LMFDB - Embedded newform 726.2.h.i.233.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(161,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,2,-2,0,-2,0,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			233.1
Root			$-1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	726.233
Dual form			726.2.h.i.215.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.0222369 - 1.73191i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.34500 + 0.437016i) q^{5} +(1.65401 + 0.514040i) q^{6} +(2.49376 - 3.43237i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-2.99901 + 0.0770245i) q^{9} -1.41421i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-4.03499 - 1.31105i) q^{13} +(2.49376 + 3.43237i) q^{14} +(0.786780 + 2.31969i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.853491 - 2.87603i) q^{18} +(1.34500 + 0.437016i) q^{20} +(-6.00000 - 4.24264i) q^{21} +1.41421i q^{23} +(-1.03598 - 1.38807i) q^{24} +(-2.42705 + 1.76336i) q^{25} +(2.49376 - 3.43237i) q^{26} +(0.200088 + 5.19230i) q^{27} +(-4.03499 + 1.31105i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-2.44929 + 0.0314477i) q^{30} +(-1.23607 + 3.80423i) q^{31} -1.00000 q^{32} +(-1.85410 + 5.70634i) q^{35} +(2.47152 + 1.70046i) q^{36} +(-1.61803 - 1.17557i) q^{37} +(-2.18089 + 7.01739i) q^{39} +(-0.831254 + 1.14412i) q^{40} +(4.85410 - 3.52671i) q^{41} +(5.88909 - 4.39529i) q^{42} -8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} +(-1.34500 - 0.437016i) q^{46} +(-5.81878 - 8.00886i) q^{47} +(1.64027 - 0.556338i) q^{48} +(-3.39919 - 10.4616i) q^{49} +(-0.927051 - 2.85317i) q^{50} +(2.49376 + 3.43237i) q^{52} +(-6.72499 - 2.18508i) q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(4.85410 - 3.52671i) q^{58} +(-6.65003 + 9.15298i) q^{59} +(0.726963 - 2.33913i) q^{60} +(-4.03499 + 1.31105i) q^{61} +(-3.23607 - 2.35114i) q^{62} +(-7.21444 + 10.4858i) q^{63} +(0.309017 - 0.951057i) q^{64} +6.00000 q^{65} -4.00000 q^{67} +(2.44929 - 0.0314477i) q^{69} +(-4.85410 - 3.52671i) q^{70} +(6.72499 - 2.18508i) q^{71} +(-2.38098 + 1.82509i) q^{72} +(1.61803 - 1.17557i) q^{74} +(3.10794 + 4.16422i) q^{75} +(-6.00000 - 4.24264i) q^{78} +(4.03499 + 1.31105i) q^{79} +(-0.831254 - 1.14412i) q^{80} +(8.98813 - 0.461994i) q^{81} +(1.85410 + 5.70634i) q^{82} +(-3.70820 - 11.4127i) q^{83} +(2.36034 + 6.95908i) q^{84} +(8.06998 + 2.62210i) q^{86} +(-6.00000 + 8.48528i) q^{87} +5.65685i q^{89} +(0.108929 + 4.24124i) q^{90} +(-14.5623 + 10.5801i) q^{91} +(0.831254 - 1.14412i) q^{92} +(6.61606 + 2.05616i) q^{93} +(9.41498 - 3.05911i) q^{94} +(0.0222369 + 1.73191i) q^{96} +(2.47214 - 7.60845i) q^{97} +11.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 8 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 48 q^{21} - 2 q^{24} - 6 q^{25} - 10 q^{27} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 8 q^{32} + 12 q^{35}+ \cdots + 88 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 8 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 48 * q^21 - 2 * q^24 - 6 * q^25 - 10 * q^27 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 8 * q^32 + 12 * q^35 + 2 * q^36 - 4 * q^37 - 12 * q^39 + 12 * q^41 - 12 * q^42 + 32 * q^45 + 2 * q^48 + 22 * q^49 + 6 * q^50 - 40 * q^54 + 12 * q^58 + 4 * q^60 - 8 * q^62 - 24 * q^63 - 2 * q^64 + 48 * q^65 - 32 * q^67 + 4 * q^69 - 12 * q^70 - 2 * q^72 + 4 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 24 * q^83 + 12 * q^84 - 48 * q^87 + 8 * q^90 - 36 * q^91 - 8 * q^93 - 2 * q^96 - 16 * q^97 + 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.0222369	−	1.73191i	−0.0128385	−	0.999918i
$3$	−0.0222369	−	1.73191i	−0.0128385	−	0.999918i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.34500	+	0.437016i	−0.601501	+	0.195440i	−0.593910	−	0.804532i	$-0.702416\pi$
$5$	−1.34500	+	0.437016i	−0.601501	+	0.195440i	−0.00759122	+	0.999971i	$0.502416\pi$
$6$	1.65401	+	0.514040i	0.675248	+	0.209856i
$7$	2.49376	−	3.43237i	0.942553	−	1.29731i	−0.0122035	−	0.999926i	$-0.503885\pi$
$7$	2.49376	−	3.43237i	0.942553	−	1.29731i	0.954757	−	0.297388i	$-0.0961154\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−2.99901	+	0.0770245i	−0.999670	+	0.0256748i
$10$		−	1.41421i		−	0.447214i
$11$		0			0
$11$		0			0
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−4.03499	−	1.31105i	−1.11911	−	0.363619i	−0.309679	−	0.950841i	$-0.600222\pi$
$13$	−4.03499	−	1.31105i	−1.11911	−	0.363619i	−0.809426	+	0.587222i	$0.800222\pi$
$14$	2.49376	+	3.43237i	0.666486	+	0.917339i
$15$	0.786780	+	2.31969i	0.203146	+	0.598942i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$17$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$18$	0.853491	−	2.87603i	0.201170	−	0.677887i
$19$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$19$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$20$	1.34500	+	0.437016i	0.300750	+	0.0977198i
$21$	−6.00000	−	4.24264i	−1.30931	−	0.925820i
$22$		0			0
$23$			1.41421i			0.294884i	0.989071	+	0.147442i	$0.0471040\pi$
$23$			1.41421i			0.294884i	−0.989071	+	0.147442i	$0.952896\pi$
$24$	−1.03598	−	1.38807i	−0.211469	−	0.283339i
$25$	−2.42705	+	1.76336i	−0.485410	+	0.352671i
$26$	2.49376	−	3.43237i	0.489067	−	0.673143i
$27$	0.200088	+	5.19230i	0.0385069	+	0.999258i
$28$	−4.03499	+	1.31105i	−0.762542	+	0.247765i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$	−2.44929	+	0.0314477i	−0.447177	+	0.00574154i
$31$	−1.23607	+	3.80423i	−0.222004	+	0.683259i	0.776578	+	0.630022i	$0.216954\pi$
$31$	−1.23607	+	3.80423i	−0.222004	+	0.683259i	−0.998582	+	0.0532375i	$0.983046\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		0			0
$35$	−1.85410	+	5.70634i	−0.313400	+	0.964547i
$36$	2.47152	+	1.70046i	0.411921	+	0.283410i
$37$	−1.61803	−	1.17557i	−0.266003	−	0.193263i	0.446786	−	0.894641i	$-0.352568\pi$
$37$	−1.61803	−	1.17557i	−0.266003	−	0.193263i	−0.712789	+	0.701378i	$0.752568\pi$
$38$		0			0
$39$	−2.18089	+	7.01739i	−0.349222	+	1.12368i
$40$	−0.831254	+	1.14412i	−0.131433	+	0.180902i
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	−0.140238	−	0.990118i	$-0.544787\pi$
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	0.898322	+	0.439338i	$0.144787\pi$
$42$	5.88909	−	4.39529i	0.908707	−	0.678208i
$43$		−	8.48528i		−	1.29399i	−0.762493	−	0.646997i	$-0.776025\pi$
$43$		−	8.48528i		−	1.29399i	0.762493	−	0.646997i	$-0.223975\pi$
$44$		0			0
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$	−1.34500	−	0.437016i	−0.198309	−	0.0644345i
$47$	−5.81878	−	8.00886i	−0.848756	−	1.16821i	−0.984136	−	0.177418i	$-0.943225\pi$
$47$	−5.81878	−	8.00886i	−0.848756	−	1.16821i	0.135380	−	0.990794i	$-0.456775\pi$
$48$	1.64027	−	0.556338i	0.236753	−	0.0803004i
$49$	−3.39919	−	10.4616i	−0.485598	−	1.49452i
$50$	−0.927051	−	2.85317i	−0.131105	−	0.403499i
$51$		0			0
$52$	2.49376	+	3.43237i	0.345823	+	0.475984i
$53$	−6.72499	−	2.18508i	−0.923748	−	0.300144i	−0.191744	−	0.981445i	$-0.561414\pi$
$53$	−6.72499	−	2.18508i	−0.923748	−	0.300144i	−0.732003	+	0.681301i	$0.761414\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$		0			0
$58$	4.85410	−	3.52671i	0.637375	−	0.463080i
$59$	−6.65003	+	9.15298i	−0.865760	+	1.19162i	0.114405	+	0.993434i	$0.463504\pi$
$59$	−6.65003	+	9.15298i	−0.865760	+	1.19162i	−0.980165	+	0.198183i	$0.936496\pi$
$60$	0.726963	−	2.33913i	0.0938505	−	0.301980i
$61$	−4.03499	+	1.31105i	−0.516628	+	0.167863i	−0.555714	−	0.831373i	$-0.687555\pi$
$61$	−4.03499	+	1.31105i	−0.516628	+	0.167863i	0.0390866	+	0.999236i	$0.487555\pi$
$62$	−3.23607	−	2.35114i	−0.410981	−	0.298595i
$63$	−7.21444	+	10.4858i	−0.908934	+	1.32109i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.00000			0.744208
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	2.44929	−	0.0314477i	0.294860	−	0.00378586i
$70$	−4.85410	−	3.52671i	−0.580176	−	0.421523i
$71$	6.72499	−	2.18508i	0.798109	−	0.259321i	0.118556	−	0.992947i	$-0.462174\pi$
$71$	6.72499	−	2.18508i	0.798109	−	0.259321i	0.679553	+	0.733626i	$0.262174\pi$
$72$	−2.38098	+	1.82509i	−0.280601	+	0.215089i
$73$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$73$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$74$	1.61803	−	1.17557i	0.188093	−	0.136657i
$75$	3.10794	+	4.16422i	0.358874	+	0.480842i
$76$		0			0
$77$		0			0
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$	4.03499	+	1.31105i	0.453972	+	0.147504i	0.527073	−	0.849820i	$-0.323290\pi$
$79$	4.03499	+	1.31105i	0.453972	+	0.147504i	−0.0731009	+	0.997325i	$0.523290\pi$
$80$	−0.831254	−	1.14412i	−0.0929370	−	0.127917i
$81$	8.98813	−	0.461994i	0.998682	−	0.0513327i
$82$	1.85410	+	5.70634i	0.204751	+	0.630160i
$83$	−3.70820	−	11.4127i	−0.407028	−	1.25270i	−0.919190	−	0.393815i	$-0.871155\pi$
$83$	−3.70820	−	11.4127i	−0.407028	−	1.25270i	0.512161	−	0.858889i	$-0.328845\pi$
$84$	2.36034	+	6.95908i	0.257534	+	0.759298i
$85$		0			0
$86$	8.06998	+	2.62210i	0.870209	+	0.282748i
$87$	−6.00000	+	8.48528i	−0.643268	+	0.909718i
$88$		0			0
$89$			5.65685i			0.599625i	0.953998	+	0.299813i	$0.0969242\pi$
$89$			5.65685i			0.599625i	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0.108929	+	4.24124i	0.0114821	+	0.447066i
$91$	−14.5623	+	10.5801i	−1.52654	+	1.10910i
$92$	0.831254	−	1.14412i	0.0866642	−	0.119283i
$93$	6.61606	+	2.05616i	0.686053	+	0.213214i
$94$	9.41498	−	3.05911i	0.971081	−	0.315523i
$95$		0			0
$96$	0.0222369	+	1.73191i	0.00226954	+	0.176762i
$97$	2.47214	−	7.60845i	0.251007	−	0.772521i	−0.743583	−	0.668644i	$-0.766875\pi$
$97$	2.47214	−	7.60845i	0.251007	−	0.772521i	0.994590	−	0.103877i	$-0.0331249\pi$
$98$	11.0000			1.11117
$99$		0			0
$100$	3.00000			0.300000
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	−0.815449	−	0.578829i	$-0.803510\pi$
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	0.999939	+	0.0110267i	$0.00350999\pi$
$102$		0			0
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	0.735689	−	0.677320i	$-0.236859\pi$
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	−0.416829	+	0.908985i	$0.636859\pi$
$104$	−4.03499	+	1.31105i	−0.395663	+	0.128559i
$105$	9.92408	+	3.08424i	0.968491	+	0.300991i
$106$	4.15627	−	5.72061i	0.403693	−	0.555635i
$107$	14.5623	−	10.5801i	1.40779	−	1.02282i	0.414152	−	0.910208i	$-0.364078\pi$
$107$	14.5623	−	10.5801i	1.40779	−	1.02282i	0.993639	−	0.112613i	$-0.0359219\pi$
$108$	2.89008	−	4.31827i	0.278098	−	0.415525i
$109$			12.7279i			1.21911i	0.792742	+	0.609557i	$0.208653\pi$
$109$			12.7279i			1.21911i	−0.792742	+	0.609557i	$0.791347\pi$
$110$		0			0
$111$	−2.00000	+	2.82843i	−0.189832	+	0.268462i
$112$	4.03499	+	1.31105i	0.381271	+	0.123882i
$113$	6.65003	+	9.15298i	0.625582	+	0.861040i	0.997744	−	0.0671276i	$-0.0213835\pi$
$113$	6.65003	+	9.15298i	0.625582	+	0.861040i	−0.372162	+	0.928168i	$0.621383\pi$
$114$		0			0
$115$	−0.618034	−	1.90211i	−0.0576320	−	0.177373i
$116$	1.85410	+	5.70634i	0.172149	+	0.529820i
$117$	12.2020	+	3.62105i	1.12807	+	0.334767i
$118$	−6.65003	−	9.15298i	−0.612185	−	0.842600i
$119$		0			0
$120$	2.00000	+	1.41421i	0.182574	+	0.129099i
$121$		0			0
$122$		−	4.24264i		−	0.384111i
$123$	−6.21588	−	8.32844i	−0.560467	−	0.750950i
$124$	3.23607	−	2.35114i	0.290607	−	0.211139i
$125$	6.65003	−	9.15298i	0.594797	−	0.818668i
$126$	−7.74320	−	10.1016i	−0.689819	−	0.899925i
$127$	12.1050	−	3.93314i	1.07414	−	0.349010i	0.282043	−	0.959402i	$-0.408988\pi$
$127$	12.1050	−	3.93314i	1.07414	−	0.349010i	0.792100	+	0.610392i	$0.208988\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−14.6957	+	0.188686i	−1.29389	+	0.0166129i
$130$	−1.85410	+	5.70634i	−0.162615	+	0.500479i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	1.23607	−	3.80423i	0.106780	−	0.328635i
$135$	−2.53824	−	6.89618i	−0.218457	−	0.593529i
$136$		0			0
$137$	2.68999	−	0.874032i	0.229822	−	0.0746736i	−0.191842	−	0.981426i	$-0.561446\pi$
$137$	2.68999	−	0.874032i	0.229822	−	0.0746736i	0.421664	+	0.906752i	$0.361446\pi$
$138$	−0.726963	+	2.33913i	−0.0618832	+	0.199120i
$139$	−9.97505	+	13.7295i	−0.846072	+	1.16452i	0.138642	+	0.990343i	$0.455726\pi$
$139$	−9.97505	+	13.7295i	−0.846072	+	1.16452i	−0.984715	+	0.174176i	$0.944274\pi$
$140$	4.85410	−	3.52671i	0.410246	−	0.298062i
$141$	−13.7412	+	10.2557i	−1.15722	+	0.863684i
$142$			7.07107i			0.593391i
$143$		0			0
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	8.06998	+	2.62210i	0.670176	+	0.217753i
$146$		0			0
$147$	−18.0430	+	6.11971i	−1.48816	+	0.504745i
$148$	0.618034	+	1.90211i	0.0508021	+	0.156353i
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	0.845939	−	0.533280i	$-0.179041\pi$
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	−0.997833	+	0.0657982i	$0.979041\pi$
$150$	−4.92081	+	1.66901i	−0.401783	+	0.136274i
$151$	−2.49376	−	3.43237i	−0.202939	−	0.279322i	0.695401	−	0.718622i	$-0.255227\pi$
$151$	−2.49376	−	3.43237i	−0.202939	−	0.279322i	−0.898341	+	0.439300i	$0.855227\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	5.65685i		−	0.454369i
$156$	5.88909	−	4.39529i	0.471505	−	0.351905i
$157$	17.7984	−	12.9313i	1.42046	−	1.03203i	0.428770	−	0.903414i	$-0.358947\pi$
$157$	17.7984	−	12.9313i	1.42046	−	1.03203i	0.991695	−	0.128615i	$-0.0410530\pi$
$158$	−2.49376	+	3.43237i	−0.198393	+	0.273065i
$159$	−3.63482	+	11.6956i	−0.288260	+	0.927525i
$160$	1.34500	−	0.437016i	0.106331	−	0.0345492i
$161$	4.85410	+	3.52671i	0.382557	+	0.277944i
$162$	−2.33810	+	8.69099i	−0.183699	+	0.682829i
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	−0.923931	−	0.382560i	$-0.875042\pi$
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	0.972339	+	0.233575i	$0.0750425\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	12.0000			0.931381
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	−0.698858	−	0.715260i	$-0.746308\pi$
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	0.985808	−	0.167879i	$-0.0536919\pi$
$168$	−7.34786	+	0.0943431i	−0.566900	+	0.00727873i
$169$	4.04508	+	2.93893i	0.311160	+	0.226071i
$170$		0			0
$171$		0			0
$172$	−4.98752	+	6.86474i	−0.380295	+	0.523431i
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	−0.756817	−	0.653627i	$-0.773247\pi$
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	0.387767	+	0.921758i	$0.373247\pi$
$174$	−6.21588	−	8.32844i	−0.471225	−	0.631377i
$175$			12.7279i			0.962140i
$176$		0			0
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$	−5.37999	−	1.74806i	−0.403247	−	0.131023i
$179$	−3.32502	−	4.57649i	−0.248523	−	0.342063i	0.666470	−	0.745532i	$-0.267804\pi$
$179$	−3.32502	−	4.57649i	−0.248523	−	0.342063i	−0.914993	+	0.403469i	$0.867804\pi$
$180$	−4.06732	−	1.20702i	−0.303160	−	0.0899658i
$181$	0.618034	+	1.90211i	0.0459381	+	0.141383i	0.971395	−	0.237471i	$-0.0763184\pi$
$181$	0.618034	+	1.90211i	0.0459381	+	0.141383i	−0.925457	+	0.378854i	$0.876318\pi$
$182$	−5.56231	−	17.1190i	−0.412306	−	1.26895i
$183$	2.36034	+	6.95908i	0.174481	+	0.514430i
$184$	0.831254	+	1.14412i	0.0612808	+	0.0843459i
$185$	2.68999	+	0.874032i	0.197772	+	0.0642601i
$186$	−4.00000	+	5.65685i	−0.293294	+	0.414781i
$187$		0			0
$188$			9.89949i			0.721995i
$189$	18.3209	+	12.2616i	1.33265	+	0.891899i
$190$		0			0
$191$	5.81878	−	8.00886i	0.421032	−	0.579501i	−0.544834	−	0.838544i	$-0.683407\pi$
$191$	5.81878	−	8.00886i	0.421032	−	0.579501i	0.965866	+	0.259043i	$0.0834072\pi$
$192$	−1.65401	−	0.514040i	−0.119368	−	0.0370977i
$193$	−8.06998	+	2.62210i	−0.580890	+	0.188743i	−0.584699	−	0.811250i	$-0.698787\pi$
$193$	−8.06998	+	2.62210i	−0.580890	+	0.188743i	0.00380923	+	0.999993i	$0.498787\pi$
$194$	6.47214	+	4.70228i	0.464672	+	0.337604i
$195$	−0.133421	−	10.3914i	−0.00955450	−	0.744147i
$196$	−3.39919	+	10.4616i	−0.242799	+	0.747259i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−0.927051	+	2.85317i	−0.0655524	+	0.201750i
$201$	0.0889475	+	6.92763i	0.00627387	+	0.488638i
$202$	4.85410	+	3.52671i	0.341533	+	0.248139i
$203$	−24.2099	+	7.86629i	−1.69921	+	0.552105i
$204$		0			0
$205$	−4.98752	+	6.86474i	−0.348344	+	0.479454i
$206$	−3.23607	+	2.35114i	−0.225468	+	0.163812i
$207$	−0.108929	−	4.24124i	−0.00757109	−	0.294787i
$208$		−	4.24264i		−	0.294174i
$209$		0			0
$210$	−6.00000	+	8.48528i	−0.414039	+	0.585540i
$211$	8.06998	+	2.62210i	0.555560	+	0.180513i	0.573323	−	0.819330i	$-0.305654\pi$
$211$	8.06998	+	2.62210i	0.555560	+	0.180513i	−0.0177622	+	0.999842i	$0.505654\pi$
$212$	4.15627	+	5.72061i	0.285454	+	0.392893i
$213$	−3.93390	−	11.5985i	−0.269546	−	0.794714i
$214$	5.56231	+	17.1190i	0.380231	+	1.17023i
$215$	3.70820	+	11.4127i	0.252897	+	0.778338i
$216$	3.21383	+	4.08305i	0.218674	+	0.277816i
$217$	9.97505	+	13.7295i	0.677150	+	0.932017i
$218$	−12.1050	−	3.93314i	−0.819852	−	0.266386i
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−2.07196	−	2.77615i	−0.139061	−	0.186323i
$223$	−6.47214	+	4.70228i	−0.433406	+	0.314888i	−0.783009	−	0.622010i	$-0.786316\pi$
$223$	−6.47214	+	4.70228i	−0.433406	+	0.314888i	0.349603	+	0.936898i	$0.386316\pi$
$224$	−2.49376	+	3.43237i	−0.166621	+	0.229335i
$225$	7.14293	−	5.47527i	0.476195	−	0.365018i
$226$	−10.7600	+	3.49613i	−0.715743	+	0.232559i
$227$	−4.85410	−	3.52671i	−0.322178	−	0.234076i	0.414926	−	0.909855i	$-0.363807\pi$
$227$	−4.85410	−	3.52671i	−0.322178	−	0.234076i	−0.737104	+	0.675779i	$0.763807\pi$
$228$		0			0
$229$	4.32624	−	13.3148i	0.285886	−	0.879866i	−0.700246	−	0.713902i	$-0.746926\pi$
$229$	4.32624	−	13.3148i	0.285886	−	0.879866i	0.986132	−	0.165964i	$-0.0530737\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−5.56231	+	17.1190i	−0.364399	+	1.12150i	0.585958	+	0.810341i	$0.300718\pi$
$233$	−5.56231	+	17.1190i	−0.364399	+	1.12150i	−0.950357	+	0.311163i	$0.899282\pi$
$234$	−7.21444	+	10.4858i	−0.471623	+	0.685478i
$235$	11.3262	+	8.22899i	0.738842	+	0.536800i
$236$	10.7600	−	3.49613i	0.700415	−	0.227579i
$237$	2.18089	−	7.01739i	0.141664	−	0.455828i
$238$		0			0
$239$	−9.70820	+	7.05342i	−0.627972	+	0.456248i	−0.855697	−	0.517477i	$-0.826871\pi$
$239$	−9.70820	+	7.05342i	−0.627972	+	0.456248i	0.227725	+	0.973725i	$0.426871\pi$
$240$	−1.96303	+	1.46510i	−0.126713	+	0.0945716i
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$		0			0
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$	4.03499	+	1.31105i	0.258314	+	0.0839313i
$245$	9.14379	+	12.5854i	0.584175	+	0.804049i
$246$	9.84163	−	3.33803i	0.627479	−	0.212825i
$247$		0			0
$248$	1.23607	+	3.80423i	0.0784904	+	0.241569i
$249$	−19.6833	+	6.67605i	−1.24738	+	0.423078i
$250$	6.65003	+	9.15298i	0.420585	+	0.578885i
$251$	5.37999	+	1.74806i	0.339582	+	0.110337i	0.473843	−	0.880609i	$-0.342866\pi$
$251$	5.37999	+	1.74806i	0.339582	+	0.110337i	−0.134262	+	0.990946i	$0.542866\pi$
$252$	12.0000	−	4.24264i	0.755929	−	0.267261i
$253$		0			0
$254$			12.7279i			0.798621i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−6.65003	+	9.15298i	−0.414818	+	0.570947i	−0.964385	−	0.264502i	$-0.914792\pi$
$257$	−6.65003	+	9.15298i	−0.414818	+	0.570947i	0.549568	+	0.835449i	$0.314792\pi$
$258$	4.36178	−	14.0348i	0.271552	−	0.873767i
$259$	−8.06998	+	2.62210i	−0.501444	+	0.162929i
$260$	−4.85410	−	3.52671i	−0.301039	−	0.218717i
$261$	14.8291	+	10.2028i	0.917901	+	0.631535i
$262$	−3.70820	+	11.4127i	−0.229094	+	0.705078i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	9.79715	−	0.125791i	0.599576	−	0.00769827i
$268$	3.23607	+	2.35114i	0.197674	+	0.143619i
$269$	6.72499	−	2.18508i	0.410030	−	0.133227i	−0.0967370	−	0.995310i	$-0.530841\pi$
$269$	6.72499	−	2.18508i	0.410030	−	0.133227i	0.506767	+	0.862083i	$0.330841\pi$
$270$	7.34302	−	0.282967i	0.446882	−	0.0172208i
$271$	7.48128	−	10.2971i	0.454456	−	0.625505i	−0.518892	−	0.854840i	$-0.673655\pi$
$271$	7.48128	−	10.2971i	0.454456	−	0.625505i	0.973347	+	0.229335i	$0.0736552\pi$
$272$		0			0
$273$	18.6476	+	24.9853i	1.12861	+	1.51218i
$274$			2.82843i			0.170872i
$275$		0			0
$276$	−2.00000	−	1.41421i	−0.120386	−	0.0851257i
$277$	−20.1750	−	6.55524i	−1.21220	−	0.393866i	−0.367962	−	0.929841i	$-0.619944\pi$
$277$	−20.1750	−	6.55524i	−1.21220	−	0.393866i	−0.844234	+	0.535975i	$0.819944\pi$
$278$	−9.97505	−	13.7295i	−0.598264	−	0.823439i
$279$	3.41396	−	11.5041i	0.204389	−	0.688734i
$280$	1.85410	+	5.70634i	0.110804	+	0.341019i
$281$	−3.70820	−	11.4127i	−0.221213	−	0.680823i	−0.998654	−	0.0518675i	$-0.983483\pi$
$281$	−3.70820	−	11.4127i	−0.221213	−	0.680823i	0.777441	−	0.628956i	$-0.216517\pi$
$282$	−5.50746	−	16.2379i	−0.327965	−	0.966950i
$283$	−4.98752	−	6.86474i	−0.296477	−	0.408066i	0.634627	−	0.772818i	$-0.281154\pi$
$283$	−4.98752	−	6.86474i	−0.296477	−	0.408066i	−0.931105	+	0.364752i	$0.881154\pi$
$284$	−6.72499	−	2.18508i	−0.399054	−	0.129661i
$285$		0			0
$286$		0			0
$287$		−	25.4558i		−	1.50261i
$288$	2.99901	−	0.0770245i	0.176718	−	0.00453871i
$289$	13.7533	−	9.99235i	0.809017	−	0.587785i
$290$	−4.98752	+	6.86474i	−0.292877	+	0.403111i
$291$	−13.2321	−	4.11232i	−0.775680	−	0.241069i
$292$		0			0
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	0.720477	−	0.693479i	$-0.243923\pi$
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	−0.436898	+	0.899511i	$0.643923\pi$
$294$	−0.244606	−	19.0510i	−0.0142657	−	1.11108i
$295$	4.94427	−	15.2169i	0.287867	−	0.885962i
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	1.85410	−	5.70634i	0.107225	−	0.330006i
$300$	−0.0667106	−	5.19572i	−0.00385154	−	0.299975i
$301$	−29.1246	−	21.1603i	−1.67871	−	1.21966i
$302$	4.03499	−	1.31105i	0.232188	−	0.0754423i
$303$	−9.92408	−	3.08424i	−0.570124	−	0.177185i
$304$		0			0
$305$	4.85410	−	3.52671i	0.277945	−	0.201939i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	4.00000	−	5.65685i	0.227552	−	0.321807i
$310$	5.37999	+	1.74806i	0.305563	+	0.0992834i
$311$	−15.7938	−	21.7383i	−0.895586	−	1.23267i	−0.971855	−	0.235581i	$-0.924301\pi$
$311$	−15.7938	−	21.7383i	−0.895586	−	1.23267i	0.0762693	−	0.997087i	$-0.475699\pi$
$312$	2.36034	+	6.95908i	0.133628	+	0.393980i
$313$	−3.09017	−	9.51057i	−0.174667	−	0.537569i	0.824951	−	0.565204i	$-0.191202\pi$
$313$	−3.09017	−	9.51057i	−0.174667	−	0.537569i	−0.999618	+	0.0276348i	$0.991202\pi$
$314$	6.79837	+	20.9232i	0.383654	+	1.18077i
$315$	5.12094	−	17.2562i	0.288533	−	0.972276i
$316$	−2.49376	−	3.43237i	−0.140285	−	0.193086i
$317$	9.41498	+	3.05911i	0.528798	+	0.171817i	0.561234	−	0.827657i	$-0.310327\pi$
$317$	9.41498	+	3.05911i	0.528798	+	0.171817i	−0.0324364	+	0.999474i	$0.510327\pi$
$318$	−10.0000	−	7.07107i	−0.560772	−	0.396526i
$319$		0			0
$320$			1.41421i			0.0790569i
$321$	−18.6476	−	24.9853i	−1.04081	−	1.39454i
$322$	−4.85410	+	3.52671i	−0.270509	+	0.196536i
$323$		0			0
$324$	−7.54311	−	4.90933i	−0.419062	−	0.272741i
$325$	12.1050	−	3.93314i	0.671463	−	0.218172i
$326$	1.61803	+	1.17557i	0.0896146	+	0.0651088i
$327$	22.0436	−	0.283029i	1.21901	−	0.0156516i
$328$	1.85410	−	5.70634i	0.102376	−	0.315080i
$329$	−42.0000			−2.31553
$330$		0			0
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$	−3.70820	+	11.4127i	−0.203514	+	0.626352i
$333$	4.94305	+	3.40092i	0.270877	+	0.186369i
$334$	9.70820	+	7.05342i	0.531209	+	0.385946i
$335$	5.37999	−	1.74806i	0.293940	−	0.0955069i
$336$	2.18089	−	7.01739i	0.118977	−	0.382830i
$337$	19.9501	−	27.4589i	1.08675	−	1.49578i	0.234886	−	0.972023i	$-0.424528\pi$
$337$	19.9501	−	27.4589i	1.08675	−	1.49578i	0.851865	−	0.523761i	$-0.175472\pi$
$338$	−4.04508	+	2.93893i	−0.220024	+	0.159857i
$339$	15.7042	−	11.7208i	0.852938	−	0.636585i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−16.1400	−	5.24419i	−0.871476	−	0.283160i
$344$	−4.98752	−	6.86474i	−0.268909	−	0.370122i
$345$	−3.28054	+	1.11268i	−0.176618	+	0.0599044i
$346$	−1.85410	−	5.70634i	−0.0996771	−	0.306775i
$347$	3.70820	+	11.4127i	0.199067	+	0.612665i	0.999905	+	0.0137839i	$0.00438768\pi$
$347$	3.70820	+	11.4127i	0.199067	+	0.612665i	−0.800838	+	0.598881i	$0.795612\pi$
$348$	9.84163	−	3.33803i	0.527566	−	0.178937i
$349$	−17.4563	−	24.0266i	−0.934416	−	1.28611i	−0.958112	−	0.286394i	$-0.907543\pi$
$349$	−17.4563	−	24.0266i	−0.934416	−	1.28611i	0.0236959	−	0.999719i	$-0.492457\pi$
$350$	−12.1050	−	3.93314i	−0.647038	−	0.210235i
$351$	6.00000	−	21.2132i	0.320256	−	1.13228i
$352$		0			0
$353$			22.6274i			1.20434i	0.798369	+	0.602168i	$0.205696\pi$
$353$			22.6274i			1.20434i	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−15.7042	+	11.7208i	−0.834671	+	0.622952i
$355$	−8.09017	+	5.87785i	−0.429382	+	0.311964i
$356$	3.32502	−	4.57649i	0.176225	−	0.242554i
$357$		0			0
$358$	5.37999	−	1.74806i	0.284341	−	0.0923881i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$	2.40481	−	3.49526i	0.126745	−	0.184217i
$361$	5.87132	−	18.0701i	0.309017	−	0.951057i
$362$	−2.00000			−0.105118
$363$		0			0
$364$	18.0000			0.943456
$365$		0			0
$366$	−7.34786	+	0.0943431i	−0.384079	+	0.00493139i
$367$	22.6525	+	16.4580i	1.18245	+	0.859100i	0.992446	−	0.122683i	$-0.0391500\pi$
$367$	22.6525	+	16.4580i	1.18245	+	0.859100i	0.190004	+	0.981783i	$0.439150\pi$
$368$	−1.34500	+	0.437016i	−0.0701128	+	0.0227810i
$369$	−14.2859	+	10.9505i	−0.743692	+	0.570062i
$370$	−1.66251	+	2.28825i	−0.0864297	+	0.118960i
$371$	−24.2705	+	17.6336i	−1.26006	+	0.915489i
$372$	−4.14392	−	5.55229i	−0.214852	−	0.287873i
$373$		−	29.6985i		−	1.53773i	−0.639412	−	0.768865i	$-0.720822\pi$
$373$		−	29.6985i		−	1.53773i	0.639412	−	0.768865i	$-0.279178\pi$
$374$		0			0
$375$	−16.0000	−	11.3137i	−0.826236	−	0.584237i
$376$	−9.41498	−	3.05911i	−0.485540	−	0.157762i
$377$	14.9626	+	20.5942i	0.770612	+	1.06066i
$378$	−17.3229	+	13.6351i	−0.890994	+	0.701315i
$379$	0.618034	+	1.90211i	0.0317463	+	0.0977050i	0.965674	−	0.259757i	$-0.0836423\pi$
$379$	0.618034	+	1.90211i	0.0317463	+	0.0977050i	−0.933928	+	0.357462i	$0.883642\pi$
$380$		0			0
$381$	−7.08102	−	20.8772i	−0.362772	−	1.06957i
$382$	5.81878	+	8.00886i	0.297715	+	0.409769i
$383$	1.34500	+	0.437016i	0.0687261	+	0.0223305i	0.343178	−	0.939270i	$-0.388496\pi$
$383$	1.34500	+	0.437016i	0.0687261	+	0.0223305i	−0.274452	+	0.961601i	$0.588496\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	0.653574	+	25.4475i	0.0332230	+	1.29357i
$388$	−6.47214	+	4.70228i	−0.328573	+	0.238722i
$389$	5.81878	−	8.00886i	0.295024	−	0.406065i	−0.635614	−	0.772007i	$-0.719253\pi$
$389$	5.81878	−	8.00886i	0.295024	−	0.406065i	0.930638	+	0.365942i	$0.119253\pi$
$390$	9.92408	+	3.08424i	0.502526	+	0.156177i
$391$		0			0
$392$	−8.89919	−	6.46564i	−0.449477	−	0.326564i
$393$	−0.266843	−	20.7829i	−0.0134604	−	1.04836i
$394$	−5.56231	+	17.1190i	−0.280225	+	0.862444i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	4.94427	−	15.2169i	0.247834	−	0.762754i
$399$		0			0
$400$	−2.42705	−	1.76336i	−0.121353	−	0.0881678i
$401$	34.9699	−	11.3624i	1.74631	−	0.567412i	0.750673	−	0.660674i	$-0.229729\pi$
$401$	34.9699	−	11.3624i	1.74631	−	0.567412i	0.995642	+	0.0932619i	$0.0297294\pi$
$402$	−6.61606	−	2.05616i	−0.329979	−	0.102552i
$403$	9.97505	−	13.7295i	0.496892	−	0.683914i
$404$	−4.85410	+	3.52671i	−0.241501	+	0.175460i
$405$	−11.8871	+	4.54934i	−0.590675	+	0.226059i
$406$		−	25.4558i		−	1.26335i
$407$		0			0
$408$		0			0
$409$	8.06998	+	2.62210i	0.399035	+	0.129654i	0.501658	−	0.865066i	$-0.332724\pi$
$409$	8.06998	+	2.62210i	0.399035	+	0.129654i	−0.102623	+	0.994720i	$0.532724\pi$
$410$	−4.98752	−	6.86474i	−0.246316	−	0.339025i
$411$	−1.57356	−	4.63939i	−0.0776180	−	0.228844i
$412$	−1.23607	−	3.80423i	−0.0608967	−	0.187421i
$413$	14.8328	+	45.6507i	0.729875	+	2.24632i
$414$	4.06732	+	1.20702i	0.199898	+	0.0593217i
$415$	9.97505	+	13.7295i	0.489656	+	0.673953i
$416$	4.03499	+	1.31105i	0.197832	+	0.0642794i
$417$	24.0000	+	16.9706i	1.17529	+	0.831052i
$418$		0			0
$419$		−	11.3137i		−	0.552711i	−0.961056	−	0.276355i	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$	−6.21588	−	8.32844i	−0.303304	−	0.406386i
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	−0.372921	−	0.927863i	$-0.621644\pi$
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	0.767211	+	0.641394i	$0.221644\pi$
$422$	−4.98752	+	6.86474i	−0.242789	+	0.334170i
$423$	18.0675	+	23.5705i	0.878470	+	1.14604i
$424$	−6.72499	+	2.18508i	−0.326594	+	0.106117i
$425$		0			0
$426$	12.2464	−	0.157238i	0.593342	−	0.00761823i
$427$	−5.56231	+	17.1190i	−0.269179	+	0.828447i
$428$	−18.0000			−0.870063
$429$		0			0
$430$	−12.0000			−0.578691
$431$	−11.1246	+	34.2380i	−0.535854	+	1.64919i	0.205944	+	0.978564i	$0.433974\pi$
$431$	−11.1246	+	34.2380i	−0.535854	+	1.64919i	−0.741797	+	0.670624i	$0.766026\pi$
$432$	−4.87634	+	1.79480i	−0.234613	+	0.0863525i
$433$	−1.61803	−	1.17557i	−0.0777578	−	0.0564943i	0.548227	−	0.836329i	$-0.315303\pi$
$433$	−1.61803	−	1.17557i	−0.0777578	−	0.0564943i	−0.625985	+	0.779835i	$0.715303\pi$
$434$	−16.1400	+	5.24419i	−0.774743	+	0.251729i
$435$	4.36178	−	14.0348i	0.209131	−	0.672916i
$436$	7.48128	−	10.2971i	0.358289	−	0.493142i
$437$		0			0
$438$		0			0
$439$		−	21.2132i		−	1.01245i	−0.862401	−	0.506225i	$-0.831040\pi$
$439$		−	21.2132i		−	1.01245i	0.862401	−	0.506225i	$-0.168960\pi$
$440$		0			0
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$		0			0
$443$	16.6251	+	22.8825i	0.789881	+	1.08718i	0.994123	+	0.108258i	$0.0345272\pi$
$443$	16.6251	+	22.8825i	0.789881	+	1.08718i	−0.204242	+	0.978921i	$0.565473\pi$
$444$	3.28054	−	1.11268i	0.155688	−	0.0528052i
$445$	−2.47214	−	7.60845i	−0.117190	−	0.360675i
$446$	−2.47214	−	7.60845i	−0.117059	−	0.360271i
$447$	−9.84163	+	3.33803i	−0.465493	+	0.157883i
$448$	−2.49376	−	3.43237i	−0.117819	−	0.162164i
$449$	29.5899	+	9.61435i	1.39644	+	0.453729i	0.908036	−	0.418891i	$-0.137581\pi$
$449$	29.5899	+	9.61435i	1.39644	+	0.453729i	0.488399	+	0.872620i	$0.337581\pi$
$450$	3.00000	+	8.48528i	0.141421	+	0.400000i
$451$		0			0
$452$		−	11.3137i		−	0.532152i
$453$	−5.88909	+	4.39529i	−0.276694	+	0.206509i
$454$	4.85410	−	3.52671i	0.227814	−	0.165517i
$455$	14.9626	−	20.5942i	0.701456	−	0.965471i
$456$		0			0
$457$	8.06998	−	2.62210i	0.377498	−	0.122656i	−0.114121	−	0.993467i	$-0.536405\pi$
$457$	8.06998	−	2.62210i	0.377498	−	0.122656i	0.491619	+	0.870810i	$0.336405\pi$
$458$	11.3262	+	8.22899i	0.529240	+	0.384516i
$459$		0			0
$460$	−0.618034	+	1.90211i	−0.0288160	+	0.0886865i
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	1.85410	−	5.70634i	0.0860745	−	0.264910i
$465$	−9.79715	+	0.125791i	−0.454332	+	0.00583341i
$466$	−14.5623	−	10.5801i	−0.674586	−	0.490115i
$467$	−29.5899	+	9.61435i	−1.36926	+	0.444899i	−0.899123	−	0.437695i	$-0.855795\pi$
$467$	−29.5899	+	9.61435i	−1.36926	+	0.444899i	−0.470135	+	0.882594i	$0.655795\pi$
$468$	−7.74320	−	10.1016i	−0.357929	−	0.466948i
$469$	−9.97505	+	13.7295i	−0.460605	+	0.633968i
$470$	−11.3262	+	8.22899i	−0.522440	+	0.379575i
$471$	−22.7916	−	30.5376i	−1.05018	−	1.40710i
$472$			11.3137i			0.520756i
$473$		0			0
$474$	6.00000	+	4.24264i	0.275589	+	0.194871i
$475$		0			0
$476$		0			0
$477$	20.3366	+	6.03509i	0.931149	+	0.276328i
$478$	−3.70820	−	11.4127i	−0.169609	−	0.522004i
$479$	−3.70820	−	11.4127i	−0.169432	−	0.521459i	0.829903	−	0.557907i	$-0.188395\pi$
$479$	−3.70820	−	11.4127i	−0.169432	−	0.521459i	−0.999336	+	0.0364486i	$0.988395\pi$
$480$	−0.786780	−	2.31969i	−0.0359114	−	0.105879i
$481$	4.98752	+	6.86474i	0.227411	+	0.313005i
$482$	8.06998	+	2.62210i	0.367578	+	0.119433i
$483$	6.00000	−	8.48528i	0.273009	−	0.386094i
$484$		0			0
$485$			11.3137i			0.513729i
$486$	15.1040	+	3.85612i	0.685131	+	0.174917i
$487$	−16.1803	+	11.7557i	−0.733201	+	0.532702i	−0.890575	−	0.454837i	$-0.849697\pi$
$487$	−16.1803	+	11.7557i	−0.733201	+	0.532702i	0.157373	+	0.987539i	$0.449697\pi$
$488$	−2.49376	+	3.43237i	−0.112887	+	0.155376i
$489$	−3.30803	−	1.02808i	−0.149594	−	0.0464914i
$490$	−14.7950	+	4.80718i	−0.668368	+	0.217166i
$491$	4.85410	+	3.52671i	0.219063	+	0.159158i	0.691905	−	0.721989i	$-0.256772\pi$
$491$	4.85410	+	3.52671i	0.219063	+	0.159158i	−0.472842	+	0.881147i	$0.656772\pi$
$492$	0.133421	+	10.3914i	0.00601510	+	0.468483i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	9.27051	−	28.5317i	0.415839	−	1.27982i
$498$	−0.266843	−	20.7829i	−0.0119575	−	0.931304i
$499$	−11.3262	−	8.22899i	−0.507032	−	0.368380i	0.304664	−	0.952460i	$-0.401456\pi$
$499$	−11.3262	−	8.22899i	−0.507032	−	0.368380i	−0.811697	+	0.584079i	$0.801456\pi$
$500$	−10.7600	+	3.49613i	−0.481201	+	0.156352i
$501$	−19.8482	−	6.16849i	−0.886751	−	0.275588i
$502$	−3.32502	+	4.57649i	−0.148403	+	0.204259i
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$	0.326787	+	12.7237i	0.0145563	+	0.566760i
$505$			8.48528i			0.377590i
$506$		0			0
$507$	5.00000	−	7.07107i	0.222058	−	0.314037i
$508$	−12.1050	−	3.93314i	−0.537071	−	0.174505i
$509$	−0.831254	−	1.14412i	−0.0368447	−	0.0507124i	0.790197	−	0.612853i	$-0.209978\pi$
$509$	−0.831254	−	1.14412i	−0.0368447	−	0.0507124i	−0.827042	+	0.562140i	$0.809978\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−6.65003	−	9.15298i	−0.293320	−	0.403721i
$515$	−5.37999	−	1.74806i	−0.237071	−	0.0770289i
$516$	12.0000	+	8.48528i	0.528271	+	0.373544i
$517$		0			0
$518$		−	8.48528i		−	0.372822i
$519$	6.21588	+	8.32844i	0.272847	+	0.365578i
$520$	4.85410	−	3.52671i	0.212866	−	0.154657i
$521$	−11.6376	+	16.0177i	−0.509851	+	0.701749i	−0.983894	−	0.178752i	$-0.942794\pi$
$521$	−11.6376	+	16.0177i	−0.509851	+	0.701749i	0.474044	+	0.880501i	$0.342794\pi$
$522$	−14.2859	+	10.9505i	−0.625275	+	0.479292i
$523$	−24.2099	+	7.86629i	−1.05863	+	0.343969i	−0.786049	−	0.618165i	$-0.787876\pi$
$523$	−24.2099	+	7.86629i	−1.05863	+	0.343969i	−0.272578	+	0.962134i	$0.587876\pi$
$524$	−9.70820	−	7.05342i	−0.424105	−	0.308130i
$525$	22.0436	−	0.283029i	0.962061	−	0.0123524i
$526$	3.70820	−	11.4127i	0.161685	−	0.497616i
$527$		0			0
$528$		0			0
$529$	21.0000			0.913043
$530$	−3.09017	+	9.51057i	−0.134228	+	0.413113i
$531$	19.2385	−	27.9621i	0.834880	−	1.21345i
$532$		0			0
$533$	−24.2099	+	7.86629i	−1.04865	+	0.340727i
$534$	−2.90785	+	9.35652i	−0.125835	+	0.404896i
$535$	−14.9626	+	20.5942i	−0.646888	+	0.890365i
$536$	−3.23607	+	2.35114i	−0.139777	+	0.101554i
$537$	−7.85212	+	5.86039i	−0.338844	+	0.252894i
$538$			7.07107i			0.304855i
$539$		0			0
$540$	−2.00000	+	7.07107i	−0.0860663	+	0.304290i
$541$	12.1050	+	3.93314i	0.520433	+	0.169099i	0.557442	−	0.830216i	$-0.311783\pi$
$541$	12.1050	+	3.93314i	0.520433	+	0.169099i	−0.0370086	+	0.999315i	$0.511783\pi$
$542$	7.48128	+	10.2971i	0.321349	+	0.442299i
$543$	3.28054	−	1.11268i	0.140782	−	0.0477495i
$544$		0			0
$545$	−5.56231	−	17.1190i	−0.238263	−	0.733298i
$546$	−29.5249	+	10.0141i	−1.26355	+	0.428563i
$547$	19.9501	+	27.4589i	0.853004	+	1.17406i	0.983193	+	0.182571i	$0.0584418\pi$
$547$	19.9501	+	27.4589i	0.853004	+	1.17406i	−0.130188	+	0.991489i	$0.541558\pi$
$548$	−2.68999	−	0.874032i	−0.114911	−	0.0373368i
$549$	12.0000	−	4.24264i	0.512148	−	0.181071i
$550$		0			0
$551$		0			0
$552$	1.96303	−	1.46510i	0.0835521	−	0.0623587i
$553$	14.5623	−	10.5801i	0.619252	−	0.449913i
$554$	12.4688	−	17.1618i	0.529749	−	0.729137i
$555$	1.45393	−	4.67826i	0.0617157	−	0.198581i
$556$	16.1400	−	5.24419i	0.684487	−	0.222403i
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	0.234856	−	0.972030i	$-0.424538\pi$
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	−0.851881	+	0.523735i	$0.824538\pi$
$558$	9.88610	+	6.80184i	0.418512	+	0.287945i
$559$	−11.1246	+	34.2380i	−0.470521	+	1.44811i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	12.0000			0.506189
$563$	9.27051	−	28.5317i	0.390705	−	1.20247i	−0.541551	−	0.840668i	$-0.682163\pi$
$563$	9.27051	−	28.5317i	0.390705	−	1.20247i	0.932256	−	0.361799i	$-0.117837\pi$
$564$	17.1450	−	0.220134i	0.721935	−	0.00926931i
$565$	−12.9443	−	9.40456i	−0.544570	−	0.395653i
$566$	8.06998	−	2.62210i	0.339207	−	0.110215i
$567$	20.8285	−	32.0027i	0.874716	−	1.34399i
$568$	4.15627	−	5.72061i	0.174393	−	0.240032i
$569$	−19.4164	+	14.1068i	−0.813978	+	0.591390i	−0.914981	−	0.403496i	$-0.867795\pi$
$569$	−19.4164	+	14.1068i	−0.813978	+	0.591390i	0.101003	+	0.994886i	$0.467795\pi$
$570$		0			0
$571$			33.9411i			1.42039i	0.704004	+	0.710196i	$0.251394\pi$
$571$			33.9411i			1.42039i	−0.704004	+	0.710196i	$0.748606\pi$
$572$		0			0
$573$	−14.0000	−	9.89949i	−0.584858	−	0.413557i
$574$	24.2099	+	7.86629i	1.01050	+	0.328333i
$575$	−2.49376	−	3.43237i	−0.103997	−	0.143140i
$576$	−0.853491	+	2.87603i	−0.0355621	+	0.119835i
$577$	6.18034	+	19.0211i	0.257291	+	0.791860i	0.993370	+	0.114964i	$0.0366753\pi$
$577$	6.18034	+	19.0211i	0.257291	+	0.791860i	−0.736079	+	0.676896i	$0.763325\pi$
$578$	5.25329	+	16.1680i	0.218508	+	0.672499i
$579$	4.72068	+	13.9182i	0.196185	+	0.578419i
$580$	−4.98752	−	6.86474i	−0.207096	−	0.285043i
$581$	−48.4199	−	15.7326i	−2.00880	−	0.652697i
$582$	8.00000	−	11.3137i	0.331611	−	0.468968i
$583$		0			0
$584$		0			0
$585$	−17.9941	+	0.462147i	−0.743963	+	0.0191074i
$586$	−4.85410	+	3.52671i	−0.200521	+	0.145687i
$587$	−16.6251	+	22.8825i	−0.686190	+	0.944460i	−0.999987	−	0.00503007i	$-0.998399\pi$
$587$	−16.6251	+	22.8825i	−0.686190	+	0.944460i	0.313797	+	0.949490i	$0.398399\pi$
$588$	18.1942	+	5.65445i	0.750314	+	0.233185i
$589$		0			0
$590$	12.9443	+	9.40456i	0.532907	+	0.387180i
$591$	−0.400264	−	31.1743i	−0.0164647	−	1.28234i
$592$	0.618034	−	1.90211i	0.0254010	−	0.0781764i
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$		0			0
$596$	−1.85410	+	5.70634i	−0.0759470	+	0.233741i
$597$	0.355790	+	27.7105i	0.0145615	+	1.13412i
$598$	4.85410	+	3.52671i	0.198499	+	0.144218i
$599$	22.8649	−	7.42927i	0.934237	−	0.303552i	0.197943	−	0.980214i	$-0.436574\pi$
$599$	22.8649	−	7.42927i	0.934237	−	0.303552i	0.736294	+	0.676662i	$0.236574\pi$
$600$	4.96204	+	1.54212i	0.202575	+	0.0629568i
$601$	−19.9501	+	27.4589i	−0.813781	+	1.12007i	0.176948	+	0.984220i	$0.443378\pi$
$601$	−19.9501	+	27.4589i	−0.813781	+	1.12007i	−0.990729	+	0.135854i	$0.956622\pi$
$602$	29.1246	−	21.1603i	1.18703	−	0.862428i
$603$	11.9960	−	0.308098i	0.488517	−	0.0125467i
$604$			4.24264i			0.172631i
$605$		0			0
$606$	6.00000	−	8.48528i	0.243733	−	0.344691i
$607$	−4.03499	−	1.31105i	−0.163775	−	0.0532138i	0.225982	−	0.974132i	$-0.427441\pi$
$607$	−4.03499	−	1.31105i	−0.163775	−	0.0532138i	−0.389757	+	0.920918i	$0.627441\pi$
$608$		0			0
$609$	14.1620	+	41.7545i	0.573875	+	1.69198i
$610$	1.85410	+	5.70634i	0.0750704	+	0.231043i
$611$	12.9787	+	39.9444i	0.525063	+	1.61598i
$612$		0			0
$613$	−7.48128	−	10.2971i	−0.302166	−	0.415896i	0.630752	−	0.775985i	$-0.282747\pi$
$613$	−7.48128	−	10.2971i	−0.302166	−	0.415896i	−0.932918	+	0.360088i	$0.882747\pi$
$614$		0			0
$615$	12.0000	+	8.48528i	0.483887	+	0.342160i
$616$		0			0
$617$			39.5980i			1.59415i	0.603877	+	0.797077i	$0.293622\pi$
$617$			39.5980i			1.59415i	−0.603877	+	0.797077i	$0.706378\pi$
$618$	4.14392	+	5.55229i	0.166693	+	0.223346i
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.440878	+	0.897567i	$0.645333\pi$
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.989876	+	0.141937i	$0.954667\pi$
$620$	−3.32502	+	4.57649i	−0.133536	+	0.183796i
$621$	−7.34302	+	0.282967i	−0.294665	+	0.0113551i
$622$	25.5549	−	8.30330i	1.02466	−	0.332932i
$623$	19.4164	+	14.1068i	0.777902	+	0.565179i
$624$	−7.34786	+	0.0943431i	−0.294150	+	0.00377675i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	10.0000			0.399680
$627$		0			0
$628$	−22.0000			−0.877896
$629$		0			0
$630$	14.8291	+	10.2028i	0.590807	+	0.406488i
$631$	−16.1803	−	11.7557i	−0.644129	−	0.467987i	0.217137	−	0.976141i	$-0.430328\pi$
$631$	−16.1803	−	11.7557i	−0.644129	−	0.467987i	−0.861266	+	0.508154i	$0.830328\pi$
$632$	4.03499	−	1.31105i	0.160503	−	0.0521507i
$633$	4.36178	−	14.0348i	0.173365	−	0.557832i
$634$	−5.81878	+	8.00886i	−0.231093	+	0.318072i
$635$	−14.5623	+	10.5801i	−0.577887	+	0.419860i
$636$	9.81516	−	7.32549i	0.389196	−	0.290474i
$637$			46.6690i			1.84909i
$638$		0			0
$639$	−20.0000	+	7.07107i	−0.791188	+	0.279727i
$640$	−1.34500	−	0.437016i	−0.0531657	−	0.0172746i
$641$	−28.2626	−	38.9002i	−1.11631	−	1.53646i	−0.811782	−	0.583960i	$-0.801502\pi$
$641$	−28.2626	−	38.9002i	−1.11631	−	1.53646i	−0.304524	−	0.952505i	$-0.598498\pi$
$642$	29.5249	−	10.0141i	1.16525	−	0.395224i
$643$	−1.23607	−	3.80423i	−0.0487458	−	0.150024i	0.923721	−	0.383066i	$-0.125132\pi$
$643$	−1.23607	−	3.80423i	−0.0487458	−	0.150024i	−0.972467	+	0.233042i	$0.925132\pi$
$644$	−1.85410	−	5.70634i	−0.0730619	−	0.224861i
$645$	19.6833	−	6.67605i	0.775027	−	0.262869i
$646$		0			0
$647$	−6.72499	−	2.18508i	−0.264386	−	0.0859044i	0.173824	−	0.984777i	$-0.444388\pi$
$647$	−6.72499	−	2.18508i	−0.264386	−	0.0859044i	−0.438211	+	0.898872i	$0.644388\pi$
$648$	7.00000	−	5.65685i	0.274986	−	0.222222i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	23.5564	−	17.5812i	0.923247	−	0.689060i
$652$	−1.61803	+	1.17557i	−0.0633671	+	0.0460389i
$653$	15.7938	−	21.7383i	0.618060	−	0.850687i	−0.379150	−	0.925335i	$-0.623784\pi$
$653$	15.7938	−	21.7383i	0.618060	−	0.850687i	0.997210	+	0.0746486i	$0.0237835\pi$
$654$	−6.54267	+	21.0522i	−0.255839	+	0.823205i
$655$	−16.1400	+	5.24419i	−0.630641	+	0.204908i
$656$	4.85410	+	3.52671i	0.189521	+	0.137695i
$657$		0			0
$658$	12.9787	−	39.9444i	0.505963	−	1.55719i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	3.09017	−	9.51057i	0.120103	−	0.369639i
$663$		0			0
$664$	−9.70820	−	7.05342i	−0.376751	−	0.273726i
$665$		0			0
$666$	−4.76195	+	3.65018i	−0.184522	+	0.141441i
$667$	4.98752	−	6.86474i	0.193118	−	0.265804i
$668$	−9.70820	+	7.05342i	−0.375622	+	0.272905i
$669$	8.28784	+	11.1046i	0.320426	+	0.429328i
$670$			5.65685i			0.218543i
$671$		0			0
$672$	6.00000	+	4.24264i	0.231455	+	0.163663i
$673$	40.3499	+	13.1105i	1.55537	+	0.505372i	0.955567	−	0.294773i	$-0.0952439\pi$
$673$	40.3499	+	13.1105i	1.55537	+	0.505372i	0.599807	+	0.800144i	$0.295244\pi$
$674$	19.9501	+	27.4589i	0.768449	+	1.05768i
$675$	−9.64149	−	12.2491i	−0.371101	−	0.471470i
$676$	−1.54508	−	4.75528i	−0.0594263	−	0.182895i
$677$	−9.27051	−	28.5317i	−0.356295	−	1.09656i	−0.955255	−	0.295783i	$-0.904419\pi$
$677$	−9.27051	−	28.5317i	−0.356295	−	1.09656i	0.598960	−	0.800779i	$-0.295581\pi$
$678$	6.29424	+	18.5575i	0.241729	+	0.712698i
$679$	−19.9501	−	27.4589i	−0.765614	−	1.05378i
$680$		0			0
$681$	−6.00000	+	8.48528i	−0.229920	+	0.325157i
$682$		0			0
$683$			5.65685i			0.216454i	0.994126	+	0.108227i	$0.0345173\pi$
$683$			5.65685i			0.216454i	−0.994126	+	0.108227i	$0.965483\pi$
$684$		0			0
$685$	−3.23607	+	2.35114i	−0.123644	+	0.0898325i
$686$	9.97505	−	13.7295i	0.380849	−	0.524194i
$687$	−23.1562	−	7.19657i	−0.883464	−	0.274566i
$688$	8.06998	−	2.62210i	0.307665	−	0.0999665i
$689$	24.2705	+	17.6336i	0.924633	+	0.671785i
$690$	−0.0444738	−	3.46382i	−0.00169309	−	0.131865i
$691$	−8.65248	+	26.6296i	−0.329156	+	1.01304i	0.640374	+	0.768063i	$0.278779\pi$
$691$	−8.65248	+	26.6296i	−0.329156	+	1.01304i	−0.969530	+	0.244974i	$0.921221\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	7.41641	−	22.8254i	0.281320	−	0.865815i
$696$	0.133421	+	10.3914i	0.00505732	+	0.393887i
$697$		0			0
$698$	28.2449	−	9.17734i	1.06909	−	0.347367i
$699$	29.7723	+	9.25273i	1.12609	+	0.349970i
$700$	7.48128	−	10.2971i	0.282766	−	0.389194i
$701$	−14.5623	+	10.5801i	−0.550011	+	0.399606i	−0.827789	−	0.561039i	$-0.810402\pi$
$701$	−14.5623	+	10.5801i	−0.550011	+	0.399606i	0.277779	+	0.960645i	$0.410402\pi$
$702$	18.3209	+	12.2616i	0.691476	+	0.462783i
$703$		0			0
$704$		0			0
$705$	14.0000	−	19.7990i	0.527271	−	0.745673i
$706$	−21.5200	−	6.99226i	−0.809914	−	0.263157i
$707$	−14.9626	−	20.5942i	−0.562725	−	0.774525i
$708$	−6.29424	−	18.5575i	−0.236552	−	0.697435i
$709$	−3.09017	−	9.51057i	−0.116054	−	0.357177i	0.876112	−	0.482108i	$-0.160129\pi$
$709$	−3.09017	−	9.51057i	−0.116054	−	0.357177i	−0.992165	+	0.124932i	$0.960129\pi$
$710$	−3.09017	−	9.51057i	−0.115972	−	0.356925i
$711$	−12.2020	−	3.62105i	−0.457609	−	0.135800i
$712$	3.32502	+	4.57649i	0.124610	+	0.171511i
$713$	−5.37999	−	1.74806i	−0.201482	−	0.0654655i
$714$		0			0
$715$		0			0
$716$			5.65685i			0.211407i
$717$	12.4318	+	16.6569i	0.464273	+	0.622062i
$718$		0			0
$719$	−19.1188	+	26.3148i	−0.713012	+	0.981377i	0.286715	+	0.958016i	$0.407437\pi$
$719$	−19.1188	+	26.3148i	−0.713012	+	0.981377i	−0.999727	+	0.0233613i	$0.992563\pi$
$720$	2.58107	+	3.36721i	0.0961906	+	0.125489i
$721$	16.1400	−	5.24419i	0.601084	−	0.195304i
$722$	15.3713	+	11.1679i	0.572061	+	0.415627i
$723$	−14.6957	+	0.188686i	−0.546540	+	0.00701732i
$724$	0.618034	−	1.90211i	0.0229691	−	0.0706915i
$725$	18.0000			0.668503
$726$		0			0
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$	−5.56231	+	17.1190i	−0.206153	+	0.634473i
$729$	−26.9199	+	2.07783i	−0.997034	+	0.0769568i
$730$		0			0
$731$		0			0
$732$	2.18089	−	7.01739i	0.0806080	−	0.259370i
$733$	−2.49376	+	3.43237i	−0.0921092	+	0.126777i	−0.852584	−	0.522590i	$-0.824966\pi$
$733$	−2.49376	+	3.43237i	−0.0921092	+	0.126777i	0.760475	+	0.649367i	$0.224966\pi$
$734$	−22.6525	+	16.4580i	−0.836118	+	0.607475i
$735$	21.5933	−	16.1161i	0.796482	−	0.594450i
$736$		−	1.41421i		−	0.0521286i
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$	−24.2099	−	7.86629i	−0.890577	−	0.289366i	−0.172235	−	0.985056i	$-0.555099\pi$
$739$	−24.2099	−	7.86629i	−0.890577	−	0.289366i	−0.718342	+	0.695690i	$0.755099\pi$
$740$	−1.66251	−	2.28825i	−0.0611150	−	0.0841176i
$741$		0			0
$742$	−9.27051	−	28.5317i	−0.340331	−	1.04743i
$743$	−7.41641	−	22.8254i	−0.272082	−	0.837381i	−0.989977	−	0.141230i	$-0.954894\pi$
$743$	−7.41641	−	22.8254i	−0.272082	−	0.837381i	0.717895	−	0.696151i	$-0.245106\pi$
$744$	6.56108	−	2.22535i	0.240541	−	0.0815853i
$745$	4.98752	+	6.86474i	0.182729	+	0.251504i
$746$	28.2449	+	9.17734i	1.03412	+	0.336006i
$747$	12.0000	+	33.9411i	0.439057	+	1.24184i
$748$		0			0
$749$		−	76.3675i		−	2.79041i
$750$	15.7042	−	11.7208i	0.573438	−	0.427982i
$751$	32.3607	−	23.5114i	1.18086	−	0.857944i	0.188590	−	0.982056i	$-0.439608\pi$
$751$	32.3607	−	23.5114i	1.18086	−	0.857944i	0.992268	+	0.124112i	$0.0396083\pi$
$752$	5.81878	−	8.00886i	0.212189	−	0.292053i
$753$	2.90785	−	9.35652i	0.105968	−	0.340970i
$754$	−24.2099	+	7.86629i	−0.881674	+	0.286473i
$755$	4.85410	+	3.52671i	0.176659	+	0.128350i
$756$	−7.61471	−	20.6886i	−0.276944	−	0.752435i
$757$	0.618034	−	1.90211i	0.0224628	−	0.0691335i	−0.939197	−	0.343380i	$-0.888428\pi$
$757$	0.618034	−	1.90211i	0.0224628	−	0.0691335i	0.961660	+	0.274246i	$0.0884283\pi$
$758$	−2.00000			−0.0726433
$759$		0			0
$760$		0			0
$761$	−7.41641	+	22.8254i	−0.268845	+	0.827419i	0.721938	+	0.691958i	$0.243252\pi$
$761$	−7.41641	+	22.8254i	−0.268845	+	0.827419i	−0.990783	+	0.135461i	$0.956748\pi$
$762$	22.0436	−	0.283029i	0.798555	−	0.0102531i
$763$	43.6869	+	31.7404i	1.58157	+	1.14908i
$764$	−9.41498	+	3.05911i	−0.340622	+	0.110675i
$765$		0			0
$766$	−0.831254	+	1.14412i	−0.0300344	+	0.0413388i
$767$	38.8328	−	28.2137i	1.40217	−	1.01874i
$768$	1.03598	+	1.38807i	0.0373827	+	0.0500878i
$769$		−	42.4264i		−	1.52994i	−0.644069	−	0.764968i	$-0.722755\pi$
$769$		−	42.4264i		−	1.52994i	0.644069	−	0.764968i	$-0.277245\pi$
$770$		0			0
$771$	16.0000	+	11.3137i	0.576226	+	0.407453i
$772$	8.06998	+	2.62210i	0.290445	+	0.0943713i
$773$	−10.8063	−	14.8736i	−0.388676	−	0.534966i	0.569181	−	0.822212i	$-0.307260\pi$
$773$	−10.8063	−	14.8736i	−0.388676	−	0.534966i	−0.957857	+	0.287246i	$0.907260\pi$
$774$	−24.4039	−	7.24211i	−0.877181	−	0.260312i
$775$	−3.70820	−	11.4127i	−0.133203	−	0.409956i
$776$	−2.47214	−	7.60845i	−0.0887445	−	0.273128i
$777$	4.72068	+	13.9182i	0.169353	+	0.499311i
$778$	5.81878	+	8.00886i	0.208613	+	0.287132i
$779$		0			0
$780$	−6.00000	+	8.48528i	−0.214834	+	0.303822i
$781$		0			0
$782$		0			0
$783$	17.3405	−	25.9096i	0.619699	−	0.925934i
$784$	8.89919	−	6.46564i	0.317828	−	0.230916i
$785$	−18.2876	+	25.1707i	−0.652712	+	0.898381i
$786$	19.8482	+	6.16849i	0.707961	+	0.220023i
$787$	40.3499	−	13.1105i	1.43832	−	0.467338i	0.516946	−	0.856018i	$-0.327069\pi$
$787$	40.3499	−	13.1105i	1.43832	−	0.467338i	0.921373	+	0.388680i	$0.127069\pi$
$788$	−14.5623	−	10.5801i	−0.518761	−	0.376902i
$789$	0.266843	+	20.7829i	0.00949985	+	0.739891i
$790$	1.85410	−	5.70634i	0.0659660	−	0.203022i
$791$	48.0000			1.70668
$792$		0			0
$793$	18.0000			0.639199
$794$	10.5066	−	32.3359i	0.372864	−	1.14756i
$795$	−0.222369	−	17.3191i	−0.00788661	−	0.614244i
$796$	12.9443	+	9.40456i	0.458798	+	0.333336i
$797$	−1.34500	+	0.437016i	−0.0476422	+	0.0154799i	−0.332741	−	0.943018i	$-0.607974\pi$
$797$	−1.34500	+	0.437016i	−0.0476422	+	0.0154799i	0.285099	+	0.958498i	$0.407974\pi$
$798$		0			0
$799$		0			0
$800$	2.42705	−	1.76336i	0.0858092	−	0.0623440i
$801$	−0.435716	−	16.9650i	−0.0153953	−	0.599428i
$802$			36.7696i			1.29838i
$803$		0			0
$804$	4.00000	−	5.65685i	0.141069	−	0.199502i
$805$	−8.06998	−	2.62210i	−0.284429	−	0.0924167i
$806$	9.97505	+	13.7295i	0.351356	+	0.483600i
$807$	−3.93390	−	11.5985i	−0.138480	−	0.408285i
$808$	−1.85410	−	5.70634i	−0.0652271	−	0.200748i
$809$	16.6869	+	51.3571i	0.586681	+	1.80562i	0.592413	+	0.805634i	$0.298175\pi$
$809$	16.6869	+	51.3571i	0.586681	+	1.80562i	−0.00573251	+	0.999984i	$0.501825\pi$
$810$	−0.653359	−	12.7111i	−0.0229567	−	0.446624i
$811$	−14.9626	−	20.5942i	−0.525407	−	0.723161i	0.461015	−	0.887392i	$-0.347485\pi$
$811$	−14.9626	−	20.5942i	−0.525407	−	0.723161i	−0.986422	+	0.164232i	$0.947485\pi$
$812$	24.2099	+	7.86629i	0.849603	+	0.276053i
$813$	−18.0000	−	12.7279i	−0.631288	−	0.446388i
$814$		0			0
$815$			2.82843i			0.0990755i
$816$		0			0
$817$		0			0
$818$	−4.98752	+	6.86474i	−0.174385	+	0.240020i
$819$	42.8576	−	32.8516i	1.49757	−	1.14793i
$820$	8.06998	−	2.62210i	0.281816	−	0.0915676i
$821$	24.2705	+	17.6336i	0.847047	+	0.615415i	0.924330	−	0.381594i	$-0.124625\pi$
$821$	24.2705	+	17.6336i	0.847047	+	0.615415i	−0.0772835	+	0.997009i	$0.524625\pi$
$822$	4.89858	−	0.0628954i	0.170857	−	0.00219373i
$823$	−12.3607	+	38.0423i	−0.430866	+	1.32607i	0.466398	+	0.884575i	$0.345552\pi$
$823$	−12.3607	+	38.0423i	−0.430866	+	1.32607i	−0.897264	+	0.441495i	$0.854448\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$	−48.0000			−1.67013
$827$	−11.1246	+	34.2380i	−0.386841	+	1.19057i	0.548296	+	0.836285i	$0.315277\pi$
$827$	−11.1246	+	34.2380i	−0.386841	+	1.19057i	−0.935136	+	0.354288i	$0.884723\pi$
$828$	−2.40481	+	3.49526i	−0.0835731	+	0.121469i
$829$	−1.61803	−	1.17557i	−0.0561966	−	0.0408293i	0.559332	−	0.828944i	$-0.311058\pi$
$829$	−1.61803	−	1.17557i	−0.0561966	−	0.0408293i	−0.615529	+	0.788114i	$0.711058\pi$
$830$	−16.1400	+	5.24419i	−0.560226	+	0.182029i
$831$	−10.9044	+	35.0869i	−0.378271	+	1.21715i
$832$	−2.49376	+	3.43237i	−0.0864556	+	0.118996i
$833$		0			0
$834$	−23.5564	+	17.5812i	−0.815690	+	0.608786i
$835$			16.9706i			0.587291i
$836$		0			0
$837$	−20.0000	−	5.65685i	−0.691301	−	0.195529i
$838$	10.7600	+	3.49613i	0.371697	+	0.120772i
$839$	9.14379	+	12.5854i	0.315679	+	0.434495i	0.937142	−	0.348949i	$-0.113461\pi$
$839$	9.14379	+	12.5854i	0.315679	+	0.434495i	−0.621463	+	0.783444i	$0.713461\pi$
$840$	9.84163	−	3.33803i	0.339568	−	0.115173i
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	3.09017	+	9.51057i	0.106494	+	0.327756i
$843$	−19.6833	+	6.67605i	−0.677927	+	0.229935i
$844$	−4.98752	−	6.86474i	−0.171678	−	0.236294i
$845$	−6.72499	−	2.18508i	−0.231347	−	0.0751690i
$846$	−28.0000	+	9.89949i	−0.962660	+	0.340352i
$847$		0			0
$848$		−	7.07107i		−	0.242821i
$849$	−11.7782	+	8.79058i	−0.404226	+	0.301692i
$850$		0			0
$851$	1.66251	−	2.28825i	0.0569900	−	0.0784400i
$852$	−3.63482	+	11.6956i	−0.124527	+	0.400686i
$853$	20.1750	−	6.55524i	0.690777	−	0.224447i	0.0574696	−	0.998347i	$-0.481697\pi$
$853$	20.1750	−	6.55524i	0.690777	−	0.224447i	0.633308	+	0.773900i	$0.281697\pi$
$854$	−14.5623	−	10.5801i	−0.498312	−	0.362045i
$855$		0			0
$856$	5.56231	−	17.1190i	0.190116	−	0.585116i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	3.70820	−	11.4127i	0.126449	−	0.389169i
$861$	−44.0872	+	0.566059i	−1.50249	+	0.0192912i
$862$	−29.1246	−	21.1603i	−0.991988	−	0.720722i
$863$	6.72499	−	2.18508i	0.228921	−	0.0743810i	−0.192310	−	0.981334i	$-0.561598\pi$
$863$	6.72499	−	2.18508i	0.228921	−	0.0743810i	0.421231	+	0.906953i	$0.361598\pi$
$864$	−0.200088	−	5.19230i	−0.00680713	−	0.176646i
$865$	4.98752	−	6.86474i	0.169581	−	0.233408i
$866$	1.61803	−	1.17557i	0.0549830	−	0.0399475i
$867$	−17.6117	−	23.5972i	−0.598123	−	0.801404i
$868$		−	16.9706i		−	0.576018i
$869$		0			0
$870$	12.0000	+	8.48528i	0.406838	+	0.287678i
$871$	16.1400	+	5.24419i	0.546882	+	0.177693i
$872$	7.48128	+	10.2971i	0.253348	+	0.348704i
$873$	−6.82793	+	23.0082i	−0.231090	+	0.778711i
$874$		0			0
$875$	−14.8328	−	45.6507i	−0.501441	−	1.54328i
$876$		0			0
$877$	17.4563	+	24.0266i	0.589458	+	0.811320i	0.994692	−	0.102893i	$-0.0328100\pi$
$877$	17.4563	+	24.0266i	0.589458	+	0.811320i	−0.405234	+	0.914213i	$0.632810\pi$
$878$	20.1750	+	6.55524i	0.680872	+	0.221229i
$879$	6.00000	−	8.48528i	0.202375	−	0.286201i
$880$		0			0
$881$			5.65685i			0.190584i	0.995449	+	0.0952921i	$0.0303785\pi$
$881$			5.65685i			0.190584i	−0.995449	+	0.0952921i	$0.969621\pi$
$882$	−32.9891	+	0.847269i	−1.11080	+	0.0285290i
$883$	−16.1803	+	11.7557i	−0.544512	+	0.395611i	−0.825758	−	0.564025i	$-0.809252\pi$
$883$	−16.1803	+	11.7557i	−0.544512	+	0.395611i	0.281246	+	0.959636i	$0.409252\pi$
$884$		0			0
$885$	−26.4642	−	8.22465i	−0.889585	−	0.276469i
$886$	−26.8999	+	8.74032i	−0.903721	+	0.293637i
$887$	−38.8328	−	28.2137i	−1.30388	−	0.947323i	−0.303893	−	0.952706i	$-0.598286\pi$
$887$	−38.8328	−	28.2137i	−1.30388	−	0.947323i	−0.999986	+	0.00538315i	$0.998286\pi$
$888$	0.0444738	+	3.46382i	0.00149244	+	0.116238i
$889$	16.6869	−	51.3571i	0.559661	−	1.72246i
$890$	8.00000			0.268161
$891$		0			0
$892$	8.00000			0.267860
$893$		0			0
$894$	−0.133421	−	10.3914i	−0.00446228	−	0.347542i
$895$	6.47214	+	4.70228i	0.216340	+	0.157180i
$896$	4.03499	−	1.31105i	0.134800	−	0.0437990i
$897$	−9.92408	−	3.08424i	−0.331356	−	0.102980i
$898$	−18.2876	+	25.1707i	−0.610265	+	0.839957i
$899$	19.4164	−	14.1068i	0.647573	−	0.470490i
$900$	−8.99703	+	0.231073i	−0.299901	+	0.00770245i
$901$		0			0
$902$		0			0
$903$	−36.0000	+	50.9117i	−1.19800	+	1.69423i
$904$	10.7600	+	3.49613i	0.357871	+	0.116279i
$905$	−1.66251	−	2.28825i	−0.0552636	−	0.0760639i
$906$	−2.36034	−	6.95908i	−0.0784171	−	0.231200i
$907$	13.5967	+	41.8465i	0.451473	+	1.38949i	0.875227	+	0.483713i	$0.160712\pi$
$907$	13.5967	+	41.8465i	0.451473	+	1.38949i	−0.423754	+	0.905777i	$0.639288\pi$
$908$	1.85410	+	5.70634i	0.0615305	+	0.189372i
$909$	−5.12094	+	17.2562i	−0.169851	+	0.572352i
$910$	14.9626	+	20.5942i	0.496004	+	0.682691i
$911$	9.41498	+	3.05911i	0.311932	+	0.101353i	0.460799	−	0.887504i	$-0.347563\pi$
$911$	9.41498	+	3.05911i	0.311932	+	0.101353i	−0.148867	+	0.988857i	$0.547563\pi$
$912$		0			0
$913$		0			0
$914$			8.48528i			0.280668i
$915$	−6.21588	−	8.32844i	−0.205491	−	0.275330i
$916$	−11.3262	+	8.22899i	−0.374229	+	0.271894i
$917$	29.9251	−	41.1884i	0.988215	−	1.36016i
$918$		0			0
$919$	−36.3149	+	11.7994i	−1.19792	+	0.389227i	−0.838995	−	0.544139i	$-0.816856\pi$
$919$	−36.3149	+	11.7994i	−1.19792	+	0.389227i	−0.358924	+	0.933367i	$0.616856\pi$
$920$	−1.61803	−	1.17557i	−0.0533450	−	0.0387574i
$921$		0			0
$922$	9.27051	−	28.5317i	0.305308	−	0.939641i
$923$	−30.0000			−0.987462
$924$		0			0
$925$	6.00000			0.197279
$926$	−9.88854	+	30.4338i	−0.324958	+	1.00012i
$927$	−9.88610	−	6.80184i	−0.324702	−	0.223402i
$928$	4.85410	+	3.52671i	0.159344	+	0.115770i
$929$	2.68999	−	0.874032i	0.0882558	−	0.0286761i	−0.264556	−	0.964370i	$-0.585225\pi$
$929$	2.68999	−	0.874032i	0.0882558	−	0.0286761i	0.352812	+	0.935694i	$0.385225\pi$
$930$	2.90785	−	9.35652i	0.0953522	−	0.306812i
$931$		0			0
$932$	14.5623	−	10.5801i	0.477004	−	0.346564i
$933$	−37.2976	+	27.8368i	−1.22107	+	0.911337i
$934$		−	31.1127i		−	1.01804i
$935$		0			0
$936$	12.0000	−	4.24264i	0.392232	−	0.138675i
$937$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$937$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$938$	−9.97505	−	13.7295i	−0.325697	−	0.448283i
$939$	−16.4027	+	5.56338i	−0.535282	+	0.181554i
$940$	−4.32624	−	13.3148i	−0.141106	−	0.434281i
$941$	−12.9787	−	39.9444i	−0.423094	−	1.30215i	−0.904808	−	0.425821i	$-0.859985\pi$
$941$	−12.9787	−	39.9444i	−0.423094	−	1.30215i	0.481714	−	0.876329i	$-0.340015\pi$
$942$	36.0860	−	12.2394i	1.17574	−	0.398782i
$943$	4.98752	+	6.86474i	0.162416	+	0.223547i
$944$	−10.7600	−	3.49613i	−0.350207	−	0.113789i
$945$	−30.0000	−	8.48528i	−0.975900	−	0.276026i
$946$		0			0
$947$			48.0833i			1.56250i	0.624221	+	0.781248i	$0.285417\pi$
$947$			48.0833i			1.56250i	−0.624221	+	0.781248i	$0.714583\pi$
$948$	−5.88909	+	4.39529i	−0.191269	+	0.142752i
$949$		0			0
$950$		0			0
$951$	5.08874	−	16.3739i	0.165014	−	0.530960i
$952$		0			0
$953$	−43.6869	−	31.7404i	−1.41516	−	1.02817i	−0.992547	−	0.121861i	$-0.961114\pi$
$953$	−43.6869	−	31.7404i	−1.41516	−	1.02817i	−0.422611	−	0.906311i	$-0.638886\pi$
$954$	−12.0241	+	17.4763i	−0.389294	+	0.565817i
$955$	−4.32624	+	13.3148i	−0.139994	+	0.430857i
$956$	12.0000			0.388108
$957$		0			0
$958$	12.0000			0.387702
$959$	3.70820	−	11.4127i	0.119744	−	0.368535i
$960$	2.44929	−	0.0314477i	0.0790504	−	0.00101497i
$961$	12.1353	+	8.81678i	0.391460	+	0.284412i
$962$	−8.06998	+	2.62210i	−0.260187	+	0.0845398i
$963$	−42.8576	+	32.8516i	−1.38107	+	1.05863i
$964$	−4.98752	+	6.86474i	−0.160637	+	0.221098i
$965$	9.70820	−	7.05342i	0.312518	−	0.227058i
$966$	6.21588	+	8.32844i	0.199993	+	0.267963i
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		0			0
$969$		0			0
$970$	−10.7600	−	3.49613i	−0.345482	−	0.112254i
$971$	26.6001	+	36.6119i	0.853639	+	1.17493i	0.983049	+	0.183342i	$0.0586915\pi$
$971$	26.6001	+	36.6119i	0.853639	+	1.17493i	−0.129411	+	0.991591i	$0.541309\pi$
$972$	−8.33478	+	13.1731i	−0.267338	+	0.422529i
$973$	22.2492	+	68.4761i	0.713277	+	2.19524i
$974$	−6.18034	−	19.0211i	−0.198031	−	0.609476i
$975$	−7.08102	−	20.8772i	−0.226774	−	0.668607i
$976$	−2.49376	−	3.43237i	−0.0798234	−	0.109867i
$977$	13.4500	+	4.37016i	0.430303	+	0.139814i	0.516157	−	0.856494i	$-0.327362\pi$
$977$	13.4500	+	4.37016i	0.430303	+	0.139814i	−0.0858545	+	0.996308i	$0.527362\pi$
$978$	2.00000	−	2.82843i	0.0639529	−	0.0904431i
$979$		0			0
$980$		−	15.5563i		−	0.496929i
$981$	−0.980361	−	38.1712i	−0.0313005	−	1.21871i
$982$	−4.85410	+	3.52671i	−0.154901	+	0.112542i
$983$	5.81878	−	8.00886i	0.185590	−	0.255443i	−0.706076	−	0.708136i	$-0.749537\pi$
$983$	5.81878	−	8.00886i	0.185590	−	0.255443i	0.891667	+	0.452693i	$0.149537\pi$
$984$	−9.92408	−	3.08424i	−0.316368	−	0.0983221i
$985$	−24.2099	+	7.86629i	−0.771393	+	0.250641i
$986$		0			0
$987$	0.933949	+	72.7401i	0.0297279	+	2.31534i
$988$		0			0
$989$	12.0000			0.381578
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	1.23607	−	3.80423i	0.0392452	−	0.120784i
$993$	0.222369	+	17.3191i	0.00705666	+	0.549604i
$994$	24.2705	+	17.6336i	0.769814	+	0.559302i
$995$	21.5200	−	6.99226i	0.682228	−	0.221669i
$996$	19.8482	+	6.16849i	0.628913	+	0.195456i
$997$	17.4563	−	24.0266i	0.552848	−	0.760929i	−0.437548	−	0.899195i	$-0.644153\pi$
$997$	17.4563	−	24.0266i	0.552848	−	0.760929i	0.990395	+	0.138266i	$0.0441528\pi$
$998$	11.3262	−	8.22899i	0.358526	−	0.260484i
$999$	5.78016	−	8.63653i	0.182876	−	0.273248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.i.233.1		8
3.2	odd	2		726.2.h.e.233.2		8
11.2	odd	10		726.2.h.e.239.1		8
11.3	even	5	inner	726.2.h.i.161.2		8
11.4	even	5		66.2.b.a.65.2	yes	2
11.5	even	5	inner	726.2.h.i.215.2		8
11.6	odd	10		726.2.h.e.215.2		8
11.7	odd	10		66.2.b.b.65.2	yes	2
11.8	odd	10		726.2.h.e.161.2		8
11.9	even	5	inner	726.2.h.i.239.1		8
11.10	odd	2		726.2.h.e.233.1		8
33.2	even	10	inner	726.2.h.i.239.2		8
33.5	odd	10		726.2.h.e.215.1		8
33.8	even	10	inner	726.2.h.i.161.1		8
33.14	odd	10		726.2.h.e.161.1		8
33.17	even	10	inner	726.2.h.i.215.1		8
33.20	odd	10		726.2.h.e.239.2		8
33.26	odd	10		66.2.b.b.65.1	yes	2
33.29	even	10		66.2.b.a.65.1	✓	2
33.32	even	2	inner	726.2.h.i.233.2		8
44.7	even	10		528.2.b.c.65.1		2
44.15	odd	10		528.2.b.b.65.1		2
55.4	even	10		1650.2.d.b.1451.1		2
55.7	even	20		1650.2.f.a.1649.4		4
55.18	even	20		1650.2.f.a.1649.1		4
55.29	odd	10		1650.2.d.a.1451.1		2
55.37	odd	20		1650.2.f.b.1649.2		4
55.48	odd	20		1650.2.f.b.1649.3		4
88.29	odd	10		2112.2.b.i.65.1		2
88.37	even	10		2112.2.b.g.65.1		2
88.51	even	10		2112.2.b.b.65.2		2
88.59	odd	10		2112.2.b.d.65.2		2
99.4	even	15		1782.2.i.f.593.2		4
99.7	odd	30		1782.2.i.c.1187.1		4
99.29	even	30		1782.2.i.f.1187.2		4
99.40	odd	30		1782.2.i.c.593.2		4
99.59	odd	30		1782.2.i.c.593.1		4
99.70	even	15		1782.2.i.f.1187.1		4
99.92	odd	30		1782.2.i.c.1187.2		4
99.95	even	30		1782.2.i.f.593.1		4
132.59	even	10		528.2.b.c.65.2		2
132.95	odd	10		528.2.b.b.65.2		2
165.29	even	10		1650.2.d.b.1451.2		2
165.59	odd	10		1650.2.d.a.1451.2		2
165.62	odd	20		1650.2.f.b.1649.1		4
165.92	even	20		1650.2.f.a.1649.3		4
165.128	odd	20		1650.2.f.b.1649.4		4
165.158	even	20		1650.2.f.a.1649.2		4
264.29	even	10		2112.2.b.g.65.2		2
264.59	even	10		2112.2.b.b.65.1		2
264.125	odd	10		2112.2.b.i.65.2		2
264.227	odd	10		2112.2.b.d.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	33.29	even	10
66.2.b.a.65.2	yes	2	11.4	even	5
66.2.b.b.65.1	yes	2	33.26	odd	10
66.2.b.b.65.2	yes	2	11.7	odd	10
528.2.b.b.65.1		2	44.15	odd	10
528.2.b.b.65.2		2	132.95	odd	10
528.2.b.c.65.1		2	44.7	even	10
528.2.b.c.65.2		2	132.59	even	10
726.2.h.e.161.1		8	33.14	odd	10
726.2.h.e.161.2		8	11.8	odd	10
726.2.h.e.215.1		8	33.5	odd	10
726.2.h.e.215.2		8	11.6	odd	10
726.2.h.e.233.1		8	11.10	odd	2
726.2.h.e.233.2		8	3.2	odd	2
726.2.h.e.239.1		8	11.2	odd	10
726.2.h.e.239.2		8	33.20	odd	10
726.2.h.i.161.1		8	33.8	even	10	inner
726.2.h.i.161.2		8	11.3	even	5	inner
726.2.h.i.215.1		8	33.17	even	10	inner
726.2.h.i.215.2		8	11.5	even	5	inner
726.2.h.i.233.1		8	1.1	even	1	trivial
726.2.h.i.233.2		8	33.32	even	2	inner
726.2.h.i.239.1		8	11.9	even	5	inner
726.2.h.i.239.2		8	33.2	even	10	inner
1650.2.d.a.1451.1		2	55.29	odd	10
1650.2.d.a.1451.2		2	165.59	odd	10
1650.2.d.b.1451.1		2	55.4	even	10
1650.2.d.b.1451.2		2	165.29	even	10
1650.2.f.a.1649.1		4	55.18	even	20
1650.2.f.a.1649.2		4	165.158	even	20
1650.2.f.a.1649.3		4	165.92	even	20
1650.2.f.a.1649.4		4	55.7	even	20
1650.2.f.b.1649.1		4	165.62	odd	20
1650.2.f.b.1649.2		4	55.37	odd	20
1650.2.f.b.1649.3		4	55.48	odd	20
1650.2.f.b.1649.4		4	165.128	odd	20
1782.2.i.c.593.1		4	99.59	odd	30
1782.2.i.c.593.2		4	99.40	odd	30
1782.2.i.c.1187.1		4	99.7	odd	30
1782.2.i.c.1187.2		4	99.92	odd	30
1782.2.i.f.593.1		4	99.95	even	30
1782.2.i.f.593.2		4	99.4	even	15
1782.2.i.f.1187.1		4	99.70	even	15
1782.2.i.f.1187.2		4	99.29	even	30
2112.2.b.b.65.1		2	264.59	even	10
2112.2.b.b.65.2		2	88.51	even	10
2112.2.b.d.65.1		2	264.227	odd	10
2112.2.b.d.65.2		2	88.59	odd	10
2112.2.b.g.65.1		2	88.37	even	10
2112.2.b.g.65.2		2	264.29	even	10
2112.2.b.i.65.1		2	88.29	odd	10
2112.2.b.i.65.2		2	264.125	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.0222369 - 1.73191i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.34500 + 0.437016i) q^{5} +(1.65401 + 0.514040i) q^{6} +(2.49376 - 3.43237i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-2.99901 + 0.0770245i) q^{9} -1.41421i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-4.03499 - 1.31105i) q^{13} +(2.49376 + 3.43237i) q^{14} +(0.786780 + 2.31969i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.853491 - 2.87603i) q^{18} +(1.34500 + 0.437016i) q^{20} +(-6.00000 - 4.24264i) q^{21} +1.41421i q^{23} +(-1.03598 - 1.38807i) q^{24} +(-2.42705 + 1.76336i) q^{25} +(2.49376 - 3.43237i) q^{26} +(0.200088 + 5.19230i) q^{27} +(-4.03499 + 1.31105i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-2.44929 + 0.0314477i) q^{30} +(-1.23607 + 3.80423i) q^{31} -1.00000 q^{32} +(-1.85410 + 5.70634i) q^{35} +(2.47152 + 1.70046i) q^{36} +(-1.61803 - 1.17557i) q^{37} +(-2.18089 + 7.01739i) q^{39} +(-0.831254 + 1.14412i) q^{40} +(4.85410 - 3.52671i) q^{41} +(5.88909 - 4.39529i) q^{42} -8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} +(-1.34500 - 0.437016i) q^{46} +(-5.81878 - 8.00886i) q^{47} +(1.64027 - 0.556338i) q^{48} +(-3.39919 - 10.4616i) q^{49} +(-0.927051 - 2.85317i) q^{50} +(2.49376 + 3.43237i) q^{52} +(-6.72499 - 2.18508i) q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(4.85410 - 3.52671i) q^{58} +(-6.65003 + 9.15298i) q^{59} +(0.726963 - 2.33913i) q^{60} +(-4.03499 + 1.31105i) q^{61} +(-3.23607 - 2.35114i) q^{62} +(-7.21444 + 10.4858i) q^{63} +(0.309017 - 0.951057i) q^{64} +6.00000 q^{65} -4.00000 q^{67} +(2.44929 - 0.0314477i) q^{69} +(-4.85410 - 3.52671i) q^{70} +(6.72499 - 2.18508i) q^{71} +(-2.38098 + 1.82509i) q^{72} +(1.61803 - 1.17557i) q^{74} +(3.10794 + 4.16422i) q^{75} +(-6.00000 - 4.24264i) q^{78} +(4.03499 + 1.31105i) q^{79} +(-0.831254 - 1.14412i) q^{80} +(8.98813 - 0.461994i) q^{81} +(1.85410 + 5.70634i) q^{82} +(-3.70820 - 11.4127i) q^{83} +(2.36034 + 6.95908i) q^{84} +(8.06998 + 2.62210i) q^{86} +(-6.00000 + 8.48528i) q^{87} +5.65685i q^{89} +(0.108929 + 4.24124i) q^{90} +(-14.5623 + 10.5801i) q^{91} +(0.831254 - 1.14412i) q^{92} +(6.61606 + 2.05616i) q^{93} +(9.41498 - 3.05911i) q^{94} +(0.0222369 + 1.73191i) q^{96} +(2.47214 - 7.60845i) q^{97} +11.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 8 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 48 q^{21} - 2 q^{24} - 6 q^{25} - 10 q^{27} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 8 q^{32} + 12 q^{35}+ \cdots + 88 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 8 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 48 * q^21 - 2 * q^24 - 6 * q^25 - 10 * q^27 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 8 * q^32 + 12 * q^35 + 2 * q^36 - 4 * q^37 - 12 * q^39 + 12 * q^41 - 12 * q^42 + 32 * q^45 + 2 * q^48 + 22 * q^49 + 6 * q^50 - 40 * q^54 + 12 * q^58 + 4 * q^60 - 8 * q^62 - 24 * q^63 - 2 * q^64 + 48 * q^65 - 32 * q^67 + 4 * q^69 - 12 * q^70 - 2 * q^72 + 4 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 24 * q^83 + 12 * q^84 - 48 * q^87 + 8 * q^90 - 36 * q^91 - 8 * q^93 - 2 * q^96 - 16 * q^97 + 88 * q^98

Introduction

L-functions

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