LMFDB - Embedded newform 546.2.bb.a.269.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.11
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.201730 - 1.72026i) q^{3} -1.00000 q^{4} +(1.75377 + 3.03762i) q^{5} +(-1.72026 - 0.201730i) q^{6} +(1.27169 + 2.32009i) q^{7} +1.00000i q^{8} +(-2.91861 - 0.694059i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.201730 - 1.72026i) q^{3} -1.00000 q^{4} +(1.75377 + 3.03762i) q^{5} +(-1.72026 - 0.201730i) q^{6} +(1.27169 + 2.32009i) q^{7} +1.00000i q^{8} +(-2.91861 - 0.694059i) q^{9} +(3.03762 - 1.75377i) q^{10} +(-3.06555 + 1.76989i) q^{11} +(-0.201730 + 1.72026i) q^{12} +(3.59167 + 0.316032i) q^{13} +(2.32009 - 1.27169i) q^{14} +(5.57930 - 2.40417i) q^{15} +1.00000 q^{16} +3.95683 q^{17} +(-0.694059 + 2.91861i) q^{18} +(5.76542 + 3.32866i) q^{19} +(-1.75377 - 3.03762i) q^{20} +(4.24770 - 1.71960i) q^{21} +(1.76989 + 3.06555i) q^{22} +1.28595i q^{23} +(1.72026 + 0.201730i) q^{24} +(-3.65143 + 6.32446i) q^{25} +(0.316032 - 3.59167i) q^{26} +(-1.78274 + 4.88076i) q^{27} +(-1.27169 - 2.32009i) q^{28} +(-5.71124 - 3.29739i) q^{29} +(-2.40417 - 5.57930i) q^{30} +(-8.14013 - 4.69971i) q^{31} -1.00000i q^{32} +(2.42627 + 5.63059i) q^{33} -3.95683i q^{34} +(-4.81731 + 7.93181i) q^{35} +(2.91861 + 0.694059i) q^{36} +10.5767 q^{37} +(3.32866 - 5.76542i) q^{38} +(1.26821 - 6.11487i) q^{39} +(-3.03762 + 1.75377i) q^{40} +(2.84220 - 4.92284i) q^{41} +(-1.71960 - 4.24770i) q^{42} +(-2.79284 - 4.83734i) q^{43} +(3.06555 - 1.76989i) q^{44} +(-3.01029 - 10.0829i) q^{45} +1.28595 q^{46} +(0.0582673 + 0.100922i) q^{47} +(0.201730 - 1.72026i) q^{48} +(-3.76563 + 5.90085i) q^{49} +(6.32446 + 3.65143i) q^{50} +(0.798214 - 6.80680i) q^{51} +(-3.59167 - 0.316032i) q^{52} +(6.70912 + 3.87351i) q^{53} +(4.88076 + 1.78274i) q^{54} +(-10.7525 - 6.20798i) q^{55} +(-2.32009 + 1.27169i) q^{56} +(6.88924 - 9.24654i) q^{57} +(-3.29739 + 5.71124i) q^{58} +5.68243 q^{59} +(-5.57930 + 2.40417i) q^{60} +(-9.51703 - 5.49466i) q^{61} +(-4.69971 + 8.14013i) q^{62} +(-2.10127 - 7.65406i) q^{63} -1.00000 q^{64} +(5.33899 + 11.4644i) q^{65} +(5.63059 - 2.42627i) q^{66} +(-3.84167 - 6.65397i) q^{67} -3.95683 q^{68} +(2.21217 + 0.259415i) q^{69} +(7.93181 + 4.81731i) q^{70} +(-8.18290 + 4.72440i) q^{71} +(0.694059 - 2.91861i) q^{72} +(3.73438 + 2.15605i) q^{73} -10.5767i q^{74} +(10.1431 + 7.55726i) q^{75} +(-5.76542 - 3.32866i) q^{76} +(-8.00472 - 4.86159i) q^{77} +(-6.11487 - 1.26821i) q^{78} +(-2.63559 - 4.56498i) q^{79} +(1.75377 + 3.03762i) q^{80} +(8.03656 + 4.05137i) q^{81} +(-4.92284 - 2.84220i) q^{82} -2.03056 q^{83} +(-4.24770 + 1.71960i) q^{84} +(6.93939 + 12.0194i) q^{85} +(-4.83734 + 2.79284i) q^{86} +(-6.82451 + 9.15966i) q^{87} +(-1.76989 - 3.06555i) q^{88} -0.354591 q^{89} +(-10.0829 + 3.01029i) q^{90} +(3.83426 + 8.73490i) q^{91} -1.28595i q^{92} +(-9.72684 + 13.0551i) q^{93} +(0.100922 - 0.0582673i) q^{94} +23.3509i q^{95} +(-1.72026 - 0.201730i) q^{96} +(0.507481 - 0.292994i) q^{97} +(5.90085 + 3.76563i) q^{98} +(10.1755 - 3.03796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.201730	−	1.72026i	0.116469	−	0.993194i
$3$	0.201730	−	1.72026i	0.116469	−	0.993194i
$4$	−1.00000			−0.500000
$5$	1.75377	+	3.03762i	0.784311	+	1.35847i	0.929410	+	0.369049i	$0.120316\pi$
$5$	1.75377	+	3.03762i	0.784311	+	1.35847i	−0.145099	+	0.989417i	$0.546350\pi$
$6$	−1.72026	−	0.201730i	−0.702294	−	0.0823561i
$7$	1.27169	+	2.32009i	0.480652	+	0.876912i
$7$	1.27169	+	2.32009i	0.480652	+	0.876912i
$8$			1.00000i			0.353553i
$9$	−2.91861	−	0.694059i	−0.972870	−	0.231353i
$10$	3.03762	−	1.75377i	0.960580	−	0.554591i
$11$	−3.06555	+	1.76989i	−0.924297	+	0.533643i	−0.885003	−	0.465585i	$-0.845844\pi$
$11$	−3.06555	+	1.76989i	−0.924297	+	0.533643i	−0.0392933	+	0.999228i	$0.512511\pi$
$12$	−0.201730	+	1.72026i	−0.0582346	+	0.496597i
$13$	3.59167	+	0.316032i	0.996151	+	0.0876514i
$13$	3.59167	+	0.316032i	0.996151	+	0.0876514i
$14$	2.32009	−	1.27169i	0.620070	−	0.339872i
$15$	5.57930	−	2.40417i	1.44057	−	0.620754i
$16$	1.00000			0.250000
$17$	3.95683			0.959673			0.479837	−	0.877358i	$-0.340696\pi$
$17$	3.95683			0.959673			0.479837	+	0.877358i	$0.340696\pi$
$18$	−0.694059	+	2.91861i	−0.163591	+	0.687923i
$19$	5.76542	+	3.32866i	1.32268	+	0.763648i	0.984155	−	0.177311i	$-0.0567397\pi$
$19$	5.76542	+	3.32866i	1.32268	+	0.763648i	0.338522	+	0.940958i	$0.390073\pi$
$20$	−1.75377	−	3.03762i	−0.392155	−	0.679233i
$21$	4.24770	−	1.71960i	0.926925	−	0.375248i
$22$	1.76989	+	3.06555i	0.377343	+	0.653576i
$23$			1.28595i			0.268139i	0.990972	+	0.134069i	$0.0428045\pi$
$23$			1.28595i			0.268139i	−0.990972	+	0.134069i	$0.957196\pi$
$24$	1.72026	+	0.201730i	0.351147	+	0.0411780i
$25$	−3.65143	+	6.32446i	−0.730286	+	1.26489i
$26$	0.316032	−	3.59167i	0.0619789	−	0.704385i
$27$	−1.78274	+	4.88076i	−0.343088	+	0.939303i
$28$	−1.27169	−	2.32009i	−0.240326	−	0.438456i
$29$	−5.71124	−	3.29739i	−1.06055	−	0.612310i	−0.134967	−	0.990850i	$-0.543093\pi$
$29$	−5.71124	−	3.29739i	−1.06055	−	0.612310i	−0.925585	+	0.378540i	$0.876426\pi$
$30$	−2.40417	−	5.57930i	−0.438939	−	1.01864i
$31$	−8.14013	−	4.69971i	−1.46201	−	0.844092i	−0.462906	−	0.886407i	$-0.653193\pi$
$31$	−8.14013	−	4.69971i	−1.46201	−	0.844092i	−0.999104	+	0.0423149i	$0.986527\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.42627	+	5.63059i	0.422359	+	0.980159i
$34$		−	3.95683i		−	0.678592i
$35$	−4.81731	+	7.93181i	−0.814274	+	1.34072i
$36$	2.91861	+	0.694059i	0.486435	+	0.115676i
$37$	10.5767			1.73880			0.869402	−	0.494106i	$-0.164504\pi$
$37$	10.5767			1.73880			0.869402	+	0.494106i	$0.164504\pi$
$38$	3.32866	−	5.76542i	0.539981	−	0.935274i
$39$	1.26821	−	6.11487i	0.203076	−	0.979163i
$40$	−3.03762	+	1.75377i	−0.480290	+	0.277296i
$41$	2.84220	−	4.92284i	0.443877	−	0.768818i	−0.554096	−	0.832453i	$-0.686936\pi$
$41$	2.84220	−	4.92284i	0.443877	−	0.768818i	0.997973	+	0.0636346i	$0.0202692\pi$
$42$	−1.71960	−	4.24770i	−0.265340	−	0.655435i
$43$	−2.79284	−	4.83734i	−0.425904	−	0.737688i	0.570600	−	0.821228i	$-0.306711\pi$
$43$	−2.79284	−	4.83734i	−0.425904	−	0.737688i	−0.996504	+	0.0835402i	$0.973377\pi$
$44$	3.06555	−	1.76989i	0.462148	−	0.266821i
$45$	−3.01029	−	10.0829i	−0.448747	−	1.50306i
$46$	1.28595			0.189603
$47$	0.0582673	+	0.100922i	0.00849915	+	0.0147210i	0.870244	−	0.492621i	$-0.163961\pi$
$47$	0.0582673	+	0.100922i	0.00849915	+	0.0147210i	−0.861745	+	0.507342i	$0.830628\pi$
$48$	0.201730	−	1.72026i	0.0291173	−	0.248299i
$49$	−3.76563	+	5.90085i	−0.537948	+	0.842978i
$50$	6.32446	+	3.65143i	0.894414	+	0.516390i
$51$	0.798214	−	6.80680i	0.111772	−	0.953142i
$52$	−3.59167	−	0.316032i	−0.498076	−	0.0438257i
$53$	6.70912	+	3.87351i	0.921568	+	0.532068i	0.884135	−	0.467231i	$-0.154749\pi$
$53$	6.70912	+	3.87351i	0.921568	+	0.532068i	0.0374333	+	0.999299i	$0.488082\pi$
$54$	4.88076	+	1.78274i	0.664188	+	0.242600i
$55$	−10.7525	−	6.20798i	−1.44987	−	0.837084i
$56$	−2.32009	+	1.27169i	−0.310035	+	0.169936i
$57$	6.88924	−	9.24654i	0.912502	−	1.22473i
$58$	−3.29739	+	5.71124i	−0.432968	+	0.749923i
$59$	5.68243			0.739789			0.369894	−	0.929074i	$-0.379394\pi$
$59$	5.68243			0.739789			0.369894	+	0.929074i	$0.379394\pi$
$60$	−5.57930	+	2.40417i	−0.720284	+	0.310377i
$61$	−9.51703	−	5.49466i	−1.21853	−	0.703519i	−0.253927	−	0.967223i	$-0.581722\pi$
$61$	−9.51703	−	5.49466i	−1.21853	−	0.703519i	−0.964603	+	0.263705i	$0.915056\pi$
$62$	−4.69971	+	8.14013i	−0.596863	+	1.03380i
$63$	−2.10127	−	7.65406i	−0.264736	−	0.964321i
$64$	−1.00000			−0.125000
$65$	5.33899	+	11.4644i	0.662220	+	1.42198i
$66$	5.63059	−	2.42627i	0.693077	−	0.298653i
$67$	−3.84167	−	6.65397i	−0.469335	−	0.812912i	0.530051	−	0.847966i	$-0.322173\pi$
$67$	−3.84167	−	6.65397i	−0.469335	−	0.812912i	−0.999385	+	0.0350543i	$0.988840\pi$
$68$	−3.95683			−0.479837
$69$	2.21217	+	0.259415i	0.266314	+	0.0312299i
$70$	7.93181	+	4.81731i	0.948032	+	0.575779i
$71$	−8.18290	+	4.72440i	−0.971132	+	0.560683i	−0.899581	−	0.436754i	$-0.856128\pi$
$71$	−8.18290	+	4.72440i	−0.971132	+	0.560683i	−0.0715506	+	0.997437i	$0.522795\pi$
$72$	0.694059	−	2.91861i	0.0817956	−	0.343961i
$73$	3.73438	+	2.15605i	0.437076	+	0.252346i	0.702357	−	0.711825i	$-0.252131\pi$
$73$	3.73438	+	2.15605i	0.437076	+	0.252346i	−0.265280	+	0.964171i	$0.585464\pi$
$74$		−	10.5767i		−	1.22952i
$75$	10.1431	+	7.55726i	1.17123	+	0.872637i
$76$	−5.76542	−	3.32866i	−0.661338	−	0.381824i
$77$	−8.00472	−	4.86159i	−0.912222	−	0.554030i
$78$	−6.11487	−	1.26821i	−0.692373	−	0.143596i
$79$	−2.63559	−	4.56498i	−0.296527	−	0.513601i	0.678812	−	0.734312i	$-0.262495\pi$
$79$	−2.63559	−	4.56498i	−0.296527	−	0.513601i	−0.975339	+	0.220712i	$0.929162\pi$
$80$	1.75377	+	3.03762i	0.196078	+	0.339616i
$81$	8.03656	+	4.05137i	0.892952	+	0.450153i
$82$	−4.92284	−	2.84220i	−0.543637	−	0.313869i
$83$	−2.03056			−0.222882			−0.111441	−	0.993771i	$-0.535547\pi$
$83$	−2.03056			−0.222882			−0.111441	+	0.993771i	$0.535547\pi$
$84$	−4.24770	+	1.71960i	−0.463462	+	0.187624i
$85$	6.93939	+	12.0194i	0.752682	+	1.30368i
$86$	−4.83734	+	2.79284i	−0.521624	+	0.301160i
$87$	−6.82451	+	9.15966i	−0.731664	+	0.982019i
$88$	−1.76989	−	3.06555i	−0.188671	−	0.326788i
$89$	−0.354591			−0.0375866			−0.0187933	−	0.999823i	$-0.505982\pi$
$89$	−0.354591			−0.0375866			−0.0187933	+	0.999823i	$0.505982\pi$
$90$	−10.0829	+	3.01029i	−1.06283	+	0.317312i
$91$	3.83426	+	8.73490i	0.401939	+	0.915666i
$92$		−	1.28595i		−	0.134069i
$93$	−9.72684	+	13.0551i	−1.00863	+	1.35375i
$94$	0.100922	−	0.0582673i	0.0104093	−	0.00600981i
$95$			23.3509i			2.39575i
$96$	−1.72026	−	0.201730i	−0.175574	−	0.0205890i
$97$	0.507481	−	0.292994i	0.0515269	−	0.0297491i	−0.474015	−	0.880517i	$-0.657196\pi$
$97$	0.507481	−	0.292994i	0.0515269	−	0.0297491i	0.525542	+	0.850768i	$0.323863\pi$
$98$	5.90085	+	3.76563i	0.596076	+	0.380386i
$99$	10.1755	−	3.03796i	1.02268	−	0.305326i
$100$	3.65143	−	6.32446i	0.365143	−	0.632446i
$101$	1.96198	+	3.39825i	0.195224	+	0.338138i	0.946974	−	0.321310i	$-0.104123\pi$
$101$	1.96198	+	3.39825i	0.195224	+	0.338138i	−0.751750	+	0.659448i	$0.770790\pi$
$102$	−6.80680	−	0.798214i	−0.673973	−	0.0790350i
$103$	−10.0847	+	5.82239i	−0.993673	+	0.573698i	−0.906370	−	0.422484i	$-0.861158\pi$
$103$	−10.0847	+	5.82239i	−0.993673	+	0.573698i	−0.0873031	+	0.996182i	$0.527825\pi$
$104$	−0.316032	+	3.59167i	−0.0309895	+	0.352193i
$105$	12.6730	+	9.88713i	1.23676	+	0.964885i
$106$	3.87351	−	6.70912i	0.376229	−	0.651647i
$107$		−	7.22910i		−	0.698863i	−0.936962	−	0.349432i	$-0.886375\pi$
$107$		−	7.22910i		−	0.698863i	0.936962	−	0.349432i	$-0.113625\pi$
$108$	1.78274	−	4.88076i	0.171544	−	0.469652i
$109$	2.42081	−	4.19296i	0.231871	−	0.401613i	−0.726487	−	0.687180i	$-0.758848\pi$
$109$	2.42081	−	4.19296i	0.231871	−	0.401613i	0.958359	+	0.285567i	$0.0921818\pi$
$110$	−6.20798	+	10.7525i	−0.591907	+	1.02521i
$111$	2.13365	−	18.1948i	0.202517	−	1.72697i
$112$	1.27169	+	2.32009i	0.120163	+	0.219228i
$113$	17.4151	−	10.0546i	1.63828	−	0.945859i	0.656848	−	0.754023i	$-0.271889\pi$
$113$	17.4151	−	10.0546i	1.63828	−	0.945859i	0.981427	−	0.191836i	$-0.0614442\pi$
$114$	−9.24654	−	6.88924i	−0.866018	−	0.645236i
$115$	−3.90622	+	2.25526i	−0.364257	+	0.210304i
$116$	5.71124	+	3.29739i	0.530276	+	0.306155i
$117$	−10.2634	−	3.41521i	−0.948847	−	0.315736i
$118$		−	5.68243i		−	0.523110i
$119$	5.03185	+	9.18021i	0.461269	+	0.841549i
$120$	2.40417	+	5.57930i	0.219470	+	0.509318i
$121$	0.765044	−	1.32510i	0.0695495	−	0.120463i
$122$	−5.49466	+	9.51703i	−0.497463	+	0.861631i
$123$	−7.89522	−	5.88242i	−0.711888	−	0.530400i
$124$	8.14013	+	4.69971i	0.731005	+	0.422046i
$125$	−8.07739			−0.722464
$126$	−7.65406	+	2.10127i	−0.681878	+	0.187196i
$127$	1.68665	−	2.92136i	0.149666	−	0.259228i	−0.781438	−	0.623983i	$-0.785514\pi$
$127$	1.68665	−	2.92136i	0.149666	−	0.259228i	0.931104	+	0.364754i	$0.118847\pi$
$128$			1.00000i			0.0883883i
$129$	−8.88490	+	3.82858i	−0.782272	+	0.337088i
$130$	11.4644	−	5.33899i	1.00549	−	0.468261i
$131$	3.63596	+	6.29766i	0.317675	+	0.550229i	0.980002	−	0.198985i	$-0.0637646\pi$
$131$	3.63596	+	6.29766i	0.317675	+	0.550229i	−0.662328	+	0.749214i	$0.730431\pi$
$132$	−2.42627	−	5.63059i	−0.211180	−	0.490080i
$133$	−0.391006	+	17.6093i	−0.0339045	+	1.52692i
$134$	−6.65397	+	3.84167i	−0.574815	+	0.331870i
$135$	−17.9524	+	3.14447i	−1.54510	+	0.270633i
$136$			3.95683i			0.339296i
$137$			7.42778i			0.634598i	0.948326	+	0.317299i	$0.102776\pi$
$137$			7.42778i			0.634598i	−0.948326	+	0.317299i	$0.897224\pi$
$138$	0.259415	−	2.21217i	0.0220829	−	0.188312i
$139$	3.55436	−	2.05211i	0.301477	−	0.174058i	−0.341629	−	0.939835i	$-0.610979\pi$
$139$	3.55436	−	2.05211i	0.301477	−	0.174058i	0.643106	+	0.765777i	$0.277645\pi$
$140$	4.81731	−	7.93181i	0.407137	−	0.670360i
$141$	0.185366	−	0.0798760i	0.0156107	−	0.00672677i
$142$	4.72440	+	8.18290i	0.396463	+	0.686694i
$143$	−11.5698	+	5.38807i	−0.967514	+	0.450573i
$144$	−2.91861	−	0.694059i	−0.243217	−	0.0578382i
$145$		−	23.1315i		−	1.92096i
$146$	2.15605	−	3.73438i	0.178436	−	0.309060i
$147$	9.39137	+	7.66826i	0.774587	+	0.632467i
$148$	−10.5767			−0.869402
$149$	2.21093	+	1.27648i	0.181126	+	0.104573i	0.587822	−	0.808991i	$-0.299986\pi$
$149$	2.21093	+	1.27648i	0.181126	+	0.104573i	−0.406695	+	0.913564i	$0.633319\pi$
$150$	7.55726	−	10.1431i	0.617048	−	0.828184i
$151$	4.89737	−	8.48249i	0.398542	−	0.690296i	−0.595004	−	0.803723i	$-0.702850\pi$
$151$	4.89737	−	8.48249i	0.398542	−	0.690296i	0.993546	+	0.113427i	$0.0361829\pi$
$152$	−3.32866	+	5.76542i	−0.269990	+	0.467637i
$153$	−11.5485	−	2.74628i	−0.933637	−	0.222023i
$154$	−4.86159	+	8.00472i	−0.391758	+	0.645039i
$155$		−	32.9689i		−	2.64812i
$156$	−1.26821	+	6.11487i	−0.101538	+	0.489582i
$157$	−11.3514	−	6.55373i	−0.905940	−	0.523045i	−0.0268175	−	0.999640i	$-0.508537\pi$
$157$	−11.3514	−	6.55373i	−0.905940	−	0.523045i	−0.879123	+	0.476596i	$0.841871\pi$
$158$	−4.56498	+	2.63559i	−0.363170	+	0.209677i
$159$	8.01689	−	10.7600i	0.635781	−	0.853327i
$160$	3.03762	−	1.75377i	0.240145	−	0.138648i
$161$	−2.98351	+	1.63532i	−0.235134	+	0.128881i
$162$	4.05137	−	8.03656i	0.318306	−	0.631412i
$163$	−7.21828	+	12.5024i	−0.565380	+	0.979266i	0.431635	+	0.902049i	$0.357937\pi$
$163$	−7.21828	+	12.5024i	−0.565380	+	0.979266i	−0.997014	+	0.0772178i	$0.975396\pi$
$164$	−2.84220	+	4.92284i	−0.221939	+	0.384409i
$165$	−12.8485	+	17.2448i	−1.00025	+	1.34251i
$166$			2.03056i			0.157602i
$167$	8.84596	−	15.3217i	0.684521	−	1.18563i	−0.289066	−	0.957309i	$-0.593345\pi$
$167$	8.84596	−	15.3217i	0.684521	−	1.18563i	0.973587	−	0.228316i	$-0.0733220\pi$
$168$	1.71960	+	4.24770i	0.132670	+	0.327717i
$169$	12.8002	+	2.27017i	0.984634	+	0.174628i
$170$	12.0194	−	6.93939i	0.921844	−	0.532227i
$171$	−14.5167	−	13.7166i	−1.11012	−	1.04894i
$172$	2.79284	+	4.83734i	0.212952	+	0.368844i
$173$	−2.85532	+	4.94555i	−0.217086	+	0.376003i	−0.953916	−	0.300075i	$-0.902988\pi$
$173$	−2.85532	+	4.94555i	−0.217086	+	0.376003i	0.736830	+	0.676078i	$0.236322\pi$
$174$	9.15966	+	6.82451i	0.694392	+	0.517365i
$175$	−19.3168	−	0.428920i	−1.46021	−	0.0324233i
$176$	−3.06555	+	1.76989i	−0.231074	+	0.133411i
$177$	1.14632	−	9.77527i	0.0861626	−	0.734754i
$178$			0.354591i			0.0265777i
$179$	13.2570	−	7.65395i	0.990877	−	0.572083i	0.0853403	−	0.996352i	$-0.472802\pi$
$179$	13.2570	−	7.65395i	0.990877	−	0.572083i	0.905536	+	0.424269i	$0.139469\pi$
$180$	3.01029	+	10.0829i	0.224374	+	0.751532i
$181$		−	16.4841i		−	1.22525i	−0.790373	−	0.612627i	$-0.790113\pi$
$181$		−	16.4841i		−	1.22525i	0.790373	−	0.612627i	$-0.209887\pi$
$182$	8.73490	−	3.83426i	0.647474	−	0.284214i
$183$	−11.3721	+	15.2633i	−0.840652	+	1.12830i
$184$	−1.28595			−0.0948013
$185$	18.5492	+	32.1281i	1.36376	+	2.36211i
$186$	13.0551	+	9.72684i	0.957246	+	0.713207i
$187$	−12.1299	+	7.00318i	−0.887023	+	0.512123i
$188$	−0.0582673	−	0.100922i	−0.00424958	−	0.00736048i
$189$	−13.5909	+	2.07069i	−0.988592	+	0.150620i
$190$	23.3509			1.69405
$191$	−6.92358	−	3.99733i	−0.500973	−	0.289237i	0.228142	−	0.973628i	$-0.426735\pi$
$191$	−6.92358	−	3.99733i	−0.500973	−	0.289237i	−0.729115	+	0.684391i	$0.760068\pi$
$192$	−0.201730	+	1.72026i	−0.0145586	+	0.124149i
$193$	7.98403	+	13.8287i	0.574703	+	0.995415i	0.996074	+	0.0885262i	$0.0282157\pi$
$193$	7.98403	+	13.8287i	0.574703	+	0.995415i	−0.421371	+	0.906888i	$0.638451\pi$
$194$	−0.292994	−	0.507481i	−0.0210358	−	0.0364350i
$195$	20.7988	−	6.87175i	1.48943	−	0.492096i
$196$	3.76563	−	5.90085i	0.268974	−	0.421489i
$197$	−23.1575	−	13.3700i	−1.64990	−	0.952571i	−0.977109	−	0.212741i	$-0.931761\pi$
$197$	−23.1575	−	13.3700i	−1.64990	−	0.952571i	−0.672794	−	0.739830i	$-0.734906\pi$
$198$	−3.03796	−	10.1755i	−0.215898	−	0.723144i
$199$		−	2.17392i		−	0.154105i	−0.997027	−	0.0770526i	$-0.975449\pi$
$199$		−	2.17392i		−	0.154105i	0.997027	−	0.0770526i	$-0.0245509\pi$
$200$	−6.32446	−	3.65143i	−0.447207	−	0.258195i
$201$	−12.2216	+	5.26638i	−0.862042	+	0.371462i
$202$	3.39825	−	1.96198i	0.239100	−	0.138044i
$203$	0.387332	−	17.4438i	0.0271854	−	1.22432i
$204$	−0.798214	+	6.80680i	−0.0558862	+	0.476571i
$205$	19.9383			1.39255
$206$	5.82239	+	10.0847i	0.405665	+	0.702633i
$207$	0.892523	−	3.75318i	0.0620347	−	0.260864i
$208$	3.59167	+	0.316032i	0.249038	+	0.0219129i
$209$	−23.5655			−1.63006
$210$	9.88713	−	12.6730i	0.682277	−	0.874520i
$211$	−2.63990	+	4.57244i	−0.181738	+	0.314779i	−0.942472	−	0.334284i	$-0.891506\pi$
$211$	−2.63990	+	4.57244i	−0.181738	+	0.314779i	0.760734	+	0.649063i	$0.224839\pi$
$212$	−6.70912	−	3.87351i	−0.460784	−	0.266034i
$213$	6.47647	+	15.0298i	0.443760	+	1.02982i
$214$	−7.22910			−0.494171
$215$	9.79601	−	16.9672i	0.668082	−	1.15715i
$216$	−4.88076	−	1.78274i	−0.332094	−	0.121300i
$217$	0.552057	−	24.8624i	0.0374761	−	1.68777i
$218$	−4.19296	−	2.42081i	−0.283983	−	0.163958i
$219$	4.46231	−	5.98918i	0.301535	−	0.404711i
$220$	10.7525	+	6.20798i	0.724936	+	0.418542i
$221$	14.2117	+	1.25049i	0.955980	+	0.0841168i
$222$	−18.1948	−	2.13365i	−1.22115	−	0.143201i
$223$	−9.21057	−	5.31772i	−0.616785	−	0.356101i	0.158831	−	0.987306i	$-0.449227\pi$
$223$	−9.21057	−	5.31772i	−0.616785	−	0.356101i	−0.775616	+	0.631205i	$0.782561\pi$
$224$	2.32009	−	1.27169i	0.155018	−	0.0849680i
$225$	15.0467	−	15.9243i	1.00311	−	1.06162i
$226$	−10.0546	−	17.4151i	−0.668823	−	1.15844i
$227$	1.95102			0.129494			0.0647468	−	0.997902i	$-0.479376\pi$
$227$	1.95102			0.129494			0.0647468	+	0.997902i	$0.479376\pi$
$228$	−6.88924	+	9.24654i	−0.456251	+	0.612367i
$229$	−10.1017	+	5.83221i	−0.667538	+	0.385403i	−0.795143	−	0.606422i	$-0.792604\pi$
$229$	−10.1017	+	5.83221i	−0.667538	+	0.385403i	0.127605	+	0.991825i	$0.459271\pi$
$230$	2.25526	+	3.90622i	0.148707	+	0.257569i
$231$	−9.97801	+	12.7895i	−0.656505	+	0.841487i
$232$	3.29739	−	5.71124i	0.216484	−	0.374962i
$233$	−11.6531	+	6.72790i	−0.763418	+	0.440759i	−0.830521	−	0.556987i	$-0.811957\pi$
$233$	−11.6531	+	6.72790i	−0.763418	+	0.440759i	0.0671038	+	0.997746i	$0.478624\pi$
$234$	−3.41521	+	10.2634i	−0.223259	+	0.670936i
$235$	−0.204375	+	0.353988i	−0.0133320	+	0.0230916i
$236$	−5.68243			−0.369894
$237$	−8.38465	+	3.61302i	−0.544641	+	0.234691i
$238$	9.18021	−	5.03185i	0.595065	−	0.326166i
$239$			4.27464i			0.276504i	0.990397	+	0.138252i	$0.0441483\pi$
$239$			4.27464i			0.276504i	−0.990397	+	0.138252i	$0.955852\pi$
$240$	5.57930	−	2.40417i	0.360142	−	0.155188i
$241$		−	14.4768i		−	0.932530i	−0.884645	−	0.466265i	$-0.845599\pi$
$241$		−	14.4768i		−	0.932530i	0.884645	−	0.466265i	$-0.154401\pi$
$242$	−1.32510	−	0.765044i	−0.0851804	−	0.0491789i
$243$	8.59065	−	13.0077i	0.551090	−	0.834446i
$244$	9.51703	+	5.49466i	0.609265	+	0.351759i
$245$	−24.5286	−	1.08983i	−1.56708	−	0.0696266i
$246$	−5.88242	+	7.89522i	−0.375050	+	0.503381i
$247$	19.6555	+	13.7775i	1.25065	+	0.876643i
$248$	4.69971	−	8.14013i	0.298432	−	0.516899i
$249$	−0.409625	+	3.49309i	−0.0259589	+	0.221366i
$250$			8.07739i			0.510859i
$251$	0.147269	+	0.255078i	0.00929556	+	0.0161004i	0.870636	−	0.491928i	$-0.163708\pi$
$251$	0.147269	+	0.255078i	0.00929556	+	0.0161004i	−0.861340	+	0.508029i	$0.830374\pi$
$252$	2.10127	+	7.65406i	0.132368	+	0.482161i
$253$	−2.27599	−	3.94213i	−0.143090	−	0.247840i
$254$	−2.92136	−	1.68665i	−0.183302	−	0.105830i
$255$	22.0764	−	9.51290i	1.38248	−	0.595721i
$256$	1.00000			0.0625000
$257$	11.1988			0.698560			0.349280	−	0.937018i	$-0.386426\pi$
$257$	11.1988			0.698560			0.349280	+	0.937018i	$0.386426\pi$
$258$	3.82858	+	8.88490i	0.238357	+	0.553150i
$259$	13.4503	+	24.5390i	0.835759	+	1.52478i
$260$	−5.33899	−	11.4644i	−0.331110	−	0.710992i
$261$	14.3803	+	13.5877i	0.890119	+	0.841059i
$262$	6.29766	−	3.63596i	0.389071	−	0.224630i
$263$	3.60427	−	2.08093i	0.222249	−	0.128315i	−0.384742	−	0.923024i	$-0.625710\pi$
$263$	3.60427	−	2.08093i	0.222249	−	0.128315i	0.606991	+	0.794709i	$0.292376\pi$
$264$	−5.63059	+	2.42627i	−0.346539	+	0.149326i
$265$			27.1730i			1.66923i
$266$	17.6093	+	0.391006i	1.07970	+	0.0239741i
$267$	−0.0715318	+	0.609990i	−0.00437768	+	0.0373308i
$268$	3.84167	+	6.65397i	0.234667	+	0.406456i
$269$	−24.2715			−1.47986			−0.739930	−	0.672683i	$-0.765142\pi$
$269$	−24.2715			−1.47986			−0.739930	+	0.672683i	$0.765142\pi$
$270$	3.14447	+	17.9524i	0.191366	+	1.09255i
$271$		−	12.3887i		−	0.752560i	−0.926506	−	0.376280i	$-0.877203\pi$
$271$		−	12.3887i		−	0.752560i	0.926506	−	0.376280i	$-0.122797\pi$
$272$	3.95683			0.239918
$273$	15.7998	−	4.83384i	0.956248	−	0.292557i
$274$	7.42778			0.448728
$275$		−	25.8506i		−	1.55885i
$276$	−2.21217	−	0.259415i	−0.133157	−	0.0156149i
$277$	−10.2959			−0.618619			−0.309310	−	0.950961i	$-0.600098\pi$
$277$	−10.2959			−0.618619			−0.309310	+	0.950961i	$0.600098\pi$
$278$	−2.05211	−	3.55436i	−0.123077	−	0.213176i
$279$	20.4960	+	19.3663i	1.22706	+	1.15943i
$280$	−7.93181	−	4.81731i	−0.474016	−	0.287889i
$281$		−	6.21604i		−	0.370818i	−0.982661	−	0.185409i	$-0.940639\pi$
$281$		−	6.21604i		−	0.370818i	0.982661	−	0.185409i	$-0.0593610\pi$
$282$	−0.0798760	−	0.185366i	−0.00475655	−	0.0110384i
$283$	−11.6400	+	6.72035i	−0.691926	+	0.399484i	−0.804333	−	0.594179i	$-0.797477\pi$
$283$	−11.6400	+	6.72035i	−0.691926	+	0.399484i	0.112407	+	0.993662i	$0.464144\pi$
$284$	8.18290	−	4.72440i	0.485566	−	0.280342i
$285$	40.1696	+	4.71058i	2.37944	+	0.279031i
$286$	5.38807	+	11.5698i	0.318603	+	0.684136i
$287$	15.0358	+	0.333863i	0.887536	+	0.0197073i
$288$	−0.694059	+	2.91861i	−0.0408978	+	0.171981i
$289$	−1.34346			−0.0790269
$290$	−23.1315			−1.35833
$291$	−0.401653	−	0.932106i	−0.0235453	−	0.0546410i
$292$	−3.73438	−	2.15605i	−0.218538	−	0.126173i
$293$	−6.36341	−	11.0218i	−0.371755	−	0.643898i	0.618081	−	0.786114i	$-0.287910\pi$
$293$	−6.36341	−	11.0218i	−0.371755	−	0.643898i	−0.989836	+	0.142217i	$0.954577\pi$
$294$	7.66826	−	9.39137i	0.447222	−	0.547716i
$295$	9.96568	+	17.2611i	0.580224	+	1.00498i
$296$			10.5767i			0.614760i
$297$	−3.17337	−	18.1175i	−0.184138	−	1.05128i
$298$	1.27648	−	2.21093i	0.0739445	−	0.128076i
$299$	−0.406400	+	4.61871i	−0.0235027	+	0.267107i
$300$	−10.1431	−	7.55726i	−0.585614	−	0.436319i
$301$	7.67145	−	12.6312i	0.442175	−	0.728051i
$302$	−8.48249	−	4.89737i	−0.488113	−	0.281812i
$303$	6.24167	−	2.68959i	0.358575	−	0.154513i
$304$	5.76542	+	3.32866i	0.330669	+	0.190912i
$305$		−	38.5455i		−	2.20711i
$306$	−2.74628	+	11.5485i	−0.156994	+	0.660181i
$307$		−	25.8938i		−	1.47784i	−0.673796	−	0.738918i	$-0.735337\pi$
$307$		−	25.8938i		−	1.47784i	0.673796	−	0.738918i	$-0.264663\pi$
$308$	8.00472	+	4.86159i	0.456111	+	0.277015i
$309$	7.98166	+	18.5229i	0.454061	+	1.05373i
$310$	−32.9689			−1.87251
$311$	2.45036	−	4.24415i	0.138947	−	0.240664i	−0.788151	−	0.615482i	$-0.788962\pi$
$311$	2.45036	−	4.24415i	0.138947	−	0.240664i	0.927098	+	0.374818i	$0.122295\pi$
$312$	6.11487	+	1.26821i	0.346186	+	0.0717981i
$313$	−18.2027	+	10.5093i	−1.02888	+	0.594022i	−0.916662	−	0.399663i	$-0.869127\pi$
$313$	−18.2027	+	10.5093i	−1.02888	+	0.594022i	−0.112213	+	0.993684i	$0.535794\pi$
$314$	−6.55373	+	11.3514i	−0.369849	+	0.640596i
$315$	19.5650	−	19.8064i	1.10236	−	1.11596i
$316$	2.63559	+	4.56498i	0.148264	+	0.256800i
$317$	12.9313	−	7.46591i	0.726296	−	0.419327i	−0.0907693	−	0.995872i	$-0.528933\pi$
$317$	12.9313	−	7.46591i	0.726296	−	0.419327i	0.817066	+	0.576545i	$0.195599\pi$
$318$	−10.7600	−	8.01689i	−0.603393	−	0.449565i
$319$	23.3441			1.30702
$320$	−1.75377	−	3.03762i	−0.0980388	−	0.169808i
$321$	−12.4359	−	1.45833i	−0.694107	−	0.0813960i
$322$	1.63532	+	2.98351i	0.0911329	+	0.166265i
$323$	22.8128	+	13.1710i	1.26934	+	0.732853i
$324$	−8.03656	−	4.05137i	−0.446476	−	0.225076i
$325$	−15.1135	+	21.5614i	−0.838345	+	1.19601i
$326$	12.5024	+	7.21828i	0.692446	+	0.399784i
$327$	−6.72465	−	5.01027i	−0.371874	−	0.277069i
$328$	4.92284	+	2.84220i	0.271818	+	0.156934i
$329$	−0.160050	+	0.263526i	−0.00882385	+	0.0145287i
$330$	17.2448	+	12.8485i	0.949298	+	0.707285i
$331$	−0.512426	+	0.887547i	−0.0281655	+	0.0487840i	−0.879765	−	0.475410i	$-0.842300\pi$
$331$	−0.512426	+	0.887547i	−0.0281655	+	0.0487840i	0.851599	+	0.524194i	$0.175633\pi$
$332$	2.03056			0.111441
$333$	−30.8693	−	7.34087i	−1.69163	−	0.402277i
$334$	−15.3217	−	8.84596i	−0.838364	−	0.484029i
$335$	13.4748	−	23.3391i	0.736208	−	1.27515i
$336$	4.24770	−	1.71960i	0.231731	−	0.0938119i
$337$	20.0548			1.09245			0.546226	−	0.837638i	$-0.316064\pi$
$337$	20.0548			1.09245			0.546226	+	0.837638i	$0.316064\pi$
$338$	2.27017	−	12.8002i	0.123481	−	0.696242i
$339$	−13.7834	−	31.9869i	−0.748613	−	1.73729i
$340$	−6.93939	−	12.0194i	−0.376341	−	0.651842i
$341$	33.2719			1.80178
$342$	−13.7166	+	14.5167i	−0.741709	+	0.784974i
$343$	−18.4792	−	1.23259i	−0.997783	−	0.0665534i
$344$	4.83734	−	2.79284i	0.260812	−	0.150580i
$345$	3.09163	+	7.17468i	0.166448	+	0.386272i
$346$	4.94555	+	2.85532i	0.265875	+	0.153503i
$347$		−	24.9526i		−	1.33953i	−0.742575	−	0.669763i	$-0.766396\pi$
$347$		−	24.9526i		−	1.33953i	0.742575	−	0.669763i	$-0.233604\pi$
$348$	6.82451	−	9.15966i	0.365832	−	0.491009i
$349$	−7.17962	−	4.14516i	−0.384316	−	0.221885i	0.295378	−	0.955380i	$-0.404554\pi$
$349$	−7.17962	−	4.14516i	−0.384316	−	0.221885i	−0.679695	+	0.733495i	$0.737888\pi$
$350$	−0.428920	+	19.3168i	−0.0229267	+	1.03253i
$351$	−7.94548	+	16.9667i	−0.424099	+	0.905616i
$352$	1.76989	+	3.06555i	0.0943356	+	0.163394i
$353$	−17.3189	−	29.9971i	−0.921789	−	1.59659i	−0.796645	−	0.604448i	$-0.793394\pi$
$353$	−17.3189	−	29.9971i	−0.921789	−	1.59659i	−0.125145	−	0.992139i	$-0.539940\pi$
$354$	−9.77527	−	1.14632i	−0.519550	−	0.0609261i
$355$	−28.7019	−	16.5710i	−1.52334	−	0.879499i
$356$	0.354591			0.0187933
$357$	16.8075	−	6.80418i	0.889545	−	0.360115i
$358$	−7.65395	−	13.2570i	−0.404524	−	0.700656i
$359$	−5.14944	+	2.97303i	−0.271777	+	0.156910i	−0.629695	−	0.776843i	$-0.716820\pi$
$359$	−5.14944	+	2.97303i	−0.271777	+	0.156910i	0.357918	+	0.933753i	$0.383487\pi$
$360$	10.0829	−	3.01029i	0.531413	−	0.158656i
$361$	12.6600	+	21.9278i	0.666316	+	1.15409i
$362$	−16.4841			−0.866385
$363$	−2.12518	−	1.58339i	−0.111543	−	0.0831064i
$364$	−3.83426	−	8.73490i	−0.200970	−	0.457833i
$365$			15.1249i			0.791671i
$366$	15.2633	+	11.3721i	0.797828	+	0.594431i
$367$	20.3845	−	11.7690i	1.06406	−	0.614336i	0.137509	−	0.990501i	$-0.456090\pi$
$367$	20.3845	−	11.7690i	1.06406	−	0.614336i	0.926553	+	0.376164i	$0.122757\pi$
$368$			1.28595i			0.0670347i
$369$	−11.7120	+	12.3952i	−0.609703	+	0.645268i
$370$	32.1281	−	18.5492i	1.67026	−	0.964326i
$371$	−0.455007	+	20.4916i	−0.0236228	+	1.06387i
$372$	9.72684	−	13.0551i	0.504313	−	0.676875i
$373$	−0.756908	+	1.31100i	−0.0391912	+	0.0678812i	−0.884956	−	0.465675i	$-0.845811\pi$
$373$	−0.756908	+	1.31100i	−0.0391912	+	0.0678812i	0.845764	+	0.533556i	$0.179145\pi$
$374$	7.00318	+	12.1299i	0.362126	+	0.627220i
$375$	−1.62946	+	13.8952i	−0.0841447	+	0.717547i
$376$	−0.100922	+	0.0582673i	−0.00520465	+	0.00300491i
$377$	−19.4709	−	13.6481i	−1.00280	−	0.702912i
$378$	2.07069	+	13.5909i	0.106505	+	0.699040i
$379$	−12.9429	+	22.4178i	−0.664832	+	1.15152i	0.314499	+	0.949258i	$0.398163\pi$
$379$	−12.9429	+	22.4178i	−0.664832	+	1.15152i	−0.979331	+	0.202265i	$0.935170\pi$
$380$		−	23.3509i		−	1.19787i
$381$	−4.68525	−	3.49080i	−0.240033	−	0.178839i
$382$	−3.99733	+	6.92358i	−0.204521	+	0.354241i
$383$	−4.81156	+	8.33387i	−0.245859	+	0.425841i	−0.962373	−	0.271732i	$-0.912403\pi$
$383$	−4.81156	+	8.33387i	−0.245859	+	0.425841i	0.716514	+	0.697573i	$0.245737\pi$
$384$	1.72026	+	0.201730i	0.0877868	+	0.0102945i
$385$	0.729228	−	32.8414i	0.0371649	−	1.67375i
$386$	13.8287	−	7.98403i	0.703864	−	0.406376i
$387$	4.79381	+	16.0567i	0.243683	+	0.816208i
$388$	−0.507481	+	0.292994i	−0.0257634	+	0.0148745i
$389$	17.2937	+	9.98452i	0.876825	+	0.506235i	0.869610	−	0.493739i	$-0.164370\pi$
$389$	17.2937	+	9.98452i	0.876825	+	0.506235i	0.00721490	+	0.999974i	$0.497703\pi$
$390$	−6.87175	−	20.7988i	−0.347965	−	1.05319i
$391$			5.08828i			0.257326i
$392$	−5.90085	−	3.76563i	−0.298038	−	0.190193i
$393$	11.5671	−	4.98437i	0.583484	−	0.251428i
$394$	−13.3700	+	23.1575i	−0.673570	+	1.16666i
$395$	9.24446	−	16.0119i	0.465139	−	0.805645i
$396$	−10.1755	+	3.03796i	−0.511340	+	0.152663i
$397$	13.0331	+	7.52468i	0.654114	+	0.377653i	0.790031	−	0.613067i	$-0.210065\pi$
$397$	13.0331	+	7.52468i	0.654114	+	0.377653i	−0.135917	+	0.990720i	$0.543398\pi$
$398$	−2.17392			−0.108969
$399$	30.2137	+	4.22496i	1.51258	+	0.211513i
$400$	−3.65143	+	6.32446i	−0.182572	+	0.316223i
$401$			30.8125i			1.53870i	0.638826	+	0.769351i	$0.279420\pi$
$401$			30.8125i			1.53870i	−0.638826	+	0.769351i	$0.720580\pi$
$402$	5.26638	+	12.2216i	0.262663	+	0.609556i
$403$	−27.7514	−	19.4524i	−1.38240	−	0.968991i
$404$	−1.96198	−	3.39825i	−0.0976121	−	0.169069i
$405$	1.78776	+	31.5172i	0.0888346	+	1.56610i
$406$	−17.4438	−	0.387332i	−0.865723	−	0.0192230i
$407$	−32.4234	+	18.7197i	−1.60717	+	0.927900i
$408$	6.80680	+	0.798214i	0.336987	+	0.0395175i
$409$			3.31277i			0.163806i	0.996640	+	0.0819028i	$0.0260997\pi$
$409$			3.31277i			0.163806i	−0.996640	+	0.0819028i	$0.973900\pi$
$410$		−	19.9383i		−	0.984682i
$411$	12.7777	+	1.49841i	0.630279	+	0.0739110i
$412$	10.0847	−	5.82239i	0.496837	−	0.286849i
$413$	7.22626	+	13.1837i	0.355581	+	0.648729i
$414$	−3.75318	−	0.892523i	−0.184459	−	0.0438651i
$415$	−3.56113	−	6.16806i	−0.174809	−	0.302778i
$416$	0.316032	−	3.59167i	0.0154947	−	0.176096i
$417$	−2.81314	−	6.52840i	−0.137760	−	0.319697i
$418$			23.5655i			1.15263i
$419$	−9.29999	+	16.1081i	−0.454334	+	0.786930i	−0.998650	−	0.0519505i	$-0.983456\pi$
$419$	−9.29999	+	16.1081i	−0.454334	+	0.786930i	0.544315	+	0.838881i	$0.316790\pi$
$420$	−12.6730	−	9.88713i	−0.618379	−	0.482442i
$421$	0.699811			0.0341067			0.0170534	−	0.999855i	$-0.494571\pi$
$421$	0.699811			0.0341067			0.0170534	+	0.999855i	$0.494571\pi$
$422$	4.57244	+	2.63990i	0.222583	+	0.128508i
$423$	−0.100014	−	0.334992i	−0.00486283	−	0.0162879i
$424$	−3.87351	+	6.70912i	−0.188114	+	0.325824i
$425$	−14.4481	+	25.0249i	−0.700836	+	1.21388i
$426$	15.0298	−	6.47647i	0.728196	−	0.313786i
$427$	0.645437	−	29.0678i	0.0312349	−	1.40669i
$428$			7.22910i			0.349432i
$429$	6.93492	+	20.9900i	0.334821	+	1.01341i
$430$	−16.9672	−	9.79601i	−0.818231	−	0.472406i
$431$	15.0353	−	8.68065i	0.724226	−	0.418132i	−0.0920801	−	0.995752i	$-0.529352\pi$
$431$	15.0353	−	8.68065i	0.724226	−	0.418132i	0.816306	+	0.577620i	$0.196018\pi$
$432$	−1.78274	+	4.88076i	−0.0857719	+	0.234826i
$433$	23.7833	−	13.7313i	1.14295	−	0.659884i	0.195793	−	0.980645i	$-0.437272\pi$
$433$	23.7833	−	13.7313i	1.14295	−	0.659884i	0.947160	+	0.320761i	$0.103939\pi$
$434$	−24.8624	−	0.552057i	−1.19343	−	0.0264996i
$435$	−39.7922	−	4.66632i	−1.90789	−	0.223733i
$436$	−2.42081	+	4.19296i	−0.115936	+	0.200806i
$437$	−4.28049	+	7.41402i	−0.204763	+	0.354661i
$438$	−5.98918	−	4.46231i	−0.286174	−	0.213217i
$439$			12.0917i			0.577106i	0.957464	+	0.288553i	$0.0931742\pi$
$439$			12.0917i			0.577106i	−0.957464	+	0.288553i	$0.906826\pi$
$440$	6.20798	−	10.7525i	0.295954	−	0.512607i
$441$	15.0859	−	14.6087i	0.718379	−	0.695652i
$442$	1.25049	−	14.2117i	0.0594795	−	0.675980i
$443$	−8.19745	+	4.73280i	−0.389473	+	0.224862i	−0.681932	−	0.731416i	$-0.738860\pi$
$443$	−8.19745	+	4.73280i	−0.389473	+	0.224862i	0.292459	+	0.956278i	$0.405527\pi$
$444$	−2.13365	+	18.1948i	−0.101258	+	0.863485i
$445$	−0.621872	−	1.07711i	−0.0294796	−	0.0510601i
$446$	−5.31772	+	9.21057i	−0.251802	+	0.436133i
$447$	2.64189	−	3.54587i	0.124957	−	0.167714i
$448$	−1.27169	−	2.32009i	−0.0600815	−	0.109614i
$449$	−1.05989	+	0.611927i	−0.0500193	+	0.0288786i	−0.524801	−	0.851225i	$-0.675860\pi$
$449$	−1.05989	+	0.611927i	−0.0500193	+	0.0288786i	0.474782	+	0.880104i	$0.342527\pi$
$450$	−15.9243	−	15.0467i	−0.750680	−	0.709306i
$451$			20.1216i			0.947488i
$452$	−17.4151	+	10.0546i	−0.819138	+	0.472929i
$453$	−13.6042	−	10.1359i	−0.639180	−	0.476228i
$454$		−	1.95102i		−	0.0915658i
$455$	−19.8089	+	26.9660i	−0.928656	+	1.26419i
$456$	9.24654	+	6.88924i	0.433009	+	0.322618i
$457$	6.13692			0.287073			0.143536	−	0.989645i	$-0.454153\pi$
$457$	6.13692			0.287073			0.143536	+	0.989645i	$0.454153\pi$
$458$	5.83221	+	10.1017i	0.272521	+	0.472020i
$459$	−7.05399	+	19.3124i	−0.329252	+	0.901425i
$460$	3.90622	−	2.25526i	0.182129	−	0.105152i
$461$	12.7435	+	22.0723i	0.593523	+	1.02801i	0.993754	+	0.111597i	$0.0355967\pi$
$461$	12.7435	+	22.0723i	0.593523	+	1.02801i	−0.400231	+	0.916414i	$0.631070\pi$
$462$	12.7895	+	9.97801i	0.595021	+	0.464219i
$463$	15.6848			0.728937			0.364468	−	0.931216i	$-0.381251\pi$
$463$	15.6848			0.728937			0.364468	+	0.931216i	$0.381251\pi$
$464$	−5.71124	−	3.29739i	−0.265138	−	0.153077i
$465$	−56.7151	−	6.65082i	−2.63010	−	0.308424i
$466$	6.72790	+	11.6531i	0.311664	+	0.539818i
$467$	−13.1716	−	22.8139i	−0.609508	−	1.05570i	−0.991322	−	0.131460i	$-0.958034\pi$
$467$	−13.1716	−	22.8139i	−0.609508	−	1.05570i	0.381813	−	0.924239i	$-0.375300\pi$
$468$	10.2634	+	3.41521i	0.474424	+	0.157868i
$469$	10.5524	−	17.3748i	0.487265	−	0.802293i
$470$	0.353988	+	0.204375i	0.0163282	+	0.00942712i
$471$	−13.5641	+	18.2053i	−0.624999	+	0.838856i
$472$			5.68243i			0.261555i
$473$	17.1232	+	9.88606i	0.787324	+	0.454562i
$474$	3.61302	+	8.38465i	0.165951	+	0.385120i
$475$	−42.1040	+	24.3088i	−1.93187	+	1.11536i
$476$	−5.03185	−	9.18021i	−0.230634	−	0.420774i
$477$	−16.8929	−	15.9618i	−0.773471	−	0.730840i
$478$	4.27464			0.195518
$479$	19.3811	+	33.5691i	0.885545	+	1.53381i	0.845087	+	0.534628i	$0.179548\pi$
$479$	19.3811	+	33.5691i	0.885545	+	1.53381i	0.0404582	+	0.999181i	$0.487118\pi$
$480$	−2.40417	−	5.57930i	−0.109735	−	0.254659i
$481$	37.9882	+	3.34258i	1.73211	+	0.152409i
$482$	−14.4768			−0.659398
$483$	2.21132	+	5.46232i	0.100618	+	0.248544i
$484$	−0.765044	+	1.32510i	−0.0347747	+	0.0602316i
$485$	1.78001	+	1.02769i	0.0808261	+	0.0466650i
$486$	−13.0077	−	8.59065i	−0.590042	−	0.389680i
$487$	−19.9536			−0.904182			−0.452091	−	0.891972i	$-0.649322\pi$
$487$	−19.9536			−0.904182			−0.452091	+	0.891972i	$0.649322\pi$
$488$	5.49466	−	9.51703i	0.248731	−	0.430816i
$489$	20.0513	+	14.9395i	0.906752	+	0.675586i
$490$	−1.08983	+	24.5286i	−0.0492335	+	1.10809i
$491$	−4.36750	−	2.52158i	−0.197103	−	0.113797i	0.398201	−	0.917298i	$-0.369635\pi$
$491$	−4.36750	−	2.52158i	−0.197103	−	0.113797i	−0.595303	+	0.803501i	$0.702968\pi$
$492$	7.89522	+	5.88242i	0.355944	+	0.265200i
$493$	−22.5985	−	13.0472i	−1.01778	−	0.587617i
$494$	13.7775	−	19.6555i	0.619880	−	0.884344i
$495$	27.0737	+	25.5816i	1.21687	+	1.14981i
$496$	−8.14013	−	4.69971i	−0.365503	−	0.211023i
$497$	−21.3671	−	12.9771i	−0.958446	−	0.582103i
$498$	3.49309	+	0.409625i	0.156529	+	0.0183557i
$499$	−18.5321	−	32.0985i	−0.829609	−	1.43693i	−0.898345	−	0.439290i	$-0.855230\pi$
$499$	−18.5321	−	32.0985i	−0.829609	−	1.43693i	0.0687359	−	0.997635i	$-0.478103\pi$
$500$	8.07739			0.361232
$501$	−24.5728	−	18.3082i	−1.09783	−	0.817951i
$502$	0.255078	−	0.147269i	0.0113847	−	0.00657296i
$503$	12.8063	+	22.1812i	0.571005	+	0.989010i	0.996463	+	0.0840317i	$0.0267797\pi$
$503$	12.8063	+	22.1812i	0.571005	+	0.989010i	−0.425458	+	0.904978i	$0.639887\pi$
$504$	7.65406	−	2.10127i	0.340939	−	0.0935982i
$505$	−6.88173	+	11.9195i	−0.306233	+	0.530411i
$506$	−3.94213	+	2.27599i	−0.175249	+	0.101180i
$507$	6.48748	−	21.5618i	0.288119	−	0.957595i
$508$	−1.68665	+	2.92136i	−0.0748328	+	0.129614i
$509$	−9.94536			−0.440820			−0.220410	−	0.975407i	$-0.570740\pi$
$509$	−9.94536			−0.440820			−0.220410	+	0.975407i	$0.570740\pi$
$510$	−9.51290	−	22.0764i	−0.421238	−	0.977558i
$511$	−0.253263	+	11.4059i	−0.0112037	+	0.504568i
$512$		−	1.00000i		−	0.0441942i
$513$	−26.5246	+	22.2055i	−1.17109	+	0.980397i
$514$		−	11.1988i		−	0.493957i
$515$	−35.3725	−	20.4223i	−1.55870	−	0.899914i
$516$	8.88490	−	3.82858i	0.391136	−	0.168544i
$517$	−0.357242	−	0.206254i	−0.0157115	−	0.00907103i
$518$	24.5390	−	13.4503i	1.07818	−	0.590971i
$519$	7.93165	+	5.90956i	0.348161	+	0.259401i
$520$	−11.4644	+	5.33899i	−0.502747	+	0.234130i
$521$	7.83412	−	13.5691i	0.343219	−	0.594473i	−0.641810	−	0.766864i	$-0.721816\pi$
$521$	7.83412	−	13.5691i	0.343219	−	0.594473i	0.985029	+	0.172391i	$0.0551494\pi$
$522$	13.5877	−	14.3803i	0.594719	−	0.629409i
$523$			37.1763i			1.62560i	0.582540	+	0.812802i	$0.302059\pi$
$523$			37.1763i			1.62560i	−0.582540	+	0.812802i	$0.697941\pi$
$524$	−3.63596	−	6.29766i	−0.158837	−	0.275115i
$525$	−4.63464	+	33.1434i	−0.202272	+	1.44650i
$526$	−2.08093	−	3.60427i	−0.0907327	−	0.157154i
$527$	−32.2092	−	18.5960i	−1.40305	−	0.810053i
$528$	2.42627	+	5.63059i	0.105590	+	0.245040i
$529$	21.3463			0.928102
$530$	27.1730			1.18032
$531$	−16.5848	−	3.94394i	−0.719718	−	0.171152i
$532$	0.391006	−	17.6093i	0.0169523	−	0.763460i
$533$	11.7640	−	16.7830i	0.509557	−	0.726953i
$534$	0.609990	+	0.0715318i	0.0263969	+	0.00309548i
$535$	21.9593	−	12.6782i	0.949382	−	0.548126i
$536$	6.65397	−	3.84167i	0.287408	−	0.165935i
$537$	−10.4925	−	24.3496i	−0.452783	−	1.05076i
$538$			24.2715i			1.04642i
$539$	1.09985	−	24.7541i	0.0473738	−	1.06623i
$540$	17.9524	−	3.14447i	0.772549	−	0.135316i
$541$	2.98669	+	5.17310i	0.128408	+	0.222409i	0.923060	−	0.384656i	$-0.125680\pi$
$541$	2.98669	+	5.17310i	0.128408	+	0.222409i	−0.794652	+	0.607065i	$0.792347\pi$
$542$	−12.3887			−0.532140
$543$	−28.3570	−	3.32534i	−1.21691	−	0.142704i
$544$		−	3.95683i		−	0.169648i
$545$	16.9822			0.727437
$546$	−4.83384	−	15.7998i	−0.206869	−	0.676169i
$547$	3.17249			0.135646			0.0678230	−	0.997697i	$-0.478395\pi$
$547$	3.17249			0.135646			0.0678230	+	0.997697i	$0.478395\pi$
$548$		−	7.42778i		−	0.317299i
$549$	23.9629	+	22.6421i	1.02271	+	0.966343i
$550$	−25.8506			−1.10227
$551$	−21.9518	−	38.0216i	−0.935178	−	1.61978i
$552$	−0.259415	+	2.21217i	−0.0110414	+	0.0941561i
$553$	7.23952	−	11.9200i	0.307856	−	0.506891i
$554$			10.2959i			0.437430i
$555$	59.0107	−	25.4282i	2.50487	−	1.07937i
$556$	−3.55436	+	2.05211i	−0.150738	+	0.0870288i
$557$	−8.07587	+	4.66261i	−0.342186	+	0.197561i	−0.661238	−	0.750176i	$-0.729969\pi$
$557$	−8.07587	+	4.66261i	−0.342186	+	0.197561i	0.319052	+	0.947737i	$0.396635\pi$
$558$	19.3663	−	20.4960i	0.819843	−	0.867665i
$559$	−8.50222	−	18.2568i	−0.359606	−	0.772180i
$560$	−4.81731	+	7.93181i	−0.203568	+	0.335180i
$561$	9.60034	+	22.2793i	0.405327	+	0.940633i
$562$	−6.21604			−0.262208
$563$	22.4508			0.946188			0.473094	−	0.881012i	$-0.343137\pi$
$563$	22.4508			0.946188			0.473094	+	0.881012i	$0.343137\pi$
$564$	−0.185366	+	0.0798760i	−0.00780534	+	0.00336339i
$565$	61.0842	+	35.2670i	2.56983	+	1.48369i
$566$	6.72035	+	11.6400i	0.282478	+	0.489265i
$567$	0.820431	+	23.7976i	0.0344549	+	0.999406i
$568$	−4.72440	−	8.18290i	−0.198231	−	0.343347i
$569$			23.7857i			0.997147i	0.866848	+	0.498573i	$0.166143\pi$
$569$			23.7857i			0.997147i	−0.866848	+	0.498573i	$0.833857\pi$
$570$	4.71058	−	40.1696i	0.197305	−	1.68252i
$571$	14.7275	−	25.5087i	0.616326	−	1.06751i	−0.373825	−	0.927499i	$-0.621954\pi$
$571$	14.7275	−	25.5087i	0.616326	−	1.06751i	0.990150	−	0.140008i	$-0.0447128\pi$
$572$	11.5698	−	5.38807i	0.483757	−	0.225287i
$573$	−8.27316	+	11.1040i	−0.345616	+	0.463876i
$574$	0.333863	−	15.0358i	0.0139352	−	0.627583i
$575$	−8.13293	−	4.69555i	−0.339167	−	0.195818i
$576$	2.91861	+	0.694059i	0.121609	+	0.0289191i
$577$	26.6927	+	15.4110i	1.11123	+	0.641570i	0.939148	−	0.343513i	$-0.111617\pi$
$577$	26.6927	+	15.4110i	1.11123	+	0.641570i	0.172083	+	0.985082i	$0.444950\pi$
$578$			1.34346i			0.0558804i
$579$	25.3997	−	10.9449i	1.05558	−	0.454857i
$580$			23.1315i			0.960482i
$581$	−2.58223	−	4.71107i	−0.107129	−	0.195448i
$582$	−0.932106	+	0.401653i	−0.0386371	+	0.0166490i
$583$	−27.4228			−1.13574
$584$	−2.15605	+	3.73438i	−0.0892178	+	0.154530i
$585$	−7.62547	−	37.1657i	−0.315274	−	1.53661i
$586$	−11.0218	+	6.36341i	−0.455304	+	0.262870i
$587$	−8.17657	+	14.1622i	−0.337483	+	0.584538i	−0.983959	−	0.178397i	$-0.942909\pi$
$587$	−8.17657	+	14.1622i	−0.337483	+	0.584538i	0.646476	+	0.762935i	$0.276242\pi$
$588$	−9.39137	−	7.66826i	−0.387293	−	0.316234i
$589$	−31.2875	−	54.1915i	−1.28918	−	2.23292i
$590$	17.2611	−	9.96568i	0.710627	−	0.410281i
$591$	−27.6714	+	37.1398i	−1.13825	+	1.52773i
$592$	10.5767			0.434701
$593$	16.4539	+	28.4990i	0.675681	+	1.17031i	0.976269	+	0.216560i	$0.0694838\pi$
$593$	16.4539	+	28.4990i	0.675681	+	1.17031i	−0.300588	+	0.953754i	$0.597183\pi$
$594$	−18.1175	+	3.17337i	−0.743368	+	0.130205i
$595$	−19.0613	+	31.3849i	−0.781437	+	1.28665i
$596$	−2.21093	−	1.27648i	−0.0905631	−	0.0522866i
$597$	−3.73972	−	0.438546i	−0.153056	−	0.0179485i
$598$	4.61871	+	0.406400i	0.188873	+	0.0166189i
$599$	−6.08634	−	3.51395i	−0.248681	−	0.143576i	0.370479	−	0.928841i	$-0.379193\pi$
$599$	−6.08634	−	3.51395i	−0.248681	−	0.143576i	−0.619160	+	0.785265i	$0.712527\pi$
$600$	−7.55726	+	10.1431i	−0.308524	+	0.414092i
$601$	5.83732	+	3.37018i	0.238109	+	0.137473i	0.614307	−	0.789067i	$-0.289435\pi$
$601$	5.83732	+	3.37018i	0.238109	+	0.137473i	−0.376198	+	0.926539i	$0.622769\pi$
$602$	−12.6312	−	7.67145i	−0.514810	−	0.312665i
$603$	6.59409	+	22.0867i	0.268532	+	0.899439i
$604$	−4.89737	+	8.48249i	−0.199271	+	0.345148i
$605$	5.36685			0.218194
$606$	−2.68959	−	6.24167i	−0.109257	−	0.253551i
$607$	−3.93516	−	2.27196i	−0.159723	−	0.0922162i	0.418008	−	0.908443i	$-0.362728\pi$
$607$	−3.93516	−	2.27196i	−0.159723	−	0.0922162i	−0.577731	+	0.816227i	$0.696062\pi$
$608$	3.32866	−	5.76542i	0.134995	−	0.233818i
$609$	−29.9299	−	4.18527i	−1.21282	−	0.169596i
$610$	−38.5455			−1.56066
$611$	0.177383	+	0.380893i	0.00717613	+	0.0154093i
$612$	11.5485	+	2.74628i	0.466819	+	0.111012i
$613$	−4.45445	−	7.71533i	−0.179913	−	0.311619i	0.761937	−	0.647651i	$-0.224248\pi$
$613$	−4.45445	−	7.71533i	−0.179913	−	0.311619i	−0.941851	+	0.336032i	$0.890915\pi$
$614$	−25.8938			−1.04499
$615$	4.02216	−	34.2991i	0.162189	−	1.38307i
$616$	4.86159	−	8.00472i	0.195879	−	0.322519i
$617$	−12.9991	+	7.50505i	−0.523325	+	0.302142i	−0.738294	−	0.674479i	$-0.764368\pi$
$617$	−12.9991	+	7.50505i	−0.523325	+	0.302142i	0.214969	+	0.976621i	$0.431035\pi$
$618$	18.5229	−	7.98166i	0.745099	−	0.321070i
$619$	−7.24862	−	4.18499i	−0.291347	−	0.168209i	0.347202	−	0.937790i	$-0.387132\pi$
$619$	−7.24862	−	4.18499i	−0.291347	−	0.168209i	−0.638549	+	0.769581i	$0.720465\pi$
$620$			32.9689i			1.32406i
$621$	−6.27641	−	2.29251i	−0.251864	−	0.0919951i
$622$	−4.24415	−	2.45036i	−0.170175	−	0.0982505i
$623$	−0.450928	−	0.822683i	−0.0180661	−	0.0329601i
$624$	1.26821	−	6.11487i	0.0507689	−	0.244791i
$625$	4.09126	+	7.08626i	0.163650	+	0.283450i
$626$	10.5093	+	18.2027i	0.420037	+	0.727525i
$627$	−4.75388	+	40.5389i	−0.189852	+	1.61897i
$628$	11.3514	+	6.55373i	0.452970	+	0.261522i
$629$	41.8504			1.66868
$630$	−19.8064	−	19.5650i	−0.789104	−	0.779488i
$631$	6.27126	+	10.8621i	0.249655	+	0.432415i	0.963430	−	0.267960i	$-0.0863494\pi$
$631$	6.27126	+	10.8621i	0.249655	+	0.432415i	−0.713775	+	0.700375i	$0.753016\pi$
$632$	4.56498	−	2.63559i	0.181585	−	0.104838i
$633$	7.33324	+	5.46372i	0.291470	+	0.217163i
$634$	−7.46591	−	12.9313i	−0.296509	−	0.513569i
$635$	11.8320			0.469537
$636$	−8.01689	+	10.7600i	−0.317890	+	0.426663i
$637$	−15.3898	+	20.0039i	−0.609765	+	0.792582i
$638$		−	23.3441i		−	0.924202i
$639$	27.1617	−	8.10927i	1.07450	−	0.320798i
$640$	−3.03762	+	1.75377i	−0.120073	+	0.0693239i
$641$			1.06251i			0.0419664i	0.999780	+	0.0209832i	$0.00667966\pi$
$641$			1.06251i			0.0419664i	−0.999780	+	0.0209832i	$0.993320\pi$
$642$	−1.45833	+	12.4359i	−0.0575556	+	0.490808i
$643$	19.3910	−	11.1954i	0.764708	−	0.441504i	−0.0662756	−	0.997801i	$-0.521112\pi$
$643$	19.3910	−	11.1954i	0.764708	−	0.441504i	0.830983	+	0.556297i	$0.187778\pi$
$644$	2.98351	−	1.63532i	0.117567	−	0.0644407i
$645$	−27.2119	−	20.2745i	−1.07147	−	0.798308i
$646$	13.1710	−	22.8128i	0.518205	−	0.897557i
$647$	4.19348	+	7.26332i	0.164863	+	0.285550i	0.936606	−	0.350383i	$-0.113949\pi$
$647$	4.19348	+	7.26332i	0.164863	+	0.285550i	−0.771744	+	0.635933i	$0.780615\pi$
$648$	−4.05137	+	8.03656i	−0.159153	+	0.315706i
$649$	−17.4197	+	10.0573i	−0.683784	+	0.394783i
$650$	21.5614	+	15.1135i	0.845710	+	0.592800i
$651$	−42.6585	−	5.96518i	−1.67192	−	0.233794i
$652$	7.21828	−	12.5024i	0.282690	−	0.489633i
$653$		−	4.81800i		−	0.188543i	−0.995547	−	0.0942715i	$-0.969948\pi$
$653$		−	4.81800i		−	0.188543i	0.995547	−	0.0942715i	$-0.0300522\pi$
$654$	−5.01027	+	6.72465i	−0.195917	+	0.262955i
$655$	−12.7533	+	22.0893i	−0.498312	+	0.863101i
$656$	2.84220	−	4.92284i	0.110969	−	0.192205i
$657$	−9.40278	−	8.88454i	−0.366837	−	0.346619i
$658$	0.263526	+	0.160050i	0.0102733	+	0.00623941i
$659$	−35.0181	+	20.2177i	−1.36411	+	0.787570i	−0.990168	−	0.139881i	$-0.955328\pi$
$659$	−35.0181	+	20.2177i	−1.36411	+	0.787570i	−0.373943	+	0.927452i	$0.621995\pi$
$660$	12.8485	−	17.2448i	0.500126	−	0.671255i
$661$	27.8415	−	16.0743i	1.08291	−	0.625219i	0.151230	−	0.988499i	$-0.451676\pi$
$661$	27.8415	−	16.0743i	1.08291	−	0.625219i	0.931680	+	0.363280i	$0.118343\pi$
$662$	0.887547	+	0.512426i	0.0344955	+	0.0199160i
$663$	5.01809	−	24.1955i	0.194886	−	0.939677i
$664$		−	2.03056i		−	0.0788009i
$665$	−54.1761	+	29.6950i	−2.10086	+	1.15152i
$666$	−7.34087	+	30.8693i	−0.284453	+	1.19616i
$667$	4.24027	−	7.34436i	0.164184	−	0.284375i
$668$	−8.84596	+	15.3217i	−0.342261	+	0.592813i
$669$	−11.0059	+	14.7719i	−0.425514	+	0.571113i
$670$	−23.3391	−	13.4748i	−0.901668	−	0.520578i
$671$	38.8998			1.50171
$672$	−1.71960	−	4.24770i	−0.0663350	−	0.163859i
$673$	−11.9937	+	20.7737i	−0.462323	+	0.800766i	−0.999076	−	0.0429727i	$-0.986317\pi$
$673$	−11.9937	+	20.7737i	−0.462323	+	0.800766i	0.536754	+	0.843739i	$0.319650\pi$
$674$		−	20.0548i		−	0.772481i
$675$	−24.3587	−	29.0966i	−0.937566	−	1.11993i
$676$	−12.8002	−	2.27017i	−0.492317	−	0.0873141i
$677$	−23.8364	−	41.2858i	−0.916107	−	1.58674i	−0.805272	−	0.592905i	$-0.797981\pi$
$677$	−23.8364	−	41.2858i	−0.916107	−	1.58674i	−0.110835	−	0.993839i	$-0.535352\pi$
$678$	−31.9869	+	13.7834i	−1.22845	+	0.529349i
$679$	1.32513	+	0.804805i	0.0508538	+	0.0308856i
$680$	−12.0194	+	6.93939i	−0.460922	+	0.266113i
$681$	0.393580	−	3.35626i	0.0150820	−	0.128612i
$682$		−	33.2719i		−	1.27405i
$683$			18.7391i			0.717031i	0.933524	+	0.358516i	$0.116717\pi$
$683$			18.7391i			0.717031i	−0.933524	+	0.358516i	$0.883283\pi$
$684$	14.5167	+	13.7166i	0.555060	+	0.524468i
$685$	−22.5628	+	13.0266i	−0.862079	+	0.497722i
$686$	−1.23259	+	18.4792i	−0.0470603	+	0.705539i
$687$	7.99511	+	18.5541i	0.305033	+	0.707882i
$688$	−2.79284	−	4.83734i	−0.106476	−	0.184422i
$689$	22.8728	+	16.0327i	0.871385	+	0.610797i
$690$	7.17468	−	3.09163i	0.273136	−	0.117697i
$691$		−	27.1896i		−	1.03434i	−0.855883	−	0.517170i	$-0.826985\pi$
$691$		−	27.1896i		−	1.03434i	0.855883	−	0.517170i	$-0.173015\pi$
$692$	2.85532	−	4.94555i	0.108543	−	0.188002i
$693$	19.9884	+	19.7448i	0.759297	+	0.750044i
$694$	−24.9526			−0.947187
$695$	12.4671	+	7.19786i	0.472903	+	0.273030i
$696$	−9.15966	−	6.82451i	−0.347196	−	0.258682i
$697$	11.2461	−	19.4789i	0.425977	−	0.737815i
$698$	−4.14516	+	7.17962i	−0.156897	+	0.271753i
$699$	9.22298	+	21.4036i	0.348845	+	0.809557i
$700$	19.3168	+	0.428920i	0.730106	+	0.0162117i
$701$		−	32.5254i		−	1.22847i	−0.789124	−	0.614233i	$-0.789465\pi$
$701$		−	32.5254i		−	1.22847i	0.789124	−	0.614233i	$-0.210535\pi$
$702$	16.9667	+	7.94548i	0.640367	+	0.299883i
$703$	60.9792	+	35.2064i	2.29988	+	1.32783i
$704$	3.06555	−	1.76989i	0.115537	−	0.0667054i
$705$	0.567724	+	0.422989i	0.0213817	+	0.0159307i
$706$	−29.9971	+	17.3189i	−1.12896	+	0.651804i
$707$	−5.38922	+	8.87347i	−0.202683	+	0.333721i
$708$	−1.14632	+	9.77527i	−0.0430813	+	0.367377i
$709$	11.4668	−	19.8611i	0.430645	−	0.745900i	−0.566284	−	0.824211i	$-0.691619\pi$
$709$	11.4668	−	19.8611i	0.430645	−	0.745900i	0.996929	+	0.0783107i	$0.0249526\pi$
$710$	−16.5710	+	28.7019i	−0.621900	+	1.07716i
$711$	4.52390	+	15.1527i	0.169660	+	0.568269i
$712$		−	0.354591i		−	0.0132889i
$713$	6.04358	−	10.4678i	0.226334	−	0.392022i
$714$	−6.80418	−	16.8075i	−0.254640	−	0.629003i
$715$	−36.6577	−	25.6952i	−1.37092	−	0.960945i
$716$	−13.2570	+	7.65395i	−0.495438	+	0.286041i
$717$	7.35351	+	0.862326i	0.274622	+	0.0322041i
$718$	2.97303	+	5.14944i	0.110952	+	0.192175i
$719$	−0.366786	+	0.635293i	−0.0136788	+	0.0236924i	−0.872784	−	0.488107i	$-0.837688\pi$
$719$	−0.366786	+	0.635293i	−0.0136788	+	0.0236924i	0.859105	+	0.511799i	$0.171021\pi$
$720$	−3.01029	−	10.0829i	−0.112187	−	0.375766i
$721$	−26.3330	−	15.9931i	−0.980693	−	0.595615i
$722$	21.9278	−	12.6600i	0.816067	−	0.471157i
$723$	−24.9038	−	2.92040i	−0.926184	−	0.108611i
$724$			16.4841i			0.612627i
$725$	41.7084	−	24.0804i	1.54901	−	0.894323i
$726$	−1.58339	+	2.12518i	−0.0587651	+	0.0788728i
$727$			45.5164i			1.68811i	0.536258	+	0.844054i	$0.319837\pi$
$727$			45.5164i			1.68811i	−0.536258	+	0.844054i	$0.680163\pi$
$728$	−8.73490	+	3.83426i	−0.323737	+	0.142107i
$729$	−20.6437	−	17.4022i	−0.764582	−	0.644527i
$730$	15.1249			0.559796
$731$	−11.0508	−	19.1406i	−0.408729	−	0.707939i
$732$	11.3721	−	15.2633i	0.420326	−	0.564150i
$733$	22.4581	−	12.9662i	0.829508	−	0.478917i	−0.0241759	−	0.999708i	$-0.507696\pi$
$733$	22.4581	−	12.9662i	0.829508	−	0.478917i	0.853684	+	0.520791i	$0.174363\pi$
$734$	−11.7690	−	20.3845i	−0.434401	−	0.752405i
$735$	−6.82296	+	41.9758i	−0.251669	+	1.54830i
$736$	1.28595			0.0474007
$737$	23.5536	+	13.5987i	0.867609	+	0.500914i
$738$	12.3952	+	11.7120i	0.456273	+	0.431125i
$739$	14.7220	+	25.4993i	0.541559	+	0.938007i	0.998815	+	0.0486721i	$0.0154989\pi$
$739$	14.7220	+	25.4993i	0.541559	+	0.938007i	−0.457256	+	0.889335i	$0.651168\pi$
$740$	−18.5492	−	32.1281i	−0.681881	−	1.18105i
$741$	27.6661	−	31.0333i	1.01634	−	1.14004i
$742$	20.4916	+	0.455007i	0.752272	+	0.0167038i
$743$	23.1459	+	13.3633i	0.849140	+	0.490251i	0.860361	−	0.509686i	$-0.170238\pi$
$743$	23.1459	+	13.3633i	0.849140	+	0.490251i	−0.0112203	+	0.999937i	$0.503572\pi$
$744$	−13.0551	−	9.72684i	−0.478623	−	0.356603i
$745$			8.95462i			0.328072i
$746$	1.31100	+	0.756908i	0.0479992	+	0.0277124i
$747$	5.92640	+	1.40933i	0.216836	+	0.0515645i
$748$	12.1299	−	7.00318i	0.443511	−	0.256061i
$749$	16.7722	−	9.19313i	0.612841	−	0.335910i
$750$	13.8952	+	1.62946i	0.507382	+	0.0594993i
$751$	27.1530			0.990827			0.495413	−	0.868657i	$-0.335017\pi$
$751$	27.1530			0.990827			0.495413	+	0.868657i	$0.335017\pi$
$752$	0.0582673	+	0.100922i	0.00212479	+	0.00368024i
$753$	0.468510	−	0.201885i	0.0170735	−	0.00735710i
$754$	−13.6481	+	19.4709i	−0.497034	+	0.709087i
$755$	34.3555			1.25032
$756$	13.5909	−	2.07069i	0.494296	−	0.0753102i
$757$	9.16804	−	15.8795i	0.333218	−	0.577151i	−0.649923	−	0.760000i	$-0.725199\pi$
$757$	9.16804	−	15.8795i	0.333218	−	0.577151i	0.983141	+	0.182849i	$0.0585321\pi$
$758$	22.4178	+	12.9429i	0.814249	+	0.470107i
$759$	−7.24064	+	3.12005i	−0.262818	+	0.113251i
$760$	−23.3509			−0.847025
$761$	−24.6931	+	42.7696i	−0.895122	+	1.55040i	−0.0614693	+	0.998109i	$0.519579\pi$
$761$	−24.6931	+	42.7696i	−0.895122	+	1.55040i	−0.833653	+	0.552288i	$0.813755\pi$
$762$	−3.49080	+	4.68525i	−0.126458	+	0.169729i
$763$	12.8066	+	0.284363i	0.463628	+	0.0102946i
$764$	6.92358	+	3.99733i	0.250486	+	0.144618i
$765$	−11.9112	−	39.8962i	−0.430651	−	1.44245i
$766$	8.33387	+	4.81156i	0.301115	+	0.173849i
$767$	20.4094	+	1.79583i	0.736942	+	0.0648436i
$768$	0.201730	−	1.72026i	0.00727932	−	0.0620746i
$769$	0.485650	+	0.280390i	0.0175130	+	0.0101111i	0.508731	−	0.860926i	$-0.330115\pi$
$769$	0.485650	+	0.280390i	0.0175130	+	0.0101111i	−0.491218	+	0.871037i	$0.663448\pi$
$770$	−32.8414	−	0.729228i	−1.18352	−	0.0262796i
$771$	2.25913	−	19.2648i	0.0813607	−	0.693806i
$772$	−7.98403	−	13.8287i	−0.287351	−	0.497707i
$773$	−31.2061			−1.12240			−0.561202	−	0.827679i	$-0.689661\pi$
$773$	−31.2061			−1.12240			−0.561202	+	0.827679i	$0.689661\pi$
$774$	16.0567	−	4.79381i	0.577147	−	0.172310i
$775$	59.4463	−	34.3213i	2.13537	−	1.23286i
$776$	0.292994	+	0.507481i	0.0105179	+	0.0182175i
$777$	44.9268	−	18.1878i	1.61174	−	0.652482i
$778$	9.98452	−	17.2937i	0.357962	−	0.620009i
$779$	32.7730	−	18.9215i	1.17421	−	0.677932i
$780$	−20.7988	+	6.87175i	−0.744717	+	0.246048i
$781$	16.7234	−	28.9657i	0.598409	−	1.03648i
$782$	5.08828			0.181957
$783$	26.2754	−	21.9969i	0.939007	−	0.786104i
$784$	−3.76563	+	5.90085i	−0.134487	+	0.210745i
$785$		−	45.9750i		−	1.64092i
$786$	−4.98437	−	11.5671i	−0.177787	−	0.412585i
$787$			5.89304i			0.210064i	0.994469	+	0.105032i	$0.0334945\pi$
$787$			5.89304i			0.210064i	−0.994469	+	0.105032i	$0.966505\pi$
$788$	23.1575	+	13.3700i	0.824951	+	0.476286i
$789$	−2.85265	−	6.62008i	−0.101557	−	0.235681i
$790$	−16.0119	−	9.24446i	−0.569677	−	0.328903i
$791$	45.4741	+	27.6183i	1.61687	+	0.981994i
$792$	3.03796	+	10.1755i	0.107949	+	0.361572i
$793$	−32.4456	−	22.7427i	−1.15218	−	0.807617i
$794$	7.52468	−	13.0331i	0.267041	−	0.462528i
$795$	46.7447	+	5.48163i	1.65787	+	0.194413i
$796$			2.17392i			0.0770526i
$797$	−24.1017	−	41.7453i	−0.853724	−	1.47869i	−0.877823	−	0.478984i	$-0.841005\pi$
$797$	−24.1017	−	41.7453i	−0.853724	−	1.47869i	0.0240989	−	0.999710i	$-0.492328\pi$
$798$	4.22496	−	30.2137i	0.149562	−	1.06955i
$799$	0.230554	+	0.399331i	0.00815641	+	0.0141273i
$800$	6.32446	+	3.65143i	0.223604	+	0.129098i
$801$	1.03491	+	0.246107i	0.0365669	+	0.00869577i
$802$	30.8125			1.08803
$803$	−15.2639			−0.538651
$804$	12.2216	−	5.26638i	0.431021	−	0.185731i
$805$	−10.1999	−	6.19481i	−0.359499	−	0.218338i
$806$	−19.4524	+	27.7514i	−0.685180	+	0.977503i
$807$	−4.89630	+	41.7534i	−0.172358	+	1.46979i
$808$	−3.39825	+	1.96198i	−0.119550	+	0.0690222i
$809$	1.24519	−	0.718909i	0.0437784	−	0.0252755i	−0.477951	−	0.878386i	$-0.658620\pi$
$809$	1.24519	−	0.718909i	0.0437784	−	0.0252755i	0.521729	+	0.853111i	$0.325287\pi$
$810$	31.5172	−	1.78776i	1.10740	−	0.0628155i
$811$			25.7211i			0.903192i	0.892223	+	0.451596i	$0.149145\pi$
$811$			25.7211i			0.903192i	−0.892223	+	0.451596i	$0.850855\pi$
$812$	−0.387332	+	17.4438i	−0.0135927	+	0.612159i
$813$	−21.3118	−	2.49918i	−0.747439	−	0.0876500i
$814$	18.7197	+	32.4234i	0.656125	+	1.13644i
$815$	−50.6369			−1.77373
$816$	0.798214	−	6.80680i	0.0279431	−	0.238286i
$817$		−	37.1857i		−	1.30096i
$818$	3.31277			0.115828
$819$	−5.12817	−	28.1550i	−0.179193	−	0.983814i
$820$	−19.9383			−0.696276
$821$		−	6.14756i		−	0.214551i	−0.994229	−	0.107276i	$-0.965787\pi$
$821$		−	6.14756i		−	0.214551i	0.994229	−	0.107276i	$-0.0342128\pi$
$822$	1.49841	−	12.7777i	0.0522630	−	0.445674i
$823$	2.53533			0.0883760			0.0441880	−	0.999023i	$-0.485930\pi$
$823$	2.53533			0.0883760			0.0441880	+	0.999023i	$0.485930\pi$
$824$	−5.82239	−	10.0847i	−0.202833	−	0.351317i
$825$	−44.4698	−	5.21485i	−1.54824	−	0.181558i
$826$	13.1837	−	7.22626i	0.458721	−	0.251434i
$827$			19.0006i			0.660717i	0.943856	+	0.330359i	$0.107170\pi$
$827$			19.0006i			0.660717i	−0.943856	+	0.330359i	$0.892830\pi$
$828$	−0.892523	+	3.75318i	−0.0310173	+	0.130432i
$829$	−14.6957	+	8.48455i	−0.510402	+	0.294681i	−0.732999	−	0.680230i	$-0.761880\pi$
$829$	−14.6957	+	8.48455i	−0.510402	+	0.294681i	0.222597	+	0.974911i	$0.428547\pi$
$830$	−6.16806	+	3.56113i	−0.214097	+	0.123609i
$831$	−2.07699	+	17.7116i	−0.0720500	+	0.614409i
$832$	−3.59167	−	0.316032i	−0.124519	−	0.0109564i
$833$	−14.9000	+	23.3487i	−0.516254	+	0.808984i
$834$	−6.52840	+	2.81314i	−0.226060	+	0.0974112i
$835$	62.0552			2.14751
$836$	23.5655			0.815031
$837$	37.4499	−	31.3517i	1.29446	−	1.08367i
$838$	16.1081	+	9.29999i	0.556444	+	0.321263i
$839$	6.69259	+	11.5919i	0.231054	+	0.400197i	0.958119	−	0.286372i	$-0.0924493\pi$
$839$	6.69259	+	11.5919i	0.231054	+	0.400197i	−0.727065	+	0.686569i	$0.759116\pi$
$840$	−9.88713	+	12.6730i	−0.341138	+	0.437260i
$841$	7.24554	+	12.5496i	0.249846	+	0.432747i
$842$		−	0.699811i		−	0.0241171i
$843$	−10.6932	−	1.25396i	−0.368294	−	0.0431888i
$844$	2.63990	−	4.57244i	0.0908690	−	0.157390i
$845$	15.5528	+	42.8637i	0.535033	+	1.47455i
$846$	−0.334992	+	0.100014i	−0.0115173	+	0.00343854i
$847$	4.04724	+	0.0898669i	0.139065	+	0.00308786i
$848$	6.70912	+	3.87351i	0.230392	+	0.133017i
$849$	9.21263	+	21.3795i	0.316177	+	0.733744i
$850$	25.0249	+	14.4481i	0.858346	+	0.495566i
$851$			13.6011i			0.466240i
$852$	−6.47647	−	15.0298i	−0.221880	−	0.514912i
$853$			9.31358i			0.318891i	0.987207	+	0.159445i	$0.0509706\pi$
$853$			9.31358i			0.318891i	−0.987207	+	0.159445i	$0.949029\pi$
$854$	−29.0678	−	0.645437i	−0.994681	−	0.0220864i
$855$	16.2069	−	68.1521i	0.554263	−	2.33075i
$856$	7.22910			0.247085
$857$	5.60469	−	9.70761i	0.191453	−	0.331606i	−0.754279	−	0.656554i	$-0.772014\pi$
$857$	5.60469	−	9.70761i	0.191453	−	0.331606i	0.945732	+	0.324948i	$0.105347\pi$
$858$	20.9900	−	6.93492i	0.716587	−	0.236754i
$859$	−22.6022	+	13.0494i	−0.771177	+	0.445239i	−0.833294	−	0.552830i	$-0.813548\pi$
$859$	−22.6022	+	13.0494i	−0.771177	+	0.445239i	0.0621172	+	0.998069i	$0.480215\pi$
$860$	−9.79601	+	16.9672i	−0.334041	+	0.578576i
$861$	3.60751	−	25.7982i	0.122944	−	0.879201i
$862$	−8.68065	−	15.0353i	−0.295664	−	0.512105i
$863$	−26.4923	+	15.2954i	−0.901809	+	0.520660i	−0.877787	−	0.479051i	$-0.840981\pi$
$863$	−26.4923	+	15.2954i	−0.901809	+	0.520660i	−0.0240226	+	0.999711i	$0.507647\pi$
$864$	4.88076	+	1.78274i	0.166047	+	0.0606499i
$865$	−20.0303			−0.681050
$866$	−13.7313	−	23.7833i	−0.466609	−	0.808190i
$867$	−0.271016	+	2.31110i	−0.00920419	+	0.0784890i
$868$	−0.552057	+	24.8624i	−0.0187380	+	0.843884i
$869$	16.1591	+	9.32944i	0.548159	+	0.316479i
$870$	−4.66632	+	39.7922i	−0.158203	+	1.34908i
$871$	−11.6952	−	25.1130i	−0.396276	−	0.850921i
$872$	4.19296	+	2.42081i	0.141992	+	0.0819789i
$873$	−1.68449	+	0.502914i	−0.0570115	+	0.0170211i
$874$	7.41402	+	4.28049i	0.250783	+	0.144790i
$875$	−10.2719	−	18.7403i	−0.347254	−	0.633537i
$876$	−4.46231	+	5.98918i	−0.150767	+	0.202356i
$877$	3.45873	−	5.99069i	0.116793	−	0.202291i	−0.801702	−	0.597724i	$-0.796072\pi$
$877$	3.45873	−	5.99069i	0.116793	−	0.202291i	0.918495	+	0.395432i	$0.129405\pi$
$878$	12.0917			0.408076
$879$	−20.2440	+	8.72332i	−0.682814	+	0.294230i
$880$	−10.7525	−	6.20798i	−0.362468	−	0.209271i
$881$	4.74525	−	8.21901i	0.159871	−	0.276905i	−0.774951	−	0.632022i	$-0.782225\pi$
$881$	4.74525	−	8.21901i	0.159871	−	0.276905i	0.934822	+	0.355116i	$0.115559\pi$
$882$	−14.6087	−	15.0859i	−0.491901	−	0.507970i
$883$	21.2743			0.715938			0.357969	−	0.933733i	$-0.383469\pi$
$883$	21.2743			0.715938			0.357969	+	0.933733i	$0.383469\pi$
$884$	−14.2117	−	1.25049i	−0.477990	−	0.0420584i
$885$	31.7039	−	13.6615i	1.06572	−	0.459227i
$886$	4.73280	+	8.19745i	0.159002	+	0.275399i
$887$	−23.7497			−0.797438			−0.398719	−	0.917073i	$-0.630545\pi$
$887$	−23.7497			−0.797438			−0.398719	+	0.917073i	$0.630545\pi$
$888$	18.1948	+	2.13365i	0.610576	+	0.0716006i
$889$	8.92269	+	0.198124i	0.299257	+	0.00664487i
$890$	−1.07711	+	0.621872i	−0.0361049	+	0.0208452i
$891$	−31.8069	+	1.80419i	−1.06557	+	0.0604428i
$892$	9.21057	+	5.31772i	0.308393	+	0.178051i
$893$			0.775809i			0.0259614i
$894$	−3.54587	−	2.64189i	−0.118592	−	0.0883581i
$895$	46.4996	+	26.8466i	1.55431	+	0.897381i
$896$	−2.32009	+	1.27169i	−0.0775088	+	0.0424840i
$897$	7.86340	+	1.63085i	0.262551	+	0.0544525i
$898$	0.611927	+	1.05989i	0.0204203	+	0.0353690i
$899$	30.9935	+	53.6824i	1.03369	+	1.79041i
$900$	−15.0467	+	15.9243i	−0.501555	+	0.530811i
$901$	26.5469	+	15.3268i	0.884405	+	0.510611i
$902$	20.1216			0.669975
$903$	−20.1815	−	15.7450i	−0.671597	−	0.523961i
$904$	10.0546	+	17.4151i	0.334412	+	0.579218i
$905$	50.0724	−	28.9093i	1.66446	−	0.960979i
$906$	−10.1359	+	13.6042i	−0.336744	+	0.451968i
$907$	−16.3615	−	28.3390i	−0.543276	−	0.940981i	−0.998713	−	0.0507133i	$-0.983851\pi$
$907$	−16.3615	−	28.3390i	−0.543276	−	0.940981i	0.455438	−	0.890268i	$-0.349483\pi$
$908$	−1.95102			−0.0647468
$909$	−3.36767	−	11.2799i	−0.111699	−	0.374130i
$910$	26.9660	+	19.8089i	0.893916	+	0.656659i
$911$			48.1424i			1.59503i	0.603299	+	0.797515i	$0.293852\pi$
$911$			48.1424i			1.59503i	−0.603299	+	0.797515i	$0.706148\pi$
$912$	6.88924	−	9.24654i	0.228125	−	0.306183i
$913$	6.22476	−	3.59387i	0.206010	−	0.118940i
$914$		−	6.13692i		−	0.202991i
$915$	−66.3084	−	7.77580i	−2.19209	−	0.257060i
$916$	10.1017	−	5.83221i	0.333769	−	0.192702i
$917$	−9.98734	+	16.4444i	−0.329811	+	0.543041i
$918$	19.3124	+	7.05399i	0.637403	+	0.232816i
$919$	−21.3079	+	36.9063i	−0.702882	+	1.21743i	0.264568	+	0.964367i	$0.414771\pi$
$919$	−21.3079	+	36.9063i	−0.702882	+	1.21743i	−0.967450	+	0.253061i	$0.918563\pi$
$920$	−2.25526	−	3.90622i	−0.0743537	−	0.128784i
$921$	−44.5441	−	5.22356i	−1.46778	−	0.172122i
$922$	22.0723	−	12.7435i	0.726914	−	0.419684i
$923$	−30.8834	+	14.3824i	−1.01654	+	0.473404i
$924$	9.97801	−	12.7895i	0.328253	−	0.420743i
$925$	−38.6202	+	66.8922i	−1.26982	+	2.19940i
$926$		−	15.6848i		−	0.515436i
$927$	33.4743	−	9.99393i	1.09944	−	0.328244i
$928$	−3.29739	+	5.71124i	−0.108242	+	0.187481i
$929$	22.0508	−	38.1931i	0.723463	−	1.25307i	−0.236141	−	0.971719i	$-0.575883\pi$
$929$	22.0508	−	38.1931i	0.723463	−	1.25307i	0.959604	−	0.281355i	$-0.0907840\pi$
$930$	−6.65082	+	56.7151i	−0.218089	+	1.85976i
$931$	−41.3524	+	21.4863i	−1.35527	+	0.704185i
$932$	11.6531	−	6.72790i	0.381709	−	0.220380i
$933$	−6.80674	−	5.07144i	−0.222843	−	0.166031i
$934$	−22.8139	+	13.1716i	−0.746492	+	0.430987i
$935$	−42.5460	−	24.5639i	−1.39140	−	0.803327i
$936$	3.41521	−	10.2634i	0.111630	−	0.335468i
$937$			30.8284i			1.00712i	0.863960	+	0.503560i	$0.167977\pi$
$937$			30.8284i			1.00712i	−0.863960	+	0.503560i	$0.832023\pi$
$938$	−17.3748	−	10.5524i	−0.567307	−	0.344548i
$939$	14.4068	+	33.4334i	0.470147	+	1.09106i
$940$	0.204375	−	0.353988i	0.00666598	−	0.0115458i
$941$	8.81522	−	15.2684i	0.287368	−	0.497736i	−0.685813	−	0.727778i	$-0.740553\pi$
$941$	8.81522	−	15.2684i	0.287368	−	0.497736i	0.973181	+	0.230042i	$0.0738865\pi$
$942$	18.2053	+	13.5641i	0.593161	+	0.441941i
$943$	6.33051	+	3.65492i	0.206150	+	0.119021i
$944$	5.68243			0.184947
$945$	−30.1253	−	37.6525i	−0.979976	−	1.22483i
$946$	9.88606	−	17.1232i	0.321424	−	0.556722i
$947$			3.58108i			0.116369i	0.998306	+	0.0581847i	$0.0185312\pi$
$947$			3.58108i			0.116369i	−0.998306	+	0.0581847i	$0.981469\pi$
$948$	8.38465	−	3.61302i	0.272321	−	0.117345i
$949$	12.7313	+	8.92400i	0.413276	+	0.289685i
$950$	24.3088	+	42.1040i	0.788681	+	1.36604i
$951$	−10.2347	−	23.7514i	−0.331883	−	0.770192i
$952$	−9.18021	+	5.03185i	−0.297532	+	0.163083i
$953$	−37.1462	+	21.4464i	−1.20328	+	0.694716i	−0.961284	−	0.275560i	$-0.911137\pi$
$953$	−37.1462	+	21.4464i	−1.20328	+	0.694716i	−0.242000	+	0.970276i	$0.577803\pi$
$954$	−15.9618	+	16.8929i	−0.516782	+	0.546926i
$955$		−	28.0416i		−	0.907406i
$956$		−	4.27464i		−	0.138252i
$957$	4.70922	−	40.1580i	0.152227	−	1.29812i
$958$	33.5691	−	19.3811i	1.08457	−	0.626175i
$959$	−17.2331	+	9.44579i	−0.556486	+	0.305021i
$960$	−5.57930	+	2.40417i	−0.180071	+	0.0775942i
$961$	28.6745	+	49.6657i	0.924984	+	1.60212i
$962$	3.34258	−	37.9882i	0.107769	−	1.22479i
$963$	−5.01742	+	21.0989i	−0.161684	+	0.679903i
$964$			14.4768i			0.466265i
$965$	−28.0043	+	48.5049i	−0.901491	+	1.56143i
$966$	5.46232	−	2.21132i	0.175747	−	0.0711479i
$967$	49.7801			1.60082			0.800411	−	0.599452i	$-0.204615\pi$
$967$	49.7801			1.60082			0.800411	+	0.599452i	$0.204615\pi$
$968$	1.32510	+	0.765044i	0.0425902	+	0.0245895i
$969$	27.2596	−	36.5870i	0.875704	−	1.17534i
$970$	1.02769	−	1.78001i	0.0329971	−	0.0571527i
$971$	21.3358	−	36.9547i	0.684698	−	1.18593i	−0.288833	−	0.957379i	$-0.593267\pi$
$971$	21.3358	−	36.9547i	0.684698	−	1.18593i	0.973532	−	0.228553i	$-0.0733993\pi$
$972$	−8.59065	+	13.0077i	−0.275545	+	0.417223i
$973$	9.28110	+	5.63679i	0.297538	+	0.180707i
$974$			19.9536i			0.639354i
$975$	34.0425	+	30.3488i	1.09023	+	0.971938i
$976$	−9.51703	−	5.49466i	−0.304633	−	0.175880i
$977$	14.9505	−	8.63169i	0.478310	−	0.276152i	−0.241402	−	0.970425i	$-0.577607\pi$
$977$	14.9505	−	8.63169i	0.478310	−	0.276152i	0.719712	+	0.694273i	$0.244274\pi$
$978$	14.9395	−	20.0513i	0.477712	−	0.641171i
$979$	1.08702	−	0.627589i	0.0347412	−	0.0200578i
$980$	24.5286	+	1.08983i	0.783538	+	0.0348133i
$981$	−9.97556	+	10.5574i	−0.318495	+	0.337073i
$982$	−2.52158	+	4.36750i	−0.0804668	+	0.139373i
$983$	15.2048	−	26.3355i	0.484957	−	0.839971i	−0.514893	−	0.857254i	$-0.672168\pi$
$983$	15.2048	−	26.3355i	0.484957	−	0.839971i	0.999851	+	0.0172834i	$0.00550176\pi$
$984$	5.88242	−	7.89522i	0.187525	−	0.251690i
$985$		−	93.7916i		−	2.98845i
$986$	−13.0472	+	22.5985i	−0.415508	+	0.719681i
$987$	0.421047	+	0.328490i	0.0134021	+	0.0104559i
$988$	−19.6555	−	13.7775i	−0.625326	−	0.438322i
$989$	6.22057	−	3.59145i	0.197803	−	0.114201i
$990$	25.5816	−	27.0737i	0.813035	−	0.860460i
$991$	3.76575	+	6.52247i	0.119623	+	0.207193i	0.919618	−	0.392813i	$-0.128498\pi$
$991$	3.76575	+	6.52247i	0.119623	+	0.207193i	−0.799995	+	0.600006i	$0.795165\pi$
$992$	−4.69971	+	8.14013i	−0.149216	+	0.258449i
$993$	1.42344	+	1.06055i	0.0451716	+	0.0336556i
$994$	−12.9771	+	21.3671i	−0.411609	+	0.677723i
$995$	6.60355	−	3.81256i	0.209347	−	0.120866i
$996$	0.409625	−	3.49309i	0.0129795	−	0.110683i
$997$			15.8809i			0.502955i	0.967863	+	0.251477i	$0.0809164\pi$
$997$			15.8809i			0.502955i	−0.967863	+	0.251477i	$0.919084\pi$
$998$	−32.0985	+	18.5321i	−1.01606	+	0.586622i
$999$	−18.8555	+	51.6225i	−0.596562	+	1.63326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.11	yes	76
3.2	odd	2	inner	546.2.bb.a.269.36	yes	76
7.5	odd	6		546.2.u.a.425.5	yes	76
13.3	even	3		546.2.u.a.185.34	yes	76
21.5	even	6		546.2.u.a.425.34	yes	76
39.29	odd	6		546.2.u.a.185.5	✓	76
91.68	odd	6	inner	546.2.bb.a.341.17	yes	76
273.68	even	6	inner	546.2.bb.a.341.30	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.5	✓	76	39.29	odd	6
546.2.u.a.185.34	yes	76	13.3	even	3
546.2.u.a.425.5	yes	76	7.5	odd	6
546.2.u.a.425.34	yes	76	21.5	even	6
546.2.bb.a.269.11	yes	76	1.1	even	1	trivial
546.2.bb.a.269.36	yes	76	3.2	odd	2	inner
546.2.bb.a.341.17	yes	76	91.68	odd	6	inner
546.2.bb.a.341.30	yes	76	273.68	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.201730 - 1.72026i) q^{3} -1.00000 q^{4} +(1.75377 + 3.03762i) q^{5} +(-1.72026 - 0.201730i) q^{6} +(1.27169 + 2.32009i) q^{7} +1.00000i q^{8} +(-2.91861 - 0.694059i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.201730 - 1.72026i) q^{3} -1.00000 q^{4} +(1.75377 + 3.03762i) q^{5} +(-1.72026 - 0.201730i) q^{6} +(1.27169 + 2.32009i) q^{7} +1.00000i q^{8} +(-2.91861 - 0.694059i) q^{9} +(3.03762 - 1.75377i) q^{10} +(-3.06555 + 1.76989i) q^{11} +(-0.201730 + 1.72026i) q^{12} +(3.59167 + 0.316032i) q^{13} +(2.32009 - 1.27169i) q^{14} +(5.57930 - 2.40417i) q^{15} +1.00000 q^{16} +3.95683 q^{17} +(-0.694059 + 2.91861i) q^{18} +(5.76542 + 3.32866i) q^{19} +(-1.75377 - 3.03762i) q^{20} +(4.24770 - 1.71960i) q^{21} +(1.76989 + 3.06555i) q^{22} +1.28595i q^{23} +(1.72026 + 0.201730i) q^{24} +(-3.65143 + 6.32446i) q^{25} +(0.316032 - 3.59167i) q^{26} +(-1.78274 + 4.88076i) q^{27} +(-1.27169 - 2.32009i) q^{28} +(-5.71124 - 3.29739i) q^{29} +(-2.40417 - 5.57930i) q^{30} +(-8.14013 - 4.69971i) q^{31} -1.00000i q^{32} +(2.42627 + 5.63059i) q^{33} -3.95683i q^{34} +(-4.81731 + 7.93181i) q^{35} +(2.91861 + 0.694059i) q^{36} +10.5767 q^{37} +(3.32866 - 5.76542i) q^{38} +(1.26821 - 6.11487i) q^{39} +(-3.03762 + 1.75377i) q^{40} +(2.84220 - 4.92284i) q^{41} +(-1.71960 - 4.24770i) q^{42} +(-2.79284 - 4.83734i) q^{43} +(3.06555 - 1.76989i) q^{44} +(-3.01029 - 10.0829i) q^{45} +1.28595 q^{46} +(0.0582673 + 0.100922i) q^{47} +(0.201730 - 1.72026i) q^{48} +(-3.76563 + 5.90085i) q^{49} +(6.32446 + 3.65143i) q^{50} +(0.798214 - 6.80680i) q^{51} +(-3.59167 - 0.316032i) q^{52} +(6.70912 + 3.87351i) q^{53} +(4.88076 + 1.78274i) q^{54} +(-10.7525 - 6.20798i) q^{55} +(-2.32009 + 1.27169i) q^{56} +(6.88924 - 9.24654i) q^{57} +(-3.29739 + 5.71124i) q^{58} +5.68243 q^{59} +(-5.57930 + 2.40417i) q^{60} +(-9.51703 - 5.49466i) q^{61} +(-4.69971 + 8.14013i) q^{62} +(-2.10127 - 7.65406i) q^{63} -1.00000 q^{64} +(5.33899 + 11.4644i) q^{65} +(5.63059 - 2.42627i) q^{66} +(-3.84167 - 6.65397i) q^{67} -3.95683 q^{68} +(2.21217 + 0.259415i) q^{69} +(7.93181 + 4.81731i) q^{70} +(-8.18290 + 4.72440i) q^{71} +(0.694059 - 2.91861i) q^{72} +(3.73438 + 2.15605i) q^{73} -10.5767i q^{74} +(10.1431 + 7.55726i) q^{75} +(-5.76542 - 3.32866i) q^{76} +(-8.00472 - 4.86159i) q^{77} +(-6.11487 - 1.26821i) q^{78} +(-2.63559 - 4.56498i) q^{79} +(1.75377 + 3.03762i) q^{80} +(8.03656 + 4.05137i) q^{81} +(-4.92284 - 2.84220i) q^{82} -2.03056 q^{83} +(-4.24770 + 1.71960i) q^{84} +(6.93939 + 12.0194i) q^{85} +(-4.83734 + 2.79284i) q^{86} +(-6.82451 + 9.15966i) q^{87} +(-1.76989 - 3.06555i) q^{88} -0.354591 q^{89} +(-10.0829 + 3.01029i) q^{90} +(3.83426 + 8.73490i) q^{91} -1.28595i q^{92} +(-9.72684 + 13.0551i) q^{93} +(0.100922 - 0.0582673i) q^{94} +23.3509i q^{95} +(-1.72026 - 0.201730i) q^{96} +(0.507481 - 0.292994i) q^{97} +(5.90085 + 3.76563i) q^{98} +(10.1755 - 3.03796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more