LMFDB - Embedded newform 264.2.q.b.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(25,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-1,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	264.25
Dual form			264.2.q.b.169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.224514i) q^{5} +(-1.30902 + 4.02874i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.04508 + 1.31433i) q^{11} +(-1.80902 + 1.31433i) q^{13} +(0.118034 - 0.363271i) q^{15} +(1.50000 + 1.08981i) q^{17} +(0.118034 + 0.363271i) q^{19} -4.23607 q^{21} +6.23607 q^{23} +(-1.50000 - 4.61653i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.145898 - 0.449028i) q^{29} +(-6.97214 + 5.06555i) q^{31} +(-0.309017 + 3.30220i) q^{33} +(1.30902 - 0.951057i) q^{35} +(1.16312 - 3.57971i) q^{37} +(-1.80902 - 1.31433i) q^{39} +(-1.54508 - 4.75528i) q^{41} +11.4721 q^{43} +0.381966 q^{45} +(0.0450850 + 0.138757i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-0.572949 + 1.76336i) q^{51} +(7.73607 - 5.62058i) q^{53} +(-0.645898 - 1.08981i) q^{55} +(-0.309017 + 0.224514i) q^{57} +(4.50000 - 13.8496i) q^{59} +(5.54508 + 4.02874i) q^{61} +(-1.30902 - 4.02874i) q^{63} +0.854102 q^{65} -4.56231 q^{67} +(1.92705 + 5.93085i) q^{69} +(-10.1631 - 7.38394i) q^{71} +(1.14590 - 3.52671i) q^{73} +(3.92705 - 2.85317i) q^{75} +(-9.28115 + 10.5474i) q^{77} +(-11.5172 + 8.36775i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.57295 + 1.14281i) q^{83} +(-0.218847 - 0.673542i) q^{85} +0.472136 q^{87} +3.47214 q^{89} +(-2.92705 - 9.00854i) q^{91} +(-6.97214 - 5.06555i) q^{93} +(0.0450850 - 0.138757i) q^{95} +(5.54508 - 4.02874i) q^{97} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + q^{5} - 3 q^{7} - q^{9} + q^{11} - 5 q^{13} - 4 q^{15} + 6 q^{17} - 4 q^{19} - 8 q^{21} + 16 q^{23} - 6 q^{25} - q^{27} + 14 q^{29} - 10 q^{31} + q^{33} + 3 q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - q^3 + q^5 - 3 * q^7 - q^9 + q^11 - 5 * q^13 - 4 * q^15 + 6 * q^17 - 4 * q^19 - 8 * q^21 + 16 * q^23 - 6 * q^25 - q^27 + 14 * q^29 - 10 * q^31 + q^33 + 3 * q^35 - 11 * q^37 - 5 * q^39 + 5 * q^41 + 28 * q^43 + 6 * q^45 - 11 * q^47 - 22 * q^49 - 9 * q^51 + 22 * q^53 - 16 * q^55 + q^57 + 18 * q^59 + 11 * q^61 - 3 * q^63 - 10 * q^65 + 22 * q^67 + q^69 - 25 * q^71 + 18 * q^73 + 9 * q^75 - 17 * q^77 - 17 * q^79 - q^81 + 13 * q^83 - 21 * q^85 - 16 * q^87 - 4 * q^89 - 5 * q^91 - 10 * q^93 - 11 * q^95 + 11 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	−0.309017	−	0.224514i	−0.138197	−	0.100406i	0.516539	−	0.856264i	$-0.327220\pi$
$5$	−0.309017	−	0.224514i	−0.138197	−	0.100406i	−0.654736	+	0.755858i	$0.727220\pi$
$6$		0			0
$7$	−1.30902	+	4.02874i	−0.494762	+	1.52272i	0.322566	+	0.946547i	$0.395455\pi$
$7$	−1.30902	+	4.02874i	−0.494762	+	1.52272i	−0.817327	+	0.576173i	$0.804545\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$12$		0			0
$13$	−1.80902	+	1.31433i	−0.501731	+	0.364529i	−0.809678	−	0.586875i	$-0.800358\pi$
$13$	−1.80902	+	1.31433i	−0.501731	+	0.364529i	0.307947	+	0.951404i	$0.400358\pi$
$14$		0			0
$15$	0.118034	−	0.363271i	0.0304762	−	0.0937962i
$16$		0			0
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	0.754637	−	0.656143i	$-0.227813\pi$
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	−0.390833	+	0.920461i	$0.627813\pi$
$18$		0			0
$19$	0.118034	+	0.363271i	0.0270789	+	0.0833401i	0.963683	−	0.267050i	$-0.0860489\pi$
$19$	0.118034	+	0.363271i	0.0270789	+	0.0833401i	−0.936604	+	0.350390i	$0.886049\pi$
$20$		0			0
$21$	−4.23607			−0.924386
$22$		0			0
$23$	6.23607			1.30031			0.650155	−	0.759802i	$-0.274704\pi$
$23$	6.23607			1.30031			0.650155	+	0.759802i	$0.274704\pi$
$24$		0			0
$25$	−1.50000	−	4.61653i	−0.300000	−	0.923305i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	0.145898	−	0.449028i	0.0270926	−	0.0833824i	−0.936596	−	0.350411i	$-0.886042\pi$
$29$	0.145898	−	0.449028i	0.0270926	−	0.0833824i	0.963689	+	0.267029i	$0.0860419\pi$
$30$		0			0
$31$	−6.97214	+	5.06555i	−1.25223	+	0.909800i	−0.998349	−	0.0574346i	$-0.981708\pi$
$31$	−6.97214	+	5.06555i	−1.25223	+	0.909800i	−0.253883	+	0.967235i	$0.581708\pi$
$32$		0			0
$33$	−0.309017	+	3.30220i	−0.0537930	+	0.574839i
$34$		0			0
$35$	1.30902	−	0.951057i	0.221264	−	0.160758i
$36$		0			0
$37$	1.16312	−	3.57971i	0.191216	−	0.588501i	−0.808784	−	0.588105i	$-0.799874\pi$
$37$	1.16312	−	3.57971i	0.191216	−	0.588501i	1.00000		0.000395703i	$-0.000125956\pi$
$38$		0			0
$39$	−1.80902	−	1.31433i	−0.289675	−	0.210461i
$40$		0			0
$41$	−1.54508	−	4.75528i	−0.241302	−	0.742650i	−0.996223	−	0.0868346i	$-0.972325\pi$
$41$	−1.54508	−	4.75528i	−0.241302	−	0.742650i	0.754921	−	0.655816i	$-0.227675\pi$
$42$		0			0
$43$	11.4721			1.74948			0.874742	−	0.484589i	$-0.161031\pi$
$43$	11.4721			1.74948			0.874742	+	0.484589i	$0.161031\pi$
$44$		0			0
$45$	0.381966			0.0569401
$46$		0			0
$47$	0.0450850	+	0.138757i	0.00657632	+	0.0202398i	0.954291	−	0.298880i	$-0.0966129\pi$
$47$	0.0450850	+	0.138757i	0.00657632	+	0.0202398i	−0.947715	+	0.319119i	$0.896613\pi$
$48$		0			0
$49$	−8.85410	−	6.43288i	−1.26487	−	0.918983i
$50$		0			0
$51$	−0.572949	+	1.76336i	−0.0802289	+	0.246919i
$52$		0			0
$53$	7.73607	−	5.62058i	1.06263	−	0.772046i	0.0880574	−	0.996115i	$-0.471934\pi$
$53$	7.73607	−	5.62058i	1.06263	−	0.772046i	0.974573	+	0.224069i	$0.0719341\pi$
$54$		0			0
$55$	−0.645898	−	1.08981i	−0.0870929	−	0.146950i
$56$		0			0
$57$	−0.309017	+	0.224514i	−0.0409303	+	0.0297376i
$58$		0			0
$59$	4.50000	−	13.8496i	0.585850	−	1.80306i	−0.00997934	−	0.999950i	$-0.503177\pi$
$59$	4.50000	−	13.8496i	0.585850	−	1.80306i	0.595829	−	0.803111i	$-0.296823\pi$
$60$		0			0
$61$	5.54508	+	4.02874i	0.709975	+	0.515827i	0.883166	−	0.469061i	$-0.155408\pi$
$61$	5.54508	+	4.02874i	0.709975	+	0.515827i	−0.173190	+	0.984888i	$0.555408\pi$
$62$		0			0
$63$	−1.30902	−	4.02874i	−0.164921	−	0.507574i
$64$		0			0
$65$	0.854102			0.105938
$66$		0			0
$67$	−4.56231			−0.557374			−0.278687	−	0.960382i	$-0.589899\pi$
$67$	−4.56231			−0.557374			−0.278687	+	0.960382i	$0.589899\pi$
$68$		0			0
$69$	1.92705	+	5.93085i	0.231990	+	0.713991i
$70$		0			0
$71$	−10.1631	−	7.38394i	−1.20614	−	0.876312i	−0.211266	−	0.977429i	$-0.567759\pi$
$71$	−10.1631	−	7.38394i	−1.20614	−	0.876312i	−0.994875	+	0.101116i	$0.967759\pi$
$72$		0			0
$73$	1.14590	−	3.52671i	0.134117	−	0.412770i	−0.861334	−	0.508038i	$-0.830371\pi$
$73$	1.14590	−	3.52671i	0.134117	−	0.412770i	0.995452	+	0.0952680i	$0.0303708\pi$
$74$		0			0
$75$	3.92705	−	2.85317i	0.453457	−	0.329456i
$76$		0			0
$77$	−9.28115	+	10.5474i	−1.05769	+	1.20199i
$78$		0			0
$79$	−11.5172	+	8.36775i	−1.29579	+	0.941446i	−0.999905	−	0.0137785i	$-0.995614\pi$
$79$	−11.5172	+	8.36775i	−1.29579	+	0.941446i	−0.295884	+	0.955224i	$0.595614\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	1.57295	+	1.14281i	0.172654	+	0.125440i	0.670756	−	0.741678i	$-0.265970\pi$
$83$	1.57295	+	1.14281i	0.172654	+	0.125440i	−0.498103	+	0.867118i	$0.665970\pi$
$84$		0			0
$85$	−0.218847	−	0.673542i	−0.0237373	−	0.0730559i
$86$		0			0
$87$	0.472136			0.0506183
$88$		0			0
$89$	3.47214			0.368046			0.184023	−	0.982922i	$-0.441088\pi$
$89$	3.47214			0.368046			0.184023	+	0.982922i	$0.441088\pi$
$90$		0			0
$91$	−2.92705	−	9.00854i	−0.306838	−	0.944351i
$92$		0			0
$93$	−6.97214	−	5.06555i	−0.722977	−	0.525273i
$94$		0			0
$95$	0.0450850	−	0.138757i	0.00462562	−	0.0142362i
$96$		0			0
$97$	5.54508	−	4.02874i	0.563018	−	0.409057i	−0.269544	−	0.962988i	$-0.586873\pi$
$97$	5.54508	−	4.02874i	0.563018	−	0.409057i	0.832562	+	0.553931i	$0.186873\pi$
$98$		0			0
$99$	−3.23607	+	0.726543i	−0.325237	+	0.0730203i
$100$		0			0
$101$	−0.427051	+	0.310271i	−0.0424932	+	0.0308731i	−0.608829	−	0.793301i	$-0.708360\pi$
$101$	−0.427051	+	0.310271i	−0.0424932	+	0.0308731i	0.566336	+	0.824174i	$0.308360\pi$
$102$		0			0
$103$	−1.09017	+	3.35520i	−0.107418	+	0.330597i	−0.990290	−	0.139015i	$-0.955606\pi$
$103$	−1.09017	+	3.35520i	−0.107418	+	0.330597i	0.882873	+	0.469613i	$0.155606\pi$
$104$		0			0
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$		0			0
$107$	3.69098	+	11.3597i	0.356821	+	1.09818i	0.954946	+	0.296779i	$0.0959125\pi$
$107$	3.69098	+	11.3597i	0.356821	+	1.09818i	−0.598125	+	0.801403i	$0.704088\pi$
$108$		0			0
$109$	17.8885			1.71341			0.856706	−	0.515805i	$-0.172507\pi$
$109$	17.8885			1.71341			0.856706	+	0.515805i	$0.172507\pi$
$110$		0			0
$111$	3.76393			0.357257
$112$		0			0
$113$	5.63525	+	17.3435i	0.530120	+	1.63154i	0.753963	+	0.656917i	$0.228140\pi$
$113$	5.63525	+	17.3435i	0.530120	+	1.63154i	−0.223843	+	0.974625i	$0.571860\pi$
$114$		0			0
$115$	−1.92705	−	1.40008i	−0.179698	−	0.130559i
$116$		0			0
$117$	0.690983	−	2.12663i	0.0638814	−	0.196607i
$118$		0			0
$119$	−6.35410	+	4.61653i	−0.582480	+	0.423196i
$120$		0			0
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$		0			0
$123$	4.04508	−	2.93893i	0.364733	−	0.264994i
$124$		0			0
$125$	−1.16312	+	3.57971i	−0.104033	+	0.320179i
$126$		0			0
$127$	−0.618034	−	0.449028i	−0.0548416	−	0.0398448i	0.560027	−	0.828475i	$-0.310791\pi$
$127$	−0.618034	−	0.449028i	−0.0548416	−	0.0398448i	−0.614868	+	0.788630i	$0.710791\pi$
$128$		0			0
$129$	3.54508	+	10.9106i	0.312127	+	0.960629i
$130$		0			0
$131$	2.32624			0.203244			0.101622	−	0.994823i	$-0.467597\pi$
$131$	2.32624			0.203244			0.101622	+	0.994823i	$0.467597\pi$
$132$		0			0
$133$	−1.61803			−0.140301
$134$		0			0
$135$	0.118034	+	0.363271i	0.0101587	+	0.0312654i
$136$		0			0
$137$	−4.42705	−	3.21644i	−0.378228	−	0.274799i	0.382386	−	0.924003i	$-0.375102\pi$
$137$	−4.42705	−	3.21644i	−0.378228	−	0.274799i	−0.760615	+	0.649203i	$0.775102\pi$
$138$		0			0
$139$	−5.75329	+	17.7068i	−0.487988	+	1.50187i	0.339619	+	0.940563i	$0.389702\pi$
$139$	−5.75329	+	17.7068i	−0.487988	+	1.50187i	−0.827607	+	0.561308i	$0.810298\pi$
$140$		0			0
$141$	−0.118034	+	0.0857567i	−0.00994026	+	0.00722202i
$142$		0			0
$143$	−7.23607	+	1.62460i	−0.605110	+	0.135856i
$144$		0			0
$145$	−0.145898	+	0.106001i	−0.0121162	+	0.00880291i
$146$		0			0
$147$	3.38197	−	10.4086i	0.278940	−	0.858489i
$148$		0			0
$149$	−6.04508	−	4.39201i	−0.495233	−	0.359808i	0.311960	−	0.950095i	$-0.399014\pi$
$149$	−6.04508	−	4.39201i	−0.495233	−	0.359808i	−0.807193	+	0.590288i	$0.799014\pi$
$150$		0			0
$151$	−4.14590	−	12.7598i	−0.337388	−	1.03837i	−0.965534	−	0.260279i	$-0.916186\pi$
$151$	−4.14590	−	12.7598i	−0.337388	−	1.03837i	0.628145	−	0.778096i	$-0.283814\pi$
$152$		0			0
$153$	−1.85410			−0.149895
$154$		0			0
$155$	3.29180			0.264403
$156$		0			0
$157$	5.00000	+	15.3884i	0.399043	+	1.22813i	0.925768	+	0.378093i	$0.123420\pi$
$157$	5.00000	+	15.3884i	0.399043	+	1.22813i	−0.526724	+	0.850036i	$0.676580\pi$
$158$		0			0
$159$	7.73607	+	5.62058i	0.613510	+	0.445741i
$160$		0			0
$161$	−8.16312	+	25.1235i	−0.643344	+	1.98001i
$162$		0			0
$163$	12.4443	−	9.04129i	0.974711	−	0.708169i	0.0181903	−	0.999835i	$-0.494210\pi$
$163$	12.4443	−	9.04129i	0.974711	−	0.708169i	0.956520	+	0.291666i	$0.0942095\pi$
$164$		0			0
$165$	0.836881	−	0.951057i	0.0651511	−	0.0740396i
$166$		0			0
$167$	−18.8713	+	13.7108i	−1.46031	+	1.06098i	−0.477024	+	0.878890i	$0.658285\pi$
$167$	−18.8713	+	13.7108i	−1.46031	+	1.06098i	−0.983283	+	0.182085i	$0.941715\pi$
$168$		0			0
$169$	−2.47214	+	7.60845i	−0.190164	+	0.585266i
$170$		0			0
$171$	−0.309017	−	0.224514i	−0.0236311	−	0.0171690i
$172$		0			0
$173$	−5.26393	−	16.2007i	−0.400209	−	1.23172i	−0.924830	−	0.380381i	$-0.875793\pi$
$173$	−5.26393	−	16.2007i	−0.400209	−	1.23172i	0.524620	−	0.851336i	$-0.324207\pi$
$174$		0			0
$175$	20.5623			1.55436
$176$		0			0
$177$	14.5623			1.09457
$178$		0			0
$179$	−6.92705	−	21.3193i	−0.517752	−	1.59348i	−0.778218	−	0.627994i	$-0.783876\pi$
$179$	−6.92705	−	21.3193i	−0.517752	−	1.59348i	0.260466	−	0.965483i	$-0.416124\pi$
$180$		0			0
$181$	−12.0451	−	8.75127i	−0.895304	−	0.650477i	0.0419514	−	0.999120i	$-0.486643\pi$
$181$	−12.0451	−	8.75127i	−0.895304	−	0.650477i	−0.937256	+	0.348643i	$0.886643\pi$
$182$		0			0
$183$	−2.11803	+	6.51864i	−0.156570	+	0.481872i
$184$		0			0
$185$	−1.16312	+	0.845055i	−0.0855142	+	0.0621297i
$186$		0			0
$187$	3.13525	+	5.29007i	0.229273	+	0.386848i
$188$		0			0
$189$	3.42705	−	2.48990i	0.249281	−	0.181113i
$190$		0			0
$191$	1.78115	−	5.48183i	0.128880	−	0.396651i	−0.865708	−	0.500549i	$-0.833132\pi$
$191$	1.78115	−	5.48183i	0.128880	−	0.396651i	0.994588	+	0.103898i	$0.0331315\pi$
$192$		0			0
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	0.597244	−	0.802060i	$-0.296262\pi$
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	−0.578246	+	0.815863i	$0.696262\pi$
$194$		0			0
$195$	0.263932	+	0.812299i	0.0189006	+	0.0581700i
$196$		0			0
$197$	−8.14590			−0.580371			−0.290186	−	0.956970i	$-0.593717\pi$
$197$	−8.14590			−0.580371			−0.290186	+	0.956970i	$0.593717\pi$
$198$		0			0
$199$	9.47214			0.671462			0.335731	−	0.941958i	$-0.391017\pi$
$199$	9.47214			0.671462			0.335731	+	0.941958i	$0.391017\pi$
$200$		0			0
$201$	−1.40983	−	4.33901i	−0.0994417	−	0.306050i
$202$		0			0
$203$	1.61803	+	1.17557i	0.113564	+	0.0825089i
$204$		0			0
$205$	−0.590170	+	1.81636i	−0.0412193	+	0.126860i
$206$		0			0
$207$	−5.04508	+	3.66547i	−0.350658	+	0.254768i
$208$		0			0
$209$	−0.118034	+	1.26133i	−0.00816458	+	0.0872478i
$210$		0			0
$211$	−2.73607	+	1.98787i	−0.188359	+	0.136851i	−0.677968	−	0.735091i	$-0.737139\pi$
$211$	−2.73607	+	1.98787i	−0.188359	+	0.136851i	0.489610	+	0.871942i	$0.337139\pi$
$212$		0			0
$213$	3.88197	−	11.9475i	0.265988	−	0.818627i
$214$		0			0
$215$	−3.54508	−	2.57565i	−0.241773	−	0.175658i
$216$		0			0
$217$	−11.2812	−	34.7198i	−0.765815	−	2.35693i
$218$		0			0
$219$	3.70820			0.250577
$220$		0			0
$221$	−4.14590			−0.278883
$222$		0			0
$223$	−3.87132	−	11.9147i	−0.259243	−	0.797868i	−0.992964	−	0.118417i	$-0.962218\pi$
$223$	−3.87132	−	11.9147i	−0.259243	−	0.797868i	0.733721	−	0.679451i	$-0.237782\pi$
$224$		0			0
$225$	3.92705	+	2.85317i	0.261803	+	0.190211i
$226$		0			0
$227$	−6.36475	+	19.5887i	−0.422443	+	1.30015i	0.482979	+	0.875632i	$0.339555\pi$
$227$	−6.36475	+	19.5887i	−0.422443	+	1.30015i	−0.905422	+	0.424514i	$0.860445\pi$
$228$		0			0
$229$	9.61803	−	6.98791i	0.635578	−	0.461774i	−0.222750	−	0.974875i	$-0.571504\pi$
$229$	9.61803	−	6.98791i	0.635578	−	0.461774i	0.858328	+	0.513101i	$0.171504\pi$
$230$		0			0
$231$	−12.8992	−	5.56758i	−0.848704	−	0.366320i
$232$		0			0
$233$	16.2533	−	11.8087i	1.06479	−	0.773614i	0.0898201	−	0.995958i	$-0.471371\pi$
$233$	16.2533	−	11.8087i	1.06479	−	0.773614i	0.974968	+	0.222344i	$0.0713708\pi$
$234$		0			0
$235$	0.0172209	−	0.0530006i	0.00112337	−	0.00345738i
$236$		0			0
$237$	−11.5172	−	8.36775i	−0.748124	−	0.543544i
$238$		0			0
$239$	4.33688	+	13.3475i	0.280530	+	0.863381i	0.987703	+	0.156341i	$0.0499699\pi$
$239$	4.33688	+	13.3475i	0.280530	+	0.863381i	−0.707174	+	0.707040i	$0.750030\pi$
$240$		0			0
$241$	−30.0689			−1.93691			−0.968454	−	0.249194i	$-0.919834\pi$
$241$	−30.0689			−1.93691			−0.968454	+	0.249194i	$0.919834\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.29180	+	3.97574i	0.0825298	+	0.254001i
$246$		0			0
$247$	−0.690983	−	0.502029i	−0.0439662	−	0.0319433i
$248$		0			0
$249$	−0.600813	+	1.84911i	−0.0380750	+	0.117183i
$250$		0			0
$251$	−1.73607	+	1.26133i	−0.109580	+	0.0796143i	−0.641226	−	0.767352i	$-0.721574\pi$
$251$	−1.73607	+	1.26133i	−0.109580	+	0.0796143i	0.531646	+	0.846967i	$0.321574\pi$
$252$		0			0
$253$	18.9894	+	8.19624i	1.19385	+	0.515293i
$254$		0			0
$255$	0.572949	−	0.416272i	0.0358795	−	0.0260680i
$256$		0			0
$257$	5.50000	−	16.9273i	0.343081	−	1.05589i	−0.619523	−	0.784979i	$-0.712674\pi$
$257$	5.50000	−	16.9273i	0.343081	−	1.05589i	0.962603	−	0.270915i	$-0.0873261\pi$
$258$		0			0
$259$	12.8992	+	9.37181i	0.801516	+	0.582336i
$260$		0			0
$261$	0.145898	+	0.449028i	0.00903086	+	0.0277941i
$262$		0			0
$263$	10.8541			0.669293			0.334646	−	0.942344i	$-0.391383\pi$
$263$	10.8541			0.669293			0.334646	+	0.942344i	$0.391383\pi$
$264$		0			0
$265$	−3.65248			−0.224370
$266$		0			0
$267$	1.07295	+	3.30220i	0.0656634	+	0.202091i
$268$		0			0
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	0.622170	−	0.782882i	$-0.286251\pi$
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	−0.552304	+	0.833643i	$0.686251\pi$
$270$		0			0
$271$	5.44427	−	16.7557i	0.330716	−	1.01784i	−0.638078	−	0.769972i	$-0.720270\pi$
$271$	5.44427	−	16.7557i	0.330716	−	1.01784i	0.968794	−	0.247867i	$-0.0797297\pi$
$272$		0			0
$273$	7.66312	−	5.56758i	0.463793	−	0.336965i
$274$		0			0
$275$	1.50000	−	16.0292i	0.0904534	−	0.966597i
$276$		0			0
$277$	1.73607	−	1.26133i	0.104310	−	0.0757858i	−0.534407	−	0.845227i	$-0.679465\pi$
$277$	1.73607	−	1.26133i	0.104310	−	0.0757858i	0.638718	+	0.769441i	$0.279465\pi$
$278$		0			0
$279$	2.66312	−	8.19624i	0.159437	−	0.490696i
$280$		0			0
$281$	−14.2361	−	10.3431i	−0.849253	−	0.617018i	0.0756872	−	0.997132i	$-0.475885\pi$
$281$	−14.2361	−	10.3431i	−0.849253	−	0.617018i	−0.924940	+	0.380113i	$0.875885\pi$
$282$		0			0
$283$	−4.85410	−	14.9394i	−0.288546	−	0.888055i	−0.985313	−	0.170757i	$-0.945379\pi$
$283$	−4.85410	−	14.9394i	−0.288546	−	0.888055i	0.696767	−	0.717298i	$-0.254621\pi$
$284$		0			0
$285$	0.145898			0.00864225
$286$		0			0
$287$	21.1803			1.25024
$288$		0			0
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$		0			0
$291$	5.54508	+	4.02874i	0.325059	+	0.236169i
$292$		0			0
$293$	8.45492	−	26.0216i	0.493941	−	1.52020i	−0.324659	−	0.945831i	$-0.605249\pi$
$293$	8.45492	−	26.0216i	0.493941	−	1.52020i	0.818600	−	0.574364i	$-0.194751\pi$
$294$		0			0
$295$	−4.50000	+	3.26944i	−0.262000	+	0.190354i
$296$		0			0
$297$	−1.69098	−	2.85317i	−0.0981208	−	0.165558i
$298$		0			0
$299$	−11.2812	+	8.19624i	−0.652406	+	0.474001i
$300$		0			0
$301$	−15.0172	+	46.2183i	−0.865578	+	2.66398i
$302$		0			0
$303$	−0.427051	−	0.310271i	−0.0245334	−	0.0178246i
$304$		0			0
$305$	−0.809017	−	2.48990i	−0.0463242	−	0.142571i
$306$		0			0
$307$	10.7984			0.616296			0.308148	−	0.951338i	$-0.400291\pi$
$307$	10.7984			0.616296			0.308148	+	0.951338i	$0.400291\pi$
$308$		0			0
$309$	−3.52786			−0.200693
$310$		0			0
$311$	4.39919	+	13.5393i	0.249455	+	0.767744i	0.994872	+	0.101145i	$0.0322505\pi$
$311$	4.39919	+	13.5393i	0.249455	+	0.767744i	−0.745417	+	0.666599i	$0.767749\pi$
$312$		0			0
$313$	−7.19098	−	5.22455i	−0.406458	−	0.295309i	0.365708	−	0.930730i	$-0.380827\pi$
$313$	−7.19098	−	5.22455i	−0.406458	−	0.295309i	−0.772166	+	0.635420i	$0.780827\pi$
$314$		0			0
$315$	−0.500000	+	1.53884i	−0.0281718	+	0.0867039i
$316$		0			0
$317$	1.57295	−	1.14281i	0.0883456	−	0.0641868i	−0.542736	−	0.839904i	$-0.682611\pi$
$317$	1.57295	−	1.14281i	0.0883456	−	0.0641868i	0.631081	+	0.775717i	$0.282611\pi$
$318$		0			0
$319$	1.03444	−	1.17557i	0.0579176	−	0.0658193i
$320$		0			0
$321$	−9.66312	+	7.02067i	−0.539343	+	0.391855i
$322$		0			0
$323$	−0.218847	+	0.673542i	−0.0121770	+	0.0374769i
$324$		0			0
$325$	8.78115	+	6.37988i	0.487091	+	0.353892i
$326$		0			0
$327$	5.52786	+	17.0130i	0.305692	+	0.940822i
$328$		0			0
$329$	−0.618034			−0.0340733
$330$		0			0
$331$	−27.0000			−1.48405			−0.742027	−	0.670370i	$-0.766135\pi$
$331$	−27.0000			−1.48405			−0.742027	+	0.670370i	$0.766135\pi$
$332$		0			0
$333$	1.16312	+	3.57971i	0.0637385	+	0.196167i
$334$		0			0
$335$	1.40983	+	1.02430i	0.0770272	+	0.0559636i
$336$		0			0
$337$	−3.18034	+	9.78808i	−0.173244	+	0.533191i	−0.999549	−	0.0300326i	$-0.990439\pi$
$337$	−3.18034	+	9.78808i	−0.173244	+	0.533191i	0.826305	+	0.563223i	$0.190439\pi$
$338$		0			0
$339$	−14.7533	+	10.7189i	−0.801289	+	0.582170i
$340$		0			0
$341$	−27.8885	+	6.26137i	−1.51025	+	0.339072i
$342$		0			0
$343$	13.5172	−	9.82084i	0.729861	−	0.530275i
$344$		0			0
$345$	0.736068	−	2.26538i	0.0396286	−	0.121964i
$346$		0			0
$347$	−12.9443	−	9.40456i	−0.694885	−	0.504863i	0.183377	−	0.983043i	$-0.441297\pi$
$347$	−12.9443	−	9.40456i	−0.694885	−	0.504863i	−0.878262	+	0.478179i	$0.841297\pi$
$348$		0			0
$349$	3.78115	+	11.6372i	0.202400	+	0.622925i	0.999810	+	0.0194863i	$0.00620306\pi$
$349$	3.78115	+	11.6372i	0.202400	+	0.622925i	−0.797410	+	0.603438i	$0.793797\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$		0			0
$353$	14.4721			0.770274			0.385137	−	0.922859i	$-0.374154\pi$
$353$	14.4721			0.770274			0.385137	+	0.922859i	$0.374154\pi$
$354$		0			0
$355$	1.48278	+	4.56352i	0.0786977	+	0.242207i
$356$		0			0
$357$	−6.35410	−	4.61653i	−0.336295	−	0.244332i
$358$		0			0
$359$	2.38197	−	7.33094i	0.125715	−	0.386912i	−0.868315	−	0.496013i	$-0.834797\pi$
$359$	2.38197	−	7.33094i	0.125715	−	0.386912i	0.994031	+	0.109100i	$0.0347970\pi$
$360$		0			0
$361$	15.2533	−	11.0822i	0.802805	−	0.583272i
$362$		0			0
$363$	−5.28115	+	9.64932i	−0.277189	+	0.506458i
$364$		0			0
$365$	−1.14590	+	0.832544i	−0.0599790	+	0.0435773i
$366$		0			0
$367$	−6.59017	+	20.2825i	−0.344004	+	1.05874i	0.618111	+	0.786091i	$0.287898\pi$
$367$	−6.59017	+	20.2825i	−0.344004	+	1.05874i	−0.962115	+	0.272645i	$0.912102\pi$
$368$		0			0
$369$	4.04508	+	2.93893i	0.210579	+	0.152994i
$370$		0			0
$371$	12.5172	+	38.5240i	0.649862	+	2.00007i
$372$		0			0
$373$	−1.94427			−0.100671			−0.0503353	−	0.998732i	$-0.516029\pi$
$373$	−1.94427			−0.100671			−0.0503353	+	0.998732i	$0.516029\pi$
$374$		0			0
$375$	−3.76393			−0.194369
$376$		0			0
$377$	0.326238	+	1.00406i	0.0168021	+	0.0517116i
$378$		0			0
$379$	−4.19098	−	3.04493i	−0.215276	−	0.156407i	0.474921	−	0.880028i	$-0.342476\pi$
$379$	−4.19098	−	3.04493i	−0.215276	−	0.156407i	−0.690198	+	0.723621i	$0.742476\pi$
$380$		0			0
$381$	0.236068	−	0.726543i	0.0120941	−	0.0372219i
$382$		0			0
$383$	15.6074	−	11.3394i	0.797500	−	0.579418i	−0.112679	−	0.993631i	$-0.535943\pi$
$383$	15.6074	−	11.3394i	0.797500	−	0.579418i	0.910180	+	0.414213i	$0.135943\pi$
$384$		0			0
$385$	5.23607	−	1.17557i	0.266855	−	0.0599126i
$386$		0			0
$387$	−9.28115	+	6.74315i	−0.471788	+	0.342774i
$388$		0			0
$389$	10.7533	−	33.0952i	0.545213	−	1.67799i	−0.175269	−	0.984521i	$-0.556079\pi$
$389$	10.7533	−	33.0952i	0.545213	−	1.67799i	0.720482	−	0.693474i	$-0.243921\pi$
$390$		0			0
$391$	9.35410	+	6.79615i	0.473057	+	0.343696i
$392$		0			0
$393$	0.718847	+	2.21238i	0.0362610	+	0.111600i
$394$		0			0
$395$	5.43769			0.273600
$396$		0			0
$397$	−21.2918			−1.06860			−0.534302	−	0.845293i	$-0.679426\pi$
$397$	−21.2918			−1.06860			−0.534302	+	0.845293i	$0.679426\pi$
$398$		0			0
$399$	−0.500000	−	1.53884i	−0.0250313	−	0.0770384i
$400$		0			0
$401$	27.0623	+	19.6619i	1.35143	+	0.981869i	0.998939	+	0.0460529i	$0.0146643\pi$
$401$	27.0623	+	19.6619i	1.35143	+	0.981869i	0.352488	+	0.935816i	$0.385336\pi$
$402$		0			0
$403$	5.95492	−	18.3273i	0.296635	−	0.912950i
$404$		0			0
$405$	−0.309017	+	0.224514i	−0.0153552	+	0.0111562i
$406$		0			0
$407$	8.24671	−	9.37181i	0.408774	−	0.464543i
$408$		0			0
$409$	−27.4164	+	19.9192i	−1.35565	+	0.984940i	−0.356946	+	0.934125i	$0.616182\pi$
$409$	−27.4164	+	19.9192i	−1.35565	+	0.984940i	−0.998708	+	0.0508154i	$0.983818\pi$
$410$		0			0
$411$	1.69098	−	5.20431i	0.0834100	−	0.256710i
$412$		0			0
$413$	49.9058	+	36.2587i	2.45570	+	1.78417i
$414$		0			0
$415$	−0.229490	−	0.706298i	−0.0112652	−	0.0346708i
$416$		0			0
$417$	−18.6180			−0.911729
$418$		0			0
$419$	−20.4508			−0.999089			−0.499545	−	0.866288i	$-0.666499\pi$
$419$	−20.4508			−0.999089			−0.499545	+	0.866288i	$0.666499\pi$
$420$		0			0
$421$	7.02786	+	21.6295i	0.342517	+	1.05416i	0.962900	+	0.269860i	$0.0869774\pi$
$421$	7.02786	+	21.6295i	0.342517	+	1.05416i	−0.620382	+	0.784299i	$0.713023\pi$
$422$		0			0
$423$	−0.118034	−	0.0857567i	−0.00573901	−	0.00416963i
$424$		0			0
$425$	2.78115	−	8.55951i	0.134906	−	0.415197i
$426$		0			0
$427$	−23.4894	+	17.0660i	−1.13673	+	0.825882i
$428$		0			0
$429$	−3.78115	−	6.37988i	−0.182556	−	0.308024i
$430$		0			0
$431$	28.2984	−	20.5600i	1.36308	−	0.990339i	0.364843	−	0.931069i	$-0.381123\pi$
$431$	28.2984	−	20.5600i	1.36308	−	0.990339i	0.998242	−	0.0592698i	$-0.0188772\pi$
$432$		0			0
$433$	−9.56231	+	29.4298i	−0.459535	+	1.41430i	0.406192	+	0.913788i	$0.366856\pi$
$433$	−9.56231	+	29.4298i	−0.459535	+	1.41430i	−0.865727	+	0.500516i	$0.833144\pi$
$434$		0			0
$435$	−0.145898	−	0.106001i	−0.00699528	−	0.00508236i
$436$		0			0
$437$	0.736068	+	2.26538i	0.0352109	+	0.108368i
$438$		0			0
$439$	29.4721			1.40663			0.703314	−	0.710879i	$-0.251703\pi$
$439$	29.4721			1.40663			0.703314	+	0.710879i	$0.251703\pi$
$440$		0			0
$441$	10.9443			0.521156
$442$		0			0
$443$	9.32624	+	28.7032i	0.443103	+	1.36373i	0.884551	+	0.466444i	$0.154465\pi$
$443$	9.32624	+	28.7032i	0.443103	+	1.36373i	−0.441448	+	0.897287i	$0.645535\pi$
$444$		0			0
$445$	−1.07295	−	0.779543i	−0.0508627	−	0.0369539i
$446$		0			0
$447$	2.30902	−	7.10642i	0.109213	−	0.336122i
$448$		0			0
$449$	−28.5623	+	20.7517i	−1.34794	+	0.979335i	−0.348827	+	0.937187i	$0.613420\pi$
$449$	−28.5623	+	20.7517i	−1.34794	+	0.979335i	−0.999111	+	0.0421476i	$0.986580\pi$
$450$		0			0
$451$	1.54508	−	16.5110i	0.0727552	−	0.777472i
$452$		0			0
$453$	10.8541	−	7.88597i	0.509970	−	0.370515i
$454$		0			0
$455$	−1.11803	+	3.44095i	−0.0524142	+	0.161314i
$456$		0			0
$457$	−1.40983	−	1.02430i	−0.0659491	−	0.0479148i	0.554322	−	0.832302i	$-0.312978\pi$
$457$	−1.40983	−	1.02430i	−0.0659491	−	0.0479148i	−0.620271	+	0.784387i	$0.712978\pi$
$458$		0			0
$459$	−0.572949	−	1.76336i	−0.0267430	−	0.0823064i
$460$		0			0
$461$	−22.0902			−1.02884			−0.514421	−	0.857538i	$-0.671993\pi$
$461$	−22.0902			−1.02884			−0.514421	+	0.857538i	$0.671993\pi$
$462$		0			0
$463$	−31.4508			−1.46164			−0.730822	−	0.682568i	$-0.760863\pi$
$463$	−31.4508			−1.46164			−0.730822	+	0.682568i	$0.760863\pi$
$464$		0			0
$465$	1.01722	+	3.13068i	0.0471725	+	0.145182i
$466$		0			0
$467$	−5.19098	−	3.77147i	−0.240210	−	0.174523i	0.461167	−	0.887313i	$-0.347431\pi$
$467$	−5.19098	−	3.77147i	−0.240210	−	0.174523i	−0.701377	+	0.712791i	$0.747431\pi$
$468$		0			0
$469$	5.97214	−	18.3803i	0.275768	−	0.848725i
$470$		0			0
$471$	−13.0902	+	9.51057i	−0.603163	+	0.438224i
$472$		0			0
$473$	34.9336	+	15.0781i	1.60625	+	0.693294i
$474$		0			0
$475$	1.50000	−	1.08981i	0.0688247	−	0.0500041i
$476$		0			0
$477$	−2.95492	+	9.09429i	−0.135296	+	0.416399i
$478$		0			0
$479$	−26.5344	−	19.2784i	−1.21239	−	0.880853i	−0.216944	−	0.976184i	$-0.569609\pi$
$479$	−26.5344	−	19.2784i	−1.21239	−	0.880853i	−0.995446	+	0.0953314i	$0.969609\pi$
$480$		0			0
$481$	2.60081	+	8.00448i	0.118587	+	0.364973i
$482$		0			0
$483$	−26.4164			−1.20199
$484$		0			0
$485$	−2.61803			−0.118879
$486$		0			0
$487$	−8.01722	−	24.6745i	−0.363295	−	1.11811i	−0.951042	−	0.309062i	$-0.899985\pi$
$487$	−8.01722	−	24.6745i	−0.363295	−	1.11811i	0.587747	−	0.809045i	$-0.300015\pi$
$488$		0			0
$489$	12.4443	+	9.04129i	0.562749	+	0.408861i
$490$		0			0
$491$	8.31559	−	25.5928i	0.375278	−	1.15499i	−0.568014	−	0.823019i	$-0.692288\pi$
$491$	8.31559	−	25.5928i	0.375278	−	1.15499i	0.943291	−	0.331966i	$-0.107712\pi$
$492$		0			0
$493$	0.708204	−	0.514540i	0.0318959	−	0.0231737i
$494$		0			0
$495$	1.16312	+	0.502029i	0.0522783	+	0.0225645i
$496$		0			0
$497$	43.0517	−	31.2789i	1.93113	−	1.40305i
$498$		0			0
$499$	0.590170	−	1.81636i	0.0264196	−	0.0813113i	−0.936977	−	0.349390i	$-0.886389\pi$
$499$	0.590170	−	1.81636i	0.0264196	−	0.0813113i	0.963397	+	0.268079i	$0.0863888\pi$
$500$		0			0
$501$	−18.8713	−	13.7108i	−0.843109	−	0.612554i
$502$		0			0
$503$	1.00000	+	3.07768i	0.0445878	+	0.137227i	0.970872	−	0.239598i	$-0.0770157\pi$
$503$	1.00000	+	3.07768i	0.0445878	+	0.137227i	−0.926284	+	0.376825i	$0.877016\pi$
$504$		0			0
$505$	0.201626			0.00897224
$506$		0			0
$507$	−8.00000			−0.355292
$508$		0			0
$509$	−4.89919	−	15.0781i	−0.217153	−	0.668327i	−0.998994	−	0.0448494i	$-0.985719\pi$
$509$	−4.89919	−	15.0781i	−0.217153	−	0.668327i	0.781841	−	0.623478i	$-0.214281\pi$
$510$		0			0
$511$	12.7082	+	9.23305i	0.562178	+	0.408446i
$512$		0			0
$513$	0.118034	−	0.363271i	0.00521133	−	0.0160388i
$514$		0			0
$515$	1.09017	−	0.792055i	0.0480386	−	0.0349021i
$516$		0			0
$517$	−0.0450850	+	0.481784i	−0.00198283	+	0.0211888i
$518$		0			0
$519$	13.7812	−	10.0126i	0.604925	−	0.439504i
$520$		0			0
$521$	−4.94427	+	15.2169i	−0.216612	+	0.666665i	0.782423	+	0.622748i	$0.213984\pi$
$521$	−4.94427	+	15.2169i	−0.216612	+	0.666665i	−0.999035	+	0.0439170i	$0.986016\pi$
$522$		0			0
$523$	5.20820	+	3.78398i	0.227739	+	0.165462i	0.695803	−	0.718232i	$-0.255049\pi$
$523$	5.20820	+	3.78398i	0.227739	+	0.165462i	−0.468064	+	0.883694i	$0.655049\pi$
$524$		0			0
$525$	6.35410	+	19.5559i	0.277316	+	0.853490i
$526$		0			0
$527$	−15.9787			−0.696044
$528$		0			0
$529$	15.8885			0.690806
$530$		0			0
$531$	4.50000	+	13.8496i	0.195283	+	0.601020i
$532$		0			0
$533$	9.04508	+	6.57164i	0.391786	+	0.284649i
$534$		0			0
$535$	1.40983	−	4.33901i	0.0609523	−	0.187592i
$536$		0			0
$537$	18.1353	−	13.1760i	0.782594	−	0.568588i
$538$		0			0
$539$	−18.5066	−	31.2259i	−0.797135	−	1.34499i
$540$		0			0
$541$	5.69098	−	4.13474i	0.244674	−	0.177766i	−0.458689	−	0.888597i	$-0.651681\pi$
$541$	5.69098	−	4.13474i	0.244674	−	0.177766i	0.703363	+	0.710831i	$0.251681\pi$
$542$		0			0
$543$	4.60081	−	14.1598i	0.197440	−	0.607657i
$544$		0			0
$545$	−5.52786	−	4.01623i	−0.236788	−	0.172036i
$546$		0			0
$547$	−4.98936	−	15.3557i	−0.213329	−	0.656561i	−0.999268	−	0.0382560i	$-0.987820\pi$
$547$	−4.98936	−	15.3557i	−0.213329	−	0.656561i	0.785938	−	0.618305i	$-0.212180\pi$
$548$		0			0
$549$	−6.85410			−0.292526
$550$		0			0
$551$	0.180340			0.00768274
$552$		0			0
$553$	−18.6353	−	57.3534i	−0.792452	−	2.43892i
$554$		0			0
$555$	−1.16312	−	0.845055i	−0.0493717	−	0.0358706i
$556$		0			0
$557$	5.35410	−	16.4782i	0.226861	−	0.698205i	−0.771237	−	0.636548i	$-0.780362\pi$
$557$	5.35410	−	16.4782i	0.226861	−	0.698205i	0.998097	−	0.0616568i	$-0.0196384\pi$
$558$		0			0
$559$	−20.7533	+	15.0781i	−0.877771	+	0.637738i
$560$		0			0
$561$	−4.06231	+	4.61653i	−0.171511	+	0.194910i
$562$		0			0
$563$	−24.4615	+	17.7723i	−1.03093	+	0.749014i	−0.968494	−	0.249035i	$-0.919886\pi$
$563$	−24.4615	+	17.7723i	−1.03093	+	0.749014i	−0.0624346	+	0.998049i	$0.519886\pi$
$564$		0			0
$565$	2.15248	−	6.62464i	0.0905553	−	0.278701i
$566$		0			0
$567$	3.42705	+	2.48990i	0.143923	+	0.104566i
$568$		0			0
$569$	−10.4164	−	32.0584i	−0.436679	−	1.34396i	−0.891357	−	0.453303i	$-0.850246\pi$
$569$	−10.4164	−	32.0584i	−0.436679	−	1.34396i	0.454678	−	0.890656i	$-0.349754\pi$
$570$		0			0
$571$	−23.1459			−0.968626			−0.484313	−	0.874895i	$-0.660930\pi$
$571$	−23.1459			−0.968626			−0.484313	+	0.874895i	$0.660930\pi$
$572$		0			0
$573$	5.76393			0.240792
$574$		0			0
$575$	−9.35410	−	28.7890i	−0.390093	−	1.20058i
$576$		0			0
$577$	22.7984	+	16.5640i	0.949109	+	0.689568i	0.950596	−	0.310431i	$-0.100473\pi$
$577$	22.7984	+	16.5640i	0.949109	+	0.689568i	−0.00148718	+	0.999999i	$0.500473\pi$
$578$		0			0
$579$	−0.100813	+	0.310271i	−0.00418965	+	0.0128944i
$580$		0			0
$581$	−6.66312	+	4.84104i	−0.276433	+	0.200840i
$582$		0			0
$583$	30.9443	−	6.94742i	1.28158	−	0.287733i
$584$		0			0
$585$	−0.690983	+	0.502029i	−0.0285686	+	0.0207563i
$586$		0			0
$587$	−3.92705	+	12.0862i	−0.162087	+	0.498852i	−0.998810	−	0.0487745i	$-0.984468\pi$
$587$	−3.92705	+	12.0862i	−0.162087	+	0.498852i	0.836723	+	0.547626i	$0.184468\pi$
$588$		0			0
$589$	−2.66312	−	1.93487i	−0.109732	−	0.0797249i
$590$		0			0
$591$	−2.51722	−	7.74721i	−0.103545	−	0.318678i
$592$		0			0
$593$	−38.5623			−1.58356			−0.791782	−	0.610804i	$-0.790846\pi$
$593$	−38.5623			−1.58356			−0.791782	+	0.610804i	$0.790846\pi$
$594$		0			0
$595$	3.00000			0.122988
$596$		0			0
$597$	2.92705	+	9.00854i	0.119796	+	0.368695i
$598$		0			0
$599$	11.5623	+	8.40051i	0.472423	+	0.343235i	0.798385	−	0.602148i	$-0.205688\pi$
$599$	11.5623	+	8.40051i	0.472423	+	0.343235i	−0.325962	+	0.945383i	$0.605688\pi$
$600$		0			0
$601$	−4.30902	+	13.2618i	−0.175768	+	0.540960i	−0.999668	−	0.0257766i	$-0.991794\pi$
$601$	−4.30902	+	13.2618i	−0.175768	+	0.540960i	0.823899	+	0.566736i	$0.191794\pi$
$602$		0			0
$603$	3.69098	−	2.68166i	0.150308	−	0.109205i
$604$		0			0
$605$	−0.534442	−	4.16750i	−0.0217282	−	0.169433i
$606$		0			0
$607$	−10.2082	+	7.41669i	−0.414338	+	0.301034i	−0.775356	−	0.631525i	$-0.782429\pi$
$607$	−10.2082	+	7.41669i	−0.414338	+	0.301034i	0.361018	+	0.932559i	$0.382429\pi$
$608$		0			0
$609$	−0.618034	+	1.90211i	−0.0250440	+	0.0770775i
$610$		0			0
$611$	−0.263932	−	0.191758i	−0.0106775	−	0.00775769i
$612$		0			0
$613$	1.79837	+	5.53483i	0.0726356	+	0.223550i	0.980783	−	0.195101i	$-0.0625034\pi$
$613$	1.79837	+	5.53483i	0.0726356	+	0.223550i	−0.908148	+	0.418650i	$0.862503\pi$
$614$		0			0
$615$	−1.90983			−0.0770118
$616$		0			0
$617$	−12.5279			−0.504353			−0.252176	−	0.967681i	$-0.581146\pi$
$617$	−12.5279			−0.504353			−0.252176	+	0.967681i	$0.581146\pi$
$618$		0			0
$619$	−5.10739	−	15.7189i	−0.205283	−	0.631797i	−0.999702	−	0.0244262i	$-0.992224\pi$
$619$	−5.10739	−	15.7189i	−0.205283	−	0.631797i	0.794418	−	0.607371i	$-0.207776\pi$
$620$		0			0
$621$	−5.04508	−	3.66547i	−0.202452	−	0.147090i
$622$		0			0
$623$	−4.54508	+	13.9883i	−0.182095	+	0.560431i
$624$		0			0
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$		0			0
$627$	−1.23607	+	0.277515i	−0.0493638	+	0.0110829i
$628$		0			0
$629$	5.64590	−	4.10199i	0.225117	−	0.163557i
$630$		0			0
$631$	8.19098	−	25.2093i	0.326078	−	1.00356i	−0.644874	−	0.764289i	$-0.723090\pi$
$631$	8.19098	−	25.2093i	0.326078	−	1.00356i	0.970952	−	0.239275i	$-0.0769099\pi$
$632$		0			0
$633$	−2.73607	−	1.98787i	−0.108749	−	0.0790107i
$634$		0			0
$635$	0.0901699	+	0.277515i	0.00357829	+	0.0110128i
$636$		0			0
$637$	24.4721			0.969621
$638$		0			0
$639$	12.5623			0.496957
$640$		0			0
$641$	5.50000	+	16.9273i	0.217237	+	0.668587i	0.998987	+	0.0449949i	$0.0143272\pi$
$641$	5.50000	+	16.9273i	0.217237	+	0.668587i	−0.781750	+	0.623592i	$0.785673\pi$
$642$		0			0
$643$	12.0623	+	8.76378i	0.475691	+	0.345610i	0.799655	−	0.600460i	$-0.205016\pi$
$643$	12.0623	+	8.76378i	0.475691	+	0.345610i	−0.323964	+	0.946069i	$0.605016\pi$
$644$		0			0
$645$	1.35410	−	4.16750i	0.0533177	−	0.164095i
$646$		0			0
$647$	32.6803	−	23.7437i	1.28480	−	0.933459i	0.285110	−	0.958495i	$-0.407970\pi$
$647$	32.6803	−	23.7437i	1.28480	−	0.933459i	0.999687	+	0.0250353i	$0.00796981\pi$
$648$		0			0
$649$	31.9058	−	36.2587i	1.25241	−	1.42328i
$650$		0			0
$651$	29.5344	−	21.4580i	1.15755	−	0.841006i
$652$		0			0
$653$	−5.48278	+	16.8743i	−0.214558	+	0.660341i	0.784627	+	0.619968i	$0.212854\pi$
$653$	−5.48278	+	16.8743i	−0.214558	+	0.660341i	−0.999185	+	0.0403726i	$0.987146\pi$
$654$		0			0
$655$	−0.718847	−	0.522273i	−0.0280877	−	0.0204069i
$656$		0			0
$657$	1.14590	+	3.52671i	0.0447057	+	0.137590i
$658$		0			0
$659$	−19.1246			−0.744989			−0.372495	−	0.928034i	$-0.621497\pi$
$659$	−19.1246			−0.744989			−0.372495	+	0.928034i	$0.621497\pi$
$660$		0			0
$661$	−8.14590			−0.316839			−0.158419	−	0.987372i	$-0.550640\pi$
$661$	−8.14590			−0.316839			−0.158419	+	0.987372i	$0.550640\pi$
$662$		0			0
$663$	−1.28115	−	3.94298i	−0.0497559	−	0.153133i
$664$		0			0
$665$	0.500000	+	0.363271i	0.0193892	+	0.0140871i
$666$		0			0
$667$	0.909830	−	2.80017i	0.0352288	−	0.108423i
$668$		0			0
$669$	10.1353	−	7.36369i	0.391852	−	0.284697i
$670$		0			0
$671$	11.5902	+	19.5559i	0.447434	+	0.754948i
$672$		0			0
$673$	6.89919	−	5.01255i	0.265944	−	0.193220i	−0.446819	−	0.894624i	$-0.647443\pi$
$673$	6.89919	−	5.01255i	0.265944	−	0.193220i	0.712763	+	0.701405i	$0.247443\pi$
$674$		0			0
$675$	−1.50000	+	4.61653i	−0.0577350	+	0.177690i
$676$		0			0
$677$	−9.23607	−	6.71040i	−0.354971	−	0.257901i	0.395980	−	0.918259i	$-0.370405\pi$
$677$	−9.23607	−	6.71040i	−0.354971	−	0.257901i	−0.750951	+	0.660357i	$0.770405\pi$
$678$		0			0
$679$	8.97214	+	27.6134i	0.344319	+	1.05970i
$680$		0			0
$681$	−20.5967			−0.789269
$682$		0			0
$683$	34.4853			1.31954			0.659772	−	0.751466i	$-0.270653\pi$
$683$	34.4853			1.31954			0.659772	+	0.751466i	$0.270653\pi$
$684$		0			0
$685$	0.645898	+	1.98787i	0.0246785	+	0.0759526i
$686$		0			0
$687$	9.61803	+	6.98791i	0.366951	+	0.266605i
$688$		0			0
$689$	−6.60739	+	20.3355i	−0.251722	+	0.774719i
$690$		0			0
$691$	−11.0000	+	7.99197i	−0.418460	+	0.304029i	−0.777018	−	0.629479i	$-0.783269\pi$
$691$	−11.0000	+	7.99197i	−0.418460	+	0.304029i	0.358558	+	0.933507i	$0.383269\pi$
$692$		0			0
$693$	1.30902	−	13.9883i	0.0497254	−	0.531373i
$694$		0			0
$695$	5.75329	−	4.18001i	0.218235	−	0.158557i
$696$		0			0
$697$	2.86475	−	8.81678i	0.108510	−	0.333959i
$698$		0			0
$699$	16.2533	+	11.8087i	0.614756	+	0.446646i
$700$		0			0
$701$	10.1738	+	31.3116i	0.384258	+	1.18262i	0.937017	+	0.349283i	$0.113575\pi$
$701$	10.1738	+	31.3116i	0.384258	+	1.18262i	−0.552760	+	0.833341i	$0.686425\pi$
$702$		0			0
$703$	1.43769			0.0542237
$704$		0			0
$705$	0.0557281			0.00209884
$706$		0			0
$707$	−0.690983	−	2.12663i	−0.0259871	−	0.0799800i
$708$		0			0
$709$	8.35410	+	6.06961i	0.313745	+	0.227949i	0.733502	−	0.679688i	$-0.237885\pi$
$709$	8.35410	+	6.06961i	0.313745	+	0.227949i	−0.419757	+	0.907637i	$0.637885\pi$
$710$		0			0
$711$	4.39919	−	13.5393i	0.164982	−	0.507764i
$712$		0			0
$713$	−43.4787	+	31.5891i	−1.62829	+	1.18302i
$714$		0			0
$715$	2.60081	+	1.12257i	0.0972649	+	0.0419817i
$716$		0			0
$717$	−11.3541	+	8.24924i	−0.424027	+	0.308073i
$718$		0			0
$719$	−9.63525	+	29.6543i	−0.359334	+	1.10592i	0.594119	+	0.804377i	$0.297501\pi$
$719$	−9.63525	+	29.6543i	−0.359334	+	1.10592i	−0.953453	+	0.301540i	$0.902499\pi$
$720$		0			0
$721$	−12.0902	−	8.78402i	−0.450261	−	0.327134i
$722$		0			0
$723$	−9.29180	−	28.5972i	−0.345566	−	1.06354i
$724$		0			0
$725$	−2.29180			−0.0851152
$726$		0			0
$727$	−31.7426			−1.17727			−0.588635	−	0.808399i	$-0.700334\pi$
$727$	−31.7426			−1.17727			−0.588635	+	0.808399i	$0.700334\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	17.2082	+	12.5025i	0.636468	+	0.462421i
$732$		0			0
$733$	11.1459	−	34.3035i	0.411683	−	1.26703i	−0.503501	−	0.863995i	$-0.667955\pi$
$733$	11.1459	−	34.3035i	0.411683	−	1.26703i	0.915184	−	0.403036i	$-0.132045\pi$
$734$		0			0
$735$	−3.38197	+	2.45714i	−0.124746	+	0.0906331i
$736$		0			0
$737$	−13.8926	−	5.99637i	−0.511741	−	0.220879i
$738$		0			0
$739$	−7.33688	+	5.33056i	−0.269892	+	0.196088i	−0.714496	−	0.699639i	$-0.753344\pi$
$739$	−7.33688	+	5.33056i	−0.269892	+	0.196088i	0.444605	+	0.895727i	$0.353344\pi$
$740$		0			0
$741$	0.263932	−	0.812299i	0.00969579	−	0.0298406i
$742$		0			0
$743$	−6.42705	−	4.66953i	−0.235786	−	0.171308i	0.463618	−	0.886035i	$-0.346551\pi$
$743$	−6.42705	−	4.66953i	−0.235786	−	0.171308i	−0.699404	+	0.714727i	$0.746551\pi$
$744$		0			0
$745$	0.881966	+	2.71441i	0.0323127	+	0.0994484i
$746$		0			0
$747$	−1.94427			−0.0711372
$748$		0			0
$749$	−50.5967			−1.84876
$750$		0			0
$751$	1.26393	+	3.88998i	0.0461215	+	0.141947i	0.971465	−	0.237182i	$-0.0762236\pi$
$751$	1.26393	+	3.88998i	0.0461215	+	0.141947i	−0.925344	+	0.379129i	$0.876224\pi$
$752$		0			0
$753$	−1.73607	−	1.26133i	−0.0632658	−	0.0459653i
$754$		0			0
$755$	−1.58359	+	4.87380i	−0.0576328	+	0.177376i
$756$		0			0
$757$	6.89919	−	5.01255i	0.250755	−	0.182184i	−0.455306	−	0.890335i	$-0.650470\pi$
$757$	6.89919	−	5.01255i	0.250755	−	0.182184i	0.706061	+	0.708151i	$0.250470\pi$
$758$		0			0
$759$	−1.92705	+	20.5927i	−0.0699475	+	0.747469i
$760$		0			0
$761$	−8.04508	+	5.84510i	−0.291634	+	0.211885i	−0.723976	−	0.689825i	$-0.757687\pi$
$761$	−8.04508	+	5.84510i	−0.291634	+	0.211885i	0.432342	+	0.901710i	$0.357687\pi$
$762$		0			0
$763$	−23.4164	+	72.0683i	−0.847731	+	2.60905i
$764$		0			0
$765$	0.572949	+	0.416272i	0.0207150	+	0.0150503i
$766$		0			0
$767$	10.0623	+	30.9686i	0.363329	+	1.11821i
$768$		0			0
$769$	26.5623			0.957861			0.478931	−	0.877853i	$-0.341025\pi$
$769$	26.5623			0.957861			0.478931	+	0.877853i	$0.341025\pi$
$770$		0			0
$771$	17.7984			0.640993
$772$		0			0
$773$	2.42047	+	7.44945i	0.0870584	+	0.267938i	0.985103	−	0.171967i	$-0.0550122\pi$
$773$	2.42047	+	7.44945i	0.0870584	+	0.267938i	−0.898044	+	0.439905i	$0.855012\pi$
$774$		0			0
$775$	33.8435	+	24.5887i	1.21569	+	0.883253i
$776$		0			0
$777$	−4.92705	+	15.1639i	−0.176757	+	0.544002i
$778$		0			0
$779$	1.54508	−	1.12257i	0.0553584	−	0.0402202i
$780$		0			0
$781$	−21.2426	−	35.8424i	−0.760122	−	1.28254i
$782$		0			0
$783$	−0.381966	+	0.277515i	−0.0136504	+	0.00991756i
$784$		0			0
$785$	1.90983	−	5.87785i	0.0681648	−	0.209790i
$786$		0			0
$787$	36.4164	+	26.4581i	1.29810	+	0.943128i	0.999935	−	0.0113846i	$-0.00362391\pi$
$787$	36.4164	+	26.4581i	1.29810	+	0.943128i	0.298170	+	0.954513i	$0.403624\pi$
$788$		0			0
$789$	3.35410	+	10.3229i	0.119409	+	0.367504i
$790$		0			0
$791$	−77.2492			−2.74667
$792$		0			0
$793$	−15.3262			−0.544251
$794$		0			0
$795$	−1.12868	−	3.47371i	−0.0400301	−	0.123200i
$796$		0			0
$797$	4.61803	+	3.35520i	0.163579	+	0.118847i	0.666563	−	0.745448i	$-0.267765\pi$
$797$	4.61803	+	3.35520i	0.163579	+	0.118847i	−0.502984	+	0.864296i	$0.667765\pi$
$798$		0			0
$799$	−0.0835921	+	0.257270i	−0.00295728	+	0.00910156i
$800$		0			0
$801$	−2.80902	+	2.04087i	−0.0992517	+	0.0721106i
$802$		0			0
$803$	8.12461	−	9.23305i	0.286711	−	0.325827i
$804$		0			0
$805$	8.16312	−	5.93085i	0.287712	−	0.209035i
$806$		0			0
$807$	−0.437694	+	1.34708i	−0.0154076	+	0.0474196i
$808$		0			0
$809$	8.30902	+	6.03685i	0.292129	+	0.212244i	0.724191	−	0.689600i	$-0.242214\pi$
$809$	8.30902	+	6.03685i	0.292129	+	0.212244i	−0.432061	+	0.901844i	$0.642214\pi$
$810$		0			0
$811$	0.100813	+	0.310271i	0.00354003	+	0.0108951i	0.952811	−	0.303564i	$-0.0981767\pi$
$811$	0.100813	+	0.310271i	0.00354003	+	0.0108951i	−0.949271	+	0.314459i	$0.898177\pi$
$812$		0			0
$813$	17.6180			0.617891
$814$		0			0
$815$	−5.87539			−0.205806
$816$		0			0
$817$	1.35410	+	4.16750i	0.0473740	+	0.145802i
$818$		0			0
$819$	7.66312	+	5.56758i	0.267771	+	0.194547i
$820$		0			0
$821$	9.57953	−	29.4828i	0.334328	−	1.02896i	−0.632724	−	0.774377i	$-0.718063\pi$
$821$	9.57953	−	29.4828i	0.334328	−	1.02896i	0.967052	−	0.254578i	$-0.0819366\pi$
$822$		0			0
$823$	33.6074	−	24.4172i	1.17148	−	0.851130i	0.180295	−	0.983613i	$-0.442295\pi$
$823$	33.6074	−	24.4172i	1.17148	−	0.851130i	0.991185	+	0.132483i	$0.0422949\pi$
$824$		0			0
$825$	15.7082	−	3.52671i	0.546889	−	0.122784i
$826$		0			0
$827$	−19.1803	+	13.9353i	−0.666966	+	0.484579i	−0.869008	−	0.494798i	$-0.835242\pi$
$827$	−19.1803	+	13.9353i	−0.666966	+	0.484579i	0.202042	+	0.979377i	$0.435242\pi$
$828$		0			0
$829$	−7.48278	+	23.0296i	−0.259888	+	0.799852i	0.732940	+	0.680294i	$0.238148\pi$
$829$	−7.48278	+	23.0296i	−0.259888	+	0.799852i	−0.992827	+	0.119558i	$0.961852\pi$
$830$		0			0
$831$	1.73607	+	1.26133i	0.0602235	+	0.0437550i
$832$		0			0
$833$	−6.27051	−	19.2986i	−0.217260	−	0.668658i
$834$		0			0
$835$	8.90983			0.308337
$836$		0			0
$837$	8.61803			0.297883
$838$		0			0
$839$	13.4336	+	41.3445i	0.463780	+	1.42737i	0.860510	+	0.509434i	$0.170145\pi$
$839$	13.4336	+	41.3445i	0.463780	+	1.42737i	−0.396730	+	0.917936i	$0.629855\pi$
$840$		0			0
$841$	23.2812	+	16.9147i	0.802798	+	0.583267i
$842$		0			0
$843$	5.43769	−	16.7355i	0.187284	−	0.576401i
$844$		0			0
$845$	2.47214	−	1.79611i	0.0850441	−	0.0617881i
$846$		0			0
$847$	−42.1246	+	19.9192i	−1.44742	+	0.684431i
$848$		0			0
$849$	12.7082	−	9.23305i	0.436144	−	0.316877i
$850$		0			0
$851$	7.25329	−	22.3233i	0.248640	−	0.765234i
$852$		0			0
$853$	−23.0795	−	16.7683i	−0.790228	−	0.574134i	0.117803	−	0.993037i	$-0.462415\pi$
$853$	−23.0795	−	16.7683i	−0.790228	−	0.574134i	−0.908031	+	0.418903i	$0.862415\pi$
$854$		0			0
$855$	0.0450850	+	0.138757i	0.00154187	+	0.00474540i
$856$		0			0
$857$	22.8885			0.781858			0.390929	−	0.920421i	$-0.372154\pi$
$857$	22.8885			0.781858			0.390929	+	0.920421i	$0.372154\pi$
$858$		0			0
$859$	19.6525			0.670534			0.335267	−	0.942123i	$-0.391174\pi$
$859$	19.6525			0.670534			0.335267	+	0.942123i	$0.391174\pi$
$860$		0			0
$861$	6.54508	+	20.1437i	0.223056	+	0.686495i
$862$		0			0
$863$	−12.3820	−	8.99602i	−0.421487	−	0.306228i	0.356749	−	0.934200i	$-0.383885\pi$
$863$	−12.3820	−	8.99602i	−0.421487	−	0.306228i	−0.778236	+	0.627972i	$0.783885\pi$
$864$		0			0
$865$	−2.01064	+	6.18812i	−0.0683639	+	0.210403i
$866$		0			0
$867$	10.9721	−	7.97172i	0.372633	−	0.270734i
$868$		0			0
$869$	−46.0689	+	10.3431i	−1.56278	+	0.350866i
$870$		0			0
$871$	8.25329	−	5.99637i	0.279652	−	0.203179i
$872$		0			0
$873$	−2.11803	+	6.51864i	−0.0716846	+	0.220622i
$874$		0			0
$875$	−12.8992	−	9.37181i	−0.436072	−	0.316825i
$876$		0			0
$877$	−3.65654	−	11.2537i	−0.123473	−	0.380010i	0.870147	−	0.492792i	$-0.164024\pi$
$877$	−3.65654	−	11.2537i	−0.123473	−	0.380010i	−0.993620	+	0.112782i	$0.964024\pi$
$878$		0			0
$879$	27.3607			0.922853
$880$		0			0
$881$	7.85410			0.264611			0.132306	−	0.991209i	$-0.457762\pi$
$881$	7.85410			0.264611			0.132306	+	0.991209i	$0.457762\pi$
$882$		0			0
$883$	10.4377	+	32.1239i	0.351256	+	1.08106i	0.958148	+	0.286272i	$0.0924160\pi$
$883$	10.4377	+	32.1239i	0.351256	+	1.08106i	−0.606892	+	0.794784i	$0.707584\pi$
$884$		0			0
$885$	−4.50000	−	3.26944i	−0.151266	−	0.109901i
$886$		0			0
$887$	5.30902	−	16.3395i	0.178259	−	0.548626i	−0.821508	−	0.570197i	$-0.806867\pi$
$887$	5.30902	−	16.3395i	0.178259	−	0.548626i	0.999767	+	0.0215712i	$0.00686685\pi$
$888$		0			0
$889$	2.61803	−	1.90211i	0.0878060	−	0.0637948i
$890$		0			0
$891$	2.19098	−	2.48990i	0.0734007	−	0.0834147i
$892$		0			0
$893$	−0.0450850	+	0.0327561i	−0.00150871	+	0.00109614i
$894$		0			0
$895$	−2.64590	+	8.14324i	−0.0884426	+	0.272198i
$896$		0			0
$897$	−11.2812	−	8.19624i	−0.376667	−	0.273664i
$898$		0			0
$899$	1.25735	+	3.86974i	0.0419351	+	0.129063i
$900$		0			0
$901$	17.7295			0.590655
$902$		0			0
$903$	−48.5967			−1.61720
$904$		0			0
$905$	1.75735	+	5.40858i	0.0584164	+	0.179787i
$906$		0			0
$907$	−4.39919	−	3.19620i	−0.146073	−	0.106128i	0.512349	−	0.858777i	$-0.328776\pi$
$907$	−4.39919	−	3.19620i	−0.146073	−	0.106128i	−0.658421	+	0.752649i	$0.728776\pi$
$908$		0			0
$909$	0.163119	−	0.502029i	0.00541031	−	0.0166512i
$910$		0			0
$911$	10.2812	−	7.46969i	0.340630	−	0.247482i	−0.404298	−	0.914627i	$-0.632484\pi$
$911$	10.2812	−	7.46969i	0.340630	−	0.247482i	0.744928	+	0.667145i	$0.232484\pi$
$912$		0			0
$913$	3.28773	+	5.54734i	0.108808	+	0.183590i
$914$		0			0
$915$	2.11803	−	1.53884i	0.0700200	−	0.0508725i
$916$		0			0
$917$	−3.04508	+	9.37181i	−0.100558	+	0.309484i
$918$		0			0
$919$	−2.33688	−	1.69784i	−0.0770866	−	0.0560067i	0.548575	−	0.836102i	$-0.315171\pi$
$919$	−2.33688	−	1.69784i	−0.0770866	−	0.0560067i	−0.625661	+	0.780095i	$0.715171\pi$
$920$		0			0
$921$	3.33688	+	10.2699i	0.109954	+	0.338404i
$922$		0			0
$923$	28.0902			0.924599
$924$		0			0
$925$	−18.2705			−0.600731
$926$		0			0
$927$	−1.09017	−	3.35520i	−0.0358059	−	0.110199i
$928$		0			0
$929$	−1.66312	−	1.20833i	−0.0545652	−	0.0396439i	0.560168	−	0.828379i	$-0.310736\pi$
$929$	−1.66312	−	1.20833i	−0.0545652	−	0.0396439i	−0.614734	+	0.788735i	$0.710736\pi$
$930$		0			0
$931$	1.29180	−	3.97574i	0.0423369	−	0.130300i
$932$		0			0
$933$	−11.5172	+	8.36775i	−0.377057	+	0.273948i
$934$		0			0
$935$	0.218847	−	2.33863i	0.00715706	−	0.0764814i
$936$		0			0
$937$	3.80902	−	2.76741i	0.124435	−	0.0904074i	−0.523827	−	0.851825i	$-0.675496\pi$
$937$	3.80902	−	2.76741i	0.124435	−	0.0904074i	0.648262	+	0.761417i	$0.275496\pi$
$938$		0			0
$939$	2.74671	−	8.45351i	0.0896355	−	0.275870i
$940$		0			0
$941$	5.02786	+	3.65296i	0.163904	+	0.119083i	0.666714	−	0.745314i	$-0.267700\pi$
$941$	5.02786	+	3.65296i	0.163904	+	0.119083i	−0.502810	+	0.864397i	$0.667700\pi$
$942$		0			0
$943$	−9.63525	−	29.6543i	−0.313767	−	0.965676i
$944$		0			0
$945$	−1.61803			−0.0526346
$946$		0			0
$947$	7.72949			0.251175			0.125587	−	0.992083i	$-0.459918\pi$
$947$	7.72949			0.251175			0.125587	+	0.992083i	$0.459918\pi$
$948$		0			0
$949$	2.56231	+	7.88597i	0.0831760	+	0.255989i
$950$		0			0
$951$	1.57295	+	1.14281i	0.0510064	+	0.0370583i
$952$		0			0
$953$	−5.76393	+	17.7396i	−0.186712	+	0.574641i	−0.999974	−	0.00725759i	$-0.997690\pi$
$953$	−5.76393	+	17.7396i	−0.186712	+	0.574641i	0.813262	+	0.581898i	$0.197690\pi$
$954$		0			0
$955$	−1.78115	+	1.29408i	−0.0576368	+	0.0418756i
$956$		0			0
$957$	1.43769	+	0.620541i	0.0464741	+	0.0200593i
$958$		0			0
$959$	18.7533	−	13.6251i	0.605575	−	0.439976i
$960$		0			0
$961$	13.3713	−	41.1527i	0.431333	−	1.32751i
$962$		0			0
$963$	−9.66312	−	7.02067i	−0.311390	−	0.226238i
$964$		0			0
$965$	−0.0385072	−	0.118513i	−0.00123959	−	0.00381506i
$966$		0			0
$967$	−22.3820			−0.719756			−0.359878	−	0.932999i	$-0.617182\pi$
$967$	−22.3820			−0.719756			−0.359878	+	0.932999i	$0.617182\pi$
$968$		0			0
$969$	−0.708204			−0.0227508
$970$		0			0
$971$	−10.9098	−	33.5770i	−0.350113	−	1.07754i	−0.958789	−	0.284119i	$-0.908299\pi$
$971$	−10.9098	−	33.5770i	−0.350113	−	1.07754i	0.608676	−	0.793419i	$-0.291701\pi$
$972$		0			0
$973$	−63.8050	−	46.3570i	−2.04549	−	1.48614i
$974$		0			0
$975$	−3.35410	+	10.3229i	−0.107417	+	0.330596i
$976$		0			0
$977$	5.19098	−	3.77147i	0.166074	−	0.120660i	−0.501644	−	0.865074i	$-0.667271\pi$
$977$	5.19098	−	3.77147i	0.166074	−	0.120660i	0.667718	+	0.744414i	$0.267271\pi$
$978$		0			0
$979$	10.5729	+	4.56352i	0.337913	+	0.145851i
$980$		0			0
$981$	−14.4721	+	10.5146i	−0.462060	+	0.335706i
$982$		0			0
$983$	−11.6738	+	35.9281i	−0.372335	+	1.14593i	0.572924	+	0.819609i	$0.305809\pi$
$983$	−11.6738	+	35.9281i	−0.372335	+	1.14593i	−0.945259	+	0.326321i	$0.894191\pi$
$984$		0			0
$985$	2.51722	+	1.82887i	0.0802053	+	0.0582726i
$986$		0			0
$987$	−0.190983	−	0.587785i	−0.00607906	−	0.0187094i
$988$		0			0
$989$	71.5410			2.27487
$990$		0			0
$991$	1.32624			0.0421293			0.0210647	−	0.999778i	$-0.493294\pi$
$991$	1.32624			0.0421293			0.0210647	+	0.999778i	$0.493294\pi$
$992$		0			0
$993$	−8.34346	−	25.6785i	−0.264772	−	0.814883i
$994$		0			0
$995$	−2.92705	−	2.12663i	−0.0927938	−	0.0674186i
$996$		0			0
$997$	8.09675	−	24.9192i	0.256427	−	0.789200i	−0.737119	−	0.675763i	$-0.763814\pi$
$997$	8.09675	−	24.9192i	0.256427	−	0.789200i	0.993545	−	0.113437i	$-0.0361859\pi$
$998$		0			0
$999$	−3.04508	+	2.21238i	−0.0963422	+	0.0699967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.q.b.25.1	✓	4
3.2	odd	2		792.2.r.d.289.1		4
4.3	odd	2		528.2.y.h.289.1		4
11.2	odd	10		2904.2.a.ba.1.1		2
11.4	even	5	inner	264.2.q.b.169.1	yes	4
11.9	even	5		2904.2.a.z.1.1		2
33.2	even	10		8712.2.a.bc.1.2		2
33.20	odd	10		8712.2.a.ba.1.2		2
33.26	odd	10		792.2.r.d.433.1		4
44.15	odd	10		528.2.y.h.433.1		4
44.31	odd	10		5808.2.a.bw.1.1		2
44.35	even	10		5808.2.a.bv.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.b.25.1	✓	4	1.1	even	1	trivial
264.2.q.b.169.1	yes	4	11.4	even	5	inner
528.2.y.h.289.1		4	4.3	odd	2
528.2.y.h.433.1		4	44.15	odd	10
792.2.r.d.289.1		4	3.2	odd	2
792.2.r.d.433.1		4	33.26	odd	10
2904.2.a.z.1.1		2	11.9	even	5
2904.2.a.ba.1.1		2	11.2	odd	10
5808.2.a.bv.1.1		2	44.35	even	10
5808.2.a.bw.1.1		2	44.31	odd	10
8712.2.a.ba.1.2		2	33.20	odd	10
8712.2.a.bc.1.2		2	33.2	even	10

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.224514i) q^{5} +(-1.30902 + 4.02874i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.04508 + 1.31433i) q^{11} +(-1.80902 + 1.31433i) q^{13} +(0.118034 - 0.363271i) q^{15} +(1.50000 + 1.08981i) q^{17} +(0.118034 + 0.363271i) q^{19} -4.23607 q^{21} +6.23607 q^{23} +(-1.50000 - 4.61653i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.145898 - 0.449028i) q^{29} +(-6.97214 + 5.06555i) q^{31} +(-0.309017 + 3.30220i) q^{33} +(1.30902 - 0.951057i) q^{35} +(1.16312 - 3.57971i) q^{37} +(-1.80902 - 1.31433i) q^{39} +(-1.54508 - 4.75528i) q^{41} +11.4721 q^{43} +0.381966 q^{45} +(0.0450850 + 0.138757i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-0.572949 + 1.76336i) q^{51} +(7.73607 - 5.62058i) q^{53} +(-0.645898 - 1.08981i) q^{55} +(-0.309017 + 0.224514i) q^{57} +(4.50000 - 13.8496i) q^{59} +(5.54508 + 4.02874i) q^{61} +(-1.30902 - 4.02874i) q^{63} +0.854102 q^{65} -4.56231 q^{67} +(1.92705 + 5.93085i) q^{69} +(-10.1631 - 7.38394i) q^{71} +(1.14590 - 3.52671i) q^{73} +(3.92705 - 2.85317i) q^{75} +(-9.28115 + 10.5474i) q^{77} +(-11.5172 + 8.36775i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.57295 + 1.14281i) q^{83} +(-0.218847 - 0.673542i) q^{85} +0.472136 q^{87} +3.47214 q^{89} +(-2.92705 - 9.00854i) q^{91} +(-6.97214 - 5.06555i) q^{93} +(0.0450850 - 0.138757i) q^{95} +(5.54508 - 4.02874i) q^{97} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + q^{5} - 3 q^{7} - q^{9} + q^{11} - 5 q^{13} - 4 q^{15} + 6 q^{17} - 4 q^{19} - 8 q^{21} + 16 q^{23} - 6 q^{25} - q^{27} + 14 q^{29} - 10 q^{31} + q^{33} + 3 q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - q^3 + q^5 - 3 * q^7 - q^9 + q^11 - 5 * q^13 - 4 * q^15 + 6 * q^17 - 4 * q^19 - 8 * q^21 + 16 * q^23 - 6 * q^25 - q^27 + 14 * q^29 - 10 * q^31 + q^33 + 3 * q^35 - 11 * q^37 - 5 * q^39 + 5 * q^41 + 28 * q^43 + 6 * q^45 - 11 * q^47 - 22 * q^49 - 9 * q^51 + 22 * q^53 - 16 * q^55 + q^57 + 18 * q^59 + 11 * q^61 - 3 * q^63 - 10 * q^65 + 22 * q^67 + q^69 - 25 * q^71 + 18 * q^73 + 9 * q^75 - 17 * q^77 - 17 * q^79 - q^81 + 13 * q^83 - 21 * q^85 - 16 * q^87 - 4 * q^89 - 5 * q^91 - 10 * q^93 - 11 * q^95 + 11 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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