LMFDB - Embedded newform 528.2.y.f.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.f.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{3} +(-0.809017 + 2.48990i) q^{5} +(2.42705 - 1.76336i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{3} +(-0.809017 + 2.48990i) q^{5} +(2.42705 - 1.76336i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-1.69098 + 2.85317i) q^{11} +(0.545085 + 1.67760i) q^{13} +(-2.11803 + 1.53884i) q^{15} +(0.500000 - 1.53884i) q^{17} +(4.73607 + 3.44095i) q^{19} +3.00000 q^{21} -3.47214 q^{23} +(-1.50000 - 1.08981i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-3.61803 + 2.62866i) q^{29} +(-0.881966 - 2.71441i) q^{31} +(-3.04508 + 1.31433i) q^{33} +(2.42705 + 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(9.66312 + 7.02067i) q^{41} -6.23607 q^{43} -2.61803 q^{45} +(1.30902 + 0.951057i) q^{47} +(0.618034 - 1.90211i) q^{49} +(1.30902 - 0.951057i) q^{51} +(-2.97214 - 9.14729i) q^{53} +(-5.73607 - 6.51864i) q^{55} +(1.80902 + 5.56758i) q^{57} +(8.35410 - 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(2.42705 + 1.76336i) q^{63} -4.61803 q^{65} +9.56231 q^{67} +(-2.80902 - 2.04087i) q^{69} +(1.71885 - 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(-0.572949 - 1.76336i) q^{75} +(0.927051 + 9.90659i) q^{77} +(-2.92705 - 9.00854i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.218847 + 0.673542i) q^{83} +(3.42705 + 2.48990i) q^{85} -4.47214 q^{87} +0.527864 q^{89} +(4.28115 + 3.11044i) q^{91} +(0.881966 - 2.71441i) q^{93} +(-12.3992 + 9.00854i) q^{95} +(-4.33688 - 13.3475i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9}+O(q^{10}) $ 4 * q + q^3 - q^5 + 3 * q^7 - q^9	$ 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9} - 9 q^{11} - 9 q^{13} - 4 q^{15} + 2 q^{17} + 10 q^{19} + 12 q^{21} + 4 q^{23} - 6 q^{25} + q^{27} - 10 q^{29} - 8 q^{31} - q^{33} + 3 q^{35} - 3 q^{37} + 9 q^{39} + 23 q^{41} - 16 q^{43} - 6 q^{45} + 3 q^{47} - 2 q^{49} + 3 q^{51} + 6 q^{53} - 14 q^{55} + 5 q^{57} + 20 q^{59} + 3 q^{61} + 3 q^{63} - 14 q^{65} - 2 q^{67} - 9 q^{69} + 27 q^{71} + 6 q^{73} - 9 q^{75} - 3 q^{77} - 5 q^{79} - q^{81} - 21 q^{83} + 7 q^{85} + 20 q^{89} - 3 q^{91} + 8 q^{93} - 25 q^{95} - 33 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 - q^5 + 3 * q^7 - q^9 - 9 * q^11 - 9 * q^13 - 4 * q^15 + 2 * q^17 + 10 * q^19 + 12 * q^21 + 4 * q^23 - 6 * q^25 + q^27 - 10 * q^29 - 8 * q^31 - q^33 + 3 * q^35 - 3 * q^37 + 9 * q^39 + 23 * q^41 - 16 * q^43 - 6 * q^45 + 3 * q^47 - 2 * q^49 + 3 * q^51 + 6 * q^53 - 14 * q^55 + 5 * q^57 + 20 * q^59 + 3 * q^61 + 3 * q^63 - 14 * q^65 - 2 * q^67 - 9 * q^69 + 27 * q^71 + 6 * q^73 - 9 * q^75 - 3 * q^77 - 5 * q^79 - q^81 - 21 * q^83 + 7 * q^85 + 20 * q^89 - 3 * q^91 + 8 * q^93 - 25 * q^95 - 33 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.809017	+	2.48990i	−0.361803	+	1.11352i	0.590155	+	0.807290i	$0.299067\pi$
$5$	−0.809017	+	2.48990i	−0.361803	+	1.11352i	−0.951959	+	0.306227i	$0.900933\pi$
$6$		0			0
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	−0.0255212	−	0.999674i	$-0.508125\pi$
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	0.942860	+	0.333188i	$0.108125\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$12$		0			0
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	0.997754	−	0.0669881i	$-0.0213390\pi$
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	−0.846574	+	0.532270i	$0.821339\pi$
$14$		0			0
$15$	−2.11803	+	1.53884i	−0.546874	+	0.397327i
$16$		0			0
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	−0.871935	−	0.489622i	$-0.837135\pi$
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	0.993203	+	0.116398i	$0.0371348\pi$
$18$		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
$21$	3.00000			0.654654
$22$		0			0
$23$	−3.47214			−0.723990			−0.361995	−	0.932180i	$-0.617904\pi$
$23$	−3.47214			−0.723990			−0.361995	+	0.932180i	$0.617904\pi$
$24$		0			0
$25$	−1.50000	−	1.08981i	−0.300000	−	0.217963i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	−0.870645	−	0.491912i	$-0.836298\pi$
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	0.198793	+	0.980042i	$0.436298\pi$
$30$		0			0
$31$	−0.881966	−	2.71441i	−0.158406	−	0.487523i	0.840084	−	0.542456i	$-0.182505\pi$
$31$	−0.881966	−	2.71441i	−0.158406	−	0.487523i	−0.998490	+	0.0549331i	$0.982505\pi$
$32$		0			0
$33$	−3.04508	+	1.31433i	−0.530081	+	0.228795i
$34$		0			0
$35$	2.42705	+	7.46969i	0.410246	+	1.26261i
$36$		0			0
$37$	−0.190983	+	0.138757i	−0.0313974	+	0.0228116i	−0.603373	−	0.797459i	$-0.706177\pi$
$37$	−0.190983	+	0.138757i	−0.0313974	+	0.0228116i	0.571976	+	0.820270i	$0.306177\pi$
$38$		0			0
$39$	−0.545085	+	1.67760i	−0.0872835	+	0.268631i
$40$		0			0
$41$	9.66312	+	7.02067i	1.50913	+	1.09644i	0.966563	+	0.256428i	$0.0825458\pi$
$41$	9.66312	+	7.02067i	1.50913	+	1.09644i	0.542562	+	0.840015i	$0.317454\pi$
$42$		0			0
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$		0			0
$45$	−2.61803			−0.390273
$46$		0			0
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	0.679148	−	0.734001i	$-0.262349\pi$
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	−0.488208	+	0.872727i	$0.662349\pi$
$48$		0			0
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$		0			0
$51$	1.30902	−	0.951057i	0.183299	−	0.133175i
$52$		0			0
$53$	−2.97214	−	9.14729i	−0.408254	−	1.25648i	−0.918147	−	0.396240i	$-0.870315\pi$
$53$	−2.97214	−	9.14729i	−0.408254	−	1.25648i	0.509893	−	0.860238i	$-0.329685\pi$
$54$		0			0
$55$	−5.73607	−	6.51864i	−0.773451	−	0.878973i
$56$		0			0
$57$	1.80902	+	5.56758i	0.239610	+	0.737444i
$58$		0			0
$59$	8.35410	−	6.06961i	1.08761	−	0.790196i	0.108617	−	0.994084i	$-0.465358\pi$
$59$	8.35410	−	6.06961i	1.08761	−	0.790196i	0.978994	+	0.203888i	$0.0653577\pi$
$60$		0			0
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	−0.666716	−	0.745312i	$-0.732301\pi$
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	0.977468	−	0.211084i	$-0.0676995\pi$
$62$		0			0
$63$	2.42705	+	1.76336i	0.305780	+	0.222162i
$64$		0			0
$65$	−4.61803			−0.572797
$66$		0			0
$67$	9.56231			1.16822			0.584111	−	0.811674i	$-0.301443\pi$
$67$	9.56231			1.16822			0.584111	+	0.811674i	$0.301443\pi$
$68$		0			0
$69$	−2.80902	−	2.04087i	−0.338166	−	0.245692i
$70$		0			0
$71$	1.71885	−	5.29007i	0.203990	−	0.627815i	−0.795764	−	0.605607i	$-0.792930\pi$
$71$	1.71885	−	5.29007i	0.203990	−	0.627815i	0.999753	−	0.0222083i	$-0.00706970\pi$
$72$		0			0
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	−0.423940	−	0.905690i	$-0.639353\pi$
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	0.730358	+	0.683065i	$0.239353\pi$
$74$		0			0
$75$	−0.572949	−	1.76336i	−0.0661585	−	0.203615i
$76$		0			0
$77$	0.927051	+	9.90659i	0.105647	+	1.12896i
$78$		0			0
$79$	−2.92705	−	9.00854i	−0.329319	−	1.01354i	−0.969453	−	0.245276i	$-0.921121\pi$
$79$	−2.92705	−	9.00854i	−0.329319	−	1.01354i	0.640134	−	0.768263i	$-0.278879\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	−0.962349	−	0.271818i	$-0.912375\pi$
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	0.938327	+	0.345749i	$0.112375\pi$
$84$		0			0
$85$	3.42705	+	2.48990i	0.371716	+	0.270067i
$86$		0			0
$87$	−4.47214			−0.479463
$88$		0			0
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$		0			0
$91$	4.28115	+	3.11044i	0.448787	+	0.326063i
$92$		0			0
$93$	0.881966	−	2.71441i	0.0914556	−	0.281471i
$94$		0			0
$95$	−12.3992	+	9.00854i	−1.27213	+	0.924256i
$96$		0			0
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	−0.887510	−	0.460788i	$-0.847567\pi$
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	0.447167	−	0.894451i	$-0.352433\pi$
$98$		0			0
$99$	−3.23607	−	0.726543i	−0.325237	−	0.0730203i
$100$		0			0
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	0.894281	−	0.447506i	$-0.147688\pi$
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	−0.986526	+	0.163605i	$0.947688\pi$
$102$		0			0
$103$	−4.85410	+	3.52671i	−0.478289	+	0.347497i	−0.800663	−	0.599115i	$-0.795519\pi$
$103$	−4.85410	+	3.52671i	−0.478289	+	0.347497i	0.322374	+	0.946612i	$0.395519\pi$
$104$		0			0
$105$	−2.42705	+	7.46969i	−0.236856	+	0.728968i
$106$		0			0
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	0.409679	−	0.912230i	$-0.365641\pi$
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	−0.740984	+	0.671522i	$0.765641\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−0.236068			−0.0224066
$112$		0			0
$113$	−0.572949	−	0.416272i	−0.0538985	−	0.0391596i	0.560510	−	0.828148i	$-0.310605\pi$
$113$	−0.572949	−	0.416272i	−0.0538985	−	0.0391596i	−0.614408	+	0.788988i	$0.710605\pi$
$114$		0			0
$115$	2.80902	−	8.64527i	0.261942	−	0.806175i
$116$		0			0
$117$	−1.42705	+	1.03681i	−0.131931	+	0.0958534i
$118$		0			0
$119$	−1.50000	−	4.61653i	−0.137505	−	0.423196i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$		0			0
$123$	3.69098	+	11.3597i	0.332805	+	1.02427i
$124$		0			0
$125$	−6.66312	+	4.84104i	−0.595967	+	0.432996i
$126$		0			0
$127$	1.14590	−	3.52671i	0.101682	−	0.312945i	−0.887255	−	0.461279i	$-0.847391\pi$
$127$	1.14590	−	3.52671i	0.101682	−	0.312945i	0.988937	+	0.148333i	$0.0473909\pi$
$128$		0			0
$129$	−5.04508	−	3.66547i	−0.444195	−	0.322727i
$130$		0			0
$131$	7.14590			0.624340			0.312170	−	0.950026i	$-0.398944\pi$
$131$	7.14590			0.624340			0.312170	+	0.950026i	$0.398944\pi$
$132$		0			0
$133$	17.5623			1.52285
$134$		0			0
$135$	−2.11803	−	1.53884i	−0.182291	−	0.132442i
$136$		0			0
$137$	2.30902	−	7.10642i	0.197273	−	0.607143i	−0.802670	−	0.596424i	$-0.796588\pi$
$137$	2.30902	−	7.10642i	0.197273	−	0.607143i	0.999943	−	0.0107192i	$-0.00341210\pi$
$138$		0			0
$139$	−0.690983	+	0.502029i	−0.0586084	+	0.0425815i	−0.616704	−	0.787195i	$-0.711532\pi$
$139$	−0.690983	+	0.502029i	−0.0586084	+	0.0425815i	0.558095	+	0.829777i	$0.311532\pi$
$140$		0			0
$141$	0.500000	+	1.53884i	0.0421076	+	0.129594i
$142$		0			0
$143$	−5.70820	−	1.28157i	−0.477344	−	0.107170i
$144$		0			0
$145$	−3.61803	−	11.1352i	−0.300461	−	0.924725i
$146$		0			0
$147$	1.61803	−	1.17557i	0.133453	−	0.0969594i
$148$		0			0
$149$	4.63525	−	14.2658i	0.379735	−	1.16870i	−0.560493	−	0.828159i	$-0.689388\pi$
$149$	4.63525	−	14.2658i	0.379735	−	1.16870i	0.940228	−	0.340545i	$-0.110612\pi$
$150$		0			0
$151$	1.61803	+	1.17557i	0.131674	+	0.0956666i	0.651673	−	0.758500i	$-0.274068\pi$
$151$	1.61803	+	1.17557i	0.131674	+	0.0956666i	−0.519999	+	0.854167i	$0.674068\pi$
$152$		0			0
$153$	1.61803			0.130810
$154$		0			0
$155$	7.47214			0.600176
$156$		0			0
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$		0			0
$159$	2.97214	−	9.14729i	0.235706	−	0.725428i
$160$		0			0
$161$	−8.42705	+	6.12261i	−0.664145	+	0.482529i
$162$		0			0
$163$	−5.64590	−	17.3763i	−0.442221	−	1.36102i	−0.885503	−	0.464634i	$-0.846186\pi$
$163$	−5.64590	−	17.3763i	−0.442221	−	1.36102i	0.443282	−	0.896382i	$-0.353814\pi$
$164$		0			0
$165$	−0.809017	−	8.64527i	−0.0629819	−	0.673033i
$166$		0			0
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	−0.996426	−	0.0844656i	$-0.973082\pi$
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	0.756478	−	0.654019i	$-0.226918\pi$
$168$		0			0
$169$	8.00000	−	5.81234i	0.615385	−	0.447103i
$170$		0			0
$171$	−1.80902	+	5.56758i	−0.138339	+	0.425764i
$172$		0			0
$173$	−12.4443	−	9.04129i	−0.946120	−	0.687397i	0.00376565	−	0.999993i	$-0.498801\pi$
$173$	−12.4443	−	9.04129i	−0.946120	−	0.687397i	−0.949886	+	0.312596i	$0.898801\pi$
$174$		0			0
$175$	−5.56231			−0.420471
$176$		0			0
$177$	10.3262			0.776168
$178$		0			0
$179$	−1.80902	−	1.31433i	−0.135212	−	0.0982375i	0.518123	−	0.855306i	$-0.326631\pi$
$179$	−1.80902	−	1.31433i	−0.135212	−	0.0982375i	−0.653335	+	0.757069i	$0.726631\pi$
$180$		0			0
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	0.522612	+	0.852571i	$0.324958\pi$
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	−0.923930	+	0.382560i	$0.875042\pi$
$182$		0			0
$183$	6.35410	−	4.61653i	0.469709	−	0.341263i
$184$		0			0
$185$	−0.190983	−	0.587785i	−0.0140413	−	0.0432148i
$186$		0			0
$187$	3.54508	+	4.02874i	0.259242	+	0.294611i
$188$		0			0
$189$	0.927051	+	2.85317i	0.0674330	+	0.207538i
$190$		0			0
$191$	−6.04508	+	4.39201i	−0.437407	+	0.317795i	−0.784604	−	0.619998i	$-0.787134\pi$
$191$	−6.04508	+	4.39201i	−0.437407	+	0.317795i	0.347197	+	0.937792i	$0.387134\pi$
$192$		0			0
$193$	−5.73607	+	17.6538i	−0.412891	+	1.27075i	0.501232	+	0.865313i	$0.332880\pi$
$193$	−5.73607	+	17.6538i	−0.412891	+	1.27075i	−0.914124	+	0.405436i	$0.867120\pi$
$194$		0			0
$195$	−3.73607	−	2.71441i	−0.267545	−	0.194383i
$196$		0			0
$197$	24.3820			1.73714			0.868572	−	0.495564i	$-0.165039\pi$
$197$	24.3820			1.73714			0.868572	+	0.495564i	$0.165039\pi$
$198$		0			0
$199$	16.7082			1.18441			0.592207	−	0.805786i	$-0.298257\pi$
$199$	16.7082			1.18441			0.592207	+	0.805786i	$0.298257\pi$
$200$		0			0
$201$	7.73607	+	5.62058i	0.545660	+	0.396445i
$202$		0			0
$203$	−4.14590	+	12.7598i	−0.290985	+	0.895560i
$204$		0			0
$205$	−25.2984	+	18.3803i	−1.76692	+	1.28374i
$206$		0			0
$207$	−1.07295	−	3.30220i	−0.0745751	−	0.229519i
$208$		0			0
$209$	−17.8262	+	7.69421i	−1.23307	+	0.532220i
$210$		0			0
$211$	6.88197	+	21.1805i	0.473774	+	1.45813i	0.847604	+	0.530629i	$0.178044\pi$
$211$	6.88197	+	21.1805i	0.473774	+	1.45813i	−0.373830	+	0.927497i	$0.621956\pi$
$212$		0			0
$213$	4.50000	−	3.26944i	0.308335	−	0.224018i
$214$		0			0
$215$	5.04508	−	15.5272i	0.344072	−	1.05894i
$216$		0			0
$217$	−6.92705	−	5.03280i	−0.470239	−	0.341649i
$218$		0			0
$219$	3.23607			0.218673
$220$		0			0
$221$	2.85410			0.191988
$222$		0			0
$223$	0.572949	+	0.416272i	0.0383675	+	0.0278756i	0.606804	−	0.794852i	$-0.292451\pi$
$223$	0.572949	+	0.416272i	0.0383675	+	0.0278756i	−0.568436	+	0.822727i	$0.692451\pi$
$224$		0			0
$225$	0.572949	−	1.76336i	0.0381966	−	0.117557i
$226$		0			0
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.336856	+	0.941556i	$0.609364\pi$
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.999567	+	0.0294127i	$0.990636\pi$
$228$		0			0
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	0.999745	+	0.0225760i	$0.00718678\pi$
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	−0.795541	+	0.605900i	$0.792813\pi$
$230$		0			0
$231$	−5.07295	+	8.55951i	−0.333776	+	0.563174i
$232$		0			0
$233$	7.51722	+	23.1356i	0.492470	+	1.51567i	0.820863	+	0.571124i	$0.193493\pi$
$233$	7.51722	+	23.1356i	0.492470	+	1.51567i	−0.328394	+	0.944541i	$0.606507\pi$
$234$		0			0
$235$	−3.42705	+	2.48990i	−0.223556	+	0.162423i
$236$		0			0
$237$	2.92705	−	9.00854i	0.190132	−	0.585167i
$238$		0			0
$239$	2.07295	+	1.50609i	0.134088	+	0.0974206i	0.652807	−	0.757524i	$-0.273591\pi$
$239$	2.07295	+	1.50609i	0.134088	+	0.0974206i	−0.518719	+	0.854945i	$0.673591\pi$
$240$		0			0
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	4.23607	+	3.07768i	0.270632	+	0.196626i
$246$		0			0
$247$	−3.19098	+	9.82084i	−0.203037	+	0.624885i
$248$		0			0
$249$	−0.572949	+	0.416272i	−0.0363092	+	0.0263802i
$250$		0			0
$251$	2.40983	+	7.41669i	0.152107	+	0.468138i	0.997856	−	0.0654431i	$-0.0208461\pi$
$251$	2.40983	+	7.41669i	0.152107	+	0.468138i	−0.845749	+	0.533581i	$0.820846\pi$
$252$		0			0
$253$	5.87132	−	9.90659i	0.369127	−	0.622822i
$254$		0			0
$255$	1.30902	+	4.02874i	0.0819738	+	0.252289i
$256$		0			0
$257$	9.44427	−	6.86167i	0.589117	−	0.428019i	−0.252882	−	0.967497i	$-0.581378\pi$
$257$	9.44427	−	6.86167i	0.589117	−	0.428019i	0.842000	+	0.539478i	$0.181378\pi$
$258$		0			0
$259$	−0.218847	+	0.673542i	−0.0135985	+	0.0418519i
$260$		0			0
$261$	−3.61803	−	2.62866i	−0.223951	−	0.162710i
$262$		0			0
$263$	16.3262			1.00672			0.503359	−	0.864077i	$-0.332097\pi$
$263$	16.3262			1.00672			0.503359	+	0.864077i	$0.332097\pi$
$264$		0			0
$265$	25.1803			1.54682
$266$		0			0
$267$	0.427051	+	0.310271i	0.0261351	+	0.0189883i
$268$		0			0
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	−0.691467	−	0.722408i	$-0.743035\pi$
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	0.984029	−	0.178006i	$-0.0569645\pi$
$270$		0			0
$271$	−22.0623	+	16.0292i	−1.34019	+	0.973705i	−0.340753	+	0.940153i	$0.610682\pi$
$271$	−22.0623	+	16.0292i	−1.34019	+	0.973705i	−0.999437	+	0.0335518i	$0.989318\pi$
$272$		0			0
$273$	1.63525	+	5.03280i	0.0989701	+	0.304599i
$274$		0			0
$275$	5.64590	−	2.43690i	0.340460	−	0.146950i
$276$		0			0
$277$	9.44427	+	29.0665i	0.567451	+	1.74644i	0.660554	+	0.750779i	$0.270322\pi$
$277$	9.44427	+	29.0665i	0.567451	+	1.74644i	−0.0931022	+	0.995657i	$0.529678\pi$
$278$		0			0
$279$	2.30902	−	1.67760i	0.138237	−	0.100435i
$280$		0			0
$281$	−0.236068	+	0.726543i	−0.0140826	+	0.0433419i	−0.957851	−	0.287266i	$-0.907254\pi$
$281$	−0.236068	+	0.726543i	−0.0140826	+	0.0433419i	0.943768	+	0.330608i	$0.107254\pi$
$282$		0			0
$283$	0.145898	+	0.106001i	0.00867274	+	0.00630111i	0.592113	−	0.805855i	$-0.298294\pi$
$283$	0.145898	+	0.106001i	0.00867274	+	0.00630111i	−0.583440	+	0.812156i	$0.698294\pi$
$284$		0			0
$285$	−15.3262			−0.907848
$286$		0			0
$287$	35.8328			2.11514
$288$		0			0
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$		0			0
$291$	4.33688	−	13.3475i	0.254232	−	0.782447i
$292$		0			0
$293$	−0.0450850	+	0.0327561i	−0.00263389	+	0.00191363i	−0.589101	−	0.808059i	$-0.700518\pi$
$293$	−0.0450850	+	0.0327561i	−0.00263389	+	0.00191363i	0.586468	+	0.809973i	$0.300518\pi$
$294$		0			0
$295$	8.35410	+	25.7113i	0.486395	+	1.49697i
$296$		0			0
$297$	−2.19098	−	2.48990i	−0.127134	−	0.144479i
$298$		0			0
$299$	−1.89261	−	5.82485i	−0.109452	−	0.336860i
$300$		0			0
$301$	−15.1353	+	10.9964i	−0.872382	+	0.633822i
$302$		0			0
$303$	0.927051	−	2.85317i	0.0532577	−	0.163910i
$304$		0			0
$305$	16.6353	+	12.0862i	0.952532	+	0.692055i
$306$		0			0
$307$	−0.562306			−0.0320925			−0.0160462	−	0.999871i	$-0.505108\pi$
$307$	−0.562306			−0.0320925			−0.0160462	+	0.999871i	$0.505108\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$		0			0
$311$	2.04508	+	1.48584i	0.115966	+	0.0842543i	0.644257	−	0.764809i	$-0.277167\pi$
$311$	2.04508	+	1.48584i	0.115966	+	0.0842543i	−0.528291	+	0.849064i	$0.677167\pi$
$312$		0			0
$313$	7.98278	−	24.5685i	0.451213	−	1.38869i	−0.424310	−	0.905517i	$-0.639483\pi$
$313$	7.98278	−	24.5685i	0.451213	−	1.38869i	0.875524	−	0.483175i	$-0.160517\pi$
$314$		0			0
$315$	−6.35410	+	4.61653i	−0.358013	+	0.260112i
$316$		0			0
$317$	−5.98278	−	18.4131i	−0.336026	−	1.03418i	−0.966214	−	0.257740i	$-0.917022\pi$
$317$	−5.98278	−	18.4131i	−0.336026	−	1.03418i	0.630188	−	0.776443i	$-0.282978\pi$
$318$		0			0
$319$	−1.38197	−	14.7679i	−0.0773752	−	0.826842i
$320$		0			0
$321$	−1.30902	−	4.02874i	−0.0730622	−	0.224862i
$322$		0			0
$323$	7.66312	−	5.56758i	0.426387	−	0.309789i
$324$		0			0
$325$	1.01064	−	3.11044i	0.0560604	−	0.172536i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.85410			0.267615
$330$		0			0
$331$	−26.5967			−1.46189			−0.730945	−	0.682437i	$-0.760920\pi$
$331$	−26.5967			−1.46189			−0.730945	+	0.682437i	$0.760920\pi$
$332$		0			0
$333$	−0.190983	−	0.138757i	−0.0104658	−	0.00760385i
$334$		0			0
$335$	−7.73607	+	23.8092i	−0.422667	+	1.30083i
$336$		0			0
$337$	0.236068	−	0.171513i	0.0128594	−	0.00934293i	−0.581337	−	0.813663i	$-0.697470\pi$
$337$	0.236068	−	0.171513i	0.0128594	−	0.00934293i	0.594196	+	0.804320i	$0.297470\pi$
$338$		0			0
$339$	−0.218847	−	0.673542i	−0.0118861	−	0.0365818i
$340$		0			0
$341$	9.23607	+	2.07363i	0.500161	+	0.112293i
$342$		0			0
$343$	4.63525	+	14.2658i	0.250280	+	0.770283i
$344$		0			0
$345$	7.35410	−	5.34307i	0.395932	−	0.287661i
$346$		0			0
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	−0.612821	−	0.790222i	$-0.709965\pi$
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	0.960263	−	0.279096i	$-0.0900348\pi$
$348$		0			0
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	0.785020	−	0.619470i	$-0.212653\pi$
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	−0.346567	+	0.938025i	$0.612653\pi$
$350$		0			0
$351$	−1.76393			−0.0941517
$352$		0			0
$353$	−10.4721			−0.557376			−0.278688	−	0.960382i	$-0.589899\pi$
$353$	−10.4721			−0.557376			−0.278688	+	0.960382i	$0.589899\pi$
$354$		0			0
$355$	11.7812	+	8.55951i	0.625279	+	0.454292i
$356$		0			0
$357$	1.50000	−	4.61653i	0.0793884	−	0.244332i
$358$		0			0
$359$	−10.3262	+	7.50245i	−0.544998	+	0.395964i	−0.825938	−	0.563761i	$-0.809354\pi$
$359$	−10.3262	+	7.50245i	−0.544998	+	0.395964i	0.280940	+	0.959725i	$0.409354\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$		0			0
$363$	1.39919	−	10.9106i	0.0734383	−	0.572661i
$364$		0			0
$365$	2.61803	+	8.05748i	0.137034	+	0.421748i
$366$		0			0
$367$	4.50000	−	3.26944i	0.234898	−	0.170663i	−0.464109	−	0.885778i	$-0.653625\pi$
$367$	4.50000	−	3.26944i	0.234898	−	0.170663i	0.699007	+	0.715115i	$0.253625\pi$
$368$		0			0
$369$	−3.69098	+	11.3597i	−0.192145	+	0.591361i
$370$		0			0
$371$	−23.3435	−	16.9600i	−1.21193	−	0.880520i
$372$		0			0
$373$	−4.41641			−0.228673			−0.114336	−	0.993442i	$-0.536474\pi$
$373$	−4.41641			−0.228673			−0.114336	+	0.993442i	$0.536474\pi$
$374$		0			0
$375$	−8.23607			−0.425309
$376$		0			0
$377$	−6.38197	−	4.63677i	−0.328688	−	0.238806i
$378$		0			0
$379$	−0.489357	+	1.50609i	−0.0251366	+	0.0773624i	−0.962838	−	0.270080i	$-0.912950\pi$
$379$	−0.489357	+	1.50609i	−0.0251366	+	0.0773624i	0.937701	+	0.347443i	$0.112950\pi$
$380$		0			0
$381$	3.00000	−	2.17963i	0.153695	−	0.111666i
$382$		0			0
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	−0.903405	−	0.428789i	$-0.858940\pi$
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	0.478834	−	0.877906i	$-0.341060\pi$
$384$		0			0
$385$	−25.4164	−	5.70634i	−1.29534	−	0.290822i
$386$		0			0
$387$	−1.92705	−	5.93085i	−0.0979575	−	0.301482i
$388$		0			0
$389$	−19.6353	+	14.2658i	−0.995547	+	0.723307i	−0.961129	−	0.276100i	$-0.910958\pi$
$389$	−19.6353	+	14.2658i	−0.995547	+	0.723307i	−0.0344181	+	0.999408i	$0.510958\pi$
$390$		0			0
$391$	−1.73607	+	5.34307i	−0.0877967	+	0.270211i
$392$		0			0
$393$	5.78115	+	4.20025i	0.291621	+	0.211875i
$394$		0			0
$395$	24.7984			1.24774
$396$		0			0
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$		0			0
$399$	14.2082	+	10.3229i	0.711300	+	0.516790i
$400$		0			0
$401$	−8.06231	+	24.8132i	−0.402612	+	1.23911i	0.520260	+	0.854008i	$0.325835\pi$
$401$	−8.06231	+	24.8132i	−0.402612	+	1.23911i	−0.922873	+	0.385106i	$0.874165\pi$
$402$		0			0
$403$	4.07295	−	2.95917i	0.202888	−	0.147407i
$404$		0			0
$405$	−0.809017	−	2.48990i	−0.0402004	−	0.123724i
$406$		0			0
$407$	−0.0729490	−	0.779543i	−0.00361595	−	0.0386405i
$408$		0			0
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	0.830374	−	0.557207i	$-0.188127\pi$
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	−0.999304	+	0.0372920i	$0.988127\pi$
$410$		0			0
$411$	6.04508	−	4.39201i	0.298182	−	0.216642i
$412$		0			0
$413$	9.57295	−	29.4625i	0.471054	−	1.44976i
$414$		0			0
$415$	−1.50000	−	1.08981i	−0.0736321	−	0.0534969i
$416$		0			0
$417$	−0.854102			−0.0418256
$418$		0			0
$419$	−16.5066			−0.806399			−0.403200	−	0.915112i	$-0.632102\pi$
$419$	−16.5066			−0.806399			−0.403200	+	0.915112i	$0.632102\pi$
$420$		0			0
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.980746	+	0.195286i	$0.0625636\pi$
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.488795	+	0.872398i	$0.337436\pi$
$422$		0			0
$423$	−0.500000	+	1.53884i	−0.0243108	+	0.0748210i
$424$		0			0
$425$	−2.42705	+	1.76336i	−0.117729	+	0.0855353i
$426$		0			0
$427$	−7.28115	−	22.4091i	−0.352360	−	1.08445i
$428$		0			0
$429$	−3.86475	−	4.39201i	−0.186592	−	0.212048i
$430$		0			0
$431$	12.2082	+	37.5730i	0.588048	+	1.80983i	0.586667	+	0.809828i	$0.300440\pi$
$431$	12.2082	+	37.5730i	0.588048	+	1.80983i	0.00138127	+	0.999999i	$0.499560\pi$
$432$		0			0
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	−0.465008	−	0.885307i	$-0.653949\pi$
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	0.698281	+	0.715824i	$0.253949\pi$
$434$		0			0
$435$	3.61803	−	11.1352i	0.173471	−	0.533890i
$436$		0			0
$437$	−16.4443	−	11.9475i	−0.786636	−	0.571525i
$438$		0			0
$439$	−3.29180			−0.157109			−0.0785544	−	0.996910i	$-0.525030\pi$
$439$	−3.29180			−0.157109			−0.0785544	+	0.996910i	$0.525030\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$		0			0
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.915853	−	0.401514i	$-0.868484\pi$
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.664877	−	0.746953i	$-0.731516\pi$
$444$		0			0
$445$	−0.427051	+	1.31433i	−0.0202442	+	0.0623051i
$446$		0			0
$447$	12.1353	−	8.81678i	0.573978	−	0.417019i
$448$		0			0
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	−0.954907	−	0.296905i	$-0.904046\pi$
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	0.598020	−	0.801481i	$-0.295954\pi$
$450$		0			0
$451$	−36.3713	+	15.6987i	−1.71266	+	0.739222i
$452$		0			0
$453$	0.618034	+	1.90211i	0.0290378	+	0.0893691i
$454$		0			0
$455$	−11.2082	+	8.14324i	−0.525449	+	0.381761i
$456$		0			0
$457$	2.53444	−	7.80021i	0.118556	−	0.364878i	−0.874116	−	0.485717i	$-0.838558\pi$
$457$	2.53444	−	7.80021i	0.118556	−	0.364878i	0.992672	+	0.120839i	$0.0385584\pi$
$458$		0			0
$459$	1.30902	+	0.951057i	0.0610997	+	0.0443915i
$460$		0			0
$461$	−21.0902			−0.982267			−0.491134	−	0.871084i	$-0.663417\pi$
$461$	−21.0902			−0.982267			−0.491134	+	0.871084i	$0.663417\pi$
$462$		0			0
$463$	15.7984			0.734213			0.367106	−	0.930179i	$-0.380349\pi$
$463$	15.7984			0.734213			0.367106	+	0.930179i	$0.380349\pi$
$464$		0			0
$465$	6.04508	+	4.39201i	0.280334	+	0.203675i
$466$		0			0
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	−0.856660	−	0.515882i	$-0.827464\pi$
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	0.996280	+	0.0861747i	$0.0274643\pi$
$468$		0			0
$469$	23.2082	−	16.8617i	1.07166	−	0.778603i
$470$		0			0
$471$	1.14590	+	3.52671i	0.0528002	+	0.162502i
$472$		0			0
$473$	10.5451	−	17.7926i	0.484864	−	0.818103i
$474$		0			0
$475$	−3.35410	−	10.3229i	−0.153897	−	0.473646i
$476$		0			0
$477$	7.78115	−	5.65334i	0.356275	−	0.258849i
$478$		0			0
$479$	8.68034	−	26.7153i	0.396615	−	1.22066i	−0.531082	−	0.847320i	$-0.678214\pi$
$479$	8.68034	−	26.7153i	0.396615	−	1.22066i	0.927697	−	0.373335i	$-0.121786\pi$
$480$		0			0
$481$	−0.336881	−	0.244758i	−0.0153605	−	0.0111600i
$482$		0			0
$483$	−10.4164			−0.473963
$484$		0			0
$485$	36.7426			1.66840
$486$		0			0
$487$	13.6074	+	9.88635i	0.616610	+	0.447993i	0.851736	−	0.523972i	$-0.175550\pi$
$487$	13.6074	+	9.88635i	0.616610	+	0.447993i	−0.235126	+	0.971965i	$0.575550\pi$
$488$		0			0
$489$	5.64590	−	17.3763i	0.255316	−	0.785783i
$490$		0			0
$491$	20.3992	−	14.8209i	0.920602	−	0.668857i	−0.0230715	−	0.999734i	$-0.507345\pi$
$491$	20.3992	−	14.8209i	0.920602	−	0.668857i	0.943674	+	0.330877i	$0.107345\pi$
$492$		0			0
$493$	2.23607	+	6.88191i	0.100707	+	0.309946i
$494$		0			0
$495$	4.42705	−	7.46969i	0.198981	−	0.335738i
$496$		0			0
$497$	−5.15654	−	15.8702i	−0.231302	−	0.711876i
$498$		0			0
$499$	−14.2082	+	10.3229i	−0.636047	+	0.462115i	−0.858490	−	0.512831i	$-0.828597\pi$
$499$	−14.2082	+	10.3229i	−0.636047	+	0.462115i	0.222443	+	0.974946i	$0.428597\pi$
$500$		0			0
$501$	3.10081	−	9.54332i	0.138534	−	0.426364i
$502$		0			0
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.964734	−	0.263227i	$-0.0847870\pi$
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.0477750	+	0.998858i	$0.484787\pi$
$504$		0			0
$505$	7.85410			0.349503
$506$		0			0
$507$	9.88854			0.439166
$508$		0			0
$509$	−19.1074	−	13.8823i	−0.846920	−	0.615324i	0.0773749	−	0.997002i	$-0.475346\pi$
$509$	−19.1074	−	13.8823i	−0.846920	−	0.615324i	−0.924295	+	0.381679i	$0.875346\pi$
$510$		0			0
$511$	3.00000	−	9.23305i	0.132712	−	0.408446i
$512$		0			0
$513$	−4.73607	+	3.44095i	−0.209103	+	0.151922i
$514$		0			0
$515$	−4.85410	−	14.9394i	−0.213897	−	0.658308i
$516$		0			0
$517$	−4.92705	+	2.12663i	−0.216691	+	0.0935289i
$518$		0			0
$519$	−4.75329	−	14.6291i	−0.208646	−	0.642147i
$520$		0			0
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	−0.293028	−	0.956104i	$-0.594663\pi$
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	0.818758	+	0.574139i	$0.194663\pi$
$522$		0			0
$523$	3.70163	−	11.3924i	0.161861	−	0.498156i	−0.836930	−	0.547309i	$-0.815652\pi$
$523$	3.70163	−	11.3924i	0.161861	−	0.498156i	0.998791	+	0.0491529i	$0.0156522\pi$
$524$		0			0
$525$	−4.50000	−	3.26944i	−0.196396	−	0.142690i
$526$		0			0
$527$	−4.61803			−0.201165
$528$		0			0
$529$	−10.9443			−0.475838
$530$		0			0
$531$	8.35410	+	6.06961i	0.362537	+	0.263399i
$532$		0			0
$533$	−6.51064	+	20.0377i	−0.282007	+	0.867929i
$534$		0			0
$535$	8.97214	−	6.51864i	0.387899	−	0.281825i
$536$		0			0
$537$	−0.690983	−	2.12663i	−0.0298181	−	0.0917707i
$538$		0			0
$539$	4.38197	+	4.97980i	0.188745	+	0.214495i
$540$		0			0
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	0.992825	+	0.119577i	$0.0381540\pi$
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	−0.732926	+	0.680308i	$0.761846\pi$
$542$		0			0
$543$	−14.1353	+	10.2699i	−0.606602	+	0.440722i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	17.4894	+	12.7068i	0.747791	+	0.543302i	0.895141	−	0.445782i	$-0.147075\pi$
$547$	17.4894	+	12.7068i	0.747791	+	0.543302i	−0.147350	+	0.989084i	$0.547075\pi$
$548$		0			0
$549$	7.85410			0.335205
$550$		0			0
$551$	−26.1803			−1.11532
$552$		0			0
$553$	−22.9894	−	16.7027i	−0.977607	−	0.710273i
$554$		0			0
$555$	0.190983	−	0.587785i	0.00810678	−	0.0249501i
$556$		0			0
$557$	−12.0623	+	8.76378i	−0.511096	+	0.371333i	−0.813239	−	0.581929i	$-0.802298\pi$
$557$	−12.0623	+	8.76378i	−0.511096	+	0.371333i	0.302143	+	0.953263i	$0.402298\pi$
$558$		0			0
$559$	−3.39919	−	10.4616i	−0.143770	−	0.442479i
$560$		0			0
$561$	0.500000	+	5.34307i	0.0211100	+	0.225585i
$562$		0			0
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	0.992105	−	0.125412i	$-0.0400251\pi$
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	−0.876345	+	0.481684i	$0.840025\pi$
$564$		0			0
$565$	1.50000	−	1.08981i	0.0631055	−	0.0458488i
$566$		0			0
$567$	−0.927051	+	2.85317i	−0.0389325	+	0.119822i
$568$		0			0
$569$	19.4721	+	14.1473i	0.816314	+	0.593087i	0.915654	−	0.401966i	$-0.131673\pi$
$569$	19.4721	+	14.1473i	0.816314	+	0.593087i	−0.0993400	+	0.995054i	$0.531673\pi$
$570$		0			0
$571$	−34.6869			−1.45160			−0.725801	−	0.687905i	$-0.758531\pi$
$571$	−34.6869			−1.45160			−0.725801	+	0.687905i	$0.758531\pi$
$572$		0			0
$573$	−7.47214			−0.312153
$574$		0			0
$575$	5.20820	+	3.78398i	0.217197	+	0.157803i
$576$		0			0
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	−0.857641	−	0.514249i	$-0.828071\pi$
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	0.996114	+	0.0880726i	$0.0280707\pi$
$578$		0			0
$579$	−15.0172	+	10.9106i	−0.624094	+	0.453431i
$580$		0			0
$581$	0.656541	+	2.02063i	0.0272379	+	0.0838297i
$582$		0			0
$583$	31.1246	+	6.98791i	1.28905	+	0.289410i
$584$		0			0
$585$	−1.42705	−	4.39201i	−0.0590013	−	0.181587i
$586$		0			0
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.999524	−	0.0308361i	$-0.990183\pi$
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.279543	+	0.960133i	$0.590183\pi$
$588$		0			0
$589$	5.16312	−	15.8904i	0.212743	−	0.654754i
$590$		0			0
$591$	19.7254	+	14.3314i	0.811396	+	0.589513i
$592$		0			0
$593$	22.2148			0.912252			0.456126	−	0.889915i	$-0.349237\pi$
$593$	22.2148			0.912252			0.456126	+	0.889915i	$0.349237\pi$
$594$		0			0
$595$	12.7082			0.520986
$596$		0			0
$597$	13.5172	+	9.82084i	0.553223	+	0.401940i
$598$		0			0
$599$	2.56231	−	7.88597i	0.104693	−	0.322212i	−0.884965	−	0.465657i	$-0.845818\pi$
$599$	2.56231	−	7.88597i	0.104693	−	0.322212i	0.989658	+	0.143445i	$0.0458181\pi$
$600$		0			0
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.983675	−	0.179955i	$-0.942405\pi$
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.132825	+	0.991140i	$0.542405\pi$
$602$		0			0
$603$	2.95492	+	9.09429i	0.120333	+	0.370348i
$604$		0			0
$605$	28.2984	−	5.34307i	1.15049	−	0.217227i
$606$		0			0
$607$	−4.11803	−	12.6740i	−0.167146	−	0.514422i	0.832042	−	0.554712i	$-0.187172\pi$
$607$	−4.11803	−	12.6740i	−0.167146	−	0.514422i	−0.999188	+	0.0402904i	$0.987172\pi$
$608$		0			0
$609$	−10.8541	+	7.88597i	−0.439830	+	0.319555i
$610$		0			0
$611$	−0.881966	+	2.71441i	−0.0356805	+	0.109813i
$612$		0			0
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.146272	−	0.989244i	$-0.546728\pi$
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.986028	+	0.166580i	$0.946728\pi$
$614$		0			0
$615$	−31.2705			−1.26095
$616$		0			0
$617$	19.5836			0.788406			0.394203	−	0.919023i	$-0.371021\pi$
$617$	19.5836			0.788406			0.394203	+	0.919023i	$0.371021\pi$
$618$		0			0
$619$	−7.13525	−	5.18407i	−0.286790	−	0.208365i	0.435084	−	0.900390i	$-0.356719\pi$
$619$	−7.13525	−	5.18407i	−0.286790	−	0.208365i	−0.721874	+	0.692025i	$0.756719\pi$
$620$		0			0
$621$	1.07295	−	3.30220i	0.0430560	−	0.132513i
$622$		0			0
$623$	1.28115	−	0.930812i	0.0513283	−	0.0372922i
$624$		0			0
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$		0			0
$627$	−18.9443	−	4.25325i	−0.756561	−	0.169859i
$628$		0			0
$629$	0.118034	+	0.363271i	0.00470632	+	0.0144846i
$630$		0			0
$631$	37.4336	−	27.1971i	1.49021	−	1.08270i	0.516125	−	0.856513i	$-0.327374\pi$
$631$	37.4336	−	27.1971i	1.49021	−	1.08270i	0.974084	−	0.226187i	$-0.0726262\pi$
$632$		0			0
$633$	−6.88197	+	21.1805i	−0.273534	+	0.841850i
$634$		0			0
$635$	7.85410	+	5.70634i	0.311681	+	0.226449i
$636$		0			0
$637$	3.52786			0.139779
$638$		0			0
$639$	5.56231			0.220041
$640$		0			0
$641$	−28.9164	−	21.0090i	−1.14213	−	0.829806i	−0.154715	−	0.987959i	$-0.549446\pi$
$641$	−28.9164	−	21.0090i	−1.14213	−	0.829806i	−0.987415	+	0.158154i	$0.949446\pi$
$642$		0			0
$643$	11.9164	−	36.6749i	0.469937	−	1.44632i	−0.382728	−	0.923861i	$-0.625015\pi$
$643$	11.9164	−	36.6749i	0.469937	−	1.44632i	0.852666	−	0.522457i	$-0.174985\pi$
$644$		0			0
$645$	13.2082	−	9.59632i	0.520073	−	0.377855i
$646$		0			0
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	−0.965369	−	0.260887i	$-0.915985\pi$
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	0.627655	−	0.778492i	$-0.284015\pi$
$648$		0			0
$649$	3.19098	+	34.0993i	0.125257	+	1.33851i
$650$		0			0
$651$	−2.64590	−	8.14324i	−0.103701	−	0.319159i
$652$		0			0
$653$	−41.2877	+	29.9973i	−1.61571	+	1.17388i	−0.776390	+	0.630252i	$0.782951\pi$
$653$	−41.2877	+	29.9973i	−1.61571	+	1.17388i	−0.839323	+	0.543632i	$0.817049\pi$
$654$		0			0
$655$	−5.78115	+	17.7926i	−0.225888	+	0.695213i
$656$		0			0
$657$	2.61803	+	1.90211i	0.102139	+	0.0742085i
$658$		0			0
$659$	10.6525			0.414962			0.207481	−	0.978239i	$-0.433474\pi$
$659$	10.6525			0.414962			0.207481	+	0.978239i	$0.433474\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$		0			0
$663$	2.30902	+	1.67760i	0.0896748	+	0.0651525i
$664$		0			0
$665$	−14.2082	+	43.7284i	−0.550971	+	1.69571i
$666$		0			0
$667$	12.5623	−	9.12705i	0.486414	−	0.353401i
$668$		0			0
$669$	0.218847	+	0.673542i	0.00846112	+	0.0260406i
$670$		0			0
$671$	17.2082	+	19.5559i	0.664315	+	0.754948i
$672$		0			0
$673$	3.83688	+	11.8087i	0.147901	+	0.455192i	0.997373	−	0.0724420i	$-0.0230792\pi$
$673$	3.83688	+	11.8087i	0.147901	+	0.455192i	−0.849472	+	0.527634i	$0.823079\pi$
$674$		0			0
$675$	1.50000	−	1.08981i	0.0577350	−	0.0419470i
$676$		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
$679$	−34.0623	−	24.7477i	−1.30719	−	0.949730i
$680$		0			0
$681$	−24.8885			−0.953731
$682$		0			0
$683$	3.11146			0.119057			0.0595283	−	0.998227i	$-0.481040\pi$
$683$	3.11146			0.119057			0.0595283	+	0.998227i	$0.481040\pi$
$684$		0			0
$685$	15.8262	+	11.4984i	0.604689	+	0.439333i
$686$		0			0
$687$	−3.09017	+	9.51057i	−0.117897	+	0.362851i
$688$		0			0
$689$	13.7254	−	9.97210i	0.522897	−	0.379907i
$690$		0			0
$691$	8.12461	+	25.0050i	0.309075	+	0.951234i	0.978125	+	0.208017i	$0.0667010\pi$
$691$	8.12461	+	25.0050i	0.309075	+	0.951234i	−0.669050	+	0.743217i	$0.733299\pi$
$692$		0			0
$693$	−9.13525	+	3.94298i	−0.347020	+	0.149782i
$694$		0			0
$695$	−0.690983	−	2.12663i	−0.0262105	−	0.0806676i
$696$		0			0
$697$	15.6353	−	11.3597i	0.592228	−	0.430278i
$698$		0			0
$699$	−7.51722	+	23.1356i	−0.284327	+	0.875070i
$700$		0			0
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	0.738966	−	0.673743i	$-0.235315\pi$
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	−0.412415	+	0.910996i	$0.635315\pi$
$702$		0			0
$703$	−1.38197			−0.0521218
$704$		0			0
$705$	−4.23607			−0.159540
$706$		0			0
$707$	−7.28115	−	5.29007i	−0.273836	−	0.198953i
$708$		0			0
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	−0.100255	−	0.994962i	$-0.531966\pi$
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	0.665932	−	0.746012i	$-0.268034\pi$
$710$		0			0
$711$	7.66312	−	5.56758i	0.287389	−	0.208801i
$712$		0			0
$713$	3.06231	+	9.42481i	0.114684	+	0.352962i
$714$		0			0
$715$	7.80902	−	13.1760i	0.292041	−	0.492756i
$716$		0			0
$717$	0.791796	+	2.43690i	0.0295702	+	0.0910076i
$718$		0			0
$719$	−1.28115	+	0.930812i	−0.0477789	+	0.0347134i	−0.611418	−	0.791307i	$-0.709401\pi$
$719$	−1.28115	+	0.930812i	−0.0477789	+	0.0347134i	0.563639	+	0.826021i	$0.309401\pi$
$720$		0			0
$721$	−5.56231	+	17.1190i	−0.207151	+	0.637546i
$722$		0			0
$723$	−18.7082	−	13.5923i	−0.695766	−	0.505503i
$724$		0			0
$725$	8.29180			0.307950
$726$		0			0
$727$	−38.8541			−1.44102			−0.720509	−	0.693445i	$-0.756092\pi$
$727$	−38.8541			−1.44102			−0.720509	+	0.693445i	$0.756092\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−3.11803	+	9.59632i	−0.115325	+	0.354933i
$732$		0			0
$733$	30.5066	−	22.1643i	1.12679	−	0.818658i	0.141562	−	0.989929i	$-0.454787\pi$
$733$	30.5066	−	22.1643i	1.12679	−	0.818658i	0.985224	+	0.171271i	$0.0547875\pi$
$734$		0			0
$735$	1.61803	+	4.97980i	0.0596821	+	0.183683i
$736$		0			0
$737$	−16.1697	+	27.2829i	−0.595618	+	1.00498i
$738$		0			0
$739$	7.72542	+	23.7764i	0.284184	+	0.874629i	0.986642	+	0.162904i	$0.0520860\pi$
$739$	7.72542	+	23.7764i	0.284184	+	0.874629i	−0.702458	+	0.711726i	$0.747914\pi$
$740$		0			0
$741$	−8.35410	+	6.06961i	−0.306896	+	0.222973i
$742$		0			0
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	0.527108	+	0.849798i	$0.323276\pi$
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	−0.925938	+	0.377675i	$0.876724\pi$
$744$		0			0
$745$	31.7705	+	23.0826i	1.16398	+	0.845682i
$746$		0			0
$747$	−0.708204			−0.0259118
$748$		0			0
$749$	−12.7082			−0.464348
$750$		0			0
$751$	9.64590	+	7.00816i	0.351984	+	0.255731i	0.749701	−	0.661777i	$-0.230197\pi$
$751$	9.64590	+	7.00816i	0.351984	+	0.255731i	−0.397717	+	0.917508i	$0.630197\pi$
$752$		0			0
$753$	−2.40983	+	7.41669i	−0.0878191	+	0.270279i
$754$		0			0
$755$	−4.23607	+	3.07768i	−0.154166	+	0.112008i
$756$		0			0
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	0.961381	−	0.275220i	$-0.0887509\pi$
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	−0.939544	+	0.342428i	$0.888751\pi$
$758$		0			0
$759$	10.5729	−	4.56352i	0.383774	−	0.165645i
$760$		0			0
$761$	−9.54508	−	29.3768i	−0.346009	−	1.06491i	−0.961041	−	0.276404i	$-0.910857\pi$
$761$	−9.54508	−	29.3768i	−0.346009	−	1.06491i	0.615032	−	0.788502i	$-0.289143\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.30902	+	4.02874i	−0.0473276	+	0.145659i
$766$		0			0
$767$	14.7361	+	10.7064i	0.532089	+	0.386585i
$768$		0			0
$769$	12.6869			0.457502			0.228751	−	0.973485i	$-0.426536\pi$
$769$	12.6869			0.457502			0.228751	+	0.973485i	$0.426536\pi$
$770$		0			0
$771$	11.6738			0.420420
$772$		0			0
$773$	25.2812	+	18.3678i	0.909300	+	0.660645i	0.940838	−	0.338858i	$-0.110040\pi$
$773$	25.2812	+	18.3678i	0.909300	+	0.660645i	−0.0315378	+	0.999503i	$0.510040\pi$
$774$		0			0
$775$	−1.63525	+	5.03280i	−0.0587401	+	0.180783i
$776$		0			0
$777$	−0.572949	+	0.416272i	−0.0205544	+	0.0149337i
$778$		0			0
$779$	21.6074	+	66.5007i	0.774165	+	2.38264i
$780$		0			0
$781$	12.1869	+	13.8496i	0.436082	+	0.495577i
$782$		0			0
$783$	−1.38197	−	4.25325i	−0.0493874	−	0.151999i
$784$		0			0
$785$	−7.85410	+	5.70634i	−0.280325	+	0.203668i
$786$		0			0
$787$	3.18034	−	9.78808i	0.113367	−	0.348907i	−0.878236	−	0.478227i	$-0.841279\pi$
$787$	3.18034	−	9.78808i	0.113367	−	0.348907i	0.991603	+	0.129320i	$0.0412795\pi$
$788$		0			0
$789$	13.2082	+	9.59632i	0.470225	+	0.341638i
$790$		0			0
$791$	−2.12461			−0.0755425
$792$		0			0
$793$	13.8541			0.491974
$794$		0			0
$795$	20.3713	+	14.8006i	0.722496	+	0.524924i
$796$		0			0
$797$	3.32624	−	10.2371i	0.117821	−	0.362617i	−0.874704	−	0.484658i	$-0.838944\pi$
$797$	3.32624	−	10.2371i	0.117821	−	0.362617i	0.992525	+	0.122041i	$0.0389440\pi$
$798$		0			0
$799$	2.11803	−	1.53884i	0.0749307	−	0.0544403i
$800$		0			0
$801$	0.163119	+	0.502029i	0.00576353	+	0.0177383i
$802$		0			0
$803$	1.00000	+	10.6861i	0.0352892	+	0.377106i
$804$		0			0
$805$	−8.42705	−	25.9358i	−0.297015	−	0.914117i
$806$		0			0
$807$	12.5623	−	9.12705i	0.442214	−	0.321287i
$808$		0			0
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	−0.884654	−	0.466249i	$-0.845605\pi$
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	0.989754	+	0.142783i	$0.0456052\pi$
$810$		0			0
$811$	2.63525	+	1.91462i	0.0925363	+	0.0672316i	0.633091	−	0.774077i	$-0.281786\pi$
$811$	2.63525	+	1.91462i	0.0925363	+	0.0672316i	−0.540555	+	0.841309i	$0.681786\pi$
$812$		0			0
$813$	−27.2705			−0.956419
$814$		0			0
$815$	47.8328			1.67551
$816$		0			0
$817$	−29.5344	−	21.4580i	−1.03328	−	0.750721i
$818$		0			0
$819$	−1.63525	+	5.03280i	−0.0571404	+	0.175860i
$820$		0			0
$821$	−32.6976	+	23.7562i	−1.14115	+	0.829096i	−0.987279	−	0.158995i	$-0.949175\pi$
$821$	−32.6976	+	23.7562i	−1.14115	+	0.829096i	−0.153873	+	0.988091i	$0.549175\pi$
$822$		0			0
$823$	10.9615	+	33.7360i	0.382094	+	1.17596i	0.938567	+	0.345098i	$0.112154\pi$
$823$	10.9615	+	33.7360i	0.382094	+	1.17596i	−0.556473	+	0.830866i	$0.687846\pi$
$824$		0			0
$825$	6.00000	+	1.34708i	0.208893	+	0.0468994i
$826$		0			0
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	−0.649880	−	0.760037i	$-0.725181\pi$
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	0.0790257	−	0.996873i	$-0.474819\pi$
$828$		0			0
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	−0.807859	−	0.589375i	$-0.799374\pi$
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	0.310887	+	0.950447i	$0.399374\pi$
$830$		0			0
$831$	−9.44427	+	29.0665i	−0.327618	+	1.00831i
$832$		0			0
$833$	−2.61803	−	1.90211i	−0.0907095	−	0.0659043i
$834$		0			0
$835$	26.2705			0.909128
$836$		0			0
$837$	2.85410			0.0986522
$838$		0			0
$839$	−29.6976	−	21.5765i	−1.02527	−	0.744905i	−0.0579164	−	0.998321i	$-0.518446\pi$
$839$	−29.6976	−	21.5765i	−1.02527	−	0.744905i	−0.967357	+	0.253417i	$0.918446\pi$
$840$		0			0
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$		0			0
$843$	−0.618034	+	0.449028i	−0.0212862	+	0.0154653i
$844$		0			0
$845$	8.00000	+	24.6215i	0.275208	+	0.847004i
$846$		0			0
$847$	−29.8328	−	14.1068i	−1.02507	−	0.484717i
$848$		0			0
$849$	0.0557281	+	0.171513i	0.00191258	+	0.00588633i
$850$		0			0
$851$	0.663119	−	0.481784i	0.0227314	−	0.0165153i
$852$		0			0
$853$	−3.07295	+	9.45756i	−0.105216	+	0.323821i	−0.989781	−	0.142596i	$-0.954455\pi$
$853$	−3.07295	+	9.45756i	−0.105216	+	0.323821i	0.884565	+	0.466416i	$0.154455\pi$
$854$		0			0
$855$	−12.3992	−	9.00854i	−0.424043	−	0.308085i
$856$		0			0
$857$	47.7214			1.63013			0.815065	−	0.579369i	$-0.196701\pi$
$857$	47.7214			1.63013			0.815065	+	0.579369i	$0.196701\pi$
$858$		0			0
$859$	−7.11146			−0.242640			−0.121320	−	0.992613i	$-0.538713\pi$
$859$	−7.11146			−0.242640			−0.121320	+	0.992613i	$0.538713\pi$
$860$		0			0
$861$	28.9894	+	21.0620i	0.987955	+	0.717791i
$862$		0			0
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	−0.993911	−	0.110183i	$-0.964856\pi$
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	0.868855	+	0.495067i	$0.164856\pi$
$864$		0			0
$865$	32.5795	−	23.6704i	1.10774	−	0.804818i
$866$		0			0
$867$	4.44427	+	13.6781i	0.150935	+	0.464531i
$868$		0			0
$869$	30.6525	+	6.88191i	1.03981	+	0.233453i
$870$		0			0
$871$	5.21227	+	16.0417i	0.176611	+	0.543553i
$872$		0			0
$873$	11.3541	−	8.24924i	0.384278	−	0.279194i
$874$		0			0
$875$	−7.63525	+	23.4989i	−0.258119	+	0.794408i
$876$		0			0
$877$	−5.19098	−	3.77147i	−0.175287	−	0.127353i	0.496682	−	0.867932i	$-0.334551\pi$
$877$	−5.19098	−	3.77147i	−0.175287	−	0.127353i	−0.671969	+	0.740579i	$0.734551\pi$
$878$		0			0
$879$	−0.0557281			−0.00187966
$880$		0			0
$881$	13.9098			0.468634			0.234317	−	0.972160i	$-0.424715\pi$
$881$	13.9098			0.468634			0.234317	+	0.972160i	$0.424715\pi$
$882$		0			0
$883$	8.56231	+	6.22088i	0.288145	+	0.209349i	0.722462	−	0.691411i	$-0.243010\pi$
$883$	8.56231	+	6.22088i	0.288145	+	0.209349i	−0.434318	+	0.900760i	$0.643010\pi$
$884$		0			0
$885$	−8.35410	+	25.7113i	−0.280820	+	0.864275i
$886$		0			0
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	−0.546293	−	0.837594i	$-0.683962\pi$
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	0.627785	+	0.778386i	$0.283962\pi$
$888$		0			0
$889$	−3.43769	−	10.5801i	−0.115297	−	0.354846i
$890$		0			0
$891$	−0.309017	−	3.30220i	−0.0103525	−	0.110628i
$892$		0			0
$893$	2.92705	+	9.00854i	0.0979500	+	0.301459i
$894$		0			0
$895$	4.73607	−	3.44095i	0.158309	−	0.115018i
$896$		0			0
$897$	1.89261	−	5.82485i	0.0631924	−	0.194486i
$898$		0			0
$899$	10.3262	+	7.50245i	0.344399	+	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$		0			0
$903$	−18.7082			−0.622570
$904$		0			0
$905$	−37.0066	−	26.8869i	−1.23014	−	0.893749i
$906$		0			0
$907$	13.2812	−	40.8752i	0.440993	−	1.35724i	−0.445825	−	0.895120i	$-0.647090\pi$
$907$	13.2812	−	40.8752i	0.440993	−	1.35724i	0.886818	−	0.462118i	$-0.152910\pi$
$908$		0			0
$909$	2.42705	−	1.76336i	0.0805002	−	0.0584868i
$910$		0			0
$911$	−5.57953	−	17.1720i	−0.184858	−	0.568934i	0.815088	−	0.579337i	$-0.196689\pi$
$911$	−5.57953	−	17.1720i	−0.184858	−	0.568934i	−0.999946	+	0.0104029i	$0.996689\pi$
$912$		0			0
$913$	−1.55166	−	1.76336i	−0.0513525	−	0.0583586i
$914$		0			0
$915$	6.35410	+	19.5559i	0.210060	+	0.646499i
$916$		0			0
$917$	17.3435	−	12.6008i	0.572731	−	0.416114i
$918$		0			0
$919$	−14.5106	+	44.6592i	−0.478662	+	1.47317i	0.362293	+	0.932064i	$0.381994\pi$
$919$	−14.5106	+	44.6592i	−0.478662	+	1.47317i	−0.840955	+	0.541106i	$0.818006\pi$
$920$		0			0
$921$	−0.454915	−	0.330515i	−0.0149900	−	0.0108908i
$922$		0			0
$923$	9.81153			0.322950
$924$		0			0
$925$	0.437694			0.0143913
$926$		0			0
$927$	−4.85410	−	3.52671i	−0.159430	−	0.115832i
$928$		0			0
$929$	−10.1631	+	31.2789i	−0.333441	+	1.02623i	0.634044	+	0.773297i	$0.281394\pi$
$929$	−10.1631	+	31.2789i	−0.333441	+	1.02623i	−0.967485	+	0.252929i	$0.918606\pi$
$930$		0			0
$931$	9.47214	−	6.88191i	0.310437	−	0.225545i
$932$		0			0
$933$	0.781153	+	2.40414i	0.0255738	+	0.0787081i
$934$		0			0
$935$	−12.8992	+	5.56758i	−0.421849	+	0.182079i
$936$		0			0
$937$	−5.12868	−	15.7844i	−0.167547	−	0.515655i	0.831668	−	0.555273i	$-0.187386\pi$
$937$	−5.12868	−	15.7844i	−0.167547	−	0.515655i	−0.999215	+	0.0396173i	$0.987386\pi$
$938$		0			0
$939$	20.8992	−	15.1841i	0.682019	−	0.495516i
$940$		0			0
$941$	−13.7918	+	42.4468i	−0.449600	+	1.38373i	0.427760	+	0.903892i	$0.359303\pi$
$941$	−13.7918	+	42.4468i	−0.449600	+	1.38373i	−0.877360	+	0.479833i	$0.840697\pi$
$942$		0			0
$943$	−33.5517	−	24.3767i	−1.09259	−	0.793815i
$944$		0			0
$945$	−7.85410			−0.255494
$946$		0			0
$947$	−18.3262			−0.595523			−0.297761	−	0.954640i	$-0.596240\pi$
$947$	−18.3262			−0.595523			−0.297761	+	0.954640i	$0.596240\pi$
$948$		0			0
$949$	4.61803	+	3.35520i	0.149908	+	0.108914i
$950$		0			0
$951$	5.98278	−	18.4131i	0.194005	−	0.597086i
$952$		0			0
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.960167	−	0.279426i	$-0.909856\pi$
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.0309585	+	0.999521i	$0.509856\pi$
$954$		0			0
$955$	−6.04508	−	18.6049i	−0.195614	−	0.602039i
$956$		0			0
$957$	7.56231	−	12.7598i	0.244455	−	0.412465i
$958$		0			0
$959$	−6.92705	−	21.3193i	−0.223686	−	0.688435i
$960$		0			0
$961$	18.4894	−	13.4333i	0.596431	−	0.433332i
$962$		0			0
$963$	1.30902	−	4.02874i	0.0421825	−	0.129824i
$964$		0			0
$965$	−39.3156	−	28.5645i	−1.26561	−	0.919522i
$966$		0			0
$967$	34.6869			1.11546			0.557728	−	0.830024i	$-0.311673\pi$
$967$	34.6869			1.11546			0.557728	+	0.830024i	$0.311673\pi$
$968$		0			0
$969$	9.47214			0.304289
$970$		0			0
$971$	30.5623	+	22.2048i	0.980791	+	0.712586i	0.957885	−	0.287151i	$-0.0927082\pi$
$971$	30.5623	+	22.2048i	0.980791	+	0.712586i	0.0229058	+	0.999738i	$0.492708\pi$
$972$		0			0
$973$	−0.791796	+	2.43690i	−0.0253838	+	0.0781234i
$974$		0			0
$975$	2.64590	−	1.92236i	0.0847366	−	0.0615647i
$976$		0			0
$977$	−1.43363	−	4.41226i	−0.0458658	−	0.141161i	0.925501	−	0.378745i	$-0.123644\pi$
$977$	−1.43363	−	4.41226i	−0.0458658	−	0.141161i	−0.971367	+	0.237585i	$0.923644\pi$
$978$		0			0
$979$	−0.892609	+	1.50609i	−0.0285279	+	0.0481347i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	−0.881416	−	0.472340i	$-0.843409\pi$
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	0.176849	+	0.984238i	$0.443409\pi$
$984$		0			0
$985$	−19.7254	+	60.7086i	−0.628504	+	1.93434i
$986$		0			0
$987$	3.92705	+	2.85317i	0.124999	+	0.0908174i
$988$		0			0
$989$	21.6525			0.688509
$990$		0			0
$991$	−21.2705			−0.675680			−0.337840	−	0.941204i	$-0.609696\pi$
$991$	−21.2705			−0.675680			−0.337840	+	0.941204i	$0.609696\pi$
$992$		0			0
$993$	−21.5172	−	15.6332i	−0.682828	−	0.496104i
$994$		0			0
$995$	−13.5172	+	41.6017i	−0.428525	+	1.31886i
$996$		0			0
$997$	10.5000	−	7.62870i	0.332538	−	0.241603i	−0.408969	−	0.912548i	$-0.634111\pi$
$997$	10.5000	−	7.62870i	0.332538	−	0.241603i	0.741507	+	0.670945i	$0.234111\pi$
$998$		0			0
$999$	−0.0729490	−	0.224514i	−0.00230800	−	0.00710331i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(-0.809017 + 2.48990i) q^{5} +(2.42705 - 1.76336i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{3} +(-0.809017 + 2.48990i) q^{5} +(2.42705 - 1.76336i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-1.69098 + 2.85317i) q^{11} +(0.545085 + 1.67760i) q^{13} +(-2.11803 + 1.53884i) q^{15} +(0.500000 - 1.53884i) q^{17} +(4.73607 + 3.44095i) q^{19} +3.00000 q^{21} -3.47214 q^{23} +(-1.50000 - 1.08981i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-3.61803 + 2.62866i) q^{29} +(-0.881966 - 2.71441i) q^{31} +(-3.04508 + 1.31433i) q^{33} +(2.42705 + 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(9.66312 + 7.02067i) q^{41} -6.23607 q^{43} -2.61803 q^{45} +(1.30902 + 0.951057i) q^{47} +(0.618034 - 1.90211i) q^{49} +(1.30902 - 0.951057i) q^{51} +(-2.97214 - 9.14729i) q^{53} +(-5.73607 - 6.51864i) q^{55} +(1.80902 + 5.56758i) q^{57} +(8.35410 - 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(2.42705 + 1.76336i) q^{63} -4.61803 q^{65} +9.56231 q^{67} +(-2.80902 - 2.04087i) q^{69} +(1.71885 - 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(-0.572949 - 1.76336i) q^{75} +(0.927051 + 9.90659i) q^{77} +(-2.92705 - 9.00854i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.218847 + 0.673542i) q^{83} +(3.42705 + 2.48990i) q^{85} -4.47214 q^{87} +0.527864 q^{89} +(4.28115 + 3.11044i) q^{91} +(0.881966 - 2.71441i) q^{93} +(-12.3992 + 9.00854i) q^{95} +(-4.33688 - 13.3475i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 - q^5 + 3 * q^7 - q^9	\( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9} - 9 q^{11} - 9 q^{13} - 4 q^{15} + 2 q^{17} + 10 q^{19} + 12 q^{21} + 4 q^{23} - 6 q^{25} + q^{27} - 10 q^{29} - 8 q^{31} - q^{33} + 3 q^{35} - 3 q^{37} + 9 q^{39} + 23 q^{41} - 16 q^{43} - 6 q^{45} + 3 q^{47} - 2 q^{49} + 3 q^{51} + 6 q^{53} - 14 q^{55} + 5 q^{57} + 20 q^{59} + 3 q^{61} + 3 q^{63} - 14 q^{65} - 2 q^{67} - 9 q^{69} + 27 q^{71} + 6 q^{73} - 9 q^{75} - 3 q^{77} - 5 q^{79} - q^{81} - 21 q^{83} + 7 q^{85} + 20 q^{89} - 3 q^{91} + 8 q^{93} - 25 q^{95} - 33 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 - q^5 + 3 * q^7 - q^9 - 9 * q^11 - 9 * q^13 - 4 * q^15 + 2 * q^17 + 10 * q^19 + 12 * q^21 + 4 * q^23 - 6 * q^25 + q^27 - 10 * q^29 - 8 * q^31 - q^33 + 3 * q^35 - 3 * q^37 + 9 * q^39 + 23 * q^41 - 16 * q^43 - 6 * q^45 + 3 * q^47 - 2 * q^49 + 3 * q^51 + 6 * q^53 - 14 * q^55 + 5 * q^57 + 20 * q^59 + 3 * q^61 + 3 * q^63 - 14 * q^65 - 2 * q^67 - 9 * q^69 + 27 * q^71 + 6 * q^73 - 9 * q^75 - 3 * q^77 - 5 * q^79 - q^81 - 21 * q^83 + 7 * q^85 + 20 * q^89 - 3 * q^91 + 8 * q^93 - 25 * q^95 - 33 * q^97 - 4 * q^99

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