LMFDB - Embedded newform 380.2.bj.a.347.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			347.49
Character	$\chi$	$=$	380.347
Dual form			380.2.bj.a.23.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29248 - 0.574023i) q^{2} +(0.745050 - 0.521689i) q^{3} +(1.34099 - 1.48382i) q^{4} +(-0.777253 - 2.09663i) q^{5} +(0.663498 - 1.10195i) q^{6} +(0.267247 + 0.0716085i) q^{7} +(0.881455 - 2.68757i) q^{8} +(-0.743121 + 2.04171i) q^{9} +O(q^{10})$	\(q+(1.29248 - 0.574023i) q^{2} +(0.745050 - 0.521689i) q^{3} +(1.34099 - 1.48382i) q^{4} +(-0.777253 - 2.09663i) q^{5} +(0.663498 - 1.10195i) q^{6} +(0.267247 + 0.0716085i) q^{7} +(0.881455 - 2.68757i) q^{8} +(-0.743121 + 2.04171i) q^{9} +(-2.20810 - 2.26369i) q^{10} +(3.13892 + 1.81226i) q^{11} +(0.225012 - 1.80511i) q^{12} +(-3.79665 - 2.65844i) q^{13} +(0.386515 - 0.0608534i) q^{14} +(-1.67288 - 1.15661i) q^{15} +(-0.403469 - 3.97960i) q^{16} +(0.779848 + 0.363649i) q^{17} +(0.211521 + 3.06543i) q^{18} +(3.17381 + 2.98779i) q^{19} +(-4.15333 - 1.65827i) q^{20} +(0.236469 - 0.0860678i) q^{21} +(5.09726 + 0.540487i) q^{22} +(-4.51633 - 0.395128i) q^{23} +(-0.745350 - 2.46222i) q^{24} +(-3.79176 + 3.25923i) q^{25} +(-6.43308 - 1.25661i) q^{26} +(1.21769 + 4.54449i) q^{27} +(0.464631 - 0.300520i) q^{28} +(0.591851 - 1.62610i) q^{29} +(-2.82609 - 0.534621i) q^{30} +(5.59259 - 3.22888i) q^{31} +(-2.80586 - 4.91194i) q^{32} +(3.28409 - 0.287320i) q^{33} +(1.21668 + 0.0223572i) q^{34} +(-0.0575813 - 0.615977i) q^{35} +(2.03302 + 3.84058i) q^{36} +(6.44328 + 6.44328i) q^{37} +(5.81714 + 2.03981i) q^{38} -4.21557 q^{39} +(-6.31997 + 0.240833i) q^{40} +(-1.29277 + 7.33165i) q^{41} +(0.256226 - 0.246980i) q^{42} +(0.546456 + 6.24603i) q^{43} +(6.89835 - 2.22738i) q^{44} +(4.85831 - 0.0288700i) q^{45} +(-6.06407 + 2.08179i) q^{46} +(5.02057 - 2.34113i) q^{47} +(-2.37672 - 2.75451i) q^{48} +(-5.99588 - 3.46173i) q^{49} +(-3.02988 + 6.38904i) q^{50} +(0.770738 - 0.135902i) q^{51} +(-9.03594 + 2.06860i) q^{52} +(0.0341874 - 0.390764i) q^{53} +(4.18248 + 5.17467i) q^{54} +(1.35991 - 7.98975i) q^{55} +(0.428019 - 0.655125i) q^{56} +(3.92335 + 0.570310i) q^{57} +(-0.168464 - 2.44143i) q^{58} +(11.4060 - 4.15144i) q^{59} +(-3.95954 + 0.931255i) q^{60} +(-9.02586 + 7.57359i) q^{61} +(5.37484 - 7.38353i) q^{62} +(-0.344800 + 0.492426i) q^{63} +(-6.44608 - 4.73794i) q^{64} +(-2.62282 + 10.0265i) q^{65} +(4.07968 - 2.25650i) q^{66} +(-8.76714 + 4.08818i) q^{67} +(1.58536 - 0.669506i) q^{68} +(-3.57103 + 2.06173i) q^{69} +(-0.428007 - 0.763083i) q^{70} +(-2.69187 + 3.20805i) q^{71} +(4.83221 + 3.79686i) q^{72} +(-9.22675 - 13.1772i) q^{73} +(12.0264 + 4.62920i) q^{74} +(-1.12474 + 4.40641i) q^{75} +(8.68943 - 0.702767i) q^{76} +(0.709093 + 0.709093i) q^{77} +(-5.44853 + 2.41984i) q^{78} +(-1.45403 + 8.24624i) q^{79} +(-8.03017 + 3.93908i) q^{80} +(-1.71519 - 1.43922i) q^{81} +(2.53767 + 10.2181i) q^{82} +(2.41674 - 9.01938i) q^{83} +(0.189395 - 0.466296i) q^{84} +(0.156300 - 1.91770i) q^{85} +(4.29165 + 7.75917i) q^{86} +(-0.407359 - 1.52029i) q^{87} +(7.63739 - 6.83865i) q^{88} +(8.79815 - 1.55135i) q^{89} +(6.26268 - 2.82610i) q^{90} +(-0.824274 - 0.982331i) q^{91} +(-6.64268 + 6.17158i) q^{92} +(2.48228 - 5.32327i) q^{93} +(5.14511 - 5.90779i) q^{94} +(3.79746 - 8.97660i) q^{95} +(-4.65301 - 2.19585i) q^{96} +(-3.94654 - 1.84030i) q^{97} +(-9.73666 - 1.03242i) q^{98} +(-6.03270 + 5.06204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.29248	−	0.574023i	0.913919	−	0.405896i
$2$	1.29248	−	0.574023i	0.913919	−	0.405896i
$3$	0.745050	−	0.521689i	0.430155	−	0.301198i	−0.338375	−	0.941011i	$-0.609877\pi$
$3$	0.745050	−	0.521689i	0.430155	−	0.301198i	0.768530	+	0.639814i	$0.220988\pi$
$4$	1.34099	−	1.48382i	0.670497	−	0.741912i
$5$	−0.777253	−	2.09663i	−0.347598	−	0.937644i
$5$	−0.777253	−	2.09663i	−0.347598	−	0.937644i
$6$	0.663498	−	1.10195i	0.270872	−	0.449868i
$7$	0.267247	+	0.0716085i	0.101010	+	0.0270655i	0.308970	−	0.951072i	$-0.400016\pi$
$7$	0.267247	+	0.0716085i	0.101010	+	0.0270655i	−0.207960	+	0.978137i	$0.566682\pi$
$8$	0.881455	−	2.68757i	0.311641	−	0.950200i
$9$	−0.743121	+	2.04171i	−0.247707	+	0.680570i
$10$	−2.20810	−	2.26369i	−0.698262	−	0.715842i
$11$	3.13892	+	1.81226i	0.946420	+	0.546416i	0.891967	−	0.452100i	$-0.149325\pi$
$11$	3.13892	+	1.81226i	0.946420	+	0.546416i	0.0544532	+	0.998516i	$0.482658\pi$
$12$	0.225012	−	1.80511i	0.0649554	−	0.521089i
$13$	−3.79665	−	2.65844i	−1.05300	−	0.737319i	−0.0870911	−	0.996200i	$-0.527757\pi$
$13$	−3.79665	−	2.65844i	−1.05300	−	0.737319i	−0.965909	+	0.258882i	$0.916646\pi$
$14$	0.386515	−	0.0608534i	0.103301	−	0.0162638i
$15$	−1.67288	−	1.15661i	−0.431937	−	0.298636i
$16$	−0.403469	−	3.97960i	−0.100867	−	0.994900i
$17$	0.779848	+	0.363649i	0.189141	+	0.0881979i	0.514882	−	0.857261i	$-0.327836\pi$
$17$	0.779848	+	0.363649i	0.189141	+	0.0881979i	−0.325741	+	0.945459i	$0.605614\pi$
$18$	0.211521	+	3.06543i	0.0498561	+	0.722529i
$19$	3.17381	+	2.98779i	0.728123	+	0.685447i
$19$	3.17381	+	2.98779i	0.728123	+	0.685447i
$20$	−4.15333	−	1.65827i	−0.928713	−	0.370800i
$21$	0.236469	−	0.0860678i	0.0516019	−	0.0187815i
$22$	5.09726	+	0.540487i	1.08674	+	0.115232i
$23$	−4.51633	−	0.395128i	−0.941721	−	0.0823899i	−0.394055	−	0.919087i	$-0.628928\pi$
$23$	−4.51633	−	0.395128i	−0.941721	−	0.0823899i	−0.547666	+	0.836697i	$0.684484\pi$
$24$	−0.745350	−	2.46222i	−0.152144	−	0.502598i
$25$	−3.79176	+	3.25923i	−0.758351	+	0.651846i
$26$	−6.43308	−	1.25661i	−1.26163	−	0.246441i
$27$	1.21769	+	4.54449i	0.234345	+	0.874588i
$28$	0.464631	−	0.300520i	0.0878069	−	0.0567930i
$29$	0.591851	−	1.62610i	0.109904	−	0.301959i	−0.872532	−	0.488556i	$-0.837524\pi$
$29$	0.591851	−	1.62610i	0.109904	−	0.301959i	0.982436	+	0.186597i	$0.0597460\pi$
$30$	−2.82609	−	0.534621i	−0.515971	−	0.0976079i
$31$	5.59259	−	3.22888i	1.00446	−	0.579924i	0.0948938	−	0.995487i	$-0.469749\pi$
$31$	5.59259	−	3.22888i	1.00446	−	0.579924i	0.909564	+	0.415563i	$0.136416\pi$
$32$	−2.80586	−	4.91194i	−0.496010	−	0.868317i
$33$	3.28409	−	0.287320i	0.571686	−	0.0500161i
$34$	1.21668	+	0.0223572i	0.208659	+	0.00383422i
$35$	−0.0575813	−	0.615977i	−0.00973301	−	0.104119i
$36$	2.03302	+	3.84058i	0.338836	+	0.640097i
$37$	6.44328	+	6.44328i	1.05927	+	1.05927i	0.998129	+	0.0611390i	$0.0194733\pi$
$37$	6.44328	+	6.44328i	1.05927	+	1.05927i	0.0611390	+	0.998129i	$0.480527\pi$
$38$	5.81714	+	2.03981i	0.943665	+	0.330901i
$39$	−4.21557			−0.675031
$40$	−6.31997	+	0.240833i	−0.999275	+	0.0380791i
$41$	−1.29277	+	7.33165i	−0.201896	+	1.14501i	0.700353	+	0.713797i	$0.253026\pi$
$41$	−1.29277	+	7.33165i	−0.201896	+	1.14501i	−0.902249	+	0.431215i	$0.858085\pi$
$42$	0.256226	−	0.246980i	0.0395366	−	0.0381098i
$43$	0.546456	+	6.24603i	0.0833338	+	0.952510i	0.916644	+	0.399704i	$0.130887\pi$
$43$	0.546456	+	6.24603i	0.0833338	+	0.952510i	−0.833310	+	0.552806i	$0.813557\pi$
$44$	6.89835	−	2.22738i	1.03996	−	0.335790i
$45$	4.85831	−	0.0288700i	0.724234	−	0.00430368i
$46$	−6.06407	+	2.08179i	−0.894098	+	0.306943i
$47$	5.02057	−	2.34113i	0.732326	−	0.341489i	−0.0204278	−	0.999791i	$-0.506503\pi$
$47$	5.02057	−	2.34113i	0.732326	−	0.341489i	0.752754	+	0.658302i	$0.228725\pi$
$48$	−2.37672	−	2.75451i	−0.343050	−	0.397580i
$49$	−5.99588	−	3.46173i	−0.856555	−	0.494532i
$50$	−3.02988	+	6.38904i	−0.428490	+	0.903546i
$51$	0.770738	−	0.135902i	0.107925	−	0.0190301i
$52$	−9.03594	+	2.06860i	−1.25306	+	0.286863i
$53$	0.0341874	−	0.390764i	0.00469600	−	0.0536756i	−0.993485	−	0.113962i	$-0.963646\pi$
$53$	0.0341874	−	0.390764i	0.00469600	−	0.0536756i	0.998181	+	0.0602863i	$0.0192014\pi$
$54$	4.18248	+	5.17467i	0.569164	+	0.704183i
$55$	1.35991	−	7.98975i	0.183370	−	1.07734i
$56$	0.428019	−	0.655125i	0.0571964	−	0.0875447i
$57$	3.92335	+	0.570310i	0.519660	+	0.0755394i
$58$	−0.168464	−	2.44143i	−0.0221204	−	0.320576i
$59$	11.4060	−	4.15144i	1.48493	−	0.540471i	0.532822	−	0.846227i	$-0.321131\pi$
$59$	11.4060	−	4.15144i	1.48493	−	0.540471i	0.952110	+	0.305756i	$0.0989092\pi$
$60$	−3.95954	+	0.931255i	−0.511174	+	0.120225i
$61$	−9.02586	+	7.57359i	−1.15564	+	0.969699i	−0.999836	−	0.0180885i	$-0.994242\pi$
$61$	−9.02586	+	7.57359i	−1.15564	+	0.969699i	−0.155806	+	0.987788i	$0.549797\pi$
$62$	5.37484	−	7.38353i	0.682605	−	0.937709i
$63$	−0.344800	+	0.492426i	−0.0434408	+	0.0620398i
$64$	−6.44608	−	4.73794i	−0.805759	−	0.592243i
$65$	−2.62282	+	10.0265i	−0.325321	+	1.24363i
$66$	4.07968	−	2.25650i	0.502174	−	0.277756i
$67$	−8.76714	+	4.08818i	−1.07108	+	0.499451i	−0.876483	−	0.481433i	$-0.840117\pi$
$67$	−8.76714	+	4.08818i	−1.07108	+	0.499451i	−0.194594	+	0.980884i	$0.562339\pi$
$68$	1.58536	−	0.669506i	0.192254	−	0.0811896i
$69$	−3.57103	+	2.06173i	−0.429901	+	0.248204i
$70$	−0.428007	−	0.763083i	−0.0511567	−	0.0912058i
$71$	−2.69187	+	3.20805i	−0.319466	+	0.380725i	−0.901748	−	0.432262i	$-0.857716\pi$
$71$	−2.69187	+	3.20805i	−0.319466	+	0.380725i	0.582282	+	0.812987i	$0.302160\pi$
$72$	4.83221	+	3.79686i	0.569481	+	0.447465i
$73$	−9.22675	−	13.1772i	−1.07991	−	1.54227i	−0.816289	−	0.577643i	$-0.803973\pi$
$73$	−9.22675	−	13.1772i	−1.07991	−	1.54227i	−0.263620	−	0.964627i	$-0.584916\pi$
$74$	12.0264	+	4.62920i	1.39804	+	0.538133i
$75$	−1.12474	+	4.40641i	−0.129874	+	0.508808i
$76$	8.68943	−	0.702767i	0.996745	−	0.0806129i
$77$	0.709093	+	0.709093i	0.0808086	+	0.0808086i
$78$	−5.44853	+	2.41984i	−0.616924	+	0.273992i
$79$	−1.45403	+	8.24624i	−0.163592	+	0.927774i	0.786913	+	0.617064i	$0.211678\pi$
$79$	−1.45403	+	8.24624i	−0.163592	+	0.927774i	−0.950505	+	0.310710i	$0.899433\pi$
$80$	−8.03017	+	3.93908i	−0.897800	+	0.440403i
$81$	−1.71519	−	1.43922i	−0.190577	−	0.159913i
$82$	2.53767	+	10.2181i	0.280238	+	1.12840i
$83$	2.41674	−	9.01938i	0.265271	−	0.990006i	−0.696813	−	0.717253i	$-0.745399\pi$
$83$	2.41674	−	9.01938i	0.265271	−	0.990006i	0.962084	−	0.272753i	$-0.0879341\pi$
$84$	0.189395	−	0.466296i	0.0206646	−	0.0508770i
$85$	0.156300	−	1.91770i	0.0169532	−	0.208004i
$86$	4.29165	+	7.75917i	0.462780	+	0.836692i
$87$	−0.407359	−	1.52029i	−0.0436735	−	0.162992i
$88$	7.63739	−	6.83865i	0.814148	−	0.729003i
$89$	8.79815	−	1.55135i	0.932602	−	0.164443i	0.313352	−	0.949637i	$-0.398548\pi$
$89$	8.79815	−	1.55135i	0.932602	−	0.164443i	0.619250	+	0.785194i	$0.287437\pi$
$90$	6.26268	−	2.82610i	0.660145	−	0.297897i
$91$	−0.824274	−	0.982331i	−0.0864074	−	0.102976i
$92$	−6.64268	+	6.17158i	−0.692547	+	0.643432i
$93$	2.48228	−	5.32327i	0.257401	−	0.551997i
$94$	5.14511	−	5.90779i	0.530678	−	0.609342i
$95$	3.79746	−	8.97660i	0.389611	−	0.920980i
$96$	−4.65301	−	2.19585i	−0.474896	−	0.224113i
$97$	−3.94654	−	1.84030i	−0.400710	−	0.186854i	0.211807	−	0.977311i	$-0.432065\pi$
$97$	−3.94654	−	1.84030i	−0.400710	−	0.186854i	−0.612517	+	0.790457i	$0.709843\pi$
$98$	−9.73666	−	1.03242i	−0.983551	−	0.104290i
$99$	−6.03270	+	5.06204i	−0.606309	+	0.508754i
$100$	−0.248598	+	9.99691i	−0.0248598	+	0.999691i
$101$	1.80652	+	10.2453i	0.179755	+	1.01944i	0.932511	+	0.361142i	$0.117613\pi$
$101$	1.80652	+	10.2453i	0.179755	+	1.01944i	−0.752756	+	0.658300i	$0.771276\pi$
$102$	0.918150	−	0.618072i	0.0909104	−	0.0611982i
$103$	−10.1187	+	2.71131i	−0.997029	+	0.267153i	−0.720200	−	0.693766i	$-0.755950\pi$
$103$	−10.1187	+	2.71131i	−0.997029	+	0.267153i	−0.276829	+	0.960919i	$0.589283\pi$
$104$	−10.4913	+	7.86046i	−1.02876	+	0.770782i
$105$	−0.364249	−	0.428894i	−0.0355471	−	0.0418557i
$106$	−0.180121	−	0.524678i	−0.0174949	−	0.0509612i
$107$	−8.12026	−	2.17582i	−0.785016	−	0.210344i	−0.156021	−	0.987754i	$-0.549867\pi$
$107$	−8.12026	−	2.17582i	−0.785016	−	0.210344i	−0.628995	+	0.777410i	$0.716533\pi$
$108$	8.37614	+	4.28729i	0.805995	+	0.412545i
$109$	0.219583	−	0.261688i	0.0210322	−	0.0250652i	−0.755426	−	0.655234i	$-0.772570\pi$
$109$	0.219583	−	0.261688i	0.0210322	−	0.0250652i	0.776458	+	0.630169i	$0.217014\pi$
$110$	−2.82866	−	11.1072i	−0.269702	−	1.05903i
$111$	8.16195	+	1.43917i	0.774698	+	0.136600i
$112$	0.177148	−	1.09243i	0.0167389	−	0.103225i
$113$	1.27332	−	1.27332i	0.119784	−	0.119784i	−0.644674	−	0.764458i	$-0.723007\pi$
$113$	1.27332	−	1.27332i	0.119784	−	0.119784i	0.764458	+	0.644674i	$0.223007\pi$
$114$	5.39821	−	1.51498i	0.505589	−	0.141891i
$115$	2.68189	+	9.77622i	0.250088	+	0.911637i
$116$	−1.61917	−	3.05879i	−0.150337	−	0.284002i
$117$	8.24913	−	5.77610i	0.762632	−	0.534001i
$118$	12.3589	−	11.9129i	1.13773	−	1.09667i
$119$	0.182371	+	0.153028i	0.0167180	+	0.0140280i
$120$	−4.58305	+	3.47649i	−0.418373	+	0.317359i
$121$	1.06855	+	1.85078i	0.0971409	+	0.168253i
$122$	−7.31829	+	14.9697i	−0.662567	+	1.35530i
$123$	2.86167	+	6.13687i	0.258028	+	0.553343i
$124$	2.70853	−	12.6283i	0.243234	−	1.13406i
$125$	9.78057	+	5.41668i	0.874801	+	0.484483i
$126$	−0.162983	+	0.834373i	−0.0145196	+	0.0743318i
$127$	−0.201401	−	0.141022i	−0.0178714	−	0.0125137i	0.564607	−	0.825360i	$-0.309028\pi$
$127$	−0.201401	−	0.141022i	−0.0178714	−	0.0125137i	−0.582478	+	0.812846i	$0.697917\pi$
$128$	−11.0511	−	2.42349i	−0.976788	−	0.214208i
$129$	3.66562	+	4.36852i	0.322740	+	0.384627i
$130$	2.36548	+	14.4645i	0.207466	+	1.26862i
$131$	0.619494	+	1.70205i	0.0541254	+	0.148708i	0.963809	−	0.266594i	$-0.0858981\pi$
$131$	0.619494	+	1.70205i	0.0541254	+	0.148708i	−0.909684	+	0.415302i	$0.863676\pi$
$132$	3.97761	−	5.25830i	0.346206	−	0.457677i
$133$	0.634239	+	1.02575i	0.0549955	+	0.0889438i
$134$	−8.98462	+	10.3164i	−0.776153	+	0.891204i
$135$	8.58168	−	6.08528i	0.738594	−	0.523737i
$136$	1.66473	−	1.77536i	0.142750	−	0.152236i
$137$	5.37552	+	0.470297i	0.459262	+	0.0401802i	0.314440	−	0.949277i	$-0.398183\pi$
$137$	5.37552	+	0.470297i	0.459262	+	0.0401802i	0.144822	+	0.989458i	$0.453739\pi$
$138$	−3.43199	+	4.71460i	−0.292150	+	0.401333i
$139$	−1.85432	−	10.5164i	−0.157281	−	0.891987i	−0.956670	−	0.291173i	$-0.905954\pi$
$139$	−1.85432	−	10.5164i	−0.157281	−	0.891987i	0.799389	−	0.600814i	$-0.205157\pi$
$140$	−0.991217	−	0.740581i	−0.0837731	−	0.0625905i
$141$	2.51923	−	4.36344i	0.212158	−	0.367468i
$142$	−1.63769	+	5.69153i	−0.137432	+	0.477622i
$143$	−7.09959	−	15.2251i	−0.593698	−	1.27319i
$144$	8.42501	+	2.13356i	0.702084	+	0.177797i
$145$	−3.86935	+	0.0229932i	−0.321332	+	0.00190948i
$146$	−19.4894	−	11.7348i	−1.61295	−	0.971180i
$147$	−6.27318	+	0.548832i	−0.517403	+	0.0452669i
$148$	18.2011	−	0.920293i	1.49612	−	0.0756476i
$149$	−5.20088	−	0.917056i	−0.426073	−	0.0751281i	−0.0434999	−	0.999053i	$-0.513851\pi$
$149$	−5.20088	−	0.917056i	−0.426073	−	0.0751281i	−0.382573	+	0.923925i	$0.624962\pi$
$150$	1.07568	+	6.34081i	0.0878289	+	0.517725i
$151$		−	10.4353i		−	0.849216i	−0.905377	−	0.424608i	$-0.860412\pi$
$151$		−	10.4353i		−	0.849216i	0.905377	−	0.424608i	$-0.139588\pi$
$152$	10.8275	−	5.89624i	0.878225	−	0.478249i
$153$	−1.32199	+	1.32199i	−0.106876	+	0.106876i
$154$	1.32352	+	0.509451i	0.106652	+	0.0410527i
$155$	−11.1166	−	9.21595i	−0.892910	−	0.740243i
$156$	−5.65306	+	6.25516i	−0.452607	+	0.500814i
$157$	−1.31952	−	15.0822i	−0.105309	−	1.20369i	−0.846497	−	0.532394i	$-0.821293\pi$
$157$	−1.31952	−	15.0822i	−0.105309	−	1.20369i	0.741187	−	0.671298i	$-0.234263\pi$
$158$	2.85423	+	11.4927i	0.227070	+	0.914312i
$159$	−0.178386	−	0.308974i	−0.0141469	−	0.0245032i
$160$	−8.11769	+	9.70068i	−0.641760	+	0.766906i
$161$	−1.17868	−	0.429005i	−0.0928930	−	0.0338103i
$162$	−3.04300	−	0.875596i	−0.239080	−	0.0687933i
$163$	2.08888	−	0.559714i	0.163614	−	0.0438402i	−0.176082	−	0.984375i	$-0.556342\pi$
$163$	2.08888	−	0.559714i	0.163614	−	0.0438402i	0.339696	+	0.940535i	$0.389676\pi$
$164$	9.14529	+	11.7499i	0.714127	+	0.917517i
$165$	−3.15497	−	6.66221i	−0.245614	−	0.518652i
$166$	−2.05376	−	13.0446i	−0.159403	−	1.01246i
$167$	0.947238	−	10.8270i	0.0732995	−	0.837817i	−0.867186	−	0.497984i	$-0.834074\pi$
$167$	0.947238	−	10.8270i	0.0732995	−	0.837817i	0.940486	−	0.339833i	$-0.110371\pi$
$168$	−0.0228763	−	0.711393i	−0.00176495	−	0.0548852i
$169$	2.90095	+	7.97031i	0.223150	+	0.613101i
$170$	−0.898793	−	2.56831i	−0.0689343	−	0.196980i
$171$	−8.45873	+	4.25971i	−0.646855	+	0.325748i
$172$	10.0008	+	7.56504i	0.762554	+	0.576829i
$173$	4.32689	−	9.27905i	0.328967	−	0.705473i	−0.670364	−	0.742032i	$-0.733862\pi$
$173$	4.32689	−	9.27905i	0.328967	−	0.705473i	0.999331	+	0.0365594i	$0.0116398\pi$
$174$	−1.39918	−	1.73110i	−0.106072	−	0.131234i
$175$	−1.24672	+	0.599496i	−0.0942434	+	0.0453177i
$176$	5.94560	−	13.2228i	0.448167	−	0.996709i
$177$	6.33226	−	9.04341i	0.475962	−	0.679744i
$178$	10.4809	−	7.05543i	0.785576	−	0.528827i
$179$	−13.2856	+	23.0114i	−0.993015	+	1.71995i	−0.394330	+	0.918969i	$0.629023\pi$
$179$	−13.2856	+	23.0114i	−0.993015	+	1.71995i	−0.598686	+	0.800984i	$0.704310\pi$
$180$	6.47213	−	7.24759i	0.482404	−	0.540204i
$181$	−10.9633	−	3.99030i	−0.814893	−	0.296597i	−0.0992493	−	0.995063i	$-0.531644\pi$
$181$	−10.9633	−	3.99030i	−0.814893	−	0.296597i	−0.715643	+	0.698466i	$0.753866\pi$
$182$	−1.62924	−	0.796488i	−0.120767	−	0.0590396i
$183$	−2.77365	+	10.3514i	−0.205034	+	0.765197i
$184$	−5.04288	+	11.7897i	−0.371766	+	0.869147i
$185$	8.50114	−	18.5173i	0.625017	−	1.36142i
$186$	0.152611	−	8.30509i	0.0111900	−	0.608959i
$187$	1.78886	+	2.55475i	0.130814	+	0.186822i
$188$	3.25873	−	10.5891i	0.237668	−	0.772289i
$189$			1.30170i			0.0946845i
$190$	−0.244652	−	13.7819i	−0.0177489	−	0.999842i
$191$			8.01689i			0.580082i	0.957014	+	0.290041i	$0.0936689\pi$
$191$			8.01689i			0.580082i	−0.957014	+	0.290041i	$0.906331\pi$
$192$	−7.27438	−	0.167155i	−0.524983	−	0.0120633i
$193$	−9.51529	−	13.5892i	−0.684926	−	0.978175i	−0.999580	−	0.0289692i	$-0.990778\pi$
$193$	−9.51529	−	13.5892i	−0.684926	−	0.978175i	0.314654	−	0.949206i	$-0.398111\pi$
$194$	−6.15718	−	0.113142i	−0.442060	−	0.00812310i
$195$	3.27656	+	8.83851i	0.234640	+	0.632939i
$196$	−13.1770	+	4.25468i	−0.941217	+	0.303906i
$197$	1.95631	−	7.30106i	0.139382	−	0.520179i	−0.860560	−	0.509349i	$-0.829886\pi$
$197$	1.95631	−	7.30106i	0.139382	−	0.520179i	0.999941	−	0.0108296i	$-0.00344722\pi$
$198$	−4.89140	+	10.0055i	−0.347617	+	0.711058i
$199$	−13.8828	−	5.05292i	−0.984124	−	0.358192i	−0.200682	−	0.979656i	$-0.564316\pi$
$199$	−13.8828	−	5.05292i	−0.984124	−	0.358192i	−0.783442	+	0.621465i	$0.786538\pi$
$200$	5.41715	+	13.0635i	0.383051	+	0.923727i
$201$	−4.39919	+	7.61962i	−0.310295	+	0.537447i
$202$	8.21590	+	12.2048i	0.578069	+	0.858726i
$203$	0.274613	−	0.392188i	0.0192740	−	0.0275262i
$204$	0.831900	−	1.32588i	0.0582447	−	0.0928304i
$205$	16.3766	−	2.98808i	1.14379	−	0.208697i
$206$	−11.5219	+	9.31269i	−0.802768	+	0.648846i
$207$	4.16292	−	8.92741i	0.289343	−	0.620498i
$208$	−9.04770	+	16.1817i	−0.627345	+	1.12200i
$209$	4.54770	+	15.1302i	0.314571	+	1.04658i
$210$	−0.716979	−	0.345248i	−0.0494762	−	0.0238243i
$211$	4.35025	+	11.9522i	0.299483	+	0.822824i	0.994586	+	0.103914i	$0.0331365\pi$
$211$	4.35025	+	11.9522i	0.299483	+	0.822824i	−0.695103	+	0.718910i	$0.744641\pi$
$212$	−0.533980	−	0.574741i	−0.0366739	−	0.0394733i
$213$	−0.331974	+	3.79448i	−0.0227465	+	0.259993i
$214$	−11.7442	+	1.84903i	−0.802819	+	0.126397i
$215$	12.6709	−	6.00046i	0.864148	−	0.409228i
$216$	13.2870	+	0.733127i	0.904065	+	0.0498830i
$217$	1.72582	−	0.462431i	0.117156	−	0.0313918i
$218$	0.133590	−	0.464272i	0.00904788	−	0.0314445i
$219$	−13.7488	−	5.00414i	−0.929056	−	0.338149i
$220$	−10.0318	−	12.7321i	−0.676341	−	0.858396i
$221$	−1.99407	−	3.45383i	−0.134136	−	0.232330i
$222$	11.3753	−	2.82505i	0.763457	−	0.189605i
$223$	1.85036	+	21.1497i	0.123909	+	1.41629i	0.762623	+	0.646843i	$0.223911\pi$
$223$	1.85036	+	21.1497i	0.123909	+	1.41629i	−0.638714	+	0.769444i	$0.720533\pi$
$224$	−0.398119	−	1.51362i	−0.0266004	−	0.101133i
$225$	−3.83667	−	10.1637i	−0.255778	−	0.677578i
$226$	0.914824	−	2.37666i	0.0608532	−	0.158093i
$227$	9.65634	−	9.65634i	0.640913	−	0.640913i	−0.309867	−	0.950780i	$-0.600284\pi$
$227$	9.65634	−	9.65634i	0.640913	−	0.640913i	0.950780	+	0.309867i	$0.100284\pi$
$228$	6.10743	−	5.05678i	0.404474	−	0.334893i
$229$		−	23.4068i		−	1.54676i	−0.633941	−	0.773381i	$-0.718564\pi$
$229$		−	23.4068i		−	1.54676i	0.633941	−	0.773381i	$-0.281436\pi$
$230$	9.07806	+	11.0961i	0.598590	+	0.731653i
$231$	0.898236	+	0.158383i	0.0590996	+	0.0104209i
$232$	−3.84856	−	3.02397i	−0.252671	−	0.198534i
$233$	5.24087	−	0.458517i	0.343341	−	0.0300384i	0.0858185	−	0.996311i	$-0.472649\pi$
$233$	5.24087	−	0.458517i	0.343341	−	0.0300384i	0.257522	+	0.966272i	$0.417094\pi$
$234$	7.34619	−	12.2007i	0.480236	−	0.797583i
$235$	−8.81076	−	8.70666i	−0.574750	−	0.567960i
$236$	9.13535	−	22.4915i	0.594661	−	1.46407i
$237$	3.21865	+	6.90241i	0.209074	+	0.448360i
$238$	0.323553	+	0.0930995i	0.0209728	+	0.00603474i
$239$	9.20133	−	15.9372i	0.595184	−	1.03089i	−0.398337	−	0.917239i	$-0.630412\pi$
$239$	9.20133	−	15.9372i	0.595184	−	1.03089i	0.993521	−	0.113650i	$-0.0362543\pi$
$240$	−3.92790	+	7.12407i	−0.253545	+	0.459856i
$241$	0.747291	+	4.23810i	0.0481373	+	0.273000i	0.999371	−	0.0354721i	$-0.0112935\pi$
$241$	0.747291	+	4.23810i	0.0481373	+	0.273000i	−0.951233	+	0.308472i	$0.900182\pi$
$242$	2.44347	+	1.77872i	0.157072	+	0.114341i
$243$	−16.0894	−	1.40764i	−1.03214	−	0.0903003i
$244$	−0.865742	+	23.5489i	−0.0554234	+	1.50757i
$245$	−2.59766	+	15.2618i	−0.165958	+	0.975042i
$246$	7.22135	+	6.28910i	0.460416	+	0.400978i
$247$	−4.10698	−	19.7810i	−0.261321	−	1.25863i
$248$	−3.74824	−	17.8766i	−0.238013	−	1.13516i
$249$	−2.90473	−	7.98067i	−0.184080	−	0.505755i
$250$	15.7505	+	1.38666i	0.996147	+	0.0877002i
$251$	13.6946	+	16.3206i	0.864395	+	1.03015i	0.999228	+	0.0392777i	$0.0125057\pi$
$251$	13.6946	+	16.3206i	0.864395	+	1.03015i	−0.134833	+	0.990868i	$0.543050\pi$
$252$	0.268298	+	1.17196i	0.0169012	+	0.0738268i
$253$	−13.4603	−	9.42503i	−0.846244	−	0.592547i
$254$	−0.341256	−	0.0666593i	−0.0214123	−	0.00418258i
$255$	−0.883995	−	1.51033i	−0.0553579	−	0.0945803i
$256$	−15.6744	+	3.21129i	−0.979652	+	0.200705i
$257$	−5.82686	−	12.4957i	−0.363470	−	0.779463i	−0.999967	−	0.00818397i	$-0.997395\pi$
$257$	−5.82686	−	12.4957i	−0.363470	−	0.779463i	0.636497	−	0.771279i	$-0.280383\pi$
$258$	7.24537	+	3.54206i	0.451077	+	0.220519i
$259$	1.26055	+	2.18334i	0.0783268	+	0.135666i
$260$	11.3603	+	17.3372i	0.704537	+	1.07521i
$261$	2.88020	+	2.41678i	0.178280	+	0.149595i
$262$	1.77770	+	1.84425i	0.109826	+	0.113938i
$263$	17.5889	−	12.3159i	1.08458	−	0.759429i	0.112397	−	0.993663i	$-0.464147\pi$
$263$	17.5889	−	12.3159i	1.08458	−	0.759429i	0.972180	+	0.234234i	$0.0752583\pi$
$264$	2.12258	−	9.07948i	0.130636	−	0.558803i
$265$	−0.845862	+	0.232044i	−0.0519609	+	0.0142543i
$266$	1.40854	+	0.961690i	0.0863634	+	0.0589650i
$267$	5.74573	−	5.74573i	0.351633	−	0.351633i
$268$	−5.69054	+	18.4911i	−0.347605	+	1.12953i
$269$	3.92353	+	0.691824i	0.239222	+	0.0421812i	0.291973	−	0.956426i	$-0.405688\pi$
$269$	3.92353	+	0.691824i	0.239222	+	0.0421812i	−0.0527518	+	0.998608i	$0.516799\pi$
$270$	7.59854	−	12.7912i	0.462432	−	0.778446i
$271$	6.31905	−	7.53075i	0.383855	−	0.457461i	−0.539172	−	0.842196i	$-0.681263\pi$
$271$	6.31905	−	7.53075i	0.383855	−	0.457461i	0.923027	+	0.384735i	$0.125707\pi$
$272$	1.13253	−	3.25021i	0.0686700	−	0.197073i
$273$	−1.12660	−	0.301871i	−0.0681847	−	0.0182700i
$274$	7.21770	−	2.47783i	0.436037	−	0.149691i
$275$	−17.8086	+	3.35883i	−1.07390	+	0.202545i
$276$	−1.72948	+	8.06355i	−0.104102	+	0.485369i
$277$	−17.3418	+	4.64671i	−1.04197	+	0.279194i	−0.738928	−	0.673784i	$-0.764668\pi$
$277$	−17.3418	+	4.64671i	−1.04197	+	0.279194i	−0.303038	+	0.952978i	$0.598001\pi$
$278$	−8.43331	−	12.5277i	−0.505796	−	0.751364i
$279$	2.43647	+	13.8179i	0.145867	+	0.827255i
$280$	−1.70624	−	0.388202i	−0.101967	−	0.0231995i
$281$	−2.04050	+	1.71218i	−0.121726	+	0.102140i	−0.701619	−	0.712553i	$-0.747539\pi$
$281$	−2.04050	+	1.71218i	−0.121726	+	0.102140i	0.579893	+	0.814693i	$0.303095\pi$
$282$	0.751335	−	7.08575i	0.0447413	−	0.421950i
$283$	14.3488	+	6.69094i	0.852945	+	0.397735i	0.799377	−	0.600829i	$-0.205163\pi$
$283$	14.3488	+	6.69094i	0.852945	+	0.397735i	0.0535680	+	0.998564i	$0.482941\pi$
$284$	1.15039	+	8.29624i	0.0682633	+	0.492291i
$285$	−1.85370	−	8.66910i	−0.109804	−	0.513513i
$286$	−17.9156	−	15.6028i	−1.05937	−	0.922613i
$287$	−0.870497	+	1.86679i	−0.0513838	+	0.110193i
$288$	12.1138	−	2.07858i	0.713815	−	0.122481i
$289$	−10.4515	−	12.4556i	−0.614792	−	0.732681i
$290$	−4.98785	+	2.25082i	−0.292897	+	0.132172i
$291$	−3.90043	+	0.687751i	−0.228647	+	0.0403167i
$292$	−31.9256	−	3.97963i	−1.86830	−	0.232890i
$293$	3.09444	+	11.5486i	0.180779	+	0.674676i	0.995495	+	0.0948159i	$0.0302263\pi$
$293$	3.09444	+	11.5486i	0.180779	+	0.674676i	−0.814716	+	0.579860i	$0.803107\pi$
$294$	−7.79290	+	4.31030i	−0.454491	+	0.251382i
$295$	−17.5694	−	20.6875i	−1.02293	−	1.20447i
$296$	22.9962	−	11.6373i	1.33663	−	0.676405i
$297$	−4.41354	+	16.4716i	−0.256100	+	0.955777i
$298$	−7.24843	+	1.80015i	−0.419890	+	0.104280i
$299$	16.0965	+	13.5066i	0.930884	+	0.781105i
$300$	5.03006	+	7.57788i	0.290411	+	0.437509i
$301$	−0.301230	+	1.70836i	−0.0173626	+	0.0984683i
$302$	−5.99013	−	13.4874i	−0.344693	−	0.776115i
$303$	6.69079	+	6.69079i	0.384376	+	0.384376i
$304$	10.6097	−	13.8360i	0.608507	−	0.793548i
$305$	22.8944	+	13.0373i	1.31093	+	0.746515i
$306$	−0.949787	+	2.46749i	−0.0542957	+	0.141057i
$307$	10.9354	+	15.6174i	0.624118	+	0.891332i	0.999366	−	0.0355918i	$-0.0113316\pi$
$307$	10.9354	+	15.6174i	0.624118	+	0.891332i	−0.375249	+	0.926924i	$0.622443\pi$
$308$	2.00306	−	0.101280i	0.114135	−	0.00577095i
$309$	−6.12450	+	7.29890i	−0.348411	+	0.415220i
$310$	−19.6582	−	5.53020i	−1.11651	−	0.314094i
$311$	12.1097	−	6.99154i	0.686678	−	0.396454i	−0.115688	−	0.993286i	$-0.536907\pi$
$311$	12.1097	−	6.99154i	0.686678	−	0.396454i	0.802366	+	0.596832i	$0.203574\pi$
$312$	−3.71583	+	11.3296i	−0.210368	+	0.641415i
$313$	9.44845	−	4.40589i	0.534058	−	0.249035i	−0.136829	−	0.990595i	$-0.543691\pi$
$313$	9.44845	−	4.40589i	0.534058	−	0.249035i	0.670887	+	0.741559i	$0.265913\pi$
$314$	−10.3630	−	18.7360i	−0.584818	−	1.05733i
$315$	1.30043	+	0.340181i	0.0732712	+	0.0191670i
$316$	10.2861	+	13.2157i	0.578639	+	0.743440i
$317$	−9.95466	+	14.2167i	−0.559110	+	0.798491i	−0.994826	−	0.101593i	$-0.967606\pi$
$317$	−9.95466	+	14.2167i	−0.559110	+	0.798491i	0.435717	+	0.900084i	$0.356495\pi$
$318$	−0.407918	−	0.296944i	−0.0228749	−	0.0166518i
$319$	4.80468	−	4.03161i	0.269010	−	0.225727i
$320$	−4.92351	+	17.1976i	−0.275233	+	0.961378i
$321$	−7.18510	+	2.61516i	−0.401033	+	0.145964i
$322$	−1.76968	+	0.122111i	−0.0986202	+	0.00680501i
$323$	1.38858	+	3.48418i	0.0772629	+	0.193865i
$324$	−4.43561	+	0.615063i	−0.246423	+	0.0341701i
$325$	23.0604	−	2.29399i	1.27916	−	0.127248i
$326$	2.37854	−	1.92248i	0.131735	−	0.106477i
$327$	0.0270799	−	0.309525i	0.00149752	−	0.0171168i
$328$	18.5648	+	9.93693i	1.02507	+	0.548675i
$329$	1.50938	−	0.266144i	0.0832146	−	0.0146730i
$330$	−7.90199	−	6.79973i	−0.434990	−	0.374313i
$331$	−12.5371	−	7.23832i	−0.689103	−	0.397854i	0.114173	−	0.993461i	$-0.463578\pi$
$331$	−12.5371	−	7.23832i	−0.689103	−	0.397854i	−0.803276	+	0.595607i	$0.796912\pi$
$332$	−10.1423	−	15.6810i	−0.556634	−	0.860604i
$333$	−17.9434	+	8.36716i	−0.983294	+	0.458518i
$334$	−4.99065	−	14.5374i	−0.273076	−	0.795449i
$335$	15.3857	+	15.2039i	0.840611	+	0.830680i
$336$	−0.437923	−	0.906328i	−0.0238907	−	0.0494442i
$337$	1.10099	+	12.5843i	0.0599746	+	0.685513i	0.965360	+	0.260922i	$0.0840265\pi$
$337$	1.10099	+	12.5843i	0.0599746	+	0.685513i	−0.905385	+	0.424591i	$0.860418\pi$
$338$	8.32456	+	8.63622i	0.452796	+	0.469749i
$339$	0.284410	−	1.61297i	0.0154470	−	0.0876045i
$340$	−2.63594	−	2.80355i	−0.142954	−	0.152044i
$341$	23.4062			1.26752
$342$	−8.48754	+	10.3611i	−0.458954	+	0.560263i
$343$	−2.72396	−	2.72396i	−0.147080	−	0.147080i
$344$	17.2683	+	4.03695i	0.931045	+	0.217658i
$345$	7.09829	+	5.88465i	0.382159	+	0.316819i
$346$	0.266017	−	14.4767i	0.0143012	−	0.778272i
$347$	−10.0280	+	0.877340i	−0.538334	+	0.0470981i	−0.353081	−	0.935593i	$-0.614866\pi$
$347$	−10.0280	+	0.877340i	−0.538334	+	0.0470981i	−0.185253	+	0.982691i	$0.559310\pi$
$348$	−2.80210	−	1.43425i	−0.150209	−	0.0768836i
$349$	−25.2352	+	14.5696i	−1.35081	+	0.779890i	−0.988363	−	0.152114i	$-0.951392\pi$
$349$	−25.2352	+	14.5696i	−1.35081	+	0.779890i	−0.362447	+	0.932005i	$0.618058\pi$
$350$	−1.26724	+	1.49048i	−0.0677366	+	0.0796697i
$351$	7.45811	−	20.4910i	0.398084	−	1.09373i
$352$	0.0943353	−	20.5031i	0.00502809	−	1.09282i
$353$	7.27865	+	27.1643i	0.387403	+	1.44581i	0.834344	+	0.551245i	$0.185847\pi$
$353$	7.27865	+	27.1643i	0.387403	+	1.44581i	−0.446940	+	0.894564i	$0.647486\pi$
$354$	2.99318	−	15.3233i	0.159086	−	0.814422i
$355$	8.81837	+	3.15041i	0.468030	+	0.167206i
$356$	9.49633	−	15.1353i	0.503305	−	0.802167i
$357$	0.215709	+	0.0188721i	0.0114165	+	0.000998816i
$358$	−3.96230	+	37.3680i	−0.209414	+	1.97496i
$359$	−30.5559	+	11.1214i	−1.61268	+	0.586967i	−0.981967	−	0.189051i	$-0.939459\pi$
$359$	−30.5559	+	11.1214i	−1.61268	+	0.586967i	−0.630711	+	0.776018i	$0.717237\pi$
$360$	4.20479	−	13.0825i	0.221612	−	0.689508i
$361$	1.14618	+	18.9654i	0.0603254	+	0.998179i
$362$	−16.4603	+	1.13580i	−0.865133	+	0.0596961i
$363$	1.76166	+	0.821474i	0.0924630	+	0.0431162i
$364$	−2.56295	−	0.0942232i	−0.134335	−	0.00493864i
$365$	−20.4562	+	29.5871i	−1.07073	+	1.54866i
$366$	2.35707	+	14.9711i	0.123206	+	0.782551i
$367$	11.2062	+	7.84665i	0.584958	+	0.409592i	0.828248	−	0.560362i	$-0.189338\pi$
$367$	11.2062	+	7.84665i	0.584958	+	0.409592i	−0.243290	+	0.969954i	$0.578227\pi$
$368$	0.249747	+	18.1326i	0.0130190	+	0.945228i
$369$	−14.0084	−	8.08776i	−0.729249	−	0.421032i
$370$	0.358198	−	28.8130i	0.0186218	−	1.49792i
$371$	0.0371185	−	0.101982i	0.00192710	−	0.00529466i
$372$	−4.57007	−	10.8217i	−0.236947	−	0.561081i
$373$	29.9450	+	8.02373i	1.55049	+	0.415453i	0.929638	−	0.368474i	$-0.120120\pi$
$373$	29.9450	+	8.02373i	1.55049	+	0.415453i	0.620853	+	0.783927i	$0.286786\pi$
$374$	3.77854	+	2.27511i	0.195384	+	0.117643i
$375$	10.1128	−	1.06672i	0.522225	−	0.0550853i
$376$	−1.86655	−	15.5568i	−0.0962600	−	0.802278i
$377$	−6.56993	+	4.60032i	−0.338369	+	0.236928i
$378$	0.747205	+	1.68241i	0.0384321	+	0.0865340i
$379$	32.4596			1.66734			0.833670	−	0.552263i	$-0.186236\pi$
$379$	32.4596			1.66734			0.833670	+	0.552263i	$0.186236\pi$
$380$	−8.22733	−	17.6723i	−0.422053	−	0.906571i
$381$	−0.223623			−0.0114566
$382$	4.60188	+	10.3616i	0.235453	+	0.530148i
$383$	−29.4218	+	20.6014i	−1.50338	+	1.05268i	−0.523754	+	0.851869i	$0.675469\pi$
$383$	−29.4218	+	20.6014i	−1.50338	+	1.05268i	−0.979630	+	0.200812i	$0.935642\pi$
$384$	−9.49792	+	3.95962i	−0.484689	+	0.202064i
$385$	0.935565	−	2.03785i	0.0476808	−	0.103859i
$386$	−20.0988	−	12.1018i	−1.02300	−	0.615965i
$387$	−13.1586	−	3.52585i	−0.668892	−	0.179229i
$388$	−8.02296	+	3.38813i	−0.407304	+	0.172006i
$389$	1.35949	−	3.73516i	0.0689288	−	0.189380i	−0.900445	−	0.434969i	$-0.856759\pi$
$389$	1.35949	−	3.73516i	0.0689288	−	0.189380i	0.969374	+	0.245589i	$0.0789814\pi$
$390$	9.30840	+	9.54275i	0.471349	+	0.483216i
$391$	−3.37837	−	1.95050i	−0.170851	−	0.0986411i
$392$	−14.5887	+	13.0630i	−0.736842	+	0.659782i
$393$	1.34949	+	0.944925i	0.0680729	+	0.0476652i
$394$	−1.66249	−	10.5594i	−0.0837550	−	0.531976i
$395$	18.4195	−	3.36083i	0.926785	−	0.169102i
$396$	−0.578644	+	15.7396i	−0.0290780	+	0.790946i
$397$	7.03618	+	3.28103i	0.353136	+	0.164670i	0.591088	−	0.806607i	$-0.298698\pi$
$397$	7.03618	+	3.28103i	0.353136	+	0.164670i	−0.237952	+	0.971277i	$0.576476\pi$
$398$	−20.8437	+	1.43826i	−1.04480	+	0.0720934i
$399$	1.00766	+	0.433359i	0.0504462	+	0.0216951i
$400$	14.5003	+	13.7747i	0.725014	+	0.688734i
$401$	18.2133	−	6.62909i	0.909527	−	0.331041i	0.155463	−	0.987842i	$-0.450313\pi$
$401$	18.2133	−	6.62909i	0.909527	−	0.331041i	0.754064	+	0.656801i	$0.228091\pi$
$402$	−1.31201	+	12.3734i	−0.0654373	+	0.617131i
$403$	−29.8169	−	2.60864i	−1.48528	−	0.129945i
$404$	17.6247	+	11.0583i	0.876862	+	0.550170i
$405$	−1.68438	+	4.71477i	−0.0836974	+	0.234279i
$406$	0.129806	−	0.664528i	0.00644215	−	0.0329799i
$407$	8.54806	+	31.9018i	0.423712	+	1.58131i
$408$	0.314125	−	2.19120i	0.0155515	−	0.108481i
$409$	−2.33827	+	6.42434i	−0.115620	+	0.317663i	−0.983982	−	0.178267i	$-0.942951\pi$
$409$	−2.33827	+	6.42434i	−0.115620	+	0.317663i	0.868362	+	0.495931i	$0.165173\pi$
$410$	19.4512	−	13.2626i	0.960624	−	0.654993i
$411$	4.25038	−	2.45396i	0.209656	−	0.121045i
$412$	−9.54607	+	18.6503i	−0.470301	+	0.918833i
$413$	3.34549	−	0.292692i	0.164621	−	0.0144024i
$414$	0.255936	−	13.9281i	0.0125786	−	0.684528i
$415$	−20.7888	+	1.94333i	−1.02048	+	0.0953941i
$416$	−2.40526	+	26.1081i	−0.117927	+	1.28006i
$417$	−6.86784	−	6.86784i	−0.336319	−	0.336319i
$418$	14.5629	+	16.9450i	0.712294	+	0.828805i
$419$	−8.27144			−0.404086			−0.202043	−	0.979377i	$-0.564758\pi$
$419$	−8.27144			−0.404086			−0.202043	+	0.979377i	$0.564758\pi$
$420$	−1.12486	−	0.0346619i	−0.0548875	−	0.00169133i
$421$	−6.25698	+	35.4851i	−0.304946	+	1.72944i	0.318810	+	0.947819i	$0.396717\pi$
$421$	−6.25698	+	35.4851i	−0.304946	+	1.72944i	−0.623757	+	0.781619i	$0.714394\pi$
$422$	12.4834	+	12.9508i	0.607684	+	0.630436i
$423$	1.04902	+	11.9903i	0.0510049	+	0.582988i
$424$	−1.02007	−	0.436322i	−0.0495391	−	0.0211897i
$425$	−4.14221	+	1.16284i	−0.200927	+	0.0564059i
$426$	1.74905	+	5.09483i	0.0847417	+	0.246846i
$427$	−2.95446	+	1.37769i	−0.142977	+	0.0666710i
$428$	−14.1178	+	9.13128i	−0.682408	+	0.441377i
$429$	−13.2323	−	7.63970i	−0.638863	−	0.368848i
$430$	12.9324	−	15.0289i	0.623658	−	0.724756i
$431$	14.4160	−	2.54193i	0.694395	−	0.122441i	0.184699	−	0.982795i	$-0.440869\pi$
$431$	14.4160	−	2.54193i	0.694395	−	0.122441i	0.509696	+	0.860354i	$0.329758\pi$
$432$	17.5940	−	6.67949i	0.846489	−	0.321367i
$433$	−1.99893	+	22.8478i	−0.0960623	+	1.09800i	0.783236	+	0.621725i	$0.213568\pi$
$433$	−1.99893	+	22.8478i	−0.0960623	+	1.09800i	−0.879298	+	0.476272i	$0.841988\pi$
$434$	1.96513	−	1.58834i	0.0943293	−	0.0762427i
$435$	−2.87086	+	2.03573i	−0.137647	+	0.0976058i
$436$	−0.0938405	−	0.676745i	−0.00449415	−	0.0324102i
$437$	−13.1534	−	14.7479i	−0.629214	−	0.705489i
$438$	−20.6425	+	1.42437i	−0.986335	+	0.0680593i
$439$	7.00284	−	2.54883i	0.334227	−	0.121649i	−0.169455	−	0.985538i	$-0.554201\pi$
$439$	7.00284	−	2.54883i	0.334227	−	0.121649i	0.503682	+	0.863889i	$0.331978\pi$
$440$	−20.2743	−	10.6974i	−0.966541	−	0.509981i
$441$	11.5235	−	9.66937i	0.548738	−	0.460446i
$442$	−4.55987	−	3.31935i	−0.216891	−	0.157885i
$443$	16.3464	−	23.3451i	0.776643	−	1.10916i	−0.214548	−	0.976714i	$-0.568828\pi$
$443$	16.3464	−	23.3451i	0.776643	−	1.10916i	0.991190	−	0.132447i	$-0.0422834\pi$
$444$	13.0806	−	10.1810i	0.620778	−	0.483168i
$445$	−10.0910	−	17.2407i	−0.478359	−	0.817288i
$446$	14.5319	+	26.2733i	0.688108	+	1.24408i
$447$	−4.35333	+	2.02999i	−0.205906	+	0.0960154i
$448$	−1.38341	−	1.72779i	−0.0653602	−	0.0816306i
$449$	−4.80987	+	2.77698i	−0.226992	+	0.131054i	−0.609184	−	0.793029i	$-0.708503\pi$
$449$	−4.80987	+	2.77698i	−0.226992	+	0.131054i	0.382192	+	0.924083i	$0.375169\pi$
$450$	−10.7930	−	10.9340i	−0.508786	−	0.515432i
$451$	−17.3447	+	20.6707i	−0.816732	+	0.973343i
$452$	−0.181869	−	3.59691i	−0.00855439	−	0.169184i
$453$	−5.44401	−	7.77485i	−0.255782	−	0.365294i
$454$	6.93763	−	18.0236i	0.325599	−	0.845887i
$455$	−1.41892	+	2.49172i	−0.0665200	+	0.116814i
$456$	4.99100	−	10.0416i	0.233725	−	0.470240i
$457$	−10.7611	−	10.7611i	−0.503384	−	0.503384i	0.409104	−	0.912488i	$-0.365841\pi$
$457$	−10.7611	−	10.7611i	−0.503384	−	0.503384i	−0.912488	+	0.409104i	$0.865841\pi$
$458$	−13.4360	−	30.2527i	−0.627825	−	1.41362i
$459$	−0.702985	+	3.98683i	−0.0328125	+	0.186089i
$460$	18.1026	+	9.13039i	0.844038	+	0.425707i
$461$	7.27233	+	6.10221i	0.338706	+	0.284208i	0.796236	−	0.604986i	$-0.206821\pi$
$461$	7.27233	+	6.10221i	0.338706	+	0.284208i	−0.457530	+	0.889194i	$0.651266\pi$
$462$	1.25186	−	0.310902i	0.0582420	−	0.0144645i
$463$	9.87721	−	36.8623i	0.459033	−	1.71313i	−0.216919	−	0.976190i	$-0.569601\pi$
$463$	9.87721	−	36.8623i	0.459033	−	1.71313i	0.675952	−	0.736945i	$-0.263732\pi$
$464$	−6.71001	−	1.69925i	−0.311504	−	0.0788858i
$465$	−13.0903	−	1.06691i	−0.607049	−	0.0494768i
$466$	6.51050	−	3.60100i	0.301593	−	0.166813i
$467$	−0.502732	−	1.87622i	−0.0232637	−	0.0868212i	0.953318	−	0.301968i	$-0.0976436\pi$
$467$	−0.502732	−	1.87622i	−0.0232637	−	0.0868212i	−0.976582	+	0.215147i	$0.930977\pi$
$468$	2.49131	−	19.9860i	0.115161	−	0.923852i
$469$	−2.63574	+	0.464752i	−0.121707	+	0.0214602i
$470$	−16.3855	−	6.19558i	−0.755808	−	0.285781i
$471$	−8.85135	−	10.5486i	−0.407848	−	0.486055i
$472$	−1.10343	−	34.3137i	−0.0507894	−	1.57942i
$473$	−9.60412	+	20.5961i	−0.441598	+	0.947010i
$474$	8.12217	+	7.07363i	0.373064	+	0.324902i
$475$	−21.7722	−	0.984794i	−0.998979	−	0.0451854i
$476$	0.471626	−	0.0653978i	0.0216169	−	0.00299750i
$477$	0.772421	+	0.360186i	0.0353667	+	0.0164918i
$478$	2.74420	−	25.8802i	0.125517	−	1.18373i
$479$	17.1579	−	14.3972i	0.783966	−	0.657826i	−0.160278	−	0.987072i	$-0.551239\pi$
$479$	17.1579	−	14.3972i	0.783966	−	0.657826i	0.944244	+	0.329246i	$0.106795\pi$
$480$	−0.987339	+	11.4624i	−0.0450657	+	0.523185i
$481$	−7.33378	−	41.5919i	−0.334391	−	1.89643i
$482$	3.39863	+	5.04868i	0.154803	+	0.229961i
$483$	−1.10198	+	0.295275i	−0.0501419	+	0.0134355i
$484$	4.17915	+	0.896349i	0.189962	+	0.0407431i
$485$	−0.790981	+	9.70482i	−0.0359166	+	0.440673i
$486$	−21.6032	+	7.41636i	−0.979943	+	0.336413i
$487$	−9.06924	−	2.43010i	−0.410967	−	0.110118i	0.0474115	−	0.998875i	$-0.484903\pi$
$487$	−9.06924	−	2.43010i	−0.410967	−	0.110118i	−0.458378	+	0.888757i	$0.651569\pi$
$488$	12.3987	+	30.9334i	0.561262	+	1.40029i
$489$	1.26432	−	1.50676i	0.0571747	−	0.0681381i
$490$	5.40323	+	21.2167i	0.244093	+	0.958471i
$491$	18.0304	+	3.17924i	0.813700	+	0.143477i	0.564987	−	0.825100i	$-0.308881\pi$
$491$	18.0304	+	3.17924i	0.813700	+	0.143477i	0.248713	+	0.968577i	$0.419992\pi$
$492$	12.9435	+	3.98329i	0.583539	+	0.179581i
$493$	1.05288	−	1.05288i	0.0474195	−	0.0474195i
$494$	−16.6629	−	23.2090i	−0.749700	−	1.04422i
$495$	15.3022	+	8.71389i	0.687782	+	0.391660i
$496$	−15.1061	−	20.9535i	−0.678283	−	0.940840i
$497$	−0.949117	+	0.664579i	−0.0425737	+	0.0298104i
$498$	−8.33539	−	8.64746i	−0.373518	−	0.387502i
$499$	30.3358	+	25.4547i	1.35802	+	1.13951i	0.976589	+	0.215112i	$0.0690116\pi$
$499$	30.3358	+	25.4547i	1.35802	+	1.13951i	0.381427	+	0.924399i	$0.375433\pi$
$500$	21.1531	−	7.24891i	0.945995	−	0.324181i
$501$	−4.94258	−	8.56080i	−0.220818	−	0.382468i
$502$	27.0683	+	13.2330i	1.20812	+	0.590616i
$503$	1.86919	+	4.00850i	0.0833433	+	0.178730i	0.943563	−	0.331194i	$-0.107451\pi$
$503$	1.86919	+	4.00850i	0.0833433	+	0.178730i	−0.860220	+	0.509924i	$0.829674\pi$
$504$	1.01950	+	1.36073i	0.0454123	+	0.0606116i
$505$	20.0765	−	11.7508i	0.893391	−	0.522902i
$506$	−22.8074	−	4.45509i	−1.01391	−	0.198053i
$507$	6.31938	+	4.42488i	0.280654	+	0.196516i
$508$	−0.479329	+	0.109733i	−0.0212668	+	0.00486862i
$509$	7.13906	+	8.50801i	0.316433	+	0.377111i	0.900693	−	0.434456i	$-0.143059\pi$
$509$	7.13906	+	8.50801i	0.316433	+	0.377111i	−0.584260	+	0.811567i	$0.698615\pi$
$510$	−2.00951	−	1.44463i	−0.0889824	−	0.0639692i
$511$	−1.52222	−	4.18227i	−0.0673391	−	0.185013i
$512$	−18.4155	+	13.1480i	−0.813857	+	0.581065i
$513$	−9.71327	+	18.0616i	−0.428851	+	0.797438i
$514$	−14.7039	−	12.8057i	−0.648563	−	0.564836i
$515$	13.5494	+	19.1079i	0.597060	+	0.841996i
$516$	11.3977	+	0.419019i	0.501755	+	0.0184463i
$517$	20.0019	+	1.74994i	0.879683	+	0.0769623i
$518$	2.88252	+	2.09833i	0.126651	+	0.0921953i
$519$	−1.61703	−	9.17065i	−0.0709798	−	0.402547i
$520$	24.6349	+	15.8869i	1.08031	+	0.696687i
$521$	21.2371	−	36.7838i	0.930416	−	1.61153i	0.147804	−	0.989017i	$-0.452779\pi$
$521$	21.2371	−	36.7838i	0.930416	−	1.61153i	0.782611	−	0.622511i	$-0.213887\pi$
$522$	5.10988	+	1.47032i	0.223653	+	0.0643543i
$523$	−4.80763	−	10.3100i	−0.210223	−	0.450825i	0.772717	−	0.634751i	$-0.218897\pi$
$523$	−4.80763	−	10.3100i	−0.210223	−	0.450825i	−0.982940	+	0.183926i	$0.941119\pi$
$524$	3.35627	+	1.36321i	0.146619	+	0.0595522i
$525$	−0.616119	+	1.09706i	−0.0268897	+	0.0478795i
$526$	15.6636	−	26.0144i	0.682967	−	1.13428i
$527$	5.53555	−	0.484298i	0.241132	−	0.0210963i
$528$	−2.46845	−	12.9534i	−0.107425	−	0.563726i
$529$	−2.40944	−	0.424849i	−0.104758	−	0.0184717i
$530$	−0.960059	+	0.785456i	−0.0417023	+	0.0341180i
$531$			26.3727i			1.14448i
$532$	2.37254	+	0.434425i	0.102863	+	0.0188347i
$533$	24.3989	−	24.3989i	1.05684	−	1.05684i
$534$	4.12804	−	10.7244i	0.178638	−	0.464091i
$535$	1.74960	+	18.7164i	0.0756419	+	0.809180i
$536$	3.25945	+	27.1659i	0.140787	+	1.17339i
$537$	2.10634	+	24.0756i	0.0908954	+	1.03894i
$538$	5.46819	−	1.35803i	0.235751	−	0.0585488i
$539$	−12.5471	−	21.7322i	−0.540441	−	0.936071i
$540$	2.47851	−	20.8940i	0.106658	−	0.899136i
$541$	−11.6931	−	4.25592i	−0.502724	−	0.182976i	0.0781949	−	0.996938i	$-0.475084\pi$
$541$	−11.6931	−	4.25592i	−0.502724	−	0.182976i	−0.580919	+	0.813962i	$0.697307\pi$
$542$	3.84440	−	13.3606i	0.165131	−	0.573887i
$543$	−10.2499	+	2.74644i	−0.439864	+	0.117861i
$544$	−0.401919	−	4.85092i	−0.0172321	−	0.207981i
$545$	−0.719337	−	0.256987i	−0.0308130	−	0.0110081i
$546$	−1.62938	+	0.256532i	−0.0697311	+	0.0109786i
$547$	−2.42315	+	27.6967i	−0.103606	+	1.18423i	0.749325	+	0.662203i	$0.230378\pi$
$547$	−2.42315	+	27.6967i	−0.103606	+	1.18423i	−0.852931	+	0.522024i	$0.825177\pi$
$548$	7.90639	−	7.34567i	0.337744	−	0.313791i
$549$	−8.75577	−	24.0563i	−0.373687	−	1.02670i
$550$	−21.0891	+	14.5638i	−0.899244	+	0.621001i
$551$	6.73687	−	3.39260i	0.287000	−	0.144530i
$552$	2.39336	+	11.4147i	0.101868	+	0.485842i
$553$	−0.979086	+	2.09966i	−0.0416350	+	0.0892865i
$554$	−19.7465	+	15.9604i	−0.838949	+	0.678091i
$555$	−3.32648	−	18.2312i	−0.141201	−	0.773873i
$556$	−18.0911	−	11.3509i	−0.767232	−	0.481386i
$557$	−10.5307	+	15.0394i	−0.446200	+	0.637239i	−0.977747	−	0.209790i	$-0.932722\pi$
$557$	−10.5307	+	15.0394i	−0.446200	+	0.637239i	0.531547	+	0.847029i	$0.321611\pi$
$558$	11.0809	+	16.4607i	0.469090	+	0.696837i
$559$	14.5300	−	25.1667i	0.614553	−	1.06444i
$560$	−2.42811	+	0.477678i	−0.102606	+	0.0201856i
$561$	2.66557	+	0.970190i	0.112541	+	0.0409614i
$562$	−1.65447	+	3.38425i	−0.0697895	+	0.142756i
$563$	0.179896	−	0.671383i	0.00758173	−	0.0282954i	−0.962031	−	0.272939i	$-0.912004\pi$
$563$	0.179896	−	0.671383i	0.00758173	−	0.0282954i	0.969613	+	0.244644i	$0.0786710\pi$
$564$	−3.09630	−	9.58945i	−0.130378	−	0.403789i
$565$	−3.65939	−	1.68000i	−0.153952	−	0.0706782i
$566$	22.3862	+	0.411359i	0.940962	+	0.0172907i
$567$	−0.355320	−	0.507449i	−0.0149220	−	0.0213109i
$568$	6.24909	+	10.0623i	0.262206	+	0.422207i
$569$		−	40.3365i		−	1.69099i	−0.533980	−	0.845497i	$-0.679304\pi$
$569$		−	40.3365i		−	1.69099i	0.533980	−	0.845497i	$-0.320696\pi$
$570$	−7.37214	−	10.1406i	−0.308785	−	0.424741i
$571$			35.8432i			1.49999i	0.661443	+	0.749996i	$0.269944\pi$
$571$			35.8432i			1.49999i	−0.661443	+	0.749996i	$0.730056\pi$
$572$	−32.1119	−	9.88226i	−1.34267	−	0.413198i
$573$	4.18233	+	5.97298i	0.174719	+	0.249525i
$574$	−0.0535182	+	2.91246i	−0.00223380	+	0.121564i
$575$	18.4126	−	13.2215i	0.767860	−	0.551376i
$576$	14.4637	−	9.64014i	0.602655	−	0.401673i
$577$	2.78161	−	10.3811i	0.115800	−	0.432172i	−0.883545	−	0.468346i	$-0.844850\pi$
$577$	2.78161	−	10.3811i	0.115800	−	0.432172i	0.999346	+	0.0361735i	$0.0115169\pi$
$578$	−20.6581	−	10.0992i	−0.859263	−	0.420070i
$579$	−14.1787	−	5.16064i	−0.589248	−	0.214469i
$580$	−5.15466	+	5.77227i	−0.214036	+	0.239680i
$581$	1.29173	−	2.23734i	0.0535900	−	0.0928205i
$582$	−4.64643	+	3.12784i	−0.192601	+	0.129653i
$583$	0.815476	−	1.16462i	0.0337736	−	0.0482337i
$584$	−43.5475	+	13.1825i	−1.80201	+	0.545494i
$585$	−18.5220	−	12.8059i	−0.765792	−	0.529460i
$586$	10.6287	+	13.1500i	0.439066	+	0.543222i
$587$	18.5327	−	39.7436i	0.764928	−	1.64039i	−0.00311391	−	0.999995i	$-0.500991\pi$
$587$	18.5327	−	39.7436i	0.764928	−	1.64039i	0.768042	−	0.640399i	$-0.221231\pi$
$588$	−7.59793	+	10.0443i	−0.313333	+	0.414219i
$589$	27.3971	+	6.46163i	1.12888	+	0.266247i
$590$	−34.5831	−	16.6528i	−1.42376	−	0.685586i
$591$	−2.35133	−	6.46024i	−0.0967210	−	0.265739i
$592$	23.0420	−	28.2413i	0.947021	−	1.16071i
$593$	2.15446	−	24.6255i	0.0884729	−	1.01125i	−0.814103	−	0.580720i	$-0.802771\pi$
$593$	2.15446	−	24.6255i	0.0884729	−	1.01125i	0.902576	−	0.430530i	$-0.141673\pi$
$594$	3.75066	+	23.8226i	0.153892	+	0.977453i
$595$	0.179095	−	0.501308i	0.00734217	−	0.0205516i
$596$	−8.33510	+	6.48743i	−0.341419	+	0.265735i
$597$	−12.9794	+	3.47782i	−0.531212	+	0.142338i
$598$	28.5574	+	8.21716i	1.16780	+	0.336025i
$599$	−8.43400	−	3.06973i	−0.344604	−	0.125426i	0.163920	−	0.986474i	$-0.447586\pi$
$599$	−8.43400	−	3.06973i	−0.344604	−	0.125426i	−0.508523	+	0.861048i	$0.669808\pi$
$600$	10.8511	+	6.90687i	0.442995	+	0.281972i
$601$	−17.0966	−	29.6121i	−0.697383	−	1.20790i	−0.969371	−	0.245602i	$-0.921014\pi$
$601$	−17.0966	−	29.6121i	−0.697383	−	1.20790i	0.271988	−	0.962301i	$-0.412319\pi$
$602$	0.591306	+	2.38093i	0.0240998	+	0.0970395i
$603$	−1.83183	−	20.9380i	−0.0745981	−	0.852660i
$604$	−15.4842	−	13.9937i	−0.630044	−	0.569397i
$605$	3.04988	−	3.67888i	0.123995	−	0.149568i
$606$	12.4884	+	4.80702i	0.507305	+	0.195272i
$607$	−0.918539	+	0.918539i	−0.0372823	+	0.0372823i	−0.725502	−	0.688220i	$-0.758392\pi$
$607$	−0.918539	+	0.918539i	−0.0372823	+	0.0372823i	0.688220	+	0.725502i	$0.258392\pi$
$608$	5.77060	−	23.9729i	0.234029	−	0.972230i
$609$		−	0.435462i		−	0.0176458i
$610$	37.0743	+	3.70851i	1.50109	+	0.150153i
$611$	−25.2851	−	4.45845i	−1.02293	−	0.180369i
$612$	0.188819	+	3.73438i	0.00763257	+	0.150953i
$613$	−41.5409	+	3.63435i	−1.67782	+	0.146790i	−0.885913	−	0.463852i	$-0.846467\pi$
$613$	−41.5409	+	3.63435i	−1.67782	+	0.146790i	−0.791907	+	0.610642i	$0.790911\pi$
$614$	23.0985	+	13.9079i	0.932181	+	0.561279i
$615$	10.6425	−	10.7698i	0.429148	−	0.434279i
$616$	2.53077	−	1.28070i	0.101968	−	0.0516011i
$617$	−3.91177	−	8.38882i	−0.157482	−	0.337721i	0.811697	−	0.584079i	$-0.198544\pi$
$617$	−3.91177	−	8.38882i	−0.157482	−	0.337721i	−0.969179	+	0.246357i	$0.920766\pi$
$618$	−3.72604	+	12.9493i	−0.149883	+	0.520896i
$619$	1.47335	−	2.55191i	0.0592188	−	0.102570i	−0.834896	−	0.550408i	$-0.814472\pi$
$619$	1.47335	−	2.55191i	0.0592188	−	0.102570i	0.894115	+	0.447837i	$0.147806\pi$
$620$	−28.5822	+	4.13659i	−1.14789	+	0.166130i
$621$	−3.70385	−	21.0056i	−0.148630	−	0.842925i
$622$	11.6382	−	15.9876i	0.466649	−	0.641046i
$623$	2.46237	+	0.215429i	0.0986526	+	0.00863098i
$624$	1.70085	+	16.7763i	0.0680885	+	0.671589i
$625$	3.75483	−	24.7164i	0.150193	−	0.988657i
$626$	9.68283	−	11.1181i	0.387004	−	0.444370i
$627$	11.2815	+	8.90027i	0.450541	+	0.355443i
$628$	−24.1488	−	18.2672i	−0.963644	−	0.728942i
$629$	2.68169	+	7.36787i	0.106926	+	0.293776i
$630$	1.87605	−	0.306804i	0.0747438	−	0.0122234i
$631$	−19.8592	−	23.6672i	−0.790581	−	0.942178i	0.208778	−	0.977963i	$-0.433051\pi$
$631$	−19.8592	−	23.6672i	−0.790581	−	0.942178i	−0.999360	+	0.0357851i	$0.988607\pi$
$632$	20.8807	+	11.1765i	0.830589	+	0.444577i
$633$	9.47649	+	6.63551i	0.376657	+	0.263738i
$634$	−4.70544	+	24.0890i	−0.186877	+	0.956697i
$635$	−0.139133	+	0.531873i	−0.00552132	+	0.0211067i
$636$	−0.697678	−	0.149639i	−0.0276647	−	0.00593355i
$637$	13.5615	+	29.0826i	0.537325	+	1.15230i
$638$	3.89570	−	7.96876i	0.154232	−	0.315486i
$639$	−4.54951	−	7.87999i	−0.179976	−	0.311727i
$640$	3.50833	+	25.0538i	0.138679	+	0.990337i
$641$	20.6542	+	17.3310i	0.815793	+	0.684532i	0.951983	−	0.306151i	$-0.0990413\pi$
$641$	20.6542	+	17.3310i	0.815793	+	0.684532i	−0.136190	+	0.990683i	$0.543486\pi$
$642$	−7.78541	+	7.50445i	−0.307266	+	0.296177i
$643$	19.6286	−	13.7441i	0.774077	−	0.542015i	−0.118476	−	0.992957i	$-0.537801\pi$
$643$	19.6286	−	13.7441i	0.774077	−	0.542015i	0.892553	+	0.450942i	$0.148912\pi$
$644$	−2.21717	+	1.17366i	−0.0873688	+	0.0462488i
$645$	6.31007	−	11.0809i	0.248459	−	0.436311i
$646$	3.79471	+	3.70614i	0.149301	+	0.145816i
$647$	−10.9984	+	10.9984i	−0.432391	+	0.432391i	−0.889441	−	0.457050i	$-0.848906\pi$
$647$	−10.9984	+	10.9984i	−0.432391	+	0.432391i	0.457050	+	0.889441i	$0.348906\pi$
$648$	−5.37987	+	3.34110i	−0.211341	+	0.131251i
$649$	43.3259	+	7.63953i	1.70069	+	0.299878i
$650$	28.4883	−	16.2022i	1.11740	−	0.635501i
$651$	1.04457	−	1.24487i	0.0409400	−	0.0487904i
$652$	1.97066	−	3.85011i	0.0771770	−	0.150782i
$653$	−15.4156	−	4.13061i	−0.603261	−	0.161643i	−0.0557539	−	0.998445i	$-0.517756\pi$
$653$	−15.4156	−	4.13061i	−0.603261	−	0.161643i	−0.547507	+	0.836801i	$0.684423\pi$
$654$	−0.142674	−	0.415598i	−0.00557901	−	0.0162512i
$655$	3.08706	−	2.62177i	0.120622	−	0.102441i
$656$	29.6986	+	2.18661i	1.15954	+	0.0853727i
$657$	33.7605	−	9.04610i	1.31712	−	0.352922i
$658$	1.79806	−	1.21040i	0.0700958	−	0.0471864i
$659$	−0.452685	−	2.56730i	−0.0176341	−	0.100008i	0.974720	−	0.223428i	$-0.0717248\pi$
$659$	−0.452685	−	2.56730i	−0.0176341	−	0.100008i	−0.992354	+	0.123420i	$0.960614\pi$
$660$	−14.1163	−	4.25256i	−0.549478	−	0.165531i
$661$	−1.94597	+	1.63286i	−0.0756893	+	0.0635109i	−0.679847	−	0.733354i	$-0.737954\pi$
$661$	−1.94597	+	1.63286i	−0.0756893	+	0.0635109i	0.604158	+	0.796864i	$0.293510\pi$
$662$	−20.3589	−	2.15875i	−0.791272	−	0.0839023i
$663$	−3.28751	−	1.53299i	−0.127676	−	0.0595364i
$664$	−22.1100	−	14.4453i	−0.858034	−	0.560587i
$665$	1.65766	−	2.12704i	0.0642812	−	0.0824829i
$666$	−18.3885	+	21.1143i	−0.712541	+	0.818163i
$667$	−3.31551	+	7.11014i	−0.128377	+	0.275306i
$668$	−14.7951	−	15.9244i	−0.572439	−	0.616135i
$669$	12.4122	+	14.7922i	0.479882	+	0.571901i
$670$	28.6131	+	10.8190i	1.10542	+	0.417974i
$671$	−42.0567	+	7.41574i	−1.62358	+	0.286281i
$672$	−1.08626	−	0.920030i	−0.0419034	−	0.0354909i
$673$	8.85491	+	33.0470i	0.341332	+	1.27387i	0.896840	+	0.442356i	$0.145857\pi$
$673$	8.85491	+	33.0470i	0.341332	+	1.27387i	−0.555508	+	0.831511i	$0.687476\pi$
$674$	8.64671	+	15.6330i	0.333059	+	0.602160i
$675$	−19.4287	−	13.2629i	−0.747812	−	0.510488i
$676$	15.7167	+	6.38363i	0.604488	+	0.245524i
$677$	6.96203	−	25.9827i	0.267573	−	0.998595i	−0.693084	−	0.720857i	$-0.743749\pi$
$677$	6.96203	−	25.9827i	0.267573	−	0.998595i	0.960657	−	0.277738i	$-0.0895847\pi$
$678$	−0.558289	−	2.24798i	−0.0214409	−	0.0863333i
$679$	−0.922917	−	0.774419i	−0.0354183	−	0.0297195i
$680$	−5.01620	−	2.11044i	−0.192362	−	0.0809316i
$681$	2.15684	−	12.2321i	0.0826504	−	0.468733i
$682$	30.2520	−	13.4357i	1.15841	−	0.514481i
$683$	28.7635	+	28.7635i	1.10060	+	1.10060i	0.994338	+	0.106267i	$0.0338899\pi$
$683$	28.7635	+	28.7635i	1.10060	+	1.10060i	0.106267	+	0.994338i	$0.466110\pi$
$684$	−5.02245	+	18.2635i	−0.192038	+	0.698323i
$685$	−3.19210	−	11.6361i	−0.121964	−	0.444591i
$686$	−5.08427	−	1.95704i	−0.194118	−	0.0747200i
$687$	−12.2111	−	17.4392i	−0.465881	−	0.665347i
$688$	24.6362	−	4.69475i	0.939246	−	0.178986i
$689$	−1.16862	+	1.39271i	−0.0445209	+	0.0530579i
$690$	12.5523	+	3.53119i	0.477858	+	0.134430i
$691$	32.6666	−	18.8601i	1.24270	−	0.717471i	0.273054	−	0.961999i	$-0.411966\pi$
$691$	32.6666	−	18.8601i	1.24270	−	0.717471i	0.969642	+	0.244527i	$0.0786328\pi$
$692$	−7.96614	−	18.8635i	−0.302827	−	0.717083i
$693$	−1.97470	+	0.920819i	−0.0750128	+	0.0349790i
$694$	−12.4574	+	6.89028i	−0.472877	+	0.261551i
$695$	−20.6077	+	12.0617i	−0.781695	+	0.457527i
$696$	−4.44495	−	0.245256i	−0.168485	−	0.00929640i
$697$	−3.67431	+	5.24746i	−0.139175	+	0.198762i
$698$	−24.2527	+	33.3164i	−0.917977	+	1.26104i
$699$	3.66550	−	3.07572i	0.138642	−	0.116335i
$700$	−0.782301	+	2.65384i	−0.0295682	+	0.100306i
$701$	−7.68634	+	2.79760i	−0.290309	+	0.105664i	−0.483070	−	0.875582i	$-0.660478\pi$
$701$	−7.68634	+	2.79760i	−0.290309	+	0.105664i	0.192760	+	0.981246i	$0.438256\pi$
$702$	−2.12287	−	30.7653i	−0.0801226	−	1.16116i
$703$	1.19858	+	39.7009i	0.0452052	+	1.49735i
$704$	−11.6473	−	26.5540i	−0.438976	−	1.00079i
$705$	−11.1066	−	1.89042i	−0.418300	−	0.0711972i
$706$	25.0004	+	30.9311i	0.940903	+	1.16411i
$707$	−0.250863	+	2.86737i	−0.00943467	+	0.107839i
$708$	−4.92730	−	21.5231i	−0.185179	−	0.808888i
$709$	27.2924	−	4.81239i	1.02499	−	0.180733i	0.364212	−	0.931316i	$-0.381338\pi$
$709$	27.2924	−	4.81239i	1.02499	−	0.180733i	0.660777	+	0.750583i	$0.270227\pi$
$710$	13.2059	−	0.990120i	0.495610	−	0.0371585i
$711$	−15.7559	−	9.09667i	−0.590892	−	0.341152i
$712$	3.58580	−	25.0131i	0.134384	−	0.937405i
$713$	−26.5338	+	12.3729i	−0.993699	+	0.463369i
$714$	0.289632	−	0.0994302i	0.0108392	−	0.00372108i
$715$	−26.4034	+	26.7190i	−0.987430	+	0.999235i
$716$	16.3289	+	50.5717i	0.610240	+	1.88995i
$717$	−1.45880	−	16.6742i	−0.0544801	−	0.622710i
$718$	−33.1088	+	31.9140i	−1.23561	+	1.19102i
$719$	5.60301	−	31.7763i	0.208957	−	1.18505i	−0.682133	−	0.731228i	$-0.738947\pi$
$719$	5.60301	−	31.7763i	0.208957	−	1.18505i	0.891090	−	0.453827i	$-0.149941\pi$
$720$	−2.07507	−	19.3225i	−0.0773332	−	0.720107i
$721$	−2.89835			−0.107940
$722$	12.3680	+	23.8544i	0.460289	+	0.887769i
$723$	2.76774	+	2.76774i	0.102933	+	0.102933i
$724$	−20.6226	+	10.9166i	−0.766432	+	0.405711i
$725$	3.05567	+	8.09475i	0.113485	+	0.300631i
$726$	2.74845	+	0.0505042i	0.102004	+	0.00187439i
$727$	−28.0599	+	2.45492i	−1.04068	+	0.0910481i	−0.594664	−	0.803974i	$-0.702715\pi$
$727$	−28.0599	+	2.45492i	−1.04068	+	0.0910481i	−0.446021	+	0.895023i	$0.647159\pi$
$728$	−3.36665	+	1.34941i	−0.124776	+	0.0500126i
$729$	−6.90461	+	3.98638i	−0.255726	+	0.147644i
$730$	−9.45545	+	49.9830i	−0.349962	+	1.84995i
$731$	−1.84521	+	5.06967i	−0.0682475	+	0.187509i
$732$	11.6402	+	17.9968i	0.430234	+	0.665180i
$733$	0.269781	+	1.00684i	0.00996460	+	0.0371884i	0.970729	−	0.240177i	$-0.0772054\pi$
$733$	0.269781	+	1.00684i	0.00996460	+	0.0371884i	−0.960765	+	0.277365i	$0.910539\pi$
$734$	18.9879	+	3.70901i	0.700856	+	0.136902i
$735$	6.02655	+	12.7260i	0.222292	+	0.469405i
$736$	10.7313	+	23.2926i	0.395562	+	0.858578i
$737$	−34.9282	−	3.05582i	−1.28660	−	0.112563i
$738$	−22.7481	−	2.41209i	−0.837370	−	0.0887903i
$739$	−15.6151	+	5.68343i	−0.574411	+	0.209068i	−0.612859	−	0.790192i	$-0.709981\pi$
$739$	−15.6151	+	5.68343i	−0.574411	+	0.209068i	0.0384483	+	0.999261i	$0.487758\pi$
$740$	−16.0764	−	37.4457i	−0.590979	−	1.37653i
$741$	−13.3794	−	12.5953i	−0.491506	−	0.462698i
$742$	−0.0105654	−	0.153117i	−0.000387867	−	0.00562109i
$743$	14.6288	+	6.82151i	0.536678	+	0.250257i	0.672008	−	0.740544i	$-0.265432\pi$
$743$	14.6288	+	6.82151i	0.536678	+	0.250257i	−0.135331	+	0.990800i	$0.543210\pi$
$744$	−12.1186	−	11.3635i	−0.444291	−	0.416607i
$745$	2.11967	+	11.6171i	0.0776587	+	0.425619i
$746$	43.3090	−	6.81862i	1.58565	−	0.249647i
$747$	16.6190	+	11.6368i	0.608058	+	0.425767i
$748$	6.18965	+	0.771559i	0.226316	+	0.0282110i
$749$	−2.01431	−	1.16296i	−0.0736011	−	0.0424936i
$750$	12.4583	−	7.18372i	0.454912	−	0.262312i
$751$	3.89111	−	10.6907i	0.141989	−	0.390110i	−0.848231	−	0.529626i	$-0.822332\pi$
$751$	3.89111	−	10.6907i	0.141989	−	0.390110i	0.990220	+	0.139516i	$0.0445546\pi$
$752$	−11.3424	−	19.0353i	−0.413615	−	0.694146i
$753$	18.7174	+	5.01532i	0.682101	+	0.182768i
$754$	−5.85080	+	9.71710i	−0.213074	+	0.353876i
$755$	−21.8791	+	8.11090i	−0.796262	+	0.295186i
$756$	1.93149	+	1.74557i	0.0702476	+	0.0634857i
$757$	27.4902	−	19.2489i	0.999150	−	0.699612i	0.0450140	−	0.998986i	$-0.485667\pi$
$757$	27.4902	−	19.2489i	0.999150	−	0.699612i	0.954136	+	0.299374i	$0.0967779\pi$
$758$	41.9533	−	18.6326i	1.52381	−	0.676766i
$759$	−14.9456			−0.542489
$760$	−20.7780	−	18.1184i	−0.753696	−	0.657223i
$761$	−16.9068			−0.612870			−0.306435	−	0.951892i	$-0.599136\pi$
$761$	−16.9068			−0.612870			−0.306435	+	0.951892i	$0.599136\pi$
$762$	−0.289028	+	0.128365i	−0.0104704	+	0.00465017i
$763$	0.0774219	−	0.0542114i	0.00280286	−	0.00196258i
$764$	11.8957	+	10.7506i	0.430370	+	0.388943i
$765$	3.79924	+	1.74421i	0.137362	+	0.0630619i
$766$	−26.2013	+	43.5156i	−0.946693	+	1.57228i
$767$	−54.3408	−	14.5606i	−1.96213	−	0.525752i
$768$	−10.0029	+	10.5697i	−0.360950	+	0.381403i
$769$	−12.3057	+	33.8097i	−0.443756	+	1.21921i	0.493248	+	0.869889i	$0.335810\pi$
$769$	−12.3057	+	33.8097i	−0.443756	+	1.21921i	−0.937003	+	0.349320i	$0.886413\pi$
$770$	0.0394202	−	3.17092i	0.00142061	−	0.114272i
$771$	−10.8602	−	6.27014i	−0.391121	−	0.225814i
$772$	−32.9240	−	4.10408i	−1.18496	−	0.147709i
$773$	2.51180	+	1.75878i	0.0903432	+	0.0632590i	0.617875	−	0.786276i	$-0.287994\pi$
$773$	2.51180	+	1.75878i	0.0903432	+	0.0632590i	−0.527532	+	0.849535i	$0.676883\pi$
$774$	−19.0312	+	2.99629i	−0.684061	+	0.107700i
$775$	−10.6821	+	30.4707i	−0.383711	+	1.09454i
$776$	−8.42463	+	8.98445i	−0.302427	+	0.322523i
$777$	2.07820	+	0.969079i	0.0745549	+	0.0347655i
$778$	−0.386964	−	5.60799i	−0.0138733	−	0.201056i
$779$	−26.0085	+	19.4068i	−0.931850	+	0.695320i
$780$	17.5086	+	6.99055i	0.626910	+	0.250302i
$781$	−14.2634	+	5.19145i	−0.510384	+	0.185765i
$782$	−5.48610	−	0.581716i	−0.196182	−	0.0208021i
$783$	8.11048	+	0.709575i	0.289845	+	0.0253581i
$784$	−11.3571	+	25.2579i	−0.405612	+	0.902069i
$785$	−30.5963	+	14.4893i	−1.09203	+	0.517144i
$786$	2.28660	+	0.446654i	0.0815602	+	0.0159316i
$787$	4.84550	+	18.0836i	0.172723	+	0.644612i	0.996928	+	0.0783206i	$0.0249558\pi$
$787$	4.84550	+	18.0836i	0.172723	+	0.644612i	−0.824205	+	0.566292i	$0.808378\pi$
$788$	−8.21008	−	12.6935i	−0.292472	−	0.452187i
$789$	6.67954	−	18.3519i	0.237798	−	0.653344i
$790$	21.8776	−	14.9170i	0.778369	−	0.530724i
$791$	0.431472	−	0.249111i	0.0153414	−	0.00885736i
$792$	8.28703	+	20.6753i	0.294467	+	0.734664i
$793$	54.4019	−	4.75955i	1.93187	−	0.169017i
$794$	10.9775	+	0.201718i	0.389577	+	0.00715869i
$795$	−0.509154	+	0.614161i	−0.0180578	+	0.0217821i
$796$	−26.1144	+	13.8237i	−0.925599	+	0.489967i
$797$	−4.11894	−	4.11894i	−0.145900	−	0.145900i	0.630384	−	0.776284i	$-0.282898\pi$
$797$	−4.11894	−	4.11894i	−0.145900	−	0.145900i	−0.776284	+	0.630384i	$0.782898\pi$
$798$	1.55114	−	0.0183159i	0.0549097	−	0.000648377i
$799$	4.76664			0.168632
$800$	26.6483	+	9.47995i	0.942159	+	0.335167i
$801$	−3.37068	+	19.1161i	−0.119097	+	0.675434i
$802$	19.7350	−	19.0228i	0.696866	−	0.671718i
$803$	−5.08163	−	58.0833i	−0.179327	−	2.04972i
$804$	5.40689	+	16.7455i	0.190686	+	0.590568i
$805$	0.0166667	+	2.80471i	0.000587423	+	0.0988529i
$806$	−40.0350	+	13.7440i	−1.41017	+	0.484111i
$807$	3.28414	−	1.53142i	0.115607	−	0.0539085i
$808$	29.1272	+	4.17560i	1.02469	+	0.146897i
$809$	20.0152	+	11.5558i	0.703697	+	0.406279i	0.808723	−	0.588190i	$-0.200159\pi$
$809$	20.0152	+	11.5558i	0.703697	+	0.406279i	−0.105026	+	0.994469i	$0.533493\pi$
$810$	0.529371	+	7.06061i	0.0186002	+	0.248085i
$811$	−48.3822	+	8.53108i	−1.69893	+	0.299567i	−0.937320	−	0.348471i	$-0.886701\pi$
$811$	−48.3822	+	8.53108i	−1.69893	+	0.299567i	−0.761608	+	0.648038i	$0.775590\pi$
$812$	−0.213683	−	0.933398i	−0.00749881	−	0.0327559i
$813$	0.779294	−	8.90737i	0.0273310	−	0.312395i
$814$	29.3606	+	36.3256i	1.02909	+	1.27321i
$815$	−2.79710	−	3.94458i	−0.0979783	−	0.138173i
$816$	−0.851803	−	3.01240i	−0.0298191	−	0.105455i
$817$	−16.9275	+	21.4564i	−0.592218	+	0.750665i
$818$	0.665563	+	9.64554i	0.0232709	+	0.337248i
$819$	2.61817	−	0.952936i	0.0914863	−	0.0332983i
$820$	17.5271	−	28.3070i	0.612074	−	0.988524i
$821$	3.59019	−	3.01253i	0.125298	−	0.105138i	−0.577985	−	0.816047i	$-0.696161\pi$
$821$	3.59019	−	3.01253i	0.125298	−	0.105138i	0.703284	+	0.710909i	$0.251716\pi$
$822$	4.08489	−	5.61150i	0.142477	−	0.195724i
$823$	−12.9682	+	18.5205i	−0.452044	+	0.645585i	−0.978893	−	0.204374i	$-0.934484\pi$
$823$	−12.9682	+	18.5205i	−0.452044	+	0.645585i	0.526849	+	0.849959i	$0.323373\pi$
$824$	−1.63238	+	29.5847i	−0.0568666	+	1.03063i
$825$	−11.5160	+	11.7930i	−0.400936	+	0.410581i
$826$	4.15596	−	2.29869i	0.144604	−	0.0799815i
$827$	37.3275	−	17.4061i	1.29800	−	0.605269i	0.354013	−	0.935241i	$-0.384817\pi$
$827$	37.3275	−	17.4061i	1.29800	−	0.605269i	0.943991	+	0.329972i	$0.107039\pi$
$828$	−7.66426	−	18.1486i	−0.266351	−	0.630709i
$829$	41.1346	−	23.7491i	1.42866	−	0.824839i	0.431647	−	0.902043i	$-0.357933\pi$
$829$	41.1346	−	23.7491i	1.42866	−	0.824839i	0.997015	+	0.0772039i	$0.0245992\pi$
$830$	−25.7535	+	14.4449i	−0.893917	+	0.501391i
$831$	−10.4963	+	12.5091i	−0.364114	+	0.433934i
$832$	11.8779	+	35.1248i	0.411793	+	1.21773i
$833$	−3.41703	−	4.88002i	−0.118393	−	0.169083i
$834$	−12.8188	−	4.93422i	−0.443880	−	0.170858i
$835$	−23.4365	+	6.42929i	−0.811052	+	0.222495i
$836$	28.5490	+	13.5415i	0.987388	+	0.468344i
$837$	21.4837	+	21.4837i	0.742584	+	0.742584i
$838$	−10.6906	+	4.74800i	−0.369302	+	0.164017i
$839$	−4.91623	+	27.8813i	−0.169727	+	0.962569i	0.774329	+	0.632784i	$0.218088\pi$
$839$	−4.91623	+	27.8813i	−0.169727	+	0.962569i	−0.944056	+	0.329786i	$0.893023\pi$
$840$	−1.47375	+	0.600896i	−0.0508492	+	0.0207329i
$841$	19.9214	+	16.7160i	0.686944	+	0.576415i
$842$	12.2823	+	49.4553i	0.423275	+	1.70434i
$843$	−0.627047	+	2.34017i	−0.0215966	+	0.0805997i
$844$	23.5686	+	9.57284i	0.811266	+	0.329511i
$845$	14.4560	−	12.2772i	0.497303	−	0.422348i
$846$	8.23854	+	14.8950i	0.283247	+	0.512102i
$847$	0.153035	+	0.571133i	0.00525833	+	0.0196243i
$848$	−1.56888	+	0.0216087i	−0.0538755	+	0.000742047i
$849$	14.1811	−	2.50052i	0.486695	−	0.0858175i
$850$	−4.68622	+	3.88067i	−0.160736	+	0.133106i
$851$	−26.5541	−	31.6459i	−0.910262	−	1.08481i
$852$	5.18516	+	5.58096i	0.177641	+	0.191201i
$853$	−1.10279	+	2.36493i	−0.0377587	+	0.0809737i	−0.924282	−	0.381709i	$-0.875335\pi$
$853$	−1.10279	+	2.36493i	−0.0377587	+	0.0809737i	0.886524	+	0.462683i	$0.153113\pi$
$854$	−3.02775	+	3.47656i	−0.103607	+	0.118966i
$855$	15.5056	+	14.4240i	0.530281	+	0.493290i
$856$	−13.0053	+	19.9059i	−0.444512	+	0.680370i
$857$	−28.4065	−	13.2462i	−0.970349	−	0.452481i	−0.128213	−	0.991747i	$-0.540924\pi$
$857$	−28.4065	−	13.2462i	−0.970349	−	0.452481i	−0.842136	+	0.539266i	$0.818702\pi$
$858$	−21.4879	−	2.27846i	−0.733583	−	0.0777853i
$859$	24.9223	−	20.9123i	0.850336	−	0.713517i	−0.109527	−	0.993984i	$-0.534934\pi$
$859$	24.9223	−	20.9123i	0.850336	−	0.713517i	0.959864	+	0.280467i	$0.0904893\pi$
$860$	8.08798	−	26.8480i	0.275798	−	0.915508i
$861$	0.325319	+	1.84498i	0.0110869	+	0.0628767i
$862$	17.1732	−	11.5605i	0.584923	−	0.393753i
$863$	10.3467	−	2.77239i	0.352206	−	0.0943733i	−0.0783783	−	0.996924i	$-0.524974\pi$
$863$	10.3467	−	2.77239i	0.352206	−	0.0943733i	0.430584	+	0.902550i	$0.358308\pi$
$864$	18.9056	−	18.7324i	0.643182	−	0.637290i
$865$	−22.8179	−	1.85975i	−0.775831	−	0.0632332i
$866$	10.5316	+	30.6777i	0.357879	+	1.04247i
$867$	−14.2848	−	3.82760i	−0.485137	−	0.129992i
$868$	1.62814	−	3.18092i	0.0552628	−	0.107968i
$869$	−19.5084	+	23.2492i	−0.661777	+	0.788675i
$870$	−2.54197	+	4.27908i	−0.0861808	+	0.145074i
$871$	44.1539	+	7.78553i	1.49610	+	0.263803i
$872$	−0.509754	−	0.820811i	−0.0172625	−	0.0277962i
$873$	6.69011	−	6.69011i	0.226426	−	0.226426i
$874$	−25.4662	−	11.5110i	−0.861406	−	0.389365i
$875$	2.22594	+	2.14796i	0.0752506	+	0.0726144i
$876$	−25.8623	+	13.6902i	−0.873806	+	0.462550i
$877$	−6.04969	+	4.23604i	−0.204283	+	0.143041i	−0.671242	−	0.741239i	$-0.734239\pi$
$877$	−6.04969	+	4.23604i	−0.204283	+	0.143041i	0.466958	+	0.884279i	$0.345350\pi$
$878$	7.58792	−	7.31409i	0.256080	−	0.246839i
$879$	8.33029	+	6.98994i	0.280974	+	0.235765i
$880$	−32.3447	−	2.18827i	−1.09034	−	0.0737665i
$881$	−16.3853	−	28.3801i	−0.552034	−	0.956151i	−0.998128	−	0.0611648i	$-0.980518\pi$
$881$	−16.3853	−	28.3801i	−0.552034	−	0.956151i	0.446094	−	0.894986i	$-0.352815\pi$
$882$	9.34342	−	19.1122i	0.314609	−	0.643541i
$883$	−5.74406	−	12.3182i	−0.193303	−	0.414540i	0.785637	−	0.618688i	$-0.212335\pi$
$883$	−5.74406	−	12.3182i	−0.193303	−	0.414540i	−0.978940	+	0.204148i	$0.934558\pi$
$884$	−7.79891	−	1.67272i	−0.262306	−	0.0562595i
$885$	−23.8825	−	6.24743i	−0.802801	−	0.210005i
$886$	7.72674	−	39.5563i	0.259585	−	1.32892i
$887$	−7.01326	−	4.91074i	−0.235482	−	0.164886i	0.449879	−	0.893089i	$-0.351467\pi$
$887$	−7.01326	−	4.91074i	−0.235482	−	0.164886i	−0.685362	+	0.728203i	$0.740356\pi$
$888$	11.0623	−	20.6673i	0.371225	−	0.693548i
$889$	−0.0437252	−	0.0521097i	−0.00146650	−	0.00174770i
$890$	−22.9390	−	16.4908i	−0.768916	−	0.552771i
$891$	−2.77563	−	7.62597i	−0.0929870	−	0.255480i
$892$	33.8637	+	25.6160i	1.13384	+	0.857687i
$893$	22.9292	+	7.57012i	0.767296	+	0.253324i
$894$	−4.46132	+	5.12263i	−0.149209	+	0.171327i
$895$	58.5728	+	9.96946i	1.95787	+	0.333242i
$896$	−2.77983	−	1.43902i	−0.0928675	−	0.0480743i
$897$	19.0389	+	1.66569i	0.635691	+	0.0556158i
$898$	−4.62260	+	6.35016i	−0.154258	+	0.211908i
$899$	−1.94050	−	11.0051i	−0.0647192	−	0.367041i
$900$	−20.2260	−	7.93648i	−0.674201	−	0.264549i
$901$	0.168762	−	0.292305i	0.00562228	−	0.00973808i
$902$	−10.5522	+	36.6726i	−0.351351	+	1.22106i
$903$	0.666802	+	1.42996i	0.0221898	+	0.0475861i
$904$	−2.29977	−	4.54453i	−0.0764892	−	0.151149i
$905$	0.155022	+	26.0874i	0.00515309	+	0.867175i
$906$	−11.4992	−	6.92383i	−0.382035	−	0.230029i
$907$	38.4405	−	3.36311i	1.27640	−	0.111670i	0.571276	−	0.820758i	$-0.306449\pi$
$907$	38.4405	−	3.36311i	1.27640	−	0.111670i	0.705120	+	0.709088i	$0.250893\pi$
$908$	−1.37921	−	27.2774i	−0.0457708	−	0.905232i
$909$	−22.2603	−	3.92509i	−0.738328	−	0.130187i
$910$	−0.403617	+	4.03499i	−0.0133798	+	0.133759i
$911$		−	7.47915i		−	0.247795i	−0.992295	−	0.123898i	$-0.960461\pi$
$911$		−	7.47915i		−	0.247795i	0.992295	−	0.123898i	$-0.0395394\pi$
$912$	0.686657	−	15.8435i	0.0227375	−	0.524629i
$913$	23.9314	−	23.9314i	0.792013	−	0.792013i
$914$	−20.0856	−	7.73137i	−0.664374	−	0.255731i
$915$	23.8589	−	2.23032i	0.788752	−	0.0737322i
$916$	−34.7315	−	31.3883i	−1.14756	−	1.03710i
$917$	0.0436767	+	0.499227i	0.00144233	+	0.0164859i
$918$	1.37994	+	5.55641i	0.0455448	+	0.183389i
$919$	−8.04595	−	13.9360i	−0.265412	−	0.459706i	0.702260	−	0.711921i	$-0.252174\pi$
$919$	−8.04595	−	13.9360i	−0.265412	−	0.459706i	−0.967671	+	0.252214i	$0.918841\pi$
$920$	28.6382	+	1.40951i	0.944175	+	0.0464702i
$921$	16.2949	+	5.93085i	0.536934	+	0.195428i
$922$	12.9021	+	3.71248i	0.424909	+	0.122264i
$923$	18.7485	−	5.02364i	0.617114	−	0.165355i
$924$	1.43954	−	1.12043i	0.0473575	−	0.0368595i
$925$	−45.4315	−	3.43121i	−1.49378	−	0.112817i
$926$	−8.39373	−	53.3134i	−0.275835	−	1.75199i
$927$	1.98375	−	22.6743i	0.0651548	−	0.744723i
$928$	−9.64795	+	1.65546i	−0.316709	+	0.0543431i
$929$	9.46330	+	26.0002i	0.310481	+	0.853039i	0.992560	+	0.121760i	$0.0388538\pi$
$929$	9.46330	+	26.0002i	0.310481	+	0.853039i	−0.682079	+	0.731279i	$0.738924\pi$
$930$	−17.5314	+	6.13519i	−0.574876	+	0.201181i
$931$	−8.68690	−	28.9013i	−0.284702	−	0.947203i
$932$	6.34762	−	8.39140i	0.207923	−	0.274869i
$933$	5.37491	−	11.5265i	0.175967	−	0.377362i
$934$	−1.72677	−	2.13639i	−0.0565015	−	0.0699050i
$935$	3.96599	−	5.73627i	0.129702	−	0.187596i
$936$	−8.25245	−	27.2615i	−0.269740	−	0.891070i
$937$	−4.80114	+	6.85673i	−0.156846	+	0.224000i	−0.889882	−	0.456190i	$-0.849214\pi$
$937$	−4.80114	+	6.85673i	−0.156846	+	0.224000i	0.733036	+	0.680190i	$0.238103\pi$
$938$	−3.13985	+	2.11366i	−0.102520	+	0.0690133i
$939$	4.74106	−	8.21176i	0.154719	−	0.267981i
$940$	−24.7343	+	1.39803i	−0.806745	+	0.0455987i
$941$	6.23416	+	2.26905i	0.203228	+	0.0739689i	0.441629	−	0.897198i	$-0.354401\pi$
$941$	6.23416	+	2.26905i	0.203228	+	0.0739689i	−0.238401	+	0.971167i	$0.576623\pi$
$942$	−17.4953	−	8.55297i	−0.570028	−	0.278671i
$943$	8.73551	−	32.6014i	0.284467	−	1.06165i
$944$	−21.1230	−	43.7163i	−0.687496	−	1.42284i
$945$	2.72918	−	1.01175i	0.0887803	−	0.0329122i
$946$	−0.590461	+	32.1330i	−0.0191976	+	1.04473i
$947$	−0.274284	−	0.391718i	−0.00891303	−	0.0127291i	0.814671	−	0.579924i	$-0.196918\pi$
$947$	−0.274284	−	0.391718i	−0.00891303	−	0.0127291i	−0.823584	+	0.567195i	$0.808029\pi$
$948$	14.5581	+	4.48019i	0.472827	+	0.145510i
$949$			74.5578i			2.42025i
$950$	−28.7054	+	11.2249i	−0.931326	+	0.364185i
$951$			15.7854i			0.511877i
$952$	0.572025	−	0.355249i	0.0185394	−	0.0115137i
$953$	−20.3971	−	29.1301i	−0.660726	−	0.943615i	−0.999996	−	0.00292587i	$-0.999069\pi$
$953$	−20.3971	−	29.1301i	−0.660726	−	0.943615i	0.339269	−	0.940689i	$-0.389820\pi$
$954$	1.20509	+	0.0221442i	0.0390163	+	0.000716946i
$955$	16.8085	−	6.23115i	0.543910	−	0.201635i
$956$	−11.3090	−	35.0248i	−0.365760	−	1.13278i
$957$	1.47648	−	5.51030i	0.0477278	−	0.178123i
$958$	13.9119	−	28.4571i	0.449473	−	0.919408i
$959$	1.40291	+	0.510619i	0.0453024	+	0.0164887i
$960$	5.30357	+	15.3816i	0.171172	+	0.496440i
$961$	5.35134	−	9.26880i	0.172624	−	0.298994i
$962$	−33.3535	−	49.5468i	−1.07536	−	1.59745i
$963$	10.4767	−	14.9623i	0.337608	−	0.482154i
$964$	7.29071	+	4.57442i	0.234818	+	0.147332i
$965$	−21.0959	+	30.5124i	−0.679101	+	0.982228i
$966$	−1.25479	+	1.01420i	−0.0403723	+	0.0326314i
$967$	−18.0334	+	38.6727i	−0.579914	+	1.24363i	0.369391	+	0.929274i	$0.379566\pi$
$967$	−18.0334	+	38.6727i	−0.579914	+	1.24363i	−0.949305	+	0.314355i	$0.898212\pi$
$968$	5.91599	−	1.24042i	0.190147	−	0.0398687i
$969$	2.85222	+	1.87148i	0.0916266	+	0.0601205i
$970$	4.54847	+	12.9973i	0.146043	+	0.417318i
$971$	−11.5854	−	31.8307i	−0.371795	−	1.02150i	−0.974667	−	0.223660i	$-0.928200\pi$
$971$	−11.5854	−	31.8307i	−0.371795	−	1.02150i	0.602873	−	0.797837i	$-0.294023\pi$
$972$	−23.6645	+	21.9862i	−0.759040	+	0.705209i
$973$	0.257501	−	2.94325i	0.00825510	−	0.0943562i
$974$	−13.1167	+	2.06511i	−0.420287	+	0.0661705i
$975$	15.9844	−	13.7395i	0.511911	−	0.440017i
$976$	33.7815	+	32.8636i	1.08132	+	1.05194i
$977$	7.60249	−	2.03708i	0.243225	−	0.0651720i	−0.135147	−	0.990826i	$-0.543151\pi$
$977$	7.60249	−	2.03708i	0.243225	−	0.0651720i	0.378372	+	0.925654i	$0.376484\pi$
$978$	0.769193	−	2.67321i	0.0245961	−	0.0854797i
$979$	30.4281	+	11.0749i	0.972487	+	0.353956i
$980$	19.1624	+	24.3205i	0.612121	+	0.776889i
$981$	0.371115	+	0.642790i	0.0118488	+	0.0205227i
$982$	25.1288	−	6.24077i	0.801893	−	0.199151i
$983$	3.19002	+	36.4621i	0.101746	+	1.16296i	0.859751	+	0.510713i	$0.170619\pi$
$983$	3.19002	+	36.4621i	0.101746	+	1.16296i	−0.758005	+	0.652249i	$0.773826\pi$
$984$	19.0157	−	2.28157i	0.606198	−	0.0727337i
$985$	−16.8282	+	1.57309i	−0.536191	+	0.0501230i
$986$	0.756448	−	1.96521i	0.0240902	−	0.0625850i
$987$	0.985716	−	0.985716i	0.0313757	−	0.0313757i
$988$	−34.8589	−	20.4322i	−1.10901	−	0.650034i
$989$		−	28.4251i		−	0.903864i
$990$	24.7797	+	2.47869i	0.787550	+	0.0787781i
$991$	23.8478	+	4.20501i	0.757550	+	0.133577i	0.539066	−	0.842264i	$-0.318777\pi$
$991$	23.8478	+	4.20501i	0.757550	+	0.133577i	0.218485	+	0.975840i	$0.429889\pi$
$992$	−31.5521	−	18.4107i	−1.00178	−	0.584539i
$993$	−13.1169	+	1.14758i	−0.416254	+	0.0364175i
$994$	−0.845228	+	1.40377i	−0.0268090	+	0.0445248i
$995$	0.196304	+	33.0345i	0.00622325	+	1.04726i
$996$	−15.7371	−	6.39193i	−0.498650	−	0.202536i
$997$	−8.23674	−	17.6637i	−0.260860	−	0.559416i	0.731636	−	0.681696i	$-0.238757\pi$
$997$	−8.23674	−	17.6637i	−0.260860	−	0.559416i	−0.992496	+	0.122280i	$0.960980\pi$
$998$	53.8199	+	15.4862i	1.70364	+	0.490208i
$999$	−21.4355	+	37.1273i	−0.678189	+	1.17466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.347.49	yes	672
4.3	odd	2	inner	380.2.bj.a.347.34	yes	672
5.3	odd	4	inner	380.2.bj.a.43.21	yes	672
19.4	even	9	inner	380.2.bj.a.327.52	yes	672
20.3	even	4	inner	380.2.bj.a.43.52	yes	672
76.23	odd	18	inner	380.2.bj.a.327.21	yes	672
95.23	odd	36	inner	380.2.bj.a.23.34	✓	672
380.23	even	36	inner	380.2.bj.a.23.49	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.34	✓	672	95.23	odd	36	inner
380.2.bj.a.23.49	yes	672	380.23	even	36	inner
380.2.bj.a.43.21	yes	672	5.3	odd	4	inner
380.2.bj.a.43.52	yes	672	20.3	even	4	inner
380.2.bj.a.327.21	yes	672	76.23	odd	18	inner
380.2.bj.a.327.52	yes	672	19.4	even	9	inner
380.2.bj.a.347.34	yes	672	4.3	odd	2	inner
380.2.bj.a.347.49	yes	672	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29248 - 0.574023i) q^{2} +(0.745050 - 0.521689i) q^{3} +(1.34099 - 1.48382i) q^{4} +(-0.777253 - 2.09663i) q^{5} +(0.663498 - 1.10195i) q^{6} +(0.267247 + 0.0716085i) q^{7} +(0.881455 - 2.68757i) q^{8} +(-0.743121 + 2.04171i) q^{9} +O(q^{10})\)	\(q+(1.29248 - 0.574023i) q^{2} +(0.745050 - 0.521689i) q^{3} +(1.34099 - 1.48382i) q^{4} +(-0.777253 - 2.09663i) q^{5} +(0.663498 - 1.10195i) q^{6} +(0.267247 + 0.0716085i) q^{7} +(0.881455 - 2.68757i) q^{8} +(-0.743121 + 2.04171i) q^{9} +(-2.20810 - 2.26369i) q^{10} +(3.13892 + 1.81226i) q^{11} +(0.225012 - 1.80511i) q^{12} +(-3.79665 - 2.65844i) q^{13} +(0.386515 - 0.0608534i) q^{14} +(-1.67288 - 1.15661i) q^{15} +(-0.403469 - 3.97960i) q^{16} +(0.779848 + 0.363649i) q^{17} +(0.211521 + 3.06543i) q^{18} +(3.17381 + 2.98779i) q^{19} +(-4.15333 - 1.65827i) q^{20} +(0.236469 - 0.0860678i) q^{21} +(5.09726 + 0.540487i) q^{22} +(-4.51633 - 0.395128i) q^{23} +(-0.745350 - 2.46222i) q^{24} +(-3.79176 + 3.25923i) q^{25} +(-6.43308 - 1.25661i) q^{26} +(1.21769 + 4.54449i) q^{27} +(0.464631 - 0.300520i) q^{28} +(0.591851 - 1.62610i) q^{29} +(-2.82609 - 0.534621i) q^{30} +(5.59259 - 3.22888i) q^{31} +(-2.80586 - 4.91194i) q^{32} +(3.28409 - 0.287320i) q^{33} +(1.21668 + 0.0223572i) q^{34} +(-0.0575813 - 0.615977i) q^{35} +(2.03302 + 3.84058i) q^{36} +(6.44328 + 6.44328i) q^{37} +(5.81714 + 2.03981i) q^{38} -4.21557 q^{39} +(-6.31997 + 0.240833i) q^{40} +(-1.29277 + 7.33165i) q^{41} +(0.256226 - 0.246980i) q^{42} +(0.546456 + 6.24603i) q^{43} +(6.89835 - 2.22738i) q^{44} +(4.85831 - 0.0288700i) q^{45} +(-6.06407 + 2.08179i) q^{46} +(5.02057 - 2.34113i) q^{47} +(-2.37672 - 2.75451i) q^{48} +(-5.99588 - 3.46173i) q^{49} +(-3.02988 + 6.38904i) q^{50} +(0.770738 - 0.135902i) q^{51} +(-9.03594 + 2.06860i) q^{52} +(0.0341874 - 0.390764i) q^{53} +(4.18248 + 5.17467i) q^{54} +(1.35991 - 7.98975i) q^{55} +(0.428019 - 0.655125i) q^{56} +(3.92335 + 0.570310i) q^{57} +(-0.168464 - 2.44143i) q^{58} +(11.4060 - 4.15144i) q^{59} +(-3.95954 + 0.931255i) q^{60} +(-9.02586 + 7.57359i) q^{61} +(5.37484 - 7.38353i) q^{62} +(-0.344800 + 0.492426i) q^{63} +(-6.44608 - 4.73794i) q^{64} +(-2.62282 + 10.0265i) q^{65} +(4.07968 - 2.25650i) q^{66} +(-8.76714 + 4.08818i) q^{67} +(1.58536 - 0.669506i) q^{68} +(-3.57103 + 2.06173i) q^{69} +(-0.428007 - 0.763083i) q^{70} +(-2.69187 + 3.20805i) q^{71} +(4.83221 + 3.79686i) q^{72} +(-9.22675 - 13.1772i) q^{73} +(12.0264 + 4.62920i) q^{74} +(-1.12474 + 4.40641i) q^{75} +(8.68943 - 0.702767i) q^{76} +(0.709093 + 0.709093i) q^{77} +(-5.44853 + 2.41984i) q^{78} +(-1.45403 + 8.24624i) q^{79} +(-8.03017 + 3.93908i) q^{80} +(-1.71519 - 1.43922i) q^{81} +(2.53767 + 10.2181i) q^{82} +(2.41674 - 9.01938i) q^{83} +(0.189395 - 0.466296i) q^{84} +(0.156300 - 1.91770i) q^{85} +(4.29165 + 7.75917i) q^{86} +(-0.407359 - 1.52029i) q^{87} +(7.63739 - 6.83865i) q^{88} +(8.79815 - 1.55135i) q^{89} +(6.26268 - 2.82610i) q^{90} +(-0.824274 - 0.982331i) q^{91} +(-6.64268 + 6.17158i) q^{92} +(2.48228 - 5.32327i) q^{93} +(5.14511 - 5.90779i) q^{94} +(3.79746 - 8.97660i) q^{95} +(-4.65301 - 2.19585i) q^{96} +(-3.94654 - 1.84030i) q^{97} +(-9.73666 - 1.03242i) q^{98} +(-6.03270 + 5.06204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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