LMFDB - Embedded newform 675.2.l.f.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	675.76
Dual form			675.2.l.f.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84958 + 1.55198i) q^{2} +(1.53931 + 0.794060i) q^{3} +(0.665000 - 3.77140i) q^{4} +(-4.07944 + 0.920299i) q^{6} +(0.0583477 + 0.330906i) q^{7} +(2.20872 + 3.82562i) q^{8} +(1.73894 + 2.44461i) q^{9} +O(q^{10})$	\(q+(-1.84958 + 1.55198i) q^{2} +(1.53931 + 0.794060i) q^{3} +(0.665000 - 3.77140i) q^{4} +(-4.07944 + 0.920299i) q^{6} +(0.0583477 + 0.330906i) q^{7} +(2.20872 + 3.82562i) q^{8} +(1.73894 + 2.44461i) q^{9} +(-4.97408 - 1.81042i) q^{11} +(4.01836 - 5.27730i) q^{12} +(4.68414 + 3.93046i) q^{13} +(-0.621479 - 0.521483i) q^{14} +(-2.82523 - 1.02830i) q^{16} +(-1.52112 + 2.63465i) q^{17} +(-7.01028 - 1.82269i) q^{18} +(-0.260295 - 0.450843i) q^{19} +(-0.172944 + 0.555698i) q^{21} +(12.0097 - 4.37117i) q^{22} +(-0.0350517 + 0.198788i) q^{23} +(0.362131 + 7.64266i) q^{24} -14.7637 q^{26} +(0.735594 + 5.14382i) q^{27} +1.28678 q^{28} +(1.41738 - 1.18933i) q^{29} +(-1.58422 + 8.98458i) q^{31} +(-1.48070 + 0.538930i) q^{32} +(-6.21906 - 6.73651i) q^{33} +(-1.27550 - 7.23373i) q^{34} +(10.3760 - 4.93257i) q^{36} +(-3.11234 + 5.39074i) q^{37} +(1.18114 + 0.429898i) q^{38} +(4.08931 + 9.76968i) q^{39} +(6.96293 + 5.84259i) q^{41} +(-0.542558 - 1.29621i) q^{42} +(-6.38441 - 2.32373i) q^{43} +(-10.1356 + 17.5553i) q^{44} +(-0.243684 - 0.422073i) q^{46} +(2.11902 + 12.0175i) q^{47} +(-3.53236 - 3.82627i) q^{48} +(6.47175 - 2.35553i) q^{49} +(-4.43354 + 2.84768i) q^{51} +(17.9383 - 15.0520i) q^{52} +2.74867 q^{53} +(-9.34365 - 8.37227i) q^{54} +(-1.13705 + 0.954096i) q^{56} +(-0.0426766 - 0.900676i) q^{57} +(-0.775751 + 4.39950i) q^{58} +(-6.56519 + 2.38954i) q^{59} +(-2.16727 - 12.2912i) q^{61} +(-11.0137 - 19.0764i) q^{62} +(-0.707472 + 0.718062i) q^{63} +(4.90880 - 8.50230i) q^{64} +(21.9576 + 2.80784i) q^{66} +(-4.29512 - 3.60403i) q^{67} +(8.92479 + 7.48879i) q^{68} +(-0.211805 + 0.278163i) q^{69} +(1.58699 - 2.74874i) q^{71} +(-5.51130 + 12.0520i) q^{72} +(0.731226 + 1.26652i) q^{73} +(-2.60980 - 14.8009i) q^{74} +(-1.87341 + 0.681865i) q^{76} +(0.308852 - 1.75159i) q^{77} +(-22.7259 - 11.7233i) q^{78} +(-2.18198 + 1.83090i) q^{79} +(-2.95220 + 8.50203i) q^{81} -21.9461 q^{82} +(-0.578595 + 0.485499i) q^{83} +(1.98075 + 1.02178i) q^{84} +(15.4149 - 5.61055i) q^{86} +(3.12618 - 0.705250i) q^{87} +(-4.06039 - 23.0276i) q^{88} +(-3.18070 - 5.50914i) q^{89} +(-1.02731 + 1.77934i) q^{91} +(0.726400 + 0.264388i) q^{92} +(-9.57291 + 12.5721i) q^{93} +(-22.5703 - 18.9387i) q^{94} +(-2.70719 - 0.346184i) q^{96} +(-10.0155 - 3.64534i) q^{97} +(-8.31429 + 14.4008i) q^{98} +(-4.22385 - 15.3079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.84958	+	1.55198i	−1.30785	+	1.09742i	−0.319118	+	0.947715i	$0.603387\pi$
$2$	−1.84958	+	1.55198i	−1.30785	+	1.09742i	−0.988731	+	0.149701i	$0.952169\pi$
$3$	1.53931	+	0.794060i	0.888720	+	0.458451i
$3$	1.53931	+	0.794060i	0.888720	+	0.458451i
$4$	0.665000	−	3.77140i	0.332500	−	1.88570i
$5$		0			0
$5$		0			0
$6$	−4.07944	+	0.920299i	−1.66542	+	0.375710i
$7$	0.0583477	+	0.330906i	0.0220534	+	0.125071i	0.993847	−	0.110762i	$-0.0353292\pi$
$7$	0.0583477	+	0.330906i	0.0220534	+	0.125071i	−0.971794	+	0.235833i	$0.924218\pi$
$8$	2.20872	+	3.82562i	0.780901	+	1.35256i
$9$	1.73894	+	2.44461i	0.579646	+	0.814869i
$10$		0			0
$11$	−4.97408	−	1.81042i	−1.49974	−	0.545861i	−0.543748	−	0.839249i	$-0.682995\pi$
$11$	−4.97408	−	1.81042i	−1.49974	−	0.545861i	−0.955994	+	0.293387i	$0.905217\pi$
$12$	4.01836	−	5.27730i	1.16000	−	1.52343i
$13$	4.68414	+	3.93046i	1.29915	+	1.09011i	0.990292	+	0.139005i	$0.0443903\pi$
$13$	4.68414	+	3.93046i	1.29915	+	1.09011i	0.308855	+	0.951109i	$0.400054\pi$
$14$	−0.621479	−	0.521483i	−0.166097	−	0.139372i
$15$		0			0
$16$	−2.82523	−	1.02830i	−0.706307	−	0.257075i
$17$	−1.52112	+	2.63465i	−0.368925	+	0.638996i	−0.989398	−	0.145231i	$-0.953607\pi$
$17$	−1.52112	+	2.63465i	−0.368925	+	0.638996i	0.620473	+	0.784228i	$0.286941\pi$
$18$	−7.01028	−	1.82269i	−1.65234	−	0.429613i
$19$	−0.260295	−	0.450843i	−0.0597157	−	0.103431i	0.834622	−	0.550823i	$-0.185686\pi$
$19$	−0.260295	−	0.450843i	−0.0597157	−	0.103431i	−0.894338	+	0.447392i	$0.852353\pi$
$20$		0			0
$21$	−0.172944	+	0.555698i	−0.0377396	+	0.121263i
$22$	12.0097	−	4.37117i	2.56047	−	0.931936i
$23$	−0.0350517	+	0.198788i	−0.00730878	+	0.0414501i	−0.988244	−	0.152885i	$-0.951144\pi$
$23$	−0.0350517	+	0.198788i	−0.00730878	+	0.0414501i	0.980935	+	0.194335i	$0.0622548\pi$
$24$	0.362131	+	7.64266i	0.0739197	+	1.56005i
$25$		0			0
$26$	−14.7637			−2.89540
$27$	0.735594	+	5.14382i	0.141565	+	0.989929i
$28$	1.28678			0.243179
$29$	1.41738	−	1.18933i	0.263201	−	0.220852i	−0.501631	−	0.865082i	$-0.667266\pi$
$29$	1.41738	−	1.18933i	0.263201	−	0.220852i	0.764832	+	0.644230i	$0.222822\pi$
$30$		0			0
$31$	−1.58422	+	8.98458i	−0.284535	+	1.61368i	0.422407	+	0.906406i	$0.361185\pi$
$31$	−1.58422	+	8.98458i	−0.284535	+	1.61368i	−0.706942	+	0.707272i	$0.749926\pi$
$32$	−1.48070	+	0.538930i	−0.261753	+	0.0952703i
$33$	−6.21906	−	6.73651i	−1.08260	−	1.17268i
$34$	−1.27550	−	7.23373i	−0.218747	−	1.24058i
$35$		0			0
$36$	10.3760	−	4.93257i	1.72933	−	0.822095i
$37$	−3.11234	+	5.39074i	−0.511666	+	0.886232i	0.488242	+	0.872708i	$0.337638\pi$
$37$	−3.11234	+	5.39074i	−0.511666	+	0.886232i	−0.999909	+	0.0135239i	$0.995695\pi$
$38$	1.18114	+	0.429898i	0.191605	+	0.0697387i
$39$	4.08931	+	9.76968i	0.654814	+	1.56440i
$40$		0			0
$41$	6.96293	+	5.84259i	1.08743	+	0.912459i	0.996516	−	0.0833996i	$-0.0265778\pi$
$41$	6.96293	+	5.84259i	1.08743	+	0.912459i	0.0909107	+	0.995859i	$0.471022\pi$
$42$	−0.542558	−	1.29621i	−0.0837186	−	0.200010i
$43$	−6.38441	−	2.32373i	−0.973613	−	0.354366i	−0.194259	−	0.980950i	$-0.562230\pi$
$43$	−6.38441	−	2.32373i	−0.973613	−	0.354366i	−0.779354	+	0.626584i	$0.784452\pi$
$44$	−10.1356	+	17.5553i	−1.52800	+	2.64657i
$45$		0			0
$46$	−0.243684	−	0.422073i	−0.0359293	−	0.0622313i
$47$	2.11902	+	12.0175i	0.309090	+	1.75294i	0.603598	+	0.797288i	$0.293733\pi$
$47$	2.11902	+	12.0175i	0.309090	+	1.75294i	−0.294508	+	0.955649i	$0.595156\pi$
$48$	−3.53236	−	3.82627i	−0.509853	−	0.552275i
$49$	6.47175	−	2.35553i	0.924536	−	0.336504i
$50$		0			0
$51$	−4.43354	+	2.84768i	−0.620819	+	0.398755i
$52$	17.9383	−	15.0520i	2.48760	−	2.08734i
$53$	2.74867			0.377558			0.188779	−	0.982020i	$-0.439547\pi$
$53$	2.74867			0.377558			0.188779	+	0.982020i	$0.439547\pi$
$54$	−9.34365	−	8.37227i	−1.27151	−	1.13932i
$55$		0			0
$56$	−1.13705	+	0.954096i	−0.151944	+	0.127496i
$57$	−0.0426766	−	0.900676i	−0.00565265	−	0.119297i
$58$	−0.775751	+	4.39950i	−0.101861	+	0.577683i
$59$	−6.56519	+	2.38954i	−0.854716	+	0.311091i	−0.731961	−	0.681346i	$-0.761395\pi$
$59$	−6.56519	+	2.38954i	−0.854716	+	0.311091i	−0.122754	+	0.992437i	$0.539173\pi$
$60$		0			0
$61$	−2.16727	−	12.2912i	−0.277491	−	1.57373i	−0.730938	−	0.682444i	$-0.760917\pi$
$61$	−2.16727	−	12.2912i	−0.277491	−	1.57373i	0.453447	−	0.891283i	$-0.350194\pi$
$62$	−11.0137	−	19.0764i	−1.39875	−	2.42270i
$63$	−0.707472	+	0.718062i	−0.0891332	+	0.0904673i
$64$	4.90880	−	8.50230i	0.613601	−	1.06279i
$65$		0			0
$66$	21.9576	+	2.80784i	2.70279	+	0.345621i
$67$	−4.29512	−	3.60403i	−0.524732	−	0.440303i	0.341545	−	0.939865i	$-0.389050\pi$
$67$	−4.29512	−	3.60403i	−0.524732	−	0.440303i	−0.866278	+	0.499562i	$0.833494\pi$
$68$	8.92479	+	7.48879i	1.08229	+	0.908149i
$69$	−0.211805	+	0.278163i	−0.0254983	+	0.0334868i
$70$		0			0
$71$	1.58699	−	2.74874i	0.188341	−	0.326216i	−0.756356	−	0.654160i	$-0.773022\pi$
$71$	1.58699	−	2.74874i	0.188341	−	0.326216i	0.944697	+	0.327944i	$0.106356\pi$
$72$	−5.51130	+	12.0520i	−0.649513	+	1.42034i
$73$	0.731226	+	1.26652i	0.0855835	+	0.148235i	0.905640	−	0.424048i	$-0.139391\pi$
$73$	0.731226	+	1.26652i	0.0855835	+	0.148235i	−0.820056	+	0.572283i	$0.806058\pi$
$74$	−2.60980	−	14.8009i	−0.303383	−	1.72057i
$75$		0			0
$76$	−1.87341	+	0.681865i	−0.214895	+	0.0782153i
$77$	0.308852	−	1.75159i	0.0351970	−	0.199612i
$78$	−22.7259	−	11.7233i	−2.57320	−	1.32740i
$79$	−2.18198	+	1.83090i	−0.245491	+	0.205992i	−0.757228	−	0.653151i	$-0.773447\pi$
$79$	−2.18198	+	1.83090i	−0.245491	+	0.205992i	0.511737	+	0.859142i	$0.329002\pi$
$80$		0			0
$81$	−2.95220	+	8.50203i	−0.328022	+	0.944670i
$82$	−21.9461			−2.42354
$83$	−0.578595	+	0.485499i	−0.0635091	+	0.0532905i	−0.673990	−	0.738741i	$-0.735421\pi$
$83$	−0.578595	+	0.485499i	−0.0635091	+	0.0532905i	0.610481	+	0.792031i	$0.290976\pi$
$84$	1.98075	+	1.02178i	0.216118	+	0.111486i
$85$		0			0
$86$	15.4149	−	5.61055i	1.66223	−	0.605001i
$87$	3.12618	−	0.705250i	0.335162	−	0.0756108i
$88$	−4.06039	−	23.0276i	−0.432840	−	2.45476i
$89$	−3.18070	−	5.50914i	−0.337154	−	0.583968i	0.646742	−	0.762709i	$-0.276131\pi$
$89$	−3.18070	−	5.50914i	−0.337154	−	0.583968i	−0.983896	+	0.178741i	$0.942798\pi$
$90$		0			0
$91$	−1.02731	+	1.77934i	−0.107691	+	0.186526i
$92$	0.726400	+	0.264388i	0.0757325	+	0.0275644i
$93$	−9.57291	+	12.5721i	−0.992664	+	1.30366i
$94$	−22.5703	−	18.9387i	−2.32794	−	1.95338i
$95$		0			0
$96$	−2.70719	−	0.346184i	−0.276302	−	0.0353323i
$97$	−10.0155	−	3.64534i	−1.01692	−	0.370128i	−0.220832	−	0.975312i	$-0.570877\pi$
$97$	−10.0155	−	3.64534i	−1.01692	−	0.370128i	−0.796086	+	0.605184i	$0.793099\pi$
$98$	−8.31429	+	14.4008i	−0.839870	+	1.45470i
$99$	−4.22385	−	15.3079i	−0.424513	−	1.53850i
$100$		0			0
$101$	−2.11146	−	11.9747i	−0.210098	−	1.19152i	−0.889213	−	0.457493i	$-0.848748\pi$
$101$	−2.11146	−	11.9747i	−0.210098	−	1.19152i	0.679116	−	0.734031i	$-0.262363\pi$
$102$	3.78063	−	12.1478i	0.374338	−	1.20281i
$103$	−2.42584	+	0.882932i	−0.239025	+	0.0869979i	−0.458755	−	0.888563i	$-0.651704\pi$
$103$	−2.42584	+	0.882932i	−0.239025	+	0.0869979i	0.219730	+	0.975561i	$0.429482\pi$
$104$	−4.69048	+	26.6010i	−0.459939	+	2.60845i
$105$		0			0
$106$	−5.08387	+	4.26588i	−0.493790	+	0.414339i
$107$	5.35813			0.517990			0.258995	−	0.965879i	$-0.416609\pi$
$107$	5.35813			0.517990			0.258995	+	0.965879i	$0.416609\pi$
$108$	19.8886	+	0.646421i	1.91378	+	0.0622019i
$109$	17.4957			1.67579			0.837893	−	0.545834i	$-0.183787\pi$
$109$	17.4957			1.67579			0.837893	+	0.545834i	$0.183787\pi$
$110$		0			0
$111$	−9.07143	+	5.82662i	−0.861022	+	0.553038i
$112$	0.175425	−	0.994885i	0.0165761	−	0.0940078i
$113$	15.7488	−	5.73211i	1.48153	−	0.539232i	0.530323	−	0.847796i	$-0.322071\pi$
$113$	15.7488	−	5.73211i	1.48153	−	0.539232i	0.951204	+	0.308564i	$0.0998485\pi$
$114$	1.47677	+	1.59964i	0.138312	+	0.149820i
$115$		0			0
$116$	−3.54287	−	6.13642i	−0.328947	−	0.569753i
$117$	−1.46300	+	18.2857i	−0.135255	+	1.69051i
$118$	8.43433	−	14.6087i	0.776443	−	1.34484i
$119$	−0.960576	−	0.349621i	−0.0880558	−	0.0320497i
$120$		0			0
$121$	13.0374	+	10.9397i	1.18522	+	0.994514i
$122$	23.0842	+	19.3700i	2.08995	+	1.75368i
$123$	6.07872	+	14.5225i	0.548100	+	1.30945i
$124$	32.8310	+	11.9495i	2.94831	+	1.07310i
$125$		0			0
$126$	0.194107	−	2.42610i	0.0172925	−	0.216134i
$127$	−4.00306	−	6.93350i	−0.355214	−	0.615249i	0.631940	−	0.775017i	$-0.282259\pi$
$127$	−4.00306	−	6.93350i	−0.355214	−	0.615249i	−0.987155	+	0.159768i	$0.948925\pi$
$128$	3.56894	+	20.2405i	0.315453	+	1.78902i
$129$	−7.98238	−	8.64655i	−0.702810	−	0.761286i
$130$		0			0
$131$	1.87834	−	10.6526i	0.164111	−	0.930721i	−0.785865	−	0.618398i	$-0.787782\pi$
$131$	1.87834	−	10.6526i	0.164111	−	0.930721i	0.949976	−	0.312323i	$-0.101107\pi$
$132$	−29.5418	+	18.9748i	−2.57128	+	1.65154i
$133$	0.133999	−	0.112439i	0.0116192	−	0.00974968i
$134$	13.5376			1.16947
$135$		0			0
$136$	−13.4389			−1.15238
$137$	−10.0791	+	8.45733i	−0.861112	+	0.722559i	−0.962207	−	0.272318i	$-0.912210\pi$
$137$	−10.0791	+	8.45733i	−0.861112	+	0.722559i	0.101095	+	0.994877i	$0.467765\pi$
$138$	−0.0399532	−	0.843201i	−0.00340105	−	0.0717780i
$139$	−1.27373	+	7.22368i	−0.108036	+	0.612705i	0.881928	+	0.471385i	$0.156246\pi$
$139$	−1.27373	+	7.22368i	−0.108036	+	0.612705i	−0.989964	+	0.141320i	$0.954865\pi$
$140$		0			0
$141$	−6.28083	+	20.1813i	−0.528941	+	1.69957i
$142$	1.33074	+	7.54699i	0.111673	+	0.633329i
$143$	−16.1835	−	28.0307i	−1.35333	−	2.34404i
$144$	−2.39911	−	8.69472i	−0.199926	−	0.724560i
$145$		0			0
$146$	−3.31807	−	1.20768i	−0.274606	−	0.0999483i
$147$	11.8325	+	1.51308i	0.975924	+	0.124797i
$148$	18.2609	+	15.3228i	1.50104	+	1.25952i
$149$	10.1927	+	8.55268i	0.835017	+	0.700663i	0.956437	−	0.291939i	$-0.0943003\pi$
$149$	10.1927	+	8.55268i	0.835017	+	0.700663i	−0.121420	+	0.992601i	$0.538745\pi$
$150$		0			0
$151$	8.57654	+	3.12160i	0.697949	+	0.254033i	0.666535	−	0.745474i	$-0.267777\pi$
$151$	8.57654	+	3.12160i	0.697949	+	0.254033i	0.0314139	+	0.999506i	$0.489999\pi$
$152$	1.14984	−	1.99158i	0.0932641	−	0.161538i
$153$	−9.08581	+	0.862960i	−0.734544	+	0.0697662i
$154$	2.14718	+	3.71903i	0.173025	+	0.299688i
$155$		0			0
$156$	39.5648	−	8.92561i	3.16772	−	0.714620i
$157$	−4.17491	+	1.51954i	−0.333194	+	0.121273i	−0.503199	−	0.864171i	$-0.667844\pi$
$157$	−4.17491	+	1.51954i	−0.333194	+	0.121273i	0.170005	+	0.985443i	$0.445622\pi$
$158$	1.19422	−	6.77277i	0.0950072	−	0.538813i
$159$	4.23104	+	2.18261i	0.335544	+	0.173092i
$160$		0			0
$161$	−0.0678253			−0.00534539
$162$	−7.73466	−	20.3069i	−0.607693	−	1.59546i
$163$	16.5806			1.29869			0.649347	−	0.760492i	$-0.275042\pi$
$163$	16.5806			1.29869			0.649347	+	0.760492i	$0.275042\pi$
$164$	26.6651	−	22.3747i	2.08220	−	1.74717i
$165$		0			0
$166$	0.316672	−	1.79594i	0.0245785	−	0.139392i
$167$	18.8502	−	6.86091i	1.45867	−	0.530913i	0.513673	−	0.857986i	$-0.328284\pi$
$167$	18.8502	−	6.86091i	1.45867	−	0.530913i	0.944999	+	0.327073i	$0.106062\pi$
$168$	−2.50788	+	0.565763i	−0.193487	+	0.0436496i
$169$	4.23523	+	24.0192i	0.325787	+	1.84763i
$170$		0			0
$171$	0.649499	−	1.42031i	0.0496684	−	0.108613i
$172$	−13.0094	+	22.5329i	−0.991955	+	1.71812i
$173$	−3.14658	−	1.14526i	−0.239230	−	0.0870725i	0.219623	−	0.975585i	$-0.429517\pi$
$173$	−3.14658	−	1.14526i	−0.239230	−	0.0870725i	−0.458853	+	0.888512i	$0.651739\pi$
$174$	−4.68759	+	6.15619i	−0.355365	+	0.466700i
$175$		0			0
$176$	12.1913	+	10.2297i	0.918951	+	0.771091i
$177$	−12.0033	−	1.53493i	−0.902223	−	0.115372i
$178$	14.4330	+	5.25320i	1.08180	+	0.393744i
$179$	−6.19883	+	10.7367i	−0.463323	+	0.802498i	−0.999124	−	0.0418458i	$-0.986676\pi$
$179$	−6.19883	+	10.7367i	−0.463323	+	0.802498i	0.535802	+	0.844344i	$0.320010\pi$
$180$		0			0
$181$	2.32049	+	4.01921i	0.172481	+	0.298746i	0.939287	−	0.343134i	$-0.111488\pi$
$181$	2.32049	+	4.01921i	0.172481	+	0.298746i	−0.766806	+	0.641879i	$0.778155\pi$
$182$	−0.861427	−	4.88540i	−0.0638532	−	0.362130i
$183$	6.42386	−	20.6409i	0.474865	−	1.52582i
$184$	−0.837906	+	0.304973i	−0.0617713	+	0.0224829i
$185$		0			0
$186$	−1.80576	−	38.1100i	−0.132405	−	2.79436i
$187$	12.3360	−	10.3511i	0.902095	−	0.756948i
$188$	46.7321			3.40829
$189$	−1.65920	+	0.543543i	−0.120689	+	0.0395369i
$190$		0			0
$191$	10.8645	−	9.11641i	0.786129	−	0.659641i	−0.158655	−	0.987334i	$-0.550716\pi$
$191$	10.8645	−	9.11641i	0.786129	−	0.659641i	0.944784	+	0.327694i	$0.106271\pi$
$192$	14.3075	−	9.18977i	1.03255	−	0.663214i
$193$	2.94460	−	16.6997i	0.211957	−	1.20207i	−0.674152	−	0.738593i	$-0.735491\pi$
$193$	2.94460	−	16.6997i	0.211957	−	1.20207i	0.886109	−	0.463477i	$-0.153398\pi$
$194$	24.1819	−	8.80149i	1.73616	−	0.631910i
$195$		0			0
$196$	−4.57992	−	25.9740i	−0.327137	−	1.85529i
$197$	−3.41348	−	5.91232i	−0.243200	−	0.421236i	0.718424	−	0.695606i	$-0.244864\pi$
$197$	−3.41348	−	5.91232i	−0.243200	−	0.421236i	−0.961624	+	0.274370i	$0.911531\pi$
$198$	31.5699	+	21.7578i	2.24357	+	1.54626i
$199$	−7.72021	+	13.3718i	−0.547271	+	0.947901i	0.451189	+	0.892428i	$0.351000\pi$
$199$	−7.72021	+	13.3718i	−0.547271	+	0.947901i	−0.998460	+	0.0554726i	$0.982333\pi$
$200$		0			0
$201$	−3.74969	−	8.95830i	−0.264483	−	0.631870i
$202$	22.4898	+	18.8711i	1.58237	+	1.32777i
$203$	0.476256	+	0.399626i	0.0334266	+	0.0280483i
$204$	7.79145	+	18.6144i	0.545510	+	1.30327i
$205$		0			0
$206$	3.11648	−	5.39790i	0.217135	−	0.376090i
$207$	−0.546911	+	0.259992i	−0.0380129	+	0.0180707i
$208$	−9.19208	−	15.9211i	−0.637356	−	1.10393i
$209$	0.478511	+	2.71377i	0.0330993	+	0.187716i
$210$		0			0
$211$	17.3343	−	6.30917i	1.19334	−	0.434341i	0.332447	−	0.943122i	$-0.392126\pi$
$211$	17.3343	−	6.30917i	1.19334	−	0.434341i	0.860896	+	0.508781i	$0.169904\pi$
$212$	1.82786	−	10.3663i	0.125538	−	0.711963i
$213$	4.62553	−	2.97100i	0.316936	−	0.203569i
$214$	−9.91028	+	8.31571i	−0.677453	+	0.568450i
$215$		0			0
$216$	−18.0536	+	14.1754i	−1.22839	+	0.964512i
$217$	−3.06549			−0.208099
$218$	−32.3597	+	27.1530i	−2.19168	+	1.83904i
$219$	0.119888	+	2.53020i	0.00810129	+	0.170975i
$220$		0			0
$221$	−17.4805	+	6.36239i	−1.17587	+	0.427980i
$222$	7.73552	−	24.8555i	0.519174	−	1.66819i
$223$	−0.541070	−	3.06856i	−0.0362328	−	0.205486i	0.961317	−	0.275444i	$-0.0888248\pi$
$223$	−0.541070	−	3.06856i	−0.0362328	−	0.205486i	−0.997550	+	0.0699575i	$0.977714\pi$
$224$	−0.264731	−	0.458527i	−0.0176881	−	0.0306366i
$225$		0			0
$226$	−20.2326	+	35.0439i	−1.34585	+	2.33108i
$227$	6.55642	+	2.38634i	0.435165	+	0.158387i	0.550308	−	0.834962i	$-0.314510\pi$
$227$	6.55642	+	2.38634i	0.435165	+	0.158387i	−0.115143	+	0.993349i	$0.536733\pi$
$228$	−3.42519	−	0.437999i	−0.226839	−	0.0290072i
$229$	−7.76380	−	6.51460i	−0.513046	−	0.430497i	0.349153	−	0.937066i	$-0.386469\pi$
$229$	−7.76380	−	6.51460i	−0.513046	−	0.430497i	−0.862200	+	0.506569i	$0.830914\pi$
$230$		0			0
$231$	1.86628	−	2.45099i	0.122793	−	0.161263i
$232$	7.68051	+	2.79548i	0.504250	+	0.183532i
$233$	−5.61343	+	9.72275i	−0.367748	+	0.636959i	−0.989213	−	0.146483i	$-0.953205\pi$
$233$	−5.61343	+	9.72275i	−0.367748	+	0.636959i	0.621465	+	0.783442i	$0.286538\pi$
$234$	−25.6731	−	36.0914i	−1.67830	−	2.35937i
$235$		0			0
$236$	4.64605	+	26.3490i	0.302432	+	1.71518i
$237$	−4.81257	+	1.08569i	−0.312610	+	0.0705232i
$238$	2.31926	−	0.844143i	0.150336	−	0.0547177i
$239$	2.49115	−	14.1280i	0.161139	−	0.913864i	−0.791818	−	0.610757i	$-0.790865\pi$
$239$	2.49115	−	14.1280i	0.161139	−	0.913864i	0.952957	−	0.303106i	$-0.0980238\pi$
$240$		0			0
$241$	−7.78696	+	6.53404i	−0.501602	+	0.420894i	−0.858163	−	0.513378i	$-0.828394\pi$
$241$	−7.78696	+	6.53404i	−0.501602	+	0.420894i	0.356560	+	0.934272i	$0.383949\pi$
$242$	−41.0918			−2.64148
$243$	−11.2955	+	10.7430i	−0.724605	+	0.689165i
$244$	−47.7963			−3.05985
$245$		0			0
$246$	−33.7818	−	17.4265i	−2.15385	−	1.11107i
$247$	0.552766	−	3.13489i	0.0351717	−	0.199468i
$248$	−37.8707	+	13.7838i	−2.40479	+	0.875273i
$249$	−1.27615	+	0.287893i	−0.0808728	+	0.0182445i
$250$		0			0
$251$	0.766397	+	1.32744i	0.0483745	+	0.0837872i	0.889199	−	0.457521i	$-0.151263\pi$
$251$	0.766397	+	1.32744i	0.0483745	+	0.0837872i	−0.840824	+	0.541308i	$0.817929\pi$
$252$	2.23763	+	3.14568i	0.140958	+	0.198159i
$253$	0.534239	−	0.925329i	0.0335873	−	0.0581749i
$254$	18.1646	+	6.61139i	1.13975	+	0.414835i
$255$		0			0
$256$	−22.9724	−	19.2761i	−1.43577	−	1.20476i
$257$	18.3627	+	15.4081i	1.14543	+	0.961131i	0.999603	−	0.0281791i	$-0.00897086\pi$
$257$	18.3627	+	15.4081i	1.14543	+	0.961131i	0.145828	+	0.989310i	$0.453415\pi$
$258$	28.1833	+	3.60396i	1.75462	+	0.224373i
$259$	−1.96543	−	0.715357i	−0.122126	−	0.0444501i
$260$		0			0
$261$	5.37217	+	1.39678i	0.332529	+	0.0864586i
$262$	13.0585	+	22.6179i	0.806755	+	1.39734i
$263$	1.42813	+	8.09931i	0.0880621	+	0.499425i	0.996654	+	0.0817395i	$0.0260475\pi$
$263$	1.42813	+	8.09931i	0.0880621	+	0.499425i	−0.908592	+	0.417686i	$0.862841\pi$
$264$	12.0351	−	38.6708i	0.740712	−	2.38002i
$265$		0			0
$266$	−0.0733394	+	0.415929i	−0.00449673	+	0.0255022i
$267$	−0.521493	−	11.0059i	−0.0319148	−	0.673552i
$268$	−16.4485	+	13.8019i	−1.00475	+	0.843088i
$269$	2.05741			0.125442			0.0627211	−	0.998031i	$-0.480022\pi$
$269$	2.05741			0.125442			0.0627211	+	0.998031i	$0.480022\pi$
$270$		0			0
$271$	−15.4436			−0.938131			−0.469066	−	0.883163i	$-0.655409\pi$
$271$	−15.4436			−0.938131			−0.469066	+	0.883163i	$0.655409\pi$
$272$	7.00671	−	5.87933i	0.424844	−	0.356486i
$273$	−2.99425	+	1.92322i	−0.181220	+	0.116398i
$274$	5.51639	−	31.2850i	0.333257	−	1.89000i
$275$		0			0
$276$	0.908213	+	0.983780i	0.0546680	+	0.0592166i
$277$	0.209051	+	1.18559i	0.0125607	+	0.0712350i	0.990444	−	0.137917i	$-0.0440407\pi$
$277$	0.209051	+	1.18559i	0.0125607	+	0.0712350i	−0.977883	+	0.209152i	$0.932930\pi$
$278$	−8.85515	−	15.3376i	−0.531097	−	0.919887i
$279$	−24.7186	+	11.7508i	−1.47987	+	0.703503i
$280$		0			0
$281$	26.1069	+	9.50212i	1.55740	+	0.566849i	0.970140	−	0.242546i	$-0.0779825\pi$
$281$	26.1069	+	9.50212i	1.55740	+	0.566849i	0.587265	+	0.809395i	$0.300205\pi$
$282$	−19.7041	−	47.0746i	−1.17336	−	2.80325i
$283$	−17.3768	−	14.5809i	−1.03295	−	0.866745i	−0.0417476	−	0.999128i	$-0.513293\pi$
$283$	−17.3768	−	14.5809i	−1.03295	−	0.866745i	−0.991199	+	0.132383i	$0.957737\pi$
$284$	−9.31127	−	7.81309i	−0.552522	−	0.463621i
$285$		0			0
$286$	73.4357	+	26.7284i	4.34235	+	1.58048i
$287$	−1.52708	+	2.64498i	−0.0901406	+	0.156128i
$288$	−3.89231	−	2.68256i	−0.229357	−	0.158071i
$289$	3.87241	+	6.70722i	0.227789	+	0.394542i
$290$		0			0
$291$	−12.5223	−	13.5642i	−0.734069	−	0.795147i
$292$	5.26282	−	1.91551i	0.307983	−	0.112097i
$293$	2.89878	−	16.4398i	0.169348	−	0.960422i	−0.775119	−	0.631816i	$-0.782310\pi$
$293$	2.89878	−	16.4398i	0.169348	−	0.960422i	0.944467	−	0.328606i	$-0.106579\pi$
$294$	−24.2333	+	15.5652i	−1.41332	+	0.907779i
$295$		0			0
$296$	−27.4972			−1.59824
$297$	5.65356	−	26.9175i	0.328053	−	1.56191i
$298$	−32.1258			−1.86100
$299$	−0.945515	+	0.793381i	−0.0546806	+	0.0458824i
$300$		0			0
$301$	0.396423	−	2.24822i	0.0228494	−	0.129586i
$302$	−20.7076	+	7.53697i	−1.19159	+	0.433704i
$303$	6.25842	−	20.1093i	0.359537	−	1.15525i
$304$	0.271790	+	1.54140i	0.0155882	+	0.0884051i
$305$		0			0
$306$	15.4656	−	15.6971i	0.884110	−	0.897344i
$307$	−3.17549	+	5.50011i	−0.181235	+	0.313908i	−0.942301	−	0.334766i	$-0.891343\pi$
$307$	−3.17549	+	5.50011i	−0.181235	+	0.313908i	0.761066	+	0.648674i	$0.224676\pi$
$308$	−6.40056	−	2.32961i	−0.364706	−	0.132742i
$309$	−4.43521	−	0.567156i	−0.252310	−	0.0322644i
$310$		0			0
$311$	−0.398806	−	0.334638i	−0.0226142	−	0.0189756i	0.631410	−	0.775449i	$-0.282476\pi$
$311$	−0.398806	−	0.334638i	−0.0226142	−	0.0189756i	−0.654025	+	0.756473i	$0.726921\pi$
$312$	−28.3429	+	37.2227i	−1.60460	+	2.10732i
$313$	15.2139	+	5.53741i	0.859942	+	0.312993i	0.734087	−	0.679056i	$-0.237610\pi$
$313$	15.2139	+	5.53741i	0.859942	+	0.312993i	0.125855	+	0.992049i	$0.459833\pi$
$314$	5.36352	−	9.28988i	0.302681	−	0.524258i
$315$		0			0
$316$	5.45403	+	9.44666i	0.306813	+	0.531416i
$317$	−1.46495	−	8.30814i	−0.0822797	−	0.466631i	−0.997911	−	0.0646113i	$-0.979419\pi$
$317$	−1.46495	−	8.30814i	−0.0822797	−	0.466631i	0.915631	−	0.402020i	$-0.131692\pi$
$318$	−11.2130	+	2.52960i	−0.628794	+	0.141853i
$319$	−9.20335	+	3.34975i	−0.515289	+	0.187550i
$320$		0			0
$321$	8.24781	+	4.25468i	0.460348	+	0.237473i
$322$	0.125448	−	0.105264i	0.00699096	−	0.00586611i
$323$	1.58375			0.0881223
$324$	30.1014	+	16.7878i	1.67230	+	0.932655i
$325$		0			0
$326$	−30.6672	+	25.7328i	−1.69850	+	1.42521i
$327$	26.9313	+	13.8927i	1.48930	+	0.768266i
$328$	−6.97235	+	39.5422i	−0.384984	+	2.18335i
$329$	−3.85304	+	1.40239i	−0.212425	+	0.0773163i
$330$		0			0
$331$	−1.19110	−	6.75507i	−0.0654688	−	0.371292i	−0.999886	−	0.0151112i	$-0.995190\pi$
$331$	−1.19110	−	6.75507i	−0.0654688	−	0.371292i	0.934417	−	0.356181i	$-0.115921\pi$
$332$	1.44625	+	2.50497i	0.0793731	+	0.137478i
$333$	−18.5904	+	1.76570i	−1.01875	+	0.0967596i
$334$	−24.2169	+	41.9449i	−1.32509	+	2.29513i
$335$		0			0
$336$	1.06003	−	1.39214i	0.0578295	−	0.0759472i
$337$	−16.1166	−	13.5234i	−0.877926	−	0.736667i	0.0878255	−	0.996136i	$-0.472008\pi$
$337$	−16.1166	−	13.5234i	−0.877926	−	0.736667i	−0.965752	+	0.259468i	$0.916453\pi$
$338$	−45.1107	−	37.8523i	−2.45370	−	2.05890i
$339$	28.7940	+	3.68205i	1.56387	+	0.199981i
$340$		0			0
$341$	24.1459	−	41.8219i	1.30757	−	2.26478i
$342$	1.00299	+	3.63498i	0.0542354	+	0.196557i
$343$	2.33311	+	4.04106i	0.125976	+	0.218197i
$344$	−5.21166	−	29.5568i	−0.280994	−	1.59360i
$345$		0			0
$346$	7.59726	−	2.76518i	0.408431	−	0.148657i
$347$	1.93708	−	10.9857i	0.103988	−	0.589744i	−0.887632	−	0.460553i	$-0.847651\pi$
$347$	1.93708	−	10.9857i	0.103988	−	0.589744i	0.991620	−	0.129190i	$-0.0412378\pi$
$348$	−0.580871	−	12.2591i	−0.0311379	−	0.657156i
$349$	−6.90169	+	5.79120i	−0.369439	+	0.309996i	−0.808540	−	0.588442i	$-0.799742\pi$
$349$	−6.90169	+	5.79120i	−0.369439	+	0.309996i	0.439101	+	0.898438i	$0.355297\pi$
$350$		0			0
$351$	−16.7720	+	26.9856i	−0.895221	+	1.44039i
$352$	8.34080			0.444566
$353$	7.32667	−	6.14780i	0.389959	−	0.327214i	−0.426638	−	0.904422i	$-0.640302\pi$
$353$	7.32667	−	6.14780i	0.389959	−	0.327214i	0.816597	+	0.577208i	$0.195858\pi$
$354$	24.5832	−	15.7899i	1.30658	−	0.839224i
$355$		0			0
$356$	−22.8924	+	8.33214i	−1.21329	+	0.441603i
$357$	−1.20100	−	1.30093i	−0.0635637	−	0.0688525i
$358$	−5.19791	−	29.4788i	−0.274718	−	1.55800i
$359$	−12.6845	−	21.9702i	−0.669463	−	1.15954i	−0.978054	−	0.208350i	$-0.933191\pi$
$359$	−12.6845	−	21.9702i	−0.669463	−	1.15954i	0.308591	−	0.951195i	$-0.400143\pi$
$360$		0			0
$361$	9.36449	−	16.2198i	0.492868	−	0.853673i
$362$	−10.5297	−	3.83249i	−0.553427	−	0.201431i
$363$	11.3818	+	27.1919i	0.597389	+	1.42721i
$364$	6.02747	+	5.05765i	0.315925	+	0.265093i
$365$		0			0
$366$	20.1528	+	48.1466i	1.05341	+	2.51667i
$367$	−25.2446	−	9.18829i	−1.31776	−	0.479625i	−0.415019	−	0.909813i	$-0.636225\pi$
$367$	−25.2446	−	9.18829i	−1.31776	−	0.479625i	−0.902740	+	0.430188i	$0.858447\pi$
$368$	0.303442	−	0.525578i	0.0158180	−	0.0273976i
$369$	−2.17474	+	27.1815i	−0.113213	+	1.41501i
$370$		0			0
$371$	0.160378	+	0.909551i	0.00832643	+	0.0472215i
$372$	41.0484	+	44.4637i	2.12826	+	2.30534i
$373$	23.6679	−	8.61440i	1.22548	−	0.446037i	0.353430	−	0.935461i	$-0.385015\pi$
$373$	23.6679	−	8.61440i	1.22548	−	0.446037i	0.872046	+	0.489424i	$0.162793\pi$
$374$	−6.75162	+	38.2904i	−0.349118	+	1.97995i
$375$		0			0
$376$	−41.2942	+	34.6499i	−2.12959	+	1.78693i
$377$	11.3138			0.582691
$378$	2.22526	−	3.58037i	0.114455	−	0.184155i
$379$	25.4242			1.30595			0.652976	−	0.757379i	$-0.273520\pi$
$379$	25.4242			1.30595			0.652976	+	0.757379i	$0.273520\pi$
$380$		0			0
$381$	−0.656322	−	13.8515i	−0.0336244	−	0.709632i
$382$	−5.94628	+	33.7230i	−0.304238	+	1.72542i
$383$	−9.29719	+	3.38390i	−0.475064	+	0.172909i	−0.568445	−	0.822721i	$-0.692455\pi$
$383$	−9.29719	+	3.38390i	−0.475064	+	0.172909i	0.0933808	+	0.995630i	$0.470233\pi$
$384$	−10.5784	+	33.9903i	−0.539829	+	1.73456i
$385$		0			0
$386$	20.4713	+	35.4573i	1.04196	+	1.80473i
$387$	−5.42146	−	19.6482i	−0.275589	−	0.998773i
$388$	−20.4083	+	35.3483i	−1.03608	+	1.79454i
$389$	−4.09700	−	1.49119i	−0.207726	−	0.0756061i	0.236061	−	0.971738i	$-0.424143\pi$
$389$	−4.09700	−	1.49119i	−0.207726	−	0.0756061i	−0.443788	+	0.896132i	$0.646366\pi$
$390$		0			0
$391$	−0.470419	−	0.394728i	−0.0237901	−	0.0199623i
$392$	23.3057	+	19.5558i	1.17711	+	0.987715i
$393$	11.3501	−	14.9061i	0.572539	−	0.751913i
$394$	15.4893	+	5.63765i	0.780340	+	0.284021i
$395$		0			0
$396$	−60.5410	+	5.75012i	−3.04230	+	0.288954i
$397$	−8.10396	−	14.0365i	−0.406726	−	0.704470i	0.587795	−	0.809010i	$-0.299996\pi$
$397$	−8.10396	−	14.0365i	−0.406726	−	0.704470i	−0.994521	+	0.104540i	$0.966663\pi$
$398$	−6.47363	−	36.7138i	−0.324494	−	1.84030i
$399$	0.295549	−	0.0666743i	0.0147960	−	0.00333789i
$400$		0			0
$401$	−0.111264	+	0.631007i	−0.00555624	+	0.0315110i	−0.987460	−	0.157870i	$-0.949537\pi$
$401$	−0.111264	+	0.631007i	−0.00555624	+	0.0315110i	0.981904	+	0.189381i	$0.0606483\pi$
$402$	20.8385	+	10.7496i	1.03933	+	0.536143i
$403$	−42.7343	+	35.8583i	−2.12875	+	1.78623i
$404$	−46.5654			−2.31672
$405$		0			0
$406$	−1.50109			−0.0744976
$407$	25.2405	−	21.1793i	1.25113	−	1.04982i
$408$	−20.6866	−	10.6713i	−1.02414	−	0.528308i
$409$	4.23533	−	24.0197i	0.209423	−	1.18770i	−0.680902	−	0.732374i	$-0.738412\pi$
$409$	4.23533	−	24.0197i	0.209423	−	1.18770i	0.890326	−	0.455325i	$-0.150477\pi$
$410$		0			0
$411$	−22.2304	+	5.01506i	−1.09654	+	0.247375i
$412$	1.71671	+	9.73596i	0.0845763	+	0.479656i
$413$	−1.17378	−	2.03304i	−0.0577577	−	0.100039i
$414$	0.608052	−	1.32967i	0.0298841	−	0.0653497i
$415$		0			0
$416$	−9.05405	−	3.29540i	−0.443911	−	0.161570i
$417$	−7.69670	+	10.1081i	−0.376909	+	0.494994i
$418$	−5.09677	−	4.27669i	−0.249291	−	0.209180i
$419$	−13.1999	−	11.0760i	−0.644855	−	0.541098i	0.260650	−	0.965433i	$-0.416063\pi$
$419$	−13.1999	−	11.0760i	−0.644855	−	0.541098i	−0.905505	+	0.424336i	$0.860508\pi$
$420$		0			0
$421$	21.2230	+	7.72454i	1.03435	+	0.376471i	0.802734	−	0.596337i	$-0.203378\pi$
$421$	21.2230	+	7.72454i	1.03435	+	0.376471i	0.231612	+	0.972808i	$0.425600\pi$
$422$	−22.2694	+	38.5718i	−1.08406	+	1.87765i
$423$	−25.6933	+	26.0779i	−1.24925	+	1.26795i
$424$	6.07104	+	10.5154i	0.294836	+	0.510671i
$425$		0			0
$426$	−3.94435	+	12.6738i	−0.191104	+	0.614049i
$427$	3.94078	−	1.43433i	0.190708	−	0.0694119i
$428$	3.56316	−	20.2077i	0.172232	−	0.976775i
$429$	−2.65337	−	55.9985i	−0.128106	−	2.70363i
$430$		0			0
$431$	−10.3129			−0.496754			−0.248377	−	0.968663i	$-0.579897\pi$
$431$	−10.3129			−0.496754			−0.248377	+	0.968663i	$0.579897\pi$
$432$	3.21117	−	15.2889i	0.154497	−	0.735587i
$433$	11.0194			0.529557			0.264778	−	0.964309i	$-0.414701\pi$
$433$	11.0194			0.529557			0.264778	+	0.964309i	$0.414701\pi$
$434$	5.66986	−	4.75758i	0.272162	−	0.228371i
$435$		0			0
$436$	11.6347	−	65.9835i	0.557199	−	3.16003i
$437$	0.0987460	−	0.0359406i	0.00472366	−	0.00171927i
$438$	−4.14856	−	4.49374i	−0.198226	−	0.214719i
$439$	−4.27981	−	24.2720i	−0.204264	−	1.15844i	−0.898593	−	0.438783i	$-0.855410\pi$
$439$	−4.27981	−	24.2720i	−0.204264	−	1.15844i	0.694329	−	0.719658i	$-0.255701\pi$
$440$		0			0
$441$	17.0123	+	11.7248i	0.810110	+	0.558323i
$442$	22.4573	−	38.8971i	1.06818	−	1.85015i
$443$	20.5698	+	7.48678i	0.977299	+	0.355708i	0.780789	−	0.624794i	$-0.214817\pi$
$443$	20.5698	+	7.48678i	0.977299	+	0.355708i	0.196509	+	0.980502i	$0.437039\pi$
$444$	15.9420	+	38.0867i	0.756575	+	1.80752i
$445$		0			0
$446$	5.76310	+	4.83582i	0.272891	+	0.228983i
$447$	8.89834	+	21.2588i	0.420877	+	1.00551i
$448$	3.09988	+	1.12826i	0.146456	+	0.0533055i
$449$	−0.0863524	+	0.149567i	−0.00407522	+	0.00705849i	−0.868056	−	0.496467i	$-0.834631\pi$
$449$	−0.0863524	+	0.149567i	−0.00407522	+	0.00705849i	0.863981	+	0.503525i	$0.167964\pi$
$450$		0			0
$451$	−24.0566	−	41.6673i	−1.13278	−	1.96204i
$452$	−11.1451	−	63.2071i	−0.524222	−	2.97301i
$453$	10.7232	+	11.6154i	0.503819	+	0.545739i
$454$	−15.8302	+	5.76171i	−0.742947	+	0.270411i
$455$		0			0
$456$	3.35138	−	2.15261i	0.156943	−	0.100805i
$457$	−6.86690	+	5.76201i	−0.321220	+	0.269536i	−0.789111	−	0.614251i	$-0.789458\pi$
$457$	−6.86690	+	5.76201i	−0.321220	+	0.269536i	0.467891	+	0.883786i	$0.345014\pi$
$458$	24.4703			1.14342
$459$	−14.6711	−	5.88632i	−0.684788	−	0.274750i
$460$		0			0
$461$	12.4655	−	10.4598i	0.580576	−	0.487161i	−0.304560	−	0.952493i	$-0.598510\pi$
$461$	12.4655	−	10.4598i	0.580576	−	0.487161i	0.885136	+	0.465332i	$0.154065\pi$
$462$	0.352042	+	7.42973i	0.0163785	+	0.345662i
$463$	−2.38861	+	13.5465i	−0.111008	+	0.629558i	0.877642	+	0.479318i	$0.159116\pi$
$463$	−2.38861	+	13.5465i	−0.111008	+	0.629558i	−0.988650	+	0.150240i	$0.951995\pi$
$464$	−5.22741	+	1.90262i	−0.242677	+	0.0883270i
$465$		0			0
$466$	−4.70704	−	26.6949i	−0.218049	−	1.23662i
$467$	2.09492	+	3.62851i	0.0969414	+	0.167907i	0.910417	−	0.413691i	$-0.135761\pi$
$467$	2.09492	+	3.62851i	0.0969414	+	0.167907i	−0.813476	+	0.581599i	$0.802427\pi$
$468$	67.9899	+	17.6776i	3.14283	+	0.817146i
$469$	0.941987	−	1.63157i	0.0434969	−	0.0753389i
$470$		0			0
$471$	−7.63307	−	0.976085i	−0.351713	−	0.0449756i
$472$	−23.6421	−	19.8381i	−1.08822	−	0.913123i
$473$	27.5496	+	23.1169i	1.26673	+	1.06292i
$474$	7.21626	−	9.47709i	0.331454	−	0.435297i
$475$		0			0
$476$	−1.95734	+	3.39022i	−0.0897148	+	0.155391i
$477$	4.77976	+	6.71941i	0.218850	+	0.307661i
$478$	17.3188	+	29.9970i	0.792143	+	1.37203i
$479$	4.29952	+	24.3838i	0.196450	+	1.11412i	0.910339	+	0.413864i	$0.135821\pi$
$479$	4.29952	+	24.3838i	0.196450	+	1.11412i	−0.713888	+	0.700259i	$0.753068\pi$
$480$		0			0
$481$	−35.7668	+	13.0180i	−1.63082	+	0.593571i
$482$	4.26190	−	24.1704i	0.194124	−	1.10093i
$483$	−0.104404	−	0.0538574i	−0.00475055	−	0.00245060i
$484$	49.9277	−	41.8943i	2.26944	−	1.90429i
$485$		0			0
$486$	4.21890	−	37.4004i	0.191373	−	1.69652i
$487$	14.2164			0.644205			0.322102	−	0.946705i	$-0.395610\pi$
$487$	14.2164			0.644205			0.322102	+	0.946705i	$0.395610\pi$
$488$	42.2346	−	35.4390i	1.91187	−	1.60425i
$489$	25.5227	+	13.1660i	1.15418	+	0.595388i
$490$		0			0
$491$	−10.7333	+	3.90659i	−0.484385	+	0.176302i	−0.572658	−	0.819795i	$-0.694088\pi$
$491$	−10.7333	+	3.90659i	−0.484385	+	0.176302i	0.0882726	+	0.996096i	$0.471865\pi$
$492$	58.8127	−	13.2678i	2.65148	−	0.598160i
$493$	0.977453	+	5.54341i	0.0440222	+	0.249663i
$494$	3.84291	+	6.65611i	0.172901	+	0.299473i
$495$		0			0
$496$	13.7146	−	23.7544i	0.615805	−	1.06661i
$497$	1.00217	+	0.364761i	0.0449536	+	0.0163618i
$498$	1.91354	−	2.51304i	0.0857477	−	0.112612i
$499$	29.0144	+	24.3459i	1.29886	+	1.08987i	0.990341	+	0.138656i	$0.0442781\pi$
$499$	29.0144	+	24.3459i	1.29886	+	1.08987i	0.308520	+	0.951218i	$0.400166\pi$
$500$		0			0
$501$	34.4642	+	4.40714i	1.53975	+	0.196897i
$502$	−3.47767	−	1.26577i	−0.155216	−	0.0564940i
$503$	18.1596	−	31.4533i	0.809694	−	1.40243i	−0.103381	−	0.994642i	$-0.532966\pi$
$503$	18.1596	−	31.4533i	0.809694	−	1.40243i	0.913076	−	0.407790i	$-0.133700\pi$
$504$	−4.30964	−	1.12052i	−0.191967	−	0.0499120i
$505$		0			0
$506$	0.447976	+	2.54060i	0.0199149	+	0.112943i
$507$	−12.5533	+	40.3359i	−0.557514	+	1.79138i
$508$	−28.8111	+	10.4864i	−1.27828	+	0.465258i
$509$	−1.95163	+	11.0682i	−0.0865043	+	0.490590i	0.910518	+	0.413470i	$0.135683\pi$
$509$	−1.95163	+	11.0682i	−0.0865043	+	0.490590i	−0.997022	+	0.0771197i	$0.975428\pi$
$510$		0			0
$511$	−0.376434	+	0.315866i	−0.0166525	+	0.0139731i
$512$	31.3000			1.38328
$513$	2.12759	−	1.67055i	0.0939352	−	0.0737564i
$514$	−57.8762			−2.55281
$515$		0			0
$516$	−37.9179	+	24.3548i	−1.66924	+	1.07216i
$517$	11.2166	−	63.6125i	0.493305	−	2.79767i
$518$	4.74543	−	1.72720i	0.208502	−	0.0758886i
$519$	−3.93414	−	4.26148i	−0.172690	−	0.187058i
$520$		0			0
$521$	2.20153	+	3.81316i	0.0964507	+	0.167057i	0.910213	−	0.414140i	$-0.135918\pi$
$521$	2.20153	+	3.81316i	0.0964507	+	0.167057i	−0.813762	+	0.581198i	$0.802584\pi$
$522$	−12.1040	+	5.75405i	−0.529779	+	0.251848i
$523$	7.79908	−	13.5084i	0.341030	−	0.590681i	−0.643594	−	0.765367i	$-0.722558\pi$
$523$	7.79908	−	13.5084i	0.341030	−	0.590681i	0.984624	+	0.174686i	$0.0558910\pi$
$524$	−38.9261	−	14.1679i	−1.70050	−	0.618930i
$525$		0			0
$526$	−15.2114	−	12.7639i	−0.663249	−	0.556532i
$527$	−21.2614	−	17.8405i	−0.926163	−	0.777143i
$528$	10.6431	+	25.4272i	0.463182	+	1.10658i
$529$	21.5746	+	7.85253i	0.938028	+	0.341414i
$530$		0			0
$531$	−17.2579	−	11.8941i	−0.748930	−	0.516158i
$532$	−0.334942	−	0.580137i	−0.0145216	−	0.0251521i
$533$	9.65127	+	54.7350i	0.418043	+	2.37084i
$534$	18.0455	+	19.5470i	0.780907	+	0.845881i
$535$		0			0
$536$	4.30093	−	24.3918i	0.185772	−	1.05357i
$537$	−18.0675	+	11.6048i	−0.779670	+	0.500785i
$538$	−3.80533	+	3.19305i	−0.164060	+	0.137662i
$539$	−36.4555			−1.57025
$540$		0			0
$541$	−1.52861			−0.0657202			−0.0328601	−	0.999460i	$-0.510462\pi$
$541$	−1.52861			−0.0657202			−0.0328601	+	0.999460i	$0.510462\pi$
$542$	28.5641	−	23.9681i	1.22693	−	1.02952i
$543$	0.380456	+	8.02941i	0.0163269	+	0.344575i
$544$	0.832422	−	4.72090i	0.0356898	−	0.202407i
$545$		0			0
$546$	2.55330	−	8.20415i	0.109271	−	0.351105i
$547$	2.13129	+	12.0871i	0.0911273	+	0.516808i	0.995865	+	0.0908404i	$0.0289553\pi$
$547$	2.13129	+	12.0871i	0.0911273	+	0.516808i	−0.904738	+	0.425968i	$0.859934\pi$
$548$	25.1934	+	43.6363i	1.07621	+	1.86405i
$549$	26.2784	−	26.6717i	1.12154	−	1.13832i
$550$		0			0
$551$	−0.905136	−	0.329443i	−0.0385601	−	0.0140347i
$552$	−1.53196	−	0.195901i	−0.0652047	−	0.00833809i
$553$	−0.733168	−	0.615201i	−0.0311775	−	0.0261610i
$554$	−2.22666	−	1.86839i	−0.0946019	−	0.0793804i
$555$		0			0
$556$	26.3964	+	9.60751i	1.11946	+	0.407449i
$557$	8.99212	−	15.5748i	0.381008	−	0.659926i	−0.610198	−	0.792249i	$-0.708910\pi$
$557$	8.99212	−	15.5748i	0.381008	−	0.659926i	0.991207	+	0.132323i	$0.0422436\pi$
$558$	27.4820	−	60.0969i	1.16341	−	2.54410i
$559$	−20.7721	−	35.9784i	−0.878567	−	1.52172i
$560$		0			0
$561$	27.2082	−	6.13804i	1.14873	−	0.259148i
$562$	−63.0338	+	22.9424i	−2.65892	+	0.967768i
$563$	1.63413	−	9.26763i	0.0688705	−	0.390584i	−0.930815	−	0.365492i	$-0.880901\pi$
$563$	1.63413	−	9.26763i	0.0688705	−	0.390584i	0.999685	−	0.0250923i	$-0.00798797\pi$
$564$	71.9351	+	37.1081i	3.02901	+	1.56253i
$565$		0			0
$566$	54.7691			2.30212
$567$	−2.98563	−	0.480827i	−0.125385	−	0.0201928i
$568$	14.0209			0.588302
$569$	−25.8778	+	21.7141i	−1.08485	+	0.910301i	−0.996315	−	0.0857719i	$-0.972664\pi$
$569$	−25.8778	+	21.7141i	−1.08485	+	0.910301i	−0.0885394	+	0.996073i	$0.528220\pi$
$570$		0			0
$571$	−0.978955	+	5.55193i	−0.0409680	+	0.232341i	−0.998416	−	0.0562653i	$-0.982081\pi$
$571$	−0.978955	+	5.55193i	−0.0409680	+	0.232341i	0.957448	+	0.288606i	$0.0931919\pi$
$572$	−116.477	+	42.3942i	−4.87015	+	1.77259i
$573$	23.9628	−	5.40588i	1.00106	−	0.225834i
$574$	−1.28050	−	7.26209i	−0.0534472	−	0.303114i
$575$		0			0
$576$	29.3209	−	2.78486i	1.22170	−	0.116036i
$577$	−7.94027	+	13.7529i	−0.330558	+	0.572543i	−0.982621	−	0.185622i	$-0.940570\pi$
$577$	−7.94027	+	13.7529i	−0.330558	+	0.572543i	0.652064	+	0.758164i	$0.273904\pi$
$578$	−17.5718	−	6.39561i	−0.730891	−	0.266022i
$579$	17.7932	−	23.3678i	0.739460	−	0.971131i
$580$		0			0
$581$	−0.194414	−	0.163133i	−0.00806567	−	0.00676790i
$582$	44.2123	+	5.65368i	1.83266	+	0.234353i
$583$	−13.6721	−	4.97623i	−0.566240	−	0.206094i
$584$	−3.23015	+	5.59478i	−0.133664	+	0.231514i
$585$		0			0
$586$	20.1527	+	34.9055i	0.832500	+	1.44193i
$587$	3.45096	+	19.5714i	0.142436	+	0.807797i	0.969390	+	0.245527i	$0.0789609\pi$
$587$	3.45096	+	19.5714i	0.142436	+	0.807797i	−0.826953	+	0.562270i	$0.809928\pi$
$588$	13.5750	−	43.6187i	0.559825	−	1.79881i
$589$	4.46300	−	1.62440i	0.183895	−	0.0669323i
$590$		0			0
$591$	−0.559657	−	11.8114i	−0.0230212	−	0.485856i
$592$	14.3364	−	12.0296i	0.589221	−	0.494416i
$593$	−43.0280			−1.76695			−0.883474	−	0.468480i	$-0.844802\pi$
$593$	−43.0280			−1.76695			−0.883474	+	0.468480i	$0.844802\pi$
$594$	31.3188	+	58.5603i	1.28502	+	2.40276i
$595$		0			0
$596$	39.0337	−	32.7532i	1.59888	−	1.34162i
$597$	−22.5018	+	14.4530i	−0.920936	+	0.591521i
$598$	0.517492	−	2.93484i	0.0211618	−	0.120015i
$599$	36.3045	−	13.2138i	1.48336	−	0.539900i	0.531671	−	0.846951i	$-0.321564\pi$
$599$	36.3045	−	13.2138i	1.48336	−	0.539900i	0.951693	+	0.307051i	$0.0993422\pi$
$600$		0			0
$601$	−1.31942	−	7.48281i	−0.0538203	−	0.305230i	0.946000	−	0.324166i	$-0.105083\pi$
$601$	−1.31942	−	7.48281i	−0.0538203	−	0.305230i	−0.999821	+	0.0189352i	$0.993972\pi$
$602$	2.75599	+	4.77351i	0.112326	+	0.194554i
$603$	1.34150	−	16.7671i	0.0546302	−	0.682808i
$604$	17.4762	−	30.2697i	0.711098	−	1.23166i
$605$		0			0
$606$	19.6338	+	46.9067i	0.797570	+	1.90546i
$607$	0.651945	+	0.547047i	0.0264616	+	0.0222040i	0.655923	−	0.754828i	$-0.272280\pi$
$607$	0.651945	+	0.547047i	0.0264616	+	0.0222040i	−0.629461	+	0.777032i	$0.716724\pi$
$608$	0.628391	+	0.527283i	0.0254846	+	0.0213841i
$609$	0.415777	+	0.993324i	0.0168482	+	0.0402515i
$610$		0			0
$611$	−37.3087	+	64.6205i	−1.50935	+	2.61427i
$612$	−2.78749	+	34.8401i	−0.112678	+	1.40833i
$613$	0.0839581	+	0.145420i	0.00339104	+	0.00587345i	0.867716	−	0.497060i	$-0.165587\pi$
$613$	0.0839581	+	0.145420i	0.00339104	+	0.00587345i	−0.864325	+	0.502934i	$0.832254\pi$
$614$	−2.66275	−	15.1012i	−0.107460	−	0.609434i
$615$		0			0
$616$	7.38308	−	2.68722i	0.297473	−	0.108271i
$617$	−2.89015	+	16.3908i	−0.116353	+	0.659871i	0.869718	+	0.493548i	$0.164300\pi$
$617$	−2.89015	+	16.3908i	−0.116353	+	0.659871i	−0.986071	+	0.166322i	$0.946811\pi$
$618$	9.08348	−	5.83436i	0.365391	−	0.234692i
$619$	−33.6283	+	28.2175i	−1.35163	+	1.13416i	−0.373165	+	0.927765i	$0.621728\pi$
$619$	−33.6283	+	28.2175i	−1.35163	+	1.13416i	−0.978470	+	0.206391i	$0.933828\pi$
$620$		0			0
$621$	−1.04831	−	0.0340724i	−0.0420674	−	0.00136728i
$622$	1.25698			0.0504001
$623$	1.63742	−	1.37396i	0.0656020	−	0.0550466i
$624$	−1.50709	−	31.8066i	−0.0603318	−	1.27328i
$625$		0			0
$626$	−36.7333	+	13.3698i	−1.46816	+	0.534366i
$627$	−1.41832	+	4.55730i	−0.0566423	+	0.182001i
$628$	2.95449	+	16.7558i	0.117897	+	0.668627i
$629$	−9.46847	−	16.3999i	−0.377533	−	0.653906i
$630$		0			0
$631$	6.62243	−	11.4704i	0.263635	−	0.456629i	−0.703570	−	0.710626i	$-0.748412\pi$
$631$	6.62243	−	11.4704i	0.263635	−	0.456629i	0.967205	+	0.253997i	$0.0817453\pi$
$632$	−11.8237	−	4.30347i	−0.470321	−	0.171183i
$633$	31.6927	+	4.05273i	1.25967	+	0.161081i
$634$	15.6036	+	13.0930i	0.619698	+	0.519989i
$635$		0			0
$636$	11.0451	−	14.5055i	0.437968	−	0.575182i
$637$	39.5729	+	14.4034i	1.56794	+	0.570682i
$638$	11.8236	−	20.4790i	0.468100	−	0.810773i
$639$	9.47927	−	0.900331i	0.374994	−	0.0356165i
$640$		0			0
$641$	−7.29257	−	41.3582i	−0.288039	−	1.63355i	−0.694223	−	0.719760i	$-0.744252\pi$
$641$	−7.29257	−	41.3582i	−0.288039	−	1.63355i	0.406183	−	0.913792i	$-0.366859\pi$
$642$	−21.8581	+	4.93108i	−0.862672	+	0.194614i
$643$	−26.4485	+	9.62646i	−1.04303	+	0.379631i	−0.806027	−	0.591879i	$-0.798386\pi$
$643$	−26.4485	+	9.62646i	−1.04303	+	0.379631i	−0.237000	+	0.971510i	$0.576164\pi$
$644$	−0.0451039	+	0.255797i	−0.00177734	+	0.0100798i
$645$		0			0
$646$	−2.92927	+	2.45795i	−0.115251	+	0.0967069i
$647$	−4.87520			−0.191664			−0.0958319	−	0.995398i	$-0.530551\pi$
$647$	−4.87520			−0.191664			−0.0958319	+	0.995398i	$0.530551\pi$
$648$	−39.0461	+	7.48464i	−1.53388	+	0.294024i
$649$	36.9819			1.45166
$650$		0			0
$651$	−4.71873	−	2.43418i	−0.184942	−	0.0954032i
$652$	11.0261	−	62.5322i	0.431816	−	2.44895i
$653$	3.30599	−	1.20328i	0.129373	−	0.0470880i	−0.276522	−	0.961008i	$-0.589182\pi$
$653$	3.30599	−	1.20328i	0.129373	−	0.0470880i	0.405895	+	0.913920i	$0.366960\pi$
$654$	−71.3727	+	16.1013i	−2.79089	+	0.629611i
$655$		0			0
$656$	−13.6639	−	23.6666i	−0.533487	−	0.924027i
$657$	−1.82459	+	3.98996i	−0.0711839	+	0.155663i
$658$	4.95001	−	8.57367i	0.192972	−	0.334236i
$659$	−3.85106	−	1.40167i	−0.150016	−	0.0546013i	0.265921	−	0.963995i	$-0.414324\pi$
$659$	−3.85106	−	1.40167i	−0.150016	−	0.0546013i	−0.415937	+	0.909394i	$0.636546\pi$
$660$		0			0
$661$	10.8180	+	9.07740i	0.420773	+	0.353070i	0.828457	−	0.560053i	$-0.189219\pi$
$661$	10.8180	+	9.07740i	0.420773	+	0.353070i	−0.407684	+	0.913123i	$0.633664\pi$
$662$	12.6868	+	10.6455i	0.493085	+	0.413748i
$663$	−31.9600	−	4.08691i	−1.24122	−	0.158722i
$664$	−3.13529	−	1.14115i	−0.121673	−	0.0442853i
$665$		0			0
$666$	31.6441	−	32.1177i	1.22618	−	1.24454i
$667$	0.186742	+	0.323446i	0.00723067	+	0.0125239i
$668$	−13.3399	−	75.6542i	−0.516136	−	2.92715i
$669$	1.60375	−	5.15311i	0.0620046	−	0.199231i
$670$		0			0
$671$	−11.4720	+	65.0611i	−0.442873	+	2.51166i
$672$	−0.0434039	−	0.916026i	−0.00167434	−	0.0353365i
$673$	−31.7224	+	26.6182i	−1.22281	+	1.02606i	−0.224134	+	0.974558i	$0.571955\pi$
$673$	−31.7224	+	26.6182i	−1.22281	+	1.02606i	−0.998673	+	0.0514985i	$0.983600\pi$
$674$	50.7970			1.95663
$675$		0			0
$676$	93.4024			3.59240
$677$	−23.8227	+	19.9896i	−0.915581	+	0.768264i	−0.973173	−	0.230077i	$-0.926102\pi$
$677$	−23.8227	+	19.9896i	−0.915581	+	0.768264i	0.0575915	+	0.998340i	$0.481658\pi$
$678$	−58.9711	+	37.8774i	−2.26477	+	1.45467i
$679$	0.621884	−	3.52688i	0.0238657	−	0.135349i
$680$		0			0
$681$	8.19745	+	8.87951i	0.314127	+	0.340264i
$682$	20.2471	+	114.827i	0.775301	+	4.39695i
$683$	−6.49887	−	11.2564i	−0.248673	−	0.430713i	0.714485	−	0.699651i	$-0.246661\pi$
$683$	−6.49887	−	11.2564i	−0.248673	−	0.430713i	−0.963158	+	0.268937i	$0.913328\pi$
$684$	−4.92463	−	3.39403i	−0.188298	−	0.129774i
$685$		0			0
$686$	−10.5869	−	3.85332i	−0.404210	−	0.147121i
$687$	−6.77789	−	16.1929i	−0.258593	−	0.617798i
$688$	15.6479	+	13.1302i	0.596571	+	0.500583i
$689$	12.8751	+	10.8035i	0.490504	+	0.411582i
$690$		0			0
$691$	−44.3322	−	16.1356i	−1.68648	−	0.613827i	−0.692301	−	0.721609i	$-0.743403\pi$
$691$	−44.3322	−	16.1356i	−1.68648	−	0.613827i	−0.994175	+	0.107782i	$0.965625\pi$
$692$	−6.41171	+	11.1054i	−0.243737	+	0.422164i
$693$	4.81902	−	2.29088i	0.183059	−	0.0870233i
$694$	13.4668	+	23.3252i	0.511194	+	0.885413i
$695$		0			0
$696$	9.60289	+	10.4019i	0.363997	+	0.394283i
$697$	−25.9846	+	9.45762i	−0.984237	+	0.358233i
$698$	3.77738	−	21.4226i	0.142976	−	0.810856i
$699$	−16.3613	+	10.5089i	−0.618839	+	0.397483i
$700$		0			0
$701$	8.98862			0.339496			0.169748	−	0.985488i	$-0.445705\pi$
$701$	8.98862			0.339496			0.169748	+	0.985488i	$0.445705\pi$
$702$	−10.8601	−	75.9418i	−0.409887	−	2.86624i
$703$	3.24051			0.122218
$704$	−39.8095	+	33.4041i	−1.50038	+	1.25897i
$705$		0			0
$706$	−4.00997	+	22.7417i	−0.150917	+	0.855895i
$707$	3.83929	−	1.39739i	0.144391	−	0.0525542i
$708$	−13.7710	+	44.2485i	−0.517547	+	1.66296i
$709$	−6.01200	−	34.0958i	−0.225785	−	1.28049i	−0.861178	−	0.508304i	$-0.830273\pi$
$709$	−6.01200	−	34.0958i	−0.225785	−	1.28049i	0.635392	−	0.772189i	$-0.280838\pi$
$710$		0			0
$711$	−8.27014	−	2.15026i	−0.310154	−	0.0806411i
$712$	14.0506	−	24.3363i	0.526568	−	0.912043i
$713$	−1.73050	−	0.629849i	−0.0648076	−	0.0235880i
$714$	4.24036	+	0.542240i	0.158692	+	0.0202928i
$715$		0			0
$716$	36.3702	+	30.5182i	1.35922	+	1.14052i
$717$	15.0531	−	19.7692i	0.562169	−	0.738294i
$718$	57.5584	+	20.9495i	2.14806	+	0.781830i
$719$	11.7846	−	20.4116i	0.439493	−	0.761224i	−0.558157	−	0.829735i	$-0.688491\pi$
$719$	11.7846	−	20.4116i	0.439493	−	0.761224i	0.997650	+	0.0685110i	$0.0218248\pi$
$720$		0			0
$721$	−0.433710	−	0.751207i	−0.0161522	−	0.0279764i
$722$	7.85242	+	44.5333i	0.292237	+	1.65736i
$723$	−17.1750	+	3.87458i	−0.638743	+	0.144097i
$724$	16.7012	−	6.07874i	0.620695	−	0.225915i
$725$		0			0
$726$	−63.2529	−	32.6293i	−2.34753	−	1.21099i
$727$	−20.7902	+	17.4450i	−0.771064	+	0.647000i	−0.940981	−	0.338459i	$-0.890094\pi$
$727$	−20.7902	+	17.4450i	−0.771064	+	0.647000i	0.169917	+	0.985458i	$0.445650\pi$
$728$	−9.07613			−0.336384
$729$	−25.9178	+	7.56753i	−0.959919	+	0.280279i
$730$		0			0
$731$	15.8336	−	13.2860i	0.585629	−	0.491401i
$732$	−73.5733	−	37.9532i	−2.71935	−	1.40279i
$733$	2.58612	−	14.6666i	0.0955205	−	0.541724i	−0.899066	−	0.437813i	$-0.855753\pi$
$733$	2.58612	−	14.6666i	0.0955205	−	0.541724i	0.994587	−	0.103911i	$-0.0331356\pi$
$734$	60.9520	−	22.1847i	2.24978	−	0.818852i
$735$		0			0
$736$	−0.0552319	−	0.313235i	−0.00203587	−	0.0115460i
$737$	14.8395	+	25.7027i	0.546619	+	0.946771i
$738$	−38.1628	−	53.6495i	−1.40479	−	1.97487i
$739$	−5.36887	+	9.29916i	−0.197497	+	0.342075i	−0.947716	−	0.319114i	$-0.896615\pi$
$739$	−5.36887	+	9.29916i	−0.197497	+	0.342075i	0.750219	+	0.661189i	$0.229948\pi$
$740$		0			0
$741$	3.34017	−	4.38663i	0.122704	−	0.161147i
$742$	−1.70824	−	1.43338i	−0.0627114	−	0.0526211i
$743$	12.7210	+	10.6742i	0.466687	+	0.391597i	0.845584	−	0.533842i	$-0.179252\pi$
$743$	12.7210	+	10.6742i	0.466687	+	0.391597i	−0.378897	+	0.925439i	$0.623697\pi$
$744$	−69.2398	−	8.85410i	−2.53846	−	0.324607i
$745$		0			0
$746$	−30.4062	+	52.6651i	−1.11325	+	1.92821i
$747$	−2.19300	−	0.570186i	−0.0802375	−	0.0208620i
$748$	−30.8348	−	53.4074i	−1.12743	−	1.95277i
$749$	0.312635	+	1.77304i	0.0114234	+	0.0647854i
$750$		0			0
$751$	−4.89963	+	1.78332i	−0.178790	+	0.0650743i	−0.429864	−	0.902894i	$-0.641439\pi$
$751$	−4.89963	+	1.78332i	−0.178790	+	0.0650743i	0.251074	+	0.967968i	$0.419216\pi$
$752$	6.37092	−	36.1313i	0.232323	−	1.31757i
$753$	0.125655	+	2.65190i	0.00457911	+	0.0966407i
$754$	−20.9258	+	17.5588i	−0.762072	+	0.639455i
$755$		0			0
$756$	0.946549	+	6.61898i	0.0344257	+	0.240730i
$757$	43.6180			1.58532			0.792662	−	0.609661i	$-0.208694\pi$
$757$	43.6180			1.58532			0.792662	+	0.609661i	$0.208694\pi$
$758$	−47.0240	+	39.4578i	−1.70799	+	1.43317i
$759$	1.55712	−	1.00015i	0.0565200	−	0.0363031i
$760$		0			0
$761$	11.6568	−	4.24273i	0.422559	−	0.153799i	−0.121984	−	0.992532i	$-0.538926\pi$
$761$	11.6568	−	4.24273i	0.422559	−	0.153799i	0.544542	+	0.838733i	$0.316703\pi$
$762$	22.7111	+	24.6008i	0.822737	+	0.891192i
$763$	1.02084	+	5.78945i	0.0369567	+	0.209592i
$764$	−27.1568	−	47.0369i	−0.982497	−	1.70174i
$765$		0			0
$766$	11.9441	−	20.6878i	0.431559	−	0.747482i
$767$	−40.1443	−	14.6113i	−1.44953	−	0.527584i
$768$	−20.0552	−	47.9133i	−0.723679	−	1.72892i
$769$	−30.8699	−	25.9030i	−1.11320	−	0.934085i	−0.114958	−	0.993370i	$-0.536673\pi$
$769$	−30.8699	−	25.9030i	−1.11320	−	0.934085i	−0.998241	+	0.0592857i	$0.981118\pi$
$770$		0			0
$771$	16.0308	+	38.2989i	0.577336	+	1.37930i
$772$	−61.0231	−	22.2106i	−2.19627	−	0.799376i
$773$	−17.2390	+	29.8587i	−0.620042	+	1.07394i	0.369435	+	0.929257i	$0.379551\pi$
$773$	−17.2390	+	29.8587i	−0.620042	+	1.07394i	−0.989477	+	0.144688i	$0.953782\pi$
$774$	40.5210	+	27.9269i	1.45650	+	1.00381i
$775$		0			0
$776$	−8.17574	−

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84958 + 1.55198i) q^{2} +(1.53931 + 0.794060i) q^{3} +(0.665000 - 3.77140i) q^{4} +(-4.07944 + 0.920299i) q^{6} +(0.0583477 + 0.330906i) q^{7} +(2.20872 + 3.82562i) q^{8} +(1.73894 + 2.44461i) q^{9} +O(q^{10})\)	\(q+(-1.84958 + 1.55198i) q^{2} +(1.53931 + 0.794060i) q^{3} +(0.665000 - 3.77140i) q^{4} +(-4.07944 + 0.920299i) q^{6} +(0.0583477 + 0.330906i) q^{7} +(2.20872 + 3.82562i) q^{8} +(1.73894 + 2.44461i) q^{9} +(-4.97408 - 1.81042i) q^{11} +(4.01836 - 5.27730i) q^{12} +(4.68414 + 3.93046i) q^{13} +(-0.621479 - 0.521483i) q^{14} +(-2.82523 - 1.02830i) q^{16} +(-1.52112 + 2.63465i) q^{17} +(-7.01028 - 1.82269i) q^{18} +(-0.260295 - 0.450843i) q^{19} +(-0.172944 + 0.555698i) q^{21} +(12.0097 - 4.37117i) q^{22} +(-0.0350517 + 0.198788i) q^{23} +(0.362131 + 7.64266i) q^{24} -14.7637 q^{26} +(0.735594 + 5.14382i) q^{27} +1.28678 q^{28} +(1.41738 - 1.18933i) q^{29} +(-1.58422 + 8.98458i) q^{31} +(-1.48070 + 0.538930i) q^{32} +(-6.21906 - 6.73651i) q^{33} +(-1.27550 - 7.23373i) q^{34} +(10.3760 - 4.93257i) q^{36} +(-3.11234 + 5.39074i) q^{37} +(1.18114 + 0.429898i) q^{38} +(4.08931 + 9.76968i) q^{39} +(6.96293 + 5.84259i) q^{41} +(-0.542558 - 1.29621i) q^{42} +(-6.38441 - 2.32373i) q^{43} +(-10.1356 + 17.5553i) q^{44} +(-0.243684 - 0.422073i) q^{46} +(2.11902 + 12.0175i) q^{47} +(-3.53236 - 3.82627i) q^{48} +(6.47175 - 2.35553i) q^{49} +(-4.43354 + 2.84768i) q^{51} +(17.9383 - 15.0520i) q^{52} +2.74867 q^{53} +(-9.34365 - 8.37227i) q^{54} +(-1.13705 + 0.954096i) q^{56} +(-0.0426766 - 0.900676i) q^{57} +(-0.775751 + 4.39950i) q^{58} +(-6.56519 + 2.38954i) q^{59} +(-2.16727 - 12.2912i) q^{61} +(-11.0137 - 19.0764i) q^{62} +(-0.707472 + 0.718062i) q^{63} +(4.90880 - 8.50230i) q^{64} +(21.9576 + 2.80784i) q^{66} +(-4.29512 - 3.60403i) q^{67} +(8.92479 + 7.48879i) q^{68} +(-0.211805 + 0.278163i) q^{69} +(1.58699 - 2.74874i) q^{71} +(-5.51130 + 12.0520i) q^{72} +(0.731226 + 1.26652i) q^{73} +(-2.60980 - 14.8009i) q^{74} +(-1.87341 + 0.681865i) q^{76} +(0.308852 - 1.75159i) q^{77} +(-22.7259 - 11.7233i) q^{78} +(-2.18198 + 1.83090i) q^{79} +(-2.95220 + 8.50203i) q^{81} -21.9461 q^{82} +(-0.578595 + 0.485499i) q^{83} +(1.98075 + 1.02178i) q^{84} +(15.4149 - 5.61055i) q^{86} +(3.12618 - 0.705250i) q^{87} +(-4.06039 - 23.0276i) q^{88} +(-3.18070 - 5.50914i) q^{89} +(-1.02731 + 1.77934i) q^{91} +(0.726400 + 0.264388i) q^{92} +(-9.57291 + 12.5721i) q^{93} +(-22.5703 - 18.9387i) q^{94} +(-2.70719 - 0.346184i) q^{96} +(-10.0155 - 3.64534i) q^{97} +(-8.31429 + 14.4008i) q^{98} +(-4.22385 - 15.3079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

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