LMFDB - Embedded newform 378.2.v.a.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	378.67
Dual form			378.2.v.a.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.829129 + 1.52071i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.684323 - 3.88099i) q^{5} +(-0.342341 - 1.69788i) q^{6} +(-1.85424 + 1.88727i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.62509 - 2.52172i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.829129 + 1.52071i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.684323 - 3.88099i) q^{5} +(-0.342341 - 1.69788i) q^{6} +(-1.85424 + 1.88727i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.62509 - 2.52172i) q^{9} +(1.97043 + 3.41288i) q^{10} +(0.594167 + 3.36969i) q^{11} +(1.35363 + 1.08060i) q^{12} +(-0.849585 + 4.81824i) q^{13} +(0.207321 - 2.63762i) q^{14} +(5.33445 + 4.25849i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.73759 + 6.47370i) q^{17} +(2.86582 + 0.887164i) q^{18} +(-0.200803 + 0.347801i) q^{19} +(-3.70320 - 1.34785i) q^{20} +(-1.33257 - 4.38455i) q^{21} +(-2.62115 - 2.19941i) q^{22} +(3.57287 + 2.99800i) q^{23} +(-1.73153 + 0.0423056i) q^{24} +(-9.89531 - 3.60160i) q^{25} +(-2.44628 - 4.23709i) q^{26} +(5.18221 - 0.380448i) q^{27} +(1.53661 + 2.15379i) q^{28} +(-0.196696 - 1.11552i) q^{29} +(-6.82373 + 0.166720i) q^{30} +(-0.893342 + 5.06639i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-5.61694 - 1.89035i) q^{33} +(-7.02438 - 2.55666i) q^{34} +(6.05556 + 8.48780i) q^{35} +(-2.76561 + 1.16251i) q^{36} -3.19278 q^{37} +(-0.0697382 - 0.395505i) q^{38} +(-6.62270 - 5.28691i) q^{39} +(3.70320 - 1.34785i) q^{40} +(0.523747 - 2.97031i) q^{41} +(3.83914 + 2.50220i) q^{42} +(-3.03657 + 2.54798i) q^{43} +3.42167 q^{44} +(-10.8989 + 4.58128i) q^{45} -4.66406 q^{46} +(0.193641 + 1.09819i) q^{47} +(1.29924 - 1.14542i) q^{48} +(-0.123556 - 6.99891i) q^{49} +(9.89531 - 3.60160i) q^{50} +(-12.9435 + 0.316242i) q^{51} +(4.59751 + 1.67336i) q^{52} +(5.46677 - 9.46872i) q^{53} +(-3.72525 + 3.62250i) q^{54} +13.4843 q^{55} +(-2.56154 - 0.662189i) q^{56} +(-0.362411 - 0.593734i) q^{57} +(0.867719 + 0.728103i) q^{58} +(-3.22777 + 1.17481i) q^{59} +(5.12012 - 4.51393i) q^{60} +(1.79132 + 10.1591i) q^{61} +(-2.57227 - 4.45531i) q^{62} +(7.77248 + 1.60891i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(18.1181 + 6.59446i) q^{65} +(5.51792 - 2.16241i) q^{66} +(1.62925 + 1.36710i) q^{67} +(7.02438 - 2.55666i) q^{68} +(-7.52145 + 2.94756i) q^{69} +(-10.0947 - 2.60959i) q^{70} +(-1.71767 + 2.97510i) q^{71} +(1.37133 - 2.66823i) q^{72} -2.19912 q^{73} +(2.44581 - 2.05228i) q^{74} +(13.6815 - 12.0617i) q^{75} +(0.307648 + 0.258147i) q^{76} +(-7.46123 - 5.12687i) q^{77} +(8.47165 - 0.206983i) q^{78} +(12.4461 - 10.4435i) q^{79} +(-1.97043 + 3.41288i) q^{80} +(-3.71817 + 8.19605i) q^{81} +(1.50807 + 2.61205i) q^{82} +(-0.188556 - 1.06935i) q^{83} +(-4.54933 + 0.550956i) q^{84} +(27.6821 - 10.0755i) q^{85} +(0.688334 - 3.90374i) q^{86} +(1.85946 + 0.625792i) q^{87} +(-2.62115 + 2.19941i) q^{88} +(-1.65052 + 2.85878i) q^{89} +(5.40422 - 10.5151i) q^{90} +(-7.51797 - 10.5376i) q^{91} +(3.57287 - 2.99800i) q^{92} +(-6.96379 - 5.55920i) q^{93} +(-0.854241 - 0.716794i) q^{94} +(1.21240 + 1.01732i) q^{95} +(-0.259015 + 1.71257i) q^{96} +(-10.4530 + 8.77109i) q^{97} +(4.59346 + 5.28206i) q^{98} +(7.53184 - 6.97436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.829129	+	1.52071i	−0.478698	+	0.877980i
$3$	−0.829129	+	1.52071i	−0.478698	+	0.877980i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.684323	−	3.88099i	0.306039	−	1.73563i	−0.312537	−	0.949906i	$-0.601179\pi$
$5$	0.684323	−	3.88099i	0.306039	−	1.73563i	0.618576	−	0.785725i	$-0.287710\pi$
$6$	−0.342341	−	1.69788i	−0.139760	−	0.693157i
$7$	−1.85424	+	1.88727i	−0.700838	+	0.713320i
$7$	−1.85424	+	1.88727i	−0.700838	+	0.713320i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.62509	−	2.52172i	−0.541696	−	0.840574i
$10$	1.97043	+	3.41288i	0.623104	+	1.07925i
$11$	0.594167	+	3.36969i	0.179148	+	1.01600i	0.933246	+	0.359237i	$0.116963\pi$
$11$	0.594167	+	3.36969i	0.179148	+	1.01600i	−0.754098	+	0.656762i	$0.771926\pi$
$12$	1.35363	+	1.08060i	0.390758	+	0.311943i
$13$	−0.849585	+	4.81824i	−0.235633	+	1.33634i	0.605645	+	0.795735i	$0.292915\pi$
$13$	−0.849585	+	4.81824i	−0.235633	+	1.33634i	−0.841277	+	0.540604i	$0.818196\pi$
$14$	0.207321	−	2.63762i	0.0554090	−	0.704933i
$15$	5.33445	+	4.25849i	1.37735	+	1.09954i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.73759	+	6.47370i	0.906499	+	1.57010i	0.818892	+	0.573948i	$0.194589\pi$
$17$	3.73759	+	6.47370i	0.906499	+	1.57010i	0.0876078	+	0.996155i	$0.472078\pi$
$18$	2.86582	+	0.887164i	0.675481	+	0.209107i
$19$	−0.200803	+	0.347801i	−0.0460674	+	0.0797910i	−0.888140	−	0.459574i	$-0.848002\pi$
$19$	−0.200803	+	0.347801i	−0.0460674	+	0.0797910i	0.842072	+	0.539365i	$0.181336\pi$
$20$	−3.70320	−	1.34785i	−0.828060	−	0.301389i
$21$	−1.33257	−	4.38455i	−0.290790	−	0.956787i
$22$	−2.62115	−	2.19941i	−0.558831	−	0.468915i
$23$	3.57287	+	2.99800i	0.744996	+	0.625126i	0.934174	−	0.356817i	$-0.116138\pi$
$23$	3.57287	+	2.99800i	0.744996	+	0.625126i	−0.189179	+	0.981943i	$0.560582\pi$
$24$	−1.73153	+	0.0423056i	−0.353448	+	0.00863560i
$25$	−9.89531	−	3.60160i	−1.97906	−	0.720320i
$26$	−2.44628	−	4.23709i	−0.479756	−	0.830961i
$27$	5.18221	−	0.380448i	0.997316	−	0.0732172i
$28$	1.53661	+	2.15379i	0.290392	+	0.407029i
$29$	−0.196696	−	1.11552i	−0.0365255	−	0.207147i	0.961083	−	0.276258i	$-0.0890946\pi$
$29$	−0.196696	−	1.11552i	−0.0365255	−	0.207147i	−0.997609	+	0.0691119i	$0.977983\pi$
$30$	−6.82373	+	0.166720i	−1.24584	+	0.0304389i
$31$	−0.893342	+	5.06639i	−0.160449	+	0.909951i	0.793185	+	0.608981i	$0.208421\pi$
$31$	−0.893342	+	5.06639i	−0.160449	+	0.909951i	−0.953634	+	0.300970i	$0.902690\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−5.61694	−	1.89035i	−0.977784	−	0.329068i
$34$	−7.02438	−	2.55666i	−1.20467	−	0.438464i
$35$	6.05556	+	8.48780i	1.02358	+	1.43470i
$36$	−2.76561	+	1.16251i	−0.460934	+	0.193751i
$37$	−3.19278			−0.524890			−0.262445	−	0.964947i	$-0.584529\pi$
$37$	−3.19278			−0.524890			−0.262445	+	0.964947i	$0.584529\pi$
$38$	−0.0697382	−	0.395505i	−0.0113130	−	0.0641594i
$39$	−6.62270	−	5.28691i	−1.06048	−	0.846583i
$40$	3.70320	−	1.34785i	0.585527	−	0.213114i
$41$	0.523747	−	2.97031i	0.0817955	−	0.463885i	−0.916207	−	0.400706i	$-0.868765\pi$
$41$	0.523747	−	2.97031i	0.0817955	−	0.463885i	0.998002	−	0.0631792i	$-0.0201240\pi$
$42$	3.83914	+	2.50220i	0.592392	+	0.386098i
$43$	−3.03657	+	2.54798i	−0.463072	+	0.388564i	−0.844260	−	0.535934i	$-0.819960\pi$
$43$	−3.03657	+	2.54798i	−0.463072	+	0.388564i	0.381188	+	0.924498i	$0.375515\pi$
$44$	3.42167			0.515836
$45$	−10.8989	+	4.58128i	−1.62471	+	0.682937i
$46$	−4.66406			−0.687678
$47$	0.193641	+	1.09819i	0.0282454	+	0.160188i	0.995668	−	0.0929791i	$-0.0296390\pi$
$47$	0.193641	+	1.09819i	0.0282454	+	0.160188i	−0.967423	+	0.253167i	$0.918528\pi$
$48$	1.29924	−	1.14542i	0.187529	−	0.165327i
$49$	−0.123556	−	6.99891i	−0.0176509	−	0.999844i
$50$	9.89531	−	3.60160i	1.39941	−	0.509343i
$51$	−12.9435	+	0.316242i	−1.81246	+	0.0442828i
$52$	4.59751	+	1.67336i	0.637560	+	0.232053i
$53$	5.46677	−	9.46872i	0.750918	−	1.30063i	−0.196460	−	0.980512i	$-0.562945\pi$
$53$	5.46677	−	9.46872i	0.750918	−	1.30063i	0.947378	−	0.320117i	$-0.103722\pi$
$54$	−3.72525	+	3.62250i	−0.506943	+	0.492960i
$55$	13.4843			1.81822
$56$	−2.56154	−	0.662189i	−0.342301	−	0.0884887i
$57$	−0.362411	−	0.593734i	−0.0480025	−	0.0786420i
$58$	0.867719	+	0.728103i	0.113937	+	0.0956046i
$59$	−3.22777	+	1.17481i	−0.420219	+	0.152947i	−0.543471	−	0.839428i	$-0.682890\pi$
$59$	−3.22777	+	1.17481i	−0.420219	+	0.152947i	0.123251	+	0.992375i	$0.460668\pi$
$60$	5.12012	−	4.51393i	0.661004	−	0.582745i
$61$	1.79132	+	10.1591i	0.229355	+	1.30074i	0.854182	+	0.519975i	$0.174059\pi$
$61$	1.79132	+	10.1591i	0.229355	+	1.30074i	−0.624826	+	0.780764i	$0.714830\pi$
$62$	−2.57227	−	4.45531i	−0.326679	−	0.565825i
$63$	7.77248	+	1.60891i	0.979240	+	0.202704i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	18.1181	+	6.59446i	2.24728	+	0.817942i
$66$	5.51792	−	2.16241i	0.679209	−	0.266174i
$67$	1.62925	+	1.36710i	0.199045	+	0.167018i	0.736862	−	0.676043i	$-0.236307\pi$
$67$	1.62925	+	1.36710i	0.199045	+	0.167018i	−0.537818	+	0.843061i	$0.680751\pi$
$68$	7.02438	−	2.55666i	0.851831	−	0.310041i
$69$	−7.52145	+	2.94756i	−0.905476	+	0.354845i
$70$	−10.0947	−	2.60959i	−1.20655	−	0.311906i
$71$	−1.71767	+	2.97510i	−0.203850	+	0.353079i	−0.949766	−	0.312961i	$-0.898679\pi$
$71$	−1.71767	+	2.97510i	−0.203850	+	0.353079i	0.745915	+	0.666041i	$0.232012\pi$
$72$	1.37133	−	2.66823i	0.161613	−	0.314454i
$73$	−2.19912			−0.257387			−0.128694	−	0.991684i	$-0.541078\pi$
$73$	−2.19912			−0.257387			−0.128694	+	0.991684i	$0.541078\pi$
$74$	2.44581	−	2.05228i	0.284320	−	0.238573i
$75$	13.6815	−	12.0617i	1.57980	−	1.39276i
$76$	0.307648	+	0.258147i	0.0352897	+	0.0296115i
$77$	−7.46123	−	5.12687i	−0.850286	−	0.584261i
$78$	8.47165	−	0.206983i	0.959225	−	0.0234362i
$79$	12.4461	−	10.4435i	1.40029	−	1.17498i	0.439322	−	0.898330i	$-0.355219\pi$
$79$	12.4461	−	10.4435i	1.40029	−	1.17498i	0.960969	−	0.276655i	$-0.0892258\pi$
$80$	−1.97043	+	3.41288i	−0.220301	+	0.381572i
$81$	−3.71817	+	8.19605i	−0.413130	+	0.910672i
$82$	1.50807	+	2.61205i	0.166538	+	0.288453i
$83$	−0.188556	−	1.06935i	−0.0206967	−	0.117377i	0.972709	−	0.232028i	$-0.0745361\pi$
$83$	−0.188556	−	1.06935i	−0.0206967	−	0.117377i	−0.993406	+	0.114651i	$0.963425\pi$
$84$	−4.54933	+	0.550956i	−0.496373	+	0.0601142i
$85$	27.6821	−	10.0755i	3.00254	−	1.09284i
$86$	0.688334	−	3.90374i	0.0742250	−	0.420951i
$87$	1.85946	+	0.625792i	0.199355	+	0.0670920i
$88$	−2.62115	+	2.19941i	−0.279416	+	0.234458i
$89$	−1.65052	+	2.85878i	−0.174954	+	0.303030i	−0.940145	−	0.340773i	$-0.889311\pi$
$89$	−1.65052	+	2.85878i	−0.174954	+	0.303030i	0.765191	+	0.643803i	$0.222644\pi$
$90$	5.40422	−	10.5151i	0.569655	−	1.10839i
$91$	−7.51797	−	10.5376i	−0.788097	−	1.10464i
$92$	3.57287	−	2.99800i	0.372498	−	0.312563i
$93$	−6.96379	−	5.55920i	−0.722112	−	0.576463i
$94$	−0.854241	−	0.716794i	−0.0881083	−	0.0739316i
$95$	1.21240	+	1.01732i	0.124389	+	0.104375i
$96$	−0.259015	+	1.71257i	−0.0264356	+	0.174789i
$97$	−10.4530	+	8.77109i	−1.06134	+	0.890569i	−0.994240	−	0.107177i	$-0.965819\pi$
$97$	−10.4530	+	8.77109i	−1.06134	+	0.890569i	−0.0670992	+	0.997746i	$0.521374\pi$
$98$	4.59346	+	5.28206i	0.464010	+	0.533568i
$99$	7.53184	−	6.97436i	0.756978	−	0.700950i
$100$	−5.26518	+	9.11957i	−0.526518	+	0.911957i
$101$	0.999192	−	0.838422i	0.0994233	−	0.0834261i	−0.591721	−	0.806143i	$-0.701551\pi$
$101$	0.999192	−	0.838422i	0.0994233	−	0.0834261i	0.691144	+	0.722717i	$0.257107\pi$
$102$	9.71205	−	8.56220i	0.961636	−	0.847784i
$103$	−1.42102	+	8.05901i	−0.140017	+	0.794078i	0.831216	+	0.555949i	$0.187645\pi$
$103$	−1.42102	+	8.05901i	−0.140017	+	0.794078i	−0.971234	+	0.238128i	$0.923466\pi$
$104$	−4.59751	+	1.67336i	−0.450823	+	0.164086i
$105$	−17.9283	+	2.17124i	−1.74962	+	0.211891i
$106$	1.89859	+	10.7674i	0.184407	+	1.04583i
$107$	−7.15354	−	12.3903i	−0.691559	−	1.19781i	−0.971327	−	0.237747i	$-0.923591\pi$
$107$	−7.15354	−	12.3903i	−0.691559	−	1.19781i	0.279768	−	0.960068i	$-0.409742\pi$
$108$	0.525213	−	5.16954i	0.0505386	−	0.497439i
$109$	−4.67627	+	8.09953i	−0.447905	+	0.775794i	−0.998249	−	0.0591435i	$-0.981163\pi$
$109$	−4.67627	+	8.09953i	−0.447905	+	0.775794i	0.550345	+	0.834938i	$0.314496\pi$
$110$	−10.3296	+	8.66755i	−0.984887	+	0.826419i
$111$	2.64723	−	4.85528i	0.251264	−	0.460843i
$112$	2.38790	−	1.13926i	0.225636	−	0.107650i
$113$	−4.30835	−	3.61514i	−0.405296	−	0.340084i	0.417241	−	0.908796i	$-0.362997\pi$
$113$	−4.30835	−	3.61514i	−0.405296	−	0.340084i	−0.822536	+	0.568713i	$0.807442\pi$
$114$	0.659268	+	0.221873i	0.0617461	+	0.0207803i
$115$	14.0802	−	11.8147i	1.31298	−	1.10173i
$116$	−1.13273			−0.105171
$117$	13.5309	−	5.68765i	1.25093	−	0.525823i
$118$	1.71746	−	2.97473i	0.158105	−	0.273846i
$119$	−19.1480	−	4.94999i	−1.75530	−	0.453764i
$120$	−1.02074	+	6.74901i	−0.0931805	+	0.616098i
$121$	−0.665134	+	0.242089i	−0.0604667	+	0.0220081i
$122$	−7.90237	−	6.63088i	−0.715447	−	0.600331i
$123$	4.08272	+	3.25924i	0.368126	+	0.293876i
$124$	4.83430	+	1.75954i	0.434133	+	0.158011i
$125$	−10.8972	+	18.8745i	−0.974675	+	1.68819i
$126$	−6.98825	+	3.76355i	−0.622563	+	0.335284i
$127$	0.680921	+	1.17939i	0.0604220	+	0.104654i	0.894654	−	0.446760i	$-0.147422\pi$
$127$	0.680921	+	1.17939i	0.0604220	+	0.104654i	−0.834232	+	0.551413i	$0.814089\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.35702	−	6.73033i	−0.119479	−	0.592573i
$130$	−18.1181	+	6.59446i	−1.58907	+	0.578373i
$131$	−13.7404	−	11.5296i	−1.20050	−	1.00734i	−0.999616	−	0.0277278i	$-0.991173\pi$
$131$	−13.7404	−	11.5296i	−1.20050	−	1.00734i	−0.200888	−	0.979614i	$-0.564383\pi$
$132$	−2.83701	+	5.20335i	−0.246930	+	0.452894i
$133$	−0.284056	−	1.02388i	−0.0246308	−	0.0887814i
$134$	−2.12683			−0.183730
$135$	2.06979	−	20.3724i	0.178139	−	1.75338i
$136$	−3.73759	+	6.47370i	−0.320496	+	0.555115i
$137$	11.5061	+	4.18787i	0.983029	+	0.357793i	0.783017	−	0.622000i	$-0.213680\pi$
$137$	11.5061	+	4.18787i	0.983029	+	0.357793i	0.200012	+	0.979793i	$0.435902\pi$
$138$	3.86711	−	7.09265i	0.329190	−	0.603767i
$139$	−5.24500	+	1.90902i	−0.444875	+	0.161921i	−0.554737	−	0.832026i	$-0.687181\pi$
$139$	−5.24500	+	1.90902i	−0.444875	+	0.161921i	0.109862	+	0.993947i	$0.464959\pi$
$140$	9.41039	−	4.48967i	0.795323	−	0.379447i
$141$	−1.83058	−	0.616072i	−0.154163	−	0.0518826i
$142$	−0.596542	−	3.38316i	−0.0500607	−	0.283908i
$143$	−16.7407			−1.39993
$144$	0.664604	+	2.92546i	0.0553837	+	0.243788i
$145$	−4.46392			−0.370708
$146$	1.68462	−	1.41357i	0.139420	−	0.116988i
$147$	10.7457	+	5.61511i	0.886292	+	0.463126i
$148$	−0.554420	+	3.14427i	−0.0455731	+	0.258458i
$149$	15.3377	−	5.58245i	1.25651	−	0.457332i	0.373913	−	0.927464i	$-0.378016\pi$
$149$	15.3377	−	5.58245i	1.25651	−	0.457332i	0.882596	+	0.470132i	$0.155794\pi$
$150$	−2.72752	+	18.0340i	−0.222701	+	1.47247i
$151$	1.91607	+	10.8666i	0.155927	+	0.884307i	0.957933	+	0.286991i	$0.0926551\pi$
$151$	1.91607	+	10.8666i	0.155927	+	0.884307i	−0.802006	+	0.597316i	$0.796234\pi$
$152$	−0.401606			−0.0325746
$153$	10.2510	−	19.9455i	0.828741	−	1.61250i
$154$	9.01112	−	0.868575i	0.726137	−	0.0699918i
$155$	19.0513	+	6.93410i	1.53024	+	0.556960i
$156$	−6.35661	+	5.60403i	−0.508936	+	0.448681i
$157$	12.6952	−	4.62067i	1.01319	−	0.368770i	0.218531	−	0.975830i	$-0.429874\pi$
$157$	12.6952	−	4.62067i	1.01319	−	0.368770i	0.794656	+	0.607060i	$0.207651\pi$
$158$	−2.82129	+	16.0004i	−0.224450	+	1.27292i
$159$	9.86648	+	16.1641i	0.782462	+	1.28190i
$160$	−0.684323	−	3.88099i	−0.0541005	−	0.306819i
$161$	−12.2830	+	1.18395i	−0.968036	+	0.0933083i
$162$	−2.42004	−	8.66853i	−0.190136	−	0.681064i
$163$	−2.08224	−	3.60655i	−0.163094	−	0.282487i	0.772883	−	0.634549i	$-0.218814\pi$
$163$	−2.08224	−	3.60655i	−0.163094	−	0.282487i	−0.935977	+	0.352062i	$0.885481\pi$
$164$	−2.83424	−	1.03158i	−0.221317	−	0.0805528i
$165$	−11.1802	+	20.5057i	−0.870381	+	1.59636i
$166$	0.831809	+	0.697971i	0.0645609	+	0.0541730i
$167$	12.0596	+	10.1192i	0.933203	+	0.783050i	0.976390	−	0.216017i	$-0.0693066\pi$
$167$	12.0596	+	10.1192i	0.933203	+	0.783050i	−0.0431868	+	0.999067i	$0.513751\pi$
$168$	3.13085	−	3.34631i	0.241550	−	0.258174i
$169$	−10.2776	−	3.74075i	−0.790587	−	0.287750i
$170$	−14.7293	+	25.5119i	−1.12969	+	1.95668i
$171$	1.20338	−	0.0588382i	0.0920248	−	0.00449947i
$172$	1.98198	+	3.43289i	0.151124	+	0.261755i
$173$	22.5104	+	8.19313i	1.71144	+	0.622912i	0.997044	−	0.0768328i	$-0.0244808\pi$
$173$	22.5104	+	8.19313i	1.71144	+	0.622912i	0.714393	+	0.699745i	$0.246703\pi$
$174$	−1.82668	+	0.715854i	−0.138480	+	0.0542687i
$175$	25.1455	−	11.9969i	1.90082	−	0.906877i
$176$	0.594167	−	3.36969i	0.0447870	−	0.254000i
$177$	0.889695	−	5.88255i	0.0668735	−	0.442160i
$178$	−0.573218	−	3.25088i	−0.0429645	−	0.243664i
$179$	−5.50168	−	9.52919i	−0.411215	−	0.712245i	0.583808	−	0.811892i	$-0.301562\pi$
$179$	−5.50168	−	9.52919i	−0.411215	−	0.712245i	−0.995023	+	0.0996466i	$0.968229\pi$
$180$	2.61911	+	11.5288i	0.195217	+	0.859307i
$181$	0.501923	+	0.869356i	0.0373076	+	0.0646187i	0.884076	−	0.467343i	$-0.154789\pi$
$181$	0.501923	+	0.869356i	0.0373076	+	0.0646187i	−0.846769	+	0.531961i	$0.821455\pi$
$182$	12.5325	+	3.23980i	0.928973	+	0.240150i
$183$	−16.9342	−	5.69913i	−1.25181	−	0.421292i
$184$	−0.809905	+	4.59320i	−0.0597070	+	0.338615i
$185$	−2.18489	+	12.3911i	−0.160636	+	0.911015i
$186$	8.90796	−	0.217643i	0.653164	−	0.0159584i
$187$	−19.5936	+	16.4410i	−1.43283	+	1.20228i
$188$	1.11513			0.0813294
$189$	−8.89107	+	10.4857i	−0.646730	+	0.762719i
$190$	−1.58267			−0.114819
$191$	−1.17773	+	0.988232i	−0.0852175	+	0.0715060i	−0.684401	−	0.729106i	$-0.739936\pi$
$191$	−1.17773	+	0.988232i	−0.0852175	+	0.0715060i	0.599184	+	0.800612i	$0.295492\pi$
$192$	−0.902405	−	1.47840i	−0.0651255	−	0.106694i
$193$	3.15080	−	17.8691i	0.226800	−	1.28624i	−0.632415	−	0.774630i	$-0.717936\pi$
$193$	3.15080	−	17.8691i	0.226800	−	1.28624i	0.859215	−	0.511615i	$-0.170953\pi$
$194$	2.36950	−	13.4381i	0.170120	−	0.964799i
$195$	−25.0505	+	22.0847i	−1.79390	+	1.58152i
$196$	−6.91404	−	1.09367i	−0.493860	−	0.0781192i
$197$	−6.04304	−	10.4669i	−0.430549	−	0.745732i	0.566372	−	0.824150i	$-0.308347\pi$
$197$	−6.04304	−	10.4669i	−0.430549	−	0.745732i	−0.996921	+	0.0784176i	$0.975013\pi$
$198$	−1.28669	+	10.1840i	−0.0914410	+	0.723749i
$199$	−0.477212	−	0.826555i	−0.0338286	−	0.0585929i	0.848615	−	0.529010i	$-0.177437\pi$
$199$	−0.477212	−	0.826555i	−0.0338286	−	0.0585929i	−0.882444	+	0.470417i	$0.844103\pi$
$200$	−1.82858	−	10.3704i	−0.129300	−	0.733297i
$201$	−3.42982	+	1.34410i	−0.241921	+	0.0948058i
$202$	−0.226498	+	1.28454i	−0.0159364	+	0.0903797i
$203$	2.47000	+	1.69723i	0.173360	+	0.119122i
$204$	−1.93618	+	12.8018i	−0.135560	+	0.896306i
$205$	−11.1693	−	4.06531i	−0.780101	−	0.283933i
$206$	−4.09166	−	7.08697i	−0.285080	−	0.493773i
$207$	1.75388	−	13.8818i	0.121903	−	0.964853i
$208$	2.44628	−	4.23709i	0.169619	−	0.293789i
$209$	−1.29129	−	0.469992i	−0.0893205	−	0.0325100i
$210$	12.3382	−	13.1873i	0.851418	−	0.910013i
$211$	−12.1201	−	10.1700i	−0.834383	−	0.700131i	0.121910	−	0.992541i	$-0.461098\pi$
$211$	−12.1201	−	10.1700i	−0.834383	−	0.700131i	−0.956293	+	0.292411i	$0.905543\pi$
$212$	−8.37557	−	7.02794i	−0.575237	−	0.482681i
$213$	−3.10007	−	5.07882i	−0.212414	−	0.347995i
$214$	13.4443	+	4.89331i	0.919030	+	0.334500i
$215$	7.81070	+	13.5285i	0.532685	+	0.922638i
$216$	2.92058	+	4.29770i	0.198720	+	0.292421i
$217$	−7.90516	−	11.0803i	−0.536637	−	0.752180i
$218$	−1.62405	−	9.21044i	−0.109995	−	0.623810i
$219$	1.82335	−	3.34421i	0.123211	−	0.225981i
$220$	2.34153	−	13.2795i	0.157866	−	0.895301i
$221$	−34.3672	+	12.5087i	−2.31179	+	0.841423i
$222$	1.09302	+	5.42096i	0.0733586	+	0.363831i
$223$	−11.7347	−	4.27109i	−0.785816	−	0.286014i	−0.0822204	−	0.996614i	$-0.526201\pi$
$223$	−11.7347	−	4.27109i	−0.785816	−	0.286014i	−0.703596	+	0.710601i	$0.748423\pi$
$224$	−1.09694	+	2.40764i	−0.0732921	+	0.160867i
$225$	6.99853	+	30.8061i	0.466569	+	2.05374i
$226$	5.62416			0.374113
$227$	3.92883	+	22.2815i	0.260766	+	1.47888i	0.780827	+	0.624747i	$0.214798\pi$
$227$	3.92883	+	22.2815i	0.260766	+	1.47888i	−0.520061	+	0.854129i	$0.674091\pi$
$228$	−0.647646	+	0.253805i	−0.0428914	+	0.0168086i
$229$	12.3882	−	4.50893i	0.818635	−	0.297959i	0.101449	−	0.994841i	$-0.467652\pi$
$229$	12.3882	−	4.50893i	0.818635	−	0.297959i	0.717186	+	0.696882i	$0.245430\pi$
$230$	−3.19172	+	18.1011i	−0.210456	+	1.19355i
$231$	13.9828	−	7.09549i	0.920000	−	0.466849i
$232$	0.867719	−	0.728103i	0.0569686	−	0.0478023i
$233$	−12.5225			−0.820378			−0.410189	−	0.912001i	$-0.634537\pi$
$233$	−12.5225			−0.820378			−0.410189	+	0.912001i	$0.634537\pi$
$234$	−6.70933	+	13.0545i	−0.438603	+	0.853399i
$235$	4.39458			0.286671
$236$	0.596467	+	3.38273i	0.0388267	+	0.220197i
$237$	5.56207	+	27.5858i	0.361295	+	1.79189i
$238$	17.8500	−	8.51620i	1.15704	−	0.552023i
$239$	21.3504	−	7.77092i	1.38104	−	0.502659i	0.458549	−	0.888669i	$-0.348369\pi$
$239$	21.3504	−	7.77092i	1.38104	−	0.502659i	0.922495	+	0.386010i	$0.126147\pi$
$240$	−3.55625	−	5.82616i	−0.229555	−	0.376077i
$241$	1.44306	+	0.525231i	0.0929558	+	0.0338331i	0.388079	−	0.921626i	$-0.373139\pi$
$241$	1.44306	+	0.525231i	0.0929558	+	0.0338331i	−0.295124	+	0.955459i	$0.595361\pi$
$242$	0.353910	−	0.612991i	0.0227502	−	0.0394045i
$243$	−9.38093	−	12.4498i	−0.601787	−	0.798657i
$244$	10.3158			0.660402
$245$	−27.2472	−	4.30999i	−1.74076	−	0.275355i
$246$	−5.22254	+	0.127600i	−0.332977	+	0.00813545i
$247$	−1.50519	−	1.26300i	−0.0957729	−	0.0803630i
$248$	−4.83430	+	1.75954i	−0.306978	+	0.111731i
$249$	1.78251	+	0.599894i	0.112962	+	0.0380168i
$250$	−3.78456	−	21.4633i	−0.239356	−	1.35746i
$251$	−4.33773	−	7.51317i	−0.273795	−	0.474227i	0.696035	−	0.718007i	$-0.254946\pi$
$251$	−4.33773	−	7.51317i	−0.273795	−	0.474227i	−0.969830	+	0.243781i	$0.921612\pi$
$252$	2.93415	−	7.37501i	0.184834	−	0.464582i
$253$	−7.97943	+	13.8208i	−0.501662	+	0.868905i
$254$	−1.27971	−	0.465777i	−0.0802963	−	0.0292255i
$255$	−7.63023	+	50.4501i	−0.477823	+	3.15931i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−10.6143	+	3.86328i	−0.662100	+	0.240985i	−0.651143	−	0.758955i	$-0.725710\pi$
$257$	−10.6143	+	3.86328i	−0.662100	+	0.240985i	−0.0109571	+	0.999940i	$0.503488\pi$
$258$	5.36571	+	4.28346i	0.334055	+	0.266676i
$259$	5.92019	−	6.02563i	0.367863	−	0.374414i
$260$	9.64046	−	16.6978i	0.597876	−	1.03555i
$261$	−2.49338	+	2.30883i	−0.154336	+	0.142913i
$262$	17.9368			1.10814
$263$	−6.30090	+	5.28708i	−0.388530	+	0.326015i	−0.816040	−	0.577995i	$-0.803835\pi$
$263$	−6.30090	+	5.28708i	−0.388530	+	0.326015i	0.427510	+	0.904011i	$0.359391\pi$
$264$	−1.17138	−	5.80959i	−0.0720932	−	0.357556i
$265$	−33.0070	−	27.6961i	−2.02760	−	1.70136i
$266$	0.875735	+	0.601748i	0.0536948	+	0.0368955i
$267$	−2.97887	−	4.88025i	−0.182304	−	0.298666i
$268$	1.62925	−	1.36710i	0.0995223	−	0.0835091i
$269$	13.8246	−	23.9449i	0.842901	−	1.45995i	−0.0445311	−	0.999008i	$-0.514179\pi$
$269$	13.8246	−	23.9449i	0.842901	−	1.45995i	0.887432	−	0.460939i	$-0.152487\pi$
$270$	11.5096	+	16.9366i	0.700452	+	1.03073i
$271$	8.35025	+	14.4631i	0.507242	+	0.878568i	0.999965	+	0.00838234i	$0.00266821\pi$
$271$	8.35025	+	14.4631i	0.507242	+	0.878568i	−0.492723	+	0.870186i	$0.663998\pi$
$272$	−1.29805	−	7.36162i	−0.0787060	−	0.446364i
$273$	22.2579	−	2.69559i	1.34711	−	0.163144i
$274$	−11.5061	+	4.18787i	−0.695107	+	0.252998i
$275$	6.25679	−	35.4840i	0.377299	−	2.13977i
$276$	1.59670	+	7.91902i	0.0961098	+	0.476669i
$277$	19.7116	−	16.5400i	1.18435	−	0.993791i	0.184414	−	0.982849i	$-0.440961\pi$
$277$	19.7116	−	16.5400i	1.18435	−	0.993791i	0.999940	−	0.0109425i	$-0.00348318\pi$
$278$	2.79080	−	4.83381i	0.167381	−	0.289913i
$279$	14.2278	−	5.98058i	0.851796	−	0.358048i
$280$	−4.32287	+	9.48817i	−0.258341	+	0.567027i
$281$	−1.53256	+	1.28597i	−0.0914249	+	0.0767146i	−0.687355	−	0.726322i	$-0.741228\pi$
$281$	−1.53256	+	1.28597i	−0.0914249	+	0.0767146i	0.595930	+	0.803037i	$0.296784\pi$
$282$	1.79831	−	0.704735i	0.107088	−	0.0419663i
$283$	20.4158	+	17.1309i	1.21360	+	1.01833i	0.999135	+	0.0415946i	$0.0132438\pi$
$283$	20.4158	+	17.1309i	1.21360	+	1.01833i	0.214461	+	0.976733i	$0.431201\pi$
$284$	2.63163	+	2.20820i	0.156158	+	0.131032i
$285$	−2.55228	+	1.00021i	−0.151184	+	0.0592472i
$286$	12.8242	−	10.7607i	0.758308	−	0.636296i
$287$	4.63462	+	6.49614i	0.273573	+	0.383455i
$288$	−2.38956	−	1.81383i	−0.140806	−	0.106881i
$289$	−19.4392	+	33.6697i	−1.14348	+	1.98057i
$290$	3.41956	−	2.86935i	0.200803	−	0.168494i
$291$	−4.67137	−	23.1683i	−0.273841	−	1.35815i
$292$	−0.381873	+	2.16571i	−0.0223474	+	0.126738i
$293$	20.0174	−	7.28576i	1.16943	−	0.425638i	0.316974	−	0.948434i	$-0.397333\pi$
$293$	20.0174	−	7.28576i	1.16943	−	0.425638i	0.852458	+	0.522796i	$0.175111\pi$
$294$	−11.8410	+	2.60579i	−0.690583	+	0.151973i
$295$	2.35059	+	13.3309i	0.136857	+	0.776154i
$296$	−1.59639	−	2.76503i	−0.0927883	−	0.160714i
$297$	4.36108	+	17.2364i	0.253056	+	1.00016i
$298$	−8.16099	+	14.1353i	−0.472754	+	0.818833i
$299$	−17.4805	+	14.6679i	−1.01093	+	0.848267i
$300$	−9.50265	−	15.5681i	−0.548636	−	0.898824i
$301$	0.821814	−	10.4554i	0.0473685	−	0.602639i
$302$	−8.45268	−	7.09264i	−0.486397	−	0.408135i
$303$	0.446533	+	2.21464i	0.0256526	+	0.127228i
$304$	0.307648	−	0.258147i	0.0176448	−	0.0148058i
$305$	40.6532			2.32779
$306$	4.96804	+	21.8683i	0.284004	+	1.25013i
$307$	6.56172	−	11.3652i	0.374497	−	0.648648i	−0.615754	−	0.787938i	$-0.711149\pi$
$307$	6.56172	−	11.3652i	0.374497	−	0.648648i	0.990252	+	0.139290i	$0.0444820\pi$
$308$	−6.34461	+	6.45760i	−0.361518	+	0.367956i
$309$	−11.0772	−	8.84291i	−0.630158	−	0.503056i
$310$	−19.0513	+	6.93410i	−1.08204	+	0.393830i
$311$	−18.0374	−	15.1352i	−1.02281	−	0.858237i	−0.0328292	−	0.999461i	$-0.510452\pi$
$311$	−18.0374	−	15.1352i	−1.02281	−	0.858237i	−0.989978	+	0.141224i	$0.954896\pi$
$312$	1.26725	−	8.37889i	0.0717438	−	0.474361i
$313$	−2.70678	−	0.985189i	−0.152996	−	0.0556862i	0.264387	−	0.964417i	$-0.414830\pi$
$313$	−2.70678	−	0.985189i	−0.152996	−	0.0556862i	−0.417383	+	0.908731i	$0.637053\pi$
$314$	−6.75497	+	11.7000i	−0.381205	+	0.660266i
$315$	11.5631	−	29.0639i	0.651504	−	1.63756i
$316$	−8.12359	−	14.0705i	−0.456988	−	0.791526i
$317$	−0.173769	−	0.985494i	−0.00975985	−	0.0553509i	0.979539	−	0.201255i	$-0.0645020\pi$
$317$	−0.173769	−	0.985494i	−0.00975985	−	0.0553509i	−0.989299	+	0.145904i	$0.953391\pi$
$318$	−17.9483	−	6.04040i	−1.00649	−	0.338729i
$319$	3.64208	−	1.32561i	0.203917	−	0.0742198i
$320$	3.01887	+	2.53314i	0.168760	+	0.141607i
$321$	24.7732	−	0.605270i	1.38270	−	0.0337829i
$322$	8.64830	−	8.80232i	0.481951	−	0.490534i
$323$	−3.00208			−0.167040
$324$	7.42588	+	5.08491i	0.412549	+	0.282495i
$325$	25.7603	−	44.6181i	1.42892	−	2.47497i
$326$	3.91334	+	1.42434i	0.216740	+	0.0788868i
$327$	−8.43977	−	13.8268i	−0.466720	−	0.764623i
$328$	2.83424	−	1.03158i	0.156495	−	0.0569594i
$329$	−2.43164	−	1.67086i	−0.134061	−	0.0921177i
$330$	−4.61623	−	22.8948i	−0.254115	−	1.26032i
$331$	−1.28437	−	7.28400i	−0.0705952	−	0.400365i	−0.999545	−	0.0301597i	$-0.990398\pi$
$331$	−1.28437	−	7.28400i	−0.0705952	−	0.400365i	0.928950	−	0.370205i	$-0.120713\pi$
$332$	−1.08585			−0.0595938
$333$	5.18855	+	8.05131i	0.284331	+	0.441209i
$334$	−15.7427			−0.861404
$335$	6.42064	−	5.38756i	0.350797	−	0.294354i
$336$	−0.247398	+	4.57589i	−0.0134967	+	0.249635i
$337$	0.107710	−	0.610855i	0.00586734	−	0.0332754i	−0.981734	−	0.190261i	$-0.939067\pi$
$337$	0.107710	−	0.610855i	0.00586734	−	0.0332754i	0.987601	+	0.156986i	$0.0501777\pi$
$338$	10.2776	−	3.74075i	0.559029	−	0.203470i
$339$	9.06974	−	3.55432i	0.492601	−	0.193044i
$340$	−5.11544	−	29.0111i	−0.277424	−	1.57335i
$341$	−17.6029			−0.953253
$342$	−0.884023	+	0.818591i	−0.0478025	+	0.0442643i
$343$	13.4379	+	12.7445i	0.725579	+	0.688139i
$344$	−3.72490	−	1.35575i	−0.200833	−	0.0730973i
$345$	6.29235	+	31.2077i	0.338769	+	1.68017i
$346$	−22.5104	+	8.19313i	−1.21017	+	0.440465i
$347$	−0.915750	+	5.19348i	−0.0491600	+	0.278800i	−0.999472	−	0.0324995i	$-0.989653\pi$
$347$	−0.915750	+	5.19348i	−0.0491600	+	0.278800i	0.950312	+	0.311300i	$0.100764\pi$
$348$	0.939177	−	1.72254i	0.0503452	−	0.0923380i
$349$	−4.38282	−	24.8562i	−0.234607	−	1.33052i	−0.843440	−	0.537224i	$-0.819473\pi$
$349$	−4.38282	−	24.8562i	−0.234607	−	1.33052i	0.608833	−	0.793298i	$-0.291638\pi$
$350$	−11.5511	+	25.3533i	−0.617435	+	1.35519i
$351$	−2.56964	+	25.2923i	−0.137157	+	1.35000i
$352$	1.71083	+	2.96325i	0.0911878	+	0.157942i
$353$	2.25447	+	0.820562i	0.119994	+	0.0436741i	0.401319	−	0.915938i	$-0.368552\pi$
$353$	2.25447	+	0.820562i	0.119994	+	0.0436741i	−0.281326	+	0.959612i	$0.590774\pi$
$354$	3.09969	+	5.07818i	0.164746	+	0.269902i
$355$	10.3709	+	8.70220i	0.550429	+	0.461865i
$356$	2.52874	+	2.12186i	0.134023	+	0.112459i
$357$	23.4036	−	25.0143i	1.23865	−	1.32390i
$358$	10.3398	+	3.76337i	0.546474	+	0.198900i
$359$	8.30082	−	14.3774i	0.438101	−	0.758812i	−0.559442	−	0.828869i	$-0.688985\pi$
$359$	8.30082	−	14.3774i	0.438101	−	0.758812i	0.997543	+	0.0700568i	$0.0223180\pi$
$360$	−9.41694	−	7.14805i	−0.496316	−	0.376735i
$361$	9.41936	+	16.3148i	0.495756	+	0.858674i
$362$	−0.943306	−	0.343335i	−0.0495791	−	0.0180453i
$363$	0.183336	−	1.21220i	0.00962265	−	0.0636238i
$364$	−11.6830	+	5.57392i	−0.612354	+	0.292153i
$365$	−1.50491	+	8.53475i	−0.0787704	+	0.446729i
$366$	16.6357	−	6.51932i	0.869562	−	0.340771i
$367$	1.62844	+	9.23532i	0.0850037	+	0.482080i	0.997356	+	0.0726734i	$0.0231531\pi$
$367$	1.62844	+	9.23532i	0.0850037	+	0.482080i	−0.912352	+	0.409406i	$0.865736\pi$
$368$	−2.33203	−	4.03919i	−0.121565	−	0.210557i
$369$	−8.34144	+	3.50628i	−0.434238	+	0.182530i
$370$	−6.29115	−	10.8966i	−0.327061	−	0.566487i
$371$	7.73328	+	27.8746i	0.401492	+	1.44718i
$372$	−6.68400	+	5.89265i	−0.346549	+	0.305520i
$373$	−4.57886	+	25.9680i	−0.237085	+	1.34457i	0.601094	+	0.799178i	$0.294732\pi$
$373$	−4.57886	+	25.9680i	−0.237085	+	1.34457i	−0.838179	+	0.545395i	$0.816379\pi$
$374$	4.44151	−	25.1890i	0.229665	−	1.30249i
$375$	−19.6674	−	32.2208i	−1.01562	−	1.66388i
$376$	−0.854241	+	0.716794i	−0.0440541	+	0.0369658i
$377$	5.54194			0.285425
$378$	0.0709076	−	13.7475i	0.00364709	−	0.707097i
$379$	21.8385			1.12177			0.560883	−	0.827895i	$-0.310462\pi$
$379$	21.8385			1.12177			0.560883	+	0.827895i	$0.310462\pi$
$380$	1.21240	−	1.01732i	0.0621947	−	0.0521875i
$381$	−2.35808	+	0.0576136i	−0.120808	+	0.00295163i
$382$	0.266970	−	1.51406i	0.0136594	−	0.0774660i
$383$	−6.70613	+	38.0324i	−0.342667	+	1.94336i	−0.0110810	+	0.999939i	$0.503527\pi$
$383$	−6.70613	+	38.0324i	−0.342667	+	1.94336i	−0.331586	+	0.943425i	$0.607584\pi$
$384$	1.64158	+	0.552465i	0.0837715	+	0.0281929i
$385$	−25.0032	+	25.4485i	−1.27428	+	1.29698i
$386$	9.07237	+	15.7138i	0.461771	+	0.799812i
$387$	11.3600	+	3.51668i	0.577461	+	0.178763i
$388$	6.82270	+	11.8173i	0.346370	+	0.599930i
$389$	−3.02050	−	17.1301i	−0.153145	−	0.868531i	−0.960462	−	0.278412i	$-0.910192\pi$
$389$	−3.02050	−	17.1301i	−0.153145	−	0.868531i	0.807316	−	0.590119i	$-0.200919\pi$
$390$	4.99404	−	33.0200i	0.252883	−	1.67203i
$391$	−6.05419	+	34.3350i	−0.306174	+	1.73640i
$392$	5.99946	−	3.60646i	0.303018	−	0.182154i
$393$	28.9256	−	11.3356i	1.45910	−	0.571805i
$394$	11.3572	+	4.13368i	0.572167	+	0.208252i
$395$	−32.0139	−	55.4497i	−1.61080	−	2.78998i
$396$	−5.56052	−	8.62850i	−0.279427	−	0.433598i
$397$	13.3155	−	23.0631i	0.668285	−	1.15750i	−0.310098	−	0.950705i	$-0.600362\pi$
$397$	13.3155	−	23.0631i	0.668285	−	1.15750i	0.978383	−	0.206799i	$-0.0663047\pi$
$398$	0.896864	+	0.326432i	0.0449558	+	0.0163626i
$399$	1.79253	+	0.416962i	0.0897390	+	0.0208742i
$400$	8.06673	+	6.76879i	0.403336	+	0.338440i
$401$	15.5276	+	13.0292i	0.775410	+	0.650646i	0.942088	−	0.335365i	$-0.108860\pi$
$401$	15.5276	+	13.0292i	0.775410	+	0.650646i	−0.166678	+	0.986011i	$0.553304\pi$
$402$	1.76342	−	3.23429i	0.0879514	−	0.161312i
$403$	−23.6521	−	8.60867i	−1.17820	−	0.428828i
$404$	−0.652176	−	1.12960i	−0.0324470	−	0.0561998i
$405$	29.2643	+	20.0389i	1.45416	+	0.995742i
$406$	−2.98309	+	0.287538i	−0.148048	+	0.0142702i
$407$	−1.89704	−	10.7587i	−0.0940329	−	0.533287i
$408$	−6.74564	−	11.0513i	−0.333959	−	0.547122i
$409$	−0.107704	+	0.610822i	−0.00532564	+	0.0302032i	−0.987355	−	0.158526i	$-0.949326\pi$
$409$	−0.107704	+	0.610822i	−0.00532564	+	0.0302032i	0.982029	+	0.188729i	$0.0604369\pi$
$410$	11.1693	−	4.06531i	0.551615	−	0.200771i
$411$	−15.9085	+	14.0251i	−0.784710	+	0.691805i
$412$	7.68981	+	2.79886i	0.378850	+	0.137890i
$413$	3.76789	−	8.27005i	0.185406	−	0.406942i
$414$	7.57951	+	11.7615i	0.372512	+	0.578044i
$415$	−4.27918			−0.210057
$416$	0.849585	+	4.81824i	0.0416544	+	0.236234i
$417$	1.44572	−	9.55892i	0.0707972	−	0.468102i
$418$	1.29129	−	0.469992i	0.0631591	−	0.0229880i
$419$	1.34242	−	7.61322i	0.0655813	−	0.371930i	−0.934300	−	0.356489i	$-0.883974\pi$
$419$	1.34242	−	7.61322i	0.0655813	−	0.371930i	0.999881	−	0.0154409i	$-0.00491518\pi$
$420$	−0.974961	+	18.0329i	−0.0475732	+	0.879918i
$421$	−0.346722	+	0.290934i	−0.0168982	+	0.0141793i	−0.651198	−	0.758908i	$-0.725733\pi$
$421$	−0.346722	+	0.290934i	−0.0168982	+	0.0141793i	0.634299	+	0.773087i	$0.281289\pi$
$422$	15.8217			0.770188
$423$	2.45465	−	2.27297i	0.119349	−	0.110515i
$424$	10.9335			0.530979
$425$	−13.6690	−	77.5206i	−0.663042	−	3.76030i
$426$	5.63939	+	1.89791i	0.273230	+	0.0919540i
$427$	−22.4945	−	15.4567i	−1.08858	−	0.748004i
$428$	−13.4443	+	4.89331i	−0.649853	+	0.236527i
$429$	13.8802	−	25.4577i	0.670145	−	1.22911i
$430$	−14.6793	−	5.34283i	−0.707899	−	0.257654i
$431$	−18.4614	+	31.9760i	−0.889253	+	1.54023i	−0.0484934	+	0.998824i	$0.515442\pi$
$431$	−18.4614	+	31.9760i	−0.889253	+	1.54023i	−0.840760	+	0.541408i	$0.817891\pi$
$432$	−4.99980	−	1.41491i	−0.240553	−	0.0680751i
$433$	−36.6719			−1.76234			−0.881169	−	0.472801i	$-0.843243\pi$
$433$	−36.6719			−1.76234			−0.881169	+	0.472801i	$0.843243\pi$
$434$	13.1780	+	3.40666i	0.632564	+	0.163525i
$435$	3.70116	−	6.78830i	0.177457	−	0.325474i
$436$	7.16445	+	6.01169i	0.343115	+	0.287908i
$437$	−1.76015	+	0.640643i	−0.0841994	+	0.0306461i
$438$	0.752847	+	3.73384i	0.0359724	+	0.178410i
$439$	3.84717	+	21.8184i	0.183615	+	1.04134i	0.927721	+	0.373273i	$0.121765\pi$
$439$	3.84717	+	21.8184i	0.183615	+	1.04134i	−0.744106	+	0.668062i	$0.767124\pi$
$440$	6.74216	+	11.6778i	0.321420	+	0.556715i
$441$	−17.4485	+	11.6854i	−0.830882	+	0.556449i
$442$	18.2864	−	31.6730i	0.869797	−	1.50653i
$443$	25.1817	+	9.16540i	1.19642	+	0.435461i	0.861974	−	0.506953i	$-0.169228\pi$
$443$	25.1817	+	9.16540i	1.19642	+	0.435461i	0.334447	+	0.942415i	$0.391450\pi$
$444$	−4.32183	−	3.45012i	−0.205105	−	0.163735i
$445$	9.96540	+	8.36196i	0.472405	+	0.396395i
$446$	11.7347	−	4.27109i	0.555656	−	0.202242i
$447$	−4.22764	+	27.9526i	−0.199960	+	1.32211i
$448$	−0.707299	−	2.54946i	−0.0334168	−	0.120450i
$449$	−4.09017	+	7.08439i	−0.193027	+	0.334333i	−0.946252	−	0.323430i	$-0.895164\pi$
$449$	−4.09017	+	7.08439i	−0.193027	+	0.334333i	0.753225	+	0.657763i	$0.228497\pi$
$450$	−25.1630	−	19.1003i	−1.18619	−	0.900397i
$451$	10.3202			0.485960
$452$	−4.30835	+	3.61514i	−0.202648	+	0.170042i
$453$	−18.1135	−	6.09600i	−0.851046	−	0.286415i
$454$	−17.3319	−	14.5432i	−0.813428	−	0.682548i
$455$	−46.0410	+	21.9660i	−2.15843	+	1.02978i
$456$	0.332983	−	0.610725i	0.0155934	−	0.0285998i
$457$	−1.42100	+	1.19236i	−0.0664715	+	0.0557762i	−0.675418	−	0.737435i	$-0.736037\pi$
$457$	−1.42100	+	1.19236i	−0.0664715	+	0.0557762i	0.608947	+	0.793211i	$0.291592\pi$
$458$	−6.59162	+	11.4170i	−0.308006	+	0.533482i
$459$	21.8319	+	32.1261i	1.01902	+	1.49952i
$460$	−9.19019	−	15.9179i	−0.428495	−	0.742175i
$461$	5.89233	+	33.4171i	0.274433	+	1.55639i	0.740757	+	0.671774i	$0.234467\pi$
$461$	5.89233	+	33.4171i	0.274433	+	1.55639i	−0.466323	+	0.884614i	$0.654422\pi$
$462$	−6.15054	+	14.4234i	−0.286149	+	0.671038i
$463$	1.39988	−	0.509514i	0.0650578	−	0.0236791i	−0.309286	−	0.950969i	$-0.600090\pi$
$463$	1.39988	−	0.509514i	0.0650578	−	0.0236791i	0.374344	+	0.927290i	$0.377868\pi$
$464$	−0.196696	+	1.11552i	−0.00913138	+	0.0517866i
$465$	−26.3407	+	23.2221i	−1.22152	+	1.07690i
$466$	9.59281	−	8.04932i	0.444378	−	0.372878i
$467$	11.9914	−	20.7696i	0.554894	−	0.961104i	−0.443018	−	0.896513i	$-0.646092\pi$
$467$	11.9914	−	20.7696i	0.554894	−	0.961104i	0.997912	−	0.0645913i	$-0.0205744\pi$
$468$	−3.25162	−	14.3130i	−0.150306	−	0.661619i
$469$	−5.60111	+	0.539887i	−0.258635	+	0.0249297i
$470$	−3.36644	+	2.82478i	−0.155283	+	0.130297i
$471$	−3.49927	+	23.1368i	−0.161238	+	1.06609i
$472$	−2.63130	−	2.20792i	−0.121115	−	0.101628i
$473$	−10.3901	−	8.71836i	−0.477739	−	0.400870i
$474$	−21.9926	−	17.5567i	−1.01015	−	0.806407i
$475$	3.23965	−	2.71839i	0.148645	−	0.124728i
$476$	−8.19980	+	17.9976i	−0.375837	+	0.824917i
$477$	−32.7615	+	1.60184i	−1.50004	+	0.0733433i
$478$	−11.3603	+	19.6767i	−0.519609	+	0.899989i
$479$	9.60833	−	8.06235i	0.439016	−	0.368378i	−0.396325	−	0.918110i	$-0.629715\pi$
$479$	9.60833	−	8.06235i	0.439016	−	0.368378i	0.835341	+	0.549732i	$0.185270\pi$
$480$	6.46923	+	2.17719i	0.295279	+	0.0993746i
$481$	2.71254	−	15.3836i	0.123681	−	0.701431i
$482$	−1.44306	+	0.525231i	−0.0657296	+	0.0239236i
$483$	8.38376	−	19.6605i	0.381474	−	0.894583i
$484$	0.122912	+	0.697067i	0.00558690	+	0.0316849i
$485$	26.8873	+	46.5701i	1.22089	+	2.11464i
$486$	15.1888	+	3.50717i	0.688978	+	0.159089i
$487$	−8.44716	+	14.6309i	−0.382777	+	0.662990i	−0.991458	−	0.130425i	$-0.958366\pi$
$487$	−8.44716	+	14.6309i	−0.382777	+	0.662990i	0.608681	+	0.793415i	$0.291699\pi$
$488$	−7.90237	+	6.63088i	−0.357724	+	0.300166i
$489$	7.21095	−	0.176181i	0.326090	−	0.00796719i
$490$	23.6430	−	14.2125i	1.06808	−	0.642057i
$491$	−1.49431	−	1.25388i	−0.0674373	−	0.0565866i	0.608446	−	0.793595i	$-0.291793\pi$
$491$	−1.49431	−	1.25388i	−0.0674373	−	0.0565866i	−0.675883	+	0.737009i	$0.736238\pi$
$492$	3.91868	−	3.45473i	0.176668	−	0.155751i
$493$	6.48636	−	5.44270i	0.292131	−	0.245127i
$494$	1.96489			0.0884044
$495$	−21.9132	−	34.0037i	−0.984926	−	1.52835i
$496$	2.57227	−	4.45531i	0.115499	−	0.200049i
$497$	−2.42982	−	8.75827i	−0.108992	−	0.392862i
$498$	−1.75109	+	0.686229i	−0.0784680	+	0.0307506i
$499$	3.77275	−	1.37317i	0.168892	−	0.0614715i	−0.256191	−	0.966626i	$-0.582467\pi$
$499$	3.77275	−	1.37317i	0.168892	−	0.0614715i	0.425082	+	0.905155i	$0.360245\pi$
$500$	16.6955	+	14.0092i	0.746644	+	0.626509i
$501$	−25.3874	+	9.94900i	−1.13422	+	0.444489i
$502$	8.15226	+	2.96718i	0.363853	+	0.132432i
$503$	11.6682	−	20.2098i	0.520257	−	0.901112i	−0.479465	−	0.877561i	$-0.659169\pi$
$503$	11.6682	−	20.2098i	0.520257	−	0.901112i	0.999723	−	0.0235513i	$-0.00749732\pi$
$504$	2.49288	+	7.53562i	0.111042	+	0.335663i
$505$	−2.57013	−	4.45160i	−0.114369	−	0.198094i
$506$	−2.77123	−	15.7164i	−0.123196	−	0.698679i
$507$	14.2101	−	12.5277i	0.631091	−	0.556374i
$508$	1.27971	−	0.465777i	0.0567781	−	0.0206655i
$509$	7.91051	+	6.63771i	0.350627	+	0.294211i	0.801042	−	0.598608i	$-0.204279\pi$
$509$	7.91051	+	6.63771i	0.350627	+	0.294211i	−0.450415	+	0.892820i	$0.648724\pi$
$510$	−26.5836	−	43.5517i	−1.17714	−	1.92850i
$511$	4.07770	−	4.15032i	0.180387	−	0.183599i
$512$	−1.00000			−0.0441942
$513$	−0.908283	+	1.87877i	−0.0401017	+	0.0829498i
$514$	5.64773	−	9.78216i	0.249111	−	0.431473i
$515$	30.3045	+	11.0299i	1.33537	+	0.486037i
$516$	−6.86373	+	0.167698i	−0.302159	+	0.00738248i
$517$	−3.58551	+	1.30502i	−0.157690	+	0.0573946i
$518$	−0.661932	+	8.42133i	−0.0290836	+	0.370012i
$519$	−31.1234	+	27.4386i	−1.36617	+	1.20442i
$520$	3.34810	+	18.9880i	0.146824	+	0.832679i
$521$	7.83528			0.343270			0.171635	−	0.985161i	$-0.445095\pi$
$521$	7.83528			0.343270			0.171635	+	0.985161i	$0.445095\pi$
$522$	0.425952	−	3.37138i	0.0186434	−	0.147561i
$523$	1.12143			0.0490366			0.0245183	−	0.999699i	$-0.492195\pi$
$523$	1.12143			0.0490366			0.0245183	+	0.999699i	$0.492195\pi$
$524$	−13.7404	+	11.5296i	−0.600252	+	0.503671i
$525$	−2.60519	+	48.1858i	−0.113700	+	2.10300i
$526$	1.42830	−	8.10028i	0.0622767	−	0.353189i
$527$	−36.1373	+	13.1529i	−1.57416	+	0.572949i
$528$	4.63166	+	3.69746i	0.201567	+	0.160911i
$529$	−0.216467	−	1.22764i	−0.00941159	−	0.0533758i
$530$	43.0875			1.87160
$531$	8.20796	+	6.23036i	0.356195	+	0.270375i
$532$	−1.05765	+	0.101946i	−0.0458549	+	0.00441991i
$533$	13.8667	+	5.04707i	0.600634	+	0.218613i
$534$	5.41891	+	1.82371i	0.234499	+	0.0789195i
$535$	−52.9819	+	19.2838i	−2.29061	+	0.833713i
$536$	−0.369321	+	2.09452i	−0.0159522	+	0.0904696i
$537$	19.0527	−	0.465504i	0.822185	−	0.0200880i
$538$	4.80123	+	27.2291i	0.206996	+	1.17393i
$539$	23.5107	−	4.57486i	1.01268	−	0.197053i
$540$	−19.7035	−	5.57598i	−0.847904	−	0.239952i
$541$	−9.55597	−	16.5514i	−0.410843	−	0.711602i	0.584139	−	0.811654i	$-0.301432\pi$
$541$	−9.55597	−	16.5514i	−0.410843	−	0.711602i	−0.994982	+	0.100052i	$0.968099\pi$
$542$	−15.6933	−	5.71191i	−0.674087	−	0.245348i
$543$	−1.73819	+	0.0424683i	−0.0745930	+	0.00182249i
$544$	5.72632	+	4.80496i	0.245514	+	0.206011i
$545$	28.2341	+	23.6912i	1.20942	+	1.01482i
$546$	−15.3179	+	16.3721i	−0.655544	+	0.700660i
$547$	8.34510	+	3.03737i	0.356811	+	0.129868i	0.514205	−	0.857667i	$-0.328087\pi$
$547$	8.34510	+	3.03737i	0.356811	+	0.129868i	−0.157394	+	0.987536i	$0.550309\pi$
$548$	6.12225	−	10.6040i	0.261530	−	0.452982i
$549$	22.7074	−	21.0267i	0.969126	−	0.897396i
$550$	18.0157	+	31.2041i	0.768193	+	1.33055i
$551$	0.427476	+	0.155588i	0.0182111	+	0.00662829i
$552$	−6.31339	−	5.03998i	−0.268716	−	0.214516i
$553$	−3.36839	+	42.8538i	−0.143239	+	1.82233i
$554$	−4.46825	+	25.3407i	−0.189838	+	1.07662i
$555$	−17.0317	−	13.5964i	−0.722956	−	0.577137i
$556$	0.969236	+	5.49681i	0.0411048	+	0.233117i
$557$	13.8003	+	23.9029i	0.584739	+	1.01280i	0.994908	+	0.100788i	$0.0321364\pi$
$557$	13.8003	+	23.9029i	0.584739	+	1.01280i	−0.410169	+	0.912010i	$0.634530\pi$
$558$	−7.05488	+	13.7268i	−0.298657	+	0.581104i
$559$	−9.69697	−	16.7956i	−0.410138	−	0.710380i
$560$	−2.78737	−	10.0470i	−0.117788	−	0.424565i
$561$	−8.75626	−	43.4278i	−0.369689	−	1.83352i
$562$	0.347403	−	1.97022i	0.0146543	−	0.0831088i
$563$	3.49757	−	19.8357i	0.147405	−	0.835974i	−0.818000	−	0.575218i	$-0.804917\pi$
$563$	3.49757	−	19.8357i	0.147405	−	0.835974i	0.965405	−	0.260756i	$-0.0839718\pi$
$564$	−0.924589	+	1.69579i	−0.0389322	+	0.0714056i
$565$	−16.9786	+	14.2467i	−0.714296	+	0.599365i
$566$	−26.6510			−1.12022
$567$	−8.57374	−	22.2147i	−0.360063	−	0.932928i
$568$	−3.43535			−0.144144
$569$	26.7988	−	22.4869i	1.12346	−	0.942698i	0.124690	−	0.992196i	$-0.460206\pi$
$569$	26.7988	−	22.4869i	1.12346	−	0.942698i	0.998774	+	0.0494973i	$0.0157619\pi$
$570$	1.31224	−	2.40678i	0.0549637	−	0.100809i
$571$	4.69403	−	26.6212i	0.196439	−	1.11406i	−0.713915	−	0.700232i	$-0.753080\pi$
$571$	4.69403	−	26.6212i	0.196439	−	1.11406i	0.910355	−	0.413829i	$-0.135809\pi$
$572$	−2.90700	+	16.4864i	−0.121548	+	0.689332i
$573$	−0.526320	−	2.61035i	−0.0219873	−	0.109049i
$574$	−7.72596	−	1.99725i	−0.322476	−	0.0833637i
$575$	−24.5571	−	42.5342i	−1.02410	−	1.77380i
$576$	2.99642	−	0.146507i	0.124851	−	0.00610447i
$577$	6.64756	+	11.5139i	0.276741	+	0.479330i	0.970573	−	0.240807i	$-0.0774121\pi$
$577$	6.64756	+	11.5139i	0.276741	+	0.479330i	−0.693832	+	0.720137i	$0.744079\pi$
$578$	−6.75116	−	38.2878i	−0.280811	−	1.59256i
$579$	24.5612	+	19.6072i	1.02073	+	0.814848i
$580$	−0.775151	+	4.39610i	−0.0321864	+	0.182538i
$581$	2.36778	+	1.62699i	0.0982322	+	0.0674988i
$582$	18.4708	+	14.7452i	0.765637	+	0.611209i
$583$	35.1548	+	12.7953i	1.45596	+	0.529927i
$584$	−1.09956	−	1.90449i	−0.0455001	−	0.0788084i
$585$	−12.8142	−	56.4055i	−0.529801	−	2.33208i
$586$	−10.6511	+	18.4482i	−0.439991	+	0.762087i
$587$	−32.7194	−	11.9089i	−1.35047	−	0.491533i	−0.437379	−	0.899277i	$-0.644093\pi$
$587$	−32.7194	−	11.9089i	−1.35047	−	0.491533i	−0.913096	+	0.407745i	$0.866315\pi$
$588$	7.39578	−	9.60742i	0.304997	−	0.396203i
$589$	−1.58271	−	1.32805i	−0.0652145	−	0.0547214i
$590$	−10.3696	−	8.70111i	−0.426909	−	0.358219i
$591$	20.9275	−	0.511309i	0.860840	−	0.0210324i
$592$	3.00023	+	1.09200i	0.123309	+	0.0448807i
$593$	−0.406959	−	0.704873i	−0.0167118	−	0.0289457i	0.857549	−	0.514403i	$-0.171986\pi$
$593$	−0.406959	−	0.704873i	−0.0167118	−	0.0289457i	−0.874260	+	0.485457i	$0.838653\pi$
$594$	−14.4201	−	10.4006i	−0.591664	−	0.426740i
$595$	−32.3143	+	70.9258i	−1.32476	+	2.90768i
$596$	−2.83428	−	16.0740i	−0.116097	−	0.658418i
$597$	1.65262	−	0.0403775i	0.0676371	−	0.00165254i
$598$	3.96251	−	22.4725i	0.162039	−	0.918970i
$599$	7.18438	−	2.61490i	0.293546	−	0.106842i	−0.191050	−	0.981580i	$-0.561189\pi$
$599$	7.18438	−	2.61490i	0.293546	−	0.106842i	0.484595	+	0.874738i	$0.338967\pi$
$600$	17.2864	+	5.81766i	0.705716	+	0.237505i
$601$	30.4980	+	11.1004i	1.24404	+	0.452793i	0.878383	−	0.477957i	$-0.158622\pi$
$601$	30.4980	+	11.1004i	1.24404	+	0.452793i	0.365656	+	0.930750i	$0.380845\pi$
$602$	6.09105	+	8.53755i	0.248253	+	0.347965i
$603$	0.799778	−	6.33018i	0.0325695	−	0.257785i
$604$	11.0342			0.448975
$605$	0.484378	+	2.74704i	0.0196928	+	0.111683i
$606$	−1.76560	−	1.40948i	−0.0717228	−	0.0572564i
$607$	−41.5419	+	15.1200i	−1.68613	+	0.613702i	−0.994130	−	0.108193i	$-0.965493\pi$
$607$	−41.5419	+	15.1200i	−1.68613	+	0.613702i	−0.692002	+	0.721895i	$0.743271\pi$
$608$	−0.0697382	+	0.395505i	−0.00282826	+	0.0160398i
$609$	−4.62893	+	2.34893i	−0.187574	+	0.0951834i
$610$	−31.1421	+	26.1314i	−1.26091	+	1.05803i
$611$	−5.45586			−0.220721
$612$	−17.8624	−	13.5587i	−0.722046	−	0.548079i
$613$	−32.7897			−1.32436			−0.662182	−	0.749343i	$-0.730369\pi$
$613$	−32.7897			−1.32436			−0.662182	+	0.749343i	$0.730369\pi$
$614$	2.27886	+	12.9241i	0.0919674	+	0.521573i
$615$	15.4430	−	13.6146i	0.622720	−	0.548994i
$616$	0.709386	−	9.02505i	0.0285820	−	0.363630i
$617$	−6.94319	+	2.52711i	−0.279522	+	0.101738i	−0.477977	−	0.878372i	$-0.658630\pi$
$617$	−6.94319	+	2.52711i	−0.279522	+	0.101738i	0.198455	+	0.980110i	$0.436408\pi$
$618$	14.1697	−	0.346201i	0.569989	−	0.0139262i
$619$	43.5369	+	15.8461i	1.74990	+	0.636910i	0.999704	−	0.0243091i	$-0.00773858\pi$
$619$	43.5369	+	15.8461i	1.74990	+	0.636910i	0.750193	+	0.661219i	$0.229961\pi$
$620$	10.1370	−	17.5578i	0.407111	−	0.705136i
$621$	19.6560	+	14.1769i	0.788766	+	0.568901i
$622$	23.5461			0.944114
$623$	−2.33482	−	8.41584i	−0.0935425	−	0.337173i
$624$	4.41508	+	7.23317i	0.176745	+	0.289559i
$625$	25.4609	+	21.3642i	1.01843	+	0.854568i
$626$	2.70678	−	0.985189i	0.108185	−	0.0393761i
$627$	1.78537	−	1.57399i	0.0713006	−	0.0628591i
$628$	−2.34598	−	13.3047i	−0.0936147	−	0.530915i
$629$	−11.9333	−	20.6691i	−0.475812	−	0.824131i
$630$	9.82409	+	29.6968i	0.391401	+	1.18315i
$631$	−4.12433	+	7.14355i	−0.164187	+	0.284380i	−0.936366	−	0.351025i	$-0.885833\pi$
$631$	−4.12433	+	7.14355i	−0.164187	+	0.284380i	0.772179	+	0.635405i	$0.219167\pi$
$632$	15.2674	+	5.55686i	0.607303	+	0.221040i
$633$	25.5147	−	9.99889i	1.01412	−	0.397420i
$634$	0.766578	+	0.643236i	0.0304447	+	0.0255462i
$635$	5.04317	−	1.83556i	0.200132	−	0.0728421i
$636$	17.6319	−	6.90971i	0.699149	−	0.273988i
$637$	33.8274	+	5.35085i	1.34029	+	0.212008i
$638$	−1.93791	+	3.35656i	−0.0767225	+	0.132887i
$639$	10.2937	−	0.503303i	0.407214	−	0.0199104i
$640$	−3.94086			−0.155776
$641$	−16.4036	+	13.7643i	−0.647904	+	0.543656i	−0.906434	−	0.422347i	$-0.861206\pi$
$641$	−16.4036	+	13.7643i	−0.647904	+	0.543656i	0.258530	+	0.966003i	$0.416762\pi$
$642$	−18.5883	+	16.3876i	−0.733622	+	0.646766i
$643$	16.9584	+	14.2298i	0.668775	+	0.561169i	0.912703	−	0.408625i	$-0.133991\pi$
$643$	16.9584	+	14.2298i	0.668775	+	0.561169i	−0.243928	+	0.969793i	$0.578436\pi$
$644$	−0.966959	+	12.3020i	−0.0381035	+	0.484766i
$645$	−27.0490	+	0.660873i	−1.06505	+	0.0260218i
$646$	2.29973	−	1.92970i	0.0904815	−	0.0759230i
$647$	9.06473	−	15.7006i	0.356371	−	0.617253i	−0.630980	−	0.775799i	$-0.717347\pi$
$647$	9.06473	−	15.7006i	0.356371	−	0.617253i	0.987352	+	0.158546i	$0.0506805\pi$
$648$	−8.95707	+	0.877995i	−0.351867	+	0.0344909i
$649$	−5.87658	−	10.1785i	−0.230676	−	0.399542i
$650$	8.94645	+	50.7378i	0.350909	+	1.99010i
$651$	23.4043	−	2.83442i	0.917286	−	0.111090i
$652$	−3.91334	+	1.42434i	−0.153258	+	0.0557814i
$653$	5.97090	−	33.8627i	0.233659	−	1.32515i	−0.611759	−	0.791044i	$-0.709538\pi$
$653$	5.97090	−	33.8627i	0.233659	−	1.32515i	0.845419	−	0.534104i	$-0.179351\pi$
$654$	15.3529	+	5.16695i	0.600347	+	0.202044i
$655$	−54.1489	+	45.4364i	−2.11577	+	1.77535i
$656$	−1.50807	+	2.61205i	−0.0588802	+	0.101983i
$657$	3.57376	+	5.54556i	0.139426	+	0.216353i
$658$	2.93675	−	0.283071i	0.114487	−	0.0110353i
$659$	−23.6717	+	19.8629i	−0.922120	+	0.773751i	−0.974386	−	0.224883i	$-0.927800\pi$
$659$	−23.6717	+	19.8629i	−0.922120	+	0.773751i	0.0522658	+	0.998633i	$0.483356\pi$
$660$	18.2527	+	14.5712i	0.710486	+	0.567182i
$661$	−5.23277	−	4.39081i	−0.203531	−	0.170783i	0.535325	−	0.844646i	$-0.320189\pi$
$661$	−5.23277	−	4.39081i	−0.203531	−	0.170783i	−0.738856	+	0.673863i	$0.764634\pi$
$662$	5.66595	+	4.75430i	0.220213	+	0.184781i
$663$	9.47291	−	62.6337i	0.367897	−	2.43249i
$664$	0.831809	−	0.697971i	0.0322805	−	0.0270865i
$665$	−4.16804	+	0.401754i	−0.161630	+	0.0155794i
$666$	−9.14994	−	2.83252i	−0.354553	−	0.109758i
$667$	2.64155	−	4.57530i	0.102281	−	0.177156i
$668$	12.0596	−	10.1192i	0.466601	−	0.391525i
$669$	16.2247	−	14.3038i	0.627283	−	0.553016i
$670$	−1.45544	+	8.25422i	−0.0562286	+	0.318888i
$671$	−33.1686	+	12.0724i	−1.28046	+	0.466049i
$672$	−2.75181	−	3.66436i	−0.106153	−	0.141356i
$673$	5.04760	+	28.6264i	0.194571	+	1.10347i	0.913029	+	0.407895i	$0.133737\pi$
$673$	5.04760	+	28.6264i	0.194571	+	1.10347i	−0.718458	+	0.695570i	$0.755152\pi$
$674$	0.310139	+	0.537176i	0.0119461	+	0.0206913i
$675$	−52.6498	−	14.8996i	−2.02649	−	0.573485i
$676$	−5.46861	+	9.47191i	−0.210331	+	0.364304i
$677$	25.9253	−	21.7539i	0.996390	−	0.836070i	0.00990959	−	0.999951i	$-0.496846\pi$
$677$	25.9253	−	21.7539i	0.996390	−	0.836070i	0.986480	+	0.163881i	$0.0524012\pi$
$678$	−4.66315	+	8.55268i	−0.179087	+	0.328464i
$679$	2.82898	−	35.9913i	0.108566	−	1.38122i
$680$	22.5666	+	18.9357i	0.865391	+	0.726149i
$681$	−37.1411	−	12.4997i	−1.42325	−	0.478988i
$682$	13.4846	−	11.3150i	0.516354	−	0.433272i
$683$	7.54155			0.288569			0.144285	−	0.989536i	$-0.453912\pi$
$683$	7.54155			0.288569			0.144285	+	0.989536i	$0.453912\pi$
$684$	0.151021	−	1.19532i	0.00577441	−	0.0457040i
$685$	24.1269	−	41.7890i	0.921842	−	1.59668i
$686$	−18.4861	−	1.12513i	−0.705801	−	0.0429577i
$687$	−3.41466	+	22.5773i	−0.130277	+	0.861377i
$688$	3.72490	−	1.35575i	0.142011	−	0.0516876i
$689$	40.9781	+	34.3847i	1.56114	+	1.30995i
$690$	−24.8802	−	19.8619i	−0.947172	−	0.756128i
$691$	15.2534	+	5.55177i	0.580266	+	0.211199i	0.615443	−	0.788182i	$-0.288977\pi$
$691$	15.2534	+	5.55177i	0.580266	+	0.211199i	−0.0351770	+	0.999381i	$0.511200\pi$
$692$	11.9776	−	20.7457i	0.455318	−	0.788634i
$693$	−0.803382	+	27.1468i	−0.0305180	+	1.03122i
$694$	−2.63680	−	4.56707i	−0.100091	−	0.173363i
$695$	3.81962	+	21.6622i	0.144887	+	0.821692i
$696$	0.387778	+	1.92324i	0.0146987	+	0.0729001i
$697$	21.1865	−	7.71125i	0.802495	−	0.292084i
$698$	19.3347	+	16.2237i	0.731829	+	0.614077i
$699$	10.3828	−	19.0431i	0.392713	−	0.720275i
$700$	−7.44812	−	26.8467i	−0.281513	−	1.01471i
$701$	−22.5406			−0.851348			−0.425674	−	0.904877i	$-0.639963\pi$
$701$	−22.5406			−0.851348			−0.425674	+	0.904877i	$0.639963\pi$
$702$	−14.2891	−	21.0268i	−0.539309	−	0.793605i
$703$	0.641120	−	1.11045i	0.0241803	−	0.0418815i
$704$	−3.21532	−	1.17028i	−0.121182	−	0.0441066i
$705$	−3.64368	+	6.68286i	−0.137229	+	0.251691i
$706$	−2.25447	+	0.820562i	−0.0848483	+	0.0308822i
$707$	−0.270420	+	3.44038i	−0.0101702	+	0.129389i
$708$	−5.63869	−	1.89767i	−0.211915	−	0.0713189i
$709$	3.77791	+	21.4256i	0.141882	+	0.804656i	0.969818	+	0.243832i	$0.0784044\pi$
$709$	3.77791	+	21.4256i	0.141882	+	0.804656i	−0.827935	+	0.560824i	$0.810484\pi$
$710$	−13.5382			−0.508080
$711$	−46.5615	−	14.4139i	−1.74619	−	0.540564i
$712$	−3.30103			−0.123711
$713$	−18.3808	+	15.4233i	−0.688367	+	0.577609i
$714$	−1.84935	+	34.2056i	−0.0692101	+	1.28011i
$715$	−11.4561	+	64.9707i	−0.428433	+	2.42976i
$716$	−10.3398	+	3.76337i	−0.386416	+	0.140644i
$717$	−5.88498	+	38.9108i	−0.219779	+	1.45315i
$718$	2.88284	+	16.3494i	0.107587	+	0.610155i
$719$	10.6086			0.395635			0.197817	−	0.980239i	$-0.436615\pi$
$719$	10.6086			0.395635			0.197817	+	0.980239i	$0.436615\pi$
$720$	11.8085	−	0.577364i	0.440076	−	0.0215171i
$721$	−12.5746	−	17.6252i	−0.468302	−	0.656397i
$722$	−17.7026	−	6.44322i	−0.658823	−	0.239792i
$723$	−1.99521	+	1.75899i	−0.0742025	+	0.0654174i
$724$	0.943306	−	0.343335i	0.0350577	−	0.0127600i
$725$	−2.07128	+	11.7468i	−0.0769254	+	0.436266i
$726$	0.638741	+	1.04644i	0.0237059	+	0.0388371i
$727$	−2.40713	−	13.6515i	−0.0892755	−	0.506306i	−0.996352	−	0.0853404i	$-0.972802\pi$
$727$	−2.40713	−	13.6515i	−0.0892755	−	0.506306i	0.907076	−	0.420966i	$-0.138309\pi$
$728$	5.36683	−	11.7795i	0.198908	−	0.436579i
$729$	26.7105	−	3.94312i	0.989278	−	0.146041i
$730$	−4.33321	−	7.50533i	−0.160379	−	0.277785i
$731$	−27.8443	−	10.1345i	−1.02986	−	0.374838i
$732$	−8.55314	+	15.6873i	−0.316133	+	0.579820i
$733$	−14.8661	−	12.4742i	−0.549094	−	0.460744i	0.325540	−	0.945528i	$-0.394454\pi$
$733$	−14.8661	−	12.4742i	−0.549094	−	0.460744i	−0.874634	+	0.484784i	$0.838898\pi$
$734$	−7.18380	−	6.02793i	−0.265159	−	0.222495i
$735$	29.1457	−	37.8615i	1.07506	−	1.39654i
$736$	4.38278	+	1.59520i	0.161551	+	0.0587999i
$737$	−3.63866	+	6.30235i	−0.134032	+	0.232150i
$738$	4.13612	−	8.04774i	0.152253	−	0.296242i
$739$	−19.6522	−	34.0386i	−0.722918	−	1.25213i	−0.959825	−	0.280598i	$-0.909467\pi$
$739$	−19.6522	−	34.0386i	−0.722918	−	1.25213i	0.236908	−	0.971532i	$-0.423866\pi$
$740$	11.8235	+	4.30340i	0.434640	+	0.158196i
$741$	3.16865	−	1.24176i	0.116403	−	0.0456170i
$742$	−23.8415	−	16.3823i	−0.875248	−	0.601413i
$743$	−1.64288	+	9.31724i	−0.0602715	+	0.341816i	−1.00000		0.000104995i	$-0.999967\pi$
$743$	−1.64288	+	9.31724i	−0.0602715	+	0.341816i	0.939729	+	0.341921i	$0.111078\pi$
$744$	1.33251	−	8.81042i	0.0488524	−	0.323006i
$745$	−11.1695	−	63.3454i	−0.409219	−	2.32080i
$746$	−13.1843	−	22.8359i	−0.482712	−	0.836082i
$747$	−2.39019	+	2.21328i	−0.0874526	+	0.0809797i
$748$	12.7888	+	22.1509i	0.467605	+	0.809916i
$749$	36.6482	+	9.47399i	1.33910	+	0.346172i
$750$	35.7772	+	12.0406i	1.30640	+	0.439662i
$751$	−1.54976	+	8.78914i	−0.0565516	+	0.320720i	−0.999940	−	0.0109704i	$-0.996508\pi$
$751$	−1.54976	+	8.78914i	−0.0565516	+	0.320720i	0.943388	+	0.331691i	$0.107619\pi$
$752$	0.193641	−	1.09819i	0.00706135	−	0.0400469i
$753$	15.0219	−	0.367021i	0.547427	−	0.0133750i
$754$	−4.24537	+	3.56229i	−0.154607	+	0.129731i
$755$	43.4842			1.58255
$756$	8.78243	+	10.5768i	0.319414	+	0.384675i
$757$	−46.7158			−1.69791			−0.848957	−	0.528462i	$-0.822769\pi$
$757$	−46.7158			−1.69791			−0.848957	+	0.528462i	$0.822769\pi$
$758$	−16.7292	+	14.0375i	−0.607633	+	0.509865i
$759$	−14.4013	−	23.5936i	−0.522736	−	0.856392i
$760$	−0.274828	+	1.55863i	−0.00996907	+	0.0565374i
$761$	0.791348	−	4.48796i	0.0286863	−	0.162688i	−0.967099	−	0.254399i	$-0.918122\pi$
$761$	0.791348	−	4.48796i	0.0286863	−	0.162688i	0.995786	+	0.0917107i	$0.0292335\pi$
$762$	1.76936	−	1.55988i	0.0640971	−	0.0565084i
$763$	−6.61504	−	23.8439i	−0.239480	−	0.863206i
$764$	0.768708	+	1.33144i	0.0278109	+	0.0481699i
$765$	−70.3933	−	53.4330i	−2.54508	−	1.93187i
$766$	−19.3095	−	33.4451i	−0.697682	−	1.20842i
$767$	−2.91826	−	16.5503i	−0.105372	−	0.597595i
$768$	−1.61264	+	0.631974i	−0.0581911	+	0.0228044i
$769$	4.65375	−	26.3927i	0.167818	−	0.951745i	−0.778292	−	0.627902i	$-0.783914\pi$
$769$	4.65375	−	26.3927i	0.167818	−	0.951745i	0.946111	−	0.323843i	$-0.104975\pi$
$770$	2.79559	−	35.5664i	0.100746	−	1.28173i
$771$	2.92569	−	19.3443i	0.105366	−	0.696669i
$772$	−17.0505	−	6.20587i	−0.613660	−	0.223354i
$773$	3.54966	+	6.14819i	0.127672	+	0.221135i	0.922774	−	0.385341i	$-0.125916\pi$
$773$	3.54966	+	6.14819i	0.127672	+	0.221135i	−0.795102	+	0.606476i	$0.792583\pi$
$774$	−10.9627	+	4.60813i	−0.394048	+	0.165636i
$775$	27.0870	−	46.9161i	0.972994	−	1.68527i
$776$	−12.8225	−	4.66700i	−0.460300	−	0.167536i
$777$	4.25460	+	13.9989i	0.152633	+	0.502208i
$778$	13.3249	+	11.1809i	0.477719	+	0.400854i
$779$	0.927909	+	0.778608i	0.0332458	+	0.0278965i
$780$	17.3992	+	28.5049i	0.622991	+	1.02064i
$781$	−11.0457	−	4.02032i	−0.395247	−	0.143858i
$782$	−17.4323	−	30.1937i	−0.623379	−	1.07972i
$783$	−1.44372	−	5.70601i	−0.0515942	−	0.203916i
$784$	−2.27766	+	6.61908i	−0.0813451	+	0.236396i
$785$	−9.24516	−	52.4319i	−0.329974	−	1.87138i
$786$	−14.8719	+	27.2766i	−0.530464	+	0.972924i
$787$	−4.05383	+	22.9904i	−0.144504	+	0.819520i	0.823261	+	0.567663i	$0.192152\pi$
$787$	−4.05383	+	22.9904i	−0.144504	+	0.819520i	−0.967764	+	0.251857i	$0.918959\pi$
$788$	−11.3572	+	4.13368i	−0.404583	+	0.147256i
$789$	−2.81583	−	13.9655i	−0.100246	−	0.497184i
$790$	60.1665	+	21.8988i	2.14063	+	0.779125i
$791$	14.8115	−	1.42767i	0.526635	−	0.0507620i
$792$	9.80590	+	3.03558i	0.348437	+	0.107865i
$793$	−50.4708			−1.79227
$794$	4.62442	+	26.2264i	0.164115	+	0.930740i
$795$	69.4847	−	27.2302i	2.46437	−	0.965755i
$796$	−0.896864	+	0.326432i	−0.0317885	+	0.0115701i
$797$	3.31354	−	18.7920i	0.117372	−	0.665648i	−0.868177	−	0.496255i	$-0.834708\pi$
$797$	3.31354	−	18.7920i	0.117372	−	0.665648i	0.985549	−	0.169393i	$-0.0541807\pi$
$798$	−1.64118	+	0.832808i	−0.0580971	+	0.0294811i
$799$	−6.38561	+	5.35817i	−0.225907	+	0.189558i
$800$	−10.5304			−0.372305
$801$	9.89128	−	0.483625i	0.349491	−	0.0170881i
$802$	−20.2698			−0.715752
$803$	−1.30664	−	7.41034i	−0.0461104	−	0.261505i
$804$	0.728102	+	3.61111i	0.0256782	+	0.127354i
$805$	−3.81065	+	48.4804i	−0.134308	+	1.70871i
$806$	23.6521	−	8.60867i	0.833110	−	0.303227i
$807$	24.9508	+	40.8766i	0.878309	+	1.43892i
$808$	1.22569	+	0.446115i	0.0431196	+	0.0156943i
$809$	6.30348	−	10.9179i	0.221619	−	0.383855i	−0.733681	−	0.679494i	$-0.762199\pi$
$809$	6.30348	−	10.9179i	0.221619	−	0.383855i	0.955300	+	0.295639i	$0.0955327\pi$
$810$	−35.2986	+	3.46005i	−1.24026	+	0.121574i
$811$	−28.3161			−0.994311			−0.497156	−	0.867661i	$-0.665622\pi$
$811$	−28.3161			−0.994311			−0.497156	+	0.867661i	$0.665622\pi$
$812$	2.10035	−	2.13776i	0.0737079	−	0.0750206i
$813$	−28.9175	+	0.706525i	−1.01418	+	0.0247789i
$814$	8.36876	+	7.02222i	0.293325	+	0.246129i
$815$	−15.4219	+	5.61311i	−0.540206	+	0.196619i
$816$	12.2711	+	4.12978i	0.429575	+	0.144571i
$817$	−0.276439	−	1.56776i	−0.00967138	−	0.0548491i
$818$	−0.310122	−	0.537148i	−0.0108432	−	0.0187809i
$819$	−14.3555	+	36.0827i	−0.501622	+	1.26083i
$820$	−5.94308	+	10.2937i	−0.207541	+	0.359472i
$821$	−11.3293	−	4.12352i	−0.395395	−	0.143912i	0.136668	−	0.990617i	$-0.456361\pi$
$821$	−11.3293	−	4.12352i	−0.395395	−	0.143912i	−0.532063	+	0.846705i	$0.678583\pi$
$822$	3.17151	−	20.9696i	0.110619	−	0.731399i
$823$	−10.7129	−	8.98922i	−0.373429	−	0.313344i	0.436687	−	0.899613i	$-0.356152\pi$
$823$	−10.7129	−	8.98922i	−0.373429	−	0.313344i	−0.810116	+	0.586269i	$0.800596\pi$
$824$	−7.68981	+	2.79886i	−0.267887	+	0.0975030i
$825$	48.7731	+	38.9356i	1.69806	+	1.35556i
$826$	2.42951	+	8.75717i	0.0845336	+	0.304701i
$827$	−5.96830	+	10.3374i	−0.207538	+	0.359467i	−0.950938	−	0.309380i	$-0.899878\pi$
$827$	−5.96830	+	10.3374i	−0.207538	+	0.359467i	0.743400	+	0.668847i	$0.233212\pi$
$828$	−13.3664	−	4.13778i	−0.464513	−	0.143798i
$829$	−4.51715			−0.156887			−0.0784435	−	0.996919i	$-0.524995\pi$
$829$	−4.51715			−0.156887			−0.0784435	+	0.996919i	$0.524995\pi$
$830$	3.27804	−	2.75060i	0.113783	−	0.0954749i
$831$	8.80899	+	43.6893i	0.305580	+	1.51556i
$832$	−3.74792	−	3.14488i	−0.129936	−	0.109029i
$833$	44.8470	−	26.9589i	1.55386	−	0.934072i
$834$	5.03687	+	8.25185i	0.174413	+	0.285738i
$835$	47.5253	−	39.8785i	1.64468	−	1.38005i
$836$	−0.687082	+	1.19006i	−0.0237632	+	0.0411591i
$837$	−2.70198	+	26.5950i	−0.0933942	+	0.919256i
$838$	3.86533	+	6.69495i	0.133526	+	0.231273i
$839$	−1.41516	−	8.02576i	−0.0488567	−	0.277080i	0.950586	−	0.310461i	$-0.100484\pi$
$839$	−1.41516	−	8.02576i	−0.0488567	−	0.277080i	−0.999443	+	0.0333813i	$0.989372\pi$
$840$	−10.8445	−	14.4407i	−0.374170	−	0.498253i
$841$	26.0454	−	9.47975i	0.898117	−	0.326888i
$842$	0.0785954	−	0.445737i	0.00270858	−	0.0153611i
$843$	−0.684892	−	3.39681i	−0.0235889	−	0.116992i
$844$	−12.1201	+	10.1700i	−0.417192	+	0.350065i
$845$	−21.5510	+	37.3275i	−0.741378	+	1.28410i
$846$	−0.419336	+	3.31901i	−0.0144171	+	0.114110i
$847$	0.776434	−	1.70418i	0.0266786	−	0.0585562i
$848$	−8.37557	+	7.02794i	−0.287618	+	0.241340i
$849$	−42.9784	+	16.8427i	−1.47502	+	0.578041i
$850$	60.3003	+	50.5980i	2.06828	+	1.73550i
$851$	−11.4074	−	9.57195i	−0.391041	−	0.328122i
$852$	−5.53998	+	2.17105i	−0.189797	+	0.0743789i
$853$	−26.4820	+	22.2210i	−0.906725	+	0.760833i	−0.971493	−	0.237067i	$-0.923814\pi$
$853$	−26.4820	+	22.2210i	−0.906725	+	0.760833i	0.0647678	+	0.997900i	$0.479369\pi$
$854$	27.1672	−	2.61862i	0.929641	−	0.0896074i
$855$	0.595151	−	4.71057i	0.0203537	−	0.161098i
$856$	7.15354	−	12.3903i	0.244503	−	0.423491i
$857$	−25.6208	+	21.4984i	−0.875188	+	0.734370i	−0.965184	−	0.261572i	$-0.915759\pi$
$857$	−25.6208	+	21.4984i	−0.875188	+	0.734370i	0.0899956	+	0.995942i	$0.471315\pi$
$858$	5.73104	+	28.4238i	0.195654	+	0.970373i
$859$	6.34566	−	35.9880i	0.216511	−	1.22790i	−0.661754	−	0.749721i	$-0.730188\pi$
$859$	6.34566	−	35.9880i	0.216511	−	1.22790i	0.878265	−	0.478174i	$-0.158701\pi$
$860$	14.6793	−	5.34283i	0.500560	−	0.182189i
$861$	−13.7214	+	1.66176i	−0.467624	+	0.0566325i
$862$	−6.41157	−	36.3618i	−0.218379	−	1.23849i
$863$	16.3210	+	28.2688i	0.555574	+	0.962282i	0.997859	+	0.0654076i	$0.0208348\pi$
$863$	16.3210	+	28.2688i	0.555574	+	0.962282i	−0.442285	+	0.896875i	$0.645832\pi$
$864$	4.73956	−	2.12992i	0.161243	−	0.0724614i
$865$	47.2018	−	81.7560i	1.60491	−	2.77979i
$866$	28.0923	−	23.5722i	0.954615	−	0.801017i
$867$	−35.0841	−	57.4778i	−1.19152	−	1.95205i
$868$	−12.2847	+	5.86099i	−0.416969	+	0.198935i
$869$	42.5863	+	35.7342i	1.44464	+	1.21220i
$870$	1.52818	+	7.57920i	0.0518102	+	0.256959i
$871$	−7.97121	+	6.68864i	−0.270094	+	0.226636i
$872$	−9.35253			−0.316717
$873$	39.1053	+	12.1057i	1.32351	+	0.409716i
$874$	0.936557	−	1.62216i	0.0316795	−	0.0548705i
$875$	−15.4152	−	55.5639i	−0.521128	−	1.87840i
$876$	−2.97678	−	2.37637i	−0.100576	−	0.0802900i
$877$	44.8679	−	16.3306i	1.51508	−	0.551445i	0.555168	−	0.831738i	$-0.312654\pi$
$877$	44.8679	−	16.3306i	1.51508	−	0.551445i	0.959915	+	0.280293i	$0.0904316\pi$
$878$	−16.9717	−	14.2409i	−0.572767	−	0.480609i
$879$	−5.51757	+	36.4815i	−0.186103	+	1.23049i
$880$	−12.6711	−	4.61191i	−0.427143	−	0.155467i
$881$	22.9571	−	39.7629i	0.773445	−	1.33965i	−0.162220	−	0.986755i	$-0.551865\pi$
$881$	22.9571	−	39.7629i	0.773445	−	1.33965i	0.935665	−	0.352891i	$-0.114801\pi$
$882$	5.85509	−	20.1672i	0.197151	−	0.679067i
$883$	−2.48770	−	4.30882i	−0.0837178	−	0.145003i	0.821126	−	0.570747i	$-0.193346\pi$
$883$	−2.48770	−	4.30882i	−0.0837178	−	0.145003i	−0.904844	+	0.425743i	$0.860013\pi$
$884$	6.35081	+	36.0172i	0.213601	+	1.21139i
$885$	−22.2213	−	7.47846i	−0.746960	−	0.251386i
$886$	−25.1817	+	9.16540i	−0.845997	+	0.307918i
$887$	11.0359	+	9.26018i	0.370548	+	0.310927i	0.808978	−	0.587839i	$-0.200021\pi$
$887$	11.0359	+	9.26018i	0.370548	+	0.310927i	−0.438430	+	0.898765i	$0.644465\pi$
$888$	5.52841	−	0.135073i	0.185521	−	0.00453274i
$889$	−3.48842	−	0.901797i	−0.116998	−	0.0302453i
$890$	−13.0089			−0.436059
$891$	−29.8273	−	7.65925i	−0.999253	−	0.256594i
$892$	−6.24392	+	10.8148i	−0.209062	+	0.362106i
$893$	−0.420836	−	0.153172i	−0.0140827	−	0.00512570i
$894$	−14.7290	−	24.1304i	−0.492613	−	0.807042i
$895$	−40.7476	+	14.8309i	−1.36204	+	0.495743i
$896$	2.18058	+	1.49835i	0.0728481	+	0.0500565i
$897$	−7.81194	−	38.7443i	−0.260833	−	1.29364i
$898$	−1.42050	−	8.05607i	−0.0474028	−	0.268834i
$899$	5.82737			0.194354
$900$	31.5534	−	1.54278i	1.05178	−	0.0514258i
$901$	81.7302			2.72283
$902$	−7.90575	+	6.63371i	−0.263233	+	0.220878i
$903$	15.2182	+	9.91861i	0.506430	+	0.330071i
$904$	0.976624	−	5.53871i	0.0324820	−	0.184215i
$905$	3.71744	−	1.35304i	0.123572	−	0.0449765i
$906$	17.7942	−	6.97332i	0.591172	−	0.231673i
$907$	−2.42403	−	13.7474i	−0.0804886	−	0.456473i	−0.998239	−	0.0593163i	$-0.981108\pi$
$907$	−2.42403	−	13.7474i	−0.0804886	−	0.456473i	0.917751	−	0.397157i	$-0.130003\pi$
$908$	22.6252			0.750845
$909$	−3.73804	−	1.15718i	−0.123983	−	0.0383811i
$910$	21.1499	−	46.4215i	0.701114	−	1.53886i
$911$	6.67210	+	2.42845i	0.221057	+	0.0804580i	0.450174	−	0.892941i	$-0.351362\pi$
$911$	6.67210	+	2.42845i	0.221057	+	0.0804580i	−0.229118	+	0.973399i	$0.573584\pi$
$912$	0.137486	+	0.681880i	0.00455262	+	0.0225793i
$913$	3.49135	−	1.27075i	0.115547	−	0.0420556i
$914$	0.322114	−	1.82680i	0.0106546	−	0.0604252i
$915$	−33.7067	+	61.8215i	−1.11431	+	2.04376i
$916$	−2.28925	−	12.9830i	−0.0756388	−	0.428969i
$917$	47.2374	−	4.55318i	1.55992	−	0.150359i
$918$	−37.3744	−	10.5768i	−1.23354	−	0.349085i
$919$	−26.5199	−	45.9338i	−0.874811	−	1.51522i	−0.856964	−	0.515376i	$-0.827652\pi$
$919$	−26.5199	−	45.9338i	−0.874811	−	1.51522i	−0.0178467	−	0.999841i	$-0.505681\pi$
$920$	17.2719	+	6.28646i	0.569438	+	0.207259i
$921$	11.8427	+	19.4017i	0.390229	+	0.639308i
$922$	−25.9939	−	21.8114i	−0.856062	−	0.718322i
$923$	−12.8754	−	10.8038i	−0.423800	−	0.355610i
$924$	−4.55961	−	15.0025i	−0.150000	−	0.493545i
$925$	31.5935	+	11.4991i	1.03879	+	0.378088i
$926$	−0.744859	+	1.29013i	−0.0244776	+	0.0423964i
$927$	22.6319	−	9.51319i	0.743328	−	0.312454i
$928$	−0.566363	−	0.980970i	−0.0185918	−	0.0322019i
$929$	7.64987	+	2.78432i	0.250984	+	0.0913507i	0.464449	−	0.885600i	$-0.346253\pi$
$929$	7.64987	+	2.78432i	0.250984	+	0.0913507i	−0.213465	+	0.976951i	$0.568475\pi$
$930$	5.25125	−	34.7206i	0.172195	−	1.13853i
$931$	2.45904	+	1.36243i	0.0805917	+	0.0446518i
$932$	−2.17451	+	12.3323i	−0.0712286	+	0.403957i
$933$	37.9715	−	14.8805i	1.24313	−	0.487167i
$934$	4.16455	+	23.6184i	0.136268	+	0.772816i
$935$	50.3989	+	87.2934i	1.64822	+	2.85480i
$936$	11.6911	+	8.87429i	0.382136	+	0.290065i
$937$	10.4893	+	18.1680i	0.342670	+	0.593522i	0.984928	−	0.172967i	$-0.0553354\pi$
$937$	10.4893	+	18.1680i	0.342670	+	0.593522i	−0.642258	+	0.766489i	$0.722002\pi$
$938$	3.94367	−	4.01390i	0.128765	−	0.131059i
$939$	3.74246	−	3.29937i	0.122130	−	0.107671i
$940$	0.763111	−	4.32782i	0.0248899	−	0.141158i
$941$	9.20701	−	52.2155i	0.300140	−	1.70218i	−0.345404	−	0.938454i	$-0.612258\pi$
$941$	9.20701	−	52.2155i	0.300140	−	1.70218i	0.645544	−	0.763723i	$-0.276631\pi$
$942$	−12.1914	−	19.9731i	−0.397218	−	0.650758i
$943$	10.7763	−	9.04237i	0.350924	−	0.294460i
$944$	3.43492			0.111797
$945$	34.6103	+	41.6817i	1.12587	+	1.35591i
$946$	13.5634			0.440983
$947$	8.40955	−	7.05645i	0.273274	−	0.229304i	−0.495843	−	0.868412i	$-0.665141\pi$
$947$	8.40955	−	7.05645i	0.273274	−	0.229304i	0.769117	+	0.639108i	$0.220696\pi$
$948$	28.1326	−	0.687347i	0.913703	−	0.0223240i
$949$	1.86834	−	10.5959i	0.0606488	−	0.343957i
$950$	−0.734369	+	4.16481i	−0.0238261	+	0.135124i
$951$	1.64272	+	0.552850i	0.0532690	+	0.0179274i
$952$	−5.28719	−	19.0577i	−0.171359	−	0.617662i
$953$	1.34851	+	2.33569i	0.0436825	+	0.0756603i	0.887040	−	0.461693i	$-0.152758\pi$
$953$	1.34851	+	2.33569i	0.0436825	+	0.0756603i	−0.843358	+	0.537353i	$0.819424\pi$
$954$	24.0671	−	22.2857i	0.779201	−	0.721528i
$955$	3.02937	+	5.24702i	0.0980281	+	0.169790i
$956$	−3.94540	−	22.3755i	−0.127603	−	0.723674i
$957$	−1.00389	+	6.63763i	−0.0324513	+	0.214564i
$958$	−2.17803	+	12.3522i	−0.0703690	+	0.399082i
$959$	−29.2387	+	13.9497i	−0.944166	+	0.450459i
$960$	−6.35519	+	2.49052i	−0.205113	+	0.0803812i
$961$	4.26020	+	1.55058i	0.137426	+	0.0500189i
$962$	7.81045	+	13.5281i	0.251819	+	0.436163i
$963$	−19.6197	+	38.1746i	−0.632237	+	1.23016i
$964$	0.767837	−	1.32993i	0.0247304	−	0.0428342i
$965$	−67.1935	−	24.4564i	−2.16304	−	0.787281i
$966$	6.21518	+	20.4498i	0.199970	+	0.657961i
$967$	12.4689	+	10.4626i	0.400972	+	0.336456i	0.820869	−	0.571116i	$-0.193489\pi$
$967$	12.4689	+	10.4626i	0.400972	+	0.336456i	−0.419897	+	0.907572i	$0.637934\pi$
$968$	−0.542222	−	0.454978i	−0.0174277	−	0.0146236i
$969$	2.48911	−	4.56528i	0.0799618	−	0.146658i
$970$	−50.5316	−	18.3920i	−1.62247	−	0.590531i
$971$	−10.8061	−	18.7167i	−0.346783	−	0.600646i	0.638893	−	0.769296i	$-0.279393\pi$
$971$	−10.8061	−	18.7167i	−0.346783	−	0.600646i	−0.985676	+	0.168650i	$0.946059\pi$
$972$	−13.8897	+	7.07652i	−0.445511	+	0.226980i
$973$	6.12267	−	13.4385i	0.196284	−	0.430819i
$974$	−2.93367	−	16.6377i	−0.0940008	−	0.533105i
$975$	46.4924	+	76.1679i	1.48895	+	2.43933i
$976$	1.79132	−	10.1591i	0.0573388	−	0.325185i
$977$	25.1963	−	9.17070i	0.806101	−	0.293397i	0.0940886	−	0.995564i	$-0.470006\pi$
$977$	25.1963	−	9.17070i	0.806101	−	0.293397i	0.712012	+	0.702167i	$0.247784\pi$
$978$	−5.41066	+	4.77007i	−0.173014	+	0.152530i
$979$	−10.6139	−	3.86313i	−0.339221	−	0.123466i
$980$	−8.97595	+	26.0849i	−0.286726	+	0.833251i
$981$	28.0241	−	1.37021i	0.894741	−	0.0437476i
$982$	1.95068			0.0622489
$983$	−0.747932	−	4.24173i	−0.0238553	−	0.135290i	0.970554	−	0.240883i	$-0.0774371\pi$
$983$	−0.747932	−	4.24173i	−0.0238553	−	0.135290i	−0.994409	+	0.105593i	$0.966326\pi$
$984$	−0.781224	+	5.16536i	−0.0249045	+	0.164666i
$985$	−44.7571	+	16.2903i	−1.42608	+	0.519051i
$986$	−1.47034	+	8.33871i	−0.0468251	+	0.265559i
$987$	4.55703	−	2.31244i	0.145052	−	0.0736059i
$988$	−1.50519	+	1.26300i	−0.0478865	+	0.0401815i
$989$	−18.4881			−0.587888
$990$	38.6437	+	11.9628i	1.22818	+	0.380203i
$991$	42.5625			1.35204			0.676020	−	0.736883i	$-0.263703\pi$
$991$	42.5625			1.35204			0.676020	+	0.736883i	$0.263703\pi$
$992$	0.893342	+	5.06639i	0.0283636	+	0.160858i
$993$	12.1417	+	4.08624i	0.385306	+	0.129673i
$994$	7.49106	+	5.14737i	0.237602	+	0.163265i
$995$	−3.53442	+	1.28642i	−0.112049	+	0.0407823i
$996$	0.900310	−	1.65126i	0.0285274	−	0.0523221i
$997$	25.5385	+	9.29526i	0.808813	+	0.294384i	0.713133	−	0.701028i	$-0.247275\pi$
$997$	25.5385	+	9.29526i	0.808813	+	0.294384i	0.0956794	+	0.995412i	$0.469498\pi$
$998$	−2.00744	+	3.47699i	−0.0635444	+	0.110062i
$999$	−16.5456	+	1.21469i	−0.523481	+	0.0384310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.67.5	✓	72
7.2	even	3		378.2.w.b.121.5	yes	72
27.25	even	9		378.2.w.b.25.5	yes	72
189.79	even	9	inner	378.2.v.a.79.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.5	✓	72	1.1	even	1	trivial
378.2.v.a.79.5	yes	72	189.79	even	9	inner
378.2.w.b.25.5	yes	72	27.25	even	9
378.2.w.b.121.5	yes	72	7.2	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.829129 + 1.52071i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.684323 - 3.88099i) q^{5} +(-0.342341 - 1.69788i) q^{6} +(-1.85424 + 1.88727i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.62509 - 2.52172i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.829129 + 1.52071i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.684323 - 3.88099i) q^{5} +(-0.342341 - 1.69788i) q^{6} +(-1.85424 + 1.88727i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.62509 - 2.52172i) q^{9} +(1.97043 + 3.41288i) q^{10} +(0.594167 + 3.36969i) q^{11} +(1.35363 + 1.08060i) q^{12} +(-0.849585 + 4.81824i) q^{13} +(0.207321 - 2.63762i) q^{14} +(5.33445 + 4.25849i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.73759 + 6.47370i) q^{17} +(2.86582 + 0.887164i) q^{18} +(-0.200803 + 0.347801i) q^{19} +(-3.70320 - 1.34785i) q^{20} +(-1.33257 - 4.38455i) q^{21} +(-2.62115 - 2.19941i) q^{22} +(3.57287 + 2.99800i) q^{23} +(-1.73153 + 0.0423056i) q^{24} +(-9.89531 - 3.60160i) q^{25} +(-2.44628 - 4.23709i) q^{26} +(5.18221 - 0.380448i) q^{27} +(1.53661 + 2.15379i) q^{28} +(-0.196696 - 1.11552i) q^{29} +(-6.82373 + 0.166720i) q^{30} +(-0.893342 + 5.06639i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-5.61694 - 1.89035i) q^{33} +(-7.02438 - 2.55666i) q^{34} +(6.05556 + 8.48780i) q^{35} +(-2.76561 + 1.16251i) q^{36} -3.19278 q^{37} +(-0.0697382 - 0.395505i) q^{38} +(-6.62270 - 5.28691i) q^{39} +(3.70320 - 1.34785i) q^{40} +(0.523747 - 2.97031i) q^{41} +(3.83914 + 2.50220i) q^{42} +(-3.03657 + 2.54798i) q^{43} +3.42167 q^{44} +(-10.8989 + 4.58128i) q^{45} -4.66406 q^{46} +(0.193641 + 1.09819i) q^{47} +(1.29924 - 1.14542i) q^{48} +(-0.123556 - 6.99891i) q^{49} +(9.89531 - 3.60160i) q^{50} +(-12.9435 + 0.316242i) q^{51} +(4.59751 + 1.67336i) q^{52} +(5.46677 - 9.46872i) q^{53} +(-3.72525 + 3.62250i) q^{54} +13.4843 q^{55} +(-2.56154 - 0.662189i) q^{56} +(-0.362411 - 0.593734i) q^{57} +(0.867719 + 0.728103i) q^{58} +(-3.22777 + 1.17481i) q^{59} +(5.12012 - 4.51393i) q^{60} +(1.79132 + 10.1591i) q^{61} +(-2.57227 - 4.45531i) q^{62} +(7.77248 + 1.60891i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(18.1181 + 6.59446i) q^{65} +(5.51792 - 2.16241i) q^{66} +(1.62925 + 1.36710i) q^{67} +(7.02438 - 2.55666i) q^{68} +(-7.52145 + 2.94756i) q^{69} +(-10.0947 - 2.60959i) q^{70} +(-1.71767 + 2.97510i) q^{71} +(1.37133 - 2.66823i) q^{72} -2.19912 q^{73} +(2.44581 - 2.05228i) q^{74} +(13.6815 - 12.0617i) q^{75} +(0.307648 + 0.258147i) q^{76} +(-7.46123 - 5.12687i) q^{77} +(8.47165 - 0.206983i) q^{78} +(12.4461 - 10.4435i) q^{79} +(-1.97043 + 3.41288i) q^{80} +(-3.71817 + 8.19605i) q^{81} +(1.50807 + 2.61205i) q^{82} +(-0.188556 - 1.06935i) q^{83} +(-4.54933 + 0.550956i) q^{84} +(27.6821 - 10.0755i) q^{85} +(0.688334 - 3.90374i) q^{86} +(1.85946 + 0.625792i) q^{87} +(-2.62115 + 2.19941i) q^{88} +(-1.65052 + 2.85878i) q^{89} +(5.40422 - 10.5151i) q^{90} +(-7.51797 - 10.5376i) q^{91} +(3.57287 - 2.99800i) q^{92} +(-6.96379 - 5.55920i) q^{93} +(-0.854241 - 0.716794i) q^{94} +(1.21240 + 1.01732i) q^{95} +(-0.259015 + 1.71257i) q^{96} +(-10.4530 + 8.77109i) q^{97} +(4.59346 + 5.28206i) q^{98} +(7.53184 - 6.97436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

L-functions

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