LMFDB - Embedded newform 738.2.e.j.247.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(247,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.247"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-7,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 12 x^{12} - 31 x^{11} + 73 x^{10} - 150 x^{9} + 297 x^{8} - 549 x^{7} + 891 x^{6} + \cdots + 2187 $ x^14 - 4x^13 + 12x^12 - 31x^11 + 73x^10 - 150x^9 + 297x^8 - 549x^7 + 891x^6 - 1350x^5 + 1971x^4 - 2511x^3 + 2916x^2 - 2916*x + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.5
Root			$1.19349 - 1.25522i$ of defining polynomial
Character	$\chi$	$=$	738.247
Dual form			738.2.e.j.493.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.19349 + 1.25522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.81416 + 3.14221i) q^{5} +(0.490312 - 1.66120i) q^{6} +(-0.330242 - 0.571996i) q^{7} +1.00000 q^{8} +(-0.151175 + 2.99619i) q^{9} +3.62831 q^{10} +(2.36839 + 4.10218i) q^{11} +(-1.68380 + 0.405978i) q^{12} +(1.96949 - 3.41126i) q^{13} +(-0.330242 + 0.571996i) q^{14} +(-6.10935 + 1.47302i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.36010 q^{17} +(2.67036 - 1.36717i) q^{18} -5.47838 q^{19} +(-1.81416 - 3.14221i) q^{20} +(0.323843 - 1.09720i) q^{21} +(2.36839 - 4.10218i) q^{22} +(3.52508 - 6.10562i) q^{23} +(1.19349 + 1.25522i) q^{24} +(-4.08232 - 7.07079i) q^{25} -3.93899 q^{26} +(-3.94131 + 3.38616i) q^{27} +0.660484 q^{28} +(4.45981 + 7.72461i) q^{29} +(4.33034 + 4.55434i) q^{30} +(-4.83343 + 8.37175i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.32250 + 7.86876i) q^{33} +(2.68005 + 4.64198i) q^{34} +2.39644 q^{35} +(-2.51919 - 1.62902i) q^{36} -6.71665 q^{37} +(2.73919 + 4.74441i) q^{38} +(6.63246 - 1.59914i) q^{39} +(-1.81416 + 3.14221i) q^{40} +(-0.500000 + 0.866025i) q^{41} +(-1.11212 + 0.268142i) q^{42} +(-1.03815 - 1.79813i) q^{43} -4.73678 q^{44} +(-9.14040 - 5.91058i) q^{45} -7.05017 q^{46} +(-2.32171 - 4.02131i) q^{47} +(0.490312 - 1.66120i) q^{48} +(3.28188 - 5.68438i) q^{49} +(-4.08232 + 7.07079i) q^{50} +(-6.39721 - 6.72813i) q^{51} +(1.96949 + 3.41126i) q^{52} +5.71582 q^{53} +(4.90315 + 1.72020i) q^{54} -17.1865 q^{55} +(-0.330242 - 0.571996i) q^{56} +(-6.53838 - 6.87659i) q^{57} +(4.45981 - 7.72461i) q^{58} +(-3.23475 + 5.60275i) q^{59} +(1.77900 - 6.02736i) q^{60} +(5.29228 + 9.16650i) q^{61} +9.66687 q^{62} +(1.76373 - 0.902996i) q^{63} +1.00000 q^{64} +(7.14593 + 12.3771i) q^{65} +(7.97580 - 1.92303i) q^{66} +(2.72835 - 4.72564i) q^{67} +(2.68005 - 4.64198i) q^{68} +(11.8711 - 2.86222i) q^{69} +(-1.19822 - 2.07538i) q^{70} -3.42340 q^{71} +(-0.151175 + 2.99619i) q^{72} -2.58783 q^{73} +(3.35833 + 5.81679i) q^{74} +(4.00322 - 13.5631i) q^{75} +(2.73919 - 4.74441i) q^{76} +(1.56428 - 2.70942i) q^{77} +(-4.70113 - 4.94431i) q^{78} +(4.88118 + 8.45445i) q^{79} +3.62831 q^{80} +(-8.95429 - 0.905897i) q^{81} +1.00000 q^{82} +(4.23404 + 7.33358i) q^{83} +(0.788279 + 0.829055i) q^{84} +(9.72406 - 16.8426i) q^{85} +(-1.03815 + 1.79813i) q^{86} +(-4.37339 + 14.8173i) q^{87} +(2.36839 + 4.10218i) q^{88} +2.36259 q^{89} +(-0.548510 + 10.8711i) q^{90} -2.60164 q^{91} +(3.52508 + 6.10562i) q^{92} +(-16.2771 + 3.92454i) q^{93} +(-2.32171 + 4.02131i) q^{94} +(9.93863 - 17.2142i) q^{95} +(-1.68380 + 0.405978i) q^{96} +(-5.34250 - 9.25348i) q^{97} -6.56376 q^{98} +(-12.6489 + 6.47600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{2} + 4 q^{3} - 7 q^{4} + 5 q^{5} - 2 q^{6} - q^{7} + 14 q^{8} - 8 q^{9} - 10 q^{10} + 10 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 5 q^{15} - 7 q^{16} - 26 q^{17} + 4 q^{18} - 2 q^{19} + 5 q^{20}+ \cdots - 34 q^{99}+O(q^{100}) $ 14 * q - 7 * q^2 + 4 * q^3 - 7 * q^4 + 5 * q^5 - 2 * q^6 - q^7 + 14 * q^8 - 8 * q^9 - 10 * q^10 + 10 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 5 * q^15 - 7 * q^16 - 26 * q^17 + 4 * q^18 - 2 * q^19 + 5 * q^20 - 17 * q^21 + 10 * q^22 + 15 * q^23 + 4 * q^24 - 14 * q^25 - 8 * q^26 + 13 * q^27 + 2 * q^28 + 30 * q^29 + 7 * q^30 - 13 * q^31 - 7 * q^32 + 23 * q^33 + 13 * q^34 - 16 * q^35 + 4 * q^36 + 14 * q^37 + q^38 - 7 * q^39 + 5 * q^40 - 7 * q^41 + 22 * q^42 + 5 * q^43 - 20 * q^44 - 5 * q^45 - 30 * q^46 + 3 * q^47 - 2 * q^48 + 12 * q^49 - 14 * q^50 + 5 * q^51 + 4 * q^52 - 24 * q^53 - 20 * q^54 - 26 * q^55 - q^56 - 13 * q^57 + 30 * q^58 + 13 * q^59 - 2 * q^60 + 55 * q^61 + 26 * q^62 + 19 * q^63 + 14 * q^64 + 25 * q^65 + 11 * q^66 + 15 * q^67 + 13 * q^68 + 39 * q^69 + 8 * q^70 - 24 * q^71 - 8 * q^72 - 7 * q^74 + 5 * q^75 + q^76 - 5 * q^77 - 10 * q^78 - 12 * q^79 - 10 * q^80 - 20 * q^81 + 14 * q^82 + 36 * q^83 - 5 * q^84 + 4 * q^85 + 5 * q^86 - 21 * q^87 + 10 * q^88 - 32 * q^89 - 2 * q^90 - 62 * q^91 + 15 * q^92 - 59 * q^93 + 3 * q^94 + 43 * q^95 - 2 * q^96 - q^97 - 24 * q^98 - 34 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.19349	+	1.25522i	0.689060	+	0.724704i
$3$	1.19349	+	1.25522i	0.689060	+	0.724704i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.81416	+	3.14221i	−0.811315	+	1.40524i	0.100629	+	0.994924i	$0.467914\pi$
$5$	−1.81416	+	3.14221i	−0.811315	+	1.40524i	−0.911944	+	0.410315i	$0.865419\pi$
$6$	0.490312	−	1.66120i	0.200169	−	0.678183i
$7$	−0.330242	−	0.571996i	−0.124820	−	0.216194i	0.796843	−	0.604187i	$-0.206502\pi$
$7$	−0.330242	−	0.571996i	−0.124820	−	0.216194i	−0.921662	+	0.387993i	$0.873169\pi$
$8$	1.00000			0.353553
$9$	−0.151175	+	2.99619i	−0.0503917	+	0.998730i
$10$	3.62831			1.14737
$11$	2.36839	+	4.10218i	0.714097	+	1.23685i	0.963307	+	0.268403i	$0.0864958\pi$
$11$	2.36839	+	4.10218i	0.714097	+	1.23685i	−0.249210	+	0.968450i	$0.580171\pi$
$12$	−1.68380	+	0.405978i	−0.486071	+	0.117196i
$13$	1.96949	−	3.41126i	0.546239	−	0.946114i	−0.452289	−	0.891872i	$-0.649392\pi$
$13$	1.96949	−	3.41126i	0.546239	−	0.946114i	0.998528	−	0.0542422i	$-0.0172743\pi$
$14$	−0.330242	+	0.571996i	−0.0882609	+	0.152872i
$15$	−6.10935	+	1.47302i	−1.57743	+	0.380331i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.36010			−1.30002			−0.650008	−	0.759928i	$-0.725234\pi$
$17$	−5.36010			−1.30002			−0.650008	+	0.759928i	$0.725234\pi$
$18$	2.67036	−	1.36717i	0.629411	−	0.322246i
$19$	−5.47838			−1.25683			−0.628413	−	0.777880i	$-0.716295\pi$
$19$	−5.47838			−1.25683			−0.628413	+	0.777880i	$0.716295\pi$
$20$	−1.81416	−	3.14221i	−0.405657	−	0.702619i
$21$	0.323843	−	1.09720i	0.0706684	−	0.239428i
$22$	2.36839	−	4.10218i	0.504943	−	0.874587i
$23$	3.52508	−	6.10562i	0.735031	−	1.27311i	−0.219679	−	0.975572i	$-0.570501\pi$
$23$	3.52508	−	6.10562i	0.735031	−	1.27311i	0.954710	−	0.297538i	$-0.0961656\pi$
$24$	1.19349	+	1.25522i	0.243620	+	0.256222i
$25$	−4.08232	−	7.07079i	−0.816464	−	1.41416i
$26$	−3.93899			−0.772499
$27$	−3.94131	+	3.38616i	−0.758506	+	0.651666i
$28$	0.660484			0.124820
$29$	4.45981	+	7.72461i	0.828165	+	1.43442i	0.899476	+	0.436970i	$0.143948\pi$
$29$	4.45981	+	7.72461i	0.828165	+	1.43442i	−0.0713112	+	0.997454i	$0.522718\pi$
$30$	4.33034	+	4.55434i	0.790609	+	0.831505i
$31$	−4.83343	+	8.37175i	−0.868110	+	1.50361i	−0.00418466	+	0.999991i	$0.501332\pi$
$31$	−4.83343	+	8.37175i	−0.868110	+	1.50361i	−0.863925	+	0.503620i	$0.832001\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.32250	+	7.86876i	−0.404296	+	1.36977i
$34$	2.68005	+	4.64198i	0.459625	+	0.796094i
$35$	2.39644			0.405072
$36$	−2.51919	−	1.62902i	−0.419865	−	0.271503i
$37$	−6.71665			−1.10421			−0.552105	−	0.833774i	$-0.686175\pi$
$37$	−6.71665			−1.10421			−0.552105	+	0.833774i	$0.686175\pi$
$38$	2.73919	+	4.74441i	0.444355	+	0.769646i
$39$	6.63246	−	1.59914i	1.06204	−	0.256068i
$40$	−1.81416	+	3.14221i	−0.286843	+	0.496827i
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i
$42$	−1.11212	+	0.268142i	−0.171604	+	0.0413752i
$43$	−1.03815	−	1.79813i	−0.158316	−	0.274212i	0.775945	−	0.630800i	$-0.217273\pi$
$43$	−1.03815	−	1.79813i	−0.158316	−	0.274212i	−0.934262	+	0.356588i	$0.883940\pi$
$44$	−4.73678			−0.714097
$45$	−9.14040	−	5.91058i	−1.36257	−	0.881097i
$46$	−7.05017			−1.03949
$47$	−2.32171	−	4.02131i	−0.338656	−	0.586569i	0.645524	−	0.763740i	$-0.276639\pi$
$47$	−2.32171	−	4.02131i	−0.338656	−	0.586569i	−0.984180	+	0.177171i	$0.943306\pi$
$48$	0.490312	−	1.66120i	0.0707705	−	0.239774i
$49$	3.28188	−	5.68438i	0.468840	−	0.812055i
$50$	−4.08232	+	7.07079i	−0.577327	+	0.999960i
$51$	−6.39721	−	6.72813i	−0.895789	−	0.942126i
$52$	1.96949	+	3.41126i	0.273120	+	0.473057i
$53$	5.71582			0.785129			0.392564	−	0.919725i	$-0.371588\pi$
$53$	5.71582			0.785129			0.392564	+	0.919725i	$0.371588\pi$
$54$	4.90315	+	1.72020i	0.667235	+	0.234090i
$55$	−17.1865			−2.31743
$56$	−0.330242	−	0.571996i	−0.0441304	−	0.0764361i
$57$	−6.53838	−	6.87659i	−0.866029	−	0.910827i
$58$	4.45981	−	7.72461i	0.585601	−	1.01429i
$59$	−3.23475	+	5.60275i	−0.421128	+	0.729416i	−0.996050	−	0.0887925i	$-0.971699\pi$
$59$	−3.23475	+	5.60275i	−0.421128	+	0.729416i	0.574922	+	0.818208i	$0.305033\pi$
$60$	1.77900	−	6.02736i	0.229669	−	0.778129i
$61$	5.29228	+	9.16650i	0.677607	+	1.17365i	0.975699	+	0.219113i	$0.0703164\pi$
$61$	5.29228	+	9.16650i	0.677607	+	1.17365i	−0.298092	+	0.954537i	$0.596350\pi$
$62$	9.66687			1.22769
$63$	1.76373	−	0.902996i	0.222209	−	0.113767i
$64$	1.00000			0.125000
$65$	7.14593	+	12.3771i	0.886344	+	1.53519i
$66$	7.97580	−	1.92303i	0.981753	−	0.236709i
$67$	2.72835	−	4.72564i	0.333321	−	0.577329i	−0.649840	−	0.760071i	$-0.725164\pi$
$67$	2.72835	−	4.72564i	0.333321	−	0.577329i	0.983161	+	0.182742i	$0.0584974\pi$
$68$	2.68005	−	4.64198i	0.325004	−	0.562923i
$69$	11.8711	−	2.86222i	1.42911	−	0.344570i
$70$	−1.19822	−	2.07538i	−0.143215	−	0.248055i
$71$	−3.42340			−0.406283			−0.203141	−	0.979149i	$-0.565115\pi$
$71$	−3.42340			−0.406283			−0.203141	+	0.979149i	$0.565115\pi$
$72$	−0.151175	+	2.99619i	−0.0178161	+	0.353104i
$73$	−2.58783			−0.302883			−0.151441	−	0.988466i	$-0.548392\pi$
$73$	−2.58783			−0.302883			−0.151441	+	0.988466i	$0.548392\pi$
$74$	3.35833	+	5.81679i	0.390397	+	0.676188i
$75$	4.00322	−	13.5631i	0.462252	−	1.56613i
$76$	2.73919	−	4.74441i	0.314207	−	0.544222i
$77$	1.56428	−	2.70942i	0.178267	−	0.308767i
$78$	−4.70113	−	4.94431i	−0.532298	−	0.559833i
$79$	4.88118	+	8.45445i	0.549176	+	0.951200i	0.998331	+	0.0577468i	$0.0183916\pi$
$79$	4.88118	+	8.45445i	0.549176	+	0.951200i	−0.449155	+	0.893454i	$0.648275\pi$
$80$	3.62831			0.405657
$81$	−8.95429	−	0.905897i	−0.994921	−	0.100655i
$82$	1.00000			0.110432
$83$	4.23404	+	7.33358i	0.464747	+	0.804965i	0.999190	−	0.0402395i	$-0.0128121\pi$
$83$	4.23404	+	7.33358i	0.464747	+	0.804965i	−0.534444	+	0.845204i	$0.679479\pi$
$84$	0.788279	+	0.829055i	0.0860083	+	0.0904573i
$85$	9.72406	−	16.8426i	1.05472	−	1.82683i
$86$	−1.03815	+	1.79813i	−0.111947	+	0.193897i
$87$	−4.37339	+	14.8173i	−0.468877	+	1.58858i
$88$	2.36839	+	4.10218i	0.252471	+	0.437293i
$89$	2.36259			0.250434			0.125217	−	0.992129i	$-0.460037\pi$
$89$	2.36259			0.250434			0.125217	+	0.992129i	$0.460037\pi$
$90$	−0.548510	+	10.8711i	−0.0578180	+	1.14591i
$91$	−2.60164			−0.272726
$92$	3.52508	+	6.10562i	0.367515	+	0.636555i
$93$	−16.2771	+	3.92454i	−1.68785	+	0.406956i
$94$	−2.32171	+	4.02131i	−0.239466	+	0.414767i
$95$	9.93863	−	17.2142i	1.01968	−	1.76614i
$96$	−1.68380	+	0.405978i	−0.171852	+	0.0414350i
$97$	−5.34250	−	9.25348i	−0.542448	−	0.939548i	−0.998763	−	0.0497295i	$-0.984164\pi$
$97$	−5.34250	−	9.25348i	−0.542448	−	0.939548i	0.456314	−	0.889819i	$-0.349169\pi$
$98$	−6.56376			−0.663040
$99$	−12.6489	+	6.47600i	−1.27127	+	0.650863i
$100$	8.16464			0.816464
$101$	4.37833	+	7.58349i	0.435660	+	0.754585i	0.997349	−	0.0727631i	$-0.0231817\pi$
$101$	4.37833	+	7.58349i	0.435660	+	0.754585i	−0.561689	+	0.827348i	$0.689848\pi$
$102$	−2.62812	+	8.90421i	−0.260223	+	0.881649i
$103$	−1.39354	+	2.41369i	−0.137310	+	0.237828i	−0.926477	−	0.376350i	$-0.877179\pi$
$103$	−1.39354	+	2.41369i	−0.137310	+	0.237828i	0.789168	+	0.614178i	$0.210512\pi$
$104$	1.96949	−	3.41126i	0.193125	−	0.334502i
$105$	2.86012	+	3.00807i	0.279119	+	0.293558i
$106$	−2.85791	−	4.95005i	−0.277585	−	0.480791i
$107$	2.61144			0.252458			0.126229	−	0.992001i	$-0.459713\pi$
$107$	2.61144			0.252458			0.126229	+	0.992001i	$0.459713\pi$
$108$	−0.961840	−	5.10636i	−0.0925531	−	0.491359i
$109$	20.5528			1.96861			0.984303	−	0.176487i	$-0.0564734\pi$
$109$	20.5528			1.96861			0.984303	+	0.176487i	$0.0564734\pi$
$110$	8.59326	+	14.8840i	0.819335	+	1.41913i
$111$	−8.01624	−	8.43090i	−0.760868	−	0.800226i
$112$	−0.330242	+	0.571996i	−0.0312049	+	0.0540485i
$113$	0.343880	−	0.595618i	0.0323495	−	0.0560310i	−0.849397	−	0.527754i	$-0.823034\pi$
$113$	0.343880	−	0.595618i	0.0323495	−	0.0560310i	0.881747	+	0.471723i	$0.156368\pi$
$114$	−2.68612	+	9.10070i	−0.251578	+	0.852358i
$115$	12.7901	+	22.1531i	1.19268	+	2.06579i
$116$	−8.91961			−0.828165
$117$	9.92305	+	6.41667i	0.917386	+	0.593221i
$118$	6.46950			0.595566
$119$	1.77013	+	3.06596i	0.162268	+	0.281056i
$120$	−6.10935	+	1.47302i	−0.557705	+	0.134467i
$121$	−5.71856	+	9.90484i	−0.519869	+	0.900440i
$122$	5.29228	−	9.16650i	0.479141	−	0.829896i
$123$	−1.68380	+	0.405978i	−0.151823	+	0.0366058i
$124$	−4.83343	−	8.37175i	−0.434055	−	0.751805i
$125$	11.4823			1.02701
$126$	−1.66388	−	1.07594i	−0.148230	−	0.0958522i
$127$	18.5262			1.64393			0.821966	−	0.569536i	$-0.192877\pi$
$127$	18.5262			1.64393			0.821966	+	0.569536i	$0.192877\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.01804	−	3.44916i	0.0896330	−	0.303681i
$130$	7.14593	−	12.3771i	0.626740	−	1.08555i
$131$	−3.48028	+	6.02802i	−0.304073	+	0.526670i	−0.977055	−	0.212989i	$-0.931680\pi$
$131$	−3.48028	+	6.02802i	−0.304073	+	0.526670i	0.672981	+	0.739659i	$0.265013\pi$
$132$	−5.65329	−	5.94573i	−0.492056	−	0.517509i
$133$	1.80919	+	3.13361i	0.156877	+	0.271718i
$134$	−5.45670			−0.471387
$135$	−3.48985	−	18.5274i	−0.300359	−	1.59459i
$136$	−5.36010			−0.459625
$137$	3.34224	+	5.78893i	0.285547	+	0.494581i	0.972742	−	0.231892i	$-0.0744915\pi$
$137$	3.34224	+	5.78893i	0.285547	+	0.494581i	−0.687195	+	0.726473i	$0.741158\pi$
$138$	−8.41429	−	8.84954i	−0.716272	−	0.753323i
$139$	10.4936	−	18.1755i	0.890059	−	1.54163i	0.0502556	−	0.998736i	$-0.483996\pi$
$139$	10.4936	−	18.1755i	0.890059	−	1.54163i	0.839803	−	0.542891i	$-0.182670\pi$
$140$	−1.19822	+	2.07538i	−0.101268	+	0.175401i
$141$	2.27672	−	7.71365i	0.191735	−	0.649607i
$142$	1.71170	+	2.96475i	0.143643	+	0.248796i
$143$	18.6581			1.56027
$144$	2.67036	−	1.36717i	0.222530	−	0.113931i
$145$	−32.3631			−2.68761
$146$	1.29392	+	2.24113i	0.107085	+	0.185477i
$147$	11.0521	−	2.66475i	0.911558	−	0.219785i
$148$	3.35833	−	5.81679i	0.276053	−	0.478137i
$149$	−9.20644	+	15.9460i	−0.754221	+	1.30635i	0.191540	+	0.981485i	$0.438652\pi$
$149$	−9.20644	+	15.9460i	−0.754221	+	1.30635i	−0.945761	+	0.324864i	$0.894681\pi$
$150$	−13.7476	+	3.31467i	−1.12249	+	0.270642i
$151$	−4.89962	−	8.48638i	−0.398725	−	0.690612i	0.594844	−	0.803841i	$-0.297214\pi$
$151$	−4.89962	−	8.48638i	−0.398725	−	0.690612i	−0.993569	+	0.113229i	$0.963881\pi$
$152$	−5.47838			−0.444355
$153$	0.810313	−	16.0599i	0.0655099	−	1.29836i
$154$	−3.12857			−0.252107
$155$	−17.5372	−	30.3753i	−1.40862	−	2.43980i
$156$	−1.93133	+	6.54345i	−0.154630	+	0.523896i
$157$	−12.2021	+	21.1346i	−0.973832	+	1.68673i	−0.290097	+	0.956997i	$0.593688\pi$
$157$	−12.2021	+	21.1346i	−0.973832	+	1.68673i	−0.683735	+	0.729730i	$0.739646\pi$
$158$	4.88118	−	8.45445i	0.388326	−	0.672600i
$159$	6.82176	+	7.17464i	0.541001	+	0.568986i
$160$	−1.81416	−	3.14221i	−0.143422	−	0.248413i
$161$	−4.65652			−0.366985
$162$	3.69262	+	8.20759i	0.290119	+	0.644849i
$163$	13.1394			1.02916			0.514580	−	0.857443i	$-0.327948\pi$
$163$	13.1394			1.02916			0.514580	+	0.857443i	$0.327948\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$	−20.5119	−	21.5729i	−1.59685	−	1.67945i
$166$	4.23404	−	7.33358i	0.328625	−	0.569196i
$167$	0.209486	−	0.362840i	0.0162105	−	0.0280774i	−0.857806	−	0.513973i	$-0.828173\pi$
$167$	0.209486	−	0.362840i	0.0162105	−	0.0280774i	0.874017	+	0.485896i	$0.161506\pi$
$168$	0.323843	−	1.09720i	0.0249850	−	0.0846506i
$169$	−1.25780	−	2.17858i	−0.0967542	−	0.167583i
$170$	−19.4481			−1.49160
$171$	0.828194	−	16.4143i	0.0633335	−	1.25523i
$172$	2.07630			0.158316
$173$	1.21748	+	2.10873i	0.0925629	+	0.160324i	0.908589	−	0.417692i	$-0.137161\pi$
$173$	1.21748	+	2.10873i	0.0925629	+	0.160324i	−0.816026	+	0.578015i	$0.803827\pi$
$174$	15.0188	−	3.62117i	1.13858	−	0.274520i
$175$	−2.69631	+	4.67014i	−0.203822	+	0.353029i
$176$	2.36839	−	4.10218i	0.178524	−	0.309213i
$177$	−10.8933	+	2.62648i	−0.818794	+	0.197418i
$178$	−1.18129	−	2.04606i	−0.0885416	−	0.153359i
$179$	9.69531			0.724662			0.362331	−	0.932050i	$-0.381981\pi$
$179$	9.69531			0.724662			0.362331	+	0.932050i	$0.381981\pi$
$180$	9.68891	−	4.96053i	0.722168	−	0.369736i
$181$	−2.80239			−0.208300			−0.104150	−	0.994562i	$-0.533212\pi$
$181$	−2.80239			−0.208300			−0.104150	+	0.994562i	$0.533212\pi$
$182$	1.30082	+	2.25308i	0.0964231	+	0.167010i
$183$	−5.18974	+	17.5831i	−0.383637	+	1.29978i
$184$	3.52508	−	6.10562i	0.259873	−	0.450113i
$185$	12.1850	−	21.1051i	0.895863	−	1.55168i
$186$	11.5373	+	12.1341i	0.845955	+	0.889714i
$187$	−12.6948	−	21.9881i	−0.928337	−	1.60793i
$188$	4.64341			0.338656
$189$	3.23845	+	1.13616i	0.235563	+	0.0826438i
$190$	−19.8773			−1.44205
$191$	3.27445	+	5.67152i	0.236931	+	0.410377i	0.959832	−	0.280575i	$-0.0905251\pi$
$191$	3.27445	+	5.67152i	0.236931	+	0.410377i	−0.722901	+	0.690952i	$0.757192\pi$
$192$	1.19349	+	1.25522i	0.0861325	+	0.0905880i
$193$	−0.705513	+	1.22198i	−0.0507840	+	0.0879604i	−0.890300	−	0.455375i	$-0.849505\pi$
$193$	−0.705513	+	1.22198i	−0.0507840	+	0.0879604i	0.839516	+	0.543335i	$0.182839\pi$
$194$	−5.34250	+	9.25348i	−0.383569	+	0.664361i
$195$	−7.00748	+	23.7417i	−0.501816	+	1.70018i
$196$	3.28188	+	5.68438i	0.234420	+	0.406027i
$197$	−10.9087			−0.777212			−0.388606	−	0.921404i	$-0.627043\pi$
$197$	−10.9087			−0.777212			−0.388606	+	0.921404i	$0.627043\pi$
$198$	11.9328	+	7.71630i	0.848031	+	0.548373i
$199$	15.3713			1.08964			0.544820	−	0.838553i	$-0.316598\pi$
$199$	15.3713			1.08964			0.544820	+	0.838553i	$0.316598\pi$
$200$	−4.08232	−	7.07079i	−0.288664	−	0.499980i
$201$	9.18798	−	2.21530i	0.648070	−	0.156255i
$202$	4.37833	−	7.58349i	0.308058	−	0.533572i
$203$	2.94563	−	5.10198i	0.206743	−	0.358089i
$204$	9.02534	−	2.17609i	0.631900	−	0.152356i
$205$	−1.81416	−	3.14221i	−0.126706	−	0.219461i
$206$	2.78709			0.194185
$207$	17.7607	+	11.4848i	1.23445	+	0.798251i
$208$	−3.93899			−0.273120
$209$	−12.9749	−	22.4733i	−0.897496	−	1.55451i
$210$	1.17500	−	3.98097i	0.0810830	−	0.274713i
$211$	6.06536	−	10.5055i	0.417557	−	0.723230i	−0.578136	−	0.815940i	$-0.696220\pi$
$211$	6.06536	−	10.5055i	0.417557	−	0.723230i	0.995693	+	0.0927106i	$0.0295531\pi$
$212$	−2.85791	+	4.95005i	−0.196282	+	0.339971i
$213$	−4.08579	−	4.29713i	−0.279953	−	0.294435i
$214$	−1.30572	−	2.26158i	−0.0892573	−	0.154598i
$215$	7.53346			0.513778
$216$	−3.94131	+	3.38616i	−0.268172	+	0.230399i
$217$	6.38481			0.433429
$218$	−10.2764	−	17.7993i	−0.696007	−	1.20552i
$219$	−3.08855	−	3.24831i	−0.208705	−	0.219500i
$220$	8.59326	−	14.8840i	0.579358	−	1.00348i
$221$	−10.5567	+	18.2847i	−0.710119	+	1.22996i
$222$	−3.29326	+	11.1577i	−0.221029	+	0.748857i
$223$	0.472110	+	0.817718i	0.0316148	+	0.0547584i	0.881400	−	0.472371i	$-0.156602\pi$
$223$	0.472110	+	0.817718i	0.0316148	+	0.0547584i	−0.849785	+	0.527129i	$0.823268\pi$
$224$	0.660484			0.0441304
$225$	21.8026	−	11.1625i	1.45350	−	0.744165i
$226$	−0.687760			−0.0457491
$227$	1.53359	+	2.65625i	0.101788	+	0.176301i	0.912421	−	0.409252i	$-0.134210\pi$
$227$	1.53359	+	2.65625i	0.101788	+	0.176301i	−0.810634	+	0.585554i	$0.800877\pi$
$228$	9.22449	−	2.22410i	0.610907	−	0.147295i
$229$	12.0947	−	20.9486i	0.799241	−	1.38433i	−0.120871	−	0.992668i	$-0.538569\pi$
$229$	12.0947	−	20.9486i	0.799241	−	1.38433i	0.920111	−	0.391657i	$-0.128098\pi$
$230$	12.7901	−	22.1531i	0.843354	−	1.46073i
$231$	5.26788	−	1.27013i	0.346601	−	0.0835685i
$232$	4.45981	+	7.72461i	0.292801	+	0.507145i
$233$	−22.4439			−1.47035			−0.735175	−	0.677877i	$-0.762900\pi$
$233$	−22.4439			−1.47035			−0.735175	+	0.677877i	$0.762900\pi$
$234$	0.595476	−	11.8019i	0.0389275	−	0.771517i
$235$	16.8477			1.09903
$236$	−3.23475	−	5.60275i	−0.210564	−	0.364708i
$237$	−4.78661	+	16.2173i	−0.310923	+	1.05342i
$238$	1.77013	−	3.06596i	0.114740	−	0.198736i
$239$	−11.5182	+	19.9501i	−0.745052	+	1.29047i	0.205119	+	0.978737i	$0.434242\pi$
$239$	−11.5182	+	19.9501i	−0.745052	+	1.29047i	−0.950171	+	0.311731i	$0.899091\pi$
$240$	4.33034	+	4.55434i	0.279522	+	0.293982i
$241$	−1.03206	−	1.78759i	−0.0664810	−	0.115149i	0.830869	−	0.556468i	$-0.187844\pi$
$241$	−1.03206	−	1.78759i	−0.0664810	−	0.115149i	−0.897350	+	0.441320i	$0.854511\pi$
$242$	11.4371			0.735206
$243$	−9.54973	−	12.3208i	−0.612616	−	0.790381i
$244$	−10.5846			−0.677607
$245$	11.9077	+	20.6247i	0.760754	+	1.31766i
$246$	1.19349	+	1.25522i	0.0760940	+	0.0800302i
$247$	−10.7896	+	18.6882i	−0.686528	+	1.18910i
$248$	−4.83343	+	8.37175i	−0.306923	+	0.531607i
$249$	−4.15201	+	14.0672i	−0.263123	+	0.891473i
$250$	−5.74115	−	9.94396i	−0.363102	−	0.628911i
$251$	13.5667			0.856324			0.428162	−	0.903702i	$-0.359161\pi$
$251$	13.5667			0.856324			0.428162	+	0.903702i	$0.359161\pi$
$252$	−0.0998486	+	1.97893i	−0.00628987	+	0.124661i
$253$	33.3951			2.09953
$254$	−9.26309	−	16.0441i	−0.581218	−	1.00670i
$255$	32.7467	−	7.89552i	2.05068	−	0.494436i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.13038	+	8.88608i	−0.320025	+	0.554299i	−0.980493	−	0.196555i	$-0.937024\pi$
$257$	−5.13038	+	8.88608i	−0.320025	+	0.554299i	0.660468	+	0.750854i	$0.270358\pi$
$258$	−3.49607	+	0.842933i	−0.217656	+	0.0524787i
$259$	2.21812	+	3.84190i	0.137827	+	0.238724i
$260$	−14.2919			−0.886344
$261$	−23.8186	+	12.1946i	−1.47433	+	0.754830i
$262$	6.96055			0.430024
$263$	−0.147800	−	0.255997i	−0.00911373	−	0.0157854i	0.861433	−	0.507872i	$-0.169568\pi$
$263$	−0.147800	−	0.255997i	−0.00911373	−	0.0157854i	−0.870546	+	0.492087i	$0.836234\pi$
$264$	−2.32250	+	7.86876i	−0.142940	+	0.484289i
$265$	−10.3694	+	17.9603i	−0.636987	+	1.10329i
$266$	1.80919	−	3.13361i	0.110929	−	0.192134i
$267$	2.81972	+	2.96557i	0.172564	+	0.181490i
$268$	2.72835	+	4.72564i	0.166660	+	0.288664i
$269$	−21.2825			−1.29762			−0.648810	−	0.760951i	$-0.724733\pi$
$269$	−21.2825			−1.29762			−0.648810	+	0.760951i	$0.724733\pi$
$270$	−14.3003	+	12.2860i	−0.870289	+	0.747704i
$271$	20.8083			1.26401			0.632006	−	0.774964i	$-0.282232\pi$
$271$	20.8083			1.26401			0.632006	+	0.774964i	$0.282232\pi$
$272$	2.68005	+	4.64198i	0.162502	+	0.281462i
$273$	−3.10502	−	3.26564i	−0.187924	−	0.197645i
$274$	3.34224	−	5.78893i	0.201912	−	0.349722i
$275$	19.3371	−	33.4928i	1.16607	−	2.01969i
$276$	−3.45678	+	11.7118i	−0.208074	+	0.704965i
$277$	1.63269	+	2.82791i	0.0980991	+	0.169913i	0.910898	−	0.412632i	$-0.135390\pi$
$277$	1.63269	+	2.82791i	0.0980991	+	0.169913i	−0.812799	+	0.582545i	$0.802057\pi$
$278$	−20.9873			−1.25873
$279$	−24.3527	−	15.7475i	−1.45796	−	0.942777i
$280$	2.39644			0.143215
$281$	0.818897	+	1.41837i	0.0488513	+	0.0846129i	0.889417	−	0.457097i	$-0.151111\pi$
$281$	0.818897	+	1.41837i	0.0488513	+	0.0846129i	−0.840566	+	0.541709i	$0.817777\pi$
$282$	−7.81858	+	1.88513i	−0.465590	+	0.112258i
$283$	2.95847	−	5.12423i	0.175863	−	0.304604i	−0.764597	−	0.644509i	$-0.777062\pi$
$283$	2.95847	−	5.12423i	0.175863	−	0.304604i	0.940460	+	0.339905i	$0.110395\pi$
$284$	1.71170	−	2.96475i	0.101571	−	0.175926i
$285$	33.4693	−	8.06974i	1.98255	−	0.478010i
$286$	−9.32906	−	16.1584i	−0.551639	−	0.955467i
$287$	0.660484			0.0389871
$288$	−2.51919	−	1.62902i	−0.148445	−	0.0959907i
$289$	11.7307			0.690040
$290$	16.1816	+	28.0273i	0.950214	+	1.64582i
$291$	5.23898	−	17.7499i	0.307115	−	1.04052i
$292$	1.29392	−	2.24113i	0.0757207	−	0.131152i
$293$	14.0380	−	24.3145i	0.820106	−	1.42047i	−0.0854967	−	0.996338i	$-0.527248\pi$
$293$	14.0380	−	24.3145i	0.820106	−	1.42047i	0.905603	−	0.424127i	$-0.139419\pi$
$294$	−7.83377	−	8.23899i	−0.456875	−	0.480508i
$295$	−11.7367	−	20.3285i	−0.683336	−	1.18357i
$296$	−6.71665			−0.390397
$297$	−23.2252	−	8.14822i	−1.34766	−	0.472807i
$298$	18.4129			1.06663
$299$	−13.8853	−	24.0500i	−0.803005	−	1.39085i
$300$	9.74440	+	10.2485i	0.562593	+	0.591695i
$301$	−0.685681	+	1.18763i	−0.0395220	+	0.0684541i
$302$	−4.89962	+	8.48638i	−0.281941	+	0.488337i
$303$	−4.29349	+	14.5466i	−0.246655	+	0.835679i
$304$	2.73919	+	4.74441i	0.157103	+	0.272111i
$305$	−38.4041			−2.19901
$306$	−14.3134	+	7.32819i	−0.818244	+	0.418924i
$307$	−16.3136			−0.931067			−0.465534	−	0.885030i	$-0.654138\pi$
$307$	−16.3136			−0.931067			−0.465534	+	0.885030i	$0.654138\pi$
$308$	1.56428	+	2.70942i	0.0891334	+	0.154384i
$309$	−4.69289	+	1.13150i	−0.266969	+	0.0643686i
$310$	−17.5372	+	30.3753i	−0.996046	+	1.72520i
$311$	7.12309	−	12.3375i	0.403913	−	0.699598i	−0.590281	−	0.807198i	$-0.700983\pi$
$311$	7.12309	−	12.3375i	0.403913	−	0.699598i	0.994194	+	0.107600i	$0.0343164\pi$
$312$	6.63246	−	1.59914i	0.375489	−	0.0905337i
$313$	12.4404	+	21.5473i	0.703170	+	1.21793i	0.967348	+	0.253453i	$0.0815663\pi$
$313$	12.4404	+	21.5473i	0.703170	+	1.21793i	−0.264177	+	0.964474i	$0.585100\pi$
$314$	24.4042			1.37721
$315$	−0.362282	+	7.18019i	−0.0204123	+	0.404558i
$316$	−9.76236			−0.549176
$317$	12.8794	+	22.3077i	0.723378	+	1.25293i	0.959638	+	0.281238i	$0.0907450\pi$
$317$	12.8794	+	22.3077i	0.723378	+	1.25293i	−0.236260	+	0.971690i	$0.575922\pi$
$318$	2.80254	−	9.49514i	0.157159	−	0.532461i
$319$	−21.1251	+	36.5898i	−1.18278	+	2.04864i
$320$	−1.81416	+	3.14221i	−0.101414	+	0.175655i
$321$	3.11673	+	3.27795i	0.173959	+	0.182957i
$322$	2.32826	+	4.03267i	0.129749	+	0.224732i
$323$	29.3647			1.63389
$324$	5.26168	−	7.30170i	0.292315	−	0.405650i
$325$	−32.1604			−1.78394
$326$	−6.56971	−	11.3791i	−0.363863	−	0.630229i
$327$	24.5296	+	25.7984i	1.35649	+	1.42666i
$328$	−0.500000	+	0.866025i	−0.0276079	+	0.0478183i
$329$	−1.53345	+	2.65601i	−0.0845418	+	0.146431i
$330$	−8.42676	+	28.5503i	−0.463878	+	1.57164i
$331$	−7.75164	−	13.4262i	−0.426069	−	0.737973i	0.570451	−	0.821332i	$-0.306769\pi$
$331$	−7.75164	−	13.4262i	−0.426069	−	0.737973i	−0.996520	+	0.0833590i	$0.973435\pi$
$332$	−8.46809			−0.464747
$333$	1.01539	−	20.1244i	0.0556430	−	1.10281i
$334$	−0.418972			−0.0229251
$335$	9.89930	+	17.1461i	0.540856	+	0.936791i
$336$	−1.11212	+	0.268142i	−0.0606713	+	0.0146284i
$337$	−11.6724	+	20.2173i	−0.635838	+	1.10130i	0.350499	+	0.936563i	$0.386012\pi$
$337$	−11.6724	+	20.2173i	−0.635838	+	1.10130i	−0.986337	+	0.164741i	$0.947321\pi$
$338$	−1.25780	+	2.17858i	−0.0684156	+	0.118499i
$339$	1.15805	−	0.279216i	0.0628967	−	0.0151649i
$340$	9.72406	+	16.8426i	0.527361	+	0.913416i
$341$	−45.7899			−2.47966
$342$	−14.6293	+	7.48989i	−0.791060	+	0.405007i
$343$	−8.95864			−0.483721
$344$	−1.03815	−	1.79813i	−0.0559733	−	0.0969486i
$345$	−12.5423	+	42.4939i	−0.675254	+	2.28779i
$346$	1.21748	−	2.10873i	0.0654519	−	0.113366i
$347$	5.80137	−	10.0483i	0.311434	−	0.539419i	−0.667239	−	0.744844i	$-0.732524\pi$
$347$	5.80137	−	10.0483i	0.311434	−	0.539419i	0.978673	+	0.205424i	$0.0658574\pi$
$348$	−10.6454	−	11.1961i	−0.570656	−	0.600174i
$349$	3.48911	+	6.04331i	0.186768	+	0.323491i	0.944171	−	0.329457i	$-0.106866\pi$
$349$	3.48911	+	6.04331i	0.186768	+	0.323491i	−0.757403	+	0.652948i	$0.773532\pi$
$350$	5.39261			0.288247
$351$	3.78867	+	20.1139i	0.202224	+	1.07360i
$352$	−4.73678			−0.252471
$353$	−4.87070	−	8.43630i	−0.259241	−	0.449019i	0.706798	−	0.707416i	$-0.250139\pi$
$353$	−4.87070	−	8.43630i	−0.259241	−	0.449019i	−0.966039	+	0.258397i	$0.916806\pi$
$354$	7.72127	+	8.12067i	0.410381	+	0.431609i
$355$	6.21058	−	10.7570i	0.329623	−	0.570924i
$356$	−1.18129	+	2.04606i	−0.0626084	+	0.108441i
$357$	−1.73583	+	5.88109i	−0.0918700	+	0.311260i
$358$	−4.84766	−	8.39639i	−0.256207	−	0.443763i
$359$	11.7818			0.621818			0.310909	−	0.950440i	$-0.399367\pi$
$359$	11.7818			0.621818			0.310909	+	0.950440i	$0.399367\pi$
$360$	−9.14040	−	5.91058i	−0.481741	−	0.311515i
$361$	11.0126			0.579612
$362$	1.40120	+	2.42694i	0.0736452	+	0.127557i
$363$	−19.2578	+	4.64323i	−1.01077	+	0.243706i
$364$	1.30082	−	2.25308i	0.0681814	−	0.118094i
$365$	4.69473	−	8.13151i	0.245733	−	0.425623i
$366$	17.8223	−	4.29711i	0.931586	−	0.224613i
$367$	−8.71736	−	15.0989i	−0.455043	−	0.788157i	0.543648	−	0.839313i	$-0.317043\pi$
$367$	−8.71736	−	15.0989i	−0.455043	−	0.788157i	−0.998691	+	0.0511563i	$0.983709\pi$
$368$	−7.05017			−0.367515
$369$	−2.51919	−	1.62902i	−0.131144	−	0.0848032i
$370$	−24.3701			−1.26694
$371$	−1.88760	−	3.26943i	−0.0979995	−	0.169740i
$372$	4.73978	−	16.0586i	0.245746	−	0.832601i
$373$	−6.91811	+	11.9825i	−0.358206	+	0.620431i	−0.987661	−	0.156606i	$-0.949945\pi$
$373$	−6.91811	+	11.9825i	−0.358206	+	0.620431i	0.629455	+	0.777037i	$0.283278\pi$
$374$	−12.6948	+	21.9881i	−0.656434	+	1.13698i
$375$	13.7040	+	14.4129i	0.707670	+	0.744277i
$376$	−2.32171	−	4.02131i	−0.119733	−	0.207383i
$377$	35.1342			1.80950
$378$	−0.635280	−	3.37267i	−0.0326753	−	0.173471i
$379$	3.18952			0.163835			0.0819174	−	0.996639i	$-0.473896\pi$
$379$	3.18952			0.163835			0.0819174	+	0.996639i	$0.473896\pi$
$380$	9.93863	+	17.2142i	0.509841	+	0.883070i
$381$	22.1108	+	23.2545i	1.13277	+	1.19136i
$382$	3.27445	−	5.67152i	0.167536	−	0.290180i
$383$	−6.76212	+	11.7123i	−0.345528	+	0.598472i	−0.985450	−	0.169968i	$-0.945633\pi$
$383$	−6.76212	+	11.7123i	−0.345528	+	0.598472i	0.639922	+	0.768440i	$0.278967\pi$
$384$	0.490312	−	1.66120i	0.0250211	−	0.0847729i
$385$	5.67571	+	9.83062i	0.289261	+	0.501015i
$386$	1.41103			0.0718194
$387$	5.54447	−	2.83866i	0.281841	−	0.144297i
$388$	10.6850			0.542448
$389$	8.73115	+	15.1228i	0.442687	+	0.766756i	0.997888	−	0.0649603i	$-0.0206921\pi$
$389$	8.73115	+	15.1228i	0.442687	+	0.766756i	−0.555201	+	0.831716i	$0.687359\pi$
$390$	24.0646	−	5.80219i	1.21856	−	0.293805i
$391$	−18.8948	+	32.7268i	−0.955551	+	1.65506i
$392$	3.28188	−	5.68438i	0.165760	−	0.287105i
$393$	−11.7202	+	2.82583i	−0.591205	+	0.142545i
$394$	5.45435	+	9.44721i	0.274786	+	0.475943i
$395$	−35.4209			−1.78222
$396$	0.716083	−	14.1923i	0.0359845	−	0.713190i
$397$	−14.0003			−0.702657			−0.351329	−	0.936252i	$-0.614270\pi$
$397$	−14.0003			−0.702657			−0.351329	+	0.936252i	$0.614270\pi$
$398$	−7.68564	−	13.3119i	−0.385246	−	0.667266i
$399$	−1.77414	+	6.01086i	−0.0888179	+	0.300919i
$400$	−4.08232	+	7.07079i	−0.204116	+	0.353539i
$401$	14.3421	−	24.8413i	0.716212	−	1.24052i	−0.246278	−	0.969199i	$-0.579208\pi$
$401$	14.3421	−	24.8413i	0.716212	−	1.24052i	0.962490	−	0.271317i	$-0.0874591\pi$
$402$	−6.51250	−	6.84938i	−0.324814	−	0.341616i
$403$	19.0388	+	32.9762i	0.948391	+	1.64266i
$404$	−8.75666			−0.435660
$405$	19.0910	−	26.4928i	0.948639	−	1.31644i
$406$	−5.89126			−0.292378
$407$	−15.9077	−	27.5529i	−0.788513	−	1.36575i
$408$	−6.39721	−	6.72813i	−0.316709	−	0.333092i
$409$	−12.5593	+	21.7533i	−0.621016	+	1.07563i	0.368280	+	0.929715i	$0.379947\pi$
$409$	−12.5593	+	21.7533i	−0.621016	+	1.07563i	−0.989297	+	0.145917i	$0.953387\pi$
$410$	−1.81416	+	3.14221i	−0.0895948	+	0.155183i
$411$	−3.27748	+	11.1043i	−0.161666	+	0.547733i
$412$	−1.39354	−	2.41369i	−0.0686549	−	0.118914i
$413$	4.27300			0.210261
$414$	1.06581	−	21.1236i	0.0523816	−	1.03817i
$415$	−30.7248			−1.50822
$416$	1.96949	+	3.41126i	0.0965623	+	0.167251i
$417$	35.3384	−	8.52038i	1.73053	−	0.417245i
$418$	−12.9749	+	22.4733i	−0.634625	+	1.09920i
$419$	13.9472	−	24.1572i	0.681363	−	1.18016i	−0.293202	−	0.956051i	$-0.594721\pi$
$419$	13.9472	−	24.1572i	0.681363	−	1.18016i	0.974565	−	0.224105i	$-0.0719459\pi$
$420$	−4.03513	+	0.972903i	−0.196894	+	0.0474728i
$421$	−3.65699	−	6.33409i	−0.178231	−	0.308705i	0.763044	−	0.646347i	$-0.223704\pi$
$421$	−3.65699	−	6.33409i	−0.178231	−	0.308705i	−0.941275	+	0.337642i	$0.890371\pi$
$422$	−12.1307			−0.590515
$423$	12.3996	−	6.34835i	0.602889	−	0.308667i
$424$	5.71582			0.277585
$425$	21.8816	+	37.9001i	1.06142	+	1.83843i
$426$	−1.67853	+	5.68696i	−0.0813253	+	0.275534i
$427$	3.49547	−	6.05433i	0.169158	−	0.292989i
$428$	−1.30572	+	2.26158i	−0.0631145	+	0.109317i
$429$	22.2682	+	23.4201i	1.07512	+	1.13073i
$430$	−3.76673	−	6.52417i	−0.181648	−	0.314623i
$431$	13.8729			0.668232			0.334116	−	0.942532i	$-0.391562\pi$
$431$	13.8729			0.668232			0.334116	+	0.942532i	$0.391562\pi$
$432$	4.90315	+	1.72020i	0.235903	+	0.0827632i
$433$	19.5255			0.938334			0.469167	−	0.883110i	$-0.344554\pi$
$433$	19.5255			0.938334			0.469167	+	0.883110i	$0.344554\pi$
$434$	−3.19240	−	5.52941i	−0.153240	−	0.265420i
$435$	−38.6250	−	40.6230i	−1.85193	−	1.94772i
$436$	−10.2764	+	17.7993i	−0.492151	+	0.852431i
$437$	−19.3117	+	33.4489i	−0.923806	+	1.60008i
$438$	−1.26885	+	4.29892i	−0.0606278	+	0.205410i
$439$	4.25502	+	7.36992i	0.203081	+	0.351747i	0.949520	−	0.313707i	$-0.101571\pi$
$439$	4.25502	+	7.36992i	0.203081	+	0.351747i	−0.746438	+	0.665454i	$0.768238\pi$
$440$	−17.1865			−0.819335
$441$	16.5353	+	10.6925i	0.787398	+	0.509165i
$442$	21.1134			1.00426
$443$	4.40699	+	7.63313i	0.209382	+	0.362661i	0.951520	−	0.307586i	$-0.0995213\pi$
$443$	4.40699	+	7.63313i	0.209382	+	0.362661i	−0.742138	+	0.670247i	$0.766188\pi$
$444$	11.3095	−	2.72682i	0.536725	−	0.129409i
$445$	−4.28610	+	7.42374i	−0.203181	+	0.351919i
$446$	0.472110	−	0.817718i	0.0223550	−	0.0387201i
$447$	−31.0036	+	7.47523i	−1.46642	+	0.353566i
$448$	−0.330242	−	0.571996i	−0.0156025	−	0.0270243i
$449$	1.50547			0.0710476			0.0355238	−	0.999369i	$-0.488690\pi$
$449$	1.50547			0.0710476			0.0355238	+	0.999369i	$0.488690\pi$
$450$	−20.5683	−	13.3003i	−0.969597	−	0.626983i
$451$	−4.73678			−0.223046
$452$	0.343880	+	0.595618i	0.0161748	+	0.0280155i
$453$	4.80468	−	16.2785i	0.225744	−	0.764831i
$454$	1.53359	−	2.65625i	0.0719748	−	0.124664i
$455$	4.71977	−	8.17489i	0.221266	−	0.383245i
$456$	−6.53838	−	6.87659i	−0.306188	−	0.322026i
$457$	15.3760	+	26.6319i	0.719257	+	1.24579i	0.961294	+	0.275523i	$0.0888510\pi$
$457$	15.3760	+	26.6319i	0.719257	+	1.24579i	−0.242037	+	0.970267i	$0.577816\pi$
$458$	−24.1894			−1.13030
$459$	21.1258	−	18.1501i	0.986070	−	0.847176i
$460$	−25.5802			−1.19268
$461$	10.7165	+	18.5616i	0.499119	+	0.864499i	0.999999	−	0.00101711i	$-0.000323756\pi$
$461$	10.7165	+	18.5616i	0.499119	+	0.864499i	−0.500881	+	0.865516i	$0.666990\pi$
$462$	−3.73391	−	3.92706i	−0.173717	−	0.182703i
$463$	9.44942	−	16.3669i	0.439152	−	0.760633i	−0.558472	−	0.829523i	$-0.688612\pi$
$463$	9.44942	−	16.3669i	0.439152	−	0.760633i	0.997624	+	0.0688898i	$0.0219457\pi$
$464$	4.45981	−	7.72461i	0.207041	−	0.358606i
$465$	17.1974	−	58.2657i	0.797510	−	2.70201i
$466$	11.2220	+	19.4370i	0.519847	+	0.900402i
$467$	10.6993			0.495104			0.247552	−	0.968875i	$-0.420374\pi$
$467$	10.6993			0.495104			0.247552	+	0.968875i	$0.420374\pi$
$468$	−10.5185	+	5.38527i	−0.486219	+	0.248934i
$469$	−3.60406			−0.166420
$470$	−8.42387	−	14.5906i	−0.388564	−	0.673013i
$471$	−41.0917	+	9.90757i	−1.89341	+	0.456517i
$472$	−3.23475	+	5.60275i	−0.148891	+	0.257887i
$473$	4.91749	−	8.51735i	0.226107	−	0.391628i
$474$	16.4379	−	3.96331i	0.755016	−	0.182041i
$475$	22.3645	+	38.7364i	1.02615	+	1.77735i
$476$	−3.54026			−0.162268
$477$	−0.864089	+	17.1257i	−0.0395639	+	0.784131i
$478$	23.0364			1.05366
$479$	11.6784	+	20.2276i	0.533600	+	0.924223i	0.999230	+	0.0392428i	$0.0124946\pi$
$479$	11.6784	+	20.2276i	0.533600	+	0.924223i	−0.465630	+	0.884980i	$0.654172\pi$
$480$	1.77900	−	6.02736i	0.0812001	−	0.275110i
$481$	−13.2284	+	22.9123i	−0.603163	+	1.04471i
$482$	−1.03206	+	1.78759i	−0.0470092	+	0.0814223i
$483$	−5.55750	−	5.84498i	−0.252875	−	0.265956i
$484$	−5.71856	−	9.90484i	−0.259935	−	0.450220i
$485$	38.7685			1.76039
$486$	−5.89528	+	14.4307i	−0.267415	+	0.654591i
$487$	3.08766			0.139915			0.0699576	−	0.997550i	$-0.477714\pi$
$487$	3.08766			0.139915			0.0699576	+	0.997550i	$0.477714\pi$
$488$	5.29228	+	9.16650i	0.239570	+	0.414948i
$489$	15.6817	+	16.4929i	0.709153	+	0.745836i
$490$	11.9077	−	20.6247i	0.537934	−	0.931729i
$491$	3.47926	−	6.02626i	0.157017	−	0.271961i	−0.776775	−	0.629779i	$-0.783146\pi$
$491$	3.47926	−	6.02626i	0.157017	−	0.271961i	0.933792	+	0.357817i	$0.116479\pi$
$492$	0.490312	−	1.66120i	0.0221050	−	0.0748928i
$493$	−23.9050	−	41.4047i	−1.07663	−	1.86477i
$494$	21.5793			0.970897
$495$	2.59817	−	51.4941i	0.116779	−	2.31449i
$496$	9.66687			0.434055
$497$	1.13055	+	1.95817i	0.0507121	+	0.0878360i
$498$	14.2586	−	3.43786i	0.638941	−	0.154054i
$499$	−8.01666	+	13.8853i	−0.358875	+	0.621590i	−0.987773	−	0.155898i	$-0.950173\pi$
$499$	−8.01666	+	13.8853i	−0.358875	+	0.621590i	0.628898	+	0.777488i	$0.283506\pi$
$500$	−5.74115	+	9.94396i	−0.256752	+	0.444707i
$501$	0.705465	−	0.170094i	0.0315178	−	0.00759922i
$502$	−6.78336	−	11.7491i	−0.302756	−	0.524389i
$503$	−12.9027			−0.575302			−0.287651	−	0.957735i	$-0.592874\pi$
$503$	−12.9027			−0.575302			−0.287651	+	0.957735i	$0.592874\pi$
$504$	1.76373	−	0.902996i	0.0785628	−	0.0402226i
$505$	−31.7719			−1.41383
$506$	−16.6976	−	28.9210i	−0.742297	−	1.28570i
$507$	1.23343	−	4.17894i	0.0547787	−	0.185593i
$508$	−9.26309	+	16.0441i	−0.410983	+	0.711844i
$509$	5.38684	−	9.33027i	0.238767	−	0.413557i	−0.721594	−	0.692317i	$-0.756590\pi$
$509$	5.38684	−	9.33027i	0.238767	−	0.413557i	0.960361	+	0.278760i	$0.0899233\pi$
$510$	−23.2111	−	24.4117i	−1.02780	−	1.08097i
$511$	0.854611	+	1.48023i	0.0378058	+	0.0654815i
$512$	1.00000			0.0441942
$513$	21.5920	−	18.5506i	0.953310	−	0.819031i
$514$	10.2608			0.452583
$515$	−5.05621	−	8.75761i	−0.222803	−	0.385906i
$516$	2.47804	+	2.60622i	0.109090	+	0.114733i
$517$	10.9974	−	19.0481i	0.483666	−	0.837734i
$518$	2.21812	−	3.84190i	0.0974586	−	0.168803i
$519$	−1.19389	+	4.04495i	−0.0524058	+	0.177553i
$520$	7.14593	+	12.3771i	0.313370	+	0.542773i
$521$	−14.9641			−0.655590			−0.327795	−	0.944749i	$-0.606306\pi$
$521$	−14.9641			−0.655590			−0.327795	+	0.944749i	$0.606306\pi$
$522$	22.4702	+	14.5302i	0.983493	+	0.635969i
$523$	12.3205			0.538736			0.269368	−	0.963037i	$-0.413185\pi$
$523$	12.3205			0.538736			0.269368	+	0.963037i	$0.413185\pi$
$524$	−3.48028	−	6.02802i	−0.152037	−	0.263335i
$525$	−9.08008	+	2.18928i	−0.396287	+	0.0955482i
$526$	−0.147800	+	0.255997i	−0.00644438	+	0.0111620i
$527$	25.9077	−	44.8734i	1.12856	−	1.95472i
$528$	7.97580	−	1.92303i	0.347102	−	0.0836892i
$529$	−13.3524	−	23.1271i	−0.580540	−	1.00553i
$530$	20.7388			0.900835
$531$	−16.2979	−	10.5389i	−0.707268	−	0.457350i
$532$	−3.61838			−0.156877
$533$	1.96949	+	3.41126i	0.0853082	+	0.147758i
$534$	1.15840	−	3.92473i	0.0501291	−	0.169840i
$535$	−4.73757	+	8.20570i	−0.204823	+	0.354764i
$536$	2.72835	−	4.72564i	0.117847	−	0.204116i
$537$	11.5712	+	12.1698i	0.499336	+	0.525165i
$538$	10.6413	+	18.4312i	0.458778	+	0.794627i
$539$	31.0911			1.33919
$540$	17.7902	+	6.24142i	0.765567	+	0.268588i
$541$	−15.1936			−0.653225			−0.326612	−	0.945158i	$-0.605907\pi$
$541$	−15.1936			−0.653225			−0.326612	+	0.945158i	$0.605907\pi$
$542$	−10.4041	−	18.0205i	−0.446896	−	0.774046i
$543$	−3.34462	−	3.51763i	−0.143531	−	0.150956i
$544$	2.68005	−	4.64198i	0.114906	−	0.199023i
$545$	−37.2861	+	64.5814i	−1.59716	+	2.76636i
$546$	−1.27561	+	4.32185i	−0.0545912	+	0.184958i
$547$	−14.3810	−	24.9087i	−0.614889	−	1.06502i	−0.990404	−	0.138203i	$-0.955867\pi$
$547$	−14.3810	−	24.9087i	−0.614889	−	1.06502i	0.375515	−	0.926816i	$-0.377466\pi$
$548$	−6.68448			−0.285547
$549$	−28.2646	+	14.4709i	−1.20631	+	0.617604i
$550$	−38.6741			−1.64907
$551$	−24.4325	−	42.3183i	−1.04086	−	1.80282i
$552$	11.8711	−	2.86222i	0.505266	−	0.121824i
$553$	3.22394	−	5.58403i	0.137096	−	0.237457i
$554$	1.63269	−	2.82791i	0.0693665	−	0.120146i
$555$	41.0344	−	9.89373i	1.74181	−	0.419966i
$556$	10.4936	+	18.1755i	0.445029	+	0.770814i
$557$	−34.5846			−1.46540			−0.732698	−	0.680554i	$-0.761739\pi$
$557$	−34.5846			−1.46540			−0.732698	+	0.680554i	$0.761739\pi$
$558$	−1.46139	+	28.9638i	−0.0618655	+	1.22613i
$559$	−8.17852			−0.345914
$560$	−1.19822	−	2.07538i	−0.0506340	−	0.0877007i
$561$	12.4489	−	42.1773i	0.525591	−	1.78073i
$562$	0.818897	−	1.41837i	0.0345431	−	0.0598304i
$563$	0.976616	−	1.69155i	0.0411594	−	0.0712903i	−0.844712	−	0.535221i	$-0.820228\pi$
$563$	0.976616	−	1.69155i	0.0411594	−	0.0712903i	0.885871	+	0.463931i	$0.153562\pi$
$564$	5.54186	+	5.82852i	0.233354	+	0.245425i
$565$	1.24770	+	2.16109i	0.0524913	+	0.0909176i
$566$	−5.91695			−0.248708
$567$	2.43891	+	5.42098i	0.102425	+	0.227660i
$568$	−3.42340			−0.143643
$569$	1.16997	+	2.02646i	0.0490479	+	0.0849534i	0.889507	−	0.456922i	$-0.151048\pi$
$569$	1.16997	+	2.02646i	0.0490479	+	0.0849534i	−0.840459	+	0.541875i	$0.817715\pi$
$570$	−23.7233	−	24.9504i	−0.993658	−	1.04506i
$571$	6.00568	−	10.4021i	0.251330	−	0.435316i	−0.712562	−	0.701609i	$-0.752465\pi$
$571$	6.00568	−	10.4021i	0.251330	−	0.435316i	0.963892	+	0.266293i	$0.0857988\pi$
$572$	−9.32906	+	16.1584i	−0.390068	+	0.675617i
$573$	−3.21101	+	10.8791i	−0.134142	+	0.454479i
$574$	−0.330242	−	0.571996i	−0.0137840	−	0.0238746i
$575$	−57.5621			−2.40050
$576$	−0.151175	+	2.99619i	−0.00629896	+	0.124841i
$577$	−16.5875			−0.690547			−0.345274	−	0.938502i	$-0.612214\pi$
$577$	−16.5875			−0.690547			−0.345274	+	0.938502i	$0.612214\pi$
$578$	−5.86534	−	10.1591i	−0.243966	−	0.422562i
$579$	−2.37589	+	0.572846i	−0.0987385	+	0.0238067i
$580$	16.1816	−	28.0273i	0.671903	−	1.16377i
$581$	2.79652	−	4.84371i	0.116019	−	0.200951i
$582$	−17.9914	+	4.33788i	−0.745767	+	0.179811i
$583$	13.5373	+	23.4473i	0.560658	+	0.971088i
$584$	−2.58783			−0.107085
$585$	−38.1645	+	19.5395i	−1.57791	+	0.807857i
$586$	−28.0759			−1.15981
$587$	−12.4396	−	21.5460i	−0.513437	−	0.889299i	−0.999879	−	0.0155860i	$-0.995039\pi$
$587$	−12.4396	−	21.5460i	−0.513437	−	0.889299i	0.486441	−	0.873713i	$-0.338295\pi$
$588$	−3.21829	+	10.9037i	−0.132720	+	0.449663i
$589$	26.4794	−	45.8636i	1.09106	−	1.88978i
$590$	−11.7367	+	20.3285i	−0.483191	+	0.836912i
$591$	−13.0194	−	13.6929i	−0.535546	−	0.563249i
$592$	3.35833	+	5.81679i	0.138026	+	0.239069i
$593$	−29.8821			−1.22711			−0.613556	−	0.789652i	$-0.710261\pi$
$593$	−29.8821			−1.22711			−0.613556	+	0.789652i	$0.710261\pi$
$594$	4.55603	+	24.1877i	0.186936	+	0.992433i
$595$	−12.8452			−0.526600
$596$	−9.20644	−	15.9460i	−0.377110	−	0.653174i
$597$	18.3454	+	19.2944i	0.750828	+	0.789667i
$598$	−13.8853	+	24.0500i	−0.567810	+	0.983476i
$599$	8.94748	−	15.4975i	0.365584	−	0.633210i	−0.623286	−	0.781994i	$-0.714203\pi$
$599$	8.94748	−	15.4975i	0.365584	−	0.633210i	0.988870	+	0.148784i	$0.0475359\pi$
$600$	4.00322	−	13.5631i	0.163431	−	0.553712i
$601$	−4.79337	−	8.30236i	−0.195526	−	0.338660i	0.751547	−	0.659680i	$-0.229308\pi$
$601$	−4.79337	−	8.30236i	−0.195526	−	0.338660i	−0.947073	+	0.321019i	$0.895975\pi$
$602$	1.37136			0.0558926
$603$	13.7464	+	8.88904i	0.559799	+	0.361990i
$604$	9.79923			0.398725
$605$	−20.7487	−	35.9378i	−0.843555	−	1.46108i
$606$	14.7445	−	3.55501i	0.598953	−	0.144413i
$607$	21.0601	−	36.4771i	0.854802	−	1.48056i	−0.0220273	−	0.999757i	$-0.507012\pi$
$607$	21.0601	−	36.4771i	0.854802	−	1.48056i	0.876829	−	0.480802i	$-0.159655\pi$
$608$	2.73919	−	4.74441i	0.111089	−	0.192411i
$609$	9.91970	−	2.39172i	0.401966	−	0.0969176i
$610$	19.2020	+	33.2589i	0.777468	+	1.34661i
$611$	−18.2903			−0.739948
$612$	13.5031	+	8.73169i	0.545831	+	0.352958i
$613$	17.2436			0.696461			0.348231	−	0.937409i	$-0.386783\pi$
$613$	17.2436			0.696461			0.348231	+	0.937409i	$0.386783\pi$
$614$	8.15681	+	14.1280i	0.329182	+	0.570160i
$615$	1.77900	−	6.02736i	0.0717364	−	0.243047i
$616$	1.56428	−	2.70942i	0.0630268	−	0.109166i
$617$	−0.279023	+	0.483282i	−0.0112330	+	0.0194562i	−0.871587	−	0.490240i	$-0.836909\pi$
$617$	−0.279023	+	0.483282i	−0.0112330	+	0.0194562i	0.860354	+	0.509697i	$0.170242\pi$
$618$	3.32635	+	3.49842i	0.133805	+	0.140727i
$619$	−11.8233	−	20.4786i	−0.475220	−	0.823105i	0.524377	−	0.851486i	$-0.324298\pi$
$619$	−11.8233	−	20.4786i	−0.475220	−	0.823105i	−0.999597	+	0.0283811i	$0.990965\pi$
$620$	35.0744			1.40862
$621$	6.78113	+	36.0007i	0.272117	+	1.44466i
$622$	−14.2462			−0.571220
$623$	−0.780225	−	1.35139i	−0.0312590	−	0.0541423i
$624$	−4.70113	−	4.94431i	−0.188196	−	0.197931i
$625$	−0.419071	+	0.725852i	−0.0167628	+	0.0290341i
$626$	12.4404	−	21.5473i	0.497217	−	0.861204i
$627$	12.7235	−	43.1080i	0.508130	−	1.72157i
$628$	−12.2021	−	21.1346i	−0.486916	−	0.843364i
$629$	36.0019			1.43549
$630$	6.39937	−	3.27635i	0.254957	−	0.130533i
$631$	28.3065			1.12686			0.563432	−	0.826163i	$-0.309481\pi$
$631$	28.3065			1.12686			0.563432	+	0.826163i	$0.309481\pi$
$632$	4.88118	+	8.45445i	0.194163	+	0.336300i
$633$	20.4257	−	4.92481i	0.811849	−	0.195744i
$634$	12.8794	−	22.3077i	0.511506	−	0.885954i
$635$	−33.6094	+	58.2131i	−1.33375	+	2.31012i
$636$	−9.62430	+	2.32050i	−0.381628	+	0.0920139i
$637$	−12.9273	−	22.3907i	−0.512198	−	0.887152i
$638$	42.2503			1.67270
$639$	0.517532	−	10.2572i	0.0204733	−	0.405767i
$640$	3.62831			0.143422
$641$	−7.38813	−	12.7966i	−0.291814	−	0.505436i	0.682425	−	0.730956i	$-0.260925\pi$
$641$	−7.38813	−	12.7966i	−0.291814	−	0.505436i	−0.974239	+	0.225520i	$0.927592\pi$
$642$	1.28042	−	4.33814i	0.0505343	−	0.171213i
$643$	2.62046	−	4.53877i	0.103341	−	0.178992i	−0.809718	−	0.586819i	$-0.800380\pi$
$643$	2.62046	−	4.53877i	0.103341	−	0.178992i	0.913059	+	0.407827i	$0.133713\pi$
$644$	2.32826	−	4.03267i	0.0917463	−	0.158909i
$645$	8.99109	+	9.45618i	0.354024	+	0.372337i
$646$	−14.6823	−	25.4305i	−0.577669	−	1.00055i
$647$	−18.0038			−0.707804			−0.353902	−	0.935283i	$-0.615145\pi$
$647$	−18.0038			−0.707804			−0.353902	+	0.935283i	$0.615145\pi$
$648$	−8.95429	−	0.905897i	−0.351758	−	0.0355870i
$649$	−30.6446			−1.20291
$650$	16.0802	+	27.8517i	0.630717	+	1.09243i
$651$	7.62019	+	8.01437i	0.298659	+	0.314108i
$652$	−6.56971	+	11.3791i	−0.257290	+	0.445639i
$653$	24.2522	−	42.0060i	0.949060	−	1.64382i	0.201650	−	0.979458i	$-0.435370\pi$
$653$	24.2522	−	42.0060i	0.949060	−	1.64382i	0.747410	−	0.664363i	$-0.231297\pi$
$654$	10.0773	−	34.1424i	0.394054	−	1.33508i
$655$	−12.6275	−	21.8715i	−0.493398	−	0.854591i
$656$	1.00000			0.0390434
$657$	0.391216	−	7.75364i	0.0152628	−	0.302498i
$658$	3.06690			0.119560
$659$	−14.3204	−	24.8037i	−0.557845	−	0.966215i	−0.997676	−	0.0681348i	$-0.978295\pi$
$659$	−14.3204	−	24.8037i	−0.557845	−	0.966215i	0.439832	−	0.898080i	$-0.355038\pi$
$660$	28.9387	−	6.97736i	1.12644	−	0.271593i
$661$	8.25787	−	14.3031i	0.321194	−	0.556325i	−0.659541	−	0.751669i	$-0.729249\pi$
$661$	8.25787	−	14.3031i	0.321194	−	0.556325i	0.980735	+	0.195344i	$0.0625825\pi$
$662$	−7.75164	+	13.4262i	−0.301276	+	0.521826i
$663$	−35.5507	+	8.57157i	−1.38067	+	0.332892i
$664$	4.23404	+	7.33358i	0.164313	+	0.284598i
$665$	−13.1286			−0.509106
$666$	−17.9359	+	9.18282i	−0.695002	+	0.355827i
$667$	62.8847			2.43491
$668$	0.209486	+	0.362840i	0.00810525	+	0.0140387i
$669$	−0.462962	+	1.56854i	−0.0178992	+	0.0606432i
$670$	9.89930	−	17.1461i	0.382443	−	0.662411i
$671$	−25.0684	+	43.4197i	−0.967755	+	1.67620i
$672$	0.788279	+	0.829055i	0.0304085	+	0.0319815i
$673$	−16.1284	−	27.9353i	−0.621705	−	1.07683i	−0.989168	−	0.146787i	$-0.953107\pi$
$673$	−16.1284	−	27.9353i	−0.621705	−	1.07683i	0.367463	−	0.930038i	$-0.380227\pi$
$674$	23.3449			0.899211
$675$	40.0325	+	14.0448i	1.54085	+	0.540585i
$676$	2.51561			0.0967542
$677$	8.16666	+	14.1451i	0.313870	+	0.543639i	0.979197	−	0.202913i	$-0.0650410\pi$
$677$	8.16666	+	14.1451i	0.313870	+	0.543639i	−0.665326	+	0.746553i	$0.731708\pi$
$678$	−0.820833	−	0.863293i	−0.0315239	−	0.0331546i
$679$	−3.52863	+	6.11177i	−0.135416	+	0.234548i
$680$	9.72406	−	16.8426i	0.372901	−	0.645883i
$681$	−1.50387	+	5.09519i	−0.0576285	+	0.195248i
$682$	22.8949	+	39.6552i	0.876692	+	1.51848i
$683$	−16.7882			−0.642382			−0.321191	−	0.947014i	$-0.604083\pi$
$683$	−16.7882			−0.642382			−0.321191	+	0.947014i	$0.604083\pi$
$684$	13.8011	+	8.92436i	0.527697	+	0.341232i
$685$	−24.2534			−0.926673
$686$	4.47932	+	7.75841i	0.171021	+	0.296218i
$687$	40.7301	−	9.82038i	1.55395	−	0.374671i
$688$	−1.03815	+	1.79813i	−0.0395791	+	0.0685530i
$689$	11.2573	−	19.4982i	0.428868	−	0.742821i
$690$	43.0719	−	10.3850i	1.63972	−	0.395351i
$691$	10.8536	+	18.7990i	0.412891	+	0.715149i	0.995205	−	0.0978156i	$-0.0311855\pi$
$691$	10.8536	+	18.7990i	0.412891	+	0.715149i	−0.582313	+	0.812965i	$0.697852\pi$
$692$	−2.43495			−0.0925629
$693$	7.88145	+	5.09649i	0.299392	+	0.193600i
$694$	−11.6027			−0.440434
$695$	38.0742	+	65.9464i	1.44424	+	2.50149i
$696$	−4.37339	+	14.8173i	−0.165773	+	0.561648i
$697$	2.68005	−	4.64198i	0.101514	−	0.175828i
$698$	3.48911	−	6.04331i	0.132065	−	0.228743i
$699$	−26.7865	−	28.1721i	−1.01316	−	1.06557i
$700$	−2.69631	−	4.67014i	−0.101911	−	0.176515i
$701$	−23.6919			−0.894830			−0.447415	−	0.894326i	$-0.647655\pi$
$701$	−23.6919			−0.894830			−0.447415	+	0.894326i	$0.647655\pi$
$702$	15.5248	−	13.3380i	0.585945	−	0.503411i
$703$	36.7963			1.38780
$704$	2.36839	+	4.10218i	0.0892621	+	0.154607i
$705$	20.1076	+	21.1477i	0.757295	+	0.796468i
$706$	−4.87070	+	8.43630i	−0.183311	+	0.317504i
$707$	2.89181	−	5.00877i	0.108758	−	0.188374i
$708$	3.17207	−	10.7471i	0.119214	−	0.403903i
$709$	9.46772	+	16.3986i	0.355568	+	0.615862i	0.987215	−	0.159394i	$-0.0509542\pi$
$709$	9.46772	+	16.3986i	0.355568	+	0.615862i	−0.631647	+	0.775256i	$0.717621\pi$
$710$	−12.4212			−0.466158
$711$	−26.0691	+	13.3468i	−0.977666	+	0.500546i
$712$	2.36259			0.0885416
$713$	34.0765	+	59.0222i	1.27618	+	2.21040i
$714$	5.96109	−	1.43727i	0.223088	−	0.0537885i
$715$	−33.8487	+	58.6277i	−1.26587	+	2.19255i
$716$	−4.84766	+	8.39639i	−0.181165	+	0.313788i
$717$	−38.7888	+	9.35230i	−1.44859	+	0.349268i
$718$	−5.89089	−	10.2033i	−0.219846	−	0.380784i
$719$	−26.0896			−0.972978			−0.486489	−	0.873687i	$-0.661723\pi$
$719$	−26.0896			−0.972978			−0.486489	+	0.873687i	$0.661723\pi$
$720$	−0.548510	+	10.8711i	−0.0204418	+	0.405142i
$721$	1.84082			0.0685559
$722$	−5.50631	−	9.53721i	−0.204924	−	0.354938i
$723$	1.01207	−	3.42893i	0.0376391	−	0.127523i
$724$	1.40120	−	2.42694i	0.0520750	−	0.0901966i
$725$	36.4127	−	63.0686i	1.35233	−	2.34231i
$726$	13.6501	+	14.3562i	0.506601	+	0.532807i
$727$	18.0771	+	31.3105i	0.670444	+	1.16124i	0.977778	+	0.209641i	$0.0672296\pi$
$727$	18.0771	+	31.3105i	0.670444	+	1.16124i	−0.307334	+	0.951602i	$0.599437\pi$
$728$	−2.60164			−0.0964231
$729$	4.06790	−	26.6918i	0.150663	−	0.988585i
$730$	−9.38946			−0.347520
$731$	5.56459	+	9.63815i	0.205814	+	0.356480i
$732$	−12.6325	−	13.2860i	−0.466912	−	0.491065i
$733$	−5.43844	+	9.41965i	−0.200873	+	0.347923i	−0.948810	−	0.315847i	$-0.897711\pi$
$733$	−5.43844	+	9.41965i	−0.200873	+	0.347923i	0.747937	+	0.663770i	$0.231045\pi$
$734$	−8.71736	+	15.0989i	−0.321764	+	0.557311i
$735$	−11.6770	+	39.5621i	−0.430711	+	1.45927i
$736$	3.52508	+	6.10562i	0.129936	+	0.225056i
$737$	25.8472			0.952094
$738$	−0.151175	+	2.99619i	−0.00556483	+	0.110291i
$739$	−49.1155			−1.80674			−0.903372	−	0.428857i	$-0.858916\pi$
$739$	−49.1155			−1.80674			−0.903372	+	0.428857i	$0.858916\pi$
$740$	12.1850	+	21.1051i	0.447931	+	0.775840i
$741$	−36.3351	+	8.76071i	−1.33480	+	0.321833i
$742$	−1.88760	+	3.26943i	−0.0692961	+	0.120024i
$743$	0.986777	−	1.70915i	0.0362013	−	0.0627025i	−0.847357	−	0.531024i	$-0.821808\pi$
$743$	0.986777	−	1.70915i	0.0362013	−	0.0627025i	0.883558	+	0.468321i	$0.155141\pi$
$744$	−16.2771	+	3.92454i	−0.596746	+	0.143881i
$745$	−33.4038	−	57.8571i	−1.22382	−	2.11972i
$746$	13.8362			0.506580
$747$	−22.6129	+	11.5773i	−0.827361	+	0.423593i
$748$	25.3896			0.928337
$749$	−0.862408	−	1.49374i	−0.0315117	−	0.0545799i
$750$	5.62991	−	19.0744i	0.205575	−	0.696499i
$751$	−3.68967	+	6.39069i	−0.134638	+	0.233200i	−0.925459	−	0.378848i	$-0.876320\pi$
$751$	−3.68967	+	6.39069i	−0.134638	+	0.233200i	0.790821	+	0.612047i	$0.209654\pi$
$752$	−2.32171	+	4.02131i	−0.0846639	+	0.146642i
$753$	16.1917	+	17.0293i	0.590059	+	0.620581i
$754$	−17.5671	−	30.4271i	−0.639756	−	1.10809i
$755$	35.5547			1.29397
$756$	−2.60317	+	2.23650i	−0.0946765	+	0.0813407i
$757$	8.30767			0.301947			0.150974	−	0.988538i	$-0.451759\pi$
$757$	8.30767			0.301947			0.150974	+	0.988538i	$0.451759\pi$
$758$	−1.59476	−	2.76221i	−0.0579243	−	0.100328i
$759$	39.8567	+	41.9184i	1.44671	+	1.52154i
$760$	9.93863	−	17.2142i	0.360512	−	0.624425i
$761$	12.5922	−	21.8103i	0.456466	−	0.790622i	−0.542305	−	0.840182i	$-0.682448\pi$
$761$	12.5922	−	21.8103i	0.456466	−	0.790622i	0.998771	+	0.0495592i	$0.0157817\pi$
$762$	9.08361	−	30.7757i	0.329065	−	1.11489i
$763$	−6.78741	−	11.7561i	−0.245721	−	0.425601i
$764$	−6.54891			−0.236931
$765$	48.9935	+	31.6813i	1.77136	+	1.14544i
$766$	13.5242			0.488650
$767$	12.7416	+	22.0692i	0.460074	+	0.796871i
$768$	−1.68380	+	0.405978i	−0.0607589	+	0.0146495i
$769$	−6.17144	+	10.6892i	−0.222548	+	0.385464i	−0.955581	−	0.294729i	$-0.904771\pi$
$769$	−6.17144	+	10.6892i	−0.222548	+	0.385464i	0.733033	+	0.680193i	$0.238104\pi$
$770$	5.67571	−	9.83062i	0.204538	−	0.354271i
$771$	−17.2771	+	4.16565i	−0.622219	+	0.150022i
$772$	−0.705513	−	1.22198i	−0.0253920	−	0.0439802i
$773$	−30.3011			−1.08985			−0.544927	−	0.838483i	$-0.683443\pi$
$773$	−30.3011			−1.08985			−0.544927	+	0.838483i	$0.683443\pi$
$774$	−5.23059	−	3.38233i	−0.188010	−	0.121575i
$775$	78.9265			2.83512
$776$	−5.34250	−	9.25348i	−0.191784	−	0.332180i
$777$	−2.17514	+	7.36949i	−0.0780328	+	0.264379i
$778$	8.73115	−	15.1228i	0.313027	−	0.542178i
$779$	2.73919	−	4.74441i	0.0981416	−	0.169986i
$780$	−17.0572	−	17.9395i	−0.610744	−	0.642337i
$781$	−8.10795	−	14.0434i	−0.290125	−	0.502512i
$782$	37.7896			1.35135
$783$	−43.7342	−	15.3435i	−1.56293	−	0.548332i
$784$	−6.56376			−0.234420
$785$	−44.2730	−	76.6830i	−1.58017	−	2.73693i
$786$	8.30733	+	8.73705i	0.296313	+	0.311640i
$787$	−1.76402	+	3.05538i	−0.0628807	+	0.108913i	−0.895752	−	0.444554i	$-0.853362\pi$
$787$	−1.76402	+	3.05538i	−0.0628807	+	0.108913i	0.832871	+	0.553467i	$0.186695\pi$
$788$	5.45435	−	9.44721i	0.194303	−	0.336543i
$789$	0.144936	−	0.491051i	0.00515986	−	0.0174819i
$790$	17.7104	+	30.6754i	0.630109	+	1.09138i
$791$	−0.454255			−0.0161514
$792$	−12.6489	+	6.47600i	−0.449460	+	0.230115i
$793$	41.6925			1.48054
$794$	7.00017	+	12.1247i	0.248427	+	0.430288i
$795$	−34.9200	+	8.41950i	−1.23848	+	0.298609i
$796$	−7.68564	+	13.3119i	−0.272410	+	0.471828i
$797$	−4.87117	+	8.43711i	−0.172546	+	0.298858i	−0.939309	−	0.343072i	$-0.888533\pi$
$797$	−4.87117	+	8.43711i	−0.172546	+	0.298858i	0.766764	+	0.641930i	$0.221866\pi$
$798$	6.09263	−	1.46898i	0.215677	−	0.0520015i
$799$	12.4446	+	21.5547i	0.440258	+	0.762549i
$800$	8.16464			0.288664
$801$	−0.357164	+	7.07875i	−0.0126198	+	0.250115i
$802$	−28.6843			−1.01288
$803$	−6.12900	−	10.6157i	−0.216288	−	0.374622i
$804$	−2.67548	+	9.06468i	−0.0943571	+	0.319687i
$805$	8.44765	−	14.6318i	0.297741	−	0.515702i
$806$	19.0388	−	32.9762i	0.670614	−	1.16154i
$807$	−25.4005	−	26.7144i	−0.894138	−	0.940390i
$808$	4.37833	+	7.58349i	0.154029	+	0.266786i
$809$	−20.5928			−0.724006			−0.362003	−	0.932177i	$-0.617907\pi$
$809$	−20.5928			−0.724006			−0.362003	+	0.932177i	$0.617907\pi$
$810$	−32.4890	−	3.28688i	−1.14155	−	0.115489i
$811$	−36.8727			−1.29478			−0.647388	−	0.762161i	$-0.724139\pi$
$811$	−36.8727			−1.29478			−0.647388	+	0.762161i	$0.724139\pi$
$812$	2.94563	+	5.10198i	0.103371	+	0.179044i
$813$	24.8344	+	26.1190i	0.870980	+	0.916034i
$814$	−15.9077	+	27.5529i	−0.557563	+	0.965728i
$815$	−23.8370	+	41.2868i	−0.834972	+	1.44621i
$816$	−2.62812	+	8.90421i	−0.0920027	+	0.311710i
$817$	5.68738	+	9.85083i	0.198976	+	0.344637i
$818$	25.1186			0.878250
$819$	0.393302	−	7.79499i	0.0137431	−	0.272379i
$820$	3.62831			0.126706
$821$	−11.2759	−	19.5304i	−0.393532	−	0.681617i	0.599381	−	0.800464i	$-0.295413\pi$
$821$	−11.2759	−	19.5304i	−0.393532	−	0.681617i	−0.992913	+	0.118847i	$0.962080\pi$
$822$	11.2553	−	2.71375i	0.392574	−	0.0946530i
$823$	24.4831	−	42.4059i	0.853426	−	1.47818i	−0.0246721	−	0.999696i	$-0.507854\pi$
$823$	24.4831	−	42.4059i	0.853426	−	1.47818i	0.878098	−	0.478481i	$-0.158812\pi$
$824$	−1.39354	+	2.41369i	−0.0485464	+	0.0840848i
$825$	65.1195	−	15.7009i	2.26717	−	0.546634i
$826$	−2.13650	−	3.70053i	−0.0743383	−	0.128758i
$827$	14.7353			0.512398			0.256199	−	0.966624i	$-0.417530\pi$
$827$	14.7353			0.512398			0.256199	+	0.966624i	$0.417530\pi$
$828$	−18.8265	+	9.63880i	−0.654266	+	0.334971i
$829$	−3.00541			−0.104382			−0.0521912	−	0.998637i	$-0.516621\pi$
$829$	−3.00541			−0.104382			−0.0521912	+	0.998637i	$0.516621\pi$
$830$	15.3624	+	26.6085i	0.533237	+	0.923594i
$831$	−1.60106	+	5.42447i	−0.0555401	+	0.188173i
$832$	1.96949	−	3.41126i	0.0682799	−	0.118264i
$833$	−17.5912	+	30.4689i	−0.609499	+	1.05568i
$834$	−25.0481	−	26.3437i	−0.867343	−	0.912209i
$835$	0.760080	+	1.31650i	0.0263037	+	0.0455593i
$836$	25.9499			0.897496
$837$	−9.29798	−	49.3624i	−0.321385	−	1.70622i
$838$	−27.8943			−0.963593
$839$	−24.7488	−	42.8662i	−0.854423	−	1.47990i	−0.877179	−	0.480164i	$-0.840577\pi$
$839$	−24.7488	−	42.8662i	−0.854423	−	1.47990i	0.0227554	−	0.999741i	$-0.492756\pi$
$840$	2.86012	+	3.00807i	0.0986836	+	0.103788i
$841$	−25.2797	+	43.7858i	−0.871715	+	1.50985i
$842$	−3.65699	+	6.33409i	−0.126028	+	0.218287i
$843$	−0.803030	+	2.72071i	−0.0276578	+	0.0937061i
$844$	6.06536	+	10.5055i	0.208778	+	0.361615i
$845$	9.12741			0.313993
$846$	−11.6976	−	7.56419i	−0.402173	−	0.260062i
$847$	7.55403			0.259560
$848$	−2.85791	−	4.95005i	−0.0981411	−	0.169985i
$849$	9.96296	−	2.40215i	0.341928	−	0.0824417i
$850$	21.8816	−	37.9001i	0.750534	−	1.29996i
$851$	−23.6768	+	41.0093i	−0.811629	+	1.40578i
$852$	5.76432	−	1.38983i	0.197482	−	0.0476147i
$853$	4.94650	+	8.56759i	0.169365	+	0.293349i	0.938197	−	0.346102i	$-0.112495\pi$
$853$	4.94650	+	8.56759i	0.169365	+	0.293349i	−0.768832	+	0.639451i	$0.779162\pi$
$854$	−6.99093			−0.239225
$855$	50.0745	+	32.3804i	1.71251	+	1.10739i
$856$	2.61144			0.0892573
$857$	8.05916	+	13.9589i	0.275296	+	0.476826i	0.970210	−	0.242267i	$-0.0778909\pi$
$857$	8.05916	+	13.9589i	0.275296	+	0.476826i	−0.694914	+	0.719093i	$0.744558\pi$
$858$	9.14831	−	30.9949i	0.312318	−	1.05815i
$859$	−23.8119	+	41.2435i	−0.812453	+	1.40721i	0.0986896	+	0.995118i	$0.468535\pi$
$859$	−23.8119	+	41.2435i	−0.812453	+	1.40721i	−0.911143	+	0.412091i	$0.864798\pi$
$860$	−3.76673	+	6.52417i	−0.128444	+	0.222472i
$861$	0.788279	+	0.829055i	0.0268645	+	0.0282541i
$862$	−6.93643	−	12.0142i	−0.236256	−	0.409207i
$863$	−10.9306			−0.372082			−0.186041	−	0.982542i	$-0.559566\pi$
$863$	−10.9306			−0.372082			−0.186041	+	0.982542i	$0.559566\pi$
$864$	−0.961840	−	5.10636i	−0.0327225	−	0.173722i
$865$	−8.83476			−0.300391
$866$	−9.76273	−	16.9095i	−0.331751	−	0.574610i
$867$	14.0004	+	14.7246i	0.475480	+	0.500075i
$868$	−3.19240	+	5.52941i	−0.108357	+	0.187680i
$869$	−23.1211	+	40.0469i	−0.784330	+	1.35850i
$870$	−15.8680	+	53.7617i	−0.537977	+	1.82269i
$871$	−10.7469	−	18.6142i	−0.364146	−	0.630719i
$872$	20.5528			0.696007
$873$	28.5328	−	14.6082i	0.965689	−	0.494414i
$874$	38.6235			1.30646
$875$	−3.79194	−	6.56782i	−0.128191	−	0.222033i
$876$	4.35739	−	1.05060i	0.147223	−	0.0354966i
$877$	25.0515	−	43.3905i	0.845930	−	1.46519i	−0.0388804	−	0.999244i	$-0.512379\pi$
$877$	25.0515	−	43.3905i	0.845930	−	1.46519i	0.884811	−	0.465951i	$-0.154288\pi$
$878$	4.25502	−	7.36992i	0.143600	−	0.248723i
$879$	47.2742	−	11.3982i	1.59452	−	0.384452i
$880$	8.59326	+	14.8840i	0.289679	+	0.501738i
$881$	33.8071			1.13899			0.569496	−	0.821994i	$-0.307139\pi$
$881$	33.8071			1.13899			0.569496	+	0.821994i	$0.307139\pi$
$882$	0.992276	−	19.6663i	0.0334117	−	0.662198i
$883$	4.02371			0.135409			0.0677043	−	0.997705i	$-0.478433\pi$
$883$	4.02371			0.135409			0.0677043	+	0.997705i	$0.478433\pi$
$884$	−10.5567	−	18.2847i	−0.355060	−	0.614981i
$885$	11.5093	−	38.9940i	0.386880	−	1.31077i
$886$	4.40699	−	7.63313i	0.148056	−	0.256440i
$887$	27.5020	−	47.6348i	0.923426	−	1.59942i	0.129353	−	0.991599i	$-0.458710\pi$
$887$	27.5020	−	47.6348i	0.923426	−	1.59942i	0.794073	−	0.607822i	$-0.207957\pi$
$888$	−8.01624	−	8.43090i	−0.269007	−	0.282923i
$889$	−6.11812	−	10.5969i	−0.205195	−	0.355409i
$890$	8.57220			0.287341
$891$	−17.4911	−	38.8776i	−0.585975	−	1.30245i
$892$	−0.944219			−0.0316148
$893$	12.7192	+	22.0303i	0.425631	+	0.737215i
$894$	21.9755	+	23.1123i	0.734972	+	0.772991i
$895$	−17.5888	+	30.4647i	−0.587929	+	1.01832i
$896$	−0.330242	+	0.571996i	−0.0110326	+	0.0191090i
$897$	13.6162	−	46.1324i	0.454632	−	1.54032i
$898$	−0.752736	−	1.30378i	−0.0251191	−	0.0435076i
$899$	−86.2247			−2.87575
$900$	−1.23429	+	24.4628i	−0.0411430	+	0.815427i
$901$	−30.6374			−1.02068
$902$	2.36839	+	4.10218i	0.0788588	+	0.136587i
$903$	−2.30910	+	0.556744i	−0.0768420	+	0.0185273i
$904$	0.343880	−	0.595618i	0.0114373	−	0.0198100i
$905$	5.08397	−	8.80570i	0.168997	−	0.292711i
$906$	−16.4999	+	3.97828i	−0.548174	+	0.132169i
$907$	−2.04026	−	3.53383i	−0.0677457	−	0.117339i	0.830163	−	0.557521i	$-0.188247\pi$
$907$	−2.04026	−	3.53383i	−0.0677457	−	0.117339i	−0.897909	+	0.440182i	$0.854914\pi$
$908$	−3.06717			−0.101788
$909$	−23.3834	+	11.9719i	−0.775580	+	0.397082i
$910$	−9.43955			−0.312918
$911$	1.02806	+	1.78065i	0.0340611	+	0.0589956i	0.882553	−	0.470212i	$-0.155823\pi$
$911$	1.02806	+	1.78065i	0.0340611	+	0.0589956i	−0.848492	+	0.529208i	$0.822489\pi$
$912$	−2.68612	+	9.10070i	−0.0889462	+	0.301354i
$913$	−20.0557	+	34.7376i	−0.663748	+	1.14965i
$914$	15.3760	−	26.6319i	0.508592	−	0.880907i
$915$	−45.8348	−	48.2057i	−1.51525	−	1.59363i
$916$	12.0947	+	20.9486i	0.399620	+	0.692163i
$917$	4.59733			0.151817
$918$	−26.2814	−	9.22045i	−0.867415	−	0.304320i
$919$	19.4256			0.640792			0.320396	−	0.947284i	$-0.396184\pi$
$919$	19.4256			0.640792			0.320396	+	0.947284i	$0.396184\pi$
$920$	12.7901	+	22.1531i	0.421677	+	0.730366i
$921$	−19.4701	−	20.4772i	−0.641561	−	0.674748i
$922$	10.7165	−	18.5616i	0.352930	−	0.611293i
$923$	−6.74236	+	11.6781i	−0.221928	+	0.384390i
$924$	−1.53398	+	5.19719i	−0.0504641	+	0.170975i
$925$	27.4195	+	47.4920i	0.901548	+	1.56153i
$926$	−18.8988			−0.621055
$927$	−7.02119	−	4.54021i	−0.230606	−	0.149120i
$928$	−8.91961			−0.292801
$929$	−14.9383	−	25.8739i	−0.490110	−	0.848895i	0.509826	−	0.860278i	$-0.329710\pi$
$929$	−14.9383	−	25.8739i	−0.490110	−	0.848895i	−0.999935	+	0.0113829i	$0.996377\pi$
$930$	−59.0583	+	14.2394i	−1.93660	+	0.466930i
$931$	−17.9794	+	31.1412i	−0.589250	+	1.02061i
$932$	11.2220	−	19.4370i	0.367588	−	0.636680i
$933$	23.9877	−	5.78364i	0.785322	−	0.189348i
$934$	−5.34964	−	9.26585i	−0.175046	−	0.303188i
$935$	92.1215			3.01270
$936$	9.92305	+	6.41667i	0.324345	+	0.209735i
$937$	14.7397			0.481524			0.240762	−	0.970584i	$-0.422603\pi$
$937$	14.7397			0.481524			0.240762	+	0.970584i	$0.422603\pi$
$938$	1.80203	+	3.12121i	0.0588384	+	0.101911i
$939$	−12.1993	+	41.3319i	−0.398110	+	1.34882i
$940$	−8.42387	+	14.5906i	−0.274756	+	0.475892i
$941$	−14.5513	+	25.2035i	−0.474358	+	0.821612i	−0.999569	−	0.0293603i	$-0.990653\pi$
$941$	−14.5513	+	25.2035i	−0.474358	+	0.821612i	0.525211	+	0.850972i	$0.323986\pi$
$942$	29.1261	+	30.6327i	0.948979	+	0.998067i
$943$	3.52508	+	6.10562i	0.114793	+	0.198826i
$944$	6.46950			0.210564
$945$	−9.44512	+	8.11472i	−0.307250	+	0.263972i
$946$	−9.83499			−0.319763
$947$	−5.14493	−	8.91129i	−0.167188	−	0.289578i	0.770242	−	0.637752i	$-0.220135\pi$
$947$	−5.14493	−	8.91129i	−0.167188	−	0.289578i	−0.937430	+	0.348174i	$0.886802\pi$
$948$	−11.6513	−	12.2540i	−0.378415	−	0.397990i
$949$	−5.09672	+	8.82778i	−0.165447	+	0.286562i
$950$	22.3645	−	38.7364i	0.725600	−	1.25678i
$951$	−12.6298	+	42.7905i	−0.409550	+	1.38758i
$952$	1.77013	+	3.06596i	0.0573702	+	0.0993682i
$953$	−45.9593			−1.48877			−0.744385	−	0.667751i	$-0.767257\pi$
$953$	−45.9593			−1.48877			−0.744385	+	0.667751i	$0.767257\pi$
$954$	15.2633	−	7.81452i	0.494168	−	0.253004i
$955$	−23.7615			−0.768903
$956$	−11.5182	−	19.9501i	−0.372526	−	0.645234i
$957$	−71.1410	+	17.1527i	−2.29966	+	0.554468i
$958$	11.6784	−	20.2276i	0.377312	−	0.653524i
$959$	2.20749	−	3.82349i	0.0712837	−	0.123467i
$960$	−6.10935	+	1.47302i	−0.197178	+	0.0475414i
$961$	−31.2241	−	54.0818i	−1.00723	−	1.74457i
$962$	26.4568			0.853001
$963$	−0.394785	+	7.82438i	−0.0127218	+	0.252137i
$964$	2.06413			0.0664810
$965$	−2.55982	−	4.43374i	−0.0824036	−	0.142727i
$966$	−2.28315	+	7.73543i	−0.0734591	+	0.248883i
$967$	−8.49482	+	14.7135i	−0.273175	+	0.473153i	−0.969673	−	0.244406i	$-0.921407\pi$
$967$	−8.49482	+	14.7135i	−0.273175	+	0.473153i	0.696498	+	0.717559i	$0.254740\pi$
$968$	−5.71856	+	9.90484i	−0.183802	+	0.318354i
$969$	35.0464	+	36.8592i	1.12585	+	1.18409i
$970$	−19.3842	−	33.5745i	−0.622390	−	1.07801i
$971$	13.5910			0.436155			0.218078	−	0.975931i	$-0.430021\pi$
$971$	13.5910			0.436155			0.218078	+	0.975931i	$0.430021\pi$
$972$	15.4450	−	2.10990i	0.495399	−	0.0676751i
$973$	−13.8618			−0.444388
$974$	−1.54383	−	2.67399i	−0.0494675	−	0.0856802i
$975$	−38.3830	−	40.3685i	−1.22924	−	1.29283i
$976$	5.29228	−	9.16650i	0.169402	−	0.293413i
$977$	10.0125	−	17.3421i	0.320327	−	0.554823i	−0.660228	−	0.751065i	$-0.729540\pi$
$977$	10.0125	−	17.3421i	0.320327	−	0.554823i	0.980555	+	0.196242i	$0.0628738\pi$
$978$	6.44242	−	21.8273i	0.206006	−	0.697959i
$979$	5.59553	+	9.69174i	0.178834	+	0.309749i
$980$	−23.8154			−0.760754
$981$	−3.10708	+	61.5802i	−0.0992013	+	1.96610i
$982$	−6.95852			−0.222055
$983$	17.0448	+	29.5225i	0.543646	+	0.941622i	0.998691	+	0.0511538i	$0.0162899\pi$
$983$	17.0448	+	29.5225i	0.543646	+	0.941622i	−0.455045	+	0.890468i	$0.650377\pi$
$984$	−1.68380	+	0.405978i	−0.0536776	+	0.0129421i
$985$	19.7901	−	34.2774i	0.630564	−	1.09217i
$986$	−23.9050	+	41.4047i	−0.761291	+	1.31859i
$987$	−5.16404	+	1.24510i	−0.164373	+	0.0396318i
$988$	−10.7896	−	18.6882i	−0.343264	−	0.594550i
$989$	−14.6383			−0.465470
$990$	−45.8943	+	23.4970i	−1.45862	+	0.746782i
$991$	51.4879			1.63557			0.817783	−	0.575526i	$-0.195203\pi$
$991$	51.4879			1.63557			0.817783	+	0.575526i	$0.195203\pi$
$992$	−4.83343	−	8.37175i	−0.153462	−	0.265803i
$993$	7.60145	−	25.7541i	0.241225	−	0.817282i
$994$	1.13055	−	1.95817i	0.0358589	−	0.0621094i
$995$	−27.8859	+	48.2998i	−0.884042	+	1.53121i
$996$	−10.1066	−	10.6293i	−0.320238	−	0.336804i
$997$	−17.5717	−	30.4350i	−0.556500	−	0.963887i	−0.997785	−	0.0665198i	$-0.978810\pi$
$997$	−17.5717	−	30.4350i	−0.556500	−	0.963887i	0.441285	−	0.897367i	$-0.354523\pi$
$998$	16.0333			0.507526
$999$	26.4724	−	22.7436i	0.837550	−	0.719576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.e.j.247.5	✓	14
3.2	odd	2		2214.2.e.j.739.7		14
9.2	odd	6		2214.2.e.j.1477.7		14
9.4	even	3		6642.2.a.bv.1.7		7
9.5	odd	6		6642.2.a.bu.1.1		7
9.7	even	3	inner	738.2.e.j.493.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.e.j.247.5	✓	14	1.1	even	1	trivial
738.2.e.j.493.5	yes	14	9.7	even	3	inner
2214.2.e.j.739.7		14	3.2	odd	2
2214.2.e.j.1477.7		14	9.2	odd	6
6642.2.a.bu.1.1		7	9.5	odd	6
6642.2.a.bv.1.7		7	9.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.19349 + 1.25522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.81416 + 3.14221i) q^{5} +(0.490312 - 1.66120i) q^{6} +(-0.330242 - 0.571996i) q^{7} +1.00000 q^{8} +(-0.151175 + 2.99619i) q^{9} +3.62831 q^{10} +(2.36839 + 4.10218i) q^{11} +(-1.68380 + 0.405978i) q^{12} +(1.96949 - 3.41126i) q^{13} +(-0.330242 + 0.571996i) q^{14} +(-6.10935 + 1.47302i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.36010 q^{17} +(2.67036 - 1.36717i) q^{18} -5.47838 q^{19} +(-1.81416 - 3.14221i) q^{20} +(0.323843 - 1.09720i) q^{21} +(2.36839 - 4.10218i) q^{22} +(3.52508 - 6.10562i) q^{23} +(1.19349 + 1.25522i) q^{24} +(-4.08232 - 7.07079i) q^{25} -3.93899 q^{26} +(-3.94131 + 3.38616i) q^{27} +0.660484 q^{28} +(4.45981 + 7.72461i) q^{29} +(4.33034 + 4.55434i) q^{30} +(-4.83343 + 8.37175i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.32250 + 7.86876i) q^{33} +(2.68005 + 4.64198i) q^{34} +2.39644 q^{35} +(-2.51919 - 1.62902i) q^{36} -6.71665 q^{37} +(2.73919 + 4.74441i) q^{38} +(6.63246 - 1.59914i) q^{39} +(-1.81416 + 3.14221i) q^{40} +(-0.500000 + 0.866025i) q^{41} +(-1.11212 + 0.268142i) q^{42} +(-1.03815 - 1.79813i) q^{43} -4.73678 q^{44} +(-9.14040 - 5.91058i) q^{45} -7.05017 q^{46} +(-2.32171 - 4.02131i) q^{47} +(0.490312 - 1.66120i) q^{48} +(3.28188 - 5.68438i) q^{49} +(-4.08232 + 7.07079i) q^{50} +(-6.39721 - 6.72813i) q^{51} +(1.96949 + 3.41126i) q^{52} +5.71582 q^{53} +(4.90315 + 1.72020i) q^{54} -17.1865 q^{55} +(-0.330242 - 0.571996i) q^{56} +(-6.53838 - 6.87659i) q^{57} +(4.45981 - 7.72461i) q^{58} +(-3.23475 + 5.60275i) q^{59} +(1.77900 - 6.02736i) q^{60} +(5.29228 + 9.16650i) q^{61} +9.66687 q^{62} +(1.76373 - 0.902996i) q^{63} +1.00000 q^{64} +(7.14593 + 12.3771i) q^{65} +(7.97580 - 1.92303i) q^{66} +(2.72835 - 4.72564i) q^{67} +(2.68005 - 4.64198i) q^{68} +(11.8711 - 2.86222i) q^{69} +(-1.19822 - 2.07538i) q^{70} -3.42340 q^{71} +(-0.151175 + 2.99619i) q^{72} -2.58783 q^{73} +(3.35833 + 5.81679i) q^{74} +(4.00322 - 13.5631i) q^{75} +(2.73919 - 4.74441i) q^{76} +(1.56428 - 2.70942i) q^{77} +(-4.70113 - 4.94431i) q^{78} +(4.88118 + 8.45445i) q^{79} +3.62831 q^{80} +(-8.95429 - 0.905897i) q^{81} +1.00000 q^{82} +(4.23404 + 7.33358i) q^{83} +(0.788279 + 0.829055i) q^{84} +(9.72406 - 16.8426i) q^{85} +(-1.03815 + 1.79813i) q^{86} +(-4.37339 + 14.8173i) q^{87} +(2.36839 + 4.10218i) q^{88} +2.36259 q^{89} +(-0.548510 + 10.8711i) q^{90} -2.60164 q^{91} +(3.52508 + 6.10562i) q^{92} +(-16.2771 + 3.92454i) q^{93} +(-2.32171 + 4.02131i) q^{94} +(9.93863 - 17.2142i) q^{95} +(-1.68380 + 0.405978i) q^{96} +(-5.34250 - 9.25348i) q^{97} -6.56376 q^{98} +(-12.6489 + 6.47600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{2} + 4 q^{3} - 7 q^{4} + 5 q^{5} - 2 q^{6} - q^{7} + 14 q^{8} - 8 q^{9} - 10 q^{10} + 10 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 5 q^{15} - 7 q^{16} - 26 q^{17} + 4 q^{18} - 2 q^{19} + 5 q^{20}+ \cdots - 34 q^{99}+O(q^{100}) \) 14 * q - 7 * q^2 + 4 * q^3 - 7 * q^4 + 5 * q^5 - 2 * q^6 - q^7 + 14 * q^8 - 8 * q^9 - 10 * q^10 + 10 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 5 * q^15 - 7 * q^16 - 26 * q^17 + 4 * q^18 - 2 * q^19 + 5 * q^20 - 17 * q^21 + 10 * q^22 + 15 * q^23 + 4 * q^24 - 14 * q^25 - 8 * q^26 + 13 * q^27 + 2 * q^28 + 30 * q^29 + 7 * q^30 - 13 * q^31 - 7 * q^32 + 23 * q^33 + 13 * q^34 - 16 * q^35 + 4 * q^36 + 14 * q^37 + q^38 - 7 * q^39 + 5 * q^40 - 7 * q^41 + 22 * q^42 + 5 * q^43 - 20 * q^44 - 5 * q^45 - 30 * q^46 + 3 * q^47 - 2 * q^48 + 12 * q^49 - 14 * q^50 + 5 * q^51 + 4 * q^52 - 24 * q^53 - 20 * q^54 - 26 * q^55 - q^56 - 13 * q^57 + 30 * q^58 + 13 * q^59 - 2 * q^60 + 55 * q^61 + 26 * q^62 + 19 * q^63 + 14 * q^64 + 25 * q^65 + 11 * q^66 + 15 * q^67 + 13 * q^68 + 39 * q^69 + 8 * q^70 - 24 * q^71 - 8 * q^72 - 7 * q^74 + 5 * q^75 + q^76 - 5 * q^77 - 10 * q^78 - 12 * q^79 - 10 * q^80 - 20 * q^81 + 14 * q^82 + 36 * q^83 - 5 * q^84 + 4 * q^85 + 5 * q^86 - 21 * q^87 + 10 * q^88 - 32 * q^89 - 2 * q^90 - 62 * q^91 + 15 * q^92 - 59 * q^93 + 3 * q^94 + 43 * q^95 - 2 * q^96 - q^97 - 24 * q^98 - 34 * q^99

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