LMFDB - Embedded newform 152.2.c.b.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(77,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("152.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.c (of order $2$, degree $1$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.4
Root			$0.340606 - 1.37258i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37258 + 0.340606i) q^{2} +2.95163i q^{3} +(1.76798 - 0.935021i) q^{4} +2.13486i q^{5} +(-1.00534 - 4.05136i) q^{6} +3.29464 q^{7} +(-2.10822 + 1.88558i) q^{8} -5.71210 q^{9} +O(q^{10})$	\(q+(-1.37258 + 0.340606i) q^{2} +2.95163i q^{3} +(1.76798 - 0.935021i) q^{4} +2.13486i q^{5} +(-1.00534 - 4.05136i) q^{6} +3.29464 q^{7} +(-2.10822 + 1.88558i) q^{8} -5.71210 q^{9} +(-0.727145 - 2.93027i) q^{10} -3.71210i q^{11} +(2.75983 + 5.21840i) q^{12} +2.32843i q^{13} +(-4.52218 + 1.12218i) q^{14} -6.30130 q^{15} +(2.25147 - 3.30619i) q^{16} -6.48822 q^{17} +(7.84034 - 1.94558i) q^{18} -1.00000i q^{19} +(1.99614 + 3.77437i) q^{20} +9.72456i q^{21} +(1.26436 + 5.09517i) q^{22} +7.32651 q^{23} +(-5.56552 - 6.22268i) q^{24} +0.442384 q^{25} +(-0.793079 - 3.19597i) q^{26} -8.00510i q^{27} +(5.82485 - 3.08056i) q^{28} -2.59857i q^{29} +(8.64907 - 2.14626i) q^{30} -1.34204 q^{31} +(-1.96423 + 5.30489i) q^{32} +10.9567 q^{33} +(8.90563 - 2.20993i) q^{34} +7.03360i q^{35} +(-10.0988 + 5.34093i) q^{36} -3.72986i q^{37} +(0.340606 + 1.37258i) q^{38} -6.87267 q^{39} +(-4.02544 - 4.50075i) q^{40} +6.52385 q^{41} +(-3.31224 - 13.3478i) q^{42} -1.97202i q^{43} +(-3.47089 - 6.56290i) q^{44} -12.1945i q^{45} +(-10.0563 + 2.49545i) q^{46} +5.45991 q^{47} +(9.75863 + 6.64550i) q^{48} +3.85468 q^{49} +(-0.607210 + 0.150679i) q^{50} -19.1508i q^{51} +(2.17714 + 4.11661i) q^{52} +4.98640i q^{53} +(2.72659 + 10.9877i) q^{54} +7.92480 q^{55} +(-6.94584 + 6.21231i) q^{56} +2.95163 q^{57} +(0.885089 + 3.56676i) q^{58} +9.67136i q^{59} +(-11.1405 + 5.89185i) q^{60} +8.15570i q^{61} +(1.84206 - 0.457105i) q^{62} -18.8193 q^{63} +(0.889191 - 7.95043i) q^{64} -4.97088 q^{65} +(-15.0390 + 3.73193i) q^{66} -0.524986i q^{67} +(-11.4710 + 6.06662i) q^{68} +21.6251i q^{69} +(-2.39569 - 9.65420i) q^{70} +7.17489 q^{71} +(12.0424 - 10.7706i) q^{72} -6.33130 q^{73} +(1.27041 + 5.11955i) q^{74} +1.30575i q^{75} +(-0.935021 - 1.76798i) q^{76} -12.2300i q^{77} +(9.43332 - 2.34087i) q^{78} -8.75644 q^{79} +(7.05824 + 4.80657i) q^{80} +6.49178 q^{81} +(-8.95453 + 2.22206i) q^{82} -7.74008i q^{83} +(9.09267 + 17.1928i) q^{84} -13.8514i q^{85} +(0.671680 + 2.70676i) q^{86} +7.67001 q^{87} +(6.99945 + 7.82592i) q^{88} -1.04368 q^{89} +(4.15353 + 16.7380i) q^{90} +7.67136i q^{91} +(12.9531 - 6.85044i) q^{92} -3.96119i q^{93} +(-7.49419 + 1.85968i) q^{94} +2.13486 q^{95} +(-15.6580 - 5.79766i) q^{96} -0.117594 q^{97} +(-5.29088 + 1.31293i) q^{98} +21.2039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.37258	+	0.340606i	−0.970564	+	0.240845i
$2$	−1.37258	+	0.340606i	−0.970564	+	0.240845i
$3$			2.95163i			1.70412i	0.523442	+	0.852061i	$0.324648\pi$
$3$			2.95163i			1.70412i	−0.523442	+	0.852061i	$0.675352\pi$
$4$	1.76798	−	0.935021i	0.883988	−	0.467510i
$5$			2.13486i			0.954737i	0.878703	+	0.477369i	$0.158409\pi$
$5$			2.13486i			0.954737i	−0.878703	+	0.477369i	$0.841591\pi$
$6$	−1.00534	−	4.05136i	−0.410429	−	1.65396i
$7$	3.29464			1.24526			0.622629	−	0.782517i	$-0.286064\pi$
$7$	3.29464			1.24526			0.622629	+	0.782517i	$0.286064\pi$
$8$	−2.10822	+	1.88558i	−0.745369	+	0.666653i
$9$	−5.71210			−1.90403
$10$	−0.727145	−	2.93027i	−0.229944	−	0.926633i
$11$		−	3.71210i		−	1.11924i	−0.828749	−	0.559620i	$-0.810947\pi$
$11$		−	3.71210i		−	1.11924i	0.828749	−	0.559620i	$-0.189053\pi$
$12$	2.75983	+	5.21840i	0.796695	+	1.50642i
$13$			2.32843i			0.645792i	0.946435	+	0.322896i	$0.104656\pi$
$13$			2.32843i			0.645792i	−0.946435	+	0.322896i	$0.895344\pi$
$14$	−4.52218	+	1.12218i	−1.20860	+	0.299914i
$15$	−6.30130			−1.62699
$16$	2.25147	−	3.30619i	0.562868	−	0.826547i
$17$	−6.48822			−1.57362			−0.786812	−	0.617192i	$-0.788270\pi$
$17$	−6.48822			−1.57362			−0.786812	+	0.617192i	$0.788270\pi$
$18$	7.84034	−	1.94558i	1.84799	−	0.458577i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	1.99614	+	3.77437i	0.446350	+	0.843976i
$21$			9.72456i			2.12207i
$22$	1.26436	+	5.09517i	0.269563	+	1.08629i
$23$	7.32651			1.52768			0.763842	−	0.645404i	$-0.223311\pi$
$23$	7.32651			1.52768			0.763842	+	0.645404i	$0.223311\pi$
$24$	−5.56552	−	6.22268i	−1.13606	−	1.27020i
$25$	0.442384			0.0884769
$26$	−0.793079	−	3.19597i	−0.155536	−	0.626782i
$27$		−	8.00510i		−	1.54058i
$28$	5.82485	−	3.08056i	1.10079	−	0.582171i
$29$		−	2.59857i		−	0.482542i	−0.970458	−	0.241271i	$-0.922436\pi$
$29$		−	2.59857i		−	0.482542i	0.970458	−	0.241271i	$-0.0775643\pi$
$30$	8.64907	−	2.14626i	1.57910	−	0.391852i
$31$	−1.34204			−0.241037			−0.120518	−	0.992711i	$-0.538456\pi$
$31$	−1.34204			−0.241037			−0.120518	+	0.992711i	$0.538456\pi$
$32$	−1.96423	+	5.30489i	−0.347230	+	0.937780i
$33$	10.9567			1.90732
$34$	8.90563	−	2.20993i	1.52730	−	0.378999i
$35$			7.03360i			1.18889i
$36$	−10.0988	+	5.34093i	−1.68314	+	0.890155i
$37$		−	3.72986i		−	0.613186i	−0.951841	−	0.306593i	$-0.900811\pi$
$37$		−	3.72986i		−	0.613186i	0.951841	−	0.306593i	$-0.0991890\pi$
$38$	0.340606	+	1.37258i	0.0552536	+	0.222663i
$39$	−6.87267			−1.10051
$40$	−4.02544	−	4.50075i	−0.636478	−	0.711631i
$41$	6.52385			1.01885			0.509427	−	0.860514i	$-0.329857\pi$
$41$	6.52385			1.01885			0.509427	+	0.860514i	$0.329857\pi$
$42$	−3.31224	−	13.3478i	−0.511090	−	2.05961i
$43$		−	1.97202i		−	0.300729i	−0.988631	−	0.150365i	$-0.951955\pi$
$43$		−	1.97202i		−	0.300729i	0.988631	−	0.150365i	$-0.0480448\pi$
$44$	−3.47089	−	6.56290i	−0.523256	−	0.989394i
$45$		−	12.1945i		−	1.81785i
$46$	−10.0563	+	2.49545i	−1.48271	+	0.367935i
$47$	5.45991			0.796410			0.398205	−	0.917297i	$-0.369633\pi$
$47$	5.45991			0.796410			0.398205	+	0.917297i	$0.369633\pi$
$48$	9.75863	+	6.64550i	1.40854	+	0.959196i
$49$	3.85468			0.550669
$50$	−0.607210	+	0.150679i	−0.0858724	+	0.0213092i
$51$		−	19.1508i		−	2.68165i
$52$	2.17714	+	4.11661i	0.301914	+	0.570872i
$53$			4.98640i			0.684935i	0.939530	+	0.342467i	$0.111263\pi$
$53$			4.98640i			0.684935i	−0.939530	+	0.342467i	$0.888737\pi$
$54$	2.72659	+	10.9877i	0.371041	+	1.49523i
$55$	7.92480			1.06858
$56$	−6.94584	+	6.21231i	−0.928177	+	0.830155i
$57$	2.95163			0.390952
$58$	0.885089	+	3.56676i	0.116218	+	0.468338i
$59$			9.67136i			1.25910i	0.776958	+	0.629552i	$0.216762\pi$
$59$			9.67136i			1.25910i	−0.776958	+	0.629552i	$0.783238\pi$
$60$	−11.1405	+	5.89185i	−1.43824	+	0.760634i
$61$			8.15570i			1.04423i	0.852875	+	0.522115i	$0.174857\pi$
$61$			8.15570i			1.04423i	−0.852875	+	0.522115i	$0.825143\pi$
$62$	1.84206	−	0.457105i	0.233941	−	0.0580525i
$63$	−18.8193			−2.37101
$64$	0.889191	−	7.95043i	0.111149	−	0.993804i
$65$	−4.97088			−0.616561
$66$	−15.0390	+	3.73193i	−1.85118	+	0.459369i
$67$		−	0.524986i		−	0.0641372i	−0.999486	−	0.0320686i	$-0.989790\pi$
$67$		−	0.524986i		−	0.0641372i	0.999486	−	0.0320686i	$-0.0102095\pi$
$68$	−11.4710	+	6.06662i	−1.39106	+	0.735686i
$69$			21.6251i			2.60336i
$70$	−2.39569	−	9.65420i	−0.286339	−	1.15390i
$71$	7.17489			0.851503			0.425751	−	0.904840i	$-0.360010\pi$
$71$	7.17489			0.851503			0.425751	+	0.904840i	$0.360010\pi$
$72$	12.0424	−	10.7706i	1.41921	−	1.26933i
$73$	−6.33130			−0.741022			−0.370511	−	0.928828i	$-0.620817\pi$
$73$	−6.33130			−0.741022			−0.370511	+	0.928828i	$0.620817\pi$
$74$	1.27041	+	5.11955i	0.147683	+	0.595136i
$75$			1.30575i			0.150775i
$76$	−0.935021	−	1.76798i	−0.107254	−	0.202801i
$77$		−	12.2300i		−	1.39374i
$78$	9.43332	−	2.34087i	1.06811	−	0.265052i
$79$	−8.75644			−0.985176			−0.492588	−	0.870263i	$-0.663949\pi$
$79$	−8.75644			−0.985176			−0.492588	+	0.870263i	$0.663949\pi$
$80$	7.05824	+	4.80657i	0.789135	+	0.537391i
$81$	6.49178			0.721309
$82$	−8.95453	+	2.22206i	−0.988862	+	0.245386i
$83$		−	7.74008i		−	0.849585i	−0.905291	−	0.424792i	$-0.860347\pi$
$83$		−	7.74008i		−	0.849585i	0.905291	−	0.424792i	$-0.139653\pi$
$84$	9.09267	+	17.1928i	0.992091	+	1.87589i
$85$		−	13.8514i		−	1.50240i
$86$	0.671680	+	2.70676i	0.0724291	+	0.291877i
$87$	7.67001			0.822311
$88$	6.99945	+	7.82592i	0.746144	+	0.834246i
$89$	−1.04368			−0.110630			−0.0553148	−	0.998469i	$-0.517616\pi$
$89$	−1.04368			−0.110630			−0.0553148	+	0.998469i	$0.517616\pi$
$90$	4.15353	+	16.7380i	0.437820	+	1.76434i
$91$			7.67136i			0.804178i
$92$	12.9531	−	6.85044i	1.35045	−	0.714208i
$93$		−	3.96119i		−	0.410756i
$94$	−7.49419	+	1.85968i	−0.772966	+	0.191811i
$95$	2.13486			0.219032
$96$	−15.6580	−	5.79766i	−1.59809	−	0.591722i
$97$	−0.117594			−0.0119398			−0.00596992	−	0.999982i	$-0.501900\pi$
$97$	−0.117594			−0.0119398			−0.00596992	+	0.999982i	$0.501900\pi$
$98$	−5.29088	+	1.31293i	−0.534459	+	0.132626i
$99$			21.2039i			2.13107i
$100$	0.782125	−	0.413639i	0.0782125	−	0.0413639i
$101$		−	10.6142i		−	1.05615i	−0.849197	−	0.528077i	$-0.822913\pi$
$101$		−	10.6142i		−	1.05615i	0.849197	−	0.528077i	$-0.177087\pi$
$102$	6.52288	+	26.2861i	0.645861	+	2.60271i
$103$	12.4190			1.22368			0.611840	−	0.790982i	$-0.290430\pi$
$103$	12.4190			1.22368			0.611840	+	0.790982i	$0.290430\pi$
$104$	−4.39045	−	4.90885i	−0.430519	−	0.481353i
$105$	−20.7605			−2.02602
$106$	−1.69840	−	6.84425i	−0.164963	−	0.664773i
$107$		−	16.5439i		−	1.59936i	−0.600430	−	0.799678i	$-0.705004\pi$
$107$		−	16.5439i		−	1.59936i	0.600430	−	0.799678i	$-0.294996\pi$
$108$	−7.48494	−	14.1528i	−0.720239	−	1.36186i
$109$		−	17.4437i		−	1.67080i	−0.549641	−	0.835401i	$-0.685235\pi$
$109$		−	17.4437i		−	1.67080i	0.549641	−	0.835401i	$-0.314765\pi$
$110$	−10.8775	+	2.69924i	−1.03712	+	0.257362i
$111$	11.0092			1.04494
$112$	7.41780	−	10.8927i	0.700916	−	1.02926i
$113$	−14.3193			−1.34705			−0.673523	−	0.739166i	$-0.735220\pi$
$113$	−14.3193			−1.34705			−0.673523	+	0.739166i	$0.735220\pi$
$114$	−4.05136	+	1.00534i	−0.379444	+	0.0941589i
$115$			15.6411i			1.45854i
$116$	−2.42972	−	4.59421i	−0.225594	−	0.426561i
$117$		−	13.3002i		−	1.22961i
$118$	−3.29413	−	13.2748i	−0.303249	−	1.22204i
$119$	−21.3764			−1.95957
$120$	13.2845	−	11.8816i	1.21271	−	1.08464i
$121$	−2.77968			−0.252698
$122$	−2.77788	−	11.1944i	−0.251498	−	1.01349i
$123$			19.2560i			1.73625i
$124$	−2.37269	+	1.25483i	−0.213073	+	0.112687i
$125$			11.6187i			1.03921i
$126$	25.8311	−	6.40998i	2.30122	−	0.571046i
$127$	2.63985			0.234248			0.117124	−	0.993117i	$-0.462632\pi$
$127$	2.63985			0.234248			0.117124	+	0.993117i	$0.462632\pi$
$128$	1.48748	+	11.2155i	0.131475	+	0.991319i
$129$	5.82065			0.512480
$130$	6.82295	−	1.69311i	0.598412	−	0.148496i
$131$		−	15.3670i		−	1.34263i	−0.741174	−	0.671313i	$-0.765731\pi$
$131$		−	15.3670i		−	1.34263i	0.741174	−	0.671313i	$-0.234269\pi$
$132$	19.3712	−	10.2448i	1.68605	−	0.891693i
$133$		−	3.29464i		−	0.285682i
$134$	0.178813	+	0.720587i	0.0154471	+	0.0622492i
$135$	17.0898			1.47085
$136$	13.6786	−	12.2340i	1.17293	−	1.04906i
$137$	−4.91853			−0.420218			−0.210109	−	0.977678i	$-0.567382\pi$
$137$	−4.91853			−0.420218			−0.210109	+	0.977678i	$0.567382\pi$
$138$	−7.36565	−	29.6823i	−0.627006	−	2.52673i
$139$			9.80377i			0.831545i	0.909469	+	0.415773i	$0.136489\pi$
$139$			9.80377i			0.831545i	−0.909469	+	0.415773i	$0.863511\pi$
$140$	6.57656	+	12.4352i	0.555821	+	1.05097i
$141$			16.1156i			1.35718i
$142$	−9.84814	+	2.44381i	−0.826438	+	0.205080i
$143$	8.64338			0.722796
$144$	−12.8606	+	18.8853i	−1.07172	+	1.57377i
$145$	5.54758			0.460701
$146$	8.69024	−	2.15648i	0.719209	−	0.178471i
$147$			11.3776i			0.938407i
$148$	−3.48750	−	6.59431i	−0.286671	−	0.542049i
$149$		−	0.724147i		−	0.0593244i	−0.999560	−	0.0296622i	$-0.990557\pi$
$149$		−	0.724147i		−	0.0593244i	0.999560	−	0.0296622i	$-0.00944316\pi$
$150$	−0.444748	−	1.79226i	−0.0363135	−	0.146337i
$151$	−15.7252			−1.27970			−0.639850	−	0.768500i	$-0.721003\pi$
$151$	−15.7252			−1.27970			−0.639850	+	0.768500i	$0.721003\pi$
$152$	1.88558	+	2.10822i	0.152941	+	0.170999i
$153$	37.0614			2.99623
$154$	4.16563	+	16.7868i	0.335676	+	1.35272i
$155$		−	2.86505i		−	0.230127i
$156$	−12.1507	+	6.42609i	−0.972835	+	0.514499i
$157$			0.141127i			0.0112632i	0.999984	+	0.00563160i	$0.00179260\pi$
$157$			0.141127i			0.0112632i	−0.999984	+	0.00563160i	$0.998207\pi$
$158$	12.0189	−	2.98249i	0.956176	−	0.237275i
$159$	−14.7180			−1.16721
$160$	−11.3252	−	4.19334i	−0.895334	−	0.331513i
$161$	24.1383			1.90236
$162$	−8.91051	+	2.21114i	−0.700076	+	0.173723i
$163$			8.41859i			0.659395i	0.944087	+	0.329697i	$0.106947\pi$
$163$			8.41859i			0.659395i	−0.944087	+	0.329697i	$0.893053\pi$
$164$	11.5340	−	6.09993i	0.900654	−	0.476325i
$165$			23.3911i			1.82099i
$166$	2.63632	+	10.6239i	0.204618	+	0.824576i
$167$	5.16538			0.399709			0.199854	−	0.979826i	$-0.435953\pi$
$167$	5.16538			0.399709			0.199854	+	0.979826i	$0.435953\pi$
$168$	−18.3364	−	20.5015i	−1.41469	−	1.58173i
$169$	7.57839			0.582953
$170$	4.71788	+	19.0123i	0.361845	+	1.45817i
$171$			5.71210i			0.436815i
$172$	−1.84388	−	3.48647i	−0.140594	−	0.265841i
$173$		−	3.13988i		−	0.238721i	−0.992851	−	0.119360i	$-0.961916\pi$
$173$		−	3.13988i		−	0.238721i	0.992851	−	0.119360i	$-0.0380844\pi$
$174$	−10.5277	+	2.61245i	−0.798105	+	0.198049i
$175$	1.45750			0.110177
$176$	−12.2729	−	8.35769i	−0.925104	−	0.629984i
$177$	−28.5463			−2.14567
$178$	1.43254	−	0.355483i	0.107373	−	0.0266446i
$179$		−	18.1898i		−	1.35957i	−0.733410	−	0.679786i	$-0.762073\pi$
$179$		−	18.1898i		−	1.35957i	0.733410	−	0.679786i	$-0.237927\pi$
$180$	−11.4021	−	21.5596i	−0.849864	−	1.60696i
$181$		−	14.0798i		−	1.04654i	−0.852166	−	0.523271i	$-0.824712\pi$
$181$		−	14.0798i		−	1.04654i	0.852166	−	0.523271i	$-0.175288\pi$
$182$	−2.61291	−	10.5296i	−0.193682	−	0.780505i
$183$	−24.0726			−1.77950
$184$	−15.4459	+	13.8147i	−1.13869	+	1.01843i
$185$	7.96273			0.585431
$186$	1.34920	+	5.43706i	0.0989285	+	0.398665i
$187$			24.0849i			1.76126i
$188$	9.65299	−	5.10513i	0.704016	−	0.372330i
$189$		−	26.3740i		−	1.91842i
$190$	−2.93027	+	0.727145i	−0.212584	+	0.0527527i
$191$	4.87409			0.352677			0.176338	−	0.984330i	$-0.443575\pi$
$191$	4.87409			0.352677			0.176338	+	0.984330i	$0.443575\pi$
$192$	23.4667	+	2.62456i	1.69356	+	0.189411i
$193$	−9.99845			−0.719704			−0.359852	−	0.933009i	$-0.617173\pi$
$193$	−9.99845			−0.719704			−0.359852	+	0.933009i	$0.617173\pi$
$194$	0.161407	−	0.0400531i	0.0115884	−	0.00287565i
$195$		−	14.6722i		−	1.05070i
$196$	6.81498	−	3.60421i	0.486785	−	0.257444i
$197$			19.2209i			1.36943i	0.728810	+	0.684716i	$0.240074\pi$
$197$			19.2209i			1.36943i	−0.728810	+	0.684716i	$0.759926\pi$
$198$	−7.22217	−	29.1041i	−0.513257	−	2.06834i
$199$	−11.7323			−0.831683			−0.415842	−	0.909437i	$-0.636513\pi$
$199$	−11.7323			−0.831683			−0.415842	+	0.909437i	$0.636513\pi$
$200$	−0.932644	+	0.834150i	−0.0659479	+	0.0589833i
$201$	1.54956			0.109298
$202$	3.61526	+	14.5689i	0.254369	+	1.02506i
$203$		−	8.56137i		−	0.600890i
$204$	−17.9064	−	33.8582i	−1.25370	−	2.37054i
$205$			13.9275i			0.972737i
$206$	−17.0461	+	4.22998i	−1.18766	+	0.294717i
$207$	−41.8498			−2.90876
$208$	7.69824	+	5.24240i	0.533777	+	0.363495i
$209$	−3.71210			−0.256771
$210$	28.4956	−	7.07117i	1.96638	−	0.487957i
$211$			0.399383i			0.0274947i	0.999906	+	0.0137473i	$0.00437605\pi$
$211$			0.399383i			0.0274947i	−0.999906	+	0.0137473i	$0.995624\pi$
$212$	4.66239	+	8.81583i	0.320214	+	0.605474i
$213$			21.1776i			1.45106i
$214$	5.63494	+	22.7078i	0.385196	+	1.55228i
$215$	4.20997			0.287118
$216$	15.0942	+	16.8765i	1.02703	+	1.14830i
$217$	−4.42153			−0.300153
$218$	5.94142	+	23.9429i	0.402404	+	1.62162i
$219$		−	18.6876i		−	1.26279i
$220$	14.0109	−	7.40986i	0.944611	−	0.499572i
$221$		−	15.1074i		−	1.01623i
$222$	−15.1110	+	3.74979i	−1.01418	+	0.251669i
$223$	−19.2548			−1.28939			−0.644697	−	0.764438i	$-0.723017\pi$
$223$	−19.2548			−1.28939			−0.644697	+	0.764438i	$0.723017\pi$
$224$	−6.47143	+	17.4777i	−0.432391	+	1.16778i
$225$	−2.52694			−0.168463
$226$	19.6545	−	4.87724i	1.30739	−	0.324429i
$227$			20.0414i			1.33019i	0.746758	+	0.665096i	$0.231609\pi$
$227$			20.0414i			1.33019i	−0.746758	+	0.665096i	$0.768391\pi$
$228$	5.21840	−	2.75983i	0.345597	−	0.182774i
$229$			18.2013i			1.20277i	0.798958	+	0.601387i	$0.205385\pi$
$229$			18.2013i			1.20277i	−0.798958	+	0.601387i	$0.794615\pi$
$230$	−5.32744	−	21.4687i	−0.351281	−	1.41560i
$231$	36.0985			2.37511
$232$	4.89981	+	5.47836i	0.321688	+	0.359672i
$233$	14.2376			0.932739			0.466369	−	0.884590i	$-0.345562\pi$
$233$	14.2376			0.932739			0.466369	+	0.884590i	$0.345562\pi$
$234$	4.53015	+	18.2557i	0.296145	+	1.19341i
$235$			11.6561i			0.760362i
$236$	9.04293	+	17.0987i	0.588645	+	1.11303i
$237$		−	25.8457i		−	1.67886i
$238$	29.3409	−	7.28093i	1.90189	−	0.471952i
$239$	8.31368			0.537767			0.268884	−	0.963173i	$-0.413345\pi$
$239$	8.31368			0.537767			0.268884	+	0.963173i	$0.413345\pi$
$240$	−14.1872	+	20.8333i	−0.915780	+	1.34478i
$241$	−26.1776			−1.68625			−0.843125	−	0.537718i	$-0.819287\pi$
$241$	−26.1776			−1.68625			−0.843125	+	0.537718i	$0.819287\pi$
$242$	3.81534	−	0.946775i	0.245260	−	0.0608610i
$243$		−	4.85401i		−	0.311385i
$244$	7.62575	+	14.4191i	0.488189	+	0.923087i
$245$			8.22920i			0.525744i
$246$	−6.55870	−	26.4304i	−0.418167	−	1.68514i
$247$	2.32843			0.148155
$248$	2.82931	−	2.53051i	0.179661	−	0.160688i
$249$	22.8458			1.44780
$250$	−3.95740	−	15.9477i	−0.250288	−	1.00862i
$251$		−	29.4740i		−	1.86038i	−0.367075	−	0.930191i	$-0.619641\pi$
$251$		−	29.4740i		−	1.86038i	0.367075	−	0.930191i	$-0.380359\pi$
$252$	−33.2721	+	17.5965i	−2.09595	+	1.10847i
$253$		−	27.1967i		−	1.70984i
$254$	−3.62341	+	0.899147i	−0.227353	+	0.0564175i
$255$	40.8842			2.56027
$256$	−5.86175	−	14.8876i	−0.366360	−	0.930473i
$257$	1.28195			0.0799657			0.0399828	−	0.999200i	$-0.487270\pi$
$257$	1.28195			0.0799657			0.0399828	+	0.999200i	$0.487270\pi$
$258$	−7.98933	+	1.98255i	−0.497394	+	0.123428i
$259$		−	12.2886i		−	0.763575i
$260$	−8.78838	+	4.64787i	−0.545032	+	0.288249i
$261$			14.8433i			0.918777i
$262$	5.23411	+	21.0926i	0.323364	+	1.30310i
$263$	−29.2736			−1.80509			−0.902544	−	0.430597i	$-0.858303\pi$
$263$	−29.2736			−1.80509			−0.902544	+	0.430597i	$0.858303\pi$
$264$	−23.0992	+	20.6598i	−1.42166	+	1.27152i
$265$	−10.6453			−0.653933
$266$	1.12218	+	4.52218i	0.0688050	+	0.277272i
$267$		−	3.08055i		−	0.188526i
$268$	−0.490873	−	0.928161i	−0.0299848	−	0.0566965i
$269$		−	14.1850i		−	0.864875i	−0.901664	−	0.432437i	$-0.857654\pi$
$269$		−	14.1850i		−	0.864875i	0.901664	−	0.432437i	$-0.142346\pi$
$270$	−23.4571	+	5.82087i	−1.42756	+	0.354247i
$271$	26.3185			1.59874			0.799369	−	0.600840i	$-0.205167\pi$
$271$	26.3185			1.59874			0.799369	+	0.600840i	$0.205167\pi$
$272$	−14.6080	+	21.4513i	−0.885743	+	1.30067i
$273$	−22.6430			−1.37042
$274$	6.75110	−	1.67528i	0.407849	−	0.101207i
$275$		−	1.64217i		−	0.0990269i
$276$	20.2199	+	38.2327i	1.21710	+	2.30134i
$277$			3.58863i			0.215620i	0.994172	+	0.107810i	$0.0343838\pi$
$277$			3.58863i			0.215620i	−0.994172	+	0.107810i	$0.965616\pi$
$278$	−3.33922	−	13.4565i	−0.200273	−	0.807068i
$279$	7.66584			0.458942
$280$	−13.2624	−	14.8284i	−0.792580	−	0.886165i
$281$	−4.42597			−0.264031			−0.132016	−	0.991248i	$-0.542145\pi$
$281$	−4.42597			−0.264031			−0.132016	+	0.991248i	$0.542145\pi$
$282$	−5.48908	−	22.1200i	−0.326870	−	1.31723i
$283$			0.493151i			0.0293148i	0.999893	+	0.0146574i	$0.00466576\pi$
$283$			0.493151i			0.0293148i	−0.999893	+	0.0146574i	$0.995334\pi$
$284$	12.6850	−	6.70867i	0.752718	−	0.398086i
$285$			6.30130i			0.373257i
$286$	−11.8638	+	2.94399i	−0.701519	+	0.174082i
$287$	21.4938			1.26874
$288$	11.2199	−	30.3020i	0.661136	−	1.78556i
$289$	25.0970			1.47630
$290$	−7.61452	+	1.88954i	−0.447140	+	0.110957i
$291$		−	0.347093i		−	0.0203469i
$292$	−11.1936	+	5.91989i	−0.655054	+	0.346436i
$293$			12.7228i			0.743275i	0.928378	+	0.371637i	$0.121204\pi$
$293$			12.7228i			0.743275i	−0.928378	+	0.371637i	$0.878796\pi$
$294$	−3.87527	−	15.6167i	−0.226011	−	0.910784i
$295$	−20.6470			−1.20211
$296$	7.03295	+	7.86338i	0.408782	+	0.457050i
$297$	−29.7157			−1.72428
$298$	0.246649	+	0.993952i	0.0142880	+	0.0575781i
$299$			17.0593i			0.986565i
$300$	1.22091	+	2.30854i	0.0704891	+	0.133284i
$301$		−	6.49709i		−	0.374486i
$302$	21.5842	−	5.35610i	1.24203	−	0.308209i
$303$	31.3292			1.79981
$304$	−3.30619	−	2.25147i	−0.189623	−	0.129131i
$305$	−17.4113			−0.996966
$306$	−50.8698	+	12.6233i	−2.90804	+	0.721627i
$307$		−	10.2166i		−	0.583092i	−0.956557	−	0.291546i	$-0.905830\pi$
$307$		−	10.2166i		−	0.583092i	0.956557	−	0.291546i	$-0.0941697\pi$
$308$	−11.4354	−	21.6224i	−0.651590	−	1.23205i
$309$			36.6562i			2.08530i
$310$	0.975855	+	3.93253i	0.0554248	+	0.223353i
$311$	0.184934			0.0104867			0.00524333	−	0.999986i	$-0.498331\pi$
$311$	0.184934			0.0104867			0.00524333	+	0.999986i	$0.498331\pi$
$312$	14.4891	−	12.9590i	0.820284	−	0.733656i
$313$	−19.0733			−1.07809			−0.539044	−	0.842278i	$-0.681214\pi$
$313$	−19.0733			−1.07809			−0.539044	+	0.842278i	$0.681214\pi$
$314$	−0.0480689	−	0.193709i	−0.00271268	−	0.0109317i
$315$		−	40.1766i		−	2.26369i
$316$	−15.4812	+	8.18745i	−0.870883	+	0.460580i
$317$			0.911635i			0.0512025i	0.999672	+	0.0256013i	$0.00815002\pi$
$317$			0.911635i			0.0512025i	−0.999672	+	0.0256013i	$0.991850\pi$
$318$	20.2017	−	5.01304i	1.13285	−	0.281117i
$319$	−9.64615			−0.540081
$320$	16.9730	+	1.89830i	0.948821	+	0.106118i
$321$	48.8313			2.72550
$322$	−33.1318	+	8.22164i	−1.84636	+	0.458174i
$323$			6.48822i			0.361014i
$324$	11.4773	−	6.06995i	0.637628	−	0.337219i
$325$			1.03006i			0.0571376i
$326$	−2.86742	−	11.5552i	−0.158812	−	0.639984i
$327$	51.4872			2.84725
$328$	−13.7537	+	12.3012i	−0.759422	+	0.679221i
$329$	17.9885			0.991736
$330$	−7.96713	−	32.1062i	−0.438576	−	1.76739i
$331$			2.45230i			0.134791i	0.997726	+	0.0673953i	$0.0214689\pi$
$331$			2.45230i			0.134791i	−0.997726	+	0.0673953i	$0.978531\pi$
$332$	−7.23714	−	13.6843i	−0.397190	−	0.751022i
$333$			21.3054i			1.16753i
$334$	−7.08992	+	1.75936i	−0.387943	+	0.0962678i
$335$	1.12077			0.0612342
$336$	32.1512	+	21.8946i	1.75399	+	1.19445i
$337$	35.1467			1.91456			0.957282	−	0.289156i	$-0.0933746\pi$
$337$	35.1467			1.91456			0.957282	+	0.289156i	$0.0933746\pi$
$338$	−10.4020	+	2.58125i	−0.565793	+	0.140401i
$339$		−	42.2652i		−	2.29553i
$340$	−12.9514	−	24.4890i	−0.702387	−	1.32810i
$341$			4.98177i			0.269778i
$342$	−1.94558	−	7.84034i	−0.105205	−	0.423957i
$343$	−10.3627			−0.559533
$344$	3.71839	+	4.15744i	0.200482	+	0.224154i
$345$	−46.1666			−2.48552
$346$	1.06946	+	4.30975i	0.0574946	+	0.231694i
$347$			5.30643i			0.284864i	0.989805	+	0.142432i	$0.0454922\pi$
$347$			5.30643i			0.284864i	−0.989805	+	0.142432i	$0.954508\pi$
$348$	13.5604	−	7.17162i	0.726913	−	0.384439i
$349$		−	26.8913i		−	1.43946i	−0.694255	−	0.719729i	$-0.744266\pi$
$349$		−	26.8913i		−	1.43946i	0.694255	−	0.719729i	$-0.255734\pi$
$350$	−2.00054	+	0.496433i	−0.106933	+	0.0265355i
$351$	18.6394			0.994895
$352$	19.6923	+	7.29140i	1.04960	+	0.388633i
$353$	−3.21383			−0.171055			−0.0855275	−	0.996336i	$-0.527258\pi$
$353$	−3.21383			−0.171055			−0.0855275	+	0.996336i	$0.527258\pi$
$354$	39.1821	−	9.72303i	2.08251	−	0.516773i
$355$			15.3174i			0.812961i
$356$	−1.84520	+	0.975861i	−0.0977952	+	0.0517205i
$357$		−	63.0951i		−	3.33935i
$358$	6.19557	+	24.9671i	0.327446	+	1.31955i
$359$	−15.6827			−0.827699			−0.413850	−	0.910345i	$-0.635816\pi$
$359$	−15.6827			−0.827699			−0.413850	+	0.910345i	$0.635816\pi$
$360$	22.9937	+	25.7087i	1.21188	+	1.35497i
$361$	−1.00000			−0.0526316
$362$	4.79566	+	19.3257i	0.252054	+	1.01574i
$363$		−	8.20457i		−	0.430628i
$364$	7.17289	+	13.5628i	0.375961	+	0.710883i
$365$		−	13.5164i		−	0.707481i
$366$	33.0417	−	8.19927i	1.72712	−	0.428583i
$367$	14.3509			0.749111			0.374555	−	0.927205i	$-0.377795\pi$
$367$	14.3509			0.749111			0.374555	+	0.927205i	$0.377795\pi$
$368$	16.4954	−	24.2228i	0.859884	−	1.26270i
$369$	−37.2649			−1.93993
$370$	−10.9295	+	2.71215i	−0.568198	+	0.140998i
$371$			16.4284i			0.852921i
$372$	−3.70379	−	7.00328i	−0.192033	−	0.363103i
$373$		−	9.08701i		−	0.470508i	−0.971934	−	0.235254i	$-0.924408\pi$
$373$		−	9.08701i		−	0.470508i	0.971934	−	0.235254i	$-0.0755921\pi$
$374$	−8.20347	−	33.0586i	−0.424191	−	1.70942i
$375$	−34.2941			−1.77094
$376$	−11.5107	+	10.2951i	−0.593619	+	0.530929i
$377$	6.05060			0.311622
$378$	8.98313	+	36.2005i	0.462043	+	1.86195i
$379$		−	18.2006i		−	0.934900i	−0.884020	−	0.467450i	$-0.845173\pi$
$379$		−	18.2006i		−	0.934900i	0.884020	−	0.467450i	$-0.154827\pi$
$380$	3.77437	−	1.99614i	0.193621	−	0.102400i
$381$			7.79184i			0.399188i
$382$	−6.69010	+	1.66015i	−0.342295	+	0.0849404i
$383$	−22.4154			−1.14537			−0.572686	−	0.819775i	$-0.694099\pi$
$383$	−22.4154			−1.14537			−0.572686	+	0.819775i	$0.694099\pi$
$384$	−33.1040	+	4.39047i	−1.68933	+	0.224050i
$385$	26.1094			1.33066
$386$	13.7237	−	3.40553i	0.698518	−	0.173337i
$387$			11.2643i			0.572599i
$388$	−0.207903	+	0.109953i	−0.0105547	+	0.00558200i
$389$			34.9213i			1.77058i	0.465038	+	0.885291i	$0.346041\pi$
$389$			34.9213i			1.77058i	−0.465038	+	0.885291i	$0.653959\pi$
$390$	4.99743	+	20.1388i	0.253055	+	1.01977i
$391$	−47.5360			−2.40400
$392$	−8.12652	+	7.26831i	−0.410451	+	0.367105i
$393$	45.3578			2.28800
$394$	−6.54676	−	26.3823i	−0.329821	−	1.32912i
$395$		−	18.6937i		−	0.940584i
$396$	19.8261	+	37.4879i	0.996297	+	1.88384i
$397$			31.3443i			1.57313i	0.617510	+	0.786563i	$0.288142\pi$
$397$			31.3443i			1.57313i	−0.617510	+	0.786563i	$0.711858\pi$
$398$	16.1036	−	3.99610i	0.807201	−	0.200307i
$399$	9.72456			0.486837
$400$	0.996016	−	1.46261i	0.0498008	−	0.0731303i
$401$	1.64321			0.0820579			0.0410290	−	0.999158i	$-0.486936\pi$
$401$	1.64321			0.0820579			0.0410290	+	0.999158i	$0.486936\pi$
$402$	−2.12690	+	0.527790i	−0.106080	+	0.0263238i
$403$		−	3.12484i		−	0.155659i
$404$	−9.92451	−	18.7657i	−0.493763	−	0.933627i
$405$			13.8590i			0.688660i
$406$	2.91605	+	11.7512i	0.144721	+	0.583202i
$407$	−13.8456			−0.686302
$408$	36.1103	+	40.3741i	1.78773	+	1.99882i
$409$	−2.46645			−0.121958			−0.0609791	−	0.998139i	$-0.519422\pi$
$409$	−2.46645			−0.121958			−0.0609791	+	0.998139i	$0.519422\pi$
$410$	−4.74378	−	19.1166i	−0.234279	−	0.944104i
$411$		−	14.5177i		−	0.716104i
$412$	21.9565	−	11.6120i	1.08172	−	0.572083i
$413$			31.8637i			1.56791i
$414$	57.4423	−	14.2543i	2.82314	−	0.700560i
$415$	16.5240			0.811130
$416$	−12.3521	−	4.57357i	−0.605611	−	0.224238i
$417$	−28.9371			−1.41705
$418$	5.09517	−	1.26436i	0.249213	−	0.0618420i
$419$			4.25063i			0.207657i	0.994595	+	0.103828i	$0.0331093\pi$
$419$			4.25063i			0.207657i	−0.994595	+	0.103828i	$0.966891\pi$
$420$	−36.7041	+	19.4115i	−1.79098	+	0.947187i
$421$			31.4900i			1.53473i	0.641212	+	0.767364i	$0.278432\pi$
$421$			31.4900i			1.53473i	−0.641212	+	0.767364i	$0.721568\pi$
$422$	−0.136032	−	0.548187i	−0.00662195	−	0.0266853i
$423$	−31.1875			−1.51639
$424$	−9.40224	−	10.5124i	−0.456613	−	0.510529i
$425$	−2.87029			−0.139229
$426$	−7.21322	−	29.0680i	−0.349482	−	1.40835i
$427$			26.8701i			1.30034i
$428$	−15.4689	−	29.2491i	−0.747715	−	1.41381i
$429$			25.5120i			1.23173i
$430$	−5.77854	+	1.43394i	−0.278666	+	0.0691508i
$431$	−21.0564			−1.01425			−0.507125	−	0.861872i	$-0.669292\pi$
$431$	−21.0564			−1.01425			−0.507125	+	0.861872i	$0.669292\pi$
$432$	−26.4664	−	18.0233i	−1.27336	−	0.867145i
$433$	−7.53125			−0.361929			−0.180964	−	0.983490i	$-0.557922\pi$
$433$	−7.53125			−0.361929			−0.180964	+	0.983490i	$0.557922\pi$
$434$	6.06892	−	1.50600i	0.291318	−	0.0722903i
$435$			16.3744i			0.785091i
$436$	−16.3102	−	30.8400i	−0.781117	−	1.47697i
$437$		−	7.32651i		−	0.350475i
$438$	6.36512	+	25.6503i	0.304137	+	1.22562i
$439$	0.823995			0.0393271			0.0196636	−	0.999807i	$-0.493740\pi$
$439$	0.823995			0.0393271			0.0196636	+	0.999807i	$0.493740\pi$
$440$	−16.7072	+	14.9428i	−0.796486	+	0.712372i
$441$	−22.0183			−1.04849
$442$	5.14567	+	20.7362i	0.244755	+	0.986319i
$443$		−	8.58526i		−	0.407898i	−0.978982	−	0.203949i	$-0.934622\pi$
$443$		−	8.58526i		−	0.407898i	0.978982	−	0.203949i	$-0.0653777\pi$
$444$	19.4639	−	10.2938i	0.923717	−	0.488522i
$445$		−	2.22810i		−	0.105622i
$446$	26.4288	−	6.55829i	1.25144	−	0.310544i
$447$	2.13741			0.101096
$448$	2.92957	−	26.1938i	0.138409	−	1.23754i
$449$	2.49451			0.117723			0.0588615	−	0.998266i	$-0.481253\pi$
$449$	2.49451			0.117723			0.0588615	+	0.998266i	$0.481253\pi$
$450$	3.46844	−	0.860692i	0.163504	−	0.0405734i
$451$		−	24.2172i		−	1.14034i
$452$	−25.3162	+	13.3888i	−1.19077	+	0.629759i
$453$		−	46.4150i		−	2.18076i
$454$	−6.82621	−	27.5085i	−0.320370	−	1.29104i
$455$	−16.3773			−0.767778
$456$	−6.22268	+	5.56552i	−0.291404	+	0.260629i
$457$	14.5004			0.678301			0.339150	−	0.940732i	$-0.389860\pi$
$457$	14.5004			0.678301			0.339150	+	0.940732i	$0.389860\pi$
$458$	−6.19947	−	24.9828i	−0.289682	−	1.16737i
$459$			51.9389i			2.42430i
$460$	14.6247	+	27.6530i	0.681881	+	1.28933i
$461$		−	23.1930i		−	1.08020i	−0.841600	−	0.540102i	$-0.818386\pi$
$461$		−	23.1930i		−	1.08020i	0.841600	−	0.540102i	$-0.181614\pi$
$462$	−49.5483	+	12.2954i	−2.30519	+	0.572033i
$463$	26.0637			1.21128			0.605642	−	0.795737i	$-0.292916\pi$
$463$	26.0637			1.21128			0.605642	+	0.795737i	$0.292916\pi$
$464$	−8.59136	−	5.85061i	−0.398844	−	0.271608i
$465$	8.45657			0.392164
$466$	−19.5424	+	4.84943i	−0.905282	+	0.224645i
$467$			12.1953i			0.564332i	0.959366	+	0.282166i	$0.0910529\pi$
$467$			12.1953i			0.564332i	−0.959366	+	0.282166i	$0.908947\pi$
$468$	−12.4360	−	23.5145i	−0.574855	−	1.08696i
$469$		−	1.72964i		−	0.0798674i
$470$	−3.97015	−	15.9990i	−0.183129	−	0.737980i
$471$	−0.416556			−0.0191939
$472$	−18.2361	−	20.3894i	−0.839385	−	0.938497i
$473$	−7.32031			−0.336588
$474$	8.80321	+	35.4754i	0.404345	+	1.62944i
$475$		−	0.442384i		−	0.0202980i
$476$	−37.7929	+	19.9874i	−1.73224	+	0.916120i
$477$		−	28.4828i		−	1.30414i
$478$	−11.4112	+	2.83169i	−0.521937	+	0.129518i
$479$	18.1883			0.831045			0.415523	−	0.909583i	$-0.363599\pi$
$479$	18.1883			0.831045			0.415523	+	0.909583i	$0.363599\pi$
$480$	12.3772	−	33.4277i	0.564939	−	1.52576i
$481$	8.68475			0.395990
$482$	35.9310	−	8.91626i	1.63661	−	0.406125i
$483$			71.2471i			3.24186i
$484$	−4.91440	+	2.59906i	−0.223382	+	0.118139i
$485$		−	0.251046i		−	0.0113994i
$486$	1.65330	+	6.66253i	0.0749954	+	0.302219i
$487$	−2.13693			−0.0968334			−0.0484167	−	0.998827i	$-0.515418\pi$
$487$	−2.13693			−0.0968334			−0.0484167	+	0.998827i	$0.515418\pi$
$488$	−15.3782	−	17.1940i	−0.696139	−	0.778337i
$489$	−24.8485			−1.12369
$490$	−2.80291	−	11.2953i	−0.126623	−	0.510268i
$491$		−	2.32773i		−	0.105049i	−0.998620	−	0.0525244i	$-0.983273\pi$
$491$		−	2.32773i		−	0.105049i	0.998620	−	0.0525244i	$-0.0167267\pi$
$492$	18.0047	+	34.0441i	0.811716	+	1.53482i
$493$			16.8601i			0.759341i
$494$	−3.19597	+	0.793079i	−0.143794	+	0.0356823i
$495$	−45.2673			−2.03461
$496$	−3.02156	+	4.43702i	−0.135672	+	0.199228i
$497$	23.6387			1.06034
$498$	−31.3578	+	7.78143i	−1.40518	+	0.348694i
$499$			16.9382i			0.758260i	0.925343	+	0.379130i	$0.123777\pi$
$499$			16.9382i			0.758260i	−0.925343	+	0.379130i	$0.876223\pi$
$500$	10.8637	+	20.5416i	0.485841	+	0.918648i
$501$			15.2463i			0.681153i
$502$	10.0390	+	40.4555i	0.448063	+	1.80562i
$503$	8.22413			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$503$	8.22413			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$504$	39.6753	−	35.4853i	1.76728	−	1.58064i
$505$	22.6598			1.00835
$506$	9.26337	+	37.3298i	0.411807	+	1.65951i
$507$			22.3686i			0.993424i
$508$	4.66718	−	2.46831i	0.207073	−	0.109514i
$509$			19.8145i			0.878261i	0.898423	+	0.439131i	$0.144713\pi$
$509$			19.8145i			0.878261i	−0.898423	+	0.439131i	$0.855287\pi$
$510$	−56.1171	+	13.9254i	−2.48491	+	0.616628i
$511$	−20.8594			−0.922764
$512$	13.1165	+	18.4379i	0.579675	+	0.814848i
$513$	−8.00510			−0.353434
$514$	−1.75958	+	0.436639i	−0.0776118	+	0.0192593i
$515$			26.5128i			1.16829i
$516$	10.2908	−	5.44243i	0.453026	−	0.239590i
$517$		−	20.2677i		−	0.891374i
$518$	4.18556	+	16.8671i	0.183903	+	0.741098i
$519$	9.26775			0.406809
$520$	10.4797	−	9.37297i	0.459565	−	0.411032i
$521$	−36.0978			−1.58147			−0.790737	−	0.612156i	$-0.790302\pi$
$521$	−36.0978			−1.58147			−0.790737	+	0.612156i	$0.790302\pi$
$522$	−5.05571	−	20.3737i	−0.221283	−	0.891731i
$523$			4.19475i			0.183424i	0.995786	+	0.0917119i	$0.0292339\pi$
$523$			4.19475i			0.183424i	−0.995786	+	0.0917119i	$0.970766\pi$
$524$	−14.3685	−	27.1686i	−0.627691	−	1.18686i
$525$			4.30199i			0.187754i
$526$	40.1805	−	9.97077i	1.75195	−	0.434746i
$527$	8.70743			0.379301
$528$	24.6688	−	36.2250i	1.07357	−	1.57649i
$529$	30.6778			1.33382
$530$	14.6115	−	3.62584i	0.634683	−	0.157496i
$531$		−	55.2438i		−	2.39738i
$532$	−3.08056	−	5.82485i	−0.133559	−	0.252539i
$533$			15.1903i			0.657967i
$534$	1.04925	+	4.22831i	0.0454056	+	0.182977i
$535$	35.3188			1.52696
$536$	0.989901	+	1.10679i	0.0427572	+	0.0478059i
$537$	53.6896			2.31688
$538$	4.83150	+	19.4701i	0.208301	+	0.839416i
$539$		−	14.3090i		−	0.616331i
$540$	30.2143	−	15.9793i	1.30021	−	0.687639i
$541$		−	6.12211i		−	0.263210i	−0.991302	−	0.131605i	$-0.957987\pi$
$541$		−	6.12211i		−	0.263210i	0.991302	−	0.131605i	$-0.0420131\pi$
$542$	−36.1244	+	8.96426i	−1.55168	+	0.385048i
$543$	41.5582			1.78343
$544$	12.7443	−	34.4193i	0.546409	−	1.47571i
$545$	37.2398			1.59518
$546$	31.0794	−	7.71234i	1.33008	−	0.330058i
$547$		−	4.88879i		−	0.209029i	−0.994523	−	0.104515i	$-0.966671\pi$
$547$		−	4.88879i		−	0.209029i	0.994523	−	0.104515i	$-0.0333289\pi$
$548$	−8.69584	+	4.59893i	−0.371468	+	0.196457i
$549$		−	46.5862i		−	1.98825i
$550$	0.559335	+	2.25402i	0.0238501	+	0.0961119i
$551$	−2.59857			−0.110703
$552$	−40.7759	−	45.5905i	−1.73554	−	1.94046i
$553$	−28.8493			−1.22680
$554$	−1.22231	−	4.92570i	−0.0519310	−	0.209273i
$555$			23.5030i			0.997647i
$556$	9.16673	+	17.3328i	0.388756	+	0.735076i
$557$			28.5987i			1.21176i	0.795554	+	0.605882i	$0.207180\pi$
$557$			28.5987i			1.21176i	−0.795554	+	0.605882i	$0.792820\pi$
$558$	−10.5220	+	2.61103i	−0.445432	+	0.110534i
$559$	4.59171			0.194209
$560$	23.2544	+	15.8359i	0.982677	+	0.669191i
$561$	−71.0897			−3.00141
$562$	6.07501	−	1.50751i	0.256259	−	0.0635905i
$563$			9.83345i			0.414431i	0.978295	+	0.207215i	$0.0664401\pi$
$563$			9.83345i			0.414431i	−0.978295	+	0.207215i	$0.933560\pi$
$564$	15.0684	+	28.4920i	0.634496	+	1.19973i
$565$		−	30.5697i		−	1.28608i
$566$	−0.167970	−	0.676891i	−0.00706032	−	0.0284519i
$567$	21.3881			0.898216
$568$	−15.1263	+	13.5288i	−0.634683	+	0.567656i
$569$	−10.3543			−0.434075			−0.217037	−	0.976163i	$-0.569639\pi$
$569$	−10.3543			−0.434075			−0.217037	+	0.976163i	$0.569639\pi$
$570$	−2.14626	−	8.64907i	−0.0898970	−	0.362270i
$571$		−	36.7988i		−	1.53998i	−0.638055	−	0.769991i	$-0.720261\pi$
$571$		−	36.7988i		−	1.53998i	0.638055	−	0.769991i	$-0.279739\pi$
$572$	15.2813	−	8.08174i	0.638942	−	0.337915i
$573$			14.3865i			0.601005i
$574$	−29.5020	+	7.32090i	−1.23139	+	0.305569i
$575$	3.24113			0.135165
$576$	−5.07915	+	45.4136i	−0.211631	+	1.89224i
$577$	−8.22871			−0.342566			−0.171283	−	0.985222i	$-0.554791\pi$
$577$	−8.22871			−0.342566			−0.171283	+	0.985222i	$0.554791\pi$
$578$	−34.4478	+	8.54820i	−1.43284	+	0.355558i
$579$		−	29.5117i		−	1.22646i
$580$	9.80798	−	5.18710i	0.407254	−	0.215383i
$581$		−	25.5008i		−	1.05795i
$582$	0.118222	+	0.476414i	0.00490046	+	0.0197480i
$583$	18.5100			0.766606
$584$	13.3478	−	11.9382i	0.552335	−	0.494004i
$585$	28.3941			1.17395
$586$	−4.33347	−	17.4631i	−0.179014	−	0.721395i
$587$		−	7.18047i		−	0.296370i	−0.988960	−	0.148185i	$-0.952657\pi$
$587$		−	7.18047i		−	0.296370i	0.988960	−	0.148185i	$-0.0473431\pi$
$588$	10.6383	+	20.1153i	0.438715	+	0.829541i
$589$			1.34204i			0.0552976i
$590$	28.3397	−	7.03249i	1.16673	−	0.289523i
$591$	−56.7329			−2.33368
$592$	−12.3316	−	8.39768i	−0.506827	−	0.345143i
$593$	−24.7687			−1.01713			−0.508564	−	0.861024i	$-0.669823\pi$
$593$	−24.7687			−1.01713			−0.508564	+	0.861024i	$0.669823\pi$
$594$	40.7874	−	10.1214i	1.67353	−	0.415284i
$595$		−	45.6355i		−	1.87087i
$596$	−0.677092	−	1.28027i	−0.0277348	−	0.0524420i
$597$		−	34.6295i		−	1.41729i
$598$	−5.81050	−	23.4153i	−0.237609	−	0.957524i
$599$	41.9307			1.71324			0.856621	−	0.515946i	$-0.172560\pi$
$599$	41.9307			1.71324			0.856621	+	0.515946i	$0.172560\pi$
$600$	−2.46210	−	2.75282i	−0.100515	−	0.112383i
$601$	2.10027			0.0856718			0.0428359	−	0.999082i	$-0.486361\pi$
$601$	2.10027			0.0856718			0.0428359	+	0.999082i	$0.486361\pi$
$602$	2.21295	+	8.91780i	0.0901930	+	0.363462i
$603$			2.99877i			0.122119i
$604$	−27.8018	+	14.7034i	−1.13124	+	0.598273i
$605$		−	5.93422i		−	0.241260i
$606$	−43.0020	+	10.6709i	−1.74683	+	0.433476i
$607$	−11.2877			−0.458152			−0.229076	−	0.973409i	$-0.573570\pi$
$607$	−11.2877			−0.458152			−0.229076	+	0.973409i	$0.573570\pi$
$608$	5.30489	+	1.96423i	0.215142	+	0.0796599i
$609$	25.2700			1.02399
$610$	23.8984	−	5.93038i	0.967619	−	0.240114i
$611$			12.7130i			0.514315i
$612$	65.5236	−	34.6532i	2.64863	−	1.40077i
$613$		−	31.4983i		−	1.27220i	−0.771605	−	0.636102i	$-0.780546\pi$
$613$		−	31.4983i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$614$	3.47984	+	14.0231i	0.140435	+	0.565928i
$615$	−41.1087			−1.65766
$616$	23.0607	+	25.7836i	0.929142	+	1.03885i
$617$	−11.4563			−0.461214			−0.230607	−	0.973047i	$-0.574071\pi$
$617$	−11.4563			−0.461214			−0.230607	+	0.973047i	$0.574071\pi$
$618$	−12.4853	−	50.3138i	−0.502234	−	2.02392i
$619$			37.6816i			1.51455i	0.653095	+	0.757276i	$0.273470\pi$
$619$			37.6816i			1.51455i	−0.653095	+	0.757276i	$0.726530\pi$
$620$	−2.67889	−	5.06534i	−0.107587	−	0.203429i
$621$		−	58.6495i		−	2.35352i
$622$	−0.253838	+	0.0629898i	−0.0101780	+	0.00252566i
$623$	−3.43855			−0.137763
$624$	−15.4736	+	22.7223i	−0.619441	+	0.909621i
$625$	−22.5924			−0.903695
$626$	26.1797	−	6.49649i	1.04635	−	0.259652i
$627$		−	10.9567i		−	0.437570i
$628$	0.131957	+	0.249510i	0.00526566	+	0.00995653i
$629$			24.2002i			0.964925i
$630$	13.6844	+	55.1458i	0.545199	+	2.19706i
$631$	6.99670			0.278534			0.139267	−	0.990255i	$-0.455525\pi$
$631$	6.99670			0.278534			0.139267	+	0.990255i	$0.455525\pi$
$632$	18.4605	−	16.5109i	0.734319	−	0.656770i
$633$	−1.17883			−0.0468543
$634$	−0.310508	−	1.25130i	−0.0123319	−	0.0496953i
$635$			5.63569i			0.223646i
$636$	−26.0210	+	13.7616i	−1.03180	+	0.545684i
$637$			8.97538i			0.355617i
$638$	13.2402	−	3.28554i	0.524183	−	0.130076i
$639$	−40.9837			−1.62129
$640$	−23.9435	+	3.17555i	−0.946450	+	0.125525i
$641$	−6.20749			−0.245181			−0.122591	−	0.992457i	$-0.539120\pi$
$641$	−6.20749			−0.245181			−0.122591	+	0.992457i	$0.539120\pi$
$642$	−67.0251	+	16.6322i	−2.64527	+	0.656422i
$643$			29.4008i			1.15945i	0.814811	+	0.579726i	$0.196841\pi$
$643$			29.4008i			1.15945i	−0.814811	+	0.579726i	$0.803159\pi$
$644$	42.6758	−	22.5698i	1.68166	−	0.889374i
$645$			12.4263i			0.489284i
$646$	−2.20993	−	8.90563i	−0.0869484	−	0.350387i
$647$	5.62285			0.221057			0.110529	−	0.993873i	$-0.464746\pi$
$647$	5.62285			0.221057			0.110529	+	0.993873i	$0.464746\pi$
$648$	−13.6861	+	12.2408i	−0.537641	+	0.480862i
$649$	35.9011			1.40924
$650$	−0.350846	−	1.41385i	−0.0137613	−	0.0554557i
$651$		−	13.0507i		−	0.511498i
$652$	7.87156	+	14.8839i	0.308274	+	0.582897i
$653$		−	34.9447i		−	1.36749i	−0.729721	−	0.683745i	$-0.760350\pi$
$653$		−	34.9447i		−	1.36749i	0.729721	−	0.683745i	$-0.239650\pi$
$654$	−70.6706	+	17.5369i	−2.76344	+	0.685746i
$655$	32.8064			1.28185
$656$	14.6883	−	21.5691i	0.573480	−	0.842130i
$657$	36.1650			1.41093
$658$	−24.6907	+	6.12698i	−0.962543	+	0.238855i
$659$			37.8768i			1.47547i	0.675090	+	0.737736i	$0.264105\pi$
$659$			37.8768i			1.47547i	−0.675090	+	0.737736i	$0.735895\pi$
$660$	21.8711	+	41.3548i	0.851332	+	1.60973i
$661$		−	6.77264i		−	0.263425i	−0.991288	−	0.131713i	$-0.957952\pi$
$661$		−	6.77264i		−	0.263425i	0.991288	−	0.131713i	$-0.0420476\pi$
$662$	−0.835268	−	3.36599i	−0.0324636	−	0.130823i
$663$	44.5914			1.73179
$664$	14.5945	+	16.3178i	0.566378	+	0.633254i
$665$	7.03360			0.272751
$666$	−7.25673	−	29.2434i	−0.281193	−	1.13316i
$667$		−	19.0385i		−	0.737172i
$668$	9.13226	−	4.82974i	0.353338	−	0.186868i
$669$		−	56.8329i		−	2.19729i
$670$	−1.53835	+	0.381741i	−0.0594317	+	0.0147479i
$671$	30.2748			1.16874
$672$	−51.5877	−	19.1012i	−1.99004	−	0.736846i
$673$	24.6355			0.949630			0.474815	−	0.880086i	$-0.342515\pi$
$673$	24.6355			0.949630			0.474815	+	0.880086i	$0.342515\pi$
$674$	−48.2418	+	11.9712i	−1.85821	+	0.461113i
$675$		−	3.54133i		−	0.136306i
$676$	13.3984	−	7.08596i	0.515323	−	0.272537i
$677$		−	28.2956i		−	1.08749i	−0.839251	−	0.543744i	$-0.817006\pi$
$677$		−	28.2956i		−	1.08749i	0.839251	−	0.543744i	$-0.182994\pi$
$678$	14.3958	+	58.0126i	0.552867	+	2.22796i
$679$	−0.387430			−0.0148682
$680$	26.1179	+	29.2019i	1.00158	+	1.11984i
$681$	−59.1546			−2.26681
$682$	−1.69682	−	6.83790i	−0.0649746	−	0.261837i
$683$			34.4333i			1.31755i	0.752339	+	0.658777i	$0.228926\pi$
$683$			34.4333i			1.31755i	−0.752339	+	0.658777i	$0.771074\pi$
$684$	5.34093	+	10.0988i	0.204216	+	0.386139i
$685$		−	10.5004i		−	0.401198i
$686$	14.2237	−	3.52960i	0.543063	−	0.134761i
$687$	−53.7234			−2.04967
$688$	−6.51985	−	4.43994i	−0.248567	−	0.169271i
$689$	−11.6105			−0.442325
$690$	63.3675	−	15.7246i	2.41236	−	0.598626i
$691$			2.19928i			0.0836646i	0.999125	+	0.0418323i	$0.0133195\pi$
$691$			2.19928i			0.0836646i	−0.999125	+	0.0418323i	$0.986680\pi$
$692$	−2.93585	−	5.55123i	−0.111604	−	0.211026i
$693$			69.8592i			2.65373i
$694$	−1.80740	−	7.28352i	−0.0686080	−	0.276479i
$695$	−20.9297			−0.793907
$696$	−16.1701	+	14.4624i	−0.612925	+	0.548196i
$697$	−42.3282			−1.60329
$698$	9.15934	+	36.9106i	0.346686	+	1.39709i
$699$			42.0242i			1.58950i
$700$	2.57682	−	1.36279i	0.0973947	−	0.0515087i
$701$			36.0608i			1.36200i	0.732285	+	0.680999i	$0.238454\pi$
$701$			36.0608i			1.36200i	−0.732285	+	0.680999i	$0.761546\pi$
$702$	−25.5841	+	6.34868i	−0.965609	+	0.239615i
$703$	−3.72986			−0.140675
$704$	−29.5128	−	3.30076i	−1.11230	−	0.124402i
$705$	−34.4045			−1.29575
$706$	4.41126	−	1.09465i	0.166020	−	0.0411977i
$707$		−	34.9701i		−	1.31518i
$708$	−50.4691	+	26.6913i	−1.89674	+	1.00312i
$709$		−	10.7299i		−	0.402970i	−0.979492	−	0.201485i	$-0.935423\pi$
$709$		−	10.7299i		−	0.402970i	0.979492	−	0.201485i	$-0.0645768\pi$
$710$	−5.21719	−	21.0244i	−0.195798	−	0.789031i
$711$	50.0176			1.87581
$712$	2.20030	−	1.96794i	0.0824599	−	0.0737515i
$713$	−9.83244			−0.368228
$714$	21.4906	+	86.6034i	0.804265	+	3.24105i
$715$			18.4524i			0.690080i
$716$	−17.0079	−	32.1592i	−0.635614	−	1.20185i
$717$			24.5389i			0.916421i
$718$	21.5258	−	5.34161i	0.803335	−	0.199347i
$719$	29.1037			1.08539			0.542693	−	0.839931i	$-0.317405\pi$
$719$	29.1037			1.08539			0.542693	+	0.839931i	$0.317405\pi$
$720$	−40.3174	−	27.4556i	−1.50254	−	1.02321i
$721$	40.9162			1.52380
$722$	1.37258	−	0.340606i	0.0510823	−	0.0126760i
$723$		−	77.2666i		−	2.87358i
$724$	−13.1649	−	24.8927i	−0.489269	−	0.925130i
$725$		−	1.14957i		−	0.0426938i
$726$	2.79453	+	11.2615i	0.103715	+	0.417952i
$727$	−40.5850			−1.50521			−0.752607	−	0.658470i	$-0.771204\pi$
$727$	−40.5850			−1.50521			−0.752607	+	0.658470i	$0.771204\pi$
$728$	−14.4650	−	16.1729i	−0.536107	−	0.599409i
$729$	33.8025			1.25195
$730$	4.60377	+	18.5524i	0.170393	+	0.686656i
$731$			12.7949i			0.473235i
$732$	−42.5597	+	22.5084i	−1.57305	+	0.831934i
$733$			18.6206i			0.687766i	0.939012	+	0.343883i	$0.111742\pi$
$733$			18.6206i			0.687766i	−0.939012	+	0.343883i	$0.888258\pi$
$734$	−19.6978	+	4.88800i	−0.727059	+	0.180419i
$735$	−24.2895			−0.895933
$736$	−14.3909	+	38.8663i	−0.530457	+	1.43263i
$737$	−1.94880			−0.0717849
$738$	51.1492	−	12.6926i	1.88283	−	0.467222i
$739$			7.89939i			0.290584i	0.989389	+	0.145292i	$0.0464121\pi$
$739$			7.89939i			0.290584i	−0.989389	+	0.145292i	$0.953588\pi$
$740$	14.0779	−	7.44532i	0.517514	−	0.273695i
$741$			6.87267i			0.252474i
$742$	−5.59562	−	22.5494i	−0.205422	−	0.827814i
$743$	−14.4064			−0.528521			−0.264261	−	0.964451i	$-0.585128\pi$
$743$	−14.4064			−0.528521			−0.264261	+	0.964451i	$0.585128\pi$
$744$	7.46913	+	8.35106i	0.273832	+	0.306165i
$745$	1.54595			0.0566392
$746$	3.09509	+	12.4727i	0.113319	+	0.456658i
$747$			44.2121i			1.61764i
$748$	22.5199	+	42.5815i	0.823409	+	1.55694i
$749$		−	54.5061i		−	1.99161i
$750$	47.0715	−	11.6808i	1.71881	−	0.426522i
$751$	14.0914			0.514204			0.257102	−	0.966384i	$-0.417232\pi$
$751$	14.0914			0.514204			0.257102	+	0.966384i	$0.417232\pi$
$752$	12.2928	−	18.0515i	0.448273	−	0.658270i
$753$	86.9962			3.17032
$754$	−8.30496	+	2.06087i	−0.302449	+	0.0750525i
$755$		−	33.5711i		−	1.22178i
$756$	−24.6602	−	46.6285i	−0.896883	−	1.69586i
$757$			50.2311i			1.82568i	0.408318	+	0.912840i	$0.366116\pi$
$757$			50.2311i			1.82568i	−0.408318	+	0.912840i	$0.633884\pi$
$758$	6.19922	+	24.9818i	0.225166	+	0.907380i
$759$	80.2746			2.91378
$760$	−4.50075	+	4.02544i	−0.163259	+	0.146018i
$761$	23.7483			0.860875			0.430437	−	0.902620i	$-0.358359\pi$
$761$	23.7483			0.860875			0.430437	+	0.902620i	$0.358359\pi$
$762$	−2.65395	−	10.6950i	−0.0961424	−	0.387437i
$763$		−	57.4707i		−	2.08058i
$764$	8.61727	−	4.55738i	0.311762	−	0.164880i
$765$			79.1207i			2.86062i
$766$	30.7670	−	7.63481i	1.11166	−	0.275857i
$767$	−22.5191			−0.813119
$768$	43.9426	−	17.3017i	1.58564	−	0.624321i
$769$	−47.4035			−1.70942			−0.854708	−	0.519109i	$-0.826264\pi$
$769$	−47.4035			−1.70942			−0.854708	+	0.519109i	$0.826264\pi$
$770$	−35.8374	+	8.89302i	−1.29149	+	0.320482i
$771$			3.78383i			0.136271i
$772$	−17.6770	+	9.34876i	−0.636209	+	0.336469i
$773$			11.8508i			0.426242i	0.977026	+	0.213121i	$0.0683628\pi$
$773$			11.8508i			0.426242i	−0.977026	+	0.213121i	$0.931637\pi$
$774$	−3.83670	−	15.4613i	−0.137907	−	0.555744i
$775$	−0.593696			−0.0213262
$776$	0.247914	−	0.221732i	0.00889958	−	0.00795972i
$777$	36.2713			1.30123
$778$	−11.8944	−	47.9325i	−0.426435	−	1.71846i
$779$		−	6.52385i		−	0.233741i
$780$	−13.7188	−	25.9400i	−0.491211	−	0.928802i
$781$		−	26.6339i		−	0.953036i
$782$	65.2472	−	16.1911i	2.33324	−	0.578991i
$783$	−20.8018			−0.743396
$784$	8.67871	−	12.7443i	0.309954	−	0.455154i
$785$	−0.301287			−0.0107534
$786$	−62.2574	+	15.4491i	−2.22065	+	0.551052i
$787$			26.3903i			0.940713i	0.882477	+	0.470356i	$0.155875\pi$
$787$			26.3903i			0.940713i	−0.882477	+	0.470356i	$0.844125\pi$
$788$	17.9719	+	33.9821i	0.640224	+	1.21056i
$789$		−	86.4048i		−	3.07609i
$790$	6.36720	+	25.6587i	0.226535	+	0.912897i
$791$	−47.1770			−1.67742
$792$	−39.9816	−	44.7025i	−1.42068	−	1.58843i
$793$	−18.9900			−0.674356
$794$	−10.6761	−	43.0227i	−0.378879	−	1.52682i
$795$		−	31.4208i		−	1.11438i
$796$	−20.7425	+	10.9700i	−0.735197	+	0.388821i
$797$			14.1893i			0.502610i	0.967908	+	0.251305i	$0.0808597\pi$
$797$			14.1893i			0.502610i	−0.967908	+	0.251305i	$0.919140\pi$
$798$	−13.3478	+	3.31224i	−0.472506	+	0.117252i
$799$	−35.4251			−1.25325
$800$	−0.868943	+	2.34680i	−0.0307218	+	0.0829719i
$801$	5.96159			0.210643
$802$	−2.25544	+	0.559687i	−0.0796424	+	0.0197632i
$803$			23.5024i			0.829382i
$804$	2.73959	−	1.44887i	0.0966177	−	0.0510978i
$805$			51.5317i			1.81625i
$806$	1.06434	+	4.28911i	0.0374898	+	0.151077i
$807$	41.8688			1.47385
$808$	20.0139	+	22.3771i	0.704087	+	0.787224i
$809$	−29.9998			−1.05474			−0.527368	−	0.849637i	$-0.676821\pi$
$809$	−29.9998			−1.05474			−0.527368	+	0.849637i	$0.676821\pi$
$810$	−4.72047	−	19.0227i	−0.165860	−	0.668389i
$811$		−	39.8833i		−	1.40049i	−0.713901	−	0.700246i	$-0.753073\pi$
$811$		−	39.8833i		−	1.40049i	0.713901	−	0.700246i	$-0.246927\pi$
$812$	−8.00506	−	15.1363i	−0.280922	−	0.531179i
$813$			77.6825i			2.72445i
$814$	19.0043	−	4.71590i	0.666100	−	0.165292i
$815$	−17.9725			−0.629549
$816$	−63.3162	−	43.1175i	−2.21651	−	1.50941i
$817$	−1.97202			−0.0689921
$818$	3.38541	−	0.840089i	0.118368	−	0.0293730i
$819$		−	43.8196i		−	1.53118i
$820$	13.0225	+	24.6234i	0.454765	+	0.859888i
$821$			56.4395i			1.96975i	0.173256	+	0.984877i	$0.444571\pi$
$821$			56.4395i			1.96975i	−0.173256	+	0.984877i	$0.555429\pi$
$822$	4.94481	+	19.9267i	0.172470	+	0.695024i
$823$	−41.7360			−1.45482			−0.727412	−	0.686201i	$-0.759277\pi$
$823$	−41.7360			−1.45482			−0.727412	+	0.686201i	$0.759277\pi$
$824$	−26.1820	+	23.4170i	−0.912093	+	0.815769i
$825$	4.84709			0.168754
$826$	−10.8530	−	43.7356i	−0.377623	−	1.52176i
$827$			17.4248i			0.605921i	0.953003	+	0.302960i	$0.0979750\pi$
$827$			17.4248i			0.605921i	−0.953003	+	0.302960i	$0.902025\pi$
$828$	−73.9893	+	39.1304i	−2.57131	+	1.35988i
$829$		−	52.2723i		−	1.81549i	−0.419519	−	0.907747i	$-0.637801\pi$
$829$		−	52.2723i		−	1.81549i	0.419519	−	0.907747i	$-0.362199\pi$
$830$	−22.6805	+	5.62817i	−0.787253	+	0.195356i
$831$	−10.5923			−0.367443
$832$	18.5121	+	2.07042i	0.641790	+	0.0717790i
$833$	−25.0100			−0.866547
$834$	39.7186	−	9.85614i	1.37534	−	0.341290i
$835$			11.0273i			0.381617i
$836$	−6.56290	+	3.47089i	−0.226983	+	0.120043i
$837$			10.7431i			0.371337i
$838$	−1.44779	−	5.83434i	−0.0500130	−	0.201544i
$839$	40.8429			1.41005			0.705027	−	0.709180i	$-0.250935\pi$
$839$	40.8429			1.41005			0.705027	+	0.709180i	$0.250935\pi$
$840$	43.7678	−	39.1456i	1.51013	−	1.35065i
$841$	22.2474			0.767153
$842$	−10.7257	−	43.2226i	−0.369631	−	1.48955i
$843$		−	13.0638i		−	0.449941i
$844$	0.373432	+	0.706100i	0.0128541	+	0.0243050i
$845$			16.1788i			0.556567i
$846$	42.8075	−	10.6227i	1.47175	−	0.365215i
$847$	−9.15805			−0.314674
$848$	16.4860	+	11.2267i	0.566131	+	0.385528i
$849$	−1.45560			−0.0499560
$850$	3.93971	−	0.977638i	0.135131	−	0.0335327i
$851$		−	27.3269i		−	0.936754i
$852$	19.8015	+	37.4415i	0.678388	+	1.28272i
$853$		−	42.8153i		−	1.46597i	−0.680245	−	0.732984i	$-0.738127\pi$
$853$		−	42.8153i		−	1.46597i	0.680245	−	0.732984i	$-0.261873\pi$
$854$	−9.15213	−	36.8815i	−0.313180	−	1.26206i
$855$	−12.1945			−0.417044
$856$	31.1947	+	34.8781i	1.06621	+	1.19211i
$857$	23.2947			0.795732			0.397866	−	0.917444i	$-0.369751\pi$
$857$	23.2947			0.795732			0.397866	+	0.917444i	$0.369751\pi$
$858$	−8.68955	−	35.0174i	−0.296656	−	1.19547i
$859$			17.5879i			0.600091i	0.953925	+	0.300045i	$0.0970018\pi$
$859$			17.5879i			0.600091i	−0.953925	+	0.300045i	$0.902998\pi$
$860$	7.44312	−	3.93641i	0.253808	−	0.134230i
$861$			63.4415i			2.16208i
$862$	28.9017	−	7.17193i	0.984394	−	0.244277i
$863$	−11.8886			−0.404692			−0.202346	−	0.979314i	$-0.564857\pi$
$863$	−11.8886			−0.404692			−0.202346	+	0.979314i	$0.564857\pi$
$864$	42.4662	+	15.7238i	1.44473	+	0.534936i
$865$	6.70319			0.227915
$866$	10.3373	−	2.56519i	0.351275	−	0.0871687i
$867$			74.0770i			2.51579i
$868$	−7.81716	+	4.13422i	−0.265332	+	0.140325i
$869$			32.5048i			1.10265i
$870$	−5.57721	−	22.4752i	−0.189085	−	0.761981i
$871$	1.22239			0.0414193
$872$	32.8914	+	36.7751i	1.11384	+	1.24536i
$873$	0.671707			0.0227338
$874$	2.49545	+	10.0563i	0.0844100	+	0.340158i
$875$			38.2795i			1.29408i
$876$	−17.4733	−	33.0392i	−0.590369	−	1.11629i
$877$			28.6698i			0.968111i	0.875037	+	0.484056i	$0.160837\pi$
$877$			28.6698i			0.968111i	−0.875037	+	0.484056i	$0.839163\pi$
$878$	−1.13100	+	0.280658i	−0.0381695	+	0.00947173i
$879$	−37.5530			−1.26663
$880$	17.8425	−	26.2009i	0.601469	−	0.883231i
$881$	−44.2297			−1.49014			−0.745069	−	0.666988i	$-0.767583\pi$
$881$	−44.2297			−1.49014			−0.745069	+	0.666988i	$0.767583\pi$
$882$	30.2220	−	7.49958i	1.01763	−	0.252524i
$883$		−	26.5869i		−	0.894719i	−0.894354	−	0.447359i	$-0.852364\pi$
$883$		−	26.5869i		−	0.894719i	0.894354	−	0.447359i	$-0.147636\pi$
$884$	−14.1257	−	26.7095i	−0.475100	−	0.898338i
$885$		−	60.9422i		−	2.04855i
$886$	2.92419	+	11.7840i	0.0982401	+	0.395891i
$887$	16.4124			0.551074			0.275537	−	0.961290i	$-0.411144\pi$
$887$	16.4124			0.551074			0.275537	+	0.961290i	$0.411144\pi$
$888$	−23.2098	+	20.7586i	−0.778868	+	0.696614i
$889$	8.69735			0.291700
$890$	0.758906	+	3.05826i	0.0254386	+	0.102513i
$891$		−	24.0981i		−	0.807317i
$892$	−34.0420	+	18.0036i	−1.13981	+	0.602806i
$893$		−	5.45991i		−	0.182709i
$894$	−2.93378	+	0.728015i	−0.0981201	+	0.0243485i
$895$	38.8327			1.29803
$896$	4.90070	+	36.9511i	0.163721	+	1.23445i
$897$	−50.3527			−1.68123
$898$	−3.42392	+	0.849644i	−0.114258	+	0.0283530i
$899$			3.48737i			0.116310i
$900$	−4.46757	+	2.36275i	−0.148919	+	0.0787582i
$901$		−	32.3529i		−	1.07783i
$902$	8.24851	+	33.2401i	0.274645	+	1.10677i
$903$	19.1770			0.638170
$904$	30.1883	−	27.0002i	1.00405	−	0.898012i
$905$	30.0583			0.999172
$906$	15.8092	+	63.7084i	0.525226	+	2.11657i
$907$		−	47.3380i		−	1.57183i	−0.618333	−	0.785916i	$-0.712192\pi$
$907$		−	47.3380i		−	1.57183i	0.618333	−	0.785916i	$-0.287808\pi$
$908$	18.7391	+	35.4326i	0.621879	+	1.17587i
$909$			60.6294i			2.01095i
$910$	22.4792	−	5.57820i	0.745178	−	0.184915i
$911$	5.30896			0.175894			0.0879469	−	0.996125i	$-0.471969\pi$
$911$	5.30896			0.175894			0.0879469	+	0.996125i	$0.471969\pi$
$912$	6.64550	−	9.75863i	0.220055	−	0.323141i
$913$	−28.7320			−0.950889
$914$	−19.9030	+	4.93893i	−0.658334	+	0.163365i
$915$		−	51.3915i		−	1.69895i
$916$	17.0186	+	32.1794i	0.562310	+	1.06324i
$917$		−	50.6290i		−	1.67192i
$918$	−17.6907	−	71.2905i	−0.583880	−	2.35294i
$919$	49.2513			1.62465			0.812326	−	0.583204i	$-0.198201\pi$
$919$	49.2513			1.62465			0.812326	+	0.583204i	$0.198201\pi$
$920$	−29.4924	−	32.9748i	−0.972337	−	1.08715i
$921$	30.1556			0.993661
$922$	7.89966	+	31.8343i	0.260162	+	1.04841i
$923$			16.7063i			0.549893i
$924$	63.8213	−	33.7529i	2.09957	−	1.11039i
$925$		−	1.65003i		−	0.0542528i
$926$	−35.7747	+	8.87746i	−1.17563	+	0.291732i
$927$	−70.9385			−2.32993
$928$	13.7851	+	5.10418i	0.452519	+	0.167553i
$929$	−29.2990			−0.961270			−0.480635	−	0.876921i	$-0.659594\pi$
$929$	−29.2990			−0.961270			−0.480635	+	0.876921i	$0.659594\pi$
$930$	−11.6074	+	2.88036i	−0.380620	+	0.0944507i
$931$		−	3.85468i		−	0.126332i
$932$	25.1718	−	13.3125i	0.824529	−	0.436065i
$933$			0.545857i			0.0178706i
$934$	−4.15380	−	16.7391i	−0.135916	−	0.547720i
$935$	−51.4179			−1.68154
$936$	25.0787	+	28.0399i	0.819722	+	0.916512i
$937$	−6.35345			−0.207558			−0.103779	−	0.994600i	$-0.533093\pi$
$937$	−6.35345			−0.207558			−0.103779	+	0.994600i	$0.533093\pi$
$938$	0.589126	+	2.37408i	0.0192357	+	0.0775164i
$939$		−	56.2973i		−	1.83719i
$940$	10.8987	+	20.6077i	0.355477	+	0.672151i
$941$			2.07523i			0.0676505i	0.999428	+	0.0338253i	$0.0107690\pi$
$941$			2.07523i			0.0676505i	−0.999428	+	0.0338253i	$0.989231\pi$
$942$	0.571758	−	0.141881i	0.0186289	−	0.00462274i
$943$	47.7970			1.55649
$944$	31.9753	+	21.7748i	1.04071	+	0.708709i
$945$	56.3047			1.83159
$946$	10.0477	−	2.49334i	0.326680	−	0.0810656i
$947$			13.3618i			0.434201i	0.976149	+	0.217101i	$0.0696600\pi$
$947$			13.3618i			0.434201i	−0.976149	+	0.217101i	$0.930340\pi$
$948$	−24.1663	−	45.6946i	−0.784885	−	1.48409i
$949$		−	14.7420i		−	0.478546i
$950$	0.150679	+	0.607210i	0.00488867	+	0.0197005i
$951$	−2.69081			−0.0872554
$952$	45.0661	−	40.3068i	1.46060	−	1.30635i
$953$	−52.6796			−1.70646			−0.853231	−	0.521534i	$-0.825360\pi$
$953$	−52.6796			−1.70646			−0.853231	+	0.521534i	$0.825360\pi$
$954$	9.70142	+	39.0950i	0.314095	+	1.26575i
$955$			10.4055i			0.336714i
$956$	14.6984	−	7.77347i	0.475380	−	0.251412i
$957$		−	28.4718i		−	0.920364i
$958$	−24.9650	+	6.19505i	−0.806582	+	0.200153i
$959$	−16.2048			−0.523281
$960$	−5.60306	+	50.0981i	−0.180838	+	1.61691i
$961$	−29.1989			−0.941901
$962$	−11.9205	+	2.95808i	−0.384334	+	0.0953722i
$963$			94.5002i			3.04522i
$964$	−46.2814	+	24.4766i	−1.49062	+	0.788339i
$965$		−	21.3453i		−	0.687128i
$966$	−24.2672	−	97.7927i	−0.780784	−	3.14643i
$967$	−7.17519			−0.230739			−0.115369	−	0.993323i	$-0.536805\pi$
$967$	−7.17519			−0.230739			−0.115369	+	0.993323i	$0.536805\pi$
$968$	5.86018	−	5.24130i	0.188353	−	0.168462i
$969$	−19.1508			−0.615213
$970$	0.0855077	+	0.344582i	0.00274549	+	0.0110638i
$971$			14.6991i			0.471718i	0.971787	+	0.235859i	$0.0757903\pi$
$971$			14.6991i			0.471718i	−0.971787	+	0.235859i	$0.924210\pi$
$972$	−4.53860	−	8.58176i	−0.145576	−	0.275260i
$973$			32.3000i			1.03549i
$974$	2.93311	−	0.727851i	0.0939830	−	0.0233218i
$975$	−3.04036			−0.0973695
$976$	26.9643	+	18.3623i	0.863106	+	0.587764i
$977$	19.5470			0.625365			0.312682	−	0.949858i	$-0.398772\pi$
$977$	19.5470			0.625365			0.312682	+	0.949858i	$0.398772\pi$
$978$	34.1067	−	8.46356i	1.09061	−	0.270635i
$979$			3.87424i			0.123821i
$980$	7.69447	+	14.5490i	0.245791	+	0.464751i
$981$			99.6401i			3.18126i
$982$	0.792838	+	3.19500i	0.0253005	+	0.101957i
$983$	24.0339			0.766562			0.383281	−	0.923632i	$-0.374794\pi$
$983$	24.0339			0.766562			0.383281	+	0.923632i	$0.374794\pi$
$984$	−36.3086	−	40.5958i	−1.15748	−	1.29415i
$985$	−41.0339			−1.30745
$986$	−5.74265	−	23.1419i	−0.182883	−	0.736988i
$987$			53.0952i			1.69004i
$988$	4.11661	−	2.17714i	0.130967	−	0.0692639i
$989$		−	14.4480i		−	0.459419i
$990$	62.1331	−	15.4183i	1.97472	−	0.490026i
$991$	50.5419			1.60552			0.802758	−	0.596305i	$-0.203365\pi$
$991$	50.5419			1.60552			0.802758	+	0.596305i	$0.203365\pi$
$992$	2.63606	−	7.11935i	0.0836951	−	0.226039i
$993$	−7.23827			−0.229700
$994$	−32.4461	+	8.05149i	−1.02913	+	0.255378i
$995$		−	25.0469i		−	0.794039i
$996$	40.3909	−	21.3613i	1.27983	−	0.676860i
$997$		−	21.9225i		−	0.694293i	−0.937811	−	0.347147i	$-0.887151\pi$
$997$		−	21.9225i		−	0.694293i	0.937811	−	0.347147i	$-0.112849\pi$
$998$	−5.76927	−	23.2492i	−0.182623	−	0.735939i
$999$	−29.8580			−0.944664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.4	yes	16
3.2	odd	2		1368.2.g.b.685.13		16
4.3	odd	2		608.2.c.b.305.2		16
8.3	odd	2		608.2.c.b.305.15		16
8.5	even	2	inner	152.2.c.b.77.3	✓	16
12.11	even	2		5472.2.g.b.2737.4		16
16.3	odd	4		4864.2.a.bp.1.8		8
16.5	even	4		4864.2.a.bo.1.8		8
16.11	odd	4		4864.2.a.bn.1.1		8
16.13	even	4		4864.2.a.bq.1.1		8
24.5	odd	2		1368.2.g.b.685.14		16
24.11	even	2		5472.2.g.b.2737.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.3	✓	16	8.5	even	2	inner
152.2.c.b.77.4	yes	16	1.1	even	1	trivial
608.2.c.b.305.2		16	4.3	odd	2
608.2.c.b.305.15		16	8.3	odd	2
1368.2.g.b.685.13		16	3.2	odd	2
1368.2.g.b.685.14		16	24.5	odd	2
4864.2.a.bn.1.1		8	16.11	odd	4
4864.2.a.bo.1.8		8	16.5	even	4
4864.2.a.bp.1.8		8	16.3	odd	4
4864.2.a.bq.1.1		8	16.13	even	4
5472.2.g.b.2737.4		16	12.11	even	2
5472.2.g.b.2737.13		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37258 + 0.340606i) q^{2} +2.95163i q^{3} +(1.76798 - 0.935021i) q^{4} +2.13486i q^{5} +(-1.00534 - 4.05136i) q^{6} +3.29464 q^{7} +(-2.10822 + 1.88558i) q^{8} -5.71210 q^{9} +O(q^{10})\)	\(q+(-1.37258 + 0.340606i) q^{2} +2.95163i q^{3} +(1.76798 - 0.935021i) q^{4} +2.13486i q^{5} +(-1.00534 - 4.05136i) q^{6} +3.29464 q^{7} +(-2.10822 + 1.88558i) q^{8} -5.71210 q^{9} +(-0.727145 - 2.93027i) q^{10} -3.71210i q^{11} +(2.75983 + 5.21840i) q^{12} +2.32843i q^{13} +(-4.52218 + 1.12218i) q^{14} -6.30130 q^{15} +(2.25147 - 3.30619i) q^{16} -6.48822 q^{17} +(7.84034 - 1.94558i) q^{18} -1.00000i q^{19} +(1.99614 + 3.77437i) q^{20} +9.72456i q^{21} +(1.26436 + 5.09517i) q^{22} +7.32651 q^{23} +(-5.56552 - 6.22268i) q^{24} +0.442384 q^{25} +(-0.793079 - 3.19597i) q^{26} -8.00510i q^{27} +(5.82485 - 3.08056i) q^{28} -2.59857i q^{29} +(8.64907 - 2.14626i) q^{30} -1.34204 q^{31} +(-1.96423 + 5.30489i) q^{32} +10.9567 q^{33} +(8.90563 - 2.20993i) q^{34} +7.03360i q^{35} +(-10.0988 + 5.34093i) q^{36} -3.72986i q^{37} +(0.340606 + 1.37258i) q^{38} -6.87267 q^{39} +(-4.02544 - 4.50075i) q^{40} +6.52385 q^{41} +(-3.31224 - 13.3478i) q^{42} -1.97202i q^{43} +(-3.47089 - 6.56290i) q^{44} -12.1945i q^{45} +(-10.0563 + 2.49545i) q^{46} +5.45991 q^{47} +(9.75863 + 6.64550i) q^{48} +3.85468 q^{49} +(-0.607210 + 0.150679i) q^{50} -19.1508i q^{51} +(2.17714 + 4.11661i) q^{52} +4.98640i q^{53} +(2.72659 + 10.9877i) q^{54} +7.92480 q^{55} +(-6.94584 + 6.21231i) q^{56} +2.95163 q^{57} +(0.885089 + 3.56676i) q^{58} +9.67136i q^{59} +(-11.1405 + 5.89185i) q^{60} +8.15570i q^{61} +(1.84206 - 0.457105i) q^{62} -18.8193 q^{63} +(0.889191 - 7.95043i) q^{64} -4.97088 q^{65} +(-15.0390 + 3.73193i) q^{66} -0.524986i q^{67} +(-11.4710 + 6.06662i) q^{68} +21.6251i q^{69} +(-2.39569 - 9.65420i) q^{70} +7.17489 q^{71} +(12.0424 - 10.7706i) q^{72} -6.33130 q^{73} +(1.27041 + 5.11955i) q^{74} +1.30575i q^{75} +(-0.935021 - 1.76798i) q^{76} -12.2300i q^{77} +(9.43332 - 2.34087i) q^{78} -8.75644 q^{79} +(7.05824 + 4.80657i) q^{80} +6.49178 q^{81} +(-8.95453 + 2.22206i) q^{82} -7.74008i q^{83} +(9.09267 + 17.1928i) q^{84} -13.8514i q^{85} +(0.671680 + 2.70676i) q^{86} +7.67001 q^{87} +(6.99945 + 7.82592i) q^{88} -1.04368 q^{89} +(4.15353 + 16.7380i) q^{90} +7.67136i q^{91} +(12.9531 - 6.85044i) q^{92} -3.96119i q^{93} +(-7.49419 + 1.85968i) q^{94} +2.13486 q^{95} +(-15.6580 - 5.79766i) q^{96} -0.117594 q^{97} +(-5.29088 + 1.31293i) q^{98} +21.2039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Introduction

L-functions

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