LMFDB - Embedded newform 69.2.e.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.2
Root			$0.480233 + 1.05156i$ of defining polynomial
Character	$\chi$	$=$	69.49
Dual form			69.2.e.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.319381 + 2.22134i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.91338 + 0.855446i) q^{4} +(-1.82263 + 2.10342i) q^{5} +(2.15328 + 0.632261i) q^{6} +(2.85304 - 1.83354i) q^{7} +(-0.966182 - 2.11564i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.319381 + 2.22134i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.91338 + 0.855446i) q^{4} +(-1.82263 + 2.10342i) q^{5} +(2.15328 + 0.632261i) q^{6} +(2.85304 - 1.83354i) q^{7} +(-0.966182 - 2.11564i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-5.25454 - 3.37689i) q^{10} +(0.730673 - 5.08195i) q^{11} +(-0.432121 + 3.00547i) q^{12} +(-1.83466 - 1.17906i) q^{13} +(4.98413 + 5.75199i) q^{14} +(1.15620 + 2.53171i) q^{15} +(-0.717732 + 0.461258i) q^{16} +(2.48322 + 0.729141i) q^{17} +(1.46963 - 1.69604i) q^{18} +(-2.21869 + 0.651466i) q^{19} +(3.51064 - 7.68724i) q^{20} +(-0.482649 - 3.35690i) q^{21} +11.5221 q^{22} +(-3.18567 + 3.58490i) q^{23} -2.32582 q^{24} +(-0.390848 - 2.71841i) q^{25} +(2.03315 - 4.45197i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-6.74351 + 7.78242i) q^{28} +(-5.12647 - 1.50527i) q^{29} +(-5.25454 + 3.37689i) q^{30} +(3.71752 + 8.14024i) q^{31} +(-4.30002 - 4.96249i) q^{32} +(-4.31917 - 2.77576i) q^{33} +(-0.826577 + 5.74897i) q^{34} +(-1.34332 + 9.34301i) q^{35} +(2.55436 + 1.64159i) q^{36} +(-1.43712 - 1.65853i) q^{37} +(-2.15574 - 4.72041i) q^{38} +(-1.83466 + 1.17906i) q^{39} +(6.21109 + 1.82374i) q^{40} +(-0.199985 + 0.230795i) q^{41} +(7.30268 - 2.14426i) q^{42} +(3.81341 - 8.35019i) q^{43} +(2.21860 + 15.4307i) q^{44} +2.78323 q^{45} +(-8.98074 - 5.93153i) q^{46} -4.99153 q^{47} +(0.121419 + 0.844485i) q^{48} +(1.87008 - 4.09490i) q^{49} +(5.91369 - 1.73642i) q^{50} +(1.69482 - 1.95592i) q^{51} +(6.35368 + 1.86561i) q^{52} +(6.89527 - 4.43132i) q^{53} +(-0.932269 - 2.04138i) q^{54} +(9.35774 + 10.7994i) q^{55} +(-6.63567 - 4.26449i) q^{56} +(-0.329083 + 2.28882i) q^{57} +(1.70642 - 11.8684i) q^{58} +(4.02428 + 2.58625i) q^{59} +(-5.53418 - 6.38679i) q^{60} +(2.43186 + 5.32504i) q^{61} +(-16.8950 + 10.8577i) q^{62} +(-3.25404 - 0.955473i) q^{63} +(8.53265 - 9.84720i) q^{64} +(5.82396 - 1.71007i) q^{65} +(4.78646 - 10.4809i) q^{66} +(0.130280 + 0.906118i) q^{67} -7.85832 q^{68} +(1.93756 + 4.38701i) q^{69} -21.1831 q^{70} +(0.189238 + 1.31618i) q^{71} +(-0.966182 + 2.11564i) q^{72} +(-9.77086 + 2.86898i) q^{73} +(3.22518 - 3.72205i) q^{74} +(-2.63512 - 0.773740i) q^{75} +(5.90660 - 3.79594i) q^{76} +(-7.23330 - 15.8387i) q^{77} +(-3.20506 - 3.69883i) q^{78} +(11.9947 + 7.70851i) q^{79} +(0.337936 - 2.35040i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.576546 - 0.370523i) q^{82} +(-1.75936 - 2.03041i) q^{83} +(4.27779 + 9.36705i) q^{84} +(-6.05968 + 3.89432i) q^{85} +(19.7666 + 5.80399i) q^{86} +(-3.49885 + 4.03789i) q^{87} +(-11.4576 + 3.36424i) q^{88} +(-0.324058 + 0.709587i) q^{89} +(0.888911 + 6.18251i) q^{90} -7.39621 q^{91} +(6.21440 - 13.1693i) q^{92} +8.94893 q^{93} +(-1.59420 - 11.0879i) q^{94} +(2.67354 - 5.85423i) q^{95} +(-6.30034 + 1.84995i) q^{96} +(2.43072 - 2.80520i) q^{97} +(9.69346 + 2.84626i) q^{98} +(-4.31917 + 2.77576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	0.319381	+	2.22134i	0.225837	+	1.57073i	0.715372	+	0.698744i	$0.246257\pi$
$2$	0.319381	+	2.22134i	0.225837	+	1.57073i	−0.489535	+	0.871984i	$0.662833\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−2.91338	+	0.855446i	−1.45669	+	0.427723i
$5$	−1.82263	+	2.10342i	−0.815104	+	0.940680i	−0.999107	−	0.0422457i	$-0.986549\pi$
$5$	−1.82263	+	2.10342i	−0.815104	+	0.940680i	0.184004	+	0.982926i	$0.441094\pi$
$6$	2.15328	+	0.632261i	0.879074	+	0.258119i
$7$	2.85304	−	1.83354i	1.07835	−	0.693013i	0.124173	−	0.992261i	$-0.460372\pi$
$7$	2.85304	−	1.83354i	1.07835	−	0.693013i	0.954175	+	0.299248i	$0.0967358\pi$
$8$	−0.966182	−	2.11564i	−0.341597	−	0.747993i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−5.25454	−	3.37689i	−1.66163	−	1.06787i
$11$	0.730673	−	5.08195i	0.220306	−	1.53226i	−0.516575	−	0.856242i	$-0.672793\pi$
$11$	0.730673	−	5.08195i	0.220306	−	1.53226i	0.736881	−	0.676022i	$-0.236298\pi$
$12$	−0.432121	+	3.00547i	−0.124743	+	0.867605i
$13$	−1.83466	−	1.17906i	−0.508842	−	0.327013i	0.260902	−	0.965365i	$-0.415980\pi$
$13$	−1.83466	−	1.17906i	−0.508842	−	0.327013i	−0.769744	+	0.638352i	$0.779616\pi$
$14$	4.98413	+	5.75199i	1.33206	+	1.53728i
$15$	1.15620	+	2.53171i	0.298528	+	0.653686i
$16$	−0.717732	+	0.461258i	−0.179433	+	0.115315i
$17$	2.48322	+	0.729141i	0.602270	+	0.176843i	0.568633	−	0.822592i	$-0.307473\pi$
$17$	2.48322	+	0.729141i	0.602270	+	0.176843i	0.0336377	+	0.999434i	$0.489291\pi$
$18$	1.46963	−	1.69604i	0.346395	−	0.399761i
$19$	−2.21869	+	0.651466i	−0.509003	+	0.149457i	−0.526142	−	0.850396i	$-0.676362\pi$
$19$	−2.21869	+	0.651466i	−0.509003	+	0.149457i	0.0171398	+	0.999853i	$0.494544\pi$
$20$	3.51064	−	7.68724i	0.785004	−	1.71892i
$21$	−0.482649	−	3.35690i	−0.105323	−	0.732535i
$22$	11.5221			2.45652
$23$	−3.18567	+	3.58490i	−0.664259	+	0.747503i
$23$	−3.18567	+	3.58490i	−0.664259	+	0.747503i
$24$	−2.32582			−0.474757
$25$	−0.390848	−	2.71841i	−0.0781696	−	0.543682i
$26$	2.03315	−	4.45197i	0.398733	−	0.873104i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	−6.74351	+	7.78242i	−1.27440	+	1.47074i
$29$	−5.12647	−	1.50527i	−0.951961	−	0.279521i	−0.231358	−	0.972869i	$-0.574317\pi$
$29$	−5.12647	−	1.50527i	−0.951961	−	0.279521i	−0.720603	+	0.693348i	$0.756135\pi$
$30$	−5.25454	+	3.37689i	−0.959344	+	0.616533i
$31$	3.71752	+	8.14024i	0.667687	+	1.46203i	0.875182	+	0.483794i	$0.160741\pi$
$31$	3.71752	+	8.14024i	0.667687	+	1.46203i	−0.207496	+	0.978236i	$0.566531\pi$
$32$	−4.30002	−	4.96249i	−0.760144	−	0.877253i
$33$	−4.31917	−	2.77576i	−0.751871	−	0.483198i
$34$	−0.826577	+	5.74897i	−0.141757	+	0.985941i
$35$	−1.34332	+	9.34301i	−0.227063	+	1.57926i
$36$	2.55436	+	1.64159i	0.425727	+	0.273598i
$37$	−1.43712	−	1.65853i	−0.236262	−	0.272661i	0.625221	−	0.780448i	$-0.285009\pi$
$37$	−1.43712	−	1.65853i	−0.236262	−	0.272661i	−0.861482	+	0.507787i	$0.830464\pi$
$38$	−2.15574	−	4.72041i	−0.349707	−	0.765752i
$39$	−1.83466	+	1.17906i	−0.293780	+	0.188801i
$40$	6.21109	+	1.82374i	0.982059	+	0.288359i
$41$	−0.199985	+	0.230795i	−0.0312323	+	0.0360440i	−0.771151	−	0.636652i	$-0.780319\pi$
$41$	−0.199985	+	0.230795i	−0.0312323	+	0.0360440i	0.739918	+	0.672697i	$0.234864\pi$
$42$	7.30268	−	2.14426i	1.12683	−	0.330866i
$43$	3.81341	−	8.35019i	0.581539	−	1.27339i	−0.358883	−	0.933383i	$-0.616842\pi$
$43$	3.81341	−	8.35019i	0.581539	−	1.27339i	0.940422	−	0.340010i	$-0.110430\pi$
$44$	2.21860	+	15.4307i	0.334467	+	2.32627i
$45$	2.78323			0.414899
$46$	−8.98074	−	5.93153i	−1.32414	−	0.874557i
$47$	−4.99153			−0.728090			−0.364045	−	0.931381i	$-0.618605\pi$
$47$	−4.99153			−0.728090			−0.364045	+	0.931381i	$0.618605\pi$
$48$	0.121419	+	0.844485i	0.0175253	+	0.121891i
$49$	1.87008	−	4.09490i	0.267154	−	0.584986i
$50$	5.91369	−	1.73642i	0.836323	−	0.245567i
$51$	1.69482	−	1.95592i	0.237322	−	0.273884i
$52$	6.35368	+	1.86561i	0.881097	+	0.258713i
$53$	6.89527	−	4.43132i	0.947138	−	0.608689i	0.0267281	−	0.999643i	$-0.491491\pi$
$53$	6.89527	−	4.43132i	0.947138	−	0.608689i	0.920410	+	0.390954i	$0.127855\pi$
$54$	−0.932269	−	2.04138i	−0.126866	−	0.277797i
$55$	9.35774	+	10.7994i	1.26180	+	1.45619i
$56$	−6.63567	−	4.26449i	−0.886729	−	0.569866i
$57$	−0.329083	+	2.28882i	−0.0435881	+	0.303162i
$58$	1.70642	−	11.8684i	0.224064	−	1.55840i
$59$	4.02428	+	2.58625i	0.523917	+	0.336701i	0.775720	−	0.631077i	$-0.217387\pi$
$59$	4.02428	+	2.58625i	0.523917	+	0.336701i	−0.251803	+	0.967779i	$0.581023\pi$
$60$	−5.53418	−	6.38679i	−0.714460	−	0.824531i
$61$	2.43186	+	5.32504i	0.311368	+	0.681801i	0.999021	−	0.0442383i	$-0.0140861\pi$
$61$	2.43186	+	5.32504i	0.311368	+	0.681801i	−0.687653	+	0.726040i	$0.741359\pi$
$62$	−16.8950	+	10.8577i	−2.14566	+	1.37893i
$63$	−3.25404	−	0.955473i	−0.409971	−	0.120378i
$64$	8.53265	−	9.84720i	1.06658	−	1.23090i
$65$	5.82396	−	1.71007i	0.722374	−	0.212108i
$66$	4.78646	−	10.4809i	0.589172	−	1.29011i
$67$	0.130280	+	0.906118i	0.0159162	+	0.110700i	0.996231	−	0.0867422i	$-0.0276456\pi$
$67$	0.130280	+	0.906118i	0.0159162	+	0.110700i	−0.980315	+	0.197442i	$0.936737\pi$
$68$	−7.85832			−0.952962
$69$	1.93756	+	4.38701i	0.233255	+	0.528134i
$70$	−21.1831			−2.53186
$71$	0.189238	+	1.31618i	0.0224585	+	0.156202i	0.997965	−	0.0637701i	$-0.0203124\pi$
$71$	0.189238	+	1.31618i	0.0224585	+	0.156202i	−0.975506	+	0.219972i	$0.929403\pi$
$72$	−0.966182	+	2.11564i	−0.113866	+	0.249331i
$73$	−9.77086	+	2.86898i	−1.14359	+	0.335789i	−0.798037	−	0.602609i	$-0.794128\pi$
$73$	−9.77086	+	2.86898i	−1.14359	+	0.335789i	−0.345556	+	0.938398i	$0.612310\pi$
$74$	3.22518	−	3.72205i	0.374919	−	0.432680i
$75$	−2.63512	−	0.773740i	−0.304277	−	0.0893438i
$76$	5.90660	−	3.79594i	0.677534	−	0.435424i
$77$	−7.23330	−	15.8387i	−0.824311	−	1.80499i
$78$	−3.20506	−	3.69883i	−0.362901	−	0.418811i
$79$	11.9947	+	7.70851i	1.34951	+	0.867275i	0.997632	−	0.0687729i	$-0.0219084\pi$
$79$	11.9947	+	7.70851i	1.34951	+	0.867275i	0.351873	+	0.936048i	$0.385545\pi$
$80$	0.337936	−	2.35040i	0.0377824	−	0.262782i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.576546	−	0.370523i	−0.0636688	−	0.0409175i
$83$	−1.75936	−	2.03041i	−0.193115	−	0.222866i	0.650932	−	0.759136i	$-0.274378\pi$
$83$	−1.75936	−	2.03041i	−0.193115	−	0.222866i	−0.844047	+	0.536270i	$0.819833\pi$
$84$	4.27779	+	9.36705i	0.466745	+	1.02203i
$85$	−6.05968	+	3.89432i	−0.657265	+	0.422399i
$86$	19.7666	+	5.80399i	2.13149	+	0.625861i
$87$	−3.49885	+	4.03789i	−0.375116	+	0.432907i
$88$	−11.4576	+	3.36424i	−1.22138	+	0.358629i
$89$	−0.324058	+	0.709587i	−0.0343500	+	0.0752161i	−0.926029	−	0.377452i	$-0.876800\pi$
$89$	−0.324058	+	0.709587i	−0.0343500	+	0.0752161i	0.891679	+	0.452668i	$0.149528\pi$
$90$	0.888911	+	6.18251i	0.0936994	+	0.651694i
$91$	−7.39621			−0.775333
$92$	6.21440	−	13.1693i	0.647896	−	1.37300i
$93$	8.94893			0.927961
$94$	−1.59420	−	11.0879i	−0.164429	−	1.14363i
$95$	2.67354	−	5.85423i	0.274299	−	0.600631i
$96$	−6.30034	+	1.84995i	−0.643025	+	0.188809i
$97$	2.43072	−	2.80520i	0.246802	−	0.284825i	−0.618809	−	0.785541i	$-0.712385\pi$
$97$	2.43072	−	2.80520i	0.246802	−	0.284825i	0.865611	+	0.500717i	$0.166930\pi$
$98$	9.69346	+	2.84626i	0.979187	+	0.287515i
$99$	−4.31917	+	2.77576i	−0.434093	+	0.278974i
$100$	3.46414	+	7.58542i	0.346414	+	0.758542i
$101$	11.3700	+	13.1217i	1.13136	+	1.30566i	0.946431	+	0.322906i	$0.104660\pi$
$101$	11.3700	+	13.1217i	1.13136	+	1.30566i	0.184928	+	0.982752i	$0.440795\pi$
$102$	4.88608	+	3.14009i	0.483794	+	0.310915i
$103$	−0.733629	+	5.10250i	−0.0722867	+	0.502765i	0.921225	+	0.389031i	$0.127190\pi$
$103$	−0.733629	+	5.10250i	−0.0722867	+	0.502765i	−0.993511	+	0.113734i	$0.963719\pi$
$104$	−0.721863	+	5.02067i	−0.0707845	+	0.492317i
$105$	7.94067	+	5.10316i	0.774930	+	0.498017i
$106$	12.0457	+	13.9015i	1.16998	+	1.35023i
$107$	−1.95225	−	4.27483i	−0.188731	−	0.413264i	0.791486	−	0.611187i	$-0.209308\pi$
$107$	−1.95225	−	4.27483i	−0.188731	−	0.413264i	−0.980218	+	0.197923i	$0.936580\pi$
$108$	2.55436	−	1.64159i	0.245794	−	0.157962i
$109$	−8.02562	−	2.35653i	−0.768715	−	0.225715i	−0.126217	−	0.992003i	$-0.540284\pi$
$109$	−8.02562	−	2.35653i	−0.768715	−	0.225715i	−0.642498	+	0.766288i	$0.722102\pi$
$110$	−21.0005	+	24.2359i	−2.00232	+	2.31080i
$111$	−2.10565	+	0.618276i	−0.199860	+	0.0586842i
$112$	−1.20198	+	2.63198i	−0.113577	+	0.248698i
$113$	−1.14304	−	7.95002i	−0.107528	−	0.747875i	−0.970234	−	0.242169i	$-0.922141\pi$
$113$	−1.14304	−	7.95002i	−0.107528	−	0.747875i	0.862706	−	0.505706i	$-0.168768\pi$
$114$	−5.18936			−0.486028
$115$	−1.73426	−	13.2348i	−0.161721	−	1.23415i
$116$	16.2230			1.50627
$117$	0.310369	+	2.15866i	0.0286936	+	0.199568i
$118$	−4.45967	+	9.76532i	−0.410546	+	0.898971i
$119$	8.42165	−	2.47282i	0.772012	−	0.226683i
$120$	4.23911	−	4.89219i	0.386976	−	0.446594i
$121$	−14.7379	−	4.32743i	−1.33981	−	0.393402i
$122$	−11.0521	+	7.10273i	−1.00061	+	0.643051i
$123$	0.126861	+	0.277788i	0.0114387	+	0.0250473i
$124$	−17.7941	−	20.5355i	−1.59796	−	1.84414i
$125$	−5.27667	−	3.39111i	−0.471960	−	0.303310i
$126$	1.08315	−	7.53351i	0.0964951	−	0.671138i
$127$	2.82649	−	19.6587i	0.250810	−	1.74442i	−0.342561	−	0.939496i	$-0.611294\pi$
$127$	2.82649	−	19.6587i	0.250810	−	1.74442i	0.593371	−	0.804929i	$-0.297797\pi$
$128$	13.5513	+	8.70890i	1.19778	+	0.769765i
$129$	−6.01146	−	6.93759i	−0.529279	−	0.610821i
$130$	5.65872	+	12.3909i	0.496302	+	1.08675i
$131$	1.48347	−	0.953370i	0.129612	−	0.0832963i	−0.474228	−	0.880402i	$-0.657273\pi$
$131$	1.48347	−	0.953370i	0.129612	−	0.0832963i	0.603840	+	0.797106i	$0.293637\pi$
$132$	14.9579	+	4.39204i	1.30192	+	0.382278i
$133$	−5.13553	+	5.92672i	−0.445307	+	0.513912i
$134$	−1.97119	+	0.578794i	−0.170285	+	0.0500002i
$135$	1.15620	−	2.53171i	0.0995094	−	0.217895i
$136$	−0.856646	−	5.95810i	−0.0734568	−	0.510903i
$137$	1.37780			0.117713			0.0588565	−	0.998266i	$-0.481255\pi$
$137$	1.37780			0.117713			0.0588565	+	0.998266i	$0.481255\pi$
$138$	−9.12624	+	5.70512i	−0.776877	+	0.485652i
$139$	−6.63501			−0.562774			−0.281387	−	0.959594i	$-0.590795\pi$
$139$	−6.63501			−0.562774			−0.281387	+	0.959594i	$0.590795\pi$
$140$	−4.07883	−	28.3689i	−0.344724	−	2.39761i
$141$	−2.07356	+	4.54046i	−0.174625	+	0.382376i
$142$	−2.86326	+	0.840728i	−0.240279	+	0.0705523i
$143$	−7.33246	+	8.46211i	−0.613171	+	0.707638i
$144$	0.818610	+	0.240366i	0.0682175	+	0.0200305i
$145$	12.5099	−	8.03960i	1.03889	−	0.667652i
$146$	−9.49363	−	20.7882i	−0.785699	−	1.72044i
$147$	−2.94799	−	3.40217i	−0.243147	−	0.280606i
$148$	5.60568	+	3.60255i	0.460784	+	0.296128i
$149$	−1.00667	+	7.00155i	−0.0824697	+	0.573589i	0.906127	+	0.423005i	$0.139025\pi$
$149$	−1.00667	+	7.00155i	−0.0824697	+	0.573589i	−0.988597	+	0.150585i	$0.951884\pi$
$150$	0.877137	−	6.10062i	0.0716179	−	0.498114i
$151$	11.1978	+	7.19637i	0.911261	+	0.585632i	0.910110	−	0.414367i	$-0.135997\pi$
$151$	11.1978	+	7.19637i	0.911261	+	0.585632i	0.00115144	+	0.999999i	$0.499633\pi$
$152$	3.52193	+	4.06452i	0.285666	+	0.329676i
$153$	−1.07512	−	2.35418i	−0.0869182	−	0.190324i
$154$	32.8731	−	21.1262i	2.64899	−	1.70240i
$155$	−23.8980	−	7.01709i	−1.91954	−	0.563627i
$156$	4.33643	−	5.00451i	0.347192	−	0.400681i
$157$	−7.40115	+	2.17317i	−0.590676	+	0.173438i	−0.563392	−	0.826190i	$-0.690504\pi$
$157$	−7.40115	+	2.17317i	−0.590676	+	0.173438i	−0.0272838	+	0.999628i	$0.508686\pi$
$158$	−13.2924	+	29.1062i	−1.05748	+	2.31557i
$159$	−1.16647	−	8.11300i	−0.0925073	−	0.643403i
$160$	18.2756			1.44481
$161$	−2.51581	+	16.0689i	−0.198274	+	1.26641i
$162$	−2.24419			−0.176320
$163$	2.87069	+	19.9661i	0.224850	+	1.56386i	0.719327	+	0.694672i	$0.244451\pi$
$163$	2.87069	+	19.9661i	0.224850	+	1.56386i	−0.494477	+	0.869191i	$0.664640\pi$
$164$	0.385199	−	0.843469i	0.0300790	−	0.0658638i
$165$	13.7108	−	4.02586i	1.06739	−	0.313413i
$166$	3.94833	−	4.55662i	0.306450	−	0.353662i
$167$	16.5069	+	4.84687i	1.27734	+	0.375062i	0.848922	−	0.528517i	$-0.177252\pi$
$167$	16.5069	+	4.84687i	1.27734	+	0.375062i	0.428421	+	0.903579i	$0.359070\pi$
$168$	−6.63567	+	4.26449i	−0.511953	+	0.329012i
$169$	−3.42462	−	7.49887i	−0.263432	−	0.576836i
$170$	−10.5860	−	12.2169i	−0.811908	−	0.936992i
$171$	1.94528	+	1.25015i	0.148759	+	0.0956017i
$172$	−3.96677	+	27.5895i	−0.302463	+	2.10368i
$173$	1.20413	−	8.37491i	0.0915483	−	0.636733i	−0.891450	−	0.453119i	$-0.850311\pi$
$173$	1.20413	−	8.37491i	0.0915483	−	0.636733i	0.982998	−	0.183614i	$-0.0587796\pi$
$174$	−10.0870	−	6.48253i	−0.764694	−	0.491439i
$175$	−6.09942	−	7.03910i	−0.461072	−	0.532106i
$176$	1.81966	+	3.98450i	0.137162	+	0.300343i
$177$	4.02428	−	2.58625i	0.302484	−	0.194394i
$178$	−1.67974	−	0.493215i	−0.125902	−	0.0369680i
$179$	8.67361	−	10.0099i	0.648296	−	0.748173i	−0.332523	−	0.943095i	$-0.607900\pi$
$179$	8.67361	−	10.0099i	0.648296	−	0.748173i	0.980819	+	0.194922i	$0.0624453\pi$
$180$	−8.10861	+	2.38090i	−0.604380	+	0.177462i
$181$	−4.05011	+	8.86850i	−0.301042	+	0.659190i	−0.998340	−	0.0575910i	$-0.981658\pi$
$181$	−4.05011	+	8.86850i	−0.301042	+	0.659190i	0.697298	+	0.716781i	$0.254385\pi$
$182$	−2.36221	−	16.4295i	−0.175099	−	1.21784i
$183$	5.85406			0.432744
$184$	10.6623	+	3.27609i	0.786036	+	0.241516i
$185$	6.10793			0.449064
$186$	2.85812	+	19.8787i	0.209568	+	1.45757i
$187$	5.51988	−	12.0868i	0.403654	−	0.883878i
$188$	14.5422	−	4.26999i	1.06060	−	0.311421i
$189$	−2.22091	+	2.56306i	−0.161547	+	0.186435i
$190$	13.8581	+	4.06912i	1.00537	+	0.295205i
$191$	0.355419	−	0.228414i	0.0257172	−	0.0165274i	−0.527719	−	0.849419i	$-0.676953\pi$
$191$	0.355419	−	0.228414i	0.0257172	−	0.0165274i	0.553436	+	0.832892i	$0.313316\pi$
$192$	−5.41274	−	11.8522i	−0.390631	−	0.855362i
$193$	−5.11910	−	5.90775i	−0.368481	−	0.425249i	0.540983	−	0.841034i	$-0.318053\pi$
$193$	−5.11910	−	5.90775i	−0.368481	−	0.425249i	−0.909463	+	0.415784i	$0.863507\pi$
$194$	7.00764	+	4.50354i	0.503119	+	0.323335i
$195$	0.863827	−	6.00805i	0.0618600	−	0.430246i
$196$	−1.94529	+	13.5298i	−0.138949	+	0.966412i
$197$	10.0653	+	6.46856i	0.717122	+	0.460866i	0.847635	−	0.530580i	$-0.178026\pi$
$197$	10.0653	+	6.46856i	0.717122	+	0.460866i	−0.130513	+	0.991447i	$0.541662\pi$
$198$	−7.54538	−	8.70783i	−0.536227	−	0.618839i
$199$	−8.08632	−	17.7066i	−0.573224	−	1.25519i	−0.945063	−	0.326888i	$-0.894000\pi$
$199$	−8.08632	−	17.7066i	−0.573224	−	1.25519i	0.371839	−	0.928297i	$-0.378727\pi$
$200$	−5.37356	+	3.45337i	−0.379968	+	0.244190i
$201$	0.878354	+	0.257908i	0.0619543	+	0.0181914i
$202$	−25.5164	+	29.4476i	−1.79533	+	2.07192i
$203$	−17.3860	+	5.10499i	−1.22026	+	0.358300i
$204$	−3.26447	+	7.14818i	−0.228558	+	0.500473i
$205$	−0.120961	−	0.841305i	−0.00844831	−	0.0587593i
$206$	−11.5687			−0.806032
$207$	4.79546	+	0.0599637i	0.333307	+	0.00416776i
$208$	1.86064			0.129012
$209$	1.68958	+	11.7513i	0.116871	+	0.812853i
$210$	−8.79977	+	19.2688i	−0.607242	+	1.32967i
$211$	−6.80564	+	1.99832i	−0.468520	+	0.137570i	−0.507466	−	0.861671i	$-0.669418\pi$
$211$	−6.80564	+	1.99832i	−0.468520	+	0.137570i	0.0389468	+	0.999241i	$0.487600\pi$
$212$	−16.2978	+	18.8087i	−1.11934	+	1.29178i
$213$	1.27585	+	0.374625i	0.0874201	+	0.0256689i
$214$	8.87237	−	5.70192i	0.606503	−	0.389776i
$215$	10.6136	+	23.2405i	0.723840	+	1.58499i
$216$	1.52309	+	1.75774i	0.103633	+	0.119599i
$217$	25.5317	+	16.4082i	1.73320	+	1.11386i
$218$	2.67144	−	18.5803i	0.180933	−	1.25842i
$219$	−1.44924	+	10.0797i	−0.0979308	+	0.681124i
$220$	−36.5010	−	23.4578i	−2.46090	−	1.58152i
$221$	−3.69616	−	4.26560i	−0.248631	−	0.286935i
$222$	−2.04591	−	4.47992i	−0.137313	−	0.300673i
$223$	−6.29845	+	4.04777i	−0.421775	+	0.271059i	−0.734265	−	0.678862i	$-0.762473\pi$
$223$	−6.29845	+	4.04777i	−0.421775	+	0.271059i	0.312490	+	0.949921i	$0.398837\pi$
$224$	−21.3671	−	6.27394i	−1.42765	−	0.419195i
$225$	−1.79849	+	2.07556i	−0.119899	+	0.138371i
$226$	17.2947	−	5.07817i	1.15042	−	0.337795i
$227$	4.18710	−	9.16846i	0.277907	−	0.608532i	−0.718282	−	0.695752i	$-0.755071\pi$
$227$	4.18710	−	9.16846i	0.277907	−	0.608532i	0.996189	+	0.0872202i	$0.0277984\pi$
$228$	−0.999219	−	6.94972i	−0.0661749	−	0.460257i
$229$	−6.55615			−0.433243			−0.216621	−	0.976256i	$-0.569504\pi$
$229$	−6.55615			−0.433243			−0.216621	+	0.976256i	$0.569504\pi$
$230$	28.8451	−	8.07932i	1.90199	−	0.532735i
$231$	−17.4122			−1.14564
$232$	1.76849	+	12.3001i	0.116107	+	0.807544i
$233$	4.57862	−	10.0258i	0.299955	−	0.656810i	−0.698303	−	0.715802i	$-0.746061\pi$
$233$	4.57862	−	10.0258i	0.299955	−	0.656810i	0.998258	+	0.0589919i	$0.0187886\pi$
$234$	−4.69601	+	1.37887i	−0.306988	+	0.0901397i
$235$	9.09770	−	10.4993i	0.593469	−	0.684900i
$236$	−13.9367	−	4.09218i	−0.907200	−	0.266378i
$237$	11.9947	−	7.70851i	0.779138	−	0.500721i
$238$	8.18270	+	17.9176i	0.530406	+	1.16143i
$239$	−4.27004	−	4.92789i	−0.276206	−	0.318759i	0.600650	−	0.799512i	$-0.294909\pi$
$239$	−4.27004	−	4.92789i	−0.276206	−	0.318759i	−0.876856	+	0.480753i	$0.840363\pi$
$240$	−1.99761	−	1.28379i	−0.128945	−	0.0828681i
$241$	−1.00354	+	6.97979i	−0.0646439	+	0.449608i	0.931633	+	0.363400i	$0.118384\pi$
$241$	−1.00354	+	6.97979i	−0.0646439	+	0.449608i	−0.996277	+	0.0862082i	$0.972525\pi$
$242$	4.90571	−	34.1200i	0.315351	−	2.19331i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−11.6402	−	13.4335i	−0.745190	−	0.859995i
$245$	5.20486	+	11.3970i	0.332526	+	0.728131i
$246$	−0.576546	+	0.370523i	−0.0367592	+	0.0236237i
$247$	4.83866	+	1.42076i	0.307876	+	0.0904006i
$248$	13.6300	−	15.7299i	0.865508	−	0.998850i
$249$	−2.57779	+	0.756907i	−0.163361	+	0.0479670i
$250$	5.84755	−	12.8044i	0.369832	−	0.809818i
$251$	0.305255	+	2.12310i	0.0192675	+	0.134009i	0.997185	−	0.0749841i	$-0.0238906\pi$
$251$	0.305255	+	2.12310i	0.0192675	+	0.134009i	−0.977917	+	0.208993i	$0.932982\pi$
$252$	10.2976			0.648689
$253$	15.8906	+	18.8088i	0.999031	+	1.18250i
$254$	44.5714			2.79666
$255$	1.02512	+	7.12984i	0.0641953	+	0.446488i
$256$	−4.19196	+	9.17911i	−0.261997	+	0.573694i
$257$	17.1552	−	5.03722i	1.07011	−	0.314213i	0.301195	−	0.953563i	$-0.402615\pi$
$257$	17.1552	−	5.03722i	1.07011	−	0.314213i	0.768916	+	0.639350i	$0.220796\pi$
$258$	13.4908	−	15.5693i	0.839903	−	0.969300i
$259$	−7.14116	−	2.09683i	−0.443730	−	0.130291i
$260$	−15.5046	+	9.96417i	−0.961552	+	0.617952i
$261$	2.21952	+	4.86007i	0.137385	+	0.300831i
$262$	2.59156	+	2.99081i	0.160107	+	0.184773i
$263$	−8.37359	−	5.38138i	−0.516338	−	0.331830i	0.256384	−	0.966575i	$-0.417469\pi$
$263$	−8.37359	−	5.38138i	−0.516338	−	0.331830i	−0.772722	+	0.634745i	$0.781105\pi$
$264$	−1.69942	+	11.8197i	−0.104592	+	0.727453i
$265$	−3.24656	+	22.5803i	−0.199435	+	1.38710i
$266$	−14.8055	−	9.51490i	−0.907782	−	0.583396i
$267$	0.510845	+	0.589547i	0.0312632	+	0.0360797i
$268$	−1.15469	−	2.52842i	−0.0705340	−	0.154448i
$269$	−13.2553	+	8.51867i	−0.808190	+	0.519392i	−0.878279	−	0.478148i	$-0.841308\pi$
$269$	−13.2553	+	8.51867i	−0.808190	+	0.519392i	0.0700887	+	0.997541i	$0.477672\pi$
$270$	5.99308	+	1.75973i	0.364727	+	0.107094i
$271$	20.1886	−	23.2989i	1.22637	−	1.41531i	0.347888	−	0.937536i	$-0.386899\pi$
$271$	20.1886	−	23.2989i	1.22637	−	1.41531i	0.878484	−	0.477772i	$-0.158556\pi$
$272$	−2.11861	+	0.622080i	−0.128460	+	0.0377192i
$273$	−3.07250	+	6.72783i	−0.185956	+	0.407187i
$274$	0.440042	+	3.06056i	0.0265839	+	0.184895i
$275$	−14.1004			−0.850285
$276$	−9.39770	−	11.1236i	−0.565675	−	0.669560i
$277$	−14.5169			−0.872236			−0.436118	−	0.899889i	$-0.643647\pi$
$277$	−14.5169			−0.872236			−0.436118	+	0.899889i	$0.643647\pi$
$278$	−2.11910	−	14.7387i	−0.127095	−	0.883966i
$279$	3.71752	−	8.14024i	0.222562	−	0.487343i
$280$	21.0644	−	6.18506i	1.25884	−	0.369628i
$281$	−11.6124	+	13.4014i	−0.692739	+	0.799463i	−0.987752	−	0.156030i	$-0.950130\pi$
$281$	−11.6124	+	13.4014i	−0.692739	+	0.799463i	0.295014	+	0.955493i	$0.404676\pi$
$282$	−10.7482	−	3.15595i	−0.640045	−	0.187934i
$283$	−4.67485	+	3.00434i	−0.277891	+	0.178590i	−0.672161	−	0.740405i	$-0.734634\pi$
$283$	−4.67485	+	3.00434i	−0.277891	+	0.178590i	0.394270	+	0.918995i	$0.370997\pi$
$284$	−1.67725	−	3.67266i	−0.0995263	−	0.217932i
$285$	−4.21457	−	4.86387i	−0.249649	−	0.288111i
$286$	−21.1391	−	13.5853i	−1.24998	−	0.803315i
$287$	−0.147394	+	1.02515i	−0.00870038	+	0.0605125i
$288$	−0.934485	+	6.49948i	−0.0550650	+	0.382986i
$289$	−8.66655	−	5.56965i	−0.509797	−	0.327627i
$290$	21.8541	+	25.2210i	1.28332	+	1.48103i
$291$	−1.54194	−	3.37638i	−0.0903902	−	0.197927i
$292$	26.0120	−	16.7169i	1.52224	−	0.978282i
$293$	−3.51241	−	1.03134i	−0.205197	−	0.0602513i	0.177519	−	0.984117i	$-0.443193\pi$
$293$	−3.51241	−	1.03134i	−0.205197	−	0.0602513i	−0.382716	+	0.923866i	$0.625011\pi$
$294$	6.61585	−	7.63510i	0.385844	−	0.445288i
$295$	−12.7748	+	3.75101i	−0.743775	+	0.218392i
$296$	−2.12033	+	4.64289i	−0.123242	+	0.269862i
$297$	0.730673	+	5.08195i	0.0423980	+	0.294884i
$298$	−15.8744			−0.919578
$299$	10.0714	−	2.82095i	0.582446	−	0.163140i
$300$	8.33899			0.481452
$301$	−4.43060	−	30.8155i	−0.255375	−	1.77617i
$302$	−12.4093	+	27.1725i	−0.714072	+	1.56360i
$303$	16.6592	−	4.89158i	0.957046	−	0.281014i
$304$	1.29193	−	1.49097i	0.0740973	−	0.0855128i
$305$	−15.6332	−	4.59032i	−0.895154	−	0.262841i
$306$	4.88608	−	3.14009i	0.279318	−	0.179507i
$307$	−9.99470	−	21.8853i	−0.570427	−	1.24906i	−0.946570	−	0.322500i	$-0.895477\pi$
$307$	−9.99470	−	21.8853i	−0.570427	−	1.24906i	0.376142	−	0.926562i	$-0.377250\pi$
$308$	34.6225	+	39.9565i	1.97280	+	2.27674i
$309$	4.33664	+	2.78699i	0.246703	+	0.158546i
$310$	7.95480	−	55.3269i	0.451803	−	3.14236i
$311$	−0.538720	+	3.74688i	−0.0305480	+	0.212466i	−0.999378	−	0.0352598i	$-0.988774\pi$
$311$	−0.538720	+	3.74688i	−0.0305480	+	0.212466i	0.968830	+	0.247726i	$0.0796832\pi$
$312$	4.26709	+	2.74229i	0.241576	+	0.155252i
$313$	−5.37205	−	6.19968i	−0.303646	−	0.350427i	0.583335	−	0.812232i	$-0.301747\pi$
$313$	−5.37205	−	6.19968i	−0.303646	−	0.350427i	−0.886982	+	0.461805i	$0.847202\pi$
$314$	−7.19115	−	15.7464i	−0.405820	−	0.888623i
$315$	7.94067	−	5.10316i	0.447406	−	0.287530i
$316$	−41.5393	−	12.1970i	−2.33677	−	0.686137i
$317$	−1.65689	+	1.91215i	−0.0930602	+	0.107397i	−0.800370	−	0.599507i	$-0.795363\pi$
$317$	−1.65689	+	1.91215i	−0.0930602	+	0.107397i	0.707309	+	0.706904i	$0.249909\pi$
$318$	17.6492	−	5.18228i	0.989719	−	0.290608i
$319$	−11.3955	+	24.9526i	−0.638023	+	1.39708i
$320$	5.16100	+	35.8956i	0.288509	+	2.00662i
$321$	−4.69952			−0.262302
$322$	−36.4981	−	0.456382i	−2.03396	−	0.0254332i
$323$	−5.98452			−0.332988
$324$	−0.432121	−	3.00547i	−0.0240067	−	0.166971i
$325$	−2.48810	+	5.44818i	−0.138015	+	0.302211i
$326$	−43.4347	+	12.7536i	−2.40562	+	0.706355i
$327$	−5.47754	+	6.32142i	−0.302909	+	0.349575i
$328$	0.681501	+	0.200107i	0.0376296	+	0.0110490i
$329$	−14.2411	+	9.15217i	−0.785135	+	0.504575i
$330$	13.3218	+	29.1707i	0.733342	+	1.60579i
$331$	20.8589	+	24.0725i	1.14651	+	1.32314i	0.938605	+	0.344993i	$0.112119\pi$
$331$	20.8589	+	24.0725i	1.14651	+	1.32314i	0.207904	+	0.978149i	$0.433336\pi$
$332$	6.86259	+	4.41032i	0.376633	+	0.242048i
$333$	−0.312317	+	2.17221i	−0.0171149	+	0.119036i
$334$	−5.49457	+	38.2155i	−0.300649	+	2.09106i
$335$	−2.14340	−	1.37748i	−0.117107	−	0.0752598i
$336$	1.89481	+	2.18673i	0.103370	+	0.119296i
$337$	7.04540	+	15.4273i	0.383787	+	0.840377i	0.998660	+	0.0517509i	$0.0164802\pi$
$337$	7.04540	+	15.4273i	0.383787	+	0.840377i	−0.614873	+	0.788626i	$0.710793\pi$
$338$	15.5638	−	10.0023i	0.846560	−	0.544051i
$339$	−7.70643	−	2.26281i	−0.418556	−	0.122899i
$340$	14.3228	−	16.5294i	0.776763	−	0.896432i
$341$	44.0845	−	12.9444i	2.38731	−	0.700978i
$342$	−2.15574	+	4.72041i	−0.116569	+	0.255251i
$343$	1.20580	+	8.38650i	0.0651069	+	0.452828i
$344$	−21.3505			−1.15114
$345$	−12.7592	−	3.92038i	−0.686932	−	0.211066i
$346$	18.9881			1.02081
$347$	−1.32556	−	9.21946i	−0.0711597	−	0.494926i	−0.993968	−	0.109668i	$-0.965021\pi$
$347$	−1.32556	−	9.21946i	−0.0711597	−	0.494926i	0.922809	−	0.385259i	$-0.125888\pi$
$348$	6.73929	−	14.7570i	0.361264	−	0.791058i
$349$	6.96469	−	2.04502i	0.372811	−	0.109467i	−0.0899592	−	0.995945i	$-0.528674\pi$
$349$	6.96469	−	2.04502i	0.372811	−	0.109467i	0.462770	+	0.886478i	$0.346855\pi$
$350$	13.6882	−	15.7971i	0.731667	−	0.844388i
$351$	2.09252	+	0.614419i	0.111690	+	0.0327953i
$352$	−28.3610	+	18.2265i	−1.51165	+	0.971477i
$353$	12.7103	+	27.8317i	0.676502	+	1.48133i	0.866308	+	0.499511i	$0.166487\pi$
$353$	12.7103	+	27.8317i	0.676502	+	1.48133i	−0.189806	+	0.981822i	$0.560786\pi$
$354$	7.03023	+	8.11332i	0.373653	+	0.431218i
$355$	−3.11340	−	2.00086i	−0.165242	−	0.106195i
$356$	0.337090	−	2.34451i	0.0178657	−	0.124259i
$357$	1.24912	−	8.68785i	0.0661107	−	0.459810i
$358$	25.0056	+	16.0701i	1.32159	+	0.849332i
$359$	3.96146	+	4.57177i	0.209078	+	0.241289i	0.850597	−	0.525819i	$-0.176241\pi$
$359$	3.96146	+	4.57177i	0.209078	+	0.241289i	−0.641519	+	0.767107i	$0.721695\pi$
$360$	−2.68911	−	5.88832i	−0.141728	−	0.310342i
$361$	−11.4856	+	7.38137i	−0.604507	+	0.388493i
$362$	−20.9935	−	6.16425i	−1.10339	−	0.323986i
$363$	−10.0587	+	11.6084i	−0.527945	+	0.609281i
$364$	21.5480	−	6.32706i	1.12942	−	0.331628i
$365$	11.7739	−	25.7814i	0.616277	−	1.34946i
$366$	1.86968	+	13.0039i	0.0977295	+	0.679724i
$367$	12.5131			0.653178			0.326589	−	0.945166i	$-0.394101\pi$
$367$	12.5131			0.653178			0.326589	+	0.945166i	$0.394101\pi$
$368$	0.632896	−	4.04241i	0.0329920	−	0.210725i
$369$	0.305385			0.0158977
$370$	1.95076	+	13.5678i	0.101415	+	0.705358i
$371$	11.5475	−	25.2855i	0.599516	−	1.31276i
$372$	−26.0717	+	7.65533i	−1.35175	+	0.396910i
$373$	22.4198	−	25.8738i	1.16085	−	1.33970i	0.230482	−	0.973077i	$-0.425970\pi$
$373$	22.4198	−	25.8738i	1.16085	−	1.33970i	0.930371	−	0.366619i	$-0.119485\pi$
$374$	28.6120	+	8.40124i	1.47949	+	0.434418i
$375$	−5.27667	+	3.39111i	−0.272486	+	0.175116i
$376$	4.82273	+	10.5603i	0.248713	+	0.544606i
$377$	7.63050	+	8.80607i	0.392991	+	0.453536i
$378$	−6.40276	−	4.11480i	−0.329322	−	0.211643i
$379$	−0.693079	+	4.82047i	−0.0356011	+	0.247611i	−0.999849	−	0.0173918i	$-0.994464\pi$
$379$	−0.693079	+	4.82047i	−0.0356011	+	0.247611i	0.964248	+	0.265003i	$0.0853728\pi$
$380$	−2.78106	+	19.3427i	−0.142665	+	0.992258i
$381$	−16.7080	−	10.7376i	−0.855976	−	0.550102i
$382$	0.620900	+	0.716557i	0.0317680	+	0.0366622i
$383$	−11.3510	−	24.8553i	−0.580011	−	1.27005i	−0.941293	−	0.337591i	$-0.890388\pi$
$383$	−11.3510	−	24.8553i	−0.580011	−	1.27005i	0.361282	−	0.932457i	$-0.382339\pi$
$384$	13.5513	−	8.70890i	0.691538	−	0.444424i
$385$	46.4992	+	13.6534i	2.36982	+	0.695841i
$386$	11.4882	−	13.2581i	0.584735	−	0.674820i
$387$	−8.80791	+	2.58623i	−0.447731	+	0.131466i
$388$	−4.68192	+	10.2520i	−0.237688	+	0.520465i
$389$	−2.04620	−	14.2316i	−0.103746	−	0.721571i	−0.973600	−	0.228261i	$-0.926696\pi$
$389$	−2.04620	−	14.2316i	−0.103746	−	0.721571i	0.869854	−	0.493310i	$-0.164213\pi$
$390$	13.6218			0.689769
$391$	−10.5246	+	6.57930i	−0.532254	+	0.332729i
$392$	−10.4702			−0.528825
$393$	−0.250959	−	1.74546i	−0.0126592	−	0.0880467i
$394$	−11.1542	+	24.4244i	−0.561943	+	1.23048i
$395$	−38.0761	+	11.1801i	−1.91582	+	0.562534i
$396$	10.2089	−	11.7817i	0.513015	−	0.592051i
$397$	−36.9854	−	10.8599i	−1.85624	−	0.545043i	−0.999574	−	0.0291790i	$-0.990711\pi$
$397$	−36.9854	−	10.8599i	−1.85624	−	0.545043i	−0.856671	−	0.515864i	$-0.827471\pi$
$398$	36.7498	−	23.6177i	1.84210	−	1.18385i
$399$	3.25776	+	7.13349i	0.163092	+	0.357121i
$400$	1.53441	+	1.77081i	0.0767206	+	0.0885403i
$401$	−25.0100	−	16.0730i	−1.24894	−	0.802646i	−0.262211	−	0.965011i	$-0.584452\pi$
$401$	−25.0100	−	16.0730i	−1.24894	−	0.802646i	−0.986731	+	0.162364i	$0.948088\pi$
$402$	−0.292373	+	2.03350i	−0.0145822	+	0.101422i
$403$	2.77747	−	19.3177i	0.138356	−	0.962285i
$404$	−44.3501	−	28.5021i	−2.20650	−	1.41803i
$405$	−1.82263	−	2.10342i	−0.0905671	−	0.104520i
$406$	−16.8927	−	36.9898i	−0.838371	−	1.83578i
$407$	−9.47863	+	6.09154i	−0.469838	+	0.301947i
$408$	−5.77554	−	1.69585i	−0.285932	−	0.0839572i
$409$	12.4112	−	14.3233i	0.613694	−	0.708241i	−0.360803	−	0.932642i	$-0.617497\pi$
$409$	12.4112	−	14.3233i	0.613694	−	0.708241i	0.974497	+	0.224401i	$0.0720427\pi$
$410$	1.83020	−	0.537394i	0.0903869	−	0.0265400i
$411$	0.572357	−	1.25329i	0.0282323	−	0.0618201i
$412$	−2.22758	−	15.4931i	−0.109745	−	0.763292i
$413$	16.2234			0.798303
$414$	1.39838	+	10.6715i	0.0687266	+	0.524476i
$415$	7.47746			0.367054
$416$	2.03798	+	14.1745i	0.0999202	+	0.694960i
$417$	−2.75628	+	6.03542i	−0.134976	+	0.295556i
$418$	−25.5640	+	7.50627i	−1.25038	+	0.367144i
$419$	12.9255	−	14.9168i	0.631452	−	0.728734i	−0.346388	−	0.938092i	$-0.612592\pi$
$419$	12.9255	−	14.9168i	0.631452	−	0.728734i	0.977839	+	0.209357i	$0.0671372\pi$
$420$	−27.4997	−	8.07464i	−1.34185	−	0.394002i
$421$	−29.0080	+	18.6423i	−1.41376	+	0.908569i	−0.999998	−	0.00181545i	$-0.999422\pi$
$421$	−29.0080	+	18.6423i	−1.41376	+	0.908569i	−0.413763	+	0.910385i	$0.635786\pi$
$422$	−6.61254	−	14.4795i	−0.321894	−	0.704849i
$423$	3.26876	+	3.77235i	0.158932	+	0.183418i
$424$	−16.0372	−	10.3065i	−0.778835	−	0.500527i
$425$	1.01154	−	7.03540i	0.0490668	−	0.341267i
$426$	−0.424687	+	2.95376i	−0.0205761	+	0.143110i
$427$	16.7019	+	10.7336i	0.808260	+	0.519437i
$428$	9.34455	+	10.7842i	0.451686	+	0.521273i
$429$	4.65139	+	10.1851i	0.224571	+	0.491743i
$430$	−48.2354	+	30.9990i	−2.32612	+	1.49490i
$431$	34.8057	+	10.2199i	1.67653	+	0.492274i	0.975341	−	0.220701i	$-0.0708347\pi$
$431$	34.8057	+	10.2199i	1.67653	+	0.492274i	0.701189	+	0.712975i	$0.252653\pi$
$432$	0.558707	−	0.644782i	0.0268808	−	0.0310221i
$433$	27.9111	−	8.19542i	1.34132	−	0.393847i	0.469179	−	0.883103i	$-0.344550\pi$
$433$	27.9111	−	8.19542i	1.34132	−	0.393847i	0.872140	+	0.489256i	$0.162732\pi$
$434$	−28.2940	+	61.9551i	−1.35815	+	2.97394i
$435$	−2.11629	−	14.7191i	−0.101468	−	0.705728i
$436$	25.3976			1.21632
$437$	4.73259	−	10.0291i	0.226390	−	0.479759i
$438$	−22.8534			−1.09198
$439$	2.42033	+	16.8338i	0.115516	+	0.803433i	0.962396	+	0.271649i	$0.0875690\pi$
$439$	2.42033	+	16.8338i	0.115516	+	0.803433i	−0.846880	+	0.531784i	$0.821522\pi$
$440$	13.8064	−	30.2318i	0.658195	−	1.44125i
$441$	−4.31936	+	1.26828i	−0.205684	+	0.0603942i
$442$	8.29488	−	9.57280i	0.394547	−	0.455332i
$443$	−14.8681	−	4.36568i	−0.706406	−	0.207420i	−0.0912538	−	0.995828i	$-0.529087\pi$
$443$	−14.8681	−	4.36568i	−0.706406	−	0.207420i	−0.615153	+	0.788408i	$0.710906\pi$
$444$	5.60568	−	3.60255i	0.266034	−	0.170969i
$445$	−0.901927	−	1.97494i	−0.0427554	−	0.0936213i
$446$	−11.0031	−	12.6982i	−0.521012	−	0.601279i
$447$	5.95065	+	3.82425i	0.281456	+	0.180881i
$448$	6.28878	−	43.7394i	0.297117	−	2.06649i
$449$	−2.20360	+	15.3264i	−0.103994	+	0.723297i	0.869391	+	0.494124i	$0.164511\pi$
$449$	−2.20360	+	15.3264i	−0.103994	+	0.723297i	−0.973386	+	0.229173i	$0.926398\pi$
$450$	−5.18494	−	3.33216i	−0.244421	−	0.157080i
$451$	1.02676	+	1.18495i	0.0483483	+	0.0557969i
$452$	10.1309	+	22.1836i	0.476519	+	1.04343i
$453$	11.1978	−	7.19637i	0.526117	−	0.338115i
$454$	21.7036	+	6.37275i	1.01860	+	0.299088i
$455$	13.4805	−	15.5574i	0.631977	−	0.729340i
$456$	5.16028	−	1.51520i	0.241652	−	0.0709556i
$457$	16.6264	−	36.4067i	0.777750	−	1.70303i	0.0689546	−	0.997620i	$-0.478034\pi$
$457$	16.6264	−	36.4067i	0.777750	−	1.70303i	0.708795	−	0.705414i	$-0.249239\pi$
$458$	−2.09391	−	14.5635i	−0.0978420	−	0.680506i
$459$	−2.58806			−0.120800
$460$	16.3742	+	37.0743i	0.763450	+	1.72860i
$461$	1.01619			0.0473287			0.0236644	−	0.999720i	$-0.492467\pi$
$461$	1.01619			0.0473287			0.0236644	+	0.999720i	$0.492467\pi$
$462$	−5.56114	−	38.6786i	−0.258728	−	1.79949i
$463$	−2.88771	+	6.32320i	−0.134203	+	0.293864i	−0.964788	−	0.263028i	$-0.915279\pi$
$463$	−2.88771	+	6.32320i	−0.134203	+	0.293864i	0.830585	+	0.556892i	$0.188006\pi$
$464$	4.37374	−	1.28425i	0.203046	−	0.0596197i
$465$	−16.3106	+	18.8234i	−0.756385	+	0.872914i
$466$	23.7330	+	6.96864i	1.09941	+	0.322816i
$467$	27.0573	−	17.3887i	1.25206	−	0.804653i	0.264887	−	0.964279i	$-0.414665\pi$
$467$	27.0573	−	17.3887i	1.25206	−	0.804653i	0.987178	+	0.159626i	$0.0510289\pi$
$468$	−2.75084	−	6.02351i	−0.127158	−	0.278437i
$469$	2.03310	+	2.34632i	0.0938797	+	0.108343i
$470$	26.2282	+	16.8559i	1.20982	+	0.777503i
$471$	−1.09776	+	7.63509i	−0.0505821	+	0.351806i
$472$	1.58339	−	11.0127i	0.0728816	−	0.506903i
$473$	−39.6489	−	25.4808i	−1.82306	−	1.17161i
$474$	20.9541	+	24.1823i	0.962455	+	1.11073i
$475$	2.63812	+	5.77669i	0.121045	+	0.265053i
$476$	−22.4201	+	14.4085i	−1.02762	+	0.660414i
$477$	−7.86441	−	2.30920i	−0.360087	−	0.105731i
$478$	9.58278	−	11.0591i	0.438306	−	0.505832i
$479$	−20.0120	+	5.87605i	−0.914371	+	0.268484i	−0.704880	−	0.709327i	$-0.748999\pi$
$479$	−20.0120	+	5.87605i	−0.914371	+	0.268484i	−0.209491	+	0.977810i	$0.567181\pi$
$480$	7.59195	−	16.6240i	0.346523	−	0.758780i
$481$	0.681120	+	4.73729i	0.0310564	+	0.216002i
$482$	−15.8250			−0.720811
$483$	13.5717	+	8.96373i	0.617533	+	0.407864i
$484$	46.6389			2.11995
$485$	1.47023	+	10.2257i	0.0667596	+	0.464323i
$486$	−0.932269	+	2.04138i	−0.0422886	+	0.0925991i
$487$	8.04267	−	2.36154i	0.364448	−	0.107012i	−0.0943810	−	0.995536i	$-0.530087\pi$
$487$	8.04267	−	2.36154i	0.364448	−	0.107012i	0.458829	+	0.888525i	$0.348269\pi$
$488$	8.91626	−	10.2899i	0.403620	−	0.465803i
$489$	19.3543	+	5.68293i	0.875232	+	0.256991i
$490$	−23.6544	+	15.2018i	−1.06860	+	0.686747i
$491$	11.2847	+	24.7101i	0.509272	+	1.11515i	0.973343	+	0.229353i	$0.0736609\pi$
$491$	11.2847	+	24.7101i	0.509272	+	1.11515i	−0.464071	+	0.885798i	$0.653612\pi$
$492$	−0.607229	−	0.700779i	−0.0273760	−	0.0315936i
$493$	−11.6326	−	7.47583i	−0.523907	−	0.336695i
$494$	−1.61062	+	11.2021i	−0.0724651	+	0.504006i
$495$	2.03363	−	14.1442i	0.0914049	−	0.635735i
$496$	−6.42293	−	4.12777i	−0.288398	−	0.185342i
$497$	2.95318	+	3.40815i	0.132468	+	0.152876i
$498$	−2.50465	−	5.48441i	−0.112236	−	0.245762i
$499$	22.3807	−	14.3832i	1.00190	−	0.643881i	0.0666147	−	0.997779i	$-0.478780\pi$
$499$	22.3807	−	14.3832i	1.00190	−	0.643881i	0.935284	+	0.353897i	$0.115144\pi$
$500$	18.2739	+	5.36569i	0.817232	+	0.239961i
$501$	11.2661	−	13.0018i	0.503332	−	0.580876i
$502$	−4.61864	+	1.35615i	−0.206140	+	0.0605281i
$503$	−3.39157	+	7.42650i	−0.151223	+	0.331131i	−0.970049	−	0.242910i	$-0.921898\pi$
$503$	−3.39157	+	7.42650i	−0.151223	+	0.331131i	0.818826	+	0.574042i	$0.194625\pi$
$504$	1.12256	+	7.80755i	0.0500026	+	0.347776i
$505$	−48.3238			−2.15038
$506$	−36.7057	+	41.3056i	−1.63177	+	1.83626i
$507$	−8.24385			−0.366122
$508$	8.58229	+	59.6911i	0.380777	+	2.64836i
$509$	−16.1453	+	35.3532i	−0.715627	+	1.56700i	0.104306	+	0.994545i	$0.466738\pi$
$509$	−16.1453	+	35.3532i	−0.715627	+	1.56700i	−0.819933	+	0.572459i	$0.805990\pi$
$510$	−15.5104	+	4.55428i	−0.686814	+	0.201667i
$511$	−22.6163	+	26.1006i	−1.00049	+	1.15462i
$512$	9.18314	+	2.69641i	0.405841	+	0.119166i
$513$	1.94528	−	1.25015i	0.0858862	−	0.0551957i
$514$	16.6684	+	36.4988i	0.735213	+	1.60989i
$515$	−9.39560	−	10.8431i	−0.414020	−	0.477804i
$516$	23.4484	+	15.0694i	1.03226	+	0.663392i
$517$	−3.64718	+	25.3667i	−0.160403	+	1.11563i
$518$	2.37704	−	16.5327i	0.104441	−	0.726403i
$519$	−7.11787	−	4.57438i	−0.312440	−	0.200793i
$520$	−9.24491	−	10.6692i	−0.405416	−	0.467875i
$521$	−17.3993	−	38.0992i	−0.762278	−	1.66916i	−0.742955	−	0.669342i	$-0.766576\pi$
$521$	−17.3993	−	38.0992i	−0.762278	−	1.66916i	−0.0193229	−	0.999813i	$-0.506151\pi$
$522$	−10.0870	+	6.48253i	−0.441496	+	0.283733i
$523$	−10.1000	−	2.96564i	−0.441644	−	0.129678i	0.0533477	−	0.998576i	$-0.483011\pi$
$523$	−10.1000	−	2.96564i	−0.441644	−	0.129678i	−0.494992	+	0.868898i	$0.664829\pi$
$524$	−3.50637	+	4.04656i	−0.153176	+	0.176775i
$525$	−8.93678	+	2.62408i	−0.390033	+	0.114524i
$526$	9.27954	−	20.3193i	0.404607	−	0.885966i
$527$	3.29606	+	22.9246i	0.143579	+	0.998613i
$528$	4.38034			0.190630
$529$	−2.70297	−	22.8406i	−0.117520	−	0.993070i
$530$	−51.1956			−2.22379
$531$	−0.680788	−	4.73499i	−0.0295437	−	0.205481i
$532$	9.89177	−	21.6600i	0.428863	−	0.939078i
$533$	0.639024	−	0.187634i	0.0276792	−	0.00812735i
$534$	−1.14643	+	1.32305i	−0.0496110	+	0.0572541i
$535$	12.5500	+	3.68502i	0.542584	+	0.159317i
$536$	1.79115	−	1.15110i	0.0773658	−	0.0497200i
$537$	−5.50216	−	12.0480i	−0.237436	−	0.519912i
$538$	−23.1564	−	26.7239i	−0.998343	−	1.15215i
$539$	−19.4437	−	12.4957i	−0.837497	−	0.538227i
$540$	−1.20269	+	8.36491i	−0.0517557	+	0.359969i
$541$	−2.44706	+	17.0197i	−0.105208	+	0.731734i	0.867118	+	0.498103i	$0.165970\pi$
$541$	−2.44706	+	17.0197i	−0.105208	+	0.731734i	−0.972325	+	0.233631i	$0.924939\pi$
$542$	58.2028	+	37.4047i	2.50002	+	1.60667i
$543$	6.38459	+	7.36821i	0.273989	+	0.316200i
$544$	−7.05957	−	15.4583i	−0.302677	−	0.662769i
$545$	19.5845	−	12.5862i	0.838908	−	0.539133i
$546$	−15.9261	−	4.67633i	−0.681575	−	0.200129i
$547$	−11.9174	+	13.7534i	−0.509551	+	0.588053i	−0.950984	−	0.309242i	$-0.899925\pi$
$547$	−11.9174	+	13.7534i	−0.509551	+	0.588053i	0.441433	+	0.897294i	$0.354470\pi$
$548$	−4.01405	+	1.17863i	−0.171472	+	0.0503486i
$549$	2.43186	−	5.32504i	0.103789	−	0.227267i
$550$	−4.50340	−	31.3218i	−0.192026	−	1.33557i
$551$	12.3547			0.526327
$552$	7.40932	−	8.33784i	0.315361	−	0.354882i
$553$	48.3551			2.05627
$554$	−4.63642	−	32.2470i	−0.196983	−	1.37005i
$555$	2.53733	−	5.55597i	0.107704	−	0.235838i
$556$	19.3303	−	5.67590i	0.819789	−	0.240712i
$557$	−27.1522	+	31.3353i	−1.15048	+	1.32772i	−0.214064	+	0.976820i	$0.568670\pi$
$557$	−27.1522	+	31.3353i	−1.15048	+	1.32772i	−0.936412	+	0.350901i	$0.885875\pi$
$558$	19.2696	+	5.65806i	0.815746	+	0.239525i
$559$	−16.8417	+	10.8235i	−0.712328	+	0.457785i
$560$	−3.34540	−	7.32539i	−0.141369	−	0.309554i
$561$	−8.70154	−	10.0421i	−0.367379	−	0.423978i
$562$	−33.4780	−	21.5150i	−1.41218	−	0.907556i
$563$	−4.78887	+	33.3073i	−0.201827	+	1.40374i	0.597031	+	0.802218i	$0.296347\pi$
$563$	−4.78887	+	33.3073i	−0.201827	+	1.40374i	−0.798858	+	0.601519i	$0.794562\pi$
$564$	2.15695	−	15.0019i	0.0908239	−	0.631694i
$565$	18.8056	+	12.0856i	0.791157	+	0.508446i
$566$	−8.16674	−	9.42492i	−0.343274	−	0.396159i
$567$	1.40885	+	3.08494i	0.0591660	+	0.129555i
$568$	2.60173	−	1.67203i	0.109166	−	0.0701570i
$569$	−14.7054	−	4.31791i	−0.616484	−	0.181016i	−0.0414433	−	0.999141i	$-0.513196\pi$
$569$	−14.7054	−	4.31791i	−0.616484	−	0.181016i	−0.575041	+	0.818125i	$0.695014\pi$
$570$	9.45828	−	10.9154i	0.396164	−	0.457197i
$571$	31.2673	−	9.18092i	1.30850	−	0.384210i	0.448169	−	0.893949i	$-0.352076\pi$
$571$	31.2673	−	9.18092i	1.30850	−	0.384210i	0.860329	+	0.509739i	$0.170258\pi$
$572$	14.1234	−	30.9259i	0.590528	−	1.29308i
$573$	−0.0601262	−	0.418187i	−0.00251181	−	0.0174700i
$574$	−2.32428			−0.0970135
$575$	10.9903	+	7.25881i	0.458328	+	0.302713i
$576$	−13.0297			−0.542905
$577$	−2.56137	−	17.8147i	−0.106631	−	0.741635i	−0.971052	−	0.238867i	$-0.923224\pi$
$577$	−2.56137	−	17.8147i	−0.106631	−	0.741635i	0.864421	−	0.502768i	$-0.167685\pi$
$578$	9.60419	−	21.0302i	0.399482	−	0.874743i
$579$	−7.50043	+	2.20233i	−0.311707	+	0.0915255i
$580$	−29.5685	+	34.1239i	−1.22777	+	1.41692i
$581$	−8.74235	−	2.56699i	−0.362694	−	0.106497i
$582$	7.00764	−	4.50354i	0.290476	−	0.186678i
$583$	−17.4815	−	38.2792i	−0.724012	−	1.58536i
$584$	15.5102	+	17.8997i	0.641816	+	0.740695i
$585$	−5.10627	−	3.28160i	−0.211118	−	0.135677i
$586$	1.16916	−	8.13165i	0.0482974	−	0.335916i
$587$	−5.13352	+	35.7044i	−0.211883	+	1.47368i	0.554978	+	0.831865i	$0.312727\pi$
$587$	−5.13352	+	35.7044i	−0.211883	+	1.47368i	−0.766861	+	0.641813i	$0.778183\pi$
$588$	11.4990	+	7.38996i	0.474211	+	0.304757i
$589$	−13.5511	−	15.6388i	−0.558364	−	0.644387i
$590$	−12.4123	−	27.1791i	−0.511006	−	1.11895i
$591$	10.0653	−	6.46856i	0.414030	−	0.266081i
$592$	1.79648	+	0.527494i	0.0738349	+	0.0216799i
$593$	−24.4354	+	28.1999i	−1.00344	+	1.15803i	−0.0160277	+	0.999872i	$0.505102\pi$
$593$	−24.4354	+	28.1999i	−1.00344	+	1.15803i	−0.987413	+	0.158161i	$0.949443\pi$
$594$	−11.0554	+	3.24616i	−0.453608	+	0.133191i
$595$	−10.1481	+	22.2213i	−0.416033	+	0.910986i
$596$	−3.05663	−	21.2593i	−0.125205	−	0.870817i
$597$	−19.4656			−0.796676
$598$	9.48292	+	21.4712i	0.387785	+	0.878021i
$599$	−1.72108			−0.0703215			−0.0351607	−	0.999382i	$-0.511194\pi$
$599$	−1.72108			−0.0703215			−0.0351607	+	0.999382i	$0.511194\pi$
$600$	0.909044	+	6.32254i	0.0371116	+	0.258117i
$601$	0.398010	−	0.871520i	0.0162352	−	0.0355501i	−0.901341	−	0.433111i	$-0.857416\pi$
$601$	0.398010	−	0.871520i	0.0162352	−	0.0355501i	0.917576	+	0.397561i	$0.130143\pi$
$602$	67.0368	−	19.6838i	2.73221	−	0.802251i
$603$	0.599483	−	0.691840i	0.0244128	−	0.0281739i
$604$	−38.7795	−	11.3867i	−1.57791	−	0.463317i
$605$	35.9640	−	23.1127i	1.46215	−	0.939664i
$606$	16.1865	+	35.4435i	0.657532	+	1.43980i
$607$	−10.5820	−	12.2123i	−0.429510	−	0.495681i	0.499200	−	0.866487i	$-0.333627\pi$
$607$	−10.5820	−	12.2123i	−0.429510	−	0.495681i	−0.928711	+	0.370805i	$0.879082\pi$
$608$	12.7733	+	8.20892i	0.518027	+	0.332916i
$609$	−2.57874	+	17.9355i	−0.104496	+	0.726785i
$610$	5.20374	−	36.1928i	0.210693	−	1.46540i
$611$	9.15775	+	5.88533i	0.370483	+	0.238095i
$612$	5.14611	+	5.93892i	0.208019	+	0.240067i
$613$	13.4019	+	29.3462i	0.541299	+	1.18528i	0.960728	+	0.277492i	$0.0895032\pi$
$613$	13.4019	+	29.3462i	0.541299	+	1.18528i	−0.419429	+	0.907788i	$0.637770\pi$
$614$	45.4228	−	29.1914i	1.83311	−	1.17807i
$615$	−0.815527	−	0.239460i	−0.0328852	−	0.00965597i
$616$	−26.5204	+	30.6062i	−1.06854	+	1.23316i
$617$	−14.4761	+	4.25056i	−0.582785	+	0.171121i	−0.559819	−	0.828615i	$-0.689129\pi$
$617$	−14.4761	+	4.25056i	−0.582785	+	0.171121i	−0.0229661	+	0.999736i	$0.507311\pi$
$618$	−4.80582	+	10.5233i	−0.193319	+	0.423309i
$619$	2.92734	+	20.3601i	0.117660	+	0.818340i	0.960121	+	0.279584i	$0.0901966\pi$
$619$	2.92734	+	20.3601i	0.117660	+	0.818340i	−0.842462	+	0.538756i	$0.818894\pi$
$620$	75.6268			3.03725
$621$	2.04665	−	4.33719i	0.0821292	−	0.174045i
$622$	−8.49517			−0.340625
$623$	0.376506	+	2.61866i	0.0150844	+	0.104914i
$624$	0.772939	−	1.69250i	0.0309423	−	0.0677542i
$625$	29.9259	−	8.78704i	1.19704	−	0.351482i
$626$	12.0559	−	13.9132i	0.481851	−	0.556085i
$627$	11.3912	+	3.34476i	0.454921	+	0.133577i
$628$	19.7033	−	12.6626i	0.786249	−	0.505292i
$629$	−2.35940	−	5.16637i	−0.0940755	−	0.205997i
$630$	13.8720	+	16.0091i	0.552673	+	0.637818i
$631$	−22.3992	−	14.3951i	−0.891699	−	0.573060i	0.0126186	−	0.999920i	$-0.495983\pi$
$631$	−22.3992	−	14.3951i	−0.891699	−	0.573060i	−0.904318	+	0.426860i	$0.859620\pi$
$632$	4.71942	−	32.8243i	0.187728	−	1.30568i
$633$	−1.00943	+	7.02076i	−0.0401214	+	0.279050i
$634$	−4.77673	−	3.06982i	−0.189708	−	0.121918i
$635$	36.1989	+	41.7757i	1.43651	+	1.65782i
$636$	10.3386	+	22.6384i	0.409953	+	0.897671i
$637$	−8.25910	+	5.30780i	−0.327237	+	0.210303i
$638$	−59.0678	−	17.3439i	−2.33851	−	0.686650i
$639$	0.870780	−	1.00493i	0.0344475	−	0.0397545i
$640$	−43.0175	+	12.6311i	−1.70042	+	0.499287i
$641$	8.55786	−	18.7391i	0.338015	−	0.740150i	−0.661941	−	0.749556i	$-0.730267\pi$
$641$	8.55786	−	18.7391i	0.338015	−	0.740150i	0.999956	+	0.00940630i	$0.00299416\pi$
$642$	−1.50094	−	10.4393i	−0.0592373	−	0.412005i
$643$	−23.7922			−0.938272			−0.469136	−	0.883126i	$-0.655435\pi$
$643$	−23.7922			−0.938272			−0.469136	+	0.883126i	$0.655435\pi$
$644$	−6.41656	−	48.9670i	−0.252848	−	1.92957i
$645$	25.5493			1.00600
$646$	−1.91134	−	13.2937i	−0.0752008	−	0.523033i
$647$	−3.88367	+	8.50406i	−0.152683	+	0.334329i	−0.970482	−	0.241176i	$-0.922467\pi$
$647$	−3.88367	+	8.50406i	−0.152683	+	0.334329i	0.817799	+	0.575505i	$0.195194\pi$
$648$	2.23161	−	0.655260i	0.0876660	−	0.0257411i
$649$	16.0836	−	18.5615i	0.631337	−	0.728602i
$650$	−12.8969	−	3.78688i	−0.505860	−	0.148534i
$651$	25.5317	−	16.4082i	1.00067	−	0.643089i
$652$	−25.4433	−	55.7131i	−0.996437	−	2.18189i
$653$	−9.81606	−	11.3283i	−0.384132	−	0.443312i	0.530448	−	0.847718i	$-0.322024\pi$
$653$	−9.81606	−	11.3283i	−0.384132	−	0.443312i	−0.914580	+	0.404406i	$0.867478\pi$
$654$	−15.7915	−	10.1486i	−0.617495	−	0.396840i
$655$	−0.698476	+	4.85801i	−0.0272917	+	0.189818i
$656$	0.0370794	−	0.257893i	0.00144771	−	0.0100690i
$657$	8.56679	+	5.50554i	0.334222	+	0.214792i
$658$	−24.8784	−	28.7113i	−0.969863	−	1.11928i
$659$	11.2927	+	24.7275i	0.439900	+	0.963246i	0.991617	+	0.129214i	$0.0412455\pi$
$659$	11.2927	+	24.7275i	0.439900	+	0.963246i	−0.551717	+	0.834031i	$0.686027\pi$
$660$	−36.5010	+	23.4578i	−1.42080	+	0.913092i
$661$	−16.1324	−	4.73689i	−0.627476	−	0.184244i	−0.0474922	−	0.998872i	$-0.515123\pi$
$661$	−16.1324	−	4.73689i	−0.627476	−	0.184244i	−0.579984	+	0.814628i	$0.696941\pi$
$662$	−46.8113	+	54.0231i	−1.81937	+	2.09967i
$663$	−5.41557	+	1.59015i	−0.210323	+	0.0617565i
$664$	−2.59576	+	5.68392i	−0.100735	+	0.220579i
$665$	−3.10624	−	21.6044i	−0.120455	−	0.837782i
$666$	−4.92498			−0.190839
$667$	21.7275	−	13.5826i	0.841291	−	0.525919i
$668$	−52.2372			−2.02112
$669$	1.06551	+	7.41077i	0.0411949	+	0.286517i
$670$	2.37530	−	5.20118i	0.0917658	−	0.200939i
$671$	28.8385	−	8.46773i	1.11330	−	0.326893i
$672$	−14.5832	+	16.8299i	−0.562558	+	0.649227i
$673$	35.7381	+	10.4937i	1.37760	+	0.404501i	0.884934	−	0.465716i	$-0.154203\pi$
$673$	35.7381	+	10.4937i	1.37760	+	0.404501i	0.492669	+	0.870217i	$0.336021\pi$
$674$	−32.0191	+	20.5774i	−1.23333	+	0.792614i
$675$	1.14088	+	2.49818i	0.0439125	+	0.0961550i
$676$	16.3921	+	18.9175i	0.630465	+	0.727596i
$677$	20.2147	+	12.9912i	0.776912	+	0.499291i	0.868008	−	0.496551i	$-0.165400\pi$
$677$	20.2147	+	12.9912i	0.776912	+	0.499291i	−0.0910951	+	0.995842i	$0.529037\pi$
$678$	2.56520	−	17.8413i	0.0985157	−	0.685192i
$679$	1.79150	−	12.4602i	0.0687515	−	0.478177i
$680$	14.0938	+	9.05751i	0.540471	+	0.347340i
$681$	−6.60054	−	7.61743i	−0.252933	−	0.291901i
$682$	42.8337	+	93.7927i	1.64019	+	3.59151i
$683$	35.2638	−	22.6626i	1.34933	−	0.867162i	0.351710	−	0.936109i	$-0.385600\pi$
$683$	35.2638	−	22.6626i	1.34933	−	0.867162i	0.997620	+	0.0689475i	$0.0219641\pi$
$684$	−6.73678	−	1.97810i	−0.257587	−	0.0756345i
$685$	−2.51121	+	2.89809i	−0.0959484	+	0.110730i
$686$	−18.2442	+	5.35698i	−0.696566	+	0.204530i
$687$	−2.72352	+	5.96368i	−0.103909	+	0.227529i
$688$	1.11459	+	7.75216i	0.0424934	+	0.295548i
$689$	−17.8753			−0.680993
$690$	4.63346	−	29.5947i	0.176393	−	1.12665i
$691$	−41.5911			−1.58220			−0.791099	−	0.611688i	$-0.790491\pi$
$691$	−41.5911			−1.58220			−0.791099	+	0.611688i	$0.790491\pi$
$692$	3.65619	+	25.4294i	0.138988	+	0.966680i
$693$	−7.23330	+	15.8387i	−0.274770	+	0.601663i
$694$	20.0562	−	5.88904i	0.761324	−	0.223545i
$695$	12.0932	−	13.9562i	0.458720	−	0.529391i
$696$	11.9233	+	3.50099i	0.451950	+	0.132705i
$697$	−0.664888	+	0.427298i	−0.0251844	+	0.0161851i
$698$	6.76708	+	14.8178i	0.256138	+	0.560863i
$699$	−7.21773	−	8.32971i	−0.273000	−	0.315059i
$700$	23.7915	+	15.2899i	0.899234	+	0.577903i
$701$	1.51073	−	10.5074i	0.0570595	−	0.396857i	−0.941198	−	0.337855i	$-0.890299\pi$
$701$	1.51073	−	10.5074i	0.0570595	−	0.396857i	0.998258	−	0.0590029i	$-0.0187921\pi$
$702$	−0.696526	+	4.84444i	−0.0262887	+	0.182842i
$703$	4.26901	+	2.74353i	0.161009	+	0.103474i
$704$	−43.8084	−	50.5575i	−1.65109	−	1.90546i
$705$	−5.77119	−	12.6371i	−0.217355	−	0.475942i
$706$	−57.7644	+	37.1229i	−2.17399	+	1.39714i
$707$	56.4983	+	16.5894i	2.12484	+	0.623908i
$708$	−9.51188	+	10.9773i	−0.357478	+	0.412552i
$709$	−2.76637	+	0.812279i	−0.103893	+	0.0305058i	−0.333266	−	0.942833i	$-0.608151\pi$
$709$	−2.76637	+	0.812279i	−0.103893	+	0.0305058i	0.229373	+	0.973339i	$0.426333\pi$
$710$	3.45024	−	7.55498i	0.129485	−	0.283533i
$711$	−2.02914	−	14.1130i	−0.0760986	−	0.529278i
$712$	1.81433			0.0679950
$713$	−41.0247	−	12.6052i	−1.53639	−	0.472069i
$714$	19.6977			0.737166
$715$	−4.43507	−	30.8466i	−0.165862	−	1.15360i
$716$	−16.7066	+	36.5824i	−0.624356	+	1.36715i
$717$	−6.25641	+	1.83705i	−0.233650	+	0.0686058i
$718$	−8.89025	+	10.2599i	−0.331781	+	0.382896i
$719$	−4.38297	−	1.28696i	−0.163457	−	0.0479954i	0.198980	−	0.980004i	$-0.436237\pi$
$719$	−4.38297	−	1.28696i	−0.163457	−	0.0479954i	−0.362437	+	0.932008i	$0.618055\pi$
$720$	−1.99761	+	1.28379i	−0.0744466	+	0.0478439i
$721$	7.26256	+	15.9028i	0.270472	+	0.592251i
$722$	−20.0649	−	23.1561i	−0.746737	−	0.861780i
$723$	5.93216	+	3.81237i	0.220619	+	0.141783i
$724$	4.21299	−	29.3020i	0.156574	−	1.08900i
$725$	−2.08826	+	14.5242i	−0.0775560	+	0.539414i
$726$	−28.9987	−	18.6363i	−1.07624	−	0.691659i
$727$	−23.2762	−	26.8622i	−0.863266	−	0.996262i	−0.999984	−	0.00565201i	$-0.998201\pi$
$727$	−23.2762	−	26.8622i	−0.863266	−	0.996262i	0.136718	−	0.990610i	$-0.456345\pi$
$728$	7.14608	+	15.6477i	0.264852	+	0.579944i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	61.0297	+	17.9199i	2.25881	+	0.663246i
$731$	15.5580	−	17.9549i	0.575434	−	0.664086i
$732$	−17.0551	+	5.00783i	−0.630375	+	0.185095i
$733$	−9.22320	+	20.1960i	−0.340667	+	0.745956i	−0.999983	−	0.00591019i	$-0.998119\pi$
$733$	−9.22320	+	20.1960i	−0.340667	+	0.745956i	0.659316	+	0.751866i	$0.270846\pi$
$734$	3.99645	+	27.7959i	0.147512	+	1.02597i
$735$	12.5293			0.462150
$736$	31.4885	+	0.393741i	1.16068	+	0.0145135i
$737$	4.70003			0.173128
$738$	0.0975342	+	0.678365i	0.00359028	+	0.0249710i
$739$	−16.8869	+	36.9771i	−0.621194	+	1.36023i	0.293453	+	0.955974i	$0.405196\pi$
$739$	−16.8869	+	36.9771i	−0.621194	+	1.36023i	−0.914647	+	0.404253i	$0.867532\pi$
$740$	−17.7947	+	5.22501i	−0.654148	+	0.192075i
$741$	3.30242	−	3.81119i	0.121317	−	0.140008i
$742$	59.8559	+	17.5753i	2.19738	+	0.645208i
$743$	−32.4043	+	20.8250i	−1.18880	+	0.763994i	−0.976983	−	0.213316i	$-0.931573\pi$
$743$	−32.4043	+	20.8250i	−1.18880	+	0.763994i	−0.211814	+	0.977310i	$0.567937\pi$
$744$	−8.64630	−	18.9328i	−0.316989	−	0.694109i
$745$	−12.8924	−	14.8787i	−0.472343	−	0.545112i
$746$	64.6351	+	41.5385i	2.36646	+	1.52083i
$747$	−0.382345	+	2.65927i	−0.0139893	+	0.0972975i
$748$	−5.74187	+	39.9356i	−0.209943	+	1.46019i
$749$	−13.4079	−	8.61675i	−0.489915	−	0.314849i
$750$	−9.21809	−	10.6382i	−0.336597	−	0.388454i
$751$	−1.10851	−	2.42730i	−0.0404501	−	0.0885734i	0.888328	−	0.459209i	$-0.151867\pi$
$751$	−1.10851	−	2.42730i	−0.0404501	−	0.0885734i	−0.928778	+	0.370636i	$0.879140\pi$
$752$	3.58258	−	2.30238i	0.130643	−	0.0839593i
$753$	2.05804	+	0.604296i	0.0749993	+	0.0220218i
$754$	−17.1243	+	19.7625i	−0.623630	+	0.719707i
$755$	−35.5464	+	10.4374i	−1.29366	+	0.379854i
$756$	4.27779	−	9.36705i	0.155582	−	0.340676i
$757$	−3.38520	−	23.5446i	−0.123037	−	0.855743i	−0.954084	−	0.299540i	$-0.903167\pi$
$757$	−3.38520	−	23.5446i	−0.123037	−	0.855743i	0.831046	−	0.556203i	$-0.187742\pi$
$758$	−10.9293			−0.396969
$759$	23.7103	−	6.64110i	0.860628	−	0.241057i
$760$	−14.9686			−0.542968
$761$	2.37376	+	16.5099i	0.0860487	+	0.598482i	0.986529	+	0.163585i	$0.0523059\pi$
$761$	2.37376	+	16.5099i	0.0860487	+	0.598482i	−0.900480	+	0.434896i	$0.856785\pi$
$762$	18.5156	−	40.5436i	0.670750	−	1.46874i
$763$	−27.2182	+	7.99199i	−0.985366	+	0.289329i
$764$	−0.840075	+	0.969499i	−0.0303929	+	0.0350752i
$765$	6.91138	+	2.02937i	0.249882	+	0.0733718i
$766$	51.5869	−	33.1529i	1.86391	−	1.19786i
$767$	−4.33383	−	9.48976i	−0.156486	−	0.342655i
$768$	6.60821	+	7.62628i	0.238453	+	0.275190i
$769$	43.1352	+	27.7213i	1.55550	+	0.999657i	0.983816	+	0.179181i	$0.0573448\pi$
$769$	43.1352	+	27.7213i	1.55550	+	0.999657i	0.571681	+	0.820476i	$0.306292\pi$
$770$	−15.4779	+	107.651i	−0.557786	+	3.87948i
$771$	2.54451	−	17.6974i	0.0916382	−	0.637358i
$772$	19.9677	+	12.8324i	0.718651	+	0.461849i
$773$	9.38915	+	10.8357i	0.337704	+	0.389732i	0.899047	−	0.437852i	$-0.144261\pi$
$773$	9.38915	+	10.8357i	0.337704	+	0.389732i	−0.561343	+	0.827583i	$0.689715\pi$
$774$	−8.55800	−	18.7394i	−0.307611	−	0.673574i
$775$	20.6755	−	13.2873i	0.742686	−	0.477295i
$776$	−8.28332	−	2.43220i	−0.297354	−	0.0873109i
$777$	−4.87389	+	5.62477i	−0.174850	+	0.201787i
$778$	30.9598	−	9.09062i	1.10996	−	0.325914i
$779$	0.293349	−	0.642345i	0.0105103	−	0.0230144i
$780$	2.62291	+	18.2427i	0.0939151	+	0.653194i
$781$	6.82704			0.244291
$782$	−17.9763	−	21.2775i	−0.642830	−	0.760883i
$783$	5.34289			0.190939
$784$	0.546592	+	3.80163i	0.0195211	+	0.135772i
$785$	8.91843	−	19.5286i	0.318312	−	0.697007i
$786$	3.79711	−	1.11493i	0.135439	−	0.0397683i
$787$	14.3000	−	16.5031i	0.509740	−	0.588271i	−0.441292	−	0.897363i	$-0.645480\pi$
$787$	14.3000	−	16.5031i	0.509740	−	0.588271i	0.951032	+	0.309093i	$0.100025\pi$
$788$	−34.8575	−	10.2351i	−1.24175	−	0.364610i
$789$	−8.37359	+	5.38138i	−0.298108	+	0.191582i
$790$	−36.9957	−	81.0094i	−1.31625	−	2.88218i
$791$	−17.8378	−	20.5859i	−0.634239	−	0.731951i
$792$	10.0456	+	6.45593i	0.356956	+	0.229401i
$793$	1.81692	−	12.6369i	0.0645206	−	0.448751i
$794$	12.3111	−	85.6258i	0.436906	−	3.03875i
$795$	19.1911	+	12.3334i	0.680639	+	0.437420i
$796$	38.7056	+	44.6686i	1.37188	+	1.58324i
$797$	5.09393	+	11.1542i	0.180436	+	0.395101i	0.978139	−	0.207950i	$-0.0666791\pi$
$797$	5.09393	+	11.1542i	0.180436	+	0.395101i	−0.797703	+	0.603050i	$0.793952\pi$
$798$	−14.8055	+	9.51490i	−0.524108	+	0.336824i
$799$	−12.3951	−	3.63953i	−0.438507	−	0.128757i
$800$	−11.8094	+	13.6288i	−0.417526	+	0.481851i
$801$	0.748483	−	0.219774i	0.0264463	−	0.00776535i
$802$	27.7159	−	60.6893i	0.978682	−	2.14301i
$803$	7.44071	+	51.7513i	0.262577	+	1.82626i
$804$	−2.77961			−0.0980292
$805$	−29.2144	−	34.5795i	−1.02967	−	1.21877i
$806$	43.7984			1.54273
$807$	2.24240	+	15.5962i	0.0789362	+	0.549013i
$808$	16.7753	−	36.7329i	0.590154	−	1.29226i
$809$	−6.43989	+	1.89092i	−0.226414	+	0.0664813i	−0.392972	−	0.919550i	$-0.628553\pi$
$809$	−6.43989	+	1.89092i	−0.226414	+	0.0664813i	0.166558	+	0.986032i	$0.446735\pi$
$810$	4.09032	−	4.72048i	0.143719	−	0.165861i
$811$	−7.85825	−	2.30739i	−0.275941	−	0.0810234i	0.140834	−	0.990033i	$-0.455021\pi$
$811$	−7.85825	−	2.30739i	−0.275941	−	0.0810234i	−0.416775	+	0.909010i	$0.636840\pi$
$812$	46.2850	−	29.7456i	1.62429	−	1.04386i
$813$	−12.8068	−	28.0429i	−0.449153	−	0.983509i
$814$	−16.5587	−	19.1098i	−0.580383	−	0.669797i
$815$	−47.2293	−	30.3524i	−1.65437	−	1.06320i
$816$	−0.314239	+	2.18558i	−0.0110006	+	0.0765105i
$817$	−3.02090	+	21.0108i	−0.105688	+	0.735075i
$818$	35.7809	+	22.9950i	1.25105	+	0.804000i
$819$	4.84349	+	5.58968i	0.169245	+	0.195319i
$820$	1.07210	+	2.34757i	0.0374393	+	0.0819806i
$821$	−32.9558	+	21.1794i	−1.15016	+	0.739166i	−0.969672	−	0.244411i	$-0.921405\pi$
$821$	−32.9558	+	21.1794i	−1.15016	+	0.739166i	−0.180492	+	0.983576i	$0.557769\pi$
$822$	2.96678	+	0.871126i	0.103478	+	0.0303840i
$823$	−1.32564	+	1.52987i	−0.0462090	+	0.0533281i	−0.778384	−	0.627789i	$-0.783960\pi$
$823$	−1.32564	+	1.52987i	−0.0462090	+	0.0533281i	0.732175	+	0.681117i	$0.238506\pi$
$824$	11.5039	−	3.37785i	0.400757	−	0.117673i
$825$	−5.85751	+	12.8262i	−0.203932	+	0.446550i
$826$	5.18146	+	36.0379i	0.180286	+	1.25392i
$827$	4.11637			0.143140			0.0715701	−	0.997436i	$-0.477199\pi$
$827$	4.11637			0.143140			0.0715701	+	0.997436i	$0.477199\pi$
$828$	−14.0223	+	3.92756i	−0.487308	+	0.136492i
$829$	19.7321			0.685323			0.342661	−	0.939459i	$-0.388672\pi$
$829$	19.7321			0.685323			0.342661	+	0.939459i	$0.388672\pi$
$830$	2.38816	+	16.6100i	0.0828943	+	0.576542i
$831$	−6.03054	+	13.2050i	−0.209197	+	0.458078i
$832$	−27.2649	+	8.00571i	−0.945242	+	0.277548i
$833$	7.62959	−	8.80501i	0.264349	−	0.305076i
$834$	−14.2871	−	4.19506i	−0.494720	−	0.145263i
$835$	−40.2810	+	25.8870i	−1.39398	+	0.895857i
$836$	−14.9750	−	32.7906i	−0.517920	−	1.13409i
$837$	−5.86031	−	6.76315i	−0.202562	−	0.233769i
$838$	37.2635	+	23.9478i	1.28725	+	0.827264i
$839$	8.08581	−	56.2380i	0.279153	−	1.94155i	−0.0536580	−	0.998559i	$-0.517088\pi$
$839$	8.08581	−	56.2380i	0.279153	−	1.94155i	0.332811	−	0.942993i	$-0.392003\pi$
$840$	3.12433	−	21.7302i	0.107800	−	0.749763i
$841$	−0.381507	−	0.245179i	−0.0131554	−	0.00845446i
$842$	−50.6755	−	58.4827i	−1.74639	−	2.01545i
$843$	7.36641	+	16.1302i	0.253713	+	0.555553i
$844$	18.1180	−	11.6437i	0.623647	−	0.400793i
$845$	22.0151	+	6.46422i	0.757343	+	0.222376i
$846$	−7.33571	+	8.46586i	−0.252207	+	0.291062i
$847$	−49.9822	+	14.6761i	−1.71741	+	0.504277i
$848$	−2.90497	+	6.36100i	−0.0997571	+	0.218438i
$849$	0.790844	+	5.50044i	0.0271417	+	0.188775i
$850$	15.9511			0.547119
$851$	10.5239	+	0.131593i	0.360754	+	0.00451096i
$852$	−4.03752			−0.138323
$853$	−4.91230	−	34.1658i	−0.168194	−	1.16981i	−0.882614	−	0.470098i	$-0.844219\pi$
$853$	−4.91230	−	34.1658i	−0.168194	−	1.16981i	0.714421	−	0.699717i	$-0.246690\pi$
$854$	−18.5089	+	40.5287i	−0.633360	+	1.38687i
$855$	−6.17512	+	1.81318i	−0.211185	+	0.0620095i
$856$	−7.15780	+	8.26054i	−0.244648	+	0.282339i
$857$	15.0191	+	4.41002i	0.513044	+	0.150643i	0.527999	−	0.849245i	$-0.322942\pi$
$857$	15.0191	+	4.41002i	0.513044	+	0.150643i	−0.0149552	+	0.999888i	$0.504761\pi$
$858$	−21.1391	+	13.5853i	−0.721678	+	0.463794i
$859$	−5.27456	−	11.5497i	−0.179966	−	0.394070i	0.798053	−	0.602587i	$-0.205863\pi$
$859$	−5.27456	−	11.5497i	−0.179966	−	0.394070i	−0.978019	+	0.208517i	$0.933136\pi$
$860$	−50.8024	−	58.6291i	−1.73235	−	1.99924i
$861$	0.871276	+	0.559935i	0.0296930	+	0.0190825i
$862$	−11.5856	+	80.5794i	−0.394606	+	2.74455i
$863$	7.03445	−	48.9257i	0.239455	−	1.66545i	−0.415357	−	0.909658i	$-0.636343\pi$
$863$	7.03445	−	48.9257i	0.239455	−	1.66545i	0.654813	−	0.755791i	$-0.272747\pi$
$864$	5.52394	+	3.55002i	0.187928	+	0.120774i
$865$	15.4213	+	17.7971i	0.524340	+	0.605121i
$866$	27.1191	+	59.3826i	0.921546	+	2.01790i
$867$	−8.66655	+	5.56965i	−0.294332	+	0.189155i
$868$	−88.4199	−	25.9624i	−3.00117	−	0.881222i
$869$	47.9384	−	55.3239i	1.62620	−	1.87673i
$870$	32.0204	−	9.40203i	1.08559	−	0.318759i
$871$	0.829350	−	1.81602i	0.0281015	−	0.0615336i
$872$	2.76862	+	19.2562i	0.0937574	+	0.652097i
$873$	−3.71181			−0.125626
$874$	23.7897	+	7.30959i	0.804698	+	0.247250i
$875$	−21.2723			−0.719134
$876$	−4.40045	−	30.6058i	−0.148677	−	1.03407i
$877$	−6.21733	+	13.6141i	−0.209944	+	0.459714i	−0.985084	−	0.172077i	$-0.944952\pi$
$877$	−6.21733	+	13.6141i	−0.209944	+	0.459714i	0.775139	+	0.631790i	$0.217680\pi$
$878$	−36.6206	+	10.7528i	−1.23589	+	0.362889i
$879$	−2.39724	+	2.76656i	−0.0808570	+	0.0933139i
$880$	−11.6977	−	3.43474i	−0.394328	−	0.115785i
$881$	−25.9272	+	16.6624i	−0.873508	+	0.561370i	−0.898824	−	0.438310i	$-0.855577\pi$
$881$	−25.9272	+	16.6624i	−0.873508	+	0.561370i	0.0253156	+	0.999680i	$0.491941\pi$
$882$	−4.19681	−	9.18973i	−0.141314	−	0.309434i
$883$	24.3213	+	28.0683i	0.818478	+	0.944574i	0.999241	−	0.0389523i	$-0.0124020\pi$
$883$	24.3213	+	28.0683i	0.818478	+	0.944574i	−0.180763	+	0.983527i	$0.557857\pi$
$884$	14.4173	+	9.26545i	0.484907	+	0.311631i
$885$	−1.89479	+	13.1785i	−0.0636926	+	0.442992i
$886$	4.94907	−	34.4216i	0.166267	−	1.15642i
$887$	−18.4129	−	11.8332i	−0.618243	−	0.397321i	0.193697	−	0.981061i	$-0.437952\pi$
$887$	−18.4129	−	11.8332i	−0.618243	−	0.397321i	−0.811940	+	0.583741i	$0.801589\pi$
$888$	3.34250	+	3.85745i	0.112167	+	0.129448i
$889$	−27.9808	−	61.2695i	−0.938447	−	2.05491i
$890$	4.09897	−	2.63425i	0.137398	−	0.0883003i
$891$	4.92623	+	1.44647i	0.165035	+	0.0484587i
$892$	14.8871	−	17.1807i	0.498458	−	0.575252i
$893$	11.0747	−	3.25182i	0.370600	−	0.108818i
$894$	−6.59445	+	14.4398i	−0.220551	+	0.482940i
$895$	5.24626	+	36.4886i	0.175363	+	1.21968i
$896$	54.6306			1.82508
$897$	1.61780	−	10.3332i	0.0540168	−	0.345014i
$898$	−34.7490			−1.15959
$899$	−6.80453	−	47.3265i	−0.226944	−	1.57843i
$900$	3.46414	−	7.58542i	0.115471	−	0.252847i
$901$	20.3536	−	5.97635i	0.678076	−	0.199101i
$902$	−2.30425	+	2.65924i	−0.0767230	+	0.0885430i
$903$	−29.8713	−	8.77100i	−0.994054	−	0.291881i
$904$	−15.7150	+	10.0994i	−0.522674	+	0.335902i
$905$	−11.2724	−	24.6831i	−0.374706	−	0.820493i
$906$	19.5620	+	22.5757i	0.649903	+	0.750028i
$907$	18.6382	+	11.9781i	0.618872	+	0.397725i	0.812175	−	0.583414i	$-0.198284\pi$
$907$	18.6382	+	11.9781i	0.618872	+	0.397725i	−0.193303	+	0.981139i	$0.561920\pi$
$908$	−4.35549	+	30.2931i	−0.144542	+	1.00531i
$909$	2.47094	−	17.1858i	0.0819559	−	0.570016i
$910$	38.8637	+	24.9762i	1.28832	+	0.827952i
$911$	−25.0315	−	28.8879i	−0.829332	−	0.957100i	0.170268	−	0.985398i	$-0.445537\pi$
$911$	−25.0315	−	28.8879i	−0.829332	−	0.957100i	−0.999600	+	0.0282982i	$0.990991\pi$
$912$	−0.819544	−	1.79455i	−0.0271378	−	0.0594235i
$913$	−11.6039	+	7.45740i	−0.384034	+	0.246804i
$914$	86.1820	+	25.3053i	2.85065	+	0.837026i
$915$	−10.6698	+	12.3136i	−0.352732	+	0.407074i
$916$	19.1006	−	5.60843i	0.631101	−	0.185308i
$917$	2.48437	−	5.44001i	0.0820411	−	0.179645i
$918$	−0.826577	−	5.74897i	−0.0272811	−	0.189744i
$919$	19.7243			0.650645			0.325322	−	0.945603i	$-0.394527\pi$
$919$	19.7243			0.650645			0.325322	+	0.945603i	$0.394527\pi$
$920$	−26.3244	+	16.4563i	−0.867890	+	0.542547i
$921$	−24.0595			−0.792789
$922$	0.324552	+	2.25731i	0.0106886	+	0.0743405i
$923$	1.20467	−	2.63787i	0.0396523	−	0.0868265i
$924$	50.7285	−	14.8952i	1.66884	−	0.490017i
$925$	−3.94687	+	4.55493i	−0.129772	+	0.149765i
$926$	−14.9683	−	4.39509i	−0.491888	−	0.144431i
$927$	4.33664	−	2.78699i	0.142434	−	0.0915368i
$928$	14.5741	+	31.9127i	0.478417	+	1.04759i
$929$	34.8707	+	40.2429i	1.14407	+	1.32033i	0.939922	+	0.341388i	$0.110897\pi$
$929$	34.8707	+	40.2429i	1.14407	+	1.32033i	0.204148	+	0.978940i	$0.434558\pi$
$930$	−47.0226	−	30.2196i	−1.54193	−	0.990938i
$931$	−1.48144	+	10.3036i	−0.0485521	+	0.337687i
$932$	−4.76275	+	33.1257i	−0.156009	+	1.08507i
$933$	3.18449	+	2.04655i	0.104255	+	0.0670009i
$934$	47.2679	+	54.5501i	1.54665	+	1.78493i
$935$	15.3631	+	33.6405i	0.502427	+	1.10016i
$936$	4.26709	−	2.74229i	0.139474	−	0.0896346i
$937$	36.1268	+	10.6078i	1.18021	+	0.346541i	0.812255	−	0.583303i	$-0.198240\pi$
$937$	36.1268	+	10.6078i	1.18021	+	0.346541i	0.367955	+	0.929844i	$0.380058\pi$
$938$	−4.56265	+	5.26558i	−0.148976	+	0.171927i
$939$	−7.87106	+	2.31115i	−0.256862	+	0.0754216i
$940$	−17.5235	+	38.3711i	−0.571553	+	1.25153i
$941$	−6.75847	−	47.0062i	−0.220320	−	1.53236i	−0.736831	−	0.676077i	$-0.763679\pi$
$941$	−6.75847	−	47.0062i	−0.220320	−	1.53236i	0.516511	−	0.856280i	$-0.327230\pi$
$942$	−17.3108			−0.564015
$943$	−0.190289	−	1.45216i	−0.00619666	−	0.0472888i
$944$	−4.08128			−0.132834
$945$	−1.34332	−	9.34301i	−0.0436983	−	0.303928i
$946$	43.9385	−	96.2119i	1.42856	−	3.12812i
$947$	6.39248	−	1.87700i	0.207728	−	0.0609944i	−0.176213	−	0.984352i	$-0.556385\pi$
$947$	6.39248	−	1.87700i	0.207728	−	0.0609944i	0.383941	+	0.923358i	$0.374567\pi$
$948$	−28.3508	+	32.7186i	−0.920793	+	1.06265i
$949$	21.3089	+	6.25685i	0.691716	+	0.203106i
$950$	−11.9894	+	7.70515i	−0.388989	+	0.249988i
$951$	1.05106	+	2.30150i	0.0340829	+	0.0746312i
$952$	−13.3685	−	15.4280i	−0.433274	−	0.500025i
$953$	40.2257	+	25.8515i	1.30304	+	0.837411i	0.993539	−	0.113489i	$-0.0362026\pi$
$953$	40.2257	+	25.8515i	1.30304	+	0.837411i	0.309498	+	0.950900i	$0.399839\pi$
$954$	2.61778	−	18.2071i	0.0847539	−	0.589476i
$955$	−0.167345	+	1.16391i	−0.00541516	+	0.0376632i
$956$	16.6558	+	10.7040i	0.538688	+	0.346193i
$957$	17.9638	+	20.7313i	0.580688	+	0.670149i
$958$	−19.4442	−	42.5768i	−0.628213	−	1.37559i
$959$	3.93091	−	2.52624i	0.126936	−	0.0815766i
$960$	34.7957	+	10.2169i	1.12303	+	0.329750i
$961$	−32.1428	+	37.0948i	−1.03686	+	1.19661i
$962$	−10.3056	+	3.02600i	−0.332267	+	0.0975623i
$963$	−1.95225	+	4.27483i	−0.0629104	+	0.137755i
$964$	−3.04713	−	21.1933i	−0.0981416	−	0.682590i
$965$	21.7567			0.700373
$966$	−15.5770	+	33.0103i	−0.501182	+	1.06209i
$967$	−14.8524			−0.477621			−0.238811	−	0.971066i	$-0.576758\pi$
$967$	−14.8524			−0.477621			−0.238811	+	0.971066i	$0.576758\pi$
$968$	5.08417	+	35.3611i	0.163411	+	1.13655i
$969$	−2.48606	+	5.44371i	−0.0798637	+	0.174877i
$970$	−22.2452	+	6.53177i	−0.714249	+	0.209722i
$971$	12.5998	−	14.5409i	0.404347	−	0.466641i	−0.516658	−	0.856192i	$-0.672824\pi$
$971$	12.5998	−	14.5409i	0.404347	−	0.466641i	0.921005	+	0.389551i	$0.127370\pi$
$972$	−2.91338	−	0.855446i	−0.0934468	−	0.0274385i
$973$	−18.9300	+	12.1656i	−0.606867	+	0.390010i
$974$	7.81447	+	17.1113i	0.250392	+	0.548282i
$975$	3.92225	+	4.52651i	0.125612	+	0.144964i
$976$	−4.20164	−	2.70023i	−0.134491	−	0.0864323i
$977$	−0.285249	+	1.98395i	−0.00912591	+	0.0634721i	−0.993875	−	0.110506i	$-0.964753\pi$
$977$	−0.285249	+	1.98395i	−0.00912591	+	0.0634721i	0.984750	+	0.173978i	$0.0556621\pi$
$978$	−6.44236	+	44.8076i	−0.206004	+	1.43279i
$979$	3.36930	+	2.16532i	0.107683	+	0.0692039i
$980$	−24.9133	−	28.7515i	−0.795826	−	0.918433i
$981$	3.47471	+	7.60856i	0.110939	+	0.242923i
$982$	−51.2855	+	32.9592i	−1.63659	+	1.05177i
$983$	−16.5833	−	4.86929i	−0.528924	−	0.155306i	0.00635737	−	0.999980i	$-0.497976\pi$
$983$	−16.5833	−	4.86929i	−0.528924	−	0.155306i	−0.535282	+	0.844674i	$0.679795\pi$
$984$	0.465129	−	0.536787i	0.0148278	−	0.0171122i
$985$	−31.9514	+	9.38178i	−1.01806	+	0.298928i
$986$	12.8912	−	28.2277i	0.410538	−	0.898953i
$987$	2.40916	+	16.7561i	0.0766844	+	0.533351i
$988$	−15.3122			−0.487147
$989$	17.7863	+	40.2717i	0.565572	+	1.28056i
$990$	32.0687			1.01921
$991$	−2.49219	−	17.3336i	−0.0791670	−	0.550618i	−0.990347	−	0.138610i	$-0.955737\pi$
$991$	−2.49219	−	17.3336i	−0.0791670	−	0.550618i	0.911180	−	0.412008i	$-0.135173\pi$
$992$	24.4104	−	53.4514i	0.775032	−	1.69708i
$993$	30.5622	−	8.97387i	0.969861	−	0.284777i
$994$	−6.62748	+	7.64852i	−0.210211	+	0.242596i
$995$	51.9828	+	15.2635i	1.64796	+	0.483886i
$996$	6.86259	−	4.41032i	0.217449	−	0.139746i
$997$	15.9380	+	34.8994i	0.504762	+	1.10527i	0.974892	+	0.222678i	$0.0714798\pi$
$997$	15.9380	+	34.8994i	0.504762	+	1.10527i	−0.470130	+	0.882597i	$0.655793\pi$
$998$	39.0981	+	45.1216i	1.23763	+	1.42830i
$999$	1.84617	+	1.18646i	0.0584103	+	0.0375380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.49.2	yes	20
3.2	odd	2		207.2.i.d.118.1		20
23.8	even	11	inner	69.2.e.c.31.2	✓	20
23.10	odd	22		1587.2.a.t.1.2		10
23.13	even	11		1587.2.a.u.1.2		10
69.8	odd	22		207.2.i.d.100.1		20
69.56	even	22		4761.2.a.bu.1.9		10
69.59	odd	22		4761.2.a.bt.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.31.2	✓	20	23.8	even	11	inner
69.2.e.c.49.2	yes	20	1.1	even	1	trivial
207.2.i.d.100.1		20	69.8	odd	22
207.2.i.d.118.1		20	3.2	odd	2
1587.2.a.t.1.2		10	23.10	odd	22
1587.2.a.u.1.2		10	23.13	even	11
4761.2.a.bt.1.9		10	69.59	odd	22
4761.2.a.bu.1.9		10	69.56	even	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.319381 + 2.22134i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.91338 + 0.855446i) q^{4} +(-1.82263 + 2.10342i) q^{5} +(2.15328 + 0.632261i) q^{6} +(2.85304 - 1.83354i) q^{7} +(-0.966182 - 2.11564i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.319381 + 2.22134i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.91338 + 0.855446i) q^{4} +(-1.82263 + 2.10342i) q^{5} +(2.15328 + 0.632261i) q^{6} +(2.85304 - 1.83354i) q^{7} +(-0.966182 - 2.11564i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-5.25454 - 3.37689i) q^{10} +(0.730673 - 5.08195i) q^{11} +(-0.432121 + 3.00547i) q^{12} +(-1.83466 - 1.17906i) q^{13} +(4.98413 + 5.75199i) q^{14} +(1.15620 + 2.53171i) q^{15} +(-0.717732 + 0.461258i) q^{16} +(2.48322 + 0.729141i) q^{17} +(1.46963 - 1.69604i) q^{18} +(-2.21869 + 0.651466i) q^{19} +(3.51064 - 7.68724i) q^{20} +(-0.482649 - 3.35690i) q^{21} +11.5221 q^{22} +(-3.18567 + 3.58490i) q^{23} -2.32582 q^{24} +(-0.390848 - 2.71841i) q^{25} +(2.03315 - 4.45197i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-6.74351 + 7.78242i) q^{28} +(-5.12647 - 1.50527i) q^{29} +(-5.25454 + 3.37689i) q^{30} +(3.71752 + 8.14024i) q^{31} +(-4.30002 - 4.96249i) q^{32} +(-4.31917 - 2.77576i) q^{33} +(-0.826577 + 5.74897i) q^{34} +(-1.34332 + 9.34301i) q^{35} +(2.55436 + 1.64159i) q^{36} +(-1.43712 - 1.65853i) q^{37} +(-2.15574 - 4.72041i) q^{38} +(-1.83466 + 1.17906i) q^{39} +(6.21109 + 1.82374i) q^{40} +(-0.199985 + 0.230795i) q^{41} +(7.30268 - 2.14426i) q^{42} +(3.81341 - 8.35019i) q^{43} +(2.21860 + 15.4307i) q^{44} +2.78323 q^{45} +(-8.98074 - 5.93153i) q^{46} -4.99153 q^{47} +(0.121419 + 0.844485i) q^{48} +(1.87008 - 4.09490i) q^{49} +(5.91369 - 1.73642i) q^{50} +(1.69482 - 1.95592i) q^{51} +(6.35368 + 1.86561i) q^{52} +(6.89527 - 4.43132i) q^{53} +(-0.932269 - 2.04138i) q^{54} +(9.35774 + 10.7994i) q^{55} +(-6.63567 - 4.26449i) q^{56} +(-0.329083 + 2.28882i) q^{57} +(1.70642 - 11.8684i) q^{58} +(4.02428 + 2.58625i) q^{59} +(-5.53418 - 6.38679i) q^{60} +(2.43186 + 5.32504i) q^{61} +(-16.8950 + 10.8577i) q^{62} +(-3.25404 - 0.955473i) q^{63} +(8.53265 - 9.84720i) q^{64} +(5.82396 - 1.71007i) q^{65} +(4.78646 - 10.4809i) q^{66} +(0.130280 + 0.906118i) q^{67} -7.85832 q^{68} +(1.93756 + 4.38701i) q^{69} -21.1831 q^{70} +(0.189238 + 1.31618i) q^{71} +(-0.966182 + 2.11564i) q^{72} +(-9.77086 + 2.86898i) q^{73} +(3.22518 - 3.72205i) q^{74} +(-2.63512 - 0.773740i) q^{75} +(5.90660 - 3.79594i) q^{76} +(-7.23330 - 15.8387i) q^{77} +(-3.20506 - 3.69883i) q^{78} +(11.9947 + 7.70851i) q^{79} +(0.337936 - 2.35040i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.576546 - 0.370523i) q^{82} +(-1.75936 - 2.03041i) q^{83} +(4.27779 + 9.36705i) q^{84} +(-6.05968 + 3.89432i) q^{85} +(19.7666 + 5.80399i) q^{86} +(-3.49885 + 4.03789i) q^{87} +(-11.4576 + 3.36424i) q^{88} +(-0.324058 + 0.709587i) q^{89} +(0.888911 + 6.18251i) q^{90} -7.39621 q^{91} +(6.21440 - 13.1693i) q^{92} +8.94893 q^{93} +(-1.59420 - 11.0879i) q^{94} +(2.67354 - 5.85423i) q^{95} +(-6.30034 + 1.84995i) q^{96} +(2.43072 - 2.80520i) q^{97} +(9.69346 + 2.84626i) q^{98} +(-4.31917 + 2.77576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

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