i	−1.81312	+	0.874918i
$995$	18.3081	−	68.3269i	0.580407	−	2.16611i
$996$	23.3374	−	17.2809i	0.739475	−	0.547567i
$997$	25.2456	−	14.5756i	0.799537	−	0.461613i	−0.0437723	−	0.999042i	$-0.513938\pi$
$997$	25.2456	−	14.5756i	0.799537	−	0.461613i	0.843309	+	0.537429i	$0.180604\pi$
$998$	−24.3902	+	4.63486i	−0.772057	+	0.146714i
$999$	1.50405	+	5.61319i	0.0475860	+	0.177593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.c.19.11	yes	48
3.2	odd	2		936.2.ed.c.19.2		48
8.3	odd	2	inner	312.2.bt.c.19.5	✓	48
13.11	odd	12	inner	312.2.bt.c.115.5	yes	48
24.11	even	2		936.2.ed.c.19.8		48
39.11	even	12		936.2.ed.c.739.8		48
104.11	even	12	inner	312.2.bt.c.115.11	yes	48
312.11	odd	12		936.2.ed.c.739.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.5	✓	48	8.3	odd	2	inner
312.2.bt.c.19.11	yes	48	1.1	even	1	trivial
312.2.bt.c.115.5	yes	48	13.11	odd	12	inner
312.2.bt.c.115.11	yes	48	104.11	even	12	inner
936.2.ed.c.19.2		48	3.2	odd	2
936.2.ed.c.19.8		48	24.11	even	2
936.2.ed.c.739.2		48	312.11	odd	12
936.2.ed.c.739.8		48	39.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16911 + 0.795730i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.733627 + 1.86059i) q^{4} +(2.47909 + 2.47909i) q^{5} +(-1.27368 + 0.614612i) q^{6} +(-3.75755 - 1.00683i) q^{7} +(-0.622837 + 2.75900i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.925639 + 4.87102i) q^{10} +(0.509830 - 0.136608i) q^{11} +(-1.97813 - 0.294955i) q^{12} +(-0.521969 - 3.56757i) q^{13} +(-3.59181 - 4.16709i) q^{14} +(-3.38651 + 0.907411i) q^{15} +(-2.92358 + 2.72996i) q^{16} +(5.38161 - 3.10707i) q^{17} +(0.104568 - 1.41034i) q^{18} +(3.55975 + 0.953832i) q^{19} +(-2.79384 + 6.43131i) q^{20} +(2.75071 - 2.75071i) q^{21} +(0.704749 + 0.245977i) q^{22} +(-1.37494 + 2.38147i) q^{23} +(-2.07794 - 1.91889i) q^{24} +7.29182i q^{25} +(2.22858 - 4.58622i) q^{26} +1.00000 q^{27} +(-0.883339 - 7.72989i) q^{28} +(-0.839483 - 0.484676i) q^{29} +(-4.68125 - 1.63388i) q^{30} +(0.348039 + 0.348039i) q^{31} +(-5.59029 + 0.865233i) q^{32} +(-0.136608 + 0.509830i) q^{33} +(8.76407 + 0.649803i) q^{34} +(-6.81928 - 11.8113i) q^{35} +(1.24450 - 1.56563i) q^{36} +(1.50405 + 5.61319i) q^{37} +(3.40274 + 3.94773i) q^{38} +(3.35059 + 1.33175i) q^{39} +(-8.38389 + 5.29575i) q^{40} +(1.71600 + 6.40421i) q^{41} +(5.40471 - 1.02706i) q^{42} +(7.50871 - 4.33516i) q^{43} +(0.628197 + 0.848364i) q^{44} +(0.907411 - 3.38651i) q^{45} +(-3.50247 + 1.69011i) q^{46} +(-1.54875 + 1.54875i) q^{47} +(-0.902421 - 3.89688i) q^{48} +(7.04327 + 4.06643i) q^{49} +(-5.80232 + 8.52492i) q^{50} +6.21414i q^{51} +(6.25485 - 3.58844i) q^{52} -14.2470i q^{53} +(1.16911 + 0.795730i) q^{54} +(1.60258 + 0.925250i) q^{55} +(5.11819 - 9.73997i) q^{56} +(-2.60592 + 2.60592i) q^{57} +(-0.595775 - 1.23464i) q^{58} +(3.44998 - 12.8755i) q^{59} +(-4.17275 - 5.63519i) q^{60} +(-5.42370 + 3.13137i) q^{61} +(0.129950 + 0.683840i) q^{62} +(1.00683 + 3.75755i) q^{63} +(-7.22415 - 3.43681i) q^{64} +(7.55033 - 10.1383i) q^{65} +(-0.565397 + 0.487342i) q^{66} +(-1.76589 - 6.59040i) q^{67} +(9.72908 + 7.73352i) q^{68} +(-1.37494 - 2.38147i) q^{69} +(1.42616 - 19.2350i) q^{70} +(2.98604 - 11.1440i) q^{71} +(2.70078 - 0.840107i) q^{72} +(-5.69573 - 5.69573i) q^{73} +(-2.70819 + 7.75924i) q^{74} +(-6.31490 - 3.64591i) q^{75} +(0.836840 + 7.32298i) q^{76} -2.05325 q^{77} +(2.85749 + 4.22312i) q^{78} +4.82868i q^{79} +(-14.0157 - 0.480014i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.08983 + 8.85268i) q^{82} +(-10.2669 + 10.2669i) q^{83} +(7.13595 + 3.09995i) q^{84} +(21.0442 + 5.63879i) q^{85} +(12.2281 + 0.906642i) q^{86} +(0.839483 - 0.484676i) q^{87} +(0.0593617 + 1.49170i) q^{88} +(-7.12395 + 1.90886i) q^{89} +(3.75561 - 3.23714i) q^{90} +(-1.63062 + 13.9308i) q^{91} +(-5.43964 - 0.811092i) q^{92} +(-0.475430 + 0.127391i) q^{93} +(-3.04304 + 0.578269i) q^{94} +(6.46031 + 11.1896i) q^{95} +(2.04583 - 5.27395i) q^{96} +(-3.76138 - 1.00786i) q^{97} +(4.99856 + 10.3586i) q^{98} +(-0.373221 - 0.373221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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