LMFDB - Embedded newform 625.2.h.b.274.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.19
Character	$\chi$	$=$	625.274
Dual form			625.2.h.b.349.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.475182 + 1.85071i) q^{2} +(-0.722462 + 0.137817i) q^{3} +(-1.44673 + 0.795344i) q^{4} +(-0.598361 - 1.27158i) q^{6} +(2.04237 - 2.81109i) q^{7} +(0.456575 + 0.486202i) q^{8} +(-2.28637 + 0.905238i) q^{9} +O(q^{10})$	\(q+(0.475182 + 1.85071i) q^{2} +(-0.722462 + 0.137817i) q^{3} +(-1.44673 + 0.795344i) q^{4} +(-0.598361 - 1.27158i) q^{6} +(2.04237 - 2.81109i) q^{7} +(0.456575 + 0.486202i) q^{8} +(-2.28637 + 0.905238i) q^{9} +(-1.60551 + 0.412224i) q^{11} +(0.935593 - 0.773989i) q^{12} +(1.71984 + 4.34382i) q^{13} +(6.17301 + 2.44407i) q^{14} +(-2.45210 + 3.86388i) q^{16} +(-1.70275 + 3.09729i) q^{17} +(-2.76178 - 3.80126i) q^{18} +(-1.54162 + 8.08148i) q^{19} +(-1.08812 + 2.31238i) q^{21} +(-1.52582 - 2.77545i) q^{22} +(5.62755 + 0.354056i) q^{23} +(-0.396865 - 0.288339i) q^{24} +(-7.22192 + 5.24704i) q^{26} +(3.39004 - 2.15139i) q^{27} +(-0.718973 + 5.69126i) q^{28} +(-2.76707 - 0.349562i) q^{29} +(3.57092 + 1.96313i) q^{31} +(-7.04747 - 2.28986i) q^{32} +(1.10311 - 0.519082i) q^{33} +(-6.54131 - 1.67952i) q^{34} +(2.58778 - 3.12808i) q^{36} +(3.80368 + 2.41389i) q^{37} +(-15.6890 + 0.987071i) q^{38} +(-1.84117 - 2.90122i) q^{39} +(-0.634417 - 10.0838i) q^{41} +(-4.79660 - 0.915001i) q^{42} +(0.711741 - 0.231259i) q^{43} +(1.99487 - 1.87330i) q^{44} +(2.01886 + 10.5832i) q^{46} +(4.35694 - 4.63967i) q^{47} +(1.23904 - 3.12945i) q^{48} +(-1.56779 - 4.82517i) q^{49} +(0.803313 - 2.47234i) q^{51} +(-5.94297 - 4.91645i) q^{52} +(-6.58904 - 3.10057i) q^{53} +(5.59249 + 5.25170i) q^{54} +(2.29925 - 0.290463i) q^{56} -6.05102i q^{57} +(-0.667923 - 5.28715i) q^{58} +(-2.95945 - 3.57736i) q^{59} +(-0.259674 + 4.12740i) q^{61} +(-1.93635 + 7.54159i) q^{62} +(-2.12492 + 8.27602i) q^{63} +(0.314349 - 4.99644i) q^{64} +(1.48485 + 1.79487i) q^{66} +(0.287826 + 2.27838i) q^{67} -5.83520i q^{68} +(-4.11449 + 0.519781i) q^{69} +(5.95709 + 5.59408i) q^{71} +(-1.48403 - 0.698331i) q^{72} +(3.49698 + 2.89295i) q^{73} +(-2.65997 + 8.18655i) q^{74} +(-4.19725 - 12.9178i) q^{76} +(-2.12024 + 5.35513i) q^{77} +(4.49444 - 4.78609i) q^{78} +(-1.69565 - 8.88892i) q^{79} +(3.22504 - 3.02851i) q^{81} +(18.3607 - 5.96575i) q^{82} +(-8.24547 - 1.57291i) q^{83} +(-0.264921 - 4.21081i) q^{84} +(0.766200 + 1.20734i) q^{86} +(2.04728 - 0.128804i) q^{87} +(-0.933457 - 0.592390i) q^{88} +(8.05754 - 9.73989i) q^{89} +(15.7234 + 4.03708i) q^{91} +(-8.42312 + 3.96362i) q^{92} +(-2.85041 - 0.926154i) q^{93} +(10.6570 + 5.85876i) q^{94} +(5.40712 + 0.683077i) q^{96} +(0.599240 - 4.74347i) q^{97} +(8.18502 - 5.19437i) q^{98} +(3.29762 - 2.39586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.475182	+	1.85071i	0.336005	+	1.30865i	0.882153	+	0.470963i	$0.156093\pi$
$2$	0.475182	+	1.85071i	0.336005	+	1.30865i	−0.546148	+	0.837688i	$0.683907\pi$
$3$	−0.722462	+	0.137817i	−0.417114	+	0.0795687i	−0.391666	−	0.920107i	$-0.628101\pi$
$3$	−0.722462	+	0.137817i	−0.417114	+	0.0795687i	−0.0254477	+	0.999676i	$0.508101\pi$
$4$	−1.44673	+	0.795344i	−0.723363	+	0.397672i
$5$		0			0
$5$		0			0
$6$	−0.598361	−	1.27158i	−0.244280	−	0.519121i
$7$	2.04237	−	2.81109i	0.771944	−	1.06249i	−0.224181	−	0.974547i	$-0.571971\pi$
$7$	2.04237	−	2.81109i	0.771944	−	1.06249i	0.996126	−	0.0879428i	$-0.0280293\pi$
$8$	0.456575	+	0.486202i	0.161423	+	0.171899i
$9$	−2.28637	+	0.905238i	−0.762124	+	0.301746i
$10$		0			0
$11$	−1.60551	+	0.412224i	−0.484078	+	0.124290i	−0.482839	−	0.875709i	$-0.660394\pi$
$11$	−1.60551	+	0.412224i	−0.484078	+	0.124290i	−0.00123904	+	0.999999i	$0.500394\pi$
$12$	0.935593	−	0.773989i	0.270082	−	0.223432i
$13$	1.71984	+	4.34382i	0.476998	+	1.20476i	0.946753	+	0.321962i	$0.104342\pi$
$13$	1.71984	+	4.34382i	0.476998	+	1.20476i	−0.469755	+	0.882797i	$0.655658\pi$
$14$	6.17301	+	2.44407i	1.64981	+	0.653205i
$15$		0			0
$16$	−2.45210	+	3.86388i	−0.613024	+	0.965971i
$17$	−1.70275	+	3.09729i	−0.412977	+	0.751203i	−0.998219	−	0.0596561i	$-0.981000\pi$
$17$	−1.70275	+	3.09729i	−0.412977	+	0.751203i	0.585242	+	0.810859i	$0.301000\pi$
$18$	−2.76178	−	3.80126i	−0.650958	−	0.895966i
$19$	−1.54162	+	8.08148i	−0.353673	+	1.85402i	0.148037	+	0.988982i	$0.452705\pi$
$19$	−1.54162	+	8.08148i	−0.353673	+	1.85402i	−0.501710	+	0.865036i	$0.667295\pi$
$20$		0			0
$21$	−1.08812	+	2.31238i	−0.237448	+	0.504602i
$22$	−1.52582	−	2.77545i	−0.325305	−	0.591727i
$23$	5.62755	+	0.354056i	1.17343	+	0.0738257i	0.637508	−	0.770444i	$-0.279965\pi$
$23$	5.62755	+	0.354056i	1.17343	+	0.0738257i	0.535919	+	0.844270i	$0.319965\pi$
$24$	−0.396865	−	0.288339i	−0.0810097	−	0.0588570i
$25$		0			0
$26$	−7.22192	+	5.24704i	−1.41634	+	1.02903i
$27$	3.39004	−	2.15139i	0.652414	−	0.414035i
$28$	−0.718973	+	5.69126i	−0.135873	+	1.07555i
$29$	−2.76707	−	0.349562i	−0.513831	−	0.0649120i	−0.135858	−	0.990728i	$-0.543379\pi$
$29$	−2.76707	−	0.349562i	−0.513831	−	0.0649120i	−0.377974	+	0.925816i	$0.623379\pi$
$30$		0			0
$31$	3.57092	+	1.96313i	0.641356	+	0.352589i	0.769016	−	0.639229i	$-0.220747\pi$
$31$	3.57092	+	1.96313i	0.641356	+	0.352589i	−0.127660	+	0.991818i	$0.540747\pi$
$32$	−7.04747	−	2.28986i	−1.24583	−	0.404794i
$33$	1.10311	−	0.519082i	0.192026	−	0.0903606i
$34$	−6.54131	−	1.67952i	−1.12182	−	0.288036i
$35$		0			0
$36$	2.58778	−	3.12808i	0.431296	−	0.521347i
$37$	3.80368	+	2.41389i	0.625321	+	0.396841i	0.810395	−	0.585884i	$-0.199253\pi$
$37$	3.80368	+	2.41389i	0.625321	+	0.396841i	−0.185074	+	0.982725i	$0.559253\pi$
$38$	−15.6890	+	0.987071i	−2.54510	+	0.160124i
$39$	−1.84117	−	2.90122i	−0.294823	−	0.464567i
$40$		0			0
$41$	−0.634417	−	10.0838i	−0.0990792	−	1.57482i	−0.662764	−	0.748829i	$-0.730617\pi$
$41$	−0.634417	−	10.0838i	−0.0990792	−	1.57482i	0.563684	−	0.825990i	$-0.309383\pi$
$42$	−4.79660	−	0.915001i	−0.740132	−	0.141188i
$43$	0.711741	−	0.231259i	0.108540	−	0.0352666i	−0.254244	−	0.967140i	$-0.581827\pi$
$43$	0.711741	−	0.231259i	0.108540	−	0.0352666i	0.362783	+	0.931874i	$0.381827\pi$
$44$	1.99487	−	1.87330i	0.300737	−	0.282411i
$45$		0			0
$46$	2.01886	+	10.5832i	0.297664	+	1.56041i
$47$	4.35694	−	4.63967i	0.635525	−	0.676766i	−0.327909	−	0.944709i	$-0.606344\pi$
$47$	4.35694	−	4.63967i	0.635525	−	0.676766i	0.963435	+	0.267943i	$0.0863440\pi$
$48$	1.23904	−	3.12945i	0.178840	−	0.451697i
$49$	−1.56779	−	4.82517i	−0.223971	−	0.689310i
$50$		0			0
$51$	0.803313	−	2.47234i	0.112486	−	0.346197i
$52$	−5.94297	−	4.91645i	−0.824141	−	0.681789i
$53$	−6.58904	−	3.10057i	−0.905074	−	0.425895i	−0.0838347	−	0.996480i	$-0.526717\pi$
$53$	−6.58904	−	3.10057i	−0.905074	−	0.425895i	−0.821239	+	0.570584i	$0.806717\pi$
$54$	5.59249	+	5.25170i	0.761041	+	0.714665i
$55$		0			0
$56$	2.29925	−	0.290463i	0.307250	−	0.0388148i
$57$		−	6.05102i		−	0.801478i
$58$	−0.667923	−	5.28715i	−0.0877025	−	0.694237i
$59$	−2.95945	−	3.57736i	−0.385288	−	0.465733i	0.541838	−	0.840483i	$-0.317729\pi$
$59$	−2.95945	−	3.57736i	−0.385288	−	0.465733i	−0.927126	+	0.374750i	$0.877729\pi$
$60$		0			0
$61$	−0.259674	+	4.12740i	−0.0332478	+	0.528459i	0.945790	+	0.324779i	$0.105290\pi$
$61$	−0.259674	+	4.12740i	−0.0332478	+	0.528459i	−0.979038	+	0.203680i	$0.934710\pi$
$62$	−1.93635	+	7.54159i	−0.245917	+	0.957783i
$63$	−2.12492	+	8.27602i	−0.267715	+	1.04268i
$64$	0.314349	−	4.99644i	0.0392937	−	0.624555i
$65$		0			0
$66$	1.48485	+	1.79487i	0.182772	+	0.220934i
$67$	0.287826	+	2.27838i	0.0351636	+	0.278348i	0.999886	+	0.0150803i	$0.00480040\pi$
$67$	0.287826	+	2.27838i	0.0351636	+	0.278348i	−0.964723	+	0.263268i	$0.915200\pi$
$68$		−	5.83520i		−	0.707622i
$69$	−4.11449	+	0.519781i	−0.495326	+	0.0625743i
$70$		0			0
$71$	5.95709	+	5.59408i	0.706977	+	0.663895i	0.952166	−	0.305580i	$-0.0988503\pi$
$71$	5.95709	+	5.59408i	0.706977	+	0.663895i	−0.245190	+	0.969475i	$0.578850\pi$
$72$	−1.48403	−	0.698331i	−0.174894	−	0.0822990i
$73$	3.49698	+	2.89295i	0.409290	+	0.338594i	0.819176	−	0.573543i	$-0.194431\pi$
$73$	3.49698	+	2.89295i	0.409290	+	0.338594i	−0.409886	+	0.912137i	$0.634431\pi$
$74$	−2.65997	+	8.18655i	−0.309215	+	0.951667i
$75$		0			0
$76$	−4.19725	−	12.9178i	−0.481457	−	1.48177i
$77$	−2.12024	+	5.35513i	−0.241624	+	0.610273i
$78$	4.49444	−	4.78609i	0.508895	−	0.541918i
$79$	−1.69565	−	8.88892i	−0.190776	−	1.00008i	−0.940874	−	0.338755i	$-0.889994\pi$
$79$	−1.69565	−	8.88892i	−0.190776	−	1.00008i	0.750099	−	0.661326i	$-0.230006\pi$
$80$		0			0
$81$	3.22504	−	3.02851i	0.358338	−	0.336502i
$82$	18.3607	−	5.96575i	2.02760	−	0.658807i
$83$	−8.24547	−	1.57291i	−0.905058	−	0.172649i	−0.286217	−	0.958165i	$-0.592398\pi$
$83$	−8.24547	−	1.57291i	−0.905058	−	0.172649i	−0.618842	+	0.785516i	$0.712398\pi$
$84$	−0.264921	−	4.21081i	−0.0289053	−	0.459437i
$85$		0			0
$86$	0.766200	+	1.20734i	0.0826215	+	0.130191i
$87$	2.04728	−	0.128804i	0.219491	−	0.0138092i
$88$	−0.933457	−	0.592390i	−0.0995069	−	0.0631490i
$89$	8.05754	−	9.73989i	0.854097	−	1.03243i	−0.144978	−	0.989435i	$-0.546311\pi$
$89$	8.05754	−	9.73989i	0.854097	−	1.03243i	0.999075	−	0.0429916i	$-0.0136889\pi$
$90$		0			0
$91$	15.7234	+	4.03708i	1.64826	+	0.423201i
$92$	−8.42312	+	3.96362i	−0.878171	+	0.413236i
$93$	−2.85041	−	0.926154i	−0.295574	−	0.0960377i
$94$	10.6570	+	5.85876i	1.09919	+	0.604285i
$95$		0			0
$96$	5.40712	+	0.683077i	0.551861	+	0.0697163i
$97$	0.599240	−	4.74347i	0.0608436	−	0.481627i	−0.932023	−	0.362398i	$-0.881958\pi$
$97$	0.599240	−	4.74347i	0.0608436	−	0.481627i	0.992867	−	0.119228i	$-0.0380420\pi$
$98$	8.18502	−	5.19437i	0.826812	−	0.524711i
$99$	3.29762	−	2.39586i	0.331423	−	0.240793i
$100$		0			0
$101$	−2.83644	−	2.06080i	−0.282236	−	0.205057i	0.437656	−	0.899143i	$-0.355809\pi$
$101$	−2.83644	−	2.06080i	−0.282236	−	0.205057i	−0.719892	+	0.694086i	$0.755809\pi$
$102$	4.95731	+	0.311888i	0.490847	+	0.0308815i
$103$	7.24504	+	13.1787i	0.713875	+	1.29853i	0.945466	+	0.325721i	$0.105607\pi$
$103$	7.24504	+	13.1787i	0.713875	+	1.29853i	−0.231591	+	0.972813i	$0.574393\pi$
$104$	−1.32674	+	2.81947i	−0.130098	+	0.276472i
$105$		0			0
$106$	2.60726	−	13.6677i	0.253240	−	1.32753i
$107$	−0.651907	−	0.897273i	−0.0630222	−	0.0867426i	0.776342	−	0.630311i	$-0.217073\pi$
$107$	−0.651907	−	0.897273i	−0.0630222	−	0.0867426i	−0.839365	+	0.543569i	$0.817073\pi$
$108$	−3.19337	+	5.80872i	−0.307282	+	0.558944i
$109$	1.54742	−	2.43834i	0.148216	−	0.233551i	−0.762106	−	0.647453i	$-0.775834\pi$
$109$	1.54742	−	2.43834i	0.148216	−	0.233551i	0.910322	+	0.413902i	$0.135834\pi$
$110$		0			0
$111$	−3.08069	−	1.21973i	−0.292406	−	0.115772i
$112$	5.85361	+	14.7845i	0.553115	+	1.39701i
$113$	14.0930	−	11.6588i	1.32576	−	1.09676i	0.337938	−	0.941168i	$-0.390271\pi$
$113$	14.0930	−	11.6588i	1.32576	−	1.09676i	0.987821	−	0.155594i	$-0.0497293\pi$
$114$	11.1987	−	2.87534i	1.04885	−	0.269300i
$115$		0			0
$116$	4.28121	−	1.69505i	0.397500	−	0.157381i
$117$	−7.86439	−	8.37472i	−0.727063	−	0.774243i
$118$	5.21439	−	7.17699i	0.480024	−	0.660696i
$119$	5.22909	+	11.1124i	0.479350	+	1.01867i
$120$		0			0
$121$	−7.23165	+	3.97564i	−0.657423	+	0.361421i
$122$	−7.76202	+	1.48068i	−0.702740	+	0.134055i
$123$	1.84806	+	7.19770i	0.166634	+	0.648995i
$124$	−6.72751			−0.604148
$125$		0			0
$126$	−16.3263			−1.45446
$127$	−0.425624	−	1.65770i	−0.0377680	−	0.147097i	0.946903	−	0.321520i	$-0.104194\pi$
$127$	−0.425624	−	1.65770i	−0.0377680	−	0.147097i	−0.984671	+	0.174424i	$0.944194\pi$
$128$	−5.16144	+	0.984598i	−0.456212	+	0.0870270i
$129$	−0.482335	+	0.265166i	−0.0424672	+	0.0233466i
$130$		0			0
$131$	−5.80892	−	12.3446i	−0.507528	−	1.07855i	−0.980327	−	0.197381i	$-0.936756\pi$
$131$	−5.80892	−	12.3446i	−0.507528	−	1.07855i	0.472799	−	0.881170i	$-0.343244\pi$
$132$	−1.18304	+	1.62832i	−0.102971	+	0.141727i
$133$	19.5691	+	20.8390i	1.69686	+	1.80697i
$134$	−4.07986	+	1.61533i	−0.352446	+	0.139543i
$135$		0			0
$136$	−2.28334	+	0.586262i	−0.195795	+	0.0502716i
$137$	−3.68923	+	3.05200i	−0.315192	+	0.260750i	−0.781545	−	0.623849i	$-0.785568\pi$
$137$	−3.68923	+	3.05200i	−0.315192	+	0.260750i	0.466352	+	0.884599i	$0.345568\pi$
$138$	−2.91710	−	7.36775i	−0.248320	−	0.627184i
$139$	−8.11895	−	3.21452i	−0.688640	−	0.272652i	−0.00236837	−	0.999997i	$-0.500754\pi$
$139$	−8.11895	−	3.21452i	−0.688640	−	0.272652i	−0.686272	+	0.727345i	$0.740754\pi$
$140$		0			0
$141$	−2.50830	+	3.95245i	−0.211237	+	0.332856i
$142$	−7.52233	+	13.6831i	−0.631260	+	1.14826i
$143$	−4.55184	−	6.26507i	−0.380644	−	0.523911i
$144$	2.10866	−	11.0540i	0.175722	−	0.921167i
$145$		0			0
$146$	−3.69232	+	7.84658i	−0.305578	+	0.649387i
$147$	1.79766	+	3.26994i	0.148269	+	0.269700i
$148$	−7.42275	−	0.467000i	−0.610146	−	0.0383871i
$149$	4.45671	+	3.23799i	0.365108	+	0.265266i	0.755179	−	0.655518i	$-0.227550\pi$
$149$	4.45671	+	3.23799i	0.365108	+	0.265266i	−0.390072	+	0.920785i	$0.627550\pi$
$150$		0			0
$151$	−15.9328	+	11.5759i	−1.29659	+	0.942031i	−0.999916	−	0.0129467i	$-0.995879\pi$
$151$	−15.9328	+	11.5759i	−1.29659	+	0.942031i	−0.296678	+	0.954978i	$0.595879\pi$
$152$	−4.63310	+	2.94025i	−0.375794	+	0.238486i
$153$	1.08933	−	8.62294i	0.0880672	−	0.697124i
$154$	−10.9183	−	1.37930i	−0.879822	−	0.111147i
$155$		0			0
$156$	4.97114	+	2.73291i	0.398010	+	0.218808i
$157$	12.7120	+	4.13038i	1.01453	+	0.329640i	0.768656	−	0.639662i	$-0.220926\pi$
$157$	12.7120	+	4.13038i	1.01453	+	0.329640i	0.245872	+	0.969302i	$0.420926\pi$
$158$	15.6451	−	7.36202i	1.24466	−	0.585691i
$159$	5.18764	+	1.33196i	0.411407	+	0.105631i
$160$		0			0
$161$	12.4888	−	15.0964i	0.984259	−	1.18976i
$162$	7.13739	+	4.52953i	0.560766	+	0.355873i
$163$	1.96179	−	0.123426i	0.153660	−	0.00966744i	0.0142256	−	0.999899i	$-0.495472\pi$
$163$	1.96179	−	0.123426i	0.153660	−	0.00966744i	0.139434	+	0.990231i	$0.455472\pi$
$164$	8.93789	+	14.0839i	0.697932	+	1.09976i
$165$		0			0
$166$	−1.00710	−	16.0074i	−0.0781662	−	1.24242i
$167$	11.2639	+	2.14871i	0.871630	+	0.166272i	0.603744	−	0.797178i	$-0.293675\pi$
$167$	11.2639	+	2.14871i	0.871630	+	0.166272i	0.267886	+	0.963451i	$0.413675\pi$
$168$	−1.62109	+	0.526725i	−0.125070	+	0.0406377i
$169$	−6.43433	+	6.04224i	−0.494948	+	0.464787i
$170$		0			0
$171$	−3.79094	−	19.8728i	−0.289900	−	1.51971i
$172$	−0.845764	+	0.900647i	−0.0644889	+	0.0686737i
$173$	4.47347	−	11.2987i	0.340112	−	0.859024i	−0.654567	−	0.756004i	$-0.727149\pi$
$173$	4.47347	−	11.2987i	0.340112	−	0.859024i	0.994679	−	0.103021i	$-0.0328508\pi$
$174$	1.21121	+	3.72772i	0.0918215	+	0.282597i
$175$		0			0
$176$	2.34407	−	7.21430i	0.176691	−	0.543798i
$177$	2.63111	+	2.17665i	0.197767	+	0.163607i
$178$	21.8545	+	10.2840i	1.63807	+	0.770816i
$179$	8.68587	+	8.15658i	0.649213	+	0.609651i	0.937539	−	0.347881i	$-0.113099\pi$
$179$	8.68587	+	8.15658i	0.649213	+	0.609651i	−0.288326	+	0.957532i	$0.593099\pi$
$180$		0			0
$181$	−7.24524	+	0.915287i	−0.538535	+	0.0680327i	−0.389896	−	0.920859i	$-0.627489\pi$
$181$	−7.24524	+	0.915287i	−0.538535	+	0.0680327i	−0.148639	+	0.988892i	$0.547489\pi$
$182$			31.0178i			2.29920i
$183$	−0.381221	−	3.01768i	−0.0281807	−	0.223073i
$184$	2.39726	+	2.89778i	0.176728	+	0.213627i
$185$		0			0
$186$	0.359581	−	5.71538i	0.0263658	−	0.419072i
$187$	1.45700	−	5.67463i	0.106546	−	0.414970i
$188$	−2.61316	+	10.1776i	−0.190585	+	0.742278i
$189$	0.876001	−	13.9236i	0.0637197	−	1.01280i
$190$		0			0
$191$	4.31730	+	5.21872i	0.312389	+	0.377613i	0.903217	−	0.429184i	$-0.141199\pi$
$191$	4.31730	+	5.21872i	0.312389	+	0.377613i	−0.590828	+	0.806797i	$0.701199\pi$
$192$	0.461489	+	3.65306i	0.0333051	+	0.263637i
$193$		−	16.9988i		−	1.22360i	−0.791014	−	0.611799i	$-0.790446\pi$
$193$		−	16.9988i		−	1.22360i	0.791014	−	0.611799i	$-0.209554\pi$
$194$	9.06355	−	1.14499i	0.650725	−	0.0822057i
$195$		0			0
$196$	6.10584	+	5.73376i	0.436131	+	0.409555i
$197$	−0.847773	−	0.398932i	−0.0604013	−	0.0284227i	0.395341	−	0.918534i	$-0.370626\pi$
$197$	−0.847773	−	0.398932i	−0.0604013	−	0.0284227i	−0.455743	+	0.890112i	$0.650626\pi$
$198$	6.00102	+	4.96448i	0.426474	+	0.352810i
$199$	0.337641	−	1.03915i	0.0239347	−	0.0736636i	−0.938376	−	0.345617i	$-0.887670\pi$
$199$	0.337641	−	1.03915i	0.0239347	−	0.0736636i	0.962310	+	0.271953i	$0.0876697\pi$
$200$		0			0
$201$	−0.521943	−	1.60638i	−0.0368150	−	0.113305i
$202$	2.46611	−	6.22869i	0.173515	−	0.438249i
$203$	−6.63403	+	7.06453i	−0.465618	+	0.495833i
$204$	0.804190	+	4.21571i	0.0563045	+	0.295159i
$205$		0			0
$206$	−20.9472	+	19.6708i	−1.45946	+	1.37053i
$207$	−13.1872	+	4.28478i	−0.916573	+	0.297812i
$208$	−21.0012	−	4.00620i	−1.45617	−	0.277780i
$209$	−0.856291	−	13.6103i	−0.0592309	−	0.941448i
$210$		0			0
$211$	5.51645	+	8.69254i	0.379768	+	0.598419i	0.979418	−	0.201844i	$-0.0646933\pi$
$211$	5.51645	+	8.69254i	0.379768	+	0.598419i	−0.599650	+	0.800263i	$0.704693\pi$
$212$	11.9985	−	0.754884i	0.824063	−	0.0518457i
$213$	−5.07473	−	3.22052i	−0.347715	−	0.220667i
$214$	1.35082	−	1.63286i	0.0923401	−	0.111620i
$215$		0			0
$216$	2.59382	+	0.665979i	0.176487	+	0.0453141i
$217$	12.8117	−	6.02872i	0.869713	−	0.409256i
$218$	5.24798	+	1.70517i	0.355438	+	0.115489i
$219$	−2.92513	−	1.60810i	−0.197662	−	0.108666i
$220$		0			0
$221$	−16.3825	−	2.06959i	−1.10201	−	0.139216i
$222$	0.793483	−	6.28106i	0.0532551	−	0.421557i
$223$	10.4347	−	6.62209i	0.698762	−	0.443448i	−0.138419	−	0.990374i	$-0.544202\pi$
$223$	10.4347	−	6.62209i	0.698762	−	0.443448i	0.837181	+	0.546926i	$0.184202\pi$
$224$	−20.8306	+	15.1343i	−1.39180	+	1.01120i
$225$		0			0
$226$	28.2737	+	20.5421i	1.88074	+	1.36644i
$227$	1.43355	+	0.0901912i	0.0951480	+	0.00598620i	0.110293	−	0.993899i	$-0.464821\pi$
$227$	1.43355	+	0.0901912i	0.0951480	+	0.00598620i	−0.0151452	+	0.999885i	$0.504821\pi$
$228$	4.81265	+	8.75417i	0.318725	+	0.579759i
$229$	−6.58367	+	13.9910i	−0.435061	+	0.924552i	0.560295	+	0.828293i	$0.310688\pi$
$229$	−6.58367	+	13.9910i	−0.435061	+	0.924552i	−0.995356	+	0.0962587i	$0.969312\pi$
$230$		0			0
$231$	0.793769	−	4.16108i	0.0522262	−	0.273779i
$232$	−1.09341	−	1.50496i	−0.0717862	−	0.0988052i
$233$	−10.4300	+	18.9720i	−0.683289	+	1.24290i	0.276186	+	0.961104i	$0.410929\pi$
$233$	−10.4300	+	18.9720i	−0.683289	+	1.24290i	−0.959475	+	0.281794i	$0.909071\pi$
$234$	11.7622	−	18.5342i	0.768918	−	1.21162i
$235$		0			0
$236$	7.12675	+	2.82168i	0.463912	+	0.183676i
$237$	2.45009	+	6.18822i	0.159150	+	0.401968i
$238$	−18.0811	+	14.9580i	−1.17202	+	0.969580i
$239$	−5.68203	+	1.45890i	−0.367540	+	0.0943683i	−0.427943	−	0.903806i	$-0.640762\pi$
$239$	−5.68203	+	1.45890i	−0.367540	+	0.0943683i	0.0604027	+	0.998174i	$0.480762\pi$
$240$		0			0
$241$	22.2432	−	8.80669i	1.43281	−	0.567289i	0.481752	−	0.876308i	$-0.340001\pi$
$241$	22.2432	−	8.80669i	1.43281	−	0.567289i	0.951056	+	0.309019i	$0.100001\pi$
$242$	−10.7941	−	11.4946i	−0.693872	−	0.738898i
$243$	−8.99260	+	12.3773i	−0.576876	+	0.794001i
$244$	−2.90702	−	6.17774i	−0.186103	−	0.395489i
$245$		0			0
$246$	−12.4427	+	6.84044i	−0.793319	+	0.436131i
$247$	−37.7558	+	7.20231i	−2.40235	+	0.458272i
$248$	0.675913	+	2.63251i	0.0429205	+	0.167164i
$249$	6.17382			0.391250
$250$		0			0
$251$	4.78921			0.302292			0.151146	−	0.988511i	$-0.451704\pi$
$251$	4.78921			0.302292			0.151146	+	0.988511i	$0.451704\pi$
$252$	−3.50811	−	13.6632i	−0.220990	−	0.860699i
$253$	−9.18102	+	1.75137i	−0.577206	+	0.110108i
$254$	2.86567	−	1.57542i	0.179808	−	0.0988504i
$255$		0			0
$256$	−8.53801	−	18.1442i	−0.533626	−	1.13401i
$257$	13.3585	−	18.3864i	0.833282	−	1.14691i	−0.154022	−	0.988067i	$-0.549223\pi$
$257$	13.3585	−	18.3864i	0.833282	−	1.14691i	0.987303	−	0.158846i	$-0.0507775\pi$
$258$	−0.719943	−	0.766661i	−0.0448217	−	0.0477302i
$259$	14.5542	−	5.76240i	0.904352	−	0.358058i
$260$		0			0
$261$	6.64298	−	1.70563i	0.411190	−	0.105576i
$262$	20.0860	−	16.6166i	1.24092	−	1.02657i
$263$	−4.07016	−	10.2800i	−0.250977	−	0.633894i	0.748599	−	0.663023i	$-0.230727\pi$
$263$	−4.07016	−	10.2800i	−0.250977	−	0.633894i	−0.999576	+	0.0291284i	$0.990727\pi$
$264$	0.756029	+	0.299333i	0.0465304	+	0.0184227i
$265$		0			0
$266$	−29.2681	+	46.1192i	−1.79454	+	2.82775i
$267$	−4.47894	+	8.14717i	−0.274107	+	0.498599i
$268$	−2.22850	−	3.06727i	−0.136127	−	0.187363i
$269$	3.04930	−	15.9850i	0.185919	−	0.974623i	−0.759927	−	0.650008i	$-0.774765\pi$
$269$	3.04930	−	15.9850i	0.185919	−	0.974623i	0.945846	−	0.324615i	$-0.105235\pi$
$270$		0			0
$271$	12.0932	−	25.6994i	0.734611	−	1.56113i	−0.0903321	−	0.995912i	$-0.528793\pi$
$271$	12.0932	−	25.6994i	0.734611	−	1.56113i	0.824943	−	0.565216i	$-0.191207\pi$
$272$	−7.79226	−	14.1741i	−0.472475	−	0.859429i
$273$	−11.9159	−	0.749688i	−0.721186	−	0.0453732i
$274$	−7.40143	−	5.37745i	−0.447137	−	0.324864i
$275$		0			0
$276$	5.53913	−	4.02442i	0.333417	−	0.242241i
$277$	24.1511	−	15.3268i	1.45110	−	0.920896i	0.451510	−	0.892266i	$-0.350886\pi$
$277$	24.1511	−	15.3268i	1.45110	−	0.920896i	0.999590	−	0.0286299i	$-0.00911442\pi$
$278$	2.09117	−	16.5533i	0.125420	−	0.992802i
$279$	−9.94155	−	1.25591i	−0.595185	−	0.0751894i
$280$		0			0
$281$	0.661101	+	0.363443i	0.0394380	+	0.0216812i	0.501351	−	0.865244i	$-0.332837\pi$
$281$	0.661101	+	0.363443i	0.0394380	+	0.0216812i	−0.461913	+	0.886925i	$0.652837\pi$
$282$	−8.50675	−	2.76401i	−0.506569	−	0.164594i
$283$	−12.0876	+	5.68799i	−0.718533	+	0.338116i	−0.750044	−	0.661388i	$-0.769968\pi$
$283$	−12.0876	+	5.68799i	−0.718533	+	0.338116i	0.0315117	+	0.999503i	$0.489968\pi$
$284$	−13.0675	−	3.35516i	−0.775413	−	0.199092i
$285$		0			0
$286$	9.43189	−	11.4012i	0.557719	−	0.674167i
$287$	−29.6420	−	18.8114i	−1.74971	−	1.11040i
$288$	18.1860	−	1.14417i	1.07162	−	0.0674207i
$289$	2.41521	+	3.80577i	0.142071	+	0.223869i
$290$		0			0
$291$	0.220803	+	3.50957i	0.0129437	+	0.205734i
$292$	−7.36005	−	1.40401i	−0.430715	−	0.0821632i
$293$	−5.25933	+	1.70886i	−0.307253	+	0.0998327i	−0.458586	−	0.888650i	$-0.651644\pi$
$293$	−5.25933	+	1.70886i	−0.307253	+	0.0998327i	0.151332	+	0.988483i	$0.451644\pi$
$294$	−5.19749	+	4.88077i	−0.303124	+	0.284652i
$295$		0			0
$296$	0.563024	+	2.95148i	0.0327251	+	0.171551i
$297$	−4.55588	+	4.85152i	−0.264359	+	0.281514i
$298$	−3.87484	+	9.78672i	−0.224463	+	0.566930i
$299$	8.14054	+	25.0540i	0.470779	+	1.44891i
$300$		0			0
$301$	0.803553	−	2.47308i	0.0463160	−	0.142546i
$302$	−28.9946	−	23.9864i	−1.66845	−	1.38026i
$303$	2.33323	+	1.09794i	0.134041	+	0.0630748i
$304$	−27.4457	−	25.7732i	−1.57412	−	1.47819i
$305$		0			0
$306$	16.4762	−	2.08143i	0.941883	−	0.118987i
$307$		−	3.63915i		−	0.207698i	−0.994593	−	0.103849i	$-0.966884\pi$
$307$		−	3.63915i		−	0.207698i	0.994593	−	0.103849i	$-0.0331158\pi$
$308$	−1.19176	−	9.43372i	−0.0679066	−	0.537536i
$309$	−7.05052	−	8.52261i	−0.401090	−	0.484834i
$310$		0			0
$311$	−1.85096	+	29.4201i	−0.104958	+	1.66826i	0.495501	+	0.868607i	$0.334984\pi$
$311$	−1.85096	+	29.4201i	−0.104958	+	1.66826i	−0.600459	+	0.799655i	$0.705016\pi$
$312$	0.569949	−	2.21981i	0.0322670	−	0.125672i
$313$	6.43068	−	25.0459i	0.363484	−	1.41568i	−0.479408	−	0.877592i	$-0.659148\pi$
$313$	6.43068	−	25.0459i	0.363484	−	1.41568i	0.842892	−	0.538084i	$-0.180852\pi$
$314$	−1.60363	+	25.4889i	−0.0904980	+	1.43842i
$315$		0			0
$316$	9.52289	+	11.5112i	0.535704	+	0.647555i
$317$	2.91267	+	23.0562i	0.163592	+	1.29496i	0.833500	+	0.552520i	$0.186334\pi$
$317$	2.91267	+	23.0562i	0.163592	+	1.29496i	−0.669908	+	0.742444i	$0.733666\pi$
$318$			10.2338i			0.573881i
$319$	4.58664	−	0.579427i	0.256803	−	0.0324417i
$320$		0			0
$321$	0.594638	+	0.558402i	0.0331894	+	0.0311670i
$322$	33.8736	+	15.9397i	1.88770	+	0.888285i
$323$	−22.4057	−	18.5356i	−1.24668	−	1.03135i
$324$	−2.25704	+	6.94645i	−0.125391	+	0.385914i
$325$		0			0
$326$	1.16063	+	3.57207i	0.0642816	+	0.197838i
$327$	−0.781907	+	1.97487i	−0.0432396	+	0.109211i
$328$	4.61309	−	4.91244i	0.254715	−	0.271244i
$329$	−4.14401	−	21.7237i	−0.228467	−	1.19767i
$330$		0			0
$331$	−11.7520	+	11.0359i	−0.645948	+	0.606585i	−0.936666	−	0.350223i	$-0.886106\pi$
$331$	−11.7520	+	11.0359i	−0.645948	+	0.606585i	0.290719	+	0.956809i	$0.406106\pi$
$332$	13.1799	−	4.28242i	0.723343	−	0.235028i
$333$	−10.8818	−	2.07581i	−0.596317	−	0.113754i
$334$	1.37578	+	21.8673i	0.0752792	+	1.19653i
$335$		0			0
$336$	−6.26658	−	9.87455i	−0.341870	−	0.538701i
$337$	−33.2123	+	2.08954i	−1.80919	+	0.113825i	−0.931121	−	0.364711i	$-0.881168\pi$
$337$	−33.2123	+	2.08954i	−1.80919	+	0.113825i	−0.878068	+	0.478535i	$0.841168\pi$
$338$	−14.2399	−	9.03693i	−0.774550	−	0.491544i
$339$	−8.57489	+	10.3653i	−0.465724	+	0.562964i
$340$		0			0
$341$	−6.54238	−	1.67980i	−0.354290	−	0.0909662i
$342$	34.9774	−	16.4591i	1.89136	−	0.890008i
$343$	6.36641	+	2.06857i	0.343754	+	0.111692i
$344$	0.437402	+	0.240464i	0.0235831	+	0.0129649i
$345$		0			0
$346$	23.0364	+	2.91017i	1.23844	+	0.156452i
$347$	0.473752	−	3.75013i	0.0254323	−	0.201317i	−0.974279	−	0.225345i	$-0.927649\pi$
$347$	0.473752	−	3.75013i	0.0254323	−	0.201317i	0.999711	+	0.0240277i	$0.00764900\pi$
$348$	−2.85940	+	1.81463i	−0.153280	+	0.0972746i
$349$	26.6127	−	19.3352i	1.42454	−	1.03499i	0.433542	−	0.901133i	$-0.357263\pi$
$349$	26.6127	−	19.3352i	1.42454	−	1.03499i	0.991001	−	0.133858i	$-0.0427365\pi$
$350$		0			0
$351$	15.1756	+	11.0257i	0.810012	+	0.588508i
$352$	12.2587	+	0.771252i	0.653390	+	0.0411078i
$353$	−10.5368	−	19.1664i	−0.560818	−	1.02012i	−0.992975	−	0.118326i	$-0.962247\pi$
$353$	−10.5368	−	19.1664i	−0.560818	−	1.02012i	0.432157	−	0.901798i	$-0.357753\pi$
$354$	−2.77809	+	5.90374i	−0.147654	+	0.313780i
$355$		0			0
$356$	−3.91048	+	20.4995i	−0.207255	+	1.08647i
$357$	−5.30930	−	7.30762i	−0.280998	−	0.386760i
$358$	−10.9681	+	19.9509i	−0.579683	+	1.05444i
$359$	−14.3562	+	22.6218i	−0.757693	+	1.19393i	0.218246	+	0.975894i	$0.429966\pi$
$359$	−14.3562	+	22.6218i	−0.757693	+	1.19393i	−0.975940	+	0.218040i	$0.930034\pi$
$360$		0			0
$361$	−45.2679	−	17.9228i	−2.38252	−	0.943307i
$362$	−5.13674	−	12.9739i	−0.269981	−	0.681895i
$363$	4.67669	−	3.86889i	0.245462	−	0.203064i
$364$	−25.9583	+	6.66496i	−1.36059	+	0.349339i
$365$		0			0
$366$	5.40370	−	2.13948i	0.282456	−	0.111832i
$367$	4.74812	+	5.05623i	0.247850	+	0.263933i	0.840849	−	0.541270i	$-0.182056\pi$
$367$	4.74812	+	5.05623i	0.247850	+	0.263933i	−0.592999	+	0.805203i	$0.702056\pi$
$368$	−15.1673	+	20.8760i	−0.790652	+	1.08824i
$369$	10.5787	+	22.4809i	0.550706	+	1.17031i
$370$		0			0
$371$	−22.1732	+	12.1898i	−1.15118	+	0.632865i
$372$	4.86037	−	0.927165i	0.251998	−	0.0480713i
$373$	−1.61695	−	6.29761i	−0.0837225	−	0.326078i	0.912901	−	0.408180i	$-0.133836\pi$
$373$	−1.61695	−	6.29761i	−0.0837225	−	0.326078i	−0.996624	+	0.0821026i	$0.973836\pi$
$374$	11.1944			0.578851
$375$		0			0
$376$	4.24509			0.218924
$377$	−3.24048	−	12.6208i	−0.166893	−	0.650006i
$378$	26.1849	−	4.99504i	1.34681	−	0.256917i
$379$	1.62501	−	0.893354i	0.0834709	−	0.0458885i	−0.439472	−	0.898257i	$-0.644834\pi$
$379$	1.62501	−	0.893354i	0.0834709	−	0.0458885i	0.522942	+	0.852368i	$0.324834\pi$
$380$		0			0
$381$	0.535956	+	1.13896i	0.0274579	+	0.0583509i
$382$	−7.60685	+	10.4699i	−0.389200	+	0.535688i
$383$	20.3148	+	21.6331i	1.03804	+	1.10540i	0.994328	+	0.106355i	$0.0339179\pi$
$383$	20.3148	+	21.6331i	1.03804	+	1.10540i	0.0437106	+	0.999044i	$0.486082\pi$
$384$	3.59325	−	1.42267i	0.183368	−	0.0726003i
$385$		0			0
$386$	31.4598	−	8.07751i	1.60126	−	0.411134i
$387$	−1.41796	+	1.17304i	−0.0720790	+	0.0596289i
$388$	2.90576	+	7.33910i	0.147517	+	0.372587i
$389$	−21.3410	−	8.44948i	−1.08203	−	0.428406i	−0.241627	−	0.970369i	$-0.577681\pi$
$389$	−21.3410	−	8.44948i	−1.08203	−	0.428406i	−0.840402	+	0.541963i	$0.817681\pi$
$390$		0			0
$391$	−10.6789	+	16.8273i	−0.540056	+	0.850993i
$392$	1.63020	−	2.96532i	0.0823373	−	0.149771i
$393$	5.89802	+	8.11793i	0.297516	+	0.409495i
$394$	0.335461	−	1.75855i	0.0169003	−	0.0885944i
$395$		0			0
$396$	−2.86522	+	6.08890i	−0.143983	+	0.305979i
$397$	5.67387	+	10.3207i	0.284763	+	0.517982i	0.979542	−	0.201242i	$-0.0644976\pi$
$397$	5.67387	+	10.3207i	0.284763	+	0.517982i	−0.694779	+	0.719224i	$0.744498\pi$
$398$	2.08361	+	0.131090i	0.104442	+	0.00657094i
$399$	−17.0099	−	12.3584i	−0.851562	−	0.618696i
$400$		0			0
$401$	−9.77910	+	7.10493i	−0.488345	+	0.354803i	−0.804547	−	0.593888i	$-0.797592\pi$
$401$	−9.77910	+	7.10493i	−0.488345	+	0.354803i	0.316203	+	0.948692i	$0.397592\pi$
$402$	2.72492	−	1.72929i	0.135907	−	0.0862491i
$403$	−2.38607	+	18.8877i	−0.118859	+	0.940864i
$404$	5.74259	+	0.725458i	0.285705	+	0.0360929i
$405$		0			0
$406$	−16.2268	−	8.92075i	−0.805322	−	0.442729i
$407$	−7.10189	−	2.30754i	−0.352027	−	0.114381i
$408$	1.56883	−	0.738236i	0.0776687	−	0.0365481i
$409$	22.4075	+	5.75326i	1.10798	+	0.284480i	0.757985	−	0.652272i	$-0.226184\pi$
$409$	22.4075	+	5.75326i	1.10798	+	0.284480i	0.349993	+	0.936752i	$0.386184\pi$
$410$		0			0
$411$	2.24471	−	2.71339i	0.110724	−	0.133842i
$412$	−20.9632	−	13.3036i	−1.03278	−	0.655423i
$413$	−16.1006	+	1.01296i	−0.792257	+	0.0498446i
$414$	−14.1962	−	22.3696i	−0.697705	−	1.09941i
$415$		0			0
$416$	−2.17377	−	34.5511i	−0.106578	−	1.69401i
$417$	6.30865	+	1.20344i	0.308936	+	0.0589327i
$418$	24.7819	−	8.05214i	1.21212	−	0.393843i
$419$	7.43275	−	6.97982i	0.363114	−	0.340987i	−0.481419	−	0.876491i	$-0.659878\pi$
$419$	7.43275	−	6.97982i	0.363114	−	0.340987i	0.844533	+	0.535504i	$0.179878\pi$
$420$		0			0
$421$	−5.33654	−	27.9751i	−0.260087	−	1.36343i	−0.837261	−	0.546804i	$-0.815844\pi$
$421$	−5.33654	−	27.9751i	−0.260087	−	1.36343i	0.577174	−	0.816621i	$-0.304156\pi$
$422$	−13.4661	+	14.3399i	−0.655518	+	0.698056i
$423$	−5.76158	+	14.5521i	−0.280138	+	0.707547i
$424$	−1.50088	−	4.61924i	−0.0728894	−	0.224330i
$425$		0			0
$426$	3.54884	−	10.9222i	0.171942	−	0.529183i
$427$	11.0721	+	9.15965i	0.535817	+	0.443266i
$428$	1.65677	+	0.779617i	0.0800830	+	0.0376842i
$429$	4.15196	+	3.89895i	0.200459	+	0.188243i
$430$		0			0
$431$	24.5473	−	3.10104i	1.18240	−	0.149372i	0.490550	−	0.871413i	$-0.336796\pi$
$431$	24.5473	−	3.10104i	1.18240	−	0.149372i	0.691850	+	0.722041i	$0.256796\pi$
$432$			18.3741i			0.884026i
$433$	−3.57155	−	28.2717i	−0.171638	−	1.35865i	−0.808873	−	0.587983i	$-0.799922\pi$
$433$	−3.57155	−	28.2717i	−0.171638	−	1.35865i	0.637236	−	0.770669i	$-0.280078\pi$
$434$	17.2453	+	20.8460i	0.827801	+	1.00064i
$435$		0			0
$436$	−0.299370	+	4.75834i	−0.0143372	+	0.227883i
$437$	−11.5369	+	44.9331i	−0.551883	+	2.14944i
$438$	1.58617	−	6.17772i	0.0757901	−	0.295183i
$439$	−1.23953	+	19.7017i	−0.0591595	+	0.940313i	0.850767	+	0.525543i	$0.176138\pi$
$439$	−1.23953	+	19.7017i	−0.0591595	+	0.940313i	−0.909926	+	0.414770i	$0.863862\pi$
$440$		0			0
$441$	7.95249	+	9.61291i	0.378690	+	0.457758i
$442$	−3.95446	−	31.3028i	−0.188094	−	1.48892i
$443$			31.5781i			1.50032i	0.661256	+	0.750161i	$0.270024\pi$
$443$			31.5781i			1.50032i	−0.661256	+	0.750161i	$0.729976\pi$
$444$	5.42701	−	0.685591i	0.257555	−	0.0325367i
$445$		0			0
$446$	17.2140	+	16.1650i	0.815106	+	0.765435i
$447$	−3.66605	−	1.72511i	−0.173398	−	0.0815951i
$448$	−13.4034	−	11.0883i	−0.633251	−	0.523871i
$449$	−9.17247	+	28.2299i	−0.432875	+	1.33225i	0.462373	+	0.886686i	$0.346998\pi$
$449$	−9.17247	+	28.2299i	−0.432875	+	1.33225i	−0.895248	+	0.445568i	$0.853002\pi$
$450$		0			0
$451$	5.17533	+	15.9280i	0.243697	+	0.750021i
$452$	−11.1160	+	28.0758i	−0.522852	+	1.32057i
$453$	9.91551	−	10.5589i	0.465871	−	0.496102i
$454$	0.514279	+	2.69594i	0.0241363	+	0.126527i
$455$		0			0
$456$	2.94202	−	2.76274i	0.137773	−	0.129377i
$457$	13.9907	−	4.54587i	0.654459	−	0.212647i	0.0370798	−	0.999312i	$-0.488194\pi$
$457$	13.9907	−	4.54587i	0.654459	−	0.212647i	0.617379	+	0.786666i	$0.288194\pi$
$458$	−29.0218	−	5.53620i	−1.35610	−	0.258690i
$459$	0.891074	+	14.1632i	0.0415918	+	0.661082i
$460$		0			0
$461$	3.16651	+	4.98962i	0.147479	+	0.232390i	0.910034	−	0.414534i	$-0.136055\pi$
$461$	3.16651	+	4.98962i	0.147479	+	0.232390i	−0.762555	+	0.646923i	$0.776055\pi$
$462$	8.07815	−	0.508234i	0.375830	−	0.0236452i
$463$	11.4026	+	7.23633i	0.529925	+	0.336301i	0.773722	−	0.633526i	$-0.218393\pi$
$463$	11.4026	+	7.23633i	0.529925	+	0.336301i	−0.243796	+	0.969826i	$0.578393\pi$
$464$	8.13578	−	9.83447i	0.377694	−	0.456554i
$465$		0			0
$466$	−40.0679	−	10.2877i	−1.85611	−	0.476568i
$467$	−6.01494	+	2.83042i	−0.278338	+	0.130976i	−0.559882	−	0.828572i	$-0.689154\pi$
$467$	−6.01494	+	2.83042i	−0.278338	+	0.130976i	0.281544	+	0.959548i	$0.409154\pi$
$468$	18.0384	+	5.86103i	0.833825	+	0.270926i
$469$	6.99257	+	3.84420i	0.322887	+	0.177509i
$470$		0			0
$471$	−9.75318	−	1.23211i	−0.449403	−	0.0567728i
$472$	0.388112	−	3.07222i	0.0178643	−	0.141411i
$473$	−1.04737	+	0.664684i	−0.0481583	+	0.0305622i
$474$	−10.2884	+	7.47494i	−0.472561	+	0.343335i
$475$		0			0
$476$	−16.4032	−	11.9176i	−0.751841	−	0.546244i
$477$	17.8717	+	1.12439i	0.818290	+	0.0514825i
$478$	−5.40000	−	9.82256i	−0.246990	−	0.449274i
$479$	13.2795	−	28.2204i	0.606757	−	1.28942i	−0.331490	−	0.943459i	$-0.607551\pi$
$479$	13.2795	−	28.2204i	0.606757	−	1.28942i	0.938247	−	0.345966i	$-0.112449\pi$
$480$		0			0
$481$	−3.94377	+	20.6740i	−0.179821	+	0.942653i
$482$	26.8682	+	36.9809i	1.22381	+	1.68443i
$483$	−6.94218	+	12.6278i	−0.315880	+	0.574583i
$484$	7.30022	−	11.5033i	0.331828	−	0.522878i
$485$		0			0
$486$	−27.1799	−	10.7613i	−1.23290	−	0.488141i
$487$	−0.159959	−	0.404011i	−0.00724844	−	0.0183075i	0.926107	−	0.377260i	$-0.123134\pi$
$487$	−0.159959	−	0.404011i	−0.00724844	−	0.0183075i	−0.933356	+	0.358953i	$0.883134\pi$
$488$	−2.12531	+	1.75821i	−0.0962083	+	0.0795904i
$489$	−1.40031	+	0.359539i	−0.0633243	+	0.0162589i
$490$		0			0
$491$	4.34727	−	1.72120i	0.196189	−	0.0776769i	−0.267975	−	0.963426i	$-0.586355\pi$
$491$	4.34727	−	1.72120i	0.196189	−	0.0776769i	0.464165	+	0.885749i	$0.346355\pi$
$492$	−8.39828	−	8.94326i	−0.378624	−	0.403193i
$493$	5.79431	−	7.97519i	0.260963	−	0.359184i
$494$	−31.2703	−	66.4528i	−1.40692	−	2.98985i
$495$		0			0
$496$	−16.3415	+	8.98384i	−0.733757	+	0.403386i
$497$	27.8920	−	5.32069i	1.25113	−	0.238666i
$498$	2.93369	+	11.4260i	0.131462	+	0.512010i
$499$	11.7643			0.526641			0.263320	−	0.964708i	$-0.415182\pi$
$499$	11.7643			0.526641			0.263320	+	0.964708i	$0.415182\pi$
$500$		0			0
$501$	−8.43390			−0.376799
$502$	2.27575	+	8.86345i	0.101572	+	0.395595i
$503$	11.1884	−	2.13429i	0.498864	−	0.0951635i	0.0681928	−	0.997672i	$-0.478277\pi$
$503$	11.1884	−	2.13429i	0.498864	−	0.0951635i	0.430672	+	0.902509i	$0.358277\pi$
$504$	−4.99401	+	2.74548i	−0.222451	+	0.122293i
$505$		0			0
$506$	−7.60395	−	16.1592i	−0.338037	−	0.718364i
$507$	3.81584	−	5.25205i	0.169467	−	0.233252i
$508$	1.93420	+	2.05971i	0.0858162	+	0.0913850i
$509$	−1.15411	+	0.456944i	−0.0511549	+	0.0202537i	−0.393563	−	0.919298i	$-0.628758\pi$
$509$	−1.15411	+	0.456944i	−0.0511549	+	0.0202537i	0.342408	+	0.939551i	$0.388758\pi$
$510$		0			0
$511$	15.2745	−	3.92181i	0.675702	−	0.173491i
$512$	21.4252	−	17.7245i	0.946870	−	0.783319i
$513$	12.1602	+	30.7132i	0.536886	+	1.35602i
$514$	40.3757	+	15.9859i	1.78090	+	0.705107i
$515$		0			0
$516$	0.486908	−	0.767244i	0.0214349	−	0.0337761i
$517$	−5.08251	+	9.24506i	−0.223529	+	0.406597i
$518$	17.5804	+	24.1974i	0.772440	+	1.06317i
$519$	−1.67476	+	8.77941i	−0.0735139	+	0.385373i
$520$		0			0
$521$	1.96892	−	4.18416i	0.0862598	−	0.183311i	−0.857043	−	0.515245i	$-0.827701\pi$
$521$	1.96892	−	4.18416i	0.0862598	−	0.183311i	0.943303	+	0.331933i	$0.107701\pi$
$522$	6.31325	+	11.4838i	0.276324	+	0.502631i
$523$	22.6027	+	1.42204i	0.988347	+	0.0621816i	0.548727	−	0.836002i	$-0.315113\pi$
$523$	22.6027	+	1.42204i	0.988347	+	0.0621816i	0.439621	+	0.898183i	$0.355113\pi$
$524$	18.2221	+	13.2391i	0.796036	+	0.578354i
$525$		0			0
$526$	17.0913	−	12.4176i	0.745218	−	0.541432i
$527$	−12.1608	+	7.71745i	−0.529731	+	0.336178i
$528$	−0.699247	+	5.53511i	−0.0304308	+	0.240885i
$529$	8.72537	+	1.10227i	0.379364	+	0.0479248i
$530$		0			0
$531$	10.0048	+	5.50017i	0.434170	+	0.238687i
$532$	−44.8854	−	14.5841i	−1.94603	−	0.632303i
$533$	42.7110	−	20.0982i	1.85002	−	0.870552i
$534$	−17.2064	−	4.41785i	−0.744593	−	0.191179i
$535$		0			0
$536$	−0.976340	+	1.18019i	−0.0421715	+	0.0509765i
$537$	−7.39933	−	4.69576i	−0.319305	−	0.202637i
$538$	31.0326	−	1.95241i	1.33791	−	0.0841743i
$539$	4.50615	+	7.10056i	0.194094	+	0.305843i
$540$		0			0
$541$	−0.0767460	−	1.21984i	−0.00329957	−	0.0524451i	0.996032	−	0.0889914i	$-0.0283644\pi$
$541$	−0.0767460	−	1.21984i	−0.00329957	−	0.0524451i	−0.999332	+	0.0365463i	$0.988364\pi$
$542$	53.3087	+	10.1692i	2.28980	+	0.436804i
$543$	5.10827	−	1.65978i	0.219217	−	0.0712279i
$544$	19.0924	−	17.9290i	0.818582	−	0.768699i
$545$		0			0
$546$	−4.27479	−	22.4092i	−0.182944	−	0.959026i
$547$	−1.59742	+	1.70108i	−0.0683008	+	0.0727329i	−0.762211	−	0.647328i	$-0.775886\pi$
$547$	−1.59742	+	1.70108i	−0.0683008	+	0.0727329i	0.693911	+	0.720061i	$0.255886\pi$
$548$	2.90992	−	7.34961i	0.124305	−	0.313960i
$549$	−3.14257	−	9.67183i	−0.134122	−	0.412784i
$550$		0			0
$551$	7.09075	−	21.8231i	0.302076	−	0.929695i
$552$	−2.13129	−	1.76316i	−0.0907137	−	0.0750449i
$553$	−28.4507	−	13.3879i	−1.20984	−	0.569310i
$554$	39.8416	+	37.4138i	1.69271	+	1.58956i
$555$		0			0
$556$	14.3025	−	1.80683i	0.606563	−	0.0766267i
$557$			21.2885i			0.902025i	0.892518	+	0.451012i	$0.148937\pi$
$557$			21.2885i			0.902025i	−0.892518	+	0.451012i	$0.851063\pi$
$558$	−2.39972	−	18.9957i	−0.101588	−	0.804154i
$559$	2.22863	+	2.69395i	0.0942609	+	0.113942i
$560$		0			0
$561$	−0.270565	+	4.30050i	−0.0114233	+	0.181567i
$562$	−0.358486	+	1.39621i	−0.0151218	+	0.0588956i
$563$	5.18651	−	20.2001i	0.218585	−	0.851334i	−0.760742	−	0.649054i	$-0.775165\pi$
$563$	5.18651	−	20.2001i	0.218585	−	0.851334i	0.979328	−	0.202280i	$-0.0648351\pi$
$564$	0.485265	−	7.71307i	0.0204334	−	0.324779i
$565$		0			0
$566$	−16.2706	−	19.6678i	−0.683906	−	0.826700i
$567$	−1.92668	−	15.2512i	−0.0809128	−	0.640491i
$568$			5.45047i			0.228697i
$569$	−37.9918	+	4.79948i	−1.59270	+	0.201205i	−0.871100	−	0.491106i	$-0.836593\pi$
$569$	−37.9918	+	4.79948i	−1.59270	+	0.201205i	−0.721600	+	0.692310i	$0.756593\pi$
$570$		0			0
$571$	5.11943	+	4.80746i	0.214241	+	0.201186i	0.784237	−	0.620462i	$-0.213055\pi$
$571$	5.11943	+	4.80746i	0.214241	+	0.201186i	−0.569995	+	0.821648i	$0.693055\pi$
$572$	11.5681	+	5.44356i	0.483688	+	0.227606i
$573$	−3.83832	−	3.17533i	−0.160348	−	0.132651i
$574$	20.7291	−	63.7977i	0.865217	−	2.66287i
$575$		0			0
$576$	3.80425	+	11.7083i	0.158510	+	0.487845i
$577$	−9.73034	+	24.5760i	−0.405079	+	1.02311i	0.573858	+	0.818955i	$0.305446\pi$
$577$	−9.73034	+	24.5760i	−0.405079	+	1.02311i	−0.978938	+	0.204159i	$0.934554\pi$
$578$	−5.89571	+	6.27830i	−0.245229	+	0.261143i
$579$	2.34272	+	12.2810i	0.0973600	+	0.510379i
$580$		0			0
$581$	−21.2619	+	19.9663i	−0.882093	+	0.828340i
$582$	−6.39027	+	2.07633i	−0.264885	+	0.0860665i
$583$	11.8569	+	2.26182i	0.491061	+	0.0936749i
$584$	0.190071	+	3.02109i	0.00786518	+	0.125013i
$585$		0			0
$586$	−5.66175	−	8.92149i	−0.233885	−	0.368543i
$587$	8.45185	−	0.531745i	0.348845	−	0.0219475i	0.112598	−	0.993641i	$-0.464083\pi$
$587$	8.45185	−	0.531745i	0.348845	−	0.0219475i	0.236247	+	0.971693i	$0.424083\pi$
$588$	−5.20145	−	3.30094i	−0.214504	−	0.136128i
$589$	−21.3700	+	25.8319i	−0.880536	+	1.06438i
$590$		0			0
$591$	0.667463	+	0.171375i	0.0274558	+	0.00704945i
$592$	−18.6540	+	8.77789i	−0.766673	+	0.360769i
$593$	−7.72851	−	2.51114i	−0.317372	−	0.103120i	0.145999	−	0.989285i	$-0.453360\pi$
$593$	−7.72851	−	2.51114i	−0.317372	−	0.103120i	−0.463371	+	0.886164i	$0.653360\pi$
$594$	−11.1436	−	6.12627i	−0.457229	−	0.251364i
$595$		0			0
$596$	−9.02295	−	1.13986i	−0.369594	−	0.0466906i
$597$	−0.100720	+	0.797281i	−0.00412220	+	0.0326305i
$598$	−42.4995	+	26.9710i	−1.73793	+	1.10293i
$599$	−5.97439	+	4.34065i	−0.244107	+	0.177354i	−0.703111	−	0.711080i	$-0.748206\pi$
$599$	−5.97439	+	4.34065i	−0.244107	+	0.177354i	0.459004	+	0.888434i	$0.348206\pi$
$600$		0			0
$601$	−4.03308	−	2.93021i	−0.164513	−	0.119526i	0.502483	−	0.864587i	$-0.332420\pi$
$601$	−4.03308	−	2.93021i	−0.164513	−	0.119526i	−0.666996	+	0.745062i	$0.732420\pi$
$602$	4.95880	+	0.311981i	0.202106	+	0.0127154i
$603$	−2.72056	−	4.94867i	−0.110790	−	0.201526i
$604$	13.8436	−	29.4192i	0.563289	−	1.19705i
$605$		0			0
$606$	−0.923254	+	4.83987i	−0.0375046	+	0.196606i
$607$	−27.6191	−	38.0144i	−1.12102	−	1.54296i	−0.804089	−	0.594509i	$-0.797347\pi$
$607$	−27.6191	−	38.0144i	−1.12102	−	1.54296i	−0.316934	−	0.948448i	$-0.602653\pi$
$608$	29.3700	−	53.4239i	1.19111	−	2.16662i
$609$	3.81923	−	6.01814i	0.154763	−	0.243867i
$610$		0			0
$611$	27.6471	+	10.9463i	1.11848	+	0.442839i
$612$	5.28224	+	13.3414i	0.213522	+	0.539295i
$613$	12.1293	−	10.0342i	0.489898	−	0.405279i	−0.359407	−	0.933181i	$-0.617021\pi$
$613$	12.1293	−	10.0342i	0.489898	−	0.405279i	0.849306	+	0.527902i	$0.177021\pi$
$614$	6.73503	−	1.72926i	0.271804	−	0.0697873i
$615$		0			0
$616$	−3.57173	+	1.41415i	−0.143909	+	0.0569776i
$617$	6.59071	+	7.01839i	0.265332	+	0.282550i	0.847814	−	0.530294i	$-0.177918\pi$
$617$	6.59071	+	7.01839i	0.265332	+	0.282550i	−0.582482	+	0.812844i	$0.697918\pi$
$618$	12.4226	−	17.0983i	0.499711	−	0.687793i
$619$	6.59026	+	14.0050i	0.264885	+	0.562909i	0.992382	−	0.123202i	$-0.0393163\pi$
$619$	6.59026	+	14.0050i	0.264885	+	0.562909i	−0.727497	+	0.686111i	$0.759316\pi$
$620$		0			0
$621$	19.8394	−	10.9068i	0.796126	−	0.437674i
$622$	−55.3277	+	10.5543i	−2.21844	+	0.423190i
$623$	−10.9232	−	42.5429i	−0.437627	−	1.70445i
$624$	15.7247			0.629492
$625$		0			0
$626$	49.4084			1.97476
$627$	2.49438	+	9.71495i	0.0996158	+	0.387978i
$628$	−21.6759	+	4.13489i	−0.864961	+	0.165000i
$629$	−13.9532	+	7.67084i	−0.556351	+	0.305856i
$630$		0			0
$631$	−1.55429	−	3.30303i	−0.0618752	−	0.131491i	0.871498	−	0.490400i	$-0.163149\pi$
$631$	−1.55429	−	3.30303i	−0.0618752	−	0.131491i	−0.933373	+	0.358908i	$0.883149\pi$
$632$	3.54762	−	4.88288i	0.141117	−	0.194231i
$633$	−5.18341	−	5.51977i	−0.206022	−	0.219391i
$634$	−41.2863	+	16.3464i	−1.63969	+	0.649199i
$635$		0			0
$636$	−8.56446	+	2.19898i	−0.339603	+	0.0871952i
$637$	18.2633	−	15.1087i	0.723619	−	0.598630i
$638$	3.25184	+	8.21322i	0.128742	+	0.325164i
$639$	−18.6841	−	7.39756i	−0.739131	−	0.292643i
$640$		0			0
$641$	7.86485	−	12.3930i	0.310643	−	0.489495i	−0.652756	−	0.757569i	$-0.726387\pi$
$641$	7.86485	−	12.3930i	0.310643	−	0.489495i	0.963398	+	0.268074i	$0.0863871\pi$
$642$	−0.750880	+	1.36585i	−0.0296349	+	0.0539056i
$643$	−23.9075	−	32.9059i	−0.942820	−	1.29768i	−0.954644	−	0.297750i	$-0.903764\pi$
$643$	−23.9075	−	32.9059i	−0.942820	−	1.29768i	0.0118237	−	0.999930i	$-0.496236\pi$
$644$	−6.06108	+	31.7733i	−0.238840	+	1.25204i
$645$		0			0
$646$	23.6573	−	50.2742i	0.930782	−	1.97801i
$647$	4.24502	+	7.72166i	0.166889	+	0.303570i	0.946506	−	0.322687i	$-0.104586\pi$
$647$	4.24502	+	7.72166i	0.166889	+	0.303570i	−0.779617	+	0.626257i	$0.784586\pi$
$648$	2.94494	+	0.185280i	0.115688	+	0.00727849i
$649$	6.22609	+	4.52352i	0.244395	+	0.177564i
$650$		0			0
$651$	−8.42509	+	6.12119i	−0.330205	+	0.239908i
$652$	−2.74001	+	1.73886i	−0.107307	+	0.0680992i
$653$	−2.27811	+	18.0331i	−0.0891493	+	0.705689i	0.882675	+	0.469983i	$0.155740\pi$
$653$	−2.27811	+	18.0331i	−0.0891493	+	0.705689i	−0.971824	+	0.235706i	$0.924260\pi$
$654$	−4.02647	−	0.508661i	−0.157447	−	0.0198902i
$655$		0			0
$656$	40.5181	+	22.2750i	1.58197	+	0.869694i
$657$	−10.6142	−	3.44876i	−0.414099	−	0.134549i
$658$	38.2351	−	17.9921i	1.49056	−	0.701404i
$659$	4.71838	+	1.21147i	0.183802	+	0.0471923i	0.339469	−	0.940617i	$-0.389753\pi$
$659$	4.71838	+	1.21147i	0.183802	+	0.0471923i	−0.155667	+	0.987810i	$0.549753\pi$
$660$		0			0
$661$	−19.7223	+	23.8402i	−0.767110	+	0.927277i	−0.998966	−	0.0454737i	$-0.985520\pi$
$661$	−19.7223	+	23.8402i	−0.767110	+	0.927277i	0.231856	+	0.972750i	$0.425520\pi$
$662$	−26.0085	−	16.5055i	−1.01085	−	0.641505i
$663$	12.1210	−	0.762587i	0.470740	−	0.0296164i
$664$	−2.99992	−	4.72712i	−0.116420	−	0.183448i
$665$		0			0
$666$	−1.32910	−	21.1254i	−0.0515015	−	0.818592i
$667$	−15.4481	−	2.94687i	−0.598151	−	0.114103i
$668$	−18.0048	+	5.85011i	−0.696626	+	0.226348i
$669$	−6.62607	+	6.22229i	−0.256179	+	0.240568i
$670$		0			0
$671$	−1.28450	−	6.73360i	−0.0495877	−	0.259948i
$672$	12.9635	−	13.8048i	0.500079	−	0.532530i
$673$	−9.54104	+	24.0979i	−0.367780	+	0.928906i	0.621571	+	0.783358i	$0.286495\pi$
$673$	−9.54104	+	24.0979i	−0.367780	+	0.928906i	−0.989351	+	0.145549i	$0.953505\pi$
$674$	−19.6490	−	60.4735i	−0.756852	−	2.32935i
$675$		0			0
$676$	4.50305	−	13.8590i	0.173194	−	0.533037i
$677$	4.06141	+	3.35989i	0.156093	+	0.129131i	0.712192	−	0.701985i	$-0.247703\pi$
$677$	4.06141	+	3.35989i	0.156093	+	0.129131i	−0.556099	+	0.831116i	$0.687703\pi$
$678$	−23.2578	−	10.9443i	−0.893209	−	0.420312i
$679$	−12.1104	−	11.3725i	−0.464756	−	0.436435i
$680$		0			0
$681$	−1.04811	+	0.132408i	−0.0401638	+	0.00507387i
$682$		−	12.9063i		−	0.494207i
$683$	1.28334	+	10.1587i	0.0491056	+	0.388711i	0.997444	+	0.0714506i	$0.0227628\pi$
$683$	1.28334	+	10.1587i	0.0491056	+	0.388711i	−0.948339	+	0.317260i	$0.897237\pi$
$684$	21.2902	+	25.7354i	0.814049	+	0.984017i
$685$		0			0
$686$	−0.803128	+	12.7653i	−0.0306636	+	0.487383i
$687$	2.82825	−	11.0153i	0.107905	−	0.420260i
$688$	−0.851701	+	3.31716i	−0.0324708	+	0.126465i
$689$	2.13621	−	33.9541i	0.0813831	−	1.29355i
$690$		0			0
$691$	17.9512	+	21.6993i	0.682895	+	0.825479i	0.992091	−	0.125520i	$-0.0400598\pi$
$691$	17.9512	+	21.6993i	0.682895	+	0.825479i	−0.309196	+	0.950998i	$0.600060\pi$
$692$	2.51447	+	19.9041i	0.0955858	+	0.756639i
$693$		−	14.1631i		−	0.538013i
$694$	7.16553	−	0.905217i	0.272000	−	0.0343616i
$695$		0			0
$696$	0.997359	+	0.936583i	0.0378048	+	0.0355011i
$697$	32.3126	+	15.2051i	1.22393	+	0.575936i
$698$	48.4298	+	40.0646i	1.83310	+	1.51647i
$699$	4.92058	−	15.1440i	0.186113	−	0.572798i
$700$		0			0
$701$	−6.89414	−	21.2180i	−0.260388	−	0.801392i	−0.992720	−	0.120444i	$-0.961568\pi$
$701$	−6.89414	−	21.2180i	−0.260388	−	0.801392i	0.732332	−	0.680948i	$-0.238432\pi$
$702$	−13.1942	+	33.3248i	−0.497984	+	1.25776i
$703$	−25.3716	+	27.0180i	−0.956908	+	1.01900i
$704$	1.55496	+	8.15140i	0.0586048	+	0.307217i
$705$		0			0
$706$	30.4646	−	28.6081i	1.14655	−	1.07668i
$707$	−11.5861	+	3.76457i	−0.435742	+	0.141581i
$708$	−5.53768	−	1.05637i	−0.208119	−	0.0397008i
$709$	−2.53129	−	40.2336i	−0.0950644	−	1.51101i	−0.699662	−	0.714474i	$-0.746666\pi$
$709$	−2.53129	−	40.2336i	−0.0950644	−	1.51101i	0.604597	−	0.796531i	$-0.293334\pi$
$710$		0			0
$711$	11.9235	+	18.7884i	0.447165	+	0.704620i
$712$	8.41443	−	0.529391i	0.315344	−	0.0198398i
$713$	19.4005	+	12.3119i	0.726554	+	0.461085i
$714$	11.0014	−	13.2984i	0.411718	−	0.497682i
$715$		0			0
$716$	−19.0534	−	4.89207i	−0.712058	−	0.182825i
$717$	3.90399	−	1.83708i	0.145797	−	0.0686070i
$718$	−48.6883	−	15.8198i	−1.81703	−	0.590389i
$719$	−21.4878	−	11.8130i	−0.801358	−	0.440550i	0.0277664	−	0.999614i	$-0.491161\pi$
$719$	−21.4878	−	11.8130i	−0.801358	−	0.440550i	−0.829124	+	0.559064i	$0.811161\pi$
$720$		0			0
$721$	51.8435	+	6.54935i	1.93075	+	0.243911i
$722$	11.6595	−	92.2945i	0.433922	−	3.43484i
$723$	−14.8561	+	9.42799i	−0.552506	+	0.350631i
$724$	9.75391	−	7.08663i	0.362501	−	0.263373i
$725$		0			0
$726$	9.38248	+	6.81677i	0.348217	+	0.252994i
$727$	9.30188	+	0.585224i	0.344987	+	0.0217048i	0.234339	−	0.972155i	$-0.424707\pi$
$727$	9.30188	+	0.585224i	0.344987	+	0.0217048i	0.110648	+	0.993860i	$0.464707\pi$
$728$	5.21606	+	9.48799i	0.193320	+	0.351648i
$729$	−0.860070	+	1.82774i	−0.0318544	+	0.0676941i
$730$		0			0
$731$	−0.495642	+	2.59824i	−0.0183320	+	0.0960995i
$732$	2.95161	+	4.06255i	0.109095	+	0.150156i
$733$	−4.77249	+	8.68112i	−0.176276	+	0.320645i	−0.949654	−	0.313300i	$-0.898565\pi$
$733$	−4.77249	+	8.68112i	−0.176276	+	0.320645i	0.773378	+	0.633945i	$0.218565\pi$
$734$	−7.10141	+	11.1900i	−0.262118	+	0.413031i
$735$		0			0
$736$	−38.8493	−	15.3815i	−1.43200	−	0.566970i
$737$	−1.40131	−	3.53930i	−0.0516179	−	0.130372i
$738$	−36.5789	+	30.2607i	−1.34649	+	1.11391i
$739$	41.3865	−	10.6263i	1.52243	−	0.390893i	0.607437	−	0.794367i	$-0.292198\pi$
$739$	41.3865	−	10.6263i	1.52243	−	0.390893i	0.914991	+	0.403474i	$0.132198\pi$
$740$		0			0
$741$	26.2846	−	10.4068i	0.965587	−	0.382303i
$742$	−33.0962	−	35.2439i	−1.21500	−	1.29384i
$743$	24.0118	−	33.0494i	0.880908	−	1.21247i	−0.0952609	−	0.995452i	$-0.530369\pi$
$743$	24.0118	−	33.0494i	0.880908	−	1.21247i	0.976169	−	0.217013i	$-0.0696315\pi$
$744$	−0.851126	−	1.80873i	−0.0312038	−	0.0663114i
$745$		0			0
$746$	10.8867	−	5.98502i	0.398591	−	0.219127i
$747$	20.2761	−	3.86787i	0.741863	−	0.141518i
$748$	2.40541	+	9.36844i	0.0879504	+	0.342544i
$749$	−3.85375			−0.140813
$750$		0			0
$751$	−50.6141			−1.84693			−0.923467	−	0.383677i	$-0.874658\pi$
$751$	−50.6141			−1.84693			−0.923467	+	0.383677i	$0.874658\pi$
$752$	7.24352	+	28.2116i	0.264144	+	1.02877i
$753$	−3.46002	+	0.660035i	−0.126090	+	0.0240530i
$754$	21.8177	−	11.9944i	0.794554	−	0.436810i
$755$		0			0
$756$	9.80675	+	20.8404i	0.356668	+	0.757958i
$757$	1.56838	−	2.15868i	0.0570036	−	0.0784587i	−0.779564	−	0.626323i	$-0.784559\pi$
$757$	1.56838	−	2.15868i	0.0570036	−	0.0784587i	0.836567	+	0.547864i	$0.184559\pi$
$758$	2.42552	+	2.58291i	0.0880987	+	0.0938156i
$759$	6.39157	−	2.53060i	0.231999	−	0.0918550i
$760$		0			0
$761$	−22.5131	+	5.78038i	−0.816099	+	0.209539i	−0.633593	−	0.773666i	$-0.718421\pi$
$761$	−22.5131	+	5.78038i	−0.816099	+	0.209539i	−0.182505	+	0.983205i	$0.558421\pi$
$762$	−1.85322	+	1.53312i	−0.0671351	+	0.0555390i
$763$	−3.69398	−	9.32993i	−0.133731	−	0.337766i
$764$	−10.3966	−	4.11632i	−0.376137	−	0.148923i
$765$		0			0
$766$	−30.3834	+	47.8766i	−1.09780	+	1.72985i
$767$	10.4496	−	19.0078i	0.377314	−	0.686332i
$768$	8.66897	+	11.9318i	0.312814	+	0.430552i
$769$	−0.192354	+	1.00835i	−0.00693645	+	0.0363622i	−0.985587	−	0.169168i	$-0.945892\pi$
$769$	−0.192354	+	1.00835i	−0.00693645	+	0.0363622i	0.978651	+	0.205530i	$0.0658919\pi$
$770$		0			0
$771$	−7.11706	+	15.1245i	−0.256315	+	0.544697i
$772$	13.5199	+	24.5925i	0.486590	+	0.885105i
$773$	1.80510	+	0.113567i	0.0649250	+	0.00408474i	0.0952198	−	0.995456i	$-0.469645\pi$
$773$	1.80510	+	0.113567i	0.0649250	+	0.00408474i	−0.0302948	+	0.999541i	$0.509645\pi$
$774$	−2.84475	−	2.06683i	−0.102252	−	0.0742907i
$775$		0			0
$776$	2.57989	−	1.87440i	0.0926125	−	0.0672869i
$777$	−9.72068	+	6.16893i	−0.348727	+	0.221309i
$778$	5.49672	−	43.5110i	0.197067	−	1.55995i
$779$	82.4697	+	10.4183i	2.95478	+	0.373276i
$780$		0			0
$781$	−11.8702	−	6.52567i	−0.424748	−	0.233507i
$782$	−36.2169	−	11.7676i	−1.29511	−	0.420808i
$783$	−10.1325	+	4.76800i	−0.362107	+	0.170395i
$784$	22.4883	+	5.77401i	0.803153	+	0.206215i
$785$		0			0
$786$	−12.2213	+	14.7730i	−0.435920	+	0.526937i
$787$	−0.931172	−	0.590940i	−0.0331927	−	0.0210647i	0.519127	−	0.854697i	$-0.326257\pi$
$787$	−0.931172	−	0.590940i	−0.0331927	−	0.0210647i	−0.552320	+	0.833632i	$0.686257\pi$
$788$	1.54378	−	0.0971266i	0.0549950	−	0.00345999i
$789$	4.35730	+	6.86600i	0.155124	+	0.244436i
$790$		0			0
$791$	−3.99056	−	63.4282i	−0.141888	−	2.25525i
$792$	2.67048	+	0.509422i	0.0948915	+	0.0181015i
$793$	−18.3753	+	5.97049i	−0.652525	+	0.212018i
$794$	−16.4046	+	15.4049i	−0.582176	+	0.546700i
$795$		0			0
$796$	0.338010	+	1.77191i	0.0119804	+	0.0628036i
$797$	3.50711	−	3.73469i	0.124228	−	0.132290i	−0.663847	−	0.747868i	$-0.731078\pi$
$797$	3.50711	−	3.73469i	0.124228	−	0.132290i	0.788076	+	0.615578i	$0.211078\pi$
$798$	14.7891	−	37.3530i	0.523529	−	1.32228i
$799$	6.95163	+	21.3949i	0.245931	+	0.756897i
$800$		0			0
$801$	−9.60560	+	29.5630i	−0.339397	+	1.04456i
$802$	−17.7960	−	14.7222i	−0.628400	−	0.519858i
$803$	−6.80696	−	3.20311i	−0.240212	−	0.113035i
$804$	2.03273	+	1.90886i	0.0716889	+	0.0673203i
$805$		0			0
$806$	−36.0895	+	4.55917i	−1.27120	+	0.160590i
$807$			11.9688i			0.421322i
$808$	−0.293083	−	2.31999i	−0.0103106	−	0.0816170i
$809$	−29.1541	−	35.2412i	−1.02500	−	1.23902i	−0.970651	−	0.240494i	$-0.922690\pi$
$809$	−29.1541	−	35.2412i	−1.02500	−	1.23902i	−0.0543527	−	0.998522i	$-0.517310\pi$
$810$		0			0
$811$	−1.51935	+	24.1494i	−0.0533515	+	0.847998i	0.876807	+	0.480842i	$0.159669\pi$
$811$	−1.51935	+	24.1494i	−0.0533515	+	0.847998i	−0.930159	+	0.367157i	$0.880331\pi$
$812$	3.97889	−	15.4968i	0.139632	−	0.543830i
$813$	−5.19508	+	20.2335i	−0.182199	+	0.709620i
$814$	0.895908	−	14.2401i	0.0314016	−	0.499114i
$815$		0			0
$816$	7.58304	+	9.16632i	0.265460	+	0.320886i
$817$	0.771675	+	6.10844i	0.0269975	+	0.213707i
$818$			44.2036i			1.54554i
$819$	−39.6041	+	5.00316i	−1.38388	+	0.174824i
$820$		0			0
$821$	6.37400	+	5.98558i	0.222454	+	0.208898i	0.787759	−	0.615984i	$-0.211241\pi$
$821$	6.37400	+	5.98558i	0.222454	+	0.208898i	−0.565305	+	0.824882i	$0.691241\pi$
$822$	6.08836	+	2.86496i	0.212356	+	0.0999271i
$823$	20.4324	+	16.9032i	0.712229	+	0.589207i	0.921374	−	0.388677i	$-0.127068\pi$
$823$	20.4324	+	16.9032i	0.712229	+	0.589207i	−0.209144	+	0.977885i	$0.567068\pi$
$824$	−3.09961	+	9.53961i	−0.107980	+	0.332328i
$825$		0			0
$826$	−9.52541	−	29.3162i	−0.331431	−	1.02004i
$827$	−12.3156	+	31.1057i	−0.428257	+	1.08165i	0.542173	+	0.840267i	$0.317602\pi$
$827$	−12.3156	+	31.1057i	−0.428257	+	1.08165i	−0.970429	+	0.241386i	$0.922398\pi$
$828$	15.6704	−	16.6872i	0.544583	−	0.579922i
$829$	9.08171	+	47.6080i	0.315421	+	1.65349i	0.688161	+	0.725558i	$0.258418\pi$
$829$	9.08171	+	47.6080i	0.315421	+	1.65349i	−0.372741	+	0.927936i	$0.621582\pi$
$830$		0			0
$831$	−15.3360	+	14.4014i	−0.531999	+	0.499581i
$832$	22.2443	−	7.22760i	0.771181	−	0.250572i
$833$	17.6145	+	3.36015i	0.610307	+	0.116422i
$834$	0.770538	+	12.2473i	0.0266815	+	0.424091i
$835$		0			0
$836$	12.0637	+	19.0094i	0.417233	+	0.657454i
$837$	16.3290	−	1.02734i	0.564414	−	0.0355099i
$838$	16.4496	+	10.4392i	0.568240	+	0.360616i
$839$	−6.76608	+	8.17879i	−0.233591	+	0.282363i	−0.874264	−	0.485451i	$-0.838655\pi$
$839$	−6.76608	+	8.17879i	−0.233591	+	0.282363i	0.640673	+	0.767814i	$0.278655\pi$
$840$		0			0
$841$	−20.5544	−	5.27748i	−0.708774	−	0.181982i
$842$	49.2381	−	23.1697i	1.69686	−	0.798481i
$843$	−0.527709	−	0.171463i	−0.0181753	−	0.00590550i
$844$	−14.8943	−	8.18824i	−0.512685	−	0.281851i
$845$		0			0
$846$	−29.6695	−	3.74813i	−1.02006	−	0.128863i
$847$	−3.59388	+	28.4485i	−0.123487	+	0.977503i
$848$	28.1372	−	17.8564i	0.966234	−	0.613191i
$849$	7.94892	−	5.77523i	0.272806	−	0.198205i
$850$		0			0
$851$	20.5507	+	14.9310i	0.704471	+	0.511828i
$852$	9.90317	+	0.623055i	0.339277	+	0.0213455i
$853$	−10.6875	−	19.4404i	−0.365931	−	0.665627i	0.627681	−	0.778470i	$-0.284004\pi$
$853$	−10.6875	−	19.4404i	−0.365931	−	0.665627i	−0.993613	+	0.112844i	$0.964004\pi$
$854$	−11.6906	+	24.8438i	−0.400044	+	0.850137i
$855$		0			0
$856$	0.138612	−	0.726631i	0.00473767	−	0.0248357i
$857$	3.31323	+	4.56026i	0.113178	+	0.155776i	0.861848	−	0.507167i	$-0.169307\pi$
$857$	3.31323	+	4.56026i	0.113178	+	0.155776i	−0.748670	+	0.662943i	$0.769307\pi$
$858$	−5.24290	+	9.53681i	−0.178990	+	0.325581i
$859$	−24.7863	+	39.0569i	−0.845696	+	1.33260i	0.0957381	+	0.995407i	$0.469479\pi$
$859$	−24.7863	+	39.0569i	−0.845696	+	1.33260i	−0.941434	+	0.337197i	$0.890521\pi$
$860$		0			0
$861$	24.0078	+	9.50535i	0.818183	+	0.323942i
$862$	17.4036	+	43.9564i	0.592768	+	1.49716i
$863$	−12.2307	+	10.1181i	−0.416337	+	0.344424i	−0.821889	−	0.569648i	$-0.807079\pi$
$863$	−12.2307	+	10.1181i	−0.416337	+	0.344424i	0.405552	+	0.914072i	$0.367079\pi$
$864$	−28.8176	+	7.39911i	−0.980395	+	0.251723i
$865$		0			0
$866$	50.6257	−	20.0441i	1.72033	−	0.681127i
$867$	−2.26940	−	2.41667i	−0.0770729	−	0.0820743i
$868$	−13.7401	+	18.9116i	−0.466369	+	0.641901i
$869$	6.38660	+	13.5722i	0.216651	+	0.460406i
$870$		0			0
$871$	−9.40186	+	5.16872i	−0.318570	+	0.175135i
$872$	1.89204	−	0.360926i	0.0640726	−	0.0122225i
$873$	2.92389	+	11.3878i	0.0989586	+	0.385418i
$874$	−88.6404			−2.99831
$875$		0			0
$876$	5.51086			0.186195
$877$	−2.95626	−	11.5139i	−0.0998258	−	0.388796i	0.898962	−	0.438027i	$-0.144323\pi$
$877$	−2.95626	−	11.5139i	−0.0998258	−	0.388796i	−0.998787	+	0.0492317i	$0.984323\pi$
$878$	−37.0513	+	7.06791i	−1.25042	+	0.238530i
$879$	3.56416	−	1.95941i	0.120216	−	0.0660894i
$880$		0			0
$881$	7.84789	+	16.6776i	0.264402	+	0.561883i	0.992308	−	0.123794i	$-0.0395061\pi$
$881$	7.84789	+	16.6776i	0.264402	+	0.561883i	−0.727906	+	0.685677i	$0.759506\pi$
$882$	−14.0118	+	19.2857i	−0.471803	+	0.649382i
$883$	−22.4361	−	23.8921i	−0.755036	−	0.804032i	0.230576	−	0.973054i	$-0.425939\pi$
$883$	−22.4361	−	23.8921i	−0.755036	−	0.804032i	−0.985612	+	0.169023i	$0.945939\pi$
$884$	25.3470	−	10.0356i	0.852513	−	0.337534i
$885$		0			0
$886$	−58.4420	+	15.0054i	−1.96340	+	0.504115i
$887$	15.0381	−	12.4406i	0.504929	−	0.417714i	−0.349771	−	0.936835i	$-0.613741\pi$
$887$	15.0381	−	12.4406i	0.504929	−	0.417714i	0.854701	+	0.519121i	$0.173741\pi$
$888$	−0.813527	−	2.05474i	−0.0273002	−	0.0689524i
$889$	−5.52921	−	2.18917i	−0.185444	−	0.0734224i
$890$		0			0
$891$	−3.92939	+	6.19174i	−0.131640	+	0.207431i
$892$	−9.82936	+	17.8795i	−0.329111	+	0.598652i
$893$	30.7786	+	42.3632i	1.02997	+	1.41763i
$894$	1.45065	−	7.60456i	0.0485169	−	0.254334i
$895$		0			0
$896$	−7.77381	+	16.5202i	−0.259705	+	0.551900i
$897$	−9.33410	−	16.9787i	−0.311657	−	0.566901i
$898$	−56.6041	−	3.56123i	−1.88890	−	0.118840i
$899$	−9.19474	−	6.68037i	−0.306662	−	0.222803i
$900$		0			0
$901$	20.8228	−	15.1287i	0.693709	−	0.504009i
$902$	−27.0190	+	17.1467i	−0.899633	+	0.570924i
$903$	−0.239704	+	1.89745i	−0.00797685	+	0.0631433i
$904$	12.1030	+	1.52897i	0.402541	+	0.0508527i
$905$		0			0
$906$	24.2532	+	13.3333i	0.805760	+	0.442970i
$907$	−21.3618	−	6.94088i	−0.709308	−	0.230468i	−0.0679268	−	0.997690i	$-0.521638\pi$
$907$	−21.3618	−	6.94088i	−0.709308	−	0.230468i	−0.641382	+	0.767222i	$0.721638\pi$
$908$	−2.14568	+	1.00968i	−0.0712070	+	0.0335075i
$909$	8.35067	+	2.14409i	0.276974	+	0.0711149i
$910$		0			0
$911$	−6.83416	+	8.26109i	−0.226426	+	0.273702i	−0.871476	−	0.490439i	$-0.836837\pi$
$911$	−6.83416	+	8.26109i	−0.226426	+	0.273702i	0.645050	+	0.764141i	$0.276837\pi$
$912$	23.3805	+	14.8377i	0.774204	+	0.491325i
$913$	13.8865	−	0.873667i	0.459578	−	0.0289142i
$914$	15.0612	+	23.7327i	0.498181	+	0.785008i
$915$		0			0
$916$	−1.60290	−	25.4774i	−0.0529614	−	0.841798i
$917$	−46.5656	−	8.88287i	−1.53773	−	0.293338i
$918$	−25.7886	+	8.37923i	−0.851151	+	0.276556i
$919$	−10.5133	+	9.87269i	−0.346803	+	0.325670i	−0.838300	−	0.545210i	$-0.816450\pi$
$919$	−10.5133	+	9.87269i	−0.346803	+	0.325670i	0.491496	+	0.870880i	$0.336450\pi$
$920$		0			0
$921$	0.501538	+	2.62915i	0.0165262	+	0.0866335i
$922$	−7.72968	+	8.23127i	−0.254564	+	0.271083i
$923$	−14.0544	+	35.4975i	−0.462607	+	1.16841i
$924$	2.16113	+	6.65126i	0.0710959	+	0.218811i
$925$		0			0
$926$	−7.97404	+	24.5416i	−0.262043	+	0.806486i
$927$	−28.4947	−	23.5729i	−0.935889	−	0.774235i
$928$	18.7004	+	8.79973i	0.613870	+	0.288865i
$929$	−33.8958	−	31.8303i	−1.11209	−	1.04432i	−0.998711	−	0.0507662i	$-0.983834\pi$
$929$	−33.8958	−	31.8303i	−1.11209	−	1.04432i	−0.113376	−	0.993552i	$-0.536166\pi$
$930$		0			0
$931$	41.4115	−	5.23148i	1.35721	−	0.171455i
$932$		−	35.7427i		−	1.17079i
$933$	−2.71735	−	21.5100i	−0.0889620	−	0.704207i
$934$	−8.09648	−	9.78696i	−0.264925	−	0.320239i
$935$		0			0
$936$	0.481132	−	7.64737i	0.0157263	−	0.249962i
$937$	5.73627	−	22.3413i	0.187396	−	0.729859i	−0.803509	−	0.595293i	$-0.797036\pi$
$937$	5.73627	−	22.3413i	0.187396	−	0.729859i	0.990905	−	0.134566i	$-0.0429640\pi$
$938$	−3.79176	+	14.7679i	−0.123805	+	0.482190i
$939$	−1.19418	+	18.9809i	−0.0389706	+	0.619420i
$940$		0			0
$941$	−30.3249	−	36.6565i	−0.988563	−	1.19497i	−0.980804	−	0.194998i	$-0.937530\pi$
$941$	−30.3249	−	36.6565i	−0.988563	−	1.19497i	−0.00775943	−	0.999970i	$-0.502470\pi$
$942$	−2.35425	−	18.6358i	−0.0767056	−	0.607188i
$943$		−	56.9715i		−	1.85525i
$944$	21.0794	−	2.66294i	0.686075	−	0.0866714i
$945$		0			0
$946$	−1.72783	−	1.62254i	−0.0561767	−	0.0527534i
$947$	45.8596	+	21.5799i	1.49024	+	0.701252i	0.986675	−	0.162706i	$-0.0520223\pi$
$947$	45.8596	+	21.5799i	1.49024	+	0.701252i	0.503563	+	0.863959i	$0.332022\pi$
$948$	−8.46637	−	7.00399i	−0.274975	−	0.227479i
$949$	−6.55222	+	20.1656i	−0.212694	+	0.654605i
$950$		0			0
$951$	−5.28183	−	16.2558i	−0.171275	−	0.527131i
$952$	−3.01540	+	7.61603i	−0.0977297	+	0.246837i
$953$	−6.34809	+	6.76003i	−0.205635	+	0.218979i	−0.823517	−	0.567292i	$-0.807991\pi$
$953$	−6.34809	+	6.76003i	−0.205635	+	0.218979i	0.617882	+	0.786271i	$0.287991\pi$
$954$	6.41140	+	33.6097i	0.207577	+	1.08816i
$955$		0			0
$956$	7.06001	−	6.62979i	0.228337	−	0.214423i
$957$	−3.23382	+	1.05073i	−0.104535	+	0.0339653i
$958$	58.5381	+	11.1667i	1.89128	+	0.360781i
$959$	1.04464	+	16.6041i	0.0337332	+	0.536173i
$960$		0			0
$961$	−7.71304	−	12.1538i	−0.248808	−	0.392058i
$962$	−40.1356	+	2.52512i	−1.29402	+	0.0814131i
$963$	2.30275	+	1.46137i	0.0742050	+	0.0470919i
$964$	−25.1754	+	30.4318i	−0.810845	+	0.980143i
$965$		0			0
$966$	−26.6692	−	6.84748i	−0.858066	−	0.220314i
$967$	10.2012	−	4.80031i	0.328048	−	0.154368i	−0.254701	−	0.967020i	$-0.581977\pi$
$967$	10.2012	−	4.80031i	0.328048	−	0.154368i	0.582749	+	0.812652i	$0.301977\pi$
$968$	−5.23475	−	1.70087i	−0.168251	−	0.0546682i
$969$	18.7418	+	10.3034i	0.602072	+	0.330992i
$970$		0			0
$971$	−0.552833	−	0.0698391i	−0.0177413	−	0.00224124i	0.116458	−	0.993196i	$-0.462846\pi$
$971$	−0.552833	−	0.0698391i	−0.0177413	−	0.00224124i	−0.134199	+	0.990954i	$0.542846\pi$
$972$	3.16565	−	25.0587i	0.101538	−	0.803758i
$973$	−25.6182	+	16.2578i	−0.821282	+	0.521201i
$974$	0.671698	−	0.488017i	0.0215226	−	0.0156371i
$975$		0			0
$976$	−15.3110	−	11.1241i	−0.490094	−	0.356074i
$977$	−7.53649	−	0.474156i	−0.241114	−	0.0151696i	−0.0582261	−	0.998303i	$-0.518544\pi$
$977$	−7.53649	−	0.474156i	−0.241114	−	0.0151696i	−0.182888	+	0.983134i	$0.558544\pi$
$978$	−1.33081	−	2.42073i	−0.0425545	−	0.0774064i
$979$	−8.92141	+	18.9590i	−0.285129	+	0.605931i
$980$		0			0
$981$	−1.33069	+	6.97574i	−0.0424858	+	0.222718i
$982$	5.25120	+	7.22765i	0.167572	+	0.230644i
$983$	−3.29505	+	5.99367i	−0.105096	+	0.191168i	−0.923626	−	0.383295i	$-0.874789\pi$
$983$	−3.29505	+	5.99367i	−0.105096	+	0.191168i	0.818530	+	0.574463i	$0.194789\pi$
$984$	−2.65577	+	4.18482i	−0.0846627	+	0.133407i
$985$		0			0
$986$	17.5131	+	6.93394i	0.557732	+	0.220822i
$987$	5.98779	+	15.1234i	0.190593	+	0.481384i
$988$	48.8940	−	40.4486i	1.55553	−	1.28684i
$989$	4.08724	−	1.04943i	0.129967	−	0.0333698i
$990$		0			0
$991$	−17.6661	+	6.99452i	−0.561184	+	0.222188i	−0.631553	−	0.775333i	$-0.717582\pi$
$991$	−17.6661	+	6.99452i	−0.561184	+	0.222188i	0.0703694	+	0.997521i	$0.477582\pi$
$992$	−20.6707	−	22.0120i	−0.656294	−	0.698882i
$993$	6.96944	−	9.59261i	0.221168	−	0.304412i
$994$	23.1009	+	49.0918i	0.732715	+	1.55710i
$995$		0			0
$996$	−8.93182	+	4.91031i	−0.283016	+	0.155589i
$997$	12.4356	−	2.37221i	0.393839	−	0.0751288i	0.0133421	−	0.999911i	$-0.495753\pi$
$997$	12.4356	−	2.37221i	0.393839	−	0.0751288i	0.380497	+	0.924782i	$0.375753\pi$
$998$	5.59017	+	21.7723i	0.176954	+	0.689189i
$999$	18.0878			0.572274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.274.19		440
5.2	odd	4		625.2.g.a.351.2		220
5.3	odd	4		125.2.g.a.21.10	yes	220
5.4	even	2	inner	625.2.h.b.274.4		440
125.6	even	25	inner	625.2.h.b.349.4		440
125.33	odd	100		125.2.g.a.6.10	✓	220
125.92	odd	100		625.2.g.a.276.2		220
125.119	even	50	inner	625.2.h.b.349.19		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.10	✓	220	125.33	odd	100
125.2.g.a.21.10	yes	220	5.3	odd	4
625.2.g.a.276.2		220	125.92	odd	100
625.2.g.a.351.2		220	5.2	odd	4
625.2.h.b.274.4		440	5.4	even	2	inner
625.2.h.b.274.19		440	1.1	even	1	trivial
625.2.h.b.349.4		440	125.6	even	25	inner
625.2.h.b.349.19		440	125.119	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.475182 + 1.85071i) q^{2} +(-0.722462 + 0.137817i) q^{3} +(-1.44673 + 0.795344i) q^{4} +(-0.598361 - 1.27158i) q^{6} +(2.04237 - 2.81109i) q^{7} +(0.456575 + 0.486202i) q^{8} +(-2.28637 + 0.905238i) q^{9} +O(q^{10})\)	\(q+(0.475182 + 1.85071i) q^{2} +(-0.722462 + 0.137817i) q^{3} +(-1.44673 + 0.795344i) q^{4} +(-0.598361 - 1.27158i) q^{6} +(2.04237 - 2.81109i) q^{7} +(0.456575 + 0.486202i) q^{8} +(-2.28637 + 0.905238i) q^{9} +(-1.60551 + 0.412224i) q^{11} +(0.935593 - 0.773989i) q^{12} +(1.71984 + 4.34382i) q^{13} +(6.17301 + 2.44407i) q^{14} +(-2.45210 + 3.86388i) q^{16} +(-1.70275 + 3.09729i) q^{17} +(-2.76178 - 3.80126i) q^{18} +(-1.54162 + 8.08148i) q^{19} +(-1.08812 + 2.31238i) q^{21} +(-1.52582 - 2.77545i) q^{22} +(5.62755 + 0.354056i) q^{23} +(-0.396865 - 0.288339i) q^{24} +(-7.22192 + 5.24704i) q^{26} +(3.39004 - 2.15139i) q^{27} +(-0.718973 + 5.69126i) q^{28} +(-2.76707 - 0.349562i) q^{29} +(3.57092 + 1.96313i) q^{31} +(-7.04747 - 2.28986i) q^{32} +(1.10311 - 0.519082i) q^{33} +(-6.54131 - 1.67952i) q^{34} +(2.58778 - 3.12808i) q^{36} +(3.80368 + 2.41389i) q^{37} +(-15.6890 + 0.987071i) q^{38} +(-1.84117 - 2.90122i) q^{39} +(-0.634417 - 10.0838i) q^{41} +(-4.79660 - 0.915001i) q^{42} +(0.711741 - 0.231259i) q^{43} +(1.99487 - 1.87330i) q^{44} +(2.01886 + 10.5832i) q^{46} +(4.35694 - 4.63967i) q^{47} +(1.23904 - 3.12945i) q^{48} +(-1.56779 - 4.82517i) q^{49} +(0.803313 - 2.47234i) q^{51} +(-5.94297 - 4.91645i) q^{52} +(-6.58904 - 3.10057i) q^{53} +(5.59249 + 5.25170i) q^{54} +(2.29925 - 0.290463i) q^{56} -6.05102i q^{57} +(-0.667923 - 5.28715i) q^{58} +(-2.95945 - 3.57736i) q^{59} +(-0.259674 + 4.12740i) q^{61} +(-1.93635 + 7.54159i) q^{62} +(-2.12492 + 8.27602i) q^{63} +(0.314349 - 4.99644i) q^{64} +(1.48485 + 1.79487i) q^{66} +(0.287826 + 2.27838i) q^{67} -5.83520i q^{68} +(-4.11449 + 0.519781i) q^{69} +(5.95709 + 5.59408i) q^{71} +(-1.48403 - 0.698331i) q^{72} +(3.49698 + 2.89295i) q^{73} +(-2.65997 + 8.18655i) q^{74} +(-4.19725 - 12.9178i) q^{76} +(-2.12024 + 5.35513i) q^{77} +(4.49444 - 4.78609i) q^{78} +(-1.69565 - 8.88892i) q^{79} +(3.22504 - 3.02851i) q^{81} +(18.3607 - 5.96575i) q^{82} +(-8.24547 - 1.57291i) q^{83} +(-0.264921 - 4.21081i) q^{84} +(0.766200 + 1.20734i) q^{86} +(2.04728 - 0.128804i) q^{87} +(-0.933457 - 0.592390i) q^{88} +(8.05754 - 9.73989i) q^{89} +(15.7234 + 4.03708i) q^{91} +(-8.42312 + 3.96362i) q^{92} +(-2.85041 - 0.926154i) q^{93} +(10.6570 + 5.85876i) q^{94} +(5.40712 + 0.683077i) q^{96} +(0.599240 - 4.74347i) q^{97} +(8.18502 - 5.19437i) q^{98} +(3.29762 - 2.39586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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