LMFDB - Embedded newform 528.2.y.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(49,528)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("528.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.y (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.21610122672$
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:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			49.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	528.49
Dual form			528.2.y.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.190983 + 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{9} +(3.30902 - 0.224514i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(0.500000 - 0.363271i) q^{15} +(-0.354102 + 1.08981i) q^{17} +(4.73607 + 3.44095i) q^{19} +1.00000 q^{21} -0.236068 q^{23} +(3.73607 + 2.71441i) q^{25} +(0.309017 - 0.951057i) q^{27} +(4.85410 - 3.52671i) q^{29} +(1.88197 + 5.79210i) q^{31} +(-2.80902 - 1.76336i) q^{33} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(0.0729490 - 0.224514i) q^{39} +(-0.190983 - 0.138757i) q^{41} +6.70820 q^{43} -0.618034 q^{45} +(-8.16312 - 5.93085i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(0.927051 - 0.673542i) q^{51} +(-0.118034 - 0.363271i) q^{53} +(-0.500000 + 1.98787i) q^{55} +(-1.80902 - 5.56758i) q^{57} +(5.97214 - 4.33901i) q^{59} +(-3.57295 + 10.9964i) q^{61} +(-0.809017 - 0.587785i) q^{63} -0.145898 q^{65} -1.85410 q^{67} +(0.190983 + 0.138757i) q^{69} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(-1.42705 - 4.39201i) q^{75} +(-2.54508 + 2.12663i) q^{77} +(-3.39919 - 10.4616i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.454915 + 1.40008i) q^{83} +(-0.572949 - 0.416272i) q^{85} -6.00000 q^{87} -8.23607 q^{89} +(-0.190983 - 0.138757i) q^{91} +(1.88197 - 5.79210i) q^{93} +(-2.92705 + 2.12663i) q^{95} +(2.42705 + 7.46969i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 3 q^{5} - q^{7} - q^{9} + 11 q^{11} + 7 q^{13} + 2 q^{15} + 12 q^{17} + 10 q^{19} + 4 q^{21} + 8 q^{23} + 6 q^{25} - q^{27} + 6 q^{29} + 12 q^{31} - 9 q^{33} - 3 q^{35} + 9 q^{37} + 7 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - q^3 - 3 * q^5 - q^7 - q^9 + 11 * q^11 + 7 * q^13 + 2 * q^15 + 12 * q^17 + 10 * q^19 + 4 * q^21 + 8 * q^23 + 6 * q^25 - q^27 + 6 * q^29 + 12 * q^31 - 9 * q^33 - 3 * q^35 + 9 * q^37 + 7 * q^39 - 3 * q^41 + 2 * q^45 - 17 * q^47 + 6 * q^49 - 3 * q^51 + 4 * q^53 - 2 * q^55 - 5 * q^57 + 6 * q^59 - 21 * q^61 - q^63 - 14 * q^65 + 6 * q^67 + 3 * q^69 - 15 * q^71 + 14 * q^73 + q^75 + q^77 + 11 * q^79 - q^81 - 13 * q^83 - 9 * q^85 - 24 * q^87 - 24 * q^89 - 3 * q^91 + 12 * q^93 - 5 * q^95 + 3 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$		0			0
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	−0.984636	−	0.174619i	$-0.944131\pi$
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	0.899226	+	0.437485i	$0.144131\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i	−0.730084	−	0.683358i	$-0.760519\pi$
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i	0.424304	+	0.905520i	$0.360519\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	0.960663	−	0.277717i	$-0.0895777\pi$
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	−0.940431	+	0.339986i	$0.889578\pi$
$14$		0			0
$15$	0.500000	−	0.363271i	0.129099	−	0.0937962i
$16$		0			0
$17$	−0.354102	+	1.08981i	−0.0858823	+	0.264319i	−0.984770	−	0.173860i	$-0.944376\pi$
$17$	−0.354102	+	1.08981i	−0.0858823	+	0.264319i	0.898888	+	0.438178i	$0.144376\pi$
$18$		0			0
$19$	4.73607	+	3.44095i	1.08653	+	0.789409i	0.978810	−	0.204772i	$-0.0656454\pi$
$19$	4.73607	+	3.44095i	1.08653	+	0.789409i	0.107719	+	0.994181i	$0.465645\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$		0			0
$23$	−0.236068			−0.0492236			−0.0246118	−	0.999697i	$-0.507835\pi$
$23$	−0.236068			−0.0492236			−0.0246118	+	0.999697i	$0.507835\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$		0			0
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$		0			0
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	−0.0374370	−	0.999299i	$-0.511919\pi$
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	0.938821	+	0.344405i	$0.111919\pi$
$30$		0			0
$31$	1.88197	+	5.79210i	0.338011	+	1.04029i	0.965220	+	0.261440i	$0.0841973\pi$
$31$	1.88197	+	5.79210i	0.338011	+	1.04029i	−0.627209	+	0.778851i	$0.715803\pi$
$32$		0			0
$33$	−2.80902	−	1.76336i	−0.488987	−	0.306961i
$34$		0			0
$35$	−0.190983	−	0.587785i	−0.0322820	−	0.0993538i
$36$		0			0
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	−0.0899846	−	0.995943i	$-0.528682\pi$
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	0.919391	+	0.393344i	$0.128682\pi$
$38$		0			0
$39$	0.0729490	−	0.224514i	0.0116812	−	0.0359510i
$40$		0			0
$41$	−0.190983	−	0.138757i	−0.0298265	−	0.0216702i	0.572772	−	0.819715i	$-0.305868\pi$
$41$	−0.190983	−	0.138757i	−0.0298265	−	0.0216702i	−0.602599	+	0.798044i	$0.705868\pi$
$42$		0			0
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$		0			0
$45$	−0.618034			−0.0921311
$46$		0			0
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.197374	−	0.980328i	$-0.563241\pi$
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.993339	+	0.115224i	$0.963241\pi$
$48$		0			0
$49$	−1.85410	+	5.70634i	−0.264872	+	0.815191i
$50$		0			0
$51$	0.927051	−	0.673542i	0.129813	−	0.0943147i
$52$		0			0
$53$	−0.118034	−	0.363271i	−0.0162132	−	0.0498991i	0.942623	−	0.333860i	$-0.108351\pi$
$53$	−0.118034	−	0.363271i	−0.0162132	−	0.0498991i	−0.958836	+	0.283961i	$0.908351\pi$
$54$		0			0
$55$	−0.500000	+	1.98787i	−0.0674200	+	0.268044i
$56$		0			0
$57$	−1.80902	−	5.56758i	−0.239610	−	0.737444i
$58$		0			0
$59$	5.97214	−	4.33901i	0.777506	−	0.564891i	−0.126724	−	0.991938i	$-0.540446\pi$
$59$	5.97214	−	4.33901i	0.777506	−	0.564891i	0.904229	+	0.427047i	$0.140446\pi$
$60$		0			0
$61$	−3.57295	+	10.9964i	−0.457469	+	1.40795i	0.410742	+	0.911751i	$0.365270\pi$
$61$	−3.57295	+	10.9964i	−0.457469	+	1.40795i	−0.868212	+	0.496194i	$0.834730\pi$
$62$		0			0
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$		0			0
$65$	−0.145898			−0.0180964
$66$		0			0
$67$	−1.85410			−0.226515			−0.113257	−	0.993566i	$-0.536128\pi$
$67$	−1.85410			−0.226515			−0.113257	+	0.993566i	$0.536128\pi$
$68$		0			0
$69$	0.190983	+	0.138757i	0.0229917	+	0.0167044i
$70$		0			0
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	0.562248	+	0.826968i	$0.309937\pi$
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	−0.940948	+	0.338550i	$0.890063\pi$
$72$		0			0
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	−0.283771	−	0.958892i	$-0.591585\pi$
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	0.824271	+	0.566196i	$0.191585\pi$
$74$		0			0
$75$	−1.42705	−	4.39201i	−0.164782	−	0.507146i
$76$		0			0
$77$	−2.54508	+	2.12663i	−0.290039	+	0.242352i
$78$		0			0
$79$	−3.39919	−	10.4616i	−0.382438	−	1.17702i	−0.938322	−	0.345764i	$-0.887620\pi$
$79$	−3.39919	−	10.4616i	−0.382438	−	1.17702i	0.555883	−	0.831260i	$-0.312380\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−0.454915	+	1.40008i	−0.0499334	+	0.153679i	−0.972914	−	0.231167i	$-0.925746\pi$
$83$	−0.454915	+	1.40008i	−0.0499334	+	0.153679i	0.922981	+	0.384846i	$0.125746\pi$
$84$		0			0
$85$	−0.572949	−	0.416272i	−0.0621450	−	0.0451510i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−8.23607			−0.873021			−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607			−0.873021			−0.436511	+	0.899699i	$0.643786\pi$
$90$		0			0
$91$	−0.190983	−	0.138757i	−0.0200205	−	0.0145457i
$92$		0			0
$93$	1.88197	−	5.79210i	0.195151	−	0.600612i
$94$		0			0
$95$	−2.92705	+	2.12663i	−0.300309	+	0.218187i
$96$		0			0
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	0.995398	+	0.0958268i	$0.0305495\pi$
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	−0.748968	+	0.662606i	$0.769451\pi$
$98$		0			0
$99$	1.23607	+	3.07768i	0.124230	+	0.309319i
$100$		0			0
$101$	−3.16312	−	9.73508i	−0.314742	−	0.968677i	−0.975860	−	0.218395i	$-0.929918\pi$
$101$	−3.16312	−	9.73508i	−0.314742	−	0.968677i	0.661118	−	0.750282i	$-0.270082\pi$
$102$		0			0
$103$	−8.85410	+	6.43288i	−0.872421	+	0.633851i	−0.931235	−	0.364418i	$-0.881268\pi$
$103$	−8.85410	+	6.43288i	−0.872421	+	0.633851i	0.0588148	+	0.998269i	$0.481268\pi$
$104$		0			0
$105$	−0.190983	+	0.587785i	−0.0186380	+	0.0573620i
$106$		0			0
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	0.0405134	−	0.999179i	$-0.487101\pi$
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	−0.937756	+	0.347294i	$0.887101\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$		0			0
$111$	−6.23607			−0.591901
$112$		0			0
$113$	−10.8992	−	7.91872i	−1.02531	−	0.744931i	−0.0579448	−	0.998320i	$-0.518455\pi$
$113$	−10.8992	−	7.91872i	−1.02531	−	0.744931i	−0.967364	+	0.253389i	$0.918455\pi$
$114$		0			0
$115$	0.0450850	−	0.138757i	0.00420420	−	0.0129392i
$116$		0			0
$117$	−0.190983	+	0.138757i	−0.0176564	+	0.0128281i
$118$		0			0
$119$	−0.354102	−	1.08981i	−0.0324605	−	0.0999031i
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$		0			0
$123$	0.0729490	+	0.224514i	0.00657759	+	0.0202437i
$124$		0			0
$125$	−4.80902	+	3.49396i	−0.430132	+	0.312509i
$126$		0			0
$127$	−2.38197	+	7.33094i	−0.211365	+	0.650516i	0.788026	+	0.615641i	$0.211103\pi$
$127$	−2.38197	+	7.33094i	−0.211365	+	0.650516i	−0.999392	+	0.0348741i	$0.988897\pi$
$128$		0			0
$129$	−5.42705	−	3.94298i	−0.477825	−	0.347160i
$130$		0			0
$131$	11.7984			1.03083			0.515414	−	0.856941i	$-0.327638\pi$
$131$	11.7984			1.03083			0.515414	+	0.856941i	$0.327638\pi$
$132$		0			0
$133$	−5.85410			−0.507615
$134$		0			0
$135$	0.500000	+	0.363271i	0.0430331	+	0.0312654i
$136$		0			0
$137$	3.01722	−	9.28605i	0.257779	−	0.793361i	−0.735491	−	0.677535i	$-0.763048\pi$
$137$	3.01722	−	9.28605i	0.257779	−	0.793361i	0.993269	−	0.115826i	$-0.0369516\pi$
$138$		0			0
$139$	11.7812	−	8.55951i	0.999264	−	0.726008i	0.0373340	−	0.999303i	$-0.488113\pi$
$139$	11.7812	−	8.55951i	0.999264	−	0.726008i	0.961930	+	0.273295i	$0.0881134\pi$
$140$		0			0
$141$	3.11803	+	9.59632i	0.262586	+	0.808156i
$142$		0			0
$143$	0.291796	+	0.726543i	0.0244012	+	0.0607565i
$144$		0			0
$145$	1.14590	+	3.52671i	0.0951617	+	0.292877i
$146$		0			0
$147$	4.85410	−	3.52671i	0.400360	−	0.290878i
$148$		0			0
$149$	−1.30902	+	4.02874i	−0.107239	+	0.330047i	−0.990249	−	0.139306i	$-0.955513\pi$
$149$	−1.30902	+	4.02874i	−0.107239	+	0.330047i	0.883011	+	0.469353i	$0.155513\pi$
$150$		0			0
$151$	0.854102	+	0.620541i	0.0695058	+	0.0504989i	0.621996	−	0.783021i	$-0.286322\pi$
$151$	0.854102	+	0.620541i	0.0695058	+	0.0504989i	−0.552490	+	0.833520i	$0.686322\pi$
$152$		0			0
$153$	−1.14590			−0.0926404
$154$		0			0
$155$	−3.76393			−0.302326
$156$		0			0
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.0491340	−	0.998792i	$-0.515646\pi$
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.965091	+	0.261915i	$0.915646\pi$
$158$		0			0
$159$	−0.118034	+	0.363271i	−0.00936070	+	0.0288093i
$160$		0			0
$161$	0.190983	−	0.138757i	0.0150516	−	0.0109356i
$162$		0			0
$163$	1.59017	+	4.89404i	0.124552	+	0.383331i	0.993819	−	0.111011i	$-0.0354090\pi$
$163$	1.59017	+	4.89404i	0.124552	+	0.383331i	−0.869267	+	0.494342i	$0.835409\pi$
$164$		0			0
$165$	1.57295	−	1.31433i	0.122454	−	0.102320i
$166$		0			0
$167$	−3.71885	−	11.4454i	−0.287773	−	0.885674i	−0.985554	−	0.169363i	$-0.945829\pi$
$167$	−3.71885	−	11.4454i	−0.287773	−	0.885674i	0.697781	−	0.716311i	$-0.254171\pi$
$168$		0			0
$169$	10.4721	−	7.60845i	0.805549	−	0.585266i
$170$		0			0
$171$	−1.80902	+	5.56758i	−0.138339	+	0.425764i
$172$		0			0
$173$	14.5902	+	10.6004i	1.10927	+	0.805932i	0.982549	−	0.186006i	$-0.0595545\pi$
$173$	14.5902	+	10.6004i	1.10927	+	0.805932i	0.126722	+	0.991938i	$0.459555\pi$
$174$		0			0
$175$	−4.61803			−0.349091
$176$		0			0
$177$	−7.38197			−0.554863
$178$		0			0
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	0.299301	−	0.954159i	$-0.403247\pi$
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	−0.814970	+	0.579503i	$0.803247\pi$
$180$		0			0
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	−0.917819	−	0.396999i	$-0.870051\pi$
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	0.975881	+	0.218301i	$0.0700515\pi$
$182$		0			0
$183$	9.35410	−	6.79615i	0.691475	−	0.502386i
$184$		0			0
$185$	1.19098	+	3.66547i	0.0875628	+	0.269491i
$186$		0			0
$187$	−0.927051	+	3.68571i	−0.0677927	+	0.269526i
$188$		0			0
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$		0			0
$191$	−0.663119	+	0.481784i	−0.0479816	+	0.0348607i	−0.611518	−	0.791231i	$-0.709441\pi$
$191$	−0.663119	+	0.481784i	−0.0479816	+	0.0348607i	0.563536	+	0.826092i	$0.309441\pi$
$192$		0			0
$193$	−0.972136	+	2.99193i	−0.0699759	+	0.215364i	−0.979929	−	0.199348i	$-0.936118\pi$
$193$	−0.972136	+	2.99193i	−0.0699759	+	0.215364i	0.909953	+	0.414712i	$0.136118\pi$
$194$		0			0
$195$	0.118034	+	0.0857567i	0.00845259	+	0.00614117i
$196$		0			0
$197$	13.0344			0.928666			0.464333	−	0.885661i	$-0.346294\pi$
$197$	13.0344			0.928666			0.464333	+	0.885661i	$0.346294\pi$
$198$		0			0
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$		0			0
$201$	1.50000	+	1.08981i	0.105802	+	0.0768695i
$202$		0			0
$203$	−1.85410	+	5.70634i	−0.130132	+	0.400506i
$204$		0			0
$205$	0.118034	−	0.0857567i	0.00824385	−	0.00598951i
$206$		0			0
$207$	−0.0729490	−	0.224514i	−0.00507031	−	0.0156048i
$208$		0			0
$209$	16.4443	+	10.3229i	1.13747	+	0.714047i
$210$		0			0
$211$	−1.11803	−	3.44095i	−0.0769686	−	0.236885i	0.905168	−	0.425054i	$-0.139745\pi$
$211$	−1.11803	−	3.44095i	−0.0769686	−	0.236885i	−0.982137	+	0.188169i	$0.939745\pi$
$212$		0			0
$213$	8.35410	−	6.06961i	0.572414	−	0.415883i
$214$		0			0
$215$	−1.28115	+	3.94298i	−0.0873739	+	0.268909i
$216$		0			0
$217$	−4.92705	−	3.57971i	−0.334470	−	0.243007i
$218$		0			0
$219$	−5.70820			−0.385725
$220$		0			0
$221$	−0.270510			−0.0181965
$222$		0			0
$223$	5.80902	+	4.22050i	0.389001	+	0.282625i	0.765046	−	0.643976i	$-0.222716\pi$
$223$	5.80902	+	4.22050i	0.389001	+	0.282625i	−0.376045	+	0.926601i	$0.622716\pi$
$224$		0			0
$225$	−1.42705	+	4.39201i	−0.0951367	+	0.292801i
$226$		0			0
$227$	10.6631	−	7.74721i	0.707736	−	0.514200i	−0.174706	−	0.984621i	$-0.555898\pi$
$227$	10.6631	−	7.74721i	0.707736	−	0.514200i	0.882443	+	0.470420i	$0.155898\pi$
$228$		0			0
$229$	0.145898	+	0.449028i	0.00964121	+	0.0296726i	0.955761	−	0.294143i	$-0.0950342\pi$
$229$	0.145898	+	0.449028i	0.00964121	+	0.0296726i	−0.946120	+	0.323816i	$0.895034\pi$
$230$		0			0
$231$	3.30902	−	0.224514i	0.217717	−	0.0147719i
$232$		0			0
$233$	−1.28115	−	3.94298i	−0.0839311	−	0.258313i	0.900280	−	0.435311i	$-0.143362\pi$
$233$	−1.28115	−	3.94298i	−0.0839311	−	0.258313i	−0.984211	+	0.176997i	$0.943362\pi$
$234$		0			0
$235$	5.04508	−	3.66547i	0.329105	−	0.239109i
$236$		0			0
$237$	−3.39919	+	10.4616i	−0.220801	+	0.679555i
$238$		0			0
$239$	0.309017	+	0.224514i	0.0199886	+	0.0145226i	0.597735	−	0.801694i	$-0.296068\pi$
$239$	0.309017	+	0.224514i	0.0199886	+	0.0145226i	−0.577746	+	0.816217i	$0.696068\pi$
$240$		0			0
$241$	8.29180			0.534122			0.267061	−	0.963680i	$-0.413948\pi$
$241$	8.29180			0.534122			0.267061	+	0.963680i	$0.413948\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−3.00000	−	2.17963i	−0.191663	−	0.139251i
$246$		0			0
$247$	−0.427051	+	1.31433i	−0.0271726	+	0.0836287i
$248$		0			0
$249$	1.19098	−	0.865300i	0.0754755	−	0.0548361i
$250$		0			0
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	0.899412	+	0.437102i	$0.143995\pi$
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	−0.470718	+	0.882284i	$0.656005\pi$
$252$		0			0
$253$	−0.781153	+	0.0530006i	−0.0491107	+	0.00333212i
$254$		0			0
$255$	0.218847	+	0.673542i	0.0137047	+	0.0421788i
$256$		0			0
$257$	−24.0623	+	17.4823i	−1.50097	+	1.09052i	−0.530970	+	0.847390i	$0.678172\pi$
$257$	−24.0623	+	17.4823i	−1.50097	+	1.09052i	−0.969995	+	0.243125i	$0.921828\pi$
$258$		0			0
$259$	−1.92705	+	5.93085i	−0.119741	+	0.368525i
$260$		0			0
$261$	4.85410	+	3.52671i	0.300461	+	0.218298i
$262$		0			0
$263$	15.2705			0.941620			0.470810	−	0.882235i	$-0.343962\pi$
$263$	15.2705			0.941620			0.470810	+	0.882235i	$0.343962\pi$
$264$		0			0
$265$	0.236068			0.0145015
$266$		0			0
$267$	6.66312	+	4.84104i	0.407776	+	0.296267i
$268$		0			0
$269$	−7.85410	+	24.1724i	−0.478873	+	1.47382i	0.361789	+	0.932260i	$0.382166\pi$
$269$	−7.85410	+	24.1724i	−0.478873	+	1.47382i	−0.840662	+	0.541560i	$0.817834\pi$
$270$		0			0
$271$	15.0623	−	10.9434i	0.914970	−	0.664765i	−0.0272970	−	0.999627i	$-0.508690\pi$
$271$	15.0623	−	10.9434i	0.914970	−	0.664765i	0.942267	+	0.334863i	$0.108690\pi$
$272$		0			0
$273$	0.0729490	+	0.224514i	0.00441508	+	0.0135882i
$274$		0			0
$275$	12.9721	+	8.14324i	0.782249	+	0.491056i
$276$		0			0
$277$	−9.02786	−	27.7849i	−0.542432	−	1.66943i	−0.727019	−	0.686617i	$-0.759095\pi$
$277$	−9.02786	−	27.7849i	−0.542432	−	1.66943i	0.184587	−	0.982816i	$-0.440905\pi$
$278$		0			0
$279$	−4.92705	+	3.57971i	−0.294975	+	0.214312i
$280$		0			0
$281$	7.65248	−	23.5519i	0.456508	−	1.40499i	−0.412847	−	0.910801i	$-0.635465\pi$
$281$	7.65248	−	23.5519i	0.456508	−	1.40499i	0.869355	−	0.494188i	$-0.164535\pi$
$282$		0			0
$283$	−4.61803	−	3.35520i	−0.274514	−	0.199446i	0.442007	−	0.897011i	$-0.354267\pi$
$283$	−4.61803	−	3.35520i	−0.274514	−	0.199446i	−0.716521	+	0.697566i	$0.754267\pi$
$284$		0			0
$285$	3.61803			0.214314
$286$		0			0
$287$	0.236068			0.0139347
$288$		0			0
$289$	12.6910	+	9.22054i	0.746528	+	0.542385i
$290$		0			0
$291$	2.42705	−	7.46969i	0.142276	−	0.437881i
$292$		0			0
$293$	17.5172	−	12.7270i	1.02337	−	0.743520i	0.0563966	−	0.998408i	$-0.482039\pi$
$293$	17.5172	−	12.7270i	1.02337	−	0.743520i	0.966970	+	0.254889i	$0.0820389\pi$
$294$		0			0
$295$	1.40983	+	4.33901i	0.0820835	+	0.252627i
$296$		0			0
$297$	0.809017	−	3.21644i	0.0469439	−	0.186637i
$298$		0			0
$299$	−0.0172209	−	0.0530006i	−0.000995912	−	0.00306510i
$300$		0			0
$301$	−5.42705	+	3.94298i	−0.312810	+	0.227270i
$302$		0			0
$303$	−3.16312	+	9.73508i	−0.181716	+	0.559266i
$304$		0			0
$305$	−5.78115	−	4.20025i	−0.331028	−	0.240506i
$306$		0			0
$307$	−27.9787			−1.59683			−0.798415	−	0.602108i	$-0.794328\pi$
$307$	−27.9787			−1.59683			−0.798415	+	0.602108i	$0.794328\pi$
$308$		0			0
$309$	10.9443			0.622598
$310$		0			0
$311$	9.42705	+	6.84915i	0.534559	+	0.388380i	0.822060	−	0.569400i	$-0.192825\pi$
$311$	9.42705	+	6.84915i	0.534559	+	0.388380i	−0.287501	+	0.957780i	$0.592825\pi$
$312$		0			0
$313$	−0.781153	+	2.40414i	−0.0441534	+	0.135890i	−0.970703	−	0.240282i	$-0.922760\pi$
$313$	−0.781153	+	2.40414i	−0.0441534	+	0.135890i	0.926550	+	0.376172i	$0.122760\pi$
$314$		0			0
$315$	0.500000	−	0.363271i	0.0281718	−	0.0204680i
$316$		0			0
$317$	−2.10739	−	6.48588i	−0.118363	−	0.364283i	0.874271	−	0.485439i	$-0.161340\pi$
$317$	−2.10739	−	6.48588i	−0.118363	−	0.364283i	−0.992634	+	0.121155i	$0.961340\pi$
$318$		0			0
$319$	15.2705	−	12.7598i	0.854984	−	0.714410i
$320$		0			0
$321$	3.54508	+	10.9106i	0.197867	+	0.608973i
$322$		0			0
$323$	−5.42705	+	3.94298i	−0.301969	+	0.219393i
$324$		0			0
$325$	−0.336881	+	1.03681i	−0.0186868	+	0.0575121i
$326$		0			0
$327$	9.70820	+	7.05342i	0.536865	+	0.390055i
$328$		0			0
$329$	10.0902			0.556289
$330$		0			0
$331$	−16.7082			−0.918366			−0.459183	−	0.888342i	$-0.651858\pi$
$331$	−16.7082			−0.918366			−0.459183	+	0.888342i	$0.651858\pi$
$332$		0			0
$333$	5.04508	+	3.66547i	0.276469	+	0.200866i
$334$		0			0
$335$	0.354102	−	1.08981i	0.0193467	−	0.0595429i
$336$		0			0
$337$	14.7082	−	10.6861i	0.801207	−	0.582111i	−0.110061	−	0.993925i	$-0.535105\pi$
$337$	14.7082	−	10.6861i	0.801207	−	0.582111i	0.911268	+	0.411814i	$0.135105\pi$
$338$		0			0
$339$	4.16312	+	12.8128i	0.226110	+	0.695894i
$340$		0			0
$341$	7.52786	+	18.7436i	0.407657	+	1.01502i
$342$		0			0
$343$	−4.01722	−	12.3637i	−0.216910	−	0.667579i
$344$		0			0
$345$	−0.118034	+	0.0857567i	−0.00635474	+	0.00461699i
$346$		0			0
$347$	0.472136	−	1.45309i	0.0253456	−	0.0780057i	−0.937584	−	0.347760i	$-0.886942\pi$
$347$	0.472136	−	1.45309i	0.0253456	−	0.0780057i	0.962929	+	0.269754i	$0.0869424\pi$
$348$		0			0
$349$	−10.2812	−	7.46969i	−0.550337	−	0.399844i	0.277572	−	0.960705i	$-0.410470\pi$
$349$	−10.2812	−	7.46969i	−0.550337	−	0.399844i	−0.827910	+	0.560861i	$0.810470\pi$
$350$		0			0
$351$	0.236068			0.0126004
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$		0			0
$355$	−5.16312	−	3.75123i	−0.274030	−	0.199094i
$356$		0			0
$357$	−0.354102	+	1.08981i	−0.0187411	+	0.0576791i
$358$		0			0
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	−0.775431	−	0.631433i	$-0.782467\pi$
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	0.360907	+	0.932602i	$0.382467\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$		0			0
$363$	−9.69098	−	5.20431i	−0.508645	−	0.273155i
$364$		0			0
$365$	1.09017	+	3.35520i	0.0570621	+	0.175619i
$366$		0			0
$367$	17.9164	−	13.0170i	0.935229	−	0.679484i	−0.0120386	−	0.999928i	$-0.503832\pi$
$367$	17.9164	−	13.0170i	0.935229	−	0.679484i	0.947267	+	0.320444i	$0.103832\pi$
$368$		0			0
$369$	0.0729490	−	0.224514i	0.00379757	−	0.0116877i
$370$		0			0
$371$	0.309017	+	0.224514i	0.0160434	+	0.0116562i
$372$		0			0
$373$	0.888544			0.0460071			0.0230035	−	0.999735i	$-0.492677\pi$
$373$	0.888544			0.0460071			0.0230035	+	0.999735i	$0.492677\pi$
$374$		0			0
$375$	5.94427			0.306961
$376$		0			0
$377$	1.14590	+	0.832544i	0.0590168	+	0.0428782i
$378$		0			0
$379$	7.69098	−	23.6704i	0.395059	−	1.21587i	−0.533856	−	0.845575i	$-0.679258\pi$
$379$	7.69098	−	23.6704i	0.395059	−	1.21587i	0.928915	−	0.370292i	$-0.120742\pi$
$380$		0			0
$381$	6.23607	−	4.53077i	0.319483	−	0.232118i
$382$		0			0
$383$	3.92705	+	12.0862i	0.200663	+	0.617577i	0.999864	+	0.0165128i	$0.00525642\pi$
$383$	3.92705	+	12.0862i	0.200663	+	0.617577i	−0.799201	+	0.601064i	$0.794744\pi$
$384$		0			0
$385$	−0.763932	−	1.90211i	−0.0389336	−	0.0969407i
$386$		0			0
$387$	2.07295	+	6.37988i	0.105374	+	0.324308i
$388$		0			0
$389$	29.7254	−	21.5968i	1.50714	−	1.09500i	0.539712	−	0.841850i	$-0.318533\pi$
$389$	29.7254	−	21.5968i	1.50714	−	1.09500i	0.967427	−	0.253151i	$-0.0814669\pi$
$390$		0			0
$391$	0.0835921	−	0.257270i	0.00422744	−	0.0130107i
$392$		0			0
$393$	−9.54508	−	6.93491i	−0.481486	−	0.349820i
$394$		0			0
$395$	6.79837			0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$		0			0
$399$	4.73607	+	3.44095i	0.237100	+	0.172263i
$400$		0			0
$401$	−9.79180	+	30.1360i	−0.488979	+	1.50492i	0.337155	+	0.941449i	$0.390535\pi$
$401$	−9.79180	+	30.1360i	−0.488979	+	1.50492i	−0.826134	+	0.563473i	$0.809465\pi$
$402$		0			0
$403$	−1.16312	+	0.845055i	−0.0579391	+	0.0420952i
$404$		0			0
$405$	−0.190983	−	0.587785i	−0.00949002	−	0.0292073i
$406$		0			0
$407$	15.8713	−	13.2618i	0.786712	−	0.657363i
$408$		0			0
$409$	−2.00000	−	6.15537i	−0.0988936	−	0.304363i	0.889355	−	0.457217i	$-0.151154\pi$
$409$	−2.00000	−	6.15537i	−0.0988936	−	0.304363i	−0.988249	+	0.152854i	$0.951154\pi$
$410$		0			0
$411$	−7.89919	+	5.73910i	−0.389638	+	0.283089i
$412$		0			0
$413$	−2.28115	+	7.02067i	−0.112248	+	0.345464i
$414$		0			0
$415$	−0.736068	−	0.534785i	−0.0361322	−	0.0262515i
$416$		0			0
$417$	−14.5623			−0.713119
$418$		0			0
$419$	−31.4508			−1.53647			−0.768237	−	0.640165i	$-0.778866\pi$
$419$	−31.4508			−1.53647			−0.768237	+	0.640165i	$0.778866\pi$
$420$		0			0
$421$	−8.50000	−	6.17561i	−0.414265	−	0.300981i	0.361061	−	0.932542i	$-0.382414\pi$
$421$	−8.50000	−	6.17561i	−0.414265	−	0.300981i	−0.775326	+	0.631561i	$0.782414\pi$
$422$		0			0
$423$	3.11803	−	9.59632i	0.151604	−	0.466589i
$424$		0			0
$425$	−4.28115	+	3.11044i	−0.207666	+	0.150878i
$426$		0			0
$427$	−3.57295	−	10.9964i	−0.172907	−	0.532153i
$428$		0			0
$429$	0.190983	−	0.759299i	0.00922075	−	0.0366593i
$430$		0			0
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	0.985357	−	0.170504i	$-0.0545395\pi$
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	−0.897390	+	0.441238i	$0.854540\pi$
$432$		0			0
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.375089	+	0.926989i	$0.622388\pi$
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.997528	+	0.0702758i	$0.977612\pi$
$434$		0			0
$435$	1.14590	−	3.52671i	0.0549416	−	0.169093i
$436$		0			0
$437$	−1.11803	−	0.812299i	−0.0534828	−	0.0388575i
$438$		0			0
$439$	−23.2918			−1.11166			−0.555828	−	0.831297i	$-0.687599\pi$
$439$	−23.2918			−1.11166			−0.555828	+	0.831297i	$0.687599\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−25.5623	−	18.5721i	−1.21450	−	0.882387i	−0.218870	−	0.975754i	$-0.570237\pi$
$443$	−25.5623	−	18.5721i	−1.21450	−	0.882387i	−0.995632	+	0.0933668i	$0.970237\pi$
$444$		0			0
$445$	1.57295	−	4.84104i	0.0745649	−	0.229487i
$446$		0			0
$447$	3.42705	−	2.48990i	0.162094	−	0.117768i
$448$		0			0
$449$	−2.79837	−	8.61251i	−0.132063	−	0.406449i	0.863058	−	0.505104i	$-0.168546\pi$
$449$	−2.79837	−	8.61251i	−0.132063	−	0.406449i	−0.995122	+	0.0986549i	$0.968546\pi$
$450$		0			0
$451$	−0.663119	−	0.416272i	−0.0312251	−	0.0196015i
$452$		0			0
$453$	−0.326238	−	1.00406i	−0.0153280	−	0.0471747i
$454$		0			0
$455$	0.118034	−	0.0857567i	0.00553352	−	0.00402034i
$456$		0			0
$457$	7.40983	−	22.8051i	0.346617	−	1.06678i	−0.614095	−	0.789232i	$-0.710479\pi$
$457$	7.40983	−	22.8051i	0.346617	−	1.06678i	0.960712	−	0.277546i	$-0.0895211\pi$
$458$		0			0
$459$	0.927051	+	0.673542i	0.0432710	+	0.0314382i
$460$		0			0
$461$	9.27051			0.431771			0.215885	−	0.976419i	$-0.430736\pi$
$461$	9.27051			0.431771			0.215885	+	0.976419i	$0.430736\pi$
$462$		0			0
$463$	−1.72949			−0.0803762			−0.0401881	−	0.999192i	$-0.512796\pi$
$463$	−1.72949			−0.0803762			−0.0401881	+	0.999192i	$0.512796\pi$
$464$		0			0
$465$	3.04508	+	2.21238i	0.141212	+	0.102597i
$466$		0			0
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	0.683256	+	0.730179i	$0.260563\pi$
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	−0.981954	+	0.189119i	$0.939437\pi$
$468$		0			0
$469$	1.50000	−	1.08981i	0.0692636	−	0.0503229i
$470$		0			0
$471$	4.85410	+	14.9394i	0.223665	+	0.688371i
$472$		0			0
$473$	22.1976	−	1.50609i	1.02064	−	0.0692499i
$474$		0			0
$475$	8.35410	+	25.7113i	0.383312	+	1.17971i
$476$		0			0
$477$	0.309017	−	0.224514i	0.0141489	−	0.0102798i
$478$		0			0
$479$	8.77051	−	26.9929i	0.400735	−	1.23333i	−0.523670	−	0.851921i	$-0.675437\pi$
$479$	8.77051	−	26.9929i	0.400735	−	1.23333i	0.924405	−	0.381414i	$-0.124563\pi$
$480$		0			0
$481$	1.19098	+	0.865300i	0.0543042	+	0.0394543i
$482$		0			0
$483$	−0.236068			−0.0107415
$484$		0			0
$485$	−4.85410			−0.220413
$486$		0			0
$487$	−10.2812	−	7.46969i	−0.465884	−	0.338484i	0.329951	−	0.943998i	$-0.392968\pi$
$487$	−10.2812	−	7.46969i	−0.465884	−	0.338484i	−0.795835	+	0.605514i	$0.792968\pi$
$488$		0			0
$489$	1.59017	−	4.89404i	0.0719100	−	0.221316i
$490$		0			0
$491$	−14.4894	+	10.5271i	−0.653896	+	0.475083i	−0.864596	−	0.502468i	$-0.832426\pi$
$491$	−14.4894	+	10.5271i	−0.653896	+	0.475083i	0.210700	+	0.977551i	$0.432426\pi$
$492$		0			0
$493$	2.12461	+	6.53888i	0.0956877	+	0.294496i
$494$		0			0
$495$	−2.04508	+	0.138757i	−0.0919197	+	0.00623668i
$496$		0			0
$497$	−3.19098	−	9.82084i	−0.143135	−	0.440525i
$498$		0			0
$499$	−14.6803	+	10.6659i	−0.657182	+	0.477471i	−0.865710	−	0.500546i	$-0.833133\pi$
$499$	−14.6803	+	10.6659i	−0.657182	+	0.477471i	0.208528	+	0.978016i	$0.433133\pi$
$500$		0			0
$501$	−3.71885	+	11.4454i	−0.166146	+	0.511344i
$502$		0			0
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	0.732803	−	0.680441i	$-0.238212\pi$
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	−0.420689	+	0.907205i	$0.638212\pi$
$504$		0			0
$505$	6.32624			0.281514
$506$		0			0
$507$	−12.9443			−0.574875
$508$		0			0
$509$	−31.3435	−	22.7724i	−1.38927	−	1.00937i	−0.995945	−	0.0899695i	$-0.971323\pi$
$509$	−31.3435	−	22.7724i	−1.38927	−	1.00937i	−0.393330	−	0.919397i	$-0.628677\pi$
$510$		0			0
$511$	−1.76393	+	5.42882i	−0.0780318	+	0.240157i
$512$		0			0
$513$	4.73607	−	3.44095i	0.209103	−	0.151922i
$514$		0			0
$515$	−2.09017	−	6.43288i	−0.0921039	−	0.283467i
$516$		0			0
$517$	−28.3435	−	17.7926i	−1.24654	−	0.782516i
$518$		0			0
$519$	−5.57295	−	17.1518i	−0.244625	−	0.752879i
$520$		0			0
$521$	−7.23607	+	5.25731i	−0.317018	+	0.230327i	−0.734902	−	0.678173i	$-0.762772\pi$
$521$	−7.23607	+	5.25731i	−0.317018	+	0.230327i	0.417884	+	0.908500i	$0.362772\pi$
$522$		0			0
$523$	−5.64590	+	17.3763i	−0.246878	+	0.759812i	0.748444	+	0.663198i	$0.230801\pi$
$523$	−5.64590	+	17.3763i	−0.246878	+	0.759812i	−0.995322	+	0.0966140i	$0.969199\pi$
$524$		0			0
$525$	3.73607	+	2.71441i	0.163055	+	0.118467i
$526$		0			0
$527$	−6.97871			−0.303998
$528$		0			0
$529$	−22.9443			−0.997577
$530$		0			0
$531$	5.97214	+	4.33901i	0.259169	+	0.188297i
$532$		0			0
$533$	0.0172209	−	0.0530006i	0.000745921	−	0.00229571i
$534$		0			0
$535$	5.73607	−	4.16750i	0.247992	−	0.180177i
$536$		0			0
$537$	2.63525	+	8.11048i	0.113720	+	0.349993i
$538$		0			0
$539$	−4.85410	+	19.2986i	−0.209081	+	0.831251i
$540$		0			0
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	0.888859	−	0.458181i	$-0.151499\pi$
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	−0.988414	+	0.151782i	$0.951499\pi$
$542$		0			0
$543$	−2.04508	+	1.48584i	−0.0877630	+	0.0637635i
$544$		0			0
$545$	2.29180	−	7.05342i	0.0981698	−	0.302135i
$546$		0			0
$547$	−24.8713	−	18.0701i	−1.06342	−	0.772621i	−0.0887027	−	0.996058i	$-0.528272\pi$
$547$	−24.8713	−	18.0701i	−1.06342	−	0.772621i	−0.974718	+	0.223438i	$0.928272\pi$
$548$		0			0
$549$	−11.5623			−0.493467
$550$		0			0
$551$	35.1246			1.49636
$552$		0			0
$553$	8.89919	+	6.46564i	0.378432	+	0.274947i
$554$		0			0
$555$	1.19098	−	3.66547i	0.0505544	−	0.155590i
$556$		0			0
$557$	−30.4443	+	22.1191i	−1.28997	+	0.937215i	−0.999805	−	0.0197634i	$-0.993709\pi$
$557$	−30.4443	+	22.1191i	−1.28997	+	0.937215i	−0.290161	+	0.956978i	$0.593709\pi$
$558$		0			0
$559$	0.489357	+	1.50609i	0.0206976	+	0.0637006i
$560$		0			0
$561$	2.91641	−	2.43690i	0.123131	−	0.102886i
$562$		0			0
$563$	−12.5451	−	38.6098i	−0.528712	−	1.62721i	−0.756856	−	0.653582i	$-0.773266\pi$
$563$	−12.5451	−	38.6098i	−0.528712	−	1.62721i	0.228144	−	0.973627i	$-0.426734\pi$
$564$		0			0
$565$	6.73607	−	4.89404i	0.283389	−	0.205894i
$566$		0			0
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$		0			0
$569$	−27.6525	−	20.0907i	−1.15925	−	0.842246i	−0.169569	−	0.985518i	$-0.554237\pi$
$569$	−27.6525	−	20.0907i	−1.15925	−	0.842246i	−0.989683	+	0.143272i	$0.954237\pi$
$570$		0			0
$571$	9.09017			0.380412			0.190206	−	0.981744i	$-0.439084\pi$
$571$	9.09017			0.380412			0.190206	+	0.981744i	$0.439084\pi$
$572$		0			0
$573$	0.819660			0.0342418
$574$		0			0
$575$	−0.881966	−	0.640786i	−0.0367805	−	0.0267226i
$576$		0			0
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	−0.510528	−	0.859861i	$-0.670550\pi$
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	0.918439	−	0.395562i	$-0.129450\pi$
$578$		0			0
$579$	2.54508	−	1.84911i	0.105770	−	0.0768465i
$580$		0			0
$581$	−0.454915	−	1.40008i	−0.0188731	−	0.0580853i
$582$		0			0
$583$	−0.472136	−	1.17557i	−0.0195539	−	0.0486872i
$584$		0			0
$585$	−0.0450850	−	0.138757i	−0.00186403	−	0.00573691i
$586$		0			0
$587$	−1.71885	+	1.24882i	−0.0709444	+	0.0515441i	−0.622692	−	0.782467i	$-0.713961\pi$
$587$	−1.71885	+	1.24882i	−0.0709444	+	0.0515441i	0.551748	+	0.834011i	$0.313961\pi$
$588$		0			0
$589$	−11.0172	+	33.9075i	−0.453957	+	1.39714i
$590$		0			0
$591$	−10.5451	−	7.66145i	−0.433767	−	0.315150i
$592$		0			0
$593$	−14.0344			−0.576325			−0.288163	−	0.957581i	$-0.593044\pi$
$593$	−14.0344			−0.576325			−0.288163	+	0.957581i	$0.593044\pi$
$594$		0			0
$595$	0.708204			0.0290335
$596$		0			0
$597$	5.42705	+	3.94298i	0.222114	+	0.161376i
$598$		0			0
$599$	−3.90983	+	12.0332i	−0.159751	+	0.491664i	−0.998611	−	0.0526833i	$-0.983223\pi$
$599$	−3.90983	+	12.0332i	−0.159751	+	0.491664i	0.838860	+	0.544347i	$0.183223\pi$
$600$		0			0
$601$	5.57295	−	4.04898i	0.227325	−	0.165162i	−0.468293	−	0.883573i	$-0.655131\pi$
$601$	5.57295	−	4.04898i	0.227325	−	0.165162i	0.695618	+	0.718412i	$0.255131\pi$
$602$		0			0
$603$	−0.572949	−	1.76336i	−0.0233323	−	0.0718094i
$604$		0			0
$605$	−1.20820	+	6.69015i	−0.0491205	+	0.271993i
$606$		0			0
$607$	5.11803	+	15.7517i	0.207735	+	0.639341i	0.999590	+	0.0286327i	$0.00911532\pi$
$607$	5.11803	+	15.7517i	0.207735	+	0.639341i	−0.791855	+	0.610709i	$0.790885\pi$
$608$		0			0
$609$	4.85410	−	3.52671i	0.196698	−	0.142910i
$610$		0			0
$611$	0.736068	−	2.26538i	0.0297781	−	0.0916476i
$612$		0			0
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	0.796270	−	0.604942i	$-0.206804\pi$
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	−0.329273	+	0.944235i	$0.606804\pi$
$614$		0			0
$615$	−0.145898			−0.00588318
$616$		0			0
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$		0			0
$619$	19.5172	+	14.1801i	0.784463	+	0.569946i	0.906315	−	0.422602i	$-0.138883\pi$
$619$	19.5172	+	14.1801i	0.784463	+	0.569946i	−0.121852	+	0.992548i	$0.538883\pi$
$620$		0			0
$621$	−0.0729490	+	0.224514i	−0.00292734	+	0.00900944i
$622$		0			0
$623$	6.66312	−	4.84104i	0.266952	−	0.193952i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$		0			0
$627$	−7.23607	−	18.0171i	−0.288981	−	0.719533i
$628$		0			0
$629$	2.20820	+	6.79615i	0.0880469	+	0.270980i
$630$		0			0
$631$	15.5451	−	11.2942i	0.618840	−	0.449614i	−0.233676	−	0.972314i	$-0.575076\pi$
$631$	15.5451	−	11.2942i	0.618840	−	0.449614i	0.852516	+	0.522701i	$0.175076\pi$
$632$		0			0
$633$	−1.11803	+	3.44095i	−0.0444379	+	0.136766i
$634$		0			0
$635$	−3.85410	−	2.80017i	−0.152945	−	0.111121i
$636$		0			0
$637$	−1.41641			−0.0561201
$638$		0			0
$639$	−10.3262			−0.408500
$640$		0			0
$641$	20.2984	+	14.7476i	0.801738	+	0.582496i	0.911423	−	0.411470i	$-0.134984\pi$
$641$	20.2984	+	14.7476i	0.801738	+	0.582496i	−0.109686	+	0.993966i	$0.534984\pi$
$642$		0			0
$643$	−6.44427	+	19.8334i	−0.254137	+	0.782154i	0.739861	+	0.672760i	$0.234891\pi$
$643$	−6.44427	+	19.8334i	−0.254137	+	0.782154i	−0.993998	+	0.109394i	$0.965109\pi$
$644$		0			0
$645$	3.35410	−	2.43690i	0.132068	−	0.0959528i
$646$		0			0
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	−0.715918	−	0.698184i	$-0.753992\pi$
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	0.168808	−	0.985649i	$-0.446008\pi$
$648$		0			0
$649$	18.7877	−	15.6987i	0.737483	−	0.616227i
$650$		0			0
$651$	1.88197	+	5.79210i	0.0737601	+	0.227010i
$652$		0			0
$653$	4.54508	−	3.30220i	0.177863	−	0.129225i	−0.495292	−	0.868727i	$-0.664939\pi$
$653$	4.54508	−	3.30220i	0.177863	−	0.129225i	0.673155	+	0.739502i	$0.264939\pi$
$654$		0			0
$655$	−2.25329	+	6.93491i	−0.0880433	+	0.270969i
$656$		0			0
$657$	4.61803	+	3.35520i	0.180167	+	0.130899i
$658$		0			0
$659$	41.1246			1.60199			0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246			1.60199			0.800994	+	0.598673i	$0.204305\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$		0			0
$663$	0.218847	+	0.159002i	0.00849932	+	0.00617511i
$664$		0			0
$665$	1.11803	−	3.44095i	0.0433555	−	0.133435i
$666$		0			0
$667$	−1.14590	+	0.832544i	−0.0443693	+	0.0322362i
$668$		0			0
$669$	−2.21885	−	6.82891i	−0.0857856	−	0.264021i
$670$		0			0
$671$	−9.35410	+	37.1895i	−0.361111	+	1.43568i
$672$		0			0
$673$	11.0729	+	34.0790i	0.426831	+	1.31365i	0.901230	+	0.433340i	$0.142665\pi$
$673$	11.0729	+	34.0790i	0.426831	+	1.31365i	−0.474399	+	0.880310i	$0.657335\pi$
$674$		0			0
$675$	3.73607	−	2.71441i	0.143801	−	0.104478i
$676$		0			0
$677$	4.18034	−	12.8658i	0.160664	−	0.494471i	−0.838027	−	0.545629i	$-0.816291\pi$
$677$	4.18034	−	12.8658i	0.160664	−	0.494471i	0.998691	+	0.0511572i	$0.0162909\pi$
$678$		0			0
$679$	−6.35410	−	4.61653i	−0.243848	−	0.177166i
$680$		0			0
$681$	−13.1803			−0.505072
$682$		0			0
$683$	−9.06888			−0.347011			−0.173506	−	0.984833i	$-0.555509\pi$
$683$	−9.06888			−0.347011			−0.173506	+	0.984833i	$0.555509\pi$
$684$		0			0
$685$	4.88197	+	3.54696i	0.186530	+	0.135522i
$686$		0			0
$687$	0.145898	−	0.449028i	0.00556636	−	0.0171315i
$688$		0			0
$689$	0.0729490	−	0.0530006i	0.00277914	−	0.00201916i
$690$		0			0
$691$	−0.416408	−	1.28157i	−0.0158409	−	0.0487533i	0.942824	−	0.333292i	$-0.108160\pi$
$691$	−0.416408	−	1.28157i	−0.0158409	−	0.0487533i	−0.958665	+	0.284539i	$0.908160\pi$
$692$		0			0
$693$	−2.80902	−	1.76336i	−0.106706	−	0.0669843i
$694$		0			0
$695$	2.78115	+	8.55951i	0.105495	+	0.324681i
$696$		0			0
$697$	0.218847	−	0.159002i	0.00828942	−	0.00602262i
$698$		0			0
$699$	−1.28115	+	3.94298i	−0.0484577	+	0.149137i
$700$		0			0
$701$	28.1525	+	20.4540i	1.06330	+	0.772536i	0.974697	−	0.223531i	$-0.0717583\pi$
$701$	28.1525	+	20.4540i	1.06330	+	0.772536i	0.0886075	+	0.996067i	$0.471758\pi$
$702$		0			0
$703$	36.5066			1.37687
$704$		0			0
$705$	−6.23607			−0.234864
$706$		0			0
$707$	8.28115	+	6.01661i	0.311445	+	0.226278i
$708$		0			0
$709$	3.46556	−	10.6659i	0.130152	−	0.400566i	−0.864653	−	0.502370i	$-0.832462\pi$
$709$	3.46556	−	10.6659i	0.130152	−	0.400566i	0.994804	+	0.101804i	$0.0324615\pi$
$710$		0			0
$711$	8.89919	−	6.46564i	0.333746	−	0.242480i
$712$		0			0
$713$	−0.444272	−	1.36733i	−0.0166381	−	0.0512068i
$714$		0			0
$715$	−0.482779	+	0.0327561i	−0.0180549	+	0.00122501i
$716$		0			0
$717$	−0.118034	−	0.363271i	−0.00440806	−	0.0135666i
$718$		0			0
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.989923	−	0.141608i	$-0.954773\pi$
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.171226	+	0.985232i	$0.554773\pi$
$720$		0			0
$721$	3.38197	−	10.4086i	0.125951	−	0.387637i
$722$		0			0
$723$	−6.70820	−	4.87380i	−0.249481	−	0.181258i
$724$		0			0
$725$	27.7082			1.02906
$726$		0			0
$727$	9.14590			0.339203			0.169601	−	0.985513i	$-0.445752\pi$
$727$	9.14590			0.339203			0.169601	+	0.985513i	$0.445752\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−2.37539	+	7.31069i	−0.0878569	+	0.270396i
$732$		0			0
$733$	0.326238	−	0.237026i	0.0120499	−	0.00875474i	−0.581744	−	0.813372i	$-0.697629\pi$
$733$	0.326238	−	0.237026i	0.0120499	−	0.00875474i	0.593794	+	0.804617i	$0.297629\pi$
$734$		0			0
$735$	1.14590	+	3.52671i	0.0422671	+	0.130085i
$736$		0			0
$737$	−6.13525	+	0.416272i	−0.225995	+	0.0153336i
$738$		0			0
$739$	−0.927051	−	2.85317i	−0.0341021	−	0.104956i	0.932557	−	0.361024i	$-0.117573\pi$
$739$	−0.927051	−	2.85317i	−0.0341021	−	0.104956i	−0.966659	+	0.256068i	$0.917573\pi$
$740$		0			0
$741$	1.11803	−	0.812299i	0.0410720	−	0.0298406i
$742$		0			0
$743$	13.2533	−	40.7894i	0.486216	−	1.49642i	−0.343996	−	0.938971i	$-0.611781\pi$
$743$	13.2533	−	40.7894i	0.486216	−	1.49642i	0.830212	−	0.557448i	$-0.188219\pi$
$744$		0			0
$745$	−2.11803	−	1.53884i	−0.0775988	−	0.0563788i
$746$		0			0
$747$	−1.47214			−0.0538626
$748$		0			0
$749$	11.4721			0.419183
$750$		0			0
$751$	13.0623	+	9.49032i	0.476650	+	0.346307i	0.800027	−	0.599963i	$-0.204818\pi$
$751$	13.0623	+	9.49032i	0.476650	+	0.346307i	−0.323377	+	0.946270i	$0.604818\pi$
$752$		0			0
$753$	6.79180	−	20.9030i	0.247507	−	0.761748i
$754$		0			0
$755$	−0.527864	+	0.383516i	−0.0192109	+	0.0139576i
$756$		0			0
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	0.975201	−	0.221322i	$-0.0710371\pi$
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	−0.919044	+	0.394156i	$0.871037\pi$
$758$		0			0
$759$	0.663119	+	0.416272i	0.0240697	+	0.0151097i
$760$		0			0
$761$	9.05166	+	27.8582i	0.328123	+	1.00986i	0.970011	+	0.243060i	$0.0781511\pi$
$761$	9.05166	+	27.8582i	0.328123	+	1.00986i	−0.641889	+	0.766798i	$0.721849\pi$
$762$		0			0
$763$	9.70820	−	7.05342i	0.351461	−	0.255351i
$764$		0			0
$765$	0.218847	−	0.673542i	0.00791243	−	0.0243520i
$766$		0			0
$767$	1.40983	+	1.02430i	0.0509060	+	0.0369854i
$768$		0			0
$769$	−34.5066			−1.24434			−0.622170	−	0.782883i	$-0.713749\pi$
$769$	−34.5066			−1.24434			−0.622170	+	0.782883i	$0.713749\pi$
$770$		0			0
$771$	29.7426			1.07116
$772$		0			0
$773$	−21.9894	−	15.9762i	−0.790902	−	0.574624i	0.117329	−	0.993093i	$-0.462567\pi$
$773$	−21.9894	−	15.9762i	−0.790902	−	0.574624i	−0.908231	+	0.418469i	$0.862567\pi$
$774$		0			0
$775$	−8.69098	+	26.7481i	−0.312189	+	0.960820i
$776$		0			0
$777$	5.04508	−	3.66547i	0.180991	−	0.131498i
$778$		0			0
$779$	−0.427051	−	1.31433i	−0.0153007	−	0.0470907i
$780$		0			0
$781$	−8.35410	+	33.2137i	−0.298933	+	1.18848i
$782$		0			0
$783$	−1.85410	−	5.70634i	−0.0662602	−	0.203928i
$784$		0			0
$785$	7.85410	−	5.70634i	0.280325	−	0.203668i
$786$		0			0
$787$	3.00000	−	9.23305i	0.106938	−	0.329123i	−0.883242	−	0.468917i	$-0.844644\pi$
$787$	3.00000	−	9.23305i	0.106938	−	0.329123i	0.990181	+	0.139795i	$0.0446442\pi$
$788$		0			0
$789$	−12.3541	−	8.97578i	−0.439818	−	0.319546i
$790$		0			0
$791$	13.4721			0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$		0			0
$795$	−0.190983	−	0.138757i	−0.00677347	−	0.00492121i
$796$		0			0
$797$	5.72949	−	17.6336i	0.202949	−	0.624613i	−0.796842	−	0.604187i	$-0.793498\pi$
$797$	5.72949	−	17.6336i	0.202949	−	0.624613i	0.999791	−	0.0204255i	$-0.00650208\pi$
$798$		0			0
$799$	9.35410	−	6.79615i	0.330924	−	0.240431i
$800$		0			0
$801$	−2.54508	−	7.83297i	−0.0899262	−	0.276764i
$802$		0			0
$803$	14.5279	−	12.1392i	0.512677	−	0.428384i
$804$		0			0
$805$	0.0450850	+	0.138757i	0.00158904	+	0.00489055i
$806$		0			0
$807$	20.5623	−	14.9394i	0.723827	−	0.525891i
$808$		0			0
$809$	8.37132	−	25.7643i	0.294320	−	0.905824i	−0.689129	−	0.724639i	$-0.742007\pi$
$809$	8.37132	−	25.7643i	0.294320	−	0.905824i	0.983449	−	0.181185i	$-0.0579933\pi$
$810$		0			0
$811$	29.5795	+	21.4908i	1.03868	+	0.754644i	0.970027	−	0.242997i	$-0.0781306\pi$
$811$	29.5795	+	21.4908i	1.03868	+	0.754644i	0.0686507	+	0.997641i	$0.478131\pi$
$812$		0			0
$813$	−18.6180			−0.652963
$814$		0			0
$815$	−3.18034			−0.111402
$816$		0			0
$817$	31.7705	+	23.0826i	1.11151	+	0.807559i
$818$		0			0
$819$	0.0729490	−	0.224514i	0.00254904	−	0.00784515i
$820$		0			0
$821$	−32.8435	+	23.8622i	−1.14624	+	0.832795i	−0.987977	−	0.154601i	$-0.950591\pi$
$821$	−32.8435	+	23.8622i	−1.14624	+	0.832795i	−0.158268	+	0.987396i	$0.550591\pi$
$822$		0			0
$823$	8.60081	+	26.4706i	0.299805	+	0.922706i	0.981565	+	0.191130i	$0.0612152\pi$
$823$	8.60081	+	26.4706i	0.299805	+	0.922706i	−0.681759	+	0.731577i	$0.738785\pi$
$824$		0			0
$825$	−5.70820	−	14.2128i	−0.198734	−	0.494828i
$826$		0			0
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	0.991835	−	0.127524i	$-0.0407030\pi$
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	−0.877369	+	0.479817i	$0.840703\pi$
$828$		0			0
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	−0.0516692	−	0.998664i	$-0.516454\pi$
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	0.933819	+	0.357745i	$0.116454\pi$
$830$		0			0
$831$	−9.02786	+	27.7849i	−0.313173	+	0.963848i
$832$		0			0
$833$	−5.56231	−	4.04125i	−0.192722	−	0.140021i
$834$		0			0
$835$	7.43769			0.257392
$836$		0			0
$837$	6.09017			0.210507
$838$		0			0
$839$	−14.4271	−	10.4819i	−0.498077	−	0.361874i	0.310205	−	0.950670i	$-0.399602\pi$
$839$	−14.4271	−	10.4819i	−0.498077	−	0.361874i	−0.808282	+	0.588796i	$0.799602\pi$
$840$		0			0
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$		0			0
$843$	−20.0344	+	14.5559i	−0.690023	+	0.501331i
$844$		0			0
$845$	2.47214	+	7.60845i	0.0850441	+	0.261739i
$846$		0			0
$847$	−7.94427	+	7.60845i	−0.272968	+	0.261430i
$848$		0			0
$849$	1.76393	+	5.42882i	0.0605380	+	0.186317i
$850$		0			0
$851$	−1.19098	+	0.865300i	−0.0408264	+	0.0296621i
$852$		0			0
$853$	−17.2533	+	53.1002i	−0.590741	+	1.81811i	−0.0158658	+	0.999874i	$0.505050\pi$
$853$	−17.2533	+	53.1002i	−0.590741	+	1.81811i	−0.574876	+	0.818241i	$0.694950\pi$
$854$		0			0
$855$	−2.92705	−	2.12663i	−0.100103	−	0.0727291i
$856$		0			0
$857$	27.7639			0.948398			0.474199	−	0.880418i	$-0.342738\pi$
$857$	27.7639			0.948398			0.474199	+	0.880418i	$0.342738\pi$
$858$		0			0
$859$	34.4164			1.17427			0.587136	−	0.809488i	$-0.300255\pi$
$859$	34.4164			1.17427			0.587136	+	0.809488i	$0.300255\pi$
$860$		0			0
$861$	−0.190983	−	0.138757i	−0.00650868	−	0.00472884i
$862$		0			0
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	−0.951641	−	0.307212i	$-0.900604\pi$
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	0.950469	+	0.310821i	$0.100604\pi$
$864$		0			0
$865$	−9.01722	+	6.55139i	−0.306595	+	0.222754i
$866$		0			0
$867$	−4.84752	−	14.9191i	−0.164631	−	0.506681i
$868$		0			0
$869$	−13.5967	−	33.8545i	−0.461238	−	1.14844i
$870$		0			0
$871$	−0.135255	−	0.416272i	−0.00458294	−	0.0141048i
$872$		0			0
$873$	−6.35410	+	4.61653i	−0.215054	+	0.156246i
$874$		0			0
$875$	1.83688	−	5.65334i	0.0620979	−	0.191118i
$876$		0			0
$877$	46.8779	+	34.0588i	1.58295	+	1.15008i	0.913208	+	0.407493i	$0.133597\pi$
$877$	46.8779	+	34.0588i	1.58295	+	1.15008i	0.669746	+	0.742590i	$0.266403\pi$
$878$		0			0
$879$	−21.6525			−0.730320
$880$		0			0
$881$	6.20163			0.208938			0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163			0.208938			0.104469	+	0.994528i	$0.466686\pi$
$882$		0			0
$883$	0.854102	+	0.620541i	0.0287428	+	0.0208829i	0.602064	−	0.798448i	$-0.294345\pi$
$883$	0.854102	+	0.620541i	0.0287428	+	0.0208829i	−0.573321	+	0.819331i	$0.694345\pi$
$884$		0			0
$885$	1.40983	−	4.33901i	0.0473909	−	0.145854i
$886$		0			0
$887$	−44.0795	+	32.0257i	−1.48005	+	1.07532i	−0.502504	+	0.864575i	$0.667588\pi$
$887$	−44.0795	+	32.0257i	−1.48005	+	1.07532i	−0.977542	+	0.210741i	$0.932412\pi$
$888$		0			0
$889$	−2.38197	−	7.33094i	−0.0798886	−	0.245872i
$890$		0			0
$891$	−2.54508	+	2.12663i	−0.0852636	+	0.0712447i
$892$		0			0
$893$	−18.2533	−	56.1778i	−0.610823	−	1.87992i
$894$		0			0
$895$	4.26393	−	3.09793i	0.142528	−	0.103552i
$896$		0			0
$897$	−0.0172209	+	0.0530006i	−0.000574990	+	0.00176964i
$898$		0			0
$899$	29.5623	+	21.4783i	0.985958	+	0.716340i
$900$		0			0
$901$	0.437694			0.0145817
$902$		0			0
$903$	6.70820			0.223235
$904$		0			0
$905$	1.26393	+	0.918300i	0.0420145	+	0.0305253i
$906$		0			0
$907$	13.1008	−	40.3202i	0.435005	−	1.33881i	−0.458076	−	0.888913i	$-0.651461\pi$
$907$	13.1008	−	40.3202i	0.435005	−	1.33881i	0.893081	−	0.449896i	$-0.148539\pi$
$908$		0			0
$909$	8.28115	−	6.01661i	0.274669	−	0.199558i
$910$		0			0
$911$	−11.9271	−	36.7077i	−0.395161	−	1.21618i	−0.928836	−	0.370491i	$-0.879190\pi$
$911$	−11.9271	−	36.7077i	−0.395161	−	1.21618i	0.533675	−	0.845689i	$-0.320810\pi$
$912$		0			0
$913$	−1.19098	+	4.73504i	−0.0394158	+	0.156707i
$914$		0			0
$915$	2.20820	+	6.79615i	0.0730010	+	0.224674i
$916$		0			0
$917$	−9.54508	+	6.93491i	−0.315206	+	0.229011i
$918$		0			0
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	0.730992	+	0.682386i	$0.239058\pi$
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	−0.992481	+	0.122395i	$0.960942\pi$
$920$		0			0
$921$	22.6353	+	16.4455i	0.745857	+	0.541897i
$922$		0			0
$923$	−2.43769			−0.0802377
$924$		0			0
$925$	28.7984			0.946885
$926$		0			0
$927$	−8.85410	−	6.43288i	−0.290807	−	0.211284i
$928$		0			0
$929$	−3.92705	+	12.0862i	−0.128842	+	0.396536i	−0.994582	−	0.103959i	$-0.966849\pi$
$929$	−3.92705	+	12.0862i	−0.128842	+	0.396536i	0.865739	+	0.500495i	$0.166849\pi$
$930$		0			0
$931$	−28.4164	+	20.6457i	−0.931310	+	0.676636i
$932$		0			0
$933$	−3.60081	−	11.0822i	−0.117885	−	0.362814i
$934$		0			0
$935$	−1.98936	−	1.24882i	−0.0650589	−	0.0408406i
$936$		0			0
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	0.907249	+	0.420593i	$0.138178\pi$
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	−0.486761	+	0.873535i	$0.661822\pi$
$938$		0			0
$939$	2.04508	−	1.48584i	0.0667388	−	0.0484886i
$940$		0			0
$941$	−4.46556	+	13.7436i	−0.145573	+	0.448028i	−0.997084	−	0.0763087i	$-0.975687\pi$
$941$	−4.46556	+	13.7436i	−0.145573	+	0.448028i	0.851511	+	0.524336i	$0.175687\pi$
$942$		0			0
$943$	0.0450850	+	0.0327561i	0.00146817	+	0.00106669i
$944$		0			0
$945$	−0.618034			−0.0201046
$946$		0			0
$947$	32.3951			1.05270			0.526350	−	0.850268i	$-0.323560\pi$
$947$	32.3951			1.05270			0.526350	+	0.850268i	$0.323560\pi$
$948$		0			0
$949$	1.09017	+	0.792055i	0.0353884	+	0.0257112i
$950$		0			0
$951$	−2.10739	+	6.48588i	−0.0683368	+	0.210319i
$952$		0			0
$953$	−9.18034	+	6.66991i	−0.297380	+	0.216059i	−0.726463	−	0.687206i	$-0.758837\pi$
$953$	−9.18034	+	6.66991i	−0.297380	+	0.216059i	0.429082	+	0.903265i	$0.358837\pi$
$954$		0			0
$955$	−0.156541	−	0.481784i	−0.00506555	−	0.0155902i
$956$		0			0
$957$	−19.8541	+	1.34708i	−0.641792	+	0.0435450i
$958$		0			0
$959$	3.01722	+	9.28605i	0.0974311	+	0.299862i
$960$		0			0
$961$	−4.92705	+	3.57971i	−0.158937	+	0.115475i
$962$		0			0
$963$	3.54508	−	10.9106i	0.114239	−	0.351591i
$964$		0			0
$965$	−1.57295	−	1.14281i	−0.0506350	−	0.0367885i
$966$		0			0
$967$	−43.9230			−1.41247			−0.706234	−	0.707978i	$-0.749607\pi$
$967$	−43.9230			−1.41247			−0.706234	+	0.707978i	$0.749607\pi$
$968$		0			0
$969$	6.70820			0.215499
$970$		0			0
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.979472	+	0.201582i	$0.935392\pi$
$972$		0			0
$973$	−4.50000	+	13.8496i	−0.144263	+	0.443997i
$974$		0			0
$975$	0.881966	−	0.640786i	0.0282455	−	0.0205216i
$976$		0			0
$977$	−0.184405	−	0.567541i	−0.00589964	−	0.0181572i	0.948063	−	0.318082i	$-0.103039\pi$
$977$	−0.184405	−	0.567541i	−0.00589964	−	0.0181572i	−0.953963	+	0.299924i	$0.903039\pi$
$978$		0			0
$979$	−27.2533	+	1.84911i	−0.871019	+	0.0590979i
$980$		0			0
$981$	−3.70820	−	11.4127i	−0.118394	−	0.364379i
$982$		0			0
$983$	−6.56231	+	4.76779i	−0.209305	+	0.152069i	−0.687499	−	0.726185i	$-0.741292\pi$
$983$	−6.56231	+	4.76779i	−0.209305	+	0.152069i	0.478194	+	0.878254i	$0.341292\pi$
$984$		0			0
$985$	−2.48936	+	7.66145i	−0.0793175	+	0.244114i
$986$		0			0
$987$	−8.16312	−	5.93085i	−0.259835	−	0.188781i
$988$		0			0
$989$	−1.58359			−0.0503553
$990$		0			0
$991$	−3.74265			−0.118889			−0.0594445	−	0.998232i	$-0.518933\pi$
$991$	−3.74265			−0.118889			−0.0594445	+	0.998232i	$0.518933\pi$
$992$		0			0
$993$	13.5172	+	9.82084i	0.428956	+	0.311655i
$994$		0			0
$995$	1.28115	−	3.94298i	0.0406153	−	0.125001i
$996$		0			0
$997$	17.1525	−	12.4620i	0.543224	−	0.394676i	−0.282057	−	0.959398i	$-0.591017\pi$
$997$	17.1525	−	12.4620i	0.543224	−	0.394676i	0.825281	+	0.564722i	$0.191017\pi$
$998$		0			0
$999$	−1.92705	−	5.93085i	−0.0609692	−	0.187644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.y.b.49.1		4
4.3	odd	2		33.2.e.b.16.1	✓	4
11.3	even	5		5808.2.a.cj.1.1		2
11.8	odd	10		5808.2.a.ci.1.1		2
11.9	even	5	inner	528.2.y.b.97.1		4
12.11	even	2		99.2.f.a.82.1		4
20.3	even	4		825.2.bx.d.49.1		8
20.7	even	4		825.2.bx.d.49.2		8
20.19	odd	2		825.2.n.c.676.1		4
36.7	odd	6		891.2.n.c.676.1		8
36.11	even	6		891.2.n.b.676.1		8
36.23	even	6		891.2.n.b.379.1		8
36.31	odd	6		891.2.n.c.379.1		8
44.3	odd	10		363.2.a.d.1.1		2
44.7	even	10		363.2.e.b.124.1		4
44.15	odd	10		363.2.e.k.124.1		4
44.19	even	10		363.2.a.i.1.2		2
44.27	odd	10		363.2.e.k.202.1		4
44.31	odd	10		33.2.e.b.31.1	yes	4
44.35	even	10		363.2.e.f.130.1		4
44.39	even	10		363.2.e.b.202.1		4
44.43	even	2		363.2.e.f.148.1		4
132.47	even	10		1089.2.a.t.1.2		2
132.107	odd	10		1089.2.a.l.1.1		2
132.119	even	10		99.2.f.a.64.1		4
220.19	even	10		9075.2.a.u.1.1		2
220.119	odd	10		825.2.n.c.526.1		4
220.163	even	20		825.2.bx.d.724.2		8
220.179	odd	10		9075.2.a.cb.1.2		2
220.207	even	20		825.2.bx.d.724.1		8
396.31	odd	30		891.2.n.c.460.1		8
396.119	even	30		891.2.n.b.757.1		8
396.295	odd	30		891.2.n.c.757.1		8
396.383	even	30		891.2.n.b.460.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	4.3	odd	2
33.2.e.b.31.1	yes	4	44.31	odd	10
99.2.f.a.64.1		4	132.119	even	10
99.2.f.a.82.1		4	12.11	even	2
363.2.a.d.1.1		2	44.3	odd	10
363.2.a.i.1.2		2	44.19	even	10
363.2.e.b.124.1		4	44.7	even	10
363.2.e.b.202.1		4	44.39	even	10
363.2.e.f.130.1		4	44.35	even	10
363.2.e.f.148.1		4	44.43	even	2
363.2.e.k.124.1		4	44.15	odd	10
363.2.e.k.202.1		4	44.27	odd	10
528.2.y.b.49.1		4	1.1	even	1	trivial
528.2.y.b.97.1		4	11.9	even	5	inner
825.2.n.c.526.1		4	220.119	odd	10
825.2.n.c.676.1		4	20.19	odd	2
825.2.bx.d.49.1		8	20.3	even	4
825.2.bx.d.49.2		8	20.7	even	4
825.2.bx.d.724.1		8	220.207	even	20
825.2.bx.d.724.2		8	220.163	even	20
891.2.n.b.379.1		8	36.23	even	6
891.2.n.b.460.1		8	396.383	even	30
891.2.n.b.676.1		8	36.11	even	6
891.2.n.b.757.1		8	396.119	even	30
891.2.n.c.379.1		8	36.31	odd	6
891.2.n.c.460.1		8	396.31	odd	30
891.2.n.c.676.1		8	36.7	odd	6
891.2.n.c.757.1		8	396.295	odd	30
1089.2.a.l.1.1		2	132.107	odd	10
1089.2.a.t.1.2		2	132.47	even	10
5808.2.a.ci.1.1		2	11.8	odd	10
5808.2.a.cj.1.1		2	11.3	even	5
9075.2.a.u.1.1		2	220.19	even	10
9075.2.a.cb.1.2		2	220.179	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.y (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.190983 + 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{9} +(3.30902 - 0.224514i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(0.500000 - 0.363271i) q^{15} +(-0.354102 + 1.08981i) q^{17} +(4.73607 + 3.44095i) q^{19} +1.00000 q^{21} -0.236068 q^{23} +(3.73607 + 2.71441i) q^{25} +(0.309017 - 0.951057i) q^{27} +(4.85410 - 3.52671i) q^{29} +(1.88197 + 5.79210i) q^{31} +(-2.80902 - 1.76336i) q^{33} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(0.0729490 - 0.224514i) q^{39} +(-0.190983 - 0.138757i) q^{41} +6.70820 q^{43} -0.618034 q^{45} +(-8.16312 - 5.93085i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(0.927051 - 0.673542i) q^{51} +(-0.118034 - 0.363271i) q^{53} +(-0.500000 + 1.98787i) q^{55} +(-1.80902 - 5.56758i) q^{57} +(5.97214 - 4.33901i) q^{59} +(-3.57295 + 10.9964i) q^{61} +(-0.809017 - 0.587785i) q^{63} -0.145898 q^{65} -1.85410 q^{67} +(0.190983 + 0.138757i) q^{69} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(-1.42705 - 4.39201i) q^{75} +(-2.54508 + 2.12663i) q^{77} +(-3.39919 - 10.4616i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.454915 + 1.40008i) q^{83} +(-0.572949 - 0.416272i) q^{85} -6.00000 q^{87} -8.23607 q^{89} +(-0.190983 - 0.138757i) q^{91} +(1.88197 - 5.79210i) q^{93} +(-2.92705 + 2.12663i) q^{95} +(2.42705 + 7.46969i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 3 q^{5} - q^{7} - q^{9} + 11 q^{11} + 7 q^{13} + 2 q^{15} + 12 q^{17} + 10 q^{19} + 4 q^{21} + 8 q^{23} + 6 q^{25} - q^{27} + 6 q^{29} + 12 q^{31} - 9 q^{33} - 3 q^{35} + 9 q^{37} + 7 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - q^3 - 3 * q^5 - q^7 - q^9 + 11 * q^11 + 7 * q^13 + 2 * q^15 + 12 * q^17 + 10 * q^19 + 4 * q^21 + 8 * q^23 + 6 * q^25 - q^27 + 6 * q^29 + 12 * q^31 - 9 * q^33 - 3 * q^35 + 9 * q^37 + 7 * q^39 - 3 * q^41 + 2 * q^45 - 17 * q^47 + 6 * q^49 - 3 * q^51 + 4 * q^53 - 2 * q^55 - 5 * q^57 + 6 * q^59 - 21 * q^61 - q^63 - 14 * q^65 + 6 * q^67 + 3 * q^69 - 15 * q^71 + 14 * q^73 + q^75 + q^77 + 11 * q^79 - q^81 - 13 * q^83 - 9 * q^85 - 24 * q^87 - 24 * q^89 - 3 * q^91 + 12 * q^93 - 5 * q^95 + 3 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more