LMFDB - Embedded newform 770.2.bi.a.27.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

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

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.19
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(0.355652 + 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.77729 - 1.35692i) q^{5} +(-2.16222 - 0.702547i) q^{6} +(2.12414 + 1.57735i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(0.355652 + 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.77729 - 1.35692i) q^{5} +(-2.16222 - 0.702547i) q^{6} +(2.12414 + 1.57735i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +(0.402154 + 2.19961i) q^{10} +(3.25893 - 0.615938i) q^{11} +(1.60760 - 1.60760i) q^{12} +(1.70240 - 3.34115i) q^{13} +(-2.36977 + 1.17652i) q^{14} +(3.67906 + 3.50831i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.00301 - 1.96852i) q^{17} +(0.339267 - 2.14205i) q^{18} +(1.06821 + 0.776101i) q^{19} +(-2.14244 - 0.640279i) q^{20} +(-2.78649 + 5.33074i) q^{21} +(-0.930718 + 3.18336i) q^{22} +(5.27438 - 5.27438i) q^{23} +(0.702547 + 2.16222i) q^{24} +(1.31752 - 4.82329i) q^{25} +(2.20411 + 3.03370i) q^{26} +(0.857967 + 1.68385i) q^{27} +(0.0275687 - 2.64561i) q^{28} +(2.67785 + 3.68574i) q^{29} +(-4.79619 + 1.68533i) q^{30} +(-4.48012 + 1.45568i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.54213 + 7.09886i) q^{33} +2.20932 q^{34} +(5.91555 - 0.0788767i) q^{35} +(1.75456 + 1.27476i) q^{36} +(-10.5411 - 1.66954i) q^{37} +(-1.17647 + 0.599441i) q^{38} +(8.10802 + 2.63445i) q^{39} +(1.54314 - 1.61825i) q^{40} +(-3.61181 + 4.97123i) q^{41} +(-3.48468 - 4.90288i) q^{42} +(4.46086 - 4.46086i) q^{43} +(-2.41385 - 2.27449i) q^{44} +(-2.75646 + 3.98990i) q^{45} +(2.30499 + 7.09402i) q^{46} +(-2.46747 + 0.390810i) q^{47} +(-2.24550 - 0.355652i) q^{48} +(2.02392 + 6.70103i) q^{49} +(3.69944 + 3.36365i) q^{50} +(4.06359 - 2.95237i) q^{51} +(-3.70370 + 0.586608i) q^{52} +(-3.08166 - 1.57019i) q^{53} -1.88983 q^{54} +(4.95628 - 5.51682i) q^{55} +(2.34474 + 1.22564i) q^{56} +(-1.36282 + 2.67469i) q^{57} +(-4.49974 + 0.712688i) q^{58} +(-10.0708 + 7.31690i) q^{59} +(0.675782 - 5.03856i) q^{60} +(-2.86642 - 0.931357i) q^{61} +(0.736912 - 4.65268i) q^{62} +(-5.43837 - 1.82990i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.50802 - 8.24823i) q^{65} +(-7.47924 - 0.957759i) q^{66} +(-7.09875 - 7.09875i) q^{67} +(-1.00301 + 1.96852i) q^{68} +(13.7195 + 9.96777i) q^{69} +(-2.61533 + 5.30661i) q^{70} +(-0.538759 + 1.65813i) q^{71} +(-1.93237 + 0.984592i) q^{72} +(-2.99166 - 0.473832i) q^{73} +(6.27312 - 8.63421i) q^{74} +(11.2993 + 1.24308i) q^{75} -1.32038i q^{76} +(7.89396 + 3.83214i) q^{77} +(-6.02828 + 6.02828i) q^{78} +(-8.50897 + 2.76473i) q^{79} +(0.741297 + 2.10962i) q^{80} +(-8.73963 + 6.34971i) q^{81} +(-2.78967 - 5.47503i) q^{82} +(-12.5881 + 6.41398i) q^{83} +(5.95051 - 0.879010i) q^{84} +(-4.45377 - 2.13762i) q^{85} +(1.94947 + 5.99984i) q^{86} +(-7.32394 + 7.32394i) q^{87} +(3.12245 - 1.11816i) q^{88} -14.2547 q^{89} +(-2.30362 - 4.26740i) q^{90} +(8.88631 - 4.41178i) q^{91} +(-7.36727 - 1.16686i) q^{92} +(-4.86209 - 9.54238i) q^{93} +(0.771996 - 2.37596i) q^{94} +(2.95163 - 0.0701237i) q^{95} +(1.33632 - 1.83929i) q^{96} +(0.802798 + 0.409046i) q^{97} +(-6.88950 - 1.23888i) q^{98} +(-6.30909 + 3.45451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	0.355652	+	2.24550i	0.205336	+	1.29644i	0.847879	+	0.530190i	$0.177879\pi$
$3$	0.355652	+	2.24550i	0.205336	+	1.29644i	−0.642543	+	0.766249i	$0.722121\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	1.77729	−	1.35692i	0.794828	−	0.606834i
$5$	1.77729	−	1.35692i	0.794828	−	0.606834i
$6$	−2.16222	−	0.702547i	−0.882721	−	0.286813i
$7$	2.12414	+	1.57735i	0.802848	+	0.596183i
$7$	2.12414	+	1.57735i	0.802848	+	0.596183i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.06261	+	0.670181i	−0.687535	+	0.223394i
$10$	0.402154	+	2.19961i	0.127172	+	0.695577i
$11$	3.25893	−	0.615938i	0.982604	−	0.185712i
$11$	3.25893	−	0.615938i	0.982604	−	0.185712i
$12$	1.60760	−	1.60760i	0.464074	−	0.464074i
$13$	1.70240	−	3.34115i	0.472161	−	0.926669i	−0.524980	−	0.851114i	$-0.675927\pi$
$13$	1.70240	−	3.34115i	0.472161	−	0.926669i	0.997142	−	0.0755546i	$-0.0240727\pi$
$14$	−2.36977	+	1.17652i	−0.633348	+	0.314437i
$15$	3.67906	+	3.50831i	0.949930	+	0.905842i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−1.00301	−	1.96852i	−0.243266	−	0.477437i	0.736799	−	0.676111i	$-0.236336\pi$
$17$	−1.00301	−	1.96852i	−0.243266	−	0.477437i	−0.980065	+	0.198675i	$0.936336\pi$
$18$	0.339267	−	2.14205i	0.0799661	−	0.504886i
$19$	1.06821	+	0.776101i	0.245064	+	0.178050i	0.703537	−	0.710659i	$-0.251603\pi$
$19$	1.06821	+	0.776101i	0.245064	+	0.178050i	−0.458472	+	0.888709i	$0.651603\pi$
$20$	−2.14244	−	0.640279i	−0.479064	−	0.143171i
$21$	−2.78649	+	5.33074i	−0.608062	+	1.16326i
$22$	−0.930718	+	3.18336i	−0.198430	+	0.678694i
$23$	5.27438	−	5.27438i	1.09978	−	1.09978i	0.105349	−	0.994435i	$-0.466404\pi$
$23$	5.27438	−	5.27438i	1.09978	−	1.09978i	0.994435	−	0.105349i	$-0.0335959\pi$
$24$	0.702547	+	2.16222i	0.143407	+	0.441361i
$25$	1.31752	−	4.82329i	0.263504	−	0.964658i
$26$	2.20411	+	3.03370i	0.432262	+	0.594958i
$27$	0.857967	+	1.68385i	0.165116	+	0.324058i
$28$	0.0275687	−	2.64561i	0.00520999	−	0.499973i
$29$	2.67785	+	3.68574i	0.497264	+	0.684425i	0.981707	−	0.190398i	$-0.0609778\pi$
$29$	2.67785	+	3.68574i	0.497264	+	0.684425i	−0.484443	+	0.874823i	$0.660978\pi$
$30$	−4.79619	+	1.68533i	−0.875660	+	0.307698i
$31$	−4.48012	+	1.45568i	−0.804653	+	0.261448i	−0.682332	−	0.731043i	$-0.739034\pi$
$31$	−4.48012	+	1.45568i	−0.804653	+	0.261448i	−0.122322	+	0.992491i	$0.539034\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.54213	+	7.09886i	0.442529	+	1.23575i
$34$	2.20932			0.378896
$35$	5.91555	−	0.0788767i	0.999911	−	0.0133326i
$36$	1.75456	+	1.27476i	0.292426	+	0.212460i
$37$	−10.5411	−	1.66954i	−1.73294	−	0.274471i	−0.791383	−	0.611320i	$-0.790639\pi$
$37$	−10.5411	−	1.66954i	−1.73294	−	0.274471i	−0.941559	+	0.336849i	$0.890639\pi$
$38$	−1.17647	+	0.599441i	−0.190848	+	0.0972421i
$39$	8.10802	+	2.63445i	1.29832	+	0.421850i
$40$	1.54314	−	1.61825i	0.243992	−	0.255867i
$41$	−3.61181	+	4.97123i	−0.564070	+	0.776375i	−0.991837	−	0.127514i	$-0.959300\pi$
$41$	−3.61181	+	4.97123i	−0.564070	+	0.776375i	0.427767	+	0.903889i	$0.359300\pi$
$42$	−3.48468	−	4.90288i	−0.537698	−	0.756531i
$43$	4.46086	−	4.46086i	0.680274	−	0.680274i	−0.279787	−	0.960062i	$-0.590264\pi$
$43$	4.46086	−	4.46086i	0.680274	−	0.680274i	0.960062	+	0.279787i	$0.0902640\pi$
$44$	−2.41385	−	2.27449i	−0.363902	−	0.342892i
$45$	−2.75646	+	3.98990i	−0.410909	+	0.594779i
$46$	2.30499	+	7.09402i	0.339852	+	1.04596i
$47$	−2.46747	+	0.390810i	−0.359918	+	0.0570054i	−0.333775	−	0.942653i	$-0.608323\pi$
$47$	−2.46747	+	0.390810i	−0.359918	+	0.0570054i	−0.0261431	+	0.999658i	$0.508323\pi$
$48$	−2.24550	−	0.355652i	−0.324110	−	0.0513339i
$49$	2.02392	+	6.70103i	0.289131	+	0.957290i
$50$	3.69944	+	3.36365i	0.523180	+	0.475692i
$51$	4.06359	−	2.95237i	0.569016	−	0.413414i
$52$	−3.70370	+	0.586608i	−0.513610	+	0.0813479i
$53$	−3.08166	−	1.57019i	−0.423299	−	0.215682i	0.229347	−	0.973345i	$-0.426341\pi$
$53$	−3.08166	−	1.57019i	−0.423299	−	0.215682i	−0.652646	+	0.757663i	$0.726341\pi$
$54$	−1.88983			−0.257174
$55$	4.95628	−	5.51682i	0.668305	−	0.743887i
$56$	2.34474	+	1.22564i	0.313329	+	0.163784i
$57$	−1.36282	+	2.67469i	−0.180510	+	0.354271i
$58$	−4.49974	+	0.712688i	−0.590844	+	0.0935806i
$59$	−10.0708	+	7.31690i	−1.31111	+	0.952579i	−0.311115	+	0.950372i	$0.600702\pi$
$59$	−10.0708	+	7.31690i	−1.31111	+	0.952579i	−0.999998	+	0.00220683i	$0.999298\pi$
$60$	0.675782	−	5.03856i	0.0872431	−	0.650475i
$61$	−2.86642	−	0.931357i	−0.367008	−	0.119248i	0.119706	−	0.992809i	$-0.461805\pi$
$61$	−2.86642	−	0.931357i	−0.367008	−	0.119248i	−0.486714	+	0.873561i	$0.661805\pi$
$62$	0.736912	−	4.65268i	0.0935879	−	0.590891i
$63$	−5.43837	−	1.82990i	−0.685170	−	0.230546i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	−1.50802	−	8.24823i	−0.187047	−	1.02307i
$66$	−7.47924	−	0.957759i	−0.920630	−	0.117892i
$67$	−7.09875	−	7.09875i	−0.867250	−	0.867250i	0.124917	−	0.992167i	$-0.460134\pi$
$67$	−7.09875	−	7.09875i	−0.867250	−	0.867250i	−0.992167	+	0.124917i	$0.960134\pi$
$68$	−1.00301	+	1.96852i	−0.121633	+	0.238718i
$69$	13.7195	+	9.96777i	1.65163	+	1.19998i
$70$	−2.61533	+	5.30661i	−0.312591	+	0.634261i
$71$	−0.538759	+	1.65813i	−0.0639389	+	0.196784i	−0.977923	−	0.208967i	$-0.932990\pi$
$71$	−0.538759	+	1.65813i	−0.0639389	+	0.196784i	0.913984	+	0.405751i	$0.132990\pi$
$72$	−1.93237	+	0.984592i	−0.227732	+	0.116035i
$73$	−2.99166	−	0.473832i	−0.350147	−	0.0554578i	−0.0211162	−	0.999777i	$-0.506722\pi$
$73$	−2.99166	−	0.473832i	−0.350147	−	0.0554578i	−0.329031	+	0.944319i	$0.606722\pi$
$74$	6.27312	−	8.63421i	0.729235	−	1.00371i
$75$	11.2993	+	1.24308i	1.30473	+	0.143538i
$76$		−	1.32038i		−	0.151458i
$77$	7.89396	+	3.83214i	0.899601	+	0.436713i
$78$	−6.02828	+	6.02828i	−0.682568	+	0.682568i
$79$	−8.50897	+	2.76473i	−0.957334	+	0.311057i	−0.745692	−	0.666291i	$-0.767881\pi$
$79$	−8.50897	+	2.76473i	−0.957334	+	0.311057i	−0.211642	+	0.977347i	$0.567881\pi$
$80$	0.741297	+	2.10962i	0.0828796	+	0.235862i
$81$	−8.73963	+	6.34971i	−0.971070	+	0.705523i
$82$	−2.78967	−	5.47503i	−0.308067	−	0.604616i
$83$	−12.5881	+	6.41398i	−1.38173	+	0.704026i	−0.977560	−	0.210658i	$-0.932439\pi$
$83$	−12.5881	+	6.41398i	−1.38173	+	0.704026i	−0.404169	+	0.914684i	$0.632439\pi$
$84$	5.95051	−	0.879010i	0.649254	−	0.0959079i
$85$	−4.45377	−	2.13762i	−0.483080	−	0.231858i
$86$	1.94947	+	5.99984i	0.210216	+	0.646979i
$87$	−7.32394	+	7.32394i	−0.785209	+	0.785209i
$88$	3.12245	−	1.11816i	0.332855	−	0.119197i
$89$	−14.2547			−1.51099			−0.755496	−	0.655153i	$-0.772604\pi$
$89$	−14.2547			−1.51099			−0.755496	+	0.655153i	$0.772604\pi$
$90$	−2.30362	−	4.26740i	−0.242823	−	0.449824i
$91$	8.88631	−	4.41178i	0.931539	−	0.462480i
$92$	−7.36727	−	1.16686i	−0.768090	−	0.121654i
$93$	−4.86209	−	9.54238i	−0.504175	−	0.989499i
$94$	0.771996	−	2.37596i	0.0796253	−	0.245061i
$95$	2.95163	−	0.0701237i	0.302831	−	0.00719454i
$96$	1.33632	−	1.83929i	0.136388	−	0.187722i
$97$	0.802798	+	0.409046i	0.0815118	+	0.0415323i	0.494271	−	0.869308i	$-0.335435\pi$
$97$	0.802798	+	0.409046i	0.0815118	+	0.0415323i	−0.412759	+	0.910840i	$0.635435\pi$
$98$	−6.88950	−	1.23888i	−0.695944	−	0.125146i
$99$	−6.30909	+	3.45451i	−0.634088	+	0.347191i
$100$	−4.67654	+	1.76916i	−0.467654	+	0.176916i
$101$	5.08501	−	1.65222i	0.505977	−	0.164402i	−0.0448947	−	0.998992i	$-0.514295\pi$
$101$	5.08501	−	1.65222i	0.505977	−	0.164402i	0.550872	+	0.834590i	$0.314295\pi$
$102$	0.785750	+	4.96103i	0.0778009	+	0.491215i
$103$	15.4800	+	2.45178i	1.52529	+	0.241581i	0.862047	−	0.506827i	$-0.169182\pi$
$103$	15.4800	+	2.45178i	1.52529	+	0.241581i	0.663238	+	0.748409i	$0.269182\pi$
$104$	1.15877	−	3.56633i	0.113627	−	0.349708i
$105$	2.28100	+	13.2553i	0.222602	+	1.29359i
$106$	2.79809	−	2.03293i	0.271775	−	0.197456i
$107$	1.74338	+	11.0073i	0.168539	+	1.06411i	0.916401	+	0.400261i	$0.131080\pi$
$107$	1.74338	+	11.0073i	0.168539	+	1.06411i	−0.747862	+	0.663854i	$0.768920\pi$
$108$	0.857967	−	1.68385i	0.0825579	−	0.162029i
$109$			14.2651i			1.36635i	0.730254	+	0.683175i	$0.239401\pi$
$109$			14.2651i			1.36635i	−0.730254	+	0.683175i	$0.760599\pi$
$110$	2.66541	+	6.92066i	0.254137	+	0.659859i
$111$		−	24.2637i		−	2.30301i
$112$	−2.15655	+	1.53275i	−0.203774	+	0.144831i
$113$	2.37812	−	0.376657i	0.223714	−	0.0354329i	−0.0435708	−	0.999050i	$-0.513873\pi$
$113$	2.37812	−	0.376657i	0.223714	−	0.0354329i	0.267285	+	0.963617i	$0.413873\pi$
$114$	−1.76446	−	2.42857i	−0.165256	−	0.227456i
$115$	2.21718	−	16.5310i	0.206753	−	1.54153i
$116$	1.40783	−	4.33285i	0.130714	−	0.402295i
$117$	−1.27221	+	8.03240i	−0.117616	+	0.742595i
$118$	−1.94734	−	12.2950i	−0.179267	−	1.13185i
$119$	0.974518	−	5.76351i	0.0893339	−	0.528340i
$120$	4.18259	+	2.88958i	0.381816	+	0.263782i
$121$	10.2412	−	4.01460i	0.931022	−	0.364963i
$122$	2.13117	−	2.13117i	0.192947	−	0.192947i
$123$	−12.4474	−	6.34228i	−1.12235	−	0.571864i
$124$	3.81102	+	2.76887i	0.342239	+	0.248651i
$125$	−4.20322	−	10.3602i	−0.375947	−	0.926641i
$126$	4.09942	−	4.01486i	0.365205	−	0.357673i
$127$	12.8210	−	6.53263i	1.13768	−	0.579677i	0.219410	−	0.975633i	$-0.429587\pi$
$127$	12.8210	−	6.53263i	1.13768	−	0.579677i	0.918269	+	0.395956i	$0.129587\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	11.6034	+	8.43034i	1.02162	+	0.742250i
$130$	8.03385	+	2.40096i	0.704615	+	0.210578i
$131$		−	13.8360i		−	1.20886i	−0.796659	−	0.604429i	$-0.793401\pi$
$131$		−	13.8360i		−	1.20886i	0.796659	−	0.604429i	$-0.206599\pi$
$132$	4.24887	−	6.22923i	0.369817	−	0.542185i
$133$	1.04484	+	3.33349i	0.0905993	+	0.289050i
$134$	9.54780	−	3.10227i	0.824804	−	0.267995i
$135$	3.80972	+	1.82850i	0.327888	+	0.157373i
$136$	−1.29861	−	1.78738i	−0.111355	−	0.153267i
$137$	−9.12611	+	4.64999i	−0.779697	+	0.397275i	−0.798077	−	0.602556i	$-0.794149\pi$
$137$	−9.12611	+	4.64999i	−0.779697	+	0.397275i	0.0183802	+	0.999831i	$0.494149\pi$
$138$	−15.1098	+	7.69885i	−1.28624	+	0.655370i
$139$	12.3649	−	8.98366i	1.04878	−	0.761984i	0.0768009	−	0.997046i	$-0.475529\pi$
$139$	12.3649	−	8.98366i	1.04878	−	0.761984i	0.971980	+	0.235062i	$0.0755294\pi$
$140$	−3.54089	−	4.73942i	−0.299260	−	0.400554i
$141$	−1.75512	−	5.40172i	−0.147808	−	0.454907i
$142$	−1.23281	−	1.23281i	−0.103455	−	0.103455i
$143$	3.49007	−	11.9372i	0.291854	−	0.998235i
$144$		−	2.16875i		−	0.180729i
$145$	9.76058	+	2.91700i	0.810572	+	0.242244i
$146$	1.78037	−	2.45047i	0.147345	−	0.202802i
$147$	−14.3273	+	6.92794i	−1.18170	+	0.571407i
$148$	4.84520	+	9.50924i	0.398273	+	0.781655i
$149$	18.5619	+	6.03113i	1.52065	+	0.494089i	0.945961	−	0.324282i	$-0.105123\pi$
$149$	18.5619	+	6.03113i	1.52065	+	0.494089i	0.574690	+	0.818371i	$0.305123\pi$
$150$	−6.23735	+	9.50338i	−0.509278	+	0.775948i
$151$	−2.32500	−	1.68921i	−0.189206	−	0.137466i	0.489150	−	0.872200i	$-0.337307\pi$
$151$	−2.32500	−	1.68921i	−0.189206	−	0.137466i	−0.678356	+	0.734734i	$0.737307\pi$
$152$	1.17647	+	0.599441i	0.0954242	+	0.0486211i
$153$	3.38808	+	3.38808i	0.273910	+	0.273910i
$154$	−6.99825	+	5.29382i	−0.563935	+	0.426588i
$155$	−5.98723	+	8.66634i	−0.480906	+	0.696097i
$156$	−2.63445	−	8.10802i	−0.210925	−	0.649161i
$157$	2.53240	−	0.401092i	0.202107	−	0.0320107i	−0.0545599	−	0.998511i	$-0.517376\pi$
$157$	2.53240	−	0.401092i	0.202107	−	0.0320107i	0.256667	+	0.966500i	$0.417376\pi$
$158$	1.39960	−	8.83671i	0.111346	−	0.703011i
$159$	2.42985	−	7.47831i	0.192700	−	0.593069i
$160$	−2.21622	−	0.297245i	−0.175208	−	0.0234992i
$161$	19.5231	−	2.88395i	1.53863	−	0.227287i
$162$	−1.68993	−	10.6698i	−0.132773	−	0.838296i
$163$	0.638438	+	0.325300i	0.0500063	+	0.0254795i	0.478815	−	0.877916i	$-0.341067\pi$
$163$	0.638438	+	0.325300i	0.0500063	+	0.0254795i	−0.428809	+	0.903395i	$0.641067\pi$
$164$	6.14477			0.479826
$165$	14.1507	+	9.16726i	1.10163	+	0.713670i
$166$		−	14.1280i		−	1.09655i
$167$	18.5659	+	9.45979i	1.43667	+	0.732020i	0.986932	−	0.161140i	$-0.0515170\pi$
$167$	18.5659	+	9.45979i	1.43667	+	0.732020i	0.449739	+	0.893160i	$0.351517\pi$
$168$	−1.91827	+	5.70101i	−0.147998	+	0.439842i
$169$	−0.623920	−	0.858753i	−0.0479939	−	0.0660579i
$170$	3.92661	−	2.99788i	0.301157	−	0.229927i
$171$	−2.72343	−	0.884895i	−0.208266	−	0.0676696i
$172$	−6.23094	−	0.986883i	−0.475104	−	0.0752492i
$173$	0.208321	+	1.31529i	0.0158383	+	0.0999994i	0.994341	−	0.106234i	$-0.0338793\pi$
$173$	0.208321	+	1.31529i	0.0158383	+	0.0999994i	−0.978503	+	0.206234i	$0.933879\pi$
$174$	−3.20068	−	9.85068i	−0.242643	−	0.746778i
$175$	10.4066	−	8.16714i	0.786667	−	0.617378i
$176$	−0.421273	+	3.28976i	−0.0317546	+	0.247975i
$177$	−20.0118	−	20.0118i	−1.50418	−	1.50418i
$178$	6.47149	−	12.7010i	0.485058	−	0.951981i
$179$	−10.4410	+	14.3709i	−0.780401	+	1.07413i	0.214837	+	0.976650i	$0.431078\pi$
$179$	−10.4410	+	14.3709i	−0.780401	+	1.07413i	−0.995238	+	0.0974793i	$0.968922\pi$
$180$	4.84811	−	0.115179i	0.361357	−	0.00858497i
$181$	−10.5540	−	3.42920i	−0.784471	−	0.254890i	−0.110723	−	0.993851i	$-0.535317\pi$
$181$	−10.5540	−	3.42920i	−0.784471	−	0.254890i	−0.673748	+	0.738961i	$0.735317\pi$
$182$	−0.103379	+	9.92067i	−0.00766294	+	0.735369i
$183$	1.07191	−	6.76779i	0.0792380	−	0.500289i
$184$	4.38435	−	6.03454i	0.323218	−	0.444872i
$185$	−21.0000	+	11.3362i	−1.54395	+	0.833451i
$186$	10.7097			0.785271
$187$	−4.48123	−	5.79748i	−0.327700	−	0.423954i
$188$	1.76652	+	1.76652i	0.128836	+	0.128836i
$189$	−0.833594	+	4.93006i	−0.0606350	+	0.358609i
$190$	−1.27753	+	2.66176i	−0.0926819	+	0.193104i
$191$	−2.32756	+	1.69107i	−0.168416	+	0.122362i	−0.668801	−	0.743442i	$-0.733192\pi$
$191$	−2.32756	+	1.69107i	−0.168416	+	0.122362i	0.500384	+	0.865803i	$0.333192\pi$
$192$	1.03214	+	2.02569i	0.0744885	+	0.146192i
$193$	−5.82405	−	11.4303i	−0.419225	−	0.822775i	−0.999962	−	0.00868384i	$-0.997236\pi$
$193$	−5.82405	−	11.4303i	−0.419225	−	0.822775i	0.580738	−	0.814091i	$-0.302764\pi$
$194$	−0.728925	+	0.529595i	−0.0523338	+	0.0380227i
$195$	17.9850	−	6.31976i	1.28794	−	0.452568i
$196$	4.23162	−	5.57615i	0.302258	−	0.398296i
$197$	−5.41938	−	5.41938i	−0.386114	−	0.386114i	0.487185	−	0.873299i	$-0.338024\pi$
$197$	−5.41938	−	5.41938i	−0.386114	−	0.386114i	−0.873299	+	0.487185i	$0.838024\pi$
$198$	−0.213722	−	7.18976i	−0.0151885	−	0.510954i
$199$	−9.45633			−0.670342			−0.335171	−	0.942157i	$-0.608794\pi$
$199$	−9.45633			−0.670342			−0.335171	+	0.942157i	$0.608794\pi$
$200$	0.546771	−	4.97001i	0.0386625	−	0.351433i
$201$	13.4155	−	18.4649i	0.946260	−	1.30241i
$202$	−0.836407	+	5.28087i	−0.0588494	+	0.371561i
$203$	−0.125598	+	12.0529i	−0.00881525	+	0.845950i
$204$	−4.77703	−	1.55215i	−0.334459	−	0.108672i
$205$	0.326341	+	13.7363i	0.0227926	+	0.959382i
$206$	−9.21231	+	12.6797i	−0.641852	+	0.883433i
$207$	−7.34417	+	14.4138i	−0.510455	+	1.00182i
$208$	2.65155	+	2.65155i	0.183852	+	0.183852i
$209$	3.95925	+	1.87131i	0.273867	+	0.129441i
$210$	−12.8461	−	3.98540i	−0.886467	−	0.275019i
$211$	−5.52230	−	16.9959i	−0.380171	−	1.17005i	−0.939923	−	0.341385i	$-0.889104\pi$
$211$	−5.52230	−	16.9959i	−0.380171	−	1.17005i	0.559753	−	0.828660i	$-0.310896\pi$
$212$	0.541049	+	3.41605i	0.0371594	+	0.234615i
$213$	−3.91494	−	0.620065i	−0.268247	−	0.0424862i
$214$	−10.5990	−	3.44384i	−0.724536	−	0.235416i
$215$	1.87520	−	13.9813i	0.127888	−	0.953515i
$216$	1.11082	+	1.52891i	0.0755815	+	0.104029i
$217$	−11.8125	−	3.97467i	−0.801885	−	0.269818i
$218$	−12.7103	−	6.47623i	−0.860851	−	0.438626i
$219$		−	6.88628i		−	0.465332i
$220$	−7.37643	−	0.767014i	−0.497319	−	0.0517120i
$221$	−8.28466			−0.557287
$222$	21.6192	+	11.0155i	1.45098	+	0.739312i
$223$	−2.67758	−	16.9056i	−0.179304	−	1.13208i	−0.899051	−	0.437844i	$-0.855742\pi$
$223$	−2.67758	−	16.9056i	−0.179304	−	1.13208i	0.719747	−	0.694237i	$-0.244258\pi$
$224$	−0.386635	−	2.61735i	−0.0258331	−	0.174879i
$225$	0.514953	+	10.8315i	0.0343302	+	0.722102i
$226$	−0.744039	+	2.28992i	−0.0494927	+	0.152323i
$227$	−4.25095	+	26.8395i	−0.282146	+	1.78140i	0.285757	+	0.958302i	$0.407755\pi$
$227$	−4.25095	+	26.8395i	−0.282146	+	1.78140i	−0.567902	+	0.823096i	$0.692245\pi$
$228$	2.96491	−	0.469596i	0.196356	−	0.0310998i
$229$	−6.20030	−	19.0826i	−0.409727	−	1.26101i	−0.916883	−	0.399156i	$-0.869303\pi$
$229$	−6.20030	−	19.0826i	−0.409727	−	1.26101i	0.507156	−	0.861855i	$-0.330697\pi$
$230$	13.7227	+	9.48045i	0.904847	+	0.625122i
$231$	−5.79757	+	19.0888i	−0.381452	+	1.25595i
$232$	3.22146	+	3.22146i	0.211499	+	0.211499i
$233$	9.35155	+	4.76485i	0.612641	+	0.312156i	0.732638	−	0.680618i	$-0.238289\pi$
$233$	9.35155	+	4.76485i	0.612641	+	0.312156i	−0.119998	+	0.992774i	$0.538289\pi$
$234$	−6.57935	−	4.78018i	−0.430105	−	0.312490i
$235$	−3.85512	+	4.04275i	−0.251480	+	0.263720i
$236$	11.8390	+	3.84672i	0.770653	+	0.250400i
$237$	−9.23443	−	18.1236i	−0.599841	−	1.17725i
$238$	4.69290	+	3.48488i	0.304196	+	0.225891i
$239$	2.41807	−	3.32818i	0.156412	−	0.215282i	−0.723618	−	0.690200i	$-0.757522\pi$
$239$	2.41807	−	3.32818i	0.156412	−	0.215282i	0.880030	+	0.474918i	$0.157522\pi$
$240$	−4.47349	+	2.41487i	−0.288763	+	0.155879i
$241$			12.5326i			0.807298i	0.914914	+	0.403649i	$0.132258\pi$
$241$			12.5326i			0.807298i	−0.914914	+	0.403649i	$0.867742\pi$
$242$	−1.07239	+	10.9476i	−0.0689361	+	0.703738i
$243$	−13.3576	−	13.3576i	−0.856889	−	0.856889i
$244$	0.931357	+	2.86642i	0.0596241	+	0.183504i
$245$	12.6899	+	9.16337i	0.810726	+	0.585426i
$246$	11.3020	−	8.21140i	0.720591	−	0.523540i
$247$	4.41160	−	2.24782i	0.280703	−	0.143025i
$248$	−4.19724	+	2.13860i	−0.266525	+	0.135801i
$249$	−18.8796	−	25.9855i	−1.19645	−	1.64677i
$250$	11.1392	+	0.958321i	0.704504	+	0.0606096i
$251$	5.14466	−	1.67160i	0.324728	−	0.105511i	−0.142116	−	0.989850i	$-0.545391\pi$
$251$	5.14466	−	1.67160i	0.324728	−	0.105511i	0.466845	+	0.884339i	$0.345391\pi$
$252$	1.71617	+	5.47532i	0.108109	+	0.344913i
$253$	13.9401	−	20.4375i	0.876409	−	1.28490i
$254$			14.3893i			0.902868i
$255$	3.21604	−	10.7612i	0.201396	−	0.673892i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.92289	−	18.4544i	0.182325	−	1.15115i	−0.711483	−	0.702703i	$-0.751976\pi$
$257$	2.92289	−	18.4544i	0.182325	−	1.15115i	0.893808	−	0.448450i	$-0.148024\pi$
$258$	−12.7793	+	6.51138i	−0.795605	+	0.405381i
$259$	−19.7572	−	20.1733i	−1.22765	−	1.25351i
$260$	−5.78656	+	6.06820i	−0.358867	+	0.376334i
$261$	−7.99346	−	5.80759i	−0.494783	−	0.359481i
$262$	12.3280	+	6.28142i	0.761625	+	0.388067i
$263$	−8.73314	+	8.73314i	−0.538509	+	0.538509i	−0.923091	−	0.384582i	$-0.874346\pi$
$263$	−8.73314	+	8.73314i	−0.538509	+	0.538509i	0.384582	+	0.923091i	$0.374346\pi$
$264$	3.62134	+	6.61378i	0.222878	+	0.407050i
$265$	−7.60764	+	1.39090i	−0.467333	+	0.0854426i
$266$	−3.44451	−	0.582412i	−0.211196	−	0.0357099i
$267$	−5.06970	−	32.0088i	−0.310261	−	1.95891i
$268$	−1.57047	+	9.91555i	−0.0959316	+	0.605689i
$269$	−3.30063	+	10.1583i	−0.201243	+	0.619361i	0.798604	+	0.601857i	$0.205572\pi$
$269$	−3.30063	+	10.1583i	−0.201243	+	0.619361i	−0.999847	+	0.0175047i	$0.994428\pi$
$270$	−3.35878	+	2.56436i	−0.204409	+	0.156062i
$271$	5.27285	+	7.25745i	0.320303	+	0.440859i	0.938560	−	0.345117i	$-0.112161\pi$
$271$	5.27285	+	7.25745i	0.320303	+	0.440859i	−0.618257	+	0.785976i	$0.712161\pi$
$272$	2.18212	−	0.345614i	0.132311	−	0.0209559i
$273$	13.0671	+	18.3851i	0.790855	+	1.11272i
$274$		−	10.2425i		−	0.618771i
$275$	1.32286	−	16.5303i	0.0797714	−	0.996813i
$276$		−	16.9582i		−	1.02076i
$277$	−3.62809	+	7.12052i	−0.217991	+	0.427831i	−0.973942	−	0.226797i	$-0.927175\pi$
$277$	−3.62809	+	7.12052i	−0.217991	+	0.427831i	0.755951	+	0.654628i	$0.227175\pi$
$278$	2.39093	+	15.0957i	0.143399	+	0.905383i
$279$	8.26515	−	6.00498i	0.494821	−	0.359509i
$280$	5.83038	−	1.00330i	0.348432	−	0.0599588i
$281$	−4.08033	+	12.5579i	−0.243412	+	0.749144i	0.752482	+	0.658613i	$0.228857\pi$
$281$	−4.08033	+	12.5579i	−0.243412	+	0.749144i	−0.995894	+	0.0905314i	$0.971143\pi$
$282$	5.60977	+	0.888501i	0.334057	+	0.0529095i
$283$	−1.42862	−	9.01995i	−0.0849226	−	0.536180i	−0.993069	−	0.117529i	$-0.962503\pi$
$283$	−1.42862	−	9.01995i	−0.0849226	−	0.536180i	0.908147	−	0.418652i	$-0.137497\pi$
$284$	1.65813	−	0.538759i	0.0983919	−	0.0319695i
$285$	1.20722	+	6.60294i	0.0715093	+	0.391124i
$286$	9.05163	+	8.52903i	0.535234	+	0.504332i
$287$	−15.5134	+	4.86247i	−0.915724	+	0.287023i
$288$	1.93237	+	0.984592i	0.113866	+	0.0580177i
$289$	7.12331	−	9.80439i	0.419018	−	0.576729i
$290$	−7.03028	+	7.37245i	−0.412832	+	0.432925i
$291$	−0.632995	+	1.94816i	−0.0371068	+	0.114203i
$292$	1.37511	+	2.69881i	0.0804724	+	0.157936i
$293$	8.43221	+	1.33553i	0.492615	+	0.0780225i	0.397799	−	0.917472i	$-0.369774\pi$
$293$	8.43221	+	1.33553i	0.492615	+	0.0780225i	0.0948152	+	0.995495i	$0.469774\pi$
$294$	0.331638	−	15.9110i	0.0193415	−	0.927946i
$295$	−7.97035	+	26.6696i	−0.464052	+	1.55277i
$296$	−10.6725			−0.620325
$297$	3.83320	+	4.95911i	0.222425	+	0.287757i
$298$	−13.8007	+	13.8007i	−0.799453	+	0.799453i
$299$	−8.64339	−	26.6016i	−0.499860	−	1.53841i
$300$	−5.63587	−	9.87197i	−0.325387	−	0.569958i
$301$	16.5118	−	2.43913i	0.951726	−	0.140589i
$302$	2.56063	−	1.30470i	0.147348	−	0.0750773i
$303$	5.51855	+	10.8308i	0.317032	+	0.622211i
$304$	−1.06821	+	0.776101i	−0.0612661	+	0.0445124i
$305$	−6.35825	+	2.23422i	−0.364072	+	0.127931i
$306$	−4.55696	+	1.48065i	−0.260504	+	0.0846429i
$307$	12.4274	−	12.4274i	0.709272	−	0.709272i	−0.257110	−	0.966382i	$-0.582770\pi$
$307$	12.4274	−	12.4274i	0.709272	−	0.709272i	0.966382	+	0.257110i	$0.0827704\pi$
$308$	−1.53969	−	8.63883i	−0.0877318	−	0.492243i
$309$			35.6322i			2.02704i
$310$	−5.00362	−	9.26909i	−0.284187	−	0.526449i
$311$	−12.9019	+	17.7580i	−0.731602	+	1.00696i	0.267456	+	0.963570i	$0.413817\pi$
$311$	−12.9019	+	17.7580i	−0.731602	+	1.00696i	−0.999058	+	0.0433934i	$0.986183\pi$
$312$	8.42031	+	1.33365i	0.476706	+	0.0755029i
$313$	−11.9862	+	6.10725i	−0.677498	+	0.345202i	−0.758649	−	0.651499i	$-0.774140\pi$
$313$	−11.9862	+	6.10725i	−0.677498	+	0.345202i	0.0811514	+	0.996702i	$0.474140\pi$
$314$	−0.792309	+	2.43847i	−0.0447126	+	0.137611i
$315$	−12.1486	+	4.12718i	−0.684495	+	0.232540i
$316$	7.23816	+	5.25883i	0.407178	+	0.295832i
$317$	−6.67856	+	13.1074i	−0.375105	+	0.736185i	−0.998971	−	0.0453460i	$-0.985561\pi$
$317$	−6.67856	+	13.1074i	−0.375105	+	0.736185i	0.623866	+	0.781531i	$0.285561\pi$
$318$	5.56010	+	5.56010i	0.311795	+	0.311795i
$319$	10.9971	+	10.3622i	0.615720	+	0.580171i
$320$	1.27099	−	1.83972i	0.0710506	−	0.102844i
$321$	−24.0968	+	7.82953i	−1.34495	+	0.437002i
$322$	−6.29367	+	18.7045i	−0.350732	+	1.04236i
$323$	0.456343	−	2.88123i	0.0253916	−	0.160316i
$324$	10.2740	+	3.33824i	0.570780	+	0.185458i
$325$	−13.8724	−	12.6132i	−0.769502	−	0.699656i
$326$	−0.579689	+	0.421169i	−0.0321060	+	0.0233264i
$327$	−32.0323	+	5.07342i	−1.77139	+	0.280561i
$328$	−2.78967	+	5.47503i	−0.154034	+	0.302308i
$329$	−5.85770	−	3.06194i	−0.322945	−	0.168810i
$330$	−14.5924	+	8.44653i	−0.803284	+	0.464966i
$331$	11.7363			0.645086			0.322543	−	0.946555i	$-0.395462\pi$
$331$	11.7363			0.645086			0.322543	+	0.946555i	$0.395462\pi$
$332$	12.5881	+	6.41398i	0.690864	+	0.352013i
$333$	22.8610	−	3.62082i	1.25277	−	0.198420i
$334$	−16.8575	+	12.2477i	−0.922399	+	0.670162i
$335$	−22.2490	−	2.98408i	−1.21559	−	0.163038i
$336$	−4.20876	−	4.29740i	−0.229607	−	0.234442i
$337$	5.08535	+	0.805441i	0.277017	+	0.0438752i	0.293397	−	0.955991i	$-0.405214\pi$
$337$	5.08535	+	0.805441i	0.277017	+	0.0438752i	−0.0163802	+	0.999866i	$0.505214\pi$
$338$	1.04841	−	0.166052i	0.0570259	−	0.00903201i
$339$	1.69156	+	5.20610i	0.0918732	+	0.282757i
$340$	0.888489	+	4.85964i	0.0481851	+	0.263551i
$341$	−13.7038	+	7.50343i	−0.742101	+	0.406334i
$342$	2.02486	−	2.02486i	0.109492	−	0.109492i
$343$	−6.27081	+	17.4263i	−0.338592	+	0.940933i
$344$	3.70811	−	5.10377i	0.199928	−	0.275177i
$345$	37.9089	−	0.900626i	2.04095	−	0.0484881i
$346$	−1.26650	−	0.411512i	−0.0680877	−	0.0221230i
$347$	25.4525	−	12.9687i	1.36636	−	0.696196i	0.391745	−	0.920074i	$-0.371871\pi$
$347$	25.4525	−	12.9687i	1.36636	−	0.696196i	0.974617	+	0.223877i	$0.0718715\pi$
$348$	10.2301	+	1.62029i	0.548391	+	0.0868566i
$349$	17.7813	+	12.9189i	0.951812	+	0.691532i	0.951235	−	0.308468i	$-0.0998162\pi$
$349$	17.7813	+	12.9189i	0.951812	+	0.691532i	0.000577532		1.00000i	$0.499816\pi$
$350$	2.55246	+	12.9802i	0.136435	+	0.693820i
$351$	7.08662			0.378256
$352$	−2.73995	−	1.86888i	−0.146040	−	0.0996115i
$353$	−13.9970	−	13.9970i	−0.744983	−	0.744983i	0.228550	−	0.973532i	$-0.426602\pi$
$353$	−13.9970	−	13.9970i	−0.744983	−	0.744983i	−0.973532	+	0.228550i	$0.926602\pi$
$354$	26.9158	−	8.74548i	1.43056	−	0.464817i
$355$	1.29242	+	3.67803i	0.0685947	+	0.195210i
$356$	8.37869	+	11.5323i	0.444069	+	0.611209i
$357$	13.2885	+	0.138474i	0.703304	+	0.00732881i
$358$	−8.06440	−	15.8273i	−0.426217	−	0.836498i
$359$	19.3895	+	26.6874i	1.02334	+	1.40851i	0.909835	+	0.414970i	$0.136208\pi$
$359$	19.3895	+	26.6874i	1.02334	+	1.40851i	0.113505	+	0.993537i	$0.463792\pi$
$360$	−2.09837	+	4.37199i	−0.110594	+	0.230424i
$361$	−5.33258	−	16.4120i	−0.280662	−	0.863789i
$362$	7.84684	−	7.84684i	0.412421	−	0.412421i
$363$	12.6571	+	21.5689i	0.664325	+	1.13207i
$364$	−8.79245	−	4.59600i	−0.460849	−	0.240896i
$365$	−5.96000	+	3.21731i	−0.311960	+	0.168402i
$366$	5.54351	+	4.02759i	0.289764	+	0.210526i
$367$	4.07290	−	25.7153i	0.212603	−	1.34233i	−0.618315	−	0.785931i	$-0.712184\pi$
$367$	4.07290	−	25.7153i	0.212603	−	1.34233i	0.830918	−	0.556395i	$-0.187816\pi$
$368$	3.38636	+	6.64611i	0.176526	+	0.346452i
$369$	4.11811	−	12.6742i	0.214380	−	0.659795i
$370$	−0.566801	−	23.8576i	−0.0294666	−	1.24030i
$371$	−4.06914	−	8.19616i	−0.211259	−	0.425524i
$372$	−4.86209	+	9.54238i	−0.252088	+	0.494750i
$373$	8.16155	−	8.16155i	0.422589	−	0.422589i	−0.463505	−	0.886094i	$-0.653408\pi$
$373$	8.16155	−	8.16155i	0.422589	−	0.422589i	0.886094	+	0.463505i	$0.153408\pi$
$374$	7.20003	−	1.36081i	0.372305	−	0.0703656i
$375$	21.7688	−	13.1229i	1.12414	−	0.677665i
$376$	−2.37596	+	0.771996i	−0.122531	+	0.0398127i
$377$	16.8734	−	2.67248i	0.869024	−	0.137640i
$378$	−4.01427	−	2.98094i	−0.206472	−	0.153323i
$379$	−30.1989	−	9.81223i	−1.55122	−	0.504021i	−0.596772	−	0.802411i	$-0.703550\pi$
$379$	−30.1989	−	9.81223i	−1.55122	−	0.504021i	−0.954444	+	0.298391i	$0.903550\pi$
$380$	−1.79166	−	2.34670i	−0.0919100	−	0.120383i
$381$	19.2288	+	26.4662i	0.985122	+	1.35590i
$382$	−0.450065	−	2.84160i	−0.0230274	−	0.145389i
$383$	0.0984998	−	0.193317i	0.00503310	−	0.00987802i	−0.888476	−	0.458923i	$-0.848236\pi$
$383$	0.0984998	−	0.193317i	0.00503310	−	0.00987802i	0.893509	+	0.449045i	$0.148236\pi$
$384$	−2.27349			−0.116018
$385$	19.2298	−	3.90067i	0.980041	−	0.198796i
$386$	12.8286			0.652958
$387$	−6.21141	+	12.1906i	−0.315744	+	0.619682i
$388$	−0.140948	−	0.889908i	−0.00715553	−	0.0451782i
$389$	7.77266	+	10.6982i	0.394090	+	0.542418i	0.959248	−	0.282564i	$-0.0911851\pi$
$389$	7.77266	+	10.6982i	0.394090	+	0.542418i	−0.565159	+	0.824982i	$0.691185\pi$
$390$	−2.53409	+	18.8939i	−0.128319	+	0.956730i
$391$	−15.6730	−	5.09246i	−0.792617	−	0.257537i
$392$	3.04727	+	6.30192i	0.153910	+	0.318295i
$393$	31.0688	−	4.92081i	1.56721	−	0.248222i
$394$	7.28904	−	2.36835i	0.367217	−	0.119316i
$395$	−11.3714	+	16.4597i	−0.572156	+	0.828180i
$396$	6.50315	+	3.07365i	0.326796	+	0.154457i
$397$	15.2405	−	15.2405i	0.764898	−	0.764898i	−0.212306	−	0.977203i	$-0.568097\pi$
$397$	15.2405	−	15.2405i	0.764898	−	0.764898i	0.977203	+	0.212306i	$0.0680972\pi$
$398$	4.29309	−	8.42565i	0.215193	−	0.422340i
$399$	−7.11375	+	3.53175i	−0.356133	+	0.176809i
$400$	4.18009	+	2.74352i	0.209004	+	0.137176i
$401$	−1.04993	+	3.23134i	−0.0524308	+	0.161366i	−0.973843	−	0.227220i	$-0.927036\pi$
$401$	−1.04993	+	3.23134i	−0.0524308	+	0.161366i	0.921413	+	0.388586i	$0.127036\pi$
$402$	10.3618	+	20.3362i	0.516801	+	1.01428i
$403$	−2.76332	+	17.4469i	−0.137651	+	0.869093i
$404$	−4.32557	−	3.14271i	−0.215205	−	0.156356i
$405$	−6.91679	+	23.1443i	−0.343698	+	1.15005i
$406$	−10.6822	−	5.58382i	−0.530150	−	0.277121i
$407$	−35.3809	+	1.05173i	−1.75377	+	0.0521323i
$408$	3.55171	−	3.55171i	0.175836	−	0.175836i
$409$	−6.55498	−	20.1742i	−0.324123	−	0.997548i	−0.971835	−	0.235663i	$-0.924274\pi$
$409$	−6.55498	−	20.1742i	−0.324123	−	0.997548i	0.647712	−	0.761885i	$-0.275726\pi$
$410$	−12.3873	−	5.94536i	−0.611763	−	0.293620i
$411$	−13.6873	−	18.8389i	−0.675143	−	0.929254i
$412$	−7.11535	−	13.9647i	−0.350548	−	0.687990i
$413$	−32.9332	−	0.343182i	−1.62054	−	0.0168869i
$414$	−9.50856	−	13.0874i	−0.467320	−	0.643211i
$415$	−13.6695	+	28.4806i	−0.671010	+	1.39806i
$416$	−3.56633	+	1.15877i	−0.174854	+	0.0568135i
$417$	24.5704	+	24.5704i	1.20322	+	1.20322i
$418$	−3.46481	+	2.67817i	−0.169469	+	0.130993i
$419$	30.4673			1.48843			0.744214	−	0.667942i	$-0.232824\pi$
$419$	30.4673			1.48843			0.744214	+	0.667942i	$0.232824\pi$
$420$	9.38304	−	9.63664i	0.457845	−	0.470220i
$421$	4.49476	+	3.26563i	0.219061	+	0.159157i	0.691904	−	0.721990i	$-0.256772\pi$
$421$	4.49476	+	3.26563i	0.219061	+	0.159157i	−0.472843	+	0.881147i	$0.656772\pi$
$422$	17.6505	+	2.79557i	0.859214	+	0.136086i
$423$	4.82751	−	2.45974i	0.234722	−	0.119597i
$424$	−3.28936	−	1.06878i	−0.159745	−	0.0519044i
$425$	−10.8162	+	2.24425i	−0.524665	+	0.108862i
$426$	2.32983	−	3.20673i	0.112881	−	0.155367i
$427$	−4.61960	−	6.49969i	−0.223558	−	0.314542i
$428$	7.88035	−	7.88035i	0.380911	−	0.380911i
$429$	28.0461	+	3.59146i	1.35408	+	0.173398i
$430$	11.6061	+	8.01818i	0.559695	+	0.386671i
$431$	−9.62443	−	29.6210i	−0.463592	−	1.42679i	−0.860744	−	0.509038i	$-0.830001\pi$
$431$	−9.62443	−	29.6210i	−0.463592	−	1.42679i	0.397152	−	0.917753i	$-0.369999\pi$
$432$	−1.86657	+	0.295635i	−0.0898053	+	0.0142238i
$433$	15.4202	+	2.44232i	0.741048	+	0.117370i	0.515534	−	0.856869i	$-0.327594\pi$
$433$	15.4202	+	2.44232i	0.741048	+	0.117370i	0.225514	+	0.974240i	$0.427594\pi$
$434$	8.90422	−	8.72056i	0.427416	−	0.418600i
$435$	−3.07875	+	22.9548i	−0.147615	+	1.10060i
$436$	11.5407	−	8.38483i	0.552700	−	0.401560i
$437$	9.72760	−	1.54070i	0.465334	−	0.0737017i
$438$	6.13572	+	3.12631i	0.293176	+	0.149381i
$439$	−8.21650			−0.392152			−0.196076	−	0.980589i	$-0.562820\pi$
$439$	−8.21650			−0.392152			−0.196076	+	0.980589i	$0.562820\pi$
$440$	4.03224	−	6.22423i	0.192230	−	0.296728i
$441$	−8.66544	−	12.4652i	−0.412640	−	0.593580i
$442$	3.76116	−	7.38169i	0.178900	−	0.351111i
$443$	−24.6688	+	3.90715i	−1.17205	+	0.185634i	−0.711948	−	0.702232i	$-0.752187\pi$
$443$	−24.6688	+	3.90715i	−1.17205	+	0.185634i	−0.460102	+	0.887866i	$0.652187\pi$
$444$	−19.6298	+	14.2619i	−0.931588	+	0.676838i
$445$	−25.3347	+	19.3425i	−1.20098	+	0.916922i
$446$	16.2786	+	5.28923i	0.770813	+	0.250452i
$447$	−6.94131	+	43.8257i	−0.328313	+	2.07289i
$448$	2.50760	+	0.843757i	0.118473	+	0.0398638i
$449$	−37.4247	+	12.1600i	−1.76618	+	0.573868i	−0.997811	−	0.0661353i	$-0.978933\pi$
$449$	−37.4247	+	12.1600i	−1.76618	+	0.573868i	−0.768372	+	0.640003i	$0.778933\pi$
$450$	−9.88474	−	4.45858i	−0.465971	−	0.210180i
$451$	−8.70866	+	18.4255i	−0.410075	+	0.867624i
$452$	−1.70254	−	1.70254i	−0.0800809	−	0.0800809i
$453$	2.96623	−	5.82156i	0.139366	−	0.273521i
$454$	−21.9842	−	15.9725i	−1.03177	−	0.749626i
$455$	9.80711	−	19.8991i	0.459765	−	0.932882i
$456$	−0.927630	+	2.85495i	−0.0434402	+	0.133695i
$457$	−29.0631	+	14.8084i	−1.35952	+	0.692708i	−0.973265	−	0.229686i	$-0.926230\pi$
$457$	−29.0631	+	14.8084i	−1.35952	+	0.692708i	−0.386251	+	0.922394i	$0.626230\pi$
$458$	19.8176	+	3.13879i	0.926014	+	0.146666i
$459$	2.45415	−	3.37785i	0.114550	−	0.157665i
$460$	−14.6771	+	7.92296i	−0.684324	+	0.369410i
$461$		−	11.8146i		−	0.550261i	−0.961407	−	0.275130i	$-0.911279\pi$
$461$		−	11.8146i		−	0.550261i	0.961407	−	0.275130i	$-0.0887210\pi$
$462$	−14.3762	−	13.8318i	−0.668841	−	0.643514i
$463$	−24.6801	+	24.6801i	−1.14698	+	1.14698i	−0.159840	+	0.987143i	$0.551098\pi$
$463$	−24.6801	+	24.6801i	−1.14698	+	1.14698i	−0.987143	+	0.159840i	$0.948902\pi$
$464$	−4.33285	+	1.40783i	−0.201147	+	0.0653568i
$465$	−21.5896	−	10.3621i	−1.00119	−	0.480531i
$466$	−8.49103	+	6.16910i	−0.393339	+	0.285778i
$467$	10.0720	+	19.7673i	0.466075	+	0.914723i	0.997703	+	0.0677452i	$0.0215805\pi$
$467$	10.0720	+	19.7673i	0.466075	+	0.914723i	−0.531628	+	0.846978i	$0.678420\pi$
$468$	7.24613	−	3.69209i	0.334952	−	0.170667i
$469$	−3.88149	−	26.2759i	−0.179230	−	1.21331i
$470$	−1.85193	−	5.27031i	−0.0854233	−	0.243101i
$471$	1.80130	+	5.54385i	0.0829997	+	0.255447i
$472$	−8.80224	+	8.80224i	−0.405156	+	0.405156i
$473$	11.7900	−	17.2852i	0.542105	−	0.794776i
$474$	20.3406			0.934274
$475$	5.15075	−	4.12976i	0.236333	−	0.189487i
$476$	−5.23559	+	2.59931i	−0.239973	+	0.119139i
$477$	7.40857	+	1.17340i	0.339215	+	0.0537264i
$478$	1.86765	+	3.66548i	0.0854245	+	0.167655i
$479$	−5.06865	+	15.5997i	−0.231593	+	0.712769i	0.765962	+	0.642885i	$0.222263\pi$
$479$	−5.06865	+	15.5997i	−0.231593	+	0.712769i	−0.997555	+	0.0698837i	$0.977737\pi$
$480$	−0.120742	−	5.08224i	−0.00551109	−	0.231972i
$481$	−23.5233	+	32.3771i	−1.07257	+	1.47627i
$482$	−11.1667	−	5.68970i	−0.508627	−	0.259159i
$483$	13.4193	+	42.8133i	0.610600	+	1.94807i
$484$	−9.26753	−	5.92562i	−0.421251	−	0.269346i
$485$	1.98185	−	0.362341i	0.0899911	−	0.0164531i
$486$	17.9659	−	5.83748i	0.814950	−	0.264793i
$487$	−2.93405	−	18.5249i	−0.132954	−	0.839441i	−0.960548	−	0.278114i	$-0.910291\pi$
$487$	−2.93405	−	18.5249i	−0.132954	−	0.839441i	0.827594	−	0.561327i	$-0.189709\pi$
$488$	−2.97683	−	0.471483i	−0.134755	−	0.0213431i
$489$	−0.503400	+	1.54930i	−0.0227645	+	0.0700620i
$490$	−13.9257	+	7.14667i	−0.629099	+	0.322854i
$491$	7.68190	−	5.58123i	0.346679	−	0.251877i	−0.400795	−	0.916168i	$-0.631266\pi$
$491$	7.68190	−	5.58123i	0.346679	−	0.251877i	0.747475	+	0.664290i	$0.231266\pi$
$492$	2.18540	+	13.7981i	0.0985255	+	0.622066i
$493$	4.56955	−	8.96824i	0.205802	−	0.403909i
$494$			4.95125i			0.222767i
$495$	−6.52559	+	14.7006i	−0.293303	+	0.660744i
$496$		−	4.71068i		−	0.211516i
$497$	−3.75985	+	2.67228i	−0.168653	+	0.119868i
$498$	31.7244	−	5.02465i	1.42161	−	0.225160i
$499$	20.3783	+	28.0484i	0.912259	+	1.25562i	0.966389	+	0.257084i	$0.0827616\pi$
$499$	20.3783	+	28.0484i	0.912259	+	1.25562i	−0.0541297	+	0.998534i	$0.517238\pi$
$500$	−5.91096	+	9.49002i	−0.264346	+	0.424407i
$501$	−14.6389	+	45.0540i	−0.654020	+	2.01287i
$502$	−0.846220	+	5.34282i	−0.0377686	+	0.238462i
$503$	−5.15210	−	32.5291i	−0.229721	−	1.45040i	−0.785393	−	0.618998i	$-0.787539\pi$
$503$	−5.15210	−	32.5291i	−0.229721	−	1.45040i	0.555672	−	0.831402i	$-0.312461\pi$
$504$	−5.65767	−	0.956622i	−0.252013	−	0.0426113i
$505$	6.79560	−	9.83644i	0.302400	−	0.437716i
$506$	11.8813	+	21.6992i	0.528187	+	0.964647i
$507$	1.70643	−	1.70643i	0.0757852	−	0.0757852i
$508$	−12.8210	−	6.53263i	−0.568840	−	0.289838i
$509$	24.2814	+	17.6415i	1.07625	+	0.781944i	0.977026	−	0.213121i	$-0.0683629\pi$
$509$	24.2814	+	17.6415i	1.07625	+	0.781944i	0.0992275	+	0.995065i	$0.468363\pi$
$510$	8.12824	+	7.75099i	0.359925	+	0.343220i
$511$	−5.60729	−	5.72538i	−0.248052	−	0.253276i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−0.390351	+	2.46458i	−0.0172344	+	0.108814i
$514$	15.1160	+	10.9824i	0.666739	+	0.484414i
$515$	30.8392	−	16.6476i	1.35894	−	0.733580i
$516$		−	14.3425i		−	0.631395i
$517$	−7.80061	+	2.79343i	−0.343070	+	0.122855i
$518$	26.9442	−	8.44532i	1.18386	−	0.371066i
$519$	−2.87938	+	0.935569i	−0.126391	+	0.0410669i
$520$	−2.77976	−	7.91077i	−0.121901	−	0.346910i
$521$	−0.593964	−	0.817521i	−0.0260220	−	0.0358162i	0.795808	−	0.605549i	$-0.207047\pi$
$521$	−0.593964	−	0.817521i	−0.0260220	−	0.0358162i	−0.821830	+	0.569733i	$0.807047\pi$
$522$	8.80355	−	4.48563i	0.385321	−	0.196331i
$523$	−15.6062	+	7.95175i	−0.682411	+	0.347706i	−0.760589	−	0.649234i	$-0.775090\pi$
$523$	−15.6062	+	7.95175i	−0.682411	+	0.347706i	0.0781779	+	0.996939i	$0.475090\pi$
$524$	−11.1936	+	8.13261i	−0.488994	+	0.355275i
$525$	22.0404	+	20.4634i	0.961923	+	0.893096i
$526$	−3.81652	−	11.7461i	−0.166408	−	0.512152i
$527$	7.35915	+	7.35915i	0.320569	+	0.320569i
$528$	−7.53698	+	0.224043i	−0.328005	+	0.00975023i
$529$		−	32.6382i		−	1.41905i
$530$	2.21449	−	7.40991i	0.0961913	−	0.321866i
$531$	15.8685	−	21.8412i	0.688636	−	0.947826i
$532$	2.08271	−	2.80467i	0.0902968	−	0.121598i
$533$	10.4609	+	20.5306i	0.453111	+	0.889280i
$534$	30.8217	+	10.0146i	1.33378	+	0.433373i
$535$	18.0345	+	17.1975i	0.779701	+	0.743513i
$536$	−8.12184	−	5.90086i	−0.350810	−	0.254878i
$537$	−35.9831	−	18.3343i	−1.55279	−	0.791185i
$538$	−7.55264	−	7.55264i	−0.325618	−	0.325618i
$539$	10.7232	+	20.5916i	0.461882	+	0.886941i
$540$	−0.760005	−	4.15689i	−0.0327054	−	0.178884i
$541$	5.87035	+	18.0671i	0.252386	+	0.776764i	0.994333	+	0.106306i	$0.0339024\pi$
$541$	5.87035	+	18.0671i	0.252386	+	0.776764i	−0.741947	+	0.670458i	$0.766098\pi$
$542$	−8.86026	+	1.40333i	−0.380581	+	0.0602780i
$543$	3.94671	−	24.9185i	0.169370	−	1.06936i
$544$	−0.682718	+	2.10119i	−0.0292713	+	0.0900878i
$545$	19.3567	+	25.3533i	0.829148	+	1.08601i
$546$	−22.3136	+	3.29617i	−0.954934	+	0.141063i
$547$	−2.06589	−	13.0435i	−0.0883309	−	0.557700i	−0.991673	−	0.128779i	$-0.958894\pi$
$547$	−2.06589	−	13.0435i	−0.0883309	−	0.557700i	0.903342	−	0.428920i	$-0.141106\pi$
$548$	9.12611	+	4.64999i	0.389848	+	0.198638i
$549$	6.53648			0.278970
$550$	14.1280	+	8.68326i	0.602421	+	0.370256i
$551$			6.01543i			0.256266i
$552$	15.1098	+	7.69885i	0.643118	+	0.327685i
$553$	−22.4352	−	7.54898i	−0.954041	−	0.321015i
$554$	−4.69731	−	6.46530i	−0.199570	−	0.274684i
$555$	−32.9240	−	43.1237i	−1.39755	−	1.83050i
$556$	−14.5359	−	4.72299i	−0.616458	−	0.200299i
$557$	2.34219	+	0.370967i	0.0992418	+	0.0157184i	0.205858	−	0.978582i	$-0.434002\pi$
$557$	2.34219	+	0.370967i	0.0992418	+	0.0157184i	−0.106616	+	0.994300i	$0.534002\pi$
$558$	1.59818	+	10.0905i	0.0676563	+	0.427165i
$559$	−7.31023	−	22.4986i	−0.309190	−	0.951589i
$560$	−1.75299	+	5.65040i	−0.0740774	+	0.238773i
$561$	11.4245	−	12.1245i	0.482341	−	0.511896i
$562$	−9.33679	−	9.33679i	−0.393849	−	0.393849i
$563$	10.2070	−	20.0324i	0.430174	−	0.844265i	−0.569576	−	0.821938i	$-0.692893\pi$
$563$	10.2070	−	20.0324i	0.430174	−	0.844265i	0.999751	−	0.0223264i	$-0.00710730\pi$
$564$	−3.33844	+	4.59497i	−0.140574	+	0.193483i
$565$	3.71551	−	3.89635i	0.156313	−	0.163921i
$566$	8.68542	+	2.82206i	0.365075	+	0.118620i
$567$	−28.5799	−	0.297818i	−1.20024	−	0.0125072i
$568$	−0.272737	+	1.72200i	−0.0114438	+	0.0722534i
$569$	5.02039	−	6.90997i	0.210466	−	0.289681i	−0.690713	−	0.723129i	$-0.742703\pi$
$569$	5.02039	−	6.90997i	0.210466	−	0.289681i	0.901179	+	0.433448i	$0.142703\pi$
$570$	−6.43133	−	1.92204i	−0.269379	−	0.0805052i
$571$	12.6265			0.528402			0.264201	−	0.964468i	$-0.414892\pi$
$571$	12.6265			0.528402			0.264201	+	0.964468i	$0.414892\pi$
$572$	−11.7088	+	4.19296i	−0.489568	+	0.175317i
$573$	−4.62510	−	4.62510i	−0.193216	−	0.193216i
$574$	2.71042	−	16.0300i	0.113131	−	0.669080i
$575$	−18.4908	−	32.3890i	−0.771118	−	1.35071i
$576$	−1.75456	+	1.27476i	−0.0731065	+	0.0531150i
$577$	0.332521	+	0.652609i	0.0138430	+	0.0271685i	0.897824	−	0.440353i	$-0.145147\pi$
$577$	0.332521	+	0.652609i	0.0138430	+	0.0271685i	−0.883981	+	0.467522i	$0.845147\pi$
$578$	5.50186	+	10.7980i	0.228847	+	0.449138i
$579$	23.5955	−	17.1431i	0.980595	−	0.712444i
$580$	−3.37722	−	9.61104i	−0.140232	−	0.399077i
$581$	−36.8561	−	6.23177i	−1.52905	−	0.258537i
$582$	−1.44845	−	1.44845i	−0.0600401	−	0.0600401i
$583$	−11.0101	−	3.21901i	−0.455990	−	0.133318i
$584$	−3.02895			−0.125339
$585$	8.63826	+	16.0022i	0.357148	+	0.661609i
$586$	−5.01811	+	6.90683i	−0.207296	+	0.285319i
$587$	5.33401	−	33.6776i	0.220158	−	1.39002i	−0.591694	−	0.806162i	$-0.701541\pi$
$587$	5.33401	−	33.6776i	0.220158	−	1.39002i	0.811853	−	0.583863i	$-0.198459\pi$
$588$	14.0262	+	7.51892i	0.578431	+	0.310075i
$589$	−5.91547	−	1.92205i	−0.243743	−	0.0791967i
$590$	−20.1443	−	19.2094i	−0.829329	−	0.790838i
$591$	10.2418	−	14.0966i	0.421291	−	0.579857i
$592$	4.84520	−	9.50924i	0.199136	−	0.390827i
$593$	−1.60358	−	1.60358i	−0.0658510	−	0.0658510i	0.673414	−	0.739265i	$-0.264827\pi$
$593$	−1.60358	−	1.60358i	−0.0658510	−	0.0658510i	−0.739265	+	0.673414i	$0.764827\pi$
$594$	−6.15884	+	1.16402i	−0.252700	+	0.0477604i
$595$	−6.08864	−	11.5658i	−0.249610	−	0.474151i
$596$	−6.03113	−	18.5619i	−0.247045	−	0.760325i
$597$	−3.36316	−	21.2342i	−0.137645	−	0.869057i
$598$	27.6262	+	4.37557i	1.12972	+	0.178930i
$599$	12.1287	+	3.94085i	0.495564	+	0.161019i	0.546127	−	0.837702i	$-0.316102\pi$
$599$	12.1287	+	3.94085i	0.495564	+	0.161019i	−0.0505629	+	0.998721i	$0.516102\pi$
$600$	11.3546	−	0.539822i	0.463550	−	0.0220381i
$601$	13.0966	+	18.0259i	0.534221	+	0.735293i	0.987766	−	0.155941i	$-0.0498409\pi$
$601$	13.0966	+	18.0259i	0.534221	+	0.735293i	−0.453545	+	0.891233i	$0.649841\pi$
$602$	−5.32293	+	15.8195i	−0.216946	+	0.644754i
$603$	19.3994	+	9.88447i	0.790003	+	0.402527i
$604$			2.87386i			0.116936i
$605$	12.7542	−	21.0317i	0.518530	−	0.855059i
$606$	−12.1557			−0.493790
$607$	−25.1086	−	12.7935i	−1.01913	−	0.519270i	−0.137142	−	0.990551i	$-0.543792\pi$
$607$	−25.1086	−	12.7935i	−1.01913	−	0.519270i	−0.881983	+	0.471281i	$0.843792\pi$
$608$	−0.206553	−	1.30413i	−0.00837684	−	0.0528893i
$609$	−27.1095	+	4.00462i	−1.09853	+	0.162275i
$610$	0.895876	−	6.67956i	0.0362730	−	0.270447i
$611$	−2.89488	+	8.90952i	−0.117114	+	0.360441i
$612$	0.749551	−	4.73248i	0.0302988	−	0.191299i
$613$	−12.6841	+	2.00897i	−0.512307	+	0.0811415i	−0.407236	−	0.913323i	$-0.633507\pi$
$613$	−12.6841	+	2.00897i	−0.512307	+	0.0811415i	−0.105072	+	0.994465i	$0.533507\pi$
$614$	5.43099	+	16.7149i	0.219177	+	0.674557i
$615$	−30.7287	+	5.61813i	−1.23910	+	0.226545i
$616$	8.39626	+	2.55008i	0.338295	+	0.102745i
$617$	7.71190	+	7.71190i	0.310469	+	0.310469i	0.845091	−	0.534622i	$-0.179546\pi$
$617$	7.71190	+	7.71190i	0.310469	+	0.310469i	−0.534622	+	0.845091i	$0.679546\pi$
$618$	−31.7485	−	16.1767i	−1.27711	−	0.650721i
$619$	26.0112	+	18.8983i	1.04548	+	0.759586i	0.971348	−	0.237663i	$-0.0763813\pi$
$619$	26.0112	+	18.8983i	1.04548	+	0.759586i	0.0741322	+	0.997248i	$0.476381\pi$
$620$	10.5304	−	0.250178i	0.422912	−	0.0100474i
$621$	13.4065	+	4.35605i	0.537986	+	0.174802i
$622$	−9.96513	−	19.5577i	−0.399565	−	0.784191i
$623$	−30.2789	−	22.4846i	−1.21310	−	0.900828i
$624$	−5.01103	+	6.89709i	−0.200602	+	0.276105i
$625$	−21.5283	−	12.7096i	−0.861131	−	0.508383i
$626$		−	13.4524i		−	0.537665i
$627$	−2.79390	+	9.55603i	−0.111577	+	0.381631i
$628$	−1.81300	−	1.81300i	−0.0723464	−	0.0723464i
$629$	7.28629	+	22.4249i	0.290523	+	0.894139i
$630$	1.83800	−	12.6982i	0.0732276	−	0.505907i
$631$	−21.5068	+	15.6256i	−0.856173	+	0.622046i	−0.926841	−	0.375453i	$-0.877487\pi$
$631$	−21.5068	+	15.6256i	−0.856173	+	0.622046i	0.0706678	+	0.997500i	$0.477487\pi$
$632$	−7.97171	+	4.06179i	−0.317098	+	0.161569i
$633$	36.2002	−	18.4449i	1.43883	−	0.733120i
$634$	−8.64678	−	11.9013i	−0.343408	−	0.472660i
$635$	13.9224	−	29.0075i	0.552492	−	1.15113i
$636$	−7.47831	+	2.42985i	−0.296534	+	0.0963499i
$637$	25.8347	+	4.64563i	1.02361	+	0.184066i
$638$	−14.2254	+	5.09416i	−0.563187	+	0.201680i
$639$		−	3.78113i		−	0.149579i
$640$	1.06219	+	1.96768i	0.0419866	+	0.0777793i
$641$	−35.8563	−	26.0511i	−1.41624	−	1.02896i	−0.992378	−	0.123231i	$-0.960674\pi$
$641$	−35.8563	−	26.0511i	−1.41624	−	1.02896i	−0.423861	−	0.905727i	$-0.639326\pi$
$642$	3.96356	−	25.0249i	0.156429	−	0.987656i
$643$	29.7745	−	15.1709i	1.17419	−	0.598281i	0.245596	−	0.969372i	$-0.421016\pi$
$643$	29.7745	−	15.1709i	1.17419	−	0.598281i	0.928596	+	0.371091i	$0.121016\pi$
$644$	−13.8085	−	14.0993i	−0.544132	−	0.555592i
$645$	32.0619	−	0.761714i	1.26243	−	0.0299924i
$646$	2.36002	+	1.71466i	0.0928539	+	0.0674623i
$647$	23.5130	+	11.9804i	0.924390	+	0.471000i	0.850328	−	0.526254i	$-0.176404\pi$
$647$	23.5130	+	11.9804i	0.924390	+	0.471000i	0.0740620	+	0.997254i	$0.476404\pi$
$648$	−7.63871	+	7.63871i	−0.300077	+	0.300077i
$649$	−28.3134	+	30.0483i	−1.11140	+	1.17950i
$650$	17.5364	−	6.63412i	0.687834	−	0.260212i
$651$	4.72396	−	27.9386i	0.185147	−	1.09500i
$652$	−0.112091	−	0.707714i	−0.00438982	−	0.0277162i
$653$	0.297806	−	1.88027i	0.0116540	−	0.0735807i	−0.981176	−	0.193116i	$-0.938141\pi$
$653$	0.297806	−	1.88027i	0.0116540	−	0.0735807i	0.992830	+	0.119536i	$0.0381406\pi$
$654$	10.0219	−	30.8443i	0.391888	−	1.20611i
$655$	−18.7744	−	24.5906i	−0.733577	−	0.960835i
$656$	−3.61181	−	4.97123i	−0.141017	−	0.194094i
$657$	6.48816	−	1.02762i	0.253127	−	0.0400914i
$658$	5.38755	−	3.82915i	0.210029	−	0.149276i
$659$		−	14.3763i		−	0.560020i	−0.959997	−	0.280010i	$-0.909662\pi$
$659$		−	14.3763i		−	0.560020i	0.959997	−	0.280010i	$-0.0903378\pi$
$660$	−0.901114	−	16.8365i	−0.0350758	−	0.655362i
$661$		−	17.9296i		−	0.697382i	−0.937238	−	0.348691i	$-0.886626\pi$
$661$		−	17.9296i		−	0.697382i	0.937238	−	0.348691i	$-0.113374\pi$
$662$	−5.32818	+	10.4571i	−0.207085	+	0.406428i
$663$	−2.94646	−	18.6032i	−0.114431	−	0.722488i
$664$	−11.4298	+	8.30423i	−0.443562	+	0.322267i
$665$	6.38028	+	4.50681i	0.247416	+	0.174767i
$666$	−7.15249	+	22.0131i	−0.277153	+	0.852990i
$667$	33.5640	+	5.31601i	1.29960	+	0.205837i
$668$	−3.25962	−	20.5804i	−0.126119	−	0.796281i
$669$	37.0091	−	12.0250i	1.43086	−	0.464913i
$670$	12.7597	−	18.4693i	0.492949	−	0.713529i
$671$	−9.91513	−	1.26969i	−0.382769	−	0.0490158i
$672$	5.73974	−	1.79905i	0.221415	−	0.0694000i
$673$	8.00921	+	4.08090i	0.308732	+	0.157307i	0.601491	−	0.798879i	$-0.294573\pi$
$673$	8.00921	+	4.08090i	0.308732	+	0.157307i	−0.292759	+	0.956186i	$0.594573\pi$
$674$	−3.02636	+	4.16542i	−0.116571	+	0.160446i
$675$	9.25211	−	1.91971i	0.356114	−	0.0738897i
$676$	−0.328014	+	1.00952i	−0.0126159	+	0.0388279i
$677$	2.00912	+	3.94313i	0.0772169	+	0.151547i	0.926387	−	0.376572i	$-0.122897\pi$
$677$	2.00912	+	3.94313i	0.0772169	+	0.151547i	−0.849170	+	0.528119i	$0.822897\pi$
$678$	−5.40662	−	0.856325i	−0.207640	−	0.0328870i
$679$	1.06004	+	2.13516i	0.0406807	+	0.0819401i
$680$	−4.73334	−	1.41458i	−0.181515	−	0.0542468i
$681$	−61.7798			−2.36741
$682$	−0.464218	−	15.6166i	−0.0177758	−	0.597992i
$683$	23.8779	−	23.8779i	0.913663	−	0.913663i	−0.0828948	−	0.996558i	$-0.526417\pi$
$683$	23.8779	−	23.8779i	0.913663	−	0.913663i	0.996558	+	0.0828948i	$0.0264166\pi$
$684$	0.884895	+	2.72343i	0.0338348	+	0.104133i
$685$	−9.91008	+	20.6478i	−0.378645	+	0.788912i
$686$	−12.6801	−	13.4987i	−0.484128	−	0.515383i
$687$	40.6447	−	20.7095i	1.55069	−	0.790117i
$688$	2.86405	+	5.62101i	0.109191	+	0.214299i
$689$	−10.4925	+	7.62322i	−0.399731	+	0.290422i
$690$	−16.4078	+	34.1860i	−0.624636	+	1.30144i
$691$	26.9051	−	8.74198i	1.02352	−	0.332561i	0.251293	−	0.967911i	$-0.419144\pi$
$691$	26.9051	−	8.74198i	1.02352	−	0.332561i	0.772224	+	0.635350i	$0.219144\pi$
$692$	0.941641	−	0.941641i	0.0357958	−	0.0357958i
$693$	−18.8504	−	2.61381i	−0.716066	−	0.0992906i
$694$			28.5660i			1.08435i
$695$	9.78597	−	32.7449i	0.371203	−	1.24208i
$696$	−6.08806	+	8.37949i	−0.230767	+	0.317624i
$697$	13.4087	+	2.12372i	0.507889	+	0.0804417i
$698$	−19.5834	+	9.97822i	−0.741241	+	0.377681i
$699$	−7.37357	+	22.6935i	−0.278894	+	0.858348i
$700$	−12.7242	−	3.61861i	−0.480930	−	0.136771i
$701$	10.0725	+	7.31813i	0.380435	+	0.276402i	0.761525	−	0.648136i	$-0.224451\pi$
$701$	10.0725	+	7.31813i	0.380435	+	0.276402i	−0.381090	+	0.924538i	$0.624451\pi$
$702$	−3.21726	+	6.31423i	−0.121428	+	0.238315i
$703$	−9.96436	−	9.96436i	−0.375813	−	0.375813i
$704$	2.90909	−	1.59286i	0.109640	−	0.0600330i
$705$	−10.4491	−	7.21885i	−0.393535	−	0.271878i
$706$	18.8259	−	6.11689i	0.708521	−	0.230212i
$707$	13.4074	+	4.51131i	0.504237	+	0.169665i
$708$	−4.42725	+	27.9525i	−0.166386	+	1.05052i
$709$	−13.8353	−	4.49536i	−0.519596	−	0.168827i	0.0374661	−	0.999298i	$-0.488071\pi$
$709$	−13.8353	−	4.49536i	−0.519596	−	0.168827i	−0.557062	+	0.830471i	$0.688071\pi$
$710$	−3.86390	−	0.518234i	−0.145010	−	0.0194490i
$711$	15.6978	−	11.4051i	0.588712	−	0.427725i
$712$	−14.0792	+	2.22992i	−0.527639	+	0.0835699i
$713$	−15.9520	+	31.3076i	−0.597409	+	1.17248i
$714$	−6.15625	+	11.7773i	−0.230392	+	0.440755i
$715$	−9.99494	−	25.9515i	−0.373790	−	0.970533i
$716$	17.7634			0.663848
$717$	8.33342	+	4.24609i	0.311217	+	0.158573i
$718$	−32.5813	+	5.16037i	−1.21592	+	0.192583i
$719$	−5.24533	+	3.81095i	−0.195618	+	0.142125i	−0.681283	−	0.732020i	$-0.738578\pi$
$719$	−5.24533	+	3.81095i	−0.195618	+	0.142125i	0.485665	+	0.874145i	$0.338578\pi$
$720$	−2.94283	−	3.85450i	−0.109673	−	0.143649i
$721$	29.0142	+	29.6253i	1.08055	+	1.10330i
$722$	17.0441	+	2.69953i	0.634317	+	0.100466i
$723$	−28.1420	+	4.45726i	−1.04661	+	0.165767i
$724$	3.42920	+	10.5540i	0.127445	+	0.392236i
$725$	21.3055	−	8.06000i	0.791267	−	0.299341i
$726$	−24.9642	+	1.48548i	−0.926509	+	0.0551313i
$727$	−12.2594	+	12.2594i	−0.454676	+	0.454676i	−0.896903	−	0.442227i	$-0.854188\pi$
$727$	−12.2594	+	12.2594i	−0.454676	+	0.454676i	0.442227	+	0.896903i	$0.354188\pi$
$728$	8.08675	−	5.74759i	0.299715	−	0.213020i
$729$	6.19465	−	8.52621i	0.229432	−	0.315785i
$730$	−0.160863	−	6.77102i	−0.00595382	−	0.250607i
$731$	−13.2556	−	4.30700i	−0.490276	−	0.159300i
$732$	−6.10531	+	3.11081i	−0.225659	+	0.114979i
$733$	37.6493	+	5.96307i	1.39061	+	0.220251i	0.806409	−	0.591359i	$-0.201408\pi$
$733$	37.6493	+	5.96307i	1.39061	+	0.220251i	0.584200	+	0.811609i	$0.301408\pi$
$734$	21.0634	+	15.3035i	0.777464	+	0.564861i
$735$	−16.0632	+	31.7540i	−0.592498	+	1.17127i
$736$	−7.45910			−0.274946
$737$	−27.5067	−	18.7619i	−1.01322	−	0.691105i
$738$	9.42325	+	9.42325i	0.346875	+	0.346875i
$739$	10.1407	−	3.29493i	0.373033	−	0.121206i	−0.116499	−	0.993191i	$-0.537167\pi$
$739$	10.1407	−	3.29493i	0.373033	−	0.121206i	0.489533	+	0.871985i	$0.337167\pi$
$740$	21.5146	+	10.3261i	0.790894	+	0.379596i
$741$	6.61647	+	9.10679i	0.243062	+	0.334546i
$742$	9.15019	+	0.0953499i	0.335914	+	0.00350040i
$743$	14.4775	+	28.4136i	0.531126	+	1.04239i	0.988229	+	0.152980i	$0.0488870\pi$
$743$	14.4775	+	28.4136i	0.531126	+	1.04239i	−0.457103	+	0.889414i	$0.651113\pi$
$744$	−6.29499	−	8.66430i	−0.230785	−	0.317649i
$745$	41.1737	−	14.4680i	1.50849	−	0.530067i
$746$	3.56673	+	10.9773i	0.130587	+	0.401906i
$747$	21.6658	−	21.6658i	0.792712	−	0.792712i
$748$	−2.05626	+	7.03306i	−0.0751842	+	0.257154i
$749$	−13.6592	+	26.1309i	−0.499096	+	0.954803i
$750$	1.80977	+	25.3539i	0.0660834	+	0.925792i
$751$	32.5501	+	23.6490i	1.18777	+	0.862966i	0.993027	−	0.117889i	$-0.0376126\pi$
$751$	32.5501	+	23.6490i	1.18777	+	0.862966i	0.194744	+	0.980854i	$0.437613\pi$
$752$	0.390810	−	2.46747i	0.0142514	−	0.0899795i
$753$	5.58329	+	10.9578i	0.203466	+	0.399325i
$754$	−5.27916	+	16.2476i	−0.192256	+	0.591702i
$755$	−6.42433	+	0.152627i	−0.233805	+	0.00555466i
$756$	4.47847	−	2.22342i	0.162880	−	0.0808651i
$757$	11.1575	−	21.8978i	0.405525	−	0.795887i	−0.594441	−	0.804139i	$-0.702627\pi$
$757$	11.1575	−	21.8978i	0.405525	−	0.795887i	0.999966	+	0.00825181i	$0.00262666\pi$
$758$	22.4528	−	22.4528i	0.815522	−	0.815522i
$759$	50.8503	+	24.0339i	1.84575	+	0.872376i
$760$	2.90432	−	0.530997i	0.105351	−	0.0192613i
$761$	0.730863	−	0.237472i	0.0264938	−	0.00860835i	−0.295740	−	0.955268i	$-0.595566\pi$
$761$	0.730863	−	0.237472i	0.0264938	−	0.00860835i	0.322234	+	0.946660i	$0.395566\pi$
$762$	−32.3112	+	5.11760i	−1.17051	+	0.185391i
$763$	−22.5011	+	30.3011i	−0.814595	+	1.09697i
$764$	2.73621	+	0.889049i	0.0989926	+	0.0321647i
$765$	10.6190	+	1.42424i	0.383930	+	0.0514935i
$766$	0.127528	+	0.175528i	0.00460779	+	0.00634208i
$767$	7.30224	+	46.1045i	0.263669	+	1.66474i
$768$	1.03214	−	2.02569i	0.0372442	−	0.0730959i
$769$	−42.1629			−1.52043			−0.760217	−	0.649670i	$-0.774907\pi$
$769$	−42.1629			−1.52043			−0.760217	+	0.649670i	$0.774907\pi$
$770$	−5.25462	+	18.9047i	−0.189363	+	0.681279i
$771$	42.4788			1.52984
$772$	−5.82405	+	11.4303i	−0.209612	+	0.411387i
$773$	−7.72274	−	48.7594i	−0.277768	−	1.75376i	−0.593432	−	0.804884i	$-0.702227\pi$
$773$	−7.72274	−	48.7594i	−0.277768	−	1.75376i	0.315664	−	0.948871i	$-0.397773\pi$
$774$	−8.04196	−	11.0688i	−0.289062	−	0.397860i
$775$	1.11851	+	23.5268i	0.0401782	+	0.845108i
$776$	0.856903	+	0.278425i	0.0307610	+	0.00999486i
$777$	38.2725	−	51.5395i	1.37302	−	1.84897i
$778$	−13.0608	+	2.06863i	−0.468254	+	0.0741641i
$779$	−7.71635	+	2.50719i	−0.276467	+	0.0898295i
$780$	−15.6841	−	10.8355i	−0.561582	−	0.387975i
$781$	−0.734472	+	5.73557i	−0.0262815	+	0.205235i
$782$	11.6528	−	11.6528i	0.416704	−	0.416704i
$783$	−3.90875	+	7.67135i	−0.139687	+	0.274152i
$784$	−6.99848	−	0.145872i	−0.249946	−	0.00520970i
$785$	3.95655	−	4.14913i	0.141215	−	0.148089i
$786$	−9.72045	+	29.9165i	−0.346717	+	1.06708i
$787$	−6.33787	−	12.4388i	−0.225921	−	0.443395i	0.750025	−	0.661410i	$-0.230042\pi$
$787$	−6.33787	−	12.4388i	−0.225921	−	0.443395i	−0.975945	+	0.218016i	$0.930042\pi$
$788$	−1.19894	+	7.56980i	−0.0427104	+	0.269663i
$789$	−22.7162	−	16.5043i	−0.808719	−	0.587569i
$790$	−9.50324	−	17.6045i	−0.338110	−	0.626341i
$791$	5.64557	+	2.95106i	0.200733	+	0.104928i
$792$	−5.69101	+	4.39894i	−0.202221	+	0.156309i
$793$	−7.99161	+	7.99161i	−0.283791	+	0.283791i
$794$	6.66033	+	20.4984i	0.236366	+	0.727461i
$795$	−5.82894	−	16.5883i	−0.206731	−	0.588325i
$796$	5.55829	+	7.65033i	0.197008	+	0.271159i
$797$	−0.192634	−	0.378065i	−0.00682344	−	0.0133918i	0.887570	−	0.460674i	$-0.152392\pi$
$797$	−0.192634	−	0.378065i	−0.00682344	−	0.0133918i	−0.894393	+	0.447282i	$0.852392\pi$
$798$	0.0827576	−	7.94178i	0.00292959	−	0.281136i
$799$	3.24422	+	4.46529i	0.114772	+	0.157971i
$800$	−4.34221	+	2.47895i	−0.153520	+	0.0876443i
$801$	29.4018	−	9.55321i	1.03886	−	0.337546i
$802$	−2.40249	−	2.40249i	−0.0848349	−	0.0848349i
$803$	−10.0415	+	0.298491i	−0.354355	+	0.0105335i
$804$	−22.8239			−0.804936
$805$	30.7849	−	31.6169i	1.08502	−	1.11435i
$806$	−14.2908	−	10.3829i	−0.503372	−	0.365721i
$807$	−23.9843	−	3.79874i	−0.844287	−	0.133722i
$808$	4.76394	−	2.42735i	0.167595	−	0.0853938i
$809$	−44.5618	−	14.4790i	−1.56671	−	0.509055i	−0.608120	−	0.793845i	$-0.708076\pi$
$809$	−44.5618	−	14.4790i	−1.56671	−	0.509055i	−0.958590	+	0.284790i	$0.908076\pi$
$810$	−17.4815	−	16.6702i	−0.614239	−	0.585730i
$811$	20.5189	−	28.2419i	0.720517	−	0.991707i	−0.278989	−	0.960294i	$-0.589999\pi$
$811$	20.5189	−	28.2419i	0.720517	−	0.991707i	0.999506	−	0.0314128i	$-0.0100006\pi$
$812$	9.82485	−	6.98292i	0.344785	−	0.245053i
$813$	−14.4213	+	14.4213i	−0.505777	+	0.505777i
$814$	15.1255	−	32.0021i	0.530149	−	1.12167i
$815$	1.57610	−	0.288158i	0.0552082	−	0.0100937i
$816$	1.55215	+	4.77703i	0.0543362	+	0.167230i
$817$	8.22721	−	1.30306i	0.287834	−	0.0455884i
$818$	20.9512	+	3.31835i	0.732542	+	0.116023i
$819$	−15.3723	+	15.0552i	−0.537150	+	0.526071i
$820$	10.9210	−	8.33798i	0.381380	−	0.291175i
$821$	−24.1688	+	17.5597i	−0.843498	+	0.612837i	−0.923346	−	0.383970i	$-0.874557\pi$
$821$	−24.1688	+	17.5597i	−0.843498	+	0.612837i	0.0798478	+	0.996807i	$0.474557\pi$
$822$	22.9995	−	3.64276i	0.802199	−	0.127056i
$823$	25.8423	+	13.1673i	0.900806	+	0.458984i	0.842118	−	0.539293i	$-0.181308\pi$
$823$	25.8423	+	13.1673i	0.900806	+	0.458984i	0.0586878	+	0.998276i	$0.481308\pi$
$824$	15.6729			0.545992
$825$	37.5892	−	2.90855i	1.30869	−	0.101263i
$826$	15.2571	−	29.1879i	0.530864	−	1.01558i
$827$	7.44051	−	14.6028i	0.258732	−	0.507790i	−0.724701	−	0.689064i	$-0.758022\pi$
$827$	7.44051	−	14.6028i	0.258732	−	0.507790i	0.983433	+	0.181274i	$0.0580220\pi$
$828$	15.9778	−	2.53063i	0.555266	−	0.0879455i
$829$	−22.8514	+	16.6025i	−0.793661	+	0.576628i	−0.909048	−	0.416692i	$-0.863189\pi$
$829$	−22.8514	+	16.6025i	−0.793661	+	0.576628i	0.115387	+	0.993321i	$0.463189\pi$
$830$	−19.1706	−	25.1096i	−0.665422	−	0.871566i
$831$	−17.2795	−	5.61444i	−0.599418	−	0.194763i
$832$	0.586608	−	3.70370i	0.0203370	−	0.128403i
$833$	11.1611	−	10.7053i	0.386709	−	0.370918i
$834$	−33.0471	+	10.7377i	−1.14433	+	0.371815i
$835$	45.8332	−	8.37968i	1.58612	−	0.289991i
$836$	−0.813273	−	4.30303i	−0.0281276	−	0.148823i
$837$	−6.29495	−	6.29495i	−0.217585	−	0.217585i
$838$	−13.8319	+	27.1466i	−0.477815	+	0.937764i
$839$	−8.37629	−	6.08573i	−0.289182	−	0.210103i	0.433731	−	0.901043i	$-0.357197\pi$
$839$	−8.37629	−	6.08573i	−0.289182	−	0.210103i	−0.722912	+	0.690940i	$0.757197\pi$
$840$	4.32650	+	12.7353i	0.149278	+	0.439409i
$841$	2.54767	−	7.84093i	0.0878508	−	0.270377i
$842$	−4.95028	+	2.52229i	−0.170598	+	0.0869239i
$843$	−29.6500	−	4.69610i	−1.02120	−	0.161742i
$844$	−10.5040	+	14.4576i	−0.361564	+	0.497650i
$845$	−2.27415	−	0.679641i	−0.0782331	−	0.0233804i
$846$			5.41804i			0.186276i
$847$	28.0862	+	7.62649i	0.965054	+	0.262049i
$848$	2.44562	−	2.44562i	0.0839830	−	0.0839830i
$849$	19.7462	−	6.41593i	0.677688	−	0.220194i
$850$	2.91083	−	10.6562i	0.0998406	−	0.365505i
$851$	−64.4034	+	46.7918i	−2.20772	+	1.60400i
$852$	1.79950	+	3.53172i	0.0616499	+	0.120995i
$853$	7.33831	−	3.73905i	0.251259	−	0.128023i	−0.323826	−	0.946117i	$-0.604969\pi$
$853$	7.33831	−	3.73905i	0.251259	−	0.128023i	0.575085	+	0.818094i	$0.304969\pi$
$854$	7.88852	−	1.16529i	0.269940	−	0.0398755i
$855$	−6.04105	+	2.12276i	−0.206600	+	0.0725970i
$856$	3.44384	+	10.5990i	0.117708	+	0.362268i
$857$	28.7616	−	28.7616i	0.982478	−	0.982478i	−0.0173714	−	0.999849i	$-0.505530\pi$
$857$	28.7616	−	28.7616i	0.982478	−	0.982478i	0.999849	+	0.0173714i	$0.00552975\pi$
$858$	−15.9327	+	23.3588i	−0.543933	+	0.797456i
$859$	29.5993			1.00991			0.504957	−	0.863145i	$-0.331508\pi$
$859$	29.5993			1.00991			0.504957	+	0.863145i	$0.331508\pi$
$860$	−12.4133	+	6.70092i	−0.423290	+	0.228500i
$861$	−16.4360	−	33.1059i	−0.560138	−	1.12824i
$862$	30.7619	+	4.87220i	1.04775	+	0.165948i
$863$	−2.40325	−	4.71664i	−0.0818075	−	0.160556i	0.846479	−	0.532422i	$-0.178718\pi$
$863$	−2.40325	−	4.71664i	−0.0818075	−	0.160556i	−0.928286	+	0.371866i	$0.878718\pi$
$864$	0.583991	−	1.79734i	0.0198678	−	0.0611467i
$865$	2.15499	+	2.05497i	0.0732718	+	0.0698711i
$866$	−9.17675	+	12.6307i	−0.311839	+	0.429209i
$867$	24.5492	+	12.5084i	0.833733	+	0.424808i
$868$	3.72764	+	11.8928i	0.126524	+	0.403667i
$869$	−26.0272	+	14.2511i	−0.882913	+	0.483434i
$870$	−19.0552	−	13.1644i	−0.646030	−	0.446316i
$871$	−35.8029	+	11.6331i	−1.21314	+	0.394172i
$872$	2.23156	+	14.0895i	0.0755700	+	0.477130i
$873$	−1.92999	−	0.305680i	−0.0653202	−	0.0103457i
$874$	−3.04346	+	9.36682i	−0.102947	+	0.316837i
$875$	7.41342	−	28.6364i	0.250619	−	0.968086i
$876$	−5.57112	+	4.04765i	−0.188231	+	0.136758i
$877$	−3.87745	−	24.4813i	−0.130932	−	0.826673i	−0.962506	−	0.271259i	$-0.912560\pi$
$877$	−3.87745	−	24.4813i	−0.130932	−	0.826673i	0.831574	−	0.555414i	$-0.187440\pi$
$878$	3.73021	−	7.32096i	0.125889	−	0.247070i
$879$			19.4095i			0.654666i
$880$	3.71523	+	6.41849i	0.125240	+	0.216367i
$881$			42.8494i			1.44363i	0.692084	+	0.721817i	$0.256693\pi$
$881$			42.8494i			1.44363i	−0.692084	+	0.721817i	$0.743307\pi$
$882$	15.0406	−	2.06189i	0.506443	−	0.0694275i
$883$	−16.3057	+	2.58256i	−0.548729	+	0.0869102i	−0.424642	−	0.905361i	$-0.639600\pi$
$883$	−16.3057	+	2.58256i	−0.548729	+	0.0869102i	−0.124087	+	0.992271i	$0.539600\pi$
$884$	4.86960	+	6.70243i	0.163782	+	0.225427i
$885$	−62.7212	−	8.41231i	−2.10835	−	0.282777i
$886$	7.71810	−	23.7539i	0.259295	−	0.798027i
$887$	−0.404297	+	2.55263i	−0.0135750	+	0.0857090i	−0.993546	−	0.113433i	$-0.963815\pi$
$887$	−0.404297	+	2.55263i	−0.0135750	+	0.0857090i	0.979971	+	0.199142i	$0.0638154\pi$
$888$	−3.79569	−	23.9650i	−0.127375	−	0.804213i
$889$	37.5378	+	6.34705i	1.25898	+	0.212873i
$890$	−5.73258	−	31.3547i	−0.192156	−	1.05101i
$891$	−24.5708	+	26.0763i	−0.823153	+	0.873590i
$892$	−12.1031	+	12.1031i	−0.405240	+	0.405240i
$893$	−2.93909	−	1.49754i	−0.0983529	−	0.0501133i
$894$	−35.8977	−	26.0812i	−1.20060	−	0.872286i
$895$	0.943389	+	39.7089i	0.0315340	+	1.32732i
$896$	−1.89022	+	1.85123i	−0.0631479	+	0.0618454i
$897$	56.6599	−	28.8696i	1.89182	−	0.963929i
$898$	6.15581	−	38.8662i	0.205422	−	1.29698i
$899$	−17.3623	−	12.6145i	−0.579066	−	0.420716i
$900$	8.46020	−	6.78322i	0.282007	−	0.226107i
$901$			7.64124i			0.254567i
$902$	−12.4636	−	16.1245i	−0.414993	−	0.536887i
$903$	11.3495	+	36.2098i	0.377688	+	1.20499i
$904$	2.28992	−	0.744039i	0.0761615	−	0.0247464i
$905$	−23.4106	+	8.22626i	−0.778196	+	0.273450i
$906$	3.84040	+	5.28586i	0.127589	+	0.175611i
$907$	17.5208	−	8.92728i	0.581768	−	0.296426i	−0.138232	−	0.990400i	$-0.544142\pi$
$907$	17.5208	−	8.92728i	0.581768	−	0.296426i	0.720000	+	0.693974i	$0.244142\pi$
$908$	24.2122	−	12.3368i	0.803511	−	0.409409i
$909$	−9.38108	+	6.81575i	−0.311151	+	0.226064i
$910$	13.2778	+	17.7722i	0.440156	+	0.589142i
$911$	6.27139	+	19.3013i	0.207780	+	0.639482i	0.999588	+	0.0287112i	$0.00914032\pi$
$911$	6.27139	+	19.3013i	0.207780	+	0.639482i	−0.791807	+	0.610771i	$0.790860\pi$
$912$	−2.12264	−	2.12264i	−0.0702878	−	0.0702878i
$913$	−37.0733	+	28.6562i	−1.22695	+	0.948383i
$914$		−	32.6183i		−	1.07892i
$915$	−7.27827	−	13.4828i	−0.240612	−	0.445729i
$916$	−11.7937	+	16.2326i	−0.389674	+	0.536340i
$917$	21.8243	−	29.3896i	0.720701	−	0.970530i
$918$	1.89553	+	3.72018i	0.0625617	+	0.122784i
$919$	−17.5970	−	5.71760i	−0.580470	−	0.188606i	0.00404107	−	0.999992i	$-0.498714\pi$
$919$	−17.5970	−	5.71760i	−0.580470	−	0.188606i	−0.584511	+	0.811386i	$0.698714\pi$
$920$	−0.396143	−	16.6743i	−0.0130604	−	0.549737i
$921$	32.3256	+	23.4860i	1.06517	+	0.773889i
$922$	10.5269	+	5.36372i	0.346685	+	0.176645i
$923$	4.62288	+	4.62288i	0.152164	+	0.152164i
$924$	18.8509	−	6.52978i	0.620149	−	0.214814i
$925$	−21.9408	+	48.6430i	−0.721408	+	1.59937i
$926$	−10.7856	−	33.1947i	−0.354437	−	1.09085i
$927$	−33.5722	+	5.31731i	−1.10265	+	0.174643i
$928$	0.712688	−	4.49974i	0.0233951	−	0.147711i
$929$	12.4265	−	38.2449i	0.407701	−	1.25477i	−0.510918	−	0.859630i	$-0.670694\pi$
$929$	12.4265	−	38.2449i	0.407701	−	1.25477i	0.918619	−	0.395145i	$-0.129306\pi$
$930$	19.0342	−	14.5322i	0.624156	−	0.476529i
$931$	−3.03870	+	8.72887i	−0.0995894	+	0.286077i
$932$	−1.64186	−	10.3663i	−0.0537808	−	0.339559i
$933$	−44.4641	−	22.6556i	−1.45569	−	0.741711i
$934$	−22.1854			−0.725928
$935$	−15.8312	−	4.22312i	−0.517735	−	0.138111i
$936$			8.13252i			0.265820i
$937$	1.70329	+	0.867871i	0.0556442	+	0.0283521i	0.481591	−	0.876396i	$-0.340059\pi$
$937$	1.70329	+	0.867871i	0.0556442	+	0.0283521i	−0.425947	+	0.904748i	$0.640059\pi$
$938$	25.1742	+	8.47060i	0.821967	+	0.276575i
$939$	−17.9767	−	24.7428i	−0.586648	−	0.807452i
$940$	5.53664	+	0.742586i	0.180585	+	0.0242205i
$941$	39.0758	+	12.6965i	1.27384	+	0.413894i	0.866405	−	0.499342i	$-0.166425\pi$
$941$	39.0758	+	12.6965i	1.27384	+	0.413894i	0.407430	+	0.913236i	$0.366425\pi$
$942$	−5.75738	−	0.911879i	−0.187585	−	0.0297106i
$943$	7.17009	+	45.2702i	0.233490	+	1.47420i
$944$	−3.84672	−	11.8390i	−0.125200	−	0.385326i
$945$	5.20817	+	9.89326i	0.169422	+	0.321828i
$946$	10.0487	+	18.3523i	0.326712	+	0.596685i
$947$	−9.02216	−	9.02216i	−0.293181	−	0.293181i	0.545155	−	0.838336i	$-0.316471\pi$
$947$	−9.02216	−	9.02216i	−0.293181	−	0.293181i	−0.838336	+	0.545155i	$0.816471\pi$
$948$	−9.23443	+	18.1236i	−0.299920	+	0.588627i
$949$	−6.67615	+	9.18893i	−0.216717	+	0.298285i
$950$	1.34125	+	6.46423i	0.0435161	+	0.209727i
$951$	−31.8079	−	10.3350i	−1.03144	−	0.335136i
$952$	0.0609081	−	5.84500i	0.00197404	−	0.189438i
$953$	−3.17570	+	20.0506i	−0.102871	+	0.649502i	0.881337	+	0.472488i	$0.156644\pi$
$953$	−3.17570	+	20.0506i	−0.102871	+	0.649502i	−0.984208	+	0.177014i	$0.943356\pi$
$954$	−4.40893	+	6.06837i	−0.142744	+	0.196471i
$955$	−1.84210	+	6.16384i	−0.0596088	+	0.199457i
$956$	−4.11386			−0.133052
$957$	−19.3571	+	28.3793i	−0.625727	+	0.917373i
$958$	−11.5983	−	11.5983i	−0.374725	−	0.374725i
$959$	−26.7198	−	4.51789i	−0.862827	−	0.145890i
$960$	4.58313	+	2.19971i	0.147920	+	0.0709953i
$961$	−7.12706	+	5.17811i	−0.229905	+	0.167036i
$962$	−18.1688	−	35.6584i	−0.585787	−	1.14967i
$963$	−10.9728	−	21.5353i	−0.353593	−	0.693966i
$964$	10.1391	−	7.36650i	0.326559	−	0.237259i
$965$	−25.8611	−	12.4123i	−0.832499	−	0.399565i
$966$	−44.2392	−	7.48014i	−1.42337	−	0.240670i
$967$	−21.3536	−	21.3536i	−0.686685	−	0.686685i	0.274813	−	0.961498i	$-0.411384\pi$
$967$	−21.3536	−	21.3536i	−0.686685	−	0.686685i	−0.961498	+	0.274813i	$0.911384\pi$
$968$	9.48713	−	5.56725i	0.304928	−	0.178938i
$969$	6.63211			0.213054
$970$	−0.576892	+	1.93034i	−0.0185229	+	0.0619795i
$971$	16.4522	−	22.6445i	0.527977	−	0.726697i	−0.458844	−	0.888517i	$-0.651736\pi$
$971$	16.4522	−	22.6445i	0.527977	−	0.726697i	0.986820	+	0.161820i	$0.0517363\pi$
$972$	−2.95512	+	18.6579i	−0.0947856	+	0.598453i
$973$	40.4352	+	0.421357i	1.29629	+	0.0135081i
$974$	17.8378	+	5.79585i	0.571560	+	0.185711i
$975$	23.3892	−	35.6364i	0.749055	−	1.14128i
$976$	1.77155	−	2.43833i	0.0567058	−	0.0780489i
$977$	23.6595	−	46.4344i	0.756934	−	1.48557i	−0.113636	−	0.993522i	$-0.536250\pi$
$977$	23.6595	−	46.4344i	0.756934	−	1.48557i	0.870570	−	0.492044i	$-0.163750\pi$
$978$	−1.15190	−	1.15190i	−0.0368338	−	0.0368338i
$979$	−46.4550	+	8.78000i	−1.48471	+	0.280610i
$980$	−0.0455929	−	15.6524i	−0.00145641	−	0.499998i
$981$	−9.56021	−	29.4233i	−0.305234	−	0.939414i
$982$	1.48540	+	9.37845i	0.0474010	+	0.299278i
$983$	19.7187	+	3.12314i	0.628930	+	0.0996127i	0.462759	−	0.886484i	$-0.346860\pi$
$983$	19.7187	+	3.12314i	0.628930	+	0.0996127i	0.166171	+	0.986097i	$0.446860\pi$
$984$	−13.2863	−	4.31699i	−0.423553	−	0.137621i
$985$	−16.9855	−	2.27813i	−0.541202	−	0.0725872i
$986$	5.91623	+	8.14299i	0.188411	+	0.259326i
$987$	4.79229	−	14.2424i	0.152540	−	0.453342i
$988$	−4.41160	−	2.24782i	−0.140352	−	0.0715127i
$989$		−	47.0565i		−	1.49631i
$990$	−10.1358	−	12.4883i	−0.322137	−	0.396904i
$991$	48.9871			1.55613			0.778064	−	0.628185i	$-0.216202\pi$
$991$	48.9871			1.55613			0.778064	+	0.628185i	$0.216202\pi$
$992$	4.19724	+	2.13860i	0.133263	+	0.0679007i
$993$	4.17404	+	26.3539i	0.132459	+	0.836315i
$994$	−0.674083	−	4.56325i	−0.0213806	−	0.144737i
$995$	−16.8066	+	12.8315i	−0.532807	+	0.406786i
$996$	−9.92558	+	30.5478i	−0.314504	+	0.967944i
$997$	−5.45404	+	34.4354i	−0.172731	+	1.09058i	0.737155	+	0.675723i	$0.236169\pi$
$997$	−5.45404	+	34.4354i	−0.172731	+	1.09058i	−0.909886	+	0.414858i	$0.863831\pi$
$998$	−34.2429	+	5.42353i	−1.08394	+	0.171679i
$999$	−6.23263	−	19.1821i	−0.197192	−	0.606893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.19	yes	384
5.3	odd	4	inner	770.2.bi.a.643.30	yes	384
7.6	odd	2	inner	770.2.bi.a.27.6	✓	384
11.9	even	5	inner	770.2.bi.a.97.43	yes	384
35.13	even	4	inner	770.2.bi.a.643.43	yes	384
55.53	odd	20	inner	770.2.bi.a.713.6	yes	384
77.20	odd	10	inner	770.2.bi.a.97.30	yes	384
385.328	even	20	inner	770.2.bi.a.713.19	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.6	✓	384	7.6	odd	2	inner
770.2.bi.a.27.19	yes	384	1.1	even	1	trivial
770.2.bi.a.97.30	yes	384	77.20	odd	10	inner
770.2.bi.a.97.43	yes	384	11.9	even	5	inner
770.2.bi.a.643.30	yes	384	5.3	odd	4	inner
770.2.bi.a.643.43	yes	384	35.13	even	4	inner
770.2.bi.a.713.6	yes	384	55.53	odd	20	inner
770.2.bi.a.713.19	yes	384	385.328	even	20	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.355652 + 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.77729 - 1.35692i) q^{5} +(-2.16222 - 0.702547i) q^{6} +(2.12414 + 1.57735i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.355652 + 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.77729 - 1.35692i) q^{5} +(-2.16222 - 0.702547i) q^{6} +(2.12414 + 1.57735i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +(0.402154 + 2.19961i) q^{10} +(3.25893 - 0.615938i) q^{11} +(1.60760 - 1.60760i) q^{12} +(1.70240 - 3.34115i) q^{13} +(-2.36977 + 1.17652i) q^{14} +(3.67906 + 3.50831i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.00301 - 1.96852i) q^{17} +(0.339267 - 2.14205i) q^{18} +(1.06821 + 0.776101i) q^{19} +(-2.14244 - 0.640279i) q^{20} +(-2.78649 + 5.33074i) q^{21} +(-0.930718 + 3.18336i) q^{22} +(5.27438 - 5.27438i) q^{23} +(0.702547 + 2.16222i) q^{24} +(1.31752 - 4.82329i) q^{25} +(2.20411 + 3.03370i) q^{26} +(0.857967 + 1.68385i) q^{27} +(0.0275687 - 2.64561i) q^{28} +(2.67785 + 3.68574i) q^{29} +(-4.79619 + 1.68533i) q^{30} +(-4.48012 + 1.45568i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.54213 + 7.09886i) q^{33} +2.20932 q^{34} +(5.91555 - 0.0788767i) q^{35} +(1.75456 + 1.27476i) q^{36} +(-10.5411 - 1.66954i) q^{37} +(-1.17647 + 0.599441i) q^{38} +(8.10802 + 2.63445i) q^{39} +(1.54314 - 1.61825i) q^{40} +(-3.61181 + 4.97123i) q^{41} +(-3.48468 - 4.90288i) q^{42} +(4.46086 - 4.46086i) q^{43} +(-2.41385 - 2.27449i) q^{44} +(-2.75646 + 3.98990i) q^{45} +(2.30499 + 7.09402i) q^{46} +(-2.46747 + 0.390810i) q^{47} +(-2.24550 - 0.355652i) q^{48} +(2.02392 + 6.70103i) q^{49} +(3.69944 + 3.36365i) q^{50} +(4.06359 - 2.95237i) q^{51} +(-3.70370 + 0.586608i) q^{52} +(-3.08166 - 1.57019i) q^{53} -1.88983 q^{54} +(4.95628 - 5.51682i) q^{55} +(2.34474 + 1.22564i) q^{56} +(-1.36282 + 2.67469i) q^{57} +(-4.49974 + 0.712688i) q^{58} +(-10.0708 + 7.31690i) q^{59} +(0.675782 - 5.03856i) q^{60} +(-2.86642 - 0.931357i) q^{61} +(0.736912 - 4.65268i) q^{62} +(-5.43837 - 1.82990i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.50802 - 8.24823i) q^{65} +(-7.47924 - 0.957759i) q^{66} +(-7.09875 - 7.09875i) q^{67} +(-1.00301 + 1.96852i) q^{68} +(13.7195 + 9.96777i) q^{69} +(-2.61533 + 5.30661i) q^{70} +(-0.538759 + 1.65813i) q^{71} +(-1.93237 + 0.984592i) q^{72} +(-2.99166 - 0.473832i) q^{73} +(6.27312 - 8.63421i) q^{74} +(11.2993 + 1.24308i) q^{75} -1.32038i q^{76} +(7.89396 + 3.83214i) q^{77} +(-6.02828 + 6.02828i) q^{78} +(-8.50897 + 2.76473i) q^{79} +(0.741297 + 2.10962i) q^{80} +(-8.73963 + 6.34971i) q^{81} +(-2.78967 - 5.47503i) q^{82} +(-12.5881 + 6.41398i) q^{83} +(5.95051 - 0.879010i) q^{84} +(-4.45377 - 2.13762i) q^{85} +(1.94947 + 5.99984i) q^{86} +(-7.32394 + 7.32394i) q^{87} +(3.12245 - 1.11816i) q^{88} -14.2547 q^{89} +(-2.30362 - 4.26740i) q^{90} +(8.88631 - 4.41178i) q^{91} +(-7.36727 - 1.16686i) q^{92} +(-4.86209 - 9.54238i) q^{93} +(0.771996 - 2.37596i) q^{94} +(2.95163 - 0.0701237i) q^{95} +(1.33632 - 1.83929i) q^{96} +(0.802798 + 0.409046i) q^{97} +(-6.88950 - 1.23888i) q^{98} +(-6.30909 + 3.45451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more