LMFDB - Embedded newform 825.2.bx.c.724.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(-3.07768 + 4.23607i) q^{7} +(1.31433 + 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(-3.07768 + 4.23607i) q^{7} +(1.31433 + 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.23607 + 3.07768i) q^{11} -0.618034i q^{12} +(-3.07768 - 1.00000i) q^{13} +(6.85410 - 4.97980i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(-1.90211 + 0.618034i) q^{17} +(0.951057 - 1.30902i) q^{18} +(4.04508 - 2.93893i) q^{19} +5.23607 q^{21} +(3.44095 - 4.11803i) q^{22} -4.61803i q^{23} +(0.690983 - 2.12663i) q^{24} +(4.23607 + 3.07768i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-3.07768 + 1.00000i) q^{28} +(0.690983 + 0.502029i) q^{29} +(2.16312 - 6.65740i) q^{31} +3.38197i q^{32} +(3.21644 - 0.809017i) q^{33} +3.23607 q^{34} +(-0.500000 + 0.363271i) q^{36} +(0.865300 - 1.19098i) q^{37} +(-7.69421 + 2.50000i) q^{38} +(1.00000 + 3.07768i) q^{39} +(-9.28115 + 6.74315i) q^{41} +(-8.05748 - 2.61803i) q^{42} -9.09017i q^{43} +(-1.73607 + 1.08981i) q^{44} +(-2.30902 + 7.10642i) q^{46} +(3.57971 + 4.92705i) q^{47} +(-2.85317 + 3.92705i) q^{48} +(-6.30902 - 19.4172i) q^{49} +(1.61803 + 1.17557i) q^{51} +(-1.17557 - 1.61803i) q^{52} +(5.11855 + 1.66312i) q^{53} -1.61803 q^{54} -11.7082 q^{56} +(-4.75528 - 1.54508i) q^{57} +(-0.812299 - 1.11803i) q^{58} +(5.42705 + 3.94298i) q^{59} +(2.16312 + 6.65740i) q^{61} +(-6.65740 + 9.16312i) q^{62} +(-3.07768 - 4.23607i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(-5.35410 - 0.363271i) q^{66} -11.6180i q^{67} +(-1.17557 - 0.381966i) q^{68} +(-3.73607 + 2.71441i) q^{69} +(-2.47214 - 7.60845i) q^{71} +(-2.12663 + 0.690983i) q^{72} +(2.66141 - 3.66312i) q^{73} +(-1.92705 + 1.40008i) q^{74} +3.09017 q^{76} +(-9.23305 - 14.7082i) q^{77} -5.23607i q^{78} +(-0.954915 + 2.93893i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(17.6538 - 5.73607i) q^{82} +(7.33094 - 2.38197i) q^{83} +(2.61803 + 1.90211i) q^{84} +(-4.54508 + 13.9883i) q^{86} -0.854102i q^{87} +(-7.19218 + 1.80902i) q^{88} -4.14590 q^{89} +(13.7082 - 9.95959i) q^{91} +(1.67760 - 2.30902i) q^{92} +(-6.65740 + 2.16312i) q^{93} +(-3.04508 - 9.37181i) q^{94} +(2.73607 - 1.98787i) q^{96} +(2.40414 + 0.781153i) q^{97} +33.0344i q^{98} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9	$ 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 28 * q^14 - 12 * q^16 + 10 * q^19 + 24 * q^21 + 10 * q^24 + 16 * q^26 + 10 * q^29 - 14 * q^31 + 8 * q^34 - 4 * q^36 + 8 * q^39 - 34 * q^41 + 4 * q^44 - 14 * q^46 - 46 * q^49 + 4 * q^51 - 4 * q^54 - 40 * q^56 + 30 * q^59 - 14 * q^61 - 6 * q^64 - 16 * q^66 - 12 * q^69 + 16 * q^71 - 2 * q^74 - 20 * q^76 - 30 * q^79 - 2 * q^81 + 12 * q^84 - 14 * q^86 - 60 * q^89 + 56 * q^91 - 2 * q^94 + 4 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

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 $

$2$	−1.53884	−	0.500000i	−1.08813	−	0.353553i	−0.290604	−	0.956844i	$-0.593856\pi$
$2$	−1.53884	−	0.500000i	−1.08813	−	0.353553i	−0.797522	+	0.603290i	$0.793856\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	0.500000	+	0.363271i	0.250000	+	0.181636i
$5$		0			0
$5$		0			0
$6$	0.500000	+	1.53884i	0.204124	+	0.628230i
$7$	−3.07768	+	4.23607i	−1.16326	+	1.60108i	−0.464830	+	0.885400i	$0.653885\pi$
$7$	−3.07768	+	4.23607i	−1.16326	+	1.60108i	−0.698425	+	0.715683i	$0.746115\pi$
$8$	1.31433	+	1.80902i	0.464685	+	0.639584i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$		−	0.618034i		−	0.178411i
$13$	−3.07768	−	1.00000i	−0.853596	−	0.277350i	−0.150644	−	0.988588i	$-0.548135\pi$
$13$	−3.07768	−	1.00000i	−0.853596	−	0.277350i	−0.702951	+	0.711238i	$0.748135\pi$
$14$	6.85410	−	4.97980i	1.83184	−	1.33091i
$15$		0			0
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	−1.90211	+	0.618034i	−0.461330	+	0.149895i	−0.530456	−	0.847713i	$-0.677979\pi$
$17$	−1.90211	+	0.618034i	−0.461330	+	0.149895i	0.0691254	+	0.997608i	$0.477979\pi$
$18$	0.951057	−	1.30902i	0.224166	−	0.308538i
$19$	4.04508	−	2.93893i	0.928006	−	0.674236i	−0.0174977	−	0.999847i	$-0.505570\pi$
$19$	4.04508	−	2.93893i	0.928006	−	0.674236i	0.945504	+	0.325611i	$0.105570\pi$
$20$		0			0
$21$	5.23607			1.14260
$22$	3.44095	−	4.11803i	0.733614	−	0.877968i
$23$		−	4.61803i		−	0.962927i	−0.876466	−	0.481463i	$-0.840105\pi$
$23$		−	4.61803i		−	0.962927i	0.876466	−	0.481463i	$-0.159895\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$		0			0
$26$	4.23607	+	3.07768i	0.830761	+	0.603583i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−3.07768	+	1.00000i	−0.581628	+	0.188982i
$29$	0.690983	+	0.502029i	0.128312	+	0.0932244i	0.650090	−	0.759857i	$-0.274731\pi$
$29$	0.690983	+	0.502029i	0.128312	+	0.0932244i	−0.521778	+	0.853081i	$0.674731\pi$
$30$		0			0
$31$	2.16312	−	6.65740i	0.388508	−	1.19570i	−0.545396	−	0.838179i	$-0.683621\pi$
$31$	2.16312	−	6.65740i	0.388508	−	1.19570i	0.933904	−	0.357525i	$-0.116379\pi$
$32$			3.38197i			0.597853i
$33$	3.21644	−	0.809017i	0.559910	−	0.140832i
$34$	3.23607			0.554981
$35$		0			0
$36$	−0.500000	+	0.363271i	−0.0833333	+	0.0605452i
$37$	0.865300	−	1.19098i	0.142254	−	0.195796i	−0.731945	−	0.681364i	$-0.761387\pi$
$37$	0.865300	−	1.19098i	0.142254	−	0.195796i	0.874199	+	0.485568i	$0.161387\pi$
$38$	−7.69421	+	2.50000i	−1.24817	+	0.405554i
$39$	1.00000	+	3.07768i	0.160128	+	0.492824i
$40$		0			0
$41$	−9.28115	+	6.74315i	−1.44947	+	1.05310i	−0.463518	+	0.886087i	$0.653413\pi$
$41$	−9.28115	+	6.74315i	−1.44947	+	1.05310i	−0.985954	+	0.167016i	$0.946587\pi$
$42$	−8.05748	−	2.61803i	−1.24330	−	0.403971i
$43$		−	9.09017i		−	1.38624i	−0.720823	−	0.693119i	$-0.756236\pi$
$43$		−	9.09017i		−	1.38624i	0.720823	−	0.693119i	$-0.243764\pi$
$44$	−1.73607	+	1.08981i	−0.261722	+	0.164296i
$45$		0			0
$46$	−2.30902	+	7.10642i	−0.340446	+	1.04778i
$47$	3.57971	+	4.92705i	0.522155	+	0.718684i	0.985910	−	0.167279i	$-0.0534982\pi$
$47$	3.57971	+	4.92705i	0.522155	+	0.718684i	−0.463755	+	0.885964i	$0.653498\pi$
$48$	−2.85317	+	3.92705i	−0.411820	+	0.566821i
$49$	−6.30902	−	19.4172i	−0.901288	−	2.77388i
$50$		0			0
$51$	1.61803	+	1.17557i	0.226570	+	0.164613i
$52$	−1.17557	−	1.61803i	−0.163022	−	0.224381i
$53$	5.11855	+	1.66312i	0.703087	+	0.228447i	0.638675	−	0.769476i	$-0.279483\pi$
$53$	5.11855	+	1.66312i	0.703087	+	0.228447i	0.0644122	+	0.997923i	$0.479483\pi$
$54$	−1.61803			−0.220187
$55$		0			0
$56$	−11.7082			−1.56457
$57$	−4.75528	−	1.54508i	−0.629853	−	0.204652i
$58$	−0.812299	−	1.11803i	−0.106660	−	0.146805i
$59$	5.42705	+	3.94298i	0.706542	+	0.513333i	0.882056	−	0.471144i	$-0.156159\pi$
$59$	5.42705	+	3.94298i	0.706542	+	0.513333i	−0.175514	+	0.984477i	$0.556159\pi$
$60$		0			0
$61$	2.16312	+	6.65740i	0.276959	+	0.852392i	0.988694	+	0.149945i	$0.0479095\pi$
$61$	2.16312	+	6.65740i	0.276959	+	0.852392i	−0.711735	+	0.702448i	$0.752090\pi$
$62$	−6.65740	+	9.16312i	−0.845490	+	1.16372i
$63$	−3.07768	−	4.23607i	−0.387752	−	0.533694i
$64$	−1.30902	+	4.02874i	−0.163627	+	0.503593i
$65$		0			0
$66$	−5.35410	−	0.363271i	−0.659044	−	0.0447156i
$67$		−	11.6180i		−	1.41937i	−0.704520	−	0.709684i	$-0.748838\pi$
$67$		−	11.6180i		−	1.41937i	0.704520	−	0.709684i	$-0.251162\pi$
$68$	−1.17557	−	0.381966i	−0.142559	−	0.0463202i
$69$	−3.73607	+	2.71441i	−0.449770	+	0.326777i
$70$		0			0
$71$	−2.47214	−	7.60845i	−0.293389	−	0.902957i	−0.983758	−	0.179500i	$-0.942552\pi$
$71$	−2.47214	−	7.60845i	−0.293389	−	0.902957i	0.690369	−	0.723457i	$-0.257448\pi$
$72$	−2.12663	+	0.690983i	−0.250625	+	0.0814331i
$73$	2.66141	−	3.66312i	0.311495	−	0.428736i	−0.624352	−	0.781143i	$-0.714637\pi$
$73$	2.66141	−	3.66312i	0.311495	−	0.428736i	0.935847	+	0.352408i	$0.114637\pi$
$74$	−1.92705	+	1.40008i	−0.224015	+	0.162757i
$75$		0			0
$76$	3.09017			0.354467
$77$	−9.23305	−	14.7082i	−1.05220	−	1.67616i
$78$		−	5.23607i		−	0.592868i
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	−0.990295	−	0.138985i	$-0.955616\pi$
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	0.882858	+	0.469640i	$0.155616\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	17.6538	−	5.73607i	1.94954	−	0.633443i
$83$	7.33094	−	2.38197i	0.804675	−	0.261455i	0.122334	−	0.992489i	$-0.460962\pi$
$83$	7.33094	−	2.38197i	0.804675	−	0.261455i	0.682341	+	0.731034i	$0.260962\pi$
$84$	2.61803	+	1.90211i	0.285651	+	0.207538i
$85$		0			0
$86$	−4.54508	+	13.9883i	−0.490109	+	1.50840i
$87$		−	0.854102i		−	0.0915693i
$88$	−7.19218	+	1.80902i	−0.766689	+	0.192842i
$89$	−4.14590			−0.439464			−0.219732	−	0.975560i	$-0.570518\pi$
$89$	−4.14590			−0.439464			−0.219732	+	0.975560i	$0.570518\pi$
$90$		0			0
$91$	13.7082	−	9.95959i	1.43701	−	1.04405i
$92$	1.67760	−	2.30902i	0.174902	−	0.240732i
$93$	−6.65740	+	2.16312i	−0.690340	+	0.224305i
$94$	−3.04508	−	9.37181i	−0.314077	−	0.966628i
$95$		0			0
$96$	2.73607	−	1.98787i	0.279249	−	0.202886i
$97$	2.40414	+	0.781153i	0.244104	+	0.0793141i	0.428514	−	0.903535i	$-0.359037\pi$
$97$	2.40414	+	0.781153i	0.244104	+	0.0793141i	−0.184410	+	0.982849i	$0.559037\pi$
$98$			33.0344i			3.33698i
$99$	−2.54508	−	2.12663i	−0.255791	−	0.213734i
$100$		0			0
$101$	6.04508	−	18.6049i	0.601508	−	1.85125i	0.0822950	−	0.996608i	$-0.473775\pi$
$101$	6.04508	−	18.6049i	0.601508	−	1.85125i	0.519213	−	0.854645i	$-0.326225\pi$
$102$	−1.90211	−	2.61803i	−0.188337	−	0.259224i
$103$	−2.71441	+	3.73607i	−0.267459	+	0.368126i	−0.921530	−	0.388308i	$-0.873060\pi$
$103$	−2.71441	+	3.73607i	−0.267459	+	0.368126i	0.654071	+	0.756433i	$0.273060\pi$
$104$	−2.23607	−	6.88191i	−0.219265	−	0.674827i
$105$		0			0
$106$	−7.04508	−	5.11855i	−0.684279	−	0.497158i
$107$	2.26538	+	3.11803i	0.219003	+	0.301432i	0.904356	−	0.426780i	$-0.140352\pi$
$107$	2.26538	+	3.11803i	0.219003	+	0.301432i	−0.685353	+	0.728211i	$0.740352\pi$
$108$	0.587785	+	0.190983i	0.0565597	+	0.0183773i
$109$	−10.8541			−1.03963			−0.519817	−	0.854278i	$-0.674000\pi$
$109$	−10.8541			−1.03963			−0.519817	+	0.854278i	$0.674000\pi$
$110$		0			0
$111$	−1.47214			−0.139729
$112$	24.1724	+	7.85410i	2.28408	+	0.742143i
$113$	−2.04087	−	2.80902i	−0.191989	−	0.264250i	0.702161	−	0.712019i	$-0.252219\pi$
$113$	−2.04087	−	2.80902i	−0.191989	−	0.264250i	−0.894150	+	0.447769i	$0.852219\pi$
$114$	6.54508	+	4.75528i	0.613003	+	0.445373i
$115$		0			0
$116$	0.163119	+	0.502029i	0.0151452	+	0.0466122i
$117$	1.90211	−	2.61803i	0.175850	−	0.242037i
$118$	−6.37988	−	8.78115i	−0.587316	−	0.808371i
$119$	3.23607	−	9.95959i	0.296650	−	0.912994i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$		−	11.3262i		−	1.02543i
$123$	10.9106	+	3.54508i	0.983780	+	0.319650i
$124$	3.50000	−	2.54290i	0.314309	−	0.228359i
$125$		0			0
$126$	2.61803	+	8.05748i	0.233233	+	0.717817i
$127$	1.84911	−	0.600813i	0.164082	−	0.0533135i	−0.225824	−	0.974168i	$-0.572507\pi$
$127$	1.84911	−	0.600813i	0.164082	−	0.0533135i	0.389906	+	0.920855i	$0.372507\pi$
$128$	8.00448	−	11.0172i	0.707503	−	0.973794i
$129$	−7.35410	+	5.34307i	−0.647493	+	0.470431i
$130$		0			0
$131$	−9.18034			−0.802090			−0.401045	−	0.916058i	$-0.631353\pi$
$131$	−9.18034			−0.802090			−0.401045	+	0.916058i	$0.631353\pi$
$132$	1.90211	+	0.763932i	0.165558	+	0.0664917i
$133$			26.1803i			2.27012i
$134$	−5.80902	+	17.8783i	−0.501823	+	1.54445i
$135$		0			0
$136$	−3.61803	−	2.62866i	−0.310244	−	0.225405i
$137$	−5.03280	+	1.63525i	−0.429981	+	0.139709i	−0.516008	−	0.856584i	$-0.672583\pi$
$137$	−5.03280	+	1.63525i	−0.429981	+	0.139709i	0.0860276	+	0.996293i	$0.472583\pi$
$138$	7.10642	−	2.30902i	0.604939	−	0.196557i
$139$	−0.954915	−	0.693786i	−0.0809948	−	0.0588462i	0.546551	−	0.837426i	$-0.315940\pi$
$139$	−0.954915	−	0.693786i	−0.0809948	−	0.0588462i	−0.627546	+	0.778580i	$0.715940\pi$
$140$		0			0
$141$	1.88197	−	5.79210i	0.158490	−	0.487782i
$142$			12.9443i			1.08626i
$143$	6.88191	−	8.23607i	0.575494	−	0.688735i
$144$	4.85410			0.404508
$145$		0			0
$146$	−5.92705	+	4.30625i	−0.490526	+	0.356388i
$147$	−12.0005	+	16.5172i	−0.989782	+	1.36232i
$148$	0.865300	−	0.281153i	0.0711272	−	0.0231106i
$149$	6.21885	+	19.1396i	0.509468	+	1.56798i	0.793127	+	0.609056i	$0.208451\pi$
$149$	6.21885	+	19.1396i	0.509468	+	1.56798i	−0.283660	+	0.958925i	$0.591549\pi$
$150$		0			0
$151$	12.3262	−	8.95554i	1.00310	−	0.728791i	0.0403454	−	0.999186i	$-0.487154\pi$
$151$	12.3262	−	8.95554i	1.00310	−	0.728791i	0.962750	+	0.270395i	$0.0871542\pi$
$152$	10.6331	+	3.45492i	0.862461	+	0.280231i
$153$		−	2.00000i		−	0.161690i
$154$	6.85410	+	27.2501i	0.552319	+	2.19588i
$155$		0			0
$156$	−0.618034	+	1.90211i	−0.0494823	+	0.152291i
$157$	−7.24518	−	9.97214i	−0.578228	−	0.795863i	0.415271	−	0.909698i	$-0.363687\pi$
$157$	−7.24518	−	9.97214i	−0.578228	−	0.795863i	−0.993500	+	0.113835i	$0.963687\pi$
$158$	2.93893	−	4.04508i	0.233808	−	0.321810i
$159$	−1.66312	−	5.11855i	−0.131894	−	0.405928i
$160$		0			0
$161$	19.5623	+	14.2128i	1.54173	+	1.12013i
$162$	0.951057	+	1.30902i	0.0747221	+	0.102846i
$163$	6.24112	+	2.02786i	0.488843	+	0.158835i	0.543059	−	0.839695i	$-0.317266\pi$
$163$	6.24112	+	2.02786i	0.488843	+	0.158835i	−0.0542163	+	0.998529i	$0.517266\pi$
$164$	−7.09017			−0.553649
$165$		0			0
$166$	−12.4721			−0.968025
$167$	8.59226	+	2.79180i	0.664889	+	0.216036i	0.621968	−	0.783043i	$-0.286333\pi$
$167$	8.59226	+	2.79180i	0.664889	+	0.216036i	0.0429216	+	0.999078i	$0.486333\pi$
$168$	6.88191	+	9.47214i	0.530951	+	0.730791i
$169$	−2.04508	−	1.48584i	−0.157314	−	0.114295i
$170$		0			0
$171$	1.54508	+	4.75528i	0.118156	+	0.363646i
$172$	3.30220	−	4.54508i	0.251790	−	0.346559i
$173$	−9.73508	−	13.3992i	−0.740144	−	1.01872i	−0.998610	−	0.0527010i	$-0.983217\pi$
$173$	−9.73508	−	13.3992i	−0.740144	−	1.01872i	0.258466	−	0.966020i	$-0.416783\pi$
$174$	−0.427051	+	1.31433i	−0.0323747	+	0.0996389i
$175$		0			0
$176$	16.0623	+	1.08981i	1.21074	+	0.0821478i
$177$		−	6.70820i		−	0.504219i
$178$	6.37988	+	2.07295i	0.478192	+	0.155374i
$179$	−8.51722	+	6.18812i	−0.636607	+	0.462522i	−0.858683	−	0.512507i	$-0.828717\pi$
$179$	−8.51722	+	6.18812i	−0.636607	+	0.462522i	0.222076	+	0.975029i	$0.428717\pi$
$180$		0			0
$181$	−0.236068	−	0.726543i	−0.0175468	−	0.0540035i	0.941900	−	0.335894i	$-0.109038\pi$
$181$	−0.236068	−	0.726543i	−0.0175468	−	0.0540035i	−0.959447	+	0.281891i	$0.909038\pi$
$182$	−26.0746	+	8.47214i	−1.93277	+	0.627996i
$183$	4.11450	−	5.66312i	0.304152	−	0.418630i
$184$	8.35410	−	6.06961i	0.615873	−	0.447458i
$185$		0			0
$186$	11.3262			0.830480
$187$	0.449028	−	6.61803i	0.0328362	−	0.483959i
$188$			3.76393i			0.274513i
$189$	−1.61803	+	4.97980i	−0.117695	+	0.362227i
$190$		0			0
$191$	13.2812	+	9.64932i	0.960991	+	0.698200i	0.953381	−	0.301771i	$-0.0975777\pi$
$191$	13.2812	+	9.64932i	0.960991	+	0.698200i	0.00760993	+	0.999971i	$0.497578\pi$
$192$	4.02874	−	1.30902i	0.290749	−	0.0944702i
$193$	7.64121	−	2.48278i	0.550026	−	0.178714i	−0.0208024	−	0.999784i	$-0.506622\pi$
$193$	7.64121	−	2.48278i	0.550026	−	0.178714i	0.570829	+	0.821069i	$0.306622\pi$
$194$	−3.30902	−	2.40414i	−0.237574	−	0.172607i
$195$		0			0
$196$	3.89919	−	12.0005i	0.278513	−	0.857176i
$197$			9.76393i			0.695651i	0.937559	+	0.347826i	$0.113080\pi$
$197$			9.76393i			0.695651i	−0.937559	+	0.347826i	$0.886920\pi$
$198$	2.85317	+	4.54508i	0.202766	+	0.323005i
$199$	4.79837			0.340148			0.170074	−	0.985431i	$-0.445599\pi$
$199$	4.79837			0.340148			0.170074	+	0.985431i	$0.445599\pi$
$200$		0			0
$201$	−9.39919	+	6.82891i	−0.662968	+	0.481674i
$202$	−18.6049	+	25.6074i	−1.30903	+	1.80173i
$203$	−4.25325	+	1.38197i	−0.298520	+	0.0969950i
$204$	0.381966	+	1.17557i	0.0267430	+	0.0823064i
$205$		0			0
$206$	6.04508	−	4.39201i	0.421181	−	0.306006i
$207$	4.39201	+	1.42705i	0.305266	+	0.0991869i
$208$			15.7082i			1.08917i
$209$	4.04508	+	16.0822i	0.279804	+	1.11243i
$210$		0			0
$211$	0.881966	−	2.71441i	0.0607170	−	0.186868i	−0.916097	−	0.400956i	$-0.868678\pi$
$211$	0.881966	−	2.71441i	0.0607170	−	0.186868i	0.976814	+	0.214088i	$0.0686780\pi$
$212$	1.95511	+	2.69098i	0.134278	+	0.184817i
$213$	−4.70228	+	6.47214i	−0.322195	+	0.443463i
$214$	−1.92705	−	5.93085i	−0.131730	−	0.405425i
$215$		0			0
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	21.5438	+	29.6525i	1.46249	+	2.01294i
$218$	16.7027	+	5.42705i	1.13125	+	0.367566i
$219$	−4.52786			−0.305965
$220$		0			0
$221$	6.47214			0.435363
$222$	2.26538	+	0.736068i	0.152043	+	0.0494016i
$223$	−12.3637	−	17.0172i	−0.827937	−	1.13956i	−0.988303	−	0.152500i	$-0.951268\pi$
$223$	−12.3637	−	17.0172i	−0.827937	−	1.13956i	0.160367	−	0.987058i	$-0.448732\pi$
$224$	−14.3262	−	10.4086i	−0.957212	−	0.695455i
$225$		0			0
$226$	1.73607	+	5.34307i	0.115482	+	0.355416i
$227$	4.73504	−	6.51722i	0.314276	−	0.432563i	−0.622433	−	0.782673i	$-0.713856\pi$
$227$	4.73504	−	6.51722i	0.314276	−	0.432563i	0.936709	+	0.350110i	$0.113856\pi$
$228$	−1.81636	−	2.50000i	−0.120291	−	0.165567i
$229$	−2.13525	+	6.57164i	−0.141102	+	0.434266i	−0.996489	−	0.0837225i	$-0.973319\pi$
$229$	−2.13525	+	6.57164i	−0.141102	+	0.434266i	0.855387	+	0.517989i	$0.173319\pi$
$230$		0			0
$231$	−6.47214	+	16.1150i	−0.425835	+	1.06029i
$232$			1.90983i			0.125386i
$233$	−9.76784	−	3.17376i	−0.639912	−	0.207920i	−0.0289512	−	0.999581i	$-0.509217\pi$
$233$	−9.76784	−	3.17376i	−0.639912	−	0.207920i	−0.610961	+	0.791661i	$0.709217\pi$
$234$	−4.23607	+	3.07768i	−0.276920	+	0.201194i
$235$		0			0
$236$	1.28115	+	3.94298i	0.0833960	+	0.256666i
$237$	2.93893	−	0.954915i	0.190904	−	0.0620284i
$238$	−9.95959	+	13.7082i	−0.645585	+	0.888571i
$239$	17.8262	−	12.9515i	1.15308	−	0.837764i	0.164196	−	0.986428i	$-0.447497\pi$
$239$	17.8262	−	12.9515i	1.15308	−	0.837764i	0.988888	+	0.148664i	$0.0474972\pi$
$240$		0			0
$241$	0.618034			0.0398111			0.0199055	−	0.999802i	$-0.493663\pi$
$241$	0.618034			0.0398111			0.0199055	+	0.999802i	$0.493663\pi$
$242$	8.42075	+	15.6803i	0.541306	+	1.00797i
$243$			1.00000i			0.0641500i
$244$	−1.33688	+	4.11450i	−0.0855850	+	0.263404i
$245$		0			0
$246$	−15.0172	−	10.9106i	−0.957463	−	0.695638i
$247$	−15.3884	+	5.00000i	−0.979142	+	0.318142i
$248$	14.8864	−	4.83688i	0.945287	−	0.307142i
$249$	−6.23607	−	4.53077i	−0.395195	−	0.287126i
$250$		0			0
$251$	5.09017	−	15.6659i	0.321289	−	0.988825i	−0.651799	−	0.758391i	$-0.725986\pi$
$251$	5.09017	−	15.6659i	0.321289	−	0.988825i	0.973088	−	0.230433i	$-0.0740144\pi$
$252$		−	3.23607i		−	0.203853i
$253$	14.2128	+	5.70820i	0.893554	+	0.358872i
$254$	−3.14590			−0.197391
$255$		0			0
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	5.62058	−	7.73607i	0.350602	−	0.482563i	−0.596898	−	0.802317i	$-0.703600\pi$
$257$	5.62058	−	7.73607i	0.350602	−	0.482563i	0.947500	+	0.319754i	$0.103600\pi$
$258$	13.9883	−	4.54508i	0.870876	−	0.282965i
$259$	2.38197	+	7.33094i	0.148008	+	0.455522i
$260$		0			0
$261$	−0.690983	+	0.502029i	−0.0427708	+	0.0310748i
$262$	14.1271	+	4.59017i	0.872775	+	0.283582i
$263$		−	24.2148i		−	1.49315i	−0.665303	−	0.746574i	$-0.731698\pi$
$263$		−	24.2148i		−	1.49315i	0.665303	−	0.746574i	$-0.268302\pi$
$264$	5.69098	+	4.75528i	0.350256	+	0.292667i
$265$		0			0
$266$	13.0902	−	40.2874i	0.802610	−	2.47018i
$267$	2.43690	+	3.35410i	0.149136	+	0.205268i
$268$	4.22050	−	5.80902i	0.257808	−	0.354842i
$269$	−0.263932	−	0.812299i	−0.0160922	−	0.0495268i	0.942688	−	0.333676i	$-0.108289\pi$
$269$	−0.263932	−	0.812299i	−0.0160922	−	0.0495268i	−0.958780	+	0.284149i	$0.908289\pi$
$270$		0			0
$271$	−14.8713	−	10.8046i	−0.903369	−	0.656336i	0.0359605	−	0.999353i	$-0.488551\pi$
$271$	−14.8713	−	10.8046i	−0.903369	−	0.656336i	−0.939329	+	0.343018i	$0.888551\pi$
$272$	5.70634	+	7.85410i	0.345998	+	0.476225i
$273$	−16.1150	−	5.23607i	−0.975322	−	0.316901i
$274$	8.56231			0.517268
$275$		0			0
$276$	−2.85410			−0.171797
$277$	21.5438	+	7.00000i	1.29444	+	0.420589i	0.873644	−	0.486566i	$-0.161751\pi$
$277$	21.5438	+	7.00000i	1.29444	+	0.420589i	0.420797	+	0.907155i	$0.361751\pi$
$278$	1.12257	+	1.54508i	0.0673273	+	0.0926680i
$279$	5.66312	+	4.11450i	0.339042	+	0.246328i
$280$		0			0
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	0.940505	−	0.339779i	$-0.110352\pi$
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	−0.960602	+	0.277928i	$0.910352\pi$
$282$	−5.79210	+	7.97214i	−0.344914	+	0.474734i
$283$	−9.42481	−	12.9721i	−0.560247	−	0.771113i	0.431111	−	0.902299i	$-0.358122\pi$
$283$	−9.42481	−	12.9721i	−0.560247	−	0.771113i	−0.991358	+	0.131185i	$0.958122\pi$
$284$	1.52786	−	4.70228i	0.0906621	−	0.279029i
$285$		0			0
$286$	−14.7082	+	9.23305i	−0.869714	+	0.545962i
$287$		−	60.0689i		−	3.54575i
$288$	−3.21644	−	1.04508i	−0.189531	−	0.0615822i
$289$	−10.5172	+	7.64121i	−0.618660	+	0.449483i
$290$		0			0
$291$	−0.781153	−	2.40414i	−0.0457920	−	0.140933i
$292$	2.66141	−	0.864745i	0.155747	−	0.0506054i
$293$	−14.9721	+	20.6074i	−0.874682	+	1.20390i	0.103183	+	0.994662i	$0.467097\pi$
$293$	−14.9721	+	20.6074i	−0.874682	+	1.20390i	−0.977866	+	0.209234i	$0.932903\pi$
$294$	26.7254	−	19.4172i	1.55866	−	1.13243i
$295$		0			0
$296$	3.29180			0.191332
$297$	−0.224514	+	3.30902i	−0.0130276	+	0.192009i
$298$		−	32.5623i		−	1.88628i
$299$	−4.61803	+	14.2128i	−0.267068	+	0.821950i
$300$		0			0
$301$	38.5066	+	27.9767i	2.21948	+	1.61255i
$302$	−23.4459	+	7.61803i	−1.34916	+	0.438369i
$303$	−18.6049	+	6.04508i	−1.06882	+	0.347281i
$304$	−19.6353	−	14.2658i	−1.12616	−	0.818202i
$305$		0			0
$306$	−1.00000	+	3.07768i	−0.0571662	+	0.175939i
$307$		−	28.1246i		−	1.60516i	−0.596547	−	0.802578i	$-0.703461\pi$
$307$		−	28.1246i		−	1.60516i	0.596547	−	0.802578i	$-0.296539\pi$
$308$	0.726543	−	10.7082i	0.0413986	−	0.610157i
$309$	4.61803			0.262711
$310$		0			0
$311$	−10.1353	+	7.36369i	−0.574718	+	0.417557i	−0.836816	−	0.547484i	$-0.815586\pi$
$311$	−10.1353	+	7.36369i	−0.574718	+	0.417557i	0.262098	+	0.965041i	$0.415586\pi$
$312$	−4.25325	+	5.85410i	−0.240793	+	0.331423i
$313$	−8.05748	+	2.61803i	−0.455436	+	0.147980i	−0.527746	−	0.849402i	$-0.676963\pi$
$313$	−8.05748	+	2.61803i	−0.455436	+	0.147980i	0.0723104	+	0.997382i	$0.476963\pi$
$314$	6.16312	+	18.9681i	0.347805	+	1.07043i
$315$		0			0
$316$	−1.54508	+	1.12257i	−0.0869178	+	0.0631495i
$317$	3.40820	+	1.10739i	0.191424	+	0.0621973i	0.403160	−	0.915130i	$-0.367912\pi$
$317$	3.40820	+	1.10739i	0.191424	+	0.0621973i	−0.211736	+	0.977327i	$0.567912\pi$
$318$			8.70820i			0.488332i
$319$	−2.39919	+	1.50609i	−0.134329	+	0.0843246i
$320$		0			0
$321$	1.19098	−	3.66547i	0.0664742	−	0.204587i
$322$	−22.9969	−	31.6525i	−1.28157	−	1.76392i
$323$	−5.87785	+	8.09017i	−0.327052	+	0.450149i
$324$	−0.190983	−	0.587785i	−0.0106102	−	0.0326547i
$325$		0			0
$326$	−8.59017	−	6.24112i	−0.475766	−	0.345664i
$327$	6.37988	+	8.78115i	0.352808	+	0.485599i
$328$	−24.3970	−	7.92705i	−1.34710	−	0.437698i
$329$	−31.8885			−1.75807
$330$		0			0
$331$	−27.5967			−1.51685			−0.758427	−	0.651758i	$-0.774032\pi$
$331$	−27.5967			−1.51685			−0.758427	+	0.651758i	$0.774032\pi$
$332$	4.53077	+	1.47214i	0.248658	+	0.0807940i
$333$	0.865300	+	1.19098i	0.0474181	+	0.0652655i
$334$	−11.8262	−	8.59226i	−0.647103	−	0.470148i
$335$		0			0
$336$	−7.85410	−	24.1724i	−0.428476	−	1.31871i
$337$	−16.9600	+	23.3435i	−0.923871	+	1.27160i	0.0383318	+	0.999265i	$0.487796\pi$
$337$	−16.9600	+	23.3435i	−0.923871	+	1.27160i	−0.962203	+	0.272334i	$0.912204\pi$
$338$	2.40414	+	3.30902i	0.130768	+	0.179987i
$339$	−1.07295	+	3.30220i	−0.0582746	+	0.179351i
$340$		0			0
$341$	17.8156	+	14.8864i	0.964769	+	0.806143i
$342$		−	8.09017i		−	0.437466i
$343$	66.8110	+	21.7082i	3.60745	+	1.17213i
$344$	16.4443	−	11.9475i	0.886616	−	0.644164i
$345$		0			0
$346$	8.28115	+	25.4868i	0.445198	+	1.37018i
$347$	−26.8011	+	8.70820i	−1.43876	+	0.467481i	−0.921510	−	0.388355i	$-0.873044\pi$
$347$	−26.8011	+	8.70820i	−1.43876	+	0.467481i	−0.517248	+	0.855835i	$0.673044\pi$
$348$	0.310271	−	0.427051i	0.0166323	−	0.0228923i
$349$	26.0795	−	18.9479i	1.39601	−	1.01426i	0.400829	−	0.916153i	$-0.368722\pi$
$349$	26.0795	−	18.9479i	1.39601	−	1.01426i	0.995176	−	0.0981041i	$-0.0312778\pi$
$350$		0			0
$351$	−3.23607			−0.172729
$352$	−10.4086	−	4.18034i	−0.554781	−	0.222813i
$353$		−	17.8328i		−	0.949145i	−0.880216	−	0.474573i	$-0.842603\pi$
$353$		−	17.8328i		−	0.949145i	0.880216	−	0.474573i	$-0.157397\pi$
$354$	−3.35410	+	10.3229i	−0.178269	+	0.548654i
$355$		0			0
$356$	−2.07295	−	1.50609i	−0.109866	−	0.0798224i
$357$	−9.95959	+	3.23607i	−0.527118	+	0.171271i
$358$	16.2007	−	5.26393i	0.856234	−	0.278207i
$359$	2.66312	+	1.93487i	0.140554	+	0.102118i	0.655840	−	0.754900i	$-0.272314\pi$
$359$	2.66312	+	1.93487i	0.140554	+	0.102118i	−0.515286	+	0.857018i	$0.672314\pi$
$360$		0			0
$361$	1.85410	−	5.70634i	0.0975843	−	0.300334i
$362$			1.23607i			0.0649663i
$363$	−1.48584	+	10.8992i	−0.0779864	+	0.572059i
$364$	10.4721			0.548889
$365$		0			0
$366$	−9.16312	+	6.65740i	−0.478964	+	0.347988i
$367$	13.0045	−	17.8992i	0.678830	−	0.934330i	−0.321089	−	0.947049i	$-0.604049\pi$
$367$	13.0045	−	17.8992i	0.678830	−	0.934330i	0.999919	+	0.0127192i	$0.00404875\pi$
$368$	−21.3193	+	6.92705i	−1.11134	+	0.361097i
$369$	−3.54508	−	10.9106i	−0.184550	−	0.567986i
$370$		0			0
$371$	−22.7984	+	16.5640i	−1.18363	+	0.859959i
$372$	−4.11450	−	1.33688i	−0.213327	−	0.0693141i
$373$			32.7426i			1.69535i	0.530516	+	0.847675i	$0.321998\pi$
$373$			32.7426i			1.69535i	−0.530516	+	0.847675i	$0.678002\pi$
$374$	−4.00000	+	9.95959i	−0.206835	+	0.514998i
$375$		0			0
$376$	−4.20820	+	12.9515i	−0.217022	+	0.667924i
$377$	−1.62460	−	2.23607i	−0.0836711	−	0.115163i
$378$	4.97980	−	6.85410i	0.256133	−	0.352537i
$379$	1.54508	+	4.75528i	0.0793657	+	0.244262i	0.982865	−	0.184327i	$-0.0590106\pi$
$379$	1.54508	+	4.75528i	0.0793657	+	0.244262i	−0.903499	+	0.428590i	$0.859011\pi$
$380$		0			0
$381$	−1.57295	−	1.14281i	−0.0805846	−	0.0585482i
$382$	−15.6129	−	21.4894i	−0.798827	−	1.09949i
$383$	−12.7068	−	4.12868i	−0.649285	−	0.210966i	−0.0341862	−	0.999415i	$-0.510884\pi$
$383$	−12.7068	−	4.12868i	−0.649285	−	0.210966i	−0.615099	+	0.788450i	$0.710884\pi$
$384$	−13.6180			−0.694942
$385$		0			0
$386$	−13.0000			−0.661683
$387$	8.64527	+	2.80902i	0.439464	+	0.142790i
$388$	0.918300	+	1.26393i	0.0466196	+	0.0641664i
$389$	−17.0344	−	12.3762i	−0.863680	−	0.627501i	0.0652033	−	0.997872i	$-0.479230\pi$
$389$	−17.0344	−	12.3762i	−0.863680	−	0.627501i	−0.928884	+	0.370371i	$0.879230\pi$
$390$		0			0
$391$	2.85410	+	8.78402i	0.144338	+	0.444227i
$392$	26.8339	−	36.9336i	1.35531	−	1.86543i
$393$	5.39607	+	7.42705i	0.272196	+	0.374645i
$394$	4.88197	−	15.0251i	0.245950	−	0.756956i
$395$		0			0
$396$	−0.500000	−	1.98787i	−0.0251259	−	0.0998942i
$397$			2.72949i			0.136989i	0.997651	+	0.0684946i	$0.0218196\pi$
$397$			2.72949i			0.136989i	−0.997651	+	0.0684946i	$0.978180\pi$
$398$	−7.38394	−	2.39919i	−0.370123	−	0.120260i
$399$	21.1803	−	15.3884i	1.06034	−	0.770384i
$400$		0			0
$401$	−9.54508	−	29.3768i	−0.476659	−	1.46700i	−0.843707	−	0.536803i	$-0.819632\pi$
$401$	−9.54508	−	29.3768i	−0.476659	−	1.46700i	0.367049	−	0.930202i	$-0.380368\pi$
$402$	17.8783	−	5.80902i	0.891689	−	0.289727i
$403$	−13.3148	+	18.3262i	−0.663257	+	0.912895i
$404$	9.78115	−	7.10642i	0.486631	−	0.353558i
$405$		0			0
$406$	7.23607			0.359120
$407$	2.59590	+	4.13525i	0.128674	+	0.204977i
$408$			4.47214i			0.221404i
$409$	8.12868	−	25.0175i	0.401937	−	1.23704i	−0.521488	−	0.853258i	$-0.674623\pi$
$409$	8.12868	−	25.0175i	0.401937	−	1.23704i	0.923426	−	0.383777i	$-0.125377\pi$
$410$		0			0
$411$	4.28115	+	3.11044i	0.211174	+	0.153427i
$412$	−2.71441	+	0.881966i	−0.133729	+	0.0434513i
$413$	−33.4055	+	10.8541i	−1.64378	+	0.534095i
$414$	−6.04508	−	4.39201i	−0.297100	−	0.215856i
$415$		0			0
$416$	3.38197	−	10.4086i	0.165815	−	0.510325i
$417$			1.18034i			0.0578015i
$418$	1.81636	−	26.7705i	0.0888409	−	1.30939i
$419$	24.5967			1.20163			0.600815	−	0.799388i	$-0.294843\pi$
$419$	24.5967			1.20163			0.600815	+	0.799388i	$0.294843\pi$
$420$		0			0
$421$	3.11803	−	2.26538i	0.151964	−	0.110408i	−0.509205	−	0.860645i	$-0.670061\pi$
$421$	3.11803	−	2.26538i	0.151964	−	0.110408i	0.661169	+	0.750237i	$0.270061\pi$
$422$	−2.71441	+	3.73607i	−0.132136	+	0.181869i
$423$	−5.79210	+	1.88197i	−0.281621	+	0.0915043i
$424$	3.71885	+	11.4454i	0.180603	+	0.555839i
$425$		0			0
$426$	10.4721	−	7.60845i	0.507377	−	0.368631i
$427$	−34.8586	−	11.3262i	−1.68692	−	0.548115i
$428$			2.38197i			0.115137i
$429$	−10.7082	−	0.726543i	−0.516997	−	0.0350778i
$430$		0			0
$431$	−4.90983	+	15.1109i	−0.236498	+	0.727867i	0.760421	+	0.649431i	$0.224993\pi$
$431$	−4.90983	+	15.1109i	−0.236498	+	0.727867i	−0.996919	+	0.0784361i	$0.975007\pi$
$432$	−2.85317	−	3.92705i	−0.137273	−	0.188940i
$433$	0.608030	−	0.836881i	0.0292200	−	0.0402179i	−0.794157	−	0.607713i	$-0.792087\pi$
$433$	0.608030	−	0.836881i	0.0292200	−	0.0402179i	0.823377	+	0.567495i	$0.192087\pi$
$434$	−18.3262	−	56.4024i	−0.879688	−	2.70740i
$435$		0			0
$436$	−5.42705	−	3.94298i	−0.259909	−	0.188835i
$437$	−13.5721	−	18.6803i	−0.649240	−	0.893602i
$438$	6.96767	+	2.26393i	0.332928	+	0.108175i
$439$	−25.3262			−1.20876			−0.604378	−	0.796698i	$-0.706578\pi$
$439$	−25.3262			−1.20876			−0.604378	+	0.796698i	$0.706578\pi$
$440$		0			0
$441$	20.4164			0.972210
$442$	−9.95959	−	3.23607i	−0.473730	−	0.153924i
$443$	−4.86128	−	6.69098i	−0.230967	−	0.317898i	0.677766	−	0.735278i	$-0.262948\pi$
$443$	−4.86128	−	6.69098i	−0.230967	−	0.317898i	−0.908732	+	0.417380i	$0.862948\pi$
$444$	−0.736068	−	0.534785i	−0.0349322	−	0.0253798i
$445$		0			0
$446$	10.5172	+	32.3687i	0.498005	+	1.53270i
$447$	11.8290	−	16.2812i	0.559490	−	0.770072i
$448$	−13.0373	−	17.9443i	−0.615953	−	0.847787i
$449$	10.5902	−	32.5932i	0.499781	−	1.53817i	−0.309590	−	0.950870i	$-0.600192\pi$
$449$	10.5902	−	32.5932i	0.499781	−	1.53817i	0.809371	−	0.587298i	$-0.199808\pi$
$450$		0			0
$451$	−9.28115	−	36.8994i	−0.437032	−	1.73753i
$452$		−	2.14590i		−	0.100935i
$453$	−14.4904	−	4.70820i	−0.680817	−	0.221211i
$454$	−10.5451	+	7.66145i	−0.494905	+	0.359570i
$455$		0			0
$456$	−3.45492	−	10.6331i	−0.161791	−	0.497942i
$457$	7.10642	−	2.30902i	0.332424	−	0.108011i	−0.138049	−	0.990425i	$-0.544083\pi$
$457$	7.10642	−	2.30902i	0.332424	−	0.108011i	0.470473	+	0.882414i	$0.344083\pi$
$458$	6.57164	−	9.04508i	0.307073	−	0.422649i
$459$	−1.61803	+	1.17557i	−0.0755234	+	0.0548709i
$460$		0			0
$461$	8.05573			0.375193			0.187596	−	0.982246i	$-0.439930\pi$
$461$	8.05573			0.375193			0.187596	+	0.982246i	$0.439930\pi$
$462$	18.0171	−	21.5623i	0.838230	−	1.00317i
$463$		−	0.270510i		−	0.0125717i	−0.999980	−	0.00628583i	$-0.997999\pi$
$463$		−	0.270510i		−	0.0125717i	0.999980	−	0.00628583i	$-0.00200085\pi$
$464$	1.28115	−	3.94298i	0.0594760	−	0.183048i
$465$		0			0
$466$	13.4443	+	9.76784i	0.622794	+	0.452486i
$467$	29.3768	−	9.54508i	1.35939	−	0.441694i	0.463553	−	0.886069i	$-0.346574\pi$
$467$	29.3768	−	9.54508i	1.35939	−	0.441694i	0.895841	+	0.444375i	$0.146574\pi$
$468$	1.90211	−	0.618034i	0.0879252	−	0.0285686i
$469$	49.2148	+	35.7566i	2.27253	+	1.65109i
$470$		0			0
$471$	−3.80902	+	11.7229i	−0.175510	+	0.540165i
$472$			15.0000i			0.690431i
$473$	27.9767	+	11.2361i	1.28637	+	0.516635i
$474$	−5.00000			−0.229658
$475$		0			0
$476$	5.23607	−	3.80423i	0.239995	−	0.174366i
$477$	−3.16344	+	4.35410i	−0.144844	+	0.199361i
$478$	−33.9075	+	11.0172i	−1.55089	+	0.503916i
$479$	−2.03444	−	6.26137i	−0.0929560	−	0.286089i	0.893760	−	0.448546i	$-0.148058\pi$
$479$	−2.03444	−	6.26137i	−0.0929560	−	0.286089i	−0.986716	+	0.162457i	$0.948058\pi$
$480$		0			0
$481$	−3.85410	+	2.80017i	−0.175732	+	0.127677i
$482$	−0.951057	−	0.309017i	−0.0433194	−	0.0140753i
$483$		−	24.1803i		−	1.10024i
$484$	−1.20820	−	6.69015i	−0.0549184	−	0.304098i
$485$		0			0
$486$	0.500000	−	1.53884i	0.0226805	−	0.0698033i
$487$	−4.80828	−	6.61803i	−0.217884	−	0.299892i	0.686058	−	0.727547i	$-0.259340\pi$
$487$	−4.80828	−	6.61803i	−0.217884	−	0.299892i	−0.903942	+	0.427655i	$0.859340\pi$
$488$	−9.20029	+	12.6631i	−0.416478	+	0.573232i
$489$	−2.02786	−	6.24112i	−0.0917032	−	0.282233i
$490$		0			0
$491$	−5.82624	−	4.23301i	−0.262934	−	0.191033i	0.448505	−	0.893780i	$-0.351957\pi$
$491$	−5.82624	−	4.23301i	−0.262934	−	0.191033i	−0.711440	+	0.702747i	$0.751957\pi$
$492$	4.16750	+	5.73607i	0.187885	+	0.258602i
$493$	−1.62460	−	0.527864i	−0.0731682	−	0.0237738i
$494$	26.1803			1.17791
$495$		0			0
$496$	−33.9787			−1.52569
$497$	39.8384	+	12.9443i	1.78700	+	0.580630i
$498$	7.33094	+	10.0902i	0.328507	+	0.452151i
$499$	9.04508	+	6.57164i	0.404914	+	0.294187i	0.771539	−	0.636182i	$-0.219487\pi$
$499$	9.04508	+	6.57164i	0.404914	+	0.294187i	−0.366626	+	0.930368i	$0.619487\pi$
$500$		0			0
$501$	−2.79180	−	8.59226i	−0.124728	−	0.383874i
$502$	−15.6659	+	21.5623i	−0.699205	+	0.962373i
$503$	8.16348	+	11.2361i	0.363992	+	0.500992i	0.951255	−	0.308404i	$-0.0997949\pi$
$503$	8.16348	+	11.2361i	0.363992	+	0.500992i	−0.587264	+	0.809396i	$0.699795\pi$
$504$	3.61803	−	11.1352i	0.161160	−	0.496000i
$505$		0			0
$506$	−19.0172	−	15.8904i	−0.845419	−	0.706416i
$507$			2.52786i			0.112266i
$508$	1.14281	+	0.371323i	0.0507042	+	0.0164748i
$509$	7.66312	−	5.56758i	0.339662	−	0.246779i	−0.404857	−	0.914380i	$-0.632679\pi$
$509$	7.66312	−	5.56758i	0.339662	−	0.246779i	0.744519	+	0.667601i	$0.232679\pi$
$510$		0			0
$511$	7.32624	+	22.5478i	0.324094	+	0.997458i
$512$	−5.03280	+	1.63525i	−0.222420	+	0.0722687i
$513$	2.93893	−	4.04508i	0.129757	−	0.178595i
$514$	−12.5172	+	9.09429i	−0.552111	+	0.401132i
$515$		0			0
$516$	−5.61803			−0.247320
$517$	−19.5887	+	4.92705i	−0.861509	+	0.216691i
$518$		−	12.4721i		−	0.547994i
$519$	−5.11803	+	15.7517i	−0.224657	+	0.691422i
$520$		0			0
$521$	−23.7533	−	17.2578i	−1.04065	−	0.756077i	−0.0702381	−	0.997530i	$-0.522376\pi$
$521$	−23.7533	−	17.2578i	−1.04065	−	0.756077i	−0.970412	+	0.241453i	$0.922376\pi$
$522$	1.31433	−	0.427051i	0.0575266	−	0.0186915i
$523$	3.57971	−	1.16312i	0.156530	−	0.0508596i	−0.229704	−	0.973261i	$-0.573776\pi$
$523$	3.57971	−	1.16312i	0.156530	−	0.0508596i	0.386234	+	0.922401i	$0.373776\pi$
$524$	−4.59017	−	3.33495i	−0.200523	−	0.145688i
$525$		0			0
$526$	−12.1074	+	37.2627i	−0.527907	+	1.62473i
$527$			14.0000i			0.609850i
$528$	−8.55951	−	13.6353i	−0.372505	−	0.593398i
$529$	1.67376			0.0727723
$530$		0			0
$531$	−5.42705	+	3.94298i	−0.235514	+	0.171111i
$532$	−9.51057	+	13.0902i	−0.412335	+	0.567531i
$533$	35.3076	−	11.4721i	1.52934	−	0.496913i
$534$	−2.07295	−	6.37988i	−0.0897053	−	0.276084i
$535$		0			0
$536$	21.0172	−	15.2699i	0.907806	−	0.659559i
$537$	10.0126	+	3.25329i	0.432075	+	0.140390i
$538$			1.38197i			0.0595808i
$539$	67.5582	+	4.58377i	2.90994	+	0.197437i
$540$		0			0
$541$	−0.500000	+	1.53884i	−0.0214967	+	0.0661600i	−0.961229	−	0.275750i	$-0.911074\pi$
$541$	−0.500000	+	1.53884i	−0.0214967	+	0.0661600i	0.939733	+	0.341910i	$0.111074\pi$
$542$	17.4823	+	24.0623i	0.750929	+	1.03356i
$543$	−0.449028	+	0.618034i	−0.0192696	+	0.0265224i
$544$	−2.09017	−	6.43288i	−0.0896153	−	0.275808i
$545$		0			0
$546$	22.1803	+	16.1150i	0.949231	+	0.689657i
$547$	−11.3799	−	15.6631i	−0.486570	−	0.669707i	0.493181	−	0.869927i	$-0.335834\pi$
$547$	−11.3799	−	15.6631i	−0.486570	−	0.669707i	−0.979751	+	0.200220i	$0.935834\pi$
$548$	−3.11044	−	1.01064i	−0.132871	−	0.0431725i
$549$	−7.00000			−0.298753
$550$		0			0
$551$	4.27051			0.181930
$552$	−9.82084	−	3.19098i	−0.418003	−	0.135817i
$553$	−9.51057	−	13.0902i	−0.404430	−	0.556651i
$554$	−29.6525	−	21.5438i	−1.25981	−	0.915308i
$555$		0			0
$556$	−0.225425	−	0.693786i	−0.00956014	−	0.0294231i
$557$	−24.9192	+	34.2984i	−1.05586	+	1.45327i	−0.172247	+	0.985054i	$0.555103\pi$
$557$	−24.9192	+	34.2984i	−1.05586	+	1.45327i	−0.883615	+	0.468215i	$0.844897\pi$
$558$	−6.65740	−	9.16312i	−0.281830	−	0.387906i
$559$	−9.09017	+	27.9767i	−0.384473	+	1.18329i
$560$		0			0
$561$	−5.61803	+	3.52671i	−0.237194	+	0.148898i
$562$			1.76393i			0.0744070i
$563$	−19.6619	−	6.38854i	−0.828651	−	0.269245i	−0.136174	−	0.990685i	$-0.543481\pi$
$563$	−19.6619	−	6.38854i	−0.828651	−	0.269245i	−0.692477	+	0.721440i	$0.743481\pi$
$564$	3.04508	−	2.21238i	0.128221	−	0.0931582i
$565$		0			0
$566$	8.01722	+	24.6745i	0.336989	+	1.03715i
$567$	4.97980	−	1.61803i	0.209132	−	0.0679510i
$568$	10.5146	−	14.4721i	0.441184	−	0.607237i
$569$	−18.2533	+	13.2618i	−0.765218	+	0.555963i	−0.900506	−	0.434843i	$-0.856804\pi$
$569$	−18.2533	+	13.2618i	−0.765218	+	0.555963i	0.135289	+	0.990806i	$0.456804\pi$
$570$		0			0
$571$	−11.0902			−0.464109			−0.232055	−	0.972703i	$-0.574545\pi$
$571$	−11.0902			−0.464109			−0.232055	+	0.972703i	$0.574545\pi$
$572$	6.43288	−	1.61803i	0.268972	−	0.0676534i
$573$		−	16.4164i		−	0.685805i
$574$	−30.0344	+	92.4365i	−1.25361	+	3.85823i
$575$		0			0
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	−28.5442	+	9.27458i	−1.18831	+	0.386106i	−0.835448	−	0.549569i	$-0.814792\pi$
$577$	−28.5442	+	9.27458i	−1.18831	+	0.386106i	−0.352863	+	0.935675i	$0.614792\pi$
$578$	20.0049	−	6.50000i	0.832096	−	0.270364i
$579$	−6.50000	−	4.72253i	−0.270131	−	0.196262i
$580$		0			0
$581$	−12.4721	+	38.3853i	−0.517431	+	1.59249i
$582$			4.09017i			0.169543i
$583$	−11.4454	+	13.6976i	−0.474021	+	0.567295i
$584$	10.1246			0.418959
$585$		0			0
$586$	33.3435	−	24.2254i	1.37741	−	1.00074i
$587$	−12.7068	+	17.4894i	−0.524464	+	0.721863i	−0.986274	−	0.165116i	$-0.947200\pi$
$587$	−12.7068	+	17.4894i	−0.524464	+	0.721863i	0.461810	+	0.886979i	$0.347200\pi$
$588$	−12.0005	+	3.89919i	−0.494891	+	0.160800i
$589$	−10.8156	−	33.2870i	−0.445649	−	1.37157i
$590$		0			0
$591$	7.89919	−	5.73910i	0.324929	−	0.236075i
$592$	−6.79615	−	2.20820i	−0.279320	−	0.0907566i
$593$		−	3.11146i		−	0.127772i	−0.997957	−	0.0638861i	$-0.979651\pi$
$593$		−	3.11146i		−	0.127772i	0.997957	−	0.0638861i	$-0.0203494\pi$
$594$	2.00000	−	4.97980i	0.0820610	−	0.204324i
$595$		0			0
$596$	−3.84346	+	11.8290i	−0.157434	+	0.484533i
$597$	−2.82041	−	3.88197i	−0.115432	−	0.158878i
$598$	14.2128	−	19.5623i	0.581207	−	0.799962i
$599$	5.48936	+	16.8945i	0.224289	+	0.690291i	0.998363	+	0.0571955i	$0.0182158\pi$
$599$	5.48936	+	16.8945i	0.224289	+	0.690291i	−0.774074	+	0.633095i	$0.781784\pi$
$600$		0			0
$601$	8.38197	+	6.08985i	0.341908	+	0.248410i	0.745466	−	0.666543i	$-0.232227\pi$
$601$	8.38197	+	6.08985i	0.341908	+	0.248410i	−0.403559	+	0.914954i	$0.632227\pi$
$602$	−45.2672	−	62.3050i	−1.84495	−	2.53936i
$603$	11.0494	+	3.59017i	0.449967	+	0.146203i
$604$	9.41641			0.383148
$605$		0			0
$606$	31.6525			1.28579
$607$	−31.3849	−	10.1976i	−1.27387	−	0.413906i	−0.407454	−	0.913226i	$-0.633583\pi$
$607$	−31.3849	−	10.1976i	−1.27387	−	0.413906i	−0.866418	+	0.499319i	$0.833583\pi$
$608$	9.93935	+	13.6803i	0.403094	+	0.554811i
$609$	3.61803	+	2.62866i	0.146610	+	0.106518i
$610$		0			0
$611$	−6.09017	−	18.7436i	−0.246382	−	0.758286i
$612$	0.726543	−	1.00000i	0.0293687	−	0.0404226i
$613$	2.21238	+	3.04508i	0.0893573	+	0.122990i	0.851355	−	0.524590i	$-0.175781\pi$
$613$	2.21238	+	3.04508i	0.0893573	+	0.122990i	−0.761998	+	0.647580i	$0.775781\pi$
$614$	−14.0623	+	43.2793i	−0.567508	+	1.74661i
$615$		0			0
$616$	14.4721	−	36.0341i	0.583099	−	1.45186i
$617$			42.2492i			1.70089i	0.526064	+	0.850445i	$0.323667\pi$
$617$			42.2492i			1.70089i	−0.526064	+	0.850445i	$0.676333\pi$
$618$	−7.10642	−	2.30902i	−0.285862	−	0.0928823i
$619$	34.6976	−	25.2093i	1.39461	−	1.01325i	0.399271	−	0.916833i	$-0.369263\pi$
$619$	34.6976	−	25.2093i	1.39461	−	1.01325i	0.995341	−	0.0964126i	$-0.0307368\pi$
$620$		0			0
$621$	−1.42705	−	4.39201i	−0.0572656	−	0.176245i
$622$	19.2784	−	6.26393i	0.772993	−	0.251161i
$623$	12.7598	−	17.5623i	0.511209	−	0.703619i
$624$	12.7082	−	9.23305i	0.508735	−	0.369618i
$625$		0			0
$626$	13.7082			0.547890
$627$	10.6331	−	12.7254i	0.424647	−	0.508205i
$628$		−	7.61803i		−	0.303993i
$629$	−0.909830	+	2.80017i	−0.0362773	+	0.111650i
$630$		0			0
$631$	32.0623	+	23.2946i	1.27638	+	0.927345i	0.999437	−	0.0335418i	$-0.0106787\pi$
$631$	32.0623	+	23.2946i	1.27638	+	0.927345i	0.276943	+	0.960886i	$0.410679\pi$
$632$	−6.57164	+	2.13525i	−0.261406	+	0.0849359i
$633$	−2.71441	+	0.881966i	−0.107888	+	0.0350550i
$634$	−4.69098	−	3.40820i	−0.186303	−	0.135357i
$635$		0			0
$636$	1.02786	−	3.16344i	0.0407575	−	0.125439i
$637$			66.0689i			2.61774i
$638$	4.44501	−	1.11803i	0.175980	−	0.0442634i
$639$	8.00000			0.316475
$640$		0			0
$641$	−3.42705	+	2.48990i	−0.135360	+	0.0983451i	−0.653405	−	0.757009i	$-0.726660\pi$
$641$	−3.42705	+	2.48990i	−0.135360	+	0.0983451i	0.518045	+	0.855354i	$0.326660\pi$
$642$	−3.66547	+	5.04508i	−0.144665	+	0.199114i
$643$	−13.0045	+	4.22542i	−0.512848	+	0.166634i	−0.553997	−	0.832519i	$-0.686898\pi$
$643$	−13.0045	+	4.22542i	−0.512848	+	0.166634i	0.0411490	+	0.999153i	$0.486898\pi$
$644$	4.61803	+	14.2128i	0.181976	+	0.560065i
$645$		0			0
$646$	13.0902	−	9.51057i	0.515026	−	0.374188i
$647$	30.0503	+	9.76393i	1.18140	+	0.383860i	0.832886	−	0.553444i	$-0.186687\pi$
$647$	30.0503	+	9.76393i	1.18140	+	0.383860i	0.348513	+	0.937304i	$0.386687\pi$
$648$		−	2.23607i		−	0.0878410i
$649$	−18.8435	+	11.8290i	−0.739670	+	0.464327i
$650$		0			0
$651$	11.3262	−	34.8586i	0.443910	−	1.36622i
$652$	2.38390	+	3.28115i	0.0933606	+	0.128500i
$653$	−25.6053	+	35.2426i	−1.00201	+	1.37915i	−0.0779293	+	0.996959i	$0.524831\pi$
$653$	−25.6053	+	35.2426i	−1.00201	+	1.37915i	−0.924083	+	0.382192i	$0.875169\pi$
$654$	−5.42705	−	16.7027i	−0.212214	−	0.653129i
$655$		0			0
$656$	45.0517	+	32.7319i	1.75897	+	1.27797i
$657$	2.66141	+	3.66312i	0.103832	+	0.142912i
$658$	49.0714	+	15.9443i	1.91300	+	0.621572i
$659$	−42.0344			−1.63743			−0.818715	−	0.574201i	$-0.805313\pi$
$659$	−42.0344			−1.63743			−0.818715	+	0.574201i	$0.805313\pi$
$660$		0			0
$661$	15.0902			0.586940			0.293470	−	0.955968i	$-0.405190\pi$
$661$	15.0902			0.586940			0.293470	+	0.955968i	$0.405190\pi$
$662$	42.4670	+	13.7984i	1.65053	+	0.536289i
$663$	−3.80423	−	5.23607i	−0.147744	−	0.203352i
$664$	13.9443	+	10.1311i	0.541143	+	0.393163i
$665$		0			0
$666$	−0.736068	−	2.26538i	−0.0285221	−	0.0877819i
$667$	2.31838	−	3.19098i	0.0897682	−	0.123555i
$668$	3.28195	+	4.51722i	0.126983	+	0.174777i
$669$	−6.50000	+	20.0049i	−0.251305	+	0.773436i
$670$		0			0
$671$	−23.1631	−	1.57160i	−0.894202	−	0.0606709i
$672$			17.7082i			0.683109i
$673$	33.5770	+	10.9098i	1.29430	+	0.420543i	0.873594	−	0.486655i	$-0.161783\pi$
$673$	33.5770	+	10.9098i	1.29430	+	0.420543i	0.420704	+	0.907198i	$0.361783\pi$
$674$	37.7705	−	27.4419i	1.45487	−	1.05702i
$675$		0			0
$676$	−0.482779	−	1.48584i	−0.0185684	−	0.0571477i
$677$	−5.65334	+	1.83688i	−0.217275	+	0.0705971i	−0.415632	−	0.909533i	$-0.636440\pi$
$677$	−5.65334	+	1.83688i	−0.217275	+	0.0705971i	0.198357	+	0.980130i	$0.436440\pi$
$678$	3.30220	−	4.54508i	0.126820	−	0.174553i
$679$	−10.7082	+	7.77997i	−0.410943	+	0.298568i
$680$		0			0
$681$	−8.05573			−0.308696
$682$	−19.9722	−	31.8156i	−0.764775	−	1.21828i
$683$			15.7082i			0.601058i	0.953773	+	0.300529i	$0.0971632\pi$
$683$			15.7082i			0.601058i	−0.953773	+	0.300529i	$0.902837\pi$
$684$	−0.954915	+	2.93893i	−0.0365121	+	0.112373i
$685$		0			0
$686$	−91.9574	−	66.8110i	−3.51095	−	2.55086i
$687$	6.57164	−	2.13525i	0.250724	−	0.0814651i
$688$	−41.9650	+	13.6353i	−1.59990	+	0.519839i
$689$	−14.0902	−	10.2371i	−0.536793	−	0.390003i
$690$		0			0
$691$	−9.05573	+	27.8707i	−0.344496	+	1.06025i	0.617357	+	0.786683i	$0.288203\pi$
$691$	−9.05573	+	27.8707i	−0.344496	+	1.06025i	−0.961853	+	0.273567i	$0.911797\pi$
$692$		−	10.2361i		−	0.389117i
$693$	16.8415	−	4.23607i	0.639756	−	0.160915i
$694$	45.5967			1.73083
$695$		0			0
$696$	1.54508	−	1.12257i	0.0585663	−	0.0425509i
$697$	13.4863	−	18.5623i	0.510830	−	0.703097i
$698$	−49.6062	+	16.1180i	−1.87762	+	0.610077i
$699$	3.17376	+	9.76784i	0.120043	+	0.369453i
$700$		0			0
$701$	−32.6976	+	23.7562i	−1.23497	+	0.897258i	−0.997253	−	0.0740763i	$-0.976399\pi$
$701$	−32.6976	+	23.7562i	−1.23497	+	0.897258i	−0.237717	+	0.971334i	$0.576399\pi$
$702$	4.97980	+	1.61803i	0.187950	+	0.0610688i
$703$		−	7.36068i		−	0.277613i
$704$	−10.7812	−	9.00854i	−0.406330	−	0.339522i
$705$		0			0
$706$	−8.91641	+	27.4419i	−0.335573	+	1.03279i
$707$	60.2066	+	82.8673i	2.26430	+	3.11654i
$708$	2.43690	−	3.35410i	0.0915842	−	0.126055i
$709$	−5.81559	−	17.8986i	−0.218409	−	0.672195i	−0.998894	−	0.0470197i	$-0.985028\pi$
$709$	−5.81559	−	17.8986i	−0.218409	−	0.672195i	0.780485	−	0.625175i	$-0.214972\pi$
$710$		0			0
$711$	−2.50000	−	1.81636i	−0.0937573	−	0.0681187i
$712$	−5.44907	−	7.50000i	−0.204212	−	0.281074i
$713$	−30.7441	−	9.98936i	−1.15137	−	0.374104i
$714$	16.9443			0.634123
$715$		0			0
$716$	−6.50658			−0.243162
$717$	−20.9560	−	6.80902i	−0.782616	−	0.254287i
$718$	−3.13068	−	4.30902i	−0.116836	−	0.160811i
$719$	21.7705	+	15.8172i	0.811903	+	0.589882i	0.914382	−	0.404853i	$-0.132677\pi$
$719$	21.7705	+	15.8172i	0.811903	+	0.589882i	−0.102479	+	0.994735i	$0.532677\pi$
$720$		0			0
$721$	−7.47214	−	22.9969i	−0.278277	−	0.856448i
$722$	−5.70634	+	7.85410i	−0.212368	+	0.292299i
$723$	−0.363271	−	0.500000i	−0.0135102	−	0.0185952i
$724$	0.145898	−	0.449028i	0.00542226	−	0.0166880i
$725$		0			0
$726$	7.73607	−	16.0292i	0.287112	−	0.594900i
$727$			21.6738i			0.803835i	0.915676	+	0.401918i	$0.131656\pi$
$727$			21.6738i			0.803835i	−0.915676	+	0.401918i	$0.868344\pi$
$728$	36.0341	+	11.7082i	1.33551	+	0.433935i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	5.61803	+	17.2905i	0.207790	+	0.639513i
$732$	4.11450	−	1.33688i	0.152076	−	0.0494125i
$733$	2.85317	−	3.92705i	0.105384	−	0.145049i	−0.753068	−	0.657943i	$-0.771427\pi$
$733$	2.85317	−	3.92705i	0.105384	−	0.145049i	0.858452	+	0.512894i	$0.171427\pi$
$734$	−28.9615	+	21.0418i	−1.06899	+	0.776665i
$735$		0			0
$736$	15.6180			0.575688
$737$	35.7566	+	14.3607i	1.31711	+	0.528982i
$738$			18.5623i			0.683288i
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	−0.770697	−	0.637201i	$-0.780092\pi$
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	0.998045	−	0.0625022i	$-0.0199080\pi$
$740$		0			0
$741$	13.0902	+	9.51057i	0.480879	+	0.349379i
$742$	43.3651	−	14.0902i	1.59198	−	0.517266i
$743$	30.1033	−	9.78115i	1.10438	−	0.358836i	0.300595	−	0.953752i	$-0.402815\pi$
$743$	30.1033	−	9.78115i	1.10438	−	0.358836i	0.803788	+	0.594916i	$0.202815\pi$
$744$	−12.6631	−	9.20029i	−0.464252	−	0.337299i
$745$		0			0
$746$	16.3713	−	50.3858i	0.599397	−	1.84475i
$747$			7.70820i			0.282028i
$748$	2.62866	−	3.14590i	0.0961132	−	0.115025i
$749$	−20.1803			−0.737374
$750$		0			0
$751$	8.18034	−	5.94336i	0.298505	−	0.216876i	−0.428444	−	0.903569i	$-0.640938\pi$
$751$	8.18034	−	5.94336i	0.298505	−	0.216876i	0.726948	+	0.686692i	$0.240938\pi$
$752$	17.3763	−	23.9164i	0.633648	−	0.872142i
$753$	−15.6659	+	5.09017i	−0.570898	+	0.185496i
$754$	1.38197	+	4.25325i	0.0503282	+	0.154894i
$755$		0			0
$756$	−2.61803	+	1.90211i	−0.0952170	+	0.0691792i
$757$	−1.73060	−	0.562306i	−0.0628997	−	0.0204374i	0.277398	−	0.960755i	$-0.410528\pi$
$757$	−1.73060	−	0.562306i	−0.0628997	−	0.0204374i	−0.340298	+	0.940318i	$0.610528\pi$
$758$		−	8.09017i		−	0.293848i
$759$	−3.73607	−	14.8536i	−0.135611	−	0.539153i
$760$		0			0
$761$	3.07953	−	9.47781i	0.111633	−	0.343570i	−0.879597	−	0.475719i	$-0.842188\pi$
$761$	3.07953	−	9.47781i	0.111633	−	0.343570i	0.991230	+	0.132149i	$0.0421878\pi$
$762$	1.84911	+	2.54508i	0.0669863	+	0.0921987i
$763$	33.4055	−	45.9787i	1.20936	−	1.66454i
$764$	3.13525	+	9.64932i	0.113430	+	0.349100i
$765$		0			0
$766$	17.4894	+	12.7068i	0.631916	+	0.459114i
$767$	−12.7598	−	17.5623i	−0.460728	−	0.634138i
$768$	12.8985	+	4.19098i	0.465435	+	0.151229i
$769$	−17.2361			−0.621549			−0.310774	−	0.950484i	$-0.600588\pi$
$769$	−17.2361			−0.621549			−0.310774	+	0.950484i	$0.600588\pi$
$770$		0			0
$771$	−9.56231			−0.344378
$772$	4.72253	+	1.53444i	0.169967	+	0.0552258i
$773$	16.1680	+	22.2533i	0.581521	+	0.800395i	0.993861	−	0.110635i	$-0.0352884\pi$
$773$	16.1680	+	22.2533i	0.581521	+	0.800395i	−0.412340	+	0.911030i	$0.635288\pi$
$774$	−11.8992	−	8.64527i	−0.427707	−	0.310748i
$775$		0			0
$776$	1.74671	+	5.37582i	0.0627033	+	0.192981i
$777$	4.53077	−	6.23607i	0.162540	−	0.223718i
$778$	20.0252	+	27.5623i	0.717938	+	0.988157i
$779$	−17.7254	+	54.5532i	−0.635079	+	1.95457i
$780$		0			0
$781$	26.4721	+	1.79611i	0.947247	+	0.0642699i
$782$		−	14.9443i		−	0.534406i
$783$	0.812299	+	0.263932i	0.0290292	+	0.00943216i
$784$	−80.1763	+	58.2515i	−2.86344	+	2.08041i
$785$		0			0
$786$	−4.59017	−	14.1271i	−0.163726	−	0.503897i
$787$	31.1931	−	10.1353i	1.11191	−	0.361283i	0.305238	−	0.952276i	$-0.401264\pi$
$787$	31.1931	−	10.1353i	1.11191	−	0.361283i	0.806676	+	0.590993i	$0.201264\pi$
$788$	−3.54696	+	4.88197i	−0.126355	+	0.173913i
$789$	−19.5902	+	14.2331i	−0.697429	+	0.506711i
$790$		0			0
$791$	18.1803			0.646418
$792$	0.502029	−	7.39919i	0.0178388	−	0.262919i
$793$		−	22.6525i		−	0.804413i
$794$	1.36475	−	4.20025i	0.0484330	−	0.149061i
$795$		0			0
$796$	2.39919	+	1.74311i	0.0850369	+	0.0617829i
$797$	−14.5434	+	4.72542i	−0.515152	+	0.167383i	−0.555044	−	0.831821i	$-0.687299\pi$
$797$	−14.5434	+	4.72542i	−0.515152	+	0.167383i	0.0398919	+	0.999204i	$0.487299\pi$
$798$	−40.2874	+	13.0902i	−1.42616	+	0.463387i
$799$	−9.85410	−	7.15942i	−0.348613	−	0.253282i
$800$		0			0
$801$	1.28115	−	3.94298i	0.0452673	−	0.139318i
$802$			49.9787i			1.76481i
$803$	7.98424	+	12.7188i	0.281758	+	0.448838i
$804$	−7.18034			−0.253231
$805$		0			0
$806$	29.6525	−	21.5438i	1.04446	−	0.758847i
$807$	−0.502029	+	0.690983i	−0.0176722	+	0.0243238i
$808$	41.6017	−	13.5172i	1.46354	−	0.475534i
$809$	−9.16970	−	28.2214i	−0.322389	−	0.992212i	−0.972605	−	0.232463i	$-0.925322\pi$
$809$	−9.16970	−	28.2214i	−0.322389	−	0.992212i	0.650216	−	0.759750i	$-0.274678\pi$
$810$		0			0
$811$	−35.2984	+	25.6458i	−1.23949	+	0.900545i	−0.997565	−	0.0697492i	$-0.977780\pi$
$811$	−35.2984	+	25.6458i	−1.23949	+	0.900545i	−0.241929	+	0.970294i	$0.577780\pi$
$812$	−2.62866	−	0.854102i	−0.0922477	−	0.0299731i
$813$			18.3820i			0.644684i
$814$	−1.92705	−	7.66145i	−0.0675431	−	0.268534i
$815$		0			0
$816$	3.00000	−	9.23305i	0.105021	−	0.323221i
$817$	−26.7153	−	36.7705i	−0.934651	−	1.28644i
$818$	−25.0175	+	34.4336i	−0.874716	+	1.20394i
$819$	5.23607	+	16.1150i	0.182963	+	0.563102i
$820$		0			0
$821$	−16.8435	−	12.2375i	−0.587841	−	0.427091i	0.253702	−	0.967283i	$-0.418352\pi$
$821$	−16.8435	−	12.2375i	−0.587841	−	0.427091i	−0.841542	+	0.540191i	$0.818352\pi$
$822$	−5.03280	−	6.92705i	−0.175539	−	0.241609i
$823$	−15.7189	−	5.10739i	−0.547928	−	0.178032i	0.0219545	−	0.999759i	$-0.493011\pi$
$823$	−15.7189	−	5.10739i	−0.547928	−	0.178032i	−0.569882	+	0.821727i	$0.693011\pi$
$824$	−10.3262			−0.359732
$825$		0			0
$826$	56.8328			1.97747
$827$	−48.8999	−	15.8885i	−1.70042	−	0.552499i	−0.711724	−	0.702459i	$-0.752086\pi$
$827$	−48.8999	−	15.8885i	−1.70042	−	0.552499i	−0.988692	+	0.149960i	$0.952086\pi$
$828$	1.67760	+	2.30902i	0.0583006	+	0.0802439i
$829$	−26.6074	−	19.3314i	−0.924113	−	0.671407i	0.0204314	−	0.999791i	$-0.493496\pi$
$829$	−26.6074	−	19.3314i	−0.924113	−	0.671407i	−0.944544	+	0.328384i	$0.893496\pi$
$830$		0			0
$831$	−7.00000	−	21.5438i	−0.242827	−	0.747346i
$832$	8.05748	−	11.0902i	0.279343	−	0.384482i
$833$	24.0009	+	33.0344i	0.831583	+	1.14458i
$834$	0.590170	−	1.81636i	0.0204359	−	0.0628953i
$835$		0			0
$836$	−3.81966	+	9.51057i	−0.132106	+	0.328930i
$837$		−	7.00000i		−	0.241955i
$838$	−37.8505	−	12.2984i	−1.30752	−	0.424840i
$839$	29.3713	−	21.3395i	1.01401	−	0.736722i	0.0489642	−	0.998801i	$-0.484408\pi$
$839$	29.3713	−	21.3395i	1.01401	−	0.736722i	0.965047	+	0.262079i	$0.0844080\pi$
$840$		0			0
$841$	−8.73607	−	26.8869i	−0.301244	−	0.927133i
$842$	−5.93085	+	1.92705i	−0.204391	+	0.0664106i
$843$	−0.640786	+	0.881966i	−0.0220698	+	0.0303765i
$844$	1.42705	−	1.03681i	0.0491211	−	0.0356886i
$845$		0			0
$846$	9.85410			0.338791
$847$	56.6799	−	10.2361i	1.94754	−	0.351715i
$848$		−	26.1246i		−	0.897123i
$849$	−4.95492	+	15.2497i	−0.170052	+	0.523367i
$850$		0			0
$851$	−5.50000	−	3.99598i	−0.188538	−	0.136981i
$852$	−4.70228	+	1.52786i	−0.161098	+	0.0523438i
$853$	22.2173	−	7.21885i	0.760707	−	0.247169i	0.0971248	−	0.995272i	$-0.469035\pi$
$853$	22.2173	−	7.21885i	0.760707	−	0.247169i	0.663582	+	0.748104i	$0.269035\pi$
$854$	47.9787	+	34.8586i	1.64180	+	1.19284i
$855$		0			0
$856$	−2.66312	+	8.19624i	−0.0910235	+	0.280142i
$857$		−	41.0132i		−	1.40098i	−0.713661	−	0.700491i	$-0.752964\pi$
$857$		−	41.0132i		−	1.40098i	0.713661	−	0.700491i	$-0.247036\pi$
$858$	16.1150	+	6.47214i	0.550156	+	0.220955i
$859$	39.2705			1.33989			0.669946	−	0.742410i	$-0.266317\pi$
$859$	39.2705			1.33989			0.669946	+	0.742410i	$0.266317\pi$
$860$		0			0
$861$	−48.5967	+	35.3076i	−1.65617	+	1.20328i
$862$	15.1109	−	20.7984i	0.514679	−	0.708395i
$863$	21.9071	−	7.11803i	0.745725	−	0.242301i	0.0885842	−	0.996069i	$-0.471766\pi$
$863$	21.9071	−	7.11803i	0.745725	−	0.242301i	0.657141	+	0.753768i	$0.271766\pi$
$864$	1.04508	+	3.21644i	0.0355545	+	0.109426i
$865$		0			0
$866$	−1.35410	+	0.983813i	−0.0460143	+	0.0334313i
$867$	12.3637	+	4.01722i	0.419894	+	0.136432i
$868$			22.6525i			0.768875i
$869$	−7.86475	−	6.57164i	−0.266793	−	0.222928i
$870$		0			0
$871$	−11.6180	+	35.7566i	−0.393662	+	1.21157i
$872$	−14.2658	−	19.6353i	−0.483103	−	0.664934i
$873$	−1.48584	+	2.04508i	−0.0502881	+	0.0692156i
$874$	11.5451	+	35.5321i	0.390518	+	1.20189i
$875$		0			0
$876$	−2.26393	−	1.64484i	−0.0764912	−	0.0555741i
$877$	−4.42477	−	6.09017i	−0.149414	−	0.205650i	0.727749	−	0.685844i	$-0.240567\pi$
$877$	−4.42477	−	6.09017i	−0.149414	−	0.205650i	−0.877163	+	0.480193i	$0.840567\pi$
$878$	38.9731	+	12.6631i	1.31528	+	0.427360i
$879$	25.4721			0.859154
$880$		0			0
$881$	−17.1459			−0.577660			−0.288830	−	0.957380i	$-0.593266\pi$
$881$	−17.1459			−0.577660			−0.288830	+	0.957380i	$0.593266\pi$
$882$	−31.4176	−	10.2082i	−1.05789	−	0.343728i
$883$	13.6578	+	18.7984i	0.459622	+	0.632616i	0.974430	−	0.224690i	$-0.0721369\pi$
$883$	13.6578	+	18.7984i	0.459622	+	0.632616i	−0.514808	+	0.857305i	$0.672137\pi$
$884$	3.23607	+	2.35114i	0.108841	+	0.0790774i
$885$		0			0
$886$	4.13525	+	12.7270i	0.138927	+	0.427572i
$887$	0.0982684	−	0.135255i	0.00329953	−	0.00454142i	−0.807364	−	0.590054i	$-0.799107\pi$
$887$	0.0982684	−	0.135255i	0.00329953	−	0.00454142i	0.810664	+	0.585512i	$0.199107\pi$
$888$	−1.93487	−	2.66312i	−0.0649300	−	0.0893684i
$889$	−3.14590	+	9.68208i	−0.105510	+	0.324726i
$890$		0			0
$891$	2.80902	−	1.76336i	0.0941056	−	0.0590746i
$892$		−	13.0000i		−	0.435272i
$893$	28.9605	+	9.40983i	0.969125	+	0.314888i
$894$	−26.3435	+	19.1396i	−0.881057	+	0.640125i
$895$		0			0
$896$	22.0344	+	67.8150i	0.736119	+	2.26554i
$897$	14.2128	−	4.61803i	0.474553	−	0.154192i
$898$	−32.5932	+	44.8607i	−1.08765	+	1.49702i
$899$	4.83688	−	3.51420i	0.161319	−	0.117205i
$900$		0			0
$901$	−10.7639			−0.358599
$902$	−4.16750	+	61.4230i	−0.138762	+	2.04516i
$903$		−	47.5967i		−	1.58392i
$904$	2.39919	−	7.38394i	0.0797958	−	0.245586i
$905$		0			0
$906$	19.9443	+	14.4904i	0.662604	+	0.481410i
$907$	−42.6915	+	13.8713i	−1.41755	+	0.460590i	−0.914823	−	0.403856i	$-0.867670\pi$
$907$	−42.6915	+	13.8713i	−1.41755	+	0.460590i	−0.502727	+	0.864445i	$0.667670\pi$
$908$	4.73504	−	1.53851i	0.157138	−	0.0510572i
$909$	15.8262	+	11.4984i	0.524923	+	0.381379i
$910$		0			0
$911$	16.3475	−	50.3125i	0.541618	−	1.66693i	−0.187281	−	0.982306i	$-0.559968\pi$
$911$	16.3475	−	50.3125i	0.541618	−	1.66693i	0.728899	−	0.684621i	$-0.240032\pi$
$912$			24.2705i			0.803677i
$913$	−1.73060	+	25.5066i	−0.0572745	+	0.844145i
$914$	−12.0902			−0.399907
$915$		0			0
$916$	−3.45492	+	2.51014i	−0.114154	+	0.0829374i
$917$	28.2542	−	38.8885i	0.933035	−	1.28421i
$918$	3.07768	−	1.00000i	0.101579	−	0.0330049i
$919$	6.87132	+	21.1478i	0.226664	+	0.697600i	0.998118	+	0.0613155i	$0.0195296\pi$
$919$	6.87132	+	21.1478i	0.226664	+	0.697600i	−0.771454	+	0.636285i	$0.780470\pi$
$920$		0			0
$921$	−22.7533	+	16.5312i	−0.749746	+	0.544723i
$922$	−12.3965	−	4.02786i	−0.408257	−	0.132651i
$923$			25.8885i			0.852132i
$924$	−9.09017	+	5.70634i	−0.299045	+	0.187725i
$925$		0			0
$926$	−0.135255	+	0.416272i	−0.00444475	+	0.0136795i
$927$	−2.71441	−	3.73607i	−0.0891530	−	0.122709i
$928$	−1.69784	+	2.33688i	−0.0557344	+	0.0767119i
$929$	3.35410	+	10.3229i	0.110045	+	0.338682i	0.990881	−	0.134738i	$-0.0430193\pi$
$929$	3.35410	+	10.3229i	0.110045	+	0.338682i	−0.880837	+	0.473420i	$0.843019\pi$
$930$		0			0
$931$	−82.5861	−	60.0023i	−2.70665	−	1.96650i
$932$	−3.73098	−	5.13525i	−0.122212	−	0.168211i
$933$	11.9147	+	3.87132i	0.390070	+	0.126741i
$934$	−49.9787			−1.63535
$935$		0			0
$936$	7.23607			0.236518
$937$	16.3597	+	5.31559i	0.534449	+	0.173653i	0.563793	−	0.825916i	$-0.309342\pi$
$937$	16.3597	+	5.31559i	0.534449	+	0.173653i	−0.0293438	+	0.999569i	$0.509342\pi$
$938$	−57.8554	−	79.6312i	−1.88905	−	2.60005i
$939$	6.85410	+	4.97980i	0.223675	+	0.162510i
$940$		0			0
$941$	−3.00000	−	9.23305i	−0.0977972	−	0.300989i	0.890175	−	0.455618i	$-0.150582\pi$
$941$	−3.00000	−	9.23305i	−0.0977972	−	0.300989i	−0.987973	+	0.154629i	$0.950582\pi$
$942$	11.7229	−	16.1353i	0.381954	−	0.525715i
$943$	31.1401	+	42.8607i	1.01406	+	1.39574i
$944$	10.0623	−	30.9686i	0.327500	−	1.00794i
$945$		0			0
$946$	−37.4336	−	31.2789i	−1.21707	−	1.01696i
$947$			4.56231i			0.148255i	0.997249	+	0.0741275i	$0.0236172\pi$
$947$			4.56231i			0.148255i	−0.997249	+	0.0741275i	$0.976383\pi$
$948$	1.81636	+	0.590170i	0.0589925	+	0.0191678i
$949$	−11.8541	+	8.61251i	−0.384800	+	0.279574i
$950$		0			0
$951$	−1.10739	−	3.40820i	−0.0359096	−	0.110518i
$952$	22.2703	−	7.23607i	0.721785	−	0.234522i
$953$	−28.8545	+	39.7148i	−0.934688	+	1.28649i	0.0233143	+	0.999728i	$0.492578\pi$
$953$	−28.8545	+	39.7148i	−0.934688	+	1.28649i	−0.958003	+	0.286760i	$0.907422\pi$
$954$	7.04508	−	5.11855i	0.228093	−	0.165719i
$955$		0			0
$956$	13.6180			0.440439
$957$	2.62866	+	1.05573i	0.0849724	+	0.0341268i
$958$			10.6525i			0.344166i
$959$	8.56231	−	26.3521i	0.276491	−	0.850953i
$960$		0			0
$961$	−14.5623	−	10.5801i	−0.469752	−	0.341295i
$962$	7.33094	−	2.38197i	0.236359	−	0.0767977i
$963$	−3.66547	+	1.19098i	−0.118118	+	0.0383789i
$964$	0.309017	+	0.224514i	0.00995277	+	0.00723111i
$965$		0			0
$966$	−12.0902	+	37.2097i	−0.388995	+	1.19720i
$967$		−	32.6738i		−	1.05072i	−0.850881	−	0.525359i	$-0.823931\pi$
$967$		−	32.6738i		−	1.05072i	0.850881	−	0.525359i	$-0.176069\pi$
$968$	3.32244	−	24.3713i	0.106787	−	0.783324i
$969$	10.0000			0.321246
$970$		0			0
$971$	25.5172	−	18.5393i	0.818887	−	0.594956i	−0.0975068	−	0.995235i	$-0.531087\pi$
$971$	25.5172	−	18.5393i	0.818887	−	0.594956i	0.916393	+	0.400279i	$0.131087\pi$
$972$	−0.363271	+	0.500000i	−0.0116519	+	0.0160375i
$973$	5.87785	−	1.90983i	0.188435	−	0.0612263i
$974$	4.09017	+	12.5882i	0.131057	+	0.403354i
$975$		0			0
$976$	27.4894	−	19.9722i	0.879913	−	0.639294i
$977$	−43.8344	−	14.2426i	−1.40239	−	0.455663i	−0.492424	−	0.870356i	$-0.663889\pi$
$977$	−43.8344	−	14.2426i	−1.40239	−	0.455663i	−0.909961	+	0.414693i	$0.863889\pi$
$978$			10.6180i			0.339527i
$979$	5.12461	−	12.7598i	0.163783	−	0.407804i
$980$		0			0
$981$	3.35410	−	10.3229i	0.107088	−	0.329584i
$982$	6.84915	+	9.42705i	0.218565	+	0.300829i
$983$	11.1679	−	15.3713i	0.356201	−	0.490269i	−0.592884	−	0.805288i	$-0.702011\pi$
$983$	11.1679	−	15.3713i	0.356201	−	0.490269i	0.949085	+	0.315019i	$0.102011\pi$
$984$	7.92705	+	24.3970i	0.252705	+	0.777746i
$985$		0			0
$986$	2.23607	+	1.62460i	0.0712109	+	0.0517378i
$987$	18.7436	+	25.7984i	0.596616	+	0.821171i
$988$	−9.51057	−	3.09017i	−0.302571	−	0.0983114i
$989$	−41.9787			−1.33485
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	22.5151	+	7.31559i	0.714855	+	0.232270i
$993$	16.2210	+	22.3262i	0.514757	+	0.708502i
$994$	−54.8328	−	39.8384i	−1.73919	−	1.26360i
$995$		0			0
$996$	−1.47214	−	4.53077i	−0.0466464	−	0.143563i
$997$	−6.63715	+	9.13525i	−0.210201	+	0.289316i	−0.901079	−	0.433654i	$-0.857224\pi$
$997$	−6.63715	+	9.13525i	−0.210201	+	0.289316i	0.690879	+	0.722971i	$0.257224\pi$
$998$	−10.6331	−	14.6353i	−0.336586	−	0.463271i
$999$	0.454915	−	1.40008i	0.0143929	−	0.0442967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.c.724.1		8
5.2	odd	4		825.2.n.d.526.1	yes	4
5.3	odd	4		825.2.n.b.526.1	✓	4
5.4	even	2	inner	825.2.bx.c.724.2		8
11.5	even	5	inner	825.2.bx.c.49.2		8
55.7	even	20		9075.2.a.bc.1.1		2
55.18	even	20		9075.2.a.bt.1.2		2
55.27	odd	20		825.2.n.d.676.1	yes	4
55.37	odd	20		9075.2.a.by.1.2		2
55.38	odd	20		825.2.n.b.676.1	yes	4
55.48	odd	20		9075.2.a.z.1.1		2
55.49	even	10	inner	825.2.bx.c.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.b.526.1	✓	4	5.3	odd	4
825.2.n.b.676.1	yes	4	55.38	odd	20
825.2.n.d.526.1	yes	4	5.2	odd	4
825.2.n.d.676.1	yes	4	55.27	odd	20
825.2.bx.c.49.1		8	55.49	even	10	inner
825.2.bx.c.49.2		8	11.5	even	5	inner
825.2.bx.c.724.1		8	1.1	even	1	trivial
825.2.bx.c.724.2		8	5.4	even	2	inner
9075.2.a.z.1.1		2	55.48	odd	20
9075.2.a.bc.1.1		2	55.7	even	20
9075.2.a.bt.1.2		2	55.18	even	20
9075.2.a.by.1.2		2	55.37	odd	20

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(-3.07768 + 4.23607i) q^{7} +(1.31433 + 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.500000 + 1.53884i) q^{6} +(-3.07768 + 4.23607i) q^{7} +(1.31433 + 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.23607 + 3.07768i) q^{11} -0.618034i q^{12} +(-3.07768 - 1.00000i) q^{13} +(6.85410 - 4.97980i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(-1.90211 + 0.618034i) q^{17} +(0.951057 - 1.30902i) q^{18} +(4.04508 - 2.93893i) q^{19} +5.23607 q^{21} +(3.44095 - 4.11803i) q^{22} -4.61803i q^{23} +(0.690983 - 2.12663i) q^{24} +(4.23607 + 3.07768i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-3.07768 + 1.00000i) q^{28} +(0.690983 + 0.502029i) q^{29} +(2.16312 - 6.65740i) q^{31} +3.38197i q^{32} +(3.21644 - 0.809017i) q^{33} +3.23607 q^{34} +(-0.500000 + 0.363271i) q^{36} +(0.865300 - 1.19098i) q^{37} +(-7.69421 + 2.50000i) q^{38} +(1.00000 + 3.07768i) q^{39} +(-9.28115 + 6.74315i) q^{41} +(-8.05748 - 2.61803i) q^{42} -9.09017i q^{43} +(-1.73607 + 1.08981i) q^{44} +(-2.30902 + 7.10642i) q^{46} +(3.57971 + 4.92705i) q^{47} +(-2.85317 + 3.92705i) q^{48} +(-6.30902 - 19.4172i) q^{49} +(1.61803 + 1.17557i) q^{51} +(-1.17557 - 1.61803i) q^{52} +(5.11855 + 1.66312i) q^{53} -1.61803 q^{54} -11.7082 q^{56} +(-4.75528 - 1.54508i) q^{57} +(-0.812299 - 1.11803i) q^{58} +(5.42705 + 3.94298i) q^{59} +(2.16312 + 6.65740i) q^{61} +(-6.65740 + 9.16312i) q^{62} +(-3.07768 - 4.23607i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(-5.35410 - 0.363271i) q^{66} -11.6180i q^{67} +(-1.17557 - 0.381966i) q^{68} +(-3.73607 + 2.71441i) q^{69} +(-2.47214 - 7.60845i) q^{71} +(-2.12663 + 0.690983i) q^{72} +(2.66141 - 3.66312i) q^{73} +(-1.92705 + 1.40008i) q^{74} +3.09017 q^{76} +(-9.23305 - 14.7082i) q^{77} -5.23607i q^{78} +(-0.954915 + 2.93893i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(17.6538 - 5.73607i) q^{82} +(7.33094 - 2.38197i) q^{83} +(2.61803 + 1.90211i) q^{84} +(-4.54508 + 13.9883i) q^{86} -0.854102i q^{87} +(-7.19218 + 1.80902i) q^{88} -4.14590 q^{89} +(13.7082 - 9.95959i) q^{91} +(1.67760 - 2.30902i) q^{92} +(-6.65740 + 2.16312i) q^{93} +(-3.04508 - 9.37181i) q^{94} +(2.73607 - 1.98787i) q^{96} +(2.40414 + 0.781153i) q^{97} +33.0344i q^{98} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9	\( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 28 * q^14 - 12 * q^16 + 10 * q^19 + 24 * q^21 + 10 * q^24 + 16 * q^26 + 10 * q^29 - 14 * q^31 + 8 * q^34 - 4 * q^36 + 8 * q^39 - 34 * q^41 + 4 * q^44 - 14 * q^46 - 46 * q^49 + 4 * q^51 - 4 * q^54 - 40 * q^56 + 30 * q^59 - 14 * q^61 - 6 * q^64 - 16 * q^66 - 12 * q^69 + 16 * q^71 - 2 * q^74 - 20 * q^76 - 30 * q^79 - 2 * q^81 + 12 * q^84 - 14 * q^86 - 60 * q^89 + 56 * q^91 - 2 * q^94 + 4 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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