LMFDB - Embedded newform 980.2.o.f.31.9

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			31.9
Character	$\chi$	$=$	980.31
Dual form			980.2.o.f.411.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.288532 + 1.38447i) q^{2} +(0.450639 - 0.780530i) q^{3} +(-1.83350 + 0.798926i) 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} +(0.942109 + 1.05472i) q^{10} +(3.24107 + 1.87123i) q^{11} +(-0.202661 + 1.79113i) q^{12} +2.41990i q^{13} -0.901278i q^{15} +(2.72344 - 2.92966i) q^{16} +(0.505515 + 0.291859i) q^{17} +(-2.30740 + 2.06105i) 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} +(-2.53823 + 0.236220i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.35028 + 0.698219i) q^{26} +4.67556 q^{27} -0.435463 q^{29} +(1.24779 - 0.260047i) q^{30} +(-1.26933 + 2.19854i) q^{31} +(4.84181 + 2.92521i) 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} +(6.49659 - 5.80297i) q^{38} +(1.88881 + 1.09050i) q^{39} +(-2.57000 - 1.18115i) q^{40} +7.35068i q^{41} +5.80096i q^{43} +(-7.43747 - 0.841528i) q^{44} +(1.89460 + 1.09385i) q^{45} +(4.06247 + 4.54805i) 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} +(-1.93332 - 4.43689i) q^{52} +(1.55746 - 2.69759i) q^{53} +(1.34905 + 6.47316i) q^{54} +3.74246 q^{55} -5.55147 q^{57} +(-0.125645 - 0.602884i) q^{58} +(-1.73534 + 3.00569i) q^{59} +(0.720054 + 1.65249i) 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} +(3.17773 + 3.55756i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(-1.16004 - 0.131255i) q^{68} -3.88640i q^{69} -9.96771i q^{71} +(2.58400 - 5.62238i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-11.9191 + 10.6466i) 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} +(0.893735 - 3.89888i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(-10.1768 + 2.12091i) q^{82} -2.59747 q^{83} +0.583719 q^{85} +(-8.03123 + 1.67376i) q^{86} +(-0.196236 + 0.339892i) q^{87} +(-0.980878 - 10.5397i) 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} +(-12.2100 + 10.9064i) q^{94} +(-5.33433 - 3.07977i) q^{95} +(4.46512 - 2.46097i) 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 $

$2$	0.288532	+	1.38447i	0.204023	+	0.978966i
$2$	0.288532	+	1.38447i	0.204023	+	0.978966i
$3$	0.450639	−	0.780530i	0.260177	−	0.450639i	−0.706112	−	0.708100i	$-0.749553\pi$
$3$	0.450639	−	0.780530i	0.260177	−	0.450639i	0.966289	+	0.257461i	$0.0828859\pi$
$4$	−1.83350	+	0.798926i	−0.916749	+	0.399463i
$5$	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
$10$	0.942109	+	1.05472i	0.297921	+	0.333531i
$11$	3.24107	+	1.87123i	0.977218	+	0.564197i	0.901429	−	0.432927i	$-0.142519\pi$
$11$	3.24107	+	1.87123i	0.977218	+	0.564197i	0.0757892	+	0.997124i	$0.475852\pi$
$12$	−0.202661	+	1.79113i	−0.0585032	+	0.517054i
$13$			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
$16$	2.72344	−	2.92966i	0.680859	−	0.732415i
$17$	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	$0.644116\pi$
$18$	−2.30740	+	2.06105i	−0.543860	+	0.485794i
$19$	−3.07977	−	5.33433i	−0.706549	−	1.22378i	−0.966130	−	0.258057i	$-0.916918\pi$
$19$	−3.07977	−	5.33433i	−0.706549	−	1.22378i	0.259581	−	0.965721i	$-0.416416\pi$
$20$	−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	−0.0572861	−	0.998358i	$-0.518245\pi$
$23$	3.73439	−	2.15605i	0.778674	−	0.449568i	0.835960	+	0.548790i	$0.184911\pi$
$24$	−2.53823	+	0.236220i	−0.518114	+	0.0482182i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−3.35028	+	0.698219i	−0.657043	+	0.136932i
$27$	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	$0.512873\pi$
$30$	1.24779	−	0.260047i	0.227814	−	0.0474779i
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	−0.957209	−	0.289399i	$-0.906545\pi$
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	0.729231	+	0.684268i	$0.239878\pi$
$32$	4.84181	+	2.92521i	0.855920	+	0.517109i
$33$	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	$0.454073\pi$
$38$	6.49659	−	5.80297i	1.05389	−	0.941366i
$39$	1.88881	+	1.09050i	0.302451	+	0.174620i
$40$	−2.57000	−	1.18115i	−0.406352	−	0.186756i
$41$			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	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	−7.43747	−	0.841528i	−1.12124	−	0.126865i
$45$	1.89460	+	1.09385i	0.282431	+	0.163061i
$46$	4.06247	+	4.54805i	0.598979	+	0.670573i
$47$	5.78826	+	10.0256i	0.844305	+	1.46238i	0.886223	+	0.463258i	$0.153320\pi$
$47$	5.78826	+	10.0256i	0.844305	+	1.46238i	−0.0419181	+	0.999121i	$0.513347\pi$
$48$	−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
$52$	−1.93332	−	4.43689i	−0.268104	−	0.615286i
$53$	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	$0.0980393\pi$
$54$	1.34905	+	6.47316i	0.183582	+	0.880885i
$55$	3.74246			0.504633
$56$		0			0
$57$	−5.55147			−0.735310
$58$	−0.125645	−	0.602884i	−0.0164980	−	0.0791625i
$59$	−1.73534	+	3.00569i	−0.225922	+	0.391308i	−0.956596	−	0.291419i	$-0.905873\pi$
$59$	−1.73534	+	3.00569i	−0.225922	+	0.391308i	0.730674	+	0.682727i	$0.239206\pi$
$60$	0.720054	+	1.65249i	0.0929586	+	0.213336i
$61$	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
$66$	3.17773	+	3.55756i	0.391152	+	0.437906i
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.121327	−	0.992613i	$-0.538715\pi$
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.920291	+	0.391234i	$0.872048\pi$
$68$	−1.16004	−	0.131255i	−0.140675	−	0.0159170i
$69$		−	3.88640i		−	0.467868i
$70$		0			0
$71$		−	9.96771i		−	1.18295i	−0.806324	−	0.591475i	$-0.798546\pi$
$71$		−	9.96771i		−	1.18295i	0.806324	−	0.591475i	$-0.201454\pi$
$72$	2.58400	−	5.62238i	0.304527	−	0.662604i
$73$	−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	$0.861058\pi$
$74$	−11.9191	+	10.6466i	−1.38557	+	1.23764i
$75$	−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	−0.477469	−	0.878648i	$-0.658446\pi$
$79$	0.397549	−	0.229525i	0.0447278	−	0.0258236i	0.522197	+	0.852825i	$0.325113\pi$
$80$	0.893735	−	3.89888i	0.0999226	−	0.435908i
$81$	−1.17456	+	2.03439i	−0.130506	+	0.226044i
$82$	−10.1768	+	2.12091i	−1.12384	+	0.234215i
$83$	−2.59747			−0.285109			−0.142554	−	0.989787i	$-0.545532\pi$
$83$	−2.59747			−0.285109			−0.142554	+	0.989787i	$0.545532\pi$
$84$		0			0
$85$	0.583719			0.0633132
$86$	−8.03123	+	1.67376i	−0.866030	+	0.180486i
$87$	−0.196236	+	0.339892i	−0.0210388	+	0.0364402i
$88$	−0.980878	−	10.5397i	−0.104562	−	1.12354i
$89$	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
$94$	−12.2100	+	10.9064i	−1.25936	+	1.12490i
$95$	−5.33433	−	3.07977i	−0.547290	−	0.315978i
$96$	4.46512	−	2.46097i	0.455720	−	0.251171i
$97$			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
$100$	−0.224860	+	1.98732i	−0.0224860	+	0.198732i
$101$	−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	$0.817010\pi$
$102$	0.495637	+	0.554880i	0.0490754	+	0.0549413i
$103$	−5.11597	−	8.86113i	−0.504092	−	0.873113i	−0.999989	−	0.00473128i	$-0.998494\pi$
$103$	−5.11597	−	8.86113i	−0.504092	−	0.873113i	0.495897	−	0.868381i	$-0.334839\pi$
$104$	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	−0.210941	−	0.977499i	$-0.567653\pi$
$107$	5.48368	−	3.16601i	0.530128	−	0.306069i	0.741068	+	0.671430i	$0.234319\pi$
$108$	−8.57263	+	3.73542i	−0.824902	+	0.359441i
$109$	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	$-0.188652\pi$
$110$	1.07982	+	5.18132i	0.102957	+	0.494019i
$111$	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	$0.437030\pi$
$114$	−1.60177	−	7.68582i	−0.150020	−	0.719843i
$115$	2.15605	−	3.73439i	0.201053	−	0.348234i
$116$	0.798420	−	0.347902i	0.0741315	−	0.0323019i
$117$	−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
$122$	9.78631	+	10.9560i	0.886010	+	0.991913i
$123$	5.73743	+	3.31250i	0.517326	+	0.298678i
$124$	0.570840	−	5.04511i	0.0512629	−	0.453064i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	−11.2145	−	1.49512i	−0.991230	−	0.132151i
$129$	4.52782	+	2.61414i	0.398652	+	0.230162i
$130$	−2.55232	+	2.27981i	−0.223853	+	0.199953i
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	−0.970691	−	0.240332i	$-0.922744\pi$
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	0.277212	−	0.960809i	$-0.410590\pi$
$132$	−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
$136$	−0.152989	−	1.64390i	−0.0131187	−	0.140963i
$137$	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	$0.0579295\pi$
$138$	5.38060	−	1.12135i	0.458027	−	0.0954557i
$139$	−17.4044			−1.47623			−0.738113	−	0.674677i	$-0.764283\pi$
$139$	−17.4044			−1.47623			−0.738113	+	0.674677i	$0.764283\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	13.8000	−	2.87600i	1.15807	−	0.241349i
$143$	−4.52820	+	7.84307i	−0.378667	+	0.655871i
$144$	8.52956	+	1.95522i	0.710797	+	0.162935i
$145$	−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	$0.854884\pi$
$150$	0.950594	−	0.849103i	0.0776157	−	0.0693289i
$151$	−6.37060	−	3.67807i	−0.518432	−	0.299317i	0.217861	−	0.975980i	$-0.430092\pi$
$151$	−6.37060	−	3.67807i	−0.518432	−	0.299317i	−0.736293	+	0.676663i	$0.763425\pi$
$152$	−7.27534	+	15.8300i	−0.590108	+	1.28398i
$153$			1.27700i			0.103239i
$154$		0			0
$155$			2.53865i			0.203909i
$156$	−4.33436	−	0.490420i	−0.347026	−	0.0392650i
$157$	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	$0.627413\pi$
$158$	0.432476	+	0.484169i	0.0344059	+	0.0385184i
$159$	−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	−0.645349	−	0.763888i	$-0.723288\pi$
$163$	−3.91284	+	2.25908i	−0.306477	+	0.176945i	0.338872	+	0.940833i	$0.389955\pi$
$164$	−5.87265	−	13.4775i	−0.458577	−	1.05241i
$165$	1.68650	−	2.92110i	0.131294	−	0.227408i
$166$	−0.749452	−	3.59611i	−0.0581687	−	0.279112i
$167$	−16.9358			−1.31053			−0.655266	−	0.755398i	$-0.727444\pi$
$167$	−16.9358			−1.31053			−0.655266	+	0.755398i	$0.727444\pi$
$168$		0			0
$169$	7.14406			0.549543
$170$	0.168421	+	0.808139i	0.0129173	+	0.0619815i
$171$	6.73762	−	11.6699i	0.515238	−	0.892419i
$172$	−4.63453	−	10.6360i	−0.353380	−	0.810991i
$173$	−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
$178$	9.30820	+	10.4208i	0.697679	+	0.781071i
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.121664	−	0.992571i	$-0.538823\pi$
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.920424	+	0.390921i	$0.872157\pi$
$180$	−4.34765	−	0.491925i	−0.324055	−	0.0366659i
$181$			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
$184$	−11.0821	−	5.09323i	−0.816983	−	0.375478i
$185$	9.78676	+	5.65039i	0.719537	+	0.415425i
$186$	−2.41323	+	2.15558i	−0.176946	+	0.158054i
$187$	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	−0.972373	−	0.233431i	$-0.925005\pi$
$191$	−17.3638	+	10.0250i	−1.25640	+	0.725385i	−0.284030	+	0.958815i	$0.591671\pi$
$192$	4.69546	+	5.47175i	0.338865	+	0.394889i
$193$	−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	$0.921614\pi$
$194$	−6.28608	+	1.31006i	−0.451315	+	0.0940568i
$195$	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	$0.518577\pi$
$198$	−11.3352	+	2.36232i	−0.805554	+	0.167883i
$199$	0.391632	−	0.678326i	0.0277621	−	0.0480853i	−0.851811	−	0.523850i	$-0.824495\pi$
$199$	0.391632	−	0.678326i	0.0277621	−	0.0480853i	0.879573	+	0.475765i	$0.157829\pi$
$200$	−2.81626	+	0.262094i	−0.199139	+	0.0185329i
$201$	−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
$206$	10.7918	−	9.63961i	0.751901	−	0.671624i
$207$	8.16972	+	4.71679i	0.567835	+	0.327839i
$208$	7.08949	+	6.59045i	0.491568	+	0.456966i
$209$		−	23.0519i		−	1.59453i
$210$		0			0
$211$		−	9.22534i		−	0.635099i	−0.948242	−	0.317549i	$-0.897140\pi$
$211$		−	9.22534i		−	0.635099i	0.948242	−	0.317549i	$-0.102860\pi$
$212$	−0.700417	+	6.19032i	−0.0481048	+	0.425153i
$213$	−7.78009	−	4.49184i	−0.533083	−	0.307776i
$214$	5.96545	+	6.67849i	0.407790	+	0.456532i
$215$	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
$220$	−6.86180	+	2.98995i	−0.462622	+	0.201582i
$221$	−0.706272	+	1.22330i	−0.0475090	+	0.0822880i
$222$	2.93874	+	14.1010i	0.197235	+	0.946397i
$223$	24.2380			1.62310			0.811550	−	0.584284i	$-0.198624\pi$
$223$	24.2380			1.62310			0.811550	+	0.584284i	$0.198624\pi$
$224$		0			0
$225$	2.18770			0.145847
$226$	1.20562	+	5.78495i	0.0801967	+	0.384809i
$227$	5.31623	−	9.20798i	0.352851	−	0.611155i	−0.633897	−	0.773417i	$-0.718546\pi$
$227$	5.31623	−	9.20798i	0.352851	−	0.611155i	0.986748	+	0.162262i	$0.0518791\pi$
$228$	10.1786	−	4.43521i	0.674095	−	0.293729i
$229$	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	$-0.538050\pi$
$234$	−4.98755	−	5.58370i	−0.326046	−	0.365018i
$235$	10.0256	+	5.78826i	0.653996	+	0.377585i
$236$	0.780415	−	6.89734i	0.0508007	−	0.448979i
$237$		−	0.413732i		−	0.0268748i
$238$		0			0
$239$		−	13.6279i		−	0.881512i	−0.897627	−	0.440756i	$-0.854710\pi$
$239$		−	13.6279i		−	0.881512i	0.897627	−	0.440756i	$-0.145290\pi$
$240$	−2.64044	−	2.45457i	−0.170439	−	0.158442i
$241$	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	$0.623399\pi$
$242$	−3.17050	+	2.83200i	−0.203808	+	0.182048i
$243$	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
$248$	7.14950	−	0.665366i	0.453993	−	0.0422508i
$249$	−1.17052	+	2.02740i	−0.0741787	+	0.128481i
$250$	1.38447	−	0.288532i	0.0875614	−	0.0182484i
$251$	−18.8826			−1.19186			−0.595928	−	0.803038i	$-0.703216\pi$
$251$	−18.8826			−1.19186			−0.595928	+	0.803038i	$0.703216\pi$
$252$		0			0
$253$	16.1379			1.01458
$254$	−6.79824	+	1.41680i	−0.426559	+	0.0888977i
$255$	0.263046	−	0.455610i	0.0164726	−	0.0285314i
$256$	−1.16580	−	15.9575i	−0.0728623	−	0.997342i
$257$	−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
$262$	16.7431	−	14.9555i	1.03439	−	0.923953i
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	0.757645	−	0.652666i	$-0.226350\pi$
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	−0.186403	+	0.982473i	$0.559683\pi$
$264$	−8.66860	−	3.98401i	−0.533515	−	0.245199i
$265$		−	3.11491i		−	0.191347i
$266$		0			0
$267$		−	8.90478i		−	0.544963i
$268$	19.5651	+	2.21374i	1.19513	+	0.135226i
$269$	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	$0.584586\pi$
$270$	4.40489	+	4.93139i	0.268073	+	0.300115i
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	0.903100	+	0.429430i	$0.141286\pi$
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	−0.0796525	+	0.996823i	$0.525381\pi$
$272$	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
$276$	3.10495	+	7.12571i	0.186896	+	0.428918i
$277$	−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	$0.198850\pi$
$278$	−5.02173	−	24.0959i	−0.301184	−	1.44517i
$279$	−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	$0.570253\pi$
$282$	3.01045	+	14.4451i	0.179269	+	0.860192i
$283$	−3.60282	+	6.24027i	−0.214165	+	0.370945i	−0.953014	−	0.302926i	$-0.902036\pi$
$283$	−3.60282	+	6.24027i	−0.214165	+	0.370945i	0.738849	+	0.673871i	$0.235370\pi$
$284$	7.96346	+	18.2758i	0.472544	+	1.08447i
$285$	−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
$290$	−0.410254	−	0.459290i	−0.0240909	−	0.0269705i
$291$	3.54395	+	2.04610i	0.207750	+	0.119944i
$292$	19.4736	+	2.20338i	1.13961	+	0.128943i
$293$			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
$296$	13.3479	−	29.0430i	0.775831	−	1.68809i
$297$	15.1538	+	8.74905i	0.879312	+	0.507671i
$298$	1.74192	−	1.55594i	0.100907	−	0.0901333i
$299$	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
$304$	−24.0153	−	5.50501i	−1.37737	−	0.315734i
$305$	5.19383	−	8.99597i	0.297398	−	0.515108i
$306$	−1.76796	+	0.368455i	−0.101068	+	0.0210632i
$307$	10.4271			0.595104			0.297552	−	0.954706i	$-0.403830\pi$
$307$	10.4271			0.595104			0.297552	+	0.954706i	$0.403830\pi$
$308$		0			0
$309$	−9.22183			−0.524612
$310$	−3.51468	+	0.732482i	−0.199620	+	0.0416022i
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	−0.956235	−	0.292600i	$-0.905480\pi$
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	0.731516	+	0.681824i	$0.238813\pi$
$312$	−0.571629	−	6.14228i	−0.0323621	−	0.347738i
$313$	−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	$0.865003\pi$
$318$	2.96101	−	2.64488i	0.166045	−	0.148317i
$319$	−1.41136	−	0.814851i	−0.0790212	−	0.0456229i
$320$	1.47625	+	7.86261i	0.0825249	+	0.439533i
$321$		−	5.70690i		−	0.318528i
$322$		0			0
$323$		−	3.59544i		−	0.200056i
$324$	0.528221	−	4.66844i	0.0293456	−	0.259358i
$325$	2.09570	+	1.20995i	0.116248	+	0.0671161i
$326$	−4.25660	−	4.76538i	−0.235751	−	0.263930i
$327$	−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	0.178629	−	0.983917i	$-0.442834\pi$
$331$	20.3773	−	11.7649i	1.12004	−	0.646655i	0.941411	+	0.337261i	$0.109501\pi$
$332$	4.76245	−	2.07518i	0.261373	−	0.113890i
$333$	−12.3613	+	21.4105i	−0.677397	+	1.17329i
$334$	−4.88652	−	23.4471i	−0.267378	−	1.28297i
$335$	−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	$0.455636\pi$
$338$	2.06129	+	9.89072i	0.112119	+	0.537984i
$339$	1.88298	−	3.26142i	0.102269	−	0.177136i
$340$	−1.07025	+	0.466348i	−0.0580423	+	0.0252913i
$341$	−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
$346$	−0.125015	−	0.139958i	−0.00672087	−	0.00752420i
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	0.538236	−	0.842794i	$-0.319091\pi$
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	−0.460763	+	0.887523i	$0.652424\pi$
$348$	0.0882513	−	0.779969i	0.00473077	−	0.0418107i
$349$		−	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
$352$	10.2189	+	18.5409i	0.544669	+	0.988236i
$353$	−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	$0.923779\pi$
$354$	−3.29920	+	2.94696i	−0.175351	+	0.156629i
$355$	−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	−0.831381	−	0.555703i	$-0.812449\pi$
$359$	−14.5102	+	8.37747i	−0.765819	+	0.442146i	0.0655619	+	0.997849i	$0.479116\pi$
$360$	−0.573383	−	6.16112i	−0.0302199	−	0.324720i
$361$	−9.47002	+	16.4026i	−0.498422	+	0.863293i
$362$	−5.52841	+	1.15216i	−0.290567	+	0.0605560i
$363$	2.70926			0.142199
$364$		0			0
$365$	−9.79892			−0.512899
$366$	12.9616	−	2.70128i	0.677514	−	0.141198i
$367$	4.22213	−	7.31294i	0.220393	−	0.381732i	−0.734534	−	0.678572i	$-0.762599\pi$
$367$	4.22213	−	7.31294i	0.220393	−	0.381732i	0.954927	+	0.296839i	$0.0959326\pi$
$368$	3.85388	−	16.8124i	0.200897	−	0.876404i
$369$	−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	$0.746754\pi$
$374$	−2.30408	+	2.05808i	−0.119141	+	0.106421i
$375$	−0.780530	−	0.450639i	−0.0403064	−	0.0232709i
$376$	13.6736	−	29.7517i	0.705162	−	1.53432i
$377$		−	1.05378i		−	0.0542723i
$378$		0			0
$379$		−	11.7976i		−	0.606002i	−0.952990	−	0.303001i	$-0.902011\pi$
$379$		−	11.7976i		−	0.606002i	0.952990	−	0.303001i	$-0.0979886\pi$
$380$	12.2410	+	1.38503i	0.627950	+	0.0710507i
$381$	3.83268	+	2.21280i	0.196354	+	0.113365i
$382$	−18.8893	−	21.1471i	−0.966462	−	1.08198i
$383$	−0.478522	−	0.828825i	−0.0244514	−	0.0423510i	0.853541	−	0.521026i	$-0.174451\pi$
$383$	−0.478522	−	0.828825i	−0.0244514	−	0.0423510i	−0.877992	+	0.478675i	$0.841117\pi$
$384$	−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
$388$	−3.62747	−	8.32488i	−0.184157	−	0.422632i
$389$	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	$-0.110441\pi$
$390$	0.629290	+	3.01953i	0.0318653	+	0.152900i
$391$	2.51705			0.127293
$392$		0			0
$393$	−14.3073			−0.721708
$394$	−0.472436	−	2.26690i	−0.0238010	−	0.114205i
$395$	0.229525	−	0.397549i	0.0115487	−	0.0200029i
$396$	−6.54110	−	15.0115i	−0.328703	−	0.754358i
$397$	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	$-0.394843\pi$
$402$	−8.35941	−	9.35859i	−0.416930	−	0.466764i
$403$	−5.32025	−	3.07165i	−0.265020	−	0.153010i
$404$	18.1729	+	2.05621i	0.904134	+	0.102300i
$405$			2.34912i			0.116728i
$406$		0			0
$407$			42.2927i			2.09637i
$408$	−1.35206	−	0.621394i	−0.0669368	−	0.0307636i
$409$	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	$0.516312\pi$
$410$	−7.75290	+	6.92515i	−0.382888	+	0.342009i
$411$	−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
$416$	−7.07872	+	11.7167i	−0.347063	+	0.574460i
$417$	−7.84312	+	13.5847i	−0.384079	+	0.665245i
$418$	31.9146	−	6.65120i	1.56099	−	0.325321i
$419$	35.2426			1.72171			0.860856	−	0.508848i	$-0.169928\pi$
$419$	35.2426			1.72171			0.860856	+	0.508848i	$0.169928\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	12.7722	−	2.66181i	0.621740	−	0.129575i
$423$	−12.6630	+	21.9329i	−0.615695	+	1.06641i
$424$	−8.77239	+	0.816400i	−0.426025	+	0.0396479i
$425$	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
$430$	−6.11837	+	5.46514i	−0.295054	+	0.263552i
$431$	1.73673	+	1.00270i	0.0836555	+	0.0482985i	0.541244	−	0.840865i	$-0.317953\pi$
$431$	1.73673	+	1.00270i	0.0836555	+	0.0482985i	−0.457589	+	0.889164i	$0.651287\pi$
$432$	12.7336	−	13.6978i	0.612645	−	0.659035i
$433$			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
$436$	−4.21849	+	37.2832i	−0.202029	+	1.78554i
$437$	−23.0022	−	13.2803i	−1.10034	−	0.635283i
$438$	−8.32029	−	9.31480i	−0.397559	−	0.445078i
$439$	−14.5247	−	25.1574i	−0.693224	−	1.20070i	−0.970776	−	0.239989i	$-0.922856\pi$
$439$	−14.5247	−	25.1574i	−0.693224	−	1.20070i	0.277552	−	0.960711i	$-0.410477\pi$
$440$	−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	−0.769922	−	0.638138i	$-0.779705\pi$
$443$	−12.6757	+	7.31831i	−0.602240	+	0.347703i	0.167683	+	0.985841i	$0.446372\pi$
$444$	−18.6744	+	8.13717i	−0.886250	+	0.386173i
$445$	4.94008	−	8.55647i	0.234182	−	0.405616i
$446$	6.99345	+	33.5568i	0.331149	+	1.58896i
$447$	−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	$0.720550\pi$
$450$	0.631220	+	3.02880i	0.0297560	+	0.142779i
$451$	−13.7548	+	23.8241i	−0.647689	+	1.12183i
$452$	−7.66122	+	3.33829i	−0.360353	+	0.157020i
$453$	−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	$0.776403\pi$
$458$	27.8043	+	31.1277i	1.29921	+	1.45450i
$459$	2.36357	+	1.36461i	0.110322	+	0.0636943i
$460$	−0.969617	+	8.56952i	−0.0452086	+	0.399556i
$461$			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	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	−1.18595	+	1.27576i	−0.0550566	+	0.0592255i
$465$	1.98149	+	1.14402i	0.0918895	+	0.0530524i
$466$	29.6062	−	26.4453i	1.37148	−	1.22505i
$467$	11.3054	+	19.5815i	0.523152	+	0.906126i	0.999637	+	0.0269432i	$0.00857731\pi$
$467$	11.3054	+	19.5815i	0.523152	+	0.906126i	−0.476485	+	0.879183i	$0.658089\pi$
$468$	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
$472$	9.77432	−	0.909644i	0.449899	−	0.0418698i
$473$	−10.8549	+	18.8013i	−0.499110	+	0.864484i
$474$	0.572798	−	0.119375i	0.0263095	−	0.00548307i
$475$	−6.15955			−0.282620
$476$		0			0
$477$	6.81448			0.312014
$478$	18.8673	−	3.93207i	0.862971	−	0.179849i
$479$	10.9907	−	19.0365i	0.502180	−	0.869801i	−0.497817	−	0.867282i	$-0.665865\pi$
$479$	10.9907	−	19.0365i	0.502180	−	0.869801i	0.999997	−	0.00251901i	$-0.000801826\pi$
$480$	2.63643	−	4.36382i	0.120336	−	0.199180i
$481$	−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
$486$	−17.0272	+	15.2093i	−0.772371	+	0.689908i
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.907095	−	0.420927i	$-0.138295\pi$
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.0890138	+	0.996030i	$0.471628\pi$
$488$	−26.6962	−	12.2694i	−1.20848	−	0.555408i
$489$			4.07212i			0.184147i
$490$		0			0
$491$			36.4635i			1.64557i	0.568350	+	0.822787i	$0.307582\pi$
$491$			36.4635i			1.64557i	−0.568350	+	0.822787i	$0.692418\pi$
$492$	−13.1660	−	1.48970i	−0.593570	−	0.0671607i
$493$	−0.220133	−	0.127094i	−0.00991429	−	0.00572402i
$494$	14.0426	+	15.7211i	0.631808	+	0.707326i
$495$	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	−0.251738	−	0.967795i	$-0.581002\pi$
$499$	10.2874	−	5.93945i	0.460528	−	0.265886i	0.712266	+	0.701909i	$0.247669\pi$
$500$	0.798926	+	1.83350i	0.0357290	+	0.0819966i
$501$	−7.63194	+	13.2189i	−0.340970	+	0.590577i
$502$	−5.44822	−	26.1423i	−0.243166	−	1.16679i
$503$	−17.3055			−0.771614			−0.385807	−	0.922580i	$-0.626077\pi$
$503$	−17.3055			−0.771614			−0.385807	+	0.922580i	$0.626077\pi$
$504$		0			0
$505$	−9.14442			−0.406921
$506$	4.65629	+	22.3424i	0.206997	+	0.993239i
$507$	3.21939	−	5.57615i	0.142978	−	0.247646i
$508$	−3.92301	−	9.00314i	−0.174056	−	0.399450i
$509$	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
$514$	−24.3389	−	27.2481i	−1.07355	−	1.20186i
$515$	−8.86113	−	5.11597i	−0.390468	−	0.225437i
$516$	−10.3903	−	1.17563i	−0.457405	−	0.0517541i
$517$			43.3247i			1.90542i
$518$		0			0
$519$			0.119597i			0.00524973i
$520$	2.85827	−	6.21915i	0.125343	−	0.272728i
$521$	−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	$0.959881\pi$
$522$	1.00479	−	0.897511i	0.0439784	−	0.0392830i
$523$	2.13211	+	3.69292i	0.0932306	+	0.161480i	0.908869	−	0.417082i	$-0.136947\pi$
$523$	2.13211	+	3.69292i	0.0932306	+	0.161480i	−0.815638	+	0.578562i	$0.803614\pi$
$524$	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
$528$	3.01457	−	13.1509i	0.131192	−	0.572320i
$529$	−2.20289	+	3.81552i	−0.0957778	+	0.165892i
$530$	4.31249	−	0.898751i	0.187323	−	0.0390392i
$531$	−7.59279			−0.329499
$532$		0			0
$533$	−17.7879			−0.770482
$534$	12.3284	−	2.56931i	0.533501	−	0.111185i
$535$	3.16601	−	5.48368i	0.136878	−	0.237080i
$536$	2.58032	+	27.7260i	0.111453	+	1.19758i
$537$	−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	$0.787448\pi$
$542$	−28.5948	+	25.5418i	−1.22825	+	1.09712i
$543$	3.11679	+	1.79948i	0.133754	+	0.0772229i
$544$	1.59386	+	2.89187i	0.0683362	+	0.123988i
$545$		−	18.7605i		−	0.803614i
$546$		0			0
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	−1.76339	+	15.5850i	−0.0753285	+	0.665757i
$549$	19.6805	+	11.3625i	0.839942	+	0.484941i
$550$	3.52581	+	3.94724i	0.150341	+	0.168311i
$551$	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
$556$	31.9110	−	13.9049i	1.35333	−	0.589697i
$557$	−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	$0.199662\pi$
$558$	−1.60245	−	7.68906i	−0.0678371	−	0.325504i
$559$	−14.0378			−0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	−2.11767	−	10.1613i	−0.0893286	−	0.428627i
$563$	1.36792	−	2.36931i	0.0576509	−	0.0998543i	−0.835760	−	0.549096i	$-0.814972\pi$
$563$	1.36792	−	2.36931i	0.0576509	−	0.0998543i	0.893410	+	0.449241i	$0.148306\pi$
$564$	−19.1301	+	8.33573i	−0.805524	+	0.350997i
$565$	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	$0.864029\pi$
$570$	−5.23009	−	5.85523i	−0.219064	−	0.245249i
$571$	4.86573	+	2.80923i	0.203625	+	0.117563i	0.598345	−	0.801239i	$-0.295825\pi$
$571$	4.86573	+	2.80923i	0.203625	+	0.117563i	−0.394720	+	0.918801i	$0.629159\pi$
$572$	2.03642	−	17.9980i	0.0851469	−	0.752532i
$573$			18.0707i			0.754912i
$574$		0			0
$575$		−	4.31210i		−	0.179827i
$576$	−17.2010	+	3.22959i	−0.716709	+	0.134566i
$577$	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	$0.413128\pi$
$578$	17.5708	−	15.6949i	0.730850	−	0.652820i
$579$	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
$584$	2.56824	+	27.5963i	0.106275	+	1.14194i
$585$	−2.64701	+	4.58475i	−0.109440	+	0.189556i
$586$	−11.7386	+	2.44640i	−0.484917	+	0.101060i
$587$	40.1422			1.65685			0.828423	−	0.560103i	$-0.189238\pi$
$587$	40.1422			1.65685			0.828423	+	0.560103i	$0.189238\pi$
$588$		0			0
$589$	15.6369			0.644309
$590$	−4.80504	+	1.00140i	−0.197820	+	0.0412270i
$591$	−0.737868	+	1.27802i	−0.0303518	+	0.0525709i
$592$	44.0603	+	10.0999i	1.81087	+	0.415103i
$593$	−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
$598$	−11.0058	+	9.83079i	−0.450063	+	0.402011i
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	0.589388	−	0.807850i	$-0.299369\pi$
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	−0.404924	+	0.914350i	$0.632702\pi$
$600$	−1.06454	+	2.31628i	−0.0434598	+	0.0945618i
$601$		−	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
$604$	14.6190	+	1.65410i	0.594838	+	0.0673042i
$605$	2.60329	+	1.50301i	0.105839	+	0.0611060i
$606$	−7.76455	−	8.69263i	−0.315413	−	0.353114i
$607$	−4.82810	−	8.36252i	−0.195967	−	0.339424i	0.751250	−	0.660017i	$-0.229451\pi$
$607$	−4.82810	−	8.36252i	−0.195967	−	0.339424i	−0.947217	+	0.320593i	$0.896118\pi$
$608$	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
$612$	−1.02023	−	2.34138i	−0.0412403	−	0.0946446i
$613$	−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	$0.217327\pi$
$614$	3.00854	+	14.4359i	0.121415	+	0.582586i
$615$	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	$0.697181\pi$
$618$	−2.66079	−	12.7673i	−0.107033	−	0.513577i
$619$	−1.24278	+	2.15256i	−0.0499517	+	0.0865189i	−0.889920	−	0.456116i	$-0.849240\pi$
$619$	−1.24278	+	2.15256i	−0.0499517	+	0.0865189i	0.839968	+	0.542635i	$0.182573\pi$
$620$	−2.02819	−	4.65461i	−0.0814542	−	0.186934i
$621$	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
$626$	−13.6292	−	15.2582i	−0.544731	−	0.609842i
$627$	−17.9927	−	10.3881i	−0.718558	−	0.414860i
$628$	−6.12592	−	0.693131i	−0.244451	−	0.0276589i
$629$			6.59647i			0.263019i
$630$		0			0
$631$		−	8.90728i		−	0.354593i	−0.984157	−	0.177297i	$-0.943265\pi$
$631$		−	8.90728i		−	0.354593i	0.984157	−	0.177297i	$-0.0567352\pi$
$632$	−1.17976	−	0.542207i	−0.0469283	−	0.0215678i
$633$	−7.20066	−	4.15730i	−0.286200	−	0.165238i
$634$	3.73060	−	3.33230i	0.148161	−	0.132342i
$635$	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
$640$	−10.4596	+	4.31243i	−0.413451	+	0.170464i
$641$	−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	$0.259984\pi$
$642$	7.90102	−	1.64662i	0.311828	−	0.0649870i
$643$	−24.2513			−0.956380			−0.478190	−	0.878256i	$-0.658707\pi$
$643$	−24.2513			−0.956380			−0.478190	+	0.878256i	$0.658707\pi$
$644$		0			0
$645$	5.22827			0.205863
$646$	4.97777	−	1.03740i	0.195848	−	0.0408160i
$647$	−14.9578	+	25.9077i	−0.588053	+	1.01854i	0.406435	+	0.913680i	$0.366772\pi$
$647$	−14.9578	+	25.9077i	−0.588053	+	1.01854i	−0.994487	+	0.104857i	$0.966561\pi$
$648$	6.61571	−	0.615690i	0.259890	−	0.0241866i
$649$	−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	$0.734839\pi$
$654$	17.8337	−	15.9296i	0.697351	−	0.622898i
$655$	−13.7477	−	7.93723i	−0.537167	−	0.310133i
$656$	21.5350	+	20.0191i	0.840800	+	0.781615i
$657$		−	21.4371i		−	0.836340i
$658$		0			0
$659$			30.2702i			1.17916i	0.807710	+	0.589580i	$0.200707\pi$
$659$			30.2702i			1.17916i	−0.807710	+	0.589580i	$0.799293\pi$
$660$	−0.758451	+	6.70323i	−0.0295227	+	0.260923i
$661$	−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	$0.779990\pi$
$662$	22.1676	+	24.8172i	0.861567	+	0.964549i
$663$	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
$668$	31.0518	−	13.5305i	1.20143	−	0.523509i
$669$	10.9226	−	18.9185i	0.422292	−	0.731432i
$670$	−2.84059	−	13.6301i	−0.109742	−	0.526576i
$671$	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	$0.366100\pi$
$674$	1.47168	+	7.06157i	0.0566868	+	0.272001i
$675$	2.33778	−	4.04915i	0.0899812	−	0.155852i
$676$	−13.0986	+	5.70758i	−0.503794	+	0.219522i
$677$	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
$682$	−8.95080	−	10.0207i	−0.342744	−	0.383711i
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	0.0869404	−	0.996214i	$-0.472291\pi$
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	−0.819276	+	0.573399i	$0.805624\pi$
$684$	−3.03003	+	26.7796i	−0.115856	+	1.02394i
$685$		−	7.84221i		−	0.299635i
$686$		0			0
$687$		−	26.5993i		−	1.01483i
$688$	16.9948	+	15.7985i	0.647921	+	0.602313i
$689$	6.52791	+	3.76889i	0.248694	+	0.143583i
$690$	4.09906	−	3.66142i	0.156048	−	0.139388i
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	0.985258	−	0.171077i	$-0.0547248\pi$
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	−0.640786	+	0.767719i	$0.721391\pi$
$692$	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
$696$	1.10530	−	0.102865i	0.0418965	−	0.00389908i
$697$	−2.14537	+	3.71588i	−0.0812615	+	0.140749i
$698$	38.2225	−	7.96581i	1.44674	−	0.301510i
$699$	−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	$0.412138\pi$
$702$	−15.6644	+	3.26456i	−0.591215	+	0.123213i
$703$	34.8038	−	60.2820i	1.31265	−	2.27358i
$704$	−22.7209	+	19.4974i	−0.856324	+	0.734835i
$705$	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	$0.588616\pi$
$710$	10.5131	−	9.39067i	0.394550	−	0.352426i
$711$	0.869718	+	0.502132i	0.0326170	+	0.0188314i
$712$	−25.3920	−	11.6699i	−0.951605	−	0.437350i
$713$			10.9469i			0.409965i
$714$		0			0
$715$			9.05640i			0.338690i
$716$	31.9940	+	3.62003i	1.19567	+	0.135287i
$717$	−10.6369	−	6.14124i	−0.397244	−	0.229349i
$718$	−15.7850	−	17.6717i	−0.589091	−	0.659503i
$719$	−10.0975	−	17.4894i	−0.376573	−	0.652243i	0.613988	−	0.789315i	$-0.289564\pi$
$719$	−10.0975	−	17.4894i	−0.376573	−	0.652243i	−0.990561	+	0.137072i	$0.956231\pi$
$720$	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
$724$	−3.19024	−	7.32147i	−0.118564	−	0.272100i
$725$	−0.217731	+	0.377122i	−0.00808634	+	0.0140060i
$726$	0.781708	+	3.75088i	0.0290119	+	0.139208i
$727$	10.7925			0.400272			0.200136	−	0.979768i	$-0.435862\pi$
$727$	10.7925			0.400272			0.200136	+	0.979768i	$0.435862\pi$
$728$		0			0
$729$	7.50278			0.277881
$730$	−2.82730	−	13.5663i	−0.104643	−	0.502111i
$731$	−1.69306	+	2.93247i	−0.0626202	+	0.108461i
$732$	7.47967	+	17.1655i	0.276457	+	0.634456i
$733$	−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
$738$	−15.1501	−	16.9610i	−0.557684	−	0.624343i
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	0.468044	−	0.883705i	$-0.344959\pi$
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	−0.531289	+	0.847191i	$0.678292\pi$
$740$	−22.4582	−	2.54109i	−0.825582	−	0.0934122i
$741$		−	13.4340i		−	0.493511i
$742$		0			0
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	2.70250	−	5.88023i	0.0990786	−	0.215580i
$745$	−1.43029	−	0.825776i	−0.0524016	−	0.0302541i
$746$	−10.9450	+	9.77648i	−0.400727	+	0.357942i
$747$	−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	−0.0682545	−	0.997668i	$-0.521743\pi$
$751$	20.8718	−	12.0504i	0.761624	−	0.439724i	0.829879	+	0.557944i	$0.188410\pi$
$752$	45.1355	+	10.3464i	1.64592	+	0.377293i
$753$	−8.50921	+	14.7384i	−0.310093	+	0.537097i
$754$	1.45892	−	0.304048i	0.0531308	−	0.0110728i
$755$	−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	$0.281533\pi$
$758$	16.3334	−	3.40398i	0.593256	−	0.123638i
$759$	7.27236	−	12.5961i	0.263970	−	0.457209i
$760$	1.61438	+	17.3469i	0.0585598	+	0.629237i
$761$	−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
$766$	1.00941	−	0.901641i	0.0364715	−	0.0325776i
$767$	−7.27349	−	4.19935i	−0.262631	−	0.151630i
$768$	−12.9806	−	6.28112i	−0.468398	−	0.226650i
$769$		−	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
$772$	4.34860	−	38.4331i	0.156509	−	1.38324i
$773$	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	$0.641749\pi$
$774$	−11.9561	−	13.3851i	−0.429752	−	0.481119i
$775$	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
$780$	−3.99887	+	1.74246i	−0.143183	+	0.0623901i
$781$	18.6519	−	32.3060i	0.667417	−	1.15600i
$782$	0.726250	+	3.48478i	0.0259707	+	0.124615i
$783$	−2.03603			−0.0727618
$784$		0			0
$785$	3.08251			0.110019
$786$	−4.12811	−	19.8080i	−0.147245	−	0.706528i
$787$	−10.5248	+	18.2295i	−0.375168	+	0.649811i	−0.990352	−	0.138573i	$-0.955748\pi$
$787$	−10.5248	+	18.2295i	−0.375168	+	0.649811i	0.615184	+	0.788384i	$0.289082\pi$
$788$	3.00214	−	1.30815i	0.106947	−	0.0466008i
$789$	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
$794$	5.84765	+	6.54661i	0.207525	+	0.232330i
$795$	−2.43128	−	1.40370i	−0.0862286	−	0.0497841i
$796$	−0.176124	+	1.55660i	−0.00624256	+	0.0551721i
$797$		−	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
$800$	4.95421	−	2.73053i	0.175158	−	0.0965388i
$801$	18.7190	+	10.8074i	0.661403	+	0.381861i
$802$	27.7528	−	24.7897i	0.979984	−	0.875355i
$803$	−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
$808$	2.39670	+	25.7530i	0.0843156	+	0.905988i
$809$	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	$0.0847632\pi$
$810$	−3.25227	+	0.677795i	−0.114273	+	0.0238153i
$811$	−18.5825			−0.652521			−0.326260	−	0.945280i	$-0.605789\pi$
$811$	−18.5825			−0.652521			−0.326260	+	0.945280i	$0.605789\pi$
$812$		0			0
$813$	24.4348			0.856967
$814$	−58.5529	+	12.2028i	−2.05228	+	0.427708i
$815$	−2.25908	+	3.91284i	−0.0791321	+	0.137061i
$816$	0.470188	−	2.05117i	0.0164599	−	0.0718054i
$817$	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	$0.740915\pi$
$822$	7.45475	−	6.65884i	0.260014	−	0.232254i
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.984547	−	0.175123i	$-0.0560323\pi$
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.340612	+	0.940204i	$0.389366\pi$
$824$	−12.0854	+	26.2961i	−0.421017	+	0.916067i
$825$		−	3.37300i		−	0.117433i
$826$		0			0
$827$			8.10796i			0.281941i	0.990014	+	0.140971i	$0.0450224\pi$
$827$			8.10796i			0.281941i	−0.990014	+	0.140971i	$0.954978\pi$
$828$	−18.7475	−	2.12123i	−0.651522	−	0.0737178i
$829$	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	$0.404682\pi$
$830$	−2.44710	−	2.73959i	−0.0849400	−	0.0950927i
$831$	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
$836$	18.4167	+	42.2656i	0.636956	+	1.46179i
$837$	−5.93481	+	10.2794i	−0.205137	+	0.355308i
$838$	10.1686	+	48.7922i	0.351269	+	1.68550i
$839$	−31.8404			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$839$	−31.8404			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	−4.52040	−	21.6903i	−0.155783	−	0.747497i
$843$	−3.30745	+	5.72868i	−0.113915	+	0.197306i
$844$	7.37036	+	16.9147i	0.253698	+	0.582227i
$845$	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
$850$	0.549927	+	0.615659i	0.0188623	+	0.0211169i
$851$	42.2015	+	24.3650i	1.44665	+	0.835223i
$852$	17.8534	+	2.02007i	0.611649	+	0.0692063i
$853$			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
$856$	−16.2733	−	7.47905i	−0.556208	−	0.255629i
$857$	−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	$0.913240\pi$
$858$	−8.60896	+	7.68981i	−0.293905	+	0.262526i
$859$	−6.02640	−	10.4380i	−0.205618	−	0.356141i	0.744711	−	0.667387i	$-0.232587\pi$
$859$	−6.02640	−	10.4380i	−0.205618	−	0.356141i	−0.950329	+	0.311246i	$0.899254\pi$
$860$	−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	−0.491562	−	0.870843i	$-0.663574\pi$
$863$	0.494372	−	0.285426i	0.0168286	−	0.00971602i	0.508391	+	0.861127i	$0.330241\pi$
$864$	22.6382	+	13.6770i	0.770167	+	0.465300i
$865$	−0.0663486	+	0.114919i	−0.00225592	+	0.00390737i
$866$	−18.8257	+	3.92340i	−0.639724	+	0.133323i
$867$	−15.0146			−0.509924
$868$		0			0
$869$	1.71798			0.0582784
$870$	−0.543366	+	0.113241i	−0.0184218	+	0.00383923i
$871$	11.9120	−	20.6321i	0.403622	−	0.699093i
$872$	−52.8345	+	4.91703i	−1.78920	+	0.166512i
$873$	−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	$0.936964\pi$
$878$	30.6388	−	27.3676i	1.03401	−	0.923613i
$879$	6.61794	+	3.82087i	0.223218	+	0.128875i
$880$	10.1924	−	10.9641i	0.343584	−	0.369601i
$881$			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	$-0.859082\pi$
$883$		−	25.4594i		−	0.856776i	0.903595	−	0.428388i	$-0.140918\pi$
$884$	0.317624	−	2.80717i	0.0106828	−	0.0944155i
$885$	2.70897	+	1.56402i	0.0910609	+	0.0525740i
$886$	−13.7893	−	15.4375i	−0.463260	−	0.518633i
$887$	−5.30243	−	9.18408i	−0.178038	−	0.308371i	0.763170	−	0.646197i	$-0.223642\pi$
$887$	−5.30243	−	9.18408i	−0.178038	−	0.308371i	−0.941209	+	0.337826i	$0.890308\pi$
$888$	−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
$892$	−44.4404	+	19.3644i	−1.48798	+	0.648368i
$893$	35.6531	−	61.7530i	1.19309	−	2.06648i
$894$	−0.429482	−	2.06079i	−0.0143640	−	0.0689231i
$895$	−16.0991			−0.538132
$896$		0			0
$897$	9.40472			0.314014
$898$	−7.81053	−	37.4774i	−0.260641	−	1.25064i
$899$	0.552744	−	0.957381i	0.0184350	−	0.0319304i
$900$	−4.01114	+	1.74781i	−0.133705	+	0.0582603i
$901$	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
$906$	−6.24611	−	6.99269i	−0.207513	−	0.232317i
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	0.262561	−	0.964915i	$-0.415433\pi$
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	−0.704361	+	0.709842i	$0.748766\pi$
$908$	−2.39081	+	21.1301i	−0.0793418	+	0.701227i
$909$		−	20.0052i		−	0.663531i
$910$		0			0
$911$		−	22.0734i		−	0.731324i	−0.930748	−	0.365662i	$-0.880843\pi$
$911$		−	22.0734i		−	0.731324i	0.930748	−	0.365662i	$-0.119157\pi$
$912$	−15.1191	+	16.2639i	−0.500642	+	0.538552i
$913$	−8.41856	−	4.86046i	−0.278614	−	0.160858i
$914$	−8.02231	+	7.16579i	−0.265354	+	0.237023i
$915$	−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	−0.999930	−	0.0117923i	$-0.996246\pi$
$919$	−45.1598	+	26.0730i	−1.48968	+	0.860069i	−0.489753	+	0.871861i	$0.662913\pi$
$920$	−12.1440	+	1.13018i	−0.400375	+	0.0372608i
$921$	4.69884	−	8.13863i	0.154832	−	0.268177i
$922$	−17.7147	+	3.69185i	−0.583401	+	0.121585i
$923$	24.1209			0.793949
$924$		0			0
$925$	11.3008			0.371567
$926$	−38.6512	+	8.05516i	−1.27016	+	0.264709i
$927$	11.1922	−	19.3855i	0.367600	−	0.636702i
$928$	−2.10843	−	1.27382i	−0.0692126	−	0.0418152i
$929$	−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
$934$	−23.8480	+	21.3019i	−0.780332	+	0.697018i
$935$	1.89187	+	1.09227i	0.0618708	+	0.0357211i
$936$	13.6056	+	6.25302i	0.444713	+	0.204386i
$937$		−	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
$940$	−23.0063	−	2.60309i	−0.750381	−	0.0849035i
$941$	−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	$0.760099\pi$
$942$	2.61736	+	2.93021i	0.0852783	+	0.0954715i
$943$	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	−0.920804	−	0.390025i	$-0.872467\pi$
$947$	−32.1100	+	18.5387i	−1.04344	+	0.602428i	−0.122631	+	0.992452i	$0.539133\pi$
$948$	0.330541	+	0.758577i	0.0107355	+	0.0246374i
$949$	11.8562	−	20.5356i	0.384869	−	0.666613i
$950$	−1.77723	−	8.52769i	−0.0576608	−	0.276675i
$951$	−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	$0.652970\pi$
$954$	1.96619	+	9.43443i	0.0636579	+	0.305451i
$955$	−10.0250	+	17.3638i	−0.324402	+	0.561881i
$956$	10.8876	+	24.9866i	0.352131	+	0.808126i
$957$	−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
$962$	−25.7637	−	28.8431i	−0.830654	−	0.929940i
$963$	11.9966	+	6.92626i	0.386586	+	0.223196i
$964$	−8.36146	−	0.946076i	−0.269305	−	0.0304711i
$965$			19.3392i			0.622550i
$966$		0			0
$967$		−	5.33936i		−	0.171702i	−0.996308	−	0.0858510i	$-0.972639\pi$
$967$		−	5.33936i		−	0.171702i	0.996308	−	0.0858510i	$-0.0273609\pi$
$968$	3.55056	−	7.72546i	0.114119	−	0.248306i
$969$	−2.80635	−	1.62025i	−0.0901530	−	0.0520498i
$970$	−4.78888	+	4.27759i	−0.153762	+	0.137345i
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	0.764197	−	0.644983i	$-0.223136\pi$
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	−0.940670	+	0.339323i	$0.889802\pi$
$972$	−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
$976$	9.28381	−	40.5002i	0.297168	−	1.29638i
$977$	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	$-0.00135275\pi$
$978$	−5.63771	+	1.17493i	−0.180274	+	0.0375703i
$979$	36.9761			1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	−50.4825	+	10.5209i	−1.61096	+	0.335735i
$983$	−17.2762	+	29.9232i	−0.551025	+	0.954402i	0.447176	+	0.894446i	$0.352430\pi$
$983$	−17.2762	+	29.9232i	−0.551025	+	0.954402i	−0.998201	+	0.0599567i	$0.980904\pi$
$984$	−1.73638	−	18.6577i	−0.0553537	−	0.594787i
$985$	−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
$990$	−8.63537	+	7.71340i	−0.274450	+	0.245148i
$991$	−47.8668	−	27.6359i	−1.52054	−	0.877884i	−0.999707	−	0.0242247i	$-0.992288\pi$
$991$	−47.8668	−	27.6359i	−1.52054	−	0.877884i	−0.520833	−	0.853659i	$-0.674378\pi$
$992$	−12.5770	+	6.93186i	−0.399321	+	0.220087i
$993$		−	21.2068i		−	0.672978i
$994$		0			0
$995$		−	0.783264i		−	0.0248311i
$996$	0.526405	−	4.65239i	0.0166798	−	0.147417i
$997$	−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	$0.744466\pi$
$998$	11.1912	+	12.5289i	0.354252	+	0.396595i
$999$	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.31.9		32
4.3	odd	2	inner	980.2.o.f.31.13		32
7.2	even	3		140.2.o.a.131.13	yes	32
7.3	odd	6		980.2.g.a.391.6		32
7.4	even	3		980.2.g.a.391.5		32
7.5	odd	6	inner	980.2.o.f.411.13		32
7.6	odd	2		140.2.o.a.31.9	✓	32
28.3	even	6		980.2.g.a.391.7		32
28.11	odd	6		980.2.g.a.391.8		32
28.19	even	6	inner	980.2.o.f.411.9		32
28.23	odd	6		140.2.o.a.131.9	yes	32
28.27	even	2		140.2.o.a.31.13	yes	32
35.2	odd	12		700.2.t.d.299.11		32
35.9	even	6		700.2.p.c.551.4		32
35.13	even	4		700.2.t.d.199.16		32
35.23	odd	12		700.2.t.c.299.6		32
35.27	even	4		700.2.t.c.199.1		32
35.34	odd	2		700.2.p.c.451.8		32
140.23	even	12		700.2.t.c.299.1		32
140.27	odd	4		700.2.t.c.199.6		32
140.79	odd	6		700.2.p.c.551.8		32
140.83	odd	4		700.2.t.d.199.11		32
140.107	even	12		700.2.t.d.299.16		32
140.139	even	2		700.2.p.c.451.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	7.6	odd	2
140.2.o.a.31.13	yes	32	28.27	even	2
140.2.o.a.131.9	yes	32	28.23	odd	6
140.2.o.a.131.13	yes	32	7.2	even	3
700.2.p.c.451.4		32	140.139	even	2
700.2.p.c.451.8		32	35.34	odd	2
700.2.p.c.551.4		32	35.9	even	6
700.2.p.c.551.8		32	140.79	odd	6
700.2.t.c.199.1		32	35.27	even	4
700.2.t.c.199.6		32	140.27	odd	4
700.2.t.c.299.1		32	140.23	even	12
700.2.t.c.299.6		32	35.23	odd	12
700.2.t.d.199.11		32	140.83	odd	4
700.2.t.d.199.16		32	35.13	even	4
700.2.t.d.299.11		32	35.2	odd	12
700.2.t.d.299.16		32	140.107	even	12
980.2.g.a.391.5		32	7.4	even	3
980.2.g.a.391.6		32	7.3	odd	6
980.2.g.a.391.7		32	28.3	even	6
980.2.g.a.391.8		32	28.11	odd	6
980.2.o.f.31.9		32	1.1	even	1	trivial
980.2.o.f.31.13		32	4.3	odd	2	inner
980.2.o.f.411.9		32	28.19	even	6	inner
980.2.o.f.411.13		32	7.5	odd	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+(0.288532 + 1.38447i) q^{2} +(0.450639 - 0.780530i) q^{3} +(-1.83350 + 0.798926i) 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} +(0.942109 + 1.05472i) q^{10} +(3.24107 + 1.87123i) q^{11} +(-0.202661 + 1.79113i) q^{12} +2.41990i q^{13} -0.901278i q^{15} +(2.72344 - 2.92966i) q^{16} +(0.505515 + 0.291859i) q^{17} +(-2.30740 + 2.06105i) 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} +(-2.53823 + 0.236220i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.35028 + 0.698219i) q^{26} +4.67556 q^{27} -0.435463 q^{29} +(1.24779 - 0.260047i) q^{30} +(-1.26933 + 2.19854i) q^{31} +(4.84181 + 2.92521i) 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} +(6.49659 - 5.80297i) q^{38} +(1.88881 + 1.09050i) q^{39} +(-2.57000 - 1.18115i) q^{40} +7.35068i q^{41} +5.80096i q^{43} +(-7.43747 - 0.841528i) q^{44} +(1.89460 + 1.09385i) q^{45} +(4.06247 + 4.54805i) 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} +(-1.93332 - 4.43689i) q^{52} +(1.55746 - 2.69759i) q^{53} +(1.34905 + 6.47316i) q^{54} +3.74246 q^{55} -5.55147 q^{57} +(-0.125645 - 0.602884i) q^{58} +(-1.73534 + 3.00569i) q^{59} +(0.720054 + 1.65249i) 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} +(3.17773 + 3.55756i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(-1.16004 - 0.131255i) q^{68} -3.88640i q^{69} -9.96771i q^{71} +(2.58400 - 5.62238i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-11.9191 + 10.6466i) 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} +(0.893735 - 3.89888i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(-10.1768 + 2.12091i) q^{82} -2.59747 q^{83} +0.583719 q^{85} +(-8.03123 + 1.67376i) q^{86} +(-0.196236 + 0.339892i) q^{87} +(-0.980878 - 10.5397i) 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} +(-12.2100 + 10.9064i) q^{94} +(-5.33433 - 3.07977i) q^{95} +(4.46512 - 2.46097i) 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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