LMFDB - Embedded newform 165.2.s.a.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(4,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("165.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.s (of order $10$, degree $4$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	165.49
Dual form			165.2.s.a.64.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.464400 - 0.150893i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.42514 + 1.03542i) q^{4} +(1.35773 - 1.77667i) q^{5} +(-0.150893 + 0.464400i) q^{6} +(3.00296 + 4.13322i) q^{7} +(-1.07962 + 1.48598i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.464400 - 0.150893i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.42514 + 1.03542i) q^{4} +(1.35773 - 1.77667i) q^{5} +(-0.150893 + 0.464400i) q^{6} +(3.00296 + 4.13322i) q^{7} +(-1.07962 + 1.48598i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.362444 - 1.02996i) q^{10} +(2.66766 + 1.97068i) q^{11} -1.76156i q^{12} +(-1.72877 + 0.561712i) q^{13} +(2.01825 + 1.46634i) q^{14} +(0.639302 + 2.14273i) q^{15} +(0.811552 - 2.49770i) q^{16} +(-0.608644 - 0.197760i) q^{17} +(-0.287015 - 0.395042i) q^{18} +(-3.55796 - 2.58501i) q^{19} +(-0.0953500 + 3.93782i) q^{20} -5.10895 q^{21} +(1.53622 + 0.512653i) q^{22} -4.37977i q^{23} +(-0.567592 - 1.74687i) q^{24} +(-1.31312 - 4.82449i) q^{25} +(-0.718083 + 0.521718i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-8.55926 - 2.78107i) q^{28} +(6.11631 - 4.44376i) q^{29} +(0.620214 + 0.898618i) q^{30} +(0.681386 + 2.09709i) q^{31} -4.95592i q^{32} +(-3.16233 + 0.999848i) q^{33} -0.312494 q^{34} +(11.4206 + 0.276537i) q^{35} +(1.42514 + 1.03542i) q^{36} +(-3.51022 - 4.83140i) q^{37} +(-2.04237 - 0.663607i) q^{38} +(0.561712 - 1.72877i) q^{39} +(1.17425 + 3.93570i) q^{40} +(1.80558 + 1.31183i) q^{41} +(-2.37259 + 0.770902i) q^{42} +3.38068i q^{43} +(-5.84226 - 0.0463305i) q^{44} +(-2.10928 - 0.742259i) q^{45} +(-0.660876 - 2.03397i) q^{46} +(-0.890969 + 1.22631i) q^{47} +(1.54366 + 2.12467i) q^{48} +(-5.90264 + 18.1664i) q^{49} +(-1.33779 - 2.04235i) q^{50} +(0.517743 - 0.376162i) q^{51} +(1.88213 - 2.59052i) q^{52} +(-8.72779 + 2.83583i) q^{53} +0.488299 q^{54} +(7.12322 - 2.06390i) q^{55} -9.38395 q^{56} +(4.18263 - 1.35902i) q^{57} +(2.16988 - 2.98659i) q^{58} +(4.34583 - 3.15743i) q^{59} +(-3.12972 - 2.39173i) q^{60} +(2.24584 - 6.91197i) q^{61} +(0.632871 + 0.871072i) q^{62} +(3.00296 - 4.13322i) q^{63} +(0.875292 + 2.69387i) q^{64} +(-1.34923 + 3.83411i) q^{65} +(-1.31771 + 0.941501i) q^{66} -7.25598i q^{67} +(1.07216 - 0.348367i) q^{68} +(3.54331 + 2.57437i) q^{69} +(5.34545 - 1.59486i) q^{70} +(1.70226 - 5.23903i) q^{71} +(1.74687 + 0.567592i) q^{72} +(4.19868 + 5.77899i) q^{73} +(-2.35917 - 1.71403i) q^{74} +(4.67493 + 1.77343i) q^{75} +7.74714 q^{76} +(-0.134369 + 16.9439i) q^{77} -0.887599i q^{78} +(-0.588726 - 1.81191i) q^{79} +(-3.33572 - 4.83307i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.03645 + 0.336765i) q^{82} +(0.153978 + 0.0500304i) q^{83} +(7.28094 - 5.28991i) q^{84} +(-1.17773 + 0.812854i) q^{85} +(0.510120 + 1.56999i) q^{86} +7.56018i q^{87} +(-5.80846 + 1.83649i) q^{88} +1.19539 q^{89} +(-1.09155 - 0.0264307i) q^{90} +(-7.51312 - 5.45860i) q^{91} +(4.53491 + 6.24177i) q^{92} +(-2.09709 - 0.681386i) q^{93} +(-0.228724 + 0.703940i) q^{94} +(-9.42346 + 2.81157i) q^{95} +(4.00943 + 2.91302i) q^{96} +(-13.5832 + 4.41347i) q^{97} +9.32716i q^{98} +(1.04987 - 3.14607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$

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 $

$2$	0.464400	−	0.150893i	0.328380	−	0.106697i	−0.140187	−	0.990125i	$-0.544770\pi$
$2$	0.464400	−	0.150893i	0.328380	−	0.106697i	0.468567	+	0.883428i	$0.344770\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−1.42514	+	1.03542i	−0.712568	+	0.517711i
$5$	1.35773	−	1.77667i	0.607197	−	0.794552i
$5$	1.35773	−	1.77667i	0.607197	−	0.794552i
$6$	−0.150893	+	0.464400i	−0.0616017	+	0.189590i
$7$	3.00296	+	4.13322i	1.13501	+	1.56221i	0.778177	+	0.628045i	$0.216145\pi$
$7$	3.00296	+	4.13322i	1.13501	+	1.56221i	0.356836	+	0.934167i	$0.383855\pi$
$8$	−1.07962	+	1.48598i	−0.381705	+	0.525372i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	0.362444	−	1.02996i	0.114615	−	0.325701i
$11$	2.66766	+	1.97068i	0.804330	+	0.594182i
$11$	2.66766	+	1.97068i	0.804330	+	0.594182i
$12$		−	1.76156i		−	0.508520i
$13$	−1.72877	+	0.561712i	−0.479475	+	0.155791i	−0.538776	−	0.842449i	$-0.681113\pi$
$13$	−1.72877	+	0.561712i	−0.479475	+	0.155791i	0.0593006	+	0.998240i	$0.481113\pi$
$14$	2.01825	+	1.46634i	0.539400	+	0.391897i
$15$	0.639302	+	2.14273i	0.165067	+	0.553251i
$16$	0.811552	−	2.49770i	0.202888	−	0.624425i
$17$	−0.608644	−	0.197760i	−0.147618	−	0.0479639i	0.234276	−	0.972170i	$-0.424728\pi$
$17$	−0.608644	−	0.197760i	−0.147618	−	0.0479639i	−0.381894	+	0.924206i	$0.624728\pi$
$18$	−0.287015	−	0.395042i	−0.0676500	−	0.0931123i
$19$	−3.55796	−	2.58501i	−0.816251	−	0.593041i	0.0993851	−	0.995049i	$-0.468312\pi$
$19$	−3.55796	−	2.58501i	−0.816251	−	0.593041i	−0.915636	+	0.402008i	$0.868312\pi$
$20$	−0.0953500	+	3.93782i	−0.0213209	+	0.880524i
$21$	−5.10895			−1.11486
$22$	1.53622	+	0.512653i	0.327524	+	0.109298i
$23$		−	4.37977i		−	0.913246i	−0.889660	−	0.456623i	$-0.849059\pi$
$23$		−	4.37977i		−	0.913246i	0.889660	−	0.456623i	$-0.150941\pi$
$24$	−0.567592	−	1.74687i	−0.115859	−	0.356578i
$25$	−1.31312	−	4.82449i	−0.262624	−	0.964898i
$26$	−0.718083	+	0.521718i	−0.140828	+	0.102317i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	−8.55926	−	2.78107i	−1.61755	−	0.525573i
$29$	6.11631	−	4.44376i	1.13577	−	0.825186i	0.149247	−	0.988800i	$-0.452315\pi$
$29$	6.11631	−	4.44376i	1.13577	−	0.825186i	0.986524	+	0.163614i	$0.0523152\pi$
$30$	0.620214	+	0.898618i	0.113235	+	0.164064i
$31$	0.681386	+	2.09709i	0.122380	+	0.376648i	0.993415	−	0.114574i	$-0.0365503\pi$
$31$	0.681386	+	2.09709i	0.122380	+	0.376648i	−0.871034	+	0.491222i	$0.836550\pi$
$32$		−	4.95592i		−	0.876092i
$33$	−3.16233	+	0.999848i	−0.550490	+	0.174051i
$34$	−0.312494			−0.0535924
$35$	11.4206	+	0.276537i	1.93043	+	0.0467433i
$36$	1.42514	+	1.03542i	0.237523	+	0.172570i
$37$	−3.51022	−	4.83140i	−0.577076	−	0.794277i	0.416295	−	0.909230i	$-0.363328\pi$
$37$	−3.51022	−	4.83140i	−0.577076	−	0.794277i	−0.993371	+	0.114953i	$0.963328\pi$
$38$	−2.04237	−	0.663607i	−0.331317	−	0.107651i
$39$	0.561712	−	1.72877i	0.0899459	−	0.276825i
$40$	1.17425	+	3.93570i	0.185665	+	0.622288i
$41$	1.80558	+	1.31183i	0.281984	+	0.204873i	0.719782	−	0.694200i	$-0.244242\pi$
$41$	1.80558	+	1.31183i	0.281984	+	0.204873i	−0.437798	+	0.899073i	$0.644242\pi$
$42$	−2.37259	+	0.770902i	−0.366099	+	0.118953i
$43$			3.38068i			0.515549i	0.966205	+	0.257775i	$0.0829892\pi$
$43$			3.38068i			0.515549i	−0.966205	+	0.257775i	$0.917011\pi$
$44$	−5.84226	−	0.0463305i	−0.880754	−	0.00698458i
$45$	−2.10928	−	0.742259i	−0.314433	−	0.110649i
$46$	−0.660876	−	2.03397i	−0.0974408	−	0.299892i
$47$	−0.890969	+	1.22631i	−0.129961	+	0.178876i	−0.869039	−	0.494744i	$-0.835262\pi$
$47$	−0.890969	+	1.22631i	−0.129961	+	0.178876i	0.739077	+	0.673620i	$0.235262\pi$
$48$	1.54366	+	2.12467i	0.222809	+	0.306670i
$49$	−5.90264	+	18.1664i	−0.843234	+	2.59521i
$50$	−1.33779	−	2.04235i	−0.189193	−	0.288832i
$51$	0.517743	−	0.376162i	0.0724985	−	0.0526733i
$52$	1.88213	−	2.59052i	0.261004	−	0.359241i
$53$	−8.72779	+	2.83583i	−1.19885	+	0.389532i	−0.839339	−	0.543608i	$-0.817058\pi$
$53$	−8.72779	+	2.83583i	−1.19885	+	0.389532i	−0.359515	+	0.933139i	$0.617058\pi$
$54$	0.488299			0.0664491
$55$	7.12322	−	2.06390i	0.960495	−	0.278296i
$56$	−9.38395			−1.25398
$57$	4.18263	−	1.35902i	0.554003	−	0.180006i
$58$	2.16988	−	2.98659i	0.284920	−	0.392158i
$59$	4.34583	−	3.15743i	0.565779	−	0.411062i	−0.267790	−	0.963477i	$-0.586294\pi$
$59$	4.34583	−	3.15743i	0.565779	−	0.411062i	0.833569	+	0.552415i	$0.186294\pi$
$60$	−3.12972	−	2.39173i	−0.404045	−	0.308772i
$61$	2.24584	−	6.91197i	0.287550	−	0.884988i	−0.698073	−	0.716027i	$-0.745959\pi$
$61$	2.24584	−	6.91197i	0.287550	−	0.884988i	0.985623	−	0.168961i	$-0.0540412\pi$
$62$	0.632871	+	0.871072i	0.0803747	+	0.110626i
$63$	3.00296	−	4.13322i	0.378338	−	0.520737i
$64$	0.875292	+	2.69387i	0.109411	+	0.336734i
$65$	−1.34923	+	3.83411i	−0.167352	+	0.475563i
$66$	−1.31771	+	0.941501i	−0.162199	+	0.115891i
$67$		−	7.25598i		−	0.886459i	−0.896408	−	0.443230i	$-0.853833\pi$
$67$		−	7.25598i		−	0.886459i	0.896408	−	0.443230i	$-0.146167\pi$
$68$	1.07216	−	0.348367i	0.130019	−	0.0422458i
$69$	3.54331	+	2.57437i	0.426565	+	0.309917i
$70$	5.34545	−	1.59486i	0.638904	−	0.190622i
$71$	1.70226	−	5.23903i	0.202022	−	0.621759i	−0.797801	−	0.602921i	$-0.794003\pi$
$71$	1.70226	−	5.23903i	0.202022	−	0.621759i	0.999823	−	0.0188376i	$-0.00599656\pi$
$72$	1.74687	+	0.567592i	0.205871	+	0.0668914i
$73$	4.19868	+	5.77899i	0.491419	+	0.676380i	0.980649	−	0.195775i	$-0.0627222\pi$
$73$	4.19868	+	5.77899i	0.491419	+	0.676380i	−0.489230	+	0.872155i	$0.662722\pi$
$74$	−2.35917	−	1.71403i	−0.274247	−	0.199252i
$75$	4.67493	+	1.77343i	0.539814	+	0.204778i
$76$	7.74714			0.888658
$77$	−0.134369	+	16.9439i	−0.0153128	+	1.93094i
$78$		−	0.887599i		−	0.100501i
$79$	−0.588726	−	1.81191i	−0.0662369	−	0.203856i	0.912460	−	0.409165i	$-0.134180\pi$
$79$	−0.588726	−	1.81191i	−0.0662369	−	0.203856i	−0.978697	+	0.205309i	$0.934180\pi$
$80$	−3.33572	−	4.83307i	−0.372945	−	0.540354i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.03645	+	0.336765i	0.114457	+	0.0371894i
$83$	0.153978	+	0.0500304i	0.0169012	+	0.00549155i	0.317455	−	0.948273i	$-0.397172\pi$
$83$	0.153978	+	0.0500304i	0.0169012	+	0.00549155i	−0.300554	+	0.953765i	$0.597172\pi$
$84$	7.28094	−	5.28991i	0.794416	−	0.577177i
$85$	−1.17773	+	0.812854i	−0.127743	+	0.0881664i
$86$	0.510120	+	1.56999i	0.0550077	+	0.169296i
$87$			7.56018i			0.810536i
$88$	−5.80846	+	1.83649i	−0.619184	+	0.195770i
$89$	1.19539			0.126711			0.0633554	−	0.997991i	$-0.479820\pi$
$89$	1.19539			0.126711			0.0633554	+	0.997991i	$0.479820\pi$
$90$	−1.09155	−	0.0264307i	−0.115059	−	0.00278604i
$91$	−7.51312	−	5.45860i	−0.787589	−	0.572217i
$92$	4.53491	+	6.24177i	0.472797	+	0.650750i
$93$	−2.09709	−	0.681386i	−0.217458	−	0.0706564i
$94$	−0.228724	+	0.703940i	−0.0235911	+	0.0726059i
$95$	−9.42346	+	2.81157i	−0.966827	+	0.288461i
$96$	4.00943	+	2.91302i	0.409210	+	0.297309i
$97$	−13.5832	+	4.41347i	−1.37917	+	0.448120i	−0.902397	−	0.430907i	$-0.858194\pi$
$97$	−13.5832	+	4.41347i	−1.37917	+	0.448120i	−0.476774	+	0.879026i	$0.658194\pi$
$98$			9.32716i			0.942185i
$99$	1.04987	−	3.14607i	0.105516	−	0.316192i
$100$	6.86676	+	5.51592i	0.686676	+	0.551592i
$101$	−1.32596	−	4.08088i	−0.131938	−	0.406063i	0.863163	−	0.504925i	$-0.168480\pi$
$101$	−1.32596	−	4.08088i	−0.131938	−	0.406063i	−0.995101	+	0.0988620i	$0.968480\pi$
$102$	0.183680	−	0.252813i	0.0181870	−	0.0250323i
$103$	5.58280	+	7.68406i	0.550089	+	0.757133i	0.990024	−	0.140896i	$-0.0449985\pi$
$103$	5.58280	+	7.68406i	0.550089	+	0.757133i	−0.439935	+	0.898030i	$0.644998\pi$
$104$	1.03173	−	3.17535i	0.101170	−	0.311369i
$105$	−6.93659	+	9.07692i	−0.676941	+	0.885816i
$106$	−3.62528	+	2.63392i	−0.352118	+	0.255829i
$107$	4.86374	−	6.69437i	0.470196	−	0.647169i	−0.506388	−	0.862306i	$-0.669020\pi$
$107$	4.86374	−	6.69437i	0.470196	−	0.647169i	0.976584	+	0.215137i	$0.0690196\pi$
$108$	−1.67535	+	0.544353i	−0.161210	+	0.0523804i
$109$	12.4980			1.19709			0.598546	−	0.801089i	$-0.295745\pi$
$109$	12.4980			1.19709			0.598546	+	0.801089i	$0.295745\pi$
$110$	2.99660	−	2.03332i	0.285714	−	0.193869i
$111$	5.97194			0.566831
$112$	12.7606	−	4.14618i	1.20576	−	0.391777i
$113$	9.52776	−	13.1138i	0.896296	−	1.23365i	−0.0753380	−	0.997158i	$-0.524004\pi$
$113$	9.52776	−	13.1138i	0.896296	−	1.23365i	0.971634	−	0.236488i	$-0.0759964\pi$
$114$	1.73735	−	1.26226i	0.162717	−	0.118221i
$115$	−7.78142	−	5.94656i	−0.725621	−	0.554520i
$116$	−4.11541	+	12.6659i	−0.382106	+	1.17600i
$117$	1.06844	+	1.47058i	0.0987773	+	0.135955i
$118$	1.54177	−	2.12206i	0.141931	−	0.195352i
$119$	−1.01035	−	3.10953i	−0.0926183	−	0.285050i
$120$	−3.87425	−	1.36336i	−0.353669	−	0.124457i
$121$	3.23284	+	10.5142i	0.293895	+	0.955838i
$122$		−	3.54880i		−	0.321293i
$123$	−2.12258	+	0.689669i	−0.191387	+	0.0621854i
$124$	−3.14244	−	2.28311i	−0.282199	−	0.205030i
$125$	−10.3544	−	4.21739i	−0.926126	−	0.377214i
$126$	0.770902	−	2.37259i	0.0686774	−	0.211367i
$127$	9.39726	+	3.05335i	0.833872	+	0.270941i	0.694675	−	0.719323i	$-0.255548\pi$
$127$	9.39726	+	3.05335i	0.833872	+	0.270941i	0.139196	+	0.990265i	$0.455548\pi$
$128$	6.63901	+	9.13781i	0.586811	+	0.807676i
$129$	−2.73503	−	1.98712i	−0.240806	−	0.174956i
$130$	−0.0480440	+	1.98415i	−0.00421374	+	0.174022i
$131$	−12.7829			−1.11685			−0.558425	−	0.829555i	$-0.688594\pi$
$131$	−12.7829			−1.11685			−0.558425	+	0.829555i	$0.688594\pi$
$132$	3.47148	−	4.69926i	0.302153	−	0.409018i
$133$		−	22.4685i		−	1.94827i
$134$	−1.09487	−	3.36968i	−0.0945827	−	0.291096i
$135$	1.84030	−	1.27015i	0.158388	−	0.109317i
$136$	0.950974	−	0.690923i	0.0815453	−	0.0592461i
$137$	−18.1261	−	5.88953i	−1.54862	−	0.503177i	−0.594880	−	0.803815i	$-0.702800\pi$
$137$	−18.1261	−	5.88953i	−1.54862	−	0.503177i	−0.953738	+	0.300638i	$0.902800\pi$
$138$	2.03397	+	0.660876i	0.173143	+	0.0562575i
$139$	−9.47734	+	6.88569i	−0.803857	+	0.584036i	−0.912043	−	0.410094i	$-0.865496\pi$
$139$	−9.47734	+	6.88569i	−0.803857	+	0.584036i	0.108186	+	0.994131i	$0.465496\pi$
$140$	−16.5622	+	11.4310i	−1.39976	+	0.966099i
$141$	−0.468410	−	1.44162i	−0.0394472	−	0.121406i
$142$		−	2.68986i		−	0.225728i
$143$	−5.71873	−	1.90840i	−0.478225	−	0.159588i
$144$	−2.62624			−0.218853
$145$	0.409218	−	16.9001i	0.0339837	−	1.40348i
$146$	2.82187	+	2.05021i	0.233540	+	0.169677i
$147$	−11.2275	−	15.4533i	−0.926027	−	1.27457i
$148$	10.0051	+	3.25084i	0.822411	+	0.267218i
$149$	−2.30442	+	7.09226i	−0.188785	+	0.581021i	−0.999993	−	0.00373714i	$-0.998810\pi$
$149$	−2.30442	+	7.09226i	−0.188785	+	0.581021i	0.811208	+	0.584758i	$0.198810\pi$
$150$	2.43863	+	0.118167i	0.199114	+	0.00964828i
$151$	4.01196	+	2.91486i	0.326489	+	0.237208i	0.738939	−	0.673772i	$-0.235327\pi$
$151$	4.01196	+	2.91486i	0.326489	+	0.237208i	−0.412451	+	0.910980i	$0.635327\pi$
$152$	7.68252	−	2.49620i	0.623134	−	0.202469i
$153$			0.639966i			0.0517382i
$154$	2.49431	+	7.88903i	0.200997	+	0.635716i
$155$	4.65098	+	1.63669i	0.373576	+	0.131462i
$156$	0.989492	+	3.04534i	0.0792228	+	0.243823i
$157$	−12.1034	+	16.6589i	−0.965958	+	1.32953i	−0.0218956	+	0.999760i	$0.506970\pi$
$157$	−12.1034	+	16.6589i	−0.965958	+	1.32953i	−0.944062	+	0.329767i	$0.893030\pi$
$158$	−0.546809	−	0.752618i	−0.0435018	−	0.0598750i
$159$	2.83583	−	8.72779i	0.224896	−	0.692159i
$160$	−8.80505	−	6.72882i	−0.696100	−	0.531960i
$161$	18.1026	−	13.1523i	1.42668	−	1.03655i
$162$	−0.287015	+	0.395042i	−0.0225500	+	0.0310374i
$163$	6.87399	−	2.23349i	0.538412	−	0.174941i	−0.0271727	−	0.999631i	$-0.508650\pi$
$163$	6.87399	−	2.23349i	0.538412	−	0.174941i	0.565585	+	0.824690i	$0.308650\pi$
$164$	−3.93149			−0.306998
$165$	−2.51719	+	6.97594i	−0.195963	+	0.543076i
$166$	0.0790564			0.00613597
$167$	−17.4167	+	5.65902i	−1.34774	+	0.437908i	−0.891933	−	0.452169i	$-0.850651\pi$
$167$	−17.4167	+	5.65902i	−1.34774	+	0.437908i	−0.455811	+	0.890077i	$0.650651\pi$
$168$	5.51574	−	7.59177i	0.425549	−	0.585718i
$169$	−7.84409	+	5.69906i	−0.603391	+	0.438390i
$170$	−0.424284	+	0.555200i	−0.0325411	+	0.0425819i
$171$	−1.35902	+	4.18263i	−0.103927	+	0.319854i
$172$	−3.50043	−	4.81793i	−0.266905	−	0.367364i
$173$	7.06265	−	9.72090i	0.536963	−	0.739066i	−0.451209	−	0.892419i	$-0.649007\pi$
$173$	7.06265	−	9.72090i	0.536963	−	0.739066i	0.988172	+	0.153352i	$0.0490069\pi$
$174$	1.14078	+	3.51095i	0.0864820	+	0.266164i
$175$	15.9974	−	19.9152i	1.20929	−	1.50545i
$176$	7.08711	−	5.06371i	0.534211	−	0.381692i
$177$			5.37174i			0.403765i
$178$	0.555138	−	0.180375i	0.0416093	−	0.0135197i
$179$	−5.42854	−	3.94406i	−0.405748	−	0.294793i	0.366130	−	0.930564i	$-0.380682\pi$
$179$	−5.42854	−	3.94406i	−0.405748	−	0.294793i	−0.771878	+	0.635771i	$0.780682\pi$
$180$	3.77456	−	1.12617i	0.281339	−	0.0839398i
$181$	−3.50264	+	10.7800i	−0.260349	+	0.801273i	0.732379	+	0.680897i	$0.238410\pi$
$181$	−3.50264	+	10.7800i	−0.260349	+	0.801273i	−0.992728	+	0.120376i	$0.961590\pi$
$182$	−4.31275	−	1.40130i	−0.319683	−	0.103871i
$183$	4.27184	+	5.87968i	0.315783	+	0.434638i
$184$	6.50824	+	4.72851i	0.479794	+	0.348591i
$185$	−13.3497	−	0.323249i	−0.981493	−	0.0237658i
$186$	−1.07670			−0.0789478
$187$	−1.23393	−	1.72700i	−0.0902341	−	0.126291i
$188$		−	2.67019i		−	0.194744i
$189$	1.57875	+	4.85890i	0.114837	+	0.353433i
$190$	−3.95201	+	2.72762i	−0.286709	+	0.197883i
$191$	−8.96911	+	6.51644i	−0.648982	+	0.471513i	−0.862924	−	0.505333i	$-0.831370\pi$
$191$	−8.96911	+	6.51644i	−0.648982	+	0.471513i	0.213942	+	0.976846i	$0.431370\pi$
$192$	−2.69387	−	0.875292i	−0.194413	−	0.0631687i
$193$	1.13371	+	0.368363i	0.0816060	+	0.0265154i	0.349535	−	0.936923i	$-0.386339\pi$
$193$	1.13371	+	0.368363i	0.0816060	+	0.0265154i	−0.267929	+	0.963439i	$0.586339\pi$
$194$	−5.64210	+	4.09922i	−0.405079	+	0.294307i
$195$	−2.30880	−	3.34519i	−0.165337	−	0.239554i
$196$	−10.3979	−	32.0014i	−0.742705	−	2.28581i
$197$		−	18.3551i		−	1.30775i	−0.756604	−	0.653873i	$-0.773143\pi$
$197$		−	18.3551i		−	1.30775i	0.756604	−	0.653873i	$-0.226857\pi$
$198$	0.0128426	−	1.61945i	0.000912686	−	0.115090i
$199$	−22.1761			−1.57202			−0.786011	−	0.618213i	$-0.787857\pi$
$199$	−22.1761			−1.57202			−0.786011	+	0.618213i	$0.787857\pi$
$200$	8.58676	+	3.25737i	0.607175	+	0.230331i
$201$	5.87021	+	4.26496i	0.414053	+	0.300827i
$202$	−1.23155	−	1.69508i	−0.0866515	−	0.119266i
$203$	36.7341	+	11.9356i	2.57823	+	0.837718i
$204$	−0.348367	+	1.07216i	−0.0243906	+	0.0750665i
$205$	4.78218	−	1.42680i	0.334002	−	0.0996523i
$206$	3.75212	+	2.72607i	0.261423	+	0.189935i
$207$	−4.16541	+	1.35342i	−0.289516	+	0.0940695i
$208$			4.77381i			0.331004i
$209$	−4.39721	−	13.9075i	−0.304161	−	0.962003i
$210$	−1.85171	+	5.26200i	−0.127780	+	0.363112i
$211$	2.56709	+	7.90070i	0.176726	+	0.543907i	0.999708	−	0.0241607i	$-0.00769134\pi$
$211$	2.56709	+	7.90070i	0.176726	+	0.543907i	−0.822982	+	0.568067i	$0.807691\pi$
$212$	9.50201	−	13.0784i	0.652601	−	0.898228i
$213$	3.23790	+	4.45659i	0.221857	+	0.305360i
$214$	1.24859	−	3.84277i	0.0853519	−	0.262686i
$215$	6.00636	+	4.59007i	0.409630	+	0.313040i
$216$	−1.48598	+	1.07962i	−0.101108	+	0.0734592i
$217$	−6.62156	+	9.11380i	−0.449501	+	0.618685i
$218$	5.80407	−	1.88586i	0.393101	−	0.127726i
$219$	−7.14322			−0.482694
$220$	−8.01455	+	10.3169i	−0.540341	+	0.695564i
$221$	1.16329			0.0782514
$222$	2.77337	−	0.901121i	0.186136	−	0.0604793i
$223$	−9.72765	+	13.3890i	−0.651412	+	0.896591i	−0.999159	−	0.0409971i	$-0.986947\pi$
$223$	−9.72765	+	13.3890i	−0.651412	+	0.896591i	0.347748	+	0.937588i	$0.386947\pi$
$224$	20.4839	−	14.8825i	1.36864	−	0.994376i
$225$	−4.18259	+	2.73970i	−0.278839	+	0.182647i
$226$	2.44591	−	7.52773i	0.162699	−	0.500737i
$227$	4.98618	+	6.86289i	0.330945	+	0.455506i	0.941769	−	0.336260i	$-0.109162\pi$
$227$	4.98618	+	6.86289i	0.330945	+	0.455506i	−0.610825	+	0.791766i	$0.709162\pi$
$228$	−4.55366	+	6.26757i	−0.301573	+	0.415080i
$229$	1.05032	+	3.23256i	0.0694073	+	0.213614i	0.979744	−	0.200255i	$-0.0641771\pi$
$229$	1.05032	+	3.23256i	0.0694073	+	0.213614i	−0.910336	+	0.413869i	$0.864177\pi$
$230$	−4.51098	−	1.58742i	−0.297445	−	0.104672i
$231$	−13.6289	−	10.0681i	−0.896719	−	0.662432i
$232$			13.8863i			0.911680i
$233$	−14.9433	+	4.85538i	−0.978969	+	0.318086i	−0.754431	−	0.656379i	$-0.772087\pi$
$233$	−14.9433	+	4.85538i	−0.978969	+	0.318086i	−0.224538	+	0.974465i	$0.572087\pi$
$234$	0.718083	+	0.521718i	0.0469426	+	0.0341058i
$235$	0.969058	+	3.24797i	0.0632144	+	0.211874i
$236$	−2.92413	+	8.99953i	−0.190344	+	0.585820i
$237$	1.81191	+	0.588726i	0.117696	+	0.0382419i
$238$	−0.938409	−	1.29161i	−0.0608280	−	0.0837226i
$239$	24.8346	+	18.0434i	1.60642	+	1.16713i	0.873521	+	0.486787i	$0.161831\pi$
$239$	24.8346	+	18.0434i	1.60642	+	1.16713i	0.732894	+	0.680342i	$0.238169\pi$
$240$	5.87072	+	0.142153i	0.378954	+	0.00917594i
$241$	5.59097			0.360146			0.180073	−	0.983653i	$-0.442367\pi$
$241$	5.59097			0.360146			0.180073	+	0.983653i	$0.442367\pi$
$242$	3.08785	+	4.39499i	0.198494	+	0.282520i
$243$		−	1.00000i		−	0.0641500i
$244$	3.95619	+	12.1759i	0.253269	+	0.779481i
$245$	24.2616	+	35.1522i	1.55002	+	2.24579i
$246$	−0.881661	+	0.640564i	−0.0562127	+	0.0408409i
$247$	7.60292	+	2.47034i	0.483762	+	0.157184i
$248$	−3.85187	−	1.25155i	−0.244594	−	0.0794733i
$249$	−0.130981	+	0.0951634i	−0.00830060	+	0.00603074i
$250$	−5.44495	−	0.396150i	−0.344369	−	0.0250547i
$251$	5.78594	+	17.8073i	0.365205	+	1.12399i	0.949852	+	0.312699i	$0.101233\pi$
$251$	5.78594	+	17.8073i	0.365205	+	1.12399i	−0.584647	+	0.811288i	$0.698767\pi$
$252$			8.99974i			0.566930i
$253$	8.63113	−	11.6838i	0.542635	−	0.734552i
$254$	4.82481			0.302736
$255$	0.0346401	−	1.43059i	0.00216925	−	0.0895869i
$256$	−0.121105	−	0.0879877i	−0.00756904	−	0.00549923i
$257$	2.92844	+	4.03065i	0.182671	+	0.251425i	0.890526	−	0.454933i	$-0.150337\pi$
$257$	2.92844	+	4.03065i	0.182671	+	0.251425i	−0.707855	+	0.706358i	$0.750337\pi$
$258$	−1.56999	−	0.510120i	−0.0977432	−	0.0317587i
$259$	9.42820	−	29.0170i	0.585840	−	1.80303i
$260$	−2.04708	−	6.86116i	−0.126955	−	0.425511i
$261$	−6.11631	−	4.44376i	−0.378590	−	0.275062i
$262$	−5.93640	+	1.92885i	−0.366752	+	0.119165i
$263$			20.0788i			1.23811i	0.785347	+	0.619055i	$0.212484\pi$
$263$			20.0788i			1.23811i	−0.785347	+	0.619055i	$0.787516\pi$
$264$	1.92838	−	5.77860i	0.118683	−	0.355648i
$265$	−6.81167	+	19.3567i	−0.418438	+	1.18907i
$266$	−3.39033	−	10.4344i	−0.207875	−	0.639772i
$267$	−0.702631	+	0.967089i	−0.0430003	+	0.0591849i
$268$	7.51300	+	10.3408i	0.458930	+	0.631662i
$269$	2.94502	−	9.06382i	0.179561	−	0.552631i	−0.820252	−	0.572003i	$-0.806167\pi$
$269$	2.94502	−	9.06382i	0.179561	−	0.552631i	0.999812	+	0.0193717i	$0.00616660\pi$
$270$	0.662979	−	0.867546i	0.0403476	−	0.0527972i
$271$	0.955407	−	0.694144i	0.0580369	−	0.0421662i	−0.558389	−	0.829580i	$-0.688580\pi$
$271$	0.955407	−	0.694144i	0.0580369	−	0.0421662i	0.616425	+	0.787413i	$0.288580\pi$
$272$	−0.987892	+	1.35972i	−0.0598997	+	0.0824449i
$273$	8.83220	−	2.86976i	0.534549	−	0.173686i
$274$	−9.30645			−0.562223
$275$	6.00456	−	15.4579i	0.362089	−	0.932144i
$276$	−7.71525			−0.464404
$277$	7.81937	−	2.54067i	0.469820	−	0.152654i	−0.0645323	−	0.997916i	$-0.520556\pi$
$277$	7.81937	−	2.54067i	0.469820	−	0.152654i	0.534352	+	0.845262i	$0.320556\pi$
$278$	−3.36227	+	4.62777i	−0.201656	+	0.277555i
$279$	1.78389	−	1.29607i	0.106799	−	0.0775938i
$280$	−12.7409	+	16.6722i	−0.761414	+	0.996354i
$281$	3.22778	−	9.93410i	0.192553	−	0.592619i	−0.807443	−	0.589946i	$-0.799149\pi$
$281$	3.22778	−	9.93410i	0.192553	−	0.592619i	0.999996	−	0.00267298i	$-0.000850837\pi$
$282$	−0.435059	−	0.598807i	−0.0259074	−	0.0356585i
$283$	14.6043	−	20.1011i	0.868136	−	1.19489i	−0.111432	−	0.993772i	$-0.535544\pi$
$283$	14.6043	−	20.1011i	0.868136	−	1.19489i	0.979568	−	0.201114i	$-0.0644563\pi$
$284$	2.99865	+	9.22889i	0.177937	+	0.547634i
$285$	3.26436	−	9.27634i	0.193364	−	0.549483i
$286$	−2.94374	−	0.0233445i	−0.174067	−	0.00138039i
$287$			11.4022i			0.673052i
$288$	−4.71336	+	1.53146i	−0.277738	+	0.0902424i
$289$	−13.4220	−	9.75162i	−0.789527	−	0.573625i
$290$	−2.36006	−	7.91016i	−0.138588	−	0.464501i
$291$	4.41347	−	13.5832i	0.258722	−	0.796264i
$292$	−11.9674	−	3.88844i	−0.700338	−	0.227554i
$293$	−14.5926	−	20.0850i	−0.852508	−	1.17338i	−0.983305	−	0.181967i	$-0.941754\pi$
$293$	−14.5926	−	20.0850i	−0.852508	−	1.17338i	0.130797	−	0.991409i	$-0.458246\pi$
$294$	−7.54583	−	5.48237i	−0.440082	−	0.319738i
$295$	0.290762	−	12.0081i	0.0169288	−	0.699136i
$296$	10.9691			0.637563
$297$	1.92812	+	2.69858i	0.111881	+	0.156588i
$298$			3.64136i			0.210939i
$299$	2.46017	+	7.57163i	0.142275	+	0.437879i
$300$	−8.49865	+	2.31315i	−0.490670	+	0.133550i
$301$	−13.9731	+	10.1521i	−0.805397	+	0.585155i
$302$	2.30298	+	0.748285i	0.132522	+	0.0430589i
$303$	4.08088	+	1.32596i	0.234440	+	0.0761743i
$304$	−9.34404	+	6.78884i	−0.535917	+	0.389367i
$305$	−9.23106	−	13.3747i	−0.528569	−	0.765835i
$306$	0.0965661	+	0.297200i	0.00552032	+	0.0169898i
$307$		−	12.4687i		−	0.711624i	−0.934557	−	0.355812i	$-0.884204\pi$
$307$		−	12.4687i		−	0.711624i	0.934557	−	0.355812i	$-0.115796\pi$
$308$	−17.3526	−	24.2865i	−0.988757	−	1.38385i
$309$	−9.49802			−0.540324
$310$	2.40688	+	0.0582799i	0.136701	+	0.00331007i
$311$	2.55580	+	1.85690i	0.144926	+	0.105295i	0.657886	−	0.753118i	$-0.271451\pi$
$311$	2.55580	+	1.85690i	0.144926	+	0.105295i	−0.512960	+	0.858413i	$0.671451\pi$
$312$	1.96248	+	2.70112i	0.111103	+	0.152921i
$313$	13.5951	+	4.41733i	0.768442	+	0.249682i	0.666898	−	0.745149i	$-0.267622\pi$
$313$	13.5951	+	4.41733i	0.768442	+	0.249682i	0.101544	+	0.994831i	$0.467622\pi$
$314$	−3.10712	+	9.56272i	−0.175345	+	0.539655i
$315$	−3.26616	−	10.9471i	−0.184027	−	0.616799i
$316$	2.71511	+	1.97264i	0.152737	+	0.110970i
$317$	25.5616	−	8.30548i	1.43568	−	0.466482i	0.515135	−	0.857109i	$-0.327742\pi$
$317$	25.5616	−	8.30548i	1.43568	−	0.466482i	0.920549	+	0.390627i	$0.127742\pi$
$318$		−	4.48109i		−	0.251287i
$319$	25.0735	+	0.198838i	1.40385	+	0.0111328i
$320$	5.97453	+	2.10245i	0.333987	+	0.117531i
$321$	2.55702	+	7.86970i	0.142719	+	0.439244i
$322$	6.42225	−	8.83947i	0.357898	−	0.492605i
$323$	1.65432	+	2.27697i	0.0920486	+	0.126694i
$324$	0.544353	−	1.67535i	0.0302418	−	0.0930748i
$325$	4.98006	+	7.60285i	0.276244	+	0.421730i
$326$	2.85526	−	2.07447i	0.158138	−	0.114894i
$327$	−7.34614	+	10.1111i	−0.406243	+	0.559145i
$328$	−3.89869	+	1.26676i	−0.215269	+	0.0699452i
$329$	−7.74418			−0.426950
$330$	−0.116366	+	3.61945i	−0.00640576	+	0.199244i
$331$	19.7763			1.08700			0.543502	−	0.839408i	$-0.317098\pi$
$331$	19.7763			1.08700			0.543502	+	0.839408i	$0.317098\pi$
$332$	−0.271241	+	0.0881317i	−0.0148863	+	0.00483686i
$333$	−3.51022	+	4.83140i	−0.192359	+	0.264759i
$334$	−7.23440	+	5.25610i	−0.395849	+	0.287601i
$335$	−12.8915	−	9.85169i	−0.704338	−	0.538255i
$336$	−4.14618	+	12.7606i	−0.226192	+	0.696149i
$337$	−8.38067	−	11.5350i	−0.456524	−	0.628352i	0.517259	−	0.855829i	$-0.326952\pi$
$337$	−8.38067	−	11.5350i	−0.456524	−	0.628352i	−0.973783	+	0.227477i	$0.926952\pi$
$338$	−2.78285	+	3.83026i	−0.151367	+	0.208339i
$339$	5.00904	+	15.4162i	0.272054	+	0.837295i
$340$	0.836779	−	2.37787i	0.0453807	−	0.128958i
$341$	−2.31498	+	6.93712i	−0.125363	+	0.375666i
$342$			2.14748i			0.116122i
$343$	−58.7991	+	19.1050i	−3.17485	+	1.03157i
$344$	−5.02361	−	3.64987i	−0.270855	−	0.196788i
$345$	9.38467	−	2.80000i	0.505254	−	0.150747i
$346$	1.81308	−	5.58008i	0.0974717	−	0.299987i
$347$	15.0223	+	4.88104i	0.806439	+	0.262028i	0.683089	−	0.730335i	$-0.260636\pi$
$347$	15.0223	+	4.88104i	0.806439	+	0.262028i	0.123350	+	0.992363i	$0.460636\pi$
$348$	−7.82797	−	10.7743i	−0.419623	−	0.577562i
$349$	1.38699	+	1.00771i	0.0742439	+	0.0539414i	0.624288	−	0.781194i	$-0.285389\pi$
$349$	1.38699	+	1.00771i	0.0742439	+	0.0539414i	−0.550044	+	0.835136i	$0.685389\pi$
$350$	4.42415	−	11.6625i	0.236481	−	0.623387i
$351$	−1.81774			−0.0970237
$352$	9.76654	−	13.2207i	0.520558	−	0.704667i
$353$		−	13.9610i		−	0.743072i	−0.928419	−	0.371536i	$-0.878831\pi$
$353$		−	13.9610i		−	0.743072i	0.928419	−	0.371536i	$-0.121169\pi$
$354$	0.810556	+	2.49464i	0.0430806	+	0.132588i
$355$	−6.99681	−	10.1376i	−0.371352	−	0.538046i
$356$	−1.70359	+	1.23773i	−0.0902901	+	0.0655996i
$357$	3.10953	+	1.01035i	0.164574	+	0.0534732i
$358$	−3.11614	−	1.01250i	−0.164693	−	0.0535121i
$359$	−27.7543	+	20.1647i	−1.46482	+	1.06425i	−0.482741	+	0.875763i	$0.660359\pi$
$359$	−27.7543	+	20.1647i	−1.46482	+	1.06425i	−0.982075	+	0.188488i	$0.939641\pi$
$360$	3.38021	−	2.33297i	0.178153	−	0.122959i
$361$	0.105471	+	0.324607i	0.00555112	+	0.0170846i
$362$			5.53476i			0.290901i
$363$	−10.4064	−	3.56468i	−0.546194	−	0.187097i
$364$	16.3592			0.857453
$365$	15.9681	+	0.386649i	0.835806	+	0.0202381i
$366$	2.87104	+	2.08593i	0.150072	+	0.109033i
$367$	−2.12335	−	2.92254i	−0.110838	−	0.152555i	0.749994	−	0.661444i	$-0.230056\pi$
$367$	−2.12335	−	2.92254i	−0.110838	−	0.152555i	−0.860832	+	0.508889i	$0.830056\pi$
$368$	−10.9394	−	3.55441i	−0.570254	−	0.185287i
$369$	0.689669	−	2.12258i	0.0359027	−	0.110497i
$370$	−6.24839	+	1.86426i	−0.324838	+	0.0969183i
$371$	−37.9304	−	27.5580i	−1.96925	−	1.43074i
$372$	3.69416	−	1.20030i	0.191533	−	0.0622329i
$373$			18.7064i			0.968579i	0.874908	+	0.484290i	$0.160922\pi$
$373$			18.7064i			0.968579i	−0.874908	+	0.484290i	$0.839078\pi$
$374$	−0.833630	−	0.615826i	−0.0431060	−	0.0318436i
$375$	9.49810	−	5.89797i	0.490480	−	0.304570i
$376$	−0.860360	−	2.64792i	−0.0443697	−	0.136556i
$377$	−8.07760	+	11.1179i	−0.416017	+	0.572599i
$378$	1.46634	+	2.01825i	0.0754206	+	0.103808i
$379$	2.89693	−	8.91585i	0.148806	−	0.457976i	−0.848675	−	0.528914i	$-0.822599\pi$
$379$	2.89693	−	8.91585i	0.148806	−	0.457976i	0.997481	+	0.0709381i	$0.0225993\pi$
$380$	10.5186	−	13.7641i	0.539590	−	0.706085i
$381$	−7.99379	+	5.80783i	−0.409534	+	0.297544i
$382$	−3.18197	+	4.37960i	−0.162804	+	0.224080i
$383$	−18.2750	+	5.93791i	−0.933809	+	0.303413i	−0.736119	−	0.676852i	$-0.763344\pi$
$383$	−18.2750	+	5.93791i	−0.933809	+	0.303413i	−0.197689	+	0.980265i	$0.563344\pi$
$384$	−11.2950			−0.576393
$385$	29.9213	+	23.2441i	1.52493	+	1.18463i
$386$	0.582076			0.0296269
$387$	3.21522	−	1.04469i	0.163439	−	0.0531045i
$388$	14.7882	−	20.3542i	0.750756	−	1.03333i
$389$	−7.52143	+	5.46464i	−0.381352	+	0.277068i	−0.761902	−	0.647692i	$-0.775734\pi$
$389$	−7.52143	+	5.46464i	−0.381352	+	0.277068i	0.380551	+	0.924760i	$0.375734\pi$
$390$	−1.57697	−	1.20512i	−0.0798531	−	0.0610238i
$391$	−0.866145	+	2.66572i	−0.0438028	+	0.134811i
$392$	−20.6223	−	28.3841i	−1.04158	−	1.43361i
$393$	7.51362	−	10.3416i	0.379012	−	0.521666i
$394$	−2.76965	−	8.52410i	−0.139533	−	0.429438i
$395$	−4.01851	−	1.41412i	−0.202193	−	0.0711522i
$396$	1.76130	+	5.57064i	0.0885085	+	0.279935i
$397$			13.8693i			0.696078i	0.937480	+	0.348039i	$0.113152\pi$
$397$			13.8693i			0.696078i	−0.937480	+	0.348039i	$0.886848\pi$
$398$	−10.2986	+	3.34621i	−0.516221	+	0.167730i
$399$	18.1774	+	13.2067i	0.910009	+	0.661160i
$400$	−13.1158	−	0.635542i	−0.655790	−	0.0317771i
$401$	3.28595	−	10.1131i	0.164093	−	0.505025i	−0.834876	−	0.550439i	$-0.814461\pi$
$401$	3.28595	−	10.1131i	0.164093	−	0.505025i	0.998968	+	0.0454134i	$0.0144605\pi$
$402$	3.36968	+	1.09487i	0.168064	+	0.0546074i
$403$	−2.35592	−	3.24265i	−0.117357	−	0.161528i
$404$	6.11510	+	4.44288i	0.304238	+	0.221042i
$405$	−0.0541280	+	2.23541i	−0.00268964	+	0.111079i
$406$	18.8603			0.936022
$407$	0.157066	−	19.8060i	0.00778549	−	0.981749i
$408$			1.17547i			0.0581943i
$409$	−1.14744	−	3.53146i	−0.0567374	−	0.174620i	0.918672	−	0.395022i	$-0.129263\pi$
$409$	−1.14744	−	3.53146i	−0.0567374	−	0.174620i	−0.975409	+	0.220402i	$0.929263\pi$
$410$	2.00555	−	1.38420i	0.0990470	−	0.0683609i
$411$	15.4190	−	11.2026i	0.760563	−	0.552581i
$412$	−15.9125	−	5.17028i	−0.783952	−	0.254721i
$413$	26.1007	+	8.48064i	1.28433	+	0.417305i
$414$	−1.73019	+	1.25706i	−0.0850344	+	0.0617811i
$415$	0.297948	−	0.205640i	0.0146257	−	0.0100945i
$416$	2.78380	+	8.56766i	0.136487	+	0.420064i
$417$		−	11.7146i		−	0.573668i
$418$	−4.14060	−	5.79514i	−0.202524	−	0.283450i
$419$	15.8996			0.776745			0.388372	−	0.921503i	$-0.373037\pi$
$419$	15.8996			0.776745			0.388372	+	0.921503i	$0.373037\pi$
$420$	0.487138	−	20.1181i	0.0237699	−	0.981664i
$421$	−3.53268	−	2.56665i	−0.172172	−	0.125091i	0.498362	−	0.866969i	$-0.333935\pi$
$421$	−3.53268	−	2.56665i	−0.172172	−	0.125091i	−0.670534	+	0.741878i	$0.733935\pi$
$422$	2.38431	+	3.28173i	0.116067	+	0.159752i
$423$	1.44162	+	0.468410i	0.0700939	+	0.0227749i
$424$	5.20876	−	16.0309i	0.252960	−	0.778531i
$425$	−0.154870	+	3.19608i	−0.00751229	+	0.155033i
$426$	2.17615	+	1.58106i	0.105435	+	0.0766027i
$427$	35.3129	−	11.4739i	1.70891	−	0.555259i
$428$			14.5764i			0.704577i
$429$	4.90531	−	3.50483i	0.236831	−	0.169215i
$430$	3.48196	+	1.22531i	0.167915	+	0.0590897i
$431$	6.21141	+	19.1168i	0.299193	+	0.920822i	0.981781	+	0.190018i	$0.0608546\pi$
$431$	6.21141	+	19.1168i	0.299193	+	0.920822i	−0.682587	+	0.730804i	$0.739145\pi$
$432$	1.54366	−	2.12467i	0.0742695	−	0.102223i
$433$	−18.0586	−	24.8556i	−0.867842	−	1.19448i	−0.979642	−	0.200751i	$-0.935662\pi$
$433$	−18.0586	−	24.8556i	−0.867842	−	1.19448i	0.111800	−	0.993731i	$-0.464338\pi$
$434$	−1.69985	+	5.23159i	−0.0815953	+	0.251124i
$435$	13.4320	+	10.2647i	0.644013	+	0.492155i
$436$	−17.8113	+	12.9407i	−0.853009	+	0.619747i
$437$	−11.3217	+	15.5830i	−0.541592	+	0.745438i
$438$	−3.31731	+	1.07786i	−0.158507	+	0.0515021i
$439$	20.6104			0.983679			0.491840	−	0.870686i	$-0.336325\pi$
$439$	20.6104			0.983679			0.491840	+	0.870686i	$0.336325\pi$
$440$	−4.62350	+	12.8132i	−0.220417	+	0.610844i
$441$	19.1013			0.909587
$442$	0.540232	−	0.175532i	0.0256962	−	0.00834920i
$443$	−8.11126	+	11.1642i	−0.385378	+	0.530427i	−0.956999	−	0.290091i	$-0.906315\pi$
$443$	−8.11126	+	11.1642i	−0.385378	+	0.530427i	0.571622	+	0.820517i	$0.306315\pi$
$444$	−8.51082	+	6.18347i	−0.403906	+	0.293455i
$445$	1.62302	−	2.12381i	0.0769384	−	0.100678i
$446$	−2.49722	+	7.68566i	−0.118247	+	0.363927i
$447$	−4.38326	−	6.03304i	−0.207321	−	0.285353i
$448$	−8.50590	+	11.7074i	−0.401866	+	0.553121i
$449$	−8.42097	−	25.9171i	−0.397410	−	1.22310i	−0.927069	−	0.374892i	$-0.877680\pi$
$449$	−8.42097	−	25.9171i	−0.397410	−	1.22310i	0.529658	−	0.848211i	$-0.322320\pi$
$450$	−1.52899	+	1.90344i	−0.0720773	+	0.0897290i
$451$	2.23148	+	7.05773i	0.105076	+	0.332336i
$452$			28.5542i			1.34308i
$453$	−4.71634	+	1.53243i	−0.221593	+	0.0719999i
$454$	3.35114	+	2.43475i	0.157277	+	0.114268i
$455$	−19.8990	+	5.93702i	−0.932877	+	0.278332i
$456$	−2.49620	+	7.68252i	−0.116895	+	0.359767i
$457$	4.39631	+	1.42845i	0.205651	+	0.0668199i	0.410031	−	0.912072i	$-0.365518\pi$
$457$	4.39631	+	1.42845i	0.205651	+	0.0668199i	−0.204380	+	0.978892i	$0.565518\pi$
$458$	0.975540	+	1.34272i	0.0455840	+	0.0627410i
$459$	−0.517743	−	0.376162i	−0.0241662	−	0.0175578i
$460$	17.2468	+	0.417612i	0.804135	+	0.0194712i
$461$	−25.3940			−1.18272			−0.591359	−	0.806409i	$-0.701408\pi$
$461$	−25.3940			−1.18272			−0.591359	+	0.806409i	$0.701408\pi$
$462$	−7.84848	−	2.61911i	−0.365144	−	0.121852i
$463$			12.8949i			0.599275i	0.954053	+	0.299638i	$0.0968658\pi$
$463$			12.8949i			0.599275i	−0.954053	+	0.299638i	$0.903134\pi$
$464$	−6.13548	−	18.8831i	−0.284832	−	0.876624i
$465$	−4.05789	+	2.80070i	−0.188180	+	0.129879i
$466$	−6.20703	+	4.50967i	−0.287535	+	0.208907i
$467$	−3.62377	−	1.17743i	−0.167688	−	0.0544851i	0.223970	−	0.974596i	$-0.428098\pi$
$467$	−3.62377	−	1.17743i	−0.167688	−	0.0544851i	−0.391658	+	0.920111i	$0.628098\pi$
$468$	−3.04534	−	0.989492i	−0.140771	−	0.0457393i
$469$	29.9906	−	21.7894i	1.38484	−	1.00614i
$470$	0.940124	+	1.36213i	0.0433647	+	0.0628304i
$471$	−6.36314	−	19.5837i	−0.293198	−	0.902371i
$472$			9.86664i			0.454149i
$473$	−6.66224	+	9.01852i	−0.306330	+	0.414672i
$474$	0.930287			0.0427295
$475$	−7.79931	+	20.5598i	−0.357857	+	0.943346i
$476$	4.65955	+	3.38536i	0.213570	+	0.155168i
$477$	5.39407	+	7.42431i	0.246978	+	0.339936i
$478$	14.2558	+	4.63199i	0.652044	+	0.211862i
$479$	−3.79836	+	11.6902i	−0.173552	+	0.534137i	−0.999564	−	0.0295147i	$-0.990604\pi$
$479$	−3.79836	+	11.6902i	−0.173552	+	0.534137i	0.826013	+	0.563651i	$0.190604\pi$
$480$	10.6192	−	3.16833i	0.484698	−	0.144614i
$481$	8.78222	+	6.38065i	0.400435	+	0.290933i
$482$	2.59645	−	0.843636i	0.118265	−	0.0384266i
$483$			22.3760i			1.01814i
$484$	−15.4939	−	11.6368i	−0.704267	−	0.528947i
$485$	−10.6012	+	30.1253i	−0.481373	+	1.36792i
$486$	−0.150893	−	0.464400i	−0.00684463	−	0.0210656i
$487$	−7.89920	+	10.8723i	−0.357947	+	0.492671i	−0.949575	−	0.313539i	$-0.898485\pi$
$487$	−7.89920	+	10.8723i	−0.357947	+	0.492671i	0.591628	+	0.806211i	$0.298485\pi$
$488$	7.84637	+	10.7996i	0.355188	+	0.488875i
$489$	−2.23349	+	6.87399i	−0.101002	+	0.310852i
$490$	16.5713	+	12.6638i	0.748615	+	0.572092i
$491$	4.92030	−	3.57480i	0.222050	−	0.161329i	−0.471199	−	0.882027i	$-0.656179\pi$
$491$	4.92030	−	3.57480i	0.222050	−	0.161329i	0.693249	+	0.720698i	$0.256179\pi$
$492$	2.31087	−	3.18064i	0.104182	−	0.143394i
$493$	−4.60145	+	1.49510i	−0.207239	+	0.0673361i
$494$	3.90355			0.175629
$495$	−4.16408	−	6.13681i	−0.187162	−	0.275829i
$496$	5.79088			0.260018
$497$	26.7659	−	8.69678i	1.20062	−	0.390104i
$498$	−0.0464682	+	0.0639580i	−0.00208229	+	0.00286602i
$499$	15.2048	−	11.0470i	0.680662	−	0.494530i	−0.192915	−	0.981215i	$-0.561794\pi$
$499$	15.2048	−	11.0470i	0.680662	−	0.494530i	0.873577	+	0.486686i	$0.161794\pi$
$500$	19.1232	−	4.71082i	0.855215	−	0.210674i
$501$	5.65902	−	17.4167i	0.252826	−	0.778120i
$502$	5.37398	+	7.39665i	0.239852	+	0.330128i
$503$	3.56554	−	4.90754i	0.158979	−	0.218816i	−0.722095	−	0.691794i	$-0.756821\pi$
$503$	3.56554	−	4.90754i	0.158979	−	0.218816i	0.881075	+	0.472977i	$0.156821\pi$
$504$	2.89980	+	8.92466i	0.129167	+	0.397536i
$505$	−9.05068	−	3.18495i	−0.402750	−	0.141729i
$506$	2.24530	−	6.72831i	0.0998159	−	0.299110i
$507$		−	9.69583i		−	0.430607i
$508$	−16.5539	+	5.37868i	−0.734459	+	0.238640i
$509$	−15.9735	−	11.6055i	−0.708014	−	0.514403i	0.174518	−	0.984654i	$-0.444163\pi$
$509$	−15.9735	−	11.6055i	−0.708014	−	0.514403i	−0.882533	+	0.470251i	$0.844163\pi$
$510$	−0.199778	−	0.669591i	−0.00884633	−	0.0296500i
$511$	−11.2774	+	34.7082i	−0.498882	+	1.53540i
$512$	−21.5538	−	7.00325i	−0.952552	−	0.309503i
$513$	−2.58501	−	3.55796i	−0.114131	−	0.157088i
$514$	1.96816	+	1.42995i	0.0868118	+	0.0630725i
$515$	21.2320	+	0.514109i	0.935594	+	0.0226544i
$516$	5.95529			0.262167
$517$	−4.79348	+	1.51558i	−0.210817	+	0.0666550i
$518$		−	14.8981i		−	0.654587i
$519$	3.71305	+	11.4276i	0.162985	+	0.501616i
$520$	−4.24074	−	6.14433i	−0.185969	−	0.269447i
$521$	34.0947	−	24.7713i	1.49372	−	1.08525i	0.520916	−	0.853608i	$-0.325590\pi$
$521$	34.0947	−	24.7713i	1.49372	−	1.08525i	0.972801	−	0.231641i	$-0.0744096\pi$
$522$	−3.51095	−	1.14078i	−0.153670	−	0.0499304i
$523$	−6.05868	−	1.96858i	−0.264927	−	0.0860801i	0.173541	−	0.984827i	$-0.444479\pi$
$523$	−6.05868	−	1.96858i	−0.264927	−	0.0860801i	−0.438469	+	0.898746i	$0.644479\pi$
$524$	18.2174	−	13.2357i	0.795832	−	0.578206i
$525$	6.70867	+	24.6481i	0.292790	+	1.07573i
$526$	3.02974	+	9.32458i	0.132103	+	0.406571i
$527$		−	1.41113i		−	0.0614698i
$528$	−0.0690720	+	8.70997i	−0.00300597	+	0.379053i
$529$	3.81758			0.165982
$530$	−0.242553	+	10.0171i	−0.0105358	+	0.435115i
$531$	−4.34583	−	3.15743i	−0.188593	−	0.137021i
$532$	23.2644	+	32.0207i	1.00864	+	1.38827i
$533$	−3.85830	−	1.25364i	−0.167122	−	0.0543011i
$534$	−0.180375	+	0.555138i	−0.00780560	+	0.0240232i
$535$	−5.29003	−	17.7304i	−0.228708	−	0.766554i
$536$	10.7822	+	7.83374i	0.465721	+	0.338366i
$537$	6.38163	−	2.07352i	0.275388	−	0.0894788i
$538$		−	4.65362i		−	0.200632i
$539$	−51.5465	+	36.8297i	−2.22026	+	1.58637i
$540$	−1.30754	+	3.71563i	−0.0562675	+	0.159895i
$541$	−3.80322	−	11.7051i	−0.163513	−	0.503242i	0.835410	−	0.549627i	$-0.185230\pi$
$541$	−3.80322	−	11.7051i	−0.163513	−	0.503242i	−0.998924	+	0.0463847i	$0.985230\pi$
$542$	0.338950	−	0.466524i	0.0145591	−	0.0200389i
$543$	−6.66242	−	9.17003i	−0.285912	−	0.393524i
$544$	−0.980085	+	3.01639i	−0.0420208	+	0.129327i
$545$	16.9690	−	22.2048i	0.726870	−	0.951151i
$546$	3.66865	−	2.66543i	0.157004	−	0.114070i
$547$	−3.22658	+	4.44101i	−0.137959	+	0.189884i	−0.872406	−	0.488782i	$-0.837441\pi$
$547$	−3.22658	+	4.44101i	−0.137959	+	0.189884i	0.734447	+	0.678666i	$0.237441\pi$
$548$	31.9303	−	10.3748i	1.36400	−	0.443189i
$549$	−7.26768			−0.310177
$550$	0.456041	−	8.08467i	0.0194456	−	0.344731i
$551$	−33.2487			−1.41644
$552$	−7.65089	+	2.48593i	−0.325644	+	0.105808i
$553$	5.72112	−	7.87445i	0.243287	−	0.334856i
$554$	3.24794	−	2.35977i	0.137992	−	0.100257i
$555$	8.10830	−	10.6102i	0.344178	−	0.450377i
$556$	6.37690	−	19.6261i	0.270441	−	0.832331i
$557$	14.9671	+	20.6005i	0.634178	+	0.872870i	0.998288	−	0.0584852i	$-0.0186270\pi$
$557$	14.9671	+	20.6005i	0.634178	+	0.872870i	−0.364111	+	0.931356i	$0.618627\pi$
$558$	0.632871	−	0.871072i	0.0267916	−	0.0368754i
$559$	−1.89897	−	5.84443i	−0.0803179	−	0.247193i
$560$	9.95912	−	28.3008i	0.420850	−	1.19593i
$561$	2.12246	+	0.0168316i	0.0896103	+	0.000710630i
$562$		−	5.10044i		−	0.215149i
$563$	−36.4756	+	11.8517i	−1.53726	+	0.499488i	−0.950620	−	0.310357i	$-0.899551\pi$
$563$	−36.4756	+	11.8517i	−1.53726	+	0.499488i	−0.586644	+	0.809845i	$0.699551\pi$
$564$	2.16023	+	1.56950i	0.0909621	+	0.0660878i
$565$	−10.3628	−	34.7328i	−0.435967	−	1.46122i
$566$	3.74913	−	11.5386i	0.157588	−	0.485005i
$567$	−4.85890	−	1.57875i	−0.204054	−	0.0663013i
$568$	5.94727	+	8.18571i	0.249542	+	0.343465i
$569$	7.40449	+	5.37967i	0.310412	+	0.225528i	0.732073	−	0.681226i	$-0.238553\pi$
$569$	7.40449	+	5.37967i	0.310412	+	0.225528i	−0.421661	+	0.906753i	$0.638553\pi$
$570$	0.116239	−	4.80050i	0.00486871	−	0.201071i
$571$	−18.3508			−0.767957			−0.383978	−	0.923342i	$-0.625446\pi$
$571$	−18.3508			−0.767957			−0.383978	+	0.923342i	$0.625446\pi$
$572$	10.1260	−	3.20158i	0.423388	−	0.133865i
$573$		−	11.0864i		−	0.463142i
$574$	1.72051	+	5.29519i	0.0718128	+	0.221017i
$575$	−21.1302	+	5.75117i	−0.881189	+	0.239841i
$576$	2.29154	−	1.66490i	0.0954810	−	0.0693710i
$577$	18.9562	+	6.15925i	0.789158	+	0.256413i	0.675745	−	0.737135i	$-0.263822\pi$
$577$	18.9562	+	6.15925i	0.789158	+	0.256413i	0.113412	+	0.993548i	$0.463822\pi$
$578$	−7.70460	−	2.50338i	−0.320469	−	0.104127i
$579$	−0.964388	+	0.700669i	−0.0400786	+	0.0291188i
$580$	16.9156	+	24.5087i	0.702380	+	1.01767i
$581$	0.255602	+	0.786663i	0.0106042	+	0.0326363i
$582$		−	6.97402i		−	0.289082i
$583$	−28.8713	−	9.63464i	−1.19573	−	0.399026i
$584$	−13.1204			−0.542928
$585$	4.06340	+	0.0983906i	0.168001	+	0.00406795i
$586$	−9.80746	−	7.12554i	−0.405143	−	0.294353i
$587$	−23.2448	−	31.9938i	−0.959417	−	1.32052i	−0.947215	−	0.320598i	$-0.896116\pi$
$587$	−23.2448	−	31.9938i	−0.959417	−	1.32052i	−0.0122016	−	0.999926i	$-0.503884\pi$
$588$	32.0014	+	10.3979i	1.31971	+	0.428801i
$589$	2.99665	−	9.22274i	0.123475	−	0.380016i
$590$	−1.67690	−	5.62041i	−0.0690368	−	0.231389i
$591$	14.8496	+	10.7889i	0.610830	+	0.443794i
$592$	−14.9161	+	4.84654i	−0.613048	+	0.199191i
$593$		−	12.3314i		−	0.506391i	−0.967415	−	0.253195i	$-0.918518\pi$
$593$		−	12.3314i		−	0.506391i	0.967415	−	0.253195i	$-0.0814816\pi$
$594$	1.30262	+	0.962280i	0.0534470	+	0.0394828i
$595$	−6.89639	−	2.42685i	−0.282724	−	0.0994913i
$596$	−4.05938	−	12.4935i	−0.166278	−	0.511753i
$597$	13.0348	−	17.9408i	0.533478	−	0.734269i
$598$	2.28501	+	3.14504i	0.0934409	+	0.128610i
$599$	−10.7382	+	33.0487i	−0.438750	+	1.35034i	0.450444	+	0.892805i	$0.351266\pi$
$599$	−10.7382	+	33.0487i	−0.438750	+	1.35034i	−0.889194	+	0.457530i	$0.848734\pi$
$600$	−7.68244	+	5.03220i	−0.313634	+	0.205439i
$601$	−31.2359	+	22.6942i	−1.27414	+	0.925717i	−0.999359	−	0.0357903i	$-0.988605\pi$
$601$	−31.2359	+	22.6942i	−1.27414	+	0.925717i	−0.274780	+	0.961507i	$0.588605\pi$
$602$	−4.95724	+	6.82306i	−0.202042	+	0.278087i
$603$	−6.90085	+	2.24222i	−0.281024	+	0.0913103i
$604$	−8.73569			−0.355450
$605$	23.0696	+	8.53180i	0.937914	+	0.346867i
$606$	2.09524			0.0851132
$607$	5.95686	−	1.93550i	0.241781	−	0.0785596i	−0.185620	−	0.982622i	$-0.559429\pi$
$607$	5.95686	−	1.93550i	0.241781	−	0.0785596i	0.427401	+	0.904062i	$0.359429\pi$
$608$	−12.8111	+	17.6330i	−0.519558	+	0.715111i
$609$	−31.2479	+	22.7029i	−1.26623	+	0.919970i
$610$	−6.30505	−	4.81832i	−0.255284	−	0.195088i
$611$	0.851447	−	2.62048i	0.0344459	−	0.106013i
$612$	−0.662634	−	0.912038i	−0.0267854	−	0.0368669i
$613$	11.1627	−	15.3641i	0.450856	−	0.620550i	−0.521725	−	0.853114i	$-0.674711\pi$
$613$	11.1627	−	15.3641i	0.450856	−	0.620550i	0.972581	+	0.232564i	$0.0747114\pi$
$614$	−1.88143	−	5.79045i	−0.0759283	−	0.233683i
$615$	−1.65659	+	4.70752i	−0.0668000	+	0.189825i
$616$	−25.0332	−	18.4928i	−1.00862	−	0.745094i
$617$			7.58574i			0.305390i	0.988273	+	0.152695i	$0.0487953\pi$
$617$			7.58574i			0.305390i	−0.988273	+	0.152695i	$0.951205\pi$
$618$	−4.41088	+	1.43318i	−0.177432	+	0.0576510i
$619$	22.6359	+	16.4460i	0.909814	+	0.661019i	0.940968	−	0.338496i	$-0.109918\pi$
$619$	22.6359	+	16.4460i	0.909814	+	0.661019i	−0.0311537	+	0.999515i	$0.509918\pi$
$620$	−8.32294	+	2.48322i	−0.334257	+	0.0997285i
$621$	1.35342	−	4.16541i	0.0543111	−	0.167152i
$622$	1.46710	+	0.476691i	0.0588255	+	0.0191136i
$623$	3.58971	+	4.94081i	0.143819	+	0.197949i
$624$	−3.86210	−	2.80598i	−0.154608	−	0.112329i
$625$	−21.5514	+	12.6703i	−0.862057	+	0.506811i
$626$	6.98012			0.278982
$627$	13.8360	+	4.61722i	0.552558	+	0.184394i
$628$		−	36.2734i		−	1.44746i
$629$	1.18101	+	3.63478i	0.0470900	+	0.144928i
$630$	−3.16864	−	4.59099i	−0.126242	−	0.182909i
$631$	20.5750	−	14.9486i	0.819078	−	0.595095i	−0.0973702	−	0.995248i	$-0.531043\pi$
$631$	20.5750	−	14.9486i	0.819078	−	0.595095i	0.916448	+	0.400153i	$0.131043\pi$
$632$	3.32806	+	1.08135i	0.132383	+	0.0430139i
$633$	−7.90070	−	2.56709i	−0.314025	−	0.102033i
$634$	10.6176	−	7.71412i	0.421678	−	0.306367i
$635$	18.1838	−	12.5502i	0.721601	−	0.498039i
$636$	4.99550	+	15.3746i	0.198084	+	0.609641i
$637$		−	34.7212i		−	1.37570i
$638$	11.6741	−	3.69106i	0.462183	−	0.146131i
$639$	−5.50864			−0.217919
$640$	25.2489	+	0.611374i	0.998050	+	0.0241667i
$641$	7.20147	+	5.23217i	0.284441	+	0.206658i	0.720852	−	0.693089i	$-0.243751\pi$
$641$	7.20147	+	5.23217i	0.284441	+	0.206658i	−0.436411	+	0.899747i	$0.643751\pi$
$642$	2.37496	+	3.26885i	0.0937322	+	0.129011i
$643$	18.5279	+	6.02009i	0.730671	+	0.237409i	0.650643	−	0.759383i	$-0.274499\pi$
$643$	18.5279	+	6.02009i	0.730671	+	0.237409i	0.0800272	+	0.996793i	$0.474499\pi$
$644$	−12.1805	+	37.4876i	−0.479978	+	1.47722i
$645$	−7.24389	+	2.16128i	−0.285228	+	0.0851002i
$646$	1.11184	+	0.807800i	0.0437448	+	0.0317825i
$647$	−31.2035	+	10.1386i	−1.22674	+	0.398591i	−0.849531	−	0.527538i	$-0.823115\pi$
$647$	−31.2035	+	10.1386i	−1.22674	+	0.398591i	−0.377206	+	0.926129i	$0.623115\pi$
$648$		−	1.83677i		−	0.0721550i
$649$	17.8155	+	0.141281i	0.699319	+	0.00554576i
$650$	3.45995	+	2.77931i	0.135711	+	0.109013i
$651$	−3.48116	−	10.7139i	−0.136438	−	0.419911i
$652$	−7.48376	+	10.3005i	−0.293086	+	0.403399i
$653$	8.75861	+	12.0552i	0.342751	+	0.471756i	0.945242	−	0.326369i	$-0.105825\pi$
$653$	8.75861	+	12.0552i	0.342751	+	0.471756i	−0.602492	+	0.798125i	$0.705825\pi$
$654$	−1.88586	+	5.80407i	−0.0737428	+	0.226957i
$655$	−17.3558	+	22.7111i	−0.678148	+	0.887396i
$656$	4.74187	−	3.44517i	0.185139	−	0.134511i
$657$	4.19868	−	5.77899i	0.163806	−	0.225460i
$658$	−3.59639	+	1.16854i	−0.140202	+	0.0455544i
$659$	25.7059			1.00136			0.500680	−	0.865633i	$-0.333083\pi$
$659$	25.7059			1.00136			0.500680	+	0.865633i	$0.333083\pi$
$660$	−3.63570	−	12.5480i	−0.141519	−	0.488431i
$661$	−12.4887			−0.485753			−0.242876	−	0.970057i	$-0.578091\pi$
$661$	−12.4887			−0.485753			−0.242876	+	0.970057i	$0.578091\pi$
$662$	9.18412	−	2.98410i	0.356951	−	0.115980i
$663$	−0.683765	+	0.941121i	−0.0265552	+	0.0365501i
$664$	−0.240582	+	0.174793i	−0.00933639	+	0.00678329i
$665$	−39.9192	−	30.5062i	−1.54800	−	1.18298i
$666$	−0.901121	+	2.77337i	−0.0349177	+	0.107466i
$667$	−19.4627	−	26.7881i	−0.753598	−	1.03724i
$668$	18.9617	−	26.0985i	0.733648	−	1.00978i
$669$	−5.11413	−	15.7397i	−0.197724	−	0.608531i
$670$	−7.47335	−	2.62989i	−0.288721	−	0.101602i
$671$	19.6124	−	14.0130i	0.757129	−	0.540965i
$672$			25.3195i			0.976723i
$673$	38.3694	−	12.4670i	1.47903	−	0.480566i	0.545208	−	0.838301i	$-0.316451\pi$
$673$	38.3694	−	12.4670i	1.47903	−	0.480566i	0.933823	+	0.357735i	$0.116451\pi$
$674$	−5.63253	−	4.09227i	−0.216957	−	0.157628i
$675$	0.241997	−	4.99414i	0.00931447	−	0.192225i
$676$	5.27796	−	16.2439i	0.202998	−	0.624765i
$677$	−5.37159	−	1.74534i	−0.206447	−	0.0670787i	0.203968	−	0.978978i	$-0.434616\pi$
$677$	−5.37159	−	1.74534i	−0.206447	−	0.0670787i	−0.410415	+	0.911899i	$0.634616\pi$
$678$	4.65239	+	6.40347i	0.178674	+	0.245924i
$679$	−59.0318	−	42.8891i	−2.26543	−	1.64593i
$680$	0.0636258	−	2.62766i	0.00243994	−	0.100766i
$681$	−8.48300			−0.325069
$682$	−0.0283181	+	3.57091i	−0.00108436	+	0.136737i
$683$		−	26.7349i		−	1.02298i	−0.859288	−	0.511492i	$-0.829093\pi$
$683$		−	26.7349i		−	1.02298i	0.859288	−	0.511492i	$-0.170907\pi$
$684$	−2.39400	−	7.36797i	−0.0915368	−	0.281721i
$685$	−35.0742	+	24.2077i	−1.34012	+	0.924930i
$686$	−24.4235	+	17.7447i	−0.932493	+	0.677496i
$687$	−3.23256	−	1.05032i	−0.123330	−	0.0400723i
$688$	8.44393	+	2.74360i	0.321922	+	0.104599i
$689$	13.4954	−	9.80501i	0.514135	−	0.373541i
$690$	3.93574	−	2.71640i	0.149831	−	0.103411i
$691$	12.1350	+	37.3476i	0.461636	+	1.42077i	0.863164	+	0.504924i	$0.168479\pi$
$691$	12.1350	+	37.3476i	0.461636	+	1.42077i	−0.401528	+	0.915847i	$0.631521\pi$
$692$			21.1664i			0.804626i
$693$	16.1562	−	5.10817i	0.613721	−	0.194043i
$694$	7.71286			0.292776
$695$	−0.634090	+	26.1870i	−0.0240524	+	0.993331i
$696$	−11.2342	−	8.16216i	−0.425833	−	0.309386i
$697$	−0.839525	−	1.15551i	−0.0317993	−	0.0437680i
$698$	0.796174	+	0.258693i	0.0301356	+	0.00979166i
$699$	4.85538	−	14.9433i	0.183647	−	0.565208i
$700$	−2.17791	+	44.9460i	−0.0823172	+	1.69880i
$701$	5.85318	+	4.25258i	0.221072	+	0.160618i	0.692809	−	0.721121i	$-0.256373\pi$
$701$	5.85318	+	4.25258i	0.221072	+	0.160618i	−0.471737	+	0.881739i	$0.656373\pi$
$702$	−0.844157	+	0.274283i	−0.0318607	+	0.0103522i
$703$			26.2638i			0.990559i
$704$	−2.97377	+	8.91126i	−0.112078	+	0.335856i
$705$	−3.19726	−	1.12512i	−0.120416	−	0.0423745i
$706$	−2.10662	−	6.48351i	−0.0792837	−	0.244010i
$707$	12.8854	−	17.7352i	0.484605	−	0.667001i
$708$	−5.56202	−	7.65546i	−0.209033	−	0.287710i
$709$	3.08055	−	9.48096i	0.115693	−	0.356065i	−0.876398	−	0.481587i	$-0.840061\pi$
$709$	3.08055	−	9.48096i	0.115693	−	0.356065i	0.992091	+	0.125522i	$0.0400606\pi$
$710$	−4.77900	−	3.65212i	−0.179353	−	0.137062i
$711$	−1.54131	+	1.11982i	−0.0578035	+	0.0419967i
$712$	−1.29057	+	1.77632i	−0.0483662	+	0.0665703i
$713$	9.18478	−	2.98431i	0.343973	−	0.111763i
$714$	1.59652			0.0597482
$715$	−11.1551	+	7.56922i	−0.417177	+	0.283073i
$716$	11.8202			0.441740
$717$	−29.1948	+	9.48596i	−1.09030	+	0.354260i
$718$	−9.84639	+	13.5524i	−0.367464	+	0.505771i
$719$	26.7790	−	19.4561i	0.998688	−	0.725589i	0.0368812	−	0.999320i	$-0.488258\pi$
$719$	26.7790	−	19.4561i	0.998688	−	0.725589i	0.961806	+	0.273731i	$0.0882577\pi$
$720$	−3.56573	+	4.66596i	−0.132887	+	0.173890i
$721$	−14.9950	+	46.1499i	−0.558444	+	1.71871i
$722$	0.0979617	+	0.134833i	0.00364576	+	0.00501795i
$723$	−3.28629	+	4.52319i	−0.122218	+	0.168219i
$724$	−6.17013	−	18.9897i	−0.229311	−	0.705747i
$725$	−29.4704	−	23.6729i	−1.09450	−	0.879189i
$726$	−5.37061	−	0.0851857i	−0.199322	−	0.00316154i
$727$		−	18.7123i		−	0.694000i	−0.937865	−	0.347000i	$-0.887200\pi$
$727$		−	18.7123i		−	0.694000i	0.937865	−	0.347000i	$-0.112800\pi$
$728$	16.2227	−	5.27108i	0.601253	−	0.195359i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	7.47390	−	2.22990i	0.276622	−	0.0825324i
$731$	0.668565	−	2.05763i	0.0247278	−	0.0761042i
$732$	−12.1759	−	3.95619i	−0.450034	−	0.146225i
$733$	6.43617	+	8.85862i	0.237725	+	0.327201i	0.911165	−	0.412041i	$-0.135184\pi$
$733$	6.43617	+	8.85862i	0.237725	+	0.327201i	−0.673440	+	0.739242i	$0.735184\pi$
$734$	−1.42707	−	1.03683i	−0.0526742	−	0.0382700i
$735$	−42.6994	−	1.03392i	−1.57499	−	0.0381366i
$736$	−21.7058			−0.800087
$737$	14.2992	−	19.3565i	0.526718	−	0.713006i
$738$		−	1.08979i		−	0.0401158i
$739$	−11.7687	−	36.2202i	−0.432917	−	1.33238i	−0.895206	−	0.445652i	$-0.852972\pi$
$739$	−11.7687	−	36.2202i	−0.432917	−	1.33238i	0.462289	−	0.886729i	$-0.347028\pi$
$740$	19.3599	−	13.3619i	0.711684	−	0.491195i
$741$	−6.46743	+	4.69887i	−0.237587	+	0.172617i
$742$	−21.7732	−	7.07453i	−0.799318	−	0.259714i
$743$	−15.7170	−	5.10677i	−0.576601	−	0.187349i	0.00617613	−	0.999981i	$-0.498034\pi$
$743$	−15.7170	−	5.10677i	−0.576601	−	0.187349i	−0.582777	+	0.812632i	$0.698034\pi$
$744$	3.27659	−	2.38058i	0.120126	−	0.0872764i
$745$	9.47183	+	13.7236i	0.347021	+	0.502793i
$746$	2.82265	+	8.68724i	0.103345	+	0.318062i
$747$		−	0.161902i		−	0.00592367i
$748$	3.54669	+	1.18357i	0.129680	+	0.0432755i
$749$	42.2750			1.54469
$750$	3.52096	−	4.17221i	0.128567	−	0.152348i
$751$	14.5070	+	10.5400i	0.529369	+	0.384609i	0.820122	−	0.572189i	$-0.193906\pi$
$751$	14.5070	+	10.5400i	0.529369	+	0.384609i	−0.290753	+	0.956798i	$0.593906\pi$
$752$	2.33990	+	3.22059i	0.0853272	+	0.117443i
$753$	−17.8073	−	5.78594i	−0.648934	−	0.210851i
$754$	−2.07363	+	6.38198i	−0.0755172	+	0.232418i
$755$	10.6259	−	3.17033i	0.386717	−	0.115380i
$756$	−7.28094	−	5.28991i	−0.264805	−	0.192392i
$757$	13.3794	−	4.34722i	0.486282	−	0.158003i	−0.0556070	−	0.998453i	$-0.517709\pi$
$757$	13.3794	−	4.34722i	0.486282	−	0.158003i	0.541889	+	0.840450i	$0.317709\pi$
$758$		−	4.57764i		−	0.166267i
$759$	4.37911	+	13.8503i	0.158952	+	0.502733i
$760$	5.99588	−	17.0385i	0.217493	−	0.618051i
$761$	3.12669	+	9.62295i	0.113342	+	0.348832i	0.991598	−	0.129360i	$-0.0412923\pi$
$761$	3.12669	+	9.62295i	0.113342	+	0.348832i	−0.878255	+	0.478192i	$0.841292\pi$
$762$	−2.83595	+	3.90336i	−0.102736	+	0.141404i
$763$	37.5310	+	51.6571i	1.35872	+	1.87011i
$764$	6.03493	−	18.5736i	0.218336	−	0.671970i
$765$	1.13701	+	0.868903i	0.0411086	+	0.0314152i
$766$	−7.59092	+	5.51512i	−0.274271	+	0.199270i
$767$	−5.73938	+	7.89958i	−0.207237	+	0.285237i
$768$	0.142367	−	0.0462579i	0.00513723	−	0.00166919i
$769$	16.0423			0.578499			0.289250	−	0.957254i	$-0.406594\pi$
$769$	16.0423			0.578499			0.289250	+	0.957254i	$0.406594\pi$
$770$	17.4028	+	6.27962i	0.627154	+	0.226302i
$771$	−4.98215			−0.179428
$772$	−1.99710	+	0.648896i	−0.0718771	+	0.0233543i
$773$	23.7675	−	32.7131i	0.854857	−	1.17661i	−0.127914	−	0.991785i	$-0.540828\pi$
$773$	23.7675	−	32.7131i	0.854857	−	1.17661i	0.982771	−	0.184825i	$-0.0591718\pi$
$774$	1.33551	−	0.970306i	0.0480040	−	0.0348769i
$775$	9.22265	−	6.04107i	0.331287	−	0.217002i
$776$	8.10651	−	24.9493i	0.291007	−	0.895627i
$777$	17.9335	+	24.6834i	0.643361	+	0.885510i
$778$	−2.66838	+	3.67270i	−0.0956659	+	0.131673i
$779$	−3.03308	−	9.33486i	−0.108671	−	0.334456i
$780$	6.75404	+	2.37676i	0.241833	+	0.0851017i
$781$	14.8655	−	10.6213i	0.531930	−	0.380062i
$782$			1.36866i			0.0489430i
$783$	7.19016	−	2.33622i	0.256955	−	0.0834898i
$784$	40.5840	+	29.4860i	1.44943	+	1.05307i
$785$	13.1642	+	44.1222i	0.469851	+	1.57479i
$786$	1.92885	−	5.93640i	0.0687999	−	0.211744i
$787$	−15.6272	−	5.07758i	−0.557049	−	0.180996i	0.0169441	−	0.999856i	$-0.494606\pi$
$787$	−15.6272	−	5.07758i	−0.557049	−	0.180996i	−0.573993	+	0.818860i	$0.694606\pi$
$788$	19.0053	+	26.1585i	0.677035	+	0.931858i
$789$	−16.2441	−	11.8020i	−0.578304	−	0.420163i
$790$	−2.07957	−	0.0503546i	−0.0739879	−	0.00179154i
$791$	82.8140			2.94453
$792$	3.54152	+	4.95666i	0.125842	+	0.176127i
$793$			13.2107i			0.469127i
$794$	2.09277	+	6.44088i	0.0742696	+	0.228578i
$795$	−11.6561	−	16.8884i	−0.413400	−	0.598968i
$796$	31.6039	−	22.9616i	1.12017	−	0.813852i
$797$	−11.3108	−	3.67509i	−0.400648	−	0.130178i	0.101760	−	0.994809i	$-0.467552\pi$
$797$	−11.3108	−	3.67509i	−0.400648	−	0.130178i	−0.502408	+	0.864631i	$0.667552\pi$
$798$	10.4344	+	3.39033i	0.369373	+	0.120016i
$799$	0.784799	−	0.570190i	0.0277642	−	0.0201719i
$800$	−23.9098	+	6.50773i	−0.845339	+	0.230083i
$801$	−0.369395	−	1.13688i	−0.0130519	−	0.0401697i
$802$		−	5.19236i		−	0.183349i
$803$	−0.187872	+	23.6906i	−0.00662987	+	0.836025i
$804$	−12.7819			−0.450782
$805$	1.21117	−	50.0197i	0.0426882	−	1.76296i
$806$	−1.58338	−	1.15039i	−0.0557722	−	0.0405209i
$807$	5.60175	+	7.71015i	0.197191	+	0.271410i
$808$	7.49563	+	2.43548i	0.263695	+	0.0856798i
$809$	−12.2690	+	37.7600i	−0.431353	+	1.32757i	0.465424	+	0.885088i	$0.345902\pi$
$809$	−12.2690	+	37.7600i	−0.431353	+	1.32757i	−0.896778	+	0.442481i	$0.854098\pi$
$810$	0.312170	+	1.04629i	0.0109685	+	0.0367630i
$811$	−23.5836	−	17.1345i	−0.828132	−	0.601673i	0.0908983	−	0.995860i	$-0.471026\pi$
$811$	−23.5836	−	17.1345i	−0.828132	−	0.601673i	−0.919030	+	0.394187i	$0.871026\pi$
$812$	−64.7095	+	21.0254i	−2.27086	+	0.737847i
$813$			1.18095i			0.0414177i
$814$	−2.91565	−	9.22162i	−0.102193	−	0.323218i
$815$	5.36486	−	15.2453i	0.187923	−	0.534020i
$816$	−0.519365	−	1.59844i	−0.0181814	−	0.0559567i
$817$	8.73909	−	12.0283i	0.305742	−	0.420818i
$818$	−1.06574	−	1.46687i	−0.0372629	−	0.0512879i
$819$	−2.86976	+	8.83220i	−0.100277	+	0.308622i
$820$	−5.33791	+	6.98496i	−0.186408	+	0.243925i
$821$	−38.5124	+	27.9809i	−1.34409	+	0.976541i	−0.344811	+	0.938672i	$0.612057\pi$
$821$	−38.5124	+	27.9809i	−1.34409	+	0.976541i	−0.999283	+	0.0378690i	$0.987943\pi$
$822$	5.47019	−	7.52908i	0.190795	−	0.262607i
$823$	−18.2829	+	5.94047i	−0.637302	+	0.207072i	−0.609807	−	0.792550i	$-0.708753\pi$
$823$	−18.2829	+	5.94047i	−0.637302	+	0.207072i	−0.0274950	+	0.999622i	$0.508753\pi$
$824$	−17.4457			−0.607748
$825$	8.97627	+	13.9437i	0.312514	+	0.485457i
$826$	13.4008			0.466275
$827$	29.1320	−	9.46557i	1.01302	−	0.329150i	0.244963	−	0.969532i	$-0.421224\pi$
$827$	29.1320	−	9.46557i	1.01302	−	0.329150i	0.768056	+	0.640382i	$0.221224\pi$
$828$	4.53491	−	6.24177i	0.157599	−	0.216917i
$829$	−36.2935	+	26.3688i	−1.26053	+	0.915826i	−0.998783	−	0.0493120i	$-0.984297\pi$
$829$	−36.2935	+	26.3688i	−1.26053	+	0.915826i	−0.261743	+	0.965138i	$0.584297\pi$
$830$	0.107337	−	0.140457i	0.00372574	−	0.00487534i
$831$	−2.54067	+	7.81937i	−0.0881347	+	0.271251i
$832$	−3.02636	−	4.16543i	−0.104920	−	0.144410i
$833$	7.18520	−	9.88958i	0.248953	−	0.342654i
$834$	−1.76765	−	5.44027i	−0.0612088	−	0.188381i
$835$	−13.5930	+	38.6272i	−0.470405	+	1.33675i
$836$	20.6668	+	15.2671i	0.714775	+	0.528025i
$837$			2.20501i			0.0762163i
$838$	7.38375	−	2.39913i	0.255068	−	0.0828765i
$839$	3.51466	+	2.55355i	0.121339	+	0.0881582i	0.646800	−	0.762660i	$-0.276107\pi$
$839$	3.51466	+	2.55355i	0.121339	+	0.0881582i	−0.525460	+	0.850818i	$0.676107\pi$
$840$	−5.99917	−	20.1073i	−0.206991	−	0.693767i
$841$	8.70078	−	26.7783i	0.300027	−	0.923388i
$842$	−2.02787	−	0.658893i	−0.0698849	−	0.0227070i
$843$	6.13961	+	8.45045i	0.211459	+	0.291049i
$844$	−11.8390	−	8.60154i	−0.407515	−	0.296077i
$845$	−0.524816	+	21.6742i	−0.0180542	+	0.745614i
$846$	0.740167			0.0254475
$847$	−33.7495	+	44.9359i	−1.15965	+	1.54401i
$848$			24.1008i			0.827626i
$849$	7.67794	+	23.6303i	0.263506	+	0.810988i
$850$	0.410343	+	1.50763i	0.0140747	+	0.0517112i
$851$	−21.1604	+	15.3740i	−0.725370	+	0.527012i
$852$	−9.22889	−	2.99865i	−0.316177	−	0.102732i
$853$	38.3828	+	12.4713i	1.31420	+	0.427010i	0.880500	−	0.474046i	$-0.157207\pi$
$853$	38.3828	+	12.4713i	1.31420	+	0.427010i	0.433702	+	0.901056i	$0.357207\pi$
$854$	14.6680	−	10.6569i	0.501928	−	0.364672i
$855$	5.58597	+	8.09342i	0.191036	+	0.276789i
$856$	4.69665	+	14.4548i	0.160528	+	0.494055i
$857$			36.6122i			1.25065i	0.780365	+	0.625324i	$0.215033\pi$
$857$			36.6122i			1.25065i	−0.780365	+	0.625324i	$0.784967\pi$
$858$	1.74917	−	2.36782i	0.0597158	−	0.0808359i
$859$	−28.5710			−0.974831			−0.487415	−	0.873170i	$-0.662060\pi$
$859$	−28.5710			−0.974831			−0.487415	+	0.873170i	$0.662060\pi$
$860$	−13.3125	−	0.322348i	−0.453954	−	0.0109920i
$861$	−9.22460	−	6.70206i	−0.314373	−	0.228406i
$862$	5.76916	+	7.94056i	0.196498	+	0.270457i
$863$	27.8749	+	9.05711i	0.948873	+	0.308307i	0.742257	−	0.670115i	$-0.233755\pi$
$863$	27.8749	+	9.05711i	0.948873	+	0.308307i	0.206615	+	0.978422i	$0.433755\pi$
$864$	1.53146	−	4.71336i	0.0521015	−	0.160352i
$865$	−7.68165	−	25.7464i	−0.261184	−	0.875403i
$866$	−12.1369	−	8.81800i	−0.412430	−	0.299648i
$867$	15.7784	−	5.12673i	0.535864	−	0.174113i
$868$		−	19.8445i		−	0.673567i
$869$	2.00018	−	5.99376i	0.0678514	−	0.203324i
$870$	7.78666	+	2.74014i	0.263993	+	0.0928996i
$871$	4.07577	+	12.5439i	0.138102	+	0.425035i
$872$	−13.4932	+	18.5717i	−0.456936	+	0.628918i
$873$	8.39491	+	11.5546i	0.284125	+	0.391064i
$874$	−2.90645	+	8.94513i	−0.0983121	+	0.302574i
$875$	−13.6625	−	55.4617i	−0.461876	−	1.87495i
$876$	10.1801	−	7.39625i	0.343952	−	0.249896i
$877$	−2.15996	+	2.97293i	−0.0729367	+	0.100389i	−0.843927	−	0.536458i	$-0.819762\pi$
$877$	−2.15996	+	2.97293i	−0.0729367	+	0.100389i	0.770990	+	0.636847i	$0.219762\pi$
$878$	9.57145	−	3.10995i	0.323021	−	0.104956i
$879$	24.8264			0.837373
$880$	0.625858	−	19.4666i	0.0210977	−	0.656220i
$881$	−11.1723			−0.376403			−0.188202	−	0.982130i	$-0.560266\pi$
$881$	−11.1723			−0.376403			−0.188202	+	0.982130i	$0.560266\pi$
$882$	8.87065	−	2.88225i	0.298690	−	0.0970504i
$883$	24.8380	−	34.1866i	0.835866	−	1.15047i	−0.150936	−	0.988544i	$-0.548229\pi$
$883$	24.8380	−	34.1866i	0.835866	−	1.15047i	0.986803	−	0.161928i	$-0.0517712\pi$
$884$	−1.65785	+	1.20450i	−0.0557594	+	0.0405116i
$885$	9.54382	+	7.29339i	0.320812	+	0.245165i
$886$	−2.08227	+	6.40858i	−0.0699553	+	0.215300i
$887$	32.8254	+	45.1803i	1.10217	+	1.51701i	0.832477	+	0.554060i	$0.186922\pi$
$887$	32.8254	+	45.1803i	1.10217	+	1.51701i	0.269693	+	0.962946i	$0.413078\pi$
$888$	−6.44745	+	8.87415i	−0.216362	+	0.297797i
$889$	15.5994	+	48.0101i	0.523188	+	1.61021i
$890$	0.433262	−	1.23120i	0.0145230	−	0.0412699i
$891$	−3.31652	−	0.0263008i	−0.111108	−	0.000881109i
$892$		−	29.1533i		−	0.976125i
$893$	6.34006	−	2.06001i	0.212162	−	0.0689356i
$894$	−2.94592	−	2.14034i	−0.0985265	−	0.0715837i
$895$	−14.3778	+	4.28974i	−0.480597	+	0.143390i
$896$	−17.8319	+	54.8810i	−0.595723	+	1.83345i
$897$	−7.57163	−	2.46017i	−0.252809	−	0.0821427i
$898$	−7.82140	−	10.7652i	−0.261003	−	0.359240i
$899$	13.4865	+	9.79854i	0.449801	+	0.326800i
$900$	3.12401	−	8.23519i	0.104134	−	0.274506i
$901$	5.87293			0.195656
$902$	2.10126	+	2.94089i	0.0699642	+	0.0979211i
$903$		−	17.2717i		−	0.574767i
$904$	9.20044	+	28.3160i	0.306002	+	0.941778i
$905$	14.3969	+	20.8594i	0.478569	+	0.693391i
$906$	−1.95903	+	1.42332i	−0.0650846	+	0.0472867i
$907$	−11.4959	−	3.73524i	−0.381714	−	0.124027i	0.111873	−	0.993722i	$-0.464315\pi$
$907$	−11.4959	−	3.73524i	−0.381714	−	0.124027i	−0.493588	+	0.869696i	$0.664315\pi$
$908$	−14.2120	−	4.61775i	−0.471641	−	0.153245i
$909$	−3.47140	+	2.52212i	−0.115139	+	0.0836535i
$910$	−8.34522	+	5.75976i	−0.276641	+	0.190934i
$911$	−12.4319	−	38.2616i	−0.411888	−	1.26766i	−0.915005	−	0.403444i	$-0.867813\pi$
$911$	−12.4319	−	38.2616i	−0.411888	−	1.26766i	0.503116	−	0.864219i	$-0.332187\pi$
$912$		−	11.5499i		−	0.382454i
$913$	0.312167	+	0.436905i	0.0103312	+	0.0144594i
$914$	2.25719			0.0746611
$915$	16.2463	+	0.393385i	0.537085	+	0.0130049i
$916$	−4.84392	−	3.51931i	−0.160048	−	0.116281i
$917$	−38.3867	−	52.8348i	−1.26764	−	1.74476i
$918$	−0.297200	−	0.0965661i	−0.00980906	−	0.00318716i
$919$	−1.12795	+	3.47148i	−0.0372077	+	0.114514i	−0.967935	−	0.251200i	$-0.919175\pi$
$919$	−1.12795	+	3.47148i	−0.0372077	+	0.114514i	0.930728	+	0.365713i	$0.119175\pi$
$920$	17.2375	−	5.14294i	0.568302	−	0.169558i
$921$	10.0874	+	7.32890i	0.332390	+	0.241495i
$922$	−11.7930	+	3.83177i	−0.388381	+	0.126193i
$923$			10.0133i			0.329591i
$924$	29.8478	+	0.236700i	0.981921	+	0.00778686i
$925$	−18.6997	+	23.2792i	−0.614842	+	0.765416i
$926$	1.94574	+	5.98837i	0.0639410	+	0.196790i
$927$	5.58280	−	7.68406i	0.183363	−	0.252378i
$928$	−22.0229	−	30.3120i	−0.722939	−	0.995040i
$929$	−3.10593	+	9.55906i	−0.101902	+	0.313623i	−0.988991	−	0.147976i	$-0.952724\pi$
$929$	−3.10593	+	9.55906i	−0.101902	+	0.313623i	0.887089	+	0.461599i	$0.152724\pi$
$930$	−1.46188	+	1.91295i	−0.0479368	+	0.0627281i
$931$	67.9617	−	49.3771i	2.22735	−	1.61827i
$932$	16.2689	−	22.3922i	0.532905	−	0.733481i
$933$	−3.00452	+	0.976228i	−0.0983636	+	0.0319603i
$934$	−1.86054			−0.0608788
$935$	−4.74366	−	0.152510i	−0.155134	−	0.00498761i
$936$	−3.33876			−0.109131
$937$	26.8518	−	8.72469i	0.877211	−	0.285023i	0.164412	−	0.986392i	$-0.447427\pi$
$937$	26.8518	−	8.72469i	0.877211	−	0.285023i	0.712799	+	0.701368i	$0.247427\pi$
$938$	10.6398	−	14.6444i	0.347401	−	0.478156i
$939$	−11.5647	+	8.40225i	−0.377400	+	0.274197i
$940$	−4.74405	−	3.62541i	−0.154734	−	0.118248i
$941$	10.0946	−	31.0680i	0.329074	−	1.01279i	−0.640494	−	0.767964i	$-0.721270\pi$
$941$	10.0946	−	31.0680i	0.329074	−	1.01279i	0.969568	−	0.244823i	$-0.0787298\pi$
$942$	−5.91008	−	8.13453i	−0.192561	−	0.265037i
$943$	5.74551	−	7.90802i	0.187100	−	0.257521i
$944$	−4.35945	−	13.4170i	−0.141888	−	0.436686i
$945$	10.7762	+	3.79216i	0.350549	+	0.123359i
$946$	−1.73312	+	5.19348i	−0.0563485	+	0.168855i
$947$		−	57.1073i		−	1.85574i	−0.372906	−	0.927869i	$-0.621639\pi$
$947$		−	57.1073i		−	1.85574i	0.372906	−	0.927869i	$-0.378361\pi$
$948$	−3.19180	+	1.03708i	−0.103665	+	0.0336828i
$949$	−10.5047	−	7.63210i	−0.340997	−	0.247749i
$950$	−0.519683	+	10.7248i	−0.0168607	+	0.347959i
$951$	−8.30548	+	25.5616i	−0.269324	+	0.828893i
$952$	5.71148	+	1.85577i	0.185110	+	0.0601459i
$953$	−2.65339	−	3.65208i	−0.0859519	−	0.118303i	0.763876	−	0.645363i	$-0.223294\pi$
$953$	−2.65339	−	3.65208i	−0.0859519	−	0.118303i	−0.849828	+	0.527061i	$0.823294\pi$
$954$	3.62528	+	2.63392i	0.117373	+	0.0852763i
$955$	−0.600086	+	24.7827i	−0.0194183	+	0.801951i
$956$	−54.0751			−1.74891
$957$	−14.8987	+	20.1680i	−0.481606	+	0.651939i
$958$			6.00205i			0.193917i
$959$	−30.0893	−	92.6053i	−0.971634	−	2.99038i
$960$	−5.21266	+	3.59771i	−0.168238	+	0.116116i
$961$	21.1460	−	15.3635i	0.682130	−	0.495596i
$962$	5.04125	+	1.63800i	0.162537	+	0.0528113i
$963$	−7.86970	−	2.55702i	−0.253598	−	0.0823989i
$964$	−7.96789	+	5.78901i	−0.256629	+	0.186452i
$965$	2.19373	−	1.51408i	0.0706187	−	0.0487401i
$966$	3.37638	+	10.3914i	0.108633	+	0.334339i
$967$			1.33608i			0.0429654i	0.999769	+	0.0214827i	$0.00683868\pi$
$967$			1.33608i			0.0429654i	−0.999769	+	0.0214827i	$0.993161\pi$
$968$	−19.1141	−	6.54748i	−0.614351	−	0.210444i
$969$	−2.81449			−0.0904144
$970$	−0.377490	+	15.5898i	−0.0121205	+	0.500559i
$971$	−2.19764	−	1.59668i	−0.0705258	−	0.0512400i	0.551964	−	0.833868i	$-0.313879\pi$
$971$	−2.19764	−	1.59668i	−0.0705258	−	0.0512400i	−0.622490	+	0.782628i	$0.713879\pi$
$972$	1.03542	+	1.42514i	0.0332112	+	0.0457112i
$973$	−56.9202	−	18.4945i	−1.82478	−	0.592906i
$974$	−2.02783	+	6.24103i	−0.0649760	+	0.199975i
$975$	−9.07804	−	0.439887i	−0.290730	−	0.0140877i
$976$	−15.4414	−	11.2189i	−0.494268	−	0.359107i
$977$	15.8664	−	5.15529i	0.507610	−	0.164932i	−0.0440051	−	0.999031i	$-0.514012\pi$
$977$	15.8664	−	5.15529i	0.507610	−	0.164932i	0.551615	+	0.834099i	$0.314012\pi$
$978$			3.52930i			0.112854i
$979$	3.18889	+	2.35573i	0.101917	+	0.0752893i
$980$	−70.9734	−	24.9757i	−2.26716	−	0.797820i
$981$	−3.86210	−	11.8863i	−0.123307	−	0.379501i
$982$	1.74557	−	2.40257i	0.0557035	−	0.0766692i
$983$	15.4303	+	21.2380i	0.492151	+	0.677388i	0.980783	−	0.195102i	$-0.0625038\pi$
$983$	15.4303	+	21.2380i	0.492151	+	0.677388i	−0.488632	+	0.872490i	$0.662504\pi$
$984$	1.26676	−	3.89869i	0.0403829	−	0.124286i
$985$	−32.6110	−	24.9213i	−1.03907	−	0.794060i
$986$	−1.91131	+	1.38865i	−0.0608686	+	0.0442237i
$987$	4.55191	−	6.26517i	0.144889	−	0.199423i
$988$	−13.3930	+	4.35166i	−0.426089	+	0.138445i
$989$	14.8066			0.470823
$990$	−2.85980	−	2.22160i	−0.0908904	−	0.0706072i
$991$	−50.3117			−1.59821			−0.799103	−	0.601195i	$-0.794692\pi$
$991$	−50.3117			−1.59821			−0.799103	+	0.601195i	$0.794692\pi$
$992$	10.3930	−	3.37689i	0.329979	−	0.107217i
$993$	−11.6242	+	15.9994i	−0.368884	+	0.507725i
$994$	11.1178	−	8.07756i	0.352636	−	0.256205i
$995$	−30.1092	+	39.3996i	−0.954526	+	1.24905i
$996$	0.0881317	−	0.271241i	0.00279256	−	0.00859462i
$997$	26.5943	+	36.6039i	0.842250	+	1.15926i	0.985518	+	0.169573i	$0.0542390\pi$
$997$	26.5943	+	36.6039i	0.842250	+	1.15926i	−0.143268	+	0.989684i	$0.545761\pi$
$998$	5.39422	−	7.42450i	0.170751	−	0.235018i
$999$	−1.84543	−	5.67965i	−0.0583868	−	0.179696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.49.8	yes	48
3.2	odd	2		495.2.ba.c.379.5		48
5.2	odd	4		825.2.n.o.676.4		24
5.3	odd	4		825.2.n.p.676.3		24
5.4	even	2	inner	165.2.s.a.49.5	✓	48
11.3	even	5		1815.2.c.j.364.10		24
11.8	odd	10		1815.2.c.k.364.15		24
11.9	even	5	inner	165.2.s.a.64.5	yes	48
15.14	odd	2		495.2.ba.c.379.8		48
33.20	odd	10		495.2.ba.c.64.8		48
55.3	odd	20		9075.2.a.dy.1.6		12
55.8	even	20		9075.2.a.ea.1.7		12
55.9	even	10	inner	165.2.s.a.64.8	yes	48
55.14	even	10		1815.2.c.j.364.15		24
55.19	odd	10		1815.2.c.k.364.10		24
55.42	odd	20		825.2.n.o.526.4		24
55.47	odd	20		9075.2.a.dz.1.7		12
55.52	even	20		9075.2.a.dx.1.6		12
55.53	odd	20		825.2.n.p.526.3		24
165.119	odd	10		495.2.ba.c.64.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.5	✓	48	5.4	even	2	inner
165.2.s.a.49.8	yes	48	1.1	even	1	trivial
165.2.s.a.64.5	yes	48	11.9	even	5	inner
165.2.s.a.64.8	yes	48	55.9	even	10	inner
495.2.ba.c.64.5		48	165.119	odd	10
495.2.ba.c.64.8		48	33.20	odd	10
495.2.ba.c.379.5		48	3.2	odd	2
495.2.ba.c.379.8		48	15.14	odd	2
825.2.n.o.526.4		24	55.42	odd	20
825.2.n.o.676.4		24	5.2	odd	4
825.2.n.p.526.3		24	55.53	odd	20
825.2.n.p.676.3		24	5.3	odd	4
1815.2.c.j.364.10		24	11.3	even	5
1815.2.c.j.364.15		24	55.14	even	10
1815.2.c.k.364.10		24	55.19	odd	10
1815.2.c.k.364.15		24	11.8	odd	10
9075.2.a.dx.1.6		12	55.52	even	20
9075.2.a.dy.1.6		12	55.3	odd	20
9075.2.a.dz.1.7		12	55.47	odd	20
9075.2.a.ea.1.7		12	55.8	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.464400 - 0.150893i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.42514 + 1.03542i) q^{4} +(1.35773 - 1.77667i) q^{5} +(-0.150893 + 0.464400i) q^{6} +(3.00296 + 4.13322i) q^{7} +(-1.07962 + 1.48598i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.464400 - 0.150893i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.42514 + 1.03542i) q^{4} +(1.35773 - 1.77667i) q^{5} +(-0.150893 + 0.464400i) q^{6} +(3.00296 + 4.13322i) q^{7} +(-1.07962 + 1.48598i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.362444 - 1.02996i) q^{10} +(2.66766 + 1.97068i) q^{11} -1.76156i q^{12} +(-1.72877 + 0.561712i) q^{13} +(2.01825 + 1.46634i) q^{14} +(0.639302 + 2.14273i) q^{15} +(0.811552 - 2.49770i) q^{16} +(-0.608644 - 0.197760i) q^{17} +(-0.287015 - 0.395042i) q^{18} +(-3.55796 - 2.58501i) q^{19} +(-0.0953500 + 3.93782i) q^{20} -5.10895 q^{21} +(1.53622 + 0.512653i) q^{22} -4.37977i q^{23} +(-0.567592 - 1.74687i) q^{24} +(-1.31312 - 4.82449i) q^{25} +(-0.718083 + 0.521718i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-8.55926 - 2.78107i) q^{28} +(6.11631 - 4.44376i) q^{29} +(0.620214 + 0.898618i) q^{30} +(0.681386 + 2.09709i) q^{31} -4.95592i q^{32} +(-3.16233 + 0.999848i) q^{33} -0.312494 q^{34} +(11.4206 + 0.276537i) q^{35} +(1.42514 + 1.03542i) q^{36} +(-3.51022 - 4.83140i) q^{37} +(-2.04237 - 0.663607i) q^{38} +(0.561712 - 1.72877i) q^{39} +(1.17425 + 3.93570i) q^{40} +(1.80558 + 1.31183i) q^{41} +(-2.37259 + 0.770902i) q^{42} +3.38068i q^{43} +(-5.84226 - 0.0463305i) q^{44} +(-2.10928 - 0.742259i) q^{45} +(-0.660876 - 2.03397i) q^{46} +(-0.890969 + 1.22631i) q^{47} +(1.54366 + 2.12467i) q^{48} +(-5.90264 + 18.1664i) q^{49} +(-1.33779 - 2.04235i) q^{50} +(0.517743 - 0.376162i) q^{51} +(1.88213 - 2.59052i) q^{52} +(-8.72779 + 2.83583i) q^{53} +0.488299 q^{54} +(7.12322 - 2.06390i) q^{55} -9.38395 q^{56} +(4.18263 - 1.35902i) q^{57} +(2.16988 - 2.98659i) q^{58} +(4.34583 - 3.15743i) q^{59} +(-3.12972 - 2.39173i) q^{60} +(2.24584 - 6.91197i) q^{61} +(0.632871 + 0.871072i) q^{62} +(3.00296 - 4.13322i) q^{63} +(0.875292 + 2.69387i) q^{64} +(-1.34923 + 3.83411i) q^{65} +(-1.31771 + 0.941501i) q^{66} -7.25598i q^{67} +(1.07216 - 0.348367i) q^{68} +(3.54331 + 2.57437i) q^{69} +(5.34545 - 1.59486i) q^{70} +(1.70226 - 5.23903i) q^{71} +(1.74687 + 0.567592i) q^{72} +(4.19868 + 5.77899i) q^{73} +(-2.35917 - 1.71403i) q^{74} +(4.67493 + 1.77343i) q^{75} +7.74714 q^{76} +(-0.134369 + 16.9439i) q^{77} -0.887599i q^{78} +(-0.588726 - 1.81191i) q^{79} +(-3.33572 - 4.83307i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.03645 + 0.336765i) q^{82} +(0.153978 + 0.0500304i) q^{83} +(7.28094 - 5.28991i) q^{84} +(-1.17773 + 0.812854i) q^{85} +(0.510120 + 1.56999i) q^{86} +7.56018i q^{87} +(-5.80846 + 1.83649i) q^{88} +1.19539 q^{89} +(-1.09155 - 0.0264307i) q^{90} +(-7.51312 - 5.45860i) q^{91} +(4.53491 + 6.24177i) q^{92} +(-2.09709 - 0.681386i) q^{93} +(-0.228724 + 0.703940i) q^{94} +(-9.42346 + 2.81157i) q^{95} +(4.00943 + 2.91302i) q^{96} +(-13.5832 + 4.41347i) q^{97} +9.32716i q^{98} +(1.04987 - 3.14607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

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