LMFDB - Embedded newform 275.2.bm.b.57.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(7,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.1
Character	$\chi$	$=$	275.57
Dual form			275.2.bm.b.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.665529 - 1.30617i) q^{2} +(0.130227 - 0.822224i) q^{3} +(-0.0875924 + 0.120561i) q^{4} +(-1.16064 + 0.377114i) q^{6} +(4.16343 - 0.659422i) q^{7} +(-2.68004 - 0.424477i) q^{8} +(2.19408 + 0.712899i) q^{9} +(-0.920480 - 3.18633i) q^{11} +(0.0877208 + 0.0877208i) q^{12} +(0.824787 - 0.420250i) q^{13} +(-3.63220 - 4.99930i) q^{14} +(1.32131 + 4.06656i) q^{16} +(-1.71765 - 0.875188i) q^{17} +(-0.529052 - 3.34030i) q^{18} +(-4.39439 + 3.19271i) q^{19} -3.50915i q^{21} +(-3.54930 + 3.32290i) q^{22} +(-1.95998 + 1.95998i) q^{23} +(-0.698030 + 2.14832i) q^{24} +(-1.09784 - 0.797627i) q^{26} +(2.00570 - 3.93640i) q^{27} +(-0.285184 + 0.559706i) q^{28} +(0.810497 + 0.588860i) q^{29} +(0.131006 - 0.403196i) q^{31} +(0.594873 - 0.594873i) q^{32} +(-2.73975 + 0.341892i) q^{33} +2.82602i q^{34} +(-0.278132 + 0.202075i) q^{36} +(0.771690 + 4.87226i) q^{37} +(7.09483 + 3.61500i) q^{38} +(-0.238130 - 0.732888i) q^{39} +(0.339428 + 0.467182i) q^{41} +(-4.58356 + 2.33544i) q^{42} +(-5.05373 - 5.05373i) q^{43} +(0.464773 + 0.168125i) q^{44} +(3.86451 + 1.25566i) q^{46} +(1.17495 + 0.186094i) q^{47} +(3.51569 - 0.556831i) q^{48} +(10.2419 - 3.32780i) q^{49} +(-0.943286 + 1.29832i) q^{51} +(-0.0215795 + 0.136247i) q^{52} +(4.12294 + 8.09173i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(2.05285 + 4.02895i) q^{57} +(0.229745 - 1.45055i) q^{58} +(5.47214 - 7.53175i) q^{59} +(7.40093 - 2.40471i) q^{61} +(-0.613832 + 0.0972215i) q^{62} +(9.60498 + 1.52128i) q^{63} +(6.96021 + 2.26151i) q^{64} +(2.26996 + 3.35105i) q^{66} +(3.05526 + 3.05526i) q^{67} +(0.255966 - 0.130421i) q^{68} +(1.35630 + 1.86679i) q^{69} +(2.65487 + 8.17086i) q^{71} +(-5.57761 - 2.84193i) q^{72} +(0.854195 + 5.39318i) q^{73} +(5.85044 - 4.25059i) q^{74} -0.809447i q^{76} +(-5.93349 - 12.6591i) q^{77} +(-0.798797 + 0.798797i) q^{78} +(-0.705861 + 2.17242i) q^{79} +(2.62377 + 1.90628i) q^{81} +(0.384322 - 0.754275i) q^{82} +(-0.902846 + 1.77193i) q^{83} +(0.423065 + 0.307374i) q^{84} +(-3.23765 + 9.96446i) q^{86} +(0.589724 - 0.589724i) q^{87} +(1.11440 + 8.93023i) q^{88} +13.9313i q^{89} +(3.15682 - 2.29356i) q^{91} +(-0.0646171 - 0.407977i) q^{92} +(-0.314457 - 0.160224i) q^{93} +(-0.538893 - 1.65854i) q^{94} +(-0.411650 - 0.566587i) q^{96} +(2.96200 - 1.50922i) q^{97} +(-11.1630 - 11.1630i) q^{98} +(0.251929 - 7.64727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.665529	−	1.30617i	−0.470600	−	0.923605i	−0.997292	−	0.0735483i	$-0.976568\pi$
$2$	−0.665529	−	1.30617i	−0.470600	−	0.923605i	0.526691	−	0.850057i	$-0.323432\pi$
$3$	0.130227	−	0.822224i	0.0751869	−	0.474711i	−0.921151	−	0.389206i	$-0.872750\pi$
$3$	0.130227	−	0.822224i	0.0751869	−	0.474711i	0.996338	−	0.0855054i	$-0.0272505\pi$
$4$	−0.0875924	+	0.120561i	−0.0437962	+	0.0602803i
$5$		0			0
$5$		0			0
$6$	−1.16064	+	0.377114i	−0.473829	+	0.153956i
$7$	4.16343	−	0.659422i	1.57363	−	0.249238i	0.692253	−	0.721655i	$-0.256618\pi$
$7$	4.16343	−	0.659422i	1.57363	−	0.249238i	0.881375	+	0.472417i	$0.156618\pi$
$8$	−2.68004	−	0.424477i	−0.947538	−	0.150075i
$9$	2.19408	+	0.712899i	0.731359	+	0.237633i
$10$		0			0
$11$	−0.920480	−	3.18633i	−0.277535	−	0.960716i
$11$	−0.920480	−	3.18633i	−0.277535	−	0.960716i
$12$	0.0877208	+	0.0877208i	0.0253228	+	0.0253228i
$13$	0.824787	−	0.420250i	0.228755	−	0.116556i	−0.335857	−	0.941913i	$-0.609026\pi$
$13$	0.824787	−	0.420250i	0.228755	−	0.116556i	0.564612	+	0.825357i	$0.309026\pi$
$14$	−3.63220	−	4.99930i	−0.970747	−	1.33612i
$15$		0			0
$16$	1.32131	+	4.06656i	0.330326	+	1.01664i
$17$	−1.71765	−	0.875188i	−0.416592	−	0.212264i	0.233115	−	0.972449i	$-0.425108\pi$
$17$	−1.71765	−	0.875188i	−0.416592	−	0.212264i	−0.649707	+	0.760185i	$0.725108\pi$
$18$	−0.529052	−	3.34030i	−0.124699	−	0.787317i
$19$	−4.39439	+	3.19271i	−1.00814	+	0.732458i	−0.963818	−	0.266560i	$-0.914113\pi$
$19$	−4.39439	+	3.19271i	−1.00814	+	0.732458i	−0.0443230	+	0.999017i	$0.514113\pi$
$20$		0			0
$21$		−	3.50915i		−	0.765758i
$22$	−3.54930	+	3.32290i	−0.756713	+	0.708446i
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	−0.881280	−	0.472595i	$-0.843317\pi$
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	0.472595	+	0.881280i	$0.343317\pi$
$24$	−0.698030	+	2.14832i	−0.142485	+	0.438523i
$25$		0			0
$26$	−1.09784	−	0.797627i	−0.215304	−	0.156428i
$27$	2.00570	−	3.93640i	0.385996	−	0.757561i
$28$	−0.285184	+	0.559706i	−0.0538948	+	0.105774i
$29$	0.810497	+	0.588860i	0.150505	+	0.109349i	0.660490	−	0.750835i	$-0.270349\pi$
$29$	0.810497	+	0.588860i	0.150505	+	0.109349i	−0.509984	+	0.860184i	$0.670349\pi$
$30$		0			0
$31$	0.131006	−	0.403196i	0.0235294	−	0.0724161i	−0.938602	−	0.345001i	$-0.887879\pi$
$31$	0.131006	−	0.403196i	0.0235294	−	0.0724161i	0.962132	+	0.272585i	$0.0878786\pi$
$32$	0.594873	−	0.594873i	0.105160	−	0.105160i
$33$	−2.73975	+	0.341892i	−0.476929	+	0.0595158i
$34$			2.82602i			0.484658i
$35$		0			0
$36$	−0.278132	+	0.202075i	−0.0463553	+	0.0336791i
$37$	0.771690	+	4.87226i	0.126865	+	0.800995i	0.966278	+	0.257501i	$0.0828990\pi$
$37$	0.771690	+	4.87226i	0.126865	+	0.800995i	−0.839413	+	0.543494i	$0.817101\pi$
$38$	7.09483	+	3.61500i	1.15093	+	0.586430i
$39$	−0.238130	−	0.732888i	−0.0381313	−	0.117356i
$40$		0			0
$41$	0.339428	+	0.467182i	0.0530097	+	0.0729616i	0.834699	−	0.550707i	$-0.185642\pi$
$41$	0.339428	+	0.467182i	0.0530097	+	0.0729616i	−0.781689	+	0.623668i	$0.785642\pi$
$42$	−4.58356	+	2.33544i	−0.707258	+	0.360366i
$43$	−5.05373	−	5.05373i	−0.770687	−	0.770687i	0.207540	−	0.978227i	$-0.433454\pi$
$43$	−5.05373	−	5.05373i	−0.770687	−	0.770687i	−0.978227	+	0.207540i	$0.933454\pi$
$44$	0.464773	+	0.168125i	0.0700672	+	0.0253458i
$45$		0			0
$46$	3.86451	+	1.25566i	0.569791	+	0.185136i
$47$	1.17495	+	0.186094i	0.171384	+	0.0271446i	0.241537	−	0.970392i	$-0.422349\pi$
$47$	1.17495	+	0.186094i	0.171384	+	0.0271446i	−0.0701524	+	0.997536i	$0.522349\pi$
$48$	3.51569	−	0.556831i	0.507447	−	0.0803717i
$49$	10.2419	−	3.32780i	1.46313	−	0.475400i
$50$		0			0
$51$	−0.943286	+	1.29832i	−0.132086	+	0.181801i
$52$	−0.0215795	+	0.136247i	−0.00299254	+	0.0188941i
$53$	4.12294	+	8.09173i	0.566330	+	1.11149i	0.979615	+	0.200883i	$0.0643812\pi$
$53$	4.12294	+	8.09173i	0.566330	+	1.11149i	−0.413285	+	0.910602i	$0.635619\pi$
$54$	−6.47647			−0.881337
$55$		0			0
$56$	−11.4381			−1.52848
$57$	2.05285	+	4.02895i	0.271907	+	0.533647i
$58$	0.229745	−	1.45055i	0.0301670	−	0.190467i
$59$	5.47214	−	7.53175i	0.712411	−	0.980550i	−0.287331	−	0.957831i	$-0.592768\pi$
$59$	5.47214	−	7.53175i	0.712411	−	0.980550i	0.999742	−	0.0227186i	$-0.00723217\pi$
$60$		0			0
$61$	7.40093	−	2.40471i	0.947591	−	0.307891i	0.205855	−	0.978583i	$-0.434002\pi$
$61$	7.40093	−	2.40471i	0.947591	−	0.307891i	0.741737	+	0.670691i	$0.234002\pi$
$62$	−0.613832	+	0.0972215i	−0.0779568	+	0.0123471i
$63$	9.60498	+	1.52128i	1.21011	+	0.191663i
$64$	6.96021	+	2.26151i	0.870026	+	0.282689i
$65$		0			0
$66$	2.26996	+	3.35105i	0.279412	+	0.412486i
$67$	3.05526	+	3.05526i	0.373259	+	0.373259i	0.868663	−	0.495404i	$-0.164980\pi$
$67$	3.05526	+	3.05526i	0.373259	+	0.373259i	−0.495404	+	0.868663i	$0.664980\pi$
$68$	0.255966	−	0.130421i	0.0310405	−	0.0158159i
$69$	1.35630	+	1.86679i	0.163280	+	0.224735i
$70$		0			0
$71$	2.65487	+	8.17086i	0.315075	+	0.969702i	0.975723	+	0.219006i	$0.0702816\pi$
$71$	2.65487	+	8.17086i	0.315075	+	0.969702i	−0.660648	+	0.750696i	$0.729718\pi$
$72$	−5.57761	−	2.84193i	−0.657328	−	0.334925i
$73$	0.854195	+	5.39318i	0.0999760	+	0.631224i	0.985893	+	0.167379i	$0.0535304\pi$
$73$	0.854195	+	5.39318i	0.0999760	+	0.631224i	−0.885917	+	0.463844i	$0.846470\pi$
$74$	5.85044	−	4.25059i	0.680100	−	0.494122i
$75$		0			0
$76$		−	0.809447i		−	0.0928499i
$77$	−5.93349	−	12.6591i	−0.676184	−	1.44264i
$78$	−0.798797	+	0.798797i	−0.0904460	+	0.0904460i
$79$	−0.705861	+	2.17242i	−0.0794156	+	0.244416i	−0.982880	−	0.184247i	$-0.941015\pi$
$79$	−0.705861	+	2.17242i	−0.0794156	+	0.244416i	0.903464	+	0.428663i	$0.141015\pi$
$80$		0			0
$81$	2.62377	+	1.90628i	0.291530	+	0.211809i
$82$	0.384322	−	0.754275i	0.0424413	−	0.0832957i
$83$	−0.902846	+	1.77193i	−0.0991002	+	0.194495i	−0.935234	−	0.354031i	$-0.884811\pi$
$83$	−0.902846	+	1.77193i	−0.0991002	+	0.194495i	0.836134	+	0.548526i	$0.184811\pi$
$84$	0.423065	+	0.307374i	0.0461601	+	0.0335373i
$85$		0			0
$86$	−3.23765	+	9.96446i	−0.349125	+	1.07450i
$87$	0.589724	−	0.589724i	0.0632250	−	0.0632250i
$88$	1.11440	+	8.93023i	0.118795	+	0.951966i
$89$			13.9313i			1.47671i	0.674410	+	0.738357i	$0.264398\pi$
$89$			13.9313i			1.47671i	−0.674410	+	0.738357i	$0.735602\pi$
$90$		0			0
$91$	3.15682	−	2.29356i	0.330925	−	0.240431i
$92$	−0.0646171	−	0.407977i	−0.00673680	−	0.0425345i
$93$	−0.314457	−	0.160224i	−0.0326076	−	0.0166144i
$94$	−0.538893	−	1.65854i	−0.0555826	−	0.171066i
$95$		0			0
$96$	−0.411650	−	0.566587i	−0.0420138	−	0.0578271i
$97$	2.96200	−	1.50922i	0.300746	−	0.153238i	−0.297105	−	0.954845i	$-0.596021\pi$
$97$	2.96200	−	1.50922i	0.300746	−	0.153238i	0.597851	+	0.801607i	$0.296021\pi$
$98$	−11.1630	−	11.1630i	−1.12763	−	1.12763i
$99$	0.251929	−	7.64727i	0.0253199	−	0.768579i
$100$		0			0
$101$	−12.6404	−	4.10712i	−1.25777	−	0.408673i	−0.397069	−	0.917789i	$-0.629973\pi$
$101$	−12.6404	−	4.10712i	−1.25777	−	0.408673i	−0.860698	+	0.509116i	$0.829973\pi$
$102$	2.32362	+	0.368025i	0.230073	+	0.0364399i
$103$	9.95825	−	1.57723i	0.981215	−	0.155409i	0.354837	−	0.934928i	$-0.384536\pi$
$103$	9.95825	−	1.57723i	0.981215	−	0.155409i	0.626378	+	0.779519i	$0.284536\pi$
$104$	−2.38885	+	0.776185i	−0.234246	+	0.0761112i
$105$		0			0
$106$	7.82528	−	10.7706i	0.760058	−	1.04613i
$107$	−0.964682	+	6.09076i	−0.0932593	+	0.588816i	0.896160	+	0.443731i	$0.146346\pi$
$107$	−0.964682	+	6.09076i	−0.0932593	+	0.588816i	−0.989419	+	0.145085i	$0.953654\pi$
$108$	0.298891	+	0.586606i	0.0287608	+	0.0564462i
$109$	−19.9193			−1.90793			−0.953964	−	0.299922i	$-0.903039\pi$
$109$	−19.9193			−1.90793			−0.953964	+	0.299922i	$0.903039\pi$
$110$		0			0
$111$	4.10659			0.389780
$112$	8.18274	+	16.0595i	0.773197	+	1.51748i
$113$	1.89632	−	11.9729i	0.178391	−	1.12632i	−0.722211	−	0.691673i	$-0.756874\pi$
$113$	1.89632	−	11.9729i	0.178391	−	1.12632i	0.900602	−	0.434644i	$-0.143126\pi$
$114$	3.89628	−	5.36277i	0.364920	−	0.502269i
$115$		0			0
$116$	−0.141987	+	0.0461342i	−0.0131831	+	0.00428346i
$117$	2.10924	−	0.334071i	0.194999	−	0.0308849i
$118$	−13.4796	−	2.13497i	−1.24090	−	0.196540i
$119$	−7.72845	−	2.51112i	−0.708465	−	0.230194i
$120$		0			0
$121$	−9.30543	+	5.86591i	−0.845949	+	0.533265i
$122$	−8.06650	−	8.06650i	−0.730306	−	0.730306i
$123$	0.428331	−	0.218246i	0.0386213	−	0.0196785i
$124$	0.0371343	+	0.0511110i	0.00333476	+	0.00458991i
$125$		0			0
$126$	−4.40534	−	13.5582i	−0.392459	−	1.20786i
$127$	1.03315	+	0.526416i	0.0916772	+	0.0467119i	0.499228	−	0.866471i	$-0.333617\pi$
$127$	1.03315	+	0.526416i	0.0916772	+	0.0467119i	−0.407551	+	0.913183i	$0.633617\pi$
$128$	−1.94151	−	12.2582i	−0.171607	−	1.08348i
$129$	−4.81343	+	3.49716i	−0.423799	+	0.307908i
$130$		0			0
$131$		−	14.4532i		−	1.26278i	−0.775465	−	0.631390i	$-0.782485\pi$
$131$		−	14.4532i		−	1.26278i	0.775465	−	0.631390i	$-0.217515\pi$
$132$	0.198763	−	0.360253i	0.0173001	−	0.0313560i
$133$	−16.1904	+	16.1904i	−1.40388	+	1.40388i
$134$	1.95734	−	6.02407i	0.169088	−	0.520400i
$135$		0			0
$136$	4.23189	+	3.07465i	0.362881	+	0.263649i
$137$	−5.61663	+	11.0232i	−0.479861	+	0.941780i	0.516479	+	0.856300i	$0.327242\pi$
$137$	−5.61663	+	11.0232i	−0.479861	+	0.941780i	−0.996340	+	0.0854799i	$0.972758\pi$
$138$	1.53570	−	3.01397i	0.130727	−	0.256566i
$139$	−0.816606	−	0.593299i	−0.0692636	−	0.0503229i	0.552615	−	0.833437i	$-0.313630\pi$
$139$	−0.816606	−	0.593299i	−0.0692636	−	0.0503229i	−0.621878	+	0.783114i	$0.713630\pi$
$140$		0			0
$141$	0.306022	−	0.941839i	0.0257717	−	0.0793172i
$142$	8.90567	−	8.90567i	0.747347	−	0.747347i
$143$	−2.09826	−	2.24121i	−0.175465	−	0.187420i
$144$			9.86430i			0.822025i
$145$		0			0
$146$	6.47594	−	4.70504i	0.535952	−	0.389392i
$147$	−1.40242	−	8.85451i	−0.115669	−	0.730308i
$148$	−0.654997	−	0.333737i	−0.0538404	−	0.0274331i
$149$	0.377177	+	1.16083i	0.0308996	+	0.0950990i	0.965317	−	0.261081i	$-0.0840790\pi$
$149$	0.377177	+	1.16083i	0.0308996	+	0.0950990i	−0.934417	+	0.356180i	$0.884079\pi$
$150$		0			0
$151$	0.932668	+	1.28371i	0.0758995	+	0.104467i	0.845279	−	0.534326i	$-0.179434\pi$
$151$	0.932668	+	1.28371i	0.0758995	+	0.104467i	−0.769379	+	0.638792i	$0.779434\pi$
$152$	13.1324	−	6.69128i	1.06518	−	0.542734i
$153$	−3.14474	−	3.14474i	−0.254237	−	0.254237i
$154$	−12.5861	+	16.1752i	−1.01421	+	1.30343i
$155$		0			0
$156$	0.109216	+	0.0354863i	0.00874425	+	0.00284118i
$157$	−7.32783	−	1.16061i	−0.584824	−	0.0926271i	−0.142991	−	0.989724i	$-0.545672\pi$
$157$	−7.32783	−	1.16061i	−0.584824	−	0.0926271i	−0.441834	+	0.897097i	$0.645672\pi$
$158$	3.30733	−	0.523829i	0.263117	−	0.0416736i
$159$	7.19014	−	2.33622i	0.570215	−	0.185274i
$160$		0			0
$161$	−6.86780	+	9.45272i	−0.541258	+	0.744978i
$162$	0.743741	−	4.69579i	0.0584338	−	0.368936i
$163$	−6.99546	−	13.7294i	−0.547927	−	1.07537i	−0.984449	−	0.175673i	$-0.943790\pi$
$163$	−6.99546	−	13.7294i	−0.547927	−	1.07537i	0.436522	−	0.899694i	$-0.356210\pi$
$164$	−0.0860550			−0.00671976
$165$		0			0
$166$	2.91533			0.226273
$167$	1.88413	+	3.69782i	0.145799	+	0.286146i	0.952344	−	0.305026i	$-0.0986653\pi$
$167$	1.88413	+	3.69782i	0.145799	+	0.286146i	−0.806545	+	0.591172i	$0.798665\pi$
$168$	−1.48955	+	9.40466i	−0.114921	+	0.725585i
$169$	−7.13754	+	9.82399i	−0.549042	+	0.755691i
$170$		0			0
$171$	−11.9177	+	3.87229i	−0.911369	+	0.296122i
$172$	1.05195	−	0.166612i	0.0802104	−	0.0127041i
$173$	4.27643	+	0.677320i	0.325131	+	0.0514957i	0.316867	−	0.948470i	$-0.397369\pi$
$173$	4.27643	+	0.677320i	0.325131	+	0.0514957i	0.00826456	+	0.999966i	$0.497369\pi$
$174$	−1.16276	−	0.377804i	−0.0881487	−	0.0286412i
$175$		0			0
$176$	11.7412	−	7.95331i	0.885025	−	0.599503i
$177$	−5.48016	−	5.48016i	−0.411914	−	0.411914i
$178$	18.1967	−	9.27168i	1.36390	−	0.694942i
$179$	−2.18633	−	3.00922i	−0.163414	−	0.224920i	0.719456	−	0.694538i	$-0.244391\pi$
$179$	−2.18633	−	3.00922i	−0.163414	−	0.224920i	−0.882869	+	0.469619i	$0.844391\pi$
$180$		0			0
$181$	1.86849	+	5.75062i	0.138884	+	0.427440i	0.996174	−	0.0873933i	$-0.0278537\pi$
$181$	1.86849	+	5.75062i	0.138884	+	0.427440i	−0.857290	+	0.514834i	$0.827854\pi$
$182$	−5.09675	−	2.59692i	−0.377796	−	0.192497i
$183$	−1.01340	−	6.39838i	−0.0749129	−	0.472982i
$184$	6.08481	−	4.42087i	0.448578	−	0.325911i
$185$		0			0
$186$			0.517369i			0.0379353i
$187$	−1.20758	+	6.27861i	−0.0883066	+	0.459137i
$188$	−0.125352	+	0.125352i	−0.00914227	+	0.00914227i
$189$	5.75482	−	17.7115i	0.418602	−	1.28832i
$190$		0			0
$191$	13.3930	+	9.73057i	0.969082	+	0.704079i	0.955242	−	0.295825i	$-0.0955945\pi$
$191$	13.3930	+	9.73057i	0.969082	+	0.704079i	0.0138398	+	0.999904i	$0.495595\pi$
$192$	2.76588	−	5.42834i	0.199610	−	0.391757i
$193$	−7.70155	+	15.1151i	−0.554370	+	1.08801i	0.428471	+	0.903556i	$0.359052\pi$
$193$	−7.70155	+	15.1151i	−0.554370	+	1.08801i	−0.982841	+	0.184456i	$0.940948\pi$
$194$	−3.94260	−	2.86447i	−0.283062	−	0.205657i
$195$		0			0
$196$	−0.495912	+	1.52626i	−0.0354223	+	0.109019i
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	−0.274915	−	0.961469i	$-0.588650\pi$
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	0.961469	+	0.274915i	$0.0886496\pi$
$198$	−10.1563	+	4.76042i	−0.721779	+	0.338308i
$199$		−	19.4166i		−	1.37640i	−0.725519	−	0.688202i	$-0.758400\pi$
$199$		−	19.4166i		−	1.37640i	0.725519	−	0.688202i	$-0.241600\pi$
$200$		0			0
$201$	2.90999	−	2.11423i	0.205255	−	0.149126i
$202$	3.04795	+	19.2440i	0.214453	+	1.35400i
$203$	3.76275	+	1.91722i	0.264093	+	0.134562i
$204$	−0.0739017	−	0.227446i	−0.00517416	−	0.0159244i
$205$		0			0
$206$	−8.68764	−	11.9575i	−0.605297	−	0.833119i
$207$	−5.69763	+	2.90309i	−0.396012	+	0.201778i
$208$	2.79877	+	2.79877i	0.194060	+	0.194060i
$209$	14.2180	+	11.0632i	0.983478	+	0.765254i
$210$		0			0
$211$	6.07815	+	1.97491i	0.418437	+	0.135959i	0.510666	−	0.859779i	$-0.329399\pi$
$211$	6.07815	+	1.97491i	0.418437	+	0.135959i	−0.0922284	+	0.995738i	$0.529399\pi$
$212$	−1.33668	−	0.211710i	−0.0918037	−	0.0145403i
$213$	7.06401	−	1.11883i	0.484018	−	0.0766609i
$214$	8.59762	−	2.79354i	0.587721	−	0.190962i
$215$		0			0
$216$	−7.04626	+	9.69835i	−0.479437	+	0.659889i
$217$	0.279559	−	1.76507i	0.0189777	−	0.119820i
$218$	13.2569	+	26.0181i	0.897871	+	1.76217i
$219$	4.54564			0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$	−2.73305	−	5.36392i	−0.183430	−	0.360003i
$223$	2.22058	−	14.0202i	0.148701	−	0.938860i	−0.794651	−	0.607066i	$-0.792346\pi$
$223$	2.22058	−	14.0202i	0.148701	−	0.938860i	0.943352	−	0.331794i	$-0.107654\pi$
$224$	2.08444	−	2.86898i	0.139272	−	0.191692i
$225$		0			0
$226$	−16.9008	+	5.49139i	−1.12422	+	0.365282i
$227$	−8.17622	+	1.29499i	−0.542675	+	0.0859512i	−0.421753	−	0.906711i	$-0.638585\pi$
$227$	−8.17622	+	1.29499i	−0.542675	+	0.0859512i	−0.120922	+	0.992662i	$0.538585\pi$
$228$	−0.665546	−	0.105412i	−0.0440769	−	0.00698109i
$229$	18.6401	+	6.05655i	1.23178	+	0.400228i	0.851357	−	0.524587i	$-0.175780\pi$
$229$	18.6401	+	6.05655i	1.23178	+	0.400228i	0.380418	+	0.924815i	$0.375780\pi$
$230$		0			0
$231$	−11.1813	+	3.23010i	−0.735676	+	0.212525i
$232$	−1.92221	−	1.92221i	−0.126199	−	0.126199i
$233$	−3.30844	+	1.68573i	−0.216743	+	0.110436i	−0.558991	−	0.829173i	$-0.688812\pi$
$233$	−3.30844	+	1.68573i	−0.216743	+	0.110436i	0.342249	+	0.939609i	$0.388812\pi$
$234$	−1.84012	−	2.53270i	−0.120292	−	0.165568i
$235$		0			0
$236$	0.428714	+	1.31945i	0.0279069	+	0.0858887i
$237$	1.69429	+	0.863285i	0.110056	+	0.0560764i
$238$	1.86354	+	11.7659i	0.120795	+	0.762672i
$239$	−2.59930	+	1.88850i	−0.168135	+	0.122157i	−0.668671	−	0.743559i	$-0.733136\pi$
$239$	−2.59930	+	1.88850i	−0.168135	+	0.122157i	0.500536	+	0.865716i	$0.333136\pi$
$240$		0			0
$241$			25.4119i			1.63693i	0.574559	+	0.818463i	$0.305174\pi$
$241$			25.4119i			1.63693i	−0.574559	+	0.818463i	$0.694826\pi$
$242$	13.8549	+	8.25059i	0.890629	+	0.530368i
$243$	11.2809	−	11.2809i	0.723671	−	0.723671i
$244$	−0.358352	+	1.10289i	−0.0229411	+	0.0706055i
$245$		0			0
$246$	−0.570133	−	0.414226i	−0.0363504	−	0.0264101i
$247$	−2.28270	+	4.48005i	−0.145245	+	0.285059i
$248$	−0.522250	+	1.02497i	−0.0331629	+	0.0650858i
$249$	1.33935	+	0.973096i	0.0848780	+	0.0616674i
$250$		0			0
$251$	5.03867	−	15.5074i	0.318038	−	0.978820i	−0.656448	−	0.754371i	$-0.727942\pi$
$251$	5.03867	−	15.5074i	0.318038	−	0.978820i	0.974486	−	0.224448i	$-0.0720580\pi$
$252$	−1.02473	+	1.02473i	−0.0645519	+	0.0645519i
$253$	8.04929	+	4.44104i	0.506055	+	0.279206i
$254$		−	1.69982i		−	0.106656i
$255$		0			0
$256$	−2.87779	+	2.09084i	−0.179862	+	0.130677i
$257$	2.53487	+	16.0045i	0.158121	+	0.998335i	0.931328	+	0.364182i	$0.118651\pi$
$257$	2.53487	+	16.0045i	0.158121	+	0.998335i	−0.773207	+	0.634154i	$0.781349\pi$
$258$	7.77139	+	3.95972i	0.483825	+	0.246521i
$259$	6.42576	+	19.7764i	0.399277	+	1.22885i
$260$		0			0
$261$	1.35849	+	1.86981i	0.0840887	+	0.115738i
$262$	−18.8784	+	9.61901i	−1.16631	+	0.594265i
$263$	0.677874	+	0.677874i	0.0417995	+	0.0417995i	0.727698	−	0.685898i	$-0.240590\pi$
$263$	0.677874	+	0.677874i	0.0417995	+	0.0417995i	−0.685898	+	0.727698i	$0.740590\pi$
$264$	7.48778	+	0.246675i	0.460841	+	0.0151818i
$265$		0			0
$266$	31.9226	+	10.3723i	1.95730	+	0.635966i
$267$	11.4546	+	1.81424i	0.701013	+	0.111030i
$268$	−0.635961	+	0.100726i	−0.0388475	+	0.00615284i
$269$	−27.0327	+	8.78345i	−1.64821	+	0.535536i	−0.978351	−	0.206951i	$-0.933646\pi$
$269$	−27.0327	+	8.78345i	−1.64821	+	0.535536i	−0.669860	+	0.742487i	$0.733646\pi$
$270$		0			0
$271$	18.0744	−	24.8772i	1.09794	−	1.51118i	0.259853	−	0.965648i	$-0.416326\pi$
$271$	18.0744	−	24.8772i	1.09794	−	1.51118i	0.838087	−	0.545536i	$-0.183674\pi$
$272$	1.28946	−	8.14133i	0.0781850	−	0.493641i
$273$	−1.47472	−	2.89430i	−0.0892540	−	0.175171i
$274$	18.1363			1.09565
$275$		0			0
$276$	−0.343863			−0.0206981
$277$	−13.6871	−	26.8625i	−0.822379	−	1.61401i	−0.788861	−	0.614571i	$-0.789329\pi$
$277$	−13.6871	−	26.8625i	−0.822379	−	1.61401i	−0.0335176	−	0.999438i	$-0.510671\pi$
$278$	−0.231477	+	1.46149i	−0.0138831	+	0.0876542i
$279$	0.574875	−	0.791248i	0.0344169	−	0.0473708i
$280$		0			0
$281$	8.10210	−	2.63253i	0.483331	−	0.157044i	−0.0572089	−	0.998362i	$-0.518220\pi$
$281$	8.10210	−	2.63253i	0.483331	−	0.157044i	0.540540	+	0.841319i	$0.318220\pi$
$282$	−1.43387	+	0.227103i	−0.0853859	+	0.0135238i
$283$	−9.42432	−	1.49267i	−0.560218	−	0.0887297i	−0.130097	−	0.991501i	$-0.541529\pi$
$283$	−9.42432	−	1.49267i	−0.560218	−	0.0887297i	−0.430120	+	0.902772i	$0.641529\pi$
$284$	−1.21763	−	0.395632i	−0.0722530	−	0.0234764i
$285$		0			0
$286$	−1.53097	+	4.23228i	−0.0905280	+	0.250260i
$287$	1.72125	+	1.72125i	0.101602	+	0.101602i
$288$	1.72928	−	0.881112i	0.101899	−	0.0519200i
$289$	−7.80797	−	10.7468i	−0.459292	−	0.632162i
$290$		0			0
$291$	−0.855180	−	2.63197i	−0.0501315	−	0.154289i
$292$	−0.725025	−	0.369419i	−0.0424289	−	0.0216186i
$293$	0.360965	+	2.27904i	0.0210878	+	0.133143i	0.995986	−	0.0895072i	$-0.0285292\pi$
$293$	0.360965	+	2.27904i	0.0210878	+	0.133143i	−0.974898	+	0.222650i	$0.928529\pi$
$294$	−10.6322	+	7.72474i	−0.620082	+	0.450516i
$295$		0			0
$296$		−	13.3854i		−	0.778013i
$297$	−14.3889	−	2.76744i	−0.834928	−	0.160583i
$298$	1.26523	−	1.26523i	0.0732926	−	0.0732926i
$299$	−0.792887	+	2.44025i	−0.0458538	+	0.141124i
$300$		0			0
$301$	−24.3734	−	17.7083i	−1.40486	−	1.02069i
$302$	1.05603	−	2.07257i	0.0607676	−	0.119263i
$303$	−5.02310	+	9.85838i	−0.288569	+	0.566349i
$304$	−18.7897	−	13.6515i	−1.07766	−	0.782967i
$305$		0			0
$306$	−2.01466	+	6.20050i	−0.115171	+	0.354459i
$307$	−12.4635	+	12.4635i	−0.711327	+	0.711327i	−0.966813	−	0.255486i	$-0.917765\pi$
$307$	−12.4635	+	12.4635i	−0.711327	+	0.711327i	0.255486	+	0.966813i	$0.417765\pi$
$308$	2.04591	+	0.393494i	0.116577	+	0.0224214i
$309$		−	8.39331i		−	0.477479i
$310$		0			0
$311$	−12.2271	+	8.88353i	−0.693337	+	0.503739i	−0.877755	−	0.479109i	$-0.840960\pi$
$311$	−12.2271	+	8.88353i	−0.693337	+	0.503739i	0.184419	+	0.982848i	$0.440960\pi$
$312$	0.327104	+	2.06525i	0.0185186	+	0.116922i
$313$	−23.2697	−	11.8565i	−1.31528	−	0.670169i	−0.351331	−	0.936251i	$-0.614271\pi$
$313$	−23.2697	−	11.8565i	−1.31528	−	0.670169i	−0.963950	+	0.266082i	$0.914271\pi$
$314$	3.36092	+	10.3438i	0.189668	+	0.583737i
$315$		0			0
$316$	−0.200080	−	0.275386i	−0.0112554	−	0.0154917i
$317$	−25.2398	+	12.8603i	−1.41761	+	0.722307i	−0.983896	−	0.178744i	$-0.942797\pi$
$317$	−25.2398	+	12.8603i	−1.41761	+	0.722307i	−0.433712	+	0.901051i	$0.642797\pi$
$318$	−7.83675	−	7.83675i	−0.439463	−	0.439463i
$319$	1.13026	−	3.12455i	0.0632824	−	0.174941i
$320$		0			0
$321$	4.88234	+	1.58637i	0.272506	+	0.0885425i
$322$	16.9176	+	2.67949i	0.942782	+	0.149322i
$323$	10.3423	−	1.63805i	0.575458	−	0.0911436i
$324$	−0.459645	+	0.149348i	−0.0255358	+	0.00829710i
$325$		0			0
$326$	−13.2773	+	18.2746i	−0.735360	+	1.01214i
$327$	−2.59405	+	16.3782i	−0.143451	+	0.905714i
$328$	−0.711372	−	1.39615i	−0.0392790	−	0.0770893i
$329$	5.01454			0.276461
$330$		0			0
$331$	−24.6455			−1.35464			−0.677319	−	0.735690i	$-0.736858\pi$
$331$	−24.6455			−1.35464			−0.677319	+	0.735690i	$0.736858\pi$
$332$	−0.134543	−	0.264055i	−0.00738401	−	0.0144919i
$333$	−1.78028	+	11.2403i	−0.0975588	+	0.615962i
$334$	3.57605	−	4.92202i	0.195673	−	0.269321i
$335$		0			0
$336$	14.2702	−	4.63665i	0.778501	−	0.252950i
$337$	30.6340	−	4.85195i	1.66874	−	0.264302i	0.750657	−	0.660692i	$-0.229737\pi$
$337$	30.6340	−	4.85195i	1.66874	−	0.264302i	0.918082	+	0.396390i	$0.129737\pi$
$338$	17.5821	+	2.78473i	0.956339	+	0.151469i
$339$	−9.59746	−	3.11840i	−0.521263	−	0.169369i
$340$		0			0
$341$	−1.40530	−	0.0462960i	−0.0761015	−	0.00250707i
$342$	12.9895	+	12.9895i	0.702390	+	0.702390i
$343$	14.1559	−	7.21277i	0.764345	−	0.389453i
$344$	11.3990	+	15.6894i	0.614594	+	0.845916i
$345$		0			0
$346$	−1.96139	−	6.03654i	−0.105445	−	0.324527i
$347$	26.8957	+	13.7041i	1.44384	+	0.735672i	0.988009	−	0.154395i	$-0.0493430\pi$
$347$	26.8957	+	13.7041i	1.44384	+	0.735672i	0.455829	+	0.890068i	$0.349343\pi$
$348$	0.0194421	+	0.122753i	0.00104221	+	0.00658024i
$349$	17.2865	−	12.5594i	0.925323	−	0.672287i	−0.0195201	−	0.999809i	$-0.506214\pi$
$349$	17.2865	−	12.5594i	0.925323	−	0.672287i	0.944843	+	0.327523i	$0.106214\pi$
$350$		0			0
$351$		−	4.08959i		−	0.218286i
$352$	−2.44303	−	1.34789i	−0.130214	−	0.0718430i
$353$	2.82626	−	2.82626i	0.150427	−	0.150427i	−0.627882	−	0.778309i	$-0.716078\pi$
$353$	2.82626	−	2.82626i	0.150427	−	0.150427i	0.778309	+	0.627882i	$0.216078\pi$
$354$	−3.51084	+	10.8053i	−0.186599	+	0.574293i
$355$		0			0
$356$	−1.67956	−	1.22027i	−0.0890167	−	0.0646744i
$357$	−3.07116	+	6.02750i	−0.162543	+	0.319009i
$358$	−2.47550	+	4.85844i	−0.130834	+	0.256777i
$359$	−8.68908	−	6.31298i	−0.458592	−	0.333187i	0.334387	−	0.942436i	$-0.391471\pi$
$359$	−8.68908	−	6.31298i	−0.458592	−	0.333187i	−0.792979	+	0.609249i	$0.791471\pi$
$360$		0			0
$361$	3.24592	−	9.98992i	0.170838	−	0.525785i
$362$	6.26778	−	6.26778i	0.329427	−	0.329427i
$363$	3.61127	+	8.41505i	0.189542	+	0.441676i
$364$			0.581487i			0.0304782i
$365$		0			0
$366$	−7.68295	+	5.58199i	−0.401594	+	0.291775i
$367$	−5.41331	−	34.1783i	−0.282572	−	1.78409i	−0.565293	−	0.824890i	$-0.691237\pi$
$367$	−5.41331	−	34.1783i	−0.282572	−	1.78409i	0.282721	−	0.959202i	$-0.408763\pi$
$368$	−10.5601	−	5.38066i	−0.550485	−	0.280486i
$369$	0.411677	+	1.26701i	0.0214310	+	0.0659579i
$370$		0			0
$371$	22.5015	+	30.9706i	1.16822	+	1.60791i
$372$	0.0468606	−	0.0238767i	0.00242961	−	0.00123795i
$373$	9.90454	+	9.90454i	0.512838	+	0.512838i	0.915395	−	0.402557i	$-0.131879\pi$
$373$	9.90454	+	9.90454i	0.512838	+	0.512838i	−0.402557	+	0.915395i	$0.631879\pi$
$374$	9.00463	−	2.60129i	0.465618	−	0.134510i
$375$		0			0
$376$	−3.06993	−	0.997480i	−0.158319	−	0.0514411i
$377$	0.915956	+	0.145073i	0.0471741	+	0.00747165i
$378$	−26.9643	+	4.27073i	−1.38690	+	0.219663i
$379$	−25.2037	+	8.18919i	−1.29463	+	0.420651i	−0.873710	−	0.486447i	$-0.838292\pi$
$379$	−25.2037	+	8.18919i	−1.29463	+	0.420651i	−0.420919	+	0.907098i	$0.638292\pi$
$380$		0			0
$381$	0.567376	−	0.780926i	0.0290676	−	0.0400081i
$382$	3.79640	−	23.9695i	0.194241	−	1.22639i
$383$	−10.9129	−	21.4177i	−0.557622	−	1.09439i	−0.981995	−	0.188907i	$-0.939505\pi$
$383$	−10.9129	−	21.4177i	−0.557622	−	1.09439i	0.424373	−	0.905487i	$-0.360495\pi$
$384$	−10.3318			−0.527243
$385$		0			0
$386$	24.8686			1.26578
$387$	−7.48548	−	14.6911i	−0.380508	−	0.746789i
$388$	−0.0774970	+	0.489297i	−0.00393431	+	0.0248403i
$389$	4.43509	−	6.10438i	0.224868	−	0.309505i	−0.681644	−	0.731684i	$-0.738735\pi$
$389$	4.43509	−	6.10438i	0.224868	−	0.309505i	0.906512	+	0.422179i	$0.138735\pi$
$390$		0			0
$391$	5.08193	−	1.65122i	0.257004	−	0.0835057i
$392$	−28.8613	+	4.57119i	−1.45772	+	0.230880i
$393$	−11.8838	−	1.88220i	−0.599456	−	0.0949445i
$394$	−18.9998	−	6.17342i	−0.957197	−	0.311012i
$395$		0			0
$396$	0.899892	+	0.700215i	0.0452213	+	0.0351871i
$397$	−16.0995	−	16.0995i	−0.808008	−	0.808008i	0.176324	−	0.984332i	$-0.443579\pi$
$397$	−16.0995	−	16.0995i	−0.808008	−	0.808008i	−0.984332	+	0.176324i	$0.943579\pi$
$398$	−25.3614	+	12.9223i	−1.27125	+	0.647736i
$399$	11.2037	+	15.4205i	0.560886	+	0.771993i
$400$		0			0
$401$	−7.46030	−	22.9604i	−0.372550	−	1.14659i	−0.945117	−	0.326732i	$-0.894053\pi$
$401$	−7.46030	−	22.9604i	−0.372550	−	1.14659i	0.572568	−	0.819858i	$-0.305947\pi$
$402$	−4.69823	−	2.39387i	−0.234327	−	0.119395i
$403$	−0.0613908	−	0.387606i	−0.00305809	−	0.0193080i
$404$	1.60236	−	1.16418i	0.0797203	−	0.0579202i
$405$		0			0
$406$		−	6.19078i		−	0.307243i
$407$	14.8143	−	6.94368i	0.734319	−	0.344185i
$408$	3.07915	−	3.07915i	0.152441	−	0.152441i
$409$	1.80956	−	5.56925i	0.0894769	−	0.275382i	−0.896298	−	0.443452i	$-0.853754\pi$
$409$	1.80956	−	5.56925i	0.0894769	−	0.275382i	0.985775	+	0.168070i	$0.0537536\pi$
$410$		0			0
$411$	8.33214	+	6.05365i	0.410994	+	0.298605i
$412$	−0.682114	+	1.33872i	−0.0336054	+	0.0659542i
$413$	17.8162	−	34.9663i	0.876680	−	1.72058i
$414$	7.58387	+	5.51001i	0.372727	+	0.270802i
$415$		0			0
$416$	0.240648	−	0.740639i	0.0117987	−	0.0363128i
$417$	−0.594169	+	0.594169i	−0.0290966	+	0.0290966i
$418$	4.98793	−	25.9340i	0.243968	−	1.26847i
$419$		−	11.0599i		−	0.540311i	−0.962817	−	0.270155i	$-0.912925\pi$
$419$		−	11.0599i		−	0.540311i	0.962817	−	0.270155i	$-0.0870751\pi$
$420$		0			0
$421$	−6.36944	+	4.62767i	−0.310428	+	0.225539i	−0.732080	−	0.681219i	$-0.761450\pi$
$421$	−6.36944	+	4.62767i	−0.310428	+	0.225539i	0.421652	+	0.906758i	$0.361450\pi$
$422$	−1.46561	−	9.25349i	−0.0713447	−	0.450453i
$423$	2.44527	+	1.24593i	0.118893	+	0.0605790i
$424$	−7.61491	−	23.4363i	−0.369813	−	1.13817i
$425$		0			0
$426$	−6.16269	−	8.48222i	−0.298583	−	0.410965i
$427$	29.2275	−	14.8922i	1.41442	−	0.720682i
$428$	−0.649807	−	0.649807i	−0.0314096	−	0.0314096i
$429$	−2.11603	+	1.43337i	−0.102163	+	0.0692037i
$430$		0			0
$431$	−6.94552	−	2.25674i	−0.334554	−	0.108703i	0.136923	−	0.990582i	$-0.456279\pi$
$431$	−6.94552	−	2.25674i	−0.334554	−	0.108703i	−0.471477	+	0.881879i	$0.656279\pi$
$432$	18.6577	+	2.95510i	0.897671	+	0.142177i
$433$	−4.98536	+	0.789604i	−0.239581	+	0.0379460i	−0.275070	−	0.961424i	$-0.588701\pi$
$433$	−4.98536	+	0.789604i	−0.239581	+	0.0379460i	0.0354890	+	0.999370i	$0.488701\pi$
$434$	−2.49154	+	0.809550i	−0.119598	+	0.0388596i
$435$		0			0
$436$	1.74478	−	2.40149i	0.0835599	−	0.115010i
$437$	2.35527	−	14.8706i	0.112668	−	0.711357i
$438$	−3.02525	−	5.93740i	−0.144552	−	0.283700i
$439$	1.29778			0.0619394			0.0309697	−	0.999520i	$-0.490140\pi$
$439$	1.29778			0.0619394			0.0309697	+	0.999520i	$0.490140\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$	1.18763	+	2.33086i	0.0564900	+	0.110868i
$443$	−2.40922	+	15.2112i	−0.114466	+	0.722707i	0.861980	+	0.506942i	$0.169224\pi$
$443$	−2.40922	+	15.2112i	−0.114466	+	0.722707i	−0.976445	+	0.215764i	$0.930776\pi$
$444$	−0.359706	+	0.495092i	−0.0170709	+	0.0234960i
$445$		0			0
$446$	−19.7907	+	6.43037i	−0.937115	+	0.304487i
$447$	1.00358	−	0.158952i	0.0474678	−	0.00751816i
$448$	30.4696	+	4.82591i	1.43955	+	0.228003i
$449$	11.5295	+	3.74615i	0.544109	+	0.176792i	0.568159	−	0.822919i	$-0.307656\pi$
$449$	11.5295	+	3.74615i	0.544109	+	0.176792i	−0.0240497	+	0.999711i	$0.507656\pi$
$450$		0			0
$451$	1.17616	−	1.51156i	0.0553833	−	0.0711766i
$452$	1.27736	+	1.27736i	0.0600818	+	0.0600818i
$453$	1.17695	−	0.599688i	0.0552981	−	0.0281758i
$454$	7.13299	+	9.81772i	0.334768	+	0.460768i
$455$		0			0
$456$	−3.79153	−	11.6691i	−0.177555	−	0.546458i
$457$	−3.12807	−	1.59383i	−0.146325	−	0.0745563i	0.379295	−	0.925276i	$-0.376167\pi$
$457$	−3.12807	−	1.59383i	−0.146325	−	0.0745563i	−0.525620	+	0.850720i	$0.676167\pi$
$458$	−4.49465	−	28.3781i	−0.210021	−	1.32602i
$459$	−6.89018	+	5.00601i	−0.321606	+	0.233660i
$460$		0			0
$461$			5.45336i			0.253988i	0.991903	+	0.126994i	$0.0405329\pi$
$461$			5.45336i			0.253988i	−0.991903	+	0.126994i	$0.959467\pi$
$462$	11.6606	+	12.4550i	0.542498	+	0.579460i
$463$	−15.3996	+	15.3996i	−0.715681	+	0.715681i	−0.967718	−	0.252037i	$-0.918900\pi$
$463$	−15.3996	+	15.3996i	−0.715681	+	0.715681i	0.252037	+	0.967718i	$0.418900\pi$
$464$	−1.32372	+	4.07400i	−0.0614523	+	0.189131i
$465$		0			0
$466$	4.40372	+	3.19949i	0.203998	+	0.148214i
$467$	−6.66632	+	13.0834i	−0.308481	+	0.605427i	−0.992248	−	0.124273i	$-0.960340\pi$
$467$	−6.66632	+	13.0834i	−0.308481	+	0.605427i	0.683768	+	0.729700i	$0.260340\pi$
$468$	−0.144478	+	0.283553i	−0.00667848	+	0.0131073i
$469$	14.7351	+	10.7057i	0.680402	+	0.494341i
$470$		0			0
$471$	−1.90857	+	5.87397i	−0.0879422	+	0.270658i
$472$	−17.8626	+	17.8626i	−0.822193	+	0.822193i
$473$	−11.4510	+	20.7547i	−0.526518	+	0.954303i
$474$		−	2.78758i		−	0.128038i
$475$		0			0
$476$	0.979695	−	0.711790i	0.0449043	−	0.0326249i
$477$	3.27747	+	20.6931i	0.150065	+	0.947473i
$478$	4.19663	+	2.13829i	0.191949	+	0.0978030i
$479$	1.51842	+	4.67321i	0.0693783	+	0.213524i	0.979734	−	0.200302i	$-0.0641922\pi$
$479$	1.51842	+	4.67321i	0.0693783	+	0.213524i	−0.910356	+	0.413826i	$0.864192\pi$
$480$		0			0
$481$	2.68405	+	3.69428i	0.122382	+	0.168444i
$482$	33.1924	−	16.9124i	1.51187	−	0.770338i
$483$	6.87787	+	6.87787i	0.312954	+	0.312954i
$484$	0.107888	−	1.63568i	0.00490399	−	0.0743490i
$485$		0			0
$486$	−22.2426	−	7.22706i	−1.00895	−	0.327826i
$487$	−10.6054	−	1.67972i	−0.480574	−	0.0761155i	−0.0885527	−	0.996071i	$-0.528224\pi$
$487$	−10.6054	−	1.67972i	−0.480574	−	0.0761155i	−0.392022	+	0.919956i	$0.628224\pi$
$488$	−20.8555	+	3.30319i	−0.944086	+	0.149529i
$489$	−12.1996	+	3.96390i	−0.551686	+	0.179254i
$490$		0			0
$491$	1.91387	−	2.63421i	0.0863715	−	0.118880i	−0.763645	−	0.645637i	$-0.776592\pi$
$491$	1.91387	−	2.63421i	0.0863715	−	0.118880i	0.850016	+	0.526757i	$0.176592\pi$
$492$	−0.0112067	+	0.0707565i	−0.000505238	+	0.00318995i
$493$	−0.876788	−	1.72079i	−0.0394886	−	0.0775007i
$494$	7.37092			0.331634
$495$		0			0
$496$	1.81272			0.0813935
$497$	16.4414	+	32.2681i	0.737498	+	1.44742i
$498$	0.379656	−	2.39705i	0.0170128	−	0.107414i
$499$	−5.25588	+	7.23410i	−0.235285	+	0.323843i	−0.910290	−	0.413971i	$-0.864142\pi$
$499$	−5.25588	+	7.23410i	−0.235285	+	0.323843i	0.675005	+	0.737813i	$0.264142\pi$
$500$		0			0
$501$	3.28580	−	1.06762i	0.146799	−	0.0476978i
$502$	−23.6088	+	3.73926i	−1.05371	+	0.166891i
$503$	−19.0954	−	3.02441i	−0.851421	−	0.134852i	−0.284553	−	0.958660i	$-0.591845\pi$
$503$	−19.0954	−	3.02441i	−0.851421	−	0.134852i	−0.566868	+	0.823808i	$0.691845\pi$
$504$	−25.0960	−	8.15419i	−1.11787	−	0.363217i
$505$		0			0
$506$	0.443733	−	13.4694i	0.0197263	−	0.598789i
$507$	7.14801	+	7.14801i	0.317454	+	0.317454i
$508$	−0.153961	+	0.0784471i	−0.00683092	+	0.00348053i
$509$	−1.65845	−	2.28267i	−0.0735097	−	0.101177i	0.770679	−	0.637224i	$-0.219917\pi$
$509$	−1.65845	−	2.28267i	−0.0735097	−	0.101177i	−0.844189	+	0.536046i	$0.819917\pi$
$510$		0			0
$511$	7.11276	+	21.8908i	0.314650	+	0.968393i
$512$	−17.4703	−	8.90156i	−0.772085	−	0.393397i
$513$	3.75398	+	23.7017i	0.165742	+	1.04645i
$514$	19.2177	−	13.9625i	0.847656	−	0.615858i
$515$		0			0
$516$		−	0.886635i		−	0.0390319i
$517$	−0.488562	−	3.91508i	−0.0214869	−	0.172185i
$518$	21.5550	−	21.5550i	0.947071	−	0.947071i
$519$	1.11382	−	3.42798i	0.0488912	−	0.150472i
$520$		0			0
$521$	−7.68839	−	5.58594i	−0.336835	−	0.244725i	0.406491	−	0.913655i	$-0.366752\pi$
$521$	−7.68839	−	5.58594i	−0.336835	−	0.244725i	−0.743325	+	0.668930i	$0.766752\pi$
$522$	1.53818	−	3.01884i	0.0673241	−	0.132131i
$523$	6.73563	−	13.2194i	0.294528	−	0.578045i	−0.695564	−	0.718465i	$-0.744845\pi$
$523$	6.73563	−	13.2194i	0.294528	−	0.578045i	0.990092	+	0.140420i	$0.0448453\pi$
$524$	1.74248	+	1.26599i	0.0761207	+	0.0553049i
$525$		0			0
$526$	0.434277	−	1.33657i	0.0189354	−	0.0582771i
$527$	−0.577895	+	0.577895i	−0.0251735	+	0.0251735i
$528$	−5.01037	−	10.6896i	−0.218049	−	0.465206i
$529$			15.3169i			0.665953i
$530$		0			0
$531$	17.3757	−	12.6242i	0.754039	−	0.547842i
$532$	−0.533767	−	3.37007i	−0.0231417	−	0.146111i
$533$	0.476289	+	0.242681i	0.0206304	+	0.0105117i
$534$	−5.25369	−	16.1692i	−0.227349	−	0.699709i
$535$		0			0
$536$	−6.89134	−	9.48511i	−0.297661	−	0.409695i
$537$	−2.75897	+	1.40577i	−0.119058	+	0.0606633i
$538$	29.4638	+	29.4638i	1.27027	+	1.27027i
$539$	−20.0309	−	29.5710i	−0.862794	−	1.27371i
$540$		0			0
$541$	−29.7351	−	9.66153i	−1.27841	−	0.415381i	−0.410392	−	0.911909i	$-0.634608\pi$
$541$	−29.7351	−	9.66153i	−1.27841	−	0.415381i	−0.868021	+	0.496528i	$0.834608\pi$
$542$	−44.5230	−	7.05176i	−1.91243	−	0.302899i
$543$	4.97163	−	0.787429i	0.213353	−	0.0337918i
$544$	−1.54241	+	0.501159i	−0.0661303	+	0.0214870i
$545$		0			0
$546$	−2.79899	+	3.85248i	−0.119786	+	0.164871i
$547$	−4.93799	+	31.1772i	−0.211133	+	1.33304i	0.623322	+	0.781966i	$0.285783\pi$
$547$	−4.93799	+	31.1772i	−0.211133	+	1.33304i	−0.834455	+	0.551076i	$0.814217\pi$
$548$	−0.836995	−	1.64270i	−0.0357547	−	0.0701725i
$549$	17.9525			0.766194
$550$		0			0
$551$	−5.44169			−0.231824
$552$	−2.84254	−	5.57880i	−0.120987	−	0.237449i
$553$	−1.50626	+	9.51017i	−0.0640528	+	0.404414i
$554$	−25.9779	+	35.7555i	−1.10370	+	1.51911i
$555$		0			0
$556$	0.143057	−	0.0464820i	0.00606696	−	0.00197128i
$557$	13.0992	−	2.07471i	0.555030	−	0.0879082i	0.127383	−	0.991854i	$-0.459342\pi$
$557$	13.0992	−	2.07471i	0.555030	−	0.0879082i	0.427648	+	0.903945i	$0.359342\pi$
$558$	−1.41610	−	0.224289i	−0.0599485	−	0.00949491i
$559$	−6.29208	−	2.04442i	−0.266127	−	0.0864698i
$560$		0			0
$561$	5.00516	+	1.81054i	0.211318	+	0.0764412i
$562$	−8.83073	−	8.83073i	−0.372502	−	0.372502i
$563$	−26.1698	+	13.3342i	−1.10292	+	0.561968i	−0.908051	−	0.418860i	$-0.862430\pi$
$563$	−26.1698	+	13.3342i	−1.10292	+	0.561968i	−0.194874	+	0.980828i	$0.562430\pi$
$564$	0.0867434	+	0.119392i	0.00365256	+	0.00502731i
$565$		0			0
$566$	4.32248	+	13.3032i	0.181687	+	0.559176i
$567$	12.1809	+	6.20650i	0.511551	+	0.260648i
$568$	−3.64683	−	23.0252i	−0.153018	−	0.966115i
$569$	−17.3540	+	12.6084i	−0.727518	+	0.528573i	−0.888777	−	0.458339i	$-0.848445\pi$
$569$	−17.3540	+	12.6084i	−0.727518	+	0.528573i	0.161259	+	0.986912i	$0.448445\pi$
$570$		0			0
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$	0.453993	−	0.0566536i	0.0189824	−	0.00236881i
$573$	9.74484	−	9.74484i	0.407097	−	0.407097i
$574$	1.10271	−	3.39380i	0.0460263	−	0.141654i
$575$		0			0
$576$	13.6590	+	9.92385i	0.569125	+	0.413494i
$577$	−3.03825	+	5.96290i	−0.126484	+	0.248239i	−0.945561	−	0.325445i	$-0.894486\pi$
$577$	−3.03825	+	5.96290i	−0.126484	+	0.248239i	0.819077	+	0.573683i	$0.194486\pi$
$578$	−8.84070	+	17.3509i	−0.367725	+	0.721700i
$579$	11.4251	+	8.30081i	0.474810	+	0.344970i
$580$		0			0
$581$	−2.59048	+	7.97268i	−0.107471	+	0.330763i
$582$	−2.86867	+	2.86867i	−0.118910	+	0.118910i
$583$	21.9879	−	20.5853i	0.910644	−	0.852558i
$584$		−	14.8165i		−	0.613112i
$585$		0			0
$586$	2.73660	−	1.98825i	0.113048	−	0.0821340i
$587$	−5.70952	−	36.0485i	−0.235657	−	1.48788i	−0.767506	−	0.641041i	$-0.778503\pi$
$587$	−5.70952	−	36.0485i	−0.235657	−	1.48788i	0.531849	−	0.846839i	$-0.321497\pi$
$588$	1.19035	+	0.606512i	0.0490890	+	0.0250121i
$589$	0.711594	+	2.19006i	0.0293207	+	0.0902400i
$590$		0			0
$591$	−6.66825	−	9.17805i	−0.274295	−	0.377535i
$592$	−18.7937	+	9.57587i	−0.772417	+	0.393566i
$593$	26.6656	+	26.6656i	1.09502	+	1.09502i	0.994983	+	0.100040i	$0.0318971\pi$
$593$	26.6656	+	26.6656i	1.09502	+	1.09502i	0.100040	+	0.994983i	$0.468103\pi$
$594$	5.96146	+	20.6362i	0.244602	+	0.846714i
$595$		0			0
$596$	−0.172988	−	0.0562073i	−0.00708588	−	0.00230234i
$597$	−15.9648	−	2.52857i	−0.653394	−	0.103487i
$598$	3.71509	−	0.588412i	0.151921	−	0.0240620i
$599$	36.7124	−	11.9286i	1.50003	−	0.487388i	0.560002	−	0.828492i	$-0.310801\pi$
$599$	36.7124	−	11.9286i	1.50003	−	0.487388i	0.940026	+	0.341103i	$0.110801\pi$
$600$		0			0
$601$	22.4050	−	30.8379i	0.913920	−	1.25790i	−0.0518905	−	0.998653i	$-0.516525\pi$
$601$	22.4050	−	30.8379i	0.913920	−	1.25790i	0.965810	−	0.259250i	$-0.0834753\pi$
$602$	−6.90894	+	43.6213i	−0.281587	+	1.77787i
$603$	4.52538	+	8.88156i	0.184288	+	0.361685i
$604$	−0.236459			−0.00962138
$605$		0			0
$606$	16.2198			0.658884
$607$	−16.4492	−	32.2834i	−0.667653	−	1.31034i	−0.937683	−	0.347491i	$-0.887034\pi$
$607$	−16.4492	−	32.2834i	−0.667653	−	1.31034i	0.270031	−	0.962852i	$-0.412966\pi$
$608$	−0.714845	+	4.51336i	−0.0289908	+	0.183041i
$609$	2.06640	−	2.84415i	0.0837346	−	0.115251i
$610$		0			0
$611$	1.04729	−	0.340286i	0.0423689	−	0.0137665i
$612$	0.654587	−	0.103676i	0.0264601	−	0.00419087i
$613$	−2.37960	−	0.376892i	−0.0961113	−	0.0152225i	0.108194	−	0.994130i	$-0.465493\pi$
$613$	−2.37960	−	0.376892i	−0.0961113	−	0.0152225i	−0.204305	+	0.978907i	$0.565493\pi$
$614$	24.5743	+	7.98466i	0.991736	+	0.322235i
$615$		0			0
$616$	10.5285	+	36.4455i	0.424206	+	1.46843i
$617$	25.5598	+	25.5598i	1.02900	+	1.02900i	0.999567	+	0.0294325i	$0.00937002\pi$
$617$	25.5598	+	25.5598i	1.02900	+	1.02900i	0.0294325	+	0.999567i	$0.490630\pi$
$618$	−10.9631	+	5.58599i	−0.441001	+	0.224701i
$619$	−0.537145	−	0.739317i	−0.0215897	−	0.0297157i	0.798086	−	0.602544i	$-0.205846\pi$
$619$	−0.537145	−	0.739317i	−0.0215897	−	0.0297157i	−0.819675	+	0.572828i	$0.805846\pi$
$620$		0			0
$621$	3.78415	+	11.6464i	0.151853	+	0.467355i
$622$	19.7409	+	10.0585i	0.791540	+	0.403310i
$623$	9.18661	+	58.0020i	0.368054	+	2.32380i
$624$	2.66569	−	1.93674i	0.106713	−	0.0775316i
$625$		0			0
$626$			38.2851i			1.53018i
$627$	10.9480	−	10.2496i	0.437219	−	0.409331i
$628$	0.781786	−	0.781786i	0.0311967	−	0.0311967i
$629$	2.93865	−	9.04423i	0.117172	−	0.360617i
$630$		0			0
$631$	−18.6941	−	13.5820i	−0.744199	−	0.540692i	0.149824	−	0.988713i	$-0.452129\pi$
$631$	−18.6941	−	13.5820i	−0.744199	−	0.540692i	−0.894023	+	0.448020i	$0.852129\pi$
$632$	2.81388	−	5.52255i	0.111930	−	0.219675i
$633$	2.41536	−	4.74042i	0.0960020	−	0.188415i
$634$	33.5956	+	24.4087i	1.33425	+	0.969392i
$635$		0			0
$636$	−0.348145	+	1.07148i	−0.0138049	+	0.0424870i
$637$	7.04889	−	7.04889i	0.279287	−	0.279287i
$638$	−4.83342	+	0.603161i	−0.191357	+	0.0238794i
$639$			19.8201i			0.784072i
$640$		0			0
$641$	−7.06172	+	5.13064i	−0.278921	+	0.202648i	−0.718447	−	0.695582i	$-0.755147\pi$
$641$	−7.06172	+	5.13064i	−0.278921	+	0.202648i	0.439525	+	0.898230i	$0.355147\pi$
$642$	−1.17727	−	7.43296i	−0.0464630	−	0.293356i
$643$	28.1018	+	14.3186i	1.10823	+	0.564670i	0.909634	−	0.415412i	$-0.136362\pi$
$643$	28.1018	+	14.3186i	1.10823	+	0.564670i	0.198594	+	0.980082i	$0.436362\pi$
$644$	−0.538058	−	1.65597i	−0.0212024	−	0.0652544i
$645$		0			0
$646$	−9.02265	−	12.4186i	−0.354991	−	0.488604i
$647$	12.2437	−	6.23845i	0.481348	−	0.245259i	−0.196441	−	0.980516i	$-0.562938\pi$
$647$	12.2437	−	6.23845i	0.481348	−	0.245259i	0.677789	+	0.735257i	$0.262938\pi$
$648$	−6.22265	−	6.22265i	−0.244449	−	0.244449i
$649$	−29.0356	−	10.5032i	−1.13975	−	0.412288i
$650$		0			0
$651$	−1.41487	−	0.459720i	−0.0554532	−	0.0180178i
$652$	2.26797	+	0.359211i	0.0888205	+	0.0140678i
$653$	5.37414	−	0.851181i	0.210307	−	0.0333093i	−0.0503921	−	0.998730i	$-0.516047\pi$
$653$	5.37414	−	0.851181i	0.210307	−	0.0333093i	0.260699	+	0.965420i	$0.416047\pi$
$654$	23.1192	−	7.51187i	0.904030	−	0.293737i
$655$		0			0
$656$	−1.45134	+	1.99759i	−0.0566652	+	0.0779929i
$657$	−1.97062	+	12.4420i	−0.0768812	+	0.485408i
$658$	−3.33733	−	6.54987i	−0.130102	−	0.255341i
$659$	42.1160			1.64061			0.820304	−	0.571928i	$-0.193805\pi$
$659$	42.1160			1.64061			0.820304	+	0.571928i	$0.193805\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$	16.4023	+	32.1913i	0.637493	+	1.25115i
$663$	−0.232390	+	1.46726i	−0.00902529	+	0.0569835i
$664$	3.17181	−	4.36562i	0.123090	−	0.169419i
$665$		0			0
$666$	15.8666	−	5.15536i	0.614817	−	0.199766i
$667$	−2.74272	+	0.434404i	−0.106198	+	0.0168202i
$668$	−0.610847	−	0.0967487i	−0.0236344	−	0.00374332i
$669$	−11.2385	−	3.65162i	−0.434507	−	0.141180i
$670$		0			0
$671$	−14.4746	−	21.3683i	−0.558786	−	0.824915i
$672$	−2.08750	−	2.08750i	−0.0805269	−	0.0805269i
$673$	4.94179	−	2.51797i	0.190492	−	0.0970605i	−0.356143	−	0.934431i	$-0.615908\pi$
$673$	4.94179	−	2.51797i	0.190492	−	0.0970605i	0.546635	+	0.837371i	$0.315908\pi$
$674$	−26.7253	−	36.7842i	−1.02942	−	1.41687i
$675$		0			0
$676$	−0.559191	−	1.72101i	−0.0215073	−	0.0661928i
$677$	2.07893	+	1.05927i	0.0798999	+	0.0407110i	0.493484	−	0.869755i	$-0.335723\pi$
$677$	2.07893	+	1.05927i	0.0798999	+	0.0407110i	−0.413584	+	0.910466i	$0.635723\pi$
$678$	2.31421	+	14.6114i	0.0888767	+	0.561146i
$679$	11.3369	−	8.23673i	0.435070	−	0.316097i
$680$		0			0
$681$			6.89132i			0.264076i
$682$	0.874800	+	1.86638i	0.0334978	+	0.0714675i
$683$	25.0400	−	25.0400i	0.958127	−	0.958127i	−0.0410307	−	0.999158i	$-0.513064\pi$
$683$	25.0400	−	25.0400i	0.958127	−	0.958127i	0.999158	+	0.0410307i	$0.0130641\pi$
$684$	0.577053	−	1.77599i	0.0220642	−	0.0679066i
$685$		0			0
$686$	−18.8423	−	13.6897i	−0.719401	−	0.522676i
$687$	7.40730	−	14.5376i	0.282606	−	0.554646i
$688$	13.8738	−	27.2288i	0.528933	−	1.03809i
$689$	6.80110	+	4.94129i	0.259101	+	0.188248i
$690$		0			0
$691$	−0.556172	+	1.71172i	−0.0211578	+	0.0651170i	−0.961078	−	0.276277i	$-0.910899\pi$
$691$	−0.556172	+	1.71172i	−0.0211578	+	0.0651170i	0.939920	+	0.341394i	$0.110899\pi$
$692$	−0.456241	+	0.456241i	−0.0173437	+	0.0173437i
$693$	−3.99389	−	32.0050i	−0.151715	−	1.21577i
$694$		−	44.2510i		−	1.67974i
$695$		0			0
$696$	−1.83081	+	1.33016i	−0.0693967	+	0.0504196i
$697$	−0.174147	−	1.09952i	−0.00659628	−	0.0416473i
$698$	−27.9094	−	14.2205i	−1.05638	−	0.538255i
$699$	0.955200	+	2.93980i	0.0361290	+	0.111194i
$700$		0			0
$701$	10.4715	+	14.4128i	0.395502	+	0.544362i	0.959608	−	0.281340i	$-0.0907790\pi$
$701$	10.4715	+	14.4128i	0.395502	+	0.544362i	−0.564106	+	0.825703i	$0.690779\pi$
$702$	−5.34171	+	2.72174i	−0.201610	+	0.102725i
$703$	−18.9468	−	18.9468i	−0.714593	−	0.714593i
$704$	0.799189	−	24.2592i	0.0301206	−	0.914304i
$705$		0			0
$706$	−5.57255	−	1.81063i	−0.209726	−	0.0681440i
$707$	−55.3357	−	8.76432i	−2.08111	−	0.329616i
$708$	1.14071	−	0.180671i	0.0428706	−	0.00679003i
$709$	9.55567	−	3.10483i	0.358871	−	0.116604i	−0.124032	−	0.992278i	$-0.539583\pi$
$709$	9.55567	−	3.10483i	0.358871	−	0.116604i	0.482903	+	0.875674i	$0.339583\pi$
$710$		0			0
$711$	−3.09743	+	4.26324i	−0.116163	+	0.159884i
$712$	5.91351	−	37.3365i	0.221618	−	1.39924i
$713$	0.533487	+	1.04703i	0.0199793	+	0.0392115i
$714$	9.91691			0.371131
$715$		0			0
$716$	0.554298			0.0207151
$717$	1.21427	+	2.38314i	0.0453478	+	0.0890001i
$718$	−2.46302	+	15.5509i	−0.0919193	+	0.580355i
$719$	−4.03181	+	5.54931i	−0.150361	+	0.206954i	−0.877553	−	0.479480i	$-0.840825\pi$
$719$	−4.03181	+	5.54931i	−0.150361	+	0.206954i	0.727191	+	0.686435i	$0.240825\pi$
$720$		0			0
$721$	40.4204	−	13.1334i	1.50533	−	0.489113i
$722$	−15.2088	+	2.40884i	−0.566014	+	0.0896478i
$723$	20.8943	+	3.30933i	0.777067	+	0.123075i
$724$	−0.856964	−	0.278444i	−0.0318488	−	0.0103483i
$725$		0			0
$726$	8.58812	−	10.3174i	0.318735	−	0.382915i
$727$	25.2212	+	25.2212i	0.935401	+	0.935401i	0.998036	−	0.0626351i	$-0.0199504\pi$
$727$	25.2212	+	25.2212i	0.935401	+	0.935401i	−0.0626351	+	0.998036i	$0.519950\pi$
$728$	−9.43398	+	4.80685i	−0.349647	+	0.178154i
$729$	−2.08750	−	2.87320i	−0.0773149	−	0.106415i
$730$		0			0
$731$	4.25759	+	13.1035i	0.157473	+	0.484651i
$732$	0.860158	+	0.438272i	0.0317924	+	0.0161990i
$733$	−1.20620	−	7.61562i	−0.0445519	−	0.281289i	0.955347	−	0.295485i	$-0.0954812\pi$
$733$	−1.20620	−	7.61562i	−0.0445519	−	0.281289i	−0.999899	+	0.0141956i	$0.995481\pi$
$734$	−41.0401	+	29.8174i	−1.51482	+	1.10058i
$735$		0			0
$736$			2.33188i			0.0859543i
$737$	6.92277	−	12.5474i	0.255004	−	0.462189i
$738$	1.38095	−	1.38095i	0.0508336	−	0.0508336i
$739$	−12.6089	+	38.8062i	−0.463825	+	1.42751i	0.396629	+	0.917979i	$0.370180\pi$
$739$	−12.6089	+	38.8062i	−0.463825	+	1.42751i	−0.860454	+	0.509528i	$0.829820\pi$
$740$		0			0
$741$	3.38633	+	2.46031i	0.124400	+	0.0903819i
$742$	25.4776	−	50.0027i	0.935313	−	1.83566i
$743$	−20.1411	+	39.5290i	−0.738904	+	1.45018i	0.148368	+	0.988932i	$0.452598\pi$
$743$	−20.1411	+	39.5290i	−0.738904	+	1.45018i	−0.887271	+	0.461248i	$0.847402\pi$
$744$	0.774746	+	0.562886i	0.0284036	+	0.0206364i
$745$		0			0
$746$	6.34530	−	19.5288i	0.232318	−	0.715001i
$747$	−3.24412	+	3.24412i	−0.118696	+	0.118696i
$748$	−0.651178	−	0.695544i	−0.0238094	−	0.0254316i
$749$			25.9946i			0.949821i
$750$		0			0
$751$	10.6518	−	7.73896i	0.388688	−	0.282399i	−0.376229	−	0.926527i	$-0.622780\pi$
$751$	10.6518	−	7.73896i	0.388688	−	0.282399i	0.764918	+	0.644128i	$0.222780\pi$
$752$	0.795708	+	5.02390i	0.0290165	+	0.183203i
$753$	−12.0944	−	6.16240i	−0.440744	−	0.224570i
$754$	−0.420104	−	1.29295i	−0.0152993	−	0.0470864i
$755$		0			0
$756$	1.63123	+	2.24520i	0.0593274	+	0.0816571i
$757$	17.7060	−	9.02166i	0.643535	−	0.327898i	−0.101586	−	0.994827i	$-0.532392\pi$
$757$	17.7060	−	9.02166i	0.643535	−	0.327898i	0.745121	+	0.666929i	$0.232392\pi$
$758$	27.4703	+	27.4703i	0.997768	+	0.997768i
$759$	4.69977	−	6.03997i	0.170591	−	0.219237i
$760$		0			0
$761$	16.8706	+	5.48158i	0.611558	+	0.198707i	0.598389	−	0.801206i	$-0.295808\pi$
$761$	16.8706	+	5.48158i	0.611558	+	0.198707i	0.0131694	+	0.999913i	$0.495808\pi$
$762$	−1.39763	−	0.221363i	−0.0506309	−	0.00801914i
$763$	−82.9328	+	13.1353i	−3.00237	+	0.475528i
$764$	−2.34625	+	0.762341i	−0.0848842	+	0.0275805i
$765$		0			0
$766$	−20.7124	+	28.5082i	−0.748371	+	1.03004i
$767$	1.34813	−	8.51175i	0.0486781	−	0.307342i
$768$	1.34437	+	2.63847i	0.0485107	+	0.0952076i
$769$	−33.4001			−1.20444			−0.602218	−	0.798331i	$-0.705716\pi$
$769$	−33.4001			−1.20444			−0.602218	+	0.798331i	$0.705716\pi$
$770$		0			0
$771$	13.4894			0.485810
$772$	−1.14769	−	2.25247i	−0.0413064	−	0.0810683i
$773$	5.96974	−	37.6915i	0.214717	−	1.35567i	−0.611021	−	0.791614i	$-0.709241\pi$
$773$	5.96974	−	37.6915i	0.214717	−	1.35567i	0.825738	−	0.564054i	$-0.190759\pi$
$774$	−14.2073	+	19.5547i	−0.510671	+	0.702878i
$775$		0			0
$776$	−8.57893	+	2.78746i	−0.307966	+	0.100064i
$777$	17.0975	−	2.70797i	0.613369	−	0.0971480i
$778$	−10.9251	−	1.73036i	−0.391683	−	0.0620365i
$779$	−2.98315	−	0.969285i	−0.106882	−	0.0347282i
$780$		0			0
$781$	23.5913	−	15.9804i	0.844163	−	0.571824i
$782$	−5.53895	−	5.53895i	−0.198072	−	0.198072i
$783$	3.94360	−	2.00936i	0.140933	−	0.0718088i
$784$	27.0654	+	37.2523i	0.966621	+	1.33044i
$785$		0			0
$786$	5.45050	+	16.7749i	0.194413	+	0.598341i
$787$	−32.7403	−	16.6820i	−1.16706	−	0.594649i	−0.240450	−	0.970662i	$-0.577295\pi$
$787$	−32.7403	−	16.6820i	−1.16706	−	0.594649i	−0.926614	+	0.376013i	$0.877295\pi$
$788$	0.317689	+	2.00581i	0.0113172	+	0.0714541i
$789$	0.645642	−	0.469086i	0.0229855	−	0.0166999i
$790$		0			0
$791$		−	51.0989i		−	1.81687i
$792$	−3.92127	+	20.3881i	−0.139336	+	0.724458i
$793$	5.09361	−	5.09361i	0.180879	−	0.180879i
$794$	−10.3140	+	31.7434i	−0.366032	+	1.12653i
$795$		0			0
$796$	2.34087	+	1.70074i	0.0829700	+	0.0602812i
$797$	9.14395	−	17.9460i	0.323895	−	0.635680i	−0.670441	−	0.741963i	$-0.733895\pi$
$797$	9.14395	−	17.9460i	0.323895	−	0.635680i	0.994336	+	0.106283i	$0.0338949\pi$
$798$	12.6855	−	24.8968i	0.449063	−	0.881337i
$799$	−1.85529	−	1.34795i	−0.0656355	−	0.0476870i
$800$		0			0
$801$	−9.93160	+	30.5663i	−0.350916	+	1.08001i
$802$	−25.0253	+	25.0253i	−0.883674	+	0.883674i
$803$	16.3982	−	7.68606i	0.578679	−	0.271235i
$804$			0.536020i			0.0189040i
$805$		0			0
$806$	−0.465424	+	0.338150i	−0.0163939	+	0.0119108i
$807$	3.70156	+	23.3708i	0.130301	+	0.822690i
$808$	32.1334	+	16.3728i	1.13045	+	0.575993i
$809$	−16.0484	−	49.3920i	−0.564233	−	1.73653i	−0.670220	−	0.742162i	$-0.733800\pi$
$809$	−16.0484	−	49.3920i	−0.564233	−	1.73653i	0.105987	−	0.994367i	$-0.466200\pi$
$810$		0			0
$811$	−23.0252	−	31.6914i	−0.808523	−	1.11284i	−0.991550	−	0.129728i	$-0.958590\pi$
$811$	−23.0252	−	31.6914i	−0.808523	−	1.11284i	0.183027	−	0.983108i	$-0.441410\pi$
$812$	−0.560729	+	0.285706i	−0.0196777	+	0.0100263i
$813$	−18.1009	−	18.1009i	−0.634826	−	0.634826i
$814$	−18.9290	−	14.7289i	−0.663462	−	0.516247i
$815$		0			0
$816$	−6.52607	−	2.12045i	−0.228458	−	0.0742306i
$817$	38.3431	+	6.07296i	1.34146	+	0.212466i
$818$	−8.47873	+	1.34290i	−0.296452	+	0.0469533i
$819$	8.56139	−	2.78176i	0.299159	−	0.0972027i
$820$		0			0
$821$	−14.6926	+	20.2226i	−0.512775	+	0.705774i	−0.984384	−	0.176034i	$-0.943673\pi$
$821$	−14.6926	+	20.2226i	−0.512775	+	0.705774i	0.471609	+	0.881808i	$0.343673\pi$
$822$	2.36185	−	14.9121i	0.0823789	−	0.520120i
$823$	−10.4310	−	20.4719i	−0.363600	−	0.713606i	0.634646	−	0.772803i	$-0.281146\pi$
$823$	−10.4310	−	20.4719i	−0.363600	−	0.713606i	−0.998246	+	0.0591972i	$0.981146\pi$
$824$	−27.3580			−0.953062
$825$		0			0
$826$	−57.5294			−2.00170
$827$	2.51391	+	4.93382i	0.0874171	+	0.171566i	0.930576	−	0.366099i	$-0.119307\pi$
$827$	2.51391	+	4.93382i	0.0874171	+	0.171566i	−0.843159	+	0.537664i	$0.819307\pi$
$828$	0.149071	−	0.941197i	0.00518057	−	0.0327089i
$829$	8.80126	−	12.1139i	0.305680	−	0.420733i	−0.628348	−	0.777933i	$-0.716268\pi$
$829$	8.80126	−	12.1139i	0.305680	−	0.420733i	0.934028	+	0.357200i	$0.116268\pi$
$830$		0			0
$831$	−23.8694	+	7.75564i	−0.828020	+	0.269040i
$832$	6.69109	−	1.05976i	0.231972	−	0.0367407i
$833$	−20.5045	−	3.24759i	−0.710439	−	0.112522i
$834$	1.17153	+	0.380652i	0.0405666	+	0.0131809i
$835$		0			0
$836$	−2.57917	+	0.745079i	−0.0892023	+	0.0257691i
$837$	−1.32438	−	1.32438i	−0.0457773	−	0.0457773i
$838$	−14.4461	+	7.36068i	−0.499034	+	0.254270i
$839$	−7.40356	−	10.1901i	−0.255599	−	0.351802i	0.661863	−	0.749625i	$-0.269766\pi$
$839$	−7.40356	−	10.1901i	−0.255599	−	0.351802i	−0.917462	+	0.397823i	$0.869766\pi$
$840$		0			0
$841$	−8.65134	−	26.6261i	−0.298322	−	0.918141i
$842$	10.2836	+	5.23975i	0.354396	+	0.180574i
$843$	−1.10941	−	7.00457i	−0.0382103	−	0.241250i
$844$	−0.770496	+	0.559798i	−0.0265216	+	0.0192691i
$845$		0			0
$846$		−	4.02315i		−	0.138319i
$847$	−34.8744	+	30.5585i	−1.19830	+	1.05000i
$848$	−27.4579	+	27.4579i	−0.942907	+	0.942907i
$849$	−2.45461	+	7.55451i	−0.0842420	+	0.259270i
$850$		0			0
$851$	−11.0621	−	8.03706i	−0.379203	−	0.275507i
$852$	−0.483867	+	0.949642i	−0.0165770	+	0.0325342i
$853$	22.5965	−	44.3481i	0.773689	−	1.51845i	−0.0794926	−	0.996835i	$-0.525330\pi$
$853$	22.5965	−	44.3481i	0.773689	−	1.51845i	0.853181	−	0.521614i	$-0.174670\pi$
$854$	−38.9035	−	28.2651i	−1.33125	−	0.967211i
$855$		0			0
$856$	5.17078	−	15.9140i	0.176734	−	0.543930i
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	−0.970044	−	0.242927i	$-0.921892\pi$
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	0.242927	+	0.970044i	$0.421892\pi$
$858$	3.28051	+	1.80996i	0.111995	+	0.0617909i
$859$		−	9.31402i		−	0.317790i	−0.987295	−	0.158895i	$-0.949207\pi$
$859$		−	9.31402i		−	0.317790i	0.987295	−	0.158895i	$-0.0507932\pi$
$860$		0			0
$861$	1.63941	−	1.19110i	0.0558709	−	0.0405926i
$862$	1.67475	+	10.5740i	0.0570424	+	0.360151i
$863$	−31.5320	−	16.0664i	−1.07336	−	0.546905i	−0.174285	−	0.984695i	$-0.555761\pi$
$863$	−31.5320	−	16.0664i	−1.07336	−	0.546905i	−0.899077	+	0.437790i	$0.855761\pi$
$864$	−1.14852	−	3.53479i	−0.0390735	−	0.120256i
$865$		0			0
$866$	4.34927	+	5.98625i	0.147794	+	0.203421i
$867$	−9.85305	+	5.02038i	−0.334627	+	0.170501i
$868$	0.188310	+	0.188310i	0.00639166	+	0.00639166i
$869$	7.57178	+	0.249443i	0.256855	+	0.00846176i
$870$		0			0
$871$	3.80391	+	1.23597i	0.128891	+	0.0418791i
$872$	53.3847	+	8.45531i	1.80783	+	0.286333i
$873$	7.57478	−	1.19973i	0.256368	−	0.0406046i
$874$	−20.9911	+	6.82042i	−0.710034	+	0.230704i
$875$		0			0
$876$	−0.398163	+	0.548025i	−0.0134527	+	0.0185160i
$877$	3.41955	−	21.5902i	0.115470	−	0.729048i	−0.860225	−	0.509915i	$-0.829677\pi$
$877$	3.41955	−	21.5902i	0.115470	−	0.729048i	0.975695	−	0.219133i	$-0.0703230\pi$
$878$	−0.863707	−	1.69512i	−0.0291487	−	0.0572076i
$879$	1.92089			0.0647901
$880$		0			0
$881$	46.4810			1.56599			0.782993	−	0.622031i	$-0.213692\pi$
$881$	46.4810			1.56599			0.782993	+	0.622031i	$0.213692\pi$
$882$	−16.5344	−	32.4505i	−0.556741	−	1.09267i
$883$	−4.36822	+	27.5798i	−0.147002	+	0.928135i	0.798376	+	0.602159i	$0.205693\pi$
$883$	−4.36822	+	27.5798i	−0.147002	+	0.928135i	−0.945378	+	0.325976i	$0.894307\pi$
$884$	0.156308	−	0.215140i	0.00525721	−	0.00723593i
$885$		0			0
$886$	21.4719	−	6.97665i	0.721363	−	0.234385i
$887$	6.95351	−	1.10133i	0.233476	−	0.0369790i	−0.0385999	−	0.999255i	$-0.512290\pi$
$887$	6.95351	−	1.10133i	0.233476	−	0.0369790i	0.272076	+	0.962276i	$0.412290\pi$
$888$	−11.0058	−	1.74315i	−0.369331	−	0.0584963i
$889$	4.64858	+	1.51041i	0.155908	+	0.0506577i
$890$		0			0
$891$	3.65892	−	10.1149i	0.122578	−	0.338862i
$892$	1.49577	+	1.49577i	0.0500822	+	0.0500822i
$893$	−5.75734	+	2.93351i	−0.192662	+	0.0981662i
$894$	−0.875532	−	1.20507i	−0.0292822	−	0.0403035i
$895$		0			0
$896$	−16.1666	−	49.7558i	−0.540090	−	1.66223i
$897$	1.90318	+	0.969718i	0.0635453	+	0.0323780i
$898$	−2.78007	−	17.5527i	−0.0927721	−	0.585740i
$899$	0.343606	−	0.249644i	0.0114599	−	0.00832611i
$900$		0			0
$901$		−	17.5071i		−	0.583247i
$902$	−2.75713	−	0.530284i	−0.0918024	−	0.0176565i
$903$	−17.7343	+	17.7343i	−0.590160	+	0.590160i
$904$	−10.1645	+	31.2830i	−0.338065	+	1.04046i
$905$		0			0
$906$	−1.56659	−	1.13820i	−0.0520466	−	0.0378141i
$907$	−13.4148	+	26.3281i	−0.445433	+	0.874211i	0.553706	+	0.832712i	$0.313213\pi$
$907$	−13.4148	+	26.3281i	−0.445433	+	0.874211i	−0.999139	+	0.0414984i	$0.986787\pi$
$908$	0.560050	−	1.09916i	0.0185859	−	0.0364769i
$909$	−24.8061	−	18.0227i	−0.822765	−	0.597774i
$910$		0			0
$911$	5.23886	−	16.1236i	0.173571	−	0.534198i	−0.825994	−	0.563679i	$-0.809386\pi$
$911$	5.23886	−	16.1236i	0.173571	−	0.534198i	0.999565	+	0.0294813i	$0.00938555\pi$
$912$	−13.6715	+	13.6715i	−0.452709	+	0.452709i
$913$	6.47702	+	1.24574i	0.214358	+	0.0412279i
$914$			5.14655i			0.170233i
$915$		0			0
$916$	−2.36292	+	1.71676i	−0.0780729	+	0.0567233i
$917$	−9.53075	−	60.1748i	−0.314733	−	1.98715i
$918$	11.1243	+	5.66813i	0.367158	+	0.187076i
$919$	−1.55222	−	4.77725i	−0.0512030	−	0.157587i	0.922185	−	0.386748i	$-0.126402\pi$
$919$	−1.55222	−	4.77725i	−0.0512030	−	0.157587i	−0.973388	+	0.229161i	$0.926402\pi$
$920$		0			0
$921$	8.62467	+	11.8708i	0.284193	+	0.391158i
$922$	7.12304	−	3.62937i	0.234585	−	0.119527i
$923$	5.62351	+	5.62351i	0.185100	+	0.185100i
$924$	0.589975	−	1.63096i	0.0194087	−	0.0536545i
$925$		0			0
$926$	30.3635	+	9.86569i	0.997805	+	0.324207i
$927$	22.9736	+	3.63865i	0.754551	+	0.119509i
$928$	0.832439	−	0.131845i	0.0273262	−	0.00432804i
$929$	11.2348	−	3.65041i	0.368602	−	0.119766i	−0.118858	−	0.992911i	$-0.537923\pi$
$929$	11.2348	−	3.65041i	0.368602	−	0.119766i	0.487460	+	0.873145i	$0.337923\pi$
$930$		0			0
$931$	−34.3822	+	47.3231i	−1.12683	+	1.55095i
$932$	0.0865609	−	0.546524i	0.00283540	−	0.0179020i
$933$	5.71194	+	11.2103i	0.187001	+	0.367009i
$934$	21.5258			0.704346
$935$		0			0
$936$	−5.79466			−0.189405
$937$	1.04060	+	2.04229i	0.0339949	+	0.0667187i	0.907379	−	0.420313i	$-0.138080\pi$
$937$	1.04060	+	2.04229i	0.0339949	+	0.0667187i	−0.873384	+	0.487032i	$0.838080\pi$
$938$	4.17683	−	26.3715i	0.136378	−	0.861060i
$939$	−12.7791	+	17.5889i	−0.417029	+	0.573991i
$940$		0			0
$941$	1.68653	−	0.547988i	0.0549794	−	0.0178639i	−0.281398	−	0.959591i	$-0.590798\pi$
$941$	1.68653	−	0.547988i	0.0549794	−	0.0178639i	0.336378	+	0.941727i	$0.390798\pi$
$942$	8.94264	−	1.41638i	0.291367	−	0.0461480i
$943$	−1.58094	−	0.250397i	−0.0514826	−	0.00815404i
$944$	37.8587	+	12.3010i	1.23219	+	0.400364i
$945$		0			0
$946$	34.7303	+	1.14415i	1.12918	+	0.0371994i
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	0.833321	−	0.552790i	$-0.186437\pi$
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	−0.552790	+	0.833321i	$0.686437\pi$
$948$	−0.252485	+	0.128648i	−0.00820033	+	0.00417828i
$949$	2.97101	+	4.08925i	0.0964431	+	0.132743i
$950$		0			0
$951$	7.28714	+	22.4275i	0.236302	+	0.727262i
$952$	19.6466	+	10.0105i	0.636752	+	0.324441i
$953$	−2.88376	−	18.2074i	−0.0934143	−	0.589794i	−0.989344	−	0.145598i	$-0.953489\pi$
$953$	−2.88376	−	18.2074i	−0.0934143	−	0.589794i	0.895930	−	0.444196i	$-0.146511\pi$
$954$	24.8476	−	18.0528i	0.804470	−	0.584482i
$955$		0			0
$956$		−	0.478792i		−	0.0154852i
$957$	−2.42189	−	1.33623i	−0.0782884	−	0.0431941i
$958$	5.09348	−	5.09348i	0.164563	−	0.164563i
$959$	−16.1154	+	49.5982i	−0.520395	+	1.60161i
$960$		0			0
$961$	24.9341	+	18.1157i	0.804327	+	0.584377i
$962$	3.03906	−	5.96448i	0.0979831	−	0.192303i
$963$	−6.45868	+	12.6759i	−0.208128	+	0.408474i
$964$	−3.06368	−	2.22589i	−0.0986743	−	0.0716911i
$965$		0			0
$966$	4.40628	−	13.5611i	0.141770	−	0.436322i
$967$	−9.49113	+	9.49113i	−0.305214	+	0.305214i	−0.843050	−	0.537836i	$-0.819242\pi$
$967$	−9.49113	+	9.49113i	−0.305214	+	0.305214i	0.537836	+	0.843050i	$0.319242\pi$
$968$	27.4289	−	11.7709i	0.881598	−	0.378333i
$969$		−	8.71697i		−	0.280029i
$970$		0			0
$971$	−41.4379	+	30.1064i	−1.32981	+	0.966161i	−0.330053	+	0.943963i	$0.607067\pi$
$971$	−41.4379	+	30.1064i	−1.32981	+	0.966161i	−0.999754	+	0.0221983i	$0.992933\pi$
$972$	0.371911	+	2.34815i	0.0119291	+	0.0753171i
$973$	−3.79111	−	1.93167i	−0.121538	−	0.0619265i
$974$	4.86416	+	14.9703i	0.155858	+	0.479681i
$975$		0			0
$976$	19.5578	+	26.9190i	0.626029	+	0.861655i
$977$	−12.9020	+	6.57391i	−0.412772	+	0.210318i	−0.648030	−	0.761615i	$-0.724407\pi$
$977$	−12.9020	+	6.57391i	−0.412772	+	0.210318i	0.235257	+	0.971933i	$0.424407\pi$
$978$	13.2967	+	13.2967i	0.425183	+	0.425183i
$979$	44.3897	−	12.8235i	1.41870	−	0.409840i
$980$		0			0
$981$	−43.7046	−	14.2005i	−1.39538	−	0.453386i
$982$	−4.71447	−	0.746699i	−0.150445	−	0.0238281i
$983$	56.8388	−	9.00238i	1.81288	−	0.287131i	0.844304	−	0.535865i	$-0.180014\pi$
$983$	56.8388	−	9.00238i	1.81288	−	0.287131i	0.968572	+	0.248734i	$0.0800143\pi$
$984$	−1.24059	+	0.403091i	−0.0395484	+	0.0128501i
$985$		0			0
$986$	−1.66413	+	2.29048i	−0.0529967	+	0.0729437i
$987$	0.653031	−	4.12308i	0.0207862	−	0.131239i
$988$	−0.340170	−	0.667621i	−0.0108222	−	0.0212399i
$989$	19.8105			0.629936
$990$		0			0
$991$	13.1102			0.416458			0.208229	−	0.978080i	$-0.433230\pi$
$991$	13.1102			0.416458			0.208229	+	0.978080i	$0.433230\pi$
$992$	−0.161918	−	0.317782i	−0.00514090	−	0.0100896i
$993$	−3.20952	+	20.2641i	−0.101851	+	0.643062i
$994$	31.2055	−	42.9507i	0.989779	−	1.36231i
$995$		0			0
$996$	−0.234634	+	0.0762372i	−0.00743466	+	0.00241567i
$997$	−2.22714	+	0.352744i	−0.0705343	+	0.0111715i	−0.191602	−	0.981473i	$-0.561368\pi$
$997$	−2.22714	+	0.352744i	−0.0705343	+	0.0111715i	0.121068	+	0.992644i	$0.461368\pi$
$998$	12.9469	+	2.05059i	0.409828	+	0.0649104i
$999$	20.7269	+	6.73459i	0.655772	+	0.213073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.b.57.1		32
5.2	odd	4		55.2.l.a.13.4	yes	32
5.3	odd	4	inner	275.2.bm.b.68.1		32
5.4	even	2		55.2.l.a.2.4	✓	32
11.6	odd	10	inner	275.2.bm.b.182.1		32
15.2	even	4		495.2.bj.a.343.1		32
15.14	odd	2		495.2.bj.a.442.1		32
20.7	even	4		880.2.cm.a.673.3		32
20.19	odd	2		880.2.cm.a.497.3		32
55.2	even	20		605.2.m.d.118.4		32
55.4	even	10		605.2.e.b.362.4		32
55.7	even	20		605.2.e.b.483.4		32
55.9	even	10		605.2.m.c.602.4		32
55.14	even	10		605.2.m.d.282.4		32
55.17	even	20		55.2.l.a.28.4	yes	32
55.19	odd	10		605.2.m.c.282.1		32
55.24	odd	10		605.2.m.d.602.1		32
55.27	odd	20		605.2.m.e.578.1		32
55.28	even	20	inner	275.2.bm.b.193.1		32
55.29	odd	10		605.2.e.b.362.13		32
55.32	even	4		605.2.m.e.233.1		32
55.37	odd	20		605.2.e.b.483.13		32
55.39	odd	10		55.2.l.a.17.4	yes	32
55.42	odd	20		605.2.m.c.118.1		32
55.47	odd	20		605.2.m.d.403.1		32
55.49	even	10		605.2.m.e.457.1		32
55.52	even	20		605.2.m.c.403.4		32
55.54	odd	2		605.2.m.e.112.1		32
165.17	odd	20		495.2.bj.a.28.1		32
165.149	even	10		495.2.bj.a.127.1		32
220.39	even	10		880.2.cm.a.17.3		32
220.127	odd	20		880.2.cm.a.193.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	5.4	even	2
55.2.l.a.13.4	yes	32	5.2	odd	4
55.2.l.a.17.4	yes	32	55.39	odd	10
55.2.l.a.28.4	yes	32	55.17	even	20
275.2.bm.b.57.1		32	1.1	even	1	trivial
275.2.bm.b.68.1		32	5.3	odd	4	inner
275.2.bm.b.182.1		32	11.6	odd	10	inner
275.2.bm.b.193.1		32	55.28	even	20	inner
495.2.bj.a.28.1		32	165.17	odd	20
495.2.bj.a.127.1		32	165.149	even	10
495.2.bj.a.343.1		32	15.2	even	4
495.2.bj.a.442.1		32	15.14	odd	2
605.2.e.b.362.4		32	55.4	even	10
605.2.e.b.362.13		32	55.29	odd	10
605.2.e.b.483.4		32	55.7	even	20
605.2.e.b.483.13		32	55.37	odd	20
605.2.m.c.118.1		32	55.42	odd	20
605.2.m.c.282.1		32	55.19	odd	10
605.2.m.c.403.4		32	55.52	even	20
605.2.m.c.602.4		32	55.9	even	10
605.2.m.d.118.4		32	55.2	even	20
605.2.m.d.282.4		32	55.14	even	10
605.2.m.d.403.1		32	55.47	odd	20
605.2.m.d.602.1		32	55.24	odd	10
605.2.m.e.112.1		32	55.54	odd	2
605.2.m.e.233.1		32	55.32	even	4
605.2.m.e.457.1		32	55.49	even	10
605.2.m.e.578.1		32	55.27	odd	20
880.2.cm.a.17.3		32	220.39	even	10
880.2.cm.a.193.3		32	220.127	odd	20
880.2.cm.a.497.3		32	20.19	odd	2
880.2.cm.a.673.3		32	20.7	even	4

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.665529 - 1.30617i) q^{2} +(0.130227 - 0.822224i) q^{3} +(-0.0875924 + 0.120561i) q^{4} +(-1.16064 + 0.377114i) q^{6} +(4.16343 - 0.659422i) q^{7} +(-2.68004 - 0.424477i) q^{8} +(2.19408 + 0.712899i) q^{9} +(-0.920480 - 3.18633i) q^{11} +(0.0877208 + 0.0877208i) q^{12} +(0.824787 - 0.420250i) q^{13} +(-3.63220 - 4.99930i) q^{14} +(1.32131 + 4.06656i) q^{16} +(-1.71765 - 0.875188i) q^{17} +(-0.529052 - 3.34030i) q^{18} +(-4.39439 + 3.19271i) q^{19} -3.50915i q^{21} +(-3.54930 + 3.32290i) q^{22} +(-1.95998 + 1.95998i) q^{23} +(-0.698030 + 2.14832i) q^{24} +(-1.09784 - 0.797627i) q^{26} +(2.00570 - 3.93640i) q^{27} +(-0.285184 + 0.559706i) q^{28} +(0.810497 + 0.588860i) q^{29} +(0.131006 - 0.403196i) q^{31} +(0.594873 - 0.594873i) q^{32} +(-2.73975 + 0.341892i) q^{33} +2.82602i q^{34} +(-0.278132 + 0.202075i) q^{36} +(0.771690 + 4.87226i) q^{37} +(7.09483 + 3.61500i) q^{38} +(-0.238130 - 0.732888i) q^{39} +(0.339428 + 0.467182i) q^{41} +(-4.58356 + 2.33544i) q^{42} +(-5.05373 - 5.05373i) q^{43} +(0.464773 + 0.168125i) q^{44} +(3.86451 + 1.25566i) q^{46} +(1.17495 + 0.186094i) q^{47} +(3.51569 - 0.556831i) q^{48} +(10.2419 - 3.32780i) q^{49} +(-0.943286 + 1.29832i) q^{51} +(-0.0215795 + 0.136247i) q^{52} +(4.12294 + 8.09173i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(2.05285 + 4.02895i) q^{57} +(0.229745 - 1.45055i) q^{58} +(5.47214 - 7.53175i) q^{59} +(7.40093 - 2.40471i) q^{61} +(-0.613832 + 0.0972215i) q^{62} +(9.60498 + 1.52128i) q^{63} +(6.96021 + 2.26151i) q^{64} +(2.26996 + 3.35105i) q^{66} +(3.05526 + 3.05526i) q^{67} +(0.255966 - 0.130421i) q^{68} +(1.35630 + 1.86679i) q^{69} +(2.65487 + 8.17086i) q^{71} +(-5.57761 - 2.84193i) q^{72} +(0.854195 + 5.39318i) q^{73} +(5.85044 - 4.25059i) q^{74} -0.809447i q^{76} +(-5.93349 - 12.6591i) q^{77} +(-0.798797 + 0.798797i) q^{78} +(-0.705861 + 2.17242i) q^{79} +(2.62377 + 1.90628i) q^{81} +(0.384322 - 0.754275i) q^{82} +(-0.902846 + 1.77193i) q^{83} +(0.423065 + 0.307374i) q^{84} +(-3.23765 + 9.96446i) q^{86} +(0.589724 - 0.589724i) q^{87} +(1.11440 + 8.93023i) q^{88} +13.9313i q^{89} +(3.15682 - 2.29356i) q^{91} +(-0.0646171 - 0.407977i) q^{92} +(-0.314457 - 0.160224i) q^{93} +(-0.538893 - 1.65854i) q^{94} +(-0.411650 - 0.566587i) q^{96} +(2.96200 - 1.50922i) q^{97} +(-11.1630 - 11.1630i) q^{98} +(0.251929 - 7.64727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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