LMFDB - Embedded newform 528.2.y.b.289.1

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			289.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	528.289
Dual form			528.2.y.b.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 + 2.48990i) q^{11} +(3.42705 - 2.48990i) q^{13} +(0.500000 - 1.53884i) q^{15} +(6.35410 + 4.61653i) q^{17} +(0.263932 + 0.812299i) q^{19} +1.00000 q^{21} +4.23607 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-1.85410 + 5.70634i) q^{29} +(4.11803 - 2.99193i) q^{31} +(-1.69098 + 2.85317i) q^{33} +(-1.30902 + 0.951057i) q^{35} +(-0.545085 + 1.67760i) q^{37} +(3.42705 + 2.48990i) q^{39} +(-1.30902 - 4.02874i) q^{41} -6.70820 q^{43} +1.61803 q^{45} +(-0.336881 - 1.03681i) q^{47} +(4.85410 + 3.52671i) q^{49} +(-2.42705 + 7.46969i) q^{51} +(2.11803 - 1.53884i) q^{53} +(-0.500000 - 5.34307i) q^{55} +(-0.690983 + 0.502029i) q^{57} +(-2.97214 + 9.14729i) q^{59} +(-6.92705 - 5.03280i) q^{61} +(0.309017 + 0.951057i) q^{63} -6.85410 q^{65} +4.85410 q^{67} +(1.30902 + 4.02874i) q^{69} +(-4.30902 - 3.13068i) q^{71} +(2.38197 - 7.33094i) q^{73} +(1.92705 - 1.40008i) q^{75} +(3.04508 - 1.31433i) q^{77} +(8.89919 - 6.46564i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-6.04508 - 4.39201i) q^{83} +(-3.92705 - 12.0862i) q^{85} -6.00000 q^{87} -3.76393 q^{89} +(-1.30902 - 4.02874i) q^{91} +(4.11803 + 2.99193i) q^{93} +(0.427051 - 1.31433i) q^{95} +(-0.927051 + 0.673542i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 3 q^{5} - q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 - 3 * q^5 - q^7 - q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	0.255260	−	0.966872i	$-0.417839\pi$
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	−0.840670	+	0.541547i	$0.817839\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i	−0.875520	−	0.483181i	$-0.839481\pi$
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i	0.992318	+	0.123716i	$0.0394811\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$12$		0			0
$13$	3.42705	−	2.48990i	0.950493	−	0.690574i	−0.000430477	−	1.00000i	$-0.500137\pi$
$13$	3.42705	−	2.48990i	0.950493	−	0.690574i	0.950923	+	0.309426i	$0.100137\pi$
$14$		0			0
$15$	0.500000	−	1.53884i	0.129099	−	0.397327i
$16$		0			0
$17$	6.35410	+	4.61653i	1.54110	+	1.11967i	0.949644	+	0.313332i	$0.101445\pi$
$17$	6.35410	+	4.61653i	1.54110	+	1.11967i	0.591452	+	0.806340i	$0.298555\pi$
$18$		0			0
$19$	0.263932	+	0.812299i	0.0605502	+	0.186354i	0.976756	−	0.214353i	$-0.0687644\pi$
$19$	0.263932	+	0.812299i	0.0605502	+	0.186354i	−0.916206	+	0.400707i	$0.868764\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$		0			0
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$		0			0
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$		0			0
$31$	4.11803	−	2.99193i	0.739621	−	0.537366i	−0.152972	−	0.988231i	$-0.548884\pi$
$31$	4.11803	−	2.99193i	0.739621	−	0.537366i	0.892592	+	0.450865i	$0.148884\pi$
$32$		0			0
$33$	−1.69098	+	2.85317i	−0.294362	+	0.496673i
$34$		0			0
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$		0			0
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	−0.985812	−	0.167854i	$-0.946316\pi$
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	0.896201	+	0.443649i	$0.146316\pi$
$38$		0			0
$39$	3.42705	+	2.48990i	0.548767	+	0.398703i
$40$		0			0
$41$	−1.30902	−	4.02874i	−0.204434	−	0.629183i	−0.999736	−	0.0229701i	$-0.992688\pi$
$41$	−1.30902	−	4.02874i	−0.204434	−	0.629183i	0.795302	−	0.606213i	$-0.207312\pi$
$42$		0			0
$43$	−6.70820			−1.02299			−0.511496	−	0.859286i	$-0.670908\pi$
$43$	−6.70820			−1.02299			−0.511496	+	0.859286i	$0.670908\pi$
$44$		0			0
$45$	1.61803			0.241202
$46$		0			0
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	0.923476	−	0.383656i	$-0.125335\pi$
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	−0.972615	+	0.232421i	$0.925335\pi$
$48$		0			0
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$		0			0
$51$	−2.42705	+	7.46969i	−0.339855	+	1.04597i
$52$		0			0
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	−0.432738	−	0.901520i	$-0.642453\pi$
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	0.723673	+	0.690143i	$0.242453\pi$
$54$		0			0
$55$	−0.500000	−	5.34307i	−0.0674200	−	0.720459i
$56$		0			0
$57$	−0.690983	+	0.502029i	−0.0915229	+	0.0664953i
$58$		0			0
$59$	−2.97214	+	9.14729i	−0.386939	+	1.19088i	0.548125	+	0.836397i	$0.315342\pi$
$59$	−2.97214	+	9.14729i	−0.386939	+	1.19088i	−0.935064	+	0.354480i	$0.884658\pi$
$60$		0			0
$61$	−6.92705	−	5.03280i	−0.886918	−	0.644384i	0.0481546	−	0.998840i	$-0.484666\pi$
$61$	−6.92705	−	5.03280i	−0.886918	−	0.644384i	−0.935073	+	0.354456i	$0.884666\pi$
$62$		0			0
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$		0			0
$65$	−6.85410			−0.850147
$66$		0			0
$67$	4.85410			0.593023			0.296511	−	0.955029i	$-0.404177\pi$
$67$	4.85410			0.593023			0.296511	+	0.955029i	$0.404177\pi$
$68$		0			0
$69$	1.30902	+	4.02874i	0.157587	+	0.485003i
$70$		0			0
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	0.301963	−	0.953320i	$-0.402358\pi$
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	−0.813349	+	0.581776i	$0.802358\pi$
$72$		0			0
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	−0.709404	−	0.704802i	$-0.751036\pi$
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	0.988192	−	0.153219i	$-0.0489641\pi$
$74$		0			0
$75$	1.92705	−	1.40008i	0.222517	−	0.161668i
$76$		0			0
$77$	3.04508	−	1.31433i	0.347020	−	0.149782i
$78$		0			0
$79$	8.89919	−	6.46564i	1.00124	−	0.727441i	0.0388837	−	0.999244i	$-0.487620\pi$
$79$	8.89919	−	6.46564i	1.00124	−	0.727441i	0.962353	+	0.271803i	$0.0876198\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−6.04508	−	4.39201i	−0.663534	−	0.482086i	0.204320	−	0.978904i	$-0.434502\pi$
$83$	−6.04508	−	4.39201i	−0.663534	−	0.482086i	−0.867855	+	0.496818i	$0.834502\pi$
$84$		0			0
$85$	−3.92705	−	12.0862i	−0.425948	−	1.31093i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−3.76393			−0.398976			−0.199488	−	0.979900i	$-0.563928\pi$
$89$	−3.76393			−0.398976			−0.199488	+	0.979900i	$0.563928\pi$
$90$		0			0
$91$	−1.30902	−	4.02874i	−0.137222	−	0.422327i
$92$		0			0
$93$	4.11803	+	2.99193i	0.427020	+	0.310248i
$94$		0			0
$95$	0.427051	−	1.31433i	0.0438145	−	0.134847i
$96$		0			0
$97$	−0.927051	+	0.673542i	−0.0941278	+	0.0683878i	−0.633854	−	0.773453i	$-0.718528\pi$
$97$	−0.927051	+	0.673542i	−0.0941278	+	0.0683878i	0.539726	+	0.841841i	$0.318528\pi$
$98$		0			0
$99$	−3.23607	−	0.726543i	−0.325237	−	0.0730203i
$100$		0			0
$101$	4.66312	−	3.38795i	0.463998	−	0.337114i	−0.331100	−	0.943596i	$-0.607420\pi$
$101$	4.66312	−	3.38795i	0.463998	−	0.337114i	0.795097	+	0.606482i	$0.207420\pi$
$102$		0			0
$103$	−2.14590	+	6.60440i	−0.211442	+	0.650750i	0.787946	+	0.615745i	$0.211145\pi$
$103$	−2.14590	+	6.60440i	−0.211442	+	0.650750i	−0.999387	+	0.0350054i	$0.988855\pi$
$104$		0			0
$105$	−1.30902	−	0.951057i	−0.127747	−	0.0928136i
$106$		0			0
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	0.981689	−	0.190493i	$-0.0610086\pi$
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	−0.906172	+	0.422910i	$0.861009\pi$
$108$		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
$111$	−1.76393			−0.167425
$112$		0			0
$113$	1.39919	+	4.30625i	0.131624	+	0.405098i	0.995050	−	0.0993784i	$-0.0316854\pi$
$113$	1.39919	+	4.30625i	0.131624	+	0.405098i	−0.863425	+	0.504477i	$0.831685\pi$
$114$		0			0
$115$	−5.54508	−	4.02874i	−0.517082	−	0.375682i
$116$		0			0
$117$	−1.30902	+	4.02874i	−0.121019	+	0.372457i
$118$		0			0
$119$	6.35410	−	4.61653i	0.582480	−	0.423196i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$		0			0
$123$	3.42705	−	2.48990i	0.309007	−	0.224507i
$124$		0			0
$125$	−3.69098	+	11.3597i	−0.330132	+	1.01604i
$126$		0			0
$127$	−4.61803	−	3.35520i	−0.409784	−	0.297726i	0.363730	−	0.931504i	$-0.381503\pi$
$127$	−4.61803	−	3.35520i	−0.409784	−	0.297726i	−0.773514	+	0.633779i	$0.781503\pi$
$128$		0			0
$129$	−2.07295	−	6.37988i	−0.182513	−	0.561717i
$130$		0			0
$131$	−12.7984			−1.11820			−0.559100	−	0.829101i	$-0.688853\pi$
$131$	−12.7984			−1.11820			−0.559100	+	0.829101i	$0.688853\pi$
$132$		0			0
$133$	0.854102			0.0740600
$134$		0			0
$135$	0.500000	+	1.53884i	0.0430331	+	0.132442i
$136$		0			0
$137$	−11.5172	−	8.36775i	−0.983983	−	0.714905i	−0.0253875	−	0.999678i	$-0.508082\pi$
$137$	−11.5172	−	8.36775i	−0.983983	−	0.714905i	−0.958595	+	0.284772i	$0.908082\pi$
$138$		0			0
$139$	1.71885	−	5.29007i	0.145791	−	0.448698i	−0.851321	−	0.524645i	$-0.824198\pi$
$139$	1.71885	−	5.29007i	0.145791	−	0.448698i	0.997112	+	0.0759473i	$0.0241981\pi$
$140$		0			0
$141$	0.881966	−	0.640786i	0.0742749	−	0.0539639i
$142$		0			0
$143$	13.7082	+	3.07768i	1.14634	+	0.257369i
$144$		0			0
$145$	7.85410	−	5.70634i	0.652248	−	0.473886i
$146$		0			0
$147$	−1.85410	+	5.70634i	−0.152924	+	0.470651i
$148$		0			0
$149$	−0.190983	−	0.138757i	−0.0156459	−	0.0113674i	0.579935	−	0.814663i	$-0.303078\pi$
$149$	−0.190983	−	0.138757i	−0.0156459	−	0.0113674i	−0.595581	+	0.803295i	$0.703078\pi$
$150$		0			0
$151$	−5.85410	−	18.0171i	−0.476400	−	1.46621i	−0.844060	−	0.536248i	$-0.819841\pi$
$151$	−5.85410	−	18.0171i	−0.476400	−	1.46621i	0.367660	−	0.929960i	$-0.380159\pi$
$152$		0			0
$153$	−7.85410			−0.634967
$154$		0			0
$155$	−8.23607			−0.661537
$156$		0			0
$157$	0.708204	+	2.17963i	0.0565208	+	0.173953i	0.975331	−	0.220745i	$-0.0708490\pi$
$157$	0.708204	+	2.17963i	0.0565208	+	0.173953i	−0.918811	+	0.394699i	$0.870849\pi$
$158$		0			0
$159$	2.11803	+	1.53884i	0.167971	+	0.122038i
$160$		0			0
$161$	1.30902	−	4.02874i	0.103165	−	0.317509i
$162$		0			0
$163$	−9.59017	+	6.96767i	−0.751160	+	0.545750i	−0.896186	−	0.443678i	$-0.853673\pi$
$163$	−9.59017	+	6.96767i	−0.751160	+	0.545750i	0.145026	+	0.989428i	$0.453673\pi$
$164$		0			0
$165$	4.92705	−	2.12663i	0.383570	−	0.165558i
$166$		0			0
$167$	−13.7812	+	10.0126i	−1.06642	+	0.774798i	−0.975265	−	0.221039i	$-0.929055\pi$
$167$	−13.7812	+	10.0126i	−1.06642	+	0.774798i	−0.0911527	+	0.995837i	$0.529055\pi$
$168$		0			0
$169$	1.52786	−	4.70228i	0.117528	−	0.361714i
$170$		0			0
$171$	−0.690983	−	0.502029i	−0.0528408	−	0.0383911i
$172$		0			0
$173$	3.40983	+	10.4944i	0.259245	+	0.797873i	0.992964	+	0.118420i	$0.0377828\pi$
$173$	3.40983	+	10.4944i	0.259245	+	0.797873i	−0.733719	+	0.679453i	$0.762217\pi$
$174$		0			0
$175$	−2.38197			−0.180060
$176$		0			0
$177$	−9.61803			−0.722936
$178$		0			0
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	0.922096	+	0.386960i	$0.126475\pi$
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	−0.518542	+	0.855052i	$0.673525\pi$
$180$		0			0
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	0.186752	−	0.982407i	$-0.440204\pi$
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	−0.876615	+	0.481192i	$0.840204\pi$
$182$		0			0
$183$	2.64590	−	8.14324i	0.195590	−	0.601965i
$184$		0			0
$185$	2.30902	−	1.67760i	0.169762	−	0.123340i
$186$		0			0
$187$	2.42705	+	25.9358i	0.177484	+	1.89661i
$188$		0			0
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$		0			0
$191$	7.16312	−	22.0458i	0.518305	−	1.59518i	−0.258882	−	0.965909i	$-0.583354\pi$
$191$	7.16312	−	22.0458i	0.518305	−	1.59518i	0.777187	−	0.629270i	$-0.216646\pi$
$192$		0			0
$193$	7.97214	+	5.79210i	0.573847	+	0.416924i	0.836501	−	0.547966i	$-0.184598\pi$
$193$	7.97214	+	5.79210i	0.573847	+	0.416924i	−0.262654	+	0.964890i	$0.584598\pi$
$194$		0			0
$195$	−2.11803	−	6.51864i	−0.151676	−	0.466809i
$196$		0			0
$197$	−16.0344			−1.14241			−0.571203	−	0.820809i	$-0.693523\pi$
$197$	−16.0344			−1.14241			−0.571203	+	0.820809i	$0.693523\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$		0			0
$201$	1.50000	+	4.61653i	0.105802	+	0.325625i
$202$		0			0
$203$	4.85410	+	3.52671i	0.340691	+	0.247527i
$204$		0			0
$205$	−2.11803	+	6.51864i	−0.147930	+	0.455281i
$206$		0			0
$207$	−3.42705	+	2.48990i	−0.238197	+	0.173060i
$208$		0			0
$209$	−1.44427	+	2.43690i	−0.0999024	+	0.168564i
$210$		0			0
$211$	1.11803	−	0.812299i	0.0769686	−	0.0559210i	−0.548636	−	0.836062i	$-0.684853\pi$
$211$	1.11803	−	0.812299i	0.0769686	−	0.0559210i	0.625604	+	0.780141i	$0.284853\pi$
$212$		0			0
$213$	1.64590	−	5.06555i	0.112775	−	0.347086i
$214$		0			0
$215$	8.78115	+	6.37988i	0.598870	+	0.435104i
$216$		0			0
$217$	−1.57295	−	4.84104i	−0.106779	−	0.328631i
$218$		0			0
$219$	7.70820			0.520872
$220$		0			0
$221$	33.2705			2.23802
$222$		0			0
$223$	4.69098	+	14.4374i	0.314131	+	0.966797i	0.976110	+	0.217275i	$0.0697168\pi$
$223$	4.69098	+	14.4374i	0.314131	+	0.966797i	−0.661979	+	0.749522i	$0.730283\pi$
$224$		0			0
$225$	1.92705	+	1.40008i	0.128470	+	0.0933390i
$226$		0			0
$227$	2.83688	−	8.73102i	0.188290	−	0.579498i	−0.811699	−	0.584076i	$-0.801457\pi$
$227$	2.83688	−	8.73102i	0.188290	−	0.579498i	0.999990	+	0.00457752i	$0.00145707\pi$
$228$		0			0
$229$	6.85410	−	4.97980i	0.452932	−	0.329074i	−0.337820	−	0.941211i	$-0.609690\pi$
$229$	6.85410	−	4.97980i	0.452932	−	0.329074i	0.790752	+	0.612136i	$0.209690\pi$
$230$		0			0
$231$	2.19098	+	2.48990i	0.144156	+	0.163823i
$232$		0			0
$233$	8.78115	−	6.37988i	0.575272	−	0.417960i	−0.261744	−	0.965137i	$-0.584298\pi$
$233$	8.78115	−	6.37988i	0.575272	−	0.417960i	0.837017	+	0.547177i	$0.184298\pi$
$234$		0			0
$235$	−0.545085	+	1.67760i	−0.0355574	+	0.109434i
$236$		0			0
$237$	8.89919	+	6.46564i	0.578064	+	0.419988i
$238$		0			0
$239$	−0.809017	−	2.48990i	−0.0523310	−	0.161058i	0.921476	−	0.388436i	$-0.126985\pi$
$239$	−0.809017	−	2.48990i	−0.0523310	−	0.161058i	−0.973807	+	0.227378i	$0.926985\pi$
$240$		0			0
$241$	21.7082			1.39835			0.699174	−	0.714951i	$-0.253551\pi$
$241$	21.7082			1.39835			0.699174	+	0.714951i	$0.253551\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−3.00000	−	9.23305i	−0.191663	−	0.589878i
$246$		0			0
$247$	2.92705	+	2.12663i	0.186244	+	0.135314i
$248$		0			0
$249$	2.30902	−	7.10642i	0.146328	−	0.450351i
$250$		0			0
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.276122	−	0.961123i	$-0.410951\pi$
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.999408	+	0.0343954i	$0.0109505\pi$
$252$		0			0
$253$	9.28115	+	10.5474i	0.583501	+	0.663108i
$254$		0			0
$255$	10.2812	−	7.46969i	0.643831	−	0.467770i
$256$		0			0
$257$	−3.93769	+	12.1190i	−0.245627	+	0.755961i	0.749906	+	0.661544i	$0.230099\pi$
$257$	−3.93769	+	12.1190i	−0.245627	+	0.755961i	−0.995533	+	0.0944167i	$0.969901\pi$
$258$		0			0
$259$	1.42705	+	1.03681i	0.0886726	+	0.0644244i
$260$		0			0
$261$	−1.85410	−	5.70634i	−0.114766	−	0.353214i
$262$		0			0
$263$	−18.2705			−1.12661			−0.563304	−	0.826250i	$-0.690470\pi$
$263$	−18.2705			−1.12661			−0.563304	+	0.826250i	$0.690470\pi$
$264$		0			0
$265$	−4.23607			−0.260220
$266$		0			0
$267$	−1.16312	−	3.57971i	−0.0711817	−	0.219075i
$268$		0			0
$269$	−1.14590	−	0.832544i	−0.0698666	−	0.0507611i	0.552304	−	0.833643i	$-0.313749\pi$
$269$	−1.14590	−	0.832544i	−0.0698666	−	0.0507611i	−0.622170	+	0.782882i	$0.713749\pi$
$270$		0			0
$271$	−5.06231	+	15.5802i	−0.307513	+	0.946428i	0.671214	+	0.741263i	$0.265773\pi$
$271$	−5.06231	+	15.5802i	−0.307513	+	0.946428i	−0.978727	+	0.205165i	$0.934227\pi$
$272$		0			0
$273$	3.42705	−	2.48990i	0.207415	−	0.150695i
$274$		0			0
$275$	4.02786	−	6.79615i	0.242889	−	0.409823i
$276$		0			0
$277$	−17.9721	+	13.0575i	−1.07984	+	0.784550i	−0.977655	−	0.210215i	$-0.932584\pi$
$277$	−17.9721	+	13.0575i	−1.07984	+	0.784550i	−0.102186	+	0.994765i	$0.532584\pi$
$278$		0			0
$279$	−1.57295	+	4.84104i	−0.0941700	+	0.289825i
$280$		0			0
$281$	−23.6525	−	17.1845i	−1.41099	−	1.02514i	−0.993178	−	0.116609i	$-0.962798\pi$
$281$	−23.6525	−	17.1845i	−1.41099	−	1.02514i	−0.417811	−	0.908534i	$-0.637202\pi$
$282$		0			0
$283$	−2.38197	−	7.33094i	−0.141593	−	0.435779i	0.854964	−	0.518687i	$-0.173579\pi$
$283$	−2.38197	−	7.33094i	−0.141593	−	0.435779i	−0.996557	+	0.0829083i	$0.973579\pi$
$284$		0			0
$285$	1.38197			0.0818606
$286$		0			0
$287$	−4.23607			−0.250047
$288$		0			0
$289$	13.8090	+	42.4998i	0.812295	+	2.49999i
$290$		0			0
$291$	−0.927051	−	0.673542i	−0.0543447	−	0.0394837i
$292$		0			0
$293$	2.98278	−	9.18005i	0.174256	−	0.536304i	−0.825343	−	0.564632i	$-0.809018\pi$
$293$	2.98278	−	9.18005i	0.174256	−	0.536304i	0.999599	+	0.0283276i	$0.00901816\pi$
$294$		0			0
$295$	12.5902	−	9.14729i	0.733028	−	0.532576i
$296$		0			0
$297$	−0.309017	−	3.30220i	−0.0179310	−	0.191613i
$298$		0			0
$299$	14.5172	−	10.5474i	0.839553	−	0.609971i
$300$		0			0
$301$	−2.07295	+	6.37988i	−0.119483	+	0.367730i
$302$		0			0
$303$	4.66312	+	3.38795i	0.267889	+	0.194633i
$304$		0			0
$305$	4.28115	+	13.1760i	0.245138	+	0.754458i
$306$		0			0
$307$	18.9787			1.08317			0.541586	−	0.840645i	$-0.317824\pi$
$307$	18.9787			1.08317			0.541586	+	0.840645i	$0.317824\pi$
$308$		0			0
$309$	−6.94427			−0.395046
$310$		0			0
$311$	6.07295	+	18.6906i	0.344365	+	1.05985i	0.961923	+	0.273322i	$0.0881223\pi$
$311$	6.07295	+	18.6906i	0.344365	+	1.05985i	−0.617557	+	0.786526i	$0.711878\pi$
$312$		0			0
$313$	9.28115	+	6.74315i	0.524602	+	0.381146i	0.818335	−	0.574742i	$-0.194898\pi$
$313$	9.28115	+	6.74315i	0.524602	+	0.381146i	−0.293733	+	0.955888i	$0.594898\pi$
$314$		0			0
$315$	0.500000	−	1.53884i	0.0281718	−	0.0867039i
$316$		0			0
$317$	23.6074	−	17.1518i	1.32592	−	0.963340i	0.326085	−	0.945340i	$-0.394270\pi$
$317$	23.6074	−	17.1518i	1.32592	−	0.963340i	0.999838	−	0.0179992i	$-0.00572963\pi$
$318$		0			0
$319$	−18.2705	+	7.88597i	−1.02295	+	0.441529i
$320$		0			0
$321$	−2.04508	+	1.48584i	−0.114146	+	0.0829316i
$322$		0			0
$323$	−2.07295	+	6.37988i	−0.115342	+	0.354986i
$324$		0			0
$325$	−8.16312	−	5.93085i	−0.452808	−	0.328985i
$326$		0			0
$327$	−3.70820	−	11.4127i	−0.205064	−	0.631123i
$328$		0			0
$329$	−1.09017			−0.0601030
$330$		0			0
$331$	−3.29180			−0.180933			−0.0904667	−	0.995899i	$-0.528836\pi$
$331$	−3.29180			−0.180933			−0.0904667	+	0.995899i	$0.528836\pi$
$332$		0			0
$333$	−0.545085	−	1.67760i	−0.0298705	−	0.0919319i
$334$		0			0
$335$	−6.35410	−	4.61653i	−0.347162	−	0.252228i
$336$		0			0
$337$	1.29180	−	3.97574i	0.0703686	−	0.216572i	−0.909687	−	0.415294i	$-0.863679\pi$
$337$	1.29180	−	3.97574i	0.0703686	−	0.216572i	0.980056	+	0.198721i	$0.0636788\pi$
$338$		0			0
$339$	−3.66312	+	2.66141i	−0.198953	+	0.144548i
$340$		0			0
$341$	16.4721	+	3.69822i	0.892016	+	0.200270i
$342$		0			0
$343$	10.5172	−	7.64121i	0.567877	−	0.412586i
$344$		0			0
$345$	2.11803	−	6.51864i	0.114031	−	0.350952i
$346$		0			0
$347$	−8.47214	−	6.15537i	−0.454808	−	0.330437i	0.336683	−	0.941618i	$-0.390695\pi$
$347$	−8.47214	−	6.15537i	−0.454808	−	0.330437i	−0.791491	+	0.611181i	$0.790695\pi$
$348$		0			0
$349$	−0.218847	−	0.673542i	−0.0117146	−	0.0360539i	0.945028	−	0.326988i	$-0.106034\pi$
$349$	−0.218847	−	0.673542i	−0.0117146	−	0.0360539i	−0.956743	+	0.290935i	$0.906034\pi$
$350$		0			0
$351$	−4.23607			−0.226105
$352$		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
$355$	2.66312	+	8.19624i	0.141344	+	0.435011i
$356$		0			0
$357$	6.35410	+	4.61653i	0.336295	+	0.244332i
$358$		0			0
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	−0.976731	−	0.214468i	$-0.931198\pi$
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	0.916253	+	0.400600i	$0.131198\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$		0			0
$363$	−10.8090	+	2.04087i	−0.567326	+	0.107118i
$364$		0			0
$365$	−10.0902	+	7.33094i	−0.528144	+	0.383719i
$366$		0			0
$367$	−8.91641	+	27.4419i	−0.465433	+	1.43245i	0.393005	+	0.919536i	$0.371436\pi$
$367$	−8.91641	+	27.4419i	−0.465433	+	1.43245i	−0.858438	+	0.512918i	$0.828564\pi$
$368$		0			0
$369$	3.42705	+	2.48990i	0.178405	+	0.129619i
$370$		0			0
$371$	−0.809017	−	2.48990i	−0.0420021	−	0.129269i
$372$		0			0
$373$	−34.8885			−1.80646			−0.903230	−	0.429156i	$-0.858811\pi$
$373$	−34.8885			−1.80646			−0.903230	+	0.429156i	$0.858811\pi$
$374$		0			0
$375$	−11.9443			−0.616800
$376$		0			0
$377$	7.85410	+	24.1724i	0.404507	+	1.24494i
$378$		0			0
$379$	8.80902	+	6.40013i	0.452489	+	0.328752i	0.790578	−	0.612362i	$-0.209780\pi$
$379$	8.80902	+	6.40013i	0.452489	+	0.328752i	−0.338089	+	0.941114i	$0.609780\pi$
$380$		0			0
$381$	1.76393	−	5.42882i	0.0903690	−	0.278127i
$382$		0			0
$383$	0.572949	−	0.416272i	0.0292763	−	0.0212705i	−0.573051	−	0.819520i	$-0.694240\pi$
$383$	0.572949	−	0.416272i	0.0292763	−	0.0212705i	0.602327	+	0.798249i	$0.294240\pi$
$384$		0			0
$385$	−5.23607	−	1.17557i	−0.266855	−	0.0599126i
$386$		0			0
$387$	5.42705	−	3.94298i	0.275873	−	0.200433i
$388$		0			0
$389$	1.77458	−	5.46158i	0.0899745	−	0.276913i	−0.895937	−	0.444181i	$-0.853495\pi$
$389$	1.77458	−	5.46158i	0.0899745	−	0.276913i	0.985911	+	0.167268i	$0.0534946\pi$
$390$		0			0
$391$	26.9164	+	19.5559i	1.36122	+	0.988985i
$392$		0			0
$393$	−3.95492	−	12.1720i	−0.199499	−	0.613995i
$394$		0			0
$395$	−17.7984			−0.895533
$396$		0			0
$397$	−5.29180			−0.265588			−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180			−0.265588			−0.132794	+	0.991144i	$0.542395\pi$
$398$		0			0
$399$	0.263932	+	0.812299i	0.0132131	+	0.0406658i
$400$		0			0
$401$	−23.2082	−	16.8617i	−1.15896	−	0.842035i	−0.169316	−	0.985562i	$-0.554156\pi$
$401$	−23.2082	−	16.8617i	−1.15896	−	0.842035i	−0.989646	+	0.143526i	$0.954156\pi$
$402$		0			0
$403$	6.66312	−	20.5070i	0.331914	−	1.02153i
$404$		0			0
$405$	−1.30902	+	0.951057i	−0.0650456	+	0.0472584i
$406$		0			0
$407$	−5.37132	+	2.31838i	−0.266247	+	0.114918i
$408$		0			0
$409$	−2.00000	+	1.45309i	−0.0988936	+	0.0718504i	−0.636133	−	0.771579i	$-0.719467\pi$
$409$	−2.00000	+	1.45309i	−0.0988936	+	0.0718504i	0.537240	+	0.843430i	$0.319467\pi$
$410$		0			0
$411$	4.39919	−	13.5393i	0.216996	−	0.667845i
$412$		0			0
$413$	7.78115	+	5.65334i	0.382886	+	0.278183i
$414$		0			0
$415$	3.73607	+	11.4984i	0.183396	+	0.564436i
$416$		0			0
$417$	5.56231			0.272387
$418$		0			0
$419$	24.4508			1.19450			0.597251	−	0.802054i	$-0.296260\pi$
$419$	24.4508			1.19450			0.597251	+	0.802054i	$0.296260\pi$
$420$		0			0
$421$	−8.50000	−	26.1603i	−0.414265	−	1.27498i	−0.912907	−	0.408168i	$-0.866168\pi$
$421$	−8.50000	−	26.1603i	−0.414265	−	1.27498i	0.498642	−	0.866808i	$-0.333832\pi$
$422$		0			0
$423$	0.881966	+	0.640786i	0.0428827	+	0.0311561i
$424$		0			0
$425$	5.78115	−	17.7926i	0.280427	−	0.863066i
$426$		0			0
$427$	−6.92705	+	5.03280i	−0.335223	+	0.243554i
$428$		0			0
$429$	1.30902	+	13.9883i	0.0631999	+	0.675363i
$430$		0			0
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	−0.868679	−	0.495375i	$-0.835031\pi$
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	0.202693	+	0.979242i	$0.435031\pi$
$432$		0			0
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	0.514996	+	0.857193i	$0.327793\pi$
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	−0.920486	+	0.390776i	$0.872207\pi$
$434$		0			0
$435$	7.85410	+	5.70634i	0.376575	+	0.273598i
$436$		0			0
$437$	1.11803	+	3.44095i	0.0534828	+	0.164603i
$438$		0			0
$439$	−36.7082			−1.75199			−0.875993	−	0.482323i	$-0.839793\pi$
$439$	−36.7082			−1.75199			−0.875993	+	0.482323i	$0.839793\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−5.43769	−	16.7355i	−0.258353	−	0.795128i	−0.993151	−	0.116842i	$-0.962723\pi$
$443$	−5.43769	−	16.7355i	−0.258353	−	0.795128i	0.734798	−	0.678286i	$-0.237277\pi$
$444$		0			0
$445$	4.92705	+	3.57971i	0.233565	+	0.169695i
$446$		0			0
$447$	0.0729490	−	0.224514i	0.00345037	−	0.0106191i
$448$		0			0
$449$	21.7984	−	15.8374i	1.02873	−	0.747415i	0.0606750	−	0.998158i	$-0.480675\pi$
$449$	21.7984	−	15.8374i	1.02873	−	0.747415i	0.968054	+	0.250742i	$0.0806747\pi$
$450$		0			0
$451$	7.16312	−	12.0862i	0.337298	−	0.569118i
$452$		0			0
$453$	15.3262	−	11.1352i	0.720089	−	0.523176i
$454$		0			0
$455$	−2.11803	+	6.51864i	−0.0992950	+	0.305598i
$456$		0			0
$457$	18.5902	+	13.5065i	0.869611	+	0.631810i	0.930483	−	0.366336i	$-0.119388\pi$
$457$	18.5902	+	13.5065i	0.869611	+	0.631810i	−0.0608712	+	0.998146i	$0.519388\pi$
$458$		0			0
$459$	−2.42705	−	7.46969i	−0.113285	−	0.348655i
$460$		0			0
$461$	−24.2705			−1.13039			−0.565195	−	0.824957i	$-0.691199\pi$
$461$	−24.2705			−1.13039			−0.565195	+	0.824957i	$0.691199\pi$
$462$		0			0
$463$	−35.2705			−1.63916			−0.819580	−	0.572965i	$-0.805793\pi$
$463$	−35.2705			−1.63916			−0.819580	+	0.572965i	$0.805793\pi$
$464$		0			0
$465$	−2.54508	−	7.83297i	−0.118025	−	0.363245i
$466$		0			0
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	0.273119	−	0.961980i	$-0.411945\pi$
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	−0.830499	+	0.557020i	$0.811945\pi$
$468$		0			0
$469$	1.50000	−	4.61653i	0.0692636	−	0.213171i
$470$		0			0
$471$	−1.85410	+	1.34708i	−0.0854325	+	0.0620704i
$472$		0			0
$473$	−14.6976	−	16.7027i	−0.675795	−	0.767993i
$474$		0			0
$475$	1.64590	−	1.19581i	0.0755190	−	0.0548678i
$476$		0			0
$477$	−0.809017	+	2.48990i	−0.0370423	+	0.114005i
$478$		0			0
$479$	−24.7705	−	17.9968i	−1.13179	−	0.822296i	−0.145839	−	0.989308i	$-0.546588\pi$
$479$	−24.7705	−	17.9968i	−1.13179	−	0.822296i	−0.985955	+	0.167012i	$0.946588\pi$
$480$		0			0
$481$	2.30902	+	7.10642i	0.105282	+	0.324025i
$482$		0			0
$483$	4.23607			0.192748
$484$		0			0
$485$	1.85410			0.0841904
$486$		0			0
$487$	−0.218847	−	0.673542i	−0.00991691	−	0.0305211i	0.945976	−	0.324238i	$-0.105108\pi$
$487$	−0.218847	−	0.673542i	−0.00991691	−	0.0305211i	−0.955893	+	0.293717i	$0.905108\pi$
$488$		0			0
$489$	−9.59017	−	6.96767i	−0.433682	−	0.315089i
$490$		0			0
$491$	8.98936	−	27.6664i	0.405684	−	1.24857i	−0.514639	−	0.857407i	$-0.672074\pi$
$491$	8.98936	−	27.6664i	0.405684	−	1.24857i	0.920323	−	0.391160i	$-0.127926\pi$
$492$		0			0
$493$	−38.1246	+	27.6992i	−1.71705	+	1.24751i
$494$		0			0
$495$	3.54508	+	4.02874i	0.159340	+	0.181078i
$496$		0			0
$497$	−4.30902	+	3.13068i	−0.193286	+	0.140430i
$498$		0			0
$499$	7.68034	−	23.6377i	0.343819	−	1.05817i	−0.618394	−	0.785868i	$-0.712216\pi$
$499$	7.68034	−	23.6377i	0.343819	−	1.05817i	0.962213	−	0.272298i	$-0.0877837\pi$
$500$		0			0
$501$	−13.7812	−	10.0126i	−0.615697	−	0.447330i
$502$		0			0
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	0.976926	+	0.213579i	$0.0685119\pi$
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	−0.664811	+	0.747011i	$0.731488\pi$
$504$		0			0
$505$	−9.32624			−0.415012
$506$		0			0
$507$	4.94427			0.219583
$508$		0			0
$509$	−1.15654	−	3.55947i	−0.0512628	−	0.157771i	0.922148	−	0.386837i	$-0.126433\pi$
$509$	−1.15654	−	3.55947i	−0.0512628	−	0.157771i	−0.973411	+	0.229067i	$0.926433\pi$
$510$		0			0
$511$	−6.23607	−	4.53077i	−0.275867	−	0.200429i
$512$		0			0
$513$	0.263932	−	0.812299i	0.0116529	−	0.0358639i
$514$		0			0
$515$	9.09017	−	6.60440i	0.400561	−	0.291024i
$516$		0			0
$517$	1.84346	−	3.11044i	0.0810752	−	0.136797i
$518$		0			0
$519$	−8.92705	+	6.48588i	−0.391854	+	0.284699i
$520$		0			0
$521$	−2.76393	+	8.50651i	−0.121090	+	0.372677i	−0.993168	−	0.116689i	$-0.962772\pi$
$521$	−2.76393	+	8.50651i	−0.121090	+	0.372677i	0.872078	+	0.489366i	$0.162772\pi$
$522$		0			0
$523$	−12.3541	−	8.97578i	−0.540207	−	0.392483i	0.283955	−	0.958838i	$-0.408353\pi$
$523$	−12.3541	−	8.97578i	−0.540207	−	0.392483i	−0.824162	+	0.566354i	$0.808353\pi$
$524$		0			0
$525$	−0.736068	−	2.26538i	−0.0321246	−	0.0988695i
$526$		0			0
$527$	39.9787			1.74150
$528$		0			0
$529$	−5.05573			−0.219814
$530$		0			0
$531$	−2.97214	−	9.14729i	−0.128980	−	0.396959i
$532$		0			0
$533$	−14.5172	−	10.5474i	−0.628811	−	0.456858i
$534$		0			0
$535$	1.26393	−	3.88998i	0.0546445	−	0.168179i
$536$		0			0
$537$	−14.1353	+	10.2699i	−0.609981	+	0.443177i
$538$		0			0
$539$	1.85410	+	19.8132i	0.0798618	+	0.853414i
$540$		0			0
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.669462	−	0.742846i	$-0.266525\pi$
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.913364	−	0.407144i	$-0.133475\pi$
$542$		0			0
$543$	3.54508	−	10.9106i	0.152134	−	0.468221i
$544$		0			0
$545$	15.7082	+	11.4127i	0.672866	+	0.488865i
$546$		0			0
$547$	−3.62868	−	11.1679i	−0.155151	−	0.477506i	0.843025	−	0.537874i	$-0.180772\pi$
$547$	−3.62868	−	11.1679i	−0.155151	−	0.477506i	−0.998176	+	0.0603684i	$0.980772\pi$
$548$		0			0
$549$	8.56231			0.365430
$550$		0			0
$551$	−5.12461			−0.218316
$552$		0			0
$553$	−3.39919	−	10.4616i	−0.144548	−	0.444873i
$554$		0			0
$555$	2.30902	+	1.67760i	0.0980123	+	0.0712101i
$556$		0			0
$557$	−12.5557	+	38.6426i	−0.532003	+	1.63734i	0.218033	+	0.975941i	$0.430036\pi$
$557$	−12.5557	+	38.6426i	−0.532003	+	1.63734i	−0.750037	+	0.661396i	$0.769964\pi$
$558$		0			0
$559$	−22.9894	+	16.7027i	−0.972346	+	0.706451i
$560$		0			0
$561$	−23.9164	+	10.3229i	−1.00975	+	0.435832i
$562$		0			0
$563$	−6.95492	+	5.05304i	−0.293115	+	0.212960i	−0.724617	−	0.689151i	$-0.757984\pi$
$563$	−6.95492	+	5.05304i	−0.293115	+	0.212960i	0.431503	+	0.902112i	$0.357984\pi$
$564$		0			0
$565$	2.26393	−	6.96767i	0.0952443	−	0.293132i
$566$		0			0
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$		0			0
$569$	3.65248	+	11.2412i	0.153120	+	0.471254i	0.997966	−	0.0637558i	$-0.0203079\pi$
$569$	3.65248	+	11.2412i	0.153120	+	0.471254i	−0.844846	+	0.535010i	$0.820308\pi$
$570$		0			0
$571$	−2.09017			−0.0874709			−0.0437354	−	0.999043i	$-0.513926\pi$
$571$	−2.09017			−0.0874709			−0.0437354	+	0.999043i	$0.513926\pi$
$572$		0			0
$573$	23.1803			0.968373
$574$		0			0
$575$	−3.11803	−	9.59632i	−0.130031	−	0.400194i
$576$		0			0
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	0.235480	−	0.971879i	$-0.424334\pi$
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	−0.851545	+	0.524282i	$0.824334\pi$
$578$		0			0
$579$	−3.04508	+	9.37181i	−0.126549	+	0.389479i
$580$		0			0
$581$	−6.04508	+	4.39201i	−0.250792	+	0.182211i
$582$		0			0
$583$	8.47214	+	1.90211i	0.350880	+	0.0787775i
$584$		0			0
$585$	5.54508	−	4.02874i	0.229261	−	0.166568i
$586$		0			0
$587$	−11.7812	+	36.2587i	−0.486260	+	1.49656i	0.343887	+	0.939011i	$0.388256\pi$
$587$	−11.7812	+	36.2587i	−0.486260	+	1.49656i	−0.830147	+	0.557544i	$0.811744\pi$
$588$		0			0
$589$	3.51722	+	2.55541i	0.144925	+	0.105294i
$590$		0			0
$591$	−4.95492	−	15.2497i	−0.203818	−	0.627287i
$592$		0			0
$593$	15.0344			0.617391			0.308695	−	0.951161i	$-0.400108\pi$
$593$	15.0344			0.617391			0.308695	+	0.951161i	$0.400108\pi$
$594$		0			0
$595$	−12.7082			−0.520986
$596$		0			0
$597$	2.07295	+	6.37988i	0.0848402	+	0.261111i
$598$		0			0
$599$	−15.0902	−	10.9637i	−0.616568	−	0.447963i	0.235153	−	0.971958i	$-0.424441\pi$
$599$	−15.0902	−	10.9637i	−0.616568	−	0.447963i	−0.851721	+	0.523996i	$0.824441\pi$
$600$		0			0
$601$	8.92705	−	27.4746i	0.364142	−	1.12071i	−0.586375	−	0.810040i	$-0.699445\pi$
$601$	8.92705	−	27.4746i	0.364142	−	1.12071i	0.950517	−	0.310674i	$-0.100555\pi$
$602$		0			0
$603$	−3.92705	+	2.85317i	−0.159922	+	0.116190i
$604$		0			0
$605$	12.2082	−	12.9515i	0.496334	−	0.526554i
$606$		0			0
$607$	2.88197	−	2.09387i	0.116975	−	0.0849876i	−0.527760	−	0.849394i	$-0.676968\pi$
$607$	2.88197	−	2.09387i	0.116975	−	0.0849876i	0.644735	+	0.764406i	$0.276968\pi$
$608$		0			0
$609$	−1.85410	+	5.70634i	−0.0751320	+	0.231233i
$610$		0			0
$611$	−3.73607	−	2.71441i	−0.151145	−	0.109813i
$612$		0			0
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	−0.961139	−	0.276065i	$-0.910969\pi$
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	0.615311	−	0.788285i	$-0.289031\pi$
$614$		0			0
$615$	−6.85410			−0.276384
$616$		0			0
$617$	−11.1803			−0.450104			−0.225052	−	0.974347i	$-0.572255\pi$
$617$	−11.1803			−0.450104			−0.225052	+	0.974347i	$0.572255\pi$
$618$		0			0
$619$	4.98278	+	15.3354i	0.200275	+	0.616382i	0.999874	+	0.0158490i	$0.00504509\pi$
$619$	4.98278	+	15.3354i	0.200275	+	0.616382i	−0.799600	+	0.600533i	$0.794955\pi$
$620$		0			0
$621$	−3.42705	−	2.48990i	−0.137523	−	0.0999162i
$622$		0			0
$623$	−1.16312	+	3.57971i	−0.0465994	+	0.143418i
$624$		0			0
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$		0			0
$627$	−2.76393	−	0.620541i	−0.110381	−	0.0247820i
$628$		0			0
$629$	−11.2082	+	8.14324i	−0.446900	+	0.324692i
$630$		0			0
$631$	9.95492	−	30.6381i	0.396299	−	1.21968i	−0.531646	−	0.846966i	$-0.678426\pi$
$631$	9.95492	−	30.6381i	0.396299	−	1.21968i	0.927945	−	0.372716i	$-0.121574\pi$
$632$		0			0
$633$	1.11803	+	0.812299i	0.0444379	+	0.0322860i
$634$		0			0
$635$	2.85410	+	8.78402i	0.113262	+	0.348583i
$636$		0			0
$637$	25.4164			1.00703
$638$		0			0
$639$	5.32624			0.210703
$640$		0			0
$641$	−4.29837	−	13.2290i	−0.169776	−	0.522515i	0.829581	−	0.558387i	$-0.188579\pi$
$641$	−4.29837	−	13.2290i	−0.169776	−	0.522515i	−0.999356	+	0.0358711i	$0.988579\pi$
$642$		0			0
$643$	11.4443	+	8.31475i	0.451318	+	0.327902i	0.790116	−	0.612957i	$-0.210020\pi$
$643$	11.4443	+	8.31475i	0.451318	+	0.327902i	−0.338798	+	0.940859i	$0.610020\pi$
$644$		0			0
$645$	−3.35410	+	10.3229i	−0.132068	+	0.406462i
$646$		0			0
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	−0.304191	−	0.952611i	$-0.598386\pi$
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	0.811987	+	0.583676i	$0.198386\pi$
$648$		0			0
$649$	−29.2877	+	12.6412i	−1.14964	+	0.496212i
$650$		0			0
$651$	4.11803	−	2.99193i	0.161398	−	0.117263i
$652$		0			0
$653$	−1.04508	+	3.21644i	−0.0408973	+	0.125869i	−0.969421	−	0.245405i	$-0.921079\pi$
$653$	−1.04508	+	3.21644i	−0.0408973	+	0.125869i	0.928523	+	0.371274i	$0.121079\pi$
$654$		0			0
$655$	16.7533	+	12.1720i	0.654605	+	0.475598i
$656$		0			0
$657$	2.38197	+	7.33094i	0.0929293	+	0.286007i
$658$		0			0
$659$	0.875388			0.0341003			0.0170501	−	0.999855i	$-0.494573\pi$
$659$	0.875388			0.0341003			0.0170501	+	0.999855i	$0.494573\pi$
$660$		0			0
$661$	16.4377			0.639352			0.319676	−	0.947527i	$-0.396426\pi$
$661$	16.4377			0.639352			0.319676	+	0.947527i	$0.396426\pi$
$662$		0			0
$663$	10.2812	+	31.6421i	0.399287	+	1.22888i
$664$		0			0
$665$	−1.11803	−	0.812299i	−0.0433555	−	0.0314996i
$666$		0			0
$667$	−7.85410	+	24.1724i	−0.304112	+	0.935961i
$668$		0			0
$669$	−12.2812	+	8.92278i	−0.474817	+	0.344975i
$670$		0			0
$671$	−2.64590	−	28.2744i	−0.102144	−	1.09152i
$672$		0			0
$673$	14.4271	−	10.4819i	0.556122	−	0.404046i	−0.273916	−	0.961754i	$-0.588319\pi$
$673$	14.4271	−	10.4819i	0.556122	−	0.404046i	0.830038	+	0.557707i	$0.188319\pi$
$674$		0			0
$675$	−0.736068	+	2.26538i	−0.0283313	+	0.0871947i
$676$		0			0
$677$	−18.1803	−	13.2088i	−0.698727	−	0.507655i	0.180790	−	0.983522i	$-0.442134\pi$
$677$	−18.1803	−	13.2088i	−0.698727	−	0.507655i	−0.879517	+	0.475867i	$0.842134\pi$
$678$		0			0
$679$	0.354102	+	1.08981i	0.0135892	+	0.0418232i
$680$		0			0
$681$	9.18034			0.351791
$682$		0			0
$683$	49.0689			1.87757			0.938784	−	0.344505i	$-0.111953\pi$
$683$	49.0689			1.87757			0.938784	+	0.344505i	$0.111953\pi$
$684$		0			0
$685$	7.11803	+	21.9071i	0.271966	+	0.837026i
$686$		0			0
$687$	6.85410	+	4.97980i	0.261500	+	0.189991i
$688$		0			0
$689$	3.42705	−	10.5474i	0.130560	−	0.401823i
$690$		0			0
$691$	26.4164	−	19.1926i	1.00493	−	0.730123i	0.0417884	−	0.999126i	$-0.486694\pi$
$691$	26.4164	−	19.1926i	1.00493	−	0.730123i	0.963139	+	0.269004i	$0.0866945\pi$
$692$		0			0
$693$	−1.69098	+	2.85317i	−0.0642351	+	0.108383i
$694$		0			0
$695$	−7.28115	+	5.29007i	−0.276190	+	0.200664i
$696$		0			0
$697$	10.2812	−	31.6421i	0.389426	−	1.19853i
$698$		0			0
$699$	8.78115	+	6.37988i	0.332134	+	0.241309i
$700$		0			0
$701$	−3.15248	−	9.70232i	−0.119067	−	0.366452i	0.873706	−	0.486454i	$-0.161710\pi$
$701$	−3.15248	−	9.70232i	−0.119067	−	0.366452i	−0.992774	+	0.120002i	$0.961710\pi$
$702$		0			0
$703$	−1.50658			−0.0568217
$704$		0			0
$705$	−1.76393			−0.0664335
$706$		0			0
$707$	−1.78115	−	5.48183i	−0.0669872	−	0.206165i
$708$		0			0
$709$	32.5344	+	23.6377i	1.22186	+	0.887731i	0.996253	−	0.0864884i	$-0.0275645\pi$
$709$	32.5344	+	23.6377i	1.22186	+	0.887731i	0.225604	+	0.974219i	$0.427565\pi$
$710$		0			0
$711$	−3.39919	+	10.4616i	−0.127479	+	0.392341i
$712$		0			0
$713$	17.4443	−	12.6740i	0.653293	−	0.474645i
$714$		0			0
$715$	−15.0172	−	17.0660i	−0.561612	−	0.638233i
$716$		0			0
$717$	2.11803	−	1.53884i	0.0790994	−	0.0574691i
$718$		0			0
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	0.206385	+	0.978471i	$0.433830\pi$
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	−0.742100	+	0.670289i	$0.766170\pi$
$720$		0			0
$721$	5.61803	+	4.08174i	0.209227	+	0.152012i
$722$		0			0
$723$	6.70820	+	20.6457i	0.249481	+	0.767823i
$724$		0			0
$725$	14.2918			0.530784
$726$		0			0
$727$	15.8541			0.587996			0.293998	−	0.955806i	$-0.405014\pi$
$727$	15.8541			0.587996			0.293998	+	0.955806i	$0.405014\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−42.6246	−	30.9686i	−1.57653	−	1.14541i
$732$		0			0
$733$	−15.3262	+	47.1693i	−0.566088	+	1.74224i	0.0986105	+	0.995126i	$0.468560\pi$
$733$	−15.3262	+	47.1693i	−0.566088	+	1.74224i	−0.664698	+	0.747112i	$0.731440\pi$
$734$		0			0
$735$	7.85410	−	5.70634i	0.289703	−	0.210481i
$736$		0			0
$737$	10.6353	+	12.0862i	0.391755	+	0.445202i
$738$		0			0
$739$	2.42705	−	1.76336i	0.0892805	−	0.0648661i	−0.542250	−	0.840218i	$-0.682427\pi$
$739$	2.42705	−	1.76336i	0.0892805	−	0.0648661i	0.631530	+	0.775351i	$0.282427\pi$
$740$		0			0
$741$	−1.11803	+	3.44095i	−0.0410720	+	0.126407i
$742$		0			0
$743$	−5.75329	−	4.18001i	−0.211068	−	0.153350i	0.477229	−	0.878779i	$-0.341641\pi$
$743$	−5.75329	−	4.18001i	−0.211068	−	0.153350i	−0.688297	+	0.725429i	$0.741641\pi$
$744$		0			0
$745$	0.118034	+	0.363271i	0.00432443	+	0.0133092i
$746$		0			0
$747$	7.47214			0.273391
$748$		0			0
$749$	2.52786			0.0923661
$750$		0			0
$751$	−7.06231	−	21.7355i	−0.257707	−	0.793141i	−0.993284	−	0.115700i	$-0.963089\pi$
$751$	−7.06231	−	21.7355i	−0.257707	−	0.793141i	0.735577	−	0.677441i	$-0.236911\pi$
$752$		0			0
$753$	20.2082	+	14.6821i	0.736428	+	0.535046i
$754$		0			0
$755$	−9.47214	+	29.1522i	−0.344726	+	1.06096i
$756$		0			0
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	−0.658864	−	0.752262i	$-0.728963\pi$
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	0.511843	+	0.859079i	$0.328963\pi$
$758$		0			0
$759$	−7.16312	+	12.0862i	−0.260005	+	0.438702i
$760$		0			0
$761$	−34.5517	+	25.1033i	−1.25250	+	0.909992i	−0.998364	−	0.0571772i	$-0.981790\pi$
$761$	−34.5517	+	25.1033i	−1.25250	+	0.909992i	−0.254133	+	0.967169i	$0.581790\pi$
$762$		0			0
$763$	−3.70820	+	11.4127i	−0.134246	+	0.413167i
$764$		0			0
$765$	10.2812	+	7.46969i	0.371716	+	0.270067i
$766$		0			0
$767$	12.5902	+	38.7486i	0.454605	+	1.39913i
$768$		0			0
$769$	3.50658			0.126450			0.0632252	−	0.997999i	$-0.479861\pi$
$769$	3.50658			0.126450			0.0632252	+	0.997999i	$0.479861\pi$
$770$		0			0
$771$	−12.7426			−0.458915
$772$		0			0
$773$	1.48936	+	4.58377i	0.0535684	+	0.164867i	0.974262	−	0.225421i	$-0.0723756\pi$
$773$	1.48936	+	4.58377i	0.0535684	+	0.164867i	−0.920693	+	0.390287i	$0.872376\pi$
$774$		0			0
$775$	−9.80902	−	7.12667i	−0.352350	−	0.255997i
$776$		0			0
$777$	−0.545085	+	1.67760i	−0.0195548	+	0.0601835i
$778$		0			0
$779$	2.92705	−	2.12663i	0.104872	−	0.0761943i
$780$		0			0
$781$	−1.64590	−	17.5883i	−0.0588949	−	0.629358i
$782$		0			0
$783$	4.85410	−	3.52671i	0.173471	−	0.126034i
$784$		0			0
$785$	1.14590	−	3.52671i	0.0408989	−	0.125874i
$786$		0			0
$787$	3.00000	+	2.17963i	0.106938	+	0.0776953i	0.639969	−	0.768400i	$-0.278947\pi$
$787$	3.00000	+	2.17963i	0.106938	+	0.0776953i	−0.533031	+	0.846096i	$0.678947\pi$
$788$		0			0
$789$	−5.64590	−	17.3763i	−0.200999	−	0.618612i
$790$		0			0
$791$	4.52786			0.160992
$792$		0			0
$793$	−36.2705			−1.28800
$794$		0			0
$795$	−1.30902	−	4.02874i	−0.0464260	−	0.142885i
$796$		0			0
$797$	39.2705	+	28.5317i	1.39103	+	1.01064i	0.995751	+	0.0920845i	$0.0293530\pi$
$797$	39.2705	+	28.5317i	1.39103	+	1.01064i	0.395282	+	0.918560i	$0.370647\pi$
$798$		0			0
$799$	2.64590	−	8.14324i	0.0936051	−	0.288087i
$800$		0			0
$801$	3.04508	−	2.21238i	0.107593	−	0.0781707i
$802$		0			0
$803$	23.4721	−	10.1311i	0.828314	−	0.357519i
$804$		0			0
$805$	−5.54508	+	4.02874i	−0.195439	+	0.141994i
$806$		0			0
$807$	0.437694	−	1.34708i	0.0154076	−	0.0474196i
$808$		0			0
$809$	−12.8713	−	9.35156i	−0.452532	−	0.328783i	0.338063	−	0.941124i	$-0.390228\pi$
$809$	−12.8713	−	9.35156i	−0.452532	−	0.328783i	−0.790594	+	0.612340i	$0.790228\pi$
$810$		0			0
$811$	−5.07953	−	15.6332i	−0.178366	−	0.548955i	0.821405	−	0.570346i	$-0.193191\pi$
$811$	−5.07953	−	15.6332i	−0.178366	−	0.548955i	−0.999771	+	0.0213905i	$0.993191\pi$
$812$		0			0
$813$	−16.3820			−0.574541
$814$		0			0
$815$	19.1803			0.671858
$816$		0			0
$817$	−1.77051	−	5.44907i	−0.0619423	−	0.190639i
$818$		0			0
$819$	3.42705	+	2.48990i	0.119751	+	0.0870041i
$820$		0			0
$821$	−2.65654	+	8.17599i	−0.0927139	+	0.285344i	−0.986651	−	0.162848i	$-0.947932\pi$
$821$	−2.65654	+	8.17599i	−0.0927139	+	0.285344i	0.893937	+	0.448192i	$0.147932\pi$
$822$		0			0
$823$	20.8992	−	15.1841i	0.728500	−	0.529286i	−0.160589	−	0.987021i	$-0.551339\pi$
$823$	20.8992	−	15.1841i	0.728500	−	0.529286i	0.889089	+	0.457735i	$0.151339\pi$
$824$		0			0
$825$	7.70820	+	1.73060i	0.268365	+	0.0602517i
$826$		0			0
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	−0.258084	−	0.966123i	$-0.583091\pi$
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	0.839085	+	0.544000i	$0.183091\pi$
$828$		0			0
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	−0.416113	−	0.909313i	$-0.636608\pi$
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	0.871123	−	0.491064i	$-0.163392\pi$
$830$		0			0
$831$	−17.9721	−	13.0575i	−0.623446	−	0.452960i
$832$		0			0
$833$	14.5623	+	44.8182i	0.504554	+	1.55286i
$834$		0			0
$835$	27.5623			0.953833
$836$		0			0
$837$	−5.09017			−0.175942
$838$		0			0
$839$	−11.0729	−	34.0790i	−0.382281	−	1.17654i	−0.938434	−	0.345459i	$-0.887723\pi$
$839$	−11.0729	−	34.0790i	−0.382281	−	1.17654i	0.556153	−	0.831080i	$-0.312277\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$		0			0
$843$	9.03444	−	27.8052i	0.311163	−	0.957660i
$844$		0			0
$845$	−6.47214	+	4.70228i	−0.222648	+	0.161763i
$846$		0			0
$847$	9.94427	+	4.70228i	0.341689	+	0.161572i
$848$		0			0
$849$	6.23607	−	4.53077i	0.214021	−	0.155496i
$850$		0			0
$851$	−2.30902	+	7.10642i	−0.0791521	+	0.243605i
$852$		0			0
$853$	1.75329	+	1.27384i	0.0600315	+	0.0436154i	0.617396	−	0.786652i	$-0.288188\pi$
$853$	1.75329	+	1.27384i	0.0600315	+	0.0436154i	−0.557365	+	0.830268i	$0.688188\pi$
$854$		0			0
$855$	0.427051	+	1.31433i	0.0146048	+	0.0449491i
$856$		0			0
$857$	32.2361			1.10116			0.550582	−	0.834781i	$-0.314406\pi$
$857$	32.2361			1.10116			0.550582	+	0.834781i	$0.314406\pi$
$858$		0			0
$859$	7.58359			0.258749			0.129374	−	0.991596i	$-0.458703\pi$
$859$	7.58359			0.258749			0.129374	+	0.991596i	$0.458703\pi$
$860$		0			0
$861$	−1.30902	−	4.02874i	−0.0446112	−	0.137299i
$862$		0			0
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.959558	−	0.281512i	$-0.0908358\pi$
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.0287861	+	0.999586i	$0.490836\pi$
$864$		0			0
$865$	5.51722	−	16.9803i	0.187591	−	0.577346i
$866$		0			0
$867$	−36.1525	+	26.2663i	−1.22780	+	0.892051i
$868$		0			0
$869$	35.5967	+	7.99197i	1.20754	+	0.271109i
$870$		0			0
$871$	16.6353	−	12.0862i	0.563664	−	0.409526i
$872$		0			0
$873$	0.354102	−	1.08981i	0.0119845	−	0.0368846i
$874$		0			0
$875$	9.66312	+	7.02067i	0.326673	+	0.237342i
$876$		0			0
$877$	−12.3779	−	38.0953i	−0.417972	−	1.28639i	−0.909565	−	0.415561i	$-0.863585\pi$
$877$	−12.3779	−	38.0953i	−0.417972	−	1.28639i	0.491593	−	0.870825i	$-0.336415\pi$
$878$		0			0
$879$	9.65248			0.325570
$880$		0			0
$881$	30.7984			1.03762			0.518812	−	0.854888i	$-0.326375\pi$
$881$	30.7984			1.03762			0.518812	+	0.854888i	$0.326375\pi$
$882$		0			0
$883$	−5.85410	−	18.0171i	−0.197006	−	0.606323i	−0.999947	−	0.0102644i	$-0.996733\pi$
$883$	−5.85410	−	18.0171i	−0.197006	−	0.606323i	0.802941	−	0.596058i	$-0.203267\pi$
$884$		0			0
$885$	12.5902	+	9.14729i	0.423214	+	0.307483i
$886$		0			0
$887$	−9.42047	+	28.9932i	−0.316309	+	0.973498i	0.658904	+	0.752227i	$0.271020\pi$
$887$	−9.42047	+	28.9932i	−0.316309	+	0.973498i	−0.975212	+	0.221270i	$0.928980\pi$
$888$		0			0
$889$	−4.61803	+	3.35520i	−0.154884	+	0.112530i
$890$		0			0
$891$	3.04508	−	1.31433i	0.102014	−	0.0440316i
$892$		0			0
$893$	0.753289	−	0.547296i	0.0252079	−	0.0183146i
$894$		0			0
$895$	8.73607	−	26.8869i	0.292015	−	0.898728i
$896$		0			0
$897$	14.5172	+	10.5474i	0.484716	+	0.352167i
$898$		0			0
$899$	9.43769	+	29.0462i	0.314765	+	0.968746i
$900$		0			0
$901$	20.5623			0.685030
$902$		0			0
$903$	−6.70820			−0.223235
$904$		0			0
$905$	5.73607	+	17.6538i	0.190673	+	0.586832i
$906$		0			0
$907$	25.3992	+	18.4536i	0.843366	+	0.612741i	0.923309	−	0.384058i	$-0.125474\pi$
$907$	25.3992	+	18.4536i	0.843366	+	0.612741i	−0.0799428	+	0.996799i	$0.525474\pi$
$908$		0			0
$909$	−1.78115	+	5.48183i	−0.0590771	+	0.181821i
$910$		0			0
$911$	−8.57295	+	6.22861i	−0.284034	+	0.206363i	−0.720675	−	0.693273i	$-0.756168\pi$
$911$	−8.57295	+	6.22861i	−0.284034	+	0.206363i	0.436641	+	0.899636i	$0.356168\pi$
$912$		0			0
$913$	−2.30902	−	24.6745i	−0.0764173	−	0.816606i
$914$		0			0
$915$	−11.2082	+	8.14324i	−0.370532	+	0.269207i
$916$		0			0
$917$	−3.95492	+	12.1720i	−0.130603	+	0.401954i
$918$		0			0
$919$	−4.57295	−	3.32244i	−0.150848	−	0.109597i	0.509801	−	0.860292i	$-0.329719\pi$
$919$	−4.57295	−	3.32244i	−0.150848	−	0.109597i	−0.660649	+	0.750695i	$0.729719\pi$
$920$		0			0
$921$	5.86475	+	18.0498i	0.193250	+	0.594762i
$922$		0			0
$923$	−22.5623			−0.742647
$924$		0			0
$925$	4.20163			0.138149
$926$		0			0
$927$	−2.14590	−	6.60440i	−0.0704805	−	0.216917i
$928$		0			0
$929$	−0.572949	−	0.416272i	−0.0187978	−	0.0136574i	0.578347	−	0.815791i	$-0.303698\pi$
$929$	−0.572949	−	0.416272i	−0.0187978	−	0.0136574i	−0.597145	+	0.802134i	$0.703698\pi$
$930$		0			0
$931$	−1.58359	+	4.87380i	−0.0519001	+	0.159732i
$932$		0			0
$933$	−15.8992	+	11.5514i	−0.520516	+	0.378177i
$934$		0			0
$935$	21.4894	−	36.2587i	0.702777	−	1.18578i
$936$		0			0
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	−0.716068	−	0.698030i	$-0.754060\pi$
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	0.442589	+	0.896725i	$0.354060\pi$
$938$		0			0
$939$	−3.54508	+	10.9106i	−0.115689	+	0.356056i
$940$		0			0
$941$	−33.5344	−	24.3642i	−1.09319	−	0.794250i	−0.113256	−	0.993566i	$-0.536128\pi$
$941$	−33.5344	−	24.3642i	−1.09319	−	0.794250i	−0.979935	+	0.199316i	$0.936128\pi$
$942$		0			0
$943$	−5.54508	−	17.0660i	−0.180573	−	0.555746i
$944$		0			0
$945$	1.61803			0.0526346
$946$		0			0
$947$	−41.3951			−1.34516			−0.672580	−	0.740024i	$-0.734814\pi$
$947$	−41.3951			−1.34516			−0.672580	+	0.740024i	$0.734814\pi$
$948$		0			0
$949$	−10.0902	−	31.0543i	−0.327541	−	1.00807i
$950$		0			0
$951$	23.6074	+	17.1518i	0.765522	+	0.556184i
$952$		0			0
$953$	13.1803	−	40.5649i	0.426953	−	1.31403i	−0.474159	−	0.880439i	$-0.657248\pi$
$953$	13.1803	−	40.5649i	0.426953	−	1.31403i	0.901112	−	0.433587i	$-0.142752\pi$
$954$		0			0
$955$	−30.3435	+	22.0458i	−0.981891	+	0.713386i
$956$		0			0
$957$	−13.1459	−	14.9394i	−0.424947	−	0.482922i
$958$		0			0
$959$	−11.5172	+	8.36775i	−0.371910	+	0.270209i
$960$		0			0
$961$	−1.57295	+	4.84104i	−0.0507403	+	0.156163i
$962$		0			0
$963$	−2.04508	−	1.48584i	−0.0659019	−	0.0478806i
$964$		0			0
$965$	−4.92705	−	15.1639i	−0.158607	−	0.488143i
$966$		0			0
$967$	20.9230			0.672838			0.336419	−	0.941712i	$-0.390784\pi$
$967$	20.9230			0.672838			0.336419	+	0.941712i	$0.390784\pi$
$968$		0			0
$969$	−6.70820			−0.215499
$970$		0			0
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	0.910896	+	0.412635i	$0.135392\pi$
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	−0.494389	+	0.869240i	$0.664608\pi$
$972$		0			0
$973$	−4.50000	−	3.26944i	−0.144263	−	0.104813i
$974$		0			0
$975$	3.11803	−	9.59632i	0.0998570	−	0.307328i
$976$		0			0
$977$	−39.3156	+	28.5645i	−1.25782	+	0.913858i	−0.998648	−	0.0519742i	$-0.983449\pi$
$977$	−39.3156	+	28.5645i	−1.25782	+	0.913858i	−0.259169	+	0.965832i	$0.583449\pi$
$978$		0			0
$979$	−8.24671	−	9.37181i	−0.263566	−	0.299524i
$980$		0			0
$981$	9.70820	−	7.05342i	0.309959	−	0.225198i
$982$		0			0
$983$	13.5623	−	41.7405i	0.432570	−	1.33131i	−0.462986	−	0.886366i	$-0.653222\pi$
$983$	13.5623	−	41.7405i	0.432570	−	1.33131i	0.895556	−	0.444949i	$-0.146778\pi$
$984$		0			0
$985$	20.9894	+	15.2497i	0.668777	+	0.485895i
$986$		0			0
$987$	−0.336881	−	1.03681i	−0.0107230	−	0.0330021i
$988$		0			0
$989$	−28.4164			−0.903589
$990$		0			0
$991$	38.7426			1.23070			0.615350	−	0.788254i	$-0.289015\pi$
$991$	38.7426			1.23070			0.615350	+	0.788254i	$0.289015\pi$
$992$		0			0
$993$	−1.01722	−	3.13068i	−0.0322805	−	0.0993493i
$994$		0			0
$995$	−8.78115	−	6.37988i	−0.278381	−	0.202256i
$996$		0			0
$997$	−14.1525	+	43.5568i	−0.448213	+	1.37946i	0.430708	+	0.902492i	$0.358264\pi$
$997$	−14.1525	+	43.5568i	−0.448213	+	1.37946i	−0.878921	+	0.476967i	$0.841736\pi$
$998$		0			0
$999$	1.42705	−	1.03681i	0.0451499	−	0.0328033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.y.b.289.1		4
4.3	odd	2		33.2.e.b.25.1	yes	4
11.2	odd	10		5808.2.a.ci.1.2		2
11.4	even	5	inner	528.2.y.b.433.1		4
11.9	even	5		5808.2.a.cj.1.2		2
12.11	even	2		99.2.f.a.91.1		4
20.3	even	4		825.2.bx.d.124.1		8
20.7	even	4		825.2.bx.d.124.2		8
20.19	odd	2		825.2.n.c.751.1		4
36.7	odd	6		891.2.n.c.190.1		8
36.11	even	6		891.2.n.b.190.1		8
36.23	even	6		891.2.n.b.784.1		8
36.31	odd	6		891.2.n.c.784.1		8
44.3	odd	10		363.2.e.k.148.1		4
44.7	even	10		363.2.e.f.202.1		4
44.15	odd	10		33.2.e.b.4.1	✓	4
44.19	even	10		363.2.e.b.148.1		4
44.27	odd	10		363.2.e.k.130.1		4
44.31	odd	10		363.2.a.d.1.2		2
44.35	even	10		363.2.a.i.1.1		2
44.39	even	10		363.2.e.b.130.1		4
44.43	even	2		363.2.e.f.124.1		4
132.35	odd	10		1089.2.a.l.1.2		2
132.59	even	10		99.2.f.a.37.1		4
132.119	even	10		1089.2.a.t.1.1		2
220.59	odd	10		825.2.n.c.301.1		4
220.79	even	10		9075.2.a.u.1.2		2
220.103	even	20		825.2.bx.d.499.2		8
220.119	odd	10		9075.2.a.cb.1.1		2
220.147	even	20		825.2.bx.d.499.1		8
396.59	even	30		891.2.n.b.136.1		8
396.103	odd	30		891.2.n.c.136.1		8
396.191	even	30		891.2.n.b.433.1		8
396.367	odd	30		891.2.n.c.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	44.15	odd	10
33.2.e.b.25.1	yes	4	4.3	odd	2
99.2.f.a.37.1		4	132.59	even	10
99.2.f.a.91.1		4	12.11	even	2
363.2.a.d.1.2		2	44.31	odd	10
363.2.a.i.1.1		2	44.35	even	10
363.2.e.b.130.1		4	44.39	even	10
363.2.e.b.148.1		4	44.19	even	10
363.2.e.f.124.1		4	44.43	even	2
363.2.e.f.202.1		4	44.7	even	10
363.2.e.k.130.1		4	44.27	odd	10
363.2.e.k.148.1		4	44.3	odd	10
528.2.y.b.289.1		4	1.1	even	1	trivial
528.2.y.b.433.1		4	11.4	even	5	inner
825.2.n.c.301.1		4	220.59	odd	10
825.2.n.c.751.1		4	20.19	odd	2
825.2.bx.d.124.1		8	20.3	even	4
825.2.bx.d.124.2		8	20.7	even	4
825.2.bx.d.499.1		8	220.147	even	20
825.2.bx.d.499.2		8	220.103	even	20
891.2.n.b.136.1		8	396.59	even	30
891.2.n.b.190.1		8	36.11	even	6
891.2.n.b.433.1		8	396.191	even	30
891.2.n.b.784.1		8	36.23	even	6
891.2.n.c.136.1		8	396.103	odd	30
891.2.n.c.190.1		8	36.7	odd	6
891.2.n.c.433.1		8	396.367	odd	30
891.2.n.c.784.1		8	36.31	odd	6
1089.2.a.l.1.2		2	132.35	odd	10
1089.2.a.t.1.1		2	132.119	even	10
5808.2.a.ci.1.2		2	11.2	odd	10
5808.2.a.cj.1.2		2	11.9	even	5
9075.2.a.u.1.2		2	220.79	even	10
9075.2.a.cb.1.1		2	220.119	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 + 2.48990i) q^{11} +(3.42705 - 2.48990i) q^{13} +(0.500000 - 1.53884i) q^{15} +(6.35410 + 4.61653i) q^{17} +(0.263932 + 0.812299i) q^{19} +1.00000 q^{21} +4.23607 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-1.85410 + 5.70634i) q^{29} +(4.11803 - 2.99193i) q^{31} +(-1.69098 + 2.85317i) q^{33} +(-1.30902 + 0.951057i) q^{35} +(-0.545085 + 1.67760i) q^{37} +(3.42705 + 2.48990i) q^{39} +(-1.30902 - 4.02874i) q^{41} -6.70820 q^{43} +1.61803 q^{45} +(-0.336881 - 1.03681i) q^{47} +(4.85410 + 3.52671i) q^{49} +(-2.42705 + 7.46969i) q^{51} +(2.11803 - 1.53884i) q^{53} +(-0.500000 - 5.34307i) q^{55} +(-0.690983 + 0.502029i) q^{57} +(-2.97214 + 9.14729i) q^{59} +(-6.92705 - 5.03280i) q^{61} +(0.309017 + 0.951057i) q^{63} -6.85410 q^{65} +4.85410 q^{67} +(1.30902 + 4.02874i) q^{69} +(-4.30902 - 3.13068i) q^{71} +(2.38197 - 7.33094i) q^{73} +(1.92705 - 1.40008i) q^{75} +(3.04508 - 1.31433i) q^{77} +(8.89919 - 6.46564i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-6.04508 - 4.39201i) q^{83} +(-3.92705 - 12.0862i) q^{85} -6.00000 q^{87} -3.76393 q^{89} +(-1.30902 - 4.02874i) q^{91} +(4.11803 + 2.99193i) q^{93} +(0.427051 - 1.31433i) q^{95} +(-0.927051 + 0.673542i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 3 q^{5} - q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 - 3 * q^5 - q^7 - q^9	\( 4 q - q^{3} - 3 q^{5} - q^{7} - q^{9} + 11 q^{11} + 7 q^{13} + 2 q^{15} + 12 q^{17} + 10 q^{19} + 4 q^{21} + 8 q^{23} + 6 q^{25} - q^{27} + 6 q^{29} + 12 q^{31} - 9 q^{33} - 3 q^{35} + 9 q^{37} + 7 q^{39} - 3 q^{41} + 2 q^{45} - 17 q^{47} + 6 q^{49} - 3 q^{51} + 4 q^{53} - 2 q^{55} - 5 q^{57} + 6 q^{59} - 21 q^{61} - q^{63} - 14 q^{65} + 6 q^{67} + 3 q^{69} - 15 q^{71} + 14 q^{73} + q^{75} + q^{77} + 11 q^{79} - q^{81} - 13 q^{83} - 9 q^{85} - 24 q^{87} - 24 q^{89} - 3 q^{91} + 12 q^{93} - 5 q^{95} + 3 q^{97} - 4 q^{99}+O(q^{100}) \) 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

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