LMFDB - Embedded newform 1190.2.ba.b.611.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(611,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.611"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.7
Character	$\chi$	$=$	1190.611
Dual form			1190.2.ba.b.781.7

$q$-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} +(-1.54039 + 0.889345i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.77869i q^{6} +(0.615368 + 2.57319i) q^{7} -1.00000 q^{8} +(0.0818691 - 0.141801i) q^{9} +(0.866025 - 0.500000i) q^{10} +(4.13329 - 2.38636i) q^{11} +(1.54039 + 0.889345i) q^{12} -2.35458 q^{13} +(2.53613 + 0.753672i) q^{14} -1.77869 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.849141 - 4.03472i) q^{17} +(-0.0818691 - 0.141801i) q^{18} +(-2.17101 + 3.76030i) q^{19} -1.00000i q^{20} +(-3.23636 - 3.41645i) q^{21} -4.77271i q^{22} +(3.99797 + 2.30823i) q^{23} +(1.54039 - 0.889345i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.17729 + 2.03913i) q^{26} -5.04483i q^{27} +(1.92077 - 1.81952i) q^{28} +10.3879i q^{29} +(-0.889345 + 1.54039i) q^{30} +(-8.16413 + 4.71356i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.24459 + 7.35184i) q^{33} +(-3.06960 - 2.75274i) q^{34} +(-0.753672 + 2.53613i) q^{35} -0.163738 q^{36} +(-3.72951 - 2.15323i) q^{37} +(2.17101 + 3.76030i) q^{38} +(3.62697 - 2.09403i) q^{39} +(-0.866025 - 0.500000i) q^{40} +11.6073i q^{41} +(-4.57691 + 1.09455i) q^{42} +2.92106 q^{43} +(-4.13329 - 2.38636i) q^{44} +(0.141801 - 0.0818691i) q^{45} +(3.99797 - 2.30823i) q^{46} +(4.95966 - 8.59039i) q^{47} -1.77869i q^{48} +(-6.24264 + 3.16692i) q^{49} +1.00000 q^{50} +(2.28025 + 6.97022i) q^{51} +(1.17729 + 2.03913i) q^{52} +(6.18762 + 10.7173i) q^{53} +(-4.36895 - 2.52242i) q^{54} +4.77271 q^{55} +(-0.615368 - 2.57319i) q^{56} -7.72310i q^{57} +(8.99621 + 5.19396i) q^{58} +(-0.925855 - 1.60363i) q^{59} +(0.889345 + 1.54039i) q^{60} +(3.26396 + 1.88445i) q^{61} +9.42712i q^{62} +(0.415262 + 0.123405i) q^{63} +1.00000 q^{64} +(-2.03913 - 1.17729i) q^{65} +(4.24459 + 7.35184i) q^{66} +(-1.37585 - 2.38305i) q^{67} +(-3.91874 + 1.28198i) q^{68} -8.21126 q^{69} +(1.81952 + 1.92077i) q^{70} +5.40325i q^{71} +(-0.0818691 + 0.141801i) q^{72} +(-1.09990 + 0.635025i) q^{73} +(-3.72951 + 2.15323i) q^{74} +(-1.54039 - 0.889345i) q^{75} +4.34202 q^{76} +(8.68405 + 9.16726i) q^{77} -4.18807i q^{78} +(9.34300 + 5.39419i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.73220 + 8.19641i) q^{81} +(10.0522 + 5.80365i) q^{82} -5.17610 q^{83} +(-1.34055 + 4.51100i) q^{84} +(2.75274 - 3.06960i) q^{85} +(1.46053 - 2.52971i) q^{86} +(-9.23845 - 16.0015i) q^{87} +(-4.13329 + 2.38636i) q^{88} +(-3.00381 + 5.20275i) q^{89} -0.163738i q^{90} +(-1.44893 - 6.05879i) q^{91} -4.61646i q^{92} +(8.38396 - 14.5214i) q^{93} +(-4.95966 - 8.59039i) q^{94} +(-3.76030 + 2.17101i) q^{95} +(-1.54039 - 0.889345i) q^{96} +1.53989i q^{97} +(-0.378686 + 6.98975i) q^{98} -0.781475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} + 24 q^{9} - 8 q^{15} - 24 q^{16} + 2 q^{17} - 24 q^{18} - 16 q^{19} - 12 q^{21} + 24 q^{25} - 4 q^{30} + 24 q^{32} + 36 q^{33} + 4 q^{34} - 4 q^{35} - 48 q^{36} + 16 q^{38}+ \cdots + 8 q^{98}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 + 24 * q^9 - 8 * q^15 - 24 * q^16 + 2 * q^17 - 24 * q^18 - 16 * q^19 - 12 * q^21 + 24 * q^25 - 4 * q^30 + 24 * q^32 + 36 * q^33 + 4 * q^34 - 4 * q^35 - 48 * q^36 + 16 * q^38 - 24 * q^42 + 8 * q^43 + 4 * q^47 + 4 * q^49 + 48 * q^50 + 16 * q^51 + 32 * q^53 - 8 * q^55 - 44 * q^59 + 4 * q^60 + 48 * q^64 - 36 * q^66 - 40 * q^67 + 2 * q^68 - 72 * q^69 - 8 * q^70 - 24 * q^72 + 32 * q^76 + 20 * q^77 - 24 * q^81 + 152 * q^83 - 12 * q^84 + 20 * q^85 + 4 * q^86 + 16 * q^87 - 16 * q^89 - 4 * q^93 - 4 * q^94 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1190\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.54039	+	0.889345i	−0.889345	+	0.513464i	−0.873728	−	0.486414i	$-0.838305\pi$
$3$	−1.54039	+	0.889345i	−0.889345	+	0.513464i	−0.0156168	+	0.999878i	$0.504971\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$			1.77869i			0.726147i
$7$	0.615368	+	2.57319i	0.232587	+	0.972576i
$7$	0.615368	+	2.57319i	0.232587	+	0.972576i
$8$	−1.00000			−0.353553
$9$	0.0818691	−	0.141801i	0.0272897	−	0.0472671i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	4.13329	−	2.38636i	1.24623	−	0.719513i	0.275878	−	0.961193i	$-0.411032\pi$
$11$	4.13329	−	2.38636i	1.24623	−	0.719513i	0.970356	+	0.241679i	$0.0776982\pi$
$12$	1.54039	+	0.889345i	0.444673	+	0.256732i
$13$	−2.35458			−0.653043			−0.326522	−	0.945190i	$-0.605877\pi$
$13$	−2.35458			−0.653043			−0.326522	+	0.945190i	$0.605877\pi$
$14$	2.53613	+	0.753672i	0.677810	+	0.201427i
$15$	−1.77869			−0.459256
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.849141	−	4.03472i	0.205947	−	0.978563i
$17$	0.849141	−	4.03472i	0.205947	−	0.978563i
$18$	−0.0818691	−	0.141801i	−0.0192967	−	0.0334229i
$19$	−2.17101	+	3.76030i	−0.498063	+	0.862671i	−0.999998	−	0.00223474i	$-0.999289\pi$
$19$	−2.17101	+	3.76030i	−0.498063	+	0.862671i	0.501934	+	0.864906i	$0.332622\pi$
$20$		−	1.00000i		−	0.223607i
$21$	−3.23636	−	3.41645i	−0.706233	−	0.745530i
$22$		−	4.77271i		−	1.01755i
$23$	3.99797	+	2.30823i	0.833635	+	0.481300i	0.855096	−	0.518470i	$-0.173498\pi$
$23$	3.99797	+	2.30823i	0.833635	+	0.481300i	−0.0214605	+	0.999770i	$0.506832\pi$
$24$	1.54039	−	0.889345i	0.314431	−	0.181537i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.17729	+	2.03913i	−0.230886	+	0.399906i
$27$		−	5.04483i		−	0.970878i
$28$	1.92077	−	1.81952i	0.362991	−	0.343857i
$29$			10.3879i			1.92899i	0.264101	+	0.964495i	$0.414925\pi$
$29$			10.3879i			1.92899i	−0.264101	+	0.964495i	$0.585075\pi$
$30$	−0.889345	+	1.54039i	−0.162371	+	0.281236i
$31$	−8.16413	+	4.71356i	−1.46632	+	0.846580i	−0.999291	−	0.0376612i	$-0.988009\pi$
$31$	−8.16413	+	4.71356i	−1.46632	+	0.846580i	−0.467030	+	0.884242i	$0.654676\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.24459	+	7.35184i	−0.738888	+	1.27979i
$34$	−3.06960	−	2.75274i	−0.526432	−	0.472091i
$35$	−0.753672	+	2.53613i	−0.127394	+	0.428685i
$36$	−0.163738			−0.0272897
$37$	−3.72951	−	2.15323i	−0.613128	−	0.353989i	0.161061	−	0.986944i	$-0.448508\pi$
$37$	−3.72951	−	2.15323i	−0.613128	−	0.353989i	−0.774189	+	0.632955i	$0.781842\pi$
$38$	2.17101	+	3.76030i	0.352184	+	0.610001i
$39$	3.62697	−	2.09403i	0.580781	−	0.335314i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$			11.6073i			1.81276i	0.422467	+	0.906378i	$0.361164\pi$
$41$			11.6073i			1.81276i	−0.422467	+	0.906378i	$0.638836\pi$
$42$	−4.57691	+	1.09455i	−0.706233	+	0.168893i
$43$	2.92106			0.445457			0.222729	−	0.974880i	$-0.428504\pi$
$43$	2.92106			0.445457			0.222729	+	0.974880i	$0.428504\pi$
$44$	−4.13329	−	2.38636i	−0.623117	−	0.359757i
$45$	0.141801	−	0.0818691i	0.0211385	−	0.0122043i
$46$	3.99797	−	2.30823i	0.589469	−	0.340330i
$47$	4.95966	−	8.59039i	0.723441	−	1.25304i	−0.236171	−	0.971711i	$-0.575893\pi$
$47$	4.95966	−	8.59039i	0.723441	−	1.25304i	0.959612	−	0.281325i	$-0.0907740\pi$
$48$		−	1.77869i		−	0.256732i
$49$	−6.24264	+	3.16692i	−0.891806	+	0.452418i
$50$	1.00000			0.141421
$51$	2.28025	+	6.97022i	0.319299	+	0.976027i
$52$	1.17729	+	2.03913i	0.163261	+	0.282776i
$53$	6.18762	+	10.7173i	0.849935	+	1.47213i	0.881266	+	0.472621i	$0.156692\pi$
$53$	6.18762	+	10.7173i	0.849935	+	1.47213i	−0.0313315	+	0.999509i	$0.509975\pi$
$54$	−4.36895	−	2.52242i	−0.594539	−	0.343257i
$55$	4.77271			0.643552
$56$	−0.615368	−	2.57319i	−0.0822321	−	0.343857i
$57$		−	7.72310i		−	1.02295i
$58$	8.99621	+	5.19396i	1.18126	+	0.682001i
$59$	−0.925855	−	1.60363i	−0.120536	−	0.208775i	0.799443	−	0.600742i	$-0.205128\pi$
$59$	−0.925855	−	1.60363i	−0.120536	−	0.208775i	−0.919979	+	0.391967i	$0.871795\pi$
$60$	0.889345	+	1.54039i	0.114814	+	0.198864i
$61$	3.26396	+	1.88445i	0.417908	+	0.241279i	0.694182	−	0.719800i	$-0.255766\pi$
$61$	3.26396	+	1.88445i	0.417908	+	0.241279i	−0.276274	+	0.961079i	$0.589100\pi$
$62$			9.42712i			1.19725i
$63$	0.415262	+	0.123405i	0.0523181	+	0.0155475i
$64$	1.00000			0.125000
$65$	−2.03913	−	1.17729i	−0.252922	−	0.146025i
$66$	4.24459	+	7.35184i	0.522473	+	0.904949i
$67$	−1.37585	−	2.38305i	−0.168087	−	0.291135i	0.769660	−	0.638454i	$-0.220426\pi$
$67$	−1.37585	−	2.38305i	−0.168087	−	0.291135i	−0.937747	+	0.347318i	$0.887092\pi$
$68$	−3.91874	+	1.28198i	−0.475217	+	0.155463i
$69$	−8.21126			−0.988519
$70$	1.81952	+	1.92077i	0.217474	+	0.229575i
$71$			5.40325i			0.641247i	0.947207	+	0.320624i	$0.103892\pi$
$71$			5.40325i			0.641247i	−0.947207	+	0.320624i	$0.896108\pi$
$72$	−0.0818691	+	0.141801i	−0.00964836	+	0.0167115i
$73$	−1.09990	+	0.635025i	−0.128733	+	0.0743240i	−0.562984	−	0.826468i	$-0.690347\pi$
$73$	−1.09990	+	0.635025i	−0.128733	+	0.0743240i	0.434251	+	0.900792i	$0.357013\pi$
$74$	−3.72951	+	2.15323i	−0.433547	+	0.250308i
$75$	−1.54039	−	0.889345i	−0.177869	−	0.102693i
$76$	4.34202			0.498063
$77$	8.68405	+	9.16726i	0.989639	+	1.04471i
$78$		−	4.18807i		−	0.474205i
$79$	9.34300	+	5.39419i	1.05117	+	0.606893i	0.922977	−	0.384856i	$-0.125749\pi$
$79$	9.34300	+	5.39419i	1.05117	+	0.606893i	0.128193	+	0.991749i	$0.459082\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	4.73220	+	8.19641i	0.525800	+	0.910713i
$82$	10.0522	+	5.80365i	1.11008	+	0.640906i
$83$	−5.17610			−0.568151			−0.284076	−	0.958802i	$-0.591687\pi$
$83$	−5.17610			−0.568151			−0.284076	+	0.958802i	$0.591687\pi$
$84$	−1.34055	+	4.51100i	−0.146266	+	0.492190i
$85$	2.75274	−	3.06960i	0.298576	−	0.332945i
$86$	1.46053	−	2.52971i	0.157493	−	0.272786i
$87$	−9.23845	−	16.0015i	−0.990466	−	1.71554i
$88$	−4.13329	+	2.38636i	−0.440610	+	0.254386i
$89$	−3.00381	+	5.20275i	−0.318403	+	0.551491i	−0.980155	−	0.198232i	$-0.936480\pi$
$89$	−3.00381	+	5.20275i	−0.318403	+	0.551491i	0.661752	+	0.749723i	$0.269813\pi$
$90$		−	0.163738i		−	0.0172595i
$91$	−1.44893	−	6.05879i	−0.151890	−	0.635134i
$92$		−	4.61646i		−	0.481300i
$93$	8.38396	−	14.5214i	0.869376	−	1.50580i
$94$	−4.95966	−	8.59039i	−0.511550	−	0.886031i
$95$	−3.76030	+	2.17101i	−0.385798	+	0.222741i
$96$	−1.54039	−	0.889345i	−0.157215	−	0.0907684i
$97$			1.53989i			0.156352i	0.996940	+	0.0781759i	$0.0249096\pi$
$97$			1.53989i			0.156352i	−0.996940	+	0.0781759i	$0.975090\pi$
$98$	−0.378686	+	6.98975i	−0.0382531	+	0.706071i
$99$		−	0.781475i		−	0.0785412i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.97519	−	3.42113i	−0.196539	−	0.340415i	0.750865	−	0.660455i	$-0.229637\pi$
$101$	−1.97519	−	3.42113i	−0.196539	−	0.340415i	−0.947404	+	0.320041i	$0.896303\pi$
$102$	7.17651	+	1.51036i	0.710581	+	0.149548i
$103$	−1.15790	+	2.00555i	−0.114092	+	0.197613i	−0.917416	−	0.397929i	$-0.869729\pi$
$103$	−1.15790	+	2.00555i	−0.114092	+	0.197613i	0.803325	+	0.595541i	$0.203062\pi$
$104$	2.35458			0.230886
$105$	−1.09455	−	4.57691i	−0.106817	−	0.446661i
$106$	12.3752			1.20199
$107$	3.52834	+	2.03709i	0.341098	+	0.196933i	0.660757	−	0.750600i	$-0.270235\pi$
$107$	3.52834	+	2.03709i	0.341098	+	0.196933i	−0.319660	+	0.947532i	$0.603569\pi$
$108$	−4.36895	+	2.52242i	−0.420403	+	0.242720i
$109$	13.6099	−	7.85771i	1.30360	−	0.752632i	0.322577	−	0.946543i	$-0.395451\pi$
$109$	13.6099	−	7.85771i	1.30360	−	0.752632i	0.981019	+	0.193912i	$0.0621175\pi$
$110$	2.38636	−	4.13329i	0.227530	−	0.394094i
$111$	7.65987			0.727043
$112$	−2.53613	−	0.753672i	−0.239642	−	0.0712153i
$113$			11.5980i			1.09105i	0.838096	+	0.545523i	$0.183669\pi$
$113$			11.5980i			1.09105i	−0.838096	+	0.545523i	$0.816331\pi$
$114$	−6.68840	−	3.86155i	−0.626426	−	0.361667i
$115$	2.30823	+	3.99797i	0.215244	+	0.372813i
$116$	8.99621	−	5.19396i	0.835277	−	0.482247i
$117$	−0.192767	+	0.333883i	−0.0178213	+	0.0308675i
$118$	−1.85171			−0.170464
$119$	10.9046	−	0.297835i	0.999627	−	0.0273025i
$120$	1.77869			0.162371
$121$	5.88939	−	10.2007i	0.535399	−	0.927338i
$122$	3.26396	−	1.88445i	0.295505	−	0.170610i
$123$	−10.3229	−	17.8798i	−0.930784	−	1.61217i
$124$	8.16413	+	4.71356i	0.733160	+	0.423290i
$125$			1.00000i			0.0894427i
$126$	0.314503	−	0.297925i	0.0280181	−	0.0265413i
$127$	−13.9116			−1.23446			−0.617228	−	0.786784i	$-0.711744\pi$
$127$	−13.9116			−1.23446			−0.617228	+	0.786784i	$0.711744\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.49957	+	2.59783i	−0.396165	+	0.228726i
$130$	−2.03913	+	1.17729i	−0.178843	+	0.103255i
$131$	−13.4849	−	7.78552i	−1.17818	−	0.680224i	−0.222589	−	0.974912i	$-0.571451\pi$
$131$	−13.4849	−	7.78552i	−1.17818	−	0.680224i	−0.955593	+	0.294688i	$0.904784\pi$
$132$	8.48917			0.738888
$133$	−11.0119	−	3.27246i	−0.954856	−	0.283758i
$134$	−2.75170			−0.237711
$135$	2.52242	−	4.36895i	0.217095	−	0.376019i
$136$	−0.849141	+	4.03472i	−0.0728132	+	0.345974i
$137$	0.135260	+	0.234277i	0.0115560	+	0.0200156i	0.871746	−	0.489959i	$-0.162988\pi$
$137$	0.135260	+	0.234277i	0.0115560	+	0.0200156i	−0.860190	+	0.509974i	$0.829655\pi$
$138$	−4.10563	+	7.11116i	−0.349494	+	0.605342i
$139$			16.9375i			1.43662i	0.695725	+	0.718308i	$0.255083\pi$
$139$			16.9375i			1.43662i	−0.695725	+	0.718308i	$0.744917\pi$
$140$	2.57319	−	0.615368i	0.217474	−	0.0520081i
$141$			17.6434i			1.48584i
$142$	4.67935	+	2.70162i	0.392682	+	0.226715i
$143$	−9.73216	+	5.61887i	−0.813844	+	0.469873i
$144$	0.0818691	+	0.141801i	0.00682242	+	0.0118168i
$145$	−5.19396	+	8.99621i	−0.431335	+	0.747095i
$146$			1.27005i			0.105110i
$147$	6.79962	−	10.4302i	0.560823	−	0.860265i
$148$			4.30647i			0.353989i
$149$	7.03050	−	12.1772i	0.575961	−	0.997594i	−0.419975	−	0.907536i	$-0.637961\pi$
$149$	7.03050	−	12.1772i	0.575961	−	0.997594i	0.995936	−	0.0900586i	$-0.0287054\pi$
$150$	−1.54039	+	0.889345i	−0.125772	+	0.0726147i
$151$	2.94380	+	5.09881i	0.239563	+	0.414935i	0.960589	−	0.277973i	$-0.0896625\pi$
$151$	2.94380	+	5.09881i	0.239563	+	0.414935i	−0.721026	+	0.692908i	$0.756329\pi$
$152$	2.17101	−	3.76030i	0.176092	−	0.305000i
$153$	−0.502610	−	0.450728i	−0.0406336	−	0.0364392i
$154$	12.2811	−	2.93698i	0.989640	−	0.236668i
$155$	−9.42712			−0.757205
$156$	−3.62697	−	2.09403i	−0.290390	−	0.167657i
$157$	11.5405	+	19.9887i	0.921032	+	1.59527i	0.797822	+	0.602893i	$0.205985\pi$
$157$	11.5405	+	19.9887i	0.921032	+	1.59527i	0.123210	+	0.992381i	$0.460681\pi$
$158$	9.34300	−	5.39419i	0.743290	−	0.429138i
$159$	−19.0627	−	11.0059i	−1.51177	−	0.872821i
$160$			1.00000i			0.0790569i
$161$	−3.47930	+	11.7080i	−0.274207	+	0.922717i
$162$	9.46440			0.743594
$163$	−18.5347	−	10.7010i	−1.45175	−	0.838167i	−0.453167	−	0.891426i	$-0.649706\pi$
$163$	−18.5347	−	10.7010i	−1.45175	−	0.838167i	−0.998581	+	0.0532586i	$0.983039\pi$
$164$	10.0522	−	5.80365i	0.784947	−	0.453189i
$165$	−7.35184	+	4.24459i	−0.572340	+	0.330441i
$166$	−2.58805	+	4.48264i	−0.200872	+	0.347920i
$167$		−	11.1036i		−	0.859219i	−0.903015	−	0.429610i	$-0.858651\pi$
$167$		−	11.1036i		−	0.859219i	0.903015	−	0.429610i	$-0.141349\pi$
$168$	3.23636	+	3.41645i	0.249691	+	0.263585i
$169$	−7.45595			−0.573535
$170$	−1.28198	−	3.91874i	−0.0983235	−	0.300554i
$171$	0.355477	+	0.615704i	0.0271840	+	0.0470840i
$172$	−1.46053	−	2.52971i	−0.111364	−	0.192889i
$173$	−10.3407	−	5.97020i	−0.786188	−	0.453906i	0.0524311	−	0.998625i	$-0.483303\pi$
$173$	−10.3407	−	5.97020i	−0.786188	−	0.453906i	−0.838619	+	0.544719i	$0.816636\pi$
$174$	−18.4769			−1.40073
$175$	−1.92077	+	1.81952i	−0.145196	+	0.137543i
$176$			4.77271i			0.359757i
$177$	2.85236	+	1.64681i	0.214396	+	0.123782i
$178$	3.00381	+	5.20275i	0.225145	+	0.389963i
$179$	−11.4362	−	19.8081i	−0.854785	−	1.48053i	−0.876845	−	0.480774i	$-0.840356\pi$
$179$	−11.4362	−	19.8081i	−0.854785	−	1.48053i	0.0220601	−	0.999757i	$-0.492977\pi$
$180$	−0.141801	−	0.0818691i	−0.0105692	−	0.00610216i
$181$		−	6.90846i		−	0.513502i	−0.966478	−	0.256751i	$-0.917348\pi$
$181$		−	6.90846i		−	0.513502i	0.966478	−	0.256751i	$-0.0826520\pi$
$182$	−5.97153	−	1.77458i	−0.442639	−	0.131541i
$183$	−6.70370			−0.495552
$184$	−3.99797	−	2.30823i	−0.294735	−	0.170165i
$185$	−2.15323	−	3.72951i	−0.158309	−	0.274199i
$186$	−8.38396	−	14.5214i	−0.614742	−	1.06476i
$187$	−6.11853	−	18.7030i	−0.447431	−	1.36770i
$188$	−9.91933			−0.723441
$189$	12.9813	−	3.10443i	0.944252	−	0.225814i
$190$			4.34202i			0.315003i
$191$	7.70175	−	13.3398i	0.557279	−	0.965236i	−0.440443	−	0.897780i	$-0.645179\pi$
$191$	7.70175	−	13.3398i	0.557279	−	0.965236i	0.997722	−	0.0674552i	$-0.0214880\pi$
$192$	−1.54039	+	0.889345i	−0.111168	+	0.0641829i
$193$	11.5001	−	6.63961i	0.827799	−	0.477930i	−0.0252996	−	0.999680i	$-0.508054\pi$
$193$	11.5001	−	6.63961i	0.827799	−	0.477930i	0.853098	+	0.521750i	$0.174721\pi$
$194$	1.33358	+	0.769943i	0.0957455	+	0.0552787i
$195$	4.18807			0.299914
$196$	5.86396	+	3.82283i	0.418854	+	0.273059i
$197$		−	8.01432i		−	0.570997i	−0.958379	−	0.285498i	$-0.907841\pi$
$197$		−	8.01432i		−	0.570997i	0.958379	−	0.285498i	$-0.0921591\pi$
$198$	−0.676777	−	0.390737i	−0.0480965	−	0.0277685i
$199$	16.5775	−	9.57103i	1.17515	−	0.678472i	0.220261	−	0.975441i	$-0.429309\pi$
$199$	16.5775	−	9.57103i	1.17515	−	0.678472i	0.954887	+	0.296969i	$0.0959757\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	4.23870	+	2.44721i	0.298975	+	0.172613i
$202$	−3.95038			−0.277948
$203$	−26.7301	+	6.39240i	−1.87609	+	0.448659i
$204$	4.89627	−	5.45986i	0.342807	−	0.382267i
$205$	−5.80365	+	10.0522i	−0.405345	+	0.702078i
$206$	1.15790	+	2.00555i	0.0806750	+	0.139733i
$207$	0.654621	−	0.377945i	0.0454993	−	0.0262690i
$208$	1.17729	−	2.03913i	0.0816304	−	0.141388i
$209$			20.7232i			1.43345i
$210$	−4.51100	−	1.34055i	−0.311288	−	0.0925066i
$211$			6.22412i			0.428486i	0.976780	+	0.214243i	$0.0687285\pi$
$211$			6.22412i			0.428486i	−0.976780	+	0.214243i	$0.931271\pi$
$212$	6.18762	−	10.7173i	0.424967	−	0.736065i
$213$	−4.80535	−	8.32311i	−0.329257	−	0.570290i
$214$	3.52834	−	2.03709i	0.241192	−	0.139252i
$215$	2.52971	+	1.46053i	0.172525	+	0.0996073i
$216$			5.04483i			0.343257i
$217$	−17.1528	−	18.1073i	−1.16441	−	1.22920i
$218$		−	15.7154i		−	1.06438i
$219$	1.12951	−	1.95637i	0.0763254	−	0.132199i
$220$	−2.38636	−	4.13329i	−0.160888	−	0.278666i
$221$	−1.99937	+	9.50007i	−0.134492	+	0.639044i
$222$	3.82993	−	6.63364i	0.257048	−	0.445221i
$223$	20.8712			1.39764			0.698819	−	0.715299i	$-0.253709\pi$
$223$	20.8712			1.39764			0.698819	+	0.715299i	$0.253709\pi$
$224$	−1.92077	+	1.81952i	−0.128337	+	0.121572i
$225$	0.163738			0.0109159
$226$	10.0441	+	5.79899i	0.668126	+	0.385743i
$227$	25.0969	−	14.4897i	1.66574	−	0.961714i	0.695842	−	0.718194i	$-0.255031\pi$
$227$	25.0969	−	14.4897i	1.66574	−	0.961714i	0.969896	−	0.243520i	$-0.0783022\pi$
$228$	−6.68840	+	3.86155i	−0.442950	+	0.255737i
$229$	−5.49875	+	9.52412i	−0.363368	+	0.629372i	−0.988513	−	0.151137i	$-0.951707\pi$
$229$	−5.49875	+	9.52412i	−0.363368	+	0.629372i	0.625145	+	0.780509i	$0.285040\pi$
$230$	4.61646			0.304401
$231$	−21.5297	−	6.39805i	−1.41655	−	0.420961i
$232$		−	10.3879i		−	0.682001i
$233$	0.0276286	+	0.0159514i	0.00181001	+	0.00104501i	0.500905	−	0.865502i	$-0.333001\pi$
$233$	0.0276286	+	0.0159514i	0.00181001	+	0.00104501i	−0.499095	+	0.866547i	$0.666334\pi$
$234$	0.192767	+	0.333883i	0.0126016	+	0.0218266i
$235$	8.59039	−	4.95966i	0.560375	−	0.323533i
$236$	−0.925855	+	1.60363i	−0.0602680	+	0.104387i
$237$	−19.1892			−1.24647
$238$	5.19439	−	9.59262i	0.336702	−	0.621797i
$239$	−1.47166			−0.0951938			−0.0475969	−	0.998867i	$-0.515156\pi$
$239$	−1.47166			−0.0951938			−0.0475969	+	0.998867i	$0.515156\pi$
$240$	0.889345	−	1.54039i	0.0574070	−	0.0994318i
$241$	−14.9165	+	8.61202i	−0.960853	+	0.554749i	−0.896436	−	0.443174i	$-0.853852\pi$
$241$	−14.9165	+	8.61202i	−0.960853	+	0.554749i	−0.0644177	+	0.997923i	$0.520519\pi$
$242$	−5.88939	−	10.2007i	−0.378584	−	0.655727i
$243$	−1.47203	−	0.849875i	−0.0944305	−	0.0545195i
$244$		−	3.76890i		−	0.241279i
$245$	−6.98975	−	0.378686i	−0.446559	−	0.0241934i
$246$	−20.6458			−1.31633
$247$	5.11181	−	8.85392i	0.325257	−	0.563361i
$248$	8.16413	−	4.71356i	0.518423	−	0.299311i
$249$	7.97322	−	4.60334i	0.505283	−	0.291725i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	17.4019			1.09840			0.549200	−	0.835691i	$-0.314933\pi$
$251$	17.4019			1.09840			0.549200	+	0.835691i	$0.314933\pi$
$252$	−0.100759	−	0.421330i	−0.00634724	−	0.0265413i
$253$	22.0330			1.38521
$254$	−6.95581	+	12.0478i	−0.436446	+	0.755947i
$255$	−1.51036	+	7.17651i	−0.0945823	+	0.449411i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.93985	−	8.55608i	0.308140	−	0.533714i	−0.669816	−	0.742527i	$-0.733627\pi$
$257$	4.93985	−	8.55608i	0.308140	−	0.533714i	0.977955	+	0.208814i	$0.0669603\pi$
$258$			5.19566i			0.323468i
$259$	3.24566	−	10.9218i	0.201676	−	0.678646i
$260$			2.35458i			0.146025i
$261$	1.47302	+	0.850450i	0.0911778	+	0.0526415i
$262$	−13.4849	+	7.78552i	−0.833101	+	0.480991i
$263$	−13.4940	−	23.3723i	−0.832074	−	1.44120i	−0.896390	−	0.443265i	$-0.853820\pi$
$263$	−13.4940	−	23.3723i	−0.832074	−	1.44120i	0.0643161	−	0.997930i	$-0.479513\pi$
$264$	4.24459	−	7.35184i	0.261236	−	0.452475i
$265$			12.3752i			0.760205i
$266$	−8.34000	+	7.90039i	−0.511358	+	0.484404i
$267$		−	10.6857i		−	0.653954i
$268$	−1.37585	+	2.38305i	−0.0840436	+	0.145568i
$269$	−7.59333	+	4.38401i	−0.462973	+	0.267298i	−0.713294	−	0.700865i	$-0.752797\pi$
$269$	−7.59333	+	4.38401i	−0.462973	+	0.267298i	0.250320	+	0.968163i	$0.419464\pi$
$270$	−2.52242	−	4.36895i	−0.153509	−	0.265886i
$271$	10.3503	−	17.9273i	0.628738	−	1.08901i	−0.359068	−	0.933311i	$-0.616905\pi$
$271$	10.3503	−	17.9273i	0.628738	−	1.08901i	0.987805	−	0.155694i	$-0.0497613\pi$
$272$	3.06960	+	2.75274i	0.186122	+	0.166909i
$273$	7.62028	+	8.04430i	0.461200	+	0.486863i
$274$	0.270519			0.0163427
$275$	4.13329	+	2.38636i	0.249247	+	0.143903i
$276$	4.10563	+	7.11116i	0.247130	+	0.428041i
$277$	20.9959	−	12.1220i	1.26152	−	0.728341i	0.288155	−	0.957584i	$-0.406958\pi$
$277$	20.9959	−	12.1220i	1.26152	−	0.728341i	0.973369	+	0.229243i	$0.0736249\pi$
$278$	14.6683	+	8.46873i	0.879745	+	0.507921i
$279$			1.54358i			0.0924117i
$280$	0.753672	−	2.53613i	0.0450405	−	0.151563i
$281$	−9.51575			−0.567662			−0.283831	−	0.958874i	$-0.591605\pi$
$281$	−9.51575			−0.567662			−0.283831	+	0.958874i	$0.591605\pi$
$282$	15.2796	+	8.82170i	0.909889	+	0.525325i
$283$	−0.0903301	+	0.0521521i	−0.00536957	+	0.00310012i	−0.502682	−	0.864471i	$-0.667653\pi$
$283$	−0.0903301	+	0.0521521i	−0.00536957	+	0.00310012i	0.497313	+	0.867571i	$0.334320\pi$
$284$	4.67935	−	2.70162i	0.277668	−	0.160312i
$285$	3.86155	−	6.68840i	0.228738	−	0.396187i
$286$			11.2377i			0.664501i
$287$	−29.8678	+	7.14277i	−1.76304	+	0.421624i
$288$	0.163738			0.00964836
$289$	−15.5579	−	6.85209i	−0.915172	−	0.403064i
$290$	5.19396	+	8.99621i	0.305000	+	0.528276i
$291$	−1.36949	−	2.37203i	−0.0802809	−	0.139051i
$292$	1.09990	+	0.635025i	0.0643665	+	0.0371620i
$293$	−1.78458			−0.104256			−0.0521282	−	0.998640i	$-0.516600\pi$
$293$	−1.78458			−0.104256			−0.0521282	+	0.998640i	$0.516600\pi$
$294$	−5.63297	−	11.1037i	−0.328522	−	0.647583i
$295$		−	1.85171i		−	0.107811i
$296$	3.72951	+	2.15323i	0.216773	+	0.125154i
$297$	−12.0388	−	20.8517i	−0.698560	−	1.20994i
$298$	−7.03050	−	12.1772i	−0.407266	−	0.705406i
$299$	−9.41355	−	5.43492i	−0.544400	−	0.314309i
$300$			1.77869i			0.102693i
$301$	1.79753	+	7.51645i	0.103608	+	0.433241i
$302$	5.88760			0.338793
$303$	6.08512	+	3.51325i	0.349581	+	0.201831i
$304$	−2.17101	−	3.76030i	−0.124516	−	0.215668i
$305$	1.88445	+	3.26396i	0.107903	+	0.186894i
$306$	−0.641647	+	0.209909i	−0.0366805	+	0.0119997i
$307$	14.9643			0.854058			0.427029	−	0.904238i	$-0.359560\pi$
$307$	14.9643			0.854058			0.427029	+	0.904238i	$0.359560\pi$
$308$	3.59706	−	12.1042i	0.204961	−	0.689703i
$309$		−	4.11911i		−	0.234328i
$310$	−4.71356	+	8.16413i	−0.267712	+	0.463691i
$311$	−6.92002	+	3.99528i	−0.392399	+	0.226551i	−0.683199	−	0.730232i	$-0.739412\pi$
$311$	−6.92002	+	3.99528i	−0.392399	+	0.226551i	0.290800	+	0.956784i	$0.406078\pi$
$312$	−3.62697	+	2.09403i	−0.205337	+	0.118551i
$313$	−2.74575	−	1.58526i	−0.155199	−	0.0896042i	0.420389	−	0.907344i	$-0.361894\pi$
$313$	−2.74575	−	1.58526i	−0.155199	−	0.0896042i	−0.575588	+	0.817740i	$0.695227\pi$
$314$	23.0810			1.30254
$315$	0.297925	+	0.314503i	0.0167862	+	0.0177202i
$316$		−	10.7884i		−	0.606893i
$317$	19.4805	+	11.2471i	1.09414	+	0.631700i	0.934675	−	0.355504i	$-0.115691\pi$
$317$	19.4805	+	11.2471i	1.09414	+	0.631700i	0.159462	+	0.987204i	$0.449024\pi$
$318$	−19.0627	+	11.0059i	−1.06898	+	0.617178i
$319$	24.7893	+	42.9363i	1.38793	+	2.40397i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−7.24670			−0.404471
$322$	8.39975	+	8.86715i	0.468100	+	0.494147i
$323$	13.3282	+	11.9524i	0.741604	+	0.665051i
$324$	4.73220	−	8.19641i	0.262900	−	0.455356i
$325$	−1.17729	−	2.03913i	−0.0653043	−	0.113110i
$326$	−18.5347	+	10.7010i	−1.02654	+	0.592674i
$327$	−13.9764	+	24.2079i	−0.772898	+	1.33870i
$328$		−	11.6073i		−	0.640906i
$329$	25.1567	+	7.47592i	1.38694	+	0.412161i
$330$			8.48917i			0.467314i
$331$	13.3731	−	23.1629i	0.735053	−	1.27315i	−0.219647	−	0.975579i	$-0.570491\pi$
$331$	13.3731	−	23.1629i	0.735053	−	1.27315i	0.954700	−	0.297570i	$-0.0961761\pi$
$332$	2.58805	+	4.48264i	0.142038	+	0.246017i
$333$	−0.610663	+	0.352566i	−0.0334641	+	0.0193205i
$334$	−9.61596	−	5.55178i	−0.526162	−	0.303780i
$335$		−	2.75170i		−	0.150342i
$336$	4.57691	−	1.09455i	0.249691	−	0.0597126i
$337$			5.89736i			0.321250i	0.987016	+	0.160625i	$0.0513509\pi$
$337$			5.89736i			0.321250i	−0.987016	+	0.160625i	$0.948649\pi$
$338$	−3.72798	+	6.45704i	−0.202775	+	0.351217i
$339$	−10.3146	−	17.8654i	−0.560212	−	0.970316i
$340$	−4.03472	−	0.849141i	−0.218813	−	0.0460511i
$341$	−22.4965	+	38.9650i	−1.21825	+	2.11007i
$342$	0.710954			0.0384440
$343$	−11.9906	−	14.1147i	−0.647433	−	0.762122i
$344$	−2.92106			−0.157493
$345$	−7.11116	−	4.10563i	−0.382852	−	0.221040i
$346$	−10.3407	+	5.97020i	−0.555919	+	0.320960i
$347$	−11.9454	+	6.89670i	−0.641265	+	0.370234i	−0.785102	−	0.619367i	$-0.787389\pi$
$347$	−11.9454	+	6.89670i	−0.641265	+	0.370234i	0.143837	+	0.989601i	$0.454056\pi$
$348$	−9.23845	+	16.0015i	−0.495233	+	0.857769i
$349$	23.0580			1.23426			0.617132	−	0.786860i	$-0.288294\pi$
$349$	23.0580			1.23426			0.617132	+	0.786860i	$0.288294\pi$
$350$	0.615368	+	2.57319i	0.0328928	+	0.137543i
$351$			11.8785i			0.634025i
$352$	4.13329	+	2.38636i	0.220305	+	0.127193i
$353$	11.5548	+	20.0134i	0.614998	+	1.06521i	0.990385	+	0.138339i	$0.0441764\pi$
$353$	11.5548	+	20.0134i	0.614998	+	1.06521i	−0.375387	+	0.926868i	$0.622490\pi$
$354$	2.85236	−	1.64681i	0.151601	−	0.0875269i
$355$	−2.70162	+	4.67935i	−0.143387	+	0.248354i
$356$	6.00762			0.318403
$357$	−16.5325	+	10.1568i	−0.874995	+	0.537553i
$358$	−22.8725			−1.20885
$359$	3.82371	−	6.62287i	0.201808	−	0.349542i	−0.747303	−	0.664483i	$-0.768652\pi$
$359$	3.82371	−	6.62287i	0.201808	−	0.349542i	0.949111	+	0.314942i	$0.101985\pi$
$360$	−0.141801	+	0.0818691i	−0.00747359	+	0.00431488i
$361$	0.0734481	+	0.127216i	0.00386569	+	0.00669557i
$362$	−5.98290	−	3.45423i	−0.314455	−	0.181550i
$363$			20.9508i			1.09963i
$364$	−4.52260	+	4.28421i	−0.237049	+	0.224554i
$365$	−1.27005			−0.0664774
$366$	−3.35185	+	5.80558i	−0.175204	+	0.303462i
$367$	−24.0073	+	13.8606i	−1.25317	+	0.723519i	−0.971738	−	0.236061i	$-0.924143\pi$
$367$	−24.0073	+	13.8606i	−1.25317	+	0.723519i	−0.281434	+	0.959581i	$0.590810\pi$
$368$	−3.99797	+	2.30823i	−0.208409	+	0.120325i
$369$	1.64593	+	0.950279i	0.0856838	+	0.0494696i
$370$	−4.30647			−0.223883
$371$	−23.7699	+	22.5170i	−1.23407	+	1.16902i
$372$	−16.7679			−0.869376
$373$	2.33190	−	4.03897i	0.120741	−	0.209130i	−0.799319	−	0.600907i	$-0.794806\pi$
$373$	2.33190	−	4.03897i	0.120741	−	0.209130i	0.920060	+	0.391777i	$0.128140\pi$
$374$	−19.2566	−	4.05271i	−0.995733	−	0.209560i
$375$	−0.889345	−	1.54039i	−0.0459256	−	0.0795454i
$376$	−4.95966	+	8.59039i	−0.255775	+	0.443015i
$377$		−	24.4592i		−	1.25971i
$378$	3.80215	−	12.7944i	0.195561	−	0.658071i
$379$		−	11.8505i		−	0.608720i	−0.952557	−	0.304360i	$-0.901557\pi$
$379$		−	11.8505i		−	0.608720i	0.952557	−	0.304360i	$-0.0984425\pi$
$380$	3.76030	+	2.17101i	0.192899	+	0.111370i
$381$	21.4293	−	12.3722i	1.09786	−	0.633848i
$382$	−7.70175	−	13.3398i	−0.394056	−	0.682525i
$383$	−3.25497	+	5.63777i	−0.166321	+	0.288076i	−0.937124	−	0.348998i	$-0.886522\pi$
$383$	−3.25497	+	5.63777i	−0.166321	+	0.288076i	0.770803	+	0.637074i	$0.219855\pi$
$384$			1.77869i			0.0907684i
$385$	2.93698	+	12.2811i	0.149682	+	0.625903i
$386$		−	13.2792i		−	0.675895i
$387$	0.239144	−	0.414210i	0.0121564	−	0.0210555i
$388$	1.33358	−	0.769943i	0.0677023	−	0.0390879i
$389$	−1.76046	−	3.04920i	−0.0892587	−	0.154601i	0.817939	−	0.575305i	$-0.195116\pi$
$389$	−1.76046	−	3.04920i	−0.0892587	−	0.154601i	−0.907198	+	0.420704i	$0.861783\pi$
$390$	2.09403	−	3.62697i	0.106036	−	0.183659i
$391$	12.7079	−	14.1707i	0.642667	−	0.716643i
$392$	6.24264	−	3.16692i	0.315301	−	0.159954i
$393$	27.6961			1.39708
$394$	−6.94061	−	4.00716i	−0.349663	−	0.201878i
$395$	5.39419	+	9.34300i	0.271411	+	0.470098i
$396$	−0.676777	+	0.390737i	−0.0340093	+	0.0196353i
$397$	10.9018	+	6.29414i	0.547145	+	0.315894i	0.747970	−	0.663733i	$-0.231029\pi$
$397$	10.9018	+	6.29414i	0.547145	+	0.315894i	−0.200825	+	0.979627i	$0.564362\pi$
$398$		−	19.1421i		−	0.959505i
$399$	19.8730	−	4.75255i	0.994896	−	0.237925i
$400$	−1.00000			−0.0500000
$401$	3.91483	+	2.26023i	0.195497	+	0.112870i	0.594553	−	0.804056i	$-0.297329\pi$
$401$	3.91483	+	2.26023i	0.195497	+	0.112870i	−0.399056	+	0.916926i	$0.630662\pi$
$402$	4.23870	−	2.44721i	0.211407	−	0.122056i
$403$	19.2231	−	11.0985i	0.957570	−	0.552853i
$404$	−1.97519	+	3.42113i	−0.0982693	+	0.170207i
$405$			9.46440i			0.470290i
$406$	−7.82909	+	26.3452i	−0.388551	+	1.30749i
$407$	−20.5535			−1.01880
$408$	−2.28025	−	6.97022i	−0.112889	−	0.345077i
$409$	−7.05852	−	12.2257i	−0.349021	−	0.604523i	0.637055	−	0.770819i	$-0.280153\pi$
$409$	−7.05852	−	12.2257i	−0.349021	−	0.604523i	−0.986076	+	0.166296i	$0.946819\pi$
$410$	5.80365	+	10.0522i	0.286622	+	0.496444i
$411$	−0.416705	−	0.240585i	−0.0205546	−	0.0118672i
$412$	2.31581			0.114092
$413$	3.55670	−	3.36923i	0.175014	−	0.165789i
$414$		−	0.755891i		−	0.0371500i
$415$	−4.48264	−	2.58805i	−0.220044	−	0.127042i
$416$	−1.17729	−	2.03913i	−0.0577214	−	0.0999764i
$417$	−15.0632	−	26.0903i	−0.737650	−	1.27765i
$418$	17.9468	+	10.3616i	0.877807	+	0.506802i
$419$			30.9819i			1.51357i	0.653666	+	0.756783i	$0.273230\pi$
$419$			30.9819i			1.51357i	−0.653666	+	0.756783i	$0.726770\pi$
$420$	−3.41645	+	3.23636i	−0.166706	+	0.157918i
$421$	−2.89695			−0.141189			−0.0705943	−	0.997505i	$-0.522490\pi$
$421$	−2.89695			−0.141189			−0.0705943	+	0.997505i	$0.522490\pi$
$422$	5.39025	+	3.11206i	0.262393	+	0.151493i
$423$	−0.812086	−	1.40657i	−0.0394850	−	0.0683900i
$424$	−6.18762	−	10.7173i	−0.300497	−	0.520476i
$425$	3.91874	−	1.28198i	0.190087	−	0.0621853i
$426$	−9.61070			−0.465640
$427$	−2.84051	+	9.55844i	−0.137462	+	0.462565i
$428$		−	4.07418i		−	0.196933i
$429$	9.99422	−	17.3105i	0.482526	−	0.835759i
$430$	2.52971	−	1.46053i	0.121993	−	0.0704330i
$431$	9.87431	−	5.70093i	0.475629	−	0.274604i	−0.242964	−	0.970035i	$-0.578120\pi$
$431$	9.87431	−	5.70093i	0.475629	−	0.274604i	0.718593	+	0.695431i	$0.244786\pi$
$432$	4.36895	+	2.52242i	0.210201	+	0.121360i
$433$	−0.208732			−0.0100310			−0.00501550	−	0.999987i	$-0.501596\pi$
$433$	−0.208732			−0.0100310			−0.00501550	+	0.999987i	$0.501596\pi$
$434$	−24.2578	+	5.80115i	−1.16441	+	0.278464i
$435$		−	18.4769i		−	0.885900i
$436$	−13.6099	−	7.85771i	−0.651798	−	0.376316i
$437$	−17.3593	+	10.0224i	−0.830406	+	0.479435i
$438$	−1.12951	−	1.95637i	−0.0539702	−	0.0934791i
$439$	−7.65138	−	4.41752i	−0.365180	−	0.210837i	0.306171	−	0.951977i	$-0.400952\pi$
$439$	−7.65138	−	4.41752i	−0.365180	−	0.210837i	−0.671351	+	0.741140i	$0.734286\pi$
$440$	−4.77271			−0.227530
$441$	−0.0620054	+	1.14449i	−0.00295264	+	0.0544994i
$442$	7.22762	+	6.48154i	0.343783	+	0.308295i
$443$	6.40902	−	11.1007i	0.304502	−	0.527412i	−0.672649	−	0.739962i	$-0.734843\pi$
$443$	6.40902	−	11.1007i	0.304502	−	0.527412i	0.977150	+	0.212550i	$0.0681768\pi$
$444$	−3.82993	−	6.63364i	−0.181761	−	0.314819i
$445$	−5.20275	+	3.00381i	−0.246634	+	0.142394i
$446$	10.4356	−	18.0750i	0.494139	−	0.855875i
$447$			25.0102i			1.18294i
$448$	0.615368	+	2.57319i	0.0290734	+	0.121572i
$449$			12.9961i			0.613324i	0.951818	+	0.306662i	$0.0992121\pi$
$449$			12.9961i			0.613324i	−0.951818	+	0.306662i	$0.900788\pi$
$450$	0.0818691	−	0.141801i	0.00385934	−	0.00668458i
$451$	27.6992	+	47.9764i	1.30430	+	2.25912i
$452$	10.0441	−	5.79899i	0.472437	−	0.272761i
$453$	−9.06920	−	5.23611i	−0.426108	−	0.246014i
$454$		−	28.9794i		−	1.36007i
$455$	1.77458	−	5.97153i	0.0831936	−	0.279950i
$456$			7.72310i			0.361667i
$457$	−12.9872	+	22.4944i	−0.607514	+	1.05225i	0.384134	+	0.923277i	$0.374500\pi$
$457$	−12.9872	+	22.4944i	−0.607514	+	1.05225i	−0.991649	+	0.128968i	$0.958833\pi$
$458$	5.49875	+	9.52412i	0.256940	+	0.445033i
$459$	−20.3545	−	4.28377i	−0.950066	−	0.199949i
$460$	2.30823	−	3.99797i	0.107622	−	0.186407i
$461$	−2.33357			−0.108685			−0.0543426	−	0.998522i	$-0.517306\pi$
$461$	−2.33357			−0.108685			−0.0543426	+	0.998522i	$0.517306\pi$
$462$	−16.3057	+	15.4462i	−0.758611	+	0.718624i
$463$	−22.7404			−1.05684			−0.528418	−	0.848984i	$-0.677215\pi$
$463$	−22.7404			−1.05684			−0.528418	+	0.848984i	$0.677215\pi$
$464$	−8.99621	−	5.19396i	−0.417639	−	0.241124i
$465$	14.5214	−	8.38396i	0.673416	−	0.388797i
$466$	0.0276286	−	0.0159514i	0.00127987	−	0.000738934i
$467$	5.02465	−	8.70295i	0.232513	−	0.402725i	−0.726034	−	0.687659i	$-0.758638\pi$
$467$	5.02465	−	8.70295i	0.232513	−	0.402725i	0.958547	+	0.284934i	$0.0919718\pi$
$468$	0.385535			0.0178213
$469$	5.28538	−	5.00678i	0.244056	−	0.231192i
$470$		−	9.91933i		−	0.457544i
$471$	−35.5537	−	20.5270i	−1.63823	−	0.945832i
$472$	0.925855	+	1.60363i	0.0426159	+	0.0738130i
$473$	12.0736	−	6.97069i	0.555144	−	0.320512i
$474$	−9.59459	+	16.6183i	−0.440694	+	0.763304i
$475$	−4.34202			−0.199225
$476$	−5.71026	−	9.29478i	−0.261729	−	0.426026i
$477$	2.02630			0.0927778
$478$	−0.735830	+	1.27450i	−0.0336561	+	0.0582940i
$479$	24.0777	−	13.9012i	1.10014	−	0.635164i	0.163879	−	0.986480i	$-0.447599\pi$
$479$	24.0777	−	13.9012i	1.10014	−	0.635164i	0.936257	+	0.351317i	$0.114266\pi$
$480$	−0.889345	−	1.54039i	−0.0405929	−	0.0703089i
$481$	8.78143	+	5.06996i	0.400399	+	0.231170i
$482$			17.2240i			0.784533i
$483$	−5.05295	−	21.1291i	−0.229917	−	0.961409i
$484$	−11.7788			−0.535399
$485$	−0.769943	+	1.33358i	−0.0349613	+	0.0605548i
$486$	−1.47203	+	0.849875i	−0.0667725	+	0.0385511i
$487$	−6.28357	+	3.62782i	−0.284736	+	0.164392i	−0.635565	−	0.772047i	$-0.719233\pi$
$487$	−6.28357	+	3.62782i	−0.284736	+	0.164392i	0.350830	+	0.936439i	$0.385900\pi$
$488$	−3.26396	−	1.88445i	−0.147753	−	0.0853050i
$489$	38.0675			1.72147
$490$	−3.82283	+	5.86396i	−0.172698	+	0.264907i
$491$	21.5976			0.974687			0.487344	−	0.873210i	$-0.337966\pi$
$491$	21.5976			0.974687			0.487344	+	0.873210i	$0.337966\pi$
$492$	−10.3229	+	17.8798i	−0.465392	+	0.806083i
$493$	41.9124	+	8.82082i	1.88764	+	0.397270i
$494$	−5.11181	−	8.85392i	−0.229991	−	0.398357i
$495$	0.390737	−	0.676777i	0.0175623	−	0.0304189i
$496$		−	9.42712i		−	0.423290i
$497$	−13.9036	+	3.32499i	−0.623661	+	0.149146i
$498$		−	9.20669i		−	0.412561i
$499$	26.9982	+	15.5874i	1.20860	+	0.697788i	0.962454	−	0.271444i	$-0.0875012\pi$
$499$	26.9982	+	15.5874i	1.20860	+	0.697788i	0.246150	+	0.969232i	$0.420835\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	9.87489	+	17.1038i	0.441178	+	0.764142i
$502$	8.70096	−	15.0705i	0.388343	−	0.672629i
$503$			20.3968i			0.909450i	0.890632	+	0.454725i	$0.150262\pi$
$503$			20.3968i			0.909450i	−0.890632	+	0.454725i	$0.849738\pi$
$504$	−0.415262	−	0.123405i	−0.0184972	−	0.00549689i
$505$		−	3.95038i		−	0.175789i
$506$	11.0165	−	19.0812i	0.489744	−	0.848262i
$507$	11.4851	−	6.63091i	0.510070	−	0.294489i
$508$	6.95581	+	12.0478i	0.308614	+	0.534535i
$509$	−6.99834	+	12.1215i	−0.310196	+	0.537275i	−0.978405	−	0.206699i	$-0.933728\pi$
$509$	−6.99834	+	12.1215i	−0.310196	+	0.537275i	0.668209	+	0.743974i	$0.267061\pi$
$510$	5.45986	+	4.89627i	0.241767	+	0.216810i
$511$	−2.31088	−	2.43947i	−0.102227	−	0.107916i
$512$	−1.00000			−0.0441942
$513$	18.9701	+	10.9524i	0.837549	+	0.483559i
$514$	−4.93985	−	8.55608i	−0.217888	−	0.377392i
$515$	−2.00555	+	1.15790i	−0.0883751	+	0.0510234i
$516$	4.49957	+	2.59783i	0.198083	+	0.114363i
$517$		−	47.3421i		−	2.08210i
$518$	−7.83571	−	8.27172i	−0.344281	−	0.363438i
$519$	21.2383			0.932256
$520$	2.03913	+	1.17729i	0.0894216	+	0.0516276i
$521$	11.0179	−	6.36120i	0.482704	−	0.278689i	−0.238839	−	0.971059i	$-0.576767\pi$
$521$	11.0179	−	6.36120i	0.482704	−	0.278689i	0.721543	+	0.692370i	$0.243433\pi$
$522$	1.47302	−	0.850450i	0.0644724	−	0.0372232i
$523$	19.8778	−	34.4294i	0.869197	−	1.50549i	0.00637867	−	0.999980i	$-0.497970\pi$
$523$	19.8778	−	34.4294i	0.869197	−	1.50549i	0.862818	−	0.505514i	$-0.168697\pi$
$524$			15.5710i			0.680224i
$525$	1.34055	−	4.51100i	0.0585063	−	0.196876i
$526$	−26.9880			−1.17673
$527$	12.0854	+	36.9424i	0.526448	+	1.60924i
$528$	−4.24459	−	7.35184i	−0.184722	−	0.319948i
$529$	−0.844135	−	1.46209i	−0.0367015	−	0.0635689i
$530$	10.7173	+	6.18762i	0.465528	+	0.268773i
$531$	−0.303196			−0.0131576
$532$	2.67194	+	11.1728i	0.115843	+	0.484404i
$533$		−	27.3303i		−	1.18381i
$534$	−9.25409	−	5.34285i	−0.400463	−	0.231208i
$535$	2.03709	+	3.52834i	0.0880710	+	0.152543i
$536$	1.37585	+	2.38305i	0.0594278	+	0.102932i
$537$	35.2326	+	20.3415i	1.52040	+	0.877802i
$538$			8.76802i			0.378016i
$539$	−18.2452	+	27.9870i	−0.785879	+	1.20548i
$540$	−5.04483			−0.217095
$541$	19.6297	+	11.3332i	0.843945	+	0.487252i	0.858603	−	0.512641i	$-0.171333\pi$
$541$	19.6297	+	11.3332i	0.843945	+	0.487252i	−0.0146583	+	0.999893i	$0.504666\pi$
$542$	−10.3503	−	17.9273i	−0.444585	−	0.770043i
$543$	6.14401	+	10.6417i	0.263665	+	0.456680i
$544$	3.91874	−	1.28198i	0.168015	−	0.0549645i
$545$	15.7154			0.673174
$546$	10.7767	−	2.57720i	0.461200	−	0.110294i
$547$			6.18369i			0.264396i	0.991223	+	0.132198i	$0.0422034\pi$
$547$			6.18369i			0.264396i	−0.991223	+	0.132198i	$0.957797\pi$
$548$	0.135260	−	0.234277i	0.00577801	−	0.0100078i
$549$	0.534435	−	0.308556i	0.0228091	−	0.0131689i
$550$	4.13329	−	2.38636i	0.176244	−	0.101755i
$551$	−39.0617	−	22.5523i	−1.66408	−	0.960759i
$552$	8.21126			0.349494
$553$	−8.13089	+	27.3608i	−0.345761	+	1.16350i
$554$		−	24.2440i		−	1.03003i
$555$	6.63364	+	3.82993i	0.281582	+	0.162572i
$556$	14.6683	−	8.46873i	0.622073	−	0.359154i
$557$	−21.9787	−	38.0683i	−0.931268	−	1.61300i	−0.781157	−	0.624334i	$-0.785370\pi$
$557$	−21.9787	−	38.0683i	−0.931268	−	1.61300i	−0.150111	−	0.988669i	$-0.547963\pi$
$558$	1.33678	+	0.771789i	0.0565904	+	0.0326725i
$559$	−6.87787			−0.290903
$560$	−1.81952	−	1.92077i	−0.0768888	−	0.0811672i
$561$	26.0584	+	23.3685i	1.10018	+	0.986617i
$562$	−4.75787	+	8.24088i	−0.200699	+	0.347621i
$563$	−14.3747	−	24.8977i	−0.605821	−	1.04931i	−0.991921	−	0.126856i	$-0.959511\pi$
$563$	−14.3747	−	24.8977i	−0.605821	−	1.04931i	0.386100	−	0.922457i	$-0.373822\pi$
$564$	15.2796	−	8.82170i	0.643389	−	0.371461i
$565$	−5.79899	+	10.0441i	−0.243965	+	0.422560i
$566$			0.104304i			0.00438423i
$567$	−18.1789	+	17.2207i	−0.763442	+	0.723201i
$568$		−	5.40325i		−	0.226715i
$569$	−9.24818	+	16.0183i	−0.387704	+	0.671523i	−0.992140	−	0.125131i	$-0.960065\pi$
$569$	−9.24818	+	16.0183i	−0.387704	+	0.671523i	0.604437	+	0.796653i	$0.293398\pi$
$570$	−3.86155	−	6.68840i	−0.161743	−	0.280146i
$571$	−2.55627	+	1.47586i	−0.106977	+	0.0617630i	−0.552534	−	0.833491i	$-0.686339\pi$
$571$	−2.55627	+	1.47586i	−0.106977	+	0.0617630i	0.445557	+	0.895254i	$0.353006\pi$
$572$	9.73216	+	5.61887i	0.406922	+	0.234937i
$573$			27.3981i			1.14457i
$574$	−8.74810	+	29.4377i	−0.365139	+	1.22871i
$575$			4.61646i			0.192520i
$576$	0.0818691	−	0.141801i	0.00341121	−	0.00590839i
$577$	−0.934037	−	1.61780i	−0.0388845	−	0.0673499i	0.845928	−	0.533297i	$-0.179047\pi$
$577$	−0.934037	−	1.61780i	−0.0388845	−	0.0673499i	−0.884813	+	0.465947i	$0.845714\pi$
$578$	−13.7130	+	10.0475i	−0.570387	+	0.417921i
$579$	−11.8098	+	20.4552i	−0.490799	+	0.850089i
$580$	10.3879			0.431335
$581$	−3.18521	−	13.3191i	−0.132145	−	0.552570i
$582$	−2.73898			−0.113534
$583$	51.1504	+	29.5317i	2.11843	+	1.22308i
$584$	1.09990	−	0.635025i	0.0455140	−	0.0262775i
$585$	−0.333883	+	0.192767i	−0.0138043	+	0.00796994i
$586$	−0.892291	+	1.54549i	−0.0368602	+	0.0638438i
$587$	14.5353			0.599937			0.299969	−	0.953949i	$-0.403024\pi$
$587$	14.5353			0.599937			0.299969	+	0.953949i	$0.403024\pi$
$588$	−12.4326	−	0.673565i	−0.512712	−	0.0277774i
$589$		−	40.9327i		−	1.68660i
$590$	−1.60363	−	0.925855i	−0.0660203	−	0.0381169i
$591$	7.12750	+	12.3452i	0.293186	+	0.507813i
$592$	3.72951	−	2.15323i	0.153282	−	0.0884973i
$593$	−21.3342	+	36.9518i	−0.876089	+	1.51743i	−0.0204908	+	0.999790i	$0.506523\pi$
$593$	−21.3342	+	36.9518i	−0.876089	+	1.51743i	−0.855598	+	0.517641i	$0.826810\pi$
$594$	−24.0775			−0.987913
$595$	9.59262	+	5.19439i	0.393259	+	0.212949i
$596$	−14.0610			−0.575961
$597$	−17.0239	+	29.4863i	−0.696742	+	1.20679i
$598$	−9.41355	+	5.43492i	−0.384949	+	0.222250i
$599$	18.7100	+	32.4066i	0.764469	+	1.32410i	0.940527	+	0.339719i	$0.110332\pi$
$599$	18.7100	+	32.4066i	0.764469	+	1.32410i	−0.176058	+	0.984380i	$0.556335\pi$
$600$	1.54039	+	0.889345i	0.0628862	+	0.0363074i
$601$		−	32.4691i		−	1.32444i	−0.749308	−	0.662222i	$-0.769614\pi$
$601$		−	32.4691i		−	1.32444i	0.749308	−	0.662222i	$-0.230386\pi$
$602$	7.40820	+	2.20152i	0.301936	+	0.0897272i
$603$	−0.450559			−0.0183482
$604$	2.94380	−	5.09881i	0.119781	−	0.207468i
$605$	10.2007	−	5.88939i	0.414718	−	0.239438i
$606$	6.08512	−	3.51325i	0.247191	−	0.142716i
$607$	−33.4932	−	19.3373i	−1.35945	−	0.784878i	−0.369899	−	0.929072i	$-0.620608\pi$
$607$	−33.4932	−	19.3373i	−1.35945	−	0.784878i	−0.989550	+	0.144194i	$0.953941\pi$
$608$	−4.34202			−0.176092
$609$	35.4898	−	33.6191i	1.43812	−	1.36232i
$610$	3.76890			0.152598
$611$	−11.6779	+	20.2268i	−0.472438	+	0.818287i
$612$	−0.139037	+	0.660637i	−0.00562023	+	0.0267047i
$613$	−2.75306	−	4.76843i	−0.111195	−	0.192595i	0.805057	−	0.593197i	$-0.202134\pi$
$613$	−2.75306	−	4.76843i	−0.111195	−	0.192595i	−0.916252	+	0.400602i	$0.868801\pi$
$614$	7.48215	−	12.9595i	0.301955	−	0.523002i
$615$		−	20.6458i		−	0.832519i
$616$	−8.68405	−	9.16726i	−0.349890	−	0.369360i
$617$		−	40.6609i		−	1.63695i	−0.574544	−	0.818473i	$-0.694821\pi$
$617$		−	40.6609i		−	1.63695i	0.574544	−	0.818473i	$-0.305179\pi$
$618$	−3.56725	−	2.05955i	−0.143496	−	0.0828474i
$619$	29.6281	−	17.1058i	1.19086	−	0.687541i	0.232355	−	0.972631i	$-0.425357\pi$
$619$	29.6281	−	17.1058i	1.19086	−	0.687541i	0.958501	+	0.285091i	$0.0920237\pi$
$620$	4.71356	+	8.16413i	0.189301	+	0.327879i
$621$	11.6446	−	20.1691i	0.467283	−	0.809358i
$622$			7.99056i			0.320392i
$623$	−15.2361	−	4.52778i	−0.610423	−	0.181402i
$624$			4.18807i			0.167657i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.74575	+	1.58526i	−0.109742	+	0.0633597i
$627$	−18.4301	−	31.9218i	−0.736026	−	1.27483i
$628$	11.5405	−	19.9887i	0.460516	−	0.797637i
$629$	−11.8546	+	13.2191i	−0.472673	+	0.527081i
$630$	0.421330	−	0.100759i	0.0167862	−	0.00401434i
$631$	27.2632			1.08533			0.542665	−	0.839949i	$-0.317415\pi$
$631$	27.2632			1.08533			0.542665	+	0.839949i	$0.317415\pi$
$632$	−9.34300	−	5.39419i	−0.371645	−	0.214569i
$633$	−5.53539	−	9.58758i	−0.220012	−	0.381072i
$634$	19.4805	−	11.2471i	0.773671	−	0.446679i
$635$	−12.0478	−	6.95581i	−0.478103	−	0.276033i
$636$			22.0117i			0.872821i
$637$	14.6988	−	7.45677i	0.582388	−	0.295448i
$638$	49.5786			1.96284
$639$	0.766188	+	0.442359i	0.0303099	+	0.0174994i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	16.6110	−	9.59037i	0.656095	−	0.378797i	−0.134692	−	0.990887i	$-0.543005\pi$
$641$	16.6110	−	9.59037i	0.656095	−	0.378797i	0.790788	+	0.612091i	$0.209671\pi$
$642$	−3.62335	+	6.27582i	−0.143002	+	0.247687i
$643$		−	31.9113i		−	1.25846i	−0.777220	−	0.629229i	$-0.783371\pi$
$643$		−	31.9113i		−	1.25846i	0.777220	−	0.629229i	$-0.216629\pi$
$644$	11.8790	−	2.84083i	0.468100	−	0.111944i
$645$	−5.19566			−0.204579
$646$	17.0152	−	5.56639i	0.669455	−	0.219007i
$647$	4.24126	+	7.34608i	0.166741	+	0.288804i	0.937272	−	0.348598i	$-0.113342\pi$
$647$	4.24126	+	7.34608i	0.166741	+	0.288804i	−0.770531	+	0.637403i	$0.780009\pi$
$648$	−4.73220	−	8.19641i	−0.185898	−	0.321986i
$649$	−7.65366	−	4.41884i	−0.300432	−	0.173455i
$650$	−2.35458			−0.0923542
$651$	42.5257	+	12.6375i	1.66671	+	0.495303i
$652$			21.4020i			0.838167i
$653$	39.7007	+	22.9212i	1.55361	+	0.896976i	0.997844	+	0.0656360i	$0.0209076\pi$
$653$	39.7007	+	22.9212i	1.55361	+	0.896976i	0.555764	+	0.831340i	$0.312426\pi$
$654$	13.9764	+	24.2079i	0.546521	+	0.946603i
$655$	−7.78552	−	13.4849i	−0.304205	−	0.526899i
$656$	−10.0522	−	5.80365i	−0.392473	−	0.226595i
$657$			0.207956i			0.00811312i
$658$	19.0527	−	18.0484i	0.742752	−	0.703601i
$659$	22.3507			0.870660			0.435330	−	0.900271i	$-0.356632\pi$
$659$	22.3507			0.870660			0.435330	+	0.900271i	$0.356632\pi$
$660$	7.35184	+	4.24459i	0.286170	+	0.165220i
$661$	−16.0686	−	27.8316i	−0.624996	−	1.08253i	−0.988542	−	0.150949i	$-0.951767\pi$
$661$	−16.0686	−	27.8316i	−0.624996	−	1.08253i	0.363545	−	0.931577i	$-0.381566\pi$
$662$	−13.3731	−	23.1629i	−0.519761	−	0.900252i
$663$	−5.36903	−	16.4119i	−0.208516	−	0.637387i
$664$	5.17610			0.200872
$665$	−7.90039	−	8.34000i	−0.306364	−	0.323411i
$666$			0.705133i			0.0273233i
$667$	−23.9777	+	41.5307i	−0.928422	+	1.60807i
$668$	−9.61596	+	5.55178i	−0.372053	+	0.214805i
$669$	−32.1498	+	18.5617i	−1.24298	+	0.717636i
$670$	−2.38305	−	1.37585i	−0.0920651	−	0.0531538i
$671$	17.9879			0.694414
$672$	1.34055	−	4.51100i	0.0517128	−	0.174015i
$673$			31.9832i			1.23286i	0.787410	+	0.616430i	$0.211422\pi$
$673$			31.9832i			1.23286i	−0.787410	+	0.616430i	$0.788578\pi$
$674$	5.10726	+	2.94868i	0.196724	+	0.113579i
$675$	4.36895	−	2.52242i	0.168161	−	0.0970878i
$676$	3.72798	+	6.45704i	0.143384	+	0.248348i
$677$	−42.6839	−	24.6435i	−1.64047	−	0.947128i	−0.980665	−	0.195695i	$-0.937304\pi$
$677$	−42.6839	−	24.6435i	−1.64047	−	0.947128i	−0.659809	−	0.751433i	$-0.729363\pi$
$678$	−20.6292			−0.792260
$679$	−3.96242	+	0.947597i	−0.152064	+	0.0363654i
$680$	−2.75274	+	3.06960i	−0.105563	+	0.117714i
$681$	−25.7727	+	44.6396i	−0.987611	+	1.71059i
$682$	22.4965	+	38.9650i	0.861434	+	1.49205i
$683$	34.2130	−	19.7529i	1.30913	−	0.755824i	0.327175	−	0.944964i	$-0.393903\pi$
$683$	34.2130	−	19.7529i	1.30913	−	0.755824i	0.981950	+	0.189140i	$0.0605699\pi$
$684$	0.355477	−	0.615704i	0.0135920	−	0.0235420i
$685$			0.270519i			0.0103360i
$686$	−18.2190	+	3.32684i	−0.695605	+	0.127019i
$687$		−	19.5612i		−	0.746305i
$688$	−1.46053	+	2.52971i	−0.0556822	+	0.0964443i
$689$	−14.5692	−	25.2347i	−0.555044	−	0.961364i
$690$	−7.11116	+	4.10563i	−0.270717	+	0.156299i
$691$	5.49552	+	3.17284i	0.209060	+	0.120701i	0.600874	−	0.799344i	$-0.294819\pi$
$691$	5.49552	+	3.17284i	0.209060	+	0.120701i	−0.391815	+	0.920044i	$0.628153\pi$
$692$			11.9404i			0.453906i
$693$	2.01089	−	0.480895i	0.0763872	−	0.0182677i
$694$			13.7934i			0.523590i
$695$	−8.46873	+	14.6683i	−0.321237	+	0.556399i
$696$	9.23845	+	16.0015i	0.350183	+	0.606534i
$697$	46.8322	+	9.85624i	1.77390	+	0.373332i
$698$	11.5290	−	19.9688i	0.436378	−	0.755829i
$699$	−0.0567452			−0.00214630
$700$	2.53613	+	0.753672i	0.0958569	+	0.0284861i
$701$	−44.2699			−1.67205			−0.836026	−	0.548690i	$-0.815127\pi$
$701$	−44.2699			−1.67205			−0.836026	+	0.548690i	$0.815127\pi$
$702$	10.2870	+	5.93923i	0.388260	+	0.224162i
$703$	16.1936	−	9.34937i	0.610753	−	0.352618i
$704$	4.13329	−	2.38636i	0.155779	−	0.0899392i
$705$	−8.82170	+	15.2796i	−0.332245	+	0.575464i
$706$	23.1095			0.869738
$707$	7.58775	−	7.18779i	0.285367	−	0.270325i
$708$		−	3.29362i		−	0.123782i
$709$	−15.8066	−	9.12596i	−0.593630	−	0.342733i	0.172901	−	0.984939i	$-0.444686\pi$
$709$	−15.8066	−	9.12596i	−0.593630	−	0.342733i	−0.766532	+	0.642207i	$0.778019\pi$
$710$	2.70162	+	4.67935i	0.101390	+	0.175613i
$711$	1.52981	−	0.883234i	0.0573722	−	0.0331239i
$712$	3.00381	−	5.20275i	0.112573	−	0.194981i
$713$	−43.5200			−1.62983
$714$	0.529756	+	19.3960i	0.0198256	+	0.725876i
$715$	−11.2377			−0.420267
$716$	−11.4362	+	19.8081i	−0.427392	+	0.740265i
$717$	2.26693	−	1.30881i	0.0846601	−	0.0488785i
$718$	−3.82371	−	6.62287i	−0.142700	−	0.247163i
$719$	21.9903	+	12.6961i	0.820100	+	0.473485i	0.850451	−	0.526054i	$-0.176329\pi$
$719$	21.9903	+	12.6961i	0.820100	+	0.473485i	−0.0303506	+	0.999539i	$0.509662\pi$
$720$			0.163738i			0.00610216i
$721$	−5.87320	−	1.74536i	−0.218730	−	0.0650006i
$722$	0.146896			0.00546691
$723$	15.3181	−	26.5317i	0.569687	−	0.986726i
$724$	−5.98290	+	3.45423i	−0.222353	+	0.128376i
$725$	−8.99621	+	5.19396i	−0.334111	+	0.192899i
$726$	18.1439	+	10.4754i	0.673384	+	0.388778i
$727$	10.6851			0.396288			0.198144	−	0.980173i	$-0.436509\pi$
$727$	10.6851			0.396288			0.198144	+	0.980173i	$0.436509\pi$
$728$	1.44893	+	6.05879i	0.0537011	+	0.224554i
$729$	−25.3699			−0.939625
$730$	−0.635025	+	1.09990i	−0.0235033	+	0.0407090i
$731$	2.48039	−	11.7857i	0.0917406	−	0.435908i
$732$	3.35185	+	5.80558i	0.123888	+	0.214580i
$733$	12.1790	−	21.0946i	0.449840	−	0.779146i	−0.548535	−	0.836127i	$-0.684814\pi$
$733$	12.1790	−	21.0946i	0.449840	−	0.779146i	0.998375	+	0.0569818i	$0.0181477\pi$
$734$			27.7213i			1.02321i
$735$	11.1037	−	5.63297i	0.409567	−	0.207775i
$736$			4.61646i			0.170165i
$737$	−11.3736	−	6.56655i	−0.418952	−	0.241882i
$738$	1.64593	−	0.950279i	0.0605876	−	0.0349803i
$739$	−7.16790	−	12.4152i	−0.263676	−	0.456700i	0.703540	−	0.710655i	$-0.251602\pi$
$739$	−7.16790	−	12.4152i	−0.263676	−	0.456700i	−0.967216	+	0.253956i	$0.918268\pi$
$740$	−2.15323	+	3.72951i	−0.0791544	+	0.137099i
$741$			18.1847i			0.668030i
$742$	7.61533	+	31.8439i	0.279567	+	1.16902i
$743$			16.3945i			0.601456i	0.953710	+	0.300728i	$0.0972297\pi$
$743$			16.3945i			0.601456i	−0.953710	+	0.300728i	$0.902770\pi$
$744$	−8.38396	+	14.5214i	−0.307371	+	0.532382i
$745$	12.1772	−	7.03050i	0.446138	−	0.257578i
$746$	−2.33190	−	4.03897i	−0.0853770	−	0.147877i
$747$	−0.423763	+	0.733979i	−0.0155047	+	0.0268549i
$748$	−13.1380	+	14.6503i	−0.480374	+	0.535668i
$749$	−3.07059	+	10.3327i	−0.112197	+	0.377547i
$750$	−1.77869			−0.0649486
$751$	−5.33116	−	3.07794i	−0.194537	−	0.112316i	0.399568	−	0.916704i	$-0.369160\pi$
$751$	−5.33116	−	3.07794i	−0.194537	−	0.112316i	−0.594105	+	0.804388i	$0.702493\pi$
$752$	4.95966	+	8.59039i	0.180860	+	0.313259i
$753$	−26.8057	+	15.4763i	−0.976856	+	0.563988i
$754$	−21.1823	−	12.2296i	−0.771414	−	0.445376i
$755$			5.88760i			0.214272i
$756$	−9.17918	−	9.68994i	−0.333843	−	0.352420i
$757$	41.9229			1.52371			0.761857	−	0.647745i	$-0.224288\pi$
$757$	41.9229			1.52371			0.761857	+	0.647745i	$0.224288\pi$
$758$	−10.2628	−	5.92525i	−0.372763	−	0.215215i
$759$	−33.9395	+	19.5950i	−1.23193	+	0.711253i
$760$	3.76030	−	2.17101i	0.136400	−	0.0787507i
$761$	−18.8631	+	32.6718i	−0.683787	+	1.18435i	0.290030	+	0.957018i	$0.406335\pi$
$761$	−18.8631	+	32.6718i	−0.683787	+	1.18435i	−0.973816	+	0.227336i	$0.926999\pi$
$762$		−	24.7445i		−	0.896397i
$763$	28.5945	+	30.1856i	1.03519	+	1.09279i
$764$	−15.4035			−0.557279
$765$	−0.209909	−	0.641647i	−0.00758929	−	0.0231988i
$766$	3.25497	+	5.63777i	0.117607	+	0.203701i
$767$	2.18000	+	3.77587i	0.0787153	+	0.136339i
$768$	1.54039	+	0.889345i	0.0555841	+	0.0320915i
$769$	13.8400			0.499084			0.249542	−	0.968364i	$-0.419720\pi$
$769$	13.8400			0.499084			0.249542	+	0.968364i	$0.419720\pi$
$770$	12.1042	+	3.59706i	0.436207	+	0.129629i
$771$			17.5729i			0.632874i
$772$	−11.5001	−	6.63961i	−0.413899	−	0.238965i
$773$	−5.16547	−	8.94686i	−0.185789	−	0.321796i	0.758053	−	0.652193i	$-0.226151\pi$
$773$	−5.16547	−	8.94686i	−0.185789	−	0.321796i	−0.943842	+	0.330397i	$0.892817\pi$
$774$	−0.239144	−	0.414210i	−0.00859587	−	0.0148885i
$775$	−8.16413	−	4.71356i	−0.293264	−	0.169316i
$776$		−	1.53989i		−	0.0552787i
$777$	4.71364	+	19.7103i	0.169101	+	0.707104i
$778$	−3.52091			−0.126231
$779$	−43.6469	−	25.1996i	−1.56381	−	0.902868i
$780$	−2.09403	−	3.62697i	−0.0749784	−	0.129866i
$781$	12.8941	+	22.3332i	0.461386	+	0.799144i
$782$	−5.91822	−	18.0907i	−0.211635	−	0.646923i
$783$	52.4053			1.87281
$784$	0.378686	−	6.98975i	0.0135245	−	0.249634i
$785$			23.0810i			0.823796i
$786$	13.8480	−	23.9855i	0.493943	−	0.855534i
$787$	−23.9547	+	13.8302i	−0.853892	+	0.492995i	−0.861962	−	0.506973i	$-0.830764\pi$
$787$	−23.9547	+	13.8302i	−0.853892	+	0.492995i	0.00807016	+	0.999967i	$0.497431\pi$
$788$	−6.94061	+	4.00716i	−0.247249	+	0.142749i
$789$	41.5720	+	24.0016i	1.48000	+	0.854480i
$790$	10.7884			0.383833
$791$	−29.8438	+	7.13702i	−1.06112	+	0.253763i
$792$			0.781475i			0.0277685i
$793$	−7.68526	−	4.43709i	−0.272912	−	0.157566i
$794$	10.9018	−	6.29414i	0.386890	−	0.223371i
$795$	−11.0059	−	19.0627i	−0.390337	−	0.676084i
$796$	−16.5775	−	9.57103i	−0.587574	−	0.339236i
$797$	20.8404			0.738206			0.369103	−	0.929388i	$-0.379665\pi$
$797$	20.8404			0.738206			0.369103	+	0.929388i	$0.379665\pi$
$798$	5.82068	−	19.5868i	0.206050	−	0.693366i
$799$	−30.4483	−	27.3053i	−1.07719	−	0.965992i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	0.491838	+	0.851889i	0.0173783	+	0.0301000i
$802$	3.91483	−	2.26023i	0.138237	−	0.0798113i
$803$	−3.03079	+	5.24948i	−0.106954	+	0.185250i
$804$		−	4.89443i		−	0.172613i
$805$	−8.86715	+	8.39975i	−0.312526	+	0.296052i
$806$		−	22.1969i		−	0.781853i
$807$	7.79779	−	13.5062i	0.274495	−	0.475440i
$808$	1.97519	+	3.42113i	0.0694869	+	0.120355i
$809$	−41.7676	+	24.1145i	−1.46847	+	0.847822i	−0.999376	−	0.0353265i	$-0.988753\pi$
$809$	−41.7676	+	24.1145i	−1.46847	+	0.847822i	−0.469094	+	0.883148i	$0.655420\pi$
$810$	8.19641	+	4.73220i	0.287993	+	0.166273i
$811$			0.805660i			0.0282906i	0.999900	+	0.0141453i	$0.00450273\pi$
$811$			0.805660i			0.0282906i	−0.999900	+	0.0141453i	$0.995497\pi$
$812$	18.9011	+	19.9528i	0.663297	+	0.700205i
$813$			36.8200i			1.29134i
$814$	−10.2768	+	17.7999i	−0.360200	+	0.623885i
$815$	−10.7010	−	18.5347i	−0.374840	−	0.649241i
$816$	−7.17651	−	1.51036i	−0.251228	−	0.0528731i
$817$	−6.34164	+	10.9840i	−0.221866	+	0.384283i
$818$	−14.1170			−0.493591
$819$	−0.977767	−	0.290567i	−0.0341660	−	0.0101532i
$820$	11.6073			0.405345
$821$	−40.6428	−	23.4651i	−1.41844	−	0.818938i	−0.422281	−	0.906465i	$-0.638770\pi$
$821$	−40.6428	−	23.4651i	−1.41844	−	0.818938i	−0.996162	+	0.0875265i	$0.972104\pi$
$822$	−0.416705	+	0.240585i	−0.0145343	+	0.00839137i
$823$	−13.1334	+	7.58259i	−0.457803	+	0.264313i	−0.711120	−	0.703071i	$-0.751812\pi$
$823$	−13.1334	+	7.58259i	−0.457803	+	0.264313i	0.253317	+	0.967383i	$0.418478\pi$
$824$	1.15790	−	2.00555i	0.0403375	−	0.0698666i
$825$	−8.48917			−0.295555
$826$	−1.13948	−	4.76481i	−0.0396477	−	0.165789i
$827$			10.6232i			0.369406i	0.982794	+	0.184703i	$0.0591324\pi$
$827$			10.6232i			0.369406i	−0.982794	+	0.184703i	$0.940868\pi$
$828$	−0.654621	−	0.377945i	−0.0227496	−	0.0131345i
$829$	15.2676	+	26.4442i	0.530264	+	0.918444i	0.999377	+	0.0353057i	$0.0112405\pi$
$829$	15.2676	+	26.4442i	0.530264	+	0.918444i	−0.469113	+	0.883138i	$0.655426\pi$
$830$	−4.48264	+	2.58805i	−0.155595	+	0.0898326i
$831$	−21.5613	+	37.3453i	−0.747953	+	1.29549i
$832$	−2.35458			−0.0816304
$833$	7.47676	+	27.8765i	0.259054	+	0.965863i
$834$	−30.1265			−1.04320
$835$	5.55178	−	9.61596i	0.192127	−	0.332774i
$836$	17.9468	−	10.3616i	0.620703	−	0.358363i
$837$	23.7791	+	41.1866i	0.821926	+	1.42362i
$838$	26.8311	+	15.4910i	0.926866	+	0.535126i
$839$			13.4485i			0.464293i	0.972681	+	0.232146i	$0.0745749\pi$
$839$			13.4485i			0.464293i	−0.972681	+	0.232146i	$0.925425\pi$
$840$	1.09455	+	4.57691i	0.0377655	+	0.157918i
$841$	−78.9091			−2.72100
$842$	−1.44847	+	2.50883i	−0.0499177	+	0.0864600i
$843$	14.6580	−	8.46278i	0.504847	−	0.291474i
$844$	5.39025	−	3.11206i	0.185540	−	0.107122i
$845$	−6.45704	−	3.72798i	−0.222129	−	0.128246i
$846$	−1.62417			−0.0558402
$847$	29.8726	+	8.87733i	1.02643	+	0.305029i
$848$	−12.3752			−0.424967
$849$	0.0927624	−	0.160669i	0.00318360	−	0.00551415i
$850$	0.849141	−	4.03472i	0.0291253	−	0.138390i
$851$	−9.94032	−	17.2171i	−0.340750	−	0.590196i
$852$	−4.80535	+	8.32311i	−0.164629	+	0.285145i
$853$			13.3016i			0.455439i	0.973727	+	0.227719i	$0.0731269\pi$
$853$			13.3016i			0.455439i	−0.973727	+	0.227719i	$0.926873\pi$
$854$	6.85759	+	7.23918i	0.234662	+	0.247720i
$855$			0.710954i			0.0243141i
$856$	−3.52834	−	2.03709i	−0.120596	−	0.0696262i
$857$	24.7964	−	14.3162i	0.847030	−	0.489033i	−0.0126175	−	0.999920i	$-0.504016\pi$
$857$	24.7964	−	14.3162i	0.847030	−	0.489033i	0.859648	+	0.510887i	$0.170683\pi$
$858$	−9.99422	−	17.3105i	−0.341197	−	0.590971i
$859$	12.3531	−	21.3961i	0.421481	−	0.730026i	−0.574604	−	0.818432i	$-0.694844\pi$
$859$	12.3531	−	21.3961i	0.421481	−	0.730026i	0.996085	+	0.0884055i	$0.0281771\pi$
$860$		−	2.92106i		−	0.0996073i
$861$	39.6558	−	37.5655i	1.35146	−	1.28023i
$862$		−	11.4019i		−	0.388349i
$863$	6.33309	−	10.9692i	0.215581	−	0.373397i	−0.737871	−	0.674941i	$-0.764169\pi$
$863$	6.33309	−	10.9692i	0.215581	−	0.373397i	0.953452	+	0.301545i	$0.0975022\pi$
$864$	4.36895	−	2.52242i	0.148635	−	0.0858143i
$865$	−5.97020	−	10.3407i	−0.202993	−	0.351594i
$866$	−0.104366	+	0.180767i	−0.00354650	+	0.00614271i
$867$	30.0591	−	3.28146i	1.02086	−	0.111444i
$868$	−7.10496	+	23.9084i	−0.241158	+	0.811506i
$869$	51.4898			1.74667
$870$	−16.0015	−	9.23845i	−0.542501	−	0.313213i
$871$	3.23955	+	5.61107i	0.109768	+	0.190124i
$872$	−13.6099	+	7.85771i	−0.460891	+	0.266095i
$873$	0.218358	+	0.126069i	0.00739030	+	0.00426679i
$874$			20.0448i			0.678024i
$875$	−2.57319	+	0.615368i	−0.0869898	+	0.0208032i
$876$	−2.25902			−0.0763254
$877$	14.6197	+	8.44069i	0.493673	+	0.285022i	0.726097	−	0.687593i	$-0.241332\pi$
$877$	14.6197	+	8.44069i	0.493673	+	0.285022i	−0.232424	+	0.972615i	$0.574666\pi$
$878$	−7.65138	+	4.41752i	−0.258221	+	0.149084i
$879$	2.74895	−	1.58711i	0.0927199	−	0.0535319i
$880$	−2.38636	+	4.13329i	−0.0804440	+	0.139333i
$881$			27.2537i			0.918201i	0.888384	+	0.459100i	$0.151828\pi$
$881$			27.2537i			0.918201i	−0.888384	+	0.459100i	$0.848172\pi$
$882$	0.960153	+	0.625942i	0.0323300	+	0.0210766i
$883$	7.22648			0.243190			0.121595	−	0.992580i	$-0.461199\pi$
$883$	7.22648			0.243190			0.121595	+	0.992580i	$0.461199\pi$
$884$	9.22699	−	3.01853i	0.310337	−	0.101524i
$885$	1.64681	+	2.85236i	0.0553569	+	0.0958810i
$886$	−6.40902	−	11.1007i	−0.215315	−	0.372937i
$887$	−18.0306	−	10.4100i	−0.605408	−	0.349533i	0.165758	−	0.986166i	$-0.446993\pi$
$887$	−18.0306	−	10.4100i	−0.605408	−	0.349533i	−0.771166	+	0.636634i	$0.780326\pi$
$888$	−7.65987			−0.257048
$889$	−8.56077	−	35.7973i	−0.287119	−	1.20060i
$890$			6.00762i			0.201376i
$891$	39.1191	+	22.5854i	1.31054	+	0.756641i
$892$	−10.4356	−	18.0750i	−0.349409	−	0.605195i
$893$	21.5349	+	37.2996i	0.720639	+	1.24818i
$894$	21.6594	+	12.5051i	0.724400	+	0.418233i
$895$		−	22.8725i		−	0.764543i
$896$	2.53613	+	0.753672i	0.0847263	+	0.0251784i
$897$	19.3341			0.645545
$898$	11.2550	+	6.49805i	0.375583	+	0.216843i
$899$	−48.9641	−	84.8084i	−1.63305	−	2.82852i
$900$	−0.0818691	−	0.141801i	−0.00272897	−	0.00472671i
$901$	48.4953	−	15.8648i	1.61561	−	0.528534i
$902$	55.3983			1.84456
$903$	−9.45361	−	9.97964i	−0.314596	−	0.332102i
$904$		−	11.5980i		−	0.385743i
$905$	3.45423	−	5.98290i	0.114823	−	0.198878i
$906$	−9.06920	+	5.23611i	−0.301304	+	0.173958i
$907$	−17.6908	+	10.2138i	−0.587414	+	0.339144i	−0.764074	−	0.645128i	$-0.776804\pi$
$907$	−17.6908	+	10.2138i	−0.587414	+	0.339144i	0.176660	+	0.984272i	$0.443471\pi$
$908$	−25.0969	−	14.4897i	−0.832869	−	0.480857i
$909$	−0.646827			−0.0214539
$910$	−4.28421	−	4.52260i	−0.142020	−	0.149923i
$911$			41.9652i			1.39037i	0.718831	+	0.695185i	$0.244678\pi$
$911$			41.9652i			1.39037i	−0.718831	+	0.695185i	$0.755322\pi$
$912$	6.68840	+	3.86155i	0.221475	+	0.127869i
$913$	−21.3943	+	12.3520i	−0.708049	+	0.408792i
$914$	12.9872	+	22.4944i	0.429577	+	0.744050i
$915$	−5.80558	−	3.35185i	−0.191927	−	0.110809i
$916$	10.9975			0.363368
$917$	11.7355	−	39.4903i	0.387539	−	1.30408i
$918$	−13.8871	+	15.4856i	−0.458342	+	0.511101i
$919$	−17.5597	+	30.4143i	−0.579241	+	1.00328i	0.416325	+	0.909216i	$0.363318\pi$
$919$	−17.5597	+	30.4143i	−0.579241	+	1.00328i	−0.995567	+	0.0940597i	$0.970016\pi$
$920$	−2.30823	−	3.99797i	−0.0761001	−	0.131809i
$921$	−23.0509	+	13.3084i	−0.759552	+	0.438528i
$922$	−1.16678	+	2.02093i	−0.0384260	+	0.0665558i
$923$		−	12.7224i		−	0.418762i
$924$	5.22397	+	21.8443i	0.171856	+	0.718624i
$925$		−	4.30647i		−	0.141596i
$926$	−11.3702	+	19.6938i	−0.373648	+	0.647178i
$927$	0.189593	+	0.328385i	0.00622706	+	0.0107856i
$928$	−8.99621	+	5.19396i	−0.295315	+	0.170500i
$929$	14.0990	+	8.14005i	0.462572	+	0.267066i	0.713125	−	0.701037i	$-0.247279\pi$
$929$	14.0990	+	8.14005i	0.462572	+	0.267066i	−0.250553	+	0.968103i	$0.580612\pi$
$930$		−	16.7679i		−	0.549842i
$931$	1.64426	−	30.3496i	0.0538885	−	0.994668i
$932$		−	0.0319028i		−	0.00104501i
$933$	7.10636	−	12.3086i	0.232652	−	0.402965i
$934$	−5.02465	−	8.70295i	−0.164412	−	0.284769i
$935$	4.05271	−	19.2566i	0.132538	−	0.629757i
$936$	0.192767	−	0.333883i	0.00630079	−	0.0109133i
$937$	1.19991			0.0391994			0.0195997	−	0.999808i	$-0.493761\pi$
$937$	1.19991			0.0391994			0.0195997	+	0.999808i	$0.493761\pi$
$938$	−1.69331	−	7.08067i	−0.0552886	−	0.231192i
$939$	5.63937			0.184034
$940$	−8.59039	−	4.95966i	−0.280188	−	0.161766i
$941$	−34.7951	+	20.0890i	−1.13429	+	0.654882i	−0.945010	−	0.327041i	$-0.893948\pi$
$941$	−34.7951	+	20.0890i	−1.13429	+	0.654882i	−0.189279	+	0.981923i	$0.560615\pi$
$942$	−35.5537	+	20.5270i	−1.15840	+	0.668805i
$943$	−26.7923	+	46.4057i	−0.872479	+	1.51118i
$944$	1.85171			0.0602680
$945$	12.7944	+	3.80215i	0.416201	+	0.123684i
$946$		−	13.9414i		−	0.453273i
$947$	27.6137	+	15.9428i	0.897325	+	0.518071i	0.876331	−	0.481709i	$-0.159984\pi$
$947$	27.6137	+	15.9428i	0.897325	+	0.518071i	0.0209933	+	0.999780i	$0.493317\pi$
$948$	9.59459	+	16.6183i	0.311618	+	0.539738i
$949$	2.58979	−	1.49522i	0.0840682	−	0.0485368i
$950$	−2.17101	+	3.76030i	−0.0704368	+	0.122000i
$951$	−40.0102			−1.29742
$952$	−10.9046	+	0.297835i	−0.353422	+	0.00965288i
$953$	−56.6897			−1.83636			−0.918180	−	0.396164i	$-0.870341\pi$
$953$	−56.6897			−1.83636			−0.918180	+	0.396164i	$0.870341\pi$
$954$	1.01315	−	1.75482i	0.0328019	−	0.0568146i
$955$	13.3398	−	7.70175i	0.431667	−	0.249223i
$956$	0.735830	+	1.27450i	0.0237984	+	0.0412201i
$957$	−76.3704	−	44.0925i	−2.46870	−	1.42531i
$958$		−	27.8025i		−	0.898257i
$959$	−0.519604	+	0.492216i	−0.0167789	+	0.0158945i
$960$	−1.77869			−0.0574070
$961$	28.9353	−	50.1174i	0.933397	−	1.61669i
$962$	8.78143	−	5.06996i	0.283125	−	0.163462i
$963$	0.577724	−	0.333549i	0.0186169	−	0.0107485i
$964$	14.9165	+	8.61202i	0.480427	+	0.277374i
$965$	13.2792			0.427473
$966$	−20.8249	−	6.18859i	−0.670029	−	0.199115i
$967$	16.3796			0.526733			0.263366	−	0.964696i	$-0.415167\pi$
$967$	16.3796			0.526733			0.263366	+	0.964696i	$0.415167\pi$
$968$	−5.88939	+	10.2007i	−0.189292	+	0.327864i
$969$	−31.1605	−	6.55800i	−1.00102	−	0.210673i
$970$	0.769943	+	1.33358i	0.0247214	+	0.0428187i
$971$	2.36317	−	4.09313i	0.0758377	−	0.131355i	−0.825613	−	0.564237i	$-0.809170\pi$
$971$	2.36317	−	4.09313i	0.0758377	−	0.131355i	0.901450	+	0.432883i	$0.142504\pi$
$972$			1.69975i			0.0545195i
$973$	−43.5834	+	10.4228i	−1.39722	+	0.334139i
$974$			7.25564i			0.232486i
$975$	3.62697	+	2.09403i	0.116156	+	0.0670628i
$976$	−3.26396	+	1.88445i	−0.104477	+	0.0603198i
$977$	5.91831	+	10.2508i	0.189343	+	0.327953i	0.945032	−	0.326979i	$-0.106031\pi$
$977$	5.91831	+	10.2508i	0.189343	+	0.327953i	−0.755688	+	0.654932i	$0.772697\pi$
$978$	19.0338	−	32.9674i	0.608633	−	1.05418i
$979$			28.6726i			0.916382i
$980$	3.16692	+	6.24264i	0.101164	+	0.199414i
$981$		−	2.57321i		−	0.0821563i
$982$	10.7988	−	18.7041i	0.344604	−	0.596872i
$983$	−43.3289	+	25.0159i	−1.38198	+	0.797885i	−0.992393	−	0.123106i	$-0.960714\pi$
$983$	−43.3289	+	25.0159i	−1.38198	+	0.797885i	−0.389584	+	0.920991i	$0.627381\pi$
$984$	10.3229	+	17.8798i	0.329082	+	0.569987i
$985$	4.00716	−	6.94061i	0.127679	−	0.221146i
$986$	28.5952	−	31.8868i	0.910658	−	1.01548i
$987$	−45.3999	+	10.8572i	−1.44509	+	0.345588i
$988$	−10.2236			−0.325257
$989$	11.6783	+	6.74248i	0.371349	+	0.214398i
$990$	−0.390737	−	0.676777i	−0.0124185	−	0.0215094i
$991$	−9.09571	+	5.25141i	−0.288935	+	0.166817i	−0.637461	−	0.770482i	$-0.720015\pi$
$991$	−9.09571	+	5.25141i	−0.288935	+	0.166817i	0.348527	+	0.937299i	$0.386682\pi$
$992$	−8.16413	−	4.71356i	−0.259211	−	0.149656i
$993$			47.5733i			1.50969i
$994$	−4.07227	+	13.7034i	−0.129165	+	0.434644i
$995$	19.1421			0.606844
$996$	−7.97322	−	4.60334i	−0.252641	−	0.145863i
$997$	24.9012	−	14.3767i	0.788630	−	0.455315i	−0.0508503	−	0.998706i	$-0.516193\pi$
$997$	24.9012	−	14.3767i	0.788630	−	0.455315i	0.839480	+	0.543391i	$0.182860\pi$
$998$	26.9982	−	15.5874i	0.854612	−	0.493410i
$999$	−10.8627	+	18.8147i	−0.343681	+	0.595272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.ba.b.611.7	✓	48
7.4	even	3	inner	1190.2.ba.b.781.18	yes	48
17.16	even	2	inner	1190.2.ba.b.611.18	yes	48
119.67	even	6	inner	1190.2.ba.b.781.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.ba.b.611.7	✓	48	1.1	even	1	trivial
1190.2.ba.b.611.18	yes	48	17.16	even	2	inner
1190.2.ba.b.781.7	yes	48	119.67	even	6	inner
1190.2.ba.b.781.18	yes	48	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.54039 + 0.889345i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.77869i q^{6} +(0.615368 + 2.57319i) q^{7} -1.00000 q^{8} +(0.0818691 - 0.141801i) q^{9} +(0.866025 - 0.500000i) q^{10} +(4.13329 - 2.38636i) q^{11} +(1.54039 + 0.889345i) q^{12} -2.35458 q^{13} +(2.53613 + 0.753672i) q^{14} -1.77869 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.849141 - 4.03472i) q^{17} +(-0.0818691 - 0.141801i) q^{18} +(-2.17101 + 3.76030i) q^{19} -1.00000i q^{20} +(-3.23636 - 3.41645i) q^{21} -4.77271i q^{22} +(3.99797 + 2.30823i) q^{23} +(1.54039 - 0.889345i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.17729 + 2.03913i) q^{26} -5.04483i q^{27} +(1.92077 - 1.81952i) q^{28} +10.3879i q^{29} +(-0.889345 + 1.54039i) q^{30} +(-8.16413 + 4.71356i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.24459 + 7.35184i) q^{33} +(-3.06960 - 2.75274i) q^{34} +(-0.753672 + 2.53613i) q^{35} -0.163738 q^{36} +(-3.72951 - 2.15323i) q^{37} +(2.17101 + 3.76030i) q^{38} +(3.62697 - 2.09403i) q^{39} +(-0.866025 - 0.500000i) q^{40} +11.6073i q^{41} +(-4.57691 + 1.09455i) q^{42} +2.92106 q^{43} +(-4.13329 - 2.38636i) q^{44} +(0.141801 - 0.0818691i) q^{45} +(3.99797 - 2.30823i) q^{46} +(4.95966 - 8.59039i) q^{47} -1.77869i q^{48} +(-6.24264 + 3.16692i) q^{49} +1.00000 q^{50} +(2.28025 + 6.97022i) q^{51} +(1.17729 + 2.03913i) q^{52} +(6.18762 + 10.7173i) q^{53} +(-4.36895 - 2.52242i) q^{54} +4.77271 q^{55} +(-0.615368 - 2.57319i) q^{56} -7.72310i q^{57} +(8.99621 + 5.19396i) q^{58} +(-0.925855 - 1.60363i) q^{59} +(0.889345 + 1.54039i) q^{60} +(3.26396 + 1.88445i) q^{61} +9.42712i q^{62} +(0.415262 + 0.123405i) q^{63} +1.00000 q^{64} +(-2.03913 - 1.17729i) q^{65} +(4.24459 + 7.35184i) q^{66} +(-1.37585 - 2.38305i) q^{67} +(-3.91874 + 1.28198i) q^{68} -8.21126 q^{69} +(1.81952 + 1.92077i) q^{70} +5.40325i q^{71} +(-0.0818691 + 0.141801i) q^{72} +(-1.09990 + 0.635025i) q^{73} +(-3.72951 + 2.15323i) q^{74} +(-1.54039 - 0.889345i) q^{75} +4.34202 q^{76} +(8.68405 + 9.16726i) q^{77} -4.18807i q^{78} +(9.34300 + 5.39419i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.73220 + 8.19641i) q^{81} +(10.0522 + 5.80365i) q^{82} -5.17610 q^{83} +(-1.34055 + 4.51100i) q^{84} +(2.75274 - 3.06960i) q^{85} +(1.46053 - 2.52971i) q^{86} +(-9.23845 - 16.0015i) q^{87} +(-4.13329 + 2.38636i) q^{88} +(-3.00381 + 5.20275i) q^{89} -0.163738i q^{90} +(-1.44893 - 6.05879i) q^{91} -4.61646i q^{92} +(8.38396 - 14.5214i) q^{93} +(-4.95966 - 8.59039i) q^{94} +(-3.76030 + 2.17101i) q^{95} +(-1.54039 - 0.889345i) q^{96} +1.53989i q^{97} +(-0.378686 + 6.98975i) q^{98} -0.781475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} + 24 q^{9} - 8 q^{15} - 24 q^{16} + 2 q^{17} - 24 q^{18} - 16 q^{19} - 12 q^{21} + 24 q^{25} - 4 q^{30} + 24 q^{32} + 36 q^{33} + 4 q^{34} - 4 q^{35} - 48 q^{36} + 16 q^{38}+ \cdots + 8 q^{98}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 + 24 * q^9 - 8 * q^15 - 24 * q^16 + 2 * q^17 - 24 * q^18 - 16 * q^19 - 12 * q^21 + 24 * q^25 - 4 * q^30 + 24 * q^32 + 36 * q^33 + 4 * q^34 - 4 * q^35 - 48 * q^36 + 16 * q^38 - 24 * q^42 + 8 * q^43 + 4 * q^47 + 4 * q^49 + 48 * q^50 + 16 * q^51 + 32 * q^53 - 8 * q^55 - 44 * q^59 + 4 * q^60 + 48 * q^64 - 36 * q^66 - 40 * q^67 + 2 * q^68 - 72 * q^69 - 8 * q^70 - 24 * q^72 + 32 * q^76 + 20 * q^77 - 24 * q^81 + 152 * q^83 - 12 * q^84 + 20 * q^85 + 4 * q^86 + 16 * q^87 - 16 * q^89 - 4 * q^93 - 4 * q^94 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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