LMFDB - Embedded newform 69.2.e.c.31.2

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			31.2
Root			$0.480233 - 1.05156i$ of defining polynomial
Character	$\chi$	$=$	69.31
Dual form			69.2.e.c.49.2

$q$-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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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	−0.489535	−	0.871984i	$-0.662833\pi$
$2$	0.319381	−	2.22134i	0.225837	−	1.57073i	0.715372	−	0.698744i	$-0.246257\pi$
$3$	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	0.184004	−	0.982926i	$-0.441094\pi$
$5$	−1.82263	−	2.10342i	−0.815104	−	0.940680i	−0.999107	+	0.0422457i	$0.986549\pi$
$6$	2.15328	−	0.632261i	0.879074	−	0.258119i
$7$	2.85304	+	1.83354i	1.07835	+	0.693013i	0.954175	−	0.299248i	$-0.0967358\pi$
$7$	2.85304	+	1.83354i	1.07835	+	0.693013i	0.124173	+	0.992261i	$0.460372\pi$
$8$	−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	0.736881	+	0.676022i	$0.236298\pi$
$11$	0.730673	+	5.08195i	0.220306	+	1.53226i	−0.516575	+	0.856242i	$0.672793\pi$
$12$	−0.432121	−	3.00547i	−0.124743	−	0.867605i
$13$	−1.83466	+	1.17906i	−0.508842	+	0.327013i	−0.769744	−	0.638352i	$-0.779616\pi$
$13$	−1.83466	+	1.17906i	−0.508842	+	0.327013i	0.260902	+	0.965365i	$0.415980\pi$
$14$	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	0.0336377	−	0.999434i	$-0.489291\pi$
$17$	2.48322	−	0.729141i	0.602270	−	0.176843i	0.568633	+	0.822592i	$0.307473\pi$
$18$	1.46963	+	1.69604i	0.346395	+	0.399761i
$19$	−2.21869	−	0.651466i	−0.509003	−	0.149457i	0.0171398	−	0.999853i	$-0.494544\pi$
$19$	−2.21869	−	0.651466i	−0.509003	−	0.149457i	−0.526142	+	0.850396i	$0.676362\pi$
$20$	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	−0.720603	−	0.693348i	$-0.756135\pi$
$29$	−5.12647	+	1.50527i	−0.951961	+	0.279521i	−0.231358	+	0.972869i	$0.574317\pi$
$30$	−5.25454	−	3.37689i	−0.959344	−	0.616533i
$31$	3.71752	−	8.14024i	0.667687	−	1.46203i	−0.207496	−	0.978236i	$-0.566531\pi$
$31$	3.71752	−	8.14024i	0.667687	−	1.46203i	0.875182	−	0.483794i	$-0.160741\pi$
$32$	−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	−0.861482	−	0.507787i	$-0.830464\pi$
$37$	−1.43712	+	1.65853i	−0.236262	+	0.272661i	0.625221	+	0.780448i	$0.285009\pi$
$38$	−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	0.739918	−	0.672697i	$-0.234864\pi$
$41$	−0.199985	−	0.230795i	−0.0312323	−	0.0360440i	−0.771151	+	0.636652i	$0.780319\pi$
$42$	7.30268	+	2.14426i	1.12683	+	0.330866i
$43$	3.81341	+	8.35019i	0.581539	+	1.27339i	0.940422	+	0.340010i	$0.110430\pi$
$43$	3.81341	+	8.35019i	0.581539	+	1.27339i	−0.358883	+	0.933383i	$0.616842\pi$
$44$	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	0.920410	−	0.390954i	$-0.127855\pi$
$53$	6.89527	+	4.43132i	0.947138	+	0.608689i	0.0267281	+	0.999643i	$0.491491\pi$
$54$	−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	−0.251803	−	0.967779i	$-0.581023\pi$
$59$	4.02428	−	2.58625i	0.523917	−	0.336701i	0.775720	+	0.631077i	$0.217387\pi$
$60$	−5.53418	+	6.38679i	−0.714460	+	0.824531i
$61$	2.43186	−	5.32504i	0.311368	−	0.681801i	−0.687653	−	0.726040i	$-0.741359\pi$
$61$	2.43186	−	5.32504i	0.311368	−	0.681801i	0.999021	+	0.0442383i	$0.0140861\pi$
$62$	−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	−0.980315	−	0.197442i	$-0.936737\pi$
$67$	0.130280	−	0.906118i	0.0159162	−	0.110700i	0.996231	+	0.0867422i	$0.0276456\pi$
$68$	−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	−0.975506	−	0.219972i	$-0.929403\pi$
$71$	0.189238	−	1.31618i	0.0224585	−	0.156202i	0.997965	+	0.0637701i	$0.0203124\pi$
$72$	−0.966182	−	2.11564i	−0.113866	−	0.249331i
$73$	−9.77086	−	2.86898i	−1.14359	−	0.335789i	−0.345556	−	0.938398i	$-0.612310\pi$
$73$	−9.77086	−	2.86898i	−1.14359	−	0.335789i	−0.798037	+	0.602609i	$0.794128\pi$
$74$	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	0.351873	−	0.936048i	$-0.385545\pi$
$79$	11.9947	−	7.70851i	1.34951	−	0.867275i	0.997632	+	0.0687729i	$0.0219084\pi$
$80$	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	−0.844047	−	0.536270i	$-0.819833\pi$
$83$	−1.75936	+	2.03041i	−0.193115	+	0.222866i	0.650932	+	0.759136i	$0.274378\pi$
$84$	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	0.891679	−	0.452668i	$-0.149528\pi$
$89$	−0.324058	−	0.709587i	−0.0343500	−	0.0752161i	−0.926029	+	0.377452i	$0.876800\pi$
$90$	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	0.865611	−	0.500717i	$-0.166930\pi$
$97$	2.43072	+	2.80520i	0.246802	+	0.284825i	−0.618809	+	0.785541i	$0.712385\pi$
$98$	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	0.184928	−	0.982752i	$-0.440795\pi$
$101$	11.3700	−	13.1217i	1.13136	−	1.30566i	0.946431	−	0.322906i	$-0.104660\pi$
$102$	4.88608	−	3.14009i	0.483794	−	0.310915i
$103$	−0.733629	−	5.10250i	−0.0722867	−	0.502765i	−0.993511	−	0.113734i	$-0.963719\pi$
$103$	−0.733629	−	5.10250i	−0.0722867	−	0.502765i	0.921225	−	0.389031i	$-0.127190\pi$
$104$	−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	−0.980218	−	0.197923i	$-0.936580\pi$
$107$	−1.95225	+	4.27483i	−0.188731	+	0.413264i	0.791486	+	0.611187i	$0.209308\pi$
$108$	2.55436	+	1.64159i	0.245794	+	0.157962i
$109$	−8.02562	+	2.35653i	−0.768715	+	0.225715i	−0.642498	−	0.766288i	$-0.722102\pi$
$109$	−8.02562	+	2.35653i	−0.768715	+	0.225715i	−0.126217	+	0.992003i	$0.540284\pi$
$110$	−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	0.862706	+	0.505706i	$0.168768\pi$
$113$	−1.14304	+	7.95002i	−0.107528	+	0.747875i	−0.970234	+	0.242169i	$0.922141\pi$
$114$	−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	0.593371	+	0.804929i	$0.297797\pi$
$127$	2.82649	+	19.6587i	0.250810	+	1.74442i	−0.342561	+	0.939496i	$0.611294\pi$
$128$	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	0.603840	−	0.797106i	$-0.293637\pi$
$131$	1.48347	+	0.953370i	0.129612	+	0.0832963i	−0.474228	+	0.880402i	$0.657273\pi$
$132$	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	−0.988597	−	0.150585i	$-0.951884\pi$
$149$	−1.00667	−	7.00155i	−0.0824697	−	0.573589i	0.906127	−	0.423005i	$-0.139025\pi$
$150$	0.877137	+	6.10062i	0.0716179	+	0.498114i
$151$	11.1978	−	7.19637i	0.911261	−	0.585632i	0.00115144	−	0.999999i	$-0.499633\pi$
$151$	11.1978	−	7.19637i	0.911261	−	0.585632i	0.910110	+	0.414367i	$0.135997\pi$
$152$	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	−0.0272838	−	0.999628i	$-0.508686\pi$
$157$	−7.40115	−	2.17317i	−0.590676	−	0.173438i	−0.563392	+	0.826190i	$0.690504\pi$
$158$	−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	−0.494477	−	0.869191i	$-0.664640\pi$
$163$	2.87069	−	19.9661i	0.224850	−	1.56386i	0.719327	−	0.694672i	$-0.244451\pi$
$164$	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	0.428421	−	0.903579i	$-0.359070\pi$
$167$	16.5069	−	4.84687i	1.27734	−	0.375062i	0.848922	+	0.528517i	$0.177252\pi$
$168$	−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	0.982998	+	0.183614i	$0.0587796\pi$
$173$	1.20413	+	8.37491i	0.0915483	+	0.636733i	−0.891450	+	0.453119i	$0.850311\pi$
$174$	−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	0.980819	−	0.194922i	$-0.0624453\pi$
$179$	8.67361	+	10.0099i	0.648296	+	0.748173i	−0.332523	+	0.943095i	$0.607900\pi$
$180$	−8.10861	−	2.38090i	−0.604380	−	0.177462i
$181$	−4.05011	−	8.86850i	−0.301042	−	0.659190i	0.697298	−	0.716781i	$-0.254385\pi$
$181$	−4.05011	−	8.86850i	−0.301042	−	0.659190i	−0.998340	+	0.0575910i	$0.981658\pi$
$182$	−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	0.553436	−	0.832892i	$-0.313316\pi$
$191$	0.355419	+	0.228414i	0.0257172	+	0.0165274i	−0.527719	+	0.849419i	$0.676953\pi$
$192$	−5.41274	+	11.8522i	−0.390631	+	0.855362i
$193$	−5.11910	+	5.90775i	−0.368481	+	0.425249i	−0.909463	−	0.415784i	$-0.863507\pi$
$193$	−5.11910	+	5.90775i	−0.368481	+	0.425249i	0.540983	+	0.841034i	$0.318053\pi$
$194$	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	−0.130513	−	0.991447i	$-0.541662\pi$
$197$	10.0653	−	6.46856i	0.717122	−	0.460866i	0.847635	+	0.530580i	$0.178026\pi$
$198$	−7.54538	+	8.70783i	−0.536227	+	0.618839i
$199$	−8.08632	+	17.7066i	−0.573224	+	1.25519i	0.371839	+	0.928297i	$0.378727\pi$
$199$	−8.08632	+	17.7066i	−0.573224	+	1.25519i	−0.945063	+	0.326888i	$0.894000\pi$
$200$	−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	0.0389468	−	0.999241i	$-0.487600\pi$
$211$	−6.80564	−	1.99832i	−0.468520	−	0.137570i	−0.507466	+	0.861671i	$0.669418\pi$
$212$	−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	0.312490	−	0.949921i	$-0.398837\pi$
$223$	−6.29845	−	4.04777i	−0.421775	−	0.271059i	−0.734265	+	0.678862i	$0.762473\pi$
$224$	−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	0.996189	−	0.0872202i	$-0.0277984\pi$
$227$	4.18710	+	9.16846i	0.277907	+	0.608532i	−0.718282	+	0.695752i	$0.755071\pi$
$228$	−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	0.998258	−	0.0589919i	$-0.0187886\pi$
$233$	4.57862	+	10.0258i	0.299955	+	0.656810i	−0.698303	+	0.715802i	$0.746061\pi$
$234$	−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	−0.876856	−	0.480753i	$-0.840363\pi$
$239$	−4.27004	+	4.92789i	−0.276206	+	0.318759i	0.600650	+	0.799512i	$0.294909\pi$
$240$	−1.99761	+	1.28379i	−0.128945	+	0.0828681i
$241$	−1.00354	−	6.97979i	−0.0646439	−	0.449608i	−0.996277	−	0.0862082i	$-0.972525\pi$
$241$	−1.00354	−	6.97979i	−0.0646439	−	0.449608i	0.931633	−	0.363400i	$-0.118384\pi$
$242$	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	−0.977917	−	0.208993i	$-0.932982\pi$
$251$	0.305255	−	2.12310i	0.0192675	−	0.134009i	0.997185	+	0.0749841i	$0.0238906\pi$
$252$	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	0.768916	−	0.639350i	$-0.220796\pi$
$257$	17.1552	+	5.03722i	1.07011	+	0.314213i	0.301195	+	0.953563i	$0.402615\pi$
$258$	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	−0.772722	−	0.634745i	$-0.781105\pi$
$263$	−8.37359	+	5.38138i	−0.516338	+	0.331830i	0.256384	+	0.966575i	$0.417469\pi$
$264$	−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	0.0700887	−	0.997541i	$-0.477672\pi$
$269$	−13.2553	−	8.51867i	−0.808190	−	0.519392i	−0.878279	+	0.478148i	$0.841308\pi$
$270$	5.99308	−	1.75973i	0.364727	−	0.107094i
$271$	20.1886	+	23.2989i	1.22637	+	1.41531i	0.878484	+	0.477772i	$0.158556\pi$
$271$	20.1886	+	23.2989i	1.22637	+	1.41531i	0.347888	+	0.937536i	$0.386899\pi$
$272$	−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	0.295014	−	0.955493i	$-0.404676\pi$
$281$	−11.6124	−	13.4014i	−0.692739	−	0.799463i	−0.987752	+	0.156030i	$0.950130\pi$
$282$	−10.7482	+	3.15595i	−0.640045	+	0.187934i
$283$	−4.67485	−	3.00434i	−0.277891	−	0.178590i	0.394270	−	0.918995i	$-0.370997\pi$
$283$	−4.67485	−	3.00434i	−0.277891	−	0.178590i	−0.672161	+	0.740405i	$0.734634\pi$
$284$	−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	−0.382716	−	0.923866i	$-0.625011\pi$
$293$	−3.51241	+	1.03134i	−0.205197	+	0.0602513i	0.177519	+	0.984117i	$0.443193\pi$
$294$	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	0.376142	+	0.926562i	$0.377250\pi$
$307$	−9.99470	+	21.8853i	−0.570427	+	1.24906i	−0.946570	+	0.322500i	$0.895477\pi$
$308$	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	0.968830	−	0.247726i	$-0.0796832\pi$
$311$	−0.538720	−	3.74688i	−0.0305480	−	0.212466i	−0.999378	+	0.0352598i	$0.988774\pi$
$312$	4.26709	−	2.74229i	0.241576	−	0.155252i
$313$	−5.37205	+	6.19968i	−0.303646	+	0.350427i	−0.886982	−	0.461805i	$-0.847202\pi$
$313$	−5.37205	+	6.19968i	−0.303646	+	0.350427i	0.583335	+	0.812232i	$0.301747\pi$
$314$	−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	0.707309	−	0.706904i	$-0.249909\pi$
$317$	−1.65689	−	1.91215i	−0.0930602	−	0.107397i	−0.800370	+	0.599507i	$0.795363\pi$
$318$	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	0.207904	−	0.978149i	$-0.433336\pi$
$331$	20.8589	−	24.0725i	1.14651	−	1.32314i	0.938605	−	0.344993i	$-0.112119\pi$
$332$	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	−0.614873	−	0.788626i	$-0.710793\pi$
$337$	7.04540	−	15.4273i	0.383787	−	0.840377i	0.998660	−	0.0517509i	$-0.0164802\pi$
$338$	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	0.922809	+	0.385259i	$0.125888\pi$
$347$	−1.32556	+	9.21946i	−0.0711597	+	0.494926i	−0.993968	+	0.109668i	$0.965021\pi$
$348$	6.73929	+	14.7570i	0.361264	+	0.791058i
$349$	6.96469	+	2.04502i	0.372811	+	0.109467i	0.462770	−	0.886478i	$-0.346855\pi$
$349$	6.96469	+	2.04502i	0.372811	+	0.109467i	−0.0899592	+	0.995945i	$0.528674\pi$
$350$	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	−0.189806	−	0.981822i	$-0.560786\pi$
$353$	12.7103	−	27.8317i	0.676502	−	1.48133i	0.866308	−	0.499511i	$-0.166487\pi$
$354$	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	−0.641519	−	0.767107i	$-0.721695\pi$
$359$	3.96146	−	4.57177i	0.209078	−	0.241289i	0.850597	+	0.525819i	$0.176241\pi$
$360$	−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	0.930371	+	0.366619i	$0.119485\pi$
$373$	22.4198	+	25.8738i	1.16085	+	1.33970i	0.230482	+	0.973077i	$0.425970\pi$
$374$	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	0.964248	−	0.265003i	$-0.0853728\pi$
$379$	−0.693079	−	4.82047i	−0.0356011	−	0.247611i	−0.999849	+	0.0173918i	$0.994464\pi$
$380$	−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	0.361282	+	0.932457i	$0.382339\pi$
$383$	−11.3510	+	24.8553i	−0.580011	+	1.27005i	−0.941293	+	0.337591i	$0.890388\pi$
$384$	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	0.869854	+	0.493310i	$0.164213\pi$
$389$	−2.04620	+	14.2316i	−0.103746	+	0.721571i	−0.973600	+	0.228261i	$0.926696\pi$
$390$	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	−0.856671	+	0.515864i	$0.827471\pi$
$397$	−36.9854	+	10.8599i	−1.85624	+	0.545043i	−0.999574	+	0.0291790i	$0.990711\pi$
$398$	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	−0.986731	−	0.162364i	$-0.948088\pi$
$401$	−25.0100	+	16.0730i	−1.24894	+	0.802646i	−0.262211	+	0.965011i	$0.584452\pi$
$402$	−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	0.974497	−	0.224401i	$-0.0720427\pi$
$409$	12.4112	+	14.3233i	0.613694	+	0.708241i	−0.360803	+	0.932642i	$0.617497\pi$
$410$	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	0.977839	−	0.209357i	$-0.0671372\pi$
$419$	12.9255	+	14.9168i	0.631452	+	0.728734i	−0.346388	+	0.938092i	$0.612592\pi$
$420$	−27.4997	+	8.07464i	−1.34185	+	0.394002i
$421$	−29.0080	−	18.6423i	−1.41376	−	0.908569i	−0.413763	−	0.910385i	$-0.635786\pi$
$421$	−29.0080	−	18.6423i	−1.41376	−	0.908569i	−0.999998	+	0.00181545i	$0.999422\pi$
$422$	−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	0.701189	−	0.712975i	$-0.252653\pi$
$431$	34.8057	−	10.2199i	1.67653	−	0.492274i	0.975341	+	0.220701i	$0.0708347\pi$
$432$	0.558707	+	0.644782i	0.0268808	+	0.0310221i
$433$	27.9111	+	8.19542i	1.34132	+	0.393847i	0.872140	−	0.489256i	$-0.162732\pi$
$433$	27.9111	+	8.19542i	1.34132	+	0.393847i	0.469179	+	0.883103i	$0.344550\pi$
$434$	−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	−0.846880	−	0.531784i	$-0.821522\pi$
$439$	2.42033	−	16.8338i	0.115516	−	0.803433i	0.962396	−	0.271649i	$-0.0875690\pi$
$440$	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	−0.615153	−	0.788408i	$-0.710906\pi$
$443$	−14.8681	+	4.36568i	−0.706406	+	0.207420i	−0.0912538	+	0.995828i	$0.529087\pi$
$444$	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	−0.973386	−	0.229173i	$-0.926398\pi$
$449$	−2.20360	−	15.3264i	−0.103994	−	0.723297i	0.869391	−	0.494124i	$-0.164511\pi$
$450$	−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	0.708795	+	0.705414i	$0.249239\pi$
$457$	16.6264	+	36.4067i	0.777750	+	1.70303i	0.0689546	+	0.997620i	$0.478034\pi$
$458$	−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	0.830585	−	0.556892i	$-0.188006\pi$
$463$	−2.88771	−	6.32320i	−0.134203	−	0.293864i	−0.964788	+	0.263028i	$0.915279\pi$
$464$	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	0.987178	−	0.159626i	$-0.0510289\pi$
$467$	27.0573	+	17.3887i	1.25206	+	0.804653i	0.264887	+	0.964279i	$0.414665\pi$
$468$	−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	−0.209491	−	0.977810i	$-0.567181\pi$
$479$	−20.0120	−	5.87605i	−0.914371	−	0.268484i	−0.704880	+	0.709327i	$0.748999\pi$
$480$	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	0.458829	−	0.888525i	$-0.348269\pi$
$487$	8.04267	+	2.36154i	0.364448	+	0.107012i	−0.0943810	+	0.995536i	$0.530087\pi$
$488$	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	−0.464071	−	0.885798i	$-0.653612\pi$
$491$	11.2847	−	24.7101i	0.509272	−	1.11515i	0.973343	−	0.229353i	$-0.0736609\pi$
$492$	−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	0.935284	−	0.353897i	$-0.115144\pi$
$499$	22.3807	+	14.3832i	1.00190	+	0.643881i	0.0666147	+	0.997779i	$0.478780\pi$
$500$	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	0.818826	−	0.574042i	$-0.194625\pi$
$503$	−3.39157	−	7.42650i	−0.151223	−	0.331131i	−0.970049	+	0.242910i	$0.921898\pi$
$504$	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	−0.819933	−	0.572459i	$-0.805990\pi$
$509$	−16.1453	−	35.3532i	−0.715627	−	1.56700i	0.104306	−	0.994545i	$-0.466738\pi$
$510$	−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	−0.0193229	+	0.999813i	$0.506151\pi$
$521$	−17.3993	+	38.0992i	−0.762278	+	1.66916i	−0.742955	+	0.669342i	$0.766576\pi$
$522$	−10.0870	−	6.48253i	−0.441496	−	0.283733i
$523$	−10.1000	+	2.96564i	−0.441644	+	0.129678i	−0.494992	−	0.868898i	$-0.664829\pi$
$523$	−10.1000	+	2.96564i	−0.441644	+	0.129678i	0.0533477	+	0.998576i	$0.483011\pi$
$524$	−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	−0.972325	−	0.233631i	$-0.924939\pi$
$541$	−2.44706	−	17.0197i	−0.105208	−	0.731734i	0.867118	−	0.498103i	$-0.165970\pi$
$542$	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	0.441433	−	0.897294i	$-0.354470\pi$
$547$	−11.9174	−	13.7534i	−0.509551	−	0.588053i	−0.950984	+	0.309242i	$0.899925\pi$
$548$	−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	−0.936412	−	0.350901i	$-0.885875\pi$
$557$	−27.1522	−	31.3353i	−1.15048	−	1.32772i	−0.214064	−	0.976820i	$-0.568670\pi$
$558$	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	−0.798858	−	0.601519i	$-0.794562\pi$
$563$	−4.78887	−	33.3073i	−0.201827	−	1.40374i	0.597031	−	0.802218i	$-0.296347\pi$
$564$	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	−0.575041	−	0.818125i	$-0.695014\pi$
$569$	−14.7054	+	4.31791i	−0.616484	+	0.181016i	−0.0414433	+	0.999141i	$0.513196\pi$
$570$	9.45828	+	10.9154i	0.396164	+	0.457197i
$571$	31.2673	+	9.18092i	1.30850	+	0.384210i	0.860329	−	0.509739i	$-0.170258\pi$
$571$	31.2673	+	9.18092i	1.30850	+	0.384210i	0.448169	+	0.893949i	$0.352076\pi$
$572$	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	0.864421	+	0.502768i	$0.167685\pi$
$577$	−2.56137	+	17.8147i	−0.106631	+	0.741635i	−0.971052	+	0.238867i	$0.923224\pi$
$578$	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	−0.766861	−	0.641813i	$-0.778183\pi$
$587$	−5.13352	−	35.7044i	−0.211883	−	1.47368i	0.554978	−	0.831865i	$-0.312727\pi$
$588$	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	−0.987413	−	0.158161i	$-0.949443\pi$
$593$	−24.4354	−	28.1999i	−1.00344	−	1.15803i	−0.0160277	−	0.999872i	$-0.505102\pi$
$594$	−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	0.917576	−	0.397561i	$-0.130143\pi$
$601$	0.398010	+	0.871520i	0.0162352	+	0.0355501i	−0.901341	+	0.433111i	$0.857416\pi$
$602$	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	−0.928711	−	0.370805i	$-0.879082\pi$
$607$	−10.5820	+	12.2123i	−0.429510	+	0.495681i	0.499200	+	0.866487i	$0.333627\pi$
$608$	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	−0.419429	−	0.907788i	$-0.637770\pi$
$613$	13.4019	−	29.3462i	0.541299	−	1.18528i	0.960728	−	0.277492i	$-0.0895032\pi$
$614$	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	−0.0229661	−	0.999736i	$-0.507311\pi$
$617$	−14.4761	−	4.25056i	−0.582785	−	0.171121i	−0.559819	+	0.828615i	$0.689129\pi$
$618$	−4.80582	−	10.5233i	−0.193319	−	0.423309i
$619$	2.92734	−	20.3601i	0.117660	−	0.818340i	−0.842462	−	0.538756i	$-0.818894\pi$
$619$	2.92734	−	20.3601i	0.117660	−	0.818340i	0.960121	−	0.279584i	$-0.0901966\pi$
$620$	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	−0.904318	−	0.426860i	$-0.859620\pi$
$631$	−22.3992	+	14.3951i	−0.891699	+	0.573060i	0.0126186	+	0.999920i	$0.495983\pi$
$632$	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	0.999956	−	0.00940630i	$-0.00299416\pi$
$641$	8.55786	+	18.7391i	0.338015	+	0.740150i	−0.661941	+	0.749556i	$0.730267\pi$
$642$	−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	0.817799	−	0.575505i	$-0.195194\pi$
$647$	−3.88367	−	8.50406i	−0.152683	−	0.334329i	−0.970482	+	0.241176i	$0.922467\pi$
$648$	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	−0.914580	−	0.404406i	$-0.867478\pi$
$653$	−9.81606	+	11.3283i	−0.384132	+	0.443312i	0.530448	+	0.847718i	$0.322024\pi$
$654$	−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	−0.551717	−	0.834031i	$-0.686027\pi$
$659$	11.2927	−	24.7275i	0.439900	−	0.963246i	0.991617	−	0.129214i	$-0.0412455\pi$
$660$	−36.5010	−	23.4578i	−1.42080	−	0.913092i
$661$	−16.1324	+	4.73689i	−0.627476	+	0.184244i	−0.579984	−	0.814628i	$-0.696941\pi$
$661$	−16.1324	+	4.73689i	−0.627476	+	0.184244i	−0.0474922	+	0.998872i	$0.515123\pi$
$662$	−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	0.492669	−	0.870217i	$-0.336021\pi$
$673$	35.7381	−	10.4937i	1.37760	−	0.404501i	0.884934	+	0.465716i	$0.154203\pi$
$674$	−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	−0.0910951	−	0.995842i	$-0.529037\pi$
$677$	20.2147	−	12.9912i	0.776912	−	0.499291i	0.868008	+	0.496551i	$0.165400\pi$
$678$	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	0.997620	−	0.0689475i	$-0.0219641\pi$
$683$	35.2638	+	22.6626i	1.34933	+	0.867162i	0.351710	+	0.936109i	$0.385600\pi$
$684$	−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	0.998258	+	0.0590029i	$0.0187921\pi$
$701$	1.51073	+	10.5074i	0.0570595	+	0.396857i	−0.941198	+	0.337855i	$0.890299\pi$
$702$	−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	0.229373	−	0.973339i	$-0.426333\pi$
$709$	−2.76637	−	0.812279i	−0.103893	−	0.0305058i	−0.333266	+	0.942833i	$0.608151\pi$
$710$	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	−0.362437	−	0.932008i	$-0.618055\pi$
$719$	−4.38297	+	1.28696i	−0.163457	+	0.0479954i	0.198980	+	0.980004i	$0.436237\pi$
$720$	−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	0.136718	+	0.990610i	$0.456345\pi$
$727$	−23.2762	+	26.8622i	−0.863266	+	0.996262i	−0.999984	+	0.00565201i	$0.998201\pi$
$728$	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	0.659316	−	0.751866i	$-0.270846\pi$
$733$	−9.22320	−	20.1960i	−0.340667	−	0.745956i	−0.999983	+	0.00591019i	$0.998119\pi$
$734$	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	−0.914647	−	0.404253i	$-0.867532\pi$
$739$	−16.8869	−	36.9771i	−0.621194	−	1.36023i	0.293453	−	0.955974i	$-0.405196\pi$
$740$	−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	−0.211814	−	0.977310i	$-0.567937\pi$
$743$	−32.4043	−	20.8250i	−1.18880	−	0.763994i	−0.976983	+	0.213316i	$0.931573\pi$
$744$	−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	−0.928778	−	0.370636i	$-0.879140\pi$
$751$	−1.10851	+	2.42730i	−0.0404501	+	0.0885734i	0.888328	+	0.459209i	$0.151867\pi$
$752$	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	0.831046	+	0.556203i	$0.187742\pi$
$757$	−3.38520	+	23.5446i	−0.123037	+	0.855743i	−0.954084	+	0.299540i	$0.903167\pi$
$758$	−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	−0.900480	−	0.434896i	$-0.856785\pi$
$761$	2.37376	−	16.5099i	0.0860487	−	0.598482i	0.986529	−	0.163585i	$-0.0523059\pi$
$762$	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	0.571681	−	0.820476i	$-0.306292\pi$
$769$	43.1352	−	27.7213i	1.55550	−	0.999657i	0.983816	−	0.179181i	$-0.0573448\pi$
$770$	−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	−0.561343	−	0.827583i	$-0.689715\pi$
$773$	9.38915	−	10.8357i	0.337704	−	0.389732i	0.899047	+	0.437852i	$0.144261\pi$
$774$	−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	0.951032	−	0.309093i	$-0.100025\pi$
$787$	14.3000	+	16.5031i	0.509740	+	0.588271i	−0.441292	+	0.897363i	$0.645480\pi$
$788$	−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	−0.797703	−	0.603050i	$-0.793952\pi$
$797$	5.09393	−	11.1542i	0.180436	−	0.395101i	0.978139	+	0.207950i	$0.0666791\pi$
$798$	−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	0.166558	−	0.986032i	$-0.446735\pi$
$809$	−6.43989	−	1.89092i	−0.226414	−	0.0664813i	−0.392972	+	0.919550i	$0.628553\pi$
$810$	4.09032	+	4.72048i	0.143719	+	0.165861i
$811$	−7.85825	+	2.30739i	−0.275941	+	0.0810234i	−0.416775	−	0.909010i	$-0.636840\pi$
$811$	−7.85825	+	2.30739i	−0.275941	+	0.0810234i	0.140834	+	0.990033i	$0.455021\pi$
$812$	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	−0.180492	−	0.983576i	$-0.557769\pi$
$821$	−32.9558	−	21.1794i	−1.15016	−	0.739166i	−0.969672	+	0.244411i	$0.921405\pi$
$822$	2.96678	−	0.871126i	0.103478	−	0.0303840i
$823$	−1.32564	−	1.52987i	−0.0462090	−	0.0533281i	0.732175	−	0.681117i	$-0.238506\pi$
$823$	−1.32564	−	1.52987i	−0.0462090	−	0.0533281i	−0.778384	+	0.627789i	$0.783960\pi$
$824$	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	0.332811	+	0.942993i	$0.392003\pi$
$839$	8.08581	+	56.2380i	0.279153	+	1.94155i	−0.0536580	+	0.998559i	$0.517088\pi$
$840$	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	0.714421	+	0.699717i	$0.246690\pi$
$853$	−4.91230	+	34.1658i	−0.168194	+	1.16981i	−0.882614	+	0.470098i	$0.844219\pi$
$854$	−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	−0.0149552	−	0.999888i	$-0.504761\pi$
$857$	15.0191	−	4.41002i	0.513044	−	0.150643i	0.527999	+	0.849245i	$0.322942\pi$
$858$	−21.1391	−	13.5853i	−0.721678	−	0.463794i
$859$	−5.27456	+	11.5497i	−0.179966	+	0.394070i	−0.978019	−	0.208517i	$-0.933136\pi$
$859$	−5.27456	+	11.5497i	−0.179966	+	0.394070i	0.798053	+	0.602587i	$0.205863\pi$
$860$	−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	0.654813	+	0.755791i	$0.272747\pi$
$863$	7.03445	+	48.9257i	0.239455	+	1.66545i	−0.415357	+	0.909658i	$0.636343\pi$
$864$	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	0.775139	−	0.631790i	$-0.217680\pi$
$877$	−6.21733	−	13.6141i	−0.209944	−	0.459714i	−0.985084	+	0.172077i	$0.944952\pi$
$878$	−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	0.0253156	−	0.999680i	$-0.491941\pi$
$881$	−25.9272	−	16.6624i	−0.873508	−	0.561370i	−0.898824	+	0.438310i	$0.855577\pi$
$882$	−4.19681	+	9.18973i	−0.141314	+	0.309434i
$883$	24.3213	−	28.0683i	0.818478	−	0.944574i	−0.180763	−	0.983527i	$-0.557857\pi$
$883$	24.3213	−	28.0683i	0.818478	−	0.944574i	0.999241	+	0.0389523i	$0.0124020\pi$
$884$	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	−0.811940	−	0.583741i	$-0.801589\pi$
$887$	−18.4129	+	11.8332i	−0.618243	+	0.397321i	0.193697	+	0.981061i	$0.437952\pi$
$888$	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	−0.193303	−	0.981139i	$-0.561920\pi$
$907$	18.6382	−	11.9781i	0.618872	−	0.397725i	0.812175	+	0.583414i	$0.198284\pi$
$908$	−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	−0.999600	−	0.0282982i	$-0.990991\pi$
$911$	−25.0315	+	28.8879i	−0.829332	+	0.957100i	0.170268	+	0.985398i	$0.445537\pi$
$912$	−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	0.204148	−	0.978940i	$-0.434558\pi$
$929$	34.8707	−	40.2429i	1.14407	−	1.32033i	0.939922	−	0.341388i	$-0.110897\pi$
$930$	−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	0.367955	−	0.929844i	$-0.380058\pi$
$937$	36.1268	−	10.6078i	1.18021	−	0.346541i	0.812255	+	0.583303i	$0.198240\pi$
$938$	−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	0.516511	+	0.856280i	$0.327230\pi$
$941$	−6.75847	+	47.0062i	−0.220320	+	1.53236i	−0.736831	+	0.676077i	$0.763679\pi$
$942$	−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	0.383941	−	0.923358i	$-0.374567\pi$
$947$	6.39248	+	1.87700i	0.207728	+	0.0609944i	−0.176213	+	0.984352i	$0.556385\pi$
$948$	−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	0.309498	−	0.950900i	$-0.399839\pi$
$953$	40.2257	−	25.8515i	1.30304	−	0.837411i	0.993539	+	0.113489i	$0.0362026\pi$
$954$	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	0.921005	−	0.389551i	$-0.127370\pi$
$971$	12.5998	+	14.5409i	0.404347	+	0.466641i	−0.516658	+	0.856192i	$0.672824\pi$
$972$	−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	0.984750	−	0.173978i	$-0.0556621\pi$
$977$	−0.285249	−	1.98395i	−0.00912591	−	0.0634721i	−0.993875	+	0.110506i	$0.964753\pi$
$978$	−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	−0.535282	−	0.844674i	$-0.679795\pi$
$983$	−16.5833	+	4.86929i	−0.528924	+	0.155306i	0.00635737	+	0.999980i	$0.497976\pi$
$984$	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	0.911180	+	0.412008i	$0.135173\pi$
$991$	−2.49219	+	17.3336i	−0.0791670	+	0.550618i	−0.990347	+	0.138610i	$0.955737\pi$
$992$	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	−0.470130	−	0.882597i	$-0.655793\pi$
$997$	15.9380	−	34.8994i	0.504762	−	1.10527i	0.974892	−	0.222678i	$-0.0714798\pi$
$998$	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.31.2	✓	20
3.2	odd	2		207.2.i.d.100.1		20
23.3	even	11	inner	69.2.e.c.49.2	yes	20
23.7	odd	22		1587.2.a.t.1.2		10
23.16	even	11		1587.2.a.u.1.2		10
69.26	odd	22		207.2.i.d.118.1		20
69.53	even	22		4761.2.a.bu.1.9		10
69.62	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	1.1	even	1	trivial
69.2.e.c.49.2	yes	20	23.3	even	11	inner
207.2.i.d.100.1		20	3.2	odd	2
207.2.i.d.118.1		20	69.26	odd	22
1587.2.a.t.1.2		10	23.7	odd	22
1587.2.a.u.1.2		10	23.16	even	11
4761.2.a.bt.1.9		10	69.62	odd	22
4761.2.a.bu.1.9		10	69.53	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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