LMFDB - Embedded newform 165.2.s.a.4.8

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			4.8
Character	$\chi$	$=$	165.4
Dual form			165.2.s.a.124.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.460901 - 0.634375i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.428031 + 1.31734i) q^{4} +(0.741158 - 2.10966i) q^{5} +(-0.634375 + 0.460901i) q^{6} +(1.44371 - 0.469090i) q^{7} +(2.52448 + 0.820252i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.460901 - 0.634375i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.428031 + 1.31734i) q^{4} +(0.741158 - 2.10966i) q^{5} +(-0.634375 + 0.460901i) q^{6} +(1.44371 - 0.469090i) q^{7} +(2.52448 + 0.820252i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.996719 - 1.44252i) q^{10} +(0.438933 - 3.28745i) q^{11} -1.38514i q^{12} +(0.274209 - 0.377416i) q^{13} +(0.367828 - 1.13206i) q^{14} +(-1.35681 + 1.77738i) q^{15} +(-0.557320 + 0.404916i) q^{16} +(-0.997064 - 1.37234i) q^{17} +(0.745753 - 0.242310i) q^{18} +(-1.73345 + 5.33501i) q^{19} +(3.09639 + 0.0733588i) q^{20} -1.51801 q^{21} +(-1.88317 - 1.79364i) q^{22} +7.68641i q^{23} +(-2.14745 - 1.56021i) q^{24} +(-3.90137 - 3.12719i) q^{25} +(-0.113040 - 0.347903i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.23591 + 1.70108i) q^{28} +(-0.822307 - 2.53080i) q^{29} +(0.502173 + 1.67992i) q^{30} +(-3.20187 - 2.32629i) q^{31} +5.84896i q^{32} +(-1.43333 + 2.99091i) q^{33} -1.33013 q^{34} +(0.0803957 - 3.39341i) q^{35} +(-0.428031 + 1.31734i) q^{36} +(-2.90965 + 0.945402i) q^{37} +(2.58545 + 3.55857i) q^{38} +(-0.377416 + 0.274209i) q^{39} +(3.60149 - 4.71786i) q^{40} +(-0.417266 + 1.28421i) q^{41} +(-0.699650 + 0.962986i) q^{42} +12.0864i q^{43} +(4.51858 - 0.828906i) q^{44} +(1.83964 - 1.27111i) q^{45} +(4.87607 + 3.54267i) q^{46} +(-2.43285 - 0.790480i) q^{47} +(0.655168 - 0.212877i) q^{48} +(-3.79887 + 2.76004i) q^{49} +(-3.78196 + 1.03361i) q^{50} +(0.524187 + 1.61328i) q^{51} +(0.614557 + 0.199682i) q^{52} +(4.71234 - 6.48598i) q^{53} -0.784131 q^{54} +(-6.61010 - 3.36252i) q^{55} +4.02938 q^{56} +(3.29722 - 4.53823i) q^{57} +(-1.98448 - 0.644797i) q^{58} +(-2.33267 - 7.17923i) q^{59} +(-2.92218 - 1.02661i) q^{60} +(8.99446 - 6.53486i) q^{61} +(-2.95149 + 0.958996i) q^{62} +(1.44371 + 0.469090i) q^{63} +(2.59580 + 1.88596i) q^{64} +(-0.592989 - 0.858214i) q^{65} +(1.23674 + 2.28778i) q^{66} -6.89959i q^{67} +(1.38107 - 1.90088i) q^{68} +(2.37523 - 7.31021i) q^{69} +(-2.11564 - 1.61503i) q^{70} +(-11.8018 + 8.57452i) q^{71} +(1.56021 + 2.14745i) q^{72} +(2.15628 - 0.700618i) q^{73} +(-0.741319 + 2.28155i) q^{74} +(2.74407 + 4.17972i) q^{75} -7.77002 q^{76} +(-0.908418 - 4.95202i) q^{77} +0.365807i q^{78} +(9.85457 + 7.15977i) q^{79} +(0.441176 + 1.47586i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.622355 + 0.856598i) q^{82} +(-6.92458 - 9.53087i) q^{83} +(-0.649754 - 1.99974i) q^{84} +(-3.63416 + 1.08635i) q^{85} +(7.66735 + 5.57065i) q^{86} +2.66104i q^{87} +(3.80462 - 7.93906i) q^{88} -1.47962 q^{89} +(0.0415286 - 1.75288i) q^{90} +(0.218836 - 0.673508i) q^{91} +(-10.1257 + 3.29002i) q^{92} +(2.32629 + 3.20187i) q^{93} +(-1.62276 + 1.17901i) q^{94} +(9.97032 + 7.61108i) q^{95} +(1.80743 - 5.56269i) q^{96} +(8.34744 - 11.4893i) q^{97} +3.68201i q^{98} +(2.28742 - 2.40161i) 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 $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.460901	−	0.634375i	0.325906	−	0.448571i	−0.614353	−	0.789031i	$-0.710583\pi$
$2$	0.460901	−	0.634375i	0.325906	−	0.448571i	0.940259	+	0.340460i	$0.110583\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.428031	+	1.31734i	0.214016	+	0.658672i
$5$	0.741158	−	2.10966i	0.331456	−	0.943471i
$5$	0.741158	−	2.10966i	0.331456	−	0.943471i
$6$	−0.634375	+	0.460901i	−0.258983	+	0.188162i
$7$	1.44371	−	0.469090i	0.545671	−	0.177299i	−0.0231928	−	0.999731i	$-0.507383\pi$
$7$	1.44371	−	0.469090i	0.545671	−	0.177299i	0.568864	+	0.822432i	$0.307383\pi$
$8$	2.52448	+	0.820252i	0.892537	+	0.290003i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.996719	−	1.44252i	−0.315190	−	0.456164i
$11$	0.438933	−	3.28745i	0.132343	−	0.991204i
$11$	0.438933	−	3.28745i	0.132343	−	0.991204i
$12$		−	1.38514i		−	0.399855i
$13$	0.274209	−	0.377416i	0.0760519	−	0.104676i	−0.769296	−	0.638892i	$-0.779393\pi$
$13$	0.274209	−	0.377416i	0.0760519	−	0.104676i	0.845348	+	0.534216i	$0.179393\pi$
$14$	0.367828	−	1.13206i	0.0983061	−	0.302555i
$15$	−1.35681	+	1.77738i	−0.350326	+	0.458917i
$16$	−0.557320	+	0.404916i	−0.139330	+	0.101229i
$17$	−0.997064	−	1.37234i	−0.241823	−	0.332841i	0.670803	−	0.741635i	$-0.265949\pi$
$17$	−0.997064	−	1.37234i	−0.241823	−	0.332841i	−0.912627	+	0.408794i	$0.865949\pi$
$18$	0.745753	−	0.242310i	0.175776	−	0.0571130i
$19$	−1.73345	+	5.33501i	−0.397681	+	1.22394i	0.529174	+	0.848514i	$0.322502\pi$
$19$	−1.73345	+	5.33501i	−0.397681	+	1.22394i	−0.926854	+	0.375422i	$0.877498\pi$
$20$	3.09639	+	0.0733588i	0.692375	+	0.0164035i
$21$	−1.51801			−0.331256
$22$	−1.88317	−	1.79364i	−0.401494	−	0.382405i
$23$			7.68641i			1.60273i	0.598177	+	0.801364i	$0.295892\pi$
$23$			7.68641i			1.60273i	−0.598177	+	0.801364i	$0.704108\pi$
$24$	−2.14745	−	1.56021i	−0.438346	−	0.318477i
$25$	−3.90137	−	3.12719i	−0.780274	−	0.625438i
$26$	−0.113040	−	0.347903i	−0.0221691	−	0.0682294i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	1.23591	+	1.70108i	0.233564	+	0.321474i
$29$	−0.822307	−	2.53080i	−0.152699	−	0.469958i	0.845222	−	0.534416i	$-0.179468\pi$
$29$	−0.822307	−	2.53080i	−0.152699	−	0.469958i	−0.997920	+	0.0644576i	$0.979468\pi$
$30$	0.502173	+	1.67992i	0.0916839	+	0.306710i
$31$	−3.20187	−	2.32629i	−0.575072	−	0.417814i	0.261872	−	0.965103i	$-0.415660\pi$
$31$	−3.20187	−	2.32629i	−0.575072	−	0.417814i	−0.836944	+	0.547288i	$0.815660\pi$
$32$			5.84896i			1.03396i
$33$	−1.43333	+	2.99091i	−0.249510	+	0.520651i
$34$	−1.33013			−0.228115
$35$	0.0803957	−	3.39341i	0.0135893	−	0.573591i
$36$	−0.428031	+	1.31734i	−0.0713385	+	0.219557i
$37$	−2.90965	+	0.945402i	−0.478343	+	0.155423i	−0.538258	−	0.842780i	$-0.680917\pi$
$37$	−2.90965	+	0.945402i	−0.478343	+	0.155423i	0.0599143	+	0.998204i	$0.480917\pi$
$38$	2.58545	+	3.55857i	0.419416	+	0.577276i
$39$	−0.377416	+	0.274209i	−0.0604350	+	0.0439086i
$40$	3.60149	−	4.71786i	0.569446	−	0.745960i
$41$	−0.417266	+	1.28421i	−0.0651660	+	0.200560i	−0.978338	−	0.207014i	$-0.933625\pi$
$41$	−0.417266	+	1.28421i	−0.0651660	+	0.200560i	0.913172	+	0.407575i	$0.133625\pi$
$42$	−0.699650	+	0.962986i	−0.107958	+	0.148592i
$43$			12.0864i			1.84317i	0.388181	+	0.921583i	$0.373104\pi$
$43$			12.0864i			1.84317i	−0.388181	+	0.921583i	$0.626896\pi$
$44$	4.51858	−	0.828906i	0.681202	−	0.124962i
$45$	1.83964	−	1.27111i	0.274237	−	0.189486i
$46$	4.87607	+	3.54267i	0.718937	+	0.522339i
$47$	−2.43285	−	0.790480i	−0.354867	−	0.115303i	0.126158	−	0.992010i	$-0.459735\pi$
$47$	−2.43285	−	0.790480i	−0.354867	−	0.115303i	−0.481025	+	0.876707i	$0.659735\pi$
$48$	0.655168	−	0.212877i	0.0945654	−	0.0307262i
$49$	−3.79887	+	2.76004i	−0.542695	+	0.394291i
$50$	−3.78196	+	1.03361i	−0.534849	+	0.146174i
$51$	0.524187	+	1.61328i	0.0734009	+	0.225905i
$52$	0.614557	+	0.199682i	0.0852238	+	0.0276909i
$53$	4.71234	−	6.48598i	0.647290	−	0.890918i	−0.351688	−	0.936117i	$-0.614392\pi$
$53$	4.71234	−	6.48598i	0.647290	−	0.890918i	0.998978	+	0.0451995i	$0.0143923\pi$
$54$	−0.784131			−0.106707
$55$	−6.61010	−	3.36252i	−0.891306	−	0.453403i
$56$	4.02938			0.538449
$57$	3.29722	−	4.53823i	0.436727	−	0.601103i
$58$	−1.98448	−	0.644797i	−0.260575	−	0.0846659i
$59$	−2.33267	−	7.17923i	−0.303688	−	0.934656i	−0.980163	−	0.198191i	$-0.936493\pi$
$59$	−2.33267	−	7.17923i	−0.303688	−	0.934656i	0.676475	−	0.736465i	$-0.263507\pi$
$60$	−2.92218	−	1.02661i	−0.377251	−	0.132534i
$61$	8.99446	−	6.53486i	1.15162	−	0.836703i	0.162927	−	0.986638i	$-0.447907\pi$
$61$	8.99446	−	6.53486i	1.15162	−	0.836703i	0.988696	+	0.149935i	$0.0479065\pi$
$62$	−2.95149	+	0.958996i	−0.374839	+	0.121793i
$63$	1.44371	+	0.469090i	0.181890	+	0.0590997i
$64$	2.59580	+	1.88596i	0.324475	+	0.235745i
$65$	−0.592989	−	0.858214i	−0.0735513	−	0.106448i
$66$	1.23674	+	2.28778i	0.152232	+	0.281607i
$67$		−	6.89959i		−	0.842919i	−0.906847	−	0.421460i	$-0.861518\pi$
$67$		−	6.89959i		−	0.842919i	0.906847	−	0.421460i	$-0.138482\pi$
$68$	1.38107	−	1.90088i	0.167479	−	0.230516i
$69$	2.37523	−	7.31021i	0.285944	−	0.880046i
$70$	−2.11564	−	1.61503i	−0.252868	−	0.193033i
$71$	−11.8018	+	8.57452i	−1.40062	+	1.01761i	−0.406013	+	0.913867i	$0.633081\pi$
$71$	−11.8018	+	8.57452i	−1.40062	+	1.01761i	−0.994604	+	0.103741i	$0.966919\pi$
$72$	1.56021	+	2.14745i	0.183873	+	0.253079i
$73$	2.15628	−	0.700618i	0.252373	−	0.0820011i	−0.180098	−	0.983649i	$-0.557642\pi$
$73$	2.15628	−	0.700618i	0.252373	−	0.0820011i	0.432472	+	0.901648i	$0.357642\pi$
$74$	−0.741319	+	2.28155i	−0.0861766	+	0.265224i
$75$	2.74407	+	4.17972i	0.316858	+	0.482633i
$76$	−7.77002			−0.891282
$77$	−0.908418	−	4.95202i	−0.103524	−	0.564336i
$78$			0.365807i			0.0414195i
$79$	9.85457	+	7.15977i	1.10873	+	0.805537i	0.982463	−	0.186460i	$-0.0597015\pi$
$79$	9.85457	+	7.15977i	1.10873	+	0.805537i	0.126264	+	0.991997i	$0.459702\pi$
$80$	0.441176	+	1.47586i	0.0493249	+	0.165007i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.622355	+	0.856598i	0.0687276	+	0.0945955i
$83$	−6.92458	−	9.53087i	−0.760071	−	1.04615i	−0.997208	−	0.0746722i	$-0.976209\pi$
$83$	−6.92458	−	9.53087i	−0.760071	−	1.04615i	0.237137	−	0.971476i	$-0.423791\pi$
$84$	−0.649754	−	1.99974i	−0.0708940	−	0.218189i
$85$	−3.63416	+	1.08635i	−0.394180	+	0.117831i
$86$	7.66735	+	5.57065i	0.826791	+	0.600699i
$87$			2.66104i			0.285294i
$88$	3.80462	−	7.93906i	0.405573	−	0.846307i
$89$	−1.47962			−0.156840			−0.0784199	−	0.996920i	$-0.524987\pi$
$89$	−1.47962			−0.156840			−0.0784199	+	0.996920i	$0.524987\pi$
$90$	0.0415286	−	1.75288i	0.00437750	−	0.184770i
$91$	0.218836	−	0.673508i	0.0229402	−	0.0706028i
$92$	−10.1257	+	3.29002i	−1.05567	+	0.343009i
$93$	2.32629	+	3.20187i	0.241225	+	0.332018i
$94$	−1.62276	+	1.17901i	−0.167375	+	0.121605i
$95$	9.97032	+	7.61108i	1.02293	+	0.780881i
$96$	1.80743	−	5.56269i	0.184470	−	0.567740i
$97$	8.34744	−	11.4893i	0.847555	−	1.16656i	−0.136842	−	0.990593i	$-0.543695\pi$
$97$	8.34744	−	11.4893i	0.847555	−	1.16656i	0.984396	−	0.175966i	$-0.0563048\pi$
$98$			3.68201i			0.371939i
$99$	2.28742	−	2.40161i	0.229894	−	0.241370i
$100$	2.44968	−	6.47798i	0.244968	−	0.647798i
$101$	2.12294	+	1.54241i	0.211240	+	0.153475i	0.688375	−	0.725355i	$-0.258325\pi$
$101$	2.12294	+	1.54241i	0.211240	+	0.153475i	−0.477134	+	0.878830i	$0.658325\pi$
$102$	1.26503	+	0.411032i	0.125256	+	0.0406982i
$103$	0.0171957	−	0.00558722i	0.00169434	−	0.000550525i	−0.308170	−	0.951331i	$-0.599716\pi$
$103$	0.0171957	−	0.00558722i	0.00169434	−	0.000550525i	0.309864	+	0.950781i	$0.399716\pi$
$104$	1.00181	−	0.727858i	0.0982356	−	0.0713724i
$105$	−1.12508	+	3.20248i	−0.109797	+	0.312530i
$106$	−1.94262	−	5.97878i	−0.188684	−	0.580711i
$107$	13.9786	+	4.54194i	1.35137	+	0.439086i	0.893152	−	0.449755i	$-0.148489\pi$
$107$	13.9786	+	4.54194i	1.35137	+	0.439086i	0.458215	+	0.888841i	$0.348489\pi$
$108$	0.814164	−	1.12060i	0.0783430	−	0.107830i
$109$	5.31791			0.509364			0.254682	−	0.967025i	$-0.418029\pi$
$109$	5.31791			0.509364			0.254682	+	0.967025i	$0.418029\pi$
$110$	−5.17970	+	2.64350i	−0.493865	+	0.252048i
$111$	3.05939			0.290384
$112$	−0.614665	+	0.846014i	−0.0580804	+	0.0799409i
$113$	−9.10816	−	2.95942i	−0.856824	−	0.278399i	−0.152523	−	0.988300i	$-0.548740\pi$
$113$	−9.10816	−	2.95942i	−0.856824	−	0.278399i	−0.704301	+	0.709901i	$0.748740\pi$
$114$	−1.35925	−	4.18335i	−0.127306	−	0.391806i
$115$	16.2158	+	5.69685i	1.51213	+	0.531234i
$116$	2.98196	−	2.16652i	0.276868	−	0.201157i
$117$	0.443679	−	0.144160i	0.0410182	−	0.0133276i
$118$	−5.62946	−	1.82912i	−0.518233	−	0.168384i
$119$	−2.08322	−	1.51355i	−0.190969	−	0.138747i
$120$	−4.88312	+	3.37403i	−0.445766	+	0.308006i
$121$	−10.6147	−	2.88594i	−0.964971	−	0.262358i
$122$		−	8.71779i		−	0.789271i
$123$	0.793688	−	1.09242i	0.0715644	−	0.0984999i
$124$	1.69403	−	5.21369i	0.152128	−	0.468203i
$125$	−9.48886	+	5.91283i	−0.848709	+	0.528860i
$126$	0.962986	−	0.699650i	0.0857896	−	0.0623298i
$127$	10.6589	+	14.6707i	0.945823	+	1.30181i	0.953358	+	0.301842i	$0.0976015\pi$
$127$	10.6589	+	14.6707i	0.945823	+	1.30181i	−0.00753504	+	0.999972i	$0.502398\pi$
$128$	−8.73257	+	2.83739i	−0.771858	+	0.250792i
$129$	3.73492	−	11.4949i	0.328841	−	1.01207i
$130$	−0.817739	−	0.0193736i	−0.0717205	−	0.00169918i
$131$	−8.67183			−0.757661			−0.378831	−	0.925466i	$-0.623674\pi$
$131$	−8.67183			−0.757661			−0.378831	+	0.925466i	$0.623674\pi$
$132$	−4.55358	−	0.607982i	−0.396338	−	0.0529181i
$133$			8.51535i			0.738374i
$134$	−4.37693	−	3.18003i	−0.378109	−	0.274712i
$135$	−2.14240	+	0.640420i	−0.184388	+	0.0551186i
$136$	−1.39140	−	4.28229i	−0.119311	−	0.367203i
$137$	−0.917391	−	1.26268i	−0.0783780	−	0.107878i	0.768028	−	0.640416i	$-0.221238\pi$
$137$	−0.917391	−	1.26268i	−0.0783780	−	0.107878i	−0.846406	+	0.532538i	$0.821238\pi$
$138$	−3.54267	−	4.87607i	−0.301572	−	0.415079i
$139$	4.41533	+	13.5890i	0.374503	+	1.15260i	0.943813	+	0.330480i	$0.107211\pi$
$139$	4.41533	+	13.5890i	0.374503	+	1.15260i	−0.569310	+	0.822123i	$0.692789\pi$
$140$	4.50471	−	1.34658i	0.380717	−	0.113807i
$141$	2.06950	+	1.50358i	0.174284	+	0.126624i
$142$			11.4388i			0.959921i
$143$	−1.12038	−	1.06711i	−0.0936907	−	0.0892361i
$144$	−0.688885			−0.0574071
$145$	−5.94860	−	0.140932i	−0.494004	−	0.0117038i
$146$	0.549376	−	1.69081i	0.0454667	−	0.139932i
$147$	4.46584	−	1.45104i	0.368336	−	0.119680i
$148$	−2.49084	−	3.42835i	−0.204746	−	0.281809i
$149$	−8.91107	+	6.47427i	−0.730023	+	0.530393i	−0.889571	−	0.456797i	$-0.848996\pi$
$149$	−8.91107	+	6.47427i	−0.730023	+	0.530393i	0.159548	+	0.987190i	$0.448996\pi$
$150$	3.91626	+	0.185670i	0.319761	+	0.0151599i
$151$	−1.33557	+	4.11048i	−0.108688	+	0.334506i	−0.990578	−	0.136948i	$-0.956271\pi$
$151$	−1.33557	+	4.11048i	−0.108688	+	0.334506i	0.881891	+	0.471454i	$0.156271\pi$
$152$	−8.75211	+	12.0462i	−0.709890	+	0.977079i
$153$		−	1.69631i		−	0.137138i
$154$	−3.56013	−	1.70611i	−0.286884	−	0.137483i
$155$	−7.28079	+	5.03071i	−0.584807	+	0.404077i
$156$	−0.522774	−	0.379817i	−0.0418554	−	0.0304097i
$157$	0.885900	+	0.287846i	0.0707025	+	0.0229727i	0.344155	−	0.938913i	$-0.388166\pi$
$157$	0.885900	+	0.287846i	0.0707025	+	0.0229727i	−0.273452	+	0.961886i	$0.588166\pi$
$158$	9.08396	−	2.95156i	0.722681	−	0.234813i
$159$	−6.48598	+	4.71234i	−0.514372	+	0.373713i
$160$	12.3393	+	4.33501i	0.975511	+	0.342712i
$161$	3.60562	+	11.0969i	0.284162	+	0.874562i
$162$	0.745753	+	0.242310i	0.0585919	+	0.0190377i
$163$	9.96788	−	13.7196i	0.780744	−	1.07460i	−0.214455	−	0.976734i	$-0.568798\pi$
$163$	9.96788	−	13.7196i	0.780744	−	1.07460i	0.995199	−	0.0978685i	$-0.0312025\pi$
$164$	−1.87035			−0.146050
$165$	5.24750	+	5.24058i	0.408518	+	0.407979i
$166$	−9.23769			−0.716984
$167$	−1.46977	+	2.02297i	−0.113735	+	0.156542i	−0.862089	−	0.506757i	$-0.830844\pi$
$167$	−1.46977	+	2.02297i	−0.113735	+	0.156542i	0.748355	+	0.663299i	$0.230844\pi$
$168$	−3.83217	−	1.24515i	−0.295658	−	0.0960653i
$169$	3.94997	+	12.1568i	0.303844	+	0.935135i
$170$	−0.985834	+	2.80612i	−0.0756100	+	0.215220i
$171$	−4.53823	+	3.29722i	−0.347047	+	0.252145i
$172$	−15.9220	+	5.17338i	−1.21404	+	0.394466i
$173$	5.34260	+	1.73592i	0.406191	+	0.131979i	0.504984	−	0.863129i	$-0.331498\pi$
$173$	5.34260	+	1.73592i	0.406191	+	0.131979i	−0.0987935	+	0.995108i	$0.531498\pi$
$174$	1.68810	+	1.22648i	0.127974	+	0.0929789i
$175$	−7.09938	−	2.68466i	−0.536662	−	0.202942i
$176$	1.08652	+	2.00989i	0.0818993	+	0.151501i
$177$			7.54869i			0.567394i
$178$	−0.681959	+	0.938636i	−0.0511150	+	0.0703538i
$179$	2.46257	−	7.57901i	0.184061	−	0.566481i	−0.815870	−	0.578235i	$-0.803741\pi$
$179$	2.46257	−	7.57901i	0.184061	−	0.566481i	0.999931	+	0.0117540i	$0.00374150\pi$
$180$	2.46192	+	1.87936i	0.183500	+	0.140079i
$181$	14.0342	−	10.1964i	1.04315	−	0.757896i	0.0722551	−	0.997386i	$-0.476980\pi$
$181$	14.0342	−	10.1964i	1.04315	−	0.757896i	0.970899	+	0.239491i	$0.0769804\pi$
$182$	−0.326395	−	0.449245i	−0.0241940	−	0.0333002i
$183$	−10.5736	+	3.43558i	−0.781625	+	0.253965i
$184$	−6.30480	+	19.4042i	−0.464796	+	1.43049i
$185$	−0.162029	+	6.83908i	−0.0119126	+	0.502819i
$186$	3.10338			0.227551
$187$	−4.94915	+	2.67543i	−0.361917	+	0.195647i
$188$		−	3.54325i		−	0.258418i
$189$	−1.22809	−	0.892262i	−0.0893306	−	0.0649025i
$190$	9.42361	−	2.81697i	0.683661	−	0.204365i
$191$	−6.85624	−	21.1013i	−0.496100	−	1.52684i	−0.815235	−	0.579131i	$-0.803392\pi$
$191$	−6.85624	−	21.1013i	−0.496100	−	1.52684i	0.319134	−	0.947709i	$-0.396608\pi$
$192$	−1.88596	−	2.59580i	−0.136107	−	0.187336i
$193$	−15.4560	−	21.2734i	−1.11255	−	1.53129i	−0.817607	−	0.575777i	$-0.804700\pi$
$193$	−15.4560	−	21.2734i	−1.11255	−	1.53129i	−0.294942	−	0.955515i	$-0.595300\pi$
$194$	−3.44117	−	10.5908i	−0.247061	−	0.760377i
$195$	0.298764	+	0.999454i	0.0213949	+	0.0715724i
$196$	−5.26196	−	3.82303i	−0.375854	−	0.273074i
$197$		−	11.5966i		−	0.826227i	−0.910680	−	0.413113i	$-0.864441\pi$
$197$		−	11.5966i		−	0.826227i	0.910680	−	0.413113i	$-0.135559\pi$
$198$	−0.469247	−	2.55798i	−0.0333479	−	0.181788i
$199$	−14.4208			−1.02226			−0.511131	−	0.859503i	$-0.670773\pi$
$199$	−14.4208			−1.02226			−0.511131	+	0.859503i	$0.670773\pi$
$200$	−7.28383	−	11.0946i	−0.515045	−	0.784509i
$201$	−2.13209	+	6.56190i	−0.150386	+	0.462841i
$202$	1.95693	−	0.635844i	0.137689	−	0.0447379i
$203$	−2.37435	−	3.26801i	−0.166646	−	0.229369i
$204$	−1.90088	+	1.38107i	−0.133088	+	0.0966943i
$205$	2.40000	+	1.83210i	0.167623	+	0.127959i
$206$	0.00438111	−	0.0134837i	0.000305247	−	0.000939453i
$207$	−4.51796	+	6.21844i	−0.314020	+	0.432211i
$208$			0.321373i			0.0222832i
$209$	16.7777	+	8.04034i	1.16054	+	0.556162i
$210$	1.51303	+	2.18975i	0.104409	+	0.151107i
$211$	2.64311	+	1.92033i	0.181959	+	0.132201i	0.675036	−	0.737785i	$-0.264128\pi$
$211$	2.64311	+	1.92033i	0.181959	+	0.132201i	−0.493077	+	0.869986i	$0.664128\pi$
$212$	10.5613	+	3.43157i	0.725353	+	0.235681i
$213$	13.8739	−	4.50789i	0.950621	−	0.308876i
$214$	9.32406	−	6.77433i	0.637380	−	0.463084i
$215$	25.4984	+	8.95797i	1.73897	+	0.610929i
$216$	−0.820252	−	2.52448i	−0.0558111	−	0.171769i
$217$	−5.71381	−	1.85653i	−0.387878	−	0.126029i
$218$	2.45103	−	3.37355i	0.166005	−	0.228486i
$219$	−2.26725			−0.153206
$220$	1.60027	−	10.1470i	0.107890	−	0.684114i
$221$	−0.791347			−0.0532318
$222$	1.41007	−	1.94080i	0.0946379	−	0.130258i
$223$	−17.2412	−	5.60199i	−1.15455	−	0.375137i	−0.331696	−	0.943386i	$-0.607621\pi$
$223$	−17.2412	−	5.60199i	−1.15455	−	0.375137i	−0.822857	+	0.568249i	$0.807621\pi$
$224$	2.74369	+	8.44420i	0.183320	+	0.564202i
$225$	−1.31816	−	4.82312i	−0.0878771	−	0.321541i
$226$	−6.07534	+	4.41400i	−0.404126	+	0.293615i
$227$	26.7707	−	8.69831i	1.77683	−	0.577327i	0.778121	−	0.628114i	$-0.216173\pi$
$227$	26.7707	−	8.69831i	1.77683	−	0.577327i	0.998709	+	0.0507872i	$0.0161730\pi$
$228$	7.38973	+	2.40107i	0.489397	+	0.159015i
$229$	−14.8547	−	10.7926i	−0.981624	−	0.713192i	−0.0235534	−	0.999723i	$-0.507498\pi$
$229$	−14.8547	−	10.7926i	−0.981624	−	0.713192i	−0.958071	+	0.286531i	$0.907498\pi$
$230$	11.0878	−	7.66119i	0.731107	−	0.505164i
$231$	−0.666303	+	4.99037i	−0.0438395	+	0.328342i
$232$		−	7.06345i		−	0.463738i
$233$	−5.31305	+	7.31279i	−0.348070	+	0.479077i	−0.946777	−	0.321891i	$-0.895681\pi$
$233$	−5.31305	+	7.31279i	−0.348070	+	0.479077i	0.598707	+	0.800968i	$0.295681\pi$
$234$	0.113040	−	0.347903i	0.00738969	−	0.0227431i
$235$	−3.47077	+	4.54662i	−0.226408	+	0.296589i
$236$	8.45906	−	6.14587i	0.550638	−	0.400062i
$237$	−7.15977	−	9.85457i	−0.465077	−	0.640123i
$238$	−1.92032	+	0.623949i	−0.124476	+	0.0404446i
$239$	3.68464	−	11.3402i	0.238340	−	0.733534i	−0.758321	−	0.651881i	$-0.773980\pi$
$239$	3.68464	−	11.3402i	0.238340	−	0.733534i	0.996661	−	0.0816530i	$-0.0260199\pi$
$240$	0.0364843	−	1.53996i	0.00235505	−	0.0994041i
$241$	25.4155			1.63715			0.818577	−	0.574396i	$-0.194763\pi$
$241$	25.4155			1.63715			0.818577	+	0.574396i	$0.194763\pi$
$242$	−6.72308	+	5.40356i	−0.432176	+	0.347354i
$243$		−	1.00000i		−	0.0641500i
$244$	12.4586	+	9.05168i	0.797578	+	0.579475i
$245$	3.00719	+	10.0600i	0.192122	+	0.642707i
$246$	−0.327191	−	1.00699i	−0.0208610	−	0.0642035i
$247$	1.53819	+	2.11714i	0.0978728	+	0.134710i
$248$	−6.17489	−	8.49901i	−0.392106	−	0.539688i
$249$	3.64047	+	11.2042i	0.230705	+	0.710038i
$250$	−0.622464	+	8.74473i	−0.0393681	+	0.553065i
$251$	11.9719	+	8.69810i	0.755660	+	0.549019i	0.897576	−	0.440859i	$-0.145326\pi$
$251$	11.9719	+	8.69810i	0.755660	+	0.549019i	−0.141916	+	0.989879i	$0.545326\pi$
$252$			2.10265i			0.132454i
$253$	25.2687	+	3.37382i	1.58863	+	0.212110i
$254$	14.2194			0.892205
$255$	3.79199	+	0.0898387i	0.237464	+	0.00562591i
$256$	−4.20790	+	12.9506i	−0.262993	+	0.809411i
$257$	7.76969	−	2.52453i	0.484660	−	0.157476i	−0.0564874	−	0.998403i	$-0.517990\pi$
$257$	7.76969	−	2.52453i	0.484660	−	0.157476i	0.541147	+	0.840928i	$0.317990\pi$
$258$	−5.57065	−	7.66735i	−0.346814	−	0.477348i
$259$	−3.75721	+	2.72977i	−0.233462	+	0.169620i
$260$	0.876746	−	1.14851i	0.0543735	−	0.0712278i
$261$	0.822307	−	2.53080i	0.0508995	−	0.156653i
$262$	−3.99685	+	5.50119i	−0.246926	+	0.339865i
$263$		−	9.66161i		−	0.595761i	−0.954603	−	0.297880i	$-0.903720\pi$
$263$		−	9.66161i		−	0.595761i	0.954603	−	0.297880i	$-0.0962796\pi$
$264$	−6.07171	+	6.37480i	−0.373688	+	0.392342i
$265$	−10.1906	−	14.7486i	−0.626007	−	0.905999i
$266$	5.40193	+	3.92473i	0.331213	+	0.240641i
$267$	1.40721	+	0.457229i	0.0861196	+	0.0279819i
$268$	9.08914	−	2.95324i	0.555208	−	0.180398i
$269$	0.307325	−	0.223285i	0.0187379	−	0.0136139i	−0.578377	−	0.815770i	$-0.696314\pi$
$269$	0.307325	−	0.223285i	0.0187379	−	0.0136139i	0.597115	+	0.802156i	$0.296314\pi$
$270$	−0.581165	+	1.65425i	−0.0353686	+	0.100675i
$271$	−2.77138	−	8.52943i	−0.168349	−	0.518126i	0.830918	−	0.556395i	$-0.187816\pi$
$271$	−2.77138	−	8.52943i	−0.168349	−	0.518126i	−0.999267	+	0.0382687i	$0.987816\pi$
$272$	1.11137	+	0.361105i	0.0673865	+	0.0218952i
$273$	−0.416251	+	0.572920i	−0.0251926	+	0.0346747i
$274$	−1.22384			−0.0739349
$275$	−11.9929	+	11.4529i	−0.723201	+	0.690638i
$276$	10.6467			0.640859
$277$	−1.98618	+	2.73375i	−0.119338	+	0.164255i	−0.864507	−	0.502621i	$-0.832369\pi$
$277$	−1.98618	+	2.73375i	−0.119338	+	0.164255i	0.745168	+	0.666876i	$0.232369\pi$
$278$	10.6556	+	3.46220i	0.639077	+	0.207649i
$279$	−1.22300	−	3.76402i	−0.0732193	−	0.225346i
$280$	2.98641	−	8.50065i	0.178472	−	0.508011i
$281$	4.10617	−	2.98331i	0.244953	−	0.177969i	−0.458534	−	0.888677i	$-0.651625\pi$
$281$	4.10617	−	2.98331i	0.244953	−	0.177969i	0.703487	+	0.710708i	$0.251625\pi$
$282$	1.90767	−	0.619840i	0.113600	−	0.0369109i
$283$	−21.2067	−	6.89047i	−1.26061	−	0.409596i	−0.398897	−	0.916996i	$-0.630607\pi$
$283$	−21.2067	−	6.89047i	−1.26061	−	0.409596i	−0.861711	+	0.507400i	$0.830607\pi$
$284$	−16.3471	−	11.8769i	−0.970024	−	0.704764i
$285$	−7.13038	−	10.3196i	−0.422367	−	0.611279i
$286$	−1.19333	+	0.218909i	−0.0705631	+	0.0129444i
$287$			2.04977i			0.120994i
$288$	−3.43793	+	4.73191i	−0.202582	+	0.278830i
$289$	4.36411	−	13.4313i	0.256712	−	0.790079i
$290$	−2.83112	+	3.70869i	−0.166249	+	0.217782i
$291$	−11.4893	+	8.34744i	−0.673513	+	0.489336i
$292$	1.84591	+	2.54068i	0.108024	+	0.148682i
$293$	−15.4229	+	5.01120i	−0.901014	+	0.292757i	−0.722655	−	0.691208i	$-0.757079\pi$
$293$	−15.4229	+	5.01120i	−0.901014	+	0.292757i	−0.178358	+	0.983966i	$0.557079\pi$
$294$	1.13780	−	3.50180i	0.0663581	−	0.204229i
$295$	−16.8746	−	0.399789i	−0.982480	−	0.0232766i
$296$	−8.12081			−0.472012
$297$	−2.91760	+	1.57721i	−0.169296	+	0.0915191i
$298$			8.63696i			0.500325i
$299$	2.90098	+	2.10768i	0.167768	+	0.121890i
$300$	−4.33159	+	5.40393i	−0.250085	+	0.311996i
$301$	5.66963	+	17.4493i	0.326792	+	1.00576i
$302$	1.99202	+	2.74178i	0.114628	+	0.157772i
$303$	−1.54241	−	2.12294i	−0.0886089	−	0.121960i
$304$	−1.19415	−	3.67521i	−0.0684890	−	0.210788i
$305$	−7.12004	−	23.8187i	−0.407692	−	1.36385i
$306$	−1.07609	−	0.781829i	−0.0615162	−	0.0446942i
$307$		−	29.9543i		−	1.70958i	−0.518973	−	0.854791i	$-0.673686\pi$
$307$		−	29.9543i		−	1.70958i	0.518973	−	0.854791i	$-0.326314\pi$
$308$	6.13469	−	3.31632i	0.349557	−	0.188965i
$309$	−0.0180806			−0.00102857
$310$	−0.164359	+	6.93741i	−0.00933496	+	0.394018i
$311$	1.57914	−	4.86011i	0.0895451	−	0.275591i	−0.896249	−	0.443552i	$-0.853718\pi$
$311$	1.57914	−	4.86011i	0.0895451	−	0.275591i	0.985794	+	0.167961i	$0.0537182\pi$
$312$	−1.17770	+	0.382658i	−0.0666741	+	0.0216637i
$313$	14.7596	+	20.3149i	0.834262	+	1.14826i	0.987115	+	0.160014i	$0.0511541\pi$
$313$	14.7596	+	20.3149i	0.834262	+	1.14826i	−0.152852	+	0.988249i	$0.548846\pi$
$314$	0.590915	−	0.429325i	0.0333473	−	0.0242282i
$315$	2.05964	−	2.69807i	0.116048	−	0.152019i
$316$	−5.21382	+	16.0465i	−0.293300	+	0.902685i
$317$	−7.29966	+	10.0471i	−0.409989	+	0.564302i	−0.963216	−	0.268729i	$-0.913396\pi$
$317$	−7.29966	+	10.0471i	−0.409989	+	0.564302i	0.553226	+	0.833031i	$0.313396\pi$
$318$			6.28647i			0.352528i
$319$	−8.68082	+	1.59244i	−0.486033	+	0.0891597i
$320$	5.90264	−	4.07847i	0.329967	−	0.227993i
$321$	−11.8909	−	8.63928i	−0.663688	−	0.482198i
$322$	8.70146	+	2.82728i	0.484914	+	0.157558i
$323$	9.04981	−	2.94046i	0.503545	−	0.163612i
$324$	−1.12060	+	0.814164i	−0.0622556	+	0.0452313i
$325$	−2.25004	+	0.614936i	−0.124810	+	0.0341105i
$326$	−4.10918	−	12.6468i	−0.227586	−	0.700439i
$327$	−5.05764	−	1.64333i	−0.279688	−	0.0908761i
$328$	−2.10676	+	2.89970i	−0.116326	+	0.160109i
$329$	−3.88313			−0.214084
$330$	5.74308	−	0.913498i	0.316146	−	0.0502864i
$331$	8.35534			0.459251			0.229626	−	0.973279i	$-0.426250\pi$
$331$	8.35534			0.459251			0.229626	+	0.973279i	$0.426250\pi$
$332$	9.59150	−	13.2016i	0.526402	−	0.724530i
$333$	−2.90965	−	0.945402i	−0.159448	−	0.0518077i
$334$	0.605903	+	1.86478i	0.0331535	+	0.102036i
$335$	−14.5558	−	5.11369i	−0.795270	−	0.279391i
$336$	0.846014	−	0.614665i	0.0461539	−	0.0335328i
$337$	3.74107	−	1.21555i	0.203789	−	0.0662150i	−0.205344	−	0.978690i	$-0.565831\pi$
$337$	3.74107	−	1.21555i	0.203789	−	0.0662150i	0.409133	+	0.912475i	$0.365831\pi$
$338$	9.53249	+	3.09729i	0.518499	+	0.168471i
$339$	7.74787	+	5.62916i	0.420806	+	0.305734i
$340$	−2.98663	−	4.32245i	−0.161973	−	0.234418i
$341$	−9.05298	+	9.50490i	−0.490246	+	0.514719i
$342$			4.39863i			0.237851i
$343$	−10.4356	+	14.3634i	−0.563469	+	0.775548i
$344$	−9.91394	+	30.5120i	−0.534524	+	1.64509i
$345$	−13.6617	−	10.4290i	−0.735520	−	0.561477i
$346$	3.56363	−	2.58913i	0.191582	−	0.139193i
$347$	5.40723	+	7.44241i	0.290275	+	0.399529i	0.929103	−	0.369820i	$-0.120581\pi$
$347$	5.40723	+	7.44241i	0.290275	+	0.399529i	−0.638828	+	0.769349i	$0.720581\pi$
$348$	−3.50551	+	1.13901i	−0.187915	+	0.0610573i
$349$	6.24065	−	19.2067i	0.334054	−	1.02811i	−0.633132	−	0.774044i	$-0.718231\pi$
$349$	6.24065	−	19.2067i	0.334054	−	1.02811i	0.967186	−	0.254069i	$-0.0817690\pi$
$350$	−4.97519	+	3.26631i	−0.265935	+	0.174591i
$351$	−0.466512			−0.0249006
$352$	19.2282	+	2.56730i	1.02487	+	0.136838i
$353$			34.8561i			1.85520i	0.373572	+	0.927601i	$0.378133\pi$
$353$			34.8561i			1.85520i	−0.373572	+	0.927601i	$0.621867\pi$
$354$	4.78870	+	3.47920i	0.254517	+	0.184917i
$355$	9.34234	+	31.2529i	0.495840	+	1.65873i
$356$	−0.633325	−	1.94917i	−0.0335662	−	0.103306i
$357$	1.51355	+	2.08322i	0.0801055	+	0.110256i
$358$	−3.67294	−	5.05536i	−0.194121	−	0.267184i
$359$	−8.78520	−	27.0381i	−0.463665	−	1.42701i	−0.860654	−	0.509191i	$-0.829945\pi$
$359$	−8.78520	−	27.0381i	−0.463665	−	1.42701i	0.396988	−	0.917824i	$-0.370055\pi$
$360$	5.68676	−	1.69993i	0.299719	−	0.0895940i
$361$	−10.0862	−	7.32802i	−0.530850	−	0.385685i
$362$		−	13.6025i		−	0.714931i
$363$	9.20335	+	6.02481i	0.483051	+	0.316220i
$364$	0.980911			0.0514137
$365$	0.120076	−	5.06829i	0.00628509	−	0.265287i
$366$	−2.69394	+	8.29111i	−0.140815	+	0.433383i
$367$	−25.2766	+	8.21286i	−1.31943	+	0.428708i	−0.882298	−	0.470692i	$-0.844004\pi$
$367$	−25.2766	+	8.21286i	−1.31943	+	0.428708i	−0.437128	+	0.899399i	$0.644004\pi$
$368$	−3.11235	−	4.28379i	−0.162243	−	0.223308i
$369$	−1.09242	+	0.793688i	−0.0568690	+	0.0413177i
$370$	4.26386	+	3.25492i	0.221668	+	0.169215i
$371$	3.76074	−	11.5744i	0.195248	−	0.600912i
$372$	−3.22224	+	4.43503i	−0.167065	+	0.229945i
$373$			19.1900i			0.993621i	0.867859	+	0.496811i	$0.165496\pi$
$373$			19.1900i			0.993621i	−0.867859	+	0.496811i	$0.834504\pi$
$374$	−0.583836	+	4.37273i	−0.0301894	+	0.226108i
$375$	10.8516	−	2.69122i	0.560374	−	0.138974i
$376$	−5.49327	−	3.99110i	−0.283294	−	0.205825i
$377$	−1.18065	−	0.383616i	−0.0608065	−	0.0197572i
$378$	−1.13206	+	0.367828i	−0.0582268	+	0.0189190i
$379$	−2.46014	+	1.78739i	−0.126369	+	0.0918122i	−0.649174	−	0.760640i	$-0.724885\pi$
$379$	−2.46014	+	1.78739i	−0.126369	+	0.0918122i	0.522806	+	0.852452i	$0.324885\pi$
$380$	−5.75881	+	16.3921i	−0.295421	+	0.840899i
$381$	−5.60371	−	17.2464i	−0.287087	−	0.883562i
$382$	−16.5462	−	5.37619i	−0.846579	−	0.275070i
$383$	−5.10988	+	7.03315i	−0.261103	+	0.359377i	−0.919361	−	0.393415i	$-0.871294\pi$
$383$	−5.10988	+	7.03315i	−0.261103	+	0.359377i	0.658258	+	0.752792i	$0.271294\pi$
$384$	9.18197			0.468566
$385$	−11.1204	−	1.75378i	−0.566748	−	0.0893807i
$386$	−20.6190			−1.04948
$387$	−7.10424	+	9.77814i	−0.361129	+	0.497051i
$388$	18.7083	+	6.07869i	0.949770	+	0.308599i
$389$	4.23102	+	13.0218i	0.214521	+	0.660229i	0.999187	+	0.0403101i	$0.0128346\pi$
$389$	4.23102	+	13.0218i	0.214521	+	0.660229i	−0.784666	+	0.619919i	$0.787165\pi$
$390$	0.771729	+	0.271121i	0.0390780	+	0.0137287i
$391$	10.5484	−	7.66384i	0.533454	−	0.387577i
$392$	−11.8541	+	3.85162i	−0.598721	+	0.194536i
$393$	8.24740	+	2.67974i	0.416026	+	0.135175i
$394$	−7.35663	−	5.34490i	−0.370621	−	0.269272i
$395$	22.4085	−	15.4833i	1.12749	−	0.779050i
$396$	4.14283	+	1.98536i	0.208185	+	0.0997680i
$397$			8.96241i			0.449811i	0.974381	+	0.224905i	$0.0722073\pi$
$397$			8.96241i			0.449811i	−0.974381	+	0.224905i	$0.927793\pi$
$398$	−6.64654	+	9.14818i	−0.333161	+	0.458557i
$399$	2.63139	−	8.09858i	0.131734	−	0.405436i
$400$	3.44056	+	0.163117i	0.172028	+	0.00815584i
$401$	−5.98370	+	4.34742i	−0.298812	+	0.217100i	−0.727081	−	0.686552i	$-0.759124\pi$
$401$	−5.98370	+	4.34742i	−0.298812	+	0.217100i	0.428269	+	0.903651i	$0.359124\pi$
$402$	3.18003	+	4.37693i	0.158605	+	0.218301i
$403$	−1.75596	+	0.570546i	−0.0874706	+	0.0284209i
$404$	−1.12320	+	3.45684i	−0.0558811	+	0.171984i
$405$	2.23544	+	0.0529614i	0.111080	+	0.00263167i
$406$	−3.16748			−0.157199
$407$	1.83082	+	9.98030i	0.0907506	+	0.494705i
$408$			4.50266i			0.222915i
$409$	−22.5760	−	16.4024i	−1.11631	−	0.811047i	−0.132665	−	0.991161i	$-0.542353\pi$
$409$	−22.5760	−	16.4024i	−1.11631	−	0.811047i	−0.983646	+	0.180114i	$0.942353\pi$
$410$	2.26840	−	0.678085i	0.112028	−	0.0334883i
$411$	0.482301	+	1.48437i	0.0237902	+	0.0732186i
$412$	0.0147206	+	0.0202612i	0.000725232	+	0.000998196i
$413$	−6.73540	−	9.27049i	−0.331428	−	0.456171i
$414$	1.86249	+	5.73217i	0.0915366	+	0.281721i
$415$	−25.2391	+	7.54466i	−1.23894	+	0.370353i
$416$	2.20749	+	1.60384i	0.108231	+	0.0786346i
$417$		−	14.2883i		−	0.699702i
$418$	12.8335	−	6.93757i	0.627705	−	0.339328i
$419$	25.4267			1.24218			0.621088	−	0.783741i	$-0.286691\pi$
$419$	25.4267			1.24218			0.621088	+	0.783741i	$0.286691\pi$
$420$	−4.70035	−	0.111359i	−0.229353	−	0.00543377i
$421$	−1.03694	+	3.19137i	−0.0505373	+	0.155538i	−0.973140	−	0.230213i	$-0.926058\pi$
$421$	−1.03694	+	3.19137i	−0.0505373	+	0.155538i	0.922603	+	0.385751i	$0.126058\pi$
$422$	2.43642	−	0.791641i	0.118603	−	0.0385365i
$423$	−1.50358	−	2.06950i	−0.0731066	−	0.100623i
$424$	17.2163	−	12.5084i	0.836099	−	0.607461i
$425$	−0.401658	+	8.47201i	−0.0194833	+	0.410953i
$426$	3.53478	−	10.8789i	0.171261	−	0.527086i
$427$	9.91995	−	13.6536i	0.480060	−	0.660746i
$428$			20.3588i			0.984079i
$429$	0.735788	+	1.36110i	0.0355242	+	0.0657144i
$430$	17.4349	−	12.0468i	0.840787	−	0.580948i
$431$	−8.39488	−	6.09924i	−0.404367	−	0.293790i	0.366950	−	0.930241i	$-0.380402\pi$
$431$	−8.39488	−	6.09924i	−0.404367	−	0.293790i	−0.771317	+	0.636451i	$0.780402\pi$
$432$	0.655168	+	0.212877i	0.0315218	+	0.0102421i
$433$	25.8371	−	8.39497i	1.24165	−	0.403437i	0.386728	−	0.922194i	$-0.373605\pi$
$433$	25.8371	−	8.39497i	1.24165	−	0.403437i	0.854922	+	0.518757i	$0.173605\pi$
$434$	−3.81123	+	2.76902i	−0.182945	+	0.132917i
$435$	5.61390	+	1.97225i	0.269166	+	0.0945623i
$436$	2.27623	+	7.00553i	0.109012	+	0.335504i
$437$	−41.0071	−	13.3240i	−1.96163	−	0.637374i
$438$	−1.04498	+	1.43829i	−0.0499309	+	0.0687239i
$439$	30.5785			1.45943			0.729715	−	0.683751i	$-0.239653\pi$
$439$	30.5785			1.45943			0.729715	+	0.683751i	$0.239653\pi$
$440$	−13.9289	−	13.9106i	−0.664036	−	0.663160i
$441$	−4.69566			−0.223603
$442$	−0.364733	+	0.502011i	−0.0173486	+	0.0238782i
$443$	−3.88499	−	1.26231i	−0.184581	−	0.0599741i	0.215268	−	0.976555i	$-0.430938\pi$
$443$	−3.88499	−	1.26231i	−0.184581	−	0.0599741i	−0.399849	+	0.916581i	$0.630938\pi$
$444$	1.30951	+	4.03027i	0.0621467	+	0.191268i
$445$	−1.09663	+	3.12151i	−0.0519855	+	0.147974i
$446$	−11.5002	+	8.35540i	−0.544551	+	0.395640i
$447$	10.4756	−	3.40372i	0.495478	−	0.160991i
$448$	4.63226	+	1.50511i	0.218854	+	0.0711099i
$449$	16.4256	+	11.9339i	0.775172	+	0.563195i	0.903526	−	0.428533i	$-0.140969\pi$
$449$	16.4256	+	11.9339i	0.775172	+	0.563195i	−0.128354	+	0.991728i	$0.540969\pi$
$450$	−3.66721	−	1.38677i	−0.172874	−	0.0653731i
$451$	4.03864	+	1.93543i	0.190172	+	0.0911356i
$452$		−	13.2653i		−	0.623948i
$453$	2.54041	−	3.49658i	0.119359	−	0.164284i
$454$	6.82062	−	20.9917i	0.320107	−	0.985189i
$455$	−1.25868	−	0.960847i	−0.0590080	−	0.0450452i
$456$	12.0462	−	8.75211i	0.564117	−	0.409855i
$457$	15.1732	+	20.8841i	0.709772	+	0.976917i	0.999802	+	0.0198993i	$0.00633455\pi$
$457$	15.1732	+	20.8841i	0.709772	+	0.976917i	−0.290030	+	0.957017i	$0.593665\pi$
$458$	−13.6931	+	4.44914i	−0.639835	+	0.207895i
$459$	−0.524187	+	1.61328i	−0.0244670	+	0.0753016i
$460$	−0.563866	+	23.8002i	−0.0262904	+	1.10969i
$461$	2.54024			0.118311			0.0591553	−	0.998249i	$-0.481159\pi$
$461$	2.54024			0.118311			0.0591553	+	0.998249i	$0.481159\pi$
$462$	2.85867	+	2.72275i	0.132997	+	0.126674i
$463$			2.87598i			0.133658i	0.997764	+	0.0668290i	$0.0212882\pi$
$463$			2.87598i			0.133658i	−0.997764	+	0.0668290i	$0.978712\pi$
$464$	1.48305	+	1.07750i	0.0688489	+	0.0500216i
$465$	8.47902	−	2.53461i	0.393205	−	0.117540i
$466$	2.19026	+	6.74094i	0.101462	+	0.312268i
$467$	−13.4207	−	18.4719i	−0.621034	−	0.854780i	0.376394	−	0.926460i	$-0.377164\pi$
$467$	−13.4207	−	18.4719i	−0.621034	−	0.854780i	−0.997428	+	0.0716801i	$0.977164\pi$
$468$	0.379817	+	0.522774i	0.0175571	+	0.0241652i
$469$	−3.23653	−	9.96101i	−0.149449	−	0.459957i
$470$	1.28458	+	4.29731i	0.0592534	+	0.198220i
$471$	−0.753592	−	0.547517i	−0.0347237	−	0.0252282i
$472$		−	20.0372i		−	0.922286i
$473$	39.7336	+	5.30514i	1.82695	+	0.243930i
$474$	−9.55144			−0.438712
$475$	23.4464	−	15.3930i	1.07580	−	0.706280i
$476$	1.10218	−	3.39217i	0.0505184	−	0.155480i
$477$	7.62473	−	2.47742i	0.349112	−	0.113433i
$478$	−5.49567	−	7.56414i	−0.251366	−	0.345976i
$479$	−19.3407	+	14.0519i	−0.883701	+	0.642046i	−0.934228	−	0.356677i	$-0.883910\pi$
$479$	−19.3407	+	14.0519i	−0.883701	+	0.642046i	0.0505272	+	0.998723i	$0.483910\pi$
$480$	−10.3958	−	7.93590i	−0.474502	−	0.362223i
$481$	−0.441042	+	1.35739i	−0.0201098	+	0.0618915i
$482$	11.7140	−	16.1230i	0.533559	−	0.734380i
$483$		−	11.6680i		−	0.530913i
$484$	−0.741635	−	15.2185i	−0.0337107	−	0.691748i
$485$	−18.0517	−	26.1257i	−0.819687	−	1.18631i
$486$	−0.634375	−	0.460901i	−0.0287759	−	0.0209069i
$487$	−12.9844	−	4.21888i	−0.588379	−	0.191176i	−0.000328069	−	1.00000i	$-0.500104\pi$
$487$	−12.9844	−	4.21888i	−0.588379	−	0.191176i	−0.588051	+	0.808824i	$0.700104\pi$
$488$	28.0665	−	9.11937i	1.27051	−	0.412815i
$489$	−13.7196	+	9.96788i	−0.620422	+	0.450763i
$490$	7.76781	+	2.72895i	0.350914	+	0.123282i
$491$	13.3256	+	41.0118i	0.601374	+	1.85084i	0.520022	+	0.854153i	$0.325924\pi$
$491$	13.3256	+	41.0118i	0.601374	+	1.85084i	0.0813521	+	0.996685i	$0.474076\pi$
$492$	1.77881	+	0.577971i	0.0801951	+	0.0260570i
$493$	−2.65323	+	3.65185i	−0.119495	+	0.164471i
$494$	2.05202			0.0923245
$495$	−3.37124	−	6.60566i	−0.151526	−	0.296902i
$496$	2.72642			0.122420
$497$	−13.0162	+	17.9152i	−0.583855	+	0.803608i
$498$	8.78557	+	2.85460i	0.393691	+	0.127918i
$499$	−3.68917	−	11.3541i	−0.165150	−	0.508279i	0.833897	−	0.551919i	$-0.186104\pi$
$499$	−3.68917	−	11.3541i	−0.165150	−	0.508279i	−0.999047	+	0.0436404i	$0.986104\pi$
$500$	−11.8508	−	9.96922i	−0.529983	−	0.445837i
$501$	2.02297	−	1.46977i	0.0903797	−	0.0656647i
$502$	11.0357	−	3.58572i	0.492548	−	0.160039i
$503$	−16.6692	−	5.41614i	−0.743241	−	0.241494i	−0.0871709	−	0.996193i	$-0.527783\pi$
$503$	−16.6692	−	5.41614i	−0.743241	−	0.241494i	−0.656071	+	0.754700i	$0.727783\pi$
$504$	3.25984	+	2.36841i	0.145205	+	0.105497i
$505$	4.82739	−	3.33552i	0.214816	−	0.148429i
$506$	13.7866	−	14.4749i	0.612891	−	0.643486i
$507$		−	12.7824i		−	0.567685i
$508$	−14.7640	+	20.3209i	−0.655048	+	0.901596i
$509$	−8.23324	+	25.3393i	−0.364932	+	1.12315i	0.585092	+	0.810967i	$0.301059\pi$
$509$	−8.23324	+	25.3393i	−0.364932	+	1.12315i	−0.950024	+	0.312178i	$0.898941\pi$
$510$	1.80472	−	2.36414i	0.0799145	−	0.104686i
$511$	2.78439	−	2.02298i	0.123174	−	0.0894912i
$512$	−4.51795	−	6.21843i	−0.199667	−	0.274818i
$513$	5.33501	−	1.73345i	0.235546	−	0.0765337i
$514$	1.97956	−	6.09246i	0.0873146	−	0.268727i
$515$	0.000957575	−	0.0404182i	4.21958e−5	−	0.00178104i
$516$	16.7414			0.736999
$517$	−3.66652	+	7.65090i	−0.161253	+	0.336486i
$518$			3.64164i			0.160004i
$519$	−4.54469	−	3.30191i	−0.199490	−	0.144938i
$520$	−0.793036	−	2.65294i	−0.0347769	−	0.116339i
$521$	8.18853	+	25.2017i	0.358746	+	1.10411i	0.953805	+	0.300425i	$0.0971285\pi$
$521$	8.18853	+	25.2017i	0.358746	+	1.10411i	−0.595060	+	0.803682i	$0.702872\pi$
$522$	−1.22648	−	1.68810i	−0.0536814	−	0.0738861i
$523$	−5.24766	−	7.22278i	−0.229464	−	0.315830i	0.678723	−	0.734394i	$-0.262534\pi$
$523$	−5.24766	−	7.22278i	−0.229464	−	0.315830i	−0.908187	+	0.418564i	$0.862534\pi$
$524$	−3.71181	−	11.4238i	−0.162151	−	0.499050i
$525$	5.92230	+	4.74710i	0.258470	+	0.207180i
$526$	−6.12909	−	4.45304i	−0.267241	−	0.194162i
$527$			6.71351i			0.292445i
$528$	−0.412248	−	2.24727i	−0.0179408	−	0.0978000i
$529$	−36.0809			−1.56874
$530$	−14.0530	−	0.332940i	−0.610424	−	0.0144620i
$531$	2.33267	−	7.17923i	0.101229	−	0.311552i
$532$	−11.2176	+	3.64484i	−0.486347	+	0.158024i
$533$	0.370265	+	0.509626i	0.0160380	+	0.0220743i
$534$	0.938636	−	0.681959i	0.0406188	−	0.0295113i
$535$	19.9424	−	26.1240i	0.862183	−	1.12944i
$536$	5.65941	−	17.4179i	0.244449	−	0.752337i
$537$	−4.68408	+	6.44709i	−0.202133	+	0.278212i
$538$		−	0.297872i		−	0.0128422i
$539$	7.40605	+	13.7001i	0.319001	+	0.590103i
$540$	−1.76067	−	2.54816i	−0.0757670	−	0.109655i
$541$	−14.3869	−	10.4527i	−0.618541	−	0.449396i	0.233871	−	0.972268i	$-0.424861\pi$
$541$	−14.3869	−	10.4527i	−0.618541	−	0.449396i	−0.852412	+	0.522871i	$0.824861\pi$
$542$	−6.68819	−	2.17312i	−0.287282	−	0.0933437i
$543$	−16.4982	+	5.36059i	−0.708005	+	0.230045i
$544$	8.02676	−	5.83179i	0.344145	−	0.250036i
$545$	3.94142	−	11.2190i	0.168832	−	0.480570i
$546$	0.171596	+	0.528119i	0.00734364	+	0.0226014i
$547$	14.5979	+	4.74315i	0.624162	+	0.202803i	0.603987	−	0.796994i	$-0.293578\pi$
$547$	14.5979	+	4.74315i	0.624162	+	0.202803i	0.0201748	+	0.999796i	$0.493578\pi$
$548$	1.27071	−	1.74899i	0.0542822	−	0.0747130i
$549$	11.1178			0.474495
$550$	1.73791	+	12.8867i	0.0741048	+	0.549490i
$551$	14.9273			0.635923
$552$	11.9924	−	16.5062i	0.510432	−	0.702549i
$553$	17.5857	+	5.71394i	0.747821	+	0.242982i
$554$	0.818789	+	2.51997i	0.0347870	+	0.107063i
$555$	2.26749	−	6.45428i	0.0962496	−	0.273969i
$556$	−16.0115	+	11.6330i	−0.679038	+	0.493350i
$557$	16.0797	−	5.22462i	0.681320	−	0.221374i	0.0521466	−	0.998639i	$-0.483394\pi$
$557$	16.0797	−	5.22462i	0.681320	−	0.221374i	0.629173	+	0.777265i	$0.283394\pi$
$558$	−2.95149	−	0.958996i	−0.124946	−	0.0405975i
$559$	4.56162	+	3.31421i	0.192936	+	0.140176i
$560$	1.32924	+	1.92377i	0.0561707	+	0.0812941i
$561$	5.53367	−	1.01512i	0.233632	−	0.0428583i
$562$		−	3.97986i		−	0.167880i
$563$	6.96105	−	9.58106i	0.293373	−	0.403793i	−0.636733	−	0.771084i	$-0.719715\pi$
$563$	6.96105	−	9.58106i	0.293373	−	0.403793i	0.930106	+	0.367291i	$0.119715\pi$
$564$	−1.09492	+	3.36983i	−0.0461046	+	0.141895i
$565$	−12.9940	+	17.0218i	−0.546661	+	0.716111i
$566$	−14.1453	+	10.2772i	−0.594573	+	0.431982i
$567$	0.892262	+	1.22809i	0.0374715	+	0.0515750i
$568$	−36.8267	+	11.9657i	−1.54521	+	0.502070i
$569$	−8.51586	+	26.2091i	−0.357003	+	1.09874i	0.597835	+	0.801619i	$0.296028\pi$
$569$	−8.51586	+	26.2091i	−0.357003	+	1.09874i	−0.954839	+	0.297124i	$0.903972\pi$
$570$	−9.83288	−	0.232957i	−0.411854	−	0.00975752i
$571$	18.4594			0.772502			0.386251	−	0.922394i	$-0.373770\pi$
$571$	18.4594			0.772502			0.386251	+	0.922394i	$0.373770\pi$
$572$	0.926194	−	1.93268i	0.0387261	−	0.0808094i
$573$			22.1873i			0.926887i
$574$	1.30032	+	0.944739i	0.0542744	+	0.0394326i
$575$	24.0369	−	29.9875i	1.00241	−	1.25057i
$576$	0.991507	+	3.05154i	0.0413128	+	0.127148i
$577$	−10.8527	−	14.9374i	−0.451803	−	0.621854i	0.520980	−	0.853569i	$-0.325566\pi$
$577$	−10.8527	−	14.9374i	−0.451803	−	0.621854i	−0.972784	+	0.231715i	$0.925566\pi$
$578$	−6.50909	−	8.95900i	−0.270743	−	0.372645i
$579$	8.12571	+	25.0084i	0.337693	+	1.03931i
$580$	−2.36053	−	7.89668i	−0.0980157	−	0.327892i
$581$	−14.4679	−	10.5116i	−0.600230	−	0.436093i
$582$			11.1359i			0.461596i
$583$	−19.2539	−	18.3385i	−0.797417	−	0.759503i
$584$	6.01816			0.249033
$585$	0.0247071	−	1.04286i	0.00102151	−	0.0431170i
$586$	−3.92943	+	12.0936i	−0.162323	+	0.499580i
$587$	9.40571	−	3.05610i	0.388215	−	0.126139i	−0.108405	−	0.994107i	$-0.534574\pi$
$587$	9.40571	−	3.05610i	0.388215	−	0.126139i	0.496620	+	0.867968i	$0.334574\pi$
$588$	3.82303	+	5.26196i	0.157659	+	0.216999i
$589$	17.9611	−	13.0495i	0.740073	−	0.537694i
$590$	−8.03115	+	10.5206i	−0.330637	+	0.433126i
$591$	−3.58356	+	11.0291i	−0.147408	+	0.453675i
$592$	1.23880	−	1.70506i	0.0509142	−	0.0700773i
$593$			20.5782i			0.845047i	0.906352	+	0.422523i	$0.138856\pi$
$593$			20.5782i			0.845047i	−0.906352	+	0.422523i	$0.861144\pi$
$594$	−0.344181	+	2.57779i	−0.0141219	+	0.105768i
$595$	−4.73708	+	3.27312i	−0.194201	+	0.134185i
$596$	−12.3431	−	8.96776i	−0.505591	−	0.367334i
$597$	13.7150	+	4.45626i	0.561316	+	0.182383i
$598$	2.67412	−	0.868876i	0.109353	−	0.0355310i
$599$	16.5591	−	12.0309i	0.676588	−	0.491570i	−0.195636	−	0.980677i	$-0.562677\pi$
$599$	16.5591	−	12.0309i	0.676588	−	0.491570i	0.872224	+	0.489107i	$0.162677\pi$
$600$	3.49890	+	12.8024i	0.142842	+	0.522658i
$601$	2.50993	+	7.72476i	0.102382	+	0.315100i	0.989107	−	0.147198i	$-0.0470253\pi$
$601$	2.50993	+	7.72476i	0.102382	+	0.315100i	−0.886725	+	0.462297i	$0.847025\pi$
$602$	13.6826	+	4.44573i	0.557659	+	0.181195i
$603$	4.05548	−	5.58189i	0.165152	−	0.227312i
$604$	−5.98658			−0.243591
$605$	−13.9555	+	20.2545i	−0.567373	+	0.823461i
$606$	−2.05764			−0.0835857
$607$	−10.6834	+	14.7044i	−0.433625	+	0.596834i	−0.968781	−	0.247920i	$-0.920253\pi$
$607$	−10.6834	+	14.7044i	−0.433625	+	0.596834i	0.535155	+	0.844754i	$0.320253\pi$
$608$	−31.2043	−	10.1389i	−1.26550	−	0.411186i
$609$	1.24827	+	3.84177i	0.0505823	+	0.155676i
$610$	−18.3916	−	6.46126i	−0.744654	−	0.261609i
$611$	−0.965448	+	0.701439i	−0.0390579	+	0.0283772i
$612$	2.23462	−	0.726072i	0.0903291	−	0.0293497i
$613$	28.7972	+	9.35677i	1.16311	+	0.377916i	0.826066	−	0.563573i	$-0.190574\pi$
$613$	28.7972	+	9.35677i	1.16311	+	0.377916i	0.337041	+	0.941490i	$0.390574\pi$
$614$	−19.0023	−	13.8060i	−0.766869	−	0.557163i
$615$	−1.71639	−	2.48407i	−0.0692113	−	0.100167i
$616$	1.76863	−	13.2464i	0.0712601	−	0.533713i
$617$			29.0856i			1.17094i	0.810694	+	0.585471i	$0.199090\pi$
$617$			29.0856i			1.17094i	−0.810694	+	0.585471i	$0.800910\pi$
$618$	−0.00833338	+	0.0114699i	−0.000335218	+	0.000461387i
$619$	−4.55168	+	14.0086i	−0.182948	+	0.563055i	−0.999907	−	0.0136403i	$-0.995658\pi$
$619$	−4.55168	+	14.0086i	−0.182948	+	0.563055i	0.816959	+	0.576695i	$0.195658\pi$
$620$	−9.74359	−	7.43800i	−0.391312	−	0.298717i
$621$	6.21844	−	4.51796i	0.249537	−	0.181299i
$622$	−2.35530	−	3.24180i	−0.0944391	−	0.129984i
$623$	−2.13615	+	0.694076i	−0.0855829	+	0.0278076i
$624$	0.0993098	−	0.305644i	0.00397557	−	0.0122356i
$625$	5.44135	+	24.4006i	0.217654	+	0.976026i
$626$	19.6900			0.786969
$627$	−13.4720	−	12.8314i	−0.538018	−	0.512438i
$628$			1.29024i			0.0514863i
$629$	4.19852	+	3.05040i	0.167406	+	0.121627i
$630$	−0.762302	−	2.55013i	−0.0303708	−	0.101600i
$631$	3.05624	+	9.40615i	0.121667	+	0.374453i	0.993279	−	0.115744i	$-0.0369251\pi$
$631$	3.05624	+	9.40615i	0.121667	+	0.374453i	−0.871612	+	0.490196i	$0.836925\pi$
$632$	19.0048	+	26.1579i	0.755972	+	1.04051i
$633$	−1.92033	−	2.64311i	−0.0763262	−	0.105054i
$634$	3.00923	+	9.26144i	0.119512	+	0.367819i
$635$	38.8502	−	11.6134i	1.54172	−	0.460862i
$636$	−8.98398	−	6.52724i	−0.356238	−	0.258822i
$637$			2.19058i			0.0867940i
$638$	−2.99079	+	6.24086i	−0.118407	+	0.247078i
$639$	−14.5878			−0.577086
$640$	−0.486290	+	20.5258i	−0.0192223	+	0.811352i
$641$	13.6718	−	42.0775i	0.540004	−	1.66196i	−0.192576	−	0.981282i	$-0.561684\pi$
$641$	13.6718	−	42.0775i	0.540004	−	1.66196i	0.732581	−	0.680680i	$-0.238316\pi$
$642$	−10.9611	+	3.56148i	−0.432600	+	0.140560i
$643$	0.749447	+	1.03153i	0.0295553	+	0.0406794i	0.823539	−	0.567260i	$-0.191996\pi$
$643$	0.749447	+	1.03153i	0.0295553	+	0.0406794i	−0.793984	+	0.607939i	$0.791996\pi$
$644$	−13.0752	+	9.49968i	−0.515235	+	0.374340i
$645$	−21.4822	−	16.3990i	−0.845861	−	0.645709i
$646$	2.30571	−	7.09624i	0.0907168	−	0.279198i
$647$	−25.3307	+	34.8647i	−0.995851	+	1.37067i	−0.0680139	+	0.997684i	$0.521666\pi$
$647$	−25.3307	+	34.8647i	−0.995851	+	1.37067i	−0.927837	+	0.372986i	$0.878334\pi$
$648$			2.65439i			0.104274i
$649$	−24.6253	+	4.51735i	−0.966626	+	0.177322i
$650$	−0.646946	+	1.71080i	−0.0253753	+	0.0671030i
$651$	4.86045	+	3.53133i	0.190496	+	0.138404i
$652$	22.3400	+	7.25871i	0.874902	+	0.284273i
$653$	18.3459	−	5.96094i	0.717930	−	0.233270i	0.0728045	−	0.997346i	$-0.476805\pi$
$653$	18.3459	−	5.96094i	0.717930	−	0.233270i	0.645125	+	0.764077i	$0.276805\pi$
$654$	−3.37355	+	2.45103i	−0.131916	+	0.0958429i
$655$	−6.42720	+	18.2946i	−0.251131	+	0.714831i
$656$	−0.287448	−	0.884675i	−0.0112230	−	0.0345408i
$657$	2.15628	+	0.700618i	0.0841245	+	0.0273337i
$658$	−1.78974	+	2.46336i	−0.0697712	+	0.0960319i
$659$	−33.4717			−1.30387			−0.651937	−	0.758273i	$-0.726043\pi$
$659$	−33.4717			−1.30387			−0.651937	+	0.758273i	$0.726043\pi$
$660$	−4.65756	+	9.15590i	−0.181295	+	0.356393i
$661$	−6.94932			−0.270297			−0.135149	−	0.990825i	$-0.543151\pi$
$661$	−6.94932			−0.270297			−0.135149	+	0.990825i	$0.543151\pi$
$662$	3.85098	−	5.30042i	0.149673	−	0.206007i
$663$	0.752616	+	0.244540i	0.0292292	+	0.00949714i
$664$	−9.66323	−	29.7404i	−0.375006	−	1.15415i
$665$	17.9645	+	6.31122i	0.696634	+	0.244739i
$666$	−1.94080	+	1.41007i	−0.0752044	+	0.0546392i
$667$	19.4528	−	6.32059i	0.753215	−	0.244734i
$668$	−3.29406	−	1.07030i	−0.127451	−	0.0414113i
$669$	14.6662	+	10.6556i	0.567028	+	0.411970i
$670$	−9.95279	+	6.87695i	−0.384510	+	0.265680i
$671$	−17.5351	−	32.4372i	−0.676934	−	1.25222i
$672$		−	8.87876i		−	0.342506i
$673$	12.8460	−	17.6810i	0.495177	−	0.681553i	−0.486155	−	0.873873i	$-0.661601\pi$
$673$	12.8460	−	17.6810i	0.495177	−	0.681553i	0.981332	+	0.192319i	$0.0616010\pi$
$674$	0.953148	−	2.93349i	0.0367139	−	0.112994i
$675$	−0.236784	+	4.99439i	−0.00911382	+	0.192234i
$676$	−14.3239	+	10.4069i	−0.550920	+	0.400267i
$677$	−0.739757	−	1.01819i	−0.0284312	−	0.0391322i	0.794565	−	0.607179i	$-0.207699\pi$
$677$	−0.739757	−	1.01819i	−0.0284312	−	0.0391322i	−0.822996	+	0.568047i	$0.807699\pi$
$678$	7.14200	−	2.32058i	0.274287	−	0.0891211i
$679$	6.66179	−	20.5029i	0.255656	−	0.786828i
$680$	−10.0654	−	0.238467i	−0.385992	−	0.00914479i
$681$	−28.1483			−1.07865
$682$	1.85715	+	10.1238i	0.0711139	+	0.387660i
$683$		−	19.8677i		−	0.760215i	−0.924942	−	0.380108i	$-0.875887\pi$
$683$		−	19.8677i		−	0.760215i	0.924942	−	0.380108i	$-0.124113\pi$
$684$	−6.28608	−	4.56710i	−0.240354	−	0.174628i
$685$	−3.34377	+	0.999541i	−0.127759	+	0.0381905i
$686$	4.30199	+	13.2402i	0.164251	+	0.505512i
$687$	10.7926	+	14.8547i	0.411762	+	0.566741i
$688$	−4.89400	−	6.73601i	−0.186582	−	0.256808i
$689$	−1.15575	−	3.55703i	−0.0440305	−	0.135512i
$690$	−12.9126	+	3.85991i	−0.491573	+	0.146944i
$691$	−6.01690	−	4.37154i	−0.228894	−	0.166301i	0.467427	−	0.884032i	$-0.345181\pi$
$691$	−6.01690	−	4.37154i	−0.228894	−	0.166301i	−0.696321	+	0.717730i	$0.745181\pi$
$692$			7.78108i			0.295792i
$693$	2.17580	−	4.54023i	0.0826518	−	0.172469i
$694$	7.21347			0.273820
$695$	31.9407	+	0.756728i	1.21158	+	0.0287043i
$696$	−2.18273	+	6.71774i	−0.0827360	+	0.254635i
$697$	2.17842	−	0.707811i	0.0825135	−	0.0268103i
$698$	−9.30796	−	12.8113i	−0.352312	−	0.484915i
$699$	7.31279	−	5.31305i	0.276595	−	0.200958i
$700$	0.497873	−	10.5014i	0.0188178	−	0.396917i
$701$	−8.95068	+	27.5474i	−0.338063	+	1.04045i	0.627131	+	0.778914i	$0.284229\pi$
$701$	−8.95068	+	27.5474i	−0.338063	+	1.04045i	−0.965194	+	0.261536i	$0.915771\pi$
$702$	−0.215016	+	0.295944i	−0.00811525	+	0.0111697i
$703$		−	17.1618i		−	0.647270i
$704$	7.33938	−	7.70575i	0.276613	−	0.290421i
$705$	4.70588	−	3.25156i	0.177234	−	0.122461i
$706$	22.1118	+	16.0652i	0.832190	+	0.604622i
$707$	3.78843	+	1.23094i	0.142479	+	0.0462941i
$708$	−9.94422	+	3.23107i	−0.373727	+	0.121431i
$709$	−21.5378	+	15.6481i	−0.808870	+	0.587678i	−0.913503	−	0.406833i	$-0.866633\pi$
$709$	−21.5378	+	15.6481i	−0.808870	+	0.587678i	0.104633	+	0.994511i	$0.466633\pi$
$710$	24.1320	+	8.47795i	0.905657	+	0.318172i
$711$	3.76411	+	11.5847i	0.141165	+	0.434462i
$712$	−3.73527	−	1.21366i	−0.139985	−	0.0454840i
$713$	17.8808	−	24.6109i	0.669643	−	0.921684i
$714$	2.01914			0.0755644
$715$	−3.08162	+	1.57273i	−0.115246	+	0.0588166i
$716$	11.0382			0.412518
$717$	−7.00861	+	9.64652i	−0.261741	+	0.360256i
$718$	−21.2014	−	6.88875i	−0.791229	−	0.257086i
$719$	−3.89316	−	11.9819i	−0.145190	−	0.446850i	0.851845	−	0.523794i	$-0.175484\pi$
$719$	−3.89316	−	11.9819i	−0.145190	−	0.446850i	−0.997035	+	0.0769437i	$0.975484\pi$
$720$	−0.510573	+	1.45332i	−0.0190279	+	0.0541619i
$721$	0.0222047	−	0.0161327i	0.000826946	−	0.000600811i
$722$	−9.29743	+	3.02092i	−0.346015	+	0.112427i
$723$	−24.1716	−	7.85381i	−0.898950	−	0.292086i
$724$	19.4393	+	14.1235i	0.722456	+	0.524895i
$725$	−4.70618	+	12.4451i	−0.174783	+	0.462199i
$726$	8.06382	−	3.06154i	0.299276	−	0.113625i
$727$			15.2116i			0.564169i	0.959390	+	0.282084i	$0.0910258\pi$
$727$			15.2116i			0.564169i	−0.959390	+	0.282084i	$0.908974\pi$
$728$	1.10489	−	1.52075i	0.0409501	−	0.0563629i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−3.15986	−	2.41215i	−0.116952	−	0.0892778i
$731$	16.5867	−	12.0510i	0.613482	−	0.445721i
$732$	−9.05168	−	12.4586i	−0.334560	−	0.460482i
$733$	−29.0602	+	9.44222i	−1.07336	+	0.348756i	−0.791796	−	0.610786i	$-0.790854\pi$
$733$	−29.0602	+	9.44222i	−1.07336	+	0.348756i	−0.281566	+	0.959542i	$0.590854\pi$
$734$	−6.43996	+	19.8201i	−0.237703	+	0.731575i
$735$	0.248688	−	10.4969i	0.00917301	−	0.387183i
$736$	−44.9575			−1.65716
$737$	−22.6821	−	3.02846i	−0.835505	−	0.111555i
$738$			1.05881i			0.0389755i
$739$	7.08598	+	5.14827i	0.260662	+	0.189382i	0.710439	−	0.703759i	$-0.248496\pi$
$739$	7.08598	+	5.14827i	0.260662	+	0.189382i	−0.449777	+	0.893141i	$0.648496\pi$
$740$	−9.07877	+	2.71389i	−0.333742	+	0.0997646i
$741$	−0.808675	−	2.48885i	−0.0297074	−	0.0914301i
$742$	−5.60917	−	7.72036i	−0.205919	−	0.283423i
$743$	−17.8143	−	24.5193i	−0.653544	−	0.899526i	0.345703	−	0.938344i	$-0.387641\pi$
$743$	−17.8143	−	24.5193i	−0.653544	−	0.899526i	−0.999246	+	0.0388185i	$0.987641\pi$
$744$	3.24633	+	9.99119i	0.119016	+	0.366295i
$745$	7.05402	+	23.5978i	0.258439	+	0.864557i
$746$	12.1737	+	8.84469i	0.445710	+	0.323827i
$747$		−	11.7808i		−	0.431037i
$748$	−5.64286	−	5.37456i	−0.206323	−	0.196513i
$749$	22.3117			0.815251
$750$	3.29427	−	8.12438i	0.120290	−	0.296660i
$751$	0.385194	−	1.18551i	0.0140559	−	0.0432597i	−0.943783	−	0.330567i	$-0.892760\pi$
$751$	0.385194	−	1.18551i	0.0140559	−	0.0432597i	0.957838	+	0.287307i	$0.0927601\pi$
$752$	1.67595	−	0.544549i	0.0611156	−	0.0198577i
$753$	−8.69810	−	11.9719i	−0.316976	−	0.436281i
$754$	−0.787519	+	0.572166i	−0.0286797	+	0.0208371i
$755$	7.68185	+	5.86413i	0.279571	+	0.213417i
$756$	0.649754	−	1.99974i	0.0236313	−	0.0727298i
$757$	8.19150	−	11.2746i	0.297725	−	0.409784i	−0.633779	−	0.773514i	$-0.718497\pi$
$757$	8.19150	−	11.2746i	0.297725	−	0.409784i	0.931504	+	0.363731i	$0.118497\pi$
$758$			2.38446i			0.0866075i
$759$	−22.9894	−	11.0172i	−0.834462	−	0.399897i
$760$	18.9268	+	27.3922i	0.686548	+	0.993619i
$761$	2.56066	+	1.86043i	0.0928238	+	0.0674404i	0.633229	−	0.773964i	$-0.281729\pi$
$761$	2.56066	+	1.86043i	0.0928238	+	0.0674404i	−0.540405	+	0.841405i	$0.681729\pi$
$762$	−13.5235	−	4.39404i	−0.489904	−	0.159179i
$763$	7.67752	−	2.49458i	0.277945	−	0.0903098i
$764$	24.8631	−	18.0641i	0.899514	−	0.653535i
$765$	−3.57864	−	1.25723i	−0.129386	−	0.0454553i
$766$	2.10651	+	6.48317i	0.0761113	+	0.234246i
$767$	−3.34920	−	1.08822i	−0.120932	−	0.0392933i
$768$	8.00389	−	11.0164i	0.288816	−	0.397521i
$769$	−1.39451			−0.0502874			−0.0251437	−	0.999684i	$-0.508004\pi$
$769$	−1.39451			−0.0502874			−0.0251437	+	0.999684i	$0.508004\pi$
$770$	−6.23795	+	6.24619i	−0.224800	+	0.225097i
$771$	−8.16954			−0.294219
$772$	21.4087	−	29.4666i	0.770517	−	1.06053i
$773$	3.17352	+	1.03114i	0.114144	+	0.0370875i	0.365532	−	0.930799i	$-0.380887\pi$
$773$	3.17352	+	1.03114i	0.114144	+	0.0370875i	−0.251388	+	0.967886i	$0.580887\pi$
$774$	2.92867	+	9.01351i	0.105269	+	0.323984i
$775$	5.21690	+	19.0886i	0.187397	+	0.685682i
$776$	30.4970	−	22.1574i	1.09478	−	0.795404i
$777$	4.41686	−	1.43513i	0.158454	−	0.0514849i
$778$	10.2108	+	3.31768i	0.366074	+	0.118945i
$779$	−6.12798	−	4.45224i	−0.219558	−	0.159518i
$780$	−1.18875	+	0.821372i	−0.0425639	+	0.0294098i
$781$	23.0081	+	42.5615i	0.823295	+	1.52297i
$782$		−	10.2239i		−	0.365606i
$783$	−1.56412	+	2.15283i	−0.0558971	+	0.0769358i
$784$	0.999598	−	3.07645i	0.0356999	−	0.109873i
$785$	1.26385	−	1.65561i	0.0451088	−	0.0590914i
$786$	5.50119	−	3.99685i	0.196221	−	0.142563i
$787$	9.25726	+	12.7415i	0.329986	+	0.454186i	0.941483	−	0.337060i	$-0.109433\pi$
$787$	9.25726	+	12.7415i	0.329986	+	0.454186i	−0.611497	+	0.791246i	$0.709433\pi$
$788$	15.2768	−	4.96373i	0.544213	−	0.176825i
$789$	−2.98560	+	9.18874i	−0.106290	+	0.327128i
$790$	0.505857	−	21.3517i	0.0179976	−	0.759659i
$791$	−14.5378			−0.516904
$792$	7.74446	−	4.18654i	0.275187	−	0.148762i
$793$		−	5.18657i		−	0.184181i
$794$	5.68554	+	4.13078i	0.201772	+	0.146596i
$795$	5.13432	+	17.1758i	0.182095	+	0.609164i
$796$	−6.17254	−	18.9971i	−0.218780	−	0.673335i
$797$	14.7552	+	20.3087i	0.522655	+	0.719372i	0.985989	−	0.166811i	$-0.0533470\pi$
$797$	14.7552	+	20.3087i	0.522655	+	0.719372i	−0.463334	+	0.886184i	$0.653347\pi$
$798$	−3.92473	−	5.40193i	−0.138934	−	0.191226i
$799$	1.34090	+	4.12685i	0.0474375	+	0.145998i
$800$	18.2908	−	22.8190i	0.646678	−	0.806772i
$801$	−1.19704	−	0.869701i	−0.0422953	−	0.0307294i
$802$			5.79964i			0.204793i
$803$	−1.35678	−	7.39619i	−0.0478799	−	0.261006i
$804$	−9.55689			−0.337045
$805$	26.0832	+	0.617954i	0.919311	+	0.0217800i
$806$	−0.447383	+	1.37690i	−0.0157584	+	0.0484994i
$807$	−0.361282	+	0.117388i	−0.0127177	+	0.00413224i
$808$	4.09415	+	5.63511i	0.144032	+	0.198243i
$809$	38.4421	−	27.9298i	1.35155	−	0.981960i	0.352620	−	0.935767i	$-0.385291\pi$
$809$	38.4421	−	27.9298i	1.35155	−	0.981960i	0.998933	−	0.0461934i	$-0.0147090\pi$
$810$	1.06391	−	1.39370i	0.0373821	−	0.0489696i
$811$	2.03052	−	6.24930i	0.0713013	−	0.219443i	−0.909056	−	0.416675i	$-0.863195\pi$
$811$	2.03052	−	6.24930i	0.0713013	−	0.219443i	0.980357	+	0.197232i	$0.0631953\pi$
$812$	3.28880	−	4.52664i	0.115414	−	0.158854i
$813$			8.96837i			0.314535i
$814$	7.17508	+	3.43850i	0.251487	+	0.120519i
$815$	−21.5560	−	31.1973i	−0.755073	−	1.09279i
$816$	−0.945384	−	0.686862i	−0.0330951	−	0.0240450i
$817$	−64.4813	−	20.9513i	−2.25592	−	0.732992i
$818$	−20.8106	+	6.76176i	−0.727625	+	0.236420i
$819$	0.572920	−	0.416251i	0.0200195	−	0.0145450i
$820$	−1.38623	+	3.94582i	−0.0484092	+	0.137794i
$821$	−5.04009	−	15.5118i	−0.175900	−	0.541365i	0.823773	−	0.566920i	$-0.191865\pi$
$821$	−5.04009	−	15.5118i	−0.175900	−	0.541365i	−0.999673	+	0.0255541i	$0.991865\pi$
$822$	1.16394	+	0.378187i	0.0405971	+	0.0131908i
$823$	17.4998	−	24.0864i	0.610004	−	0.839599i	−0.386574	−	0.922259i	$-0.626342\pi$
$823$	17.4998	−	24.0864i	0.610004	−	0.839599i	0.996578	+	0.0826599i	$0.0263415\pi$
$824$	0.0479931			0.00167192
$825$	14.9451	−	7.18637i	0.520322	−	0.250197i
$826$	−8.98532			−0.312639
$827$	10.0515	−	13.8347i	0.349524	−	0.481078i	−0.597669	−	0.801743i	$-0.703906\pi$
$827$	10.0515	−	13.8347i	0.349524	−	0.481078i	0.947193	+	0.320665i	$0.103906\pi$
$828$	−10.1257	−	3.29002i	−0.351891	−	0.114336i
$829$	−11.8730	−	36.5413i	−0.412366	−	1.26913i	−0.914585	−	0.404393i	$-0.867483\pi$
$829$	−11.8730	−	36.5413i	−0.412366	−	1.26913i	0.502219	−	0.864740i	$-0.332517\pi$
$830$	−6.84659	+	19.4884i	−0.237649	+	0.676453i
$831$	2.73375	−	1.98618i	0.0948326	−	0.0689000i
$832$	1.42358	−	0.462550i	0.0493538	−	0.0160360i
$833$	7.57542	+	2.46140i	0.262473	+	0.0852826i
$834$	−9.06415	−	6.58549i	−0.313866	−	0.228037i
$835$	3.17845	+	4.60007i	0.109995	+	0.159192i
$836$	−3.41051	+	25.5436i	−0.117955	+	0.883442i
$837$			3.95772i			0.136799i
$838$	11.7192	−	16.1301i	0.404832	−	0.557204i
$839$	−12.2300	+	37.6401i	−0.422227	+	1.29948i	0.483397	+	0.875401i	$0.339403\pi$
$839$	−12.2300	+	37.6401i	−0.422227	+	1.29948i	−0.905624	+	0.424081i	$0.860597\pi$
$840$	−5.46709	+	7.16174i	−0.188633	+	0.247104i
$841$	17.7327	−	12.8836i	0.611473	−	0.444261i
$842$	1.54660	+	2.12871i	0.0532994	+	0.0733603i
$843$	−4.82709	+	1.56842i	−0.166254	+	0.0540191i
$844$	−1.39840	+	4.30384i	−0.0481350	+	0.148144i
$845$	28.5742	+	0.676971i	0.982983	+	0.0232885i
$846$	−2.00584			−0.0689623
$847$	−16.6783	+	0.812776i	−0.573072	+	0.0279273i
$848$			5.52287i			0.189656i
$849$	18.0395	+	13.1065i	0.619114	+	0.449813i
$850$	5.18931	+	4.15956i	0.177992	+	0.142672i
$851$	−7.26675	−	22.3648i	−0.249101	−	0.766654i
$852$	11.8769	+	16.3471i	0.406896	+	0.560044i
$853$	−25.5412	−	35.1544i	−0.874513	−	1.20366i	−0.977911	−	0.209024i	$-0.932971\pi$
$853$	−25.5412	−	35.1544i	−0.874513	−	1.20366i	0.103397	−	0.994640i	$-0.467029\pi$
$854$	−4.08942	−	12.5860i	−0.139937	−	0.430682i
$855$	3.59247	+	12.0179i	0.122860	+	0.411004i
$856$	31.5632	+	22.9320i	1.07881	+	0.783801i
$857$			22.0266i			0.752415i	0.926536	+	0.376207i	$0.122772\pi$
$857$			22.0266i			0.752415i	−0.926536	+	0.376207i	$0.877228\pi$
$858$	1.20257	+	0.160565i	0.0410551	+	0.00548158i
$859$	42.4022			1.44675			0.723373	−	0.690458i	$-0.242591\pi$
$859$	42.4022			1.44675			0.723373	+	0.690458i	$0.242591\pi$
$860$	−0.886647	+	37.4244i	−0.0302344	+	1.27616i
$861$	0.633413	−	1.94944i	0.0215866	−	0.0664369i
$862$	−7.73841	+	2.51436i	−0.263571	+	0.0856395i
$863$	4.72668	+	6.50571i	0.160898	+	0.221457i	0.881853	−	0.471525i	$-0.156296\pi$
$863$	4.72668	+	6.50571i	0.160898	+	0.221457i	−0.720955	+	0.692982i	$0.756296\pi$
$864$	4.73191	−	3.43793i	0.160983	−	0.116961i
$865$	7.62192	−	9.98451i	0.259153	−	0.339484i
$866$	6.58276	−	20.2596i	0.223691	−	0.688451i
$867$	−8.30102	+	11.4254i	−0.281918	+	0.388026i
$868$		−	8.32170i		−	0.282457i
$869$	27.8629	−	29.2538i	0.945183	−	0.992366i
$870$	3.83860	−	2.65231i	0.130141	−	0.0899217i
$871$	−2.60402	−	1.89193i	−0.0882338	−	0.0641056i
$872$	13.4250	+	4.36203i	0.454626	+	0.147717i
$873$	13.5064	−	4.38851i	0.457124	−	0.148529i
$874$	−27.3526	+	19.8728i	−0.925216	+	0.672209i
$875$	−10.9255	+	12.9875i	−0.369349	+	0.439059i
$876$	−0.970452	−	2.98674i	−0.0327885	−	0.100913i
$877$	54.6399	+	17.7536i	1.84506	+	0.599496i	0.997647	+	0.0685570i	$0.0218395\pi$
$877$	54.6399	+	17.7536i	1.84506	+	0.599496i	0.847410	+	0.530939i	$0.178161\pi$
$878$	14.0936	−	19.3982i	0.475637	−	0.654658i
$879$	16.2166			0.546971
$880$	5.04548	−	0.802538i	0.170083	−	0.0270536i
$881$	−49.5171			−1.66827			−0.834137	−	0.551557i	$-0.814034\pi$
$881$	−49.5171			−1.66827			−0.834137	+	0.551557i	$0.814034\pi$
$882$	−2.16423	+	2.97881i	−0.0728735	+	0.100302i
$883$	−24.8174	−	8.06367i	−0.835173	−	0.271364i	−0.139950	−	0.990159i	$-0.544694\pi$
$883$	−24.8174	−	8.06367i	−0.835173	−	0.271364i	−0.695223	+	0.718794i	$0.744694\pi$
$884$	−0.338721	−	1.04248i	−0.0113924	−	0.0350623i
$885$	15.9252	+	5.59477i	0.535320	+	0.188066i
$886$	−2.59137	+	1.88274i	−0.0870588	+	0.0632519i
$887$	−10.0166	+	3.25459i	−0.336324	+	0.109278i	−0.472310	−	0.881432i	$-0.656580\pi$
$887$	−10.0166	+	3.25459i	−0.336324	+	0.109278i	0.135986	+	0.990711i	$0.456580\pi$
$888$	7.72335	+	2.50947i	0.259179	+	0.0842122i
$889$	22.2702	+	16.1803i	0.746919	+	0.542668i
$890$	1.47477	+	2.13438i	0.0494343	+	0.0715447i
$891$	3.26219	−	0.598429i	0.109287	−	0.0200481i
$892$		−	25.1104i		−	0.840757i
$893$	8.43443	−	11.6090i	0.282248	−	0.388480i
$894$	2.66897	−	8.21423i	0.0892636	−	0.274725i
$895$	−14.1640	−	10.8124i	−0.473450	−	0.361420i
$896$	−11.2763	+	8.19272i	−0.376715	+	0.273700i
$897$	−2.10768	−	2.90098i	−0.0703735	−	0.0968608i
$898$	15.1411	−	4.91965i	0.505266	−	0.164171i
$899$	−3.25447	+	10.0162i	−0.108542	+	0.334059i
$900$	5.78950	−	3.80091i	0.192983	−	0.126697i
$901$	−13.5995			−0.453064
$902$	3.08920	−	1.66997i	0.102859	−	0.0556040i
$903$		−	18.3473i		−	0.610560i
$904$	−20.5659	−	14.9420i	−0.684011	−	0.496963i
$905$	−11.1095	−	37.1646i	−0.369293	−	1.23539i
$906$	−1.04727	−	3.22315i	−0.0347931	−	0.107082i
$907$	−8.79742	−	12.1086i	−0.292114	−	0.402060i	0.637586	−	0.770379i	$-0.279933\pi$
$907$	−8.79742	−	12.1086i	−0.292114	−	0.402060i	−0.929699	+	0.368320i	$0.879933\pi$
$908$	22.9174	+	31.5430i	0.760539	+	1.04679i
$909$	0.810890	+	2.49566i	0.0268955	+	0.0827760i
$910$	−1.18967	+	0.355623i	−0.0394370	+	0.0117888i
$911$	−1.62459	−	1.18034i	−0.0538252	−	0.0391063i	0.560547	−	0.828122i	$-0.310591\pi$
$911$	−1.62459	−	1.18034i	−0.0538252	−	0.0391063i	−0.614373	+	0.789016i	$0.710591\pi$
$912$			3.86434i			0.127961i
$913$	−34.3717	+	18.5808i	−1.13754	+	0.614935i
$914$	20.2417			0.669535
$915$	−0.588812	+	24.8531i	−0.0194655	+	0.821618i
$916$	7.85925	−	24.1883i	0.259677	−	0.799203i
$917$	−12.5196	+	4.06787i	−0.413434	+	0.134333i
$918$	0.781829	+	1.07609i	0.0258042	+	0.0355164i
$919$	−13.5903	+	9.87393i	−0.448303	+	0.325711i	−0.788925	−	0.614489i	$-0.789362\pi$
$919$	−13.5903	+	9.87393i	−0.448303	+	0.325711i	0.340623	+	0.940200i	$0.389362\pi$
$920$	36.2634	+	27.6826i	1.19557	+	0.912667i
$921$	−9.25638	+	28.4882i	−0.305008	+	0.938719i
$922$	1.17080	−	1.61146i	0.0385581	−	0.0530707i
$923$			6.80541i			0.224003i
$924$	−6.85924	+	1.25829i	−0.225652	+	0.0413945i
$925$	14.3081	+	5.41067i	0.470446	+	0.177902i
$926$	1.82445	+	1.32554i	0.0599551	+	0.0435600i
$927$	0.0171957	+	0.00558722i	0.000564781	+	0.000183508i
$928$	14.8026	−	4.80964i	0.485918	−	0.157884i
$929$	27.4390	−	19.9356i	0.900246	−	0.654067i	−0.0382835	−	0.999267i	$-0.512189\pi$
$929$	27.4390	−	19.9356i	0.900246	−	0.654067i	0.938529	+	0.345200i	$0.112189\pi$
$930$	2.30009	−	6.54708i	0.0754230	−	0.214687i
$931$	−8.13969	−	25.0514i	−0.266767	−	0.821026i
$932$	−11.9076	−	3.86902i	−0.390047	−	0.126734i
$933$	−3.00371	+	4.13425i	−0.0983371	+	0.135349i
$934$	−17.9037			−0.585828
$935$	1.97617	+	12.4240i	0.0646275	+	0.406307i
$936$	1.23831			0.0404753
$937$	−12.0742	+	16.6188i	−0.394448	+	0.542911i	−0.959340	−	0.282254i	$-0.908918\pi$
$937$	−12.0742	+	16.6188i	−0.394448	+	0.542911i	0.564892	+	0.825165i	$0.308918\pi$
$938$	−7.81074	−	2.53786i	−0.255030	−	0.0828641i
$939$	−7.75958	−	23.8815i	−0.253224	−	0.779345i
$940$	−7.47506	−	2.62611i	−0.243810	−	0.0856542i
$941$	−42.7681	+	31.0728i	−1.39420	+	1.01295i	−0.398810	+	0.917034i	$0.630577\pi$
$941$	−42.7681	+	31.0728i	−1.39420	+	1.01295i	−0.995390	+	0.0959115i	$0.969423\pi$
$942$	−0.694662	+	0.225709i	−0.0226333	+	0.00735401i
$943$	−9.87099	−	3.20728i	−0.321444	−	0.104443i
$944$	4.20703	+	3.05659i	0.136927	+	0.0994834i
$945$	−2.79258	+	1.92956i	−0.0908428	+	0.0627685i
$946$	21.6787	−	22.7609i	0.704835	−	0.740020i
$947$		−	28.1947i		−	0.916206i	−0.888899	−	0.458103i	$-0.848529\pi$
$947$		−	28.1947i		−	0.916206i	0.888899	−	0.458103i	$-0.151471\pi$
$948$	9.91727	−	13.6499i	0.322098	−	0.443330i
$949$	0.326847	−	1.00593i	0.0106099	−	0.0326539i
$950$	1.04153	−	21.9685i	0.0337915	−	0.712752i
$951$	10.0471	−	7.29966i	0.325800	−	0.236708i
$952$	−4.01755	−	5.52969i	−0.130210	−	0.179218i
$953$	10.4792	−	3.40489i	0.339453	−	0.110295i	−0.134330	−	0.990937i	$-0.542888\pi$
$953$	10.4792	−	3.40489i	0.339453	−	0.110295i	0.473783	+	0.880642i	$0.342888\pi$
$954$	1.94262	−	5.97878i	0.0628948	−	0.193570i
$955$	−49.5983	−	1.17507i	−1.60496	−	0.0380243i
$956$	16.5160			0.534167
$957$	8.74805	+	1.16802i	0.282784	+	0.0377567i
$958$			18.7458i			0.605649i
$959$	−1.91676	−	1.39261i	−0.0618953	−	0.0449696i
$960$	−6.87406	+	2.05484i	−0.221859	+	0.0663197i
$961$	−4.73921	−	14.5858i	−0.152878	−	0.470510i
$962$	0.657816	+	0.905406i	0.0212088	+	0.0291915i
$963$	8.63928	+	11.8909i	0.278397	+	0.383180i
$964$	10.8786	+	33.4809i	0.350377	+	1.07835i
$965$	−56.3351	+	16.8401i	−1.81349	+	0.542101i
$966$	−7.40191	−	5.37780i	−0.238152	−	0.173028i
$967$			49.0215i			1.57643i	0.615403	+	0.788213i	$0.288993\pi$
$967$			49.0215i			1.57643i	−0.615403	+	0.788213i	$0.711007\pi$
$968$	−24.4293	−	15.9922i	−0.785188	−	0.514009i
$969$	−9.51553			−0.305683
$970$	−24.8935	−	0.589770i	−0.799283	−	0.0189364i
$971$	0.315326	−	0.970472i	0.0101193	−	0.0311439i	−0.945869	−	0.324548i	$-0.894788\pi$
$971$	0.315326	−	0.970472i	0.0101193	−	0.0311439i	0.955989	+	0.293404i	$0.0947880\pi$
$972$	1.31734	−	0.428031i	0.0422539	−	0.0137291i
$973$	12.7489	+	17.5474i	0.408711	+	0.562543i
$974$	−8.66087	+	6.29249i	−0.277512	+	0.201624i
$975$	2.32994	+	0.110463i	0.0746179	+	0.00353763i
$976$	−2.36672	+	7.28401i	−0.0757568	+	0.233155i
$977$	28.4364	−	39.1393i	0.909760	−	1.25218i	−0.0574890	−	0.998346i	$-0.518309\pi$
$977$	28.4364	−	39.1393i	0.909760	−	1.25218i	0.967249	−	0.253831i	$-0.0816906\pi$
$978$			13.2976i			0.425210i
$979$	−0.649455	+	4.86419i	−0.0207567	+	0.155460i
$980$	−11.9653	+	8.26749i	−0.382216	+	0.264095i
$981$	4.30228	+	3.12579i	0.137361	+	0.0997988i
$982$	32.1587	+	10.4490i	1.02622	+	0.333440i
$983$	−58.5062	+	19.0098i	−1.86606	+	0.606319i	−0.873146	+	0.487460i	$0.837924\pi$
$983$	−58.5062	+	19.0098i	−1.86606	+	0.606319i	−0.992911	+	0.118859i	$0.962076\pi$
$984$	2.89970	−	2.10676i	0.0924392	−	0.0671610i
$985$	−24.4650	−	8.59495i	−0.779521	−	0.273858i
$986$	1.09377	+	3.36628i	0.0348328	+	0.107204i
$987$	3.69308	+	1.19995i	0.117552	+	0.0381949i
$988$	−2.13061	+	2.93253i	−0.0677837	+	0.0932962i
$989$	−92.9014			−2.95409
$990$	−5.74428	−	0.905919i	−0.182565	−	0.0287920i
$991$	31.0431			0.986117			0.493059	−	0.869996i	$-0.335879\pi$
$991$	31.0431			0.986117			0.493059	+	0.869996i	$0.335879\pi$
$992$	13.6064	−	18.7276i	0.432003	−	0.594602i
$993$	−7.94640	−	2.58194i	−0.252171	−	0.0819355i
$994$	5.36581	+	16.5143i	0.170193	+	0.523801i
$995$	−10.6881	+	30.4230i	−0.338835	+	0.964474i
$996$	−13.2016	+	9.59150i	−0.418308	+	0.303918i
$997$	−45.2735	+	14.7103i	−1.43383	+	0.465879i	−0.919967	−	0.391996i	$-0.871785\pi$
$997$	−45.2735	+	14.7103i	−1.43383	+	0.465879i	−0.513860	+	0.857874i	$0.671785\pi$
$998$	−8.90310	−	2.89279i	−0.281823	−	0.0915697i
$999$	2.47509	+	1.79826i	0.0783085	+	0.0568945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.4.8	yes	48
3.2	odd	2		495.2.ba.c.334.5		48
5.2	odd	4		825.2.n.o.301.5		24
5.3	odd	4		825.2.n.p.301.2		24
5.4	even	2	inner	165.2.s.a.4.5	✓	48
11.3	even	5	inner	165.2.s.a.124.5	yes	48
11.5	even	5		1815.2.c.j.364.16		24
11.6	odd	10		1815.2.c.k.364.9		24
15.14	odd	2		495.2.ba.c.334.8		48
33.14	odd	10		495.2.ba.c.289.8		48
55.3	odd	20		825.2.n.p.751.2		24
55.14	even	10	inner	165.2.s.a.124.8	yes	48
55.17	even	20		9075.2.a.dx.1.9		12
55.27	odd	20		9075.2.a.dz.1.4		12
55.28	even	20		9075.2.a.ea.1.4		12
55.38	odd	20		9075.2.a.dy.1.9		12
55.39	odd	10		1815.2.c.k.364.16		24
55.47	odd	20		825.2.n.o.751.5		24
55.49	even	10		1815.2.c.j.364.9		24
165.14	odd	10		495.2.ba.c.289.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.5	✓	48	5.4	even	2	inner
165.2.s.a.4.8	yes	48	1.1	even	1	trivial
165.2.s.a.124.5	yes	48	11.3	even	5	inner
165.2.s.a.124.8	yes	48	55.14	even	10	inner
495.2.ba.c.289.5		48	165.14	odd	10
495.2.ba.c.289.8		48	33.14	odd	10
495.2.ba.c.334.5		48	3.2	odd	2
495.2.ba.c.334.8		48	15.14	odd	2
825.2.n.o.301.5		24	5.2	odd	4
825.2.n.o.751.5		24	55.47	odd	20
825.2.n.p.301.2		24	5.3	odd	4
825.2.n.p.751.2		24	55.3	odd	20
1815.2.c.j.364.9		24	55.49	even	10
1815.2.c.j.364.16		24	11.5	even	5
1815.2.c.k.364.9		24	11.6	odd	10
1815.2.c.k.364.16		24	55.39	odd	10
9075.2.a.dx.1.9		12	55.17	even	20
9075.2.a.dy.1.9		12	55.38	odd	20
9075.2.a.dz.1.4		12	55.27	odd	20
9075.2.a.ea.1.4		12	55.28	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)

\(f(q)\)	\(=\)	\(q+(0.460901 - 0.634375i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.428031 + 1.31734i) q^{4} +(0.741158 - 2.10966i) q^{5} +(-0.634375 + 0.460901i) q^{6} +(1.44371 - 0.469090i) q^{7} +(2.52448 + 0.820252i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.460901 - 0.634375i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.428031 + 1.31734i) q^{4} +(0.741158 - 2.10966i) q^{5} +(-0.634375 + 0.460901i) q^{6} +(1.44371 - 0.469090i) q^{7} +(2.52448 + 0.820252i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.996719 - 1.44252i) q^{10} +(0.438933 - 3.28745i) q^{11} -1.38514i q^{12} +(0.274209 - 0.377416i) q^{13} +(0.367828 - 1.13206i) q^{14} +(-1.35681 + 1.77738i) q^{15} +(-0.557320 + 0.404916i) q^{16} +(-0.997064 - 1.37234i) q^{17} +(0.745753 - 0.242310i) q^{18} +(-1.73345 + 5.33501i) q^{19} +(3.09639 + 0.0733588i) q^{20} -1.51801 q^{21} +(-1.88317 - 1.79364i) q^{22} +7.68641i q^{23} +(-2.14745 - 1.56021i) q^{24} +(-3.90137 - 3.12719i) q^{25} +(-0.113040 - 0.347903i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.23591 + 1.70108i) q^{28} +(-0.822307 - 2.53080i) q^{29} +(0.502173 + 1.67992i) q^{30} +(-3.20187 - 2.32629i) q^{31} +5.84896i q^{32} +(-1.43333 + 2.99091i) q^{33} -1.33013 q^{34} +(0.0803957 - 3.39341i) q^{35} +(-0.428031 + 1.31734i) q^{36} +(-2.90965 + 0.945402i) q^{37} +(2.58545 + 3.55857i) q^{38} +(-0.377416 + 0.274209i) q^{39} +(3.60149 - 4.71786i) q^{40} +(-0.417266 + 1.28421i) q^{41} +(-0.699650 + 0.962986i) q^{42} +12.0864i q^{43} +(4.51858 - 0.828906i) q^{44} +(1.83964 - 1.27111i) q^{45} +(4.87607 + 3.54267i) q^{46} +(-2.43285 - 0.790480i) q^{47} +(0.655168 - 0.212877i) q^{48} +(-3.79887 + 2.76004i) q^{49} +(-3.78196 + 1.03361i) q^{50} +(0.524187 + 1.61328i) q^{51} +(0.614557 + 0.199682i) q^{52} +(4.71234 - 6.48598i) q^{53} -0.784131 q^{54} +(-6.61010 - 3.36252i) q^{55} +4.02938 q^{56} +(3.29722 - 4.53823i) q^{57} +(-1.98448 - 0.644797i) q^{58} +(-2.33267 - 7.17923i) q^{59} +(-2.92218 - 1.02661i) q^{60} +(8.99446 - 6.53486i) q^{61} +(-2.95149 + 0.958996i) q^{62} +(1.44371 + 0.469090i) q^{63} +(2.59580 + 1.88596i) q^{64} +(-0.592989 - 0.858214i) q^{65} +(1.23674 + 2.28778i) q^{66} -6.89959i q^{67} +(1.38107 - 1.90088i) q^{68} +(2.37523 - 7.31021i) q^{69} +(-2.11564 - 1.61503i) q^{70} +(-11.8018 + 8.57452i) q^{71} +(1.56021 + 2.14745i) q^{72} +(2.15628 - 0.700618i) q^{73} +(-0.741319 + 2.28155i) q^{74} +(2.74407 + 4.17972i) q^{75} -7.77002 q^{76} +(-0.908418 - 4.95202i) q^{77} +0.365807i q^{78} +(9.85457 + 7.15977i) q^{79} +(0.441176 + 1.47586i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.622355 + 0.856598i) q^{82} +(-6.92458 - 9.53087i) q^{83} +(-0.649754 - 1.99974i) q^{84} +(-3.63416 + 1.08635i) q^{85} +(7.66735 + 5.57065i) q^{86} +2.66104i q^{87} +(3.80462 - 7.93906i) q^{88} -1.47962 q^{89} +(0.0415286 - 1.75288i) q^{90} +(0.218836 - 0.673508i) q^{91} +(-10.1257 + 3.29002i) q^{92} +(2.32629 + 3.20187i) q^{93} +(-1.62276 + 1.17901i) q^{94} +(9.97032 + 7.61108i) q^{95} +(1.80743 - 5.56269i) q^{96} +(8.34744 - 11.4893i) q^{97} +3.68201i q^{98} +(2.28742 - 2.40161i) 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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