LMFDB - Embedded newform 414.2.e.d.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, degree $2$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$0.827154 - 1.43267i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.d.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.958787 - 1.44247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.217761 + 0.377174i) q^{5} +(-1.72861 + 0.109097i) q^{6} +(2.31474 - 4.00925i) q^{7} -1.00000 q^{8} +(-1.16146 + 2.76605i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.958787 - 1.44247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.217761 + 0.377174i) q^{5} +(-1.72861 + 0.109097i) q^{6} +(2.31474 - 4.00925i) q^{7} -1.00000 q^{8} +(-1.16146 + 2.76605i) q^{9} +0.435523 q^{10} +(2.10068 - 3.63849i) q^{11} +(-0.769825 + 1.55157i) q^{12} +(1.60224 + 2.77517i) q^{13} +(-2.31474 - 4.00925i) q^{14} +(0.335276 - 0.675744i) q^{15} +(-0.500000 + 0.866025i) q^{16} -5.97604 q^{17} +(1.81474 + 2.38887i) q^{18} -6.45604 q^{19} +(0.217761 - 0.377174i) q^{20} +(-8.00257 + 0.505064i) q^{21} +(-2.10068 - 3.63849i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.958787 + 1.44247i) q^{24} +(2.40516 - 4.16586i) q^{25} +3.20449 q^{26} +(5.10354 - 0.976682i) q^{27} -4.62948 q^{28} +(-1.77412 + 3.07286i) q^{29} +(-0.417574 - 0.628230i) q^{30} +(2.03777 + 3.52952i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.26252 + 0.458358i) q^{33} +(-2.98802 + 5.17540i) q^{34} +2.01624 q^{35} +(2.97620 - 0.377174i) q^{36} +7.64429 q^{37} +(-3.22802 + 5.59110i) q^{38} +(2.46689 - 4.97199i) q^{39} +(-0.217761 - 0.377174i) q^{40} +(1.97990 + 3.42928i) q^{41} +(-3.56389 + 7.18296i) q^{42} +(6.28438 - 10.8849i) q^{43} -4.20136 q^{44} +(-1.29620 + 0.164268i) q^{45} -1.00000 q^{46} +(-4.71761 + 8.17113i) q^{47} +(1.72861 - 0.109097i) q^{48} +(-7.21604 - 12.4986i) q^{49} +(-2.40516 - 4.16586i) q^{50} +(5.72975 + 8.62028i) q^{51} +(1.60224 - 2.77517i) q^{52} +0.713953 q^{53} +(1.70594 - 4.90813i) q^{54} +1.82979 q^{55} +(-2.31474 + 4.00925i) q^{56} +(6.18997 + 9.31267i) q^{57} +(1.77412 + 3.07286i) q^{58} +(-1.06162 - 1.83878i) q^{59} +(-0.752850 + 0.0475144i) q^{60} +(4.20052 - 7.27551i) q^{61} +4.07554 q^{62} +(8.40130 + 11.0592i) q^{63} +1.00000 q^{64} +(-0.697814 + 1.20865i) q^{65} +(-3.23431 + 6.51871i) q^{66} +(2.31474 + 4.00925i) q^{67} +(2.98802 + 5.17540i) q^{68} +(-0.769825 + 1.55157i) q^{69} +(1.00812 - 1.74612i) q^{70} +7.53311 q^{71} +(1.16146 - 2.76605i) q^{72} +11.5243 q^{73} +(3.82214 - 6.62015i) q^{74} +(-8.31517 + 0.524793i) q^{75} +(3.22802 + 5.59110i) q^{76} +(-9.72506 - 16.8443i) q^{77} +(-3.07242 - 4.62239i) q^{78} +(-3.42225 + 5.92751i) q^{79} -0.435523 q^{80} +(-6.30204 - 6.42528i) q^{81} +3.95980 q^{82} +(3.57688 - 6.19533i) q^{83} +(4.43868 + 6.67790i) q^{84} +(-1.30135 - 2.25401i) q^{85} +(-6.28438 - 10.8849i) q^{86} +(6.13351 - 0.387103i) q^{87} +(-2.10068 + 3.63849i) q^{88} +10.8502 q^{89} +(-0.505841 + 1.20468i) q^{90} +14.8351 q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.13745 - 6.32348i) q^{93} +(4.71761 + 8.17113i) q^{94} +(-1.40588 - 2.43505i) q^{95} +(0.769825 - 1.55157i) q^{96} +(3.77412 - 6.53696i) q^{97} -14.4321 q^{98} +(7.62438 + 10.0365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.958787	−	1.44247i	−0.553556	−	0.832812i
$3$	−0.958787	−	1.44247i	−0.553556	−	0.832812i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.217761	+	0.377174i	0.0973859	+	0.168677i	0.910602	−	0.413285i	$-0.135619\pi$
$5$	0.217761	+	0.377174i	0.0973859	+	0.168677i	−0.813216	+	0.581962i	$0.802285\pi$
$6$	−1.72861	+	0.109097i	−0.705703	+	0.0445388i
$7$	2.31474	−	4.00925i	0.874889	−	1.51535i	0.0180091	−	0.999838i	$-0.494267\pi$
$7$	2.31474	−	4.00925i	0.874889	−	1.51535i	0.856880	−	0.515515i	$-0.172399\pi$
$8$	−1.00000			−0.353553
$9$	−1.16146	+	2.76605i	−0.387152	+	0.922016i
$10$	0.435523			0.137724
$11$	2.10068	−	3.63849i	0.633379	−	1.09704i	−0.353477	−	0.935443i	$-0.615001\pi$
$11$	2.10068	−	3.63849i	0.633379	−	1.09704i	0.986856	−	0.161602i	$-0.0516659\pi$
$12$	−0.769825	+	1.55157i	−0.222229	+	0.447900i
$13$	1.60224	+	2.77517i	0.444383	+	0.769693i	0.998009	−	0.0630718i	$-0.0200897\pi$
$13$	1.60224	+	2.77517i	0.444383	+	0.769693i	−0.553626	+	0.832765i	$0.686756\pi$
$14$	−2.31474	−	4.00925i	−0.618640	−	1.07152i
$15$	0.335276	−	0.675744i	0.0865680	−	0.174476i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.97604			−1.44940			−0.724701	−	0.689063i	$-0.758022\pi$
$17$	−5.97604			−1.44940			−0.724701	+	0.689063i	$0.758022\pi$
$18$	1.81474	+	2.38887i	0.427738	+	0.563063i
$19$	−6.45604			−1.48112			−0.740559	−	0.671991i	$-0.765439\pi$
$19$	−6.45604			−1.48112			−0.740559	+	0.671991i	$0.765439\pi$
$20$	0.217761	−	0.377174i	0.0486930	−	0.0843387i
$21$	−8.00257	+	0.505064i	−1.74630	+	0.110214i
$22$	−2.10068	−	3.63849i	−0.447867	−	0.775728i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	0.958787	+	1.44247i	0.195712	+	0.294444i
$25$	2.40516	−	4.16586i	0.481032	−	0.833172i
$26$	3.20449			0.628452
$27$	5.10354	−	0.976682i	0.982176	−	0.187963i
$28$	−4.62948			−0.874889
$29$	−1.77412	+	3.07286i	−0.329445	+	0.570616i	−0.982402	−	0.186780i	$-0.940195\pi$
$29$	−1.77412	+	3.07286i	−0.329445	+	0.570616i	0.652957	+	0.757395i	$0.273528\pi$
$30$	−0.417574	−	0.628230i	−0.0762382	−	0.114699i
$31$	2.03777	+	3.52952i	0.365994	+	0.633920i	0.988935	−	0.148349i	$-0.0473958\pi$
$31$	2.03777	+	3.52952i	0.365994	+	0.633920i	−0.622941	+	0.782269i	$0.714062\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−7.26252	+	0.458358i	−1.26424	+	0.0797898i
$34$	−2.98802	+	5.17540i	−0.512441	+	0.887574i
$35$	2.01624			0.340808
$36$	2.97620	−	0.377174i	0.496033	−	0.0628623i
$37$	7.64429			1.25671			0.628357	−	0.777925i	$-0.283728\pi$
$37$	7.64429			1.25671			0.628357	+	0.777925i	$0.283728\pi$
$38$	−3.22802	+	5.59110i	−0.523654	+	0.906996i
$39$	2.46689	−	4.97199i	0.395019	−	0.796156i
$40$	−0.217761	−	0.377174i	−0.0344311	−	0.0596364i
$41$	1.97990	+	3.42928i	0.309208	+	0.535564i	0.978189	−	0.207715i	$-0.0666027\pi$
$41$	1.97990	+	3.42928i	0.309208	+	0.535564i	−0.668981	+	0.743279i	$0.733269\pi$
$42$	−3.56389	+	7.18296i	−0.549920	+	1.10836i
$43$	6.28438	−	10.8849i	0.958358	−	1.65993i	0.231870	−	0.972747i	$-0.425516\pi$
$43$	6.28438	−	10.8849i	0.958358	−	1.65993i	0.726488	−	0.687179i	$-0.241151\pi$
$44$	−4.20136			−0.633379
$45$	−1.29620	+	0.164268i	−0.193226	+	0.0244876i
$46$	−1.00000			−0.147442
$47$	−4.71761	+	8.17113i	−0.688134	+	1.19188i	0.284307	+	0.958733i	$0.408236\pi$
$47$	−4.71761	+	8.17113i	−0.688134	+	1.19188i	−0.972441	+	0.233149i	$0.925097\pi$
$48$	1.72861	−	0.109097i	0.249504	−	0.0157469i
$49$	−7.21604	−	12.4986i	−1.03086	−	1.78551i
$50$	−2.40516	−	4.16586i	−0.340141	−	0.589141i
$51$	5.72975	+	8.62028i	0.802325	+	1.20708i
$52$	1.60224	−	2.77517i	0.222191	−	0.384847i
$53$	0.713953			0.0980690			0.0490345	−	0.998797i	$-0.484386\pi$
$53$	0.713953			0.0980690			0.0490345	+	0.998797i	$0.484386\pi$
$54$	1.70594	−	4.90813i	0.232149	−	0.667912i
$55$	1.82979			0.246729
$56$	−2.31474	+	4.00925i	−0.309320	+	0.535758i
$57$	6.18997	+	9.31267i	0.819882	+	1.23349i
$58$	1.77412	+	3.07286i	0.232953	+	0.403486i
$59$	−1.06162	−	1.83878i	−0.138211	−	0.239389i	0.788608	−	0.614896i	$-0.210802\pi$
$59$	−1.06162	−	1.83878i	−0.138211	−	0.239389i	−0.926820	+	0.375507i	$0.877469\pi$
$60$	−0.752850	+	0.0475144i	−0.0971925	+	0.00613408i
$61$	4.20052	−	7.27551i	0.537821	−	0.931533i	−0.461200	−	0.887296i	$-0.652581\pi$
$61$	4.20052	−	7.27551i	0.537821	−	0.931533i	0.999021	−	0.0442370i	$-0.0140857\pi$
$62$	4.07554			0.517593
$63$	8.40130	+	11.0592i	1.05846	+	1.39333i
$64$	1.00000			0.125000
$65$	−0.697814	+	1.20865i	−0.0865532	+	0.149915i
$66$	−3.23431	+	6.51871i	−0.398116	+	0.802397i
$67$	2.31474	+	4.00925i	0.282790	+	0.489808i	0.972071	−	0.234687i	$-0.0754065\pi$
$67$	2.31474	+	4.00925i	0.282790	+	0.489808i	−0.689280	+	0.724495i	$0.742073\pi$
$68$	2.98802	+	5.17540i	0.362351	+	0.627610i
$69$	−0.769825	+	1.55157i	−0.0926760	+	0.186787i
$70$	1.00812	−	1.74612i	0.120494	−	0.208701i
$71$	7.53311			0.894016			0.447008	−	0.894530i	$-0.352490\pi$
$71$	7.53311			0.894016			0.447008	+	0.894530i	$0.352490\pi$
$72$	1.16146	−	2.76605i	0.136879	−	0.325982i
$73$	11.5243			1.34881			0.674407	−	0.738360i	$-0.264399\pi$
$73$	11.5243			1.34881			0.674407	+	0.738360i	$0.264399\pi$
$74$	3.82214	−	6.62015i	0.444315	−	0.769577i
$75$	−8.31517	+	0.524793i	−0.960154	+	0.0605979i
$76$	3.22802	+	5.59110i	0.370280	+	0.641343i
$77$	−9.72506	−	16.8443i	−1.10827	−	1.91959i
$78$	−3.07242	−	4.62239i	−0.347883	−	0.523382i
$79$	−3.42225	+	5.92751i	−0.385033	+	0.666897i	−0.991774	−	0.128003i	$-0.959143\pi$
$79$	−3.42225	+	5.92751i	−0.385033	+	0.666897i	0.606741	+	0.794900i	$0.292477\pi$
$80$	−0.435523			−0.0486930
$81$	−6.30204	−	6.42528i	−0.700227	−	0.713920i
$82$	3.95980			0.437286
$83$	3.57688	−	6.19533i	0.392613	−	0.680026i	−0.600180	−	0.799865i	$-0.704904\pi$
$83$	3.57688	−	6.19533i	0.392613	−	0.680026i	0.992793	+	0.119839i	$0.0382378\pi$
$84$	4.43868	+	6.67790i	0.484300	+	0.728619i
$85$	−1.30135	−	2.25401i	−0.141151	−	0.244481i
$86$	−6.28438	−	10.8849i	−0.677662	−	1.17374i
$87$	6.13351	−	0.387103i	0.657582	−	0.0415018i
$88$	−2.10068	+	3.63849i	−0.223933	+	0.387864i
$89$	10.8502			1.15012			0.575060	−	0.818111i	$-0.304979\pi$
$89$	10.8502			1.15012			0.575060	+	0.818111i	$0.304979\pi$
$90$	−0.505841	+	1.20468i	−0.0533203	+	0.126984i
$91$	14.8351			1.55514
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$	3.13745	−	6.32348i	0.325338	−	0.655714i
$94$	4.71761	+	8.17113i	0.486584	+	0.842788i
$95$	−1.40588	−	2.43505i	−0.144240	−	0.249831i
$96$	0.769825	−	1.55157i	0.0785699	−	0.158356i
$97$	3.77412	−	6.53696i	0.383203	−	0.663728i	−0.608315	−	0.793696i	$-0.708154\pi$
$97$	3.77412	−	6.53696i	0.383203	−	0.663728i	0.991518	+	0.129968i	$0.0414875\pi$
$98$	−14.4321			−1.45786
$99$	7.62438	+	10.0365i	0.766279	+	1.00871i
$100$	−4.81032			−0.481032
$101$	−0.371813	+	0.643998i	−0.0369967	+	0.0640802i	−0.883931	−	0.467618i	$-0.845112\pi$
$101$	−0.371813	+	0.643998i	−0.0369967	+	0.0640802i	0.846934	+	0.531698i	$0.178446\pi$
$102$	10.3303	−	0.651970i	1.02285	−	0.0645547i
$103$	6.35827	+	11.0128i	0.626499	+	1.08513i	0.988249	+	0.152853i	$0.0488460\pi$
$103$	6.35827	+	11.0128i	0.626499	+	1.08513i	−0.361750	+	0.932275i	$0.617821\pi$
$104$	−1.60224	−	2.77517i	−0.157113	−	0.272128i
$105$	−1.93315	−	2.90838i	−0.188656	−	0.283829i
$106$	0.356976	−	0.618301i	0.0346726	−	0.0600547i
$107$	−7.41469			−0.716805			−0.358403	−	0.933567i	$-0.616678\pi$
$107$	−7.41469			−0.716805			−0.358403	+	0.933567i	$0.616678\pi$
$108$	−3.39760	−	3.93145i	−0.326934	−	0.378304i
$109$	−14.8914			−1.42633			−0.713167	−	0.700995i	$-0.752740\pi$
$109$	−14.8914			−1.42633			−0.713167	+	0.700995i	$0.752740\pi$
$110$	0.914895	−	1.58464i	0.0872318	−	0.151090i
$111$	−7.32924	−	11.0267i	−0.695661	−	1.04661i
$112$	2.31474	+	4.00925i	0.218722	+	0.378838i
$113$	6.46792	+	11.2028i	0.608451	+	1.05387i	0.991496	+	0.130138i	$0.0415419\pi$
$113$	6.46792	+	11.2028i	0.608451	+	1.05387i	−0.383045	+	0.923730i	$0.625125\pi$
$114$	11.1600	−	0.704338i	1.04523	−	0.0659673i
$115$	0.217761	−	0.377174i	0.0203064	−	0.0351717i
$116$	3.54823			0.329445
$117$	−9.53719	+	1.20865i	−0.881713	+	0.111740i
$118$	−2.12324			−0.195460
$119$	−13.8330	+	23.9594i	−1.26807	+	2.19636i
$120$	−0.335276	+	0.675744i	−0.0306064	+	0.0616867i
$121$	−3.32572	−	5.76031i	−0.302338	−	0.523665i
$122$	−4.20052	−	7.27551i	−0.380297	−	0.658693i
$123$	3.04835	−	6.14390i	0.274860	−	0.553977i
$124$	2.03777	−	3.52952i	0.182997	−	0.316960i
$125$	4.27262			0.382155
$126$	13.7782	−	1.74612i	1.22746	−	0.155557i
$127$	7.43240			0.659518			0.329759	−	0.944065i	$-0.393032\pi$
$127$	7.43240			0.659518			0.329759	+	0.944065i	$0.393032\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−21.7265	+	1.37122i	−1.91291	+	0.120729i
$130$	0.697814	+	1.20865i	0.0612024	+	0.106006i
$131$	−7.23302	−	12.5280i	−0.631952	−	1.09457i	−0.987152	−	0.159782i	$-0.948921\pi$
$131$	−7.23302	−	12.5280i	−0.631952	−	1.09457i	0.355201	−	0.934790i	$-0.384413\pi$
$132$	4.02821	+	6.06035i	0.350611	+	0.527486i
$133$	−14.9441	+	25.8839i	−1.29581	+	2.24442i
$134$	4.62948			0.399926
$135$	1.47973	+	1.71224i	0.127355	+	0.147366i
$136$	5.97604			0.512441
$137$	−9.39974	+	16.2808i	−0.803074	+	1.39096i	0.114510	+	0.993422i	$0.463470\pi$
$137$	−9.39974	+	16.2808i	−0.803074	+	1.39096i	−0.917584	+	0.397543i	$0.869863\pi$
$138$	0.958787	+	1.44247i	0.0816174	+	0.122791i
$139$	2.03255	+	3.52048i	0.172399	+	0.298603i	0.939258	−	0.343212i	$-0.111515\pi$
$139$	2.03255	+	3.52048i	0.172399	+	0.298603i	−0.766859	+	0.641815i	$0.778182\pi$
$140$	−1.00812	−	1.74612i	−0.0852019	−	0.147574i
$141$	16.3098	−	1.02936i	1.37353	−	0.0866875i
$142$	3.76656	−	6.52387i	0.316082	−	0.547471i
$143$	13.4632			1.12585
$144$	−1.81474	−	2.38887i	−0.151228	−	0.199073i
$145$	−1.54534			−0.128333
$146$	5.76214	−	9.98031i	0.476878	−	0.825977i
$147$	−11.1102	+	22.3924i	−0.916352	+	1.84689i
$148$	−3.82214	−	6.62015i	−0.314178	−	0.544173i
$149$	−6.07929	−	10.5296i	−0.498035	−	0.862621i	0.501963	−	0.864889i	$-0.332611\pi$
$149$	−6.07929	−	10.5296i	−0.498035	−	0.862621i	−0.999997	+	0.00226808i	$0.999278\pi$
$150$	−3.70310	+	7.46355i	−0.302357	+	0.609396i
$151$	5.08214	−	8.80253i	0.413579	−	0.716340i	−0.581699	−	0.813404i	$-0.697612\pi$
$151$	5.08214	−	8.80253i	0.413579	−	0.716340i	0.995278	+	0.0970643i	$0.0309453\pi$
$152$	6.45604			0.523654
$153$	6.94091	−	16.5300i	0.561139	−	1.33637i
$154$	−19.4501			−1.56734
$155$	−0.887495	+	1.53719i	−0.0712853	+	0.123470i
$156$	−5.53932	+	0.349601i	−0.443500	+	0.0279905i
$157$	4.78208	+	8.28281i	0.381652	+	0.661040i	0.991299	−	0.131633i	$-0.0420220\pi$
$157$	4.78208	+	8.28281i	0.381652	+	0.661040i	−0.609647	+	0.792673i	$0.708689\pi$
$158$	3.42225	+	5.92751i	0.272260	+	0.471568i
$159$	−0.684529	−	1.02986i	−0.0542866	−	0.0816730i
$160$	−0.217761	+	0.377174i	−0.0172156	+	0.0298182i
$161$	−4.62948			−0.364854
$162$	−8.71548	+	2.24509i	−0.684753	+	0.176391i
$163$	−8.54769			−0.669507			−0.334753	−	0.942306i	$-0.608653\pi$
$163$	−8.54769			−0.669507			−0.334753	+	0.942306i	$0.608653\pi$
$164$	1.97990	−	3.42928i	0.154604	−	0.267782i
$165$	−1.75438	−	2.63942i	−0.136578	−	0.205479i
$166$	−3.57688	−	6.19533i	−0.277619	−	0.480851i
$167$	7.40786	+	12.8308i	0.573238	+	0.992876i	0.996231	+	0.0867436i	$0.0276461\pi$
$167$	7.40786	+	12.8308i	0.573238	+	0.992876i	−0.422993	+	0.906133i	$0.639021\pi$
$168$	8.00257	−	0.505064i	0.617412	−	0.0389665i
$169$	1.36562	−	2.36533i	0.105048	−	0.181949i
$170$	−2.60270			−0.199618
$171$	7.49841	−	17.8577i	0.573418	−	1.36561i
$172$	−12.5688			−0.958358
$173$	−4.45239	+	7.71177i	−0.338509	+	0.586315i	−0.984152	−	0.177324i	$-0.943256\pi$
$173$	−4.45239	+	7.71177i	−0.338509	+	0.586315i	0.645643	+	0.763639i	$0.276589\pi$
$174$	2.73152	−	5.50533i	0.207076	−	0.417358i
$175$	−11.1346	−	19.2858i	−0.841700	−	1.45787i
$176$	2.10068	+	3.63849i	0.158345	+	0.274261i
$177$	−1.63452	+	3.29436i	−0.122858	+	0.247619i
$178$	5.42511	−	9.39656i	0.406629	−	0.704302i
$179$	0.543955			0.0406571			0.0203286	−	0.999793i	$-0.493529\pi$
$179$	0.543955			0.0406571			0.0203286	+	0.999793i	$0.493529\pi$
$180$	0.790361	+	1.04041i	0.0589100	+	0.0775475i
$181$	1.79810			0.133651			0.0668257	−	0.997765i	$-0.478713\pi$
$181$	1.79810			0.133651			0.0668257	+	0.997765i	$0.478713\pi$
$182$	7.41756	−	12.8476i	0.549826	−	0.952327i
$183$	−14.5221	+	0.916530i	−1.07351	+	0.0677519i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	1.66463	+	2.88323i	0.122386	+	0.211979i
$186$	−3.90757	−	5.87885i	−0.286517	−	0.431058i
$187$	−12.5538	+	21.7437i	−0.918021	+	1.59006i
$188$	9.43521			0.688134
$189$	7.89760	−	22.7221i	0.574466	−	1.65279i
$190$	−2.81176			−0.203986
$191$	11.8864	−	20.5878i	0.860066	−	1.48968i	−0.0117980	−	0.999930i	$-0.503756\pi$
$191$	11.8864	−	20.5878i	0.860066	−	1.48968i	0.871864	−	0.489748i	$-0.162911\pi$
$192$	−0.958787	−	1.44247i	−0.0691945	−	0.104102i
$193$	4.63979	+	8.03635i	0.333979	+	0.578469i	0.983288	−	0.182056i	$-0.0582751\pi$
$193$	4.63979	+	8.03635i	0.333979	+	0.578469i	−0.649309	+	0.760525i	$0.724942\pi$
$194$	−3.77412	−	6.53696i	−0.270966	−	0.469326i
$195$	2.41250	−	0.152259i	0.172763	−	0.0109035i
$196$	−7.21604	+	12.4986i	−0.515432	+	0.892754i
$197$	−0.921570			−0.0656591			−0.0328296	−	0.999461i	$-0.510452\pi$
$197$	−0.921570			−0.0656591			−0.0328296	+	0.999461i	$0.510452\pi$
$198$	12.5041	−	1.58464i	0.888626	−	0.112616i
$199$	−9.68718			−0.686706			−0.343353	−	0.939206i	$-0.611563\pi$
$199$	−9.68718			−0.686706			−0.343353	+	0.939206i	$0.611563\pi$
$200$	−2.40516	+	4.16586i	−0.170070	+	0.294571i
$201$	3.56389	−	7.18296i	0.251377	−	0.506647i
$202$	0.371813	+	0.643998i	0.0261606	+	0.0453116i
$203$	8.21323	+	14.2257i	0.576456	+	0.998451i
$204$	4.60050	−	9.27225i	0.322100	−	0.649187i
$205$	−0.862291	+	1.49353i	−0.0602250	+	0.104313i
$206$	12.7165			0.886003
$207$	2.97620	−	0.377174i	0.206860	−	0.0262154i
$208$	−3.20449			−0.222191
$209$	−13.5621	+	23.4902i	−0.938109	+	1.62485i
$210$	−3.48530	+	0.219967i	−0.240509	+	0.0151792i
$211$	0.902750	+	1.56361i	0.0621479	+	0.107643i	0.895425	−	0.445212i	$-0.146872\pi$
$211$	0.902750	+	1.56361i	0.0621479	+	0.107643i	−0.833277	+	0.552855i	$0.813538\pi$
$212$	−0.356976	−	0.618301i	−0.0245172	−	0.0424651i
$213$	−7.22265	−	10.8663i	−0.494888	−	0.744547i
$214$	−3.70735	+	6.42131i	−0.253429	+	0.438952i
$215$	5.47398			0.373322
$216$	−5.10354	+	0.976682i	−0.347252	+	0.0664548i
$217$	18.8676			1.28082
$218$	−7.44568	+	12.8963i	−0.504285	+	0.873447i
$219$	−11.0493	−	16.6234i	−0.746644	−	1.12331i
$220$	−0.914895	−	1.58464i	−0.0616822	−	0.106837i
$221$	−9.57508	−	16.5845i	−0.644089	−	1.11560i
$222$	−13.2140	+	0.833972i	−0.886866	+	0.0559725i
$223$	−3.03682	+	5.25992i	−0.203360	+	0.352230i	−0.949609	−	0.313437i	$-0.898520\pi$
$223$	−3.03682	+	5.25992i	−0.203360	+	0.352230i	0.746249	+	0.665667i	$0.231853\pi$
$224$	4.62948			0.309320
$225$	8.72948	+	11.4912i	0.581965	+	0.766083i
$226$	12.9358			0.860479
$227$	2.17687	−	3.77044i	0.144484	−	0.250253i	−0.784697	−	0.619880i	$-0.787181\pi$
$227$	2.17687	−	3.77044i	0.144484	−	0.250253i	0.929180	+	0.369627i	$0.120515\pi$
$228$	4.97002	−	10.0170i	0.329148	−	0.663392i
$229$	2.54308	+	4.40475i	0.168052	+	0.291074i	0.937735	−	0.347352i	$-0.112919\pi$
$229$	2.54308	+	4.40475i	0.168052	+	0.291074i	−0.769683	+	0.638426i	$0.779586\pi$
$230$	−0.217761	−	0.377174i	−0.0143588	−	0.0248701i
$231$	−14.9732	+	30.1782i	−0.985163	+	1.98558i
$232$	1.77412	−	3.07286i	0.116476	−	0.201743i
$233$	−26.8186			−1.75694			−0.878471	−	0.477795i	$-0.841436\pi$
$233$	−26.8186			−1.75694			−0.878471	+	0.477795i	$0.841436\pi$
$234$	−3.72187	+	8.86377i	−0.243306	+	0.579443i
$235$	−4.10925			−0.268058
$236$	−1.06162	+	1.83878i	−0.0691056	+	0.119694i
$237$	11.8315	−	0.746717i	0.768537	−	0.0485045i
$238$	13.8330	+	23.9594i	0.896659	+	1.55306i
$239$	7.40208	+	12.8208i	0.478801	+	0.829307i	0.999705	−	0.0243081i	$-0.00773828\pi$
$239$	7.40208	+	12.8208i	0.478801	+	0.829307i	−0.520904	+	0.853615i	$0.674405\pi$
$240$	0.417574	+	0.628230i	0.0269543	+	0.0405521i
$241$	−13.7842	+	23.8750i	−0.887921	+	1.53792i	−0.0455913	+	0.998960i	$0.514517\pi$
$241$	−13.7842	+	23.8750i	−0.887921	+	1.53792i	−0.842329	+	0.538963i	$0.818816\pi$
$242$	−6.65144			−0.427571
$243$	−3.22598	+	15.2510i	−0.206947	+	0.978352i
$244$	−8.40103			−0.537821
$245$	3.14275	−	5.44341i	0.200783	−	0.347767i
$246$	−3.79660	−	5.71190i	−0.242062	−	0.364177i
$247$	−10.3442	−	17.9166i	−0.658183	−	1.14001i
$248$	−2.03777	−	3.52952i	−0.129398	−	0.224125i
$249$	−12.3661	+	0.780456i	−0.783667	+	0.0494594i
$250$	2.13631	−	3.70020i	0.135112	−	0.234021i
$251$	−5.65292			−0.356809			−0.178404	−	0.983957i	$-0.557094\pi$
$251$	−5.65292			−0.356809			−0.178404	+	0.983957i	$0.557094\pi$
$252$	5.37694	−	12.8054i	0.338715	−	0.806662i
$253$	−4.20136			−0.264137
$254$	3.71620	−	6.43664i	0.233175	−	0.403871i
$255$	−2.00362	+	4.03828i	−0.125472	+	0.252887i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.82050	+	4.88525i	0.175938	+	0.304734i	0.940486	−	0.339834i	$-0.110371\pi$
$257$	2.82050	+	4.88525i	0.175938	+	0.304734i	−0.764547	+	0.644567i	$0.777037\pi$
$258$	−9.67574	+	19.5013i	−0.602385	+	1.21410i
$259$	17.6945	−	30.6478i	1.09949	−	1.90436i
$260$	1.39563			0.0865532
$261$	−6.43912	−	8.47628i	−0.398571	−	0.524669i
$262$	−14.4660			−0.893715
$263$	7.20692	−	12.4828i	0.444398	−	0.769719i	−0.553612	−	0.832774i	$-0.686751\pi$
$263$	7.20692	−	12.4828i	0.444398	−	0.769719i	0.998010	+	0.0630551i	$0.0200844\pi$
$264$	7.26252	−	0.458358i	0.446977	−	0.0282100i
$265$	0.155471	+	0.269284i	0.00955053	+	0.0165420i
$266$	14.9441	+	25.8839i	0.916279	+	1.58704i
$267$	−10.4030	−	15.6511i	−0.636656	−	0.957834i
$268$	2.31474	−	4.00925i	0.141395	−	0.244904i
$269$	0.980220			0.0597651			0.0298825	−	0.999553i	$-0.490487\pi$
$269$	0.980220			0.0597651			0.0298825	+	0.999553i	$0.490487\pi$
$270$	2.22271	−	0.425368i	0.135270	−	0.0258870i
$271$	0.0900885			0.00547249			0.00273624	−	0.999996i	$-0.499129\pi$
$271$	0.0900885			0.00547249			0.00273624	+	0.999996i	$0.499129\pi$
$272$	2.98802	−	5.17540i	0.181175	−	0.313805i
$273$	−14.2237	−	21.3993i	−0.860858	−	1.29514i
$274$	9.39974	+	16.2808i	0.567859	+	0.983561i
$275$	−10.1049	−	17.5023i	−0.609351	−	1.05543i
$276$	1.72861	−	0.109097i	0.104050	−	0.00656689i
$277$	1.54449	−	2.67514i	0.0927995	−	0.160733i	−0.815889	−	0.578209i	$-0.803752\pi$
$277$	1.54449	−	2.67514i	0.0927995	−	0.160733i	0.908688	+	0.417476i	$0.137085\pi$
$278$	4.06510			0.243809
$279$	−12.1296	+	1.53719i	−0.726180	+	0.0920289i
$280$	−2.01624			−0.120494
$281$	1.66280	−	2.88005i	0.0991941	−	0.171809i	−0.812157	−	0.583439i	$-0.801707\pi$
$281$	1.66280	−	2.88005i	0.0991941	−	0.171809i	0.911351	+	0.411629i	$0.135040\pi$
$282$	7.26346	−	14.6394i	0.432533	−	0.871763i
$283$	−5.45975	−	9.45656i	−0.324548	−	0.562134i	0.656873	−	0.754002i	$-0.271879\pi$
$283$	−5.45975	−	9.45656i	−0.324548	−	0.562134i	−0.981421	+	0.191868i	$0.938546\pi$
$284$	−3.76656	−	6.52387i	−0.223504	−	0.387120i
$285$	−2.16456	+	4.36264i	−0.128217	+	0.258420i
$286$	6.73161	−	11.6595i	0.398048	−	0.689440i
$287$	18.3318			1.08209
$288$	−2.97620	+	0.377174i	−0.175374	+	0.0222252i
$289$	18.7131			1.10077
$290$	−0.772668	+	1.33830i	−0.0453726	+	0.0785877i
$291$	−13.0480	+	0.823492i	−0.764885	+	0.0482740i
$292$	−5.76214	−	9.98031i	−0.337204	−	0.584054i
$293$	−1.94896	−	3.37570i	−0.113859	−	0.197210i	0.803464	−	0.595354i	$-0.202988\pi$
$293$	−1.94896	−	3.37570i	−0.113859	−	0.197210i	−0.917323	+	0.398143i	$0.869655\pi$
$294$	13.8373	+	20.8179i	0.807007	+	1.21412i
$295$	0.462360	−	0.800831i	0.0269196	−	0.0466262i
$296$	−7.64429			−0.444315
$297$	7.16726	−	20.6208i	0.415886	−	1.19654i
$298$	−12.1586			−0.704327
$299$	1.60224	−	2.77517i	0.0926602	−	0.160492i
$300$	4.61207	+	6.93876i	0.266278	+	0.400609i
$301$	−29.0934	−	50.3912i	−1.67692	−	2.90450i
$302$	−5.08214	−	8.80253i	−0.292444	−	0.506529i
$303$	1.28544	−	0.0811276i	0.0738465	−	0.00466066i
$304$	3.22802	−	5.59110i	0.185140	−	0.320672i
$305$	3.65884			0.209505
$306$	−10.8450	−	14.2760i	−0.619965	−	0.816105i
$307$	−32.6824			−1.86529			−0.932643	−	0.360802i	$-0.882503\pi$
$307$	−32.6824			−1.86529			−0.932643	+	0.360802i	$0.882503\pi$
$308$	−9.72506	+	16.8443i	−0.554137	+	0.959793i
$309$	9.78950	−	19.7306i	0.556905	−	1.12243i
$310$	0.887495	+	1.53719i	0.0504063	+	0.0873063i
$311$	2.81771	+	4.88042i	0.159778	+	0.276743i	0.934788	−	0.355205i	$-0.115589\pi$
$311$	2.81771	+	4.88042i	0.159778	+	0.276743i	−0.775011	+	0.631948i	$0.782256\pi$
$312$	−2.46689	+	4.97199i	−0.139660	+	0.281483i
$313$	−7.65418	+	13.2574i	−0.432640	+	0.749354i	−0.997100	−	0.0761064i	$-0.975751\pi$
$313$	−7.65418	+	13.2574i	−0.432640	+	0.749354i	0.564460	+	0.825460i	$0.309084\pi$
$314$	9.56417			0.539737
$315$	−2.34178	+	5.57703i	−0.131944	+	0.314230i
$316$	6.84450			0.385033
$317$	15.5534	−	26.9394i	0.873568	−	1.51306i	0.0152884	−	0.999883i	$-0.495133\pi$
$317$	15.5534	−	26.9394i	0.873568	−	1.51306i	0.858280	−	0.513182i	$-0.171533\pi$
$318$	−1.23415	+	0.0778904i	−0.0692075	+	0.00436788i
$319$	7.45370	+	12.9102i	0.417327	+	0.722832i
$320$	0.217761	+	0.377174i	0.0121732	+	0.0210847i
$321$	7.10911	+	10.6955i	0.396792	+	0.596964i
$322$	−2.31474	+	4.00925i	−0.128995	+	0.223427i
$323$	38.5816			2.14674
$324$	−2.41344	+	8.67037i	−0.134080	+	0.481687i
$325$	15.4146			0.855049
$326$	−4.27384	+	7.40252i	−0.236706	+	0.409987i
$327$	14.2776	+	21.4804i	0.789555	+	1.18787i
$328$	−1.97990	−	3.42928i	−0.109322	−	0.189351i
$329$	21.8401	+	37.8281i	1.20408	+	2.08553i
$330$	−3.16300	+	0.199625i	−0.174117	+	0.0109890i
$331$	−14.0945	+	24.4125i	−0.774706	+	1.34183i	0.160253	+	0.987076i	$0.448769\pi$
$331$	−14.0945	+	24.4125i	−0.774706	+	1.34183i	−0.934960	+	0.354754i	$0.884564\pi$
$332$	−7.15375			−0.392613
$333$	−8.87850	+	21.1445i	−0.486539	+	1.15871i
$334$	14.8157			0.810680
$335$	−1.00812	+	1.74612i	−0.0550796	+	0.0954007i
$336$	3.56389	−	7.18296i	0.194426	−	0.391863i
$337$	4.72176	+	8.17832i	0.257210	+	0.445501i	0.965494	−	0.260427i	$-0.0838633\pi$
$337$	4.72176	+	8.17832i	0.257210	+	0.445501i	−0.708283	+	0.705928i	$0.750530\pi$
$338$	−1.36562	−	2.36533i	−0.0742802	−	0.128657i
$339$	9.95833	−	20.0709i	0.540862	−	1.09010i
$340$	−1.30135	+	2.25401i	−0.0705757	+	0.122241i
$341$	17.1228			0.927251
$342$	−11.7160	−	15.4227i	−0.633531	−	0.833963i
$343$	−34.4067			−1.85779
$344$	−6.28438	+	10.8849i	−0.338831	+	0.586872i
$345$	−0.752850	+	0.0475144i	−0.0405321	+	0.00255809i
$346$	4.45239	+	7.71177i	0.239362	+	0.414587i
$347$	12.2666	+	21.2464i	0.658508	+	1.14057i	0.981002	+	0.193997i	$0.0621453\pi$
$347$	12.2666	+	21.2464i	0.658508	+	1.14057i	−0.322495	+	0.946571i	$0.604521\pi$
$348$	−3.40200	−	5.11823i	−0.182366	−	0.274366i
$349$	−8.54208	+	14.7953i	−0.457247	+	0.791975i	−0.998814	−	0.0486822i	$-0.984498\pi$
$349$	−8.54208	+	14.7953i	−0.457247	+	0.791975i	0.541567	+	0.840657i	$0.317831\pi$
$350$	−22.2693			−1.19034
$351$	10.8876	+	12.5983i	0.581136	+	0.672447i
$352$	4.20136			0.223933
$353$	−6.42640	+	11.1309i	−0.342043	+	0.592435i	−0.984812	−	0.173624i	$-0.944452\pi$
$353$	−6.42640	+	11.1309i	−0.342043	+	0.592435i	0.642769	+	0.766060i	$0.277785\pi$
$354$	2.03574	+	3.06272i	0.108198	+	0.162782i
$355$	1.64042	+	2.84129i	0.0870646	+	0.150800i
$356$	−5.42511	−	9.39656i	−0.287530	−	0.498017i
$357$	47.8237	−	3.01828i	2.53110	−	0.159745i
$358$	0.271978	−	0.471079i	0.0143745	−	0.0248973i
$359$	35.5998			1.87889			0.939444	−	0.342704i	$-0.111343\pi$
$359$	35.5998			1.87889			0.939444	+	0.342704i	$0.111343\pi$
$360$	1.29620	−	0.164268i	0.0683158	−	0.00865768i
$361$	22.6805			1.19371
$362$	0.899048	−	1.55720i	0.0472529	−	0.0818445i
$363$	−5.12044	+	10.3202i	−0.268753	+	0.541669i
$364$	−7.41756	−	12.8476i	−0.388786	−	0.673397i
$365$	2.50954	+	4.34666i	0.131355	+	0.227514i
$366$	−6.46732	+	13.0348i	−0.338052	+	0.681339i
$367$	−0.228597	+	0.395941i	−0.0119327	+	0.0206680i	−0.871930	−	0.489630i	$-0.837132\pi$
$367$	−0.228597	+	0.395941i	−0.0119327	+	0.0206680i	0.859997	+	0.510298i	$0.170465\pi$
$368$	1.00000			0.0521286
$369$	−11.7851	+	1.49353i	−0.613509	+	0.0777502i
$370$	3.32926			0.173080
$371$	1.65261	−	2.86241i	0.0857995	−	0.148609i
$372$	−7.04502	+	0.444630i	−0.365267	+	0.0230530i
$373$	1.06866	+	1.85097i	0.0553329	+	0.0958395i	0.892365	−	0.451314i	$-0.149045\pi$
$373$	1.06866	+	1.85097i	0.0553329	+	0.0958395i	−0.837032	+	0.547154i	$0.815711\pi$
$374$	12.5538	+	21.7437i	0.649139	+	1.12434i
$375$	−4.09653	−	6.16314i	−0.211544	−	0.318263i
$376$	4.71761	−	8.17113i	0.243292	−	0.421394i
$377$	−11.3703			−0.585599
$378$	−15.7291	−	18.2006i	−0.809019	−	0.936137i
$379$	0.0602809			0.00309642			0.00154821	−	0.999999i	$-0.499507\pi$
$379$	0.0602809			0.00309642			0.00154821	+	0.999999i	$0.499507\pi$
$380$	−1.40588	+	2.43505i	−0.0721200	+	0.124916i
$381$	−7.12608	−	10.7210i	−0.365080	−	0.549255i
$382$	−11.8864	−	20.5878i	−0.608159	−	1.05336i
$383$	−6.41495	−	11.1110i	−0.327788	−	0.567746i	0.654284	−	0.756249i	$-0.272970\pi$
$383$	−6.41495	−	11.1110i	−0.327788	−	0.567746i	−0.982073	+	0.188502i	$0.939637\pi$
$384$	−1.72861	+	0.109097i	−0.0882128	+	0.00556735i
$385$	4.23549	−	7.33608i	0.215860	−	0.373881i
$386$	9.27958			0.472318
$387$	22.8090	+	30.0252i	1.15945	+	1.52627i
$388$	−7.54823			−0.383203
$389$	4.00954	−	6.94473i	0.203292	−	0.352112i	−0.746295	−	0.665615i	$-0.768169\pi$
$389$	4.00954	−	6.94473i	0.203292	−	0.352112i	0.949587	+	0.313503i	$0.101503\pi$
$390$	1.07439	−	2.16542i	0.0544038	−	0.109650i
$391$	2.98802	+	5.17540i	0.151111	+	0.261731i
$392$	7.21604	+	12.4986i	0.364465	+	0.631272i
$393$	−11.1363	+	22.4451i	−0.561753	+	1.13220i
$394$	−0.460785	+	0.798103i	−0.0232140	+	0.0402078i
$395$	−2.98094			−0.149987
$396$	4.87969	−	11.6212i	0.245214	−	0.583986i
$397$	23.1224			1.16048			0.580240	−	0.814446i	$-0.302959\pi$
$397$	23.1224			1.16048			0.580240	+	0.814446i	$0.302959\pi$
$398$	−4.84359	+	8.38934i	−0.242787	+	0.420520i
$399$	51.6650	−	3.26072i	2.58648	−	0.163240i
$400$	2.40516	+	4.16586i	0.120258	+	0.208293i
$401$	−6.31865	−	10.9442i	−0.315538	−	0.546528i	0.664014	−	0.747720i	$-0.268852\pi$
$401$	−6.31865	−	10.9442i	−0.315538	−	0.546528i	−0.979552	+	0.201192i	$0.935518\pi$
$402$	−4.43868	−	6.67790i	−0.221381	−	0.333063i
$403$	−6.53000	+	11.3103i	−0.325283	+	0.563406i
$404$	0.743625			0.0369967
$405$	1.05111	−	3.77615i	0.0522300	−	0.187638i
$406$	16.4265			0.815232
$407$	16.0582	−	27.8136i	0.795976	−	1.37867i
$408$	−5.72975	−	8.62028i	−0.283665	−	0.426767i
$409$	−6.62673	−	11.4778i	−0.327671	−	0.567542i	0.654379	−	0.756167i	$-0.272930\pi$
$409$	−6.62673	−	11.4778i	−0.327671	−	0.567542i	−0.982049	+	0.188625i	$0.939597\pi$
$410$	0.862291	+	1.49353i	0.0425855	+	0.0737603i
$411$	32.4970	−	2.05097i	1.60296	−	0.101167i
$412$	6.35827	−	11.0128i	0.313249	−	0.542564i
$413$	−9.82950			−0.483678
$414$	1.16146	−	2.76605i	0.0570824	−	0.135944i
$415$	3.11562			0.152940
$416$	−1.60224	+	2.77517i	−0.0785565	+	0.136064i
$417$	3.12941	−	6.30729i	0.153248	−	0.308869i
$418$	13.5621	+	23.4902i	0.663343	+	1.14894i
$419$	−2.78746	−	4.82802i	−0.136176	−	0.235864i	0.789870	−	0.613274i	$-0.210148\pi$
$419$	−2.78746	−	4.82802i	−0.136176	−	0.235864i	−0.926046	+	0.377410i	$0.876815\pi$
$420$	−1.55216	+	3.12835i	−0.0757374	+	0.152648i
$421$	−12.0656	+	20.8983i	−0.588044	+	1.01852i	0.406445	+	0.913675i	$0.366768\pi$
$421$	−12.0656	+	20.8983i	−0.588044	+	1.01852i	−0.994488	+	0.104846i	$0.966565\pi$
$422$	1.80550			0.0878904
$423$	−17.1225	−	22.5395i	−0.832522	−	1.09591i
$424$	−0.713953			−0.0346726
$425$	−14.3733	+	24.8953i	−0.697209	+	1.20760i
$426$	−13.0218	+	0.821843i	−0.630910	+	0.0398184i
$427$	−19.4462	−	33.6818i	−0.941068	−	1.62998i
$428$	3.70735	+	6.42131i	0.179201	+	0.310386i
$429$	−12.9084	−	19.4203i	−0.623221	−	0.937622i
$430$	2.73699	−	4.74061i	0.131989	−	0.228612i
$431$	4.23209			0.203852			0.101926	−	0.994792i	$-0.467499\pi$
$431$	4.23209			0.203852			0.101926	+	0.994792i	$0.467499\pi$
$432$	−1.70594	+	4.90813i	−0.0820769	+	0.236143i
$433$	7.59737			0.365107			0.182553	−	0.983196i	$-0.441564\pi$
$433$	7.59737			0.365107			0.182553	+	0.983196i	$0.441564\pi$
$434$	9.43380	−	16.3398i	0.452837	−	0.784337i
$435$	1.48165	+	2.22911i	0.0710396	+	0.106877i
$436$	7.44568	+	12.8963i	0.356583	+	0.617620i
$437$	3.22802	+	5.59110i	0.154417	+	0.267459i
$438$	−19.9210	+	1.25727i	−0.951862	+	0.0600746i
$439$	5.03882	−	8.72749i	0.240490	−	0.416540i	−0.720364	−	0.693596i	$-0.756025\pi$
$439$	5.03882	−	8.72749i	0.240490	−	0.416540i	0.960854	+	0.277056i	$0.0893587\pi$
$440$	−1.82979			−0.0872318
$441$	42.9527	−	5.44341i	2.04537	−	0.259210i
$442$	−19.1502			−0.910880
$443$	1.45152	−	2.51411i	0.0689640	−	0.119449i	−0.829482	−	0.558534i	$-0.811364\pi$
$443$	1.45152	−	2.51411i	0.0689640	−	0.119449i	0.898446	+	0.439085i	$0.144697\pi$
$444$	−5.88476	+	11.8607i	−0.279278	+	0.562882i
$445$	2.36276	+	4.09242i	0.112006	+	0.193999i
$446$	3.03682	+	5.25992i	0.143797	+	0.249064i
$447$	−9.35997	+	18.8649i	−0.442711	+	0.892278i
$448$	2.31474	−	4.00925i	0.109361	−	0.189419i
$449$	−24.3808			−1.15060			−0.575300	−	0.817943i	$-0.695115\pi$
$449$	−24.3808			−1.15060			−0.575300	+	0.817943i	$0.695115\pi$
$450$	14.3165	−	1.81433i	0.674884	−	0.0855282i
$451$	16.6365			0.783384
$452$	6.46792	−	11.2028i	0.304225	−	0.526934i
$453$	−17.5701	+	1.10890i	−0.825515	+	0.0521005i
$454$	−2.17687	−	3.77044i	−0.102165	−	0.176956i
$455$	3.23052	+	5.59542i	0.151449	+	0.262317i
$456$	−6.18997	−	9.31267i	−0.289872	−	0.436106i
$457$	−4.79877	+	8.31171i	−0.224477	+	0.388805i	−0.956162	−	0.292837i	$-0.905401\pi$
$457$	−4.79877	+	8.31171i	−0.224477	+	0.388805i	0.731686	+	0.681642i	$0.238734\pi$
$458$	5.08616			0.237661
$459$	−30.4989	+	5.83669i	−1.42357	+	0.272434i
$460$	−0.435523			−0.0203064
$461$	−8.31611	+	14.4039i	−0.387320	+	0.670858i	−0.992088	−	0.125544i	$-0.959932\pi$
$461$	−8.31611	+	14.4039i	−0.387320	+	0.670858i	0.604768	+	0.796402i	$0.293266\pi$
$462$	18.6485	+	28.0563i	0.867608	+	1.30530i
$463$	9.29582	+	16.1008i	0.432014	+	0.748269i	0.997047	−	0.0767988i	$-0.0244699\pi$
$463$	9.29582	+	16.1008i	0.432014	+	0.748269i	−0.565033	+	0.825068i	$0.691137\pi$
$464$	−1.77412	−	3.07286i	−0.0823613	−	0.142654i
$465$	3.06827	−	0.193647i	0.142287	−	0.00898015i
$466$	−13.4093	+	23.2256i	−0.621173	+	1.07590i
$467$	−0.707813			−0.0327537			−0.0163768	−	0.999866i	$-0.505213\pi$
$467$	−0.707813			−0.0327537			−0.0163768	+	0.999866i	$0.505213\pi$
$468$	5.81531	+	7.65512i	0.268813	+	0.353858i
$469$	21.4321			0.989642
$470$	−2.05463	+	3.55872i	−0.0947728	+	0.164151i
$471$	7.36273	−	14.8395i	0.339257	−	0.683767i
$472$	1.06162	+	1.83878i	0.0488650	+	0.0846367i
$473$	−26.4029	−	45.7312i	−1.21401	−	2.10272i
$474$	5.26907	−	10.6197i	0.242016	−	0.487780i
$475$	−15.5278	+	26.8950i	−0.712465	+	1.23403i
$476$	27.6660			1.26807
$477$	−0.829224	+	1.97483i	−0.0379676	+	0.0904211i
$478$	14.8042			0.677127
$479$	−20.8161	+	36.0546i	−0.951113	+	1.64738i	−0.208090	+	0.978110i	$0.566725\pi$
$479$	−20.8161	+	36.0546i	−0.951113	+	1.64738i	−0.743023	+	0.669266i	$0.766609\pi$
$480$	0.752850	−	0.0475144i	0.0343627	−	0.00216873i
$481$	12.2480	+	21.2142i	0.558462	+	0.967284i
$482$	13.7842	+	23.8750i	0.627855	+	1.08748i
$483$	4.43868	+	6.67790i	0.201967	+	0.303855i
$484$	−3.32572	+	5.76031i	−0.151169	+	0.261832i
$485$	3.28743			0.149274
$486$	11.5948	+	10.4193i	0.525949	+	0.472628i
$487$	−16.1155			−0.730265			−0.365133	−	0.930956i	$-0.618976\pi$
$487$	−16.1155			−0.730265			−0.365133	+	0.930956i	$0.618976\pi$
$488$	−4.20052	+	7.27551i	−0.190148	+	0.329347i
$489$	8.19541	+	12.3298i	0.370609	+	0.557573i
$490$	−3.14275	−	5.44341i	−0.141975	−	0.245908i
$491$	−4.99631	−	8.65386i	−0.225480	−	0.390543i	0.730983	−	0.682396i	$-0.239062\pi$
$491$	−4.99631	−	8.65386i	−0.225480	−	0.390543i	−0.956463	+	0.291852i	$0.905728\pi$
$492$	−6.84495	+	0.432003i	−0.308594	+	0.0194762i
$493$	10.6022	−	18.3635i	0.477499	−	0.827052i
$494$	−20.6883			−0.930812
$495$	−2.12522	+	5.06129i	−0.0955215	+	0.227488i
$496$	−4.07554			−0.182997
$497$	17.4372	−	30.2021i	0.782165	−	1.35475i
$498$	−5.50714	+	11.0995i	−0.246781	+	0.497383i
$499$	−2.48566	−	4.30529i	−0.111273	−	0.192731i	0.805011	−	0.593260i	$-0.202160\pi$
$499$	−2.48566	−	4.30529i	−0.111273	−	0.192731i	−0.916284	+	0.400529i	$0.868826\pi$
$500$	−2.13631	−	3.70020i	−0.0955387	−	0.165478i
$501$	11.4055	−	22.9876i	0.509561	−	1.02701i
$502$	−2.82646	+	4.89557i	−0.126151	+	0.218500i
$503$	−5.41695			−0.241530			−0.120765	−	0.992681i	$-0.538535\pi$
$503$	−5.41695			−0.241530			−0.120765	+	0.992681i	$0.538535\pi$
$504$	−8.40130	−	11.0592i	−0.374224	−	0.492618i
$505$	−0.323866			−0.0144118
$506$	−2.10068	+	3.63849i	−0.0933866	+	0.161750i
$507$	−4.72127	+	0.297972i	−0.209679	+	0.0132334i
$508$	−3.71620	−	6.43664i	−0.164880	−	0.285580i
$509$	−8.96080	−	15.5206i	−0.397180	−	0.687936i	0.596197	−	0.802839i	$-0.296678\pi$
$509$	−8.96080	−	15.5206i	−0.397180	−	0.687936i	−0.993377	+	0.114902i	$0.963345\pi$
$510$	2.49544	+	3.75433i	0.110500	+	0.166244i
$511$	26.6757	−	46.2037i	1.18006	−	2.04393i
$512$	−1.00000			−0.0441942
$513$	−32.9487	+	6.30551i	−1.45472	+	0.278395i
$514$	5.64100			0.248814
$515$	−2.76917	+	4.79635i	−0.122024	+	0.211352i
$516$	12.0508	+	18.1301i	0.530505	+	0.798133i
$517$	19.8204	+	34.3299i	0.871699	+	1.50983i
$518$	−17.6945	−	30.6478i	−0.777454	−	1.34659i
$519$	15.3929	−	0.971488i	0.675674	−	0.0426436i
$520$	0.697814	−	1.20865i	0.0306012	−	0.0530028i
$521$	44.4983			1.94951			0.974753	−	0.223286i	$-0.0716785\pi$
$521$	44.4983			1.94951			0.974753	+	0.223286i	$0.0716785\pi$
$522$	−10.5602	+	1.33830i	−0.462209	+	0.0585758i
$523$	−1.42361			−0.0622501			−0.0311251	−	0.999515i	$-0.509909\pi$
$523$	−1.42361			−0.0622501			−0.0311251	+	0.999515i	$0.509909\pi$
$524$	−7.23302	+	12.5280i	−0.315976	+	0.547286i
$525$	−17.1434	+	34.5523i	−0.748201	+	1.50799i
$526$	−7.20692	−	12.4828i	−0.314237	−	0.544274i
$527$	−12.1778	−	21.0925i	−0.530472	−	0.918805i
$528$	3.23431	−	6.51871i	0.140755	−	0.283690i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.310943			0.0135065
$531$	6.31918	−	0.800831i	0.274229	−	0.0347531i
$532$	29.8881			1.29581
$533$	−6.34456	+	10.9891i	−0.274813	+	0.475991i
$534$	−18.7558	+	1.18373i	−0.811643	+	0.0512250i
$535$	−1.61463	−	2.79663i	−0.0698067	−	0.120909i
$536$	−2.31474	−	4.00925i	−0.0999815	−	0.173173i
$537$	−0.521537	−	0.784641i	−0.0225060	−	0.0338597i
$538$	0.490110	−	0.848895i	0.0211301	−	0.0365985i
$539$	−60.6344			−2.61171
$540$	0.742975	−	2.13761i	0.0319725	−	0.0919879i
$541$	9.66320			0.415453			0.207727	−	0.978187i	$-0.433394\pi$
$541$	9.66320			0.415453			0.207727	+	0.978187i	$0.433394\pi$
$542$	0.0450442	−	0.0780189i	0.00193482	−	0.00335120i
$543$	−1.72399	−	2.59370i	−0.0739835	−	0.111307i
$544$	−2.98802	−	5.17540i	−0.128110	−	0.221894i
$545$	−3.24276	−	5.61663i	−0.138905	−	0.240590i
$546$	−25.6442	+	1.61847i	−1.09747	+	0.0692642i
$547$	0.592206	−	1.02573i	0.0253209	−	0.0438571i	−0.853087	−	0.521768i	$-0.825273\pi$
$547$	0.592206	−	1.02573i	0.0253209	−	0.0438571i	0.878408	+	0.477911i	$0.158606\pi$
$548$	18.7995			0.803074
$549$	15.2457	+	20.0690i	0.650670	+	0.856524i
$550$	−20.2099			−0.861753
$551$	11.4538	−	19.8385i	0.487947	−	0.845149i
$552$	0.769825	−	1.55157i	0.0327659	−	0.0660392i
$553$	15.8432	+	27.4413i	0.673723	+	1.16692i
$554$	−1.54449	−	2.67514i	−0.0656191	−	0.113656i
$555$	2.56295	−	5.16559i	0.108791	−	0.219267i
$556$	2.03255	−	3.52048i	0.0861993	−	0.149302i
$557$	9.20364			0.389971			0.194985	−	0.980806i	$-0.437534\pi$
$557$	9.20364			0.389971			0.194985	+	0.980806i	$0.437534\pi$
$558$	−4.73355	+	11.2731i	−0.200387	+	0.477229i
$559$	40.2764			1.70351
$560$	−1.00812	+	1.74612i	−0.0426010	+	0.0737870i
$561$	43.4011	−	2.73916i	1.83240	−	0.115648i
$562$	−1.66280	−	2.88005i	−0.0701408	−	0.121488i
$563$	−5.76234	−	9.98067i	−0.242854	−	0.420635i	0.718672	−	0.695349i	$-0.244750\pi$
$563$	−5.76234	−	9.98067i	−0.242854	−	0.420635i	−0.961526	+	0.274714i	$0.911417\pi$
$564$	−9.04636	−	13.6100i	−0.380920	−	0.573086i
$565$	−2.81693	+	4.87906i	−0.118509	+	0.205264i
$566$	−10.9195			−0.458981
$567$	−40.3481	+	10.3936i	−1.69446	+	0.436490i
$568$	−7.53311			−0.316082
$569$	−7.41744	+	12.8474i	−0.310955	+	0.538591i	−0.978569	−	0.205917i	$-0.933982\pi$
$569$	−7.41744	+	12.8474i	−0.310955	+	0.538591i	0.667614	+	0.744508i	$0.267316\pi$
$570$	2.69587	+	4.05588i	0.112918	+	0.169882i
$571$	2.87907	+	4.98670i	0.120485	+	0.208687i	0.919959	−	0.392014i	$-0.128222\pi$
$571$	2.87907	+	4.98670i	0.120485	+	0.208687i	−0.799474	+	0.600701i	$0.794888\pi$
$572$	−6.73161	−	11.6595i	−0.281463	−	0.487508i
$573$	−41.0938	+	2.59354i	−1.71672	+	0.108347i
$574$	9.16590	−	15.8758i	0.382577	−	0.662643i
$575$	−4.81032			−0.200604
$576$	−1.16146	+	2.76605i	−0.0483940	+	0.115252i
$577$	−23.0209			−0.958371			−0.479186	−	0.877714i	$-0.659068\pi$
$577$	−23.0209			−0.958371			−0.479186	+	0.877714i	$0.659068\pi$
$578$	9.35653	−	16.2060i	0.389180	−	0.674080i
$579$	7.14365	−	14.3979i	0.296880	−	0.598357i
$580$	0.772668	+	1.33830i	0.0320833	+	0.0555699i
$581$	−16.5591	−	28.6812i	−0.686986	−	1.18990i
$582$	−5.81082	+	11.7116i	−0.240866	+	0.485462i
$583$	1.49979	−	2.59771i	0.0621148	−	0.107586i
$584$	−11.5243			−0.476878
$585$	−2.53270	−	3.33398i	−0.104714	−	0.137843i
$586$	−3.89792			−0.161022
$587$	0.975904	−	1.69031i	0.0402799	−	0.0697668i	−0.845183	−	0.534478i	$-0.820508\pi$
$587$	0.975904	−	1.69031i	0.0402799	−	0.0697668i	0.885462	+	0.464711i	$0.153842\pi$
$588$	24.9475	−	1.57450i	1.02882	−	0.0649314i
$589$	−13.1559	−	22.7867i	−0.542080	−	0.938910i
$590$	−0.462360	−	0.800831i	−0.0190351	−	0.0329697i
$591$	0.883589	+	1.32934i	0.0363460	+	0.0546817i
$592$	−3.82214	+	6.62015i	−0.157089	+	0.272086i
$593$	−24.3221			−0.998787			−0.499394	−	0.866375i	$-0.666444\pi$
$593$	−24.3221			−0.998787			−0.499394	+	0.866375i	$0.666444\pi$
$594$	−14.2745	−	16.5174i	−0.585692	−	0.677719i
$595$	−12.0492			−0.493967
$596$	−6.07929	+	10.5296i	−0.249017	+	0.431311i
$597$	9.28794	+	13.9735i	0.380130	+	0.571897i
$598$	−1.60224	−	2.77517i	−0.0655207	−	0.113485i
$599$	−16.7619	−	29.0325i	−0.684874	−	1.18624i	−0.973476	−	0.228788i	$-0.926524\pi$
$599$	−16.7619	−	29.0325i	−0.684874	−	1.18624i	0.288602	−	0.957449i	$-0.406810\pi$
$600$	8.31517	−	0.524793i	0.339466	−	0.0214246i
$601$	−6.29502	+	10.9033i	−0.256779	+	0.444754i	−0.965377	−	0.260858i	$-0.915995\pi$
$601$	−6.29502	+	10.9033i	−0.256779	+	0.444754i	0.708598	+	0.705612i	$0.249328\pi$
$602$	−58.1868			−2.37152
$603$	−13.7782	+	1.74612i	−0.561093	+	0.0711075i
$604$	−10.1643			−0.413579
$605$	1.44843	−	2.50875i	0.0588869	−	0.101995i
$606$	0.572461	−	1.15379i	0.0232546	−	0.0468694i
$607$	2.25445	+	3.90482i	0.0915053	+	0.158492i	0.908145	−	0.418656i	$-0.137499\pi$
$607$	2.25445	+	3.90482i	0.0915053	+	0.158492i	−0.816639	+	0.577148i	$0.804166\pi$
$608$	−3.22802	−	5.59110i	−0.130914	−	0.226749i
$609$	12.6455	−	25.4868i	0.512422	−	1.03278i
$610$	1.82942	−	3.16865i	0.0740711	−	0.128295i
$611$	−30.2350			−1.22318
$612$	−17.7859	+	2.25401i	−0.718951	+	0.0911128i
$613$	−25.5888			−1.03352			−0.516760	−	0.856130i	$-0.672862\pi$
$613$	−25.5888			−1.03352			−0.516760	+	0.856130i	$0.672862\pi$
$614$	−16.3412	+	28.3038i	−0.659478	+	1.14225i
$615$	2.98113	−	0.188147i	0.120211	−	0.00758683i
$616$	9.72506	+	16.8443i	0.391834	+	0.678676i
$617$	20.5875	+	35.6586i	0.828821	+	1.43556i	0.898964	+	0.438023i	$0.144321\pi$
$617$	20.5875	+	35.6586i	0.828821	+	1.43556i	−0.0701425	+	0.997537i	$0.522345\pi$
$618$	−12.1924	−	18.3433i	−0.490452	−	0.737874i
$619$	14.0068	−	24.2605i	0.562982	−	0.975113i	−0.434253	−	0.900791i	$-0.642987\pi$
$619$	14.0068	−	24.2605i	0.562982	−	0.975113i	0.997234	−	0.0743218i	$-0.0236792\pi$
$620$	1.77499			0.0712853
$621$	−3.39760	−	3.93145i	−0.136341	−	0.157764i
$622$	5.63543			0.225960
$623$	25.1154	−	43.5012i	1.00623	−	1.74284i
$624$	3.07242	+	4.62239i	0.122995	+	0.185044i
$625$	−11.0954	−	19.2178i	−0.443815	−	0.768711i
$626$	7.65418	+	13.2574i	0.305923	+	0.529873i
$627$	46.8872	−	2.95918i	1.87249	−	0.118178i
$628$	4.78208	−	8.28281i	0.190826	−	0.330520i
$629$	−45.6826			−1.82148
$630$	3.65896	+	4.81656i	0.145776	+	0.191896i
$631$	−40.1274			−1.59745			−0.798723	−	0.601698i	$-0.794491\pi$
$631$	−40.1274			−1.59745			−0.798723	+	0.601698i	$0.794491\pi$
$632$	3.42225	−	5.92751i	0.136130	−	0.235784i
$633$	1.38992	−	2.80136i	0.0552443	−	0.111344i
$634$	−15.5534	−	26.9394i	−0.617706	−	1.06990i
$635$	1.61849	+	2.80331i	0.0642278	+	0.111246i
$636$	−0.549618	+	1.10775i	−0.0217938	+	0.0439251i
$637$	23.1237	−	40.0515i	0.916196	−	1.58690i
$638$	14.9074			0.590190
$639$	−8.74938	+	20.8370i	−0.346120	+	0.824297i
$640$	0.435523			0.0172156
$641$	14.1763	−	24.5540i	0.559929	−	0.969826i	−0.437573	−	0.899183i	$-0.644162\pi$
$641$	14.1763	−	24.5540i	0.559929	−	0.969826i	0.997502	−	0.0706426i	$-0.0225050\pi$
$642$	12.8171	−	0.808923i	0.505851	−	0.0319257i
$643$	2.19080	+	3.79457i	0.0863966	+	0.149643i	0.905985	−	0.423309i	$-0.139131\pi$
$643$	2.19080	+	3.79457i	0.0863966	+	0.149643i	−0.819589	+	0.572952i	$0.805798\pi$
$644$	2.31474	+	4.00925i	0.0912135	+	0.157986i
$645$	−5.24838	−	7.89607i	−0.206655	−	0.310907i
$646$	19.2908	−	33.4126i	0.758986	−	1.31460i
$647$	20.3298			0.799247			0.399624	−	0.916679i	$-0.369141\pi$
$647$	20.3298			0.799247			0.399624	+	0.916679i	$0.369141\pi$
$648$	6.30204	+	6.42528i	0.247568	+	0.252409i
$649$	−8.92050			−0.350160
$650$	7.70731	−	13.3494i	0.302306	−	0.523609i
$651$	−18.0900	−	27.2160i	−0.709004	−	1.06668i
$652$	4.27384	+	7.40252i	0.167377	+	0.289905i
$653$	22.1343	+	38.3377i	0.866182	+	1.50027i	0.865869	+	0.500271i	$0.166766\pi$
$653$	22.1343	+	38.3377i	0.866182	+	1.50027i	0.000312861		1.00000i	$0.499900\pi$
$654$	25.7414	−	1.62461i	1.00657	−	0.0635272i
$655$	3.15015	−	5.45621i	0.123086	−	0.213192i
$656$	−3.95980			−0.154604
$657$	−13.3849	+	31.8767i	−0.522196	+	1.24363i
$658$	43.6801			1.70283
$659$	13.6768	−	23.6890i	0.532774	−	0.922791i	−0.466494	−	0.884524i	$-0.654483\pi$
$659$	13.6768	−	23.6890i	0.532774	−	0.922791i	0.999268	−	0.0382665i	$-0.0121836\pi$
$660$	−1.40862	+	2.83905i	−0.0548303	+	0.110510i
$661$	−6.86841	−	11.8964i	−0.267150	−	0.462718i	0.700974	−	0.713186i	$-0.252749\pi$
$661$	−6.86841	−	11.8964i	−0.267150	−	0.462718i	−0.968125	+	0.250468i	$0.919415\pi$
$662$	14.0945	+	24.4125i	0.547800	+	0.948817i
$663$	−14.7423	+	29.7128i	−0.572542	+	1.15395i
$664$	−3.57688	+	6.19533i	−0.138810	+	0.240425i
$665$	−13.0170			−0.504776
$666$	13.8724	+	18.2612i	0.537544	+	0.707609i
$667$	3.54823			0.137388
$668$	7.40786	−	12.8308i	0.286619	−	0.496438i
$669$	10.4989	−	0.662617i	0.405913	−	0.0256183i
$670$	1.00812	+	1.74612i	0.0389472	+	0.0674585i
$671$	−17.6479	−	30.5670i	−0.681289	−	1.18003i
$672$	−4.43868	−	6.67790i	−0.171226	−	0.257606i
$673$	−23.8044	+	41.2305i	−0.917593	+	1.58932i	−0.114534	+	0.993419i	$0.536538\pi$
$673$	−23.8044	+	41.2305i	−0.917593	+	1.58932i	−0.803059	+	0.595899i	$0.796796\pi$
$674$	9.44351			0.363750
$675$	8.20610	−	23.6097i	0.315853	−	0.908738i
$676$	−2.73125			−0.105048
$677$	0.266420	−	0.461453i	0.0102393	−	0.0177351i	−0.860860	−	0.508841i	$-0.830074\pi$
$677$	0.266420	−	0.461453i	0.0102393	−	0.0177351i	0.871100	+	0.491106i	$0.163407\pi$
$678$	−12.4027	−	18.6596i	−0.476323	−	0.716617i
$679$	−17.4722	−	30.2627i	−0.670521	−	1.16138i
$680$	1.30135	+	2.25401i	0.0499046	+	0.0864372i
$681$	−7.52591	+	0.474981i	−0.288394	+	0.0182013i
$682$	8.56140	−	14.8288i	0.327833	−	0.567823i
$683$	−38.7409			−1.48238			−0.741190	−	0.671295i	$-0.765738\pi$
$683$	−38.7409			−1.48238			−0.741190	+	0.671295i	$0.765738\pi$
$684$	−19.2145	+	2.43505i	−0.734683	+	0.0931065i
$685$	−8.18760			−0.312832
$686$	−17.2033	+	29.7971i	−0.656827	+	1.13766i
$687$	3.91545	−	7.89154i	0.149384	−	0.301081i
$688$	6.28438	+	10.8849i	0.239590	+	0.414981i
$689$	1.14393	+	1.98134i	0.0435801	+	0.0754830i
$690$	−0.335276	+	0.675744i	−0.0127638	+	0.0257252i
$691$	−15.4566	+	26.7717i	−0.587998	+	1.01844i	0.406497	+	0.913652i	$0.366750\pi$
$691$	−15.4566	+	26.7717i	−0.587998	+	1.01844i	−0.994494	+	0.104790i	$0.966583\pi$
$692$	8.90478			0.338509
$693$	57.8874	−	7.33608i	2.19896	−	0.278675i
$694$	24.5333			0.931270
$695$	−0.885222	+	1.53325i	−0.0335784	+	0.0581595i
$696$	−6.13351	+	0.387103i	−0.232490	+	0.0146731i
$697$	−11.8319	−	20.4935i	−0.448167	−	0.776248i
$698$	8.54208	+	14.7953i	0.323323	+	0.560011i
$699$	25.7133	+	38.6850i	0.972566	+	1.46320i
$700$	−11.1346	+	19.2858i	−0.420850	+	0.728933i
$701$	−46.7636			−1.76624			−0.883119	−	0.469150i	$-0.844560\pi$
$701$	−46.7636			−1.76624			−0.883119	+	0.469150i	$0.844560\pi$
$702$	16.3542	−	3.12977i	0.617251	−	0.118125i
$703$	−49.3519			−1.86134
$704$	2.10068	−	3.63849i	0.0791724	−	0.137131i
$705$	3.93990	+	5.92748i	0.148385	+	0.223242i
$706$	6.42640	+	11.1309i	0.241861	+	0.418915i
$707$	1.72130	+	2.98138i	0.0647361	+	0.112126i
$708$	3.67026	−	0.231640i	0.137937	−	0.00870557i
$709$	13.1841	−	22.8355i	0.495138	−	0.857604i	−0.504846	−	0.863209i	$-0.668451\pi$
$709$	13.1841	−	22.8355i	0.495138	−	0.857604i	0.999984	+	0.00560505i	$0.00178415\pi$
$710$	3.28084			0.123128
$711$	−12.4210	−	16.3507i	−0.465824	−	0.613197i
$712$	−10.8502			−0.406629
$713$	2.03777	−	3.52952i	0.0763150	−	0.132181i
$714$	21.2979	−	42.9257i	0.797055	−	1.60645i
$715$	2.93177	+	5.07797i	0.109642	+	0.189905i
$716$	−0.271978	−	0.471079i	−0.0101643	−	0.0176051i
$717$	11.3966	−	22.9697i	0.425614	−	0.857819i
$718$	17.7999	−	30.8304i	0.664287	−	1.15058i
$719$	−46.8541			−1.74736			−0.873682	−	0.486498i	$-0.838274\pi$
$719$	−46.8541			−1.74736			−0.873682	+	0.486498i	$0.838274\pi$
$720$	0.505841	−	1.20468i	0.0188516	−	0.0448957i
$721$	58.8710			2.19247
$722$	11.3403	−	19.6419i	0.422041	−	0.730996i
$723$	47.6552	−	3.00765i	1.77231	−	0.111856i
$724$	−0.899048	−	1.55720i	−0.0334129	−	0.0578728i
$725$	8.53407	+	14.7814i	0.316947	+	0.548969i
$726$	6.37731	+	9.59452i	0.236684	+	0.356086i
$727$	−5.23445	+	9.06634i	−0.194135	+	0.336252i	−0.946617	−	0.322361i	$-0.895523\pi$
$727$	−5.23445	+	9.06634i	−0.194135	+	0.336252i	0.752482	+	0.658613i	$0.228857\pi$
$728$	−14.8351			−0.549826
$729$	25.0922	−	9.96907i	0.929340	−	0.369225i
$730$	5.01909			0.185765
$731$	−37.5557	+	65.0484i	−1.38905	+	2.40590i
$732$	8.05480	+	12.1183i	0.297714	+	0.447904i
$733$	1.16327	+	2.01485i	0.0429664	+	0.0744200i	0.886709	−	0.462328i	$-0.152986\pi$
$733$	1.16327	+	2.01485i	0.0429664	+	0.0744200i	−0.843742	+	0.536748i	$0.819652\pi$
$734$	0.228597	+	0.395941i	0.00843766	+	0.0146145i
$735$	−10.8652	+	0.685732i	−0.400769	+	0.0252936i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	19.4501			0.716454
$738$	−4.59913	+	10.9530i	−0.169296	+	0.403185i
$739$	11.2490			0.413802			0.206901	−	0.978362i	$-0.433662\pi$
$739$	11.2490			0.413802			0.206901	+	0.978362i	$0.433662\pi$
$740$	1.66463	−	2.88323i	0.0611931	−	0.105990i
$741$	−15.9264	+	32.0994i	−0.585070	+	1.17920i
$742$	−1.65261	−	2.86241i	−0.0606694	−	0.105082i
$743$	0.148648	+	0.257467i	0.00545338	+	0.00944554i	0.868739	−	0.495270i	$-0.164931\pi$
$743$	0.148648	+	0.257467i	0.00545338	+	0.00944554i	−0.863286	+	0.504715i	$0.831597\pi$
$744$	−3.13745	+	6.32348i	−0.115024	+	0.231830i
$745$	2.64767	−	4.58590i	0.0970031	−	0.168014i
$746$	2.13731			0.0782526
$747$	12.9822	+	17.0894i	0.474994	+	0.625269i
$748$	25.1075			0.918021
$749$	−17.1631	+	29.7273i	−0.627125	+	1.08621i
$750$	−7.38570	+	0.466132i	−0.269688	+	0.0170207i
$751$	4.22109	+	7.31115i	0.154030	+	0.266788i	0.932705	−	0.360639i	$-0.117441\pi$
$751$	4.22109	+	7.31115i	0.154030	+	0.266788i	−0.778675	+	0.627427i	$0.784108\pi$
$752$	−4.71761	−	8.17113i	−0.172033	−	0.297971i
$753$	5.41994	+	8.15418i	0.197514	+	0.297155i
$754$	−5.68514	+	9.84694i	−0.207040	+	0.358605i
$755$	4.42678			0.161107
$756$	−23.6267	+	4.52153i	−0.859296	+	0.164447i
$757$	5.44738			0.197988			0.0989942	−	0.995088i	$-0.468437\pi$
$757$	5.44738			0.197988			0.0989942	+	0.995088i	$0.468437\pi$
$758$	0.0301405	−	0.0522048i	0.00109475	−	0.00189616i
$759$	4.02821	+	6.06035i	0.146215	+	0.219977i
$760$	1.40588	+	2.43505i	0.0509966	+	0.0883286i
$761$	−0.866614	−	1.50102i	−0.0314147	−	0.0544119i	0.849891	−	0.526959i	$-0.176668\pi$
$761$	−0.866614	−	1.50102i	−0.0314147	−	0.0544119i	−0.881305	+	0.472547i	$0.843335\pi$
$762$	−12.8477	+	0.810855i	−0.465424	+	0.0293742i
$763$	−34.4696	+	59.7031i	−1.24788	+	2.16140i
$764$	−23.7727			−0.860066
$765$	7.74615	−	0.981672i	0.280063	−	0.0354924i
$766$	−12.8299			−0.463563
$767$	3.40195	−	5.89235i	0.122837	−	0.212761i
$768$	−0.769825	+	1.55157i	−0.0277787	+	0.0559875i
$769$	21.3192	+	36.9260i	0.768791	+	1.33158i	0.938219	+	0.346042i	$0.112474\pi$
$769$	21.3192	+	36.9260i	0.768791	+	1.33158i	−0.169429	+	0.985542i	$0.554192\pi$
$770$	−4.23549	−	7.33608i	−0.152636	−	0.264374i
$771$	4.34258	−	8.75241i	0.156394	−	0.315210i
$772$	4.63979	−	8.03635i	0.166990	−	0.289235i
$773$	14.1875			0.510288			0.255144	−	0.966903i	$-0.417877\pi$
$773$	14.1875			0.510288			0.255144	+	0.966903i	$0.417877\pi$
$774$	37.4071	−	4.74061i	1.34457	−	0.170398i
$775$	19.6046			0.704219
$776$	−3.77412	+	6.53696i	−0.135483	+	0.234663i
$777$	−61.1740	+	3.86086i	−2.19460	+	0.138507i
$778$	−4.00954	−	6.94473i	−0.143749	−	0.248981i
$779$	−12.7823	−	22.1396i	−0.457974	−	0.793234i
$780$	−1.33811	−	2.01316i	−0.0479120	−	0.0720826i
$781$	15.8247	−	27.4091i	0.566251	−	0.980776i
$782$	5.97604			0.213703
$783$	−6.05306	+	17.4152i	−0.216319	+	0.622368i
$784$	14.4321			0.515432
$785$	−2.08271	+	3.60735i	−0.0743350	+	0.128752i
$786$	13.8698	+	20.8669i	0.494721	+	0.744296i
$787$	−13.6683	−	23.6742i	−0.487222	−	0.843893i	0.512670	−	0.858586i	$-0.328656\pi$
$787$	−13.6683	−	23.6742i	−0.487222	−	0.843893i	−0.999892	+	0.0146925i	$0.995323\pi$
$788$	0.460785	+	0.798103i	0.0164148	+	0.0284312i
$789$	−24.9159	+	1.57251i	−0.887030	+	0.0559829i
$790$	−1.49047	+	2.58157i	−0.0530285	+	0.0918481i
$791$	59.8862			2.12931
$792$	−7.62438	−	10.0365i	−0.270920	−	0.356632i
$793$	26.9210			0.955993
$794$	11.5612	−	20.0246i	0.410291	−	0.710646i
$795$	0.239371	−	0.482450i	0.00848963	−	0.0171107i
$796$	4.84359	+	8.38934i	0.171676	+	0.297352i
$797$	9.64903	+	16.7126i	0.341786	+	0.591991i	0.984764	−	0.173893i	$-0.0556348\pi$
$797$	9.64903	+	16.7126i	0.341786	+	0.591991i	−0.642978	+	0.765884i	$0.722301\pi$
$798$	23.0086	−	46.3735i	0.814496	−	1.64161i
$799$	28.1926	−	48.8310i	0.997383	−	1.72752i
$800$	4.81032			0.170070
$801$	−12.6020	+	30.0122i	−0.445271	+	1.06043i
$802$	−12.6373			−0.446238
$803$	24.2088	−	41.9309i	0.854311	−	1.47971i
$804$	−8.00257	+	0.505064i	−0.282229	+	0.0178122i
$805$	−1.00812	−	1.74612i	−0.0355316	−	0.0615426i
$806$	6.53000	+	11.3103i	0.230010	+	0.398388i
$807$	−0.939822	−	1.41394i	−0.0330833	−	0.0497731i
$808$	0.371813	−	0.643998i	0.0130803	−	0.0226558i
$809$	−29.9263			−1.05215			−0.526076	−	0.850438i	$-0.676337\pi$
$809$	−29.9263			−1.05215			−0.526076	+	0.850438i	$0.676337\pi$
$810$	−2.74468	−	2.79836i	−0.0964384	−	0.0983243i
$811$	21.4708			0.753941			0.376971	−	0.926225i	$-0.376966\pi$
$811$	21.4708			0.753941			0.376971	+	0.926225i	$0.376966\pi$
$812$	8.21323	−	14.2257i	0.288228	−	0.499226i
$813$	−0.0863757	−	0.129950i	−0.00302933	−	0.00455755i
$814$	−16.0582	−	27.8136i	−0.562840	−	0.974867i
$815$	−1.86136	−	3.22397i	−0.0652005	−	0.112931i
$816$	−10.3303	+	0.651970i	−0.361631	+	0.0228235i
$817$	−40.5722	+	70.2731i	−1.41944	+	2.45855i
$818$	−13.2535			−0.463396
$819$	−17.2303	+	41.0346i	−0.602076	+	1.43387i
$820$	1.72458			0.0602250
$821$	21.4212	−	37.1025i	0.747604	−	1.29489i	−0.201364	−	0.979516i	$-0.564538\pi$
$821$	21.4212	−	37.1025i	0.747604	−	1.29489i	0.948968	−	0.315371i	$-0.102129\pi$
$822$	14.4723	−	29.1687i	0.504779	−	1.01738i
$823$	−17.6598	−	30.5878i	−0.615584	−	1.06622i	−0.990282	−	0.139075i	$-0.955587\pi$
$823$	−17.6598	−	30.5878i	−0.615584	−	1.06622i	0.374698	−	0.927147i	$-0.377746\pi$
$824$	−6.35827	−	11.0128i	−0.221501	−	0.383651i
$825$	−15.5581	+	31.3571i	−0.541663	+	1.09171i
$826$	−4.91475	+	8.51260i	−0.171006	+	0.296191i
$827$	6.71444			0.233484			0.116742	−	0.993162i	$-0.462755\pi$
$827$	6.71444			0.233484			0.116742	+	0.993162i	$0.462755\pi$
$828$	−1.81474	−	2.38887i	−0.0630666	−	0.0830191i
$829$	−40.2072			−1.39645			−0.698227	−	0.715876i	$-0.746027\pi$
$829$	−40.2072			−1.39645			−0.698227	+	0.715876i	$0.746027\pi$
$830$	1.55781	−	2.69821i	0.0540724	−	0.0936562i
$831$	−5.33965	+	0.337000i	−0.185230	+	0.0116904i
$832$	1.60224	+	2.77517i	0.0555478	+	0.0962117i
$833$	43.1234	+	74.6919i	1.49414	+	2.58792i
$834$	−3.89756	−	5.86380i	−0.134962	−	0.203047i
$835$	−3.22629	+	5.58810i	−0.111651	+	0.193384i
$836$	27.1242			0.938109
$837$	13.8470	+	16.0228i	0.478624	+	0.553828i
$838$	−5.57491			−0.192582
$839$	12.4982	−	21.6475i	0.431486	−	0.747356i	−0.565516	−	0.824738i	$-0.691323\pi$
$839$	12.4982	−	21.6475i	0.431486	−	0.747356i	0.997002	+	0.0773820i	$0.0246561\pi$
$840$	1.93315	+	2.90838i	0.0667000	+	0.100349i
$841$	8.20502	+	14.2115i	0.282932	+	0.490052i
$842$	12.0656	+	20.8983i	0.415810	+	0.720203i
$843$	−5.74866	+	0.362814i	−0.197994	+	0.0124960i
$844$	0.902750	−	1.56361i	0.0310739	−	0.0538217i
$845$	1.18952			0.0409208
$846$	−28.0810	+	3.55872i	−0.965446	+	0.122351i
$847$	−30.7927			−1.05805
$848$	−0.356976	+	0.618301i	−0.0122586	+	0.0212326i
$849$	−8.40610	+	16.9424i	−0.288496	+	0.581460i
$850$	14.3733	+	24.8953i	0.493001	+	0.853903i
$851$	−3.82214	−	6.62015i	−0.131021	−	0.226936i
$852$	−5.79918	+	11.6882i	−0.198677	+	0.400430i
$853$	21.7021	−	37.5891i	0.743064	−	1.28702i	−0.208030	−	0.978123i	$-0.566705\pi$
$853$	21.7021	−	37.5891i	0.743064	−	1.28702i	0.951094	−	0.308902i	$-0.0999616\pi$
$854$	−38.8924			−1.33087
$855$	8.36834	−	1.06052i	0.286191	−	0.0362691i
$856$	7.41469			0.253429
$857$	−1.37403	+	2.37989i	−0.0469360	+	0.0812955i	−0.888539	−	0.458801i	$-0.848279\pi$
$857$	−1.37403	+	2.37989i	−0.0469360	+	0.0812955i	0.841603	+	0.540097i	$0.181612\pi$
$858$	−23.2727	+	1.46880i	−0.794516	+	0.0501441i
$859$	14.8783	+	25.7700i	0.507642	+	0.879262i	0.999961	+	0.00884669i	$0.00281603\pi$
$859$	14.8783	+	25.7700i	0.507642	+	0.879262i	−0.492319	+	0.870415i	$0.663851\pi$
$860$	−2.73699	−	4.74061i	−0.0933306	−	0.161653i
$861$	−17.5763	−	26.4431i	−0.598998	−	0.901179i
$862$	2.11604	−	3.66509i	0.0720727	−	0.124834i
$863$	−15.4133			−0.524675			−0.262338	−	0.964976i	$-0.584493\pi$
$863$	−15.4133			−0.524675			−0.262338	+	0.964976i	$0.584493\pi$
$864$	3.39760	+	3.93145i	0.115589	+	0.133751i
$865$	−3.87824			−0.131864
$866$	3.79869	−	6.57952i	0.129085	−	0.223581i
$867$	−17.9418	−	26.9931i	−0.609337	−	0.916733i
$868$	−9.43380	−	16.3398i	−0.320204	−	0.554610i
$869$	14.3781	+	24.9036i	0.487744	+	0.844797i
$870$	2.67129	−	0.168592i	0.0905651	−	0.00571581i
$871$	−7.41756	+	12.8476i	−0.251334	+	0.435324i
$872$	14.8914			0.504285
$873$	13.6981	+	18.0318i	0.463610	+	0.610283i
$874$	6.45604			0.218379
$875$	9.89000	−	17.1300i	0.334343	−	0.579099i
$876$	−8.87167	+	17.8807i	−0.299746	+	0.604133i
$877$	7.86522	+	13.6230i	0.265590	+	0.460015i	0.967718	−	0.252036i	$-0.0811001\pi$
$877$	7.86522	+	13.6230i	0.265590	+	0.460015i	−0.702128	+	0.712050i	$0.747767\pi$
$878$	−5.03882	−	8.72749i	−0.170052	−	0.294538i
$879$	−3.00072	+	6.04790i	−0.101212	+	0.203990i
$880$	−0.914895	+	1.58464i	−0.0308411	+	0.0534183i
$881$	17.2562			0.581377			0.290689	−	0.956818i	$-0.406116\pi$
$881$	17.2562			0.581377			0.290689	+	0.956818i	$0.406116\pi$
$882$	16.7622	−	39.9198i	0.564413	−	1.34417i
$883$	33.0703			1.11290			0.556452	−	0.830880i	$-0.312162\pi$
$883$	33.0703			1.11290			0.556452	+	0.830880i	$0.312162\pi$
$884$	−9.57508	+	16.5845i	−0.322045	+	0.557798i
$885$	−1.59848	+	0.100885i	−0.0537324	+	0.00339120i
$886$	−1.45152	−	2.51411i	−0.0487649	−	0.0844633i
$887$	15.3024	+	26.5046i	0.513806	+	0.889938i	0.999872	+	0.0160155i	$0.00509810\pi$
$887$	15.3024	+	26.5046i	0.513806	+	0.889938i	−0.486066	+	0.873922i	$0.661569\pi$
$888$	7.32924	+	11.0267i	0.245953	+	0.370031i
$889$	17.2041	−	29.7983i	0.577006	−	0.999403i
$890$	4.72552			0.158400
$891$	−36.6169	+	9.43242i	−1.22671	+	0.315998i
$892$	6.07363			0.203360
$893$	30.4571	−	52.7532i	1.01921	−	1.76532i
$894$	11.6575	+	17.5384i	0.389884	+	0.586572i
$895$	0.118453	+	0.205166i	0.00395943	+	0.00685794i
$896$	−2.31474	−	4.00925i	−0.0773300	−	0.133940i
$897$	−5.53932	+	0.349601i	−0.184952	+	0.0116728i
$898$	−12.1904	+	21.1144i	−0.406798	+	0.704595i
$899$	−14.4609			−0.482299
$900$	5.58697	−	13.3056i	0.186232	−	0.443519i
$901$	−4.26661			−0.142141
$902$	8.31827	−	14.4077i	0.276968	−	0.479723i
$903$	−44.7936	+	90.2809i	−1.49064	+	3.00436i
$904$	−6.46792	−	11.2028i	−0.215120	−	0.372598i
$905$	0.391556	+	0.678195i	0.0130158	+	0.0225440i
$906$	−7.82472	+	15.7706i	−0.259959	+	0.523943i
$907$	−8.93204	+	15.4708i	−0.296584	+	0.513698i	−0.975352	−	0.220654i	$-0.929181\pi$
$907$	−8.93204	+	15.4708i	−0.296584	+	0.513698i	0.678768	+	0.734352i	$0.262514\pi$
$908$	−4.35373			−0.144484
$909$	−1.34949	−	1.77643i	−0.0447596	−	0.0589204i
$910$	6.46103			0.214181
$911$	−15.8558	+	27.4630i	−0.525325	+	0.909890i	0.474240	+	0.880396i	$0.342723\pi$
$911$	−15.8558	+	27.4630i	−0.525325	+	0.909890i	−0.999565	+	0.0294942i	$0.990610\pi$
$912$	−11.1600	+	0.704338i	−0.369544	+	0.0233229i
$913$	−15.0277	−	26.0288i	−0.497346	−	0.861428i
$914$	4.79877	+	8.31171i	0.158729	+	0.274927i
$915$	−3.50805	−	5.27778i	−0.115973	−	0.174478i
$916$	2.54308	−	4.40475i	0.0840258	−	0.145537i
$917$	−66.9702			−2.21155
$918$	−10.1947	+	29.3312i	−0.336477	+	0.968074i
$919$	−40.6594			−1.34123			−0.670616	−	0.741805i	$-0.733970\pi$
$919$	−40.6594			−1.34123			−0.670616	+	0.741805i	$0.733970\pi$
$920$	−0.217761	+	0.377174i	−0.00717938	+	0.0124351i
$921$	31.3355	+	47.1435i	1.03254	+	1.55343i
$922$	8.31611	+	14.4039i	0.273877	+	0.474368i
$923$	12.0699	+	20.9057i	0.397285	+	0.688118i
$924$	33.6217	−	2.12196i	1.10607	−	0.0698073i
$925$	18.3857	−	31.8450i	0.604519	−	1.04706i
$926$	18.5916			0.610959
$927$	−37.8469	+	4.79635i	−1.24306	+	0.157533i
$928$	−3.54823			−0.116476
$929$	0.178966	−	0.309978i	0.00587167	−	0.0101700i	−0.863075	−	0.505076i	$-0.831464\pi$
$929$	0.178966	−	0.309978i	0.00587167	−	0.0101700i	0.868946	+	0.494906i	$0.164798\pi$
$930$	1.36643	−	2.75402i	0.0448070	−	0.0903079i
$931$	46.5871	+	80.6912i	1.52683	+	2.64455i
$932$	13.4093	+	23.2256i	0.439236	+	0.760778i
$933$	4.33829	−	8.74376i	0.142029	−	0.286258i
$934$	−0.353907	+	0.612984i	−0.0115802	+	0.0200575i
$935$	−10.9349			−0.357609
$936$	9.53719	−	1.20865i	0.311733	−	0.0395060i
$937$	47.0619			1.53744			0.768722	−	0.639583i	$-0.220893\pi$
$937$	47.0619			1.53744			0.768722	+	0.639583i	$0.220893\pi$
$938$	10.7160	−	18.5607i	0.349891	−	0.606029i
$939$	26.4622	−	1.67010i	0.863561	−	0.0545017i
$940$	2.05463	+	3.55872i	0.0670145	+	0.116073i
$941$	−9.59941	−	16.6267i	−0.312932	−	0.542014i	0.666064	−	0.745895i	$-0.267978\pi$
$941$	−9.59941	−	16.6267i	−0.312932	−	0.542014i	−0.978996	+	0.203881i	$0.934644\pi$
$942$	−9.17000	−	13.7961i	−0.298775	−	0.449500i
$943$	1.97990	−	3.42928i	0.0644743	−	0.111673i
$944$	2.12324			0.0691056
$945$	10.2900	−	1.96923i	0.334733	−	0.0640591i
$946$	−52.8059			−1.71687
$947$	27.6131	−	47.8272i	0.897304	−	1.55418i	0.0663762	−	0.997795i	$-0.478856\pi$
$947$	27.6131	−	47.8272i	0.897304	−	1.55418i	0.830927	−	0.556381i	$-0.187810\pi$
$948$	−6.56242	−	9.87301i	−0.213137	−	0.320660i
$949$	18.4647	+	31.9818i	0.599390	+	1.03817i
$950$	15.5278	+	26.8950i	0.503789	+	0.872588i
$951$	−53.7717	+	3.39368i	−1.74367	+	0.110048i
$952$	13.8330	−	23.9594i	0.448329	−	0.776529i
$953$	49.6992			1.60991			0.804957	−	0.593333i	$-0.202188\pi$
$953$	49.6992			1.60991			0.804957	+	0.593333i	$0.202188\pi$
$954$	1.29564	+	1.70554i	0.0419478	+	0.0552190i
$955$	10.3536			0.335033
$956$	7.40208	−	12.8208i	0.239400	−	0.414654i
$957$	11.4761	−	23.1299i	0.370969	−	0.747683i
$958$	20.8161	+	36.0546i	0.672538	+	1.16487i
$959$	43.5159	+	75.3718i	1.40520	+	2.43388i
$960$	0.335276	−	0.675744i	0.0108210	−	0.0218096i
$961$	7.19501	−	12.4621i	0.232097	−	0.402004i
$962$	24.4960			0.789784
$963$	8.61183	−	20.5094i	0.277512	−	0.660906i
$964$	27.5685			0.887921
$965$	−2.02073	+	3.50002i	−0.0650498	+	0.112669i
$966$	8.00257	−	0.505064i	0.257479	−	0.0162502i
$967$	−8.54366	−	14.7980i	−0.274745	−	0.475873i	0.695325	−	0.718695i	$-0.255260\pi$
$967$	−8.54366	−	14.7980i	−0.274745	−	0.475873i	−0.970071	+	0.242822i	$0.921927\pi$
$968$	3.32572	+	5.76031i	0.106893	+	0.185144i
$969$	−36.9915	−	55.6529i	−1.18834	−	1.78783i
$970$	1.64371	−	2.84700i	0.0527765	−	0.0914116i
$971$	42.9555			1.37851			0.689254	−	0.724520i	$-0.257938\pi$
$971$	42.9555			1.37851			0.689254	+	0.724520i	$0.257938\pi$
$972$	14.8207	−	4.83172i	0.475376	−	0.154977i
$973$	18.8193			0.603319
$974$	−8.05777	+	13.9565i	−0.258188	+	0.447194i
$975$	−14.7793	−	22.2352i	−0.473317	−	0.712095i
$976$	4.20052	+	7.27551i	0.134455	+	0.232883i
$977$	14.4870	+	25.0923i	0.463481	+	0.802773i	0.999132	−	0.0416666i	$-0.0132667\pi$
$977$	14.4870	+	25.0923i	0.463481	+	0.802773i	−0.535650	+	0.844440i	$0.679933\pi$
$978$	14.7756	−	0.932531i	0.472473	−	0.0298190i
$979$	22.7928	−	39.4783i	0.728462	−	1.26173i
$980$	−6.28550			−0.200783
$981$	17.2956	−	41.1902i	0.552207	−	1.31510i
$982$	−9.99262			−0.318877
$983$	−24.8332	+	43.0124i	−0.792056	+	1.37188i	0.132635	+	0.991165i	$0.457656\pi$
$983$	−24.8332	+	43.0124i	−0.792056	+	1.37188i	−0.924692	+	0.380717i	$0.875677\pi$
$984$	−3.04835	+	6.14390i	−0.0971778	+	0.195860i
$985$	−0.200682	−	0.347592i	−0.00639427	−	0.0110752i
$986$	−10.6022	−	18.3635i	−0.337642	−	0.584814i
$987$	33.6260	−	67.7728i	1.07033	−	2.15723i
$988$	−10.3442	+	17.9166i	−0.329092	+	0.570003i
$989$	−12.5688			−0.399663
$990$	3.32059	+	4.37114i	0.105535	+	0.138924i
$991$	−21.8471			−0.693997			−0.346998	−	0.937866i	$-0.612799\pi$
$991$	−21.8471			−0.693997			−0.346998	+	0.937866i	$0.612799\pi$
$992$	−2.03777	+	3.52952i	−0.0646992	+	0.112062i
$993$	48.7280	−	3.07536i	1.54634	−	0.0975934i
$994$	−17.4372	−	30.2021i	−0.553074	−	0.957953i
$995$	−2.10949	−	3.65375i	−0.0668755	−	0.115832i
$996$	6.85892	+	10.3191i	0.217333	+	0.326973i
$997$	−16.2651	+	28.1719i	−0.515120	+	0.892215i	0.484726	+	0.874666i	$0.338919\pi$
$997$	−16.2651	+	28.1719i	−0.515120	+	0.892215i	−0.999846	+	0.0175483i	$0.994414\pi$
$998$	−4.97132			−0.157364
$999$	39.0129	−	7.46604i	1.23431	−	0.236215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.d.277.2	yes	10
3.2	odd	2		1242.2.e.b.829.3		10
9.2	odd	6		3726.2.a.u.1.3		5
9.4	even	3	inner	414.2.e.d.139.2	✓	10
9.5	odd	6		1242.2.e.b.415.3		10
9.7	even	3		3726.2.a.r.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.2	✓	10	9.4	even	3	inner
414.2.e.d.277.2	yes	10	1.1	even	1	trivial
1242.2.e.b.415.3		10	9.5	odd	6
1242.2.e.b.829.3		10	3.2	odd	2
3726.2.a.r.1.3		5	9.7	even	3
3726.2.a.u.1.3		5	9.2	odd	6

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.958787 - 1.44247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.217761 + 0.377174i) q^{5} +(-1.72861 + 0.109097i) q^{6} +(2.31474 - 4.00925i) q^{7} -1.00000 q^{8} +(-1.16146 + 2.76605i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.958787 - 1.44247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.217761 + 0.377174i) q^{5} +(-1.72861 + 0.109097i) q^{6} +(2.31474 - 4.00925i) q^{7} -1.00000 q^{8} +(-1.16146 + 2.76605i) q^{9} +0.435523 q^{10} +(2.10068 - 3.63849i) q^{11} +(-0.769825 + 1.55157i) q^{12} +(1.60224 + 2.77517i) q^{13} +(-2.31474 - 4.00925i) q^{14} +(0.335276 - 0.675744i) q^{15} +(-0.500000 + 0.866025i) q^{16} -5.97604 q^{17} +(1.81474 + 2.38887i) q^{18} -6.45604 q^{19} +(0.217761 - 0.377174i) q^{20} +(-8.00257 + 0.505064i) q^{21} +(-2.10068 - 3.63849i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.958787 + 1.44247i) q^{24} +(2.40516 - 4.16586i) q^{25} +3.20449 q^{26} +(5.10354 - 0.976682i) q^{27} -4.62948 q^{28} +(-1.77412 + 3.07286i) q^{29} +(-0.417574 - 0.628230i) q^{30} +(2.03777 + 3.52952i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.26252 + 0.458358i) q^{33} +(-2.98802 + 5.17540i) q^{34} +2.01624 q^{35} +(2.97620 - 0.377174i) q^{36} +7.64429 q^{37} +(-3.22802 + 5.59110i) q^{38} +(2.46689 - 4.97199i) q^{39} +(-0.217761 - 0.377174i) q^{40} +(1.97990 + 3.42928i) q^{41} +(-3.56389 + 7.18296i) q^{42} +(6.28438 - 10.8849i) q^{43} -4.20136 q^{44} +(-1.29620 + 0.164268i) q^{45} -1.00000 q^{46} +(-4.71761 + 8.17113i) q^{47} +(1.72861 - 0.109097i) q^{48} +(-7.21604 - 12.4986i) q^{49} +(-2.40516 - 4.16586i) q^{50} +(5.72975 + 8.62028i) q^{51} +(1.60224 - 2.77517i) q^{52} +0.713953 q^{53} +(1.70594 - 4.90813i) q^{54} +1.82979 q^{55} +(-2.31474 + 4.00925i) q^{56} +(6.18997 + 9.31267i) q^{57} +(1.77412 + 3.07286i) q^{58} +(-1.06162 - 1.83878i) q^{59} +(-0.752850 + 0.0475144i) q^{60} +(4.20052 - 7.27551i) q^{61} +4.07554 q^{62} +(8.40130 + 11.0592i) q^{63} +1.00000 q^{64} +(-0.697814 + 1.20865i) q^{65} +(-3.23431 + 6.51871i) q^{66} +(2.31474 + 4.00925i) q^{67} +(2.98802 + 5.17540i) q^{68} +(-0.769825 + 1.55157i) q^{69} +(1.00812 - 1.74612i) q^{70} +7.53311 q^{71} +(1.16146 - 2.76605i) q^{72} +11.5243 q^{73} +(3.82214 - 6.62015i) q^{74} +(-8.31517 + 0.524793i) q^{75} +(3.22802 + 5.59110i) q^{76} +(-9.72506 - 16.8443i) q^{77} +(-3.07242 - 4.62239i) q^{78} +(-3.42225 + 5.92751i) q^{79} -0.435523 q^{80} +(-6.30204 - 6.42528i) q^{81} +3.95980 q^{82} +(3.57688 - 6.19533i) q^{83} +(4.43868 + 6.67790i) q^{84} +(-1.30135 - 2.25401i) q^{85} +(-6.28438 - 10.8849i) q^{86} +(6.13351 - 0.387103i) q^{87} +(-2.10068 + 3.63849i) q^{88} +10.8502 q^{89} +(-0.505841 + 1.20468i) q^{90} +14.8351 q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.13745 - 6.32348i) q^{93} +(4.71761 + 8.17113i) q^{94} +(-1.40588 - 2.43505i) q^{95} +(0.769825 - 1.55157i) q^{96} +(3.77412 - 6.53696i) q^{97} -14.4321 q^{98} +(7.62438 + 10.0365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more