LMFDB - Embedded newform 980.2.o.f.31.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(31,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.13
Character	$\chi$	$=$	980.31
Dual form			980.2.o.f.411.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05472 + 0.942109i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.21064 + 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(1.38447 + 0.288532i) q^{10} +(-3.24107 - 1.87123i) q^{11} +(-1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +0.901278i q^{15} +(-3.89888 + 0.893735i) q^{16} +(0.505515 + 0.291859i) q^{17} +(-0.631220 + 3.02880i) q^{18} +(3.07977 + 5.33433i) q^{19} +(1.18839 + 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} +(-3.73439 + 2.15605i) q^{23} +(-1.06454 - 2.31628i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.27981 + 2.55232i) q^{26} -4.67556 q^{27} -0.435463 q^{29} +(-0.849103 + 0.950594i) q^{30} +(1.26933 - 2.19854i) q^{31} +(-4.95421 - 2.73053i) q^{32} +(2.92110 - 1.68650i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(5.65039 + 9.78676i) q^{37} +(-1.77723 + 8.52769i) q^{38} +(-1.88881 - 1.09050i) q^{39} +(-0.262094 + 2.81626i) q^{40} +7.35068i q^{41} -5.80096i q^{43} +(2.98995 - 6.86180i) q^{44} +(1.89460 + 1.09385i) q^{45} +(-5.96996 - 1.24418i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 - 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} +(-0.455610 + 0.263046i) q^{51} +(-4.80912 + 0.544138i) q^{52} +(1.55746 - 2.69759i) q^{53} +(-4.93139 - 4.40489i) q^{54} -3.74246 q^{55} -5.55147 q^{57} +(-0.459290 - 0.410254i) q^{58} +(1.73534 - 3.00569i) q^{59} +(-1.79113 + 0.202661i) q^{60} +(8.99597 - 5.19383i) q^{61} +(3.41004 - 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} +(1.20995 + 2.09570i) q^{65} +(4.66981 + 0.973217i) q^{66} +(8.52602 + 4.92250i) q^{67} +(-0.466348 + 1.07025i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(-6.16112 - 0.573383i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-3.26063 + 15.6456i) q^{74} +(0.450639 + 0.780530i) q^{75} +(-9.90849 + 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} +(-0.397549 + 0.229525i) q^{79} +(-2.92966 + 2.72344i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(-6.92515 + 7.75290i) q^{82} +2.59747 q^{83} +0.583719 q^{85} +(5.46514 - 6.11837i) q^{86} +(0.196236 - 0.339892i) q^{87} +(9.61812 - 4.42040i) q^{88} +(8.55647 - 4.94008i) q^{89} +(0.967745 + 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} +(1.14402 + 1.98149i) q^{93} +(3.34020 - 16.0273i) q^{94} +(5.33433 + 3.07977i) q^{95} +(4.36382 - 2.63643i) q^{96} +4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + 30 q^{12} - 14 q^{16} - 8 q^{22} - 36 q^{24} + 16 q^{25} - 30 q^{26} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} + 60 q^{38} - 18 q^{44} - 12 q^{45} + 2 q^{46}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 + 30 * q^12 - 14 * q^16 - 8 * q^22 - 36 * q^24 + 16 * q^25 - 30 * q^26 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 + 60 * q^38 - 18 * q^44 - 12 * q^45 + 2 * q^46 + 4 * q^50 + 36 * q^52 - 8 * q^53 - 12 * q^54 + 48 * q^57 + 2 * q^58 + 14 * q^60 - 24 * q^61 + 4 * q^64 + 4 * q^65 - 24 * q^66 - 60 * q^68 + 4 * q^72 + 72 * q^73 + 38 * q^74 + 120 * q^78 - 36 * q^81 - 42 * q^82 + 28 * q^86 + 4 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^93 - 18 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	1.05472	+	0.942109i	0.745798	+	0.666172i
$2$	1.05472	+	0.942109i	0.745798	+	0.666172i
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	−0.966289	−	0.257461i	$-0.917114\pi$
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	0.706112	+	0.708100i	$0.250447\pi$
$4$	0.224860	+	1.98732i	0.112430	+	0.993660i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.21064	+	0.398687i	−0.494242	+	0.162763i
$7$		0			0
$7$		0			0
$8$	−1.63511	+	2.30790i	−0.578098	+	0.815967i
$9$	1.09385	+	1.89460i	0.364616	+	0.631534i
$10$	1.38447	+	0.288532i	0.437807	+	0.0912418i
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.0757892	−	0.997124i	$-0.524148\pi$
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.901429	+	0.432927i	$0.857481\pi$
$12$	−1.65249	−	0.720054i	−0.477033	−	0.207862i
$13$			2.41990i			0.671161i	0.942012	+	0.335580i	$0.108932\pi$
$13$			2.41990i			0.671161i	−0.942012	+	0.335580i	$0.891068\pi$
$14$		0			0
$15$			0.901278i			0.232709i
$16$	−3.89888	+	0.893735i	−0.974719	+	0.223434i
$17$	0.505515	+	0.291859i	0.122605	+	0.0707863i	0.560048	−	0.828460i	$-0.310782\pi$
$17$	0.505515	+	0.291859i	0.122605	+	0.0707863i	−0.437443	+	0.899246i	$0.644116\pi$
$18$	−0.631220	+	3.02880i	−0.148780	+	0.713894i
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	0.966130	+	0.258057i	$0.0830822\pi$
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	−0.259581	+	0.965721i	$0.583584\pi$
$20$	1.18839	+	1.60864i	0.265733	+	0.359703i
$21$		0			0
$22$	−1.65551	−	5.02706i	−0.352955	−	1.07177i
$23$	−3.73439	+	2.15605i	−0.778674	+	0.449568i	−0.835960	−	0.548790i	$-0.815089\pi$
$23$	−3.73439	+	2.15605i	−0.778674	+	0.449568i	0.0572861	+	0.998358i	$0.481755\pi$
$24$	−1.06454	−	2.31628i	−0.217299	−	0.472809i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.27981	+	2.55232i	−0.447108	+	0.500550i
$27$	−4.67556			−0.899812
$28$		0			0
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$	−0.849103	+	0.950594i	−0.155024	+	0.173554i
$31$	1.26933	−	2.19854i	0.227978	−	0.394869i	−0.729231	−	0.684268i	$-0.760122\pi$
$31$	1.26933	−	2.19854i	0.227978	−	0.394869i	0.957209	+	0.289399i	$0.0934554\pi$
$32$	−4.95421	−	2.73053i	−0.875789	−	0.482694i
$33$	2.92110	−	1.68650i	0.508499	−	0.293582i
$34$	0.258212	+	0.784080i	0.0442831	+	0.134469i
$35$		0			0
$36$	−3.51922	+	2.59985i	−0.586536	+	0.433308i
$37$	5.65039	+	9.78676i	0.928918	+	1.60893i	0.785136	+	0.619324i	$0.212593\pi$
$37$	5.65039	+	9.78676i	0.928918	+	1.60893i	0.143782	+	0.989609i	$0.454073\pi$
$38$	−1.77723	+	8.52769i	−0.288304	+	1.38337i
$39$	−1.88881	−	1.09050i	−0.302451	−	0.174620i
$40$	−0.262094	+	2.81626i	−0.0414407	+	0.445289i
$41$			7.35068i			1.14798i	0.818861	+	0.573992i	$0.194606\pi$
$41$			7.35068i			1.14798i	−0.818861	+	0.573992i	$0.805394\pi$
$42$		0			0
$43$		−	5.80096i		−	0.884637i	−0.896858	−	0.442319i	$-0.854156\pi$
$43$		−	5.80096i		−	0.884637i	0.896858	−	0.442319i	$-0.145844\pi$
$44$	2.98995	−	6.86180i	0.450752	−	1.03446i
$45$	1.89460	+	1.09385i	0.282431	+	0.163061i
$46$	−5.96996	−	1.24418i	−0.880223	−	0.183444i
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	−0.886223	−	0.463258i	$-0.846680\pi$
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	0.0419181	−	0.999121i	$-0.486653\pi$
$48$	1.05940	−	3.44594i	0.152911	−	0.497379i
$49$		0			0
$50$	1.34325	−	0.442358i	0.189964	−	0.0625588i
$51$	−0.455610	+	0.263046i	−0.0637981	+	0.0368339i
$52$	−4.80912	+	0.544138i	−0.666905	+	0.0754584i
$53$	1.55746	−	2.69759i	0.213933	−	0.370543i	−0.739009	−	0.673696i	$-0.764706\pi$
$53$	1.55746	−	2.69759i	0.213933	−	0.370543i	0.952942	+	0.303153i	$0.0980393\pi$
$54$	−4.93139	−	4.40489i	−0.671078	−	0.599429i
$55$	−3.74246			−0.504633
$56$		0			0
$57$	−5.55147			−0.735310
$58$	−0.459290	−	0.410254i	−0.0603078	−	0.0538689i
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	−0.730674	−	0.682727i	$-0.760794\pi$
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	0.956596	+	0.291419i	$0.0941273\pi$
$60$	−1.79113	+	0.202661i	−0.231234	+	0.0261634i
$61$	8.99597	−	5.19383i	1.15182	−	0.665001i	0.202487	−	0.979285i	$-0.435098\pi$
$61$	8.99597	−	5.19383i	1.15182	−	0.665001i	0.949329	+	0.314284i	$0.101764\pi$
$62$	3.41004	−	1.12299i	0.433076	−	0.142620i
$63$		0			0
$64$	−2.65284	−	7.54735i	−0.331605	−	0.943418i
$65$	1.20995	+	2.09570i	0.150076	+	0.259939i
$66$	4.66981	+	0.973217i	0.574813	+	0.119795i
$67$	8.52602	+	4.92250i	1.04162	+	0.601379i	0.920291	−	0.391234i	$-0.127952\pi$
$67$	8.52602	+	4.92250i	1.04162	+	0.601379i	0.121327	+	0.992613i	$0.461285\pi$
$68$	−0.466348	+	1.07025i	−0.0565530	+	0.129787i
$69$		−	3.88640i		−	0.467868i
$70$		0			0
$71$			9.96771i			1.18295i	0.806324	+	0.591475i	$0.201454\pi$
$71$			9.96771i			1.18295i	−0.806324	+	0.591475i	$0.798546\pi$
$72$	−6.16112	−	0.573383i	−0.726095	−	0.0675738i
$73$	−8.48612	−	4.89946i	−0.993225	−	0.573439i	−0.0869881	−	0.996209i	$-0.527724\pi$
$73$	−8.48612	−	4.89946i	−0.993225	−	0.573439i	−0.906237	+	0.422771i	$0.861058\pi$
$74$	−3.26063	+	15.6456i	−0.379041	+	1.81876i
$75$	0.450639	+	0.780530i	0.0520353	+	0.0901278i
$76$	−9.90849	+	7.31997i	−1.13658	+	0.839658i
$77$		0			0
$78$	−0.964785	−	2.92964i	−0.109240	−	0.331716i
$79$	−0.397549	+	0.229525i	−0.0447278	+	0.0258236i	−0.522197	−	0.852825i	$-0.674887\pi$
$79$	−0.397549	+	0.229525i	−0.0447278	+	0.0258236i	0.477469	+	0.878648i	$0.341554\pi$
$80$	−2.92966	+	2.72344i	−0.327546	+	0.304489i
$81$	−1.17456	+	2.03439i	−0.130506	+	0.226044i
$82$	−6.92515	+	7.75290i	−0.764755	+	0.856164i
$83$	2.59747			0.285109			0.142554	−	0.989787i	$-0.454468\pi$
$83$	2.59747			0.285109			0.142554	+	0.989787i	$0.454468\pi$
$84$		0			0
$85$	0.583719			0.0633132
$86$	5.46514	−	6.11837i	0.589321	−	0.659761i
$87$	0.196236	−	0.339892i	0.0210388	−	0.0364402i
$88$	9.61812	−	4.42040i	1.02529	−	0.471217i
$89$	8.55647	−	4.94008i	0.906984	−	0.523648i	0.0275247	−	0.999621i	$-0.491237\pi$
$89$	8.55647	−	4.94008i	0.906984	−	0.523648i	0.879460	+	0.475973i	$0.157904\pi$
$90$	0.967745	+	2.93862i	0.102009	+	0.309758i
$91$		0			0
$92$	−5.12447	−	6.93662i	−0.534263	−	0.723192i
$93$	1.14402	+	1.98149i	0.118629	+	0.205471i
$94$	3.34020	−	16.0273i	0.344515	−	1.65309i
$95$	5.33433	+	3.07977i	0.547290	+	0.315978i
$96$	4.36382	−	2.63643i	0.445381	−	0.269079i
$97$			4.54044i			0.461011i	0.973071	+	0.230506i	$0.0740380\pi$
$97$			4.54044i			0.461011i	−0.973071	+	0.230506i	$0.925962\pi$
$98$		0			0
$99$		−	8.18738i		−	0.822862i
$100$	1.83350	+	0.798926i	0.183350	+	0.0798926i
$101$	−7.91930	−	4.57221i	−0.787999	−	0.454952i	0.0512584	−	0.998685i	$-0.483677\pi$
$101$	−7.91930	−	4.57221i	−0.787999	−	0.454952i	−0.839258	+	0.543734i	$0.817010\pi$
$102$	−0.728358	−	0.151795i	−0.0721182	−	0.0150299i
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	0.999989	+	0.00473128i	$0.00150602\pi$
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	−0.495897	+	0.868381i	$0.665161\pi$
$104$	−5.58490	−	3.95681i	−0.547645	−	0.387997i
$105$		0			0
$106$	4.18410	−	1.37790i	0.406396	−	0.133834i
$107$	−5.48368	+	3.16601i	−0.530128	+	0.306069i	−0.741068	−	0.671430i	$-0.765681\pi$
$107$	−5.48368	+	3.16601i	−0.530128	+	0.306069i	0.210941	+	0.977499i	$0.432347\pi$
$108$	−1.05134	−	9.29183i	−0.101166	−	0.894107i
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.0690134	−	0.997616i	$-0.478015\pi$
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.829454	−	0.558575i	$-0.188652\pi$
$110$	−3.94724	−	3.52581i	−0.376355	−	0.336173i
$111$	−10.1851			−0.966731
$112$		0			0
$113$	4.17847			0.393077			0.196539	−	0.980496i	$-0.437030\pi$
$113$	4.17847			0.393077			0.196539	+	0.980496i	$0.437030\pi$
$114$	−5.85523	−	5.23009i	−0.548393	−	0.489843i
$115$	−2.15605	+	3.73439i	−0.201053	+	0.348234i
$116$	−0.0979179	−	0.865403i	−0.00909145	−	0.0803507i
$117$	−4.58475	+	2.64701i	−0.423861	+	0.244716i
$118$	4.66198	−	1.53528i	0.429170	−	0.141334i
$119$		0			0
$120$	−2.08006	−	1.47369i	−0.189883	−	0.134529i
$121$	1.50301	+	2.60329i	0.136637	+	0.236663i
$122$	14.3814	+	2.99717i	1.30203	+	0.271351i
$123$	−5.73743	−	3.31250i	−0.517326	−	0.298678i
$124$	4.65461	+	2.02819i	0.417997	+	0.182137i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	4.91036i		−	0.435724i	−0.975980	−	0.217862i	$-0.930092\pi$
$127$		−	4.91036i		−	0.435724i	0.975980	−	0.217862i	$-0.0699083\pi$
$128$	4.31243	−	10.4596i	0.381169	−	0.924505i
$129$	4.52782	+	2.61414i	0.398652	+	0.230162i
$130$	−0.698219	+	3.35028i	−0.0612379	+	0.293839i
$131$	7.93723	+	13.7477i	0.693479	+	1.20114i	0.970691	+	0.240332i	$0.0772564\pi$
$131$	7.93723	+	13.7477i	0.693479	+	1.20114i	−0.277212	+	0.960809i	$0.589410\pi$
$132$	4.00845	+	5.42594i	0.348891	+	0.472267i
$133$		0			0
$134$	4.35501	+	13.2243i	0.376216	+	1.14240i
$135$	−4.04915	+	2.33778i	−0.348496	+	0.201204i
$136$	−1.50016	+	0.689459i	−0.128637	+	0.0591206i
$137$	3.92110	−	6.79155i	0.335002	−	0.580241i	−0.648483	−	0.761229i	$-0.724596\pi$
$137$	3.92110	−	6.79155i	0.335002	−	0.580241i	0.983485	+	0.180988i	$0.0579295\pi$
$138$	3.66142	−	4.09906i	0.311680	−	0.348935i
$139$	17.4044			1.47623			0.738113	−	0.674677i	$-0.235717\pi$
$139$	17.4044			1.47623			0.738113	+	0.674677i	$0.235717\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	−9.39067	+	10.5131i	−0.788048	+	0.882242i
$143$	4.52820	−	7.84307i	0.378667	−	0.655871i
$144$	−5.95805	−	6.40921i	−0.496505	−	0.534101i
$145$	−0.377122	+	0.217731i	−0.0313183	+	0.0180816i
$146$	−4.33463	−	13.1624i	−0.358736	−	1.08933i
$147$		0			0
$148$	−18.1789	+	13.4298i	−1.49429	+	1.10392i
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	0.830216	−	0.557441i	$-0.188217\pi$
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	−0.897867	+	0.440268i	$0.854884\pi$
$150$	−0.260047	+	1.24779i	−0.0212328	+	0.101882i
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	0.736293	−	0.676663i	$-0.236575\pi$
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	−0.217861	+	0.975980i	$0.569908\pi$
$152$	−17.3469	−	1.61438i	−1.40702	−	0.130944i
$153$			1.27700i			0.103239i
$154$		0			0
$155$		−	2.53865i		−	0.203909i
$156$	1.74246	−	3.99887i	0.139509	−	0.320166i
$157$	2.66953	+	1.54125i	0.213052	+	0.123005i	0.602729	−	0.797946i	$-0.294080\pi$
$157$	2.66953	+	1.54125i	0.213052	+	0.123005i	−0.389677	+	0.920952i	$0.627413\pi$
$158$	−0.635540	−	0.132451i	−0.0505609	−	0.0105372i
$159$	1.40370	+	2.43128i	0.111321	+	0.192813i
$160$	−5.65574	+	0.112397i	−0.447125	+	0.00888579i
$161$		0			0
$162$	−3.15545	+	1.03915i	−0.247915	+	0.0816433i
$163$	3.91284	−	2.25908i	0.306477	−	0.176945i	−0.338872	−	0.940833i	$-0.610045\pi$
$163$	3.91284	−	2.25908i	0.306477	−	0.176945i	0.645349	+	0.763888i	$0.276712\pi$
$164$	−14.6082	+	1.65287i	−1.14071	+	0.129068i
$165$	1.68650	−	2.92110i	0.131294	−	0.227408i
$166$	2.73959	+	2.44710i	0.212634	+	0.189932i
$167$	16.9358			1.31053			0.655266	−	0.755398i	$-0.272556\pi$
$167$	16.9358			1.31053			0.655266	+	0.755398i	$0.272556\pi$
$168$		0			0
$169$	7.14406			0.549543
$170$	0.615659	+	0.549927i	0.0472189	+	0.0421775i
$171$	−6.73762	+	11.6699i	−0.515238	+	0.892419i
$172$	11.5284	−	1.30440i	0.879029	−	0.0994596i
$173$	−0.114919	+	0.0663486i	−0.00873715	+	0.00504439i	−0.504362	−	0.863492i	$-0.668272\pi$
$173$	−0.114919	+	0.0663486i	−0.00873715	+	0.00504439i	0.495625	+	0.868537i	$0.334939\pi$
$174$	0.527189	−	0.173613i	0.0399661	−	0.0131616i
$175$		0			0
$176$	14.3089	+	4.39904i	1.07857	+	0.331590i
$177$	1.56402	+	2.70897i	0.117559	+	0.203618i
$178$	13.6788	+	2.85074i	1.02527	+	0.213672i
$179$	13.9422	+	8.04953i	1.04209	+	0.601650i	0.920424	−	0.390921i	$-0.127843\pi$
$179$	13.9422	+	8.04953i	1.04209	+	0.601650i	0.121664	+	0.992571i	$0.461177\pi$
$180$	−1.74781	+	4.01114i	−0.130274	+	0.298973i
$181$			3.99317i			0.296810i	0.988927	+	0.148405i	$0.0474139\pi$
$181$			3.99317i			0.296810i	−0.988927	+	0.148405i	$0.952586\pi$
$182$		0			0
$183$			9.36216i			0.692071i
$184$	1.13018	−	12.1440i	0.0833177	−	0.895267i
$185$	9.78676	+	5.65039i	0.719537	+	0.415425i
$186$	−0.660170	+	3.16770i	−0.0484060	+	0.232267i
$187$	−1.09227	−	1.89187i	−0.0798749	−	0.138347i
$188$	18.6225	−	13.7575i	1.35818	−	1.00337i
$189$		0			0
$190$	2.72472	+	8.27381i	0.197672	+	0.600245i
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.284030	−	0.958815i	$-0.408329\pi$
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.972373	+	0.233431i	$0.0749953\pi$
$192$	7.08640	+	1.33051i	0.511417	+	0.0960214i
$193$	−9.66959	+	16.7482i	−0.696032	+	1.20556i	0.273799	+	0.961787i	$0.411720\pi$
$193$	−9.66959	+	16.7482i	−0.696032	+	1.20556i	−0.969832	+	0.243776i	$0.921614\pi$
$194$	−4.27759	+	4.78888i	−0.307113	+	0.343821i
$195$	−2.18101			−0.156185
$196$		0			0
$197$	−1.63738			−0.116659			−0.0583293	−	0.998297i	$-0.518577\pi$
$197$	−1.63738			−0.116659			−0.0583293	+	0.998297i	$0.518577\pi$
$198$	7.71340	−	8.63537i	0.548168	−	0.613689i
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	−0.879573	−	0.475765i	$-0.842171\pi$
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	0.851811	+	0.523850i	$0.175505\pi$
$200$	1.18115	+	2.57000i	0.0835198	+	0.181726i
$201$	−7.68431	+	4.43654i	−0.542009	+	0.312929i
$202$	−4.04510	−	12.2832i	−0.284612	−	0.864245i
$203$		0			0
$204$	−0.625205	−	0.846294i	−0.0437731	−	0.0592524i
$205$	3.67534	+	6.36588i	0.256697	+	0.444612i
$206$	−2.95224	+	14.1658i	−0.205692	+	0.986978i
$207$	−8.16972	−	4.71679i	−0.567835	−	0.327839i
$208$	−2.16275	−	9.43491i	−0.149960	−	0.654193i
$209$		−	23.0519i		−	1.59453i
$210$		0			0
$211$			9.22534i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$211$			9.22534i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$212$	5.71118	+	2.48858i	0.392246	+	0.170916i
$213$	−7.78009	−	4.49184i	−0.533083	−	0.307776i
$214$	−8.76646	−	1.82699i	−0.599263	−	0.124890i
$215$	−2.90048	−	5.02378i	−0.197811	−	0.342619i
$216$	7.64505	−	10.7907i	0.520180	−	0.734217i
$217$		0			0
$218$	25.2001	−	8.29887i	1.70677	−	0.562071i
$219$	7.64835	−	4.41578i	0.516828	−	0.298391i
$220$	−0.841528	−	7.43747i	−0.0567358	−	0.501434i
$221$	−0.706272	+	1.22330i	−0.0475090	+	0.0822880i
$222$	−10.7425	−	9.59552i	−0.720986	−	0.644009i
$223$	−24.2380			−1.62310			−0.811550	−	0.584284i	$-0.801376\pi$
$223$	−24.2380			−1.62310			−0.811550	+	0.584284i	$0.801376\pi$
$224$		0			0
$225$	2.18770			0.145847
$226$	4.40710	+	3.93657i	0.293156	+	0.261857i
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	−0.986748	−	0.162262i	$-0.948121\pi$
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	0.633897	+	0.773417i	$0.281454\pi$
$228$	−1.24830	−	11.0325i	−0.0826707	−	0.730648i
$229$	25.5589	−	14.7564i	1.68898	−	0.975132i	0.733676	−	0.679499i	$-0.237803\pi$
$229$	25.5589	−	14.7564i	1.68898	−	0.975132i	0.955302	−	0.295633i	$-0.0955304\pi$
$230$	−5.79223	+	1.90749i	−0.381928	+	0.125776i
$231$		0			0
$232$	0.712029	−	1.00501i	0.0467470	−	0.0659819i
$233$	−14.0351	−	24.3096i	−0.919472	−	1.59257i	−0.800218	−	0.599709i	$-0.795283\pi$
$233$	−14.0351	−	24.3096i	−0.919472	−	1.59257i	−0.119254	−	0.992864i	$-0.538050\pi$
$234$	−7.32940	−	1.52749i	−0.479138	−	0.0998553i
$235$	−10.0256	−	5.78826i	−0.653996	−	0.377585i
$236$	6.36348	+	2.77281i	0.414227	+	0.180495i
$237$		−	0.413732i		−	0.0268748i
$238$		0			0
$239$			13.6279i			0.881512i	0.897627	+	0.440756i	$0.145290\pi$
$239$			13.6279i			0.881512i	−0.897627	+	0.440756i	$0.854710\pi$
$240$	−0.805504	−	3.51397i	−0.0519951	−	0.226826i
$241$	3.64372	+	2.10370i	0.234713	+	0.135512i	0.612744	−	0.790281i	$-0.290066\pi$
$241$	3.64372	+	2.10370i	0.234713	+	0.135512i	−0.378031	+	0.925793i	$0.623399\pi$
$242$	−0.867332	+	4.16174i	−0.0557542	+	0.267527i
$243$	−8.07194	−	13.9810i	−0.517815	−	0.896882i
$244$	12.3446	+	16.7100i	0.790283	+	1.06975i
$245$		0			0
$246$	−2.93062	−	8.89904i	−0.186850	−	0.567382i
$247$	−12.9086	+	7.45276i	−0.821352	+	0.474208i
$248$	2.99852	+	6.52433i	0.190406	+	0.414295i
$249$	−1.17052	+	2.02740i	−0.0741787	+	0.128481i
$250$	0.942109	−	1.05472i	0.0595842	−	0.0667062i
$251$	18.8826			1.19186			0.595928	−	0.803038i	$-0.296784\pi$
$251$	18.8826			1.19186			0.595928	+	0.803038i	$0.296784\pi$
$252$		0			0
$253$	16.1379			1.01458
$254$	4.62610	−	5.17905i	0.290267	−	0.324962i
$255$	−0.263046	+	0.455610i	−0.0164726	+	0.0285314i
$256$	14.4025	−	6.96913i	0.900155	−	0.435570i
$257$	−22.3734	+	12.9173i	−1.39561	+	0.805757i	−0.993929	−	0.110022i	$-0.964908\pi$
$257$	−22.3734	+	12.9173i	−1.39561	+	0.805757i	−0.401682	+	0.915779i	$0.631574\pi$
$258$	2.31277	+	7.02288i	0.143987	+	0.437225i
$259$		0			0
$260$	−3.89275	+	2.87580i	−0.241418	+	0.178349i
$261$	−0.476330	−	0.825028i	−0.0294841	−	0.0510680i
$262$	−4.58029	+	21.9777i	−0.282971	+	1.35779i
$263$	−9.26400	−	5.34857i	−0.571243	−	0.329807i	0.186403	−	0.982473i	$-0.440317\pi$
$263$	−9.26400	−	5.34857i	−0.571243	−	0.329807i	−0.757645	+	0.652666i	$0.773650\pi$
$264$	−0.884043	+	9.49923i	−0.0544091	+	0.584637i
$265$		−	3.11491i		−	0.191347i
$266$		0			0
$267$			8.90478i			0.544963i
$268$	−7.86542	+	18.0508i	−0.480457	+	1.10263i
$269$	7.24441	+	4.18256i	0.441699	+	0.255015i	0.704318	−	0.709884i	$-0.251253\pi$
$269$	7.24441	+	4.18256i	0.441699	+	0.255015i	−0.262619	+	0.964900i	$0.584586\pi$
$270$	−6.47316	−	1.34905i	−0.393944	−	0.0821004i
$271$	−13.5557	−	23.4791i	−0.823448	−	1.42625i	−0.903100	−	0.429430i	$-0.858714\pi$
$271$	−13.5557	−	23.4791i	−0.823448	−	1.42625i	0.0796525	−	0.996823i	$-0.474619\pi$
$272$	−2.23179	−	0.686127i	−0.135322	−	0.0416025i
$273$		0			0
$274$	10.5340	−	3.46906i	0.636385	−	0.209574i
$275$	−3.24107	+	1.87123i	−0.195444	+	0.112839i
$276$	7.72352	−	0.873895i	0.464901	−	0.0526023i
$277$	−1.67991	+	2.90970i	−0.100936	+	0.174827i	−0.912071	−	0.410033i	$-0.865517\pi$
$277$	−1.67991	+	2.90970i	−0.100936	+	0.174827i	0.811134	+	0.584860i	$0.198850\pi$
$278$	18.3568	+	16.3969i	1.10097	+	0.983420i
$279$	5.55380			0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	11.0046	+	9.82966i	0.655313	+	0.585348i
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	−0.738849	−	0.673871i	$-0.764630\pi$
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	0.953014	+	0.302926i	$0.0979635\pi$
$284$	−19.8090	+	2.24133i	−1.17545	+	0.132999i
$285$	−4.80771	+	2.77573i	−0.284784	+	0.164420i
$286$	12.1650	−	4.00617i	0.719332	−	0.236890i
$287$		0			0
$288$	−0.245892	−	12.3730i	−0.0144893	−	0.729089i
$289$	−8.32964	−	14.4274i	−0.489979	−	0.848668i
$290$	−0.602884	−	0.125645i	−0.0354026	−	0.00737812i
$291$	−3.54395	−	2.04610i	−0.207750	−	0.119944i
$292$	7.82861	−	17.9663i	0.458135	−	1.05140i
$293$			8.47879i			0.495336i	0.968845	+	0.247668i	$0.0796642\pi$
$293$			8.47879i			0.495336i	−0.968845	+	0.247668i	$0.920336\pi$
$294$		0			0
$295$		−	3.47068i		−	0.202071i
$296$	−31.8259	−	2.96187i	−1.84984	−	0.172155i
$297$	15.1538	+	8.74905i	0.879312	+	0.507671i
$298$	0.476525	−	2.28652i	0.0276044	−	0.132455i
$299$	−5.21744	−	9.03686i	−0.301732	−	0.522615i
$300$	−1.44983	+	1.07107i	−0.0837060	+	0.0618384i
$301$		0			0
$302$	3.25404	+	9.88112i	0.187249	+	0.568595i
$303$	7.13749	−	4.12083i	0.410038	−	0.236736i
$304$	−16.7751	−	18.0454i	−0.962120	−	1.03497i
$305$	5.19383	−	8.99597i	0.297398	−	0.515108i
$306$	−1.20307	+	1.34687i	−0.0687752	+	0.0769957i
$307$	−10.4271			−0.595104			−0.297552	−	0.954706i	$-0.596170\pi$
$307$	−10.4271			−0.595104			−0.297552	+	0.954706i	$0.596170\pi$
$308$		0			0
$309$	−9.22183			−0.524612
$310$	2.39169	−	2.67756i	0.135839	−	0.152075i
$311$	3.96296	−	6.86404i	0.224719	−	0.389224i	−0.731516	−	0.681824i	$-0.761187\pi$
$311$	3.96296	−	6.86404i	0.224719	−	0.389224i	0.956235	+	0.292600i	$0.0945203\pi$
$312$	5.60518	−	2.57609i	0.317331	−	0.145843i
$313$	−12.5285	+	7.23333i	−0.708152	+	0.408852i	−0.810376	−	0.585910i	$-0.800737\pi$
$313$	−12.5285	+	7.23333i	−0.708152	+	0.408852i	0.102224	+	0.994761i	$0.467404\pi$
$314$	1.36357	+	4.14058i	0.0769507	+	0.233666i
$315$		0			0
$316$	−0.545533	−	0.738447i	−0.0306886	−	0.0415409i
$317$	−1.76853	−	3.06318i	−0.0993305	−	0.172046i	0.812077	−	0.583550i	$-0.198337\pi$
$317$	−1.76853	−	3.06318i	−0.0993305	−	0.172046i	−0.911408	+	0.411504i	$0.865003\pi$
$318$	−0.810024	+	3.88675i	−0.0454239	+	0.217958i
$319$	1.41136	+	0.814851i	0.0790212	+	0.0456229i
$320$	−6.07110	−	5.20978i	−0.339385	−	0.291235i
$321$		−	5.70690i		−	0.318528i
$322$		0			0
$323$			3.59544i			0.200056i
$324$	−4.30710	−	1.87677i	−0.239283	−	0.104265i
$325$	2.09570	+	1.20995i	0.116248	+	0.0671161i
$326$	6.25524	+	1.30363i	0.346446	+	0.0722015i
$327$	8.45423	+	14.6432i	0.467520	+	0.809769i
$328$	−16.9647	−	12.0192i	−0.936717	−	0.663648i
$329$		0			0
$330$	4.53078	−	1.49207i	0.249411	−	0.0821359i
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.941411	−	0.337261i	$-0.890499\pi$
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.178629	+	0.983917i	$0.557166\pi$
$332$	0.584065	+	5.16199i	0.0320547	+	0.283301i
$333$	−12.3613	+	21.4105i	−0.677397	+	1.17329i
$334$	17.8625	+	15.9554i	0.977393	+	0.873040i
$335$	9.84499			0.537890
$336$		0			0
$337$	5.10057			0.277846			0.138923	−	0.990303i	$-0.455636\pi$
$337$	5.10057			0.277846			0.138923	+	0.990303i	$0.455636\pi$
$338$	7.53497	+	6.73049i	0.409848	+	0.366090i
$339$	−1.88298	+	3.26142i	−0.102269	+	0.177136i
$340$	0.131255	+	1.16004i	0.00711829	+	0.0629118i
$341$	−8.22794	+	4.75040i	−0.445568	+	0.257249i
$342$	−18.1006	+	5.96087i	−0.978768	+	0.322327i
$343$		0			0
$344$	13.3880	+	9.48520i	0.721835	+	0.511407i
$345$	−1.94320	−	3.36572i	−0.104618	−	0.181204i
$346$	−0.183715	−	0.0382874i	−0.00987658	−	0.00205834i
$347$	−1.44316	−	0.833209i	−0.0774729	−	0.0447290i	0.460763	−	0.887523i	$-0.347576\pi$
$347$	−1.44316	−	0.833209i	−0.0774729	−	0.0447290i	−0.538236	+	0.842794i	$0.680909\pi$
$348$	0.719599	+	0.313557i	0.0385745	+	0.0168084i
$349$		−	27.6081i		−	1.47783i	−0.673801	−	0.738913i	$-0.735339\pi$
$349$		−	27.6081i		−	1.47783i	0.673801	−	0.738913i	$-0.264661\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	10.9475	+	18.1203i	0.583503	+	0.965815i
$353$	−23.5193	−	13.5789i	−1.25180	−	0.722730i	−0.280337	−	0.959902i	$-0.590446\pi$
$353$	−23.5193	−	13.5789i	−1.25180	−	0.722730i	−0.971468	+	0.237172i	$0.923779\pi$
$354$	−0.902540	+	4.33067i	−0.0479695	+	0.230173i
$355$	4.98385	+	8.63229i	0.264516	+	0.458154i
$356$	11.7415	+	15.8936i	0.622300	+	0.842360i
$357$		0			0
$358$	7.12154	+	21.6251i	0.376385	+	1.14292i
$359$	14.5102	−	8.37747i	0.765819	−	0.442146i	−0.0655619	−	0.997849i	$-0.520884\pi$
$359$	14.5102	−	8.37747i	0.765819	−	0.442146i	0.831381	+	0.555703i	$0.187551\pi$
$360$	−5.62238	+	2.58400i	−0.296325	+	0.136189i
$361$	−9.47002	+	16.4026i	−0.498422	+	0.863293i
$362$	−3.76200	+	4.21166i	−0.197726	+	0.221360i
$363$	−2.70926			−0.142199
$364$		0			0
$365$	−9.79892			−0.512899
$366$	−8.82018	+	9.87444i	−0.461038	+	0.516145i
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	−0.954927	−	0.296839i	$-0.904067\pi$
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	0.734534	+	0.678572i	$0.237401\pi$
$368$	12.6330	−	11.7437i	0.658540	−	0.612184i
$369$	−13.9266	+	8.04054i	−0.724991	+	0.418574i
$370$	4.99899	+	15.1798i	0.259885	+	0.789158i
$371$		0			0
$372$	−3.68062	+	2.71908i	−0.190831	+	0.140978i
$373$	5.18861	+	8.98694i	0.268656	+	0.465326i	0.968515	−	0.248955i	$-0.0800871\pi$
$373$	5.18861	+	8.98694i	0.268656	+	0.465326i	−0.699859	+	0.714281i	$0.746754\pi$
$374$	0.630311	−	3.02443i	0.0325926	−	0.156390i
$375$	0.780530	+	0.450639i	0.0403064	+	0.0232709i
$376$	32.6025	+	3.03414i	1.68134	+	0.156474i
$377$		−	1.05378i		−	0.0542723i
$378$		0			0
$379$			11.7976i			0.606002i	0.952990	+	0.303001i	$0.0979886\pi$
$379$			11.7976i			0.606002i	−0.952990	+	0.303001i	$0.902011\pi$
$380$	−4.92102	+	11.2935i	−0.252443	+	0.579346i
$381$	3.83268	+	2.21280i	0.196354	+	0.113365i
$382$	27.7586	+	5.78507i	1.42025	+	0.295990i
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	0.877992	−	0.478675i	$-0.158883\pi$
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	−0.853541	+	0.521026i	$0.825549\pi$
$384$	6.22067	+	8.07948i	0.317447	+	0.412304i
$385$		0			0
$386$	−25.9773	+	8.55483i	−1.32221	+	0.435430i
$387$	10.9905	−	6.34537i	0.558679	−	0.322553i
$388$	−9.02330	+	1.02096i	−0.458088	+	0.0518314i
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	−0.175722	−	0.984440i	$-0.556226\pi$
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	0.940411	−	0.340041i	$-0.110441\pi$
$390$	−2.30035	−	2.05475i	−0.116483	−	0.104046i
$391$	−2.51705			−0.127293
$392$		0			0
$393$	−14.3073			−0.721708
$394$	−1.72697	−	1.54259i	−0.0870037	−	0.0777147i
$395$	−0.229525	+	0.397549i	−0.0115487	+	0.0200029i
$396$	16.2709	−	1.84101i	0.817645	−	0.0925142i
$397$	5.37540	−	3.10349i	0.269783	−	0.155760i	−0.359006	−	0.933335i	$-0.616884\pi$
$397$	5.37540	−	3.10349i	0.269783	−	0.155760i	0.628789	+	0.777576i	$0.283551\pi$
$398$	−1.05212	+	0.346483i	−0.0527380	+	0.0173676i
$399$		0			0
$400$	−1.17544	+	3.82339i	−0.0587720	+	0.191170i
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	−0.981387	−	0.192038i	$-0.938490\pi$
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	0.324384	−	0.945926i	$-0.394843\pi$
$402$	−12.2845	−	2.56017i	−0.612694	−	0.127689i
$403$	5.32025	+	3.07165i	0.265020	+	0.153010i
$404$	7.30571	−	16.7663i	0.363473	−	0.834153i
$405$			2.34912i			0.116728i
$406$		0			0
$407$		−	42.2927i		−	2.09637i
$408$	0.137886	−	1.48161i	0.00682637	−	0.0733508i
$409$	15.9374	+	9.20148i	0.788055	+	0.454984i	0.839277	−	0.543703i	$-0.182978\pi$
$409$	15.9374	+	9.20148i	0.788055	+	0.454984i	−0.0512223	+	0.998687i	$0.516312\pi$
$410$	−2.12091	+	10.1768i	−0.104744	+	0.502595i
$411$	3.53400	+	6.12107i	0.174320	+	0.301930i
$412$	−16.4595	+	12.1596i	−0.810902	+	0.599060i
$413$		0			0
$414$	−4.17302	−	12.6716i	−0.205093	−	0.622777i
$415$	2.24947	−	1.29873i	0.110422	−	0.0637523i
$416$	6.60762	−	11.9887i	0.323965	−	0.587795i
$417$	−7.84312	+	13.5847i	−0.384079	+	0.665245i
$418$	21.7174	−	24.3132i	1.06223	−	1.18920i
$419$	−35.2426			−1.72171			−0.860856	−	0.508848i	$-0.830072\pi$
$419$	−35.2426			−1.72171			−0.860856	+	0.508848i	$0.830072\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−8.69128	+	9.73014i	−0.423085	+	0.473656i
$423$	12.6630	−	21.9329i	0.615695	−	1.06641i
$424$	3.67917	+	8.00531i	0.178676	+	0.388772i
$425$	0.505515	−	0.291859i	0.0245211	−	0.0141573i
$426$	−3.97400	−	12.0673i	−0.192541	−	0.584664i
$427$		0			0
$428$	−7.52492	−	10.1859i	−0.363731	−	0.492355i
$429$	4.08117	+	7.06879i	0.197041	+	0.341284i
$430$	1.67376	−	8.03123i	0.0807159	−	0.387300i
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	0.457589	−	0.889164i	$-0.348713\pi$
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	−0.541244	+	0.840865i	$0.682047\pi$
$432$	18.2294	−	4.17871i	0.877064	−	0.201048i
$433$			13.5978i			0.653469i	0.945116	+	0.326734i	$0.105948\pi$
$433$			13.5978i			0.653469i	−0.945116	+	0.326734i	$0.894052\pi$
$434$		0			0
$435$		−	0.392473i		−	0.0188176i
$436$	34.3974	+	14.9883i	1.64734	+	0.717809i
$437$	−23.0022	−	13.2803i	−1.10034	−	0.635283i
$438$	12.2270	+	2.54818i	0.584228	+	0.121757i
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	0.970776	+	0.239989i	$0.0771437\pi$
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	−0.277552	+	0.960711i	$0.589523\pi$
$440$	6.11933	−	8.63724i	0.291728	−	0.411764i
$441$		0			0
$442$	−1.89740	+	0.624849i	−0.0902500	+	0.0297211i
$443$	12.6757	−	7.31831i	0.602240	−	0.347703i	−0.167683	−	0.985841i	$-0.553628\pi$
$443$	12.6757	−	7.31831i	0.602240	−	0.347703i	0.769922	+	0.638138i	$0.220295\pi$
$444$	−2.29023	−	20.2411i	−0.108689	−	0.960601i
$445$	4.94008	−	8.55647i	0.234182	−	0.405616i
$446$	−25.5643	−	22.8349i	−1.21050	−	1.08126i
$447$	1.48851			0.0704040
$448$		0			0
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$	2.30740	+	2.06105i	0.108772	+	0.0971589i
$451$	13.7548	−	23.8241i	0.647689	−	1.12183i
$452$	0.939568	+	8.30395i	0.0441936	+	0.390585i
$453$	−5.74168	+	3.31496i	−0.269768	+	0.155750i
$454$	−14.2820	+	4.70335i	−0.670290	+	0.220739i
$455$		0			0
$456$	9.07725	−	12.8122i	0.425081	−	0.599989i
$457$	3.80306	+	6.58709i	0.177900	+	0.308131i	0.941161	−	0.337959i	$-0.109736\pi$
$457$	3.80306	+	6.58709i	0.177900	+	0.308131i	−0.763261	+	0.646090i	$0.776403\pi$
$458$	40.8596	+	8.51539i	1.90924	+	0.397898i
$459$	−2.36357	−	1.36461i	−0.110322	−	0.0636943i
$460$	−7.90623	−	3.44505i	−0.368630	−	0.160626i
$461$			12.7953i			0.595936i	0.954576	+	0.297968i	$0.0963089\pi$
$461$			12.7953i			0.595936i	−0.954576	+	0.297968i	$0.903691\pi$
$462$		0			0
$463$		−	27.9178i		−	1.29745i	−0.761024	−	0.648724i	$-0.775303\pi$
$463$		−	27.9178i		−	1.29745i	0.761024	−	0.648724i	$-0.224697\pi$
$464$	1.69782	−	0.389188i	0.0788191	−	0.0180676i
$465$	1.98149	+	1.14402i	0.0918895	+	0.0530524i
$466$	8.09917	−	38.8624i	0.375187	−	1.80026i
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	−0.999637	−	0.0269432i	$-0.991423\pi$
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	0.476485	−	0.879183i	$-0.341911\pi$
$468$	−6.29138	−	8.51617i	−0.290819	−	0.393660i
$469$		0			0
$470$	−5.12097	−	15.5502i	−0.236213	−	0.717276i
$471$	−2.40599	+	1.38910i	−0.110862	+	0.0640062i
$472$	4.09938	+	8.91963i	0.188689	+	0.410559i
$473$	−10.8549	+	18.8013i	−0.499110	+	0.864484i
$474$	0.389781	−	0.436371i	0.0179032	−	0.0200432i
$475$	6.15955			0.282620
$476$		0			0
$477$	6.81448			0.312014
$478$	−12.8389	+	14.3735i	−0.587239	+	0.657430i
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	0.497817	+	0.867282i	$0.334135\pi$
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	−0.999997	+	0.00251901i	$0.999198\pi$
$480$	2.46097	−	4.46512i	0.112327	−	0.203804i
$481$	−23.6830	+	13.6734i	−1.07985	+	0.623453i
$482$	1.86118	+	5.65160i	0.0847744	+	0.257423i
$483$		0			0
$484$	−4.83560	+	3.57234i	−0.219800	+	0.162379i
$485$	2.27022	+	3.93213i	0.103085	+	0.178549i
$486$	4.65802	−	22.3507i	0.211292	−	1.01385i
$487$	−21.9822	−	12.6914i	−0.996108	−	0.575103i	−0.0890138	−	0.996030i	$-0.528372\pi$
$487$	−21.9822	−	12.6914i	−0.996108	−	0.575103i	−0.907095	+	0.420927i	$0.861705\pi$
$488$	−2.72254	+	29.2543i	−0.123244	+	1.32428i
$489$			4.07212i			0.184147i
$490$		0			0
$491$		−	36.4635i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$491$		−	36.4635i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$492$	5.29289	−	12.1469i	0.238622	−	0.547627i
$493$	−0.220133	−	0.127094i	−0.00991429	−	0.00572402i
$494$	−20.6362	−	4.30072i	−0.928467	−	0.193498i
$495$	−4.09369	−	7.09048i	−0.183998	−	0.318693i
$496$	−2.98403	+	9.70626i	−0.133987	+	0.435824i
$497$		0			0
$498$	−3.14460	+	1.03558i	−0.140913	+	0.0464053i
$499$	−10.2874	+	5.93945i	−0.460528	+	0.265886i	−0.712266	−	0.701909i	$-0.752331\pi$
$499$	−10.2874	+	5.93945i	−0.460528	+	0.265886i	0.251738	+	0.967795i	$0.418998\pi$
$500$	1.98732	−	0.224860i	0.0888756	−	0.0100560i
$501$	−7.63194	+	13.2189i	−0.340970	+	0.590577i
$502$	19.9158	+	17.7894i	0.888884	+	0.793981i
$503$	17.3055			0.771614			0.385807	−	0.922580i	$-0.373923\pi$
$503$	17.3055			0.771614			0.385807	+	0.922580i	$0.373923\pi$
$504$		0			0
$505$	−9.14442			−0.406921
$506$	17.0209	+	15.2036i	0.756672	+	0.675884i
$507$	−3.21939	+	5.57615i	−0.142978	+	0.247646i
$508$	9.75846	−	1.10414i	0.432962	−	0.0489884i
$509$	11.8717	−	6.85414i	0.526205	−	0.303805i	−0.213265	−	0.976994i	$-0.568410\pi$
$509$	11.8717	−	6.85414i	0.526205	−	0.303805i	0.739470	+	0.673190i	$0.235076\pi$
$510$	−0.706674	+	0.232721i	−0.0312921	+	0.0103051i
$511$		0			0
$512$	21.7562	+	6.21824i	0.961498	+	0.274810i
$513$	−14.3997	−	24.9410i	−0.635761	−	1.10117i
$514$	−35.7671	−	7.45408i	−1.57762	−	0.328785i
$515$	8.86113	+	5.11597i	0.390468	+	0.225437i
$516$	−4.17700	+	9.58603i	−0.183882	+	0.422002i
$517$			43.3247i			1.90542i
$518$		0			0
$519$		−	0.119597i		−	0.00524973i
$520$	−6.81507	−	0.634243i	−0.298861	−	0.0278134i
$521$	−31.4817	−	18.1760i	−1.37924	−	0.796304i	−0.387171	−	0.922008i	$-0.626548\pi$
$521$	−31.4817	−	18.1760i	−1.37924	−	0.796304i	−0.992068	+	0.125704i	$0.959881\pi$
$522$	0.274873	−	1.31893i	0.0120309	−	0.0577279i
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	0.815638	−	0.578562i	$-0.196386\pi$
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	−0.908869	+	0.417082i	$0.863053\pi$
$524$	−25.5363	+	18.8651i	−1.11556	+	0.824126i
$525$		0			0
$526$	−4.73196	−	14.3689i	−0.206323	−	0.626515i
$527$	1.28333	−	0.740929i	0.0559026	−	0.0322754i
$528$	−9.88173	+	9.18614i	−0.430047	+	0.399776i
$529$	−2.20289	+	3.81552i	−0.0957778	+	0.165892i
$530$	2.93459	−	3.28535i	0.127470	−	0.142707i
$531$	7.59279			0.329499
$532$		0			0
$533$	−17.7879			−0.770482
$534$	−8.38927	+	9.39203i	−0.363039	+	0.406433i
$535$	−3.16601	+	5.48368i	−0.136878	+	0.237080i
$536$	−25.3016	+	11.6284i	−1.09286	+	0.502270i
$537$	−12.5658	+	7.25487i	−0.542254	+	0.313071i
$538$	3.70038	+	11.2364i	0.159535	+	0.484438i
$539$		0			0
$540$	−5.55640	−	7.52129i	−0.239110	−	0.323665i
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	0.928870	−	0.370405i	$-0.120781\pi$
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	−0.785215	+	0.619223i	$0.787448\pi$
$542$	7.82248	−	37.5347i	0.336004	−	1.61225i
$543$	−3.11679	−	1.79948i	−0.133754	−	0.0772229i
$544$	−1.70750	−	2.82626i	−0.0732084	−	0.121175i
$545$		−	18.7605i		−	0.803614i
$546$		0			0
$547$			45.6888i			1.95351i	0.214353	+	0.976756i	$0.431236\pi$
$547$			45.6888i			1.95351i	−0.214353	+	0.976756i	$0.568764\pi$
$548$	14.3787	+	6.26534i	0.614226	+	0.267642i
$549$	19.6805	+	11.3625i	0.839942	+	0.484941i
$550$	−5.18132	−	1.07982i	−0.220932	−	0.0460436i
$551$	−1.34113	−	2.32290i	−0.0571339	−	0.0989589i
$552$	8.96944	+	6.35469i	0.381765	+	0.270474i
$553$		0			0
$554$	−4.51309	+	1.48625i	−0.191743	+	0.0631445i
$555$	−8.82059	+	5.09257i	−0.374413	+	0.216168i
$556$	3.91355	+	34.5882i	0.165972	+	1.46687i
$557$	−2.44203	+	4.22972i	−0.103472	+	0.179219i	−0.913113	−	0.407707i	$-0.866329\pi$
$557$	−2.44203	+	4.22972i	−0.103472	+	0.179219i	0.809641	+	0.586926i	$0.199662\pi$
$558$	5.85769	+	5.23229i	0.247976	+	0.221500i
$559$	14.0378			0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	−7.74107	−	6.91459i	−0.326538	−	0.291674i
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	−0.893410	−	0.449241i	$-0.851694\pi$
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	0.835760	+	0.549096i	$0.185028\pi$
$564$	2.34611	+	20.7350i	0.0987891	+	0.873103i
$565$	3.61866	−	2.08923i	0.152238	−	0.0878947i
$566$	9.67897	−	3.18747i	0.406838	−	0.133979i
$567$		0			0
$568$	−23.0045	−	16.2983i	−0.965248	−	0.683861i
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	0.813860	−	0.581062i	$-0.197362\pi$
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	−0.910144	+	0.414292i	$0.864029\pi$
$570$	−7.68582	−	1.60177i	−0.321924	−	0.0670910i
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	0.394720	−	0.918801i	$-0.370841\pi$
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	−0.598345	+	0.801239i	$0.704175\pi$
$572$	16.6049	+	7.23539i	0.694286	+	0.302527i
$573$			18.0707i			0.754912i
$574$		0			0
$575$			4.31210i			0.179827i
$576$	11.3974	−	13.2817i	0.474892	−	0.553405i
$577$	29.7446	+	17.1731i	1.23828	+	0.714924i	0.968743	−	0.248065i	$-0.0797948\pi$
$577$	29.7446	+	17.1731i	1.23828	+	0.714924i	0.269541	+	0.962989i	$0.413128\pi$
$578$	4.80673	−	23.0642i	0.199934	−	0.959345i
$579$	−8.71499	−	15.0948i	−0.362182	−	0.627318i
$580$	−0.517501	−	0.700502i	−0.0214881	−	0.0290868i
$581$		0			0
$582$	−1.81021	−	5.49684i	−0.0750358	−	0.227851i
$583$	−10.0956	+	5.82872i	−0.418118	+	0.241401i
$584$	25.1832	−	11.5740i	1.04209	−	0.478935i
$585$	−2.64701	+	4.58475i	−0.109440	+	0.189556i
$586$	−7.98795	+	8.94273i	−0.329979	+	0.369421i
$587$	−40.1422			−1.65685			−0.828423	−	0.560103i	$-0.810762\pi$
$587$	−40.1422			−1.65685			−0.828423	+	0.560103i	$0.810762\pi$
$588$		0			0
$589$	15.6369			0.644309
$590$	3.26976	−	3.66058i	0.134614	−	0.150704i
$591$	0.737868	−	1.27802i	0.0303518	−	0.0525709i
$592$	−30.7769	−	33.1074i	−1.26492	−	1.36071i
$593$	−9.46884	+	5.46684i	−0.388839	+	0.224496i	−0.681657	−	0.731672i	$-0.738740\pi$
$593$	−9.46884	+	5.46684i	−0.388839	+	0.224496i	0.292818	+	0.956168i	$0.405407\pi$
$594$	7.74042	+	23.5043i	0.317593	+	0.964394i
$595$		0			0
$596$	2.65675	−	1.96269i	0.108825	−	0.0803951i
$597$	−0.352969	−	0.611361i	−0.0144461	−	0.0250213i
$598$	3.01079	−	14.4467i	0.123120	−	0.590771i
$599$	−4.51466	−	2.60654i	−0.184464	−	0.106500i	0.404924	−	0.914350i	$-0.367298\pi$
$599$	−4.51466	−	2.60654i	−0.184464	−	0.106500i	−0.589388	+	0.807850i	$0.700631\pi$
$600$	−2.53823	−	0.236220i	−0.103623	−	0.00964363i
$601$		−	16.1103i		−	0.657154i	−0.944477	−	0.328577i	$-0.893431\pi$
$601$		−	16.1103i		−	0.657154i	0.944477	−	0.328577i	$-0.106569\pi$
$602$		0			0
$603$			21.5379i			0.877090i
$604$	−5.87700	+	13.4875i	−0.239132	+	0.548797i
$605$	2.60329	+	1.50301i	0.105839	+	0.0611060i
$606$	11.4103	+	2.37798i	0.463512	+	0.0965989i
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	0.947217	−	0.320593i	$-0.103882\pi$
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	−0.751250	+	0.660017i	$0.770549\pi$
$608$	−0.692317	−	34.8368i	−0.0280772	−	1.41282i
$609$		0			0
$610$	13.9532	−	4.59506i	0.564949	−	0.186048i
$611$	24.2609	−	14.0070i	0.981491	−	0.566664i
$612$	−2.53781	+	0.287146i	−0.102585	+	0.0116072i
$613$	−3.92388	+	6.79635i	−0.158484	+	0.274502i	−0.934322	−	0.356430i	$-0.883994\pi$
$613$	−3.92388	+	6.79635i	−0.158484	+	0.274502i	0.775838	+	0.630932i	$0.217327\pi$
$614$	−10.9976	−	9.82343i	−0.443827	−	0.396441i
$615$	−6.62501			−0.267146
$616$		0			0
$617$	−28.8434			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$617$	−28.8434			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$618$	−9.72643	−	8.68797i	−0.391254	−	0.349481i
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	−0.839968	−	0.542635i	$-0.817427\pi$
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	0.889920	+	0.456116i	$0.150760\pi$
$620$	5.04511	−	0.570840i	0.202617	−	0.0229255i
$621$	17.4604	−	10.0807i	0.700660	−	0.404526i
$622$	10.6465	−	3.50609i	0.426885	−	0.140581i
$623$		0			0
$624$	8.33885	+	2.56364i	0.333821	+	0.102628i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−20.0286	−	4.17409i	−0.800504	−	0.166830i
$627$	17.9927	+	10.3881i	0.718558	+	0.414860i
$628$	−2.46269	+	5.65177i	−0.0982722	+	0.225530i
$629$			6.59647i			0.263019i
$630$		0			0
$631$			8.90728i			0.354593i	0.984157	+	0.177297i	$0.0567352\pi$
$631$			8.90728i			0.354593i	−0.984157	+	0.177297i	$0.943265\pi$
$632$	0.120314	−	1.29280i	0.00478585	−	0.0514250i
$633$	−7.20066	−	4.15730i	−0.286200	−	0.165238i
$634$	1.02055	−	4.89694i	0.0405314	−	0.194482i
$635$	−2.45518	−	4.25250i	−0.0974309	−	0.168755i
$636$	−4.51609	+	3.33630i	−0.179075	+	0.132293i
$637$		0			0
$638$	0.720911	+	2.18910i	0.0285412	+	0.0866672i
$639$	−18.8848	+	10.9032i	−0.747073	+	0.431323i
$640$	−1.49512	−	11.2145i	−0.0590996	−	0.443291i
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	−0.973568	−	0.228398i	$-0.926651\pi$
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	0.684583	+	0.728935i	$0.259984\pi$
$642$	5.37653	−	6.01917i	0.212195	−	0.237558i
$643$	24.2513			0.956380			0.478190	−	0.878256i	$-0.341293\pi$
$643$	24.2513			0.956380			0.478190	+	0.878256i	$0.341293\pi$
$644$		0			0
$645$	5.22827			0.205863
$646$	−3.38730	+	3.79218i	−0.133272	+	0.149201i
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	−0.406435	−	0.913680i	$-0.633228\pi$
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	0.994487	−	0.104857i	$-0.0334386\pi$
$648$	−2.77465	−	6.03722i	−0.108999	−	0.237164i
$649$	−11.2487	+	6.49444i	−0.441550	+	0.254929i
$650$	1.07046	+	3.25054i	0.0419870	+	0.127496i
$651$		0			0
$652$	5.36935	+	7.26808i	0.210280	+	0.284640i
$653$	7.78155	+	13.4780i	0.304516	+	0.527436i	0.977153	−	0.212535i	$-0.0681721\pi$
$653$	7.78155	+	13.4780i	0.304516	+	0.527436i	−0.672638	+	0.739972i	$0.734839\pi$
$654$	−4.87863	+	23.4092i	−0.190770	+	0.915373i
$655$	13.7477	+	7.93723i	0.537167	+	0.310133i
$656$	−6.56957	−	28.6594i	−0.256498	−	1.11896i
$657$		−	21.4371i		−	0.836340i
$658$		0			0
$659$		−	30.2702i		−	1.17916i	−0.807710	−	0.589580i	$-0.799293\pi$
$659$		−	30.2702i		−	1.17916i	0.807710	−	0.589580i	$-0.200707\pi$
$660$	6.18439	+	2.69478i	0.240727	+	0.104894i
$661$	−15.5209	−	8.96099i	−0.603693	−	0.348542i	0.166800	−	0.985991i	$-0.446656\pi$
$661$	−15.5209	−	8.96099i	−0.603693	−	0.348542i	−0.770493	+	0.637449i	$0.779990\pi$
$662$	−32.5761	−	6.78907i	−1.26611	−	0.263865i
$663$	−0.636547	−	1.10253i	−0.0247214	−	0.0428188i
$664$	−4.24714	+	5.99470i	−0.164821	+	0.232640i
$665$		0			0
$666$	−33.2087	+	10.9363i	−1.28681	+	0.423772i
$667$	1.62619	−	0.938880i	0.0629662	−	0.0363536i
$668$	3.80818	+	33.6569i	0.147343	+	1.30222i
$669$	10.9226	−	18.9185i	0.422292	−	0.731432i
$670$	10.3837	+	9.27506i	0.401157	+	0.358327i
$671$	−38.8754			−1.50077
$672$		0			0
$673$	21.1876			0.816723			0.408362	−	0.912820i	$-0.366100\pi$
$673$	21.1876			0.816723			0.408362	+	0.912820i	$0.366100\pi$
$674$	5.37966	+	4.80529i	0.207217	+	0.185093i
$675$	−2.33778	+	4.04915i	−0.0899812	+	0.155852i
$676$	1.60641	+	14.1975i	0.0617850	+	0.546059i
$677$	21.8732	−	12.6285i	0.840657	−	0.485353i	−0.0168308	−	0.999858i	$-0.505358\pi$
$677$	21.8732	−	12.6285i	0.840657	−	0.485353i	0.857487	+	0.514505i	$0.172024\pi$
$678$	−5.05863	+	1.66590i	−0.194275	+	0.0639786i
$679$		0			0
$680$	−0.954444	+	1.34717i	−0.0366012	+	0.0516615i
$681$	−4.79140	−	8.29895i	−0.183607	−	0.318016i
$682$	−13.1536	−	2.74128i	−0.503676	−	0.104969i
$683$	19.1391	+	11.0499i	0.732336	+	0.422814i	0.819276	−	0.573399i	$-0.194376\pi$
$683$	19.1391	+	11.0499i	0.732336	+	0.422814i	−0.0869404	+	0.996214i	$0.527709\pi$
$684$	−24.7068	−	10.7657i	−0.944689	−	0.411637i
$685$		−	7.84221i		−	0.299635i
$686$		0			0
$687$			26.5993i			1.01483i
$688$	5.18452	+	22.6172i	0.197658	+	0.862273i
$689$	6.52791	+	3.76889i	0.248694	+	0.143583i
$690$	1.12135	−	5.38060i	0.0426891	−	0.204836i
$691$	−9.05508	−	15.6839i	−0.344471	−	0.596642i	0.640786	−	0.767719i	$-0.278609\pi$
$691$	−9.05508	−	15.6839i	−0.344471	−	0.596642i	−0.985258	+	0.171077i	$0.945275\pi$
$692$	−0.157697	−	0.213462i	−0.00599473	−	0.00811461i
$693$		0			0
$694$	−0.737153	−	2.23841i	−0.0279819	−	0.0849691i
$695$	15.0727	−	8.70222i	0.571740	−	0.330094i
$696$	0.463569	+	1.00865i	0.0175715	+	0.0382330i
$697$	−2.14537	+	3.71588i	−0.0812615	+	0.140749i
$698$	26.0098	−	29.1187i	0.984486	−	1.10216i
$699$	25.2991			0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	10.6594	−	11.9335i	0.402313	−	0.450401i
$703$	−34.8038	+	60.2820i	−1.31265	+	2.27358i
$704$	−5.52481	+	29.4255i	−0.208224	+	1.10902i
$705$	9.03582	−	5.21684i	0.340309	−	0.196477i
$706$	−12.0134	−	36.4796i	−0.452131	−	1.37293i
$707$		0			0
$708$	−5.03189	+	3.71735i	−0.189110	+	0.139706i
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	0.970088	+	0.242753i	$0.0780505\pi$
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	−0.274814	+	0.961498i	$0.588616\pi$
$710$	−2.87600	+	13.8000i	−0.107934	+	0.517904i
$711$	−0.869718	−	0.502132i	−0.0326170	−	0.0188314i
$712$	−2.58953	+	27.8251i	−0.0970469	+	1.04279i
$713$			10.9469i			0.409965i
$714$		0			0
$715$		−	9.05640i		−	0.338690i
$716$	−12.8620	+	29.5176i	−0.480674	+	1.10312i
$717$	−10.6369	−	6.14124i	−0.397244	−	0.229349i
$718$	23.1967	+	4.83433i	0.865692	+	0.180416i
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	0.990561	−	0.137072i	$-0.0437692\pi$
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	−0.613988	+	0.789315i	$0.710436\pi$
$720$	−8.36443	−	2.57151i	−0.311724	−	0.0958345i
$721$		0			0
$722$	−25.4412	+	8.37828i	−0.946824	+	0.311807i
$723$	−3.28401	+	1.89602i	−0.122134	+	0.0705138i
$724$	−7.93570	+	0.897902i	−0.294928	+	0.0333703i
$725$	−0.217731	+	0.377122i	−0.00808634	+	0.0140060i
$726$	−2.85750	−	2.55242i	−0.106052	−	0.0947292i
$727$	−10.7925			−0.400272			−0.200136	−	0.979768i	$-0.564138\pi$
$727$	−10.7925			−0.400272			−0.200136	+	0.979768i	$0.564138\pi$
$728$		0			0
$729$	7.50278			0.277881
$730$	−10.3351	−	9.23166i	−0.382519	−	0.341679i
$731$	1.69306	−	2.93247i	0.0626202	−	0.108461i
$732$	−18.6056	+	2.10517i	−0.687683	+	0.0778094i
$733$	−6.26329	+	3.61611i	−0.231340	+	0.133564i	−0.611190	−	0.791484i	$-0.709309\pi$
$733$	−6.26329	+	3.61611i	−0.231340	+	0.133564i	0.379850	+	0.925048i	$0.375976\pi$
$734$	−11.3427	+	3.73538i	−0.418668	+	0.137875i
$735$		0			0
$736$	24.3881	−	0.484669i	0.898958	−	0.0178651i
$737$	−18.4223	−	31.9083i	−0.678593	−	1.17536i
$738$	−22.2637	−	4.63990i	−0.819539	−	0.170797i
$739$	1.71927	+	0.992622i	0.0632444	+	0.0365142i	0.531289	−	0.847191i	$-0.321708\pi$
$739$	1.71927	+	0.992622i	0.0632444	+	0.0365142i	−0.468044	+	0.883705i	$0.655041\pi$
$740$	−9.02848	+	20.7200i	−0.331893	+	0.761681i
$741$		−	13.4340i		−	0.493511i
$742$		0			0
$743$			19.8225i			0.727216i	0.931552	+	0.363608i	$0.118455\pi$
$743$			19.8225i			0.727216i	−0.931552	+	0.363608i	$0.881545\pi$
$744$	−6.44368	−	0.599680i	−0.236237	−	0.0219853i
$745$	−1.43029	−	0.825776i	−0.0524016	−	0.0302541i
$746$	−2.99416	+	14.3669i	−0.109624	+	0.526011i
$747$	2.84124	+	4.92116i	0.103955	+	0.180056i
$748$	3.51414	−	2.59610i	0.128490	−	0.0949228i
$749$		0			0
$750$	0.398687	+	1.21064i	0.0145580	+	0.0442064i
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	−0.829879	−	0.557944i	$-0.811590\pi$
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	0.0682545	+	0.997668i	$0.478257\pi$
$752$	31.5279	+	33.9153i	1.14971	+	1.23676i
$753$	−8.50921	+	14.7384i	−0.310093	+	0.537097i
$754$	0.992774	−	1.11144i	0.0361547	−	0.0404762i
$755$	7.35613			0.267717
$756$		0			0
$757$	34.8711			1.26741			0.633706	−	0.773574i	$-0.281533\pi$
$757$	34.8711			1.26741			0.633706	+	0.773574i	$0.281533\pi$
$758$	−11.1146	+	12.4431i	−0.403702	+	0.451955i
$759$	−7.27236	+	12.5961i	−0.263970	+	0.457209i
$760$	−15.8300	+	7.27534i	−0.574215	+	0.263904i
$761$	−7.76620	+	4.48382i	−0.281524	+	0.162538i	−0.634113	−	0.773240i	$-0.718635\pi$
$761$	−7.76620	+	4.48382i	−0.281524	+	0.162538i	0.352589	+	0.935778i	$0.385301\pi$
$762$	1.95770	+	5.94469i	0.0709200	+	0.215353i
$763$		0			0
$764$	23.8273	+	32.2533i	0.862043	+	1.16688i
$765$	0.638500	+	1.10591i	0.0230850	+	0.0399844i
$766$	−0.276138	+	1.32500i	−0.00997727	+	0.0478741i
$767$	7.27349	+	4.19935i	0.262631	+	0.151630i
$768$	−1.05071	+	14.3821i	−0.0379141	+	0.518970i
$769$		−	0.573577i		−	0.0206837i	−0.999947	−	0.0103419i	$-0.996708\pi$
$769$		−	0.573577i		−	0.0206837i	0.999947	−	0.0103419i	$-0.00329197\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	−35.4584	−	15.4506i	−1.27617	−	0.556078i
$773$	3.76591	+	2.17425i	0.135450	+	0.0782023i	0.566194	−	0.824272i	$-0.308415\pi$
$773$	3.76591	+	2.17425i	0.135450	+	0.0782023i	−0.430744	+	0.902474i	$0.641749\pi$
$774$	17.5699	+	3.66168i	0.631537	+	0.131616i
$775$	−1.26933	−	2.19854i	−0.0455955	−	0.0789738i
$776$	−10.4789	−	7.42411i	−0.376170	−	0.266510i
$777$		0			0
$778$	40.5179	−	13.3433i	1.45264	−	0.478381i
$779$	−39.2109	+	22.6384i	−1.40488	+	0.811107i
$780$	−0.490420	−	4.33436i	−0.0175599	−	0.155195i
$781$	18.6519	−	32.3060i	0.667417	−	1.15600i
$782$	−2.65478	−	2.37134i	−0.0949348	−	0.0847990i
$783$	2.03603			0.0727618
$784$		0			0
$785$	3.08251			0.110019
$786$	−15.0902	−	13.4790i	−0.538249	−	0.480782i
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	−0.615184	−	0.788384i	$-0.710918\pi$
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	0.990352	+	0.138573i	$0.0442516\pi$
$788$	−0.368181	−	3.25400i	−0.0131159	−	0.115919i
$789$	8.34944	−	4.82055i	0.297248	−	0.171616i
$790$	−0.616619	+	0.203065i	−0.0219383	+	0.00722471i
$791$		0			0
$792$	18.8957	+	13.3873i	0.671428	+	0.475695i
$793$	12.5686	+	21.7694i	0.446323	+	0.773054i
$794$	8.59335	+	1.79091i	0.304967	+	0.0635570i
$795$	2.43128	+	1.40370i	0.0862286	+	0.0497841i
$796$	−1.43611	−	0.625770i	−0.0509017	−	0.0221798i
$797$		−	14.7349i		−	0.521938i	−0.965347	−	0.260969i	$-0.915958\pi$
$797$		−	14.7349i		−	0.521938i	0.965347	−	0.260969i	$-0.0840420\pi$
$798$		0			0
$799$		−	6.75744i		−	0.239061i
$800$	−4.84181	+	2.92521i	−0.171184	+	0.103422i
$801$	18.7190	+	10.8074i	0.661403	+	0.381861i
$802$	7.59213	−	36.4295i	0.268087	−	1.28637i
$803$	18.3360	+	31.7590i	0.647065	+	1.12075i
$804$	−10.5447	−	14.2736i	−0.371883	−	0.503390i
$805$		0			0
$806$	2.71753	+	8.25198i	0.0957210	+	0.290663i
$807$	−6.52923	+	3.76965i	−0.229840	+	0.132698i
$808$	23.5011	−	10.8009i	0.826767	−	0.379975i
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	−0.710276	−	0.703923i	$-0.751430\pi$
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	0.964753	+	0.263156i	$0.0847632\pi$
$810$	−2.21312	+	2.47765i	−0.0777613	+	0.0870559i
$811$	18.5825			0.652521			0.326260	−	0.945280i	$-0.394211\pi$
$811$	18.5825			0.652521			0.326260	+	0.945280i	$0.394211\pi$
$812$		0			0
$813$	24.4348			0.856967
$814$	39.8444	−	44.6069i	1.39654	−	1.56347i
$815$	2.25908	−	3.91284i	0.0791321	−	0.137061i
$816$	1.54127	−	1.43278i	0.0539553	−	0.0501573i
$817$	30.9442	−	17.8656i	1.08260	−	0.625040i
$818$	8.14069	+	24.7198i	0.284633	+	0.864306i
$819$		0			0
$820$	−11.8246	+	8.73551i	−0.412933	+	0.305057i
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	0.972918	−	0.231149i	$-0.0742486\pi$
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	−0.686640	+	0.726997i	$0.740915\pi$
$822$	−2.03934	+	9.78542i	−0.0711303	+	0.341306i
$823$	−38.0161	−	21.9486i	−1.32516	−	0.765081i	−0.340612	−	0.940204i	$-0.610634\pi$
$823$	−38.0161	−	21.9486i	−1.32516	−	0.765081i	−0.984547	+	0.175123i	$0.943968\pi$
$824$	−28.8158	−	2.68173i	−1.00385	−	0.0934226i
$825$		−	3.37300i		−	0.117433i
$826$		0			0
$827$		−	8.10796i		−	0.281941i	−0.990014	−	0.140971i	$-0.954978\pi$
$827$		−	8.10796i		−	0.281941i	0.990014	−	0.140971i	$-0.0450224\pi$
$828$	7.53673	−	17.2964i	0.261919	−	0.601093i
$829$	36.5657	+	21.1112i	1.26998	+	0.733223i	0.974984	−	0.222276i	$-0.0713486\pi$
$829$	36.5657	+	21.1112i	1.26998	+	0.733223i	0.294995	+	0.955499i	$0.404682\pi$
$830$	3.59611	+	0.749452i	0.124823	+	0.0260138i
$831$	−1.51407	−	2.62245i	−0.0525225	−	0.0909716i
$832$	18.2639	−	6.41961i	0.633185	−	0.222560i
$833$		0			0
$834$	−21.0705	+	6.93893i	−0.729613	+	0.240275i
$835$	14.6668	−	8.46791i	0.507567	−	0.293044i
$836$	45.8114	−	5.18343i	1.58442	−	0.179273i
$837$	−5.93481	+	10.2794i	−0.205137	+	0.355308i
$838$	−37.1710	−	33.2024i	−1.28405	−	1.14696i
$839$	31.8404			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$839$	31.8404			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	−16.5242	−	14.7599i	−0.569460	−	0.508661i
$843$	3.30745	−	5.72868i	0.113915	−	0.197306i
$844$	−18.3337	+	2.07441i	−0.631072	+	0.0714040i
$845$	6.18694	−	3.57203i	0.212837	−	0.122882i
$846$	34.0191	−	11.2031i	1.16960	−	0.385171i
$847$		0			0
$848$	−3.66139	+	11.9095i	−0.125733	+	0.408975i
$849$	3.24714	+	5.62422i	0.111442	+	0.193023i
$850$	0.808139	+	0.168421i	0.0277190	+	0.00577681i
$851$	−42.2015	−	24.3650i	−1.44665	−	0.835223i
$852$	7.17729	−	16.4716i	0.245890	−	0.564306i
$853$			16.2023i			0.554755i	0.960761	+	0.277378i	$0.0894653\pi$
$853$			16.2023i			0.554755i	−0.960761	+	0.277378i	$0.910535\pi$
$854$		0			0
$855$			13.4752i			0.460843i
$856$	1.65958	−	17.8326i	0.0567234	−	0.609505i
$857$	−35.4659	−	20.4762i	−1.21149	−	0.699455i	−0.248407	−	0.968656i	$-0.579907\pi$
$857$	−35.4659	−	20.4762i	−1.21149	−	0.699455i	−0.963084	+	0.269201i	$0.913240\pi$
$858$	−2.35509	+	11.3005i	−0.0804015	+	0.385792i
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	0.950329	−	0.311246i	$-0.100746\pi$
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	−0.744711	+	0.667387i	$0.767413\pi$
$860$	9.33165	−	6.89382i	0.318206	−	0.235077i
$861$		0			0
$862$	−0.887107	−	2.69376i	−0.0302150	−	0.0917499i
$863$	−0.494372	+	0.285426i	−0.0168286	+	0.00971602i	−0.508391	−	0.861127i	$-0.669759\pi$
$863$	−0.494372	+	0.285426i	−0.0168286	+	0.00971602i	0.491562	+	0.870843i	$0.336426\pi$
$864$	23.1637	+	12.7668i	0.788045	+	0.434334i
$865$	−0.0663486	+	0.114919i	−0.00225592	+	0.00390737i
$866$	−12.8106	+	14.3418i	−0.435323	+	0.487356i
$867$	15.0146			0.509924
$868$		0			0
$869$	1.71798			0.0582784
$870$	0.369753	−	0.413948i	0.0125358	−	0.0140342i
$871$	−11.9120	+	20.6321i	−0.403622	+	0.699093i
$872$	22.1590	+	48.2146i	0.750398	+	1.63275i
$873$	−8.60232	+	4.96655i	−0.291144	+	0.168092i
$874$	−11.7493	−	35.6775i	−0.397426	−	1.20681i
$875$		0			0
$876$	10.4954	+	14.2068i	0.354605	+	0.480003i
$877$	−9.47193	−	16.4059i	−0.319844	−	0.553987i	0.660611	−	0.750728i	$-0.270297\pi$
$877$	−9.47193	−	16.4059i	−0.319844	−	0.553987i	−0.980455	+	0.196742i	$0.936964\pi$
$878$	−8.38165	+	40.2178i	−0.282867	+	1.35729i
$879$	−6.61794	−	3.82087i	−0.223218	−	0.128875i
$880$	14.5914	−	3.34477i	0.491876	−	0.112752i
$881$			35.7695i			1.20511i	0.798079	+	0.602553i	$0.205850\pi$
$881$			35.7695i			1.20511i	−0.798079	+	0.602553i	$0.794150\pi$
$882$		0			0
$883$			25.4594i			0.856776i	0.903595	+	0.428388i	$0.140918\pi$
$883$			25.4594i			0.856776i	−0.903595	+	0.428388i	$0.859082\pi$
$884$	−2.58990	−	1.12852i	−0.0871076	−	0.0379561i
$885$	2.70897	+	1.56402i	0.0910609	+	0.0525740i
$886$	20.2639	+	4.22313i	0.680779	+	0.141879i
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	0.941209	−	0.337826i	$-0.109692\pi$
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	−0.763170	+	0.646197i	$0.776358\pi$
$888$	16.6538	−	23.5063i	0.558865	−	0.788821i
$889$		0			0
$890$	13.2715	−	4.37057i	0.444863	−	0.146502i
$891$	7.61364	−	4.39574i	0.255067	−	0.147263i
$892$	−5.45015	−	48.1687i	−0.182485	−	1.61281i
$893$	35.6531	−	61.7530i	1.19309	−	2.06648i
$894$	1.56996	+	1.40234i	0.0525072	+	0.0469012i
$895$	16.0991			0.538132
$896$		0			0
$897$	9.40472			0.314014
$898$	−28.5511	−	25.5028i	−0.952763	−	0.851040i
$899$	−0.552744	+	0.957381i	−0.0184350	+	0.0319304i
$900$	0.491925	+	4.34765i	0.0163975	+	0.144922i
$901$	1.57463	−	0.909116i	0.0524587	−	0.0302870i
$902$	36.9523	−	12.1691i	1.23038	−	0.405187i
$903$		0			0
$904$	−6.83225	+	9.64350i	−0.227237	+	0.320738i
$905$	1.99658	+	3.45818i	0.0663687	+	0.114954i
$906$	−9.17891	−	1.91294i	−0.304949	−	0.0635533i
$907$	13.3054	+	7.68190i	0.441800	+	0.255073i	0.704361	−	0.709842i	$-0.251234\pi$
$907$	13.3054	+	7.68190i	0.441800	+	0.255073i	−0.262561	+	0.964915i	$0.584567\pi$
$908$	−19.4946	−	8.49454i	−0.646951	−	0.281901i
$909$		−	20.0052i		−	0.663531i
$910$		0			0
$911$			22.0734i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$911$			22.0734i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$912$	21.6445	−	4.96154i	0.716720	−	0.164293i
$913$	−8.41856	−	4.86046i	−0.278614	−	0.160858i
$914$	−2.19461	+	10.5304i	−0.0725911	+	0.348315i
$915$	4.68108	+	8.10787i	0.154752	+	0.268038i
$916$	35.0729	+	47.4755i	1.15884	+	1.56864i
$917$		0			0
$918$	−1.20729	−	3.66601i	−0.0398464	−	0.120996i
$919$	45.1598	−	26.0730i	1.48968	−	0.860069i	0.489753	−	0.871861i	$-0.337087\pi$
$919$	45.1598	−	26.0730i	1.48968	−	0.860069i	0.999930	+	0.0117923i	$0.00375369\pi$
$920$	−5.09323	−	11.0821i	−0.167919	−	0.365366i
$921$	4.69884	−	8.13863i	0.154832	−	0.268177i
$922$	−12.0546	+	13.4954i	−0.396996	+	0.444448i
$923$	−24.1209			−0.793949
$924$		0			0
$925$	11.3008			0.371567
$926$	26.3016	−	29.4454i	0.864323	−	0.967634i
$927$	−11.1922	+	19.3855i	−0.367600	+	0.636702i
$928$	2.15737	+	1.18904i	0.0708193	+	0.0390323i
$929$	−24.8707	+	14.3591i	−0.815982	+	0.471107i	−0.849029	−	0.528346i	$-0.822812\pi$
$929$	−24.8707	+	14.3591i	−0.815982	+	0.471107i	0.0330469	+	0.999454i	$0.489479\pi$
$930$	1.01213	+	3.07340i	0.0331890	+	0.100781i
$931$		0			0
$932$	45.1549	−	33.3585i	1.47910	−	1.09270i
$933$	3.57173	+	6.18641i	0.116933	+	0.202534i
$934$	6.52394	−	31.3039i	0.213470	−	1.02430i
$935$	−1.89187	−	1.09227i	−0.0618708	−	0.0357211i
$936$	1.38753	−	14.9093i	0.0453529	−	0.487326i
$937$		−	44.9045i		−	1.46697i	−0.679707	−	0.733484i	$-0.737893\pi$
$937$		−	44.9045i		−	1.46697i	0.679707	−	0.733484i	$-0.262107\pi$
$938$		0			0
$939$		−	13.0385i		−	0.425495i
$940$	9.24879	−	21.2256i	0.301662	−	0.692301i
$941$	−15.3727	−	8.87541i	−0.501134	−	0.289330i	0.228048	−	0.973650i	$-0.426766\pi$
$941$	−15.3727	−	8.87541i	−0.501134	−	0.289330i	−0.729182	+	0.684320i	$0.760099\pi$
$942$	−3.84632	−	0.801598i	−0.125320	−	0.0261175i
$943$	−15.8484	−	27.4503i	−0.516096	−	0.893905i
$944$	−4.07957	+	13.2698i	−0.132779	+	0.431894i
$945$		0			0
$946$	−29.1618	+	9.60352i	−0.948130	+	0.312237i
$947$	32.1100	−	18.5387i	1.04344	−	0.602428i	0.122631	−	0.992452i	$-0.460867\pi$
$947$	32.1100	−	18.5387i	1.04344	−	0.602428i	0.920804	+	0.390025i	$0.127533\pi$
$948$	0.822218	−	0.0930316i	0.0267044	−	0.00302153i
$949$	11.8562	−	20.5356i	0.384869	−	0.666613i
$950$	6.49659	+	5.80297i	0.210777	+	0.188273i
$951$	3.18787			0.103374
$952$		0			0
$953$	−28.5420			−0.924567			−0.462283	−	0.886732i	$-0.652970\pi$
$953$	−28.5420			−0.924567			−0.462283	+	0.886732i	$0.652970\pi$
$954$	7.18736	+	6.41999i	0.232699	+	0.207855i
$955$	10.0250	−	17.3638i	0.324402	−	0.561881i
$956$	−27.0829	+	3.06435i	−0.875923	+	0.0991082i
$957$	−1.27203	+	0.734408i	−0.0411189	+	0.0237400i
$958$	−29.5266	+	9.72368i	−0.953962	+	0.314158i
$959$		0			0
$960$	6.80226	−	2.39094i	0.219542	−	0.0771674i
$961$	12.2776	+	21.2655i	0.396052	+	0.685983i
$962$	−37.8607	−	7.89042i	−1.22068	−	0.254397i
$963$	−11.9966	−	6.92626i	−0.386586	−	0.223196i
$964$	−3.36141	+	7.71428i	−0.108264	+	0.248460i
$965$			19.3392i			0.622550i
$966$		0			0
$967$			5.33936i			0.171702i	0.996308	+	0.0858510i	$0.0273609\pi$
$967$			5.33936i			0.171702i	−0.996308	+	0.0858510i	$0.972639\pi$
$968$	−8.46573	−	0.787860i	−0.272099	−	0.0253228i
$969$	−2.80635	−	1.62025i	−0.0901530	−	0.0520498i
$970$	−1.31006	+	6.28608i	−0.0420635	+	0.201834i
$971$	5.49906	+	9.52465i	0.176473	+	0.305660i	0.940670	−	0.339323i	$-0.110198\pi$
$971$	5.49906	+	9.52465i	0.176473	+	0.305660i	−0.764197	+	0.644983i	$0.776864\pi$
$972$	25.9697	−	19.1853i	0.832978	−	0.615368i
$973$		0			0
$974$	−11.2283	−	34.0955i	−0.359778	−	1.09249i
$975$	−1.88881	+	1.09050i	−0.0604902	+	0.0349241i
$976$	−30.4323	+	28.2901i	−0.974113	+	0.905544i
$977$	15.7434	−	27.2684i	0.503676	−	0.872392i	−0.496315	−	0.868142i	$-0.665314\pi$
$977$	15.7434	−	27.2684i	0.503676	−	0.872392i	0.999991	−	0.00424979i	$-0.00135275\pi$
$978$	−3.83638	+	4.29493i	−0.122674	+	0.137337i
$979$	−36.9761			−1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	34.3526	−	38.4587i	1.09624	−	1.22727i
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	−0.447176	−	0.894446i	$-0.647570\pi$
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	0.998201	−	0.0599567i	$-0.0190963\pi$
$984$	17.0263	−	7.82512i	0.542777	−	0.249456i
$985$	−1.41801	+	0.818690i	−0.0451817	+	0.0260856i
$986$	−0.112442	−	0.341438i	−0.00358088	−	0.0108736i
$987$		0			0
$988$	−17.7136	−	23.9776i	−0.563545	−	0.762829i
$989$	12.5072	+	21.6630i	0.397704	+	0.688844i
$990$	2.36232	−	11.3352i	0.0750794	−	0.360255i
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.999707	+	0.0242247i	$0.00771173\pi$
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.520833	+	0.853659i	$0.325622\pi$
$992$	−12.2917	+	7.42608i	−0.390261	+	0.235778i
$993$		−	21.2068i		−	0.672978i
$994$		0			0
$995$			0.783264i			0.0248311i
$996$	−4.29229	−	1.87032i	−0.136007	−	0.0592632i
$997$	−13.2344	−	7.64087i	−0.419137	−	0.241989i	0.275571	−	0.961281i	$-0.411133\pi$
$997$	−13.2344	−	7.64087i	−0.419137	−	0.241989i	−0.694708	+	0.719292i	$0.744466\pi$
$998$	−16.4459	−	3.42744i	−0.520587	−	0.108494i
$999$	−26.4187	−	45.7586i	−0.835851	−	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.f.31.13		32
4.3	odd	2	inner	980.2.o.f.31.9		32
7.2	even	3		140.2.o.a.131.9	yes	32
7.3	odd	6		980.2.g.a.391.7		32
7.4	even	3		980.2.g.a.391.8		32
7.5	odd	6	inner	980.2.o.f.411.9		32
7.6	odd	2		140.2.o.a.31.13	yes	32
28.3	even	6		980.2.g.a.391.6		32
28.11	odd	6		980.2.g.a.391.5		32
28.19	even	6	inner	980.2.o.f.411.13		32
28.23	odd	6		140.2.o.a.131.13	yes	32
28.27	even	2		140.2.o.a.31.9	✓	32
35.2	odd	12		700.2.t.d.299.16		32
35.9	even	6		700.2.p.c.551.8		32
35.13	even	4		700.2.t.d.199.11		32
35.23	odd	12		700.2.t.c.299.1		32
35.27	even	4		700.2.t.c.199.6		32
35.34	odd	2		700.2.p.c.451.4		32
140.23	even	12		700.2.t.c.299.6		32
140.27	odd	4		700.2.t.c.199.1		32
140.79	odd	6		700.2.p.c.551.4		32
140.83	odd	4		700.2.t.d.199.16		32
140.107	even	12		700.2.t.d.299.11		32
140.139	even	2		700.2.p.c.451.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	28.27	even	2
140.2.o.a.31.13	yes	32	7.6	odd	2
140.2.o.a.131.9	yes	32	7.2	even	3
140.2.o.a.131.13	yes	32	28.23	odd	6
700.2.p.c.451.4		32	35.34	odd	2
700.2.p.c.451.8		32	140.139	even	2
700.2.p.c.551.4		32	140.79	odd	6
700.2.p.c.551.8		32	35.9	even	6
700.2.t.c.199.1		32	140.27	odd	4
700.2.t.c.199.6		32	35.27	even	4
700.2.t.c.299.1		32	35.23	odd	12
700.2.t.c.299.6		32	140.23	even	12
700.2.t.d.199.11		32	35.13	even	4
700.2.t.d.199.16		32	140.83	odd	4
700.2.t.d.299.11		32	140.107	even	12
700.2.t.d.299.16		32	35.2	odd	12
980.2.g.a.391.5		32	28.11	odd	6
980.2.g.a.391.6		32	28.3	even	6
980.2.g.a.391.7		32	7.3	odd	6
980.2.g.a.391.8		32	7.4	even	3
980.2.o.f.31.9		32	4.3	odd	2	inner
980.2.o.f.31.13		32	1.1	even	1	trivial
980.2.o.f.411.9		32	7.5	odd	6	inner
980.2.o.f.411.13		32	28.19	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05472 + 0.942109i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.21064 + 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(1.38447 + 0.288532i) q^{10} +(-3.24107 - 1.87123i) q^{11} +(-1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +0.901278i q^{15} +(-3.89888 + 0.893735i) q^{16} +(0.505515 + 0.291859i) q^{17} +(-0.631220 + 3.02880i) q^{18} +(3.07977 + 5.33433i) q^{19} +(1.18839 + 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} +(-3.73439 + 2.15605i) q^{23} +(-1.06454 - 2.31628i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.27981 + 2.55232i) q^{26} -4.67556 q^{27} -0.435463 q^{29} +(-0.849103 + 0.950594i) q^{30} +(1.26933 - 2.19854i) q^{31} +(-4.95421 - 2.73053i) q^{32} +(2.92110 - 1.68650i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(5.65039 + 9.78676i) q^{37} +(-1.77723 + 8.52769i) q^{38} +(-1.88881 - 1.09050i) q^{39} +(-0.262094 + 2.81626i) q^{40} +7.35068i q^{41} -5.80096i q^{43} +(2.98995 - 6.86180i) q^{44} +(1.89460 + 1.09385i) q^{45} +(-5.96996 - 1.24418i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 - 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} +(-0.455610 + 0.263046i) q^{51} +(-4.80912 + 0.544138i) q^{52} +(1.55746 - 2.69759i) q^{53} +(-4.93139 - 4.40489i) q^{54} -3.74246 q^{55} -5.55147 q^{57} +(-0.459290 - 0.410254i) q^{58} +(1.73534 - 3.00569i) q^{59} +(-1.79113 + 0.202661i) q^{60} +(8.99597 - 5.19383i) q^{61} +(3.41004 - 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} +(1.20995 + 2.09570i) q^{65} +(4.66981 + 0.973217i) q^{66} +(8.52602 + 4.92250i) q^{67} +(-0.466348 + 1.07025i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(-6.16112 - 0.573383i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-3.26063 + 15.6456i) q^{74} +(0.450639 + 0.780530i) q^{75} +(-9.90849 + 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} +(-0.397549 + 0.229525i) q^{79} +(-2.92966 + 2.72344i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(-6.92515 + 7.75290i) q^{82} +2.59747 q^{83} +0.583719 q^{85} +(5.46514 - 6.11837i) q^{86} +(0.196236 - 0.339892i) q^{87} +(9.61812 - 4.42040i) q^{88} +(8.55647 - 4.94008i) q^{89} +(0.967745 + 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} +(1.14402 + 1.98149i) q^{93} +(3.34020 - 16.0273i) q^{94} +(5.33433 + 3.07977i) q^{95} +(4.36382 - 2.63643i) q^{96} +4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + 30 q^{12} - 14 q^{16} - 8 q^{22} - 36 q^{24} + 16 q^{25} - 30 q^{26} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} + 60 q^{38} - 18 q^{44} - 12 q^{45} + 2 q^{46}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 + 30 * q^12 - 14 * q^16 - 8 * q^22 - 36 * q^24 + 16 * q^25 - 30 * q^26 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 + 60 * q^38 - 18 * q^44 - 12 * q^45 + 2 * q^46 + 4 * q^50 + 36 * q^52 - 8 * q^53 - 12 * q^54 + 48 * q^57 + 2 * q^58 + 14 * q^60 - 24 * q^61 + 4 * q^64 + 4 * q^65 - 24 * q^66 - 60 * q^68 + 4 * q^72 + 72 * q^73 + 38 * q^74 + 120 * q^78 - 36 * q^81 - 42 * q^82 + 28 * q^86 + 4 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^93 - 18 * q^94 + 60 * q^96

Introduction

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