LMFDB - Embedded newform 966.2.j.a.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.1
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.70593 + 0.299664i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.915921 - 1.58642i) q^{5} +(1.32755 - 1.11248i) q^{6} +(1.74832 + 1.98579i) q^{7} +1.00000i q^{8} +(2.82040 - 1.02241i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70593 + 0.299664i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.915921 - 1.58642i) q^{5} +(1.32755 - 1.11248i) q^{6} +(1.74832 + 1.98579i) q^{7} +1.00000i q^{8} +(2.82040 - 1.02241i) q^{9} +(1.58642 + 0.915921i) q^{10} +(0.402421 - 0.697013i) q^{11} +(-0.593449 + 1.62721i) q^{12} -0.357435 q^{13} +(-2.50699 - 0.845586i) q^{14} +(2.03789 + 2.43186i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.02572 - 3.50866i) q^{17} +(-1.93133 + 2.29564i) q^{18} +(-4.35925 + 2.51681i) q^{19} -1.83184 q^{20} +(-3.57759 - 2.86372i) q^{21} +0.804842i q^{22} +(-4.54585 + 1.52815i) q^{23} +(-0.299664 - 1.70593i) q^{24} +(0.822177 - 1.42405i) q^{25} +(0.309548 - 0.178718i) q^{26} +(-4.50503 + 2.58934i) q^{27} +(2.59391 - 0.521194i) q^{28} +8.17926i q^{29} +(-2.98080 - 1.08711i) q^{30} +(1.44317 - 2.49965i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.477633 + 1.30965i) q^{33} +4.05145i q^{34} +(1.54898 - 4.59241i) q^{35} +(0.524767 - 2.95375i) q^{36} +(7.82094 - 4.51542i) q^{37} +(2.51681 - 4.35925i) q^{38} +(0.609760 - 0.107110i) q^{39} +(1.58642 - 0.915921i) q^{40} -4.77613i q^{41} +(4.53014 + 0.691258i) q^{42} -1.59064i q^{43} +(-0.402421 - 0.697013i) q^{44} +(-4.20524 - 3.53790i) q^{45} +(3.17275 - 3.59634i) q^{46} +(7.75220 - 4.47573i) q^{47} +(1.11248 + 1.32755i) q^{48} +(-0.886745 + 6.94361i) q^{49} +1.64435i q^{50} +(-2.40433 + 6.59256i) q^{51} +(-0.178718 + 0.309548i) q^{52} +(4.72870 - 8.19035i) q^{53} +(2.60680 - 4.49495i) q^{54} -1.47434 q^{55} +(-1.98579 + 1.74832i) q^{56} +(6.68238 - 5.59982i) q^{57} +(-4.08963 - 7.08344i) q^{58} +(-11.4528 - 6.61227i) q^{59} +(3.12500 - 0.548937i) q^{60} +(9.42234 - 5.43999i) q^{61} +2.88635i q^{62} +(6.96127 + 3.81323i) q^{63} -1.00000 q^{64} +(0.327382 + 0.567043i) q^{65} +(-0.241182 - 1.37300i) q^{66} +(9.94959 + 5.74440i) q^{67} +(-2.02572 - 3.50866i) q^{68} +(7.29698 - 3.96915i) q^{69} +(0.954746 + 4.75163i) q^{70} +3.72566i q^{71} +(1.02241 + 2.82040i) q^{72} +(2.04854 - 3.54818i) q^{73} +(-4.51542 + 7.82094i) q^{74} +(-0.975840 + 2.67571i) q^{75} +5.03363i q^{76} +(2.08769 - 0.419479i) q^{77} +(-0.474512 + 0.397640i) q^{78} +(8.99349 - 5.19239i) q^{79} +(-0.915921 + 1.58642i) q^{80} +(6.90935 - 5.76723i) q^{81} +(2.38807 + 4.13625i) q^{82} +11.7730 q^{83} +(-4.26884 + 1.66642i) q^{84} -7.42162 q^{85} +(0.795320 + 1.37753i) q^{86} +(-2.45103 - 13.9532i) q^{87} +(0.697013 + 0.402421i) q^{88} +(3.94235 + 6.82835i) q^{89} +(5.41080 + 0.961290i) q^{90} +(-0.624911 - 0.709792i) q^{91} +(-0.949509 + 4.70090i) q^{92} +(-1.71290 + 4.69670i) q^{93} +(-4.47573 + 7.75220i) q^{94} +(7.98546 + 4.61041i) q^{95} +(-1.62721 - 0.593449i) q^{96} -7.26241i q^{97} +(-2.70386 - 6.45671i) q^{98} +(0.422354 - 2.37730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.70593	+	0.299664i	−0.984920	+	0.173011i
$3$	−1.70593	+	0.299664i	−0.984920	+	0.173011i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.915921	−	1.58642i	−0.409612	−	0.709470i	0.585234	−	0.810865i	$-0.301003\pi$
$5$	−0.915921	−	1.58642i	−0.409612	−	0.709470i	−0.994846	+	0.101395i	$0.967669\pi$
$6$	1.32755	−	1.11248i	0.541969	−	0.454169i
$7$	1.74832	+	1.98579i	0.660803	+	0.750559i
$7$	1.74832	+	1.98579i	0.660803	+	0.750559i
$8$			1.00000i			0.353553i
$9$	2.82040	−	1.02241i	0.940134	−	0.340804i
$10$	1.58642	+	0.915921i	0.501671	+	0.289640i
$11$	0.402421	−	0.697013i	0.121334	−	0.210157i	−0.798960	−	0.601385i	$-0.794616\pi$
$11$	0.402421	−	0.697013i	0.121334	−	0.210157i	0.920294	+	0.391227i	$0.127949\pi$
$12$	−0.593449	+	1.62721i	−0.171314	+	0.469736i
$13$	−0.357435			−0.0991347			−0.0495673	−	0.998771i	$-0.515784\pi$
$13$	−0.357435			−0.0991347			−0.0495673	+	0.998771i	$0.515784\pi$
$14$	−2.50699	−	0.845586i	−0.670020	−	0.225992i
$15$	2.03789	+	2.43186i	0.526181	+	0.627903i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.02572	−	3.50866i	0.491310	−	0.850974i	−0.508640	−	0.860980i	$-0.669851\pi$
$17$	2.02572	−	3.50866i	0.491310	−	0.850974i	0.999950	+	0.0100051i	$0.00318478\pi$
$18$	−1.93133	+	2.29564i	−0.455220	+	0.541087i
$19$	−4.35925	+	2.51681i	−1.00008	+	0.577397i	−0.908272	−	0.418380i	$-0.862598\pi$
$19$	−4.35925	+	2.51681i	−1.00008	+	0.577397i	−0.0918086	+	0.995777i	$0.529265\pi$
$20$	−1.83184			−0.409612
$21$	−3.57759	−	2.86372i	−0.780693	−	0.624914i
$22$			0.804842i			0.171593i
$23$	−4.54585	+	1.52815i	−0.947875	+	0.318641i
$23$	−4.54585	+	1.52815i	−0.947875	+	0.318641i
$24$	−0.299664	−	1.70593i	−0.0611686	−	0.348222i
$25$	0.822177	−	1.42405i	0.164435	−	0.284810i
$26$	0.309548	−	0.178718i	0.0607073	−	0.0350494i
$27$	−4.50503	+	2.58934i	−0.866994	+	0.498318i
$28$	2.59391	−	0.521194i	0.490202	−	0.0984965i
$29$			8.17926i			1.51885i	0.650595	+	0.759425i	$0.274520\pi$
$29$			8.17926i			1.51885i	−0.650595	+	0.759425i	$0.725480\pi$
$30$	−2.98080	−	1.08711i	−0.544216	−	0.198477i
$31$	1.44317	−	2.49965i	0.259202	−	0.448951i	−0.706827	−	0.707387i	$-0.749874\pi$
$31$	1.44317	−	2.49965i	0.259202	−	0.448951i	0.966028	+	0.258436i	$0.0832072\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.477633	+	1.30965i	−0.0831452	+	0.227980i
$34$			4.05145i			0.694818i
$35$	1.54898	−	4.59241i	0.261826	−	0.776258i
$36$	0.524767	−	2.95375i	0.0874611	−	0.492291i
$37$	7.82094	−	4.51542i	1.28575	−	0.742331i	0.307860	−	0.951432i	$-0.400387\pi$
$37$	7.82094	−	4.51542i	1.28575	−	0.742331i	0.977894	+	0.209101i	$0.0670538\pi$
$38$	2.51681	−	4.35925i	0.408281	−	0.707164i
$39$	0.609760	−	0.107110i	0.0976397	−	0.0171514i
$40$	1.58642	−	0.915921i	0.250835	−	0.144820i
$41$		−	4.77613i		−	0.745907i	−0.927850	−	0.372953i	$-0.878345\pi$
$41$		−	4.77613i		−	0.745907i	0.927850	−	0.372953i	$-0.121655\pi$
$42$	4.53014	+	0.691258i	0.699016	+	0.106663i
$43$		−	1.59064i		−	0.242570i	−0.992618	−	0.121285i	$-0.961298\pi$
$43$		−	1.59064i		−	0.242570i	0.992618	−	0.121285i	$-0.0387016\pi$
$44$	−0.402421	−	0.697013i	−0.0606672	−	0.105079i
$45$	−4.20524	−	3.53790i	−0.626881	−	0.527399i
$46$	3.17275	−	3.59634i	0.467796	−	0.530252i
$47$	7.75220	−	4.47573i	1.13077	−	0.652853i	0.186644	−	0.982428i	$-0.440239\pi$
$47$	7.75220	−	4.47573i	1.13077	−	0.652853i	0.944129	+	0.329575i	$0.106905\pi$
$48$	1.11248	+	1.32755i	0.160573	+	0.191615i
$49$	−0.886745	+	6.94361i	−0.126678	+	0.991944i
$50$			1.64435i			0.232547i
$51$	−2.40433	+	6.59256i	−0.336673	+	0.923144i
$52$	−0.178718	+	0.309548i	−0.0247837	+	0.0429266i
$53$	4.72870	−	8.19035i	0.649537	−	1.12503i	−0.333696	−	0.942681i	$-0.608296\pi$
$53$	4.72870	−	8.19035i	0.649537	−	1.12503i	0.983234	−	0.182351i	$-0.0583706\pi$
$54$	2.60680	−	4.49495i	0.354741	−	0.611685i
$55$	−1.47434			−0.198800
$56$	−1.98579	+	1.74832i	−0.265363	+	0.233629i
$57$	6.68238	−	5.59982i	0.885103	−	0.741715i
$58$	−4.08963	−	7.08344i	−0.536994	−	0.930102i
$59$	−11.4528	−	6.61227i	−1.49103	−	0.860844i	−0.491079	−	0.871115i	$-0.663397\pi$
$59$	−11.4528	−	6.61227i	−1.49103	−	0.860844i	−0.999947	+	0.0102708i	$0.996731\pi$
$60$	3.12500	−	0.548937i	0.403435	−	0.0708675i
$61$	9.42234	−	5.43999i	1.20641	−	0.696519i	0.244434	−	0.969666i	$-0.421398\pi$
$61$	9.42234	−	5.43999i	1.20641	−	0.696519i	0.961972	+	0.273147i	$0.0880645\pi$
$62$			2.88635i			0.366567i
$63$	6.96127	+	3.81323i	0.877037	+	0.480422i
$64$	−1.00000			−0.125000
$65$	0.327382	+	0.567043i	0.0406068	+	0.0703330i
$66$	−0.241182	−	1.37300i	−0.0296875	−	0.169005i
$67$	9.94959	+	5.74440i	1.21554	+	0.701790i	0.963960	−	0.266048i	$-0.0857179\pi$
$67$	9.94959	+	5.74440i	1.21554	+	0.701790i	0.251576	+	0.967838i	$0.419051\pi$
$68$	−2.02572	−	3.50866i	−0.245655	−	0.425487i
$69$	7.29698	−	3.96915i	0.878453	−	0.477829i
$70$	0.954746	+	4.75163i	0.114114	+	0.567928i
$71$			3.72566i			0.442155i	0.975256	+	0.221077i	$0.0709573\pi$
$71$			3.72566i			0.442155i	−0.975256	+	0.221077i	$0.929043\pi$
$72$	1.02241	+	2.82040i	0.120492	+	0.332388i
$73$	2.04854	−	3.54818i	0.239764	−	0.415283i	−0.720883	−	0.693057i	$-0.756263\pi$
$73$	2.04854	−	3.54818i	0.239764	−	0.415283i	0.960646	+	0.277774i	$0.0895967\pi$
$74$	−4.51542	+	7.82094i	−0.524907	+	0.909166i
$75$	−0.975840	+	2.67571i	−0.112680	+	0.308964i
$76$			5.03363i			0.577397i
$77$	2.08769	−	0.419479i	0.237914	−	0.0478041i
$78$	−0.474512	+	0.397640i	−0.0537279	+	0.0450239i
$79$	8.99349	−	5.19239i	1.01185	−	0.584190i	0.100114	−	0.994976i	$-0.468079\pi$
$79$	8.99349	−	5.19239i	1.01185	−	0.584190i	0.911732	+	0.410786i	$0.134746\pi$
$80$	−0.915921	+	1.58642i	−0.102403	+	0.177367i
$81$	6.90935	−	5.76723i	0.767705	−	0.640803i
$82$	2.38807	+	4.13625i	0.263718	+	0.456773i
$83$	11.7730			1.29225			0.646125	−	0.763231i	$-0.276388\pi$
$83$	11.7730			1.29225			0.646125	+	0.763231i	$0.276388\pi$
$84$	−4.26884	+	1.66642i	−0.465769	+	0.181822i
$85$	−7.42162			−0.804987
$86$	0.795320	+	1.37753i	0.0857616	+	0.148543i
$87$	−2.45103	−	13.9532i	−0.262778	−	1.49595i
$88$	0.697013	+	0.402421i	0.0743019	+	0.0428982i
$89$	3.94235	+	6.82835i	0.417888	+	0.723804i	0.995727	−	0.0923473i	$-0.0294370\pi$
$89$	3.94235	+	6.82835i	0.417888	+	0.723804i	−0.577839	+	0.816151i	$0.696104\pi$
$90$	5.41080	+	0.961290i	0.570348	+	0.101329i
$91$	−0.624911	−	0.709792i	−0.0655085	−	0.0744064i
$92$	−0.949509	+	4.70090i	−0.0989932	+	0.490102i
$93$	−1.71290	+	4.69670i	−0.177620	+	0.487025i
$94$	−4.47573	+	7.75220i	−0.461637	+	0.799578i
$95$	7.98546	+	4.61041i	0.819291	+	0.473018i
$96$	−1.62721	−	0.593449i	−0.166077	−	0.0605686i
$97$		−	7.26241i		−	0.737386i	−0.929551	−	0.368693i	$-0.879805\pi$
$97$		−	7.26241i		−	0.737386i	0.929551	−	0.368693i	$-0.120195\pi$
$98$	−2.70386	−	6.45671i	−0.273131	−	0.652226i
$99$	0.422354	−	2.37730i	0.0424482	−	0.238928i
$100$	−0.822177	−	1.42405i	−0.0822177	−	0.142405i
$101$	−12.1841	−	7.03449i	−1.21236	−	0.699958i	−0.249089	−	0.968481i	$-0.580131\pi$
$101$	−12.1841	−	7.03449i	−1.21236	−	0.699958i	−0.963273	+	0.268523i	$0.913464\pi$
$102$	−1.21407	−	6.91149i	−0.120211	−	0.684340i
$103$	7.12583	−	4.11410i	0.702128	−	0.405374i	−0.106011	−	0.994365i	$-0.533808\pi$
$103$	7.12583	−	4.11410i	0.702128	−	0.405374i	0.808140	+	0.588991i	$0.200475\pi$
$104$		−	0.357435i		−	0.0350494i
$105$	−1.26628	+	8.29850i	−0.123576	+	0.809851i
$106$			9.45740i			0.918584i
$107$	−2.02051	−	3.49963i	−0.195330	−	0.338322i	0.751679	−	0.659530i	$-0.229245\pi$
$107$	−2.02051	−	3.49963i	−0.195330	−	0.338322i	−0.947009	+	0.321208i	$0.895911\pi$
$108$	−0.0100848	+	5.19614i	−0.000970406	+	0.499999i
$109$	−9.59033	−	5.53698i	−0.918587	−	0.530347i	−0.0354033	−	0.999373i	$-0.511272\pi$
$109$	−9.59033	−	5.53698i	−0.918587	−	0.530347i	−0.883184	+	0.469026i	$0.844605\pi$
$110$	1.27682	−	0.737172i	0.121740	−	0.0702866i
$111$	−11.9889	+	10.0466i	−1.13793	+	0.953586i
$112$	0.845586	−	2.50699i	0.0799004	−	0.236888i
$113$	16.2921			1.53264			0.766318	−	0.642461i	$-0.222087\pi$
$113$	16.2921			1.53264			0.766318	+	0.642461i	$0.222087\pi$
$114$	−2.98720	+	8.19078i	−0.279777	+	0.767137i
$115$	6.58793	+	5.81197i	0.614328	+	0.541969i
$116$	7.08344	+	4.08963i	0.657681	+	0.379712i
$117$	−1.00811	+	0.365446i	−0.0931999	+	0.0337855i
$118$	13.2245			1.21742
$119$	10.5091	−	2.11159i	0.963366	−	0.193569i
$120$	−2.43186	+	2.03789i	−0.221997	+	0.186033i
$121$	5.17611	+	8.96529i	0.470556	+	0.815027i
$122$	−5.43999	+	9.42234i	−0.492513	+	0.853058i
$123$	1.43124	+	8.14776i	0.129050	+	0.734659i
$124$	−1.44317	−	2.49965i	−0.129601	−	0.224475i
$125$	−12.1714			−1.08864
$126$	−7.93525	+	0.178280i	−0.706928	+	0.0158824i
$127$	−1.31179			−0.116403			−0.0582014	−	0.998305i	$-0.518537\pi$
$127$	−1.31179			−0.116403			−0.0582014	+	0.998305i	$0.518537\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.476657	+	2.71352i	0.0419673	+	0.238912i
$130$	−0.567043	−	0.327382i	−0.0497330	−	0.0287133i
$131$	−11.0937	+	6.40496i	−0.969262	+	0.559604i	−0.899011	−	0.437925i	$-0.855713\pi$
$131$	−11.0937	+	6.40496i	−0.969262	+	0.559604i	−0.0702511	+	0.997529i	$0.522380\pi$
$132$	0.895372	+	1.06847i	0.0779321	+	0.0929980i
$133$	−12.6192	−	4.25637i	−1.09423	−	0.369074i
$134$	−11.4888			−0.992481
$135$	8.23404	+	4.77526i	0.708673	+	0.410989i
$136$	3.50866	+	2.02572i	0.300865	+	0.173704i
$137$	−0.261105	+	0.452247i	−0.0223077	+	0.0386381i	−0.876964	−	0.480557i	$-0.840435\pi$
$137$	−0.261105	+	0.452247i	−0.0223077	+	0.0386381i	0.854656	+	0.519195i	$0.173768\pi$
$138$	−4.33480	+	7.08587i	−0.369002	+	0.603189i
$139$	2.36891			0.200928			0.100464	−	0.994941i	$-0.467967\pi$
$139$	2.36891			0.200928			0.100464	+	0.994941i	$0.467967\pi$
$140$	−3.20265	−	3.63766i	−0.270673	−	0.307438i
$141$	−11.8835	+	9.95834i	−1.00077	+	0.838644i
$142$	−1.86283	−	3.22652i	−0.156325	−	0.270763i
$143$	−0.143839	+	0.249137i	−0.0120285	+	0.0208339i
$144$	−2.29564	−	1.93133i	−0.191303	−	0.160945i
$145$	12.9758	−	7.49155i	1.07758	−	0.622140i
$146$			4.09708i			0.339077i
$147$	−0.568023	−	12.1110i	−0.0468498	−	0.998902i
$148$		−	9.03084i		−	0.742331i
$149$	2.33799	+	4.04952i	0.191536	+	0.331750i	0.945759	−	0.324868i	$-0.105320\pi$
$149$	2.33799	+	4.04952i	0.191536	+	0.331750i	−0.754224	+	0.656618i	$0.771987\pi$
$150$	−0.492753	−	2.80515i	−0.0402331	−	0.229040i
$151$	10.7404	−	18.6029i	0.874041	−	1.51388i	0.0162597	−	0.999868i	$-0.494824\pi$
$151$	10.7404	−	18.6029i	0.874041	−	1.51388i	0.857781	−	0.514015i	$-0.171843\pi$
$152$	−2.51681	−	4.35925i	−0.204141	−	0.353582i
$153$	2.12607	−	11.9670i	0.171882	−	0.967471i
$154$	−1.59825	+	1.40712i	−0.128791	+	0.113389i
$155$	−5.28734			−0.424689
$156$	0.212120	−	0.581623i	0.0169832	−	0.0465671i
$157$	−16.7025	−	9.64319i	−1.33300	−	0.769610i	−0.347245	−	0.937774i	$-0.612883\pi$
$157$	−16.7025	−	9.64319i	−1.33300	−	0.769610i	−0.985759	+	0.168164i	$0.946216\pi$
$158$	−5.19239	+	8.99349i	−0.413084	+	0.715483i
$159$	−5.61249	+	15.3892i	−0.445099	+	1.22044i
$160$		−	1.83184i		−	0.144820i
$161$	−10.9822	−	6.35542i	−0.865518	−	0.500877i
$162$	−3.10006	+	8.44924i	−0.243563	+	0.663835i
$163$	4.77983	+	8.27890i	0.374385	+	0.648454i	0.990235	−	0.139410i	$-0.0445206\pi$
$163$	4.77983	+	8.27890i	0.374385	+	0.648454i	−0.615850	+	0.787863i	$0.711187\pi$
$164$	−4.13625	−	2.38807i	−0.322987	−	0.186477i
$165$	2.51513	−	0.441808i	0.195802	−	0.0343947i
$166$	−10.1957	+	5.88648i	−0.791339	+	0.456880i
$167$			5.01224i			0.387858i	0.981016	+	0.193929i	$0.0621232\pi$
$167$			5.01224i			0.387858i	−0.981016	+	0.193929i	$0.937877\pi$
$168$	2.86372	−	3.57759i	0.220941	−	0.276017i
$169$	−12.8722			−0.990172
$170$	6.42731	−	3.71081i	0.492952	−	0.284606i
$171$	−9.72162	+	11.5554i	−0.743431	+	0.883662i
$172$	−1.37753	−	0.795320i	−0.105036	−	0.0606426i
$173$	14.3021	−	8.25732i	1.08737	−	0.627793i	0.154494	−	0.987994i	$-0.450625\pi$
$173$	14.3021	−	8.25732i	1.08737	−	0.627793i	0.932875	+	0.360201i	$0.117292\pi$
$174$	9.09928	+	10.8584i	0.689814	+	0.823170i
$175$	4.26530	−	0.857028i	0.322426	−	0.0647852i
$176$	−0.804842			−0.0606672
$177$	21.5191	+	7.84809i	1.61748	+	0.589899i
$178$	−6.82835	−	3.94235i	−0.511807	−	0.295492i
$179$	12.8803	+	7.43646i	0.962721	+	0.555827i	0.897009	−	0.442012i	$-0.145735\pi$
$179$	12.8803	+	7.43646i	0.962721	+	0.555827i	0.0657115	+	0.997839i	$0.479068\pi$
$180$	−5.16653	+	1.87290i	−0.385091	+	0.139598i
$181$		−	21.3335i		−	1.58571i	−0.609411	−	0.792854i	$-0.708594\pi$
$181$		−	21.3335i		−	1.58571i	0.609411	−	0.792854i	$-0.291406\pi$
$182$	0.896085	+	0.302242i	0.0664223	+	0.0224037i
$183$	−14.4437	+	12.1038i	−1.06771	+	0.894737i
$184$	−1.52815	−	4.54585i	−0.112657	−	0.335125i
$185$	−14.3267	−	8.27154i	−1.05332	−	0.608136i
$186$	−0.864935	−	4.92391i	−0.0634201	−	0.361039i
$187$	−1.63039	−	2.82391i	−0.119226	−	0.206505i
$188$		−	8.95146i		−	0.652853i
$189$	−13.0181	−	4.41907i	−0.946930	−	0.321440i
$190$	−9.22082			−0.668948
$191$	−6.81664	−	11.8068i	−0.493235	−	0.854308i	0.506735	−	0.862102i	$-0.330852\pi$
$191$	−6.81664	−	11.8068i	−0.493235	−	0.854308i	−0.999970	+	0.00779424i	$0.997519\pi$
$192$	1.70593	−	0.299664i	0.123115	−	0.0216264i
$193$	9.90920	−	17.1632i	0.713280	−	1.23544i	−0.250340	−	0.968158i	$-0.580542\pi$
$193$	9.90920	−	17.1632i	0.713280	−	1.23544i	0.963619	−	0.267279i	$-0.0861244\pi$
$194$	3.63120	+	6.28943i	0.260705	+	0.451555i
$195$	−0.728414	−	0.869232i	−0.0521628	−	0.0622470i
$196$	5.56997	+	4.23975i	0.397855	+	0.302839i
$197$			0.297461i			0.0211932i	0.999944	+	0.0105966i	$0.00337307\pi$
$197$			0.297461i			0.0211932i	−0.999944	+	0.0105966i	$0.996627\pi$
$198$	0.822880	+	2.26998i	0.0584795	+	0.161320i
$199$	6.90105	+	3.98432i	0.489203	+	0.282441i	0.724244	−	0.689544i	$-0.242189\pi$
$199$	6.90105	+	3.98432i	0.489203	+	0.282441i	−0.235041	+	0.971985i	$0.575522\pi$
$200$	1.42405	+	0.822177i	0.100696	+	0.0581367i
$201$	−18.6947	−	6.81802i	−1.31862	−	0.480906i
$202$	14.0690			0.989890
$203$	−16.2423	+	14.3000i	−1.13999	+	1.00366i
$204$	4.50716	+	5.37849i	0.315565	+	0.376570i
$205$	−7.57697	+	4.37456i	−0.529198	+	0.305533i
$206$	−4.11410	+	7.12583i	−0.286643	+	0.496480i
$207$	−11.2587	+	8.95773i	−0.782536	+	0.622605i
$208$	0.178718	+	0.309548i	0.0123918	+	0.0214633i
$209$			4.05128i			0.280233i
$210$	−3.05262	−	7.81985i	−0.210651	−	0.539621i
$211$	−14.8691			−1.02363			−0.511817	−	0.859094i	$-0.671027\pi$
$211$	−14.8691			−1.02363			−0.511817	+	0.859094i	$0.671027\pi$
$212$	−4.72870	−	8.19035i	−0.324769	−	0.562516i
$213$	−1.11645	−	6.35572i	−0.0764976	−	0.435487i
$214$	3.49963	+	2.02051i	0.239230	+	0.138119i
$215$	−2.52343	+	1.45690i	−0.172096	+	0.0993598i
$216$	−2.58934	−	4.50503i	−0.176182	−	0.306529i
$217$	7.48692	−	1.50435i	0.508245	−	0.102122i
$218$	11.0740			0.750023
$219$	−2.43141	+	6.66682i	−0.164299	+	0.450502i
$220$	−0.737172	+	1.27682i	−0.0497001	+	0.0860831i
$221$	−0.724065	+	1.25412i	−0.0487059	+	0.0843611i
$222$	5.35934	−	14.6951i	0.359696	−	0.986270i
$223$	3.89019			0.260506			0.130253	−	0.991481i	$-0.458421\pi$
$223$	3.89019			0.260506			0.130253	+	0.991481i	$0.458421\pi$
$224$	0.521194	+	2.59391i	0.0348238	+	0.173313i
$225$	0.862902	−	4.85700i	0.0575268	−	0.323800i
$226$	−14.1094	+	8.14607i	−0.938544	+	0.541869i
$227$	−0.594170	+	1.02913i	−0.0394365	+	0.0683060i	−0.885070	−	0.465458i	$-0.845890\pi$
$227$	−0.594170	+	1.02913i	−0.0394365	+	0.0683060i	0.845633	+	0.533764i	$0.179223\pi$
$228$	−1.50840	−	8.58703i	−0.0998960	−	0.568690i
$229$	−20.0397	+	11.5699i	−1.32426	+	0.764561i	−0.984405	−	0.175917i	$-0.943711\pi$
$229$	−20.0397	+	11.5699i	−1.32426	+	0.764561i	−0.339853	+	0.940478i	$0.610377\pi$
$230$	−8.61130	−	1.73935i	−0.567812	−	0.114689i
$231$	−3.43574	+	1.34121i	−0.226055	+	0.0882449i
$232$	−8.17926			−0.536994
$233$	0.249994	−	0.144334i	0.0163777	−	0.00945565i	−0.491789	−	0.870715i	$-0.663657\pi$
$233$	0.249994	−	0.144334i	0.0163777	−	0.00945565i	0.508166	+	0.861259i	$0.330323\pi$
$234$	0.690327	−	0.820541i	0.0451281	−	0.0536404i
$235$	−14.2008	−	8.19884i	−0.926358	−	0.534833i
$236$	−11.4528	+	6.61227i	−0.745513	+	0.430422i
$237$	−13.7863	+	11.5529i	−0.895516	+	0.750441i
$238$	−8.04534	+	7.08323i	−0.521502	+	0.459138i
$239$			16.2421i			1.05061i	0.850913	+	0.525306i	$0.176049\pi$
$239$			16.2421i			1.05061i	−0.850913	+	0.525306i	$0.823951\pi$
$240$	1.08711	−	2.98080i	0.0701723	−	0.192410i
$241$	0.171545	+	0.0990416i	0.0110502	+	0.00637983i	0.505515	−	0.862818i	$-0.331303\pi$
$241$	0.171545	+	0.0990416i	0.0110502	+	0.00637983i	−0.494465	+	0.869198i	$0.664636\pi$
$242$	−8.96529	−	5.17611i	−0.576311	−	0.332733i
$243$	−10.0586	+	11.9090i	−0.645262	+	0.763961i
$244$		−	10.8800i		−	0.696519i
$245$	11.8277	−	4.95305i	0.755643	−	0.316439i
$246$	−5.31336	−	6.34055i	−0.338768	−	0.404259i
$247$	1.55815	−	0.899598i	0.0991427	−	0.0572400i
$248$	2.49965	+	1.44317i	0.158728	+	0.0916417i
$249$	−20.0839	+	3.52793i	−1.27276	+	0.223574i
$250$	10.5407	−	6.08570i	0.666655	−	0.384894i
$251$	2.68500			0.169476			0.0847378	−	0.996403i	$-0.472995\pi$
$251$	2.68500			0.169476			0.0847378	+	0.996403i	$0.472995\pi$
$252$	6.78299	−	4.12202i	0.427288	−	0.259663i
$253$	−0.764205	+	3.78348i	−0.0480451	+	0.237865i
$254$	1.13605	−	0.655897i	0.0712819	−	0.0411546i
$255$	12.6608	−	2.22399i	0.792848	−	0.139272i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.09634	+	1.21032i	−0.130766	+	0.0754978i	−0.563956	−	0.825805i	$-0.690721\pi$
$257$	−2.09634	+	1.21032i	−0.130766	+	0.0754978i	0.433190	+	0.901303i	$0.357388\pi$
$258$	−1.76956	−	2.11165i	−0.110168	−	0.131466i
$259$	22.6402	+	7.63635i	1.40679	+	0.474500i
$260$	0.654765			0.0406068
$261$	8.36257	+	23.0688i	0.517630	+	1.42792i
$262$	6.40496	−	11.0937i	0.395700	−	0.685372i
$263$	0.447581	−	0.775233i	0.0275990	−	0.0478029i	−0.851896	−	0.523711i	$-0.824547\pi$
$263$	0.447581	−	0.775233i	0.0275990	−	0.0478029i	0.879495	+	0.475908i	$0.157881\pi$
$264$	−1.30965	−	0.477633i	−0.0806033	−	0.0293963i
$265$	−17.3245			−1.06423
$266$	13.0568	−	2.62350i	0.800562	−	0.160857i
$267$	−8.77159	−	10.4673i	−0.536813	−	0.640589i
$268$	9.94959	−	5.74440i	0.607768	−	0.350895i
$269$	18.0453	+	10.4185i	1.10024	+	0.635225i	0.936284	−	0.351243i	$-0.114241\pi$
$269$	18.0453	+	10.4185i	1.10024	+	0.635225i	0.163957	+	0.986467i	$0.447574\pi$
$270$	−9.51851	−	0.0184737i	−0.579278	−	0.00112427i
$271$	1.12394	+	1.94671i	0.0682742	+	0.118254i	0.898142	−	0.439706i	$-0.144917\pi$
$271$	1.12394	+	1.94671i	0.0682742	+	0.118254i	−0.829867	+	0.557961i	$0.811584\pi$
$272$	−4.05145			−0.245655
$273$	1.27876	+	1.02359i	0.0773938	+	0.0619507i
$274$		−	0.522210i		−	0.0315479i
$275$	−0.661722	−	1.14614i	−0.0399033	−	0.0691146i
$276$	0.211108	−	8.30394i	0.0127072	−	0.499839i
$277$	−8.79533	+	15.2340i	−0.528460	+	0.915319i	0.470989	+	0.882139i	$0.343897\pi$
$277$	−8.79533	+	15.2340i	−0.528460	+	0.915319i	−0.999449	+	0.0331806i	$0.989436\pi$
$278$	−2.05153	+	1.18445i	−0.123043	+	0.0710388i
$279$	1.51466	−	8.52554i	0.0906803	−	0.510411i
$280$	4.59241	+	1.54898i	0.274449	+	0.0925693i
$281$	15.7613			0.940241			0.470120	−	0.882602i	$-0.344210\pi$
$281$	15.7613			0.940241			0.470120	+	0.882602i	$0.344210\pi$
$282$	5.31224	−	14.5659i	0.316339	−	0.867388i
$283$	−1.00904	−	0.582570i	−0.0599813	−	0.0346302i	0.469709	−	0.882821i	$-0.344359\pi$
$283$	−1.00904	−	0.582570i	−0.0599813	−	0.0346302i	−0.529691	+	0.848191i	$0.677692\pi$
$284$	3.22652	+	1.86283i	0.191459	+	0.110539i
$285$	−15.0042	−	5.47208i	−0.888773	−	0.324138i
$286$		−	0.287679i		−	0.0170108i
$287$	9.48441	−	8.35022i	0.559847	−	0.492898i
$288$	2.95375	+	0.524767i	0.174051	+	0.0309222i
$289$	0.292883	+	0.507288i	0.0172284	+	0.0298405i
$290$	−7.49155	+	12.9758i	−0.439919	+	0.761962i
$291$	2.17628	+	12.3892i	0.127576	+	0.726266i
$292$	−2.04854	−	3.54818i	−0.119882	−	0.207641i
$293$	20.0277			1.17003			0.585017	−	0.811021i	$-0.301088\pi$
$293$	20.0277			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$294$	6.54744	+	10.2045i	0.381855	+	0.595136i
$295$			24.2253i			1.41045i
$296$	4.51542	+	7.82094i	0.262453	+	0.454583i
$297$	−0.00811663	+	4.18207i	−0.000470975	+	0.242668i
$298$	−4.04952	−	2.33799i	−0.234582	−	0.135436i
$299$	1.62485	−	0.546214i	0.0939673	−	0.0315884i
$300$	1.82931	+	2.18296i	0.105615	+	0.126033i
$301$	3.15868	−	2.78095i	0.182063	−	0.160291i
$302$			21.4808i			1.23608i
$303$	22.8932	+	8.34922i	1.31518	+	0.479650i
$304$	4.35925	+	2.51681i	0.250020	+	0.144349i
$305$	−17.2602	−	9.96520i	−0.988318	−	0.570606i
$306$	4.14225	+	11.4267i	0.236797	+	0.653222i
$307$	−0.477093			−0.0272291			−0.0136146	−	0.999907i	$-0.504334\pi$
$307$	−0.477093			−0.0272291			−0.0136146	+	0.999907i	$0.504334\pi$
$308$	0.680563	−	2.01773i	0.0387787	−	0.114971i
$309$	−10.9233	+	9.15372i	−0.621406	+	0.520737i
$310$	4.57897	−	2.64367i	0.260068	−	0.150150i
$311$	−13.9644	−	8.06232i	−0.791846	−	0.457172i	0.0487661	−	0.998810i	$-0.484471\pi$
$311$	−13.9644	−	8.06232i	−0.791846	−	0.457172i	−0.840612	+	0.541638i	$0.817804\pi$
$312$	0.107110	+	0.609760i	0.00606393	+	0.0345208i
$313$	−13.7951	+	7.96462i	−0.779747	+	0.450187i	−0.836341	−	0.548210i	$-0.815309\pi$
$313$	−13.7951	+	7.96462i	−0.779747	+	0.450187i	0.0565937	+	0.998397i	$0.481976\pi$
$314$	19.2864			1.08839
$315$	−0.326581	−	14.5361i	−0.0184007	−	0.819018i
$316$		−	10.3848i		−	0.584190i
$317$	−12.9259	+	7.46277i	−0.725990	+	0.419151i	−0.816954	−	0.576704i	$-0.804339\pi$
$317$	−12.9259	+	7.46277i	−0.725990	+	0.419151i	0.0909631	+	0.995854i	$0.471005\pi$
$318$	−2.83404	−	16.1337i	−0.158925	−	0.904732i
$319$	5.70105	+	3.29150i	0.319198	+	0.184289i
$320$	0.915921	+	1.58642i	0.0512016	+	0.0886837i
$321$	4.49557	+	5.36465i	0.250918	+	0.299426i
$322$	12.6886	+	0.0128574i	0.707106	+	0.000716517i
$323$			20.3935i			1.13472i
$324$	−1.53989	−	8.86728i	−0.0855496	−	0.492627i
$325$	−0.293875	+	0.509006i	−0.0163012	+	0.0282346i
$326$	−8.27890	−	4.77983i	−0.458526	−	0.264730i
$327$	18.0197	+	6.57183i	0.996491	+	0.363423i
$328$	4.77613			0.263718
$329$	22.4412	+	7.56923i	1.23722	+	0.417305i
$330$	−1.95726	+	1.64018i	−0.107744	+	0.0902890i
$331$	8.54378	+	14.7983i	0.469609	+	0.813386i	0.999396	−	0.0347442i	$-0.0110617\pi$
$331$	8.54378	+	14.7983i	0.469609	+	0.813386i	−0.529788	+	0.848130i	$0.677728\pi$
$332$	5.88648	−	10.1957i	0.323063	−	0.559561i
$333$	17.4416	−	20.7315i	0.955792	−	1.13608i
$334$	−2.50612	−	4.34072i	−0.137129	−	0.237514i
$335$		−	21.0457i		−	1.14985i
$336$	−0.691258	+	4.53014i	−0.0377112	+	0.247139i
$337$		−	27.4583i		−	1.49575i	−0.663840	−	0.747875i	$-0.731074\pi$
$337$		−	27.4583i		−	1.49575i	0.663840	−	0.747875i	$-0.268926\pi$
$338$	11.1477	−	6.43612i	0.606354	−	0.350079i
$339$	−27.7933	+	4.88217i	−1.50952	+	0.265163i
$340$	−3.71081	+	6.42731i	−0.201247	+	0.348570i
$341$	−1.16153	−	2.01182i	−0.0629002	−	0.108946i
$342$	2.64148	−	14.8681i	0.142835	−	0.803973i
$343$	−15.3389	+	10.3788i	−0.828222	+	0.560401i
$344$	1.59064			0.0857616
$345$	−12.9802	−	7.94066i	−0.698830	−	0.427511i
$346$	−8.25732	+	14.3021i	−0.443916	+	0.768886i
$347$	1.33072	+	0.768294i	0.0714370	+	0.0412442i	0.535293	−	0.844666i	$-0.320201\pi$
$347$	1.33072	+	0.768294i	0.0714370	+	0.0412442i	−0.463856	+	0.885911i	$0.653535\pi$
$348$	−13.3094	−	4.85397i	−0.713458	−	0.260200i
$349$	6.80845			0.364448			0.182224	−	0.983257i	$-0.441670\pi$
$349$	6.80845			0.364448			0.182224	+	0.983257i	$0.441670\pi$
$350$	−3.26534	+	2.87486i	−0.174540	+	0.153668i
$351$	1.61026	−	0.925520i	0.0859492	−	0.0494006i
$352$	0.697013	−	0.402421i	0.0371509	−	0.0214491i
$353$	−5.05570	−	2.91891i	−0.269088	−	0.155358i	0.359385	−	0.933189i	$-0.382986\pi$
$353$	−5.05570	−	2.91891i	−0.269088	−	0.155358i	−0.628473	+	0.777831i	$0.716320\pi$
$354$	−22.5602	+	3.96292i	−1.19906	+	0.210627i
$355$	5.91047	−	3.41241i	0.313695	−	0.181112i
$356$	7.88470			0.417888
$357$	−17.2950	+	6.75142i	−0.915349	+	0.357323i
$358$	−14.8729			−0.786058
$359$	−8.34516	−	14.4542i	−0.440440	−	0.762865i	0.557282	−	0.830324i	$-0.311844\pi$
$359$	−8.34516	−	14.4542i	−0.440440	−	0.762865i	−0.997722	+	0.0674583i	$0.978511\pi$
$360$	3.53790	−	4.20524i	0.186464	−	0.221636i
$361$	3.16871	−	5.48837i	0.166774	−	0.288862i
$362$	10.6668	+	18.4754i	0.560633	+	0.971044i
$363$	−11.5167	−	13.7431i	−0.604468	−	0.721325i
$364$	−0.927154	+	0.186293i	−0.0485961	+	0.00976442i
$365$	−7.50521			−0.392841
$366$	6.45671	−	17.7040i	0.337498	−	0.925404i
$367$	24.8982	+	14.3750i	1.29968	+	0.750368i	0.980348	−	0.197276i	$-0.0632095\pi$
$367$	24.8982	+	14.3750i	1.29968	+	0.750368i	0.319328	+	0.947644i	$0.396543\pi$
$368$	3.59634	+	3.17275i	0.187472	+	0.165391i
$369$	−4.88318	−	13.4706i	−0.254208	−	0.701253i
$370$	16.5431			0.860034
$371$	24.5316	−	4.92915i	1.27362	−	0.255909i
$372$	3.21101	+	3.83177i	0.166483	+	0.198668i
$373$	−29.4930	+	17.0278i	−1.52709	+	0.881665i	−0.527606	+	0.849489i	$0.676910\pi$
$373$	−29.4930	+	17.0278i	−1.52709	+	0.881665i	−0.999482	+	0.0321754i	$0.989756\pi$
$374$	2.82391	+	1.63039i	0.146021	+	0.0843053i
$375$	20.7636	−	3.64733i	1.07223	−	0.188347i
$376$	4.47573	+	7.75220i	0.230818	+	0.399789i
$377$		−	2.92355i		−	0.150571i
$378$	13.4836	−	2.68204i	0.693520	−	0.137949i
$379$		−	6.08992i		−	0.312818i	−0.987692	−	0.156409i	$-0.950008\pi$
$379$		−	6.08992i		−	0.312818i	0.987692	−	0.156409i	$-0.0499918\pi$
$380$	7.98546	−	4.61041i	0.409646	−	0.236509i
$381$	2.23783	−	0.393097i	0.114648	−	0.0201390i
$382$	11.8068	+	6.81664i	0.604087	+	0.348770i
$383$	7.34779	+	12.7268i	0.375455	+	0.650307i	0.990395	−	0.138267i	$-0.0441532\pi$
$383$	7.34779	+	12.7268i	0.375455	+	0.650307i	−0.614940	+	0.788574i	$0.710820\pi$
$384$	−1.32755	+	1.11248i	−0.0677461	+	0.0567711i
$385$	−2.57763	−	2.92774i	−0.131368	−	0.149211i
$386$			19.8184i			1.00873i
$387$	−1.62629	−	4.48625i	−0.0826689	−	0.228049i
$388$	−6.28943	−	3.63120i	−0.319297	−	0.184346i
$389$	−11.9662	+	20.7260i	−0.606710	+	1.05085i	0.385069	+	0.922888i	$0.374178\pi$
$389$	−11.9662	+	20.7260i	−0.606710	+	1.05085i	−0.991779	+	0.127964i	$0.959156\pi$
$390$	1.06544	+	0.388570i	0.0539507	+	0.0196760i
$391$	−3.84689	+	19.0454i	−0.194545	+	0.963169i
$392$	−6.94361	−	0.886745i	−0.350705	−	0.0447874i
$393$	17.0058	−	14.2508i	0.857828	−	0.718858i
$394$	−0.148731	−	0.257609i	−0.00749294	−	0.0129781i
$395$	−16.4746	−	9.51164i	−0.828930	−	0.478583i
$396$	−1.84762	−	1.55442i	−0.0928466	−	0.0781125i
$397$	−14.0462	−	24.3288i	−0.704961	−	1.22103i	−0.966706	−	0.255891i	$-0.917631\pi$
$397$	−14.0462	−	24.3288i	−0.704961	−	1.22103i	0.261745	−	0.965137i	$-0.415702\pi$
$398$	−7.96865			−0.399432
$399$	22.8030	+	3.47954i	1.14158	+	0.174195i
$400$	−1.64435			−0.0822177
$401$	2.51540	+	4.35680i	0.125613	+	0.217568i	0.921972	−	0.387256i	$-0.126577\pi$
$401$	2.51540	+	4.35680i	0.125613	+	0.217568i	−0.796359	+	0.604824i	$0.793244\pi$
$402$	19.5991	−	3.44278i	0.977514	−	0.171710i
$403$	−0.515841	+	0.893463i	−0.0256959	+	0.0445066i
$404$	−12.1841	+	7.03449i	−0.606181	+	0.349979i
$405$	−15.4777	−	5.67881i	−0.769092	−	0.282183i
$406$	6.91627	−	20.5053i	0.343249	−	1.01766i
$407$		−	7.26840i		−	0.360281i
$408$	−6.59256	−	2.40433i	−0.326381	−	0.119032i
$409$	0.998771	−	1.72992i	0.0493861	−	0.0855392i	−0.840276	−	0.542159i	$-0.817607\pi$
$409$	0.998771	−	1.72992i	0.0493861	−	0.0855392i	0.889662	+	0.456620i	$0.150940\pi$
$410$	4.37456	−	7.57697i	0.216044	−	0.374200i
$411$	0.309905	−	0.849747i	0.0152865	−	0.0419149i
$412$		−	8.22819i		−	0.405374i
$413$	−6.89256	−	34.3032i	−0.339161	−	1.68795i
$414$	5.27148	−	13.3870i	0.259079	−	0.657935i
$415$	−10.7831	−	18.6769i	−0.529322	−	0.916813i
$416$	−0.309548	−	0.178718i	−0.0151768	−	0.00876235i
$417$	−4.04119	+	0.709876i	−0.197898	+	0.0347628i
$418$	−2.02564	−	3.50851i	−0.0990772	−	0.171607i
$419$	15.3396			0.749390			0.374695	−	0.927148i	$-0.377747\pi$
$419$	15.3396			0.749390			0.374695	+	0.927148i	$0.377747\pi$
$420$	6.55358	+	5.24588i	0.319782	+	0.255973i
$421$			23.9544i			1.16747i	0.811946	+	0.583733i	$0.198408\pi$
$421$			23.9544i			1.16747i	−0.811946	+	0.583733i	$0.801592\pi$
$422$	12.8771	−	7.43457i	0.626845	−	0.361909i
$423$	17.2883	−	20.5493i	0.840585	−	0.999141i
$424$	8.19035	+	4.72870i	0.397759	+	0.229646i
$425$	−3.33101	−	5.76947i	−0.161578	−	0.279860i
$426$	4.14473	+	4.94599i	0.200813	+	0.239634i
$427$	27.2760	+	9.19996i	1.31998	+	0.445217i
$428$	−4.04102			−0.195330
$429$	0.170723	−	0.468114i	0.00824257	−	0.0226008i
$430$	1.45690	−	2.52343i	0.0702580	−	0.121690i
$431$	3.52095	−	6.09847i	0.169598	−	0.293753i	−0.768680	−	0.639633i	$-0.779086\pi$
$431$	3.52095	−	6.09847i	0.169598	−	0.293753i	0.938279	+	0.345880i	$0.112420\pi$
$432$	4.49495	+	2.60680i	0.216263	+	0.125420i
$433$			29.6558i			1.42517i	0.701588	+	0.712583i	$0.252475\pi$
$433$			29.6558i			1.42517i	−0.701588	+	0.712583i	$0.747525\pi$
$434$	−5.73169	+	5.04627i	−0.275130	+	0.242229i
$435$	−19.8908	+	16.6684i	−0.953691	+	0.799191i
$436$	−9.59033	+	5.53698i	−0.459294	+	0.265173i
$437$	15.9704	−	18.1027i	0.763970	−	0.865967i
$438$	−1.22775	−	6.98934i	−0.0586641	−	0.333964i
$439$	1.86777	+	3.23506i	0.0891436	+	0.154401i	0.907149	−	0.420809i	$-0.138254\pi$
$439$	1.86777	+	3.23506i	0.0891436	+	0.154401i	−0.818006	+	0.575210i	$0.804920\pi$
$440$		−	1.47434i		−	0.0702866i
$441$	4.59825	+	20.4904i	0.218964	+	0.975733i
$442$		−	1.44813i		−	0.0688805i
$443$	22.1855	−	12.8088i	1.05407	−	0.608566i	0.130282	−	0.991477i	$-0.458412\pi$
$443$	22.1855	−	12.8088i	1.05407	−	0.608566i	0.923785	+	0.382911i	$0.125079\pi$
$444$	2.70622	+	15.4060i	0.128431	+	0.731136i
$445$	7.22177	−	12.5085i	0.342345	−	0.592958i
$446$	−3.36900	+	1.94509i	−0.159527	+	0.0921029i
$447$	−5.20195	−	6.20759i	−0.246044	−	0.293609i
$448$	−1.74832	−	1.98579i	−0.0826004	−	0.0938199i
$449$		−	14.3161i		−	0.675619i	−0.941214	−	0.337810i	$-0.890314\pi$
$449$		−	14.3161i		−	0.675619i	0.941214	−	0.337810i	$-0.109686\pi$
$450$	1.68121	+	4.63774i	0.0792528	+	0.218625i
$451$	−3.32903	−	1.92202i	−0.156758	−	0.0905042i
$452$	8.14607	−	14.1094i	0.383159	−	0.663651i
$453$	−12.7478	+	34.9538i	−0.598942	+	1.64227i
$454$		−	1.18834i		−	0.0557716i
$455$	−0.553660	+	1.64149i	−0.0259560	+	0.0769541i
$456$	5.59982	+	6.68238i	0.262236	+	0.312931i
$457$	23.8191	−	13.7520i	1.11421	−	0.643289i	0.174293	−	0.984694i	$-0.444236\pi$
$457$	23.8191	−	13.7520i	1.11421	−	0.643289i	0.939916	+	0.341405i	$0.110903\pi$
$458$	11.5699	−	20.0397i	0.540626	−	0.936392i
$459$	−0.0408579	+	21.0519i	−0.00190708	+	0.982619i
$460$	8.32728	−	2.79933i	0.388262	−	0.130519i
$461$		−	1.92543i		−	0.0896764i	−0.998994	−	0.0448382i	$-0.985723\pi$
$461$		−	1.92543i		−	0.0896764i	0.998994	−	0.0448382i	$-0.0142772\pi$
$462$	2.30484	−	2.87939i	0.107231	−	0.133961i
$463$	−17.7630			−0.825515			−0.412757	−	0.910841i	$-0.635434\pi$
$463$	−17.7630			−0.825515			−0.412757	+	0.910841i	$0.635434\pi$
$464$	7.08344	−	4.08963i	0.328841	−	0.189856i
$465$	9.01983	−	1.58442i	0.418285	−	0.0734759i
$466$	−0.144334	+	0.249994i	−0.00668616	+	0.0115808i
$467$	−12.2024	−	21.1352i	−0.564660	−	0.978020i	−0.997081	−	0.0763484i	$-0.975674\pi$
$467$	−12.2024	−	21.1352i	−0.564660	−	0.978020i	0.432421	−	0.901672i	$-0.357659\pi$
$468$	−0.187570	+	1.05577i	−0.00867043	+	0.0488031i
$469$	5.98790	+	29.8009i	0.276495	+	1.37608i
$470$	16.3977			0.756368
$471$	31.3830	+	11.4455i	1.44605	+	0.527380i
$472$	6.61227	−	11.4528i	0.304354	−	0.527157i
$473$	−1.10870	−	0.640107i	−0.0509780	−	0.0294321i
$474$	6.16284	−	16.8982i	0.283069	−	0.776162i
$475$			8.27706i			0.379778i
$476$	3.42585	−	10.1569i	0.157024	−	0.465542i
$477$	4.96293	−	27.9348i	0.227237	−	1.27905i
$478$	−8.12104	−	14.0661i	−0.371448	−	0.643366i
$479$	−20.2378	+	35.0529i	−0.924689	+	1.60161i	−0.132629	+	0.991166i	$0.542342\pi$
$479$	−20.2378	+	35.0529i	−0.924689	+	1.60161i	−0.792060	+	0.610443i	$0.790991\pi$
$480$	0.548937	+	3.12500i	0.0250554	+	0.142636i
$481$	−2.79548	+	1.61397i	−0.127463	+	0.0735907i
$482$	−0.198083			−0.00902244
$483$	20.6394	+	7.55094i	0.939123	+	0.343580i
$484$	10.3522			0.470556
$485$	−11.5212	+	6.65180i	−0.523153	+	0.302042i
$486$	2.75655	−	15.3428i	0.125040	−	0.695963i
$487$	−3.71232	+	6.42992i	−0.168221	+	0.291367i	−0.937794	−	0.347191i	$-0.887136\pi$
$487$	−3.71232	+	6.42992i	−0.168221	+	0.291367i	0.769573	+	0.638558i	$0.220469\pi$
$488$	5.43999	+	9.42234i	0.246257	+	0.426529i
$489$	−10.6349	−	12.6909i	−0.480929	−	0.573902i
$490$	−7.76655	+	10.2033i	−0.350857	+	0.460938i
$491$			0.0699917i			0.00315868i	0.999999	+	0.00157934i	$0.000502720\pi$
$491$			0.0699917i			0.00315868i	−0.999999	+	0.00157934i	$0.999497\pi$
$492$	7.77178	+	2.83439i	0.350379	+	0.127784i
$493$	28.6982	+	16.5689i	1.29250	+	0.746227i
$494$	−0.899598	+	1.55815i	−0.0404748	+	0.0701045i
$495$	−4.15824	+	1.50739i	−0.186899	+	0.0677520i
$496$	−2.88635			−0.129601
$497$	−7.39839	+	6.51365i	−0.331863	+	0.292177i
$498$	15.6292	−	13.0972i	0.700360	−	0.586900i
$499$	−9.29940	−	16.1070i	−0.416298	−	0.721050i	0.579265	−	0.815139i	$-0.303339\pi$
$499$	−9.29940	−	16.1070i	−0.416298	−	0.721050i	−0.995564	+	0.0940892i	$0.970006\pi$
$500$	−6.08570	+	10.5407i	−0.272161	+	0.471397i
$501$	−1.50199	−	8.55053i	−0.0671038	−	0.382010i
$502$	−2.32528	+	1.34250i	−0.103782	+	0.0599186i
$503$	−25.5400			−1.13877			−0.569387	−	0.822070i	$-0.692819\pi$
$503$	−25.5400			−1.13877			−0.569387	+	0.822070i	$0.692819\pi$
$504$	−3.81323	+	6.96127i	−0.169855	+	0.310080i
$505$			25.7721i			1.14685i
$506$	−1.22992	−	3.65869i	−0.0546766	−	0.162649i
$507$	21.9592	−	3.85735i	0.975240	−	0.171311i
$508$	−0.655897	+	1.13605i	−0.0291007	+	0.0504039i
$509$	1.54514	−	0.892085i	0.0684870	−	0.0395410i	−0.465365	−	0.885119i	$-0.654077\pi$
$509$	1.54514	−	0.892085i	0.0684870	−	0.0395410i	0.533852	+	0.845578i	$0.320744\pi$
$510$	−9.85255	+	8.25642i	−0.436278	+	0.365600i
$511$	10.6275	−	2.13538i	0.470131	−	0.0944635i
$512$		−	1.00000i		−	0.0441942i
$513$	13.1217	−	22.6259i	0.579337	−	0.998958i
$514$	1.21032	−	2.09634i	0.0533850	−	0.0924656i
$515$	−13.0534	−	7.53638i	−0.575201	−	0.332093i
$516$	2.58831	+	0.943964i	0.113944	+	0.0415557i
$517$		−	7.20451i		−	0.316854i
$518$	−23.4252	+	4.70682i	−1.02924	+	0.206806i
$519$	−21.9240	+	18.3722i	−0.962356	+	0.806452i
$520$	−0.567043	+	0.327382i	−0.0248665	+	0.0143567i
$521$	2.01344	−	3.48737i	0.0882102	−	0.152785i	−0.818544	−	0.574443i	$-0.805219\pi$
$521$	2.01344	−	3.48737i	0.0882102	−	0.152785i	0.906755	+	0.421659i	$0.138552\pi$
$522$	−18.7766	−	15.7969i	−0.821829	−	0.691411i
$523$	16.3672	−	9.44959i	0.715686	−	0.413202i	−0.0974766	−	0.995238i	$-0.531077\pi$
$523$	16.3672	−	9.44959i	0.715686	−	0.413202i	0.813163	+	0.582036i	$0.197744\pi$
$524$			12.8099i			0.559604i
$525$	−7.01949	+	2.74019i	−0.306356	+	0.119592i
$526$			0.895162i			0.0390309i
$527$	−5.84695	−	10.1272i	−0.254697	−	0.441148i
$528$	1.37300	−	0.241182i	0.0597524	−	0.0104961i
$529$	18.3295	−	13.8935i	0.796936	−	0.604064i
$530$	15.0034	−	8.66224i	0.651708	−	0.376264i
$531$	−39.0619	−	6.93980i	−1.69514	−	0.301162i
$532$	−9.99574	+	8.80040i	−0.433370	+	0.381546i
$533$			1.70716i			0.0739452i
$534$	12.8301	+	4.67917i	0.555212	+	0.202487i
$535$	−3.70126	+	6.41077i	−0.160019	+	0.277162i
$536$	−5.74440	+	9.94959i	−0.248120	+	0.429757i
$537$	−24.2014	−	8.82632i	−1.04437	−	0.380884i
$538$	−20.8369			−0.898343
$539$	4.48294	+	3.41233i	0.193094	+	0.146979i
$540$	8.25251	−	4.74326i	0.355132	−	0.204117i
$541$	21.8894	+	37.9135i	0.941099	+	1.63003i	0.763380	+	0.645949i	$0.223538\pi$
$541$	21.8894	+	37.9135i	0.941099	+	1.63003i	0.177718	+	0.984081i	$0.443128\pi$
$542$	−1.94671	−	1.12394i	−0.0836185	−	0.0482772i
$543$	6.39289	+	36.3935i	0.274345	+	1.56180i
$544$	3.50866	−	2.02572i	0.150432	−	0.0868522i
$545$			20.2858i			0.868946i
$546$	−1.61923	−	0.247080i	−0.0692967	−	0.0105740i
$547$	2.04122			0.0872764			0.0436382	−	0.999047i	$-0.486105\pi$
$547$	2.04122			0.0872764			0.0436382	+	0.999047i	$0.486105\pi$
$548$	0.261105	+	0.452247i	0.0111539	+	0.0193190i
$549$	21.0129	−	24.9765i	0.896808	−	1.06597i
$550$	1.14614	+	0.661722i	0.0488714	+	0.0282159i
$551$	−20.5857	−	35.6554i	−0.876979	−	1.51897i
$552$	3.96915	+	7.29698i	0.168938	+	0.310580i
$553$	26.0345	+	8.78123i	1.10710	+	0.373416i
$554$		−	17.5907i		−	0.747355i
$555$	26.9191	+	9.81747i	1.14265	+	0.416729i
$556$	1.18445	−	2.05153i	0.0502320	−	0.0870044i
$557$	20.9425	−	36.2735i	0.887363	−	1.53696i	0.0443821	−	0.999015i	$-0.485868\pi$
$557$	20.9425	−	36.2735i	0.887363	−	1.53696i	0.842981	−	0.537943i	$-0.180799\pi$
$558$	2.95104	+	8.14067i	0.124927	+	0.344622i
$559$			0.568551i			0.0240471i
$560$	−4.75163	+	0.954746i	−0.200793	+	0.0403454i
$561$	3.62755	+	4.32884i	0.153155	+	0.182764i
$562$	−13.6497	+	7.88065i	−0.575778	+	0.332425i
$563$	5.49924	−	9.52496i	0.231765	−	0.401429i	−0.726562	−	0.687101i	$-0.758883\pi$
$563$	5.49924	−	9.52496i	0.231765	−	0.401429i	0.958328	+	0.285671i	$0.0922165\pi$
$564$	2.68243	+	15.2706i	0.112951	+	0.643008i
$565$	−14.9223	−	25.8462i	−0.627787	−	1.08736i
$566$	1.16514			0.0489745
$567$	23.5323	+	3.63756i	0.988263	+	0.152763i
$568$	−3.72566			−0.156325
$569$	20.7509	+	35.9416i	0.869922	+	1.50675i	0.862075	+	0.506780i	$0.169165\pi$
$569$	20.7509	+	35.9416i	0.869922	+	1.50675i	0.00784722	+	0.999969i	$0.497502\pi$
$570$	15.7301	−	2.76315i	0.658860	−	0.115735i
$571$	−27.6537	−	15.9659i	−1.15727	−	0.668152i	−0.206624	−	0.978420i	$-0.566248\pi$
$571$	−27.6537	−	15.9659i	−1.15727	−	0.668152i	−0.950649	+	0.310268i	$0.899581\pi$
$572$	0.143839	+	0.249137i	0.00601423	+	0.0104169i
$573$	15.1668	+	18.0988i	0.633601	+	0.756090i
$574$	−4.03863	+	11.9737i	−0.168569	+	0.499773i
$575$	−1.56133	+	7.72993i	−0.0651119	+	0.322361i
$576$	−2.82040	+	1.02241i	−0.117517	+	0.0426005i
$577$	−14.8814	+	25.7753i	−0.619520	+	1.07304i	0.370053	+	0.929011i	$0.379340\pi$
$577$	−14.8814	+	25.7753i	−0.619520	+	1.07304i	−0.989573	+	0.144030i	$0.953994\pi$
$578$	−0.507288	−	0.292883i	−0.0211004	−	0.0121823i
$579$	−11.7612	+	32.2487i	−0.488779	+	1.34021i
$580$		−	14.9831i		−	0.622140i
$581$	20.5829	+	23.3787i	0.853924	+	0.969911i
$582$	−8.07930	−	9.64120i	−0.334898	−	0.399640i
$583$	−3.80586	−	6.59194i	−0.157622	−	0.273010i
$584$	3.54818	+	2.04854i	0.146825	+	0.0847693i
$585$	1.50310	+	1.26457i	0.0621456	+	0.0522835i
$586$	−17.3445	+	10.0139i	−0.716496	+	0.413669i
$587$			16.2133i			0.669194i	0.942361	+	0.334597i	$0.108600\pi$
$587$			16.2133i			0.669194i	−0.942361	+	0.334597i	$0.891400\pi$
$588$	−10.7725	−	5.56360i	−0.444250	−	0.229439i
$589$			14.5288i			0.598649i
$590$	−12.1126	−	20.9797i	−0.498669	−	0.863721i
$591$	−0.0891384	−	0.507448i	−0.00366666	−	0.0208736i
$592$	−7.82094	−	4.51542i	−0.321439	−	0.185583i
$593$	4.74859	−	2.74160i	0.195001	−	0.112584i	−0.399321	−	0.916811i	$-0.630754\pi$
$593$	4.74859	−	2.74160i	0.195001	−	0.112584i	0.594322	+	0.804227i	$0.297421\pi$
$594$	−2.08401	−	3.62584i	−0.0855079	−	0.148770i
$595$	−12.9754	−	14.7378i	−0.531938	−	0.604190i
$596$	4.67598			0.191536
$597$	−12.9667	−	4.72899i	−0.530691	−	0.193545i
$598$	−1.13405	+	1.28546i	−0.0463748	+	0.0525663i
$599$	−10.9423	−	6.31752i	−0.447089	−	0.258127i	0.259511	−	0.965740i	$-0.416439\pi$
$599$	−10.9423	−	6.31752i	−0.447089	−	0.258127i	−0.706600	+	0.707613i	$0.749772\pi$
$600$	−2.67571	−	0.975840i	−0.109235	−	0.0398385i
$601$	12.6617			0.516480			0.258240	−	0.966081i	$-0.416857\pi$
$601$	12.6617			0.516480			0.258240	+	0.966081i	$0.416857\pi$
$602$	−1.34502	+	3.98771i	−0.0548191	+	0.162527i
$603$	33.9350	+	6.02894i	1.38194	+	0.245517i
$604$	−10.7404	−	18.6029i	−0.437020	−	0.756942i
$605$	9.48183	−	16.4230i	0.385491	−	0.667690i
$606$	−24.0007	+	4.21596i	−0.974962	+	0.171262i
$607$	17.6948	+	30.6484i	0.718211	+	1.24398i	0.961708	+	0.274077i	$0.0883723\pi$
$607$	17.6948	+	30.6484i	0.718211	+	1.24398i	−0.243496	+	0.969902i	$0.578294\pi$
$608$	−5.03363			−0.204141
$609$	23.4231	−	29.2620i	0.949151	−	1.18576i
$610$	19.9304			0.806958
$611$	−2.77091	+	1.59978i	−0.112099	+	0.0647203i
$612$	−9.30065	−	7.82470i	−0.375957	−	0.316295i
$613$	−26.2221	−	15.1393i	−1.05910	−	0.611472i	−0.133917	−	0.990993i	$-0.542756\pi$
$613$	−26.2221	−	15.1393i	−1.05910	−	0.611472i	−0.925183	+	0.379521i	$0.876089\pi$
$614$	0.413175	−	0.238546i	0.0166744	−	0.00962695i
$615$	11.6149	−	9.73325i	0.468357	−	0.392482i
$616$	0.419479	+	2.08769i	0.0169013	+	0.0841152i
$617$	−23.3163			−0.938678			−0.469339	−	0.883018i	$-0.655508\pi$
$617$	−23.3163			−0.938678			−0.469339	+	0.883018i	$0.655508\pi$
$618$	4.88301	−	13.3890i	0.196424	−	0.538585i
$619$	−21.6219	−	12.4834i	−0.869059	−	0.501751i	−0.00202345	−	0.999998i	$-0.500644\pi$
$619$	−21.6219	−	12.4834i	−0.869059	−	0.501751i	−0.867035	+	0.498247i	$0.833977\pi$
$620$	−2.64367	+	4.57897i	−0.106172	+	0.183896i
$621$	16.5223	−	18.6551i	0.663018	−	0.748604i
$622$	16.1246			0.646539
$623$	−6.66719	+	19.7668i	−0.267116	+	0.791942i
$624$	−0.397640	−	0.474512i	−0.0159183	−	0.0189957i
$625$	7.03717	+	12.1887i	0.281487	+	0.487549i
$626$	7.96462	−	13.7951i	0.318330	−	0.551364i
$627$	−1.21402	−	6.91120i	−0.0484833	−	0.276007i
$628$	−16.7025	+	9.64319i	−0.666502	+	0.384805i
$629$		−	36.5880i		−	1.45886i
$630$	7.55089	+	12.4254i	0.300835	+	0.495039i
$631$		−	14.4122i		−	0.573740i	−0.957970	−	0.286870i	$-0.907385\pi$
$631$		−	14.4122i		−	0.573740i	0.957970	−	0.286870i	$-0.0926147\pi$
$632$	5.19239	+	8.99349i	0.206542	+	0.357742i
$633$	25.3657	−	4.45575i	1.00820	−	0.177100i
$634$	7.46277	−	12.9259i	0.296384	−	0.513353i
$635$	1.20150	+	2.08106i	0.0476801	+	0.0825843i
$636$	10.5212	+	12.5552i	0.417192	+	0.497844i
$637$	0.316954	−	2.48189i	0.0125582	−	0.0983360i
$638$	−6.58301			−0.260624
$639$	3.80916	+	10.5079i	0.150688	+	0.415685i
$640$	−1.58642	−	0.915921i	−0.0627088	−	0.0362050i
$641$	−2.60812	+	4.51740i	−0.103015	+	0.178426i	−0.912925	−	0.408127i	$-0.866182\pi$
$641$	−2.60812	+	4.51740i	−0.103015	+	0.178426i	0.809911	+	0.586553i	$0.199515\pi$
$642$	−6.57560	−	2.39814i	−0.259518	−	0.0946471i
$643$			22.5755i			0.890292i	0.895458	+	0.445146i	$0.146848\pi$
$643$			22.5755i			0.890292i	−0.895458	+	0.445146i	$0.853152\pi$
$644$	−10.9951	+	6.33315i	−0.433266	+	0.249561i
$645$	3.86821	−	3.24155i	0.152311	−	0.127636i
$646$	−10.1967	−	17.6613i	−0.401186	−	0.694874i
$647$	−42.0212	−	24.2609i	−1.65202	−	0.953796i	−0.976239	−	0.216696i	$-0.930472\pi$
$647$	−42.0212	−	24.2609i	−1.65202	−	0.953796i	−0.675784	−	0.737100i	$-0.736195\pi$
$648$	5.76723	+	6.90935i	0.226558	+	0.271425i
$649$	−9.21768	+	5.32183i	−0.361826	+	0.208900i
$650$		−	0.587750i		−	0.0230534i
$651$	−12.3214	+	4.80988i	−0.482913	+	0.188514i
$652$	9.55965			0.374385
$653$	13.6931	−	7.90573i	0.535853	−	0.309375i	−0.207544	−	0.978226i	$-0.566547\pi$
$653$	13.6931	−	7.90573i	0.535853	−	0.309375i	0.743397	+	0.668851i	$0.233214\pi$
$654$	−18.8914	+	3.31847i	−0.738713	+	0.129762i
$655$	20.3219	+	11.7329i	0.794044	+	0.458441i
$656$	−4.13625	+	2.38807i	−0.161494	+	0.0932384i
$657$	2.15001	−	12.1017i	0.0838800	−	0.472134i
$658$	−23.2193	+	4.66545i	−0.905181	+	0.181878i
$659$	27.4602			1.06970			0.534849	−	0.844948i	$-0.320368\pi$
$659$	27.4602			1.06970			0.534849	+	0.844948i	$0.320368\pi$
$660$	0.874948	−	2.39907i	0.0340573	−	0.0933836i
$661$	−19.8954	−	11.4866i	−0.773842	−	0.446778i	0.0604012	−	0.998174i	$-0.480762\pi$
$661$	−19.8954	−	11.4866i	−0.773842	−	0.446778i	−0.834244	+	0.551396i	$0.814095\pi$
$662$	−14.7983	−	8.54378i	−0.575151	−	0.332064i
$663$	0.859391	−	2.35641i	0.0333760	−	0.0915155i
$664$			11.7730i			0.456880i
$665$	4.80584	+	23.9179i	0.186362	+	0.927498i
$666$	−4.73908	+	26.6748i	−0.183636	+	1.03363i
$667$	−12.4991	−	37.1817i	−0.483968	−	1.43968i
$668$	4.34072	+	2.50612i	0.167948	+	0.0969646i
$669$	−6.63639	+	1.16575i	−0.256578	+	0.0450705i
$670$	10.5228	+	18.2261i	0.406532	+	0.704135i
$671$		−	8.75666i		−	0.338047i
$672$	−1.66642	−	4.26884i	−0.0642836	−	0.164674i
$673$	−13.8445			−0.533666			−0.266833	−	0.963743i	$-0.585977\pi$
$673$	−13.8445			−0.533666			−0.266833	+	0.963743i	$0.585977\pi$
$674$	13.7292	+	23.7796i	0.528827	+	0.915956i
$675$	−0.0165829	+	8.54429i	−0.000638276	+	0.328870i
$676$	−6.43612	+	11.1477i	−0.247543	+	0.428757i
$677$	2.44452	+	4.23404i	0.0939507	+	0.162727i	0.909170	−	0.416425i	$-0.136717\pi$
$677$	2.44452	+	4.23404i	0.0939507	+	0.162727i	−0.815219	+	0.579152i	$0.803384\pi$
$678$	21.6286	−	18.1247i	0.830642	−	0.696076i
$679$	14.4216	−	12.6970i	0.553452	−	0.487267i
$680$		−	7.42162i		−	0.284606i
$681$	0.705220	−	1.93368i	0.0270241	−	0.0740989i
$682$	2.01182	+	1.16153i	0.0770367	+	0.0444772i
$683$	−7.90958	−	4.56660i	−0.302652	−	0.174736i	0.340982	−	0.940070i	$-0.389241\pi$
$683$	−7.90958	−	4.56660i	−0.302652	−	0.174736i	−0.643633	+	0.765334i	$0.722574\pi$
$684$	5.14644	+	14.1969i	0.196779	+	0.542831i
$685$	0.956607			0.0365501
$686$	8.09448	−	16.6577i	0.309049	−	0.635995i
$687$	30.7192	−	25.7426i	1.17201	−	0.982143i
$688$	−1.37753	+	0.795320i	−0.0525180	+	0.0303213i
$689$	−1.69020	+	2.92752i	−0.0643916	+	0.111530i
$690$	15.2115	+	0.386717i	0.579092	+	0.0147221i
$691$	−14.0502	−	24.3357i	−0.534495	−	0.925773i	−0.999188	−	0.0403009i	$-0.987168\pi$
$691$	−14.0502	−	24.3357i	−0.534495	−	0.925773i	0.464692	−	0.885472i	$-0.346165\pi$
$692$		−	16.5146i		−	0.627793i
$693$	5.45923	−	3.31757i	0.207379	−	0.126024i
$694$	−1.53659			−0.0583281
$695$	−2.16973	−	3.75808i	−0.0823026	−	0.142552i
$696$	13.9532	−	2.45103i	0.528897	−	0.0929060i
$697$	−16.7578	−	9.67513i	−0.634748	−	0.366472i
$698$	−5.89629	+	3.40423i	−0.223178	+	0.128852i
$699$	−0.383221	+	0.321139i	−0.0144948	+	0.0121466i
$700$	1.39044	−	4.12237i	0.0525538	−	0.155811i
$701$	−1.99728			−0.0754364			−0.0377182	−	0.999288i	$-0.512009\pi$
$701$	−1.99728			−0.0754364			−0.0377182	+	0.999288i	$0.512009\pi$
$702$	−0.931764	+	1.60665i	−0.0351672	+	0.0606392i
$703$	−22.7290	+	39.3677i	−0.857239	+	1.48478i
$704$	−0.402421	+	0.697013i	−0.0151668	+	0.0262697i
$705$	26.6825	+	9.73118i	1.00492	+	0.366498i
$706$	5.83782			0.219709
$707$	−7.33267	−	36.4936i	−0.275773	−	1.37248i
$708$	17.5562	−	14.7121i	0.659803	−	0.552913i
$709$	−35.4918	+	20.4912i	−1.33292	+	0.769563i	−0.985747	−	0.168237i	$-0.946193\pi$
$709$	−35.4918	+	20.4912i	−1.33292	+	0.769563i	−0.347176	+	0.937800i	$0.612859\pi$
$710$	−3.41241	+	5.91047i	−0.128066	+	0.221816i
$711$	20.0565	−	23.8397i	0.752177	−	0.894058i
$712$	−6.82835	+	3.94235i	−0.255903	+	0.147746i
$713$	−2.74061	+	13.5684i	−0.102637	+	0.508142i
$714$	11.6022	−	14.4944i	0.434201	−	0.542440i
$715$	0.526982			0.0197080
$716$	12.8803	−	7.43646i	0.481360	−	0.277914i
$717$	−4.86716	−	27.7079i	−0.181768	−	1.03477i
$718$	14.4542	+	8.34516i	0.539427	+	0.311438i
$719$	−4.94088	+	2.85262i	−0.184264	+	0.106385i	−0.589294	−	0.807918i	$-0.700594\pi$
$719$	−4.94088	+	2.85262i	−0.184264	+	0.106385i	0.405031	+	0.914303i	$0.367261\pi$
$720$	−0.961290	+	5.41080i	−0.0358252	+	0.201649i
$721$	20.6280	+	6.95765i	0.768226	+	0.259116i
$722$			6.33742i			0.235855i
$723$	−0.322323	−	0.117552i	−0.0119873	−	0.00437182i
$724$	−18.4754	−	10.6668i	−0.686632	−	0.396427i
$725$	11.6477	+	6.72479i	0.432584	+	0.249753i
$726$	16.8453	+	6.14352i	0.625187	+	0.228007i
$727$			42.2173i			1.56575i	0.622176	+	0.782877i	$0.286249\pi$
$727$			42.2173i			1.56575i	−0.622176	+	0.782877i	$0.713751\pi$
$728$	0.709792	−	0.624911i	0.0263066	−	0.0231608i
$729$	13.5907	−	23.3301i	0.503358	−	0.864078i
$730$	6.49970	−	3.75261i	0.240565	−	0.138890i
$731$	−5.58101	−	3.22220i	−0.206421	−	0.119177i
$732$	3.26034	+	18.5605i	0.120505	+	0.686016i
$733$	−26.3050	+	15.1872i	−0.971597	+	0.560952i	−0.899723	−	0.436462i	$-0.856231\pi$
$733$	−26.3050	+	15.1872i	−0.971597	+	0.560952i	−0.0718744	+	0.997414i	$0.522898\pi$
$734$	−28.7500			−1.06118
$735$	−18.6930	+	11.9939i	−0.689500	+	0.442401i
$736$	−4.70090	−	0.949509i	−0.173277	−	0.0349994i
$737$	8.00785	−	4.62333i	0.294973	−	0.170303i
$738$	10.9643	+	9.22431i	0.403600	+	0.339552i
$739$	−3.10211	+	5.37301i	−0.114113	+	0.197649i	−0.917425	−	0.397909i	$-0.869736\pi$
$739$	−3.10211	+	5.37301i	−0.114113	+	0.197649i	0.803312	+	0.595559i	$0.203069\pi$
$740$	−14.3267	+	8.27154i	−0.526661	+	0.304068i
$741$	−2.38852	+	2.00157i	−0.0877444	+	0.0735296i
$742$	−18.7804	+	16.5346i	−0.689452	+	0.607004i
$743$	2.39891			0.0880075			0.0440037	−	0.999031i	$-0.485989\pi$
$743$	2.39891			0.0880075			0.0440037	+	0.999031i	$0.485989\pi$
$744$	−4.69670	−	1.71290i	−0.172189	−	0.0627980i
$745$	4.28283	−	7.41808i	0.156911	−	0.271777i
$746$	17.0278	−	29.4930i	0.623431	−	1.07981i
$747$	33.2045	−	12.0368i	1.21489	−	0.440404i
$748$	−3.26078			−0.119226
$749$	3.41703	−	10.1308i	0.124856	−	0.370171i
$750$	−16.1581	+	13.5405i	−0.590011	+	0.494428i
$751$	19.3679	−	11.1820i	0.706743	−	0.408038i	−0.103111	−	0.994670i	$-0.532880\pi$
$751$	19.3679	−	11.1820i	0.706743	−	0.408038i	0.809854	+	0.586631i	$0.199546\pi$
$752$	−7.75220	−	4.47573i	−0.282693	−	0.163213i
$753$	−4.58042	+	0.804597i	−0.166920	+	0.0293211i
$754$	1.46178	+	2.53187i	0.0532348	+	0.0922053i
$755$	−39.3494			−1.43207
$756$	−10.3361	+	9.06450i	−0.375920	+	0.329673i
$757$			27.2258i			0.989540i	0.869024	+	0.494770i	$0.164748\pi$
$757$			27.2258i			0.989540i	−0.869024	+	0.494770i	$0.835252\pi$
$758$	3.04496	+	5.27402i	0.110598	+	0.191561i
$759$	0.169909	−	6.68336i	0.00616729	−	0.242591i
$760$	−4.61041	+	7.98546i	−0.167237	+	0.289663i
$761$	36.9318	−	21.3226i	1.33878	−	0.772944i	0.352152	−	0.935943i	$-0.385450\pi$
$761$	36.9318	−	21.3226i	1.33878	−	0.772944i	0.986626	+	0.162999i	$0.0521167\pi$
$762$	−1.74147	+	1.45935i	−0.0630868	+	0.0528666i
$763$	−5.77169	−	28.7248i	−0.208949	−	1.03991i
$764$	−13.6333			−0.493235
$765$	−20.9319	+	7.58795i	−0.756796	+	0.274343i
$766$	−12.7268	−	7.34779i	−0.459836	−	0.265487i
$767$	4.09363	+	2.36346i	0.147812	+	0.0853395i
$768$	0.593449	−	1.62721i	0.0214142	−	0.0587169i
$769$		−	45.4796i		−	1.64004i	−0.572338	−	0.820018i	$-0.693964\pi$
$769$		−	45.4796i		−	1.64004i	0.572338	−	0.820018i	$-0.306036\pi$
$770$	3.69616	+	1.24668i	0.133200	+	0.0449274i
$771$	3.21352	−	2.69292i	0.115732	−	0.0969833i
$772$	−9.90920	−	17.1632i	−0.356640	−	0.617718i
$773$	−20.5266	+	35.5531i	−0.738290	+	1.27876i	0.214975	+	0.976620i	$0.431033\pi$
$773$	−20.5266	+	35.5531i	−0.738290	+	1.27876i	−0.953265	+	0.302136i	$0.902300\pi$
$774$	3.65153	+	3.07206i	0.131252	+	0.110423i
$775$	−2.37309	−	4.11031i	−0.0852439	−	0.147647i
$776$	7.26241			0.260705
$777$	−40.9110	−	6.24264i	−1.46767	−	0.223954i
$778$		−	23.9324i		−	0.858017i
$779$	12.0206	+	20.8204i	0.430684	+	0.745967i
$780$	−1.11698	+	0.196209i	−0.0399944	+	0.00702542i
$781$	2.59684	+	1.49928i	0.0929221	+	0.0536486i
$782$	−6.19122	−	18.4173i	−0.221398	−	0.658601i
$783$	−21.1789	−	36.8478i	−0.756871	−	1.31683i
$784$	6.45671	−	2.70386i	0.230597	−	0.0965664i
$785$			35.3296i			1.26097i
$786$	−7.60203	+	20.8445i	−0.271156	+	0.743497i
$787$	−28.3409	−	16.3626i	−1.01024	−	0.583265i	−0.0989808	−	0.995089i	$-0.531558\pi$
$787$	−28.3409	−	16.3626i	−1.01024	−	0.583265i	−0.911263	+	0.411825i	$0.864892\pi$
$788$	0.257609	+	0.148731i	0.00917694	+	0.00529831i
$789$	−0.531233	+	1.45662i	−0.0189124	+	0.0518570i
$790$	19.0233			0.676818
$791$	28.4839	+	32.3528i	1.01277	+	1.15033i
$792$	2.37730	+	0.422354i	0.0844736	+	0.0150077i
$793$	−3.36787	+	1.94444i	−0.119597	+	0.0690492i
$794$	24.3288	+	14.0462i	0.863397	+	0.498483i
$795$	29.5544	−	5.19152i	1.04819	−	0.184124i
$796$	6.90105	−	3.98432i	0.244601	−	0.141221i
$797$	39.0654			1.38377			0.691883	−	0.722009i	$-0.256781\pi$
$797$	39.0654			1.38377			0.691883	+	0.722009i	$0.256781\pi$
$798$	−21.4878	+	8.38815i	−0.760659	+	0.296937i
$799$		−	36.2664i		−	1.28301i
$800$	1.42405	−	0.822177i	0.0503478	−	0.0290683i
$801$	18.1004	+	15.2280i	0.639546	+	0.538055i
$802$	−4.35680	−	2.51540i	−0.153844	−	0.0888219i
$803$	−1.64875	−	2.85572i	−0.0581832	−	0.100776i
$804$	−15.2519	+	12.7811i	−0.537894	+	0.450754i
$805$	−0.0235528	+	23.2435i	−0.000830128	+	0.819224i
$806$		−	1.03168i		−	0.0363395i
$807$	−33.9061	−	12.3657i	−1.19355	−	0.435292i
$808$	7.03449	−	12.1841i	0.247472	−	0.428635i
$809$	22.4772	+	12.9772i	0.790256	+	0.456254i	0.840052	−	0.542505i	$-0.182524\pi$
$809$	22.4772	+	12.9772i	0.790256	+	0.456254i	−0.0497970	+	0.998759i	$0.515857\pi$
$810$	16.2435	−	2.82084i	0.570737	−	0.0991142i
$811$	16.3095			0.572705			0.286353	−	0.958124i	$-0.407557\pi$
$811$	16.3095			0.572705			0.286353	+	0.958124i	$0.407557\pi$
$812$	4.26298	+	21.2162i	0.149601	+	0.744544i
$813$	−2.50072	−	2.98416i	−0.0877040	−	0.104659i
$814$	3.63420	+	6.29462i	0.127379	+	0.220626i
$815$	8.75589	−	15.1656i	0.306705	−	0.531229i
$816$	6.91149	−	1.21407i	0.241951	−	0.0425011i
$817$	4.00335	+	6.93400i	0.140059	+	0.242590i
$818$			1.99754i			0.0698425i
$819$	−2.48820	−	1.36298i	−0.0869448	−	0.0476265i
$820$			8.74913i			0.305533i
$821$	−14.2998	+	8.25599i	−0.499067	+	0.288136i	−0.728328	−	0.685229i	$-0.759702\pi$
$821$	−14.2998	+	8.25599i	−0.499067	+	0.288136i	0.229261	+	0.973365i	$0.426369\pi$
$822$	0.156488	+	0.890855i	0.00545813	+	0.0310721i
$823$	0.360323	−	0.624098i	0.0125601	−	0.0217547i	−0.859677	−	0.510838i	$-0.829335\pi$
$823$	0.360323	−	0.624098i	0.0125601	−	0.0217547i	0.872237	+	0.489083i	$0.162669\pi$
$824$	4.11410	+	7.12583i	0.143321	+	0.248240i
$825$	1.47231	+	1.75694i	0.0512592	+	0.0611686i
$826$	23.1207	+	26.2612i	0.804474	+	0.913744i
$827$	−22.3249			−0.776313			−0.388157	−	0.921593i	$-0.626888\pi$
$827$	−22.3249			−0.776313			−0.388157	+	0.921593i	$0.626888\pi$
$828$	2.12826	+	14.2292i	0.0739620	+	0.494499i
$829$	−21.2589	+	36.8215i	−0.738352	+	1.27886i	0.214885	+	0.976639i	$0.431062\pi$
$829$	−21.2589	+	36.8215i	−0.738352	+	1.27886i	−0.953237	+	0.302224i	$0.902271\pi$
$830$	18.6769	+	10.7831i	0.648284	+	0.374287i
$831$	10.4392	−	28.6237i	0.362130	−	0.992946i
$832$	0.357435			0.0123918
$833$	22.5664	+	17.1771i	0.781881	+	0.595152i
$834$	3.14484	−	2.63537i	0.108897	−	0.0912553i
$835$	7.95152	−	4.59081i	0.275174	−	0.158872i
$836$	3.50851	+	2.02564i	0.121344	+	0.0700581i
$837$	−0.0291081	+	14.9979i	−0.00100612	+	0.518403i
$838$	−13.2845	+	7.66981i	−0.458906	+	0.264949i
$839$	−10.1138			−0.349167			−0.174583	−	0.984642i	$-0.555858\pi$
$839$	−10.1138			−0.349167			−0.174583	+	0.984642i	$0.555858\pi$
$840$	−8.29850	−	1.26628i	−0.286326	−	0.0436907i
$841$	−37.9002			−1.30690
$842$	−11.9772	−	20.7451i	−0.412761	−	0.714924i
$843$	−26.8877	+	4.72309i	−0.926062	+	0.162672i
$844$	−7.43457	+	12.8771i	−0.255909	+	0.443247i
$845$	11.7900	+	20.4208i	0.405587	+	0.702497i
$846$	−4.69743	+	26.4404i	−0.161501	+	0.909038i
$847$	−8.75370	+	25.9529i	−0.300781	+	0.891752i
$848$	−9.45740			−0.324769
$849$	1.89593	+	0.691452i	0.0650682	+	0.0237306i
$850$	5.76947	+	3.33101i	0.197891	+	0.114253i
$851$	−28.6526	+	32.4780i	−0.982198	+	1.11333i
$852$	−6.06244	−	2.21099i	−0.207696	−	0.0757473i
$853$	47.4496			1.62464			0.812322	−	0.583209i	$-0.198203\pi$
$853$	47.4496			1.62464			0.812322	+	0.583209i	$0.198203\pi$
$854$	−28.2217	+	5.67058i	−0.965725	+	0.194043i
$855$	27.2360	+	4.83878i	0.931450	+	0.165483i
$856$	3.49963	−	2.02051i	0.119615	−	0.0690597i
$857$	38.5659	+	22.2661i	1.31739	+	0.760594i	0.983308	−	0.181951i	$-0.0582412\pi$
$857$	38.5659	+	22.2661i	1.31739	+	0.760594i	0.334080	+	0.942545i	$0.391574\pi$
$858$	0.0862069	+	0.490760i	0.00294306	+	0.0167543i
$859$	−9.33086	−	16.1615i	−0.318365	−	0.551424i	0.661782	−	0.749696i	$-0.269800\pi$
$859$	−9.33086	−	16.1615i	−0.318365	−	0.551424i	−0.980147	+	0.198272i	$0.936467\pi$
$860$			2.91380i			0.0993598i
$861$	−13.6775	+	17.0870i	−0.466128	+	0.582325i
$862$			7.04190i			0.239848i
$863$	−44.0420	+	25.4277i	−1.49921	+	0.865568i	−1.00000		0.000913662i	$-0.999709\pi$
$863$	−44.0420	+	25.4277i	−1.49921	+	0.865568i	−0.499209	+	0.866482i	$0.666376\pi$
$864$	−5.19614	−	0.0100848i	−0.176776	−	0.000343090i
$865$	−26.1992	−	15.1261i	−0.890799	−	0.514303i
$866$	−14.8279	−	25.6827i	−0.503872	−	0.872733i
$867$	−0.651654	−	0.777632i	−0.0221313	−	0.0264098i
$868$	2.44066	−	7.23604i	0.0828413	−	0.245607i
$869$		−	8.35811i		−	0.283529i
$870$	8.89171	−	24.3807i	0.301457	−	0.826583i
$871$	−3.55633	−	2.05325i	−0.120502	−	0.0695717i
$872$	5.53698	−	9.59033i	0.187506	−	0.324770i
$873$	−7.42517	−	20.4829i	−0.251304	−	0.693242i
$874$	−4.77948	+	23.6626i	−0.161668	+	0.800398i
$875$	−21.2795	−	24.1699i	−0.719380	−	0.817092i
$876$	4.55793	+	5.43907i	0.153998	+	0.183769i
$877$	−9.68056	−	16.7672i	−0.326889	−	0.566189i	0.655004	−	0.755626i	$-0.272667\pi$
$877$	−9.68056	−	16.7672i	−0.326889	−	0.566189i	−0.981893	+	0.189437i	$0.939334\pi$
$878$	−3.23506	−	1.86777i	−0.109178	−	0.0630340i
$879$	−34.1660	+	6.00159i	−1.15239	+	0.202429i
$880$	0.737172	+	1.27682i	0.0248501	+	0.0430416i
$881$	−10.1703			−0.342645			−0.171322	−	0.985215i	$-0.554804\pi$
$881$	−10.1703			−0.342645			−0.171322	+	0.985215i	$0.554804\pi$
$882$	−14.2274	−	15.4461i	−0.479061	−	0.520096i
$883$	−13.6801			−0.460373			−0.230187	−	0.973146i	$-0.573934\pi$
$883$	−13.6801			−0.460373			−0.230187	+	0.973146i	$0.573934\pi$
$884$	0.724065	+	1.25412i	0.0243529	+	0.0421805i
$885$	−7.25944	−	41.3267i	−0.244023	−	1.38918i
$886$	−12.8088	+	22.1855i	−0.430321	+	0.745338i
$887$	33.4594	−	19.3178i	1.12346	−	0.648627i	0.181174	−	0.983451i	$-0.442010\pi$
$887$	33.4594	−	19.3178i	1.12346	−	0.648627i	0.942281	+	0.334824i	$0.108677\pi$
$888$	−10.0466	−	11.9889i	−0.337143	−	0.402320i
$889$	−2.29344	−	2.60495i	−0.0769194	−	0.0873672i
$890$			14.4435i			0.484148i
$891$	−1.23937	−	7.13676i	−0.0415205	−	0.239090i
$892$	1.94509	−	3.36900i	0.0651266	−	0.112803i
$893$	−22.5292	+	39.0217i	−0.753910	+	1.30581i
$894$	7.60881	+	2.77496i	0.254477	+	0.0928085i
$895$		−	27.2448i		−	0.910695i
$896$	2.50699	+	0.845586i	0.0837526	+	0.0282491i
$897$	−2.60820	+	1.41871i	−0.0870851	+	0.0473694i
$898$	7.15806	+	12.3981i	0.238867	+	0.413731i
$899$	20.4453	+	11.8041i	0.681889	+	0.393689i
$900$	−3.77484	−	3.17580i	−0.125828	−	0.105860i
$901$	−19.1581	−	33.1828i	−0.638249	−	1.10548i
$902$	3.84403			0.127992
$903$	−4.55514	+	5.69065i	−0.151586	+	0.189373i
$904$			16.2921i			0.541869i
$905$	−33.8440	+	19.5398i	−1.12501	+	0.649526i
$906$	−6.43702	−	36.6447i	−0.213856	−	1.21744i
$907$	6.05837	+	3.49780i	0.201165	+	0.116143i	0.597199	−	0.802093i	$-0.296280\pi$
$907$	6.05837	+	3.49780i	0.201165	+	0.116143i	−0.396034	+	0.918236i	$0.629614\pi$
$908$	0.594170	+	1.02913i	0.0197182	+	0.0341530i
$909$	−41.5562	−	7.38293i	−1.37833	−	0.244876i
$910$	−0.341260	−	1.69840i	−0.0113127	−	0.0563014i
$911$	−34.3159			−1.13694			−0.568468	−	0.822705i	$-0.692464\pi$
$911$	−34.3159			−1.13694			−0.568468	+	0.822705i	$0.692464\pi$
$912$	−8.19078	−	2.98720i	−0.271224	−	0.0989162i
$913$	4.73769	−	8.20592i	0.156795	−	0.271576i
$914$	−13.7520	+	23.8191i	−0.454874	+	0.787865i
$915$	32.4310	+	11.8277i	1.07214	+	0.391011i
$916$			23.1398i			0.764561i
$917$	−32.1143	−	10.8319i	−1.06051	−	0.357701i
$918$	−10.4906	−	18.2519i	−0.346240	−	0.602403i
$919$	−23.2368	+	13.4158i	−0.766512	+	0.442546i	−0.831629	−	0.555332i	$-0.812591\pi$
$919$	−23.2368	+	13.4158i	−0.766512	+	0.442546i	0.0651169	+	0.997878i	$0.479258\pi$
$920$	−5.81197	+	6.58793i	−0.191615	+	0.217198i
$921$	0.813888	−	0.142968i	0.0268185	−	0.00471094i
$922$	0.962717	+	1.66748i	0.0317054	+	0.0549154i
$923$		−	1.33168i		−	0.0438328i
$924$	−0.556354	+	3.64605i	−0.0183027	+	0.119946i
$925$		−	14.8499i		−	0.488261i
$926$	15.3832	−	8.88148i	0.505522	−	0.291864i
$927$	15.8914	−	18.8889i	0.521942	−	0.620394i
$928$	−4.08963	+	7.08344i	−0.134249	+	0.232525i
$929$	−19.1649	+	11.0649i	−0.628780	+	0.363026i	−0.780279	−	0.625431i	$-0.784923\pi$
$929$	−19.1649	+	11.0649i	−0.628780	+	0.363026i	0.151500	+	0.988457i	$0.451590\pi$
$930$	−7.01919	+	5.88207i	−0.230168	+	0.192881i
$931$	−13.6102	−	32.5007i	−0.446057	−	1.06517i
$932$		−	0.288669i		−	0.00945565i
$933$	26.2382	+	9.56916i	0.859001	+	0.313280i
$934$	21.1352	+	12.2024i	0.691565	+	0.399275i
$935$	−2.98661	+	5.17297i	−0.0976727	+	0.169174i
$936$	−0.365446	−	1.00811i	−0.0119450	−	0.0329511i
$937$		−	42.2587i		−	1.38053i	−0.723556	−	0.690266i	$-0.757494\pi$
$937$		−	42.2587i		−	1.38053i	0.723556	−	0.690266i	$-0.242506\pi$
$938$	−20.0861	−	22.8144i	−0.655835	−	0.744915i
$939$	21.1468	−	17.7210i	0.690101	−	0.578303i
$940$	−14.2008	+	8.19884i	−0.463179	+	0.267417i
$941$	−6.31335	+	10.9350i	−0.205809	+	0.356472i	−0.950390	−	0.311060i	$-0.899316\pi$
$941$	−6.31335	+	10.9350i	−0.205809	+	0.356472i	0.744581	+	0.667532i	$0.232649\pi$
$942$	−32.9012	+	5.77943i	−1.07198	+	0.188304i
$943$	7.29865	+	21.7116i	0.237677	+	0.707027i
$944$			13.2245i			0.430422i
$945$	4.91308	+	24.6998i	0.159822	+	0.803484i
$946$	1.28021			0.0416233
$947$	−21.2041	+	12.2422i	−0.689041	+	0.397818i	−0.803253	−	0.595638i	$-0.796899\pi$
$947$	−21.2041	+	12.2422i	−0.689041	+	0.397818i	0.114212	+	0.993456i	$0.463566\pi$
$948$	3.11194	+	17.7157i	0.101071	+	0.575380i
$949$	−0.732221	+	1.26824i	−0.0237689	+	0.0411689i
$950$	−4.13853	−	7.16815i	−0.134272	−	0.232565i
$951$	19.8144	−	16.6044i	0.642525	−	0.538434i
$952$	2.11159	+	10.5091i	0.0684371	+	0.340601i
$953$	−12.7820			−0.414050			−0.207025	−	0.978336i	$-0.566378\pi$
$953$	−12.7820			−0.414050			−0.207025	+	0.978336i	$0.566378\pi$
$954$	9.66936	+	26.6737i	0.313057	+	0.863593i
$955$	−12.4870	+	21.6281i	−0.404070	+	0.699870i
$956$	14.0661	+	8.12104i	0.454929	+	0.262653i
$957$	−10.7119	−	3.90668i	−0.346268	−	0.126285i
$958$		−	40.4756i		−	1.30771i
$959$	−1.35457	+	0.272173i	−0.0437412	+	0.00878893i
$960$	−2.03789	−	2.43186i	−0.0657727	−	0.0784879i
$961$	11.3345	+	19.6319i	0.365629	+	0.633288i
$962$	1.61397	−	2.79548i	0.0520365	−	0.0901298i
$963$	−9.27672	−	7.80457i	−0.298938	−	0.251499i
$964$	0.171545	−	0.0990416i	0.00552510	−	0.00318992i
$965$	−36.3042			−1.16867
$966$	−21.6497	+	3.78037i	−0.696567	+	0.121631i
$967$	23.4058			0.752681			0.376341	−	0.926481i	$-0.377182\pi$
$967$	23.4058			0.752681			0.376341	+	0.926481i	$0.377182\pi$
$968$	−8.96529	+	5.17611i	−0.288155	+	0.166367i
$969$	−6.11119	−	34.7899i	−0.196320	−	1.11761i
$970$	6.65180	−	11.5212i	0.213576	−	0.369925i
$971$	3.53216	+	6.11789i	0.113352	+	0.196332i	0.917120	−	0.398611i	$-0.130508\pi$
$971$	3.53216	+	6.11789i	0.113352	+	0.196332i	−0.803767	+	0.594944i	$0.797174\pi$
$972$	5.28416	+	14.6655i	0.169489	+	0.470397i
$973$	4.14161	+	4.70416i	0.132774	+	0.150808i
$974$		−	7.42463i		−	0.237900i
$975$	0.348799	−	0.956393i	0.0111705	−	0.0306291i
$976$	−9.42234	−	5.43999i	−0.301602	−	0.174130i
$977$	−10.6227	+	18.3990i	−0.339849	+	0.588635i	−0.984404	−	0.175922i	$-0.943709\pi$
$977$	−10.6227	+	18.3990i	−0.339849	+	0.588635i	0.644555	+	0.764558i	$0.277043\pi$
$978$	15.5556	+	5.67317i	0.497412	+	0.181408i
$979$	6.34594			0.202817
$980$	1.62438	−	12.7196i	0.0518888	−	0.406313i
$981$	−32.7097	−	5.81125i	−1.04434	−	0.185539i
$982$	−0.0349959	−	0.0606146i	−0.00111676	−	0.00193429i
$983$	−3.69198	+	6.39469i	−0.117756	+	0.203959i	−0.918878	−	0.394542i	$-0.870903\pi$
$983$	−3.69198	+	6.39469i	−0.117756	+	0.203959i	0.801122	+	0.598501i	$0.204237\pi$
$984$	−8.14776	+	1.43124i	−0.259741	+	0.0456261i
$985$	0.471899	−	0.272451i	0.0150359	−	0.00868101i
$986$	−33.1378			−1.05532
$987$	−40.5514	−	6.18777i	−1.29076	−	0.196959i
$988$		−	1.79920i		−	0.0572400i
$989$	2.43074	+	7.23081i	0.0772929	+	0.229926i
$990$	2.84745	−	3.38456i	0.0904979	−	0.107568i
$991$	−11.7459	+	20.3445i	−0.373121	+	0.646264i	−0.990044	−	0.140759i	$-0.955046\pi$
$991$	−11.7459	+	20.3445i	−0.373121	+	0.646264i	0.616923	+	0.787023i	$0.288379\pi$
$992$	2.49965	−	1.44317i	0.0793640	−	0.0458208i
$993$	−19.0096	−	22.6846i	−0.603252	−	0.719873i
$994$	3.15037	−	9.34018i	0.0999236	−	0.296253i
$995$		−	14.5973i		−	0.462766i
$996$	−6.98666	+	19.1571i	−0.221381	+	0.607016i
$997$	−3.96205	+	6.86247i	−0.125479	+	0.217337i	−0.921920	−	0.387380i	$-0.873380\pi$
$997$	−3.96205	+	6.86247i	−0.125479	+	0.217337i	0.796441	+	0.604716i	$0.206714\pi$
$998$	16.1070	+	9.29940i	0.509859	+	0.294367i
$999$	−23.5416	+	40.5932i	−0.744825	+	1.28431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.1	✓	128
3.2	odd	2	inner	966.2.j.a.137.52	yes	128
7.2	even	3	inner	966.2.j.a.275.51	yes	128
21.2	odd	6	inner	966.2.j.a.275.2	yes	128
23.22	odd	2	inner	966.2.j.a.137.2	yes	128
69.68	even	2	inner	966.2.j.a.137.51	yes	128
161.114	odd	6	inner	966.2.j.a.275.52	yes	128
483.275	even	6	inner	966.2.j.a.275.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.1	✓	128	1.1	even	1	trivial
966.2.j.a.137.2	yes	128	23.22	odd	2	inner
966.2.j.a.137.51	yes	128	69.68	even	2	inner
966.2.j.a.137.52	yes	128	3.2	odd	2	inner
966.2.j.a.275.1	yes	128	483.275	even	6	inner
966.2.j.a.275.2	yes	128	21.2	odd	6	inner
966.2.j.a.275.51	yes	128	7.2	even	3	inner
966.2.j.a.275.52	yes	128	161.114	odd	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70593 + 0.299664i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.915921 - 1.58642i) q^{5} +(1.32755 - 1.11248i) q^{6} +(1.74832 + 1.98579i) q^{7} +1.00000i q^{8} +(2.82040 - 1.02241i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70593 + 0.299664i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.915921 - 1.58642i) q^{5} +(1.32755 - 1.11248i) q^{6} +(1.74832 + 1.98579i) q^{7} +1.00000i q^{8} +(2.82040 - 1.02241i) q^{9} +(1.58642 + 0.915921i) q^{10} +(0.402421 - 0.697013i) q^{11} +(-0.593449 + 1.62721i) q^{12} -0.357435 q^{13} +(-2.50699 - 0.845586i) q^{14} +(2.03789 + 2.43186i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.02572 - 3.50866i) q^{17} +(-1.93133 + 2.29564i) q^{18} +(-4.35925 + 2.51681i) q^{19} -1.83184 q^{20} +(-3.57759 - 2.86372i) q^{21} +0.804842i q^{22} +(-4.54585 + 1.52815i) q^{23} +(-0.299664 - 1.70593i) q^{24} +(0.822177 - 1.42405i) q^{25} +(0.309548 - 0.178718i) q^{26} +(-4.50503 + 2.58934i) q^{27} +(2.59391 - 0.521194i) q^{28} +8.17926i q^{29} +(-2.98080 - 1.08711i) q^{30} +(1.44317 - 2.49965i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.477633 + 1.30965i) q^{33} +4.05145i q^{34} +(1.54898 - 4.59241i) q^{35} +(0.524767 - 2.95375i) q^{36} +(7.82094 - 4.51542i) q^{37} +(2.51681 - 4.35925i) q^{38} +(0.609760 - 0.107110i) q^{39} +(1.58642 - 0.915921i) q^{40} -4.77613i q^{41} +(4.53014 + 0.691258i) q^{42} -1.59064i q^{43} +(-0.402421 - 0.697013i) q^{44} +(-4.20524 - 3.53790i) q^{45} +(3.17275 - 3.59634i) q^{46} +(7.75220 - 4.47573i) q^{47} +(1.11248 + 1.32755i) q^{48} +(-0.886745 + 6.94361i) q^{49} +1.64435i q^{50} +(-2.40433 + 6.59256i) q^{51} +(-0.178718 + 0.309548i) q^{52} +(4.72870 - 8.19035i) q^{53} +(2.60680 - 4.49495i) q^{54} -1.47434 q^{55} +(-1.98579 + 1.74832i) q^{56} +(6.68238 - 5.59982i) q^{57} +(-4.08963 - 7.08344i) q^{58} +(-11.4528 - 6.61227i) q^{59} +(3.12500 - 0.548937i) q^{60} +(9.42234 - 5.43999i) q^{61} +2.88635i q^{62} +(6.96127 + 3.81323i) q^{63} -1.00000 q^{64} +(0.327382 + 0.567043i) q^{65} +(-0.241182 - 1.37300i) q^{66} +(9.94959 + 5.74440i) q^{67} +(-2.02572 - 3.50866i) q^{68} +(7.29698 - 3.96915i) q^{69} +(0.954746 + 4.75163i) q^{70} +3.72566i q^{71} +(1.02241 + 2.82040i) q^{72} +(2.04854 - 3.54818i) q^{73} +(-4.51542 + 7.82094i) q^{74} +(-0.975840 + 2.67571i) q^{75} +5.03363i q^{76} +(2.08769 - 0.419479i) q^{77} +(-0.474512 + 0.397640i) q^{78} +(8.99349 - 5.19239i) q^{79} +(-0.915921 + 1.58642i) q^{80} +(6.90935 - 5.76723i) q^{81} +(2.38807 + 4.13625i) q^{82} +11.7730 q^{83} +(-4.26884 + 1.66642i) q^{84} -7.42162 q^{85} +(0.795320 + 1.37753i) q^{86} +(-2.45103 - 13.9532i) q^{87} +(0.697013 + 0.402421i) q^{88} +(3.94235 + 6.82835i) q^{89} +(5.41080 + 0.961290i) q^{90} +(-0.624911 - 0.709792i) q^{91} +(-0.949509 + 4.70090i) q^{92} +(-1.71290 + 4.69670i) q^{93} +(-4.47573 + 7.75220i) q^{94} +(7.98546 + 4.61041i) q^{95} +(-1.62721 - 0.593449i) q^{96} -7.26241i q^{97} +(-2.70386 - 6.45671i) q^{98} +(0.422354 - 2.37730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more