LMFDB - Embedded newform 275.2.bm.b.68.1

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			68.1
Character	$\chi$	$=$	275.68
Dual form			275.2.bm.b.182.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30617 + 0.665529i) q^{2} +(0.822224 + 0.130227i) q^{3} +(0.0875924 - 0.120561i) q^{4} +(-1.16064 + 0.377114i) q^{6} +(-0.659422 - 4.16343i) q^{7} +(0.424477 - 2.68004i) q^{8} +(-2.19408 - 0.712899i) q^{9} +(-0.920480 - 3.18633i) q^{11} +(0.0877208 - 0.0877208i) q^{12} +(0.420250 + 0.824787i) q^{13} +(3.63220 + 4.99930i) q^{14} +(1.32131 + 4.06656i) q^{16} +(-0.875188 + 1.71765i) q^{17} +(3.34030 - 0.529052i) q^{18} +(4.39439 - 3.19271i) q^{19} -3.50915i q^{21} +(3.32290 + 3.54930i) q^{22} +(-1.95998 - 1.95998i) q^{23} +(0.698030 - 2.14832i) q^{24} +(-1.09784 - 0.797627i) q^{26} +(-3.93640 - 2.00570i) q^{27} +(-0.559706 - 0.285184i) q^{28} +(-0.810497 - 0.588860i) q^{29} +(0.131006 - 0.403196i) q^{31} +(-0.594873 - 0.594873i) q^{32} +(-0.341892 - 2.73975i) q^{33} -2.82602i q^{34} +(-0.278132 + 0.202075i) q^{36} +(4.87226 - 0.771690i) q^{37} +(-3.61500 + 7.09483i) q^{38} +(0.238130 + 0.732888i) q^{39} +(0.339428 + 0.467182i) q^{41} +(2.33544 + 4.58356i) q^{42} +(5.05373 - 5.05373i) q^{43} +(-0.464773 - 0.168125i) q^{44} +(3.86451 + 1.25566i) q^{46} +(0.186094 - 1.17495i) q^{47} +(0.556831 + 3.51569i) q^{48} +(-10.2419 + 3.32780i) q^{49} +(-0.943286 + 1.29832i) q^{51} +(0.136247 + 0.0215795i) q^{52} +(-8.09173 + 4.12294i) q^{53} +6.47647 q^{54} -11.4381 q^{56} +(4.02895 - 2.05285i) q^{57} +(1.45055 + 0.229745i) q^{58} +(-5.47214 + 7.53175i) q^{59} +(7.40093 - 2.40471i) q^{61} +(0.0972215 + 0.613832i) q^{62} +(-1.52128 + 9.60498i) q^{63} +(-6.96021 - 2.26151i) q^{64} +(2.26996 + 3.35105i) q^{66} +(3.05526 - 3.05526i) q^{67} +(0.130421 + 0.255966i) q^{68} +(-1.35630 - 1.86679i) q^{69} +(2.65487 + 8.17086i) q^{71} +(-2.84193 + 5.57761i) q^{72} +(-5.39318 + 0.854195i) q^{73} +(-5.85044 + 4.25059i) q^{74} -0.809447i q^{76} +(-12.6591 + 5.93349i) q^{77} +(-0.798797 - 0.798797i) q^{78} +(0.705861 - 2.17242i) q^{79} +(2.62377 + 1.90628i) q^{81} +(-0.754275 - 0.384322i) q^{82} +(-1.77193 - 0.902846i) q^{83} +(-0.423065 - 0.307374i) q^{84} +(-3.23765 + 9.96446i) q^{86} +(-0.589724 - 0.589724i) q^{87} +(-8.93023 + 1.11440i) q^{88} -13.9313i q^{89} +(3.15682 - 2.29356i) q^{91} +(-0.407977 + 0.0646171i) q^{92} +(0.160224 - 0.314457i) q^{93} +(0.538893 + 1.65854i) q^{94} +(-0.411650 - 0.566587i) q^{96} +(-1.50922 - 2.96200i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30617	+	0.665529i	−0.923605	+	0.470600i	−0.850057	−	0.526691i	$-0.823432\pi$
$2$	−1.30617	+	0.665529i	−0.923605	+	0.470600i	−0.0735483	+	0.997292i	$0.523432\pi$
$3$	0.822224	+	0.130227i	0.474711	+	0.0751869i	0.389206	−	0.921151i	$-0.372750\pi$
$3$	0.822224	+	0.130227i	0.474711	+	0.0751869i	0.0855054	+	0.996338i	$0.472750\pi$
$4$	0.0875924	−	0.120561i	0.0437962	−	0.0602803i
$5$		0			0
$5$		0			0
$6$	−1.16064	+	0.377114i	−0.473829	+	0.153956i
$7$	−0.659422	−	4.16343i	−0.249238	−	1.57363i	−0.721655	−	0.692253i	$-0.756618\pi$
$7$	−0.659422	−	4.16343i	−0.249238	−	1.57363i	0.472417	−	0.881375i	$-0.343382\pi$
$8$	0.424477	−	2.68004i	0.150075	−	0.947538i
$9$	−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
$13$	0.420250	+	0.824787i	0.116556	+	0.228755i	0.941913	−	0.335857i	$-0.109026\pi$
$13$	0.420250	+	0.824787i	0.116556	+	0.228755i	−0.825357	+	0.564612i	$0.809026\pi$
$14$	3.63220	+	4.99930i	0.970747	+	1.33612i
$15$		0			0
$16$	1.32131	+	4.06656i	0.330326	+	1.01664i
$17$	−0.875188	+	1.71765i	−0.212264	+	0.416592i	−0.972449	−	0.233115i	$-0.925108\pi$
$17$	−0.875188	+	1.71765i	−0.212264	+	0.416592i	0.760185	+	0.649707i	$0.225108\pi$
$18$	3.34030	−	0.529052i	0.787317	−	0.124699i
$19$	4.39439	−	3.19271i	1.00814	−	0.732458i	0.0443230	−	0.999017i	$-0.485887\pi$
$19$	4.39439	−	3.19271i	1.00814	−	0.732458i	0.963818	+	0.266560i	$0.0858869\pi$
$20$		0			0
$21$		−	3.50915i		−	0.765758i
$22$	3.32290	+	3.54930i	0.708446	+	0.756713i
$23$	−1.95998	−	1.95998i	−0.408685	−	0.408685i	0.472595	−	0.881280i	$-0.343317\pi$
$23$	−1.95998	−	1.95998i	−0.408685	−	0.408685i	−0.881280	+	0.472595i	$0.843317\pi$
$24$	0.698030	−	2.14832i	0.142485	−	0.438523i
$25$		0			0
$26$	−1.09784	−	0.797627i	−0.215304	−	0.156428i
$27$	−3.93640	−	2.00570i	−0.757561	−	0.385996i
$28$	−0.559706	−	0.285184i	−0.105774	−	0.0538948i
$29$	−0.810497	−	0.588860i	−0.150505	−	0.109349i	0.509984	−	0.860184i	$-0.329651\pi$
$29$	−0.810497	−	0.588860i	−0.150505	−	0.109349i	−0.660490	+	0.750835i	$0.729651\pi$
$30$		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
$33$	−0.341892	−	2.73975i	−0.0595158	−	0.476929i
$34$		−	2.82602i		−	0.484658i
$35$		0			0
$36$	−0.278132	+	0.202075i	−0.0463553	+	0.0336791i
$37$	4.87226	−	0.771690i	0.800995	−	0.126865i	0.257501	−	0.966278i	$-0.417101\pi$
$37$	4.87226	−	0.771690i	0.800995	−	0.126865i	0.543494	+	0.839413i	$0.317101\pi$
$38$	−3.61500	+	7.09483i	−0.586430	+	1.15093i
$39$	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	$0.785642\pi$
$42$	2.33544	+	4.58356i	0.360366	+	0.707258i
$43$	5.05373	−	5.05373i	0.770687	−	0.770687i	−0.207540	−	0.978227i	$-0.566546\pi$
$43$	5.05373	−	5.05373i	0.770687	−	0.770687i	0.978227	+	0.207540i	$0.0665456\pi$
$44$	−0.464773	−	0.168125i	−0.0700672	−	0.0253458i
$45$		0			0
$46$	3.86451	+	1.25566i	0.569791	+	0.185136i
$47$	0.186094	−	1.17495i	0.0271446	−	0.171384i	−0.970392	−	0.241537i	$-0.922349\pi$
$47$	0.186094	−	1.17495i	0.0271446	−	0.171384i	0.997536	+	0.0701524i	$0.0223486\pi$
$48$	0.556831	+	3.51569i	0.0803717	+	0.507447i
$49$	−10.2419	+	3.32780i	−1.46313	+	0.475400i
$50$		0			0
$51$	−0.943286	+	1.29832i	−0.132086	+	0.181801i
$52$	0.136247	+	0.0215795i	0.0188941	+	0.00299254i
$53$	−8.09173	+	4.12294i	−1.11149	+	0.566330i	−0.910602	−	0.413285i	$-0.864381\pi$
$53$	−8.09173	+	4.12294i	−1.11149	+	0.566330i	−0.200883	+	0.979615i	$0.564381\pi$
$54$	6.47647			0.881337
$55$		0			0
$56$	−11.4381			−1.52848
$57$	4.02895	−	2.05285i	0.533647	−	0.271907i
$58$	1.45055	+	0.229745i	0.190467	+	0.0301670i
$59$	−5.47214	+	7.53175i	−0.712411	+	0.980550i	0.287331	+	0.957831i	$0.407232\pi$
$59$	−5.47214	+	7.53175i	−0.712411	+	0.980550i	−0.999742	+	0.0227186i	$0.992768\pi$
$60$		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	$0.234002\pi$
$62$	0.0972215	+	0.613832i	0.0123471	+	0.0779568i
$63$	−1.52128	+	9.60498i	−0.191663	+	1.21011i
$64$	−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	−0.495404	−	0.868663i	$-0.664980\pi$
$67$	3.05526	−	3.05526i	0.373259	−	0.373259i	0.868663	+	0.495404i	$0.164980\pi$
$68$	0.130421	+	0.255966i	0.0158159	+	0.0310405i
$69$	−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	$0.729718\pi$
$72$	−2.84193	+	5.57761i	−0.334925	+	0.657328i
$73$	−5.39318	+	0.854195i	−0.631224	+	0.0999760i	−0.463844	−	0.885917i	$-0.653530\pi$
$73$	−5.39318	+	0.854195i	−0.631224	+	0.0999760i	−0.167379	+	0.985893i	$0.553530\pi$
$74$	−5.85044	+	4.25059i	−0.680100	+	0.494122i
$75$		0			0
$76$		−	0.809447i		−	0.0928499i
$77$	−12.6591	+	5.93349i	−1.44264	+	0.676184i
$78$	−0.798797	−	0.798797i	−0.0904460	−	0.0904460i
$79$	0.705861	−	2.17242i	0.0794156	−	0.244416i	−0.903464	−	0.428663i	$-0.858985\pi$
$79$	0.705861	−	2.17242i	0.0794156	−	0.244416i	0.982880	+	0.184247i	$0.0589847\pi$
$80$		0			0
$81$	2.62377	+	1.90628i	0.291530	+	0.211809i
$82$	−0.754275	−	0.384322i	−0.0832957	−	0.0424413i
$83$	−1.77193	−	0.902846i	−0.194495	−	0.0991002i	0.354031	−	0.935234i	$-0.384811\pi$
$83$	−1.77193	−	0.902846i	−0.194495	−	0.0991002i	−0.548526	+	0.836134i	$0.684811\pi$
$84$	−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
$88$	−8.93023	+	1.11440i	−0.951966	+	0.118795i
$89$		−	13.9313i		−	1.47671i	−0.674410	−	0.738357i	$-0.735602\pi$
$89$		−	13.9313i		−	1.47671i	0.674410	−	0.738357i	$-0.264398\pi$
$90$		0			0
$91$	3.15682	−	2.29356i	0.330925	−	0.240431i
$92$	−0.407977	+	0.0646171i	−0.0425345	+	0.00673680i
$93$	0.160224	−	0.314457i	0.0166144	−	0.0326076i
$94$	0.538893	+	1.65854i	0.0555826	+	0.171066i
$95$		0			0
$96$	−0.411650	−	0.566587i	−0.0420138	−	0.0578271i
$97$	−1.50922	−	2.96200i	−0.153238	−	0.300746i	0.801607	−	0.597851i	$-0.203979\pi$
$97$	−1.50922	−	2.96200i	−0.153238	−	0.300746i	−0.954845	+	0.297105i	$0.903979\pi$
$98$	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	$0.829973\pi$
$102$	0.368025	−	2.32362i	0.0364399	−	0.230073i
$103$	1.57723	+	9.95825i	0.155409	+	0.981215i	0.934928	+	0.354837i	$0.115464\pi$
$103$	1.57723	+	9.95825i	0.155409	+	0.981215i	−0.779519	+	0.626378i	$0.784536\pi$
$104$	2.38885	−	0.776185i	0.234246	−	0.0761112i
$105$		0			0
$106$	7.82528	−	10.7706i	0.760058	−	1.04613i
$107$	6.09076	+	0.964682i	0.588816	+	0.0932593i	0.443731	−	0.896160i	$-0.353654\pi$
$107$	6.09076	+	0.964682i	0.588816	+	0.0932593i	0.145085	+	0.989419i	$0.453654\pi$
$108$	−0.586606	+	0.298891i	−0.0564462	+	0.0287608i
$109$	19.9193			1.90793			0.953964	−	0.299922i	$-0.0969607\pi$
$109$	19.9193			1.90793			0.953964	+	0.299922i	$0.0969607\pi$
$110$		0			0
$111$	4.10659			0.389780
$112$	16.0595	−	8.18274i	1.51748	−	0.773197i
$113$	11.9729	+	1.89632i	1.12632	+	0.178391i	0.691673	−	0.722211i	$-0.256874\pi$
$113$	11.9729	+	1.89632i	1.12632	+	0.178391i	0.434644	+	0.900602i	$0.356874\pi$
$114$	−3.89628	+	5.36277i	−0.364920	+	0.502269i
$115$		0			0
$116$	−0.141987	+	0.0461342i	−0.0131831	+	0.00428346i
$117$	−0.334071	−	2.10924i	−0.0308849	−	0.194999i
$118$	2.13497	−	13.4796i	0.196540	−	1.24090i
$119$	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
$123$	0.218246	+	0.428331i	0.0196785	+	0.0386213i
$124$	−0.0371343	−	0.0511110i	−0.00333476	−	0.00458991i
$125$		0			0
$126$	−4.40534	−	13.5582i	−0.392459	−	1.20786i
$127$	0.526416	−	1.03315i	0.0467119	−	0.0916772i	−0.866471	−	0.499228i	$-0.833617\pi$
$127$	0.526416	−	1.03315i	0.0467119	−	0.0916772i	0.913183	+	0.407551i	$0.133617\pi$
$128$	12.2582	−	1.94151i	1.08348	−	0.171607i
$129$	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	$-0.217515\pi$
$132$	−0.360253	−	0.198763i	−0.0313560	−	0.0173001i
$133$	−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
$137$	11.0232	+	5.61663i	0.941780	+	0.479861i	0.856300	−	0.516479i	$-0.172758\pi$
$137$	11.0232	+	5.61663i	0.941780	+	0.479861i	0.0854799	+	0.996340i	$0.472758\pi$
$138$	3.01397	+	1.53570i	0.256566	+	0.130727i
$139$	0.816606	+	0.593299i	0.0692636	+	0.0503229i	0.621878	−	0.783114i	$-0.286370\pi$
$139$	0.816606	+	0.593299i	0.0692636	+	0.0503229i	−0.552615	+	0.833437i	$0.686370\pi$
$140$		0			0
$141$	0.306022	−	0.941839i	0.0257717	−	0.0793172i
$142$	−8.90567	−	8.90567i	−0.747347	−	0.747347i
$143$	2.24121	−	2.09826i	0.187420	−	0.175465i
$144$		−	9.86430i		−	0.822025i
$145$		0			0
$146$	6.47594	−	4.70504i	0.535952	−	0.389392i
$147$	−8.85451	+	1.40242i	−0.730308	+	0.115669i
$148$	0.333737	−	0.654997i	0.0274331	−	0.0538404i
$149$	−0.377177	−	1.16083i	−0.0308996	−	0.0950990i	0.934417	−	0.356180i	$-0.115921\pi$
$149$	−0.377177	−	1.16083i	−0.0308996	−	0.0950990i	−0.965317	+	0.261081i	$0.915921\pi$
$150$		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	$0.779434\pi$
$152$	−6.69128	−	13.1324i	−0.542734	−	1.06518i
$153$	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
$157$	−1.16061	+	7.32783i	−0.0926271	+	0.584824i	0.897097	+	0.441834i	$0.145672\pi$
$157$	−1.16061	+	7.32783i	−0.0926271	+	0.584824i	−0.989724	+	0.142991i	$0.954328\pi$
$158$	0.523829	+	3.30733i	0.0416736	+	0.263117i
$159$	−7.19014	+	2.33622i	−0.570215	+	0.185274i
$160$		0			0
$161$	−6.86780	+	9.45272i	−0.541258	+	0.744978i
$162$	−4.69579	−	0.743741i	−0.368936	−	0.0584338i
$163$	13.7294	−	6.99546i	1.07537	−	0.547927i	0.175673	−	0.984449i	$-0.443790\pi$
$163$	13.7294	−	6.99546i	1.07537	−	0.547927i	0.899694	+	0.436522i	$0.143790\pi$
$164$	0.0860550			0.00671976
$165$		0			0
$166$	2.91533			0.226273
$167$	3.69782	−	1.88413i	0.286146	−	0.145799i	−0.305026	−	0.952344i	$-0.598665\pi$
$167$	3.69782	−	1.88413i	0.286146	−	0.145799i	0.591172	+	0.806545i	$0.298665\pi$
$168$	−9.40466	−	1.48955i	−0.725585	−	0.114921i
$169$	7.13754	−	9.82399i	0.549042	−	0.755691i
$170$		0			0
$171$	−11.9177	+	3.87229i	−0.911369	+	0.296122i
$172$	−0.166612	−	1.05195i	−0.0127041	−	0.0802104i
$173$	−0.677320	+	4.27643i	−0.0514957	+	0.325131i	0.948470	+	0.316867i	$0.102631\pi$
$173$	−0.677320	+	4.27643i	−0.0514957	+	0.325131i	−0.999966	+	0.00826456i	$0.997369\pi$
$174$	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
$178$	9.27168	+	18.1967i	0.694942	+	1.36390i
$179$	2.18633	+	3.00922i	0.163414	+	0.224920i	0.882869	−	0.469619i	$-0.155609\pi$
$179$	2.18633	+	3.00922i	0.163414	+	0.224920i	−0.719456	+	0.694538i	$0.755609\pi$
$180$		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	$0.827854\pi$
$182$	−2.59692	+	5.09675i	−0.192497	+	0.377796i
$183$	6.39838	−	1.01340i	0.472982	−	0.0749129i
$184$	−6.08481	+	4.42087i	−0.448578	+	0.325911i
$185$		0			0
$186$			0.517369i			0.0379353i
$187$	6.27861	+	1.20758i	0.459137	+	0.0883066i
$188$	−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	$0.495595\pi$
$192$	−5.42834	−	2.76588i	−0.391757	−	0.199610i
$193$	−15.1151	−	7.70155i	−1.08801	−	0.554370i	−0.184456	−	0.982841i	$-0.559052\pi$
$193$	−15.1151	−	7.70155i	−1.08801	−	0.554370i	−0.903556	+	0.428471i	$0.859052\pi$
$194$	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	$-0.411350\pi$
$197$	−9.63624	−	9.63624i	−0.686554	−	0.686554i	−0.961469	+	0.274915i	$0.911350\pi$
$198$	−4.76042	−	10.1563i	−0.338308	−	0.721779i
$199$			19.4166i			1.37640i	0.725519	+	0.688202i	$0.241600\pi$
$199$			19.4166i			1.37640i	−0.725519	+	0.688202i	$0.758400\pi$
$200$		0			0
$201$	2.90999	−	2.11423i	0.205255	−	0.149126i
$202$	19.2440	−	3.04795i	1.35400	−	0.214453i
$203$	−1.91722	+	3.76275i	−0.134562	+	0.264093i
$204$	0.0739017	+	0.227446i	0.00517416	+	0.0159244i
$205$		0			0
$206$	−8.68764	−	11.9575i	−0.605297	−	0.833119i
$207$	2.90309	+	5.69763i	0.201778	+	0.396012i
$208$	−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	$0.529399\pi$
$212$	−0.211710	+	1.33668i	−0.0145403	+	0.0918037i
$213$	1.11883	+	7.06401i	0.0766609	+	0.484018i
$214$	−8.59762	+	2.79354i	−0.587721	+	0.190962i
$215$		0			0
$216$	−7.04626	+	9.69835i	−0.479437	+	0.659889i
$217$	−1.76507	−	0.279559i	−0.119820	−	0.0189777i
$218$	−26.0181	+	13.2569i	−1.76217	+	0.897871i
$219$	−4.54564			−0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$	−5.36392	+	2.73305i	−0.360003	+	0.183430i
$223$	14.0202	+	2.22058i	0.938860	+	0.148701i	0.607066	−	0.794651i	$-0.292346\pi$
$223$	14.0202	+	2.22058i	0.938860	+	0.148701i	0.331794	+	0.943352i	$0.392346\pi$
$224$	−2.08444	+	2.86898i	−0.139272	+	0.191692i
$225$		0			0
$226$	−16.9008	+	5.49139i	−1.12422	+	0.365282i
$227$	1.29499	+	8.17622i	0.0859512	+	0.542675i	0.992662	+	0.120922i	$0.0385850\pi$
$227$	1.29499	+	8.17622i	0.0859512	+	0.542675i	−0.906711	+	0.421753i	$0.861415\pi$
$228$	0.105412	−	0.665546i	0.00698109	−	0.0440769i
$229$	−18.6401	−	6.05655i	−1.23178	−	0.400228i	−0.380418	−	0.924815i	$-0.624220\pi$
$229$	−18.6401	−	6.05655i	−1.23178	−	0.400228i	−0.851357	+	0.524587i	$0.824220\pi$
$230$		0			0
$231$	−11.1813	+	3.23010i	−0.735676	+	0.212525i
$232$	−1.92221	+	1.92221i	−0.126199	+	0.126199i
$233$	−1.68573	−	3.30844i	−0.110436	−	0.216743i	0.829173	−	0.558991i	$-0.188812\pi$
$233$	−1.68573	−	3.30844i	−0.110436	−	0.216743i	−0.939609	+	0.342249i	$0.888812\pi$
$234$	1.84012	+	2.53270i	0.120292	+	0.165568i
$235$		0			0
$236$	0.428714	+	1.31945i	0.0279069	+	0.0858887i
$237$	0.863285	−	1.69429i	0.0560764	−	0.110056i
$238$	−11.7659	+	1.86354i	−0.762672	+	0.120795i
$239$	2.59930	−	1.88850i	0.168135	−	0.122157i	−0.500536	−	0.865716i	$-0.666864\pi$
$239$	2.59930	−	1.88850i	0.168135	−	0.122157i	0.668671	+	0.743559i	$0.266864\pi$
$240$		0			0
$241$			25.4119i			1.63693i	0.574559	+	0.818463i	$0.305174\pi$
$241$			25.4119i			1.63693i	−0.574559	+	0.818463i	$0.694826\pi$
$242$	8.25059	−	13.8549i	0.530368	−	0.890629i
$243$	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
$247$	4.48005	+	2.28270i	0.285059	+	0.145245i
$248$	−1.02497	−	0.522250i	−0.0650858	−	0.0331629i
$249$	−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
$253$	−4.44104	+	8.04929i	−0.279206	+	0.506055i
$254$			1.69982i			0.106656i
$255$		0			0
$256$	−2.87779	+	2.09084i	−0.179862	+	0.130677i
$257$	16.0045	−	2.53487i	0.998335	−	0.158121i	0.364182	−	0.931328i	$-0.381349\pi$
$257$	16.0045	−	2.53487i	0.998335	−	0.158121i	0.634154	+	0.773207i	$0.281349\pi$
$258$	−3.95972	+	7.77139i	−0.246521	+	0.483825i
$259$	−6.42576	−	19.7764i	−0.399277	−	1.22885i
$260$		0			0
$261$	1.35849	+	1.86981i	0.0840887	+	0.115738i
$262$	9.61901	+	18.8784i	0.594265	+	1.16631i
$263$	−0.677874	+	0.677874i	−0.0417995	+	0.0417995i	−0.727698	−	0.685898i	$-0.759410\pi$
$263$	−0.677874	+	0.677874i	−0.0417995	+	0.0417995i	0.685898	+	0.727698i	$0.259410\pi$
$264$	−7.48778	−	0.246675i	−0.460841	−	0.0151818i
$265$		0			0
$266$	31.9226	+	10.3723i	1.95730	+	0.635966i
$267$	1.81424	−	11.4546i	0.111030	−	0.701013i
$268$	−0.100726	−	0.635961i	−0.00615284	−	0.0388475i
$269$	27.0327	−	8.78345i	1.64821	−	0.535536i	0.669860	−	0.742487i	$-0.266354\pi$
$269$	27.0327	−	8.78345i	1.64821	−	0.535536i	0.978351	+	0.206951i	$0.0663541\pi$
$270$		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	$-0.183674\pi$
$272$	−8.14133	−	1.28946i	−0.493641	−	0.0781850i
$273$	2.89430	−	1.47472i	0.175171	−	0.0892540i
$274$	−18.1363			−1.09565
$275$		0			0
$276$	−0.343863			−0.0206981
$277$	−26.8625	+	13.6871i	−1.61401	+	0.822379i	−0.614571	+	0.788861i	$0.710671\pi$
$277$	−26.8625	+	13.6871i	−1.61401	+	0.822379i	−0.999438	+	0.0335176i	$0.989329\pi$
$278$	−1.46149	−	0.231477i	−0.0876542	−	0.0138831i
$279$	−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	$0.318220\pi$
$282$	0.227103	+	1.43387i	0.0135238	+	0.0853859i
$283$	1.49267	−	9.42432i	0.0887297	−	0.560218i	−0.902772	−	0.430120i	$-0.858471\pi$
$283$	1.49267	−	9.42432i	0.0887297	−	0.560218i	0.991501	−	0.130097i	$-0.0415289\pi$
$284$	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
$288$	0.881112	+	1.72928i	0.0519200	+	0.101899i
$289$	7.80797	+	10.7468i	0.459292	+	0.632162i
$290$		0			0
$291$	−0.855180	−	2.63197i	−0.0501315	−	0.154289i
$292$	−0.369419	+	0.725025i	−0.0216186	+	0.0424289i
$293$	−2.27904	+	0.360965i	−0.133143	+	0.0210878i	−0.222650	−	0.974898i	$-0.571471\pi$
$293$	−2.27904	+	0.360965i	−0.133143	+	0.0210878i	0.0895072	+	0.995986i	$0.471471\pi$
$294$	10.6322	−	7.72474i	0.620082	−	0.450516i
$295$		0			0
$296$		−	13.3854i		−	0.778013i
$297$	−2.76744	+	14.3889i	−0.160583	+	0.834928i
$298$	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
$302$	−2.07257	−	1.05603i	−0.119263	−	0.0607676i
$303$	−9.85838	−	5.02310i	−0.566349	−	0.288569i
$304$	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	$-0.0822353\pi$
$307$	12.4635	+	12.4635i	0.711327	+	0.711327i	−0.255486	+	0.966813i	$0.582235\pi$
$308$	−0.393494	+	2.04591i	−0.0224214	+	0.116577i
$309$			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	$0.440960\pi$
$312$	2.06525	−	0.327104i	0.116922	−	0.0185186i
$313$	11.8565	−	23.2697i	0.670169	−	1.31528i	−0.266082	−	0.963950i	$-0.585729\pi$
$313$	11.8565	−	23.2697i	0.670169	−	1.31528i	0.936251	−	0.351331i	$-0.114271\pi$
$314$	−3.36092	−	10.3438i	−0.189668	−	0.583737i
$315$		0			0
$316$	−0.200080	−	0.275386i	−0.0112554	−	0.0154917i
$317$	12.8603	+	25.2398i	0.722307	+	1.41761i	0.901051	+	0.433712i	$0.142797\pi$
$317$	12.8603	+	25.2398i	0.722307	+	1.41761i	−0.178744	+	0.983896i	$0.557203\pi$
$318$	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
$322$	2.67949	−	16.9176i	0.149322	−	0.942782i
$323$	1.63805	+	10.3423i	0.0911436	+	0.575458i
$324$	0.459645	−	0.149348i	0.0255358	−	0.00829710i
$325$		0			0
$326$	−13.2773	+	18.2746i	−0.735360	+	1.01214i
$327$	16.3782	+	2.59405i	0.905714	+	0.143451i
$328$	1.39615	−	0.711372i	0.0770893	−	0.0392790i
$329$	−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	$0.736858\pi$
$332$	−0.264055	+	0.134543i	−0.0144919	+	0.00738401i
$333$	−11.2403	−	1.78028i	−0.615962	−	0.0975588i
$334$	−3.57605	+	4.92202i	−0.195673	+	0.269321i
$335$		0			0
$336$	14.2702	−	4.63665i	0.778501	−	0.252950i
$337$	−4.85195	−	30.6340i	−0.264302	−	1.66874i	−0.660692	−	0.750657i	$-0.729737\pi$
$337$	−4.85195	−	30.6340i	−0.264302	−	1.66874i	0.396390	−	0.918082i	$-0.370263\pi$
$338$	−2.78473	+	17.5821i	−0.151469	+	0.956339i
$339$	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
$343$	7.21277	+	14.1559i	0.389453	+	0.764345i
$344$	−11.3990	−	15.6894i	−0.614594	−	0.845916i
$345$		0			0
$346$	−1.96139	−	6.03654i	−0.105445	−	0.324527i
$347$	13.7041	−	26.8957i	0.735672	−	1.44384i	−0.154395	−	0.988009i	$-0.549343\pi$
$347$	13.7041	−	26.8957i	0.735672	−	1.44384i	0.890068	−	0.455829i	$-0.150657\pi$
$348$	−0.122753	+	0.0194421i	−0.00658024	+	0.00104221i
$349$	−17.2865	+	12.5594i	−0.925323	+	0.672287i	−0.944843	−	0.327523i	$-0.893786\pi$
$349$	−17.2865	+	12.5594i	−0.925323	+	0.672287i	0.0195201	+	0.999809i	$0.493786\pi$
$350$		0			0
$351$		−	4.08959i		−	0.218286i
$352$	−1.34789	+	2.44303i	−0.0718430	+	0.130214i
$353$	2.82626	+	2.82626i	0.150427	+	0.150427i	0.778309	−	0.627882i	$-0.216078\pi$
$353$	2.82626	+	2.82626i	0.150427	+	0.150427i	−0.627882	+	0.778309i	$0.716078\pi$
$354$	3.51084	−	10.8053i	0.186599	−	0.574293i
$355$		0			0
$356$	−1.67956	−	1.22027i	−0.0890167	−	0.0646744i
$357$	6.02750	+	3.07116i	0.319009	+	0.162543i
$358$	−4.85844	−	2.47550i	−0.256777	−	0.130834i
$359$	8.68908	+	6.31298i	0.458592	+	0.333187i	0.792979	−	0.609249i	$-0.208529\pi$
$359$	8.68908	+	6.31298i	0.458592	+	0.333187i	−0.334387	+	0.942436i	$0.608529\pi$
$360$		0			0
$361$	3.24592	−	9.98992i	0.170838	−	0.525785i
$362$	−6.26778	−	6.26778i	−0.329427	−	0.329427i
$363$	−8.41505	+	3.61127i	−0.441676	+	0.189542i
$364$		−	0.581487i		−	0.0304782i
$365$		0			0
$366$	−7.68295	+	5.58199i	−0.401594	+	0.291775i
$367$	−34.1783	+	5.41331i	−1.78409	+	0.282572i	−0.959202	−	0.282721i	$-0.908763\pi$
$367$	−34.1783	+	5.41331i	−1.78409	+	0.282572i	−0.824890	+	0.565293i	$0.808763\pi$
$368$	5.38066	−	10.5601i	0.280486	−	0.550485i
$369$	−0.411677	−	1.26701i	−0.0214310	−	0.0659579i
$370$		0			0
$371$	22.5015	+	30.9706i	1.16822	+	1.60791i
$372$	−0.0238767	−	0.0468606i	−0.00123795	−	0.00242961i
$373$	−9.90454	+	9.90454i	−0.512838	+	0.512838i	−0.915395	−	0.402557i	$-0.868121\pi$
$373$	−9.90454	+	9.90454i	−0.512838	+	0.512838i	0.402557	+	0.915395i	$0.368121\pi$
$374$	−9.00463	+	2.60129i	−0.465618	+	0.134510i
$375$		0			0
$376$	−3.06993	−	0.997480i	−0.158319	−	0.0514411i
$377$	0.145073	−	0.915956i	0.00747165	−	0.0471741i
$378$	−4.27073	−	26.9643i	−0.219663	−	1.38690i
$379$	25.2037	−	8.18919i	1.29463	−	0.420651i	0.420919	−	0.907098i	$-0.361708\pi$
$379$	25.2037	−	8.18919i	1.29463	−	0.420651i	0.873710	+	0.486447i	$0.161708\pi$
$380$		0			0
$381$	0.567376	−	0.780926i	0.0290676	−	0.0400081i
$382$	−23.9695	−	3.79640i	−1.22639	−	0.194241i
$383$	21.4177	−	10.9129i	1.09439	−	0.557622i	0.188907	−	0.981995i	$-0.439505\pi$
$383$	21.4177	−	10.9129i	1.09439	−	0.557622i	0.905487	+	0.424373i	$0.139505\pi$
$384$	10.3318			0.527243
$385$		0			0
$386$	24.8686			1.26578
$387$	−14.6911	+	7.48548i	−0.746789	+	0.380508i
$388$	−0.489297	−	0.0774970i	−0.0248403	−	0.00393431i
$389$	−4.43509	+	6.10438i	−0.224868	+	0.309505i	−0.906512	−	0.422179i	$-0.861265\pi$
$389$	−4.43509	+	6.10438i	−0.224868	+	0.309505i	0.681644	+	0.731684i	$0.261265\pi$
$390$		0			0
$391$	5.08193	−	1.65122i	0.257004	−	0.0835057i
$392$	4.57119	+	28.8613i	0.230880	+	1.45772i
$393$	1.88220	−	11.8838i	0.0949445	−	0.599456i
$394$	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	−0.984332	−	0.176324i	$-0.943579\pi$
$397$	−16.0995	+	16.0995i	−0.808008	+	0.808008i	0.176324	+	0.984332i	$0.443579\pi$
$398$	−12.9223	−	25.3614i	−0.647736	−	1.27125i
$399$	−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	$-0.305947\pi$
$402$	−2.39387	+	4.69823i	−0.119395	+	0.234327i
$403$	0.387606	−	0.0613908i	0.0193080	−	0.00305809i
$404$	−1.60236	+	1.16418i	−0.0797203	+	0.0579202i
$405$		0			0
$406$		−	6.19078i		−	0.307243i
$407$	−6.94368	−	14.8143i	−0.344185	−	0.734319i
$408$	3.07915	+	3.07915i	0.152441	+	0.152441i
$409$	−1.80956	+	5.56925i	−0.0894769	+	0.275382i	−0.985775	−	0.168070i	$-0.946246\pi$
$409$	−1.80956	+	5.56925i	−0.0894769	+	0.275382i	0.896298	+	0.443452i	$0.146246\pi$
$410$		0			0
$411$	8.33214	+	6.05365i	0.410994	+	0.298605i
$412$	1.33872	+	0.682114i	0.0659542	+	0.0336054i
$413$	34.9663	+	17.8162i	1.72058	+	0.876680i
$414$	−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
$418$	25.9340	+	4.98793i	1.26847	+	0.243968i
$419$			11.0599i			0.540311i	0.962817	+	0.270155i	$0.0870751\pi$
$419$			11.0599i			0.540311i	−0.962817	+	0.270155i	$0.912925\pi$
$420$		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	$0.361450\pi$
$422$	−9.25349	+	1.46561i	−0.450453	+	0.0713447i
$423$	−1.24593	+	2.44527i	−0.0605790	+	0.118893i
$424$	7.61491	+	23.4363i	0.369813	+	1.13817i
$425$		0			0
$426$	−6.16269	−	8.48222i	−0.298583	−	0.410965i
$427$	−14.8922	−	29.2275i	−0.720682	−	1.41442i
$428$	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	$0.656279\pi$
$432$	2.95510	−	18.6577i	0.142177	−	0.897671i
$433$	−0.789604	−	4.98536i	−0.0379460	−	0.239581i	0.961424	−	0.275070i	$-0.0887011\pi$
$433$	−0.789604	−	4.98536i	−0.0379460	−	0.239581i	−0.999370	+	0.0354890i	$0.988701\pi$
$434$	2.49154	−	0.809550i	0.119598	−	0.0388596i
$435$		0			0
$436$	1.74478	−	2.40149i	0.0835599	−	0.115010i
$437$	−14.8706	−	2.35527i	−0.711357	−	0.112668i
$438$	5.93740	−	3.02525i	0.283700	−	0.144552i
$439$	−1.29778			−0.0619394			−0.0309697	−	0.999520i	$-0.509860\pi$
$439$	−1.29778			−0.0619394			−0.0309697	+	0.999520i	$0.509860\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$	2.33086	−	1.18763i	0.110868	−	0.0564900i
$443$	−15.2112	−	2.40922i	−0.722707	−	0.114466i	−0.215764	−	0.976445i	$-0.569224\pi$
$443$	−15.2112	−	2.40922i	−0.722707	−	0.114466i	−0.506942	+	0.861980i	$0.669224\pi$
$444$	0.359706	−	0.495092i	0.0170709	−	0.0234960i
$445$		0			0
$446$	−19.7907	+	6.43037i	−0.937115	+	0.304487i
$447$	−0.158952	−	1.00358i	−0.00751816	−	0.0474678i
$448$	−4.82591	+	30.4696i	−0.228003	+	1.43955i
$449$	−11.5295	−	3.74615i	−0.544109	−	0.176792i	0.0240497	−	0.999711i	$-0.492344\pi$
$449$	−11.5295	−	3.74615i	−0.544109	−	0.176792i	−0.568159	+	0.822919i	$0.692344\pi$
$450$		0			0
$451$	1.17616	−	1.51156i	0.0553833	−	0.0711766i
$452$	1.27736	−	1.27736i	0.0600818	−	0.0600818i
$453$	0.599688	+	1.17695i	0.0281758	+	0.0552981i
$454$	−7.13299	−	9.81772i	−0.334768	−	0.460768i
$455$		0			0
$456$	−3.79153	−	11.6691i	−0.177555	−	0.546458i
$457$	−1.59383	+	3.12807i	−0.0745563	+	0.146325i	−0.925276	−	0.379295i	$-0.876167\pi$
$457$	−1.59383	+	3.12807i	−0.0745563	+	0.146325i	0.850720	+	0.525620i	$0.176167\pi$
$458$	28.3781	−	4.49465i	1.32602	−	0.210021i
$459$	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	$0.959467\pi$
$462$	12.4550	−	11.6606i	0.579460	−	0.542498i
$463$	−15.3996	−	15.3996i	−0.715681	−	0.715681i	0.252037	−	0.967718i	$-0.418900\pi$
$463$	−15.3996	−	15.3996i	−0.715681	−	0.715681i	−0.967718	+	0.252037i	$0.918900\pi$
$464$	1.32372	−	4.07400i	0.0614523	−	0.189131i
$465$		0			0
$466$	4.40372	+	3.19949i	0.203998	+	0.148214i
$467$	13.0834	+	6.66632i	0.605427	+	0.308481i	0.729700	−	0.683768i	$-0.239660\pi$
$467$	13.0834	+	6.66632i	0.605427	+	0.308481i	−0.124273	+	0.992248i	$0.539660\pi$
$468$	−0.283553	−	0.144478i	−0.0131073	−	0.00667848i
$469$	−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
$473$	−20.7547	−	11.4510i	−0.954303	−	0.526518i
$474$			2.78758i			0.128038i
$475$		0			0
$476$	0.979695	−	0.711790i	0.0449043	−	0.0326249i
$477$	20.6931	−	3.27747i	0.947473	−	0.150065i
$478$	−2.13829	+	4.19663i	−0.0978030	+	0.191949i
$479$	−1.51842	−	4.67321i	−0.0693783	−	0.213524i	0.910356	−	0.413826i	$-0.135808\pi$
$479$	−1.51842	−	4.67321i	−0.0693783	−	0.213524i	−0.979734	+	0.200302i	$0.935808\pi$
$480$		0			0
$481$	2.68405	+	3.69428i	0.122382	+	0.168444i
$482$	−16.9124	−	33.1924i	−0.770338	−	1.51187i
$483$	−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
$487$	−1.67972	+	10.6054i	−0.0761155	+	0.480574i	0.919956	+	0.392022i	$0.128224\pi$
$487$	−1.67972	+	10.6054i	−0.0761155	+	0.480574i	−0.996071	+	0.0885527i	$0.971776\pi$
$488$	−3.30319	−	20.8555i	−0.149529	−	0.944086i
$489$	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	$0.176592\pi$
$492$	0.0707565	+	0.0112067i	0.00318995	+	0.000505238i
$493$	1.72079	−	0.876788i	0.0775007	−	0.0394886i
$494$	−7.37092			−0.331634
$495$		0			0
$496$	1.81272			0.0813935
$497$	32.2681	−	16.4414i	1.44742	−	0.737498i
$498$	2.39705	+	0.379656i	0.107414	+	0.0170128i
$499$	5.25588	−	7.23410i	0.235285	−	0.323843i	−0.675005	−	0.737813i	$-0.735858\pi$
$499$	5.25588	−	7.23410i	0.235285	−	0.323843i	0.910290	+	0.413971i	$0.135858\pi$
$500$		0			0
$501$	3.28580	−	1.06762i	0.146799	−	0.0476978i
$502$	3.73926	+	23.6088i	0.166891	+	1.05371i
$503$	3.02441	−	19.0954i	0.134852	−	0.851421i	−0.823808	−	0.566868i	$-0.808155\pi$
$503$	3.02441	−	19.0954i	0.134852	−	0.851421i	0.958660	−	0.284553i	$-0.0918451\pi$
$504$	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
$508$	−0.0784471	−	0.153961i	−0.00348053	−	0.00683092i
$509$	1.65845	+	2.28267i	0.0735097	+	0.101177i	0.844189	−	0.536046i	$-0.180083\pi$
$509$	1.65845	+	2.28267i	0.0735097	+	0.101177i	−0.770679	+	0.637224i	$0.780083\pi$
$510$		0			0
$511$	7.11276	+	21.8908i	0.314650	+	0.968393i
$512$	−8.90156	+	17.4703i	−0.393397	+	0.772085i
$513$	−23.7017	+	3.75398i	−1.04645	+	0.165742i
$514$	−19.2177	+	13.9625i	−0.847656	+	0.615858i
$515$		0			0
$516$		−	0.886635i		−	0.0390319i
$517$	−3.91508	+	0.488562i	−0.172185	+	0.0214869i
$518$	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	$0.766752\pi$
$522$	−3.01884	−	1.53818i	−0.132131	−	0.0673241i
$523$	13.2194	+	6.73563i	0.578045	+	0.294528i	0.718465	−	0.695564i	$-0.244845\pi$
$523$	13.2194	+	6.73563i	0.578045	+	0.294528i	−0.140420	+	0.990092i	$0.544845\pi$
$524$	−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
$528$	10.6896	−	5.01037i	0.465206	−	0.218049i
$529$		−	15.3169i		−	0.665953i
$530$		0			0
$531$	17.3757	−	12.6242i	0.754039	−	0.547842i
$532$	−3.37007	+	0.533767i	−0.146111	+	0.0231417i
$533$	−0.242681	+	0.476289i	−0.0105117	+	0.0206304i
$534$	5.25369	+	16.1692i	0.227349	+	0.699709i
$535$		0			0
$536$	−6.89134	−	9.48511i	−0.297661	−	0.409695i
$537$	1.40577	+	2.75897i	0.0606633	+	0.119058i
$538$	−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	$0.834608\pi$
$542$	−7.05176	+	44.5230i	−0.302899	+	1.91243i
$543$	0.787429	+	4.97163i	0.0337918	+	0.213353i
$544$	1.54241	−	0.501159i	0.0661303	−	0.0214870i
$545$		0			0
$546$	−2.79899	+	3.85248i	−0.119786	+	0.164871i
$547$	31.1772	+	4.93799i	1.33304	+	0.211133i	0.781966	−	0.623322i	$-0.214217\pi$
$547$	31.1772	+	4.93799i	1.33304	+	0.211133i	0.551076	+	0.834455i	$0.314217\pi$
$548$	1.64270	−	0.836995i	0.0701725	−	0.0357547i
$549$	−17.9525			−0.766194
$550$		0			0
$551$	−5.44169			−0.231824
$552$	−5.57880	+	2.84254i	−0.237449	+	0.120987i
$553$	−9.51017	−	1.50626i	−0.404414	−	0.0640528i
$554$	25.9779	−	35.7555i	1.10370	−	1.51911i
$555$		0			0
$556$	0.143057	−	0.0464820i	0.00606696	−	0.00197128i
$557$	−2.07471	−	13.0992i	−0.0879082	−	0.555030i	−0.991854	−	0.127383i	$-0.959342\pi$
$557$	−2.07471	−	13.0992i	−0.0879082	−	0.555030i	0.903945	−	0.427648i	$-0.140658\pi$
$558$	0.224289	−	1.41610i	0.00949491	−	0.0599485i
$559$	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
$563$	−13.3342	−	26.1698i	−0.561968	−	1.10292i	−0.980828	−	0.194874i	$-0.937570\pi$
$563$	−13.3342	−	26.1698i	−0.561968	−	1.10292i	0.418860	−	0.908051i	$-0.362430\pi$
$564$	−0.0867434	−	0.119392i	−0.00365256	−	0.00502731i
$565$		0			0
$566$	4.32248	+	13.3032i	0.181687	+	0.559176i
$567$	6.20650	−	12.1809i	0.260648	−	0.511551i
$568$	23.0252	−	3.64683i	0.966115	−	0.153018i
$569$	17.3540	−	12.6084i	0.727518	−	0.528573i	−0.161259	−	0.986912i	$-0.551555\pi$
$569$	17.3540	−	12.6084i	0.727518	−	0.528573i	0.888777	+	0.458339i	$0.151555\pi$
$570$		0			0
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$	−0.0566536	−	0.453993i	−0.00236881	−	0.0189824i
$573$	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
$577$	5.96290	+	3.03825i	0.248239	+	0.126484i	0.573683	−	0.819077i	$-0.305514\pi$
$577$	5.96290	+	3.03825i	0.248239	+	0.126484i	−0.325445	+	0.945561i	$0.605514\pi$
$578$	−17.3509	−	8.84070i	−0.721700	−	0.367725i
$579$	−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
$583$	20.5853	+	21.9879i	0.852558	+	0.910644i
$584$			14.8165i			0.613112i
$585$		0			0
$586$	2.73660	−	1.98825i	0.113048	−	0.0821340i
$587$	−36.0485	+	5.70952i	−1.48788	+	0.235657i	−0.846839	−	0.531849i	$-0.821497\pi$
$587$	−36.0485	+	5.70952i	−1.48788	+	0.235657i	−0.641041	+	0.767506i	$0.721497\pi$
$588$	−0.606512	+	1.19035i	−0.0250121	+	0.0490890i
$589$	−0.711594	−	2.19006i	−0.0293207	−	0.0902400i
$590$		0			0
$591$	−6.66825	−	9.17805i	−0.274295	−	0.377535i
$592$	9.57587	+	18.7937i	0.393566	+	0.772417i
$593$	−26.6656	+	26.6656i	−1.09502	+	1.09502i	−0.100040	+	0.994983i	$0.531897\pi$
$593$	−26.6656	+	26.6656i	−1.09502	+	1.09502i	−0.994983	+	0.100040i	$0.968103\pi$
$594$	−5.96146	−	20.6362i	−0.244602	−	0.846714i
$595$		0			0
$596$	−0.172988	−	0.0562073i	−0.00708588	−	0.00230234i
$597$	−2.52857	+	15.9648i	−0.103487	+	0.653394i
$598$	0.588412	+	3.71509i	0.0240620	+	0.151921i
$599$	−36.7124	+	11.9286i	−1.50003	+	0.487388i	−0.940026	−	0.341103i	$-0.889199\pi$
$599$	−36.7124	+	11.9286i	−1.50003	+	0.487388i	−0.560002	+	0.828492i	$0.689199\pi$
$600$		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	$-0.0834753\pi$
$602$	43.6213	+	6.90894i	1.77787	+	0.281587i
$603$	−8.88156	+	4.52538i	−0.361685	+	0.184288i
$604$	0.236459			0.00962138
$605$		0			0
$606$	16.2198			0.658884
$607$	−32.2834	+	16.4492i	−1.31034	+	0.667653i	−0.962852	−	0.270031i	$-0.912966\pi$
$607$	−32.2834	+	16.4492i	−1.31034	+	0.667653i	−0.347491	+	0.937683i	$0.612966\pi$
$608$	−4.51336	−	0.714845i	−0.183041	−	0.0289908i
$609$	−2.06640	+	2.84415i	−0.0837346	+	0.115251i
$610$		0			0
$611$	1.04729	−	0.340286i	0.0423689	−	0.0137665i
$612$	−0.103676	−	0.654587i	−0.00419087	−	0.0264601i
$613$	0.376892	−	2.37960i	0.0152225	−	0.0961113i	−0.978907	−	0.204305i	$-0.934507\pi$
$613$	0.376892	−	2.37960i	0.0152225	−	0.0961113i	0.994130	+	0.108194i	$0.0345066\pi$
$614$	−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	0.0294325	−	0.999567i	$-0.490630\pi$
$617$	25.5598	−	25.5598i	1.02900	−	1.02900i	0.999567	−	0.0294325i	$-0.00937002\pi$
$618$	−5.58599	−	10.9631i	−0.224701	−	0.441001i
$619$	0.537145	+	0.739317i	0.0215897	+	0.0297157i	0.819675	−	0.572828i	$-0.194154\pi$
$619$	0.537145	+	0.739317i	0.0215897	+	0.0297157i	−0.798086	+	0.602544i	$0.794154\pi$
$620$		0			0
$621$	3.78415	+	11.6464i	0.151853	+	0.467355i
$622$	10.0585	−	19.7409i	0.403310	−	0.791540i
$623$	−58.0020	+	9.18661i	−2.32380	+	0.368054i
$624$	−2.66569	+	1.93674i	−0.106713	+	0.0775316i
$625$		0			0
$626$			38.2851i			1.53018i
$627$	−10.2496	−	10.9480i	−0.409331	−	0.437219i
$628$	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	$0.852129\pi$
$632$	−5.52255	−	2.81388i	−0.219675	−	0.111930i
$633$	4.74042	+	2.41536i	0.188415	+	0.0960020i
$634$	−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
$638$	−0.603161	−	4.83342i	−0.0238794	−	0.191357i
$639$		−	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	$0.355147\pi$
$642$	−7.43296	+	1.17727i	−0.293356	+	0.0464630i
$643$	−14.3186	+	28.1018i	−0.564670	+	1.10823i	0.415412	+	0.909634i	$0.363638\pi$
$643$	−14.3186	+	28.1018i	−0.564670	+	1.10823i	−0.980082	+	0.198594i	$0.936362\pi$
$644$	0.538058	+	1.65597i	0.0212024	+	0.0652544i
$645$		0			0
$646$	−9.02265	−	12.4186i	−0.354991	−	0.488604i
$647$	−6.23845	−	12.2437i	−0.245259	−	0.481348i	0.735257	−	0.677789i	$-0.237062\pi$
$647$	−6.23845	−	12.2437i	−0.245259	−	0.481348i	−0.980516	+	0.196441i	$0.937062\pi$
$648$	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
$652$	0.359211	−	2.26797i	0.0140678	−	0.0888205i
$653$	0.851181	+	5.37414i	0.0333093	+	0.210307i	0.998730	−	0.0503921i	$-0.0160471\pi$
$653$	0.851181	+	5.37414i	0.0333093	+	0.210307i	−0.965420	+	0.260699i	$0.916047\pi$
$654$	−23.1192	+	7.51187i	−0.904030	+	0.293737i
$655$		0			0
$656$	−1.45134	+	1.99759i	−0.0566652	+	0.0779929i
$657$	12.4420	+	1.97062i	0.485408	+	0.0768812i
$658$	6.54987	−	3.33733i	0.255341	−	0.130102i
$659$	−42.1160			−1.64061			−0.820304	−	0.571928i	$-0.806195\pi$
$659$	−42.1160			−1.64061			−0.820304	+	0.571928i	$0.806195\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$	32.1913	−	16.4023i	1.25115	−	0.637493i
$663$	−1.46726	−	0.232390i	−0.0569835	−	0.00902529i
$664$	−3.17181	+	4.36562i	−0.123090	+	0.169419i
$665$		0			0
$666$	15.8666	−	5.15536i	0.614817	−	0.199766i
$667$	0.434404	+	2.74272i	0.0168202	+	0.106198i
$668$	0.0967487	−	0.610847i	0.00374332	−	0.0236344i
$669$	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
$673$	2.51797	+	4.94179i	0.0970605	+	0.190492i	0.934431	−	0.356143i	$-0.115908\pi$
$673$	2.51797	+	4.94179i	0.0970605	+	0.190492i	−0.837371	+	0.546635i	$0.815908\pi$
$674$	26.7253	+	36.7842i	1.02942	+	1.41687i
$675$		0			0
$676$	−0.559191	−	1.72101i	−0.0215073	−	0.0661928i
$677$	1.05927	−	2.07893i	0.0407110	−	0.0798999i	−0.869755	−	0.493484i	$-0.835723\pi$
$677$	1.05927	−	2.07893i	0.0407110	−	0.0798999i	0.910466	+	0.413584i	$0.135723\pi$
$678$	−14.6114	+	2.31421i	−0.561146	+	0.0888767i
$679$	−11.3369	+	8.23673i	−0.435070	+	0.316097i
$680$		0			0
$681$			6.89132i			0.264076i
$682$	1.86638	−	0.874800i	0.0714675	−	0.0334978i
$683$	25.0400	+	25.0400i	0.958127	+	0.958127i	0.999158	−	0.0410307i	$-0.0130641\pi$
$683$	25.0400	+	25.0400i	0.958127	+	0.958127i	−0.0410307	+	0.999158i	$0.513064\pi$
$684$	−0.577053	+	1.77599i	−0.0220642	+	0.0679066i
$685$		0			0
$686$	−18.8423	−	13.6897i	−0.719401	−	0.522676i
$687$	−14.5376	−	7.40730i	−0.554646	−	0.282606i
$688$	27.2288	+	13.8738i	1.03809	+	0.528933i
$689$	−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
$693$	32.0050	−	3.99389i	1.21577	−	0.151715i
$694$			44.2510i			1.67974i
$695$		0			0
$696$	−1.83081	+	1.33016i	−0.0693967	+	0.0504196i
$697$	−1.09952	+	0.174147i	−0.0416473	+	0.00659628i
$698$	14.2205	−	27.9094i	0.538255	−	1.05638i
$699$	−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	$0.690779\pi$
$702$	2.72174	+	5.34171i	0.102725	+	0.201610i
$703$	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
$707$	−8.76432	+	55.3357i	−0.329616	+	2.08111i
$708$	0.180671	+	1.14071i	0.00679003	+	0.0428706i
$709$	−9.55567	+	3.10483i	−0.358871	+	0.116604i	−0.482903	−	0.875674i	$-0.660417\pi$
$709$	−9.55567	+	3.10483i	−0.358871	+	0.116604i	0.124032	+	0.992278i	$0.460417\pi$
$710$		0			0
$711$	−3.09743	+	4.26324i	−0.116163	+	0.159884i
$712$	−37.3365	−	5.91351i	−1.39924	−	0.221618i
$713$	−1.04703	+	0.533487i	−0.0392115	+	0.0199793i
$714$	−9.91691			−0.371131
$715$		0			0
$716$	0.554298			0.0207151
$717$	2.38314	−	1.21427i	0.0890001	−	0.0453478i
$718$	−15.5509	−	2.46302i	−0.580355	−	0.0919193i
$719$	4.03181	−	5.54931i	0.150361	−	0.206954i	−0.727191	−	0.686435i	$-0.759175\pi$
$719$	4.03181	−	5.54931i	0.150361	−	0.206954i	0.877553	+	0.479480i	$0.159175\pi$
$720$		0			0
$721$	40.4204	−	13.1334i	1.50533	−	0.489113i
$722$	2.40884	+	15.2088i	0.0896478	+	0.566014i
$723$	−3.30933	+	20.8943i	−0.123075	+	0.777067i
$724$	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	−0.0626351	−	0.998036i	$-0.519950\pi$
$727$	25.2212	−	25.2212i	0.935401	−	0.935401i	0.998036	+	0.0626351i	$0.0199504\pi$
$728$	−4.80685	−	9.43398i	−0.178154	−	0.349647i
$729$	2.08750	+	2.87320i	0.0773149	+	0.106415i
$730$		0			0
$731$	4.25759	+	13.1035i	0.157473	+	0.484651i
$732$	0.438272	−	0.860158i	0.0161990	−	0.0317924i
$733$	7.61562	−	1.20620i	0.281289	−	0.0445519i	−0.0141956	−	0.999899i	$-0.504519\pi$
$733$	7.61562	−	1.20620i	0.281289	−	0.0445519i	0.295485	+	0.955347i	$0.404519\pi$
$734$	41.0401	−	29.8174i	1.51482	−	1.10058i
$735$		0			0
$736$			2.33188i			0.0859543i
$737$	−12.5474	−	6.92277i	−0.462189	−	0.255004i
$738$	1.38095	+	1.38095i	0.0508336	+	0.0508336i
$739$	12.6089	−	38.8062i	0.463825	−	1.42751i	−0.396629	−	0.917979i	$-0.629820\pi$
$739$	12.6089	−	38.8062i	0.463825	−	1.42751i	0.860454	−	0.509528i	$-0.170180\pi$
$740$		0			0
$741$	3.38633	+	2.46031i	0.124400	+	0.0903819i
$742$	−50.0027	−	25.4776i	−1.83566	−	0.935313i
$743$	−39.5290	−	20.1411i	−1.45018	−	0.738904i	−0.461248	−	0.887271i	$-0.652598\pi$
$743$	−39.5290	−	20.1411i	−1.45018	−	0.738904i	−0.988932	+	0.148368i	$0.952598\pi$
$744$	−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
$748$	0.695544	−	0.651178i	0.0254316	−	0.0238094i
$749$		−	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	$0.222780\pi$
$752$	5.02390	−	0.795708i	0.183203	−	0.0290165i
$753$	6.16240	−	12.0944i	0.224570	−	0.440744i
$754$	0.420104	+	1.29295i	0.0152993	+	0.0470864i
$755$		0			0
$756$	1.63123	+	2.24520i	0.0593274	+	0.0816571i
$757$	−9.02166	−	17.7060i	−0.327898	−	0.643535i	0.666929	−	0.745121i	$-0.267608\pi$
$757$	−9.02166	−	17.7060i	−0.327898	−	0.643535i	−0.994827	+	0.101586i	$0.967608\pi$
$758$	−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	$0.495808\pi$
$762$	−0.221363	+	1.39763i	−0.00801914	+	0.0506309i
$763$	−13.1353	−	82.9328i	−0.475528	−	3.00237i
$764$	2.34625	−	0.762341i	0.0848842	−	0.0275805i
$765$		0			0
$766$	−20.7124	+	28.5082i	−0.748371	+	1.03004i
$767$	−8.51175	−	1.34813i	−0.307342	−	0.0486781i
$768$	−2.63847	+	1.34437i	−0.0952076	+	0.0485107i
$769$	33.4001			1.20444			0.602218	−	0.798331i	$-0.294284\pi$
$769$	33.4001			1.20444			0.602218	+	0.798331i	$0.294284\pi$
$770$		0			0
$771$	13.4894			0.485810
$772$	−2.25247	+	1.14769i	−0.0810683	+	0.0413064i
$773$	37.6915	+	5.96974i	1.35567	+	0.214717i	0.791614	−	0.611021i	$-0.209241\pi$
$773$	37.6915	+	5.96974i	1.35567	+	0.214717i	0.564054	+	0.825738i	$0.309241\pi$
$774$	14.2073	−	19.5547i	0.510671	−	0.702878i
$775$		0			0
$776$	−8.57893	+	2.78746i	−0.307966	+	0.100064i
$777$	−2.70797	−	17.0975i	−0.0971480	−	0.613369i
$778$	1.73036	−	10.9251i	0.0620365	−	0.391683i
$779$	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
$783$	2.00936	+	3.94360i	0.0718088	+	0.140933i
$784$	−27.0654	−	37.2523i	−0.966621	−	1.33044i
$785$		0			0
$786$	5.45050	+	16.7749i	0.194413	+	0.598341i
$787$	−16.6820	+	32.7403i	−0.594649	+	1.16706i	0.376013	+	0.926614i	$0.377295\pi$
$787$	−16.6820	+	32.7403i	−0.594649	+	1.16706i	−0.970662	+	0.240450i	$0.922705\pi$
$788$	−2.00581	+	0.317689i	−0.0714541	+	0.0113172i
$789$	−0.645642	+	0.469086i	−0.0229855	+	0.0166999i
$790$		0			0
$791$		−	51.0989i		−	1.81687i
$792$	20.3881	+	3.92127i	0.724458	+	0.139336i
$793$	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
$797$	−17.9460	−	9.14395i	−0.635680	−	0.323895i	0.106283	−	0.994336i	$-0.466105\pi$
$797$	−17.9460	−	9.14395i	−0.635680	−	0.323895i	−0.741963	+	0.670441i	$0.766105\pi$
$798$	24.8968	+	12.6855i	0.881337	+	0.449063i
$799$	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
$803$	7.68606	+	16.3982i	0.271235	+	0.578679i
$804$		−	0.536020i		−	0.0189040i
$805$		0			0
$806$	−0.465424	+	0.338150i	−0.0163939	+	0.0119108i
$807$	23.3708	−	3.70156i	0.822690	−	0.130301i
$808$	−16.3728	+	32.1334i	−0.575993	+	1.13045i
$809$	16.0484	+	49.3920i	0.564233	+	1.73653i	0.670220	+	0.742162i	$0.266200\pi$
$809$	16.0484	+	49.3920i	0.564233	+	1.73653i	−0.105987	+	0.994367i	$0.533800\pi$
$810$		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	$-0.441410\pi$
$812$	0.285706	+	0.560729i	0.0100263	+	0.0196777i
$813$	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
$817$	6.07296	−	38.3431i	0.212466	−	1.34146i
$818$	−1.34290	−	8.47873i	−0.0469533	−	0.296452i
$819$	−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	$0.343673\pi$
$822$	−14.9121	−	2.36185i	−0.520120	−	0.0823789i
$823$	20.4719	−	10.4310i	0.713606	−	0.363600i	−0.0591972	−	0.998246i	$-0.518854\pi$
$823$	20.4719	−	10.4310i	0.713606	−	0.363600i	0.772803	+	0.634646i	$0.218854\pi$
$824$	27.3580			0.953062
$825$		0			0
$826$	−57.5294			−2.00170
$827$	4.93382	−	2.51391i	0.171566	−	0.0874171i	−0.366099	−	0.930576i	$-0.619307\pi$
$827$	4.93382	−	2.51391i	0.171566	−	0.0874171i	0.537664	+	0.843159i	$0.319307\pi$
$828$	0.941197	+	0.149071i	0.0327089	+	0.00518057i
$829$	−8.80126	+	12.1139i	−0.305680	+	0.420733i	−0.934028	−	0.357200i	$-0.883732\pi$
$829$	−8.80126	+	12.1139i	−0.305680	+	0.420733i	0.628348	+	0.777933i	$0.283732\pi$
$830$		0			0
$831$	−23.8694	+	7.75564i	−0.828020	+	0.269040i
$832$	−1.05976	−	6.69109i	−0.0367407	−	0.231972i
$833$	3.24759	−	20.5045i	0.112522	−	0.710439i
$834$	−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
$838$	−7.36068	−	14.4461i	−0.254270	−	0.499034i
$839$	7.40356	+	10.1901i	0.255599	+	0.351802i	0.917462	−	0.397823i	$-0.130234\pi$
$839$	7.40356	+	10.1901i	0.255599	+	0.351802i	−0.661863	+	0.749625i	$0.730234\pi$
$840$		0			0
$841$	−8.65134	−	26.6261i	−0.298322	−	0.918141i
$842$	5.23975	−	10.2836i	0.180574	−	0.354396i
$843$	7.00457	−	1.10941i	0.241250	−	0.0382103i
$844$	0.770496	−	0.559798i	0.0265216	−	0.0192691i
$845$		0			0
$846$		−	4.02315i		−	0.138319i
$847$	30.5585	+	34.8744i	1.05000	+	1.19830i
$848$	−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
$852$	0.949642	+	0.483867i	0.0325342	+	0.0165770i
$853$	44.3481	+	22.5965i	1.51845	+	0.773689i	0.996835	−	0.0794926i	$-0.0253300\pi$
$853$	44.3481	+	22.5965i	1.51845	+	0.773689i	0.521614	+	0.853181i	$0.325330\pi$
$854$	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	$-0.0781077\pi$
$857$	21.2860	+	21.2860i	0.727117	+	0.727117i	−0.242927	+	0.970044i	$0.578108\pi$
$858$	−1.80996	+	3.28051i	−0.0617909	+	0.111995i
$859$			9.31402i			0.317790i	0.987295	+	0.158895i	$0.0507932\pi$
$859$			9.31402i			0.317790i	−0.987295	+	0.158895i	$0.949207\pi$
$860$		0			0
$861$	1.63941	−	1.19110i	0.0558709	−	0.0405926i
$862$	10.5740	−	1.67475i	0.360151	−	0.0570424i
$863$	16.0664	−	31.5320i	0.546905	−	1.07336i	−0.437790	−	0.899077i	$-0.644239\pi$
$863$	16.0664	−	31.5320i	0.546905	−	1.07336i	0.984695	−	0.174285i	$-0.0557613\pi$
$864$	1.14852	+	3.53479i	0.0390735	+	0.120256i
$865$		0			0
$866$	4.34927	+	5.98625i	0.147794	+	0.203421i
$867$	5.02038	+	9.85305i	0.170501	+	0.334627i
$868$	−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
$872$	8.45531	−	53.3847i	0.286333	−	1.80783i
$873$	1.19973	+	7.57478i	0.0406046	+	0.256368i
$874$	20.9911	−	6.82042i	0.710034	−	0.230704i
$875$		0			0
$876$	−0.398163	+	0.548025i	−0.0134527	+	0.0185160i
$877$	−21.5902	−	3.41955i	−0.729048	−	0.115470i	−0.219133	−	0.975695i	$-0.570323\pi$
$877$	−21.5902	−	3.41955i	−0.729048	−	0.115470i	−0.509915	+	0.860225i	$0.670323\pi$
$878$	1.69512	−	0.863707i	0.0572076	−	0.0291487i
$879$	−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	$0.213692\pi$
$882$	−32.4505	+	16.5344i	−1.09267	+	0.556741i
$883$	−27.5798	−	4.36822i	−0.928135	−	0.147002i	−0.325976	−	0.945378i	$-0.605693\pi$
$883$	−27.5798	−	4.36822i	−0.928135	−	0.147002i	−0.602159	+	0.798376i	$0.705693\pi$
$884$	−0.156308	+	0.215140i	−0.00525721	+	0.00723593i
$885$		0			0
$886$	21.4719	−	6.97665i	0.721363	−	0.234385i
$887$	−1.10133	−	6.95351i	−0.0369790	−	0.233476i	0.962276	−	0.272076i	$-0.0877102\pi$
$887$	−1.10133	−	6.95351i	−0.0369790	−	0.233476i	−0.999255	+	0.0385999i	$0.987710\pi$
$888$	1.74315	−	11.0058i	0.0584963	−	0.369331i
$889$	−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
$893$	−2.93351	−	5.75734i	−0.0981662	−	0.192662i
$894$	0.875532	+	1.20507i	0.0292822	+	0.0403035i
$895$		0			0
$896$	−16.1666	−	49.7558i	−0.540090	−	1.66223i
$897$	0.969718	−	1.90318i	0.0323780	−	0.0635453i
$898$	17.5527	−	2.78007i	0.585740	−	0.0927721i
$899$	−0.343606	+	0.249644i	−0.0114599	+	0.00832611i
$900$		0			0
$901$		−	17.5071i		−	0.583247i
$902$	−0.530284	+	2.75713i	−0.0176565	+	0.0918024i
$903$	−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
$907$	26.3281	+	13.4148i	0.874211	+	0.445433i	0.832712	−	0.553706i	$-0.186787\pi$
$907$	26.3281	+	13.4148i	0.874211	+	0.445433i	0.0414984	+	0.999139i	$0.486787\pi$
$908$	1.09916	+	0.560050i	0.0364769	+	0.0185859i
$909$	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
$913$	−1.24574	+	6.47702i	−0.0412279	+	0.214358i
$914$		−	5.14655i		−	0.170233i
$915$		0			0
$916$	−2.36292	+	1.71676i	−0.0780729	+	0.0567233i
$917$	−60.1748	+	9.53075i	−1.98715	+	0.314733i
$918$	−5.66813	+	11.1243i	−0.187076	+	0.367158i
$919$	1.55222	+	4.77725i	0.0512030	+	0.157587i	0.973388	−	0.229161i	$-0.0735983\pi$
$919$	1.55222	+	4.77725i	0.0512030	+	0.157587i	−0.922185	+	0.386748i	$0.873598\pi$
$920$		0			0
$921$	8.62467	+	11.8708i	0.284193	+	0.391158i
$922$	−3.62937	−	7.12304i	−0.119527	−	0.234585i
$923$	−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
$927$	3.63865	−	22.9736i	0.119509	−	0.754551i
$928$	0.131845	+	0.832439i	0.00432804	+	0.0273262i
$929$	−11.2348	+	3.65041i	−0.368602	+	0.119766i	−0.487460	−	0.873145i	$-0.662077\pi$
$929$	−11.2348	+	3.65041i	−0.368602	+	0.119766i	0.118858	+	0.992911i	$0.462077\pi$
$930$		0			0
$931$	−34.3822	+	47.3231i	−1.12683	+	1.55095i
$932$	−0.546524	−	0.0865609i	−0.0179020	−	0.00283540i
$933$	−11.2103	+	5.71194i	−0.367009	+	0.187001i
$934$	−21.5258			−0.704346
$935$		0			0
$936$	−5.79466			−0.189405
$937$	2.04229	−	1.04060i	0.0667187	−	0.0339949i	−0.420313	−	0.907379i	$-0.638080\pi$
$937$	2.04229	−	1.04060i	0.0667187	−	0.0339949i	0.487032	+	0.873384i	$0.338080\pi$
$938$	26.3715	+	4.17683i	0.861060	+	0.136378i
$939$	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	$0.390798\pi$
$942$	−1.41638	−	8.94264i	−0.0461480	−	0.291367i
$943$	0.250397	−	1.58094i	0.00815404	−	0.0514826i
$944$	−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	−0.552790	−	0.833321i	$-0.686437\pi$
$947$	8.63289	−	8.63289i	0.280531	−	0.280531i	0.833321	+	0.552790i	$0.186437\pi$
$948$	−0.128648	−	0.252485i	−0.00417828	−	0.00820033i
$949$	−2.97101	−	4.08925i	−0.0964431	−	0.132743i
$950$		0			0
$951$	7.28714	+	22.4275i	0.236302	+	0.727262i
$952$	10.0105	−	19.6466i	0.324441	−	0.636752i
$953$	18.2074	−	2.88376i	0.589794	−	0.0934143i	0.145598	−	0.989344i	$-0.453489\pi$
$953$	18.2074	−	2.88376i	0.589794	−	0.0934143i	0.444196	+	0.895930i	$0.353489\pi$
$954$	−24.8476	+	18.0528i	−0.804470	+	0.584482i
$955$		0			0
$956$		−	0.478792i		−	0.0154852i
$957$	−1.33623	+	2.42189i	−0.0431941	+	0.0782884i
$958$	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
$962$	−5.96448	−	3.03906i	−0.192303	−	0.0979831i
$963$	−12.6759	−	6.45868i	−0.408474	−	0.208128i
$964$	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	$-0.180758\pi$
$967$	9.49113	+	9.49113i	0.305214	+	0.305214i	−0.537836	+	0.843050i	$0.680758\pi$
$968$	11.7709	+	27.4289i	0.378333	+	0.881598i
$969$			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	$0.992933\pi$
$972$	2.34815	−	0.371911i	0.0753171	−	0.0119291i
$973$	1.93167	−	3.79111i	0.0619265	−	0.121538i
$974$	−4.86416	−	14.9703i	−0.155858	−	0.479681i
$975$		0			0
$976$	19.5578	+	26.9190i	0.626029	+	0.861655i
$977$	6.57391	+	12.9020i	0.210318	+	0.412772i	0.971933	−	0.235257i	$-0.0755933\pi$
$977$	6.57391	+	12.9020i	0.210318	+	0.412772i	−0.761615	+	0.648030i	$0.775593\pi$
$978$	−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
$982$	−0.746699	+	4.71447i	−0.0238281	+	0.150445i
$983$	9.00238	+	56.8388i	0.287131	+	1.81288i	0.535865	+	0.844304i	$0.319986\pi$
$983$	9.00238	+	56.8388i	0.287131	+	1.81288i	−0.248734	+	0.968572i	$0.580014\pi$
$984$	1.24059	−	0.403091i	0.0395484	−	0.0128501i
$985$		0			0
$986$	−1.66413	+	2.29048i	−0.0529967	+	0.0729437i
$987$	−4.12308	−	0.653031i	−0.131239	−	0.0207862i
$988$	0.667621	−	0.340170i	0.0212399	−	0.0108222i
$989$	−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	$0.433230\pi$
$992$	−0.317782	+	0.161918i	−0.0100896	+	0.00514090i
$993$	−20.2641	−	3.20952i	−0.643062	−	0.101851i
$994$	−31.2055	+	42.9507i	−0.989779	+	1.36231i
$995$		0			0
$996$	−0.234634	+	0.0762372i	−0.00743466	+	0.00241567i
$997$	0.352744	+	2.22714i	0.0111715	+	0.0705343i	0.992644	−	0.121068i	$-0.0386318\pi$
$997$	0.352744	+	2.22714i	0.0111715	+	0.0705343i	−0.981473	+	0.191602i	$0.938632\pi$
$998$	−2.05059	+	12.9469i	−0.0649104	+	0.409828i
$999$	−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.68.1		32
5.2	odd	4	inner	275.2.bm.b.57.1		32
5.3	odd	4		55.2.l.a.2.4	✓	32
5.4	even	2		55.2.l.a.13.4	yes	32
11.6	odd	10	inner	275.2.bm.b.193.1		32
15.8	even	4		495.2.bj.a.442.1		32
15.14	odd	2		495.2.bj.a.343.1		32
20.3	even	4		880.2.cm.a.497.3		32
20.19	odd	2		880.2.cm.a.673.3		32
55.3	odd	20		605.2.m.d.282.4		32
55.4	even	10		605.2.e.b.483.13		32
55.8	even	20		605.2.m.c.282.1		32
55.9	even	10		605.2.m.c.118.1		32
55.13	even	20		605.2.m.d.602.1		32
55.14	even	10		605.2.m.d.403.1		32
55.17	even	20	inner	275.2.bm.b.182.1		32
55.18	even	20		605.2.e.b.362.13		32
55.19	odd	10		605.2.m.c.403.4		32
55.24	odd	10		605.2.m.d.118.4		32
55.28	even	20		55.2.l.a.17.4	yes	32
55.29	odd	10		605.2.e.b.483.4		32
55.38	odd	20		605.2.m.e.457.1		32
55.39	odd	10		55.2.l.a.28.4	yes	32
55.43	even	4		605.2.m.e.112.1		32
55.48	odd	20		605.2.e.b.362.4		32
55.49	even	10		605.2.m.e.578.1		32
55.53	odd	20		605.2.m.c.602.4		32
55.54	odd	2		605.2.m.e.233.1		32
165.83	odd	20		495.2.bj.a.127.1		32
165.149	even	10		495.2.bj.a.28.1		32
220.39	even	10		880.2.cm.a.193.3		32
220.83	odd	20		880.2.cm.a.17.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	5.3	odd	4
55.2.l.a.13.4	yes	32	5.4	even	2
55.2.l.a.17.4	yes	32	55.28	even	20
55.2.l.a.28.4	yes	32	55.39	odd	10
275.2.bm.b.57.1		32	5.2	odd	4	inner
275.2.bm.b.68.1		32	1.1	even	1	trivial
275.2.bm.b.182.1		32	55.17	even	20	inner
275.2.bm.b.193.1		32	11.6	odd	10	inner
495.2.bj.a.28.1		32	165.149	even	10
495.2.bj.a.127.1		32	165.83	odd	20
495.2.bj.a.343.1		32	15.14	odd	2
495.2.bj.a.442.1		32	15.8	even	4
605.2.e.b.362.4		32	55.48	odd	20
605.2.e.b.362.13		32	55.18	even	20
605.2.e.b.483.4		32	55.29	odd	10
605.2.e.b.483.13		32	55.4	even	10
605.2.m.c.118.1		32	55.9	even	10
605.2.m.c.282.1		32	55.8	even	20
605.2.m.c.403.4		32	55.19	odd	10
605.2.m.c.602.4		32	55.53	odd	20
605.2.m.d.118.4		32	55.24	odd	10
605.2.m.d.282.4		32	55.3	odd	20
605.2.m.d.403.1		32	55.14	even	10
605.2.m.d.602.1		32	55.13	even	20
605.2.m.e.112.1		32	55.43	even	4
605.2.m.e.233.1		32	55.54	odd	2
605.2.m.e.457.1		32	55.38	odd	20
605.2.m.e.578.1		32	55.49	even	10
880.2.cm.a.17.3		32	220.83	odd	20
880.2.cm.a.193.3		32	220.39	even	10
880.2.cm.a.497.3		32	20.3	even	4
880.2.cm.a.673.3		32	20.19	odd	2

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

Fields

Representations

Groups

Database

Properties

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