LMFDB - Embedded newform 220.2.m.a.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(81,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.m (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16$ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$1.40799 + 0.132563i$ of defining polynomial
Character	$\chi$	$=$	220.201
Dual form			220.2.m.a.81.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.346820 - 1.06740i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.714347 - 2.19853i) q^{7} +(1.40799 - 1.02296i) q^{9} +(-3.14835 + 1.04301i) q^{11} +(4.18616 - 3.04142i) q^{13} +(0.346820 - 1.06740i) q^{15} +(-0.339863 - 0.246925i) q^{17} +(-0.537803 - 1.65519i) q^{19} -2.59447 q^{21} +4.90614 q^{23} +(0.309017 + 0.951057i) q^{25} +(-4.30419 - 3.12718i) q^{27} +(-0.849477 + 2.61442i) q^{29} +(-5.30849 + 3.85684i) q^{31} +(2.20522 + 2.99883i) q^{33} +(1.87018 - 1.35877i) q^{35} +(-3.22859 + 9.93656i) q^{37} +(-4.69826 - 3.41349i) q^{39} +(2.61055 + 8.03445i) q^{41} +6.16578 q^{43} +1.74037 q^{45} +(-0.320799 - 0.987319i) q^{47} +(1.33986 + 0.973468i) q^{49} +(-0.145697 + 0.448410i) q^{51} +(-4.38495 + 3.18585i) q^{53} +(-3.16014 - 1.00675i) q^{55} +(-1.58023 + 1.14810i) q^{57} +(-4.45471 + 13.7102i) q^{59} +(-10.2838 - 7.47163i) q^{61} +(-1.24323 - 3.82626i) q^{63} +5.17438 q^{65} -0.559626 q^{67} +(-1.70155 - 5.23683i) q^{69} +(-4.17060 - 3.03012i) q^{71} +(3.83770 - 11.8112i) q^{73} +(0.907987 - 0.659691i) q^{75} +(0.0440700 + 7.66683i) q^{77} +(3.91229 - 2.84244i) q^{79} +(-0.231768 + 0.713310i) q^{81} +(5.83021 + 4.23590i) q^{83} +(-0.129816 - 0.399533i) q^{85} +3.08526 q^{87} +8.95287 q^{89} +(-3.69630 - 11.3760i) q^{91} +(5.95790 + 4.32867i) q^{93} +(0.537803 - 1.65519i) q^{95} +(0.633590 - 0.460330i) q^{97} +(-3.36588 + 4.68919i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - q^{3} + 2 q^{5} + q^{7} + 3 q^{9} + 5 q^{11} + 6 q^{13} + q^{15} - 13 q^{17} - 7 q^{19} + 28 q^{21} - 22 q^{23} - 2 q^{25} + 2 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 4 q^{35} + 16 q^{37} - 17 q^{39}+ \cdots - 20 q^{99}+O(q^{100})$ 8 * q - q^3 + 2 * q^5 + q^7 + 3 * q^9 + 5 * q^11 + 6 * q^13 + q^15 - 13 * q^17 - 7 * q^19 + 28 * q^21 - 22 * q^23 - 2 * q^25 + 2 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 4 * q^35 + 16 * q^37 - 17 * q^39 - 12 * q^41 + 10 * q^43 - 8 * q^45 - 18 * q^47 + 21 * q^49 + 21 * q^51 - 23 * q^53 - 15 * q^55 - q^57 - 9 * q^59 - 34 * q^61 - 29 * q^63 - 6 * q^65 + 26 * q^67 - q^69 - 26 * q^71 + q^73 - q^75 - 10 * q^77 + 19 * q^79 + 12 * q^81 - 7 * q^83 - 12 * q^85 + 94 * q^87 - 8 * q^89 - 18 * q^91 + 49 * q^93 + 7 * q^95 - 24 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.346820	−	1.06740i	−0.200237	−	0.616265i	−0.999875	−	0.0157838i	$-0.994976\pi$
$3$	−0.346820	−	1.06740i	−0.200237	−	0.616265i	0.799639	−	0.600481i	$-0.205024\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	0.714347	−	2.19853i	0.269998	−	0.830967i	−0.720502	−	0.693453i	$-0.756089\pi$
$7$	0.714347	−	2.19853i	0.269998	−	0.830967i	0.990500	−	0.137515i	$-0.0439114\pi$
$8$		0			0
$9$	1.40799	−	1.02296i	0.469329	−	0.340987i
$10$		0			0
$11$	−3.14835	+	1.04301i	−0.949265	+	0.314479i
$11$	−3.14835	+	1.04301i	−0.949265	+	0.314479i
$12$		0			0
$13$	4.18616	−	3.04142i	1.16103	−	0.843539i	0.171123	−	0.985250i	$-0.445260\pi$
$13$	4.18616	−	3.04142i	1.16103	−	0.843539i	0.989908	+	0.141711i	$0.0452604\pi$
$14$		0			0
$15$	0.346820	−	1.06740i	0.0895486	−	0.275602i
$16$		0			0
$17$	−0.339863	−	0.246925i	−0.0824290	−	0.0598882i	0.545808	−	0.837911i	$-0.316223\pi$
$17$	−0.339863	−	0.246925i	−0.0824290	−	0.0598882i	−0.628237	+	0.778022i	$0.716223\pi$
$18$		0			0
$19$	−0.537803	−	1.65519i	−0.123381	−	0.379726i	0.870222	−	0.492660i	$-0.163975\pi$
$19$	−0.537803	−	1.65519i	−0.123381	−	0.379726i	−0.993603	+	0.112934i	$0.963975\pi$
$20$		0			0
$21$	−2.59447			−0.566160
$22$		0			0
$23$	4.90614			1.02300			0.511501	−	0.859283i	$-0.329090\pi$
$23$	4.90614			1.02300			0.511501	+	0.859283i	$0.329090\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−4.30419	−	3.12718i	−0.828342	−	0.601826i
$28$		0			0
$29$	−0.849477	+	2.61442i	−0.157744	+	0.485486i	−0.998429	−	0.0560390i	$-0.982153\pi$
$29$	−0.849477	+	2.61442i	−0.157744	+	0.485486i	0.840685	+	0.541525i	$0.182153\pi$
$30$		0			0
$31$	−5.30849	+	3.85684i	−0.953433	+	0.692710i	−0.951616	−	0.307289i	$-0.900578\pi$
$31$	−5.30849	+	3.85684i	−0.953433	+	0.692710i	−0.00181677	+	0.999998i	$0.500578\pi$
$32$		0			0
$33$	2.20522	+	2.99883i	0.383880	+	0.522029i
$34$		0			0
$35$	1.87018	−	1.35877i	0.316119	−	0.229674i
$36$		0			0
$37$	−3.22859	+	9.93656i	−0.530776	+	1.63356i	0.221827	+	0.975086i	$0.428798\pi$
$37$	−3.22859	+	9.93656i	−0.530776	+	1.63356i	−0.752603	+	0.658475i	$0.771202\pi$
$38$		0			0
$39$	−4.69826	−	3.41349i	−0.752324	−	0.546596i
$40$		0			0
$41$	2.61055	+	8.03445i	0.407700	+	1.25477i	0.918620	+	0.395142i	$0.129305\pi$
$41$	2.61055	+	8.03445i	0.407700	+	1.25477i	−0.510920	+	0.859628i	$0.670695\pi$
$42$		0			0
$43$	6.16578			0.940272			0.470136	−	0.882594i	$-0.344205\pi$
$43$	6.16578			0.940272			0.470136	+	0.882594i	$0.344205\pi$
$44$		0			0
$45$	1.74037			0.259439
$46$		0			0
$47$	−0.320799	−	0.987319i	−0.0467934	−	0.144015i	0.924930	−	0.380138i	$-0.124123\pi$
$47$	−0.320799	−	0.987319i	−0.0467934	−	0.144015i	−0.971723	+	0.236122i	$0.924123\pi$
$48$		0			0
$49$	1.33986	+	0.973468i	0.191409	+	0.139067i
$50$		0			0
$51$	−0.145697	+	0.448410i	−0.0204017	+	0.0627899i
$52$		0			0
$53$	−4.38495	+	3.18585i	−0.602319	+	0.437610i	−0.846701	−	0.532069i	$-0.821415\pi$
$53$	−4.38495	+	3.18585i	−0.602319	+	0.437610i	0.244382	+	0.969679i	$0.421415\pi$
$54$		0			0
$55$	−3.16014	−	1.00675i	−0.426113	−	0.135750i
$56$		0			0
$57$	−1.58023	+	1.14810i	−0.209307	+	0.152070i
$58$		0			0
$59$	−4.45471	+	13.7102i	−0.579954	+	1.78492i	0.0386977	+	0.999251i	$0.487679\pi$
$59$	−4.45471	+	13.7102i	−0.579954	+	1.78492i	−0.618652	+	0.785665i	$0.712321\pi$
$60$		0			0
$61$	−10.2838	−	7.47163i	−1.31671	−	0.956644i	−0.999967	−	0.00813122i	$-0.997412\pi$
$61$	−10.2838	−	7.47163i	−1.31671	−	0.956644i	−0.316740	−	0.948512i	$-0.602588\pi$
$62$		0			0
$63$	−1.24323	−	3.82626i	−0.156632	−	0.482063i
$64$		0			0
$65$	5.17438			0.641802
$66$		0			0
$67$	−0.559626			−0.0683692			−0.0341846	−	0.999416i	$-0.510883\pi$
$67$	−0.559626			−0.0683692			−0.0341846	+	0.999416i	$0.510883\pi$
$68$		0			0
$69$	−1.70155	−	5.23683i	−0.204842	−	0.630440i
$70$		0			0
$71$	−4.17060	−	3.03012i	−0.494959	−	0.359609i	0.312129	−	0.950040i	$-0.398958\pi$
$71$	−4.17060	−	3.03012i	−0.494959	−	0.359609i	−0.807088	+	0.590431i	$0.798958\pi$
$72$		0			0
$73$	3.83770	−	11.8112i	0.449168	−	1.38240i	−0.428679	−	0.903457i	$-0.641021\pi$
$73$	3.83770	−	11.8112i	0.449168	−	1.38240i	0.877847	−	0.478941i	$-0.158979\pi$
$74$		0			0
$75$	0.907987	−	0.659691i	0.104845	−	0.0761746i
$76$		0			0
$77$	0.0440700	+	7.66683i	0.00502224	+	0.873716i
$78$		0			0
$79$	3.91229	−	2.84244i	0.440167	−	0.319800i	−0.345535	−	0.938406i	$-0.612302\pi$
$79$	3.91229	−	2.84244i	0.440167	−	0.319800i	0.785701	+	0.618606i	$0.212302\pi$
$80$		0			0
$81$	−0.231768	+	0.713310i	−0.0257521	+	0.0792567i
$82$		0			0
$83$	5.83021	+	4.23590i	0.639949	+	0.464950i	0.859833	−	0.510576i	$-0.170568\pi$
$83$	5.83021	+	4.23590i	0.639949	+	0.464950i	−0.219884	+	0.975526i	$0.570568\pi$
$84$		0			0
$85$	−0.129816	−	0.399533i	−0.0140805	−	0.0433355i
$86$		0			0
$87$	3.08526			0.330774
$88$		0			0
$89$	8.95287			0.949002			0.474501	−	0.880255i	$-0.342628\pi$
$89$	8.95287			0.949002			0.474501	+	0.880255i	$0.342628\pi$
$90$		0			0
$91$	−3.69630	−	11.3760i	−0.387477	−	1.19253i
$92$		0			0
$93$	5.95790	+	4.32867i	0.617805	+	0.448862i
$94$		0			0
$95$	0.537803	−	1.65519i	0.0551774	−	0.169819i
$96$		0			0
$97$	0.633590	−	0.460330i	0.0643313	−	0.0467394i	−0.555155	−	0.831747i	$-0.687341\pi$
$97$	0.633590	−	0.460330i	0.0643313	−	0.0467394i	0.619486	+	0.785008i	$0.287341\pi$
$98$		0			0
$99$	−3.36588	+	4.68919i	−0.338284	+	0.471281i
$100$		0			0
$101$	−8.95520	+	6.50634i	−0.891076	+	0.647405i	−0.936158	−	0.351579i	$-0.885645\pi$
$101$	−8.95520	+	6.50634i	−0.891076	+	0.647405i	0.0450823	+	0.998983i	$0.485645\pi$
$102$		0			0
$103$	1.24201	−	3.82251i	0.122379	−	0.376643i	−0.871036	−	0.491220i	$-0.836551\pi$
$103$	1.24201	−	3.82251i	0.122379	−	0.376643i	0.993414	+	0.114577i	$0.0365511\pi$
$104$		0			0
$105$	−2.09897	−	1.52499i	−0.204838	−	0.148824i
$106$		0			0
$107$	−0.206864	−	0.636662i	−0.0199983	−	0.0615484i	0.940559	−	0.339629i	$-0.110302\pi$
$107$	−0.206864	−	0.636662i	−0.0199983	−	0.0615484i	−0.960558	+	0.278081i	$0.910302\pi$
$108$		0			0
$109$	6.43834			0.616682			0.308341	−	0.951276i	$-0.400226\pi$
$109$	6.43834			0.616682			0.308341	+	0.951276i	$0.400226\pi$
$110$		0			0
$111$	11.7261			1.11299
$112$		0			0
$113$	−1.48658	−	4.57521i	−0.139845	−	0.430399i	0.856467	−	0.516202i	$-0.172655\pi$
$113$	−1.48658	−	4.57521i	−0.139845	−	0.430399i	−0.996312	+	0.0858025i	$0.972655\pi$
$114$		0			0
$115$	3.96915	+	2.88376i	0.370125	+	0.268912i
$116$		0			0
$117$	2.78280	−	8.56456i	0.257270	−	0.791794i
$118$		0			0
$119$	−0.785653	+	0.570811i	−0.0720207	+	0.0523261i
$120$		0			0
$121$	8.82427	−	6.56751i	0.802206	−	0.597047i
$122$		0			0
$123$	7.67060	−	5.57302i	0.691635	−	0.502502i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−11.7385	−	8.52854i	−1.04163	−	0.756785i	−0.0710234	−	0.997475i	$-0.522626\pi$
$127$	−11.7385	−	8.52854i	−1.04163	−	0.756785i	−0.970602	+	0.240689i	$0.922626\pi$
$128$		0			0
$129$	−2.13842	−	6.58137i	−0.188277	−	0.579457i
$130$		0			0
$131$	14.2108			1.24160			0.620802	−	0.783968i	$-0.286807\pi$
$131$	14.2108			1.24160			0.620802	+	0.783968i	$0.286807\pi$
$132$		0			0
$133$	−4.02316			−0.348852
$134$		0			0
$135$	−1.64405	−	5.05988i	−0.141498	−	0.435485i
$136$		0			0
$137$	2.18186	+	1.58521i	0.186409	+	0.135434i	0.677076	−	0.735913i	$-0.263247\pi$
$137$	2.18186	+	1.58521i	0.186409	+	0.135434i	−0.490667	+	0.871347i	$0.663247\pi$
$138$		0			0
$139$	2.11219	−	6.50066i	0.179154	−	0.551379i	−0.820645	−	0.571439i	$-0.806386\pi$
$139$	2.11219	−	6.50066i	0.179154	−	0.551379i	0.999799	+	0.0200595i	$0.00638556\pi$
$140$		0			0
$141$	−0.942607	+	0.684844i	−0.0793818	+	0.0576743i
$142$		0			0
$143$	−10.0073	+	13.9417i	−0.836851	+	1.16586i
$144$		0			0
$145$	−2.22396	+	1.61580i	−0.184690	+	0.134185i
$146$		0			0
$147$	0.574390	−	1.76779i	0.0473749	−	0.145805i
$148$		0			0
$149$	−16.0588	−	11.6674i	−1.31559	−	0.955831i	−0.999976	−	0.00694229i	$-0.997790\pi$
$149$	−16.0588	−	11.6674i	−1.31559	−	0.955831i	−0.315612	−	0.948888i	$-0.602210\pi$
$150$		0			0
$151$	5.22714	+	16.0875i	0.425379	+	1.30918i	0.902631	+	0.430415i	$0.141633\pi$
$151$	5.22714	+	16.0875i	0.425379	+	1.30918i	−0.477252	+	0.878766i	$0.658367\pi$
$152$		0			0
$153$	−0.731118			−0.0591074
$154$		0			0
$155$	−6.56166			−0.527045
$156$		0			0
$157$	3.58072	+	11.0203i	0.285773	+	0.879517i	0.986166	+	0.165761i	$0.0530079\pi$
$157$	3.58072	+	11.0203i	0.285773	+	0.879517i	−0.700393	+	0.713757i	$0.746992\pi$
$158$		0			0
$159$	4.92137	+	3.57559i	0.390290	+	0.283563i
$160$		0			0
$161$	3.50469	−	10.7863i	0.276208	−	0.850081i
$162$		0			0
$163$	−18.3592	+	13.3388i	−1.43800	+	1.04477i	−0.449550	+	0.893255i	$0.648416\pi$
$163$	−18.3592	+	13.3388i	−1.43800	+	1.04477i	−0.988455	+	0.151516i	$0.951584\pi$
$164$		0			0
$165$	0.0213963	+	3.72230i	0.00166570	+	0.289780i
$166$		0			0
$167$	13.3632	−	9.70893i	1.03407	−	0.751299i	0.0649545	−	0.997888i	$-0.479310\pi$
$167$	13.3632	−	9.70893i	1.03407	−	0.751299i	0.969120	+	0.246589i	$0.0793098\pi$
$168$		0			0
$169$	4.25645	−	13.1000i	0.327419	−	1.00769i
$170$		0			0
$171$	−2.45041	−	1.78033i	−0.187388	−	0.136145i
$172$		0			0
$173$	−4.44674	−	13.6857i	−0.338080	−	1.04050i	−0.965185	−	0.261568i	$-0.915761\pi$
$173$	−4.44674	−	13.6857i	−0.338080	−	1.04050i	0.627106	−	0.778934i	$-0.284239\pi$
$174$		0			0
$175$	2.31167			0.174746
$176$		0			0
$177$	16.1793			1.21611
$178$		0			0
$179$	6.03442	+	18.5720i	0.451034	+	1.38814i	0.875729	+	0.482803i	$0.160381\pi$
$179$	6.03442	+	18.5720i	0.451034	+	1.38814i	−0.424696	+	0.905336i	$0.639619\pi$
$180$		0			0
$181$	−1.05851	−	0.769052i	−0.0786784	−	0.0571632i	0.547751	−	0.836642i	$-0.315484\pi$
$181$	−1.05851	−	0.769052i	−0.0786784	−	0.0571632i	−0.626429	+	0.779478i	$0.715484\pi$
$182$		0			0
$183$	−4.40860	+	13.5683i	−0.325893	+	1.00300i
$184$		0			0
$185$	−8.45255	+	6.14113i	−0.621444	+	0.451505i
$186$		0			0
$187$	1.32756	+	0.422928i	0.0970804	+	0.0309276i
$188$		0			0
$189$	−9.94989	+	7.22902i	−0.723748	+	0.525834i
$190$		0			0
$191$	−5.47398	+	16.8472i	−0.396083	+	1.21902i	0.532032	+	0.846725i	$0.321429\pi$
$191$	−5.47398	+	16.8472i	−0.396083	+	1.21902i	−0.928115	+	0.372294i	$0.878571\pi$
$192$		0			0
$193$	−11.8441	−	8.60526i	−0.852559	−	0.619420i	0.0732915	−	0.997311i	$-0.476650\pi$
$193$	−11.8441	−	8.60526i	−0.852559	−	0.619420i	−0.925850	+	0.377890i	$0.876650\pi$
$194$		0			0
$195$	−1.79458	−	5.52314i	−0.128512	−	0.395520i
$196$		0			0
$197$	−23.4114			−1.66799			−0.833997	−	0.551768i	$-0.813953\pi$
$197$	−23.4114			−1.66799			−0.833997	+	0.551768i	$0.813953\pi$
$198$		0			0
$199$	0.478502			0.0339201			0.0169601	−	0.999856i	$-0.494601\pi$
$199$	0.478502			0.0339201			0.0169601	+	0.999856i	$0.494601\pi$
$200$		0			0
$201$	0.194089	+	0.597346i	0.0136900	+	0.0421335i
$202$		0			0
$203$	5.14107	+	3.73521i	0.360833	+	0.262160i
$204$		0			0
$205$	−2.61055	+	8.03445i	−0.182329	+	0.561150i
$206$		0			0
$207$	6.90779	−	5.01880i	0.480124	−	0.348831i
$208$		0			0
$209$	3.41957	+	4.65019i	0.236536	+	0.321660i
$210$		0			0
$211$	−7.50479	+	5.45255i	−0.516651	+	0.375369i	−0.815341	−	0.578981i	$-0.803450\pi$
$211$	−7.50479	+	5.45255i	−0.516651	+	0.375369i	0.298690	+	0.954350i	$0.403450\pi$
$212$		0			0
$213$	−1.78791	+	5.50262i	−0.122505	+	0.377033i
$214$		0			0
$215$	4.98822	+	3.62415i	0.340194	+	0.247165i
$216$		0			0
$217$	4.68730	+	14.4260i	0.318194	+	0.979302i
$218$		0			0
$219$	−13.9383			−0.941864
$220$		0			0
$221$	−2.17373			−0.146221
$222$		0			0
$223$	2.18338	+	6.71974i	0.146210	+	0.449987i	0.997165	−	0.0752516i	$-0.0239760\pi$
$223$	2.18338	+	6.71974i	0.146210	+	0.449987i	−0.850955	+	0.525239i	$0.823976\pi$
$224$		0			0
$225$	1.40799	+	1.02296i	0.0938658	+	0.0681975i
$226$		0			0
$227$	1.16342	−	3.58064i	0.0772190	−	0.237656i	−0.904994	−	0.425423i	$-0.860125\pi$
$227$	1.16342	−	3.58064i	0.0772190	−	0.237656i	0.982213	+	0.187768i	$0.0601252\pi$
$228$		0			0
$229$	9.27282	−	6.73710i	0.612765	−	0.445200i	−0.237622	−	0.971358i	$-0.576368\pi$
$229$	9.27282	−	6.73710i	0.612765	−	0.445200i	0.850387	+	0.526158i	$0.176368\pi$
$230$		0			0
$231$	8.16831	−	2.70605i	0.537435	−	0.178045i
$232$		0			0
$233$	−5.02034	+	3.64749i	−0.328894	+	0.238955i	−0.739961	−	0.672650i	$-0.765156\pi$
$233$	−5.02034	+	3.64749i	−0.328894	+	0.238955i	0.411067	+	0.911605i	$0.365156\pi$
$234$		0			0
$235$	0.320799	−	0.987319i	0.0209266	−	0.0644056i
$236$		0			0
$237$	−4.39089	−	3.19017i	−0.285219	−	0.207224i
$238$		0			0
$239$	5.21504	+	16.0502i	0.337333	+	1.03820i	0.965562	+	0.260175i	$0.0837801\pi$
$239$	5.21504	+	16.0502i	0.337333	+	1.03820i	−0.628229	+	0.778029i	$0.716220\pi$
$240$		0			0
$241$	27.7757			1.78919			0.894596	−	0.446875i	$-0.147463\pi$
$241$	27.7757			1.78919			0.894596	+	0.446875i	$0.147463\pi$
$242$		0			0
$243$	−15.1190			−0.969887
$244$		0			0
$245$	0.511782	+	1.57510i	0.0326966	+	0.100630i
$246$		0			0
$247$	−7.28545	−	5.29319i	−0.463562	−	0.336798i
$248$		0			0
$249$	2.49937	−	7.69228i	0.158391	−	0.487478i
$250$		0			0
$251$	20.4086	−	14.8277i	1.28818	−	0.935917i	0.288412	−	0.957506i	$-0.406873\pi$
$251$	20.4086	−	14.8277i	1.28818	−	0.935917i	0.999767	+	0.0215891i	$0.00687257\pi$
$252$		0			0
$253$	−15.4463	+	5.11714i	−0.971099	+	0.321712i
$254$		0			0
$255$	−0.381440	+	0.277132i	−0.0238867	+	0.0173547i
$256$		0			0
$257$	2.22694	−	6.85383i	0.138913	−	0.427530i	−0.857265	−	0.514875i	$-0.827838\pi$
$257$	2.22694	−	6.85383i	0.138913	−	0.427530i	0.996178	+	0.0873452i	$0.0278383\pi$
$258$		0			0
$259$	19.5395	+	14.1963i	1.21413	+	0.882115i
$260$		0			0
$261$	1.47840	+	4.55006i	0.0915108	+	0.281641i
$262$		0			0
$263$	−11.1830			−0.689572			−0.344786	−	0.938681i	$-0.612048\pi$
$263$	−11.1830			−0.689572			−0.344786	+	0.938681i	$0.612048\pi$
$264$		0			0
$265$	−5.42009			−0.332954
$266$		0			0
$267$	−3.10504	−	9.55632i	−0.190025	−	0.584837i
$268$		0			0
$269$	−13.4968	−	9.80598i	−0.822913	−	0.597881i	0.0946323	−	0.995512i	$-0.469832\pi$
$269$	−13.4968	−	9.80598i	−0.822913	−	0.597881i	−0.917545	+	0.397631i	$0.869832\pi$
$270$		0			0
$271$	0.354916	−	1.09232i	0.0215596	−	0.0663537i	−0.939698	−	0.342006i	$-0.888894\pi$
$271$	0.354916	−	1.09232i	0.0215596	−	0.0663537i	0.961257	+	0.275652i	$0.0888938\pi$
$272$		0			0
$273$	−10.8609	+	7.89088i	−0.657329	+	0.477577i
$274$		0			0
$275$	−1.96485	−	2.67196i	−0.118485	−	0.161125i
$276$		0			0
$277$	−19.5666	+	14.2160i	−1.17564	+	0.854155i	−0.991674	−	0.128777i	$-0.958895\pi$
$277$	−19.5666	+	14.2160i	−1.17564	+	0.854155i	−0.183970	+	0.982932i	$0.558895\pi$
$278$		0			0
$279$	−3.52888	+	10.8608i	−0.211268	+	0.650217i
$280$		0			0
$281$	−1.08607	−	0.789077i	−0.0647896	−	0.0470724i	0.554919	−	0.831904i	$-0.312749\pi$
$281$	−1.08607	−	0.789077i	−0.0647896	−	0.0470724i	−0.619709	+	0.784832i	$0.712749\pi$
$282$		0			0
$283$	−9.13341	−	28.1098i	−0.542925	−	1.67095i	−0.725873	−	0.687829i	$-0.758564\pi$
$283$	−9.13341	−	28.1098i	−0.542925	−	1.67095i	0.182948	−	0.983123i	$-0.441436\pi$
$284$		0			0
$285$	−1.95327			−0.115702
$286$		0			0
$287$	19.5288			1.15275
$288$		0			0
$289$	−5.19875	−	16.0001i	−0.305809	−	0.941183i
$290$		0			0
$291$	−0.711099	−	0.516644i	−0.0416854	−	0.0302862i
$292$		0			0
$293$	2.67950	−	8.24666i	0.156538	−	0.481775i	−0.841775	−	0.539828i	$-0.818489\pi$
$293$	2.67950	−	8.24666i	0.156538	−	0.481775i	0.998314	+	0.0580530i	$0.0184892\pi$
$294$		0			0
$295$	−11.6626	+	8.47337i	−0.679022	+	0.493339i
$296$		0			0
$297$	16.8128	+	5.35616i	0.975577	+	0.310796i
$298$		0			0
$299$	20.5379	−	14.9217i	1.18774	−	0.862941i
$300$		0			0
$301$	4.40450	−	13.5557i	0.253871	−	0.781335i
$302$		0			0
$303$	10.0507	+	7.30228i	0.577399	+	0.419505i
$304$		0			0
$305$	−3.92807	−	12.0893i	−0.224920	−	0.692234i
$306$		0			0
$307$	3.11110			0.177560			0.0887799	−	0.996051i	$-0.471703\pi$
$307$	3.11110			0.177560			0.0887799	+	0.996051i	$0.471703\pi$
$308$		0			0
$309$	−4.51091			−0.256617
$310$		0			0
$311$	−7.10193	−	21.8575i	−0.402713	−	1.23942i	−0.922789	−	0.385305i	$-0.874096\pi$
$311$	−7.10193	−	21.8575i	−0.402713	−	1.23942i	0.520076	−	0.854120i	$-0.325904\pi$
$312$		0			0
$313$	16.6517	+	12.0981i	0.941208	+	0.683827i	0.948711	−	0.316145i	$-0.102388\pi$
$313$	16.6517	+	12.0981i	0.941208	+	0.683827i	−0.00750347	+	0.999972i	$0.502388\pi$
$314$		0			0
$315$	1.24323	−	3.82626i	0.0700478	−	0.215585i
$316$		0			0
$317$	26.4316	−	19.2037i	1.48455	−	1.07859i	0.508493	−	0.861066i	$-0.330203\pi$
$317$	26.4316	−	19.2037i	1.48455	−	1.07859i	0.976055	−	0.217522i	$-0.0697973\pi$
$318$		0			0
$319$	−0.0524066	−	9.11714i	−0.00293421	−	0.510462i
$320$		0			0
$321$	−0.607830	+	0.441614i	−0.0339257	+	0.0246485i
$322$		0			0
$323$	−0.225928	+	0.695335i	−0.0125710	+	0.0386895i
$324$		0			0
$325$	4.18616	+	3.04142i	0.232206	+	0.168708i
$326$		0			0
$327$	−2.23295	−	6.87231i	−0.123482	−	0.380039i
$328$		0			0
$329$	−2.39981			−0.132306
$330$		0			0
$331$	16.5065			0.907281			0.453641	−	0.891185i	$-0.350125\pi$
$331$	16.5065			0.907281			0.453641	+	0.891185i	$0.350125\pi$
$332$		0			0
$333$	5.61892	+	17.2933i	0.307915	+	0.947665i
$334$		0			0
$335$	−0.452747	−	0.328940i	−0.0247362	−	0.0179719i
$336$		0			0
$337$	−4.77683	+	14.7016i	−0.260211	+	0.800846i	0.732548	+	0.680716i	$0.238331\pi$
$337$	−4.77683	+	14.7016i	−0.260211	+	0.800846i	−0.992758	+	0.120130i	$0.961669\pi$
$338$		0			0
$339$	−4.36802	+	3.17355i	−0.237238	+	0.172364i
$340$		0			0
$341$	12.6903	−	17.6795i	0.687218	−	0.957399i
$342$		0			0
$343$	16.1886	−	11.7617i	0.874103	−	0.635073i
$344$		0			0
$345$	1.70155	−	5.23683i	0.0916083	−	0.281941i
$346$		0			0
$347$	7.16099	+	5.20276i	0.384422	+	0.279299i	0.763166	−	0.646203i	$-0.223644\pi$
$347$	7.16099	+	5.20276i	0.384422	+	0.279299i	−0.378744	+	0.925501i	$0.623644\pi$
$348$		0			0
$349$	1.82441	+	5.61495i	0.0976584	+	0.300562i	0.987937	−	0.154854i	$-0.0494907\pi$
$349$	1.82441	+	5.61495i	0.0976584	+	0.300562i	−0.890279	+	0.455416i	$0.849491\pi$
$350$		0			0
$351$	−27.5291			−1.46939
$352$		0			0
$353$	−35.4813			−1.88848			−0.944240	−	0.329258i	$-0.893201\pi$
$353$	−35.4813			−1.88848			−0.944240	+	0.329258i	$0.893201\pi$
$354$		0			0
$355$	−1.59303	−	4.90284i	−0.0845492	−	0.260216i
$356$		0			0
$357$	0.881765	+	0.640640i	0.0466680	+	0.0339063i
$358$		0			0
$359$	0.723147	−	2.22562i	0.0381662	−	0.117464i	−0.930158	−	0.367159i	$-0.880331\pi$
$359$	0.723147	−	2.22562i	0.0381662	−	0.117464i	0.968324	+	0.249695i	$0.0803305\pi$
$360$		0			0
$361$	12.9209	−	9.38759i	0.680048	−	0.494084i
$362$		0			0
$363$	−10.0706	−	7.14130i	−0.528570	−	0.374821i
$364$		0			0
$365$	10.0472	−	7.29973i	0.525895	−	0.382085i
$366$		0			0
$367$	−6.40910	+	19.7252i	−0.334552	+	1.02965i	0.632390	+	0.774650i	$0.282074\pi$
$367$	−6.40910	+	19.7252i	−0.334552	+	1.02965i	−0.966942	+	0.254996i	$0.917926\pi$
$368$		0			0
$369$	11.8946	+	8.64191i	0.619206	+	0.449880i
$370$		0			0
$371$	3.87183	+	11.9163i	0.201015	+	0.618661i
$372$		0			0
$373$	35.2190			1.82357			0.911786	−	0.410665i	$-0.134703\pi$
$373$	35.2190			1.82357			0.911786	+	0.410665i	$0.134703\pi$
$374$		0			0
$375$	1.12233			0.0579571
$376$		0			0
$377$	4.39551	+	13.5280i	0.226381	+	0.696728i
$378$		0			0
$379$	−17.2585	−	12.5391i	−0.886512	−	0.644089i	0.0484543	−	0.998825i	$-0.484570\pi$
$379$	−17.2585	−	12.5391i	−0.886512	−	0.644089i	−0.934966	+	0.354737i	$0.884570\pi$
$380$		0			0
$381$	−5.03223	+	15.4876i	−0.257809	+	0.793454i
$382$		0			0
$383$	6.52120	−	4.73793i	0.333218	−	0.242097i	−0.408577	−	0.912724i	$-0.633975\pi$
$383$	6.52120	−	4.73793i	0.333218	−	0.242097i	0.741795	+	0.670627i	$0.233975\pi$
$384$		0			0
$385$	−4.47080	+	6.22850i	−0.227853	+	0.317434i
$386$		0			0
$387$	8.68133	−	6.30736i	0.441297	−	0.320621i
$388$		0			0
$389$	3.33258	−	10.2566i	0.168969	−	0.520032i	−0.830338	−	0.557260i	$-0.811853\pi$
$389$	3.33258	−	10.2566i	0.168969	−	0.520032i	0.999307	+	0.0372279i	$0.0118528\pi$
$390$		0			0
$391$	−1.66742	−	1.21145i	−0.0843250	−	0.0612657i
$392$		0			0
$393$	−4.92859	−	15.1686i	−0.248615	−	0.765157i
$394$		0			0
$395$	4.83585			0.243318
$396$		0			0
$397$	−20.4389			−1.02580			−0.512900	−	0.858448i	$-0.671429\pi$
$397$	−20.4389			−1.02580			−0.512900	+	0.858448i	$0.671429\pi$
$398$		0			0
$399$	1.39531	+	4.29433i	0.0698531	+	0.214986i
$400$		0			0
$401$	−13.2079	−	9.59609i	−0.659570	−	0.479206i	0.206948	−	0.978352i	$-0.433647\pi$
$401$	−13.2079	−	9.59609i	−0.659570	−	0.479206i	−0.866518	+	0.499146i	$0.833647\pi$
$402$		0			0
$403$	−10.4919	+	32.2907i	−0.522638	+	1.60852i
$404$		0			0
$405$	−0.606778	+	0.440850i	−0.0301510	+	0.0219060i
$406$		0			0
$407$	−0.199180	−	34.6513i	−0.00987300	−	1.71760i
$408$		0			0
$409$	−15.6595	+	11.3773i	−0.774311	+	0.562570i	−0.903266	−	0.429081i	$-0.858838\pi$
$409$	−15.6595	+	11.3773i	−0.774311	+	0.562570i	0.128955	+	0.991650i	$0.458838\pi$
$410$		0			0
$411$	0.935348	−	2.87870i	0.0461373	−	0.141996i
$412$		0			0
$413$	26.9601	+	19.5877i	1.32662	+	0.963846i
$414$		0			0
$415$	2.22694	+	6.85383i	0.109316	+	0.336441i
$416$		0			0
$417$	−7.67138			−0.375669
$418$		0			0
$419$	−11.0672			−0.540669			−0.270334	−	0.962767i	$-0.587134\pi$
$419$	−11.0672			−0.540669			−0.270334	+	0.962767i	$0.587134\pi$
$420$		0			0
$421$	6.68747	+	20.5819i	0.325928	+	1.00310i	0.971020	+	0.238998i	$0.0768188\pi$
$421$	6.68747	+	20.5819i	0.325928	+	1.00310i	−0.645093	+	0.764104i	$0.723181\pi$
$422$		0			0
$423$	−1.46167	−	1.06197i	−0.0710689	−	0.0516346i
$424$		0			0
$425$	0.129816	−	0.399533i	0.00629701	−	0.0193802i
$426$		0			0
$427$	−23.7728	+	17.2720i	−1.15045	+	0.835849i
$428$		0			0
$429$	18.3521	+	5.84655i	0.886048	+	0.282274i
$430$		0			0
$431$	−15.9413	+	11.5820i	−0.767865	+	0.557887i	−0.901313	−	0.433169i	$-0.857395\pi$
$431$	−15.9413	+	11.5820i	−0.767865	+	0.557887i	0.133448	+	0.991056i	$0.457395\pi$
$432$		0			0
$433$	12.1300	−	37.3323i	0.582931	−	1.79408i	−0.0244951	−	0.999700i	$-0.507798\pi$
$433$	12.1300	−	37.3323i	0.582931	−	1.79408i	0.607426	−	0.794376i	$-0.292202\pi$
$434$		0			0
$435$	2.49603	+	1.81347i	0.119675	+	0.0869492i
$436$		0			0
$437$	−2.63854	−	8.12059i	−0.126218	−	0.388460i
$438$		0			0
$439$	8.40014			0.400917			0.200458	−	0.979702i	$-0.435757\pi$
$439$	8.40014			0.400917			0.200458	+	0.979702i	$0.435757\pi$
$440$		0			0
$441$	2.88233			0.137254
$442$		0			0
$443$	−1.62643	−	5.00564i	−0.0772741	−	0.237825i	0.904956	−	0.425505i	$-0.139903\pi$
$443$	−1.62643	−	5.00564i	−0.0772741	−	0.237825i	−0.982230	+	0.187679i	$0.939903\pi$
$444$		0			0
$445$	7.24302	+	5.26237i	0.343352	+	0.249460i
$446$		0			0
$447$	−6.88430	+	21.1877i	−0.325616	+	1.00214i
$448$		0			0
$449$	−22.2573	+	16.1709i	−1.05039	+	0.763152i	−0.972286	−	0.233794i	$-0.924886\pi$
$449$	−22.2573	+	16.1709i	−1.05039	+	0.763152i	−0.0781020	+	0.996945i	$0.524886\pi$
$450$		0			0
$451$	−16.5989	−	22.5725i	−0.781613	−	1.06290i
$452$		0			0
$453$	15.3590	−	11.1589i	0.721627	−	0.524292i
$454$		0			0
$455$	3.69630	−	11.3760i	0.173285	−	0.533317i
$456$		0			0
$457$	15.0241	+	10.9157i	0.702799	+	0.510613i	0.880842	−	0.473409i	$-0.156977\pi$
$457$	15.0241	+	10.9157i	0.702799	+	0.510613i	−0.178044	+	0.984023i	$0.556977\pi$
$458$		0			0
$459$	0.690658	+	2.12563i	0.0322372	+	0.0992158i
$460$		0			0
$461$	−33.4696			−1.55884			−0.779418	−	0.626504i	$-0.784485\pi$
$461$	−33.4696			−1.55884			−0.779418	+	0.626504i	$0.784485\pi$
$462$		0			0
$463$	−7.19202			−0.334242			−0.167121	−	0.985936i	$-0.553447\pi$
$463$	−7.19202			−0.334242			−0.167121	+	0.985936i	$0.553447\pi$
$464$		0			0
$465$	2.27571	+	7.00393i	0.105534	+	0.324799i
$466$		0			0
$467$	−14.3010	−	10.3903i	−0.661772	−	0.480805i	0.205489	−	0.978659i	$-0.434122\pi$
$467$	−14.3010	−	10.3903i	−0.661772	−	0.480805i	−0.867261	+	0.497854i	$0.834122\pi$
$468$		0			0
$469$	−0.399767	+	1.23036i	−0.0184595	+	0.0568125i
$470$		0			0
$471$	10.5213	−	7.64414i	0.484794	−	0.352223i
$472$		0			0
$473$	−19.4120	+	6.43095i	−0.892567	+	0.295695i
$474$		0			0
$475$	1.40799	−	1.02296i	0.0646029	−	0.0469367i
$476$		0			0
$477$	−2.91494	+	8.97127i	−0.133466	+	0.410766i
$478$		0			0
$479$	3.90215	+	2.83508i	0.178294	+	0.129538i	0.673353	−	0.739321i	$-0.264854\pi$
$479$	3.90215	+	2.83508i	0.178294	+	0.129538i	−0.495059	+	0.868859i	$0.664854\pi$
$480$		0			0
$481$	16.7059	+	51.4155i	0.761724	+	2.34435i
$482$		0			0
$483$	−12.7288			−0.579182
$484$		0			0
$485$	0.783160			0.0355615
$486$		0			0
$487$	−6.87203	−	21.1499i	−0.311401	−	0.958395i	−0.977211	−	0.212273i	$-0.931914\pi$
$487$	−6.87203	−	21.1499i	−0.311401	−	0.958395i	0.665809	−	0.746122i	$-0.268086\pi$
$488$		0			0
$489$	20.6052	+	14.9705i	0.931798	+	0.676991i
$490$		0			0
$491$	−6.49346	+	19.9848i	−0.293046	+	0.901901i	0.690825	+	0.723022i	$0.257247\pi$
$491$	−6.49346	+	19.9848i	−0.293046	+	0.901901i	−0.983871	+	0.178880i	$0.942753\pi$
$492$		0			0
$493$	0.934273	−	0.678789i	0.0420775	−	0.0305711i
$494$		0			0
$495$	−5.47929	+	1.81522i	−0.246276	+	0.0815879i
$496$		0			0
$497$	−9.64107	+	7.00465i	−0.432461	+	0.314201i
$498$		0			0
$499$	4.12469	−	12.6945i	0.184646	−	0.568283i	−0.815296	−	0.579045i	$-0.803426\pi$
$499$	4.12469	−	12.6945i	0.184646	−	0.568283i	0.999942	+	0.0107616i	$0.00342560\pi$
$500$		0			0
$501$	−14.9980	−	10.8967i	−0.670059	−	0.486827i
$502$		0			0
$503$	−8.59700	−	26.4589i	−0.383321	−	1.17974i	−0.937691	−	0.347471i	$-0.887040\pi$
$503$	−8.59700	−	26.4589i	−0.383321	−	1.17974i	0.554369	−	0.832271i	$-0.312960\pi$
$504$		0			0
$505$	−11.0692			−0.492575
$506$		0			0
$507$	−15.4592			−0.686567
$508$		0			0
$509$	2.64140	+	8.12939i	0.117078	+	0.360329i	0.992375	−	0.123257i	$-0.0393340\pi$
$509$	2.64140	+	8.12939i	0.117078	+	0.360329i	−0.875297	+	0.483586i	$0.839334\pi$
$510$		0			0
$511$	−23.2259	−	16.8746i	−1.02745	−	0.746488i
$512$		0			0
$513$	−2.86126	+	8.80605i	−0.126328	+	0.388797i
$514$		0			0
$515$	3.25162	−	2.36244i	0.143284	−	0.104102i
$516$		0			0
$517$	2.03977	+	2.77383i	0.0897090	+	0.121993i
$518$		0			0
$519$	−13.0659	+	9.49293i	−0.573529	+	0.416693i
$520$		0			0
$521$	−2.90594	+	8.94357i	−0.127312	+	0.391825i	−0.994315	−	0.106477i	$-0.966043\pi$
$521$	−2.90594	+	8.94357i	−0.127312	+	0.391825i	0.867003	+	0.498302i	$0.166043\pi$
$522$		0			0
$523$	33.0969	+	24.0463i	1.44723	+	1.05147i	0.986469	+	0.163948i	$0.0524229\pi$
$523$	33.0969	+	24.0463i	1.44723	+	1.05147i	0.460760	+	0.887525i	$0.347577\pi$
$524$		0			0
$525$	−0.801735	−	2.46749i	−0.0349906	−	0.107690i
$526$		0			0
$527$	2.75651			0.120076
$528$		0			0
$529$	1.07025			0.0465324
$530$		0			0
$531$	7.75284	+	23.8608i	0.336445	+	1.03547i
$532$		0			0
$533$	35.3643	+	25.6937i	1.53180	+	1.11292i
$534$		0			0
$535$	0.206864	−	0.636662i	0.00894351	−	0.0275253i
$536$		0			0
$537$	17.7310	−	12.8823i	0.765148	−	0.555913i
$538$		0			0
$539$	−5.23370	−	1.66733i	−0.225431	−	0.0718171i
$540$		0			0
$541$	−25.6654	+	18.6470i	−1.10344	+	0.801697i	−0.981618	−	0.190855i	$-0.938874\pi$
$541$	−25.6654	+	18.6470i	−1.10344	+	0.801697i	−0.121822	+	0.992552i	$0.538874\pi$
$542$		0			0
$543$	−0.453776	+	1.39658i	−0.0194734	+	0.0599329i
$544$		0			0
$545$	5.20873	+	3.78436i	0.223117	+	0.162104i
$546$		0			0
$547$	11.7089	+	36.0362i	0.500635	+	1.54080i	0.807987	+	0.589201i	$0.200557\pi$
$547$	11.7089	+	36.0362i	0.500635	+	1.54080i	−0.307352	+	0.951596i	$0.599443\pi$
$548$		0			0
$549$	−22.1227			−0.944172
$550$		0			0
$551$	4.78421			0.203814
$552$		0			0
$553$	−3.45447	−	10.6318i	−0.146899	−	0.452109i
$554$		0			0
$555$	9.48658	+	6.89240i	0.402683	+	0.292566i
$556$		0			0
$557$	6.52612	−	20.0853i	0.276521	−	0.851043i	−0.712292	−	0.701883i	$-0.752343\pi$
$557$	6.52612	−	20.0853i	0.276521	−	0.851043i	0.988813	−	0.149160i	$-0.0476570\pi$
$558$		0			0
$559$	25.8109	−	18.7527i	1.09169	−	0.793156i
$560$		0			0
$561$	−0.00898845	−	1.56372i	−0.000379493	−	0.0660201i
$562$		0			0
$563$	29.4806	−	21.4189i	1.24246	−	0.902698i	0.244698	−	0.969599i	$-0.421311\pi$
$563$	29.4806	−	21.4189i	1.24246	−	0.902698i	0.997760	+	0.0669013i	$0.0213113\pi$
$564$		0			0
$565$	1.48658	−	4.57521i	0.0625407	−	0.192480i
$566$		0			0
$567$	1.40267	+	1.01910i	0.0589067	+	0.0427982i
$568$		0			0
$569$	−3.54762	−	10.9184i	−0.148724	−	0.457725i	0.848747	−	0.528799i	$-0.177357\pi$
$569$	−3.54762	−	10.9184i	−0.148724	−	0.457725i	−0.997471	+	0.0710738i	$0.977357\pi$
$570$		0			0
$571$	−33.4382			−1.39934			−0.699672	−	0.714464i	$-0.746671\pi$
$571$	−33.4382			−1.39934			−0.699672	+	0.714464i	$0.746671\pi$
$572$		0			0
$573$	19.8812			0.830549
$574$		0			0
$575$	1.51608	+	4.66602i	0.0632250	+	0.194586i
$576$		0			0
$577$	−4.57859	−	3.32654i	−0.190609	−	0.138486i	0.488388	−	0.872627i	$-0.337585\pi$
$577$	−4.57859	−	3.32654i	−0.190609	−	0.138486i	−0.678997	+	0.734141i	$0.737585\pi$
$578$		0			0
$579$	−5.07750	+	15.6269i	−0.211014	+	0.649433i
$580$		0			0
$581$	13.4776	−	9.79201i	0.559143	−	0.406241i
$582$		0			0
$583$	10.4825	−	14.6037i	0.434141	−	0.604824i
$584$		0			0
$585$	7.28545	−	5.29319i	0.301216	−	0.218847i
$586$		0			0
$587$	10.4907	−	32.2870i	0.432996	−	1.33263i	−0.462129	−	0.886813i	$-0.652914\pi$
$587$	10.4907	−	32.2870i	0.432996	−	1.33263i	0.895126	−	0.445814i	$-0.147086\pi$
$588$		0			0
$589$	9.23873	+	6.71233i	0.380675	+	0.276577i
$590$		0			0
$591$	8.11955	+	24.9894i	0.333994	+	1.02793i
$592$		0			0
$593$	8.42927			0.346149			0.173074	−	0.984909i	$-0.444630\pi$
$593$	8.42927			0.346149			0.173074	+	0.984909i	$0.444630\pi$
$594$		0			0
$595$	−0.971121			−0.0398121
$596$		0			0
$597$	−0.165954	−	0.510755i	−0.00679206	−	0.0209038i
$598$		0			0
$599$	−32.0192	−	23.2633i	−1.30827	−	0.950512i	−0.308267	−	0.951300i	$-0.599749\pi$
$599$	−32.0192	−	23.2633i	−1.30827	−	0.950512i	−1.00000		0.000788105i	$0.999749\pi$
$600$		0			0
$601$	0.357186	−	1.09930i	0.0145699	−	0.0448416i	−0.943507	−	0.331352i	$-0.892495\pi$
$601$	0.357186	−	1.09930i	0.0145699	−	0.0448416i	0.958077	+	0.286510i	$0.0924953\pi$
$602$		0			0
$603$	−0.787946	+	0.572476i	−0.0320876	+	0.0233130i
$604$		0			0
$605$	10.9993	−	0.126455i	0.447184	−	0.00514112i
$606$		0			0
$607$	−35.2814	+	25.6334i	−1.43203	+	1.04043i	−0.442393	+	0.896821i	$0.645870\pi$
$607$	−35.2814	+	25.6334i	−1.43203	+	1.04043i	−0.989635	+	0.143608i	$0.954130\pi$
$608$		0			0
$609$	2.20394	−	6.78304i	0.0893083	−	0.274863i
$610$		0			0
$611$	−4.34577	−	3.15739i	−0.175811	−	0.127734i
$612$		0			0
$613$	−7.46362	−	22.9706i	−0.301453	−	0.927776i	−0.980977	−	0.194123i	$-0.937814\pi$
$613$	−7.46362	−	22.9706i	−0.301453	−	0.927776i	0.679525	−	0.733653i	$-0.262186\pi$
$614$		0			0
$615$	9.48139			0.382326
$616$		0			0
$617$	−30.2901			−1.21943			−0.609716	−	0.792620i	$-0.708717\pi$
$617$	−30.2901			−1.21943			−0.609716	+	0.792620i	$0.708717\pi$
$618$		0			0
$619$	−7.74826	−	23.8467i	−0.311429	−	0.958480i	−0.977199	−	0.212323i	$-0.931897\pi$
$619$	−7.74826	−	23.8467i	−0.311429	−	0.958480i	0.665771	−	0.746157i	$-0.268103\pi$
$620$		0			0
$621$	−21.1170	−	15.3424i	−0.847395	−	0.615669i
$622$		0			0
$623$	6.39545	−	19.6832i	0.256228	−	0.788590i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	3.77764	−	5.26283i	0.150865	−	0.210177i
$628$		0			0
$629$	3.55087	−	2.57985i	0.141582	−	0.102866i
$630$		0			0
$631$	0.854729	−	2.63059i	0.0340262	−	0.104722i	−0.932601	−	0.360909i	$-0.882466\pi$
$631$	0.854729	−	2.63059i	0.0340262	−	0.104722i	0.966627	+	0.256187i	$0.0824664\pi$
$632$		0			0
$633$	8.42288	+	6.11958i	0.334779	+	0.243231i
$634$		0			0
$635$	−4.48372	−	13.7995i	−0.177931	−	0.547615i
$636$		0			0
$637$	8.56960			0.339540
$638$		0			0
$639$	−8.97185			−0.354921
$640$		0			0
$641$	5.10346	+	15.7068i	0.201574	+	0.620382i	0.999837	+	0.0180722i	$0.00575288\pi$
$641$	5.10346	+	15.7068i	0.201574	+	0.620382i	−0.798262	+	0.602310i	$0.794247\pi$
$642$		0			0
$643$	33.5405	+	24.3686i	1.32271	+	0.961005i	0.999894	+	0.0145433i	$0.00462945\pi$
$643$	33.5405	+	24.3686i	1.32271	+	0.961005i	0.322816	+	0.946462i	$0.395371\pi$
$644$		0			0
$645$	2.13842	−	6.58137i	0.0842000	−	0.259141i
$646$		0			0
$647$	20.7768	−	15.0952i	0.816821	−	0.593455i	−0.0989792	−	0.995090i	$-0.531558\pi$
$647$	20.7768	−	15.0952i	0.816821	−	0.593455i	0.915800	+	0.401634i	$0.131558\pi$
$648$		0			0
$649$	−0.274823	−	47.8109i	−0.0107878	−	1.87674i
$650$		0			0
$651$	13.7727	−	10.0065i	0.539795	−	0.392184i
$652$		0			0
$653$	10.1771	−	31.3220i	0.398262	−	1.22572i	−0.528130	−	0.849164i	$-0.677107\pi$
$653$	10.1771	−	31.3220i	0.398262	−	1.22572i	0.926392	−	0.376561i	$-0.122893\pi$
$654$		0			0
$655$	11.4968	+	8.35290i	0.449216	+	0.326375i
$656$		0			0
$657$	−6.67900	−	20.5558i	−0.260573	−	0.801960i
$658$		0			0
$659$	−4.58757			−0.178706			−0.0893532	−	0.996000i	$-0.528480\pi$
$659$	−4.58757			−0.178706			−0.0893532	+	0.996000i	$0.528480\pi$
$660$		0			0
$661$	−21.6825			−0.843353			−0.421676	−	0.906746i	$-0.638558\pi$
$661$	−21.6825			−0.843353			−0.421676	+	0.906746i	$0.638558\pi$
$662$		0			0
$663$	0.753892	+	2.32024i	0.0292787	+	0.0901106i
$664$		0			0
$665$	−3.25481	−	2.36476i	−0.126216	−	0.0917013i
$666$		0			0
$667$	−4.16766	+	12.8267i	−0.161372	+	0.496653i
$668$		0			0
$669$	6.41543	−	4.66108i	0.248035	−	0.180208i
$670$		0			0
$671$	40.1700	+	12.7972i	1.55075	+	0.494032i
$672$		0			0
$673$	−14.4381	+	10.4899i	−0.556547	+	0.404355i	−0.830193	−	0.557475i	$-0.811770\pi$
$673$	−14.4381	+	10.4899i	−0.556547	+	0.404355i	0.273647	+	0.961830i	$0.411770\pi$
$674$		0			0
$675$	1.64405	−	5.05988i	0.0632797	−	0.194755i
$676$		0			0
$677$	−8.04338	−	5.84386i	−0.309132	−	0.224598i	0.422392	−	0.906413i	$-0.361191\pi$
$677$	−8.04338	−	5.84386i	−0.309132	−	0.224598i	−0.731524	+	0.681816i	$0.761191\pi$
$678$		0			0
$679$	−0.559448	−	1.72180i	−0.0214696	−	0.0660767i
$680$		0			0
$681$	−4.22548			−0.161921
$682$		0			0
$683$	10.6508			0.407541			0.203770	−	0.979019i	$-0.434680\pi$
$683$	10.6508			0.407541			0.203770	+	0.979019i	$0.434680\pi$
$684$		0			0
$685$	0.833396	+	2.56493i	0.0318424	+	0.0980009i
$686$		0			0
$687$	−10.4072	−	7.56127i	−0.397059	−	0.288480i
$688$		0			0
$689$	−8.66657	+	26.6730i	−0.330170	+	1.01616i
$690$		0			0
$691$	8.95202	−	6.50402i	0.340551	−	0.247425i	−0.404343	−	0.914607i	$-0.632500\pi$
$691$	8.95202	−	6.50402i	0.340551	−	0.247425i	0.744894	+	0.667183i	$0.232500\pi$
$692$		0			0
$693$	7.90493	+	10.7497i	0.300283	+	0.408348i
$694$		0			0
$695$	5.52979	−	4.01763i	0.209757	−	0.152397i
$696$		0			0
$697$	1.09668	−	3.37523i	0.0415396	−	0.127846i
$698$		0			0
$699$	5.63450	+	4.09370i	0.213116	+	0.154838i
$700$		0			0
$701$	−13.1808	−	40.5663i	−0.497832	−	1.53217i	−0.812496	−	0.582967i	$-0.801892\pi$
$701$	−13.1808	−	40.5663i	−0.497832	−	1.53217i	0.314664	−	0.949203i	$-0.398108\pi$
$702$		0			0
$703$	18.1832			0.685793
$704$		0			0
$705$	−1.16513			−0.0438812
$706$		0			0
$707$	7.90727	+	24.3361i	0.297384	+	0.915253i
$708$		0			0
$709$	42.6989	+	31.0226i	1.60359	+	1.16508i	0.880156	+	0.474685i	$0.157438\pi$
$709$	42.6989	+	31.0226i	1.60359	+	1.16508i	0.723435	+	0.690392i	$0.242562\pi$
$710$		0			0
$711$	2.60074	−	8.00424i	0.0975352	−	0.300183i
$712$		0			0
$713$	−26.0442	+	18.9222i	−0.975364	+	0.708643i
$714$		0			0
$715$	−16.2908	+	5.39691i	−0.609240	+	0.201833i
$716$		0			0
$717$	15.3234	−	11.1331i	0.572262	−	0.415773i
$718$		0			0
$719$	−4.14399	+	12.7539i	−0.154545	+	0.475640i	−0.998114	−	0.0613797i	$-0.980450\pi$
$719$	−4.14399	+	12.7539i	−0.154545	+	0.475640i	0.843570	+	0.537020i	$0.180450\pi$
$720$		0			0
$721$	−7.51669	−	5.46120i	−0.279936	−	0.203386i
$722$		0			0
$723$	−9.63319	−	29.6479i	−0.358262	−	1.10262i
$724$		0			0
$725$	−2.74897			−0.102094
$726$		0			0
$727$	11.7639			0.436300			0.218150	−	0.975915i	$-0.429998\pi$
$727$	11.7639			0.436300			0.218150	+	0.975915i	$0.429998\pi$
$728$		0			0
$729$	5.93890	+	18.2780i	0.219959	+	0.676965i
$730$		0			0
$731$	−2.09552	−	1.52249i	−0.0775057	−	0.0563112i
$732$		0			0
$733$	3.90057	−	12.0047i	0.144071	−	0.443404i	−0.852820	−	0.522206i	$-0.825109\pi$
$733$	3.90057	−	12.0047i	0.144071	−	0.443404i	0.996890	+	0.0788016i	$0.0251093\pi$
$734$		0			0
$735$	1.50377	−	1.09256i	0.0554675	−	0.0402995i
$736$		0			0
$737$	1.76190	−	0.583694i	0.0649004	−	0.0215006i
$738$		0			0
$739$	1.57009	−	1.14074i	0.0577567	−	0.0419627i	−0.558532	−	0.829483i	$-0.688635\pi$
$739$	1.57009	−	1.14074i	0.0577567	−	0.0419627i	0.616289	+	0.787520i	$0.288635\pi$
$740$		0			0
$741$	−3.12322	+	9.61230i	−0.114735	+	0.353117i
$742$		0			0
$743$	−9.56920	−	6.95243i	−0.351060	−	0.255060i	0.398254	−	0.917275i	$-0.369616\pi$
$743$	−9.56920	−	6.95243i	−0.351060	−	0.255060i	−0.749314	+	0.662215i	$0.769616\pi$
$744$		0			0
$745$	−6.13391	−	18.8782i	−0.224729	−	0.691646i
$746$		0			0
$747$	12.5420			0.458889
$748$		0			0
$749$	−1.54749			−0.0565442
$750$		0			0
$751$	−6.42808	−	19.7836i	−0.234564	−	0.721914i	−0.997179	−	0.0750610i	$-0.976085\pi$
$751$	−6.42808	−	19.7836i	−0.234564	−	0.721914i	0.762615	−	0.646853i	$-0.223915\pi$
$752$		0			0
$753$	−22.9053	−	16.6416i	−0.834714	−	0.606455i
$754$		0			0
$755$	−5.22714	+	16.0875i	−0.190235	+	0.585484i
$756$		0			0
$757$	−18.9704	+	13.7828i	−0.689491	+	0.500944i	−0.876493	−	0.481415i	$-0.840123\pi$
$757$	−18.9704	+	13.7828i	−0.689491	+	0.500944i	0.187002	+	0.982360i	$0.440123\pi$
$758$		0			0
$759$	10.8191	+	14.7127i	0.392710	+	0.534036i
$760$		0			0
$761$	−20.8441	+	15.1441i	−0.755599	+	0.548975i	−0.897557	−	0.440898i	$-0.854660\pi$
$761$	−20.8441	+	15.1441i	−0.755599	+	0.548975i	0.141958	+	0.989873i	$0.454660\pi$
$762$		0			0
$763$	4.59921	−	14.1549i	0.166503	−	0.512442i
$764$		0			0
$765$	−0.591487	−	0.429741i	−0.0213853	−	0.0155373i
$766$		0			0
$767$	23.0504	+	70.9417i	0.832300	+	2.56156i
$768$		0			0
$769$	16.4583			0.593500			0.296750	−	0.954955i	$-0.404097\pi$
$769$	16.4583			0.593500			0.296750	+	0.954955i	$0.404097\pi$
$770$		0			0
$771$	−8.08814			−0.291287
$772$		0			0
$773$	11.8797	+	36.5620i	0.427283	+	1.31504i	0.900791	+	0.434253i	$0.142987\pi$
$773$	11.8797	+	36.5620i	0.427283	+	1.31504i	−0.473508	+	0.880789i	$0.657013\pi$
$774$		0			0
$775$	−5.30849	−	3.85684i	−0.190687	−	0.138542i
$776$		0			0
$777$	8.37647	−	25.7801i	0.300504	−	0.924856i
$778$		0			0
$779$	11.8946	−	8.64191i	0.426167	−	0.309628i
$780$		0			0
$781$	16.2910	+	5.18992i	0.582937	+	0.185710i
$782$		0			0
$783$	11.8321	−	8.59651i	0.422844	−	0.307214i
$784$		0			0
$785$	−3.58072	+	11.0203i	−0.127801	+	0.393332i
$786$		0			0
$787$	−1.50000	−	1.08981i	−0.0534692	−	0.0388477i	0.560730	−	0.827999i	$-0.310521\pi$
$787$	−1.50000	−	1.08981i	−0.0534692	−	0.0388477i	−0.614199	+	0.789151i	$0.710521\pi$
$788$		0			0
$789$	3.87848	+	11.9367i	0.138078	+	0.424959i
$790$		0			0
$791$	−11.1207			−0.395406
$792$		0			0
$793$	−65.7740			−2.33570
$794$		0			0
$795$	1.87980	+	5.78542i	0.0666696	+	0.205188i
$796$		0			0
$797$	−9.15265	−	6.64979i	−0.324204	−	0.235548i	0.413763	−	0.910384i	$-0.364214\pi$
$797$	−9.15265	−	6.64979i	−0.324204	−	0.235548i	−0.737967	+	0.674837i	$0.764214\pi$
$798$		0			0
$799$	−0.134766	+	0.414767i	−0.00476768	+	0.0146734i
$800$		0			0
$801$	12.6055	−	9.15845i	0.445394	−	0.323598i
$802$		0			0
$803$	0.236758	+	41.1886i	0.00835500	+	1.45351i
$804$		0			0
$805$	9.17539	−	6.66631i	0.323390	−	0.234957i
$806$		0			0
$807$	−5.78598	+	17.8074i	−0.203676	+	0.626851i
$808$		0			0
$809$	−21.2679	−	15.4520i	−0.747739	−	0.543264i	0.147386	−	0.989079i	$-0.452914\pi$
$809$	−21.2679	−	15.4520i	−0.747739	−	0.543264i	−0.895125	+	0.445815i	$0.852914\pi$
$810$		0			0
$811$	−6.68613	−	20.5778i	−0.234782	−	0.722585i	−0.997150	−	0.0754411i	$-0.975964\pi$
$811$	−6.68613	−	20.5778i	−0.234782	−	0.722585i	0.762368	−	0.647143i	$-0.224036\pi$
$812$		0			0
$813$	−1.28904			−0.0452085
$814$		0			0
$815$	−22.6932			−0.794909
$816$		0			0
$817$	−3.31597	−	10.2055i	−0.116011	−	0.357046i
$818$		0			0
$819$	−16.8416	−	12.2361i	−0.588493	−	0.427565i
$820$		0			0
$821$	10.6314	−	32.7200i	0.371037	−	1.14194i	−0.575076	−	0.818100i	$-0.695028\pi$
$821$	10.6314	−	32.7200i	0.371037	−	1.14194i	0.946113	−	0.323835i	$-0.104972\pi$
$822$		0			0
$823$	−23.2211	+	16.8711i	−0.809435	+	0.588089i	−0.913667	−	0.406464i	$-0.866762\pi$
$823$	−23.2211	+	16.8711i	−0.809435	+	0.588089i	0.104231	+	0.994553i	$0.466762\pi$
$824$		0			0
$825$	−2.17060	+	3.02398i	−0.0755707	+	0.105281i
$826$		0			0
$827$	−29.4541	+	21.3997i	−1.02422	+	0.744139i	−0.967144	−	0.254231i	$-0.918178\pi$
$827$	−29.4541	+	21.3997i	−1.02422	+	0.744139i	−0.0570762	+	0.998370i	$0.518178\pi$
$828$		0			0
$829$	0.499497	−	1.53729i	0.0173482	−	0.0533924i	−0.942008	−	0.335591i	$-0.891064\pi$
$829$	0.499497	−	1.53729i	0.0173482	−	0.0533924i	0.959356	+	0.282199i	$0.0910639\pi$
$830$		0			0
$831$	21.9603	+	15.9551i	0.761793	+	0.553475i
$832$		0			0
$833$	−0.214997	−	0.661692i	−0.00744920	−	0.0229263i
$834$		0			0
$835$	16.5178			0.571622
$836$		0			0
$837$	34.9098			1.20666
$838$		0			0
$839$	8.60378	+	26.4797i	0.297036	+	0.914181i	0.982530	+	0.186104i	$0.0595860\pi$
$839$	8.60378	+	26.4797i	0.297036	+	0.914181i	−0.685495	+	0.728078i	$0.740414\pi$
$840$		0			0
$841$	17.3479	+	12.6040i	0.598203	+	0.434620i
$842$		0			0
$843$	−0.465591	+	1.43294i	−0.0160358	+	0.0493532i
$844$		0			0
$845$	11.1435	−	8.09625i	0.383349	−	0.278519i
$846$		0			0
$847$	−8.13531	−	24.0919i	−0.279533	−	0.827809i
$848$		0			0
$849$	−26.8368	+	19.4981i	−0.921036	+	0.669172i
$850$		0			0
$851$	−15.8399	+	48.7502i	−0.542985	+	1.67114i
$852$		0			0
$853$	21.7239	+	15.7834i	0.743813	+	0.540412i	0.893903	−	0.448261i	$-0.147956\pi$
$853$	21.7239	+	15.7834i	0.743813	+	0.540412i	−0.150090	+	0.988672i	$0.547956\pi$
$854$		0			0
$855$	−0.935975	−	2.88064i	−0.0320097	−	0.0985156i
$856$		0			0
$857$	−34.8384			−1.19006			−0.595029	−	0.803704i	$-0.702859\pi$
$857$	−34.8384			−1.19006			−0.595029	+	0.803704i	$0.702859\pi$
$858$		0			0
$859$	21.1475			0.721543			0.360771	−	0.932654i	$-0.382513\pi$
$859$	21.1475			0.721543			0.360771	+	0.932654i	$0.382513\pi$
$860$		0			0
$861$	−6.77300	−	20.8451i	−0.230823	−	0.710400i
$862$		0			0
$863$	5.02412	+	3.65024i	0.171023	+	0.124255i	0.670004	−	0.742357i	$-0.266292\pi$
$863$	5.02412	+	3.65024i	0.171023	+	0.124255i	−0.498981	+	0.866613i	$0.666292\pi$
$864$		0			0
$865$	4.44674	−	13.6857i	0.151194	−	0.465327i
$866$		0			0
$867$	−15.2755	+	11.0983i	−0.518784	+	0.376919i
$868$		0			0
$869$	−9.35258	+	13.0296i	−0.317264	+	0.441998i
$870$		0			0
$871$	−2.34268	+	1.70206i	−0.0793787	+	0.0576720i
$872$		0			0
$873$	0.421186	−	1.29628i	0.0142550	−	0.0438723i
$874$		0			0
$875$	1.87018	+	1.35877i	0.0632238	+	0.0459347i
$876$		0			0
$877$	−0.180719	−	0.556195i	−0.00610244	−	0.0187814i	0.947959	−	0.318393i	$-0.103143\pi$
$877$	−0.180719	−	0.556195i	−0.00610244	−	0.0187814i	−0.954061	+	0.299611i	$0.903143\pi$
$878$		0			0
$879$	−9.73181			−0.328246
$880$		0			0
$881$	24.6436			0.830262			0.415131	−	0.909762i	$-0.363736\pi$
$881$	24.6436			0.830262			0.415131	+	0.909762i	$0.363736\pi$
$882$		0			0
$883$	−7.44571	−	22.9155i	−0.250568	−	0.771170i	−0.994671	−	0.103104i	$-0.967123\pi$
$883$	−7.44571	−	22.9155i	−0.250568	−	0.771170i	0.744102	−	0.668066i	$-0.232877\pi$
$884$		0			0
$885$	13.0893	+	9.50995i	0.439993	+	0.319673i
$886$		0			0
$887$	−10.3441	+	31.8360i	−0.347322	+	1.06895i	0.613007	+	0.790078i	$0.289960\pi$
$887$	−10.3441	+	31.8360i	−0.347322	+	1.06895i	−0.960329	+	0.278870i	$0.910040\pi$
$888$		0			0
$889$	−27.1356	+	19.7152i	−0.910100	+	0.661227i
$890$		0			0
$891$	−0.0142984	−	2.48749i	−0.000479015	−	0.0833340i
$892$		0			0
$893$	−1.46167	+	1.06197i	−0.0489130	+	0.0355373i
$894$		0			0
$895$	−6.03442	+	18.5720i	−0.201708	+	0.620795i
$896$		0			0
$897$	−23.0504	−	16.7471i	−0.769629	−	0.559168i
$898$		0			0
$899$	−5.57398	−	17.1549i	−0.185903	−	0.572149i
$900$		0			0
$901$	2.27695			0.0758562
$902$		0			0
$903$	−15.9969			−0.532344
$904$		0			0
$905$	−0.404315	−	1.24435i	−0.0134399	−	0.0413637i
$906$		0			0
$907$	44.7221	+	32.4925i	1.48497	+	1.07890i	0.975911	+	0.218168i	$0.0700081\pi$
$907$	44.7221	+	32.4925i	1.48497	+	1.07890i	0.509063	+	0.860729i	$0.329992\pi$
$908$		0			0
$909$	−5.95307	+	18.3217i	−0.197451	+	0.607691i
$910$		0			0
$911$	15.7635	−	11.4529i	0.522269	−	0.379451i	−0.295189	−	0.955439i	$-0.595383\pi$
$911$	15.7635	−	11.4529i	0.522269	−	0.379451i	0.817458	+	0.575988i	$0.195383\pi$
$912$		0			0
$913$	−22.7736	−	7.25515i	−0.753698	−	0.240110i
$914$		0			0
$915$	−11.5419	+	8.38566i	−0.381562	+	0.277221i
$916$		0			0
$917$	10.1514	−	31.2429i	0.335230	−	1.03173i
$918$		0			0
$919$	−40.2356	−	29.2329i	−1.32725	−	0.964303i	−0.999811	−	0.0194309i	$-0.993815\pi$
$919$	−40.2356	−	29.2329i	−1.32725	−	0.964303i	−0.327439	−	0.944872i	$-0.606185\pi$
$920$		0			0
$921$	−1.07899	−	3.32080i	−0.0355540	−	0.109424i
$922$		0			0
$923$	−26.6747			−0.878007
$924$		0			0
$925$	−10.4479			−0.343526
$926$		0			0
$927$	−2.16155	−	6.65258i	−0.0709947	−	0.218499i
$928$		0			0
$929$	36.9997	+	26.8819i	1.21392	+	0.881966i	0.995581	−	0.0939069i	$-0.0299356\pi$
$929$	36.9997	+	26.8819i	1.21392	+	0.881966i	0.218341	+	0.975873i	$0.429936\pi$
$930$		0			0
$931$	0.890689	−	2.74126i	0.0291912	−	0.0898412i
$932$		0			0
$933$	−20.8677	+	15.1612i	−0.683176	+	0.496357i
$934$		0			0
$935$	0.825424	+	1.12247i	0.0269942	+	0.0367088i
$936$		0			0
$937$	9.70092	−	7.04813i	0.316915	−	0.230252i	−0.417943	−	0.908473i	$-0.637249\pi$
$937$	9.70092	−	7.04813i	0.316915	−	0.230252i	0.734858	+	0.678221i	$0.237249\pi$
$938$		0			0
$939$	7.13846	−	21.9699i	0.232955	−	0.716961i
$940$		0			0
$941$	20.3860	+	14.8113i	0.664564	+	0.482834i	0.868201	−	0.496212i	$-0.165276\pi$
$941$	20.3860	+	14.8113i	0.664564	+	0.482834i	−0.203637	+	0.979046i	$0.565276\pi$
$942$		0			0
$943$	12.8077	+	39.4182i	0.417077	+	1.28363i
$944$		0			0
$945$	−12.2987			−0.400078
$946$		0			0
$947$	9.65426			0.313721			0.156861	−	0.987621i	$-0.449863\pi$
$947$	9.65426			0.313721			0.156861	+	0.987621i	$0.449863\pi$
$948$		0			0
$949$	−19.8577	−	61.1156i	−0.644607	−	1.98390i
$950$		0			0
$951$	−29.6651	−	21.5530i	−0.961957	−	0.698903i
$952$		0			0
$953$	−9.93492	+	30.5765i	−0.321824	+	0.990472i	0.651030	+	0.759052i	$0.274337\pi$
$953$	−9.93492	+	30.5765i	−0.321824	+	0.990472i	−0.972854	+	0.231420i	$0.925663\pi$
$954$		0			0
$955$	−14.3311	+	10.4121i	−0.463742	+	0.336929i
$956$		0			0
$957$	−9.71348	+	3.21795i	−0.313992	+	0.104021i
$958$		0			0
$959$	5.04374	−	3.66450i	0.162871	−	0.118333i
$960$		0			0
$961$	3.72530	−	11.4653i	0.120171	−	0.369848i
$962$		0			0
$963$	−0.942542	−	0.684797i	−0.0303730	−	0.0220673i
$964$		0			0
$965$	−4.52405	−	13.9236i	−0.145634	−	0.448217i
$966$		0			0
$967$	46.4330			1.49318			0.746592	−	0.665283i	$-0.231689\pi$
$967$	46.4330			1.49318			0.746592	+	0.665283i	$0.231689\pi$
$968$		0			0
$969$	0.820559			0.0263601
$970$		0			0
$971$	5.66699	+	17.4412i	0.181862	+	0.559715i	0.999880	−	0.0154779i	$-0.00492697\pi$
$971$	5.66699	+	17.4412i	0.181862	+	0.559715i	−0.818018	+	0.575193i	$0.804927\pi$
$972$		0			0
$973$	−12.7831	−	9.28745i	−0.409807	−	0.297742i
$974$		0			0
$975$	1.79458	−	5.52314i	0.0574725	−	0.176882i
$976$		0			0
$977$	25.3866	−	18.4444i	0.812189	−	0.590090i	−0.102276	−	0.994756i	$-0.532612\pi$
$977$	25.3866	−	18.4444i	0.812189	−	0.590090i	0.914464	+	0.404667i	$0.132612\pi$
$978$		0			0
$979$	−28.1868	+	9.33791i	−0.900854	+	0.298441i
$980$		0			0
$981$	9.06510	−	6.58618i	0.289427	−	0.210281i
$982$		0			0
$983$	−6.32332	+	19.4612i	−0.201683	+	0.620715i	0.798151	+	0.602458i	$0.205812\pi$
$983$	−6.32332	+	19.4612i	−0.201683	+	0.620715i	−0.999833	+	0.0182573i	$0.994188\pi$
$984$		0			0
$985$	−18.9402	−	13.7609i	−0.603486	−	0.438458i
$986$		0			0
$987$	0.832304	+	2.56157i	0.0264925	+	0.0815356i
$988$		0			0
$989$	30.2502			0.961900
$990$		0			0
$991$	44.5692			1.41579			0.707894	−	0.706318i	$-0.249645\pi$
$991$	44.5692			1.41579			0.707894	+	0.706318i	$0.249645\pi$
$992$		0			0
$993$	−5.72480	−	17.6191i	−0.181671	−	0.559126i
$994$		0			0
$995$	0.387117	+	0.281257i	0.0122724	+	0.00891644i
$996$		0			0
$997$	6.52704	−	20.0882i	0.206713	−	0.636198i	−0.792925	−	0.609319i	$-0.791443\pi$
$997$	6.52704	−	20.0882i	0.206713	−	0.636198i	0.999639	−	0.0268794i	$-0.00855700\pi$
$998$		0			0
$999$	44.9699	−	32.6725i	1.42278	−	1.03371i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.m.a.201.1	yes	8
3.2	odd	2		1980.2.z.c.1081.2		8
4.3	odd	2		880.2.bo.f.641.2		8
5.2	odd	4		1100.2.cb.c.949.2		16
5.3	odd	4		1100.2.cb.c.949.3		16
5.4	even	2		1100.2.n.c.201.2		8
11.2	odd	10		2420.2.a.m.1.2		4
11.4	even	5	inner	220.2.m.a.81.1	✓	8
11.9	even	5		2420.2.a.n.1.2		4
33.26	odd	10		1980.2.z.c.1621.2		8
44.15	odd	10		880.2.bo.f.81.2		8
44.31	odd	10		9680.2.a.ck.1.3		4
44.35	even	10		9680.2.a.cl.1.3		4
55.4	even	10		1100.2.n.c.301.2		8
55.37	odd	20		1100.2.cb.c.1049.3		16
55.48	odd	20		1100.2.cb.c.1049.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.a.81.1	✓	8	11.4	even	5	inner
220.2.m.a.201.1	yes	8	1.1	even	1	trivial
880.2.bo.f.81.2		8	44.15	odd	10
880.2.bo.f.641.2		8	4.3	odd	2
1100.2.n.c.201.2		8	5.4	even	2
1100.2.n.c.301.2		8	55.4	even	10
1100.2.cb.c.949.2		16	5.2	odd	4
1100.2.cb.c.949.3		16	5.3	odd	4
1100.2.cb.c.1049.2		16	55.48	odd	20
1100.2.cb.c.1049.3		16	55.37	odd	20
1980.2.z.c.1081.2		8	3.2	odd	2
1980.2.z.c.1621.2		8	33.26	odd	10
2420.2.a.m.1.2		4	11.2	odd	10
2420.2.a.n.1.2		4	11.9	even	5
9680.2.a.ck.1.3		4	44.31	odd	10
9680.2.a.cl.1.3		4	44.35	even	10

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.m.a.201.1

Level	$220$
Weight	$2$
Character	220.201
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$