LMFDB - Embedded newform 483.2.r.a.181.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.7
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261645 - 1.81978i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-1.32416 + 0.388808i) q^{4} +(1.39776 - 1.61310i) q^{5} +(-0.517964 + 1.76402i) q^{6} +(2.31938 + 1.27299i) q^{7} +(-0.473472 - 1.03676i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.261645 - 1.81978i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-1.32416 + 0.388808i) q^{4} +(1.39776 - 1.61310i) q^{5} +(-0.517964 + 1.76402i) q^{6} +(2.31938 + 1.27299i) q^{7} +(-0.473472 - 1.03676i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-3.30121 - 2.12156i) q^{10} +(5.55772 + 0.799079i) q^{11} +(1.36601 + 0.196403i) q^{12} +(2.77826 - 4.32305i) q^{13} +(1.70970 - 4.55383i) q^{14} +(-1.94155 + 0.886678i) q^{15} +(-4.08475 + 2.62511i) q^{16} +(0.617581 + 0.181338i) q^{17} +(1.20396 - 1.38944i) q^{18} +(-5.98902 + 1.75853i) q^{19} +(-1.22367 + 2.67946i) q^{20} +(-1.58096 - 2.12145i) q^{21} -10.3229i q^{22} +(4.55545 - 1.49929i) q^{23} +1.13976i q^{24} +(0.0632123 + 0.439651i) q^{25} +(-8.59392 - 3.92471i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-3.56617 - 0.783844i) q^{28} +(-2.25990 - 0.663565i) q^{29} +(2.12156 + 3.30121i) q^{30} +(-2.95658 + 1.35022i) q^{31} +(4.35312 + 5.02377i) q^{32} +(-4.72353 - 3.03563i) q^{33} +(0.168409 - 1.17131i) q^{34} +(5.29539 - 1.96206i) q^{35} +(-1.16098 - 0.746117i) q^{36} +(-4.96767 + 4.30451i) q^{37} +(4.76714 + 10.4386i) q^{38} +(-4.32305 + 2.77826i) q^{39} +(-2.33420 - 0.685382i) q^{40} +(-4.12951 - 3.57824i) q^{41} +(-3.44693 + 3.43207i) q^{42} +(-2.53503 - 1.15771i) q^{43} +(-7.66999 + 1.10278i) q^{44} +2.13444 q^{45} +(-3.92030 - 7.89764i) q^{46} +7.97650i q^{47} +(4.80613 - 0.691017i) q^{48} +(3.75901 + 5.90507i) q^{49} +(0.783529 - 0.230065i) q^{50} +(-0.486441 - 0.421503i) q^{51} +(-1.99801 + 6.80461i) q^{52} +(-4.63224 - 7.20790i) q^{53} +(-1.67235 + 0.763738i) q^{54} +(9.05735 - 7.84824i) q^{55} +(0.221621 - 3.00736i) q^{56} +(6.17832 + 0.888309i) q^{57} +(-0.616253 + 4.28613i) q^{58} +(-0.0452540 + 0.0704165i) q^{59} +(2.22618 - 1.92899i) q^{60} +(-2.78250 - 6.09283i) q^{61} +(3.23068 + 5.02704i) q^{62} +(0.556809 + 2.58650i) q^{63} +(1.64376 - 1.89700i) q^{64} +(-3.09018 - 10.5242i) q^{65} +(-4.28829 + 9.39004i) q^{66} +(0.832194 - 0.119651i) q^{67} -0.888280 q^{68} +(-4.76661 - 0.528597i) q^{69} +(-4.95603 - 9.12308i) q^{70} +(0.233434 + 1.62357i) q^{71} +(0.473472 - 1.03676i) q^{72} +(2.78031 + 9.46888i) q^{73} +(9.13303 + 7.91382i) q^{74} +(0.125138 - 0.426180i) q^{75} +(7.24667 - 4.65715i) q^{76} +(11.8732 + 8.92827i) q^{77} +(6.18692 + 7.14009i) q^{78} +(0.516710 - 0.804016i) q^{79} +(-1.47493 + 10.2584i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-5.43115 + 8.45103i) q^{82} +(7.27635 + 8.39735i) q^{83} +(2.91828 + 2.19445i) q^{84} +(1.15575 - 0.742753i) q^{85} +(-1.44350 + 4.91611i) q^{86} +(1.78002 + 1.54240i) q^{87} +(-1.80297 - 6.14035i) q^{88} +(-2.29948 + 5.03515i) q^{89} +(-0.558465 - 3.88421i) q^{90} +(11.9470 - 6.49010i) q^{91} +(-5.44920 + 3.75650i) q^{92} +3.25030 q^{93} +(14.5155 - 2.08701i) q^{94} +(-5.53452 + 12.1189i) q^{95} +(-1.87279 - 6.37813i) q^{96} +(-2.94110 + 3.39421i) q^{97} +(9.76241 - 8.38561i) q^{98} +(3.03563 + 4.72353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

Coefficient data

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

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

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

$2$	−0.261645	−	1.81978i	−0.185011	−	1.28678i	−0.844700	−	0.535240i	$-0.820221\pi$
$2$	−0.261645	−	1.81978i	−0.185011	−	1.28678i	0.659689	−	0.751539i	$-0.270688\pi$
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	−1.32416	+	0.388808i	−0.662079	+	0.194404i
$5$	1.39776	−	1.61310i	0.625097	−	0.721401i	−0.351569	−	0.936162i	$-0.614352\pi$
$5$	1.39776	−	1.61310i	0.625097	−	0.721401i	0.976667	+	0.214761i	$0.0688973\pi$
$6$	−0.517964	+	1.76402i	−0.211458	+	0.720159i
$7$	2.31938	+	1.27299i	0.876642	+	0.481144i
$7$	2.31938	+	1.27299i	0.876642	+	0.481144i
$8$	−0.473472	−	1.03676i	−0.167398	−	0.366549i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−3.30121	−	2.12156i	−1.04393	−	0.670895i
$11$	5.55772	+	0.799079i	1.67572	+	0.240931i	0.913630	−	0.406546i	$-0.133267\pi$
$11$	5.55772	+	0.799079i	1.67572	+	0.240931i	0.762085	+	0.647477i	$0.224176\pi$
$12$	1.36601	+	0.196403i	0.394334	+	0.0566967i
$13$	2.77826	−	4.32305i	0.770550	−	1.19900i	−0.204902	−	0.978783i	$-0.565687\pi$
$13$	2.77826	−	4.32305i	0.770550	−	1.19900i	0.975451	−	0.220216i	$-0.0706762\pi$
$14$	1.70970	−	4.55383i	0.456937	−	1.21706i
$15$	−1.94155	+	0.886678i	−0.501307	+	0.228939i
$16$	−4.08475	+	2.62511i	−1.02119	+	0.656278i
$17$	0.617581	+	0.181338i	0.149785	+	0.0439809i	0.355766	−	0.934575i	$-0.384220\pi$
$17$	0.617581	+	0.181338i	0.149785	+	0.0439809i	−0.205980	+	0.978556i	$0.566038\pi$
$18$	1.20396	−	1.38944i	0.283776	−	0.327494i
$19$	−5.98902	+	1.75853i	−1.37397	+	0.403435i	−0.883668	−	0.468115i	$-0.844933\pi$
$19$	−5.98902	+	1.75853i	−1.37397	+	0.403435i	−0.490307	+	0.871550i	$0.663115\pi$
$20$	−1.22367	+	2.67946i	−0.273621	+	0.599146i
$21$	−1.58096	−	2.12145i	−0.344994	−	0.462939i
$22$		−	10.3229i		−	2.20085i
$23$	4.55545	−	1.49929i	0.949877	−	0.312624i
$23$	4.55545	−	1.49929i	0.949877	−	0.312624i
$24$			1.13976i			0.232652i
$25$	0.0632123	+	0.439651i	0.0126425	+	0.0879302i
$26$	−8.59392	−	3.92471i	−1.68541	−	0.769699i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−3.56617	−	0.783844i	−0.673942	−	0.148133i
$29$	−2.25990	−	0.663565i	−0.419652	−	0.123221i	0.0650873	−	0.997880i	$-0.479267\pi$
$29$	−2.25990	−	0.663565i	−0.419652	−	0.123221i	−0.484740	+	0.874659i	$0.661086\pi$
$30$	2.12156	+	3.30121i	0.387342	+	0.602715i
$31$	−2.95658	+	1.35022i	−0.531017	+	0.242507i	−0.662833	−	0.748767i	$-0.730646\pi$
$31$	−2.95658	+	1.35022i	−0.531017	+	0.242507i	0.131817	+	0.991274i	$0.457919\pi$
$32$	4.35312	+	5.02377i	0.769530	+	0.888085i
$33$	−4.72353	−	3.03563i	−0.822261	−	0.528435i
$34$	0.168409	−	1.17131i	0.0288818	−	0.200878i
$35$	5.29539	−	1.96206i	0.895084	−	0.331648i
$36$	−1.16098	−	0.746117i	−0.193497	−	0.124353i
$37$	−4.96767	+	4.30451i	−0.816680	+	0.707657i	−0.959383	−	0.282108i	$-0.908966\pi$
$37$	−4.96767	+	4.30451i	−0.816680	+	0.707657i	0.142703	+	0.989766i	$0.454421\pi$
$38$	4.76714	+	10.4386i	0.773333	+	1.69336i
$39$	−4.32305	+	2.77826i	−0.692242	+	0.444877i
$40$	−2.33420	−	0.685382i	−0.369069	−	0.108368i
$41$	−4.12951	−	3.57824i	−0.644921	−	0.558827i	0.269798	−	0.962917i	$-0.413043\pi$
$41$	−4.12951	−	3.57824i	−0.644921	−	0.558827i	−0.914719	+	0.404089i	$0.867588\pi$
$42$	−3.44693	+	3.43207i	−0.531873	+	0.529580i
$43$	−2.53503	−	1.15771i	−0.386589	−	0.176549i	0.212633	−	0.977132i	$-0.431796\pi$
$43$	−2.53503	−	1.15771i	−0.386589	−	0.176549i	−0.599222	+	0.800583i	$0.704523\pi$
$44$	−7.66999	+	1.10278i	−1.15629	+	0.166250i
$45$	2.13444			0.318183
$46$	−3.92030	−	7.89764i	−0.578016	−	1.16444i
$47$			7.97650i			1.16349i	0.813370	+	0.581746i	$0.197630\pi$
$47$			7.97650i			1.16349i	−0.813370	+	0.581746i	$0.802370\pi$
$48$	4.80613	−	0.691017i	0.693705	−	0.0997398i
$49$	3.75901	+	5.90507i	0.537001	+	0.843581i
$50$	0.783529	−	0.230065i	0.110808	−	0.0325361i
$51$	−0.486441	−	0.421503i	−0.0681153	−	0.0590222i
$52$	−1.99801	+	6.80461i	−0.277075	+	0.943629i
$53$	−4.63224	−	7.20790i	−0.636286	−	0.990081i	−0.998321	−	0.0579165i	$-0.981554\pi$
$53$	−4.63224	−	7.20790i	−0.636286	−	0.990081i	0.362035	−	0.932165i	$-0.382082\pi$
$54$	−1.67235	+	0.763738i	−0.227578	+	0.103932i
$55$	9.05735	−	7.84824i	1.22129	−	1.05826i
$56$	0.221621	−	3.00736i	0.0296153	−	0.401875i
$57$	6.17832	+	0.888309i	0.818339	+	0.117659i
$58$	−0.616253	+	4.28613i	−0.0809180	+	0.562797i
$59$	−0.0452540	+	0.0704165i	−0.00589156	+	0.00916745i	−0.844187	−	0.536049i	$-0.819916\pi$
$59$	−0.0452540	+	0.0704165i	−0.00589156	+	0.00916745i	0.838295	+	0.545217i	$0.183553\pi$
$60$	2.22618	−	1.92899i	0.287398	−	0.249032i
$61$	−2.78250	−	6.09283i	−0.356263	−	0.780107i	−0.999891	−	0.0147686i	$-0.995299\pi$
$61$	−2.78250	−	6.09283i	−0.356263	−	0.780107i	0.643628	−	0.765339i	$-0.277428\pi$
$62$	3.23068	+	5.02704i	0.410297	+	0.638435i
$63$	0.556809	+	2.58650i	0.0701514	+	0.325868i
$64$	1.64376	−	1.89700i	0.205470	−	0.237125i
$65$	−3.09018	−	10.5242i	−0.383290	−	1.30537i
$66$	−4.28829	+	9.39004i	−0.527852	+	1.15583i
$67$	0.832194	−	0.119651i	0.101669	−	0.0146177i	−0.0912927	−	0.995824i	$-0.529100\pi$
$67$	0.832194	−	0.119651i	0.101669	−	0.0146177i	0.192961	+	0.981206i	$0.438191\pi$
$68$	−0.888280			−0.107720
$69$	−4.76661	−	0.528597i	−0.573833	−	0.0636356i
$70$	−4.95603	−	9.12308i	−0.592358	−	1.09042i
$71$	0.233434	+	1.62357i	0.0277035	+	0.192682i	0.998974	−	0.0452981i	$-0.0144238\pi$
$71$	0.233434	+	1.62357i	0.0277035	+	0.192682i	−0.971270	+	0.237980i	$0.923515\pi$
$72$	0.473472	−	1.03676i	0.0557992	−	0.122183i
$73$	2.78031	+	9.46888i	0.325411	+	1.10825i	0.946015	+	0.324124i	$0.105069\pi$
$73$	2.78031	+	9.46888i	0.325411	+	1.10825i	−0.620604	+	0.784124i	$0.713112\pi$
$74$	9.13303	+	7.91382i	1.06169	+	0.919963i
$75$	0.125138	−	0.426180i	0.0144497	−	0.0492110i
$76$	7.24667	−	4.65715i	0.831250	−	0.534212i
$77$	11.8732	+	8.92827i	1.35308	+	1.01747i
$78$	6.18692	+	7.14009i	0.700531	+	0.808456i
$79$	0.516710	−	0.804016i	0.0581344	−	0.0904588i	−0.810970	−	0.585088i	$-0.801060\pi$
$79$	0.516710	−	0.804016i	0.0581344	−	0.0904588i	0.869104	+	0.494629i	$0.164696\pi$
$80$	−1.47493	+	10.2584i	−0.164903	+	1.14692i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−5.43115	+	8.45103i	−0.599770	+	0.933261i
$83$	7.27635	+	8.39735i	0.798683	+	0.921729i	0.998308	−	0.0581431i	$-0.0185180\pi$
$83$	7.27635	+	8.39735i	0.798683	+	0.921729i	−0.199625	+	0.979872i	$0.563973\pi$
$84$	2.91828	+	2.19445i	0.318410	+	0.239434i
$85$	1.15575	−	0.742753i	0.125358	−	0.0805629i
$86$	−1.44350	+	4.91611i	−0.155657	+	0.530118i
$87$	1.78002	+	1.54240i	0.190838	+	0.165362i
$88$	−1.80297	−	6.14035i	−0.192197	−	0.654564i
$89$	−2.29948	+	5.03515i	−0.243744	+	0.533725i	−0.991478	−	0.130273i	$-0.958415\pi$
$89$	−2.29948	+	5.03515i	−0.243744	+	0.533725i	0.747734	+	0.663998i	$0.231142\pi$
$90$	−0.558465	−	3.88421i	−0.0588674	−	0.409432i
$91$	11.9470	−	6.49010i	1.25239	−	0.680347i
$92$	−5.44920	+	3.75650i	−0.568118	+	0.391642i
$93$	3.25030			0.337040
$94$	14.5155	−	2.08701i	1.49716	−	0.215259i
$95$	−5.53452	+	12.1189i	−0.567829	+	1.24337i
$96$	−1.87279	−	6.37813i	−0.191141	−	0.650965i
$97$	−2.94110	+	3.39421i	−0.298623	+	0.344630i	−0.885155	−	0.465297i	$-0.845948\pi$
$97$	−2.94110	+	3.39421i	−0.298623	+	0.344630i	0.586531	+	0.809927i	$0.300493\pi$
$98$	9.76241	−	8.38561i	0.986152	−	0.847074i
$99$	3.03563	+	4.72353i	0.305092	+	0.474733i
$100$	−0.254643	−	0.557590i	−0.0254643	−	0.0557590i
$101$	7.30866	−	6.33299i	0.727239	−	0.630156i	−0.210461	−	0.977602i	$-0.567496\pi$
$101$	7.30866	−	6.33299i	0.727239	−	0.630156i	0.937700	+	0.347446i	$0.112951\pi$
$102$	−0.639769	+	0.995499i	−0.0633465	+	0.0985691i
$103$	2.25327	−	15.6719i	0.222022	−	1.54419i	−0.508354	−	0.861148i	$-0.669746\pi$
$103$	2.25327	−	15.6719i	0.222022	−	1.54419i	0.730375	−	0.683046i	$-0.239345\pi$
$104$	−5.79739	−	0.833538i	−0.568480	−	0.0817351i
$105$	−5.63192	−	0.415033i	−0.549619	−	0.0405030i
$106$	−11.9048	+	10.3156i	−1.15630	+	1.00194i
$107$	12.5412	−	5.72739i	1.21241	−	0.553688i	0.296483	−	0.955038i	$-0.404186\pi$
$107$	12.5412	−	5.72739i	1.21241	−	0.553688i	0.915925	+	0.401350i	$0.131459\pi$
$108$	0.746117	+	1.16098i	0.0717951	+	0.111715i
$109$	2.31743	−	7.89244i	0.221970	−	0.755959i	−0.770921	−	0.636930i	$-0.780204\pi$
$109$	2.31743	−	7.89244i	0.221970	−	0.755959i	0.992891	−	0.119028i	$-0.0379780\pi$
$110$	−16.6519	−	14.4289i	−1.58770	−	1.37575i
$111$	6.30691	−	1.85188i	0.598625	−	0.175772i
$112$	−12.8158	+	0.888784i	−1.21098	+	0.0839822i
$113$	−4.45898	+	0.641105i	−0.419466	+	0.0603101i	−0.348816	−	0.937191i	$-0.613416\pi$
$113$	−4.45898	+	0.641105i	−0.419466	+	0.0603101i	−0.0706495	+	0.997501i	$0.522507\pi$
$114$		−	11.4756i		−	1.07479i
$115$	3.94891	−	9.44405i	0.368238	−	0.880662i
$116$	3.25046			0.301798
$117$	5.08651	−	0.731330i	0.470248	−	0.0676115i
$118$	0.139983	+	0.0639281i	0.0128865	+	0.00588506i
$119$	1.20156	+	1.20676i	0.110147	+	0.110624i
$120$	1.83854	+	1.59311i	0.167835	+	0.145430i
$121$	19.6953	+	5.78306i	1.79048	+	0.525733i
$122$	−10.3596	+	6.65770i	−0.937913	+	0.602760i
$123$	2.26988	+	4.97034i	0.204668	+	0.448161i
$124$	3.38999	−	2.93745i	0.304431	−	0.263791i
$125$	9.77558	+	6.28238i	0.874354	+	0.561913i
$126$	4.56117	−	1.69001i	0.406341	−	0.150558i
$127$	−0.138595	+	0.963949i	−0.0122983	+	0.0855366i	−0.995046	−	0.0994136i	$-0.968303\pi$
$127$	−0.138595	+	0.963949i	−0.0122983	+	0.0855366i	0.982748	+	0.184950i	$0.0592124\pi$
$128$	7.30209	+	4.69277i	0.645420	+	0.414786i
$129$	1.82501	+	2.10618i	0.160684	+	0.185439i
$130$	−18.3432	+	8.37706i	−1.60880	+	0.734716i
$131$	−7.96195	−	12.3890i	−0.695639	−	1.08244i	−0.991862	−	0.127316i	$-0.959364\pi$
$131$	−7.96195	−	12.3890i	−0.695639	−	1.08244i	0.296223	−	0.955119i	$-0.404273\pi$
$132$	7.43497	+	2.18311i	0.647131	+	0.190015i
$133$	−16.1294	−	3.54524i	−1.39859	−	0.307411i
$134$	−0.435479	−	1.48310i	−0.0376196	−	0.128121i
$135$	−1.94155	−	0.886678i	−0.167102	−	0.0763131i
$136$	−0.104403	−	0.726140i	−0.00895250	−	0.0622660i
$137$			8.88276i			0.758906i	0.925211	+	0.379453i	$0.123888\pi$
$137$			8.88276i			0.758906i	−0.925211	+	0.379453i	$0.876112\pi$
$138$	0.285230	+	8.81249i	0.0242804	+	0.750169i
$139$			22.0612i			1.87121i	0.353055	+	0.935603i	$0.385143\pi$
$139$			22.0612i			1.87121i	−0.353055	+	0.935603i	$0.614857\pi$
$140$	−6.24906	+	4.65696i	−0.528142	+	0.393585i
$141$	3.31356	−	7.25568i	0.279052	−	0.611038i
$142$	2.89346	−	0.849597i	0.242814	−	0.0712966i
$143$	18.8952	−	21.8063i	1.58010	−	1.82353i
$144$	−4.65887	−	1.36797i	−0.388239	−	0.113997i
$145$	−4.22919	+	2.71794i	−0.351215	+	0.225712i
$146$	16.5038	−	7.53704i	1.36587	−	0.623770i
$147$	−0.966261	−	6.93299i	−0.0796959	−	0.571823i
$148$	4.90435	−	7.63132i	0.403135	−	0.627291i
$149$	−18.8967	−	2.71693i	−1.54808	−	0.222580i	−0.685336	−	0.728227i	$-0.740345\pi$
$149$	−18.8967	−	2.71693i	−1.54808	−	0.222580i	−0.862740	+	0.505647i	$0.831254\pi$
$150$	−0.808296	−	0.116215i	−0.0659971	−	0.00948895i
$151$	7.36484	+	4.73309i	0.599342	+	0.385174i	0.804847	−	0.593482i	$-0.202247\pi$
$151$	7.36484	+	4.73309i	0.599342	+	0.385174i	−0.205505	+	0.978656i	$0.565884\pi$
$152$	4.65881	+	5.37655i	0.377879	+	0.436096i
$153$	0.267383	+	0.585487i	0.0216166	+	0.0473339i
$154$	13.1409	−	23.9427i	1.05893	−	1.92936i
$155$	−1.95454	+	6.65654i	−0.156992	+	0.534666i
$156$	4.64419	−	5.35969i	0.371833	−	0.429118i
$157$	−12.3580	+	3.62863i	−0.986273	+	0.289596i	−0.734812	−	0.678271i	$-0.762729\pi$
$157$	−12.3580	+	3.62863i	−0.986273	+	0.289596i	−0.251462	+	0.967867i	$0.580911\pi$
$158$	−1.59833	−	0.729931i	−0.127156	−	0.0580702i
$159$	1.21936	+	8.48084i	0.0967015	+	0.672574i
$160$	14.1885			1.12170
$161$	12.4744	+	2.32160i	0.983119	+	0.182968i
$162$	1.83849			0.144446
$163$	1.23405	+	8.58300i	0.0966582	+	0.672273i	0.979328	+	0.202279i	$0.0648347\pi$
$163$	1.23405	+	8.58300i	0.0966582	+	0.672273i	−0.882670	+	0.469994i	$0.844256\pi$
$164$	6.85937	+	3.13257i	0.535627	+	0.244613i
$165$	−11.4991	+	3.37645i	−0.895206	+	0.262856i
$166$	13.3775	−	15.4385i	1.03830	−	1.19826i
$167$	−0.745175	+	2.53783i	−0.0576633	+	0.196383i	−0.983287	−	0.182062i	$-0.941723\pi$
$167$	−0.745175	+	2.53783i	−0.0576633	+	0.196383i	0.925624	+	0.378445i	$0.123541\pi$
$168$	−1.45089	+	2.64352i	−0.111939	+	0.203952i
$169$	−5.56967	−	12.1959i	−0.428436	−	0.938144i
$170$	−1.65404	−	1.90887i	−0.126859	−	0.146403i
$171$	−5.25098	−	3.37460i	−0.401553	−	0.258062i
$172$	3.80691	+	0.547351i	0.290274	+	0.0417351i
$173$	−4.40967	−	0.634015i	−0.335261	−	0.0482033i	−0.0273715	−	0.999625i	$-0.508714\pi$
$173$	−4.40967	−	0.634015i	−0.335261	−	0.0482033i	−0.307890	+	0.951422i	$0.599623\pi$
$174$	2.34109	−	3.64280i	0.177477	−	0.276160i
$175$	−0.413057	+	1.10018i	−0.0312242	+	0.0831661i
$176$	−24.7996	+	11.3256i	−1.86934	+	0.853698i
$177$	0.0704165	−	0.0452540i	0.00529283	−	0.00340150i
$178$	9.76452	+	2.86712i	0.731882	+	0.214900i
$179$	6.38356	−	7.36703i	0.477130	−	0.550637i	−0.465251	−	0.885179i	$-0.654036\pi$
$179$	6.38356	−	7.36703i	0.477130	−	0.550637i	0.942381	+	0.334541i	$0.108581\pi$
$180$	−2.82633	+	0.829886i	−0.210662	+	0.0618561i
$181$	−8.62098	+	18.8773i	−0.640792	+	1.40314i	0.258594	+	0.965986i	$0.416741\pi$
$181$	−8.62098	+	18.8773i	−0.640792	+	1.40314i	−0.899387	+	0.437154i	$0.855987\pi$
$182$	−14.9364	−	20.0428i	−1.10716	−	1.48567i
$183$			6.69813i			0.495140i
$184$	−3.71128	−	4.01303i	−0.273599	−	0.295844i
$185$			14.0300i			1.03151i
$186$	−0.850424	−	5.91483i	−0.0623561	−	0.433696i
$187$	3.28744	+	1.50132i	0.240401	+	0.109788i
$188$	−3.10133	−	10.5621i	−0.226187	−	0.770324i
$189$	0.567978	−	2.58407i	0.0413143	−	0.187963i
$190$	23.5018	+	6.90076i	1.70500	+	0.500633i
$191$	−9.90028	−	15.4051i	−0.716359	−	1.11468i	−0.988324	−	0.152369i	$-0.951310\pi$
$191$	−9.90028	−	15.4051i	−0.716359	−	1.11468i	0.271965	−	0.962307i	$-0.412327\pi$
$192$	−2.28326	+	1.04273i	−0.164780	+	0.0752524i
$193$	13.2120	+	15.2475i	0.951024	+	1.09754i	0.995136	+	0.0985133i	$0.0314087\pi$
$193$	13.2120	+	15.2475i	0.951024	+	1.09754i	−0.0441120	+	0.999027i	$0.514046\pi$
$194$	6.94624	+	4.46408i	0.498711	+	0.320502i
$195$	−1.56098	+	10.8569i	−0.111784	+	0.777475i
$196$	−7.27346	−	6.35771i	−0.519533	−	0.454122i
$197$	−22.1553	−	14.2384i	−1.57850	−	1.01444i	−0.976386	−	0.216033i	$-0.930688\pi$
$197$	−22.1553	−	14.2384i	−1.57850	−	1.01444i	−0.602116	−	0.798409i	$-0.705675\pi$
$198$	7.80153	−	6.76007i	0.554431	−	0.480417i
$199$	8.58096	+	18.7897i	0.608288	+	1.33197i	0.923739	+	0.383023i	$0.125117\pi$
$199$	8.58096	+	18.7897i	0.608288	+	1.33197i	−0.315451	+	0.948942i	$0.602156\pi$
$200$	0.425883	−	0.273698i	0.0301145	−	0.0193534i
$201$	−0.806695	−	0.236867i	−0.0568999	−	0.0167073i
$202$	−13.4369	−	11.6432i	−0.945419	−	0.819210i
$203$	−4.39684	−	4.41588i	−0.308598	−	0.309934i
$204$	0.808008	+	0.369005i	0.0565719	+	0.0258355i
$205$	−11.5441	+	1.65980i	−0.806277	+	0.115925i
$206$	−29.1089			−2.02811
$207$	4.11628	+	2.46095i	0.286101	+	0.171048i
$208$			24.9518i			1.73010i
$209$	−34.6905	+	4.98774i	−2.39959	+	0.345009i
$210$	0.718296	+	10.3575i	0.0495671	+	0.714732i
$211$	12.8672	−	3.77816i	0.885817	−	0.260099i	0.192988	−	0.981201i	$-0.438182\pi$
$211$	12.8672	−	3.77816i	0.885817	−	0.260099i	0.692829	+	0.721102i	$0.256364\pi$
$212$	8.93630	+	7.74335i	0.613747	+	0.531815i
$213$	0.462116	−	1.57382i	0.0316636	−	0.107836i
$214$	−13.7040	−	21.3238i	−0.936783	−	1.45766i
$215$	−5.41087	+	2.47106i	−0.369018	+	0.168525i
$216$	−0.861370	+	0.746381i	−0.0586088	+	0.0507848i
$217$	−8.57622	−	0.632007i	−0.582192	−	0.0429034i
$218$	−14.9689	−	2.15220i	−1.01382	−	0.145765i
$219$	1.40445	−	9.76818i	0.0949040	−	0.660072i
$220$	−8.94191	+	13.9139i	−0.602863	+	0.938074i
$221$	2.49973	−	2.16603i	0.168150	−	0.145703i
$222$	−5.02018	−	10.9927i	−0.336932	−	0.737779i
$223$	11.5752	+	18.0114i	0.775133	+	1.20613i	0.974098	+	0.226124i	$0.0726056\pi$
$223$	11.5752	+	18.0114i	0.775133	+	1.20613i	−0.198965	+	0.980007i	$0.563758\pi$
$224$	3.70133	+	17.1935i	0.247306	+	1.14879i
$225$	−0.290871	+	0.335683i	−0.0193914	+	0.0223789i
$226$	2.33334	+	7.94663i	0.155212	+	0.528602i
$227$	−3.52025	+	7.70828i	−0.233647	+	0.511616i	−0.989746	−	0.142842i	$-0.954376\pi$
$227$	−3.52025	+	7.70828i	−0.233647	+	0.511616i	0.756098	+	0.654458i	$0.227103\pi$
$228$	−8.52646	+	1.22592i	−0.564678	+	0.0811885i
$229$	−11.0180			−0.728089			−0.364045	−	0.931382i	$-0.618604\pi$
$229$	−11.0180			−0.728089			−0.364045	+	0.931382i	$0.618604\pi$
$230$	−18.2193	−	4.71517i	−1.20135	−	0.310909i
$231$	−7.09133	−	13.0538i	−0.466575	−	0.858874i
$232$	0.382040	+	2.65715i	0.0250822	+	0.174450i
$233$	−2.50121	+	5.47688i	−0.163860	+	0.358802i	−0.973695	−	0.227854i	$-0.926829\pi$
$233$	−2.50121	+	5.47688i	−0.163860	+	0.358802i	0.809836	+	0.586657i	$0.199556\pi$
$234$	−2.66172	−	9.06499i	−0.174002	−	0.592597i
$235$	12.8669	+	11.1492i	0.839344	+	0.727296i
$236$	0.0325449	−	0.110838i	0.00211849	−	0.00721492i
$237$	−0.804016	+	0.516710i	−0.0522264	+	0.0335639i
$238$	1.88166	−	2.50232i	0.121970	−	0.162201i
$239$	13.4240	+	15.4921i	0.868327	+	1.00210i	0.999942	+	0.0108019i	$0.00343843\pi$
$239$	13.4240	+	15.4921i	0.868327	+	1.00210i	−0.131615	+	0.991301i	$0.542016\pi$
$240$	5.60314	−	8.71865i	0.361681	−	0.562787i
$241$	−2.03659	+	14.1648i	−0.131188	+	0.912433i	0.812821	+	0.582513i	$0.197931\pi$
$241$	−2.03659	+	14.1648i	−0.131188	+	0.912433i	−0.944009	+	0.329919i	$0.892978\pi$
$242$	5.37073	−	37.3542i	0.345243	−	2.40122i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	6.05341	+	6.98601i	0.387530	+	0.447234i
$245$	14.7797	+	2.19021i	0.944238	+	0.139927i
$246$	8.45103	−	5.43115i	0.538818	−	0.346277i
$247$	−9.03679	+	30.7765i	−0.574997	+	1.95826i
$248$	2.79971	+	2.42596i	0.177782	+	0.154049i
$249$	−3.13041	−	10.6612i	−0.198382	−	0.675626i
$250$	8.87483	−	19.4332i	0.561293	−	1.22906i
$251$	0.101556	+	0.706340i	0.00641018	+	0.0445838i	0.992775	−	0.119987i	$-0.0382852\pi$
$251$	0.101556	+	0.706340i	0.00641018	+	0.0445838i	−0.986365	+	0.164571i	$0.947376\pi$
$252$	−1.74295	−	3.20844i	−0.109796	−	0.202113i
$253$	26.5160	−	4.69249i	1.66704	−	0.295014i
$254$	1.79044			0.112342
$255$	−1.35985	+	0.195518i	−0.0851574	+	0.0122438i
$256$	8.71471	−	19.0826i	0.544669	−	1.19266i
$257$	2.31784	+	7.89384i	0.144583	+	0.492404i	0.999659	−	0.0260978i	$-0.00830814\pi$
$257$	2.31784	+	7.89384i	0.144583	+	0.492404i	−0.855077	+	0.518502i	$0.826490\pi$
$258$	3.35528	−	3.87220i	0.208891	−	0.241073i
$259$	−17.0015	+	3.66000i	−1.05642	+	0.227421i
$260$	8.18378	+	12.7342i	0.507536	+	0.789742i
$261$	−0.978428	−	2.14246i	−0.0605632	−	0.132615i
$262$	−20.4621	+	17.7305i	−1.26415	+	1.09540i
$263$	14.7978	−	23.0258i	0.912469	−	1.41983i	0.00487108	−	0.999988i	$-0.498449\pi$
$263$	14.7978	−	23.0258i	0.912469	−	1.41983i	0.907598	−	0.419841i	$-0.137914\pi$
$264$	−0.910755	+	6.33444i	−0.0560531	+	0.389858i
$265$	−18.1018	−	2.60265i	−1.11199	−	0.159879i
$266$	−2.23139	+	30.2795i	−0.136815	+	1.85656i
$267$	4.18336	−	3.62490i	0.256017	−	0.221840i
$268$	−1.05543	+	0.482001i	−0.0644709	+	0.0294429i
$269$	−1.52686	−	2.37585i	−0.0930945	−	0.144858i	0.791583	−	0.611062i	$-0.209258\pi$
$269$	−1.52686	−	2.37585i	−0.0930945	−	0.144858i	−0.884677	+	0.466204i	$0.845621\pi$
$270$	−1.10556	+	3.76520i	−0.0672823	+	0.229143i
$271$	−22.0513	−	19.1076i	−1.33952	−	1.16070i	−0.973133	−	0.230243i	$-0.926048\pi$
$271$	−22.0513	−	19.1076i	−1.33952	−	1.16070i	−0.366391	−	0.930461i	$-0.619407\pi$
$272$	−2.99870	+	0.880497i	−0.181823	+	0.0533879i
$273$	−13.5635	+	0.940634i	−0.820898	+	0.0569298i
$274$	16.1647	−	2.32413i	0.976544	−	0.140406i
$275$			2.49397i			0.150392i
$276$	6.51727	−	1.15335i	0.392293	−	0.0694235i
$277$	−20.8366			−1.25195			−0.625974	−	0.779844i	$-0.715298\pi$
$277$	−20.8366			−1.25195			−0.625974	+	0.779844i	$0.715298\pi$
$278$	40.1465	−	5.77220i	2.40783	−	0.346193i
$279$	−2.95658	−	1.35022i	−0.177006	−	0.0808357i
$280$	−4.54140	−	4.56106i	−0.271400	−	0.272575i
$281$	−22.8779	−	19.8238i	−1.36478	−	1.18259i	−0.963838	−	0.266490i	$-0.914136\pi$
$281$	−22.8779	−	19.8238i	−1.36478	−	1.18259i	−0.400946	−	0.916102i	$-0.631318\pi$
$282$	−14.0707	−	4.13154i	−0.837899	−	0.246029i
$283$	16.1200	−	10.3597i	0.958235	−	0.615820i	0.0347257	−	0.999397i	$-0.488944\pi$
$283$	16.1200	−	10.3597i	0.958235	−	0.615820i	0.923509	+	0.383577i	$0.125308\pi$
$284$	−0.940359	−	2.05910i	−0.0558000	−	0.122185i
$285$	10.0687	−	8.72462i	0.596421	−	0.516802i
$286$	−44.6264	−	28.6797i	−2.63882	−	1.69586i
$287$	−5.02283	−	13.5561i	−0.296489	−	0.800191i
$288$	−0.946023	+	6.57973i	−0.0557449	+	0.387715i
$289$	−13.9528	−	8.96691i	−0.820752	−	0.527465i
$290$	6.05259	+	6.98507i	0.355421	+	0.410177i
$291$	4.08532	−	1.86570i	0.239486	−	0.109370i
$292$	−7.36315	−	11.4573i	−0.430896	−	0.670487i
$293$	16.3102	+	4.78911i	0.952852	+	0.279783i	0.720974	−	0.692962i	$-0.243695\pi$
$293$	16.3102	+	4.78911i	0.952852	+	0.279783i	0.231878	+	0.972745i	$0.425513\pi$
$294$	−12.3637	+	3.57237i	−0.721066	+	0.208345i
$295$	0.0503348	+	0.171425i	0.00293061	+	0.00998073i
$296$	6.81479	+	3.11221i	0.396102	+	0.180894i
$297$	−0.799079	−	5.55772i	−0.0463673	−	0.322492i
$298$			35.0987i			2.03321i
$299$	6.17468	−	23.8589i	0.357091	−	1.37979i
$300$			0.612984i			0.0353906i
$301$	−4.40594	−	5.91222i	−0.253954	−	0.340775i
$302$	6.68622	−	14.6408i	0.384749	−	0.842482i
$303$	−9.27901	+	2.72456i	−0.533065	+	0.156522i
$304$	19.8473	−	22.9050i	1.13832	−	1.31369i
$305$	−13.7176	−	4.02786i	−0.785469	−	0.230634i
$306$	0.995499	−	0.639769i	0.0569089	−	0.0365731i
$307$	12.1758	−	5.56051i	0.694911	−	0.317355i	−0.0364599	−	0.999335i	$-0.511608\pi$
$307$	12.1758	−	5.56051i	0.694911	−	0.317355i	0.731371	+	0.681980i	$0.238881\pi$
$308$	−19.1934	−	7.20603i	−1.09365	−	0.410602i
$309$	−8.55998	+	13.3196i	−0.486960	+	0.757724i
$310$	12.6248	+	1.81518i	0.717043	+	0.103095i
$311$	10.1655	+	1.46158i	0.576435	+	0.0828788i	0.424365	−	0.905491i	$-0.360497\pi$
$311$	10.1655	+	1.46158i	0.576435	+	0.0828788i	0.152069	+	0.988370i	$0.451406\pi$
$312$	4.92722	+	3.16653i	0.278949	+	0.179270i
$313$	5.58463	+	6.44501i	0.315662	+	0.364293i	0.891302	−	0.453410i	$-0.149793\pi$
$313$	5.58463	+	6.44501i	0.315662	+	0.364293i	−0.575640	+	0.817703i	$0.695247\pi$
$314$	9.83671	+	21.5394i	0.555117	+	1.21554i
$315$	4.95057	+	2.71711i	0.278933	+	0.153092i
$316$	−0.371597	+	1.26554i	−0.0209040	+	0.0711924i
$317$	13.1401	−	15.1645i	0.738023	−	0.851724i	−0.255328	−	0.966855i	$-0.582183\pi$
$317$	13.1401	−	15.1645i	0.738023	−	0.851724i	0.993350	+	0.115131i	$0.0367288\pi$
$318$	15.1142	−	4.43794i	0.847563	−	0.248867i
$319$	−12.0296	−	5.49375i	−0.673530	−	0.307591i
$320$	−0.762470	−	5.30309i	−0.0426234	−	0.296452i
$321$	−13.7872			−0.769524
$322$	0.960946	−	23.3081i	0.0535514	−	1.29891i
$323$	−4.01759			−0.223545
$324$	−0.196403	−	1.36601i	−0.0109113	−	0.0758896i
$325$	2.07625	+	0.948193i	0.115170	+	0.0525963i
$326$	15.2963	−	4.49140i	0.847184	−	0.248756i
$327$	−5.38665	+	6.21652i	−0.297882	+	0.343774i
$328$	−1.75457	+	5.97550i	−0.0968797	+	0.329942i
$329$	−10.1540	+	18.5005i	−0.559807	+	1.01997i
$330$	9.15309	+	20.0425i	0.503861	+	1.10330i
$331$	−5.93290	−	6.84693i	−0.326101	−	0.376341i	0.568898	−	0.822408i	$-0.307370\pi$
$331$	−5.93290	−	6.84693i	−0.326101	−	0.376341i	−0.895000	+	0.446067i	$0.852824\pi$
$332$	−12.9000	−	8.29032i	−0.707979	−	0.454990i
$333$	−6.50626	−	0.935460i	−0.356541	−	0.0512629i
$334$	4.81327	+	0.692043i	0.263370	+	0.0378669i
$335$	0.970198	−	1.50966i	0.0530076	−	0.0824814i
$336$	12.0269	+	4.51541i	0.656120	+	0.246336i
$337$	25.2939	−	11.5513i	1.37785	−	0.629241i	0.417660	−	0.908603i	$-0.362850\pi$
$337$	25.2939	−	11.5513i	1.37785	−	0.629241i	0.960186	+	0.279363i	$0.0901231\pi$
$338$	−20.7365	+	13.3266i	−1.12792	+	0.724869i
$339$	4.32236	+	1.26916i	0.234758	+	0.0689312i
$340$	−1.24160	+	1.43289i	−0.0673353	+	0.0777091i
$341$	−17.5107	+	5.14162i	−0.948260	+	0.278434i
$342$	−4.76714	+	10.4386i	−0.257778	+	0.564454i
$343$	1.20148	+	18.4812i	0.0648740	+	0.997893i
$344$			3.17636i			0.171258i
$345$	−7.51526	+	6.95017i	−0.404608	+	0.374185i
$346$			8.19053i			0.440325i
$347$	2.56220	+	17.8205i	0.137546	+	0.956653i	0.935347	+	0.353732i	$0.115088\pi$
$347$	2.56220	+	17.8205i	0.137546	+	0.956653i	−0.797801	+	0.602921i	$0.794003\pi$
$348$	−2.95672	−	1.35029i	−0.158497	−	0.0723831i
$349$	−7.60384	−	25.8963i	−0.407024	−	1.38620i	−0.867019	−	0.498275i	$-0.833967\pi$
$349$	−7.60384	−	25.8963i	−0.407024	−	1.38620i	0.459995	−	0.887922i	$-0.347851\pi$
$350$	2.11017	+	0.463815i	0.112793	+	0.0247920i
$351$	−4.93066	−	1.44777i	−0.263179	−	0.0772764i
$352$	20.1790	+	31.3992i	1.07555	+	1.67358i
$353$	25.2995	−	11.5539i	1.34656	−	0.614952i	0.393943	−	0.919135i	$-0.371111\pi$
$353$	25.2995	−	11.5539i	1.34656	−	0.614952i	0.952613	+	0.304184i	$0.0983836\pi$
$354$	−0.100776	−	0.116302i	−0.00535621	−	0.00618139i
$355$	2.94526	+	1.89281i	0.156318	+	0.100460i
$356$	1.08716	−	7.56139i	0.0576196	−	0.400753i
$357$	−0.591671	−	1.59686i	−0.0313145	−	0.0845146i
$358$	−15.0766	−	9.68914i	−0.796823	−	0.512087i
$359$	−1.71642	+	1.48729i	−0.0905893	+	0.0784961i	−0.698978	−	0.715143i	$-0.746362\pi$
$359$	−1.71642	+	1.48729i	−0.0905893	+	0.0784961i	0.608389	+	0.793639i	$0.291816\pi$
$360$	−1.01060	−	2.21290i	−0.0532631	−	0.116630i
$361$	16.7921	−	10.7916i	0.883793	−	0.567979i
$362$	36.6082	+	10.7491i	1.92408	+	0.564962i
$363$	−15.5131	−	13.4422i	−0.814226	−	0.705531i
$364$	−13.2963	+	13.2390i	−0.696917	+	0.693912i
$365$	19.1605	+	8.75029i	1.00290	+	0.458011i
$366$	12.1891	−	1.75253i	0.637136	−	0.0916063i
$367$	−7.91666			−0.413246			−0.206623	−	0.978421i	$-0.566247\pi$
$367$	−7.91666			−0.413246			−0.206623	+	0.978421i	$0.566247\pi$
$368$	−14.6721	+	18.0828i	−0.764835	+	0.942631i
$369$		−	5.46413i		−	0.284451i
$370$	25.5316	−	3.67089i	1.32732	−	0.190840i
$371$	−1.56834	−	22.6146i	−0.0814240	−	1.17409i
$372$	−4.30391	+	1.26374i	−0.223147	+	0.0655219i
$373$	17.4695	+	15.1374i	0.904534	+	0.783784i	0.976923	−	0.213593i	$-0.0685166\pi$
$373$	17.4695	+	15.1374i	0.904534	+	0.783784i	−0.0723883	+	0.997377i	$0.523062\pi$
$374$	1.87194	−	6.37523i	0.0967955	−	0.329655i
$375$	−6.28238	−	9.77558i	−0.324421	−	0.504809i
$376$	8.26970	−	3.77665i	0.426477	−	0.194766i
$377$	−9.14720	+	7.92609i	−0.471105	+	0.408214i
$378$	−4.85104	−	0.357487i	−0.249511	−	0.0183872i
$379$	−18.4717	−	2.65583i	−0.948826	−	0.136421i	−0.349510	−	0.936933i	$-0.613652\pi$
$379$	−18.4717	−	2.65583i	−0.948826	−	0.136421i	−0.599316	+	0.800512i	$0.704561\pi$
$380$	2.61665	−	18.1992i	0.134231	−	0.933599i
$381$	0.526509	−	0.819264i	0.0269739	−	0.0419722i
$382$	−25.4436	+	22.0470i	−1.30181	+	1.12802i
$383$	−9.89157	−	21.6595i	−0.505435	−	1.10675i	−0.974664	−	0.223673i	$-0.928195\pi$
$383$	−9.89157	−	21.6595i	−0.505435	−	1.10675i	0.469229	−	0.883077i	$-0.344532\pi$
$384$	−4.69277	−	7.30209i	−0.239477	−	0.372633i
$385$	30.9981	−	6.67313i	1.57981	−	0.340094i
$386$	24.2903	−	28.0325i	1.23634	−	1.42681i
$387$	−0.785153	−	2.67399i	−0.0399116	−	0.135926i
$388$	2.57478	−	5.63799i	0.130715	−	0.286226i
$389$	20.3739	−	2.92932i	1.03300	−	0.148523i	0.395095	−	0.918640i	$-0.370712\pi$
$389$	20.3739	−	2.92932i	1.03300	−	0.148523i	0.637902	+	0.770117i	$0.279802\pi$
$390$	20.1655			1.02112
$391$	3.08524	−	0.0998583i	0.156027	−	0.00505005i
$392$	4.34235	−	6.69307i	0.219322	−	0.338051i
$393$	2.09585	+	14.5770i	0.105722	+	0.735311i
$394$	−20.1139	+	44.0432i	−1.01332	+	2.21887i
$395$	−0.574723	−	1.95733i	−0.0289174	−	0.0984837i
$396$	−5.85620	−	5.07442i	−0.294285	−	0.254999i
$397$	7.34315	−	25.0085i	0.368542	−	1.25514i	−0.541527	−	0.840683i	$-0.682154\pi$
$397$	7.34315	−	25.0085i	0.368542	−	1.25514i	0.910069	−	0.414456i	$-0.136028\pi$
$398$	31.9479	−	20.5317i	1.60141	−	1.02916i
$399$	13.1990	+	9.92524i	0.660779	+	0.496884i
$400$	−1.41234	−	1.62993i	−0.0706170	−	0.0814963i
$401$	3.68479	−	5.73364i	0.184010	−	0.286325i	−0.736978	−	0.675917i	$-0.763748\pi$
$401$	3.68479	−	5.73364i	0.184010	−	0.286325i	0.920987	+	0.389592i	$0.127384\pi$
$402$	−0.219978	+	1.52998i	−0.0109715	+	0.0763086i
$403$	−2.37704	+	16.5327i	−0.118409	+	0.823552i
$404$	−7.21550	+	11.2275i	−0.358985	+	0.558591i
$405$	1.39776	+	1.61310i	0.0694553	+	0.0801556i
$406$	−6.88551	+	9.15667i	−0.341722	+	0.454438i
$407$	−31.0486	+	19.9537i	−1.53902	+	0.989068i
$408$	−0.206681	+	0.703891i	−0.0102322	+	0.0348478i
$409$	−2.47390	−	2.14364i	−0.122326	−	0.105996i	0.591549	−	0.806269i	$-0.298516\pi$
$409$	−2.47390	−	2.14364i	−0.122326	−	0.105996i	−0.713876	+	0.700272i	$0.753062\pi$
$410$	6.04093	+	20.5735i	0.298340	+	1.01605i
$411$	3.69003	−	8.08005i	0.182016	−	0.398559i
$412$	3.10965	+	21.6281i	0.153202	+	1.06554i
$413$	−0.194600	+	0.105715i	−0.00957565	+	0.00520188i
$414$	3.40139	−	8.13461i	0.167169	−	0.399794i
$415$	23.7164			1.16419
$416$	33.8121	−	4.86144i	1.65777	−	0.238352i
$417$	9.16455	−	20.0676i	0.448790	−	0.982713i
$418$	18.1532	+	61.8241i	0.887901	+	3.02391i
$419$	−0.200757	+	0.231686i	−0.00980762	+	0.0113186i	−0.760632	−	0.649183i	$-0.775111\pi$
$419$	−0.200757	+	0.231686i	−0.00980762	+	0.0113186i	0.750825	+	0.660502i	$0.229656\pi$
$420$	7.61892	−	1.64017i	0.371765	−	0.0800319i
$421$	16.6584	+	25.9210i	0.811880	+	1.26331i	0.961565	+	0.274576i	$0.0885376\pi$
$421$	16.6584	+	25.9210i	0.811880	+	1.26331i	−0.149685	+	0.988734i	$0.547826\pi$
$422$	−10.2421	−	22.4270i	−0.498576	−	1.09173i
$423$	−6.02824	+	5.22350i	−0.293103	+	0.253975i
$424$	−5.27962	+	8.21525i	−0.256401	+	0.398968i
$425$	−0.0406868	+	0.282983i	−0.00197360	+	0.0137267i
$426$	−2.98492	−	0.429167i	−0.144620	−	0.0207932i
$427$	1.30242	−	17.6737i	0.0630287	−	0.855288i
$428$	−14.3797	+	12.4601i	−0.695070	+	0.602282i
$429$	−26.2463	+	11.9863i	−1.26719	+	0.578704i
$430$	5.91251	+	9.20005i	0.285127	+	0.443666i
$431$	−7.33280	+	24.9732i	−0.353209	+	1.20292i	0.570974	+	0.820968i	$0.306566\pi$
$431$	−7.33280	+	24.9732i	−0.353209	+	1.20292i	−0.924183	+	0.381950i	$0.875253\pi$
$432$	3.66958	+	3.17971i	0.176553	+	0.152984i
$433$	−36.6632	+	10.7653i	−1.76192	+	0.517346i	−0.992591	−	0.121507i	$-0.961227\pi$
$433$	−36.6632	+	10.7653i	−1.76192	+	0.517346i	−0.769329	+	0.638853i	$0.779409\pi$
$434$	1.09381	+	15.7722i	0.0525047	+	0.757090i
$435$	4.97608	−	0.715452i	0.238585	−	0.0343033i
$436$			11.3519i			0.543656i
$437$	−24.6461	+	16.9902i	−1.17898	+	0.812752i
$438$	−18.1434			−0.866925
$439$	7.86800	−	1.13125i	0.375519	−	0.0539915i	0.0480285	−	0.998846i	$-0.484706\pi$
$439$	7.86800	−	1.13125i	0.375519	−	0.0539915i	0.327490	+	0.944854i	$0.393797\pi$
$440$	−12.4251	−	5.67437i	−0.592345	−	0.270515i
$441$	−2.00113	+	6.70787i	−0.0952917	+	0.319422i
$442$	−4.59574	−	3.98223i	−0.218597	−	0.189415i
$443$	−13.2322	−	3.88534i	−0.628683	−	0.184598i	−0.0481570	−	0.998840i	$-0.515335\pi$
$443$	−13.2322	−	3.88534i	−0.628683	−	0.184598i	−0.580526	+	0.814242i	$0.697153\pi$
$444$	−7.63132	+	4.90435i	−0.362166	+	0.232750i
$445$	4.90809	+	10.7472i	0.232666	+	0.509467i
$446$	29.7482	−	25.7769i	1.40862	−	1.22057i
$447$	16.0604	+	10.3214i	0.759629	+	0.488184i
$448$	6.22734	−	2.30737i	0.294214	−	0.109013i
$449$	0.515315	−	3.58409i	0.0243192	−	0.169144i	−0.974042	−	0.226366i	$-0.927315\pi$
$449$	0.515315	−	3.58409i	0.0243192	−	0.169144i	0.998361	+	0.0572225i	$0.0182245\pi$
$450$	0.686974	+	0.441491i	0.0323843	+	0.0208121i
$451$	−20.0914	−	23.1867i	−0.946065	−	1.09182i
$452$	5.65513	−	2.58261i	0.265995	−	0.121476i
$453$	−4.73309	−	7.36484i	−0.222380	−	0.346030i
$454$	14.9484	+	4.38926i	0.701565	+	0.205998i
$455$	6.22986	−	28.3433i	0.292061	−	1.32876i
$456$	−2.00430	−	6.82602i	−0.0938599	−	0.319658i
$457$	1.60325	+	0.732178i	0.0749967	+	0.0342499i	0.452560	−	0.891734i	$-0.350511\pi$
$457$	1.60325	+	0.732178i	0.0749967	+	0.0342499i	−0.377564	+	0.925984i	$0.623238\pi$
$458$	2.88280	+	20.0503i	0.134704	+	0.936890i
$459$		−	0.643653i		−	0.0300432i
$460$	−1.55706	+	14.0408i	−0.0725984	+	0.654655i
$461$		−	38.4017i		−	1.78854i	−0.447524	−	0.894272i	$-0.647694\pi$
$461$		−	38.4017i		−	1.78854i	0.447524	−	0.894272i	$-0.352306\pi$
$462$	−21.8996	+	16.3201i	−1.01886	+	0.759280i
$463$	15.0436	−	32.9408i	0.699133	−	1.53089i	−0.141886	−	0.989883i	$-0.545317\pi$
$463$	15.0436	−	32.9408i	0.699133	−	1.53089i	0.841019	−	0.541005i	$-0.181956\pi$
$464$	10.9730	−	3.22198i	0.509411	−	0.149577i
$465$	4.54314	−	5.24306i	0.210683	−	0.243141i
$466$	10.6212	+	3.11865i	0.492015	+	0.144469i
$467$	8.10357	−	5.20785i	0.374989	−	0.240991i	−0.339548	−	0.940589i	$-0.610274\pi$
$467$	8.10357	−	5.20785i	0.374989	−	0.240991i	0.714536	+	0.699598i	$0.246638\pi$
$468$	−6.45100	+	2.94607i	−0.298198	+	0.136182i
$469$	2.08249	+	0.781855i	0.0961602	+	0.0361027i
$470$	16.9226	−	26.3321i	0.780581	−	1.21461i
$471$	12.7486	+	1.83297i	0.587424	+	0.0844588i
$472$	0.0944314	+	0.0135772i	0.00434656	+	0.000624941i
$473$	−13.1639	−	8.45991i	−0.605276	−	0.388987i
$474$	1.15066	+	1.32794i	0.0528518	+	0.0609942i
$475$	−1.15172	−	2.52192i	−0.0528446	−	0.115713i
$476$	−2.06025	−	1.13077i	−0.0944316	−	0.0518287i
$477$	2.41390	−	8.22098i	0.110525	−	0.376413i
$478$	24.6800	−	28.4822i	1.12884	−	1.30275i
$479$	−8.84215	+	2.59629i	−0.404008	+	0.118627i	−0.477422	−	0.878674i	$-0.658429\pi$
$479$	−8.84215	+	2.59629i	−0.404008	+	0.118627i	0.0734141	+	0.997302i	$0.476611\pi$
$480$	−12.9063	−	5.89410i	−0.589088	−	0.269028i
$481$	4.80716	+	33.4345i	0.219188	+	1.52448i
$482$	26.3096			1.19837
$483$	−10.3827	−	7.29385i	−0.472428	−	0.331882i
$484$	−28.3282			−1.28764
$485$	1.36425	+	9.48858i	0.0619475	+	0.430854i
$486$	−1.67235	−	0.763738i	−0.0758595	−	0.0346439i
$487$	−7.09307	+	2.08271i	−0.321418	+	0.0943768i	−0.438461	−	0.898750i	$-0.644476\pi$
$487$	−7.09307	+	2.08271i	−0.321418	+	0.0943768i	0.117044	+	0.993127i	$0.462658\pi$
$488$	−4.99936	+	5.76957i	−0.226310	+	0.261176i
$489$	2.44298	−	8.32002i	0.110475	−	0.376244i
$490$	0.118671	−	27.4688i	0.00536102	−	1.24091i
$491$	3.85083	+	8.43213i	0.173785	+	0.380537i	0.976403	−	0.215957i	$-0.0692872\pi$
$491$	3.85083	+	8.43213i	0.173785	+	0.380537i	−0.802617	+	0.596494i	$0.796560\pi$
$492$	−4.93819	−	5.69897i	−0.222631	−	0.256930i
$493$	−1.27534	−	0.819610i	−0.0574384	−	0.0369134i
$494$	58.3709	+	8.39246i	2.62623	+	0.377595i
$495$	11.8626	+	1.70559i	0.533185	+	0.0766604i
$496$	8.53239	−	13.2767i	0.383116	−	0.596140i
$497$	−1.52536	+	4.06282i	−0.0684217	+	0.182243i
$498$	−18.5820	+	8.48611i	−0.832679	+	0.380272i
$499$	8.57098	−	5.50824i	0.383690	−	0.246583i	−0.334550	−	0.942378i	$-0.608584\pi$
$499$	8.57098	−	5.50824i	0.383690	−	0.246583i	0.718240	+	0.695795i	$0.244948\pi$
$500$	−15.3870	−	4.51804i	−0.688130	−	0.202053i
$501$	1.73209	−	1.99894i	0.0773840	−	0.0893059i
$502$	1.25881	−	0.369621i	0.0561836	−	0.0164970i
$503$	−16.9832	+	37.1881i	−0.757245	+	1.65813i	−0.00435321	+	0.999991i	$0.501386\pi$
$503$	−16.9832	+	37.1881i	−0.757245	+	1.65813i	−0.752892	+	0.658144i	$0.771342\pi$
$504$	2.41794	−	1.80191i	0.107704	−	0.0802634i
$505$		−	20.6416i		−	0.918540i
$506$	−15.4771	−	47.0255i	−0.688039	−	2.09054i
$507$			13.4075i			0.595447i
$508$	−0.191269	−	1.33031i	−0.00848620	−	0.0590228i
$509$	30.4940	+	13.9262i	1.35162	+	0.617266i	0.953868	−	0.300225i	$-0.0970617\pi$
$509$	30.4940	+	13.9262i	1.35162	+	0.617266i	0.397756	+	0.917491i	$0.369789\pi$
$510$	0.711598	+	2.42348i	0.0315101	+	0.107314i
$511$	−5.60516	+	25.5012i	−0.247958	+	1.12811i
$512$	−20.3494	−	5.97512i	−0.899325	−	0.264066i
$513$	3.37460	+	5.25098i	0.148992	+	0.231837i
$514$	13.7586	−	6.28334i	0.606866	−	0.277146i
$515$	−22.1308	−	25.5403i	−0.975198	−	1.12544i
$516$	−3.23551	−	2.07933i	−0.142435	−	0.0915376i
$517$	−6.37386	+	44.3311i	−0.280322	+	1.94968i
$518$	11.1088	+	29.9813i	0.488090	+	1.31730i
$519$	3.74780	+	2.40857i	0.164510	+	0.105724i
$520$	−9.44793	+	8.18668i	−0.414319	+	0.359010i
$521$	−5.31450	−	11.6371i	−0.232833	−	0.509832i	0.756766	−	0.653685i	$-0.226778\pi$
$521$	−5.31450	−	11.6371i	−0.232833	−	0.509832i	−0.989599	+	0.143853i	$0.954051\pi$
$522$	−3.64280	+	2.34109i	−0.159441	+	0.102467i
$523$	−2.27794	−	0.668863i	−0.0996072	−	0.0292473i	0.231549	−	0.972823i	$-0.425621\pi$
$523$	−2.27794	−	0.668863i	−0.0996072	−	0.0292473i	−0.331156	+	0.943576i	$0.607439\pi$
$524$	15.3598	+	13.3094i	0.670997	+	0.581423i
$525$	0.832763	−	0.829173i	0.0363447	−	0.0361881i
$526$	−45.7736	−	20.9041i	−1.99582	−	0.911462i
$527$	−2.07077	+	0.297732i	−0.0902042	+	0.0129694i
$528$	27.2633			1.18648
$529$	18.5042	−	13.6599i	0.804532	−	0.593909i
$530$			33.6223i			1.46046i
$531$	−0.0828523	+	0.0119124i	−0.00359548	+	0.000516952i
$532$	22.7363	−	1.57677i	0.985741	−	0.0683618i
$533$	−26.9418	+	7.91081i	−1.16698	+	0.342655i
$534$	−7.69108	−	6.66435i	−0.332825	−	0.288395i
$535$	8.29078	−	28.2358i	0.358442	−	1.22074i
$536$	−0.518070	−	0.806133i	−0.0223772	−	0.0348196i
$537$	−8.86707	+	4.04945i	−0.382642	+	0.174747i
$538$	−3.92402	+	3.40018i	−0.169177	+	0.146592i
$539$	16.1729	+	35.8225i	0.696616	+	1.54298i
$540$	2.91567	+	0.419210i	0.125470	+	0.0180399i
$541$	−1.93069	+	13.4282i	−0.0830067	+	0.577324i	0.905292	+	0.424791i	$0.139652\pi$
$541$	−1.93069	+	13.4282i	−0.0830067	+	0.577324i	−0.988298	+	0.152534i	$0.951257\pi$
$542$	−29.0020	+	45.1280i	−1.24574	+	1.93841i
$543$	15.6838	−	13.5901i	0.673058	−	0.583208i
$544$	1.77740	+	3.89197i	0.0762055	+	0.166867i
$545$	−9.49210	−	14.7700i	−0.406597	−	0.632677i
$546$	5.26056	+	24.4364i	0.225131	+	1.04578i
$547$	−23.3464	+	26.9431i	−0.998218	+	1.15200i	−0.00984567	+	0.999952i	$0.503134\pi$
$547$	−23.3464	+	26.9431i	−0.998218	+	1.15200i	−0.988372	+	0.152053i	$0.951411\pi$
$548$	−3.45369	−	11.7622i	−0.147534	−	0.502455i
$549$	2.78250	−	6.09283i	0.118754	−	0.260036i
$550$	4.53848	−	0.652534i	0.193521	−	0.0278242i
$551$	14.7015			0.626303
$552$	1.70883	+	5.19210i	0.0727326	+	0.220990i
$553$	2.22194	−	1.20705i	0.0944867	−	0.0513290i
$554$	5.45178	+	37.9180i	0.231624	+	1.61098i
$555$	5.82828	−	12.7622i	0.247397	−	0.541724i
$556$	−8.57756	−	29.2125i	−0.363770	−	1.23889i
$557$	8.97502	+	7.77690i	0.380284	+	0.329518i	0.823938	−	0.566681i	$-0.191773\pi$
$557$	8.97502	+	7.77690i	0.380284	+	0.329518i	−0.443654	+	0.896198i	$0.646318\pi$
$558$	−1.68354	+	5.73360i	−0.0712698	+	0.242723i
$559$	−12.0478	+	7.74265i	−0.509568	+	0.327479i
$560$	−16.4797	+	21.9155i	−0.696395	+	0.926099i
$561$	−2.36669	−	2.73130i	−0.0999215	−	0.115316i
$562$	−30.0892	+	46.8196i	−1.26923	+	1.97497i
$563$	0.518811	−	3.60841i	0.0218653	−	0.152076i	−0.975964	−	0.217932i	$-0.930069\pi$
$563$	0.518811	−	3.60841i	0.0218653	−	0.152076i	0.997829	+	0.0658562i	$0.0209779\pi$
$564$	−1.56661	+	10.8960i	−0.0659661	+	0.458804i
$565$	−5.19842	+	8.08890i	−0.218699	+	0.340303i
$566$	−23.0701	−	26.6243i	−0.969708	−	1.11910i
$567$	−1.59011	+	2.11460i	−0.0667784	+	0.0888050i
$568$	1.57272	−	1.01073i	0.0659900	−	0.0424092i
$569$	−2.51269	+	8.55745i	−0.105338	+	0.358747i	−0.995246	−	0.0973922i	$-0.968950\pi$
$569$	−2.51269	+	8.55745i	−0.105338	+	0.358747i	0.889909	+	0.456139i	$0.150768\pi$
$570$	−18.5113	−	16.0402i	−0.775354	−	0.671848i
$571$	10.5007	+	35.7622i	0.439441	+	1.49660i	0.820282	+	0.571959i	$0.193817\pi$
$571$	10.5007	+	35.7622i	0.439441	+	1.49660i	−0.380841	+	0.924641i	$0.624365\pi$
$572$	−16.5418	+	36.2215i	−0.691648	+	1.51450i
$573$	2.60609	+	18.1257i	0.108871	+	0.757213i
$574$	−23.3549	+	12.6873i	−0.974816	+	0.529560i
$575$	0.947126	+	1.90803i	0.0394979	+	0.0795705i
$576$	2.51009			0.104587
$577$	18.5891	−	2.67271i	0.773876	−	0.111267i	0.255948	−	0.966691i	$-0.417613\pi$
$577$	18.5891	−	2.67271i	0.773876	−	0.111267i	0.517928	+	0.855424i	$0.326703\pi$
$578$	−12.6671	+	27.7372i	−0.526883	+	1.15371i
$579$	−5.68405	−	19.3581i	−0.236221	−	0.804495i
$580$	4.54336	−	5.24332i	0.188653	−	0.217717i
$581$	6.18687	+	28.7393i	0.256675	+	1.19231i
$582$	−4.46408	−	6.94624i	−0.185042	−	0.287931i
$583$	−19.9850	−	43.7610i	−0.827693	−	1.81240i
$584$	8.50054	−	7.36576i	0.351755	−	0.304797i
$585$	5.93002	−	9.22729i	0.245176	−	0.381501i
$586$	4.44764	−	30.9340i	0.183730	−	1.27787i
$587$	35.5200	+	5.10700i	1.46607	+	0.210788i	0.828665	−	0.559744i	$-0.189101\pi$
$587$	35.5200	+	5.10700i	1.46607	+	0.210788i	0.637400	+	0.770533i	$0.280010\pi$
$588$	3.97508	+	8.80468i	0.163930	+	0.363099i
$589$	15.3326	−	13.2857i	0.631767	−	0.547430i
$590$	0.298785	−	0.136451i	0.0123008	−	0.00561759i
$591$	14.2384	+	22.1553i	0.585688	+	0.911348i
$592$	8.99188	−	30.6235i	0.369564	−	1.25862i
$593$	−20.8106	−	18.0325i	−0.854589	−	0.740505i	0.112850	−	0.993612i	$-0.464002\pi$
$593$	−20.8106	−	18.0325i	−0.854589	−	0.740505i	−0.967438	+	0.253107i	$0.918548\pi$
$594$	−9.90475	+	2.90830i	−0.406397	+	0.119329i
$595$	3.62612	−	0.251474i	0.148657	−	0.0103094i
$596$	26.0785	−	3.74953i	1.06822	−	0.153587i
$597$		−	20.6564i		−	0.845408i
$598$	−45.0335	−	4.99402i	−1.84156	−	0.204221i
$599$	−25.6471			−1.04791			−0.523955	−	0.851746i	$-0.675544\pi$
$599$	−25.6471			−1.04791			−0.523955	+	0.851746i	$0.675544\pi$
$600$	−0.501095	+	0.0720466i	−0.0204571	+	0.00294129i
$601$	−30.4264	−	13.8953i	−1.24112	−	0.566801i	−0.316827	−	0.948483i	$-0.602617\pi$
$601$	−30.4264	−	13.8953i	−1.24112	−	0.566801i	−0.924293	+	0.381683i	$0.875345\pi$
$602$	−9.60616	+	9.56475i	−0.391518	+	0.389830i
$603$	0.635398	+	0.550575i	0.0258754	+	0.0224212i
$604$	−11.5925	−	3.40386i	−0.471691	−	0.138501i
$605$	36.8579	−	23.6872i	1.49849	−	0.963020i
$606$	7.38592	+	16.1729i	0.300032	+	0.656979i
$607$	−14.2847	+	12.3777i	−0.579797	+	0.502397i	−0.894664	−	0.446739i	$-0.852585\pi$
$607$	−14.2847	+	12.3777i	−0.579797	+	0.502397i	0.314868	+	0.949136i	$0.398040\pi$
$608$	−34.9054	−	22.4323i	−1.41560	−	0.909750i
$609$	2.16508	+	5.84333i	0.0877337	+	0.236784i
$610$	−3.74067	+	26.0169i	−0.151455	+	1.05339i
$611$	34.4828	+	22.1608i	1.39503	+	0.896528i
$612$	−0.581700	−	0.671317i	−0.0235138	−	0.0271364i
$613$	7.11048	−	3.24725i	0.287190	−	0.131155i	−0.266611	−	0.963804i	$-0.585904\pi$
$613$	7.11048	−	3.24725i	0.287190	−	0.131155i	0.553801	+	0.832649i	$0.313177\pi$
$614$	−13.3047	−	20.7024i	−0.536932	−	0.835483i
$615$	11.1904	+	3.28580i	0.451241	+	0.132496i
$616$	3.63482	−	16.5369i	0.146451	−	0.666293i
$617$	2.70296	+	9.20544i	0.108817	+	0.370597i	0.995839	−	0.0911304i	$-0.0290480\pi$
$617$	2.70296	+	9.20544i	0.108817	+	0.370597i	−0.887022	+	0.461727i	$0.847230\pi$
$618$	26.4784	+	12.0923i	1.06512	+	0.486423i
$619$	−4.09203	−	28.4607i	−0.164472	−	1.14393i	−0.890074	−	0.455816i	$-0.849348\pi$
$619$	−4.09203	−	28.4607i	−0.164472	−	1.14393i	0.725602	−	0.688115i	$-0.241561\pi$
$620$		−	9.57425i		−	0.384511i
$621$	−2.72198	−	3.94852i	−0.109229	−	0.158449i
$622$		−	18.8815i		−	0.757078i
$623$	−11.7430	+	8.75121i	−0.470475	+	0.350610i
$624$	10.3654	−	22.6970i	0.414947	−	0.908606i
$625$	21.6671	−	6.36204i	0.866685	−	0.254482i
$626$	10.2673	−	11.8491i	0.410364	−	0.473585i
$627$	33.6276	+	9.87394i	1.34296	+	0.394327i
$628$	14.9531	−	9.60975i	0.596692	−	0.383471i
$629$	−3.84851	+	1.75755i	−0.153450	+	0.0700783i
$630$	3.64926	−	9.71986i	0.145390	−	0.387249i
$631$	−9.98834	+	15.5422i	−0.397630	+	0.618724i	−0.981121	−	0.193396i	$-0.938050\pi$
$631$	−9.98834	+	15.5422i	−0.397630	+	0.618724i	0.583491	+	0.812119i	$0.301686\pi$
$632$	−1.07822	−	0.155024i	−0.0428892	−	0.00616653i
$633$	−13.2740	−	1.90851i	−0.527592	−	0.0758563i
$634$	−31.0341	−	19.9444i	−1.23252	−	0.792094i
$635$	1.36122	+	1.57094i	0.0540185	+	0.0623407i
$636$	−4.91204	−	10.7559i	−0.194775	−	0.426498i
$637$	35.9714	+	0.155404i	1.42524	+	0.00615734i
$638$	−6.84992	+	23.3287i	−0.271191	+	0.923592i
$639$	−1.07414	+	1.23963i	−0.0424925	+	0.0490389i
$640$	17.7765	−	5.21964i	0.702677	−	0.206325i
$641$	−34.8666	−	15.9231i	−1.37715	−	0.628923i	−0.417127	−	0.908848i	$-0.636963\pi$
$641$	−34.8666	−	15.9231i	−1.37715	−	0.628923i	−0.960022	+	0.279925i	$0.909690\pi$
$642$	3.60734	+	25.0896i	0.142370	+	0.990208i
$643$	33.3852			1.31658			0.658292	−	0.752763i	$-0.271279\pi$
$643$	33.3852			1.31658			0.658292	+	0.752763i	$0.271279\pi$
$644$	−17.4207	+	1.77597i	−0.686472	+	0.0699830i
$645$	5.94841			0.234219
$646$	1.05118	+	7.31113i	0.0413582	+	0.287653i
$647$	−38.2391	−	17.4632i	−1.50333	−	0.686549i	−0.517717	−	0.855552i	$-0.673218\pi$
$647$	−38.2391	−	17.4632i	−1.50333	−	0.686549i	−0.985616	+	0.169002i	$0.945945\pi$
$648$	1.09359	−	0.321106i	0.0429602	−	0.0126142i
$649$	−0.307777	+	0.355194i	−0.0120813	+	0.0139426i
$650$	1.18226	−	4.02642i	0.0463721	−	0.157929i
$651$	7.53866	+	4.13759i	0.295464	+	0.162165i
$652$	−4.97121	−	10.8854i	−0.194688	−	0.426307i
$653$	−13.2235	−	15.2607i	−0.517474	−	0.597197i	0.435522	−	0.900178i	$-0.356564\pi$
$653$	−13.2235	−	15.2607i	−0.517474	−	0.597197i	−0.952997	+	0.302981i	$0.902018\pi$
$654$	12.7221	+	8.17600i	0.497473	+	0.319707i
$655$	−31.1137	−	4.47347i	−1.21571	−	0.174793i
$656$	26.2613	+	3.77581i	1.02533	+	0.147420i
$657$	−5.33538	+	8.30202i	−0.208153	+	0.323892i
$658$	36.3236	+	13.6374i	1.41604	+	0.531643i
$659$	5.45241	−	2.49003i	0.212396	−	0.0969979i	−0.306376	−	0.951910i	$-0.599117\pi$
$659$	5.45241	−	2.49003i	0.212396	−	0.0969979i	0.518772	+	0.854913i	$0.326389\pi$
$660$	13.9139	−	8.94191i	0.541597	−	0.348063i
$661$	−18.8643	−	5.53905i	−0.733735	−	0.215444i	−0.106542	−	0.994308i	$-0.533978\pi$
$661$	−18.8643	−	5.53905i	−0.733735	−	0.215444i	−0.627193	+	0.778864i	$0.715796\pi$
$662$	−10.9076	+	12.5880i	−0.423936	+	0.489248i
$663$	−3.17364	+	0.931863i	−0.123254	+	0.0361906i
$664$	5.26088	−	11.5197i	0.204162	−	0.447052i
$665$	−28.2638	+	21.0629i	−1.09602	+	0.816785i
$666$			12.0847i			0.468274i
$667$	−11.2897	+	0.365409i	−0.437140	+	0.0141487i
$668$		−	3.65022i		−	0.141231i
$669$	−3.04698	−	21.1922i	−0.117803	−	0.819339i
$670$	−3.00109	−	1.37055i	−0.115942	−	0.0529491i
$671$	−10.5957	−	36.0857i	−0.409043	−	1.39307i
$672$	3.77557	−	17.1773i	0.145646	−	0.662629i
$673$	8.78422	+	2.57928i	0.338607	+	0.0994240i	0.446615	−	0.894726i	$-0.352629\pi$
$673$	8.78422	+	2.57928i	0.338607	+	0.0994240i	−0.108009	+	0.994150i	$0.534447\pi$
$674$	−27.6389	−	43.0070i	−1.06461	−	1.65657i
$675$	0.404033	−	0.184516i	0.0155512	−	0.00710201i
$676$	12.1170	+	13.9837i	0.466037	+	0.537835i
$677$	−27.1700	−	17.4611i	−1.04423	−	0.671086i	−0.0982004	−	0.995167i	$-0.531309\pi$
$677$	−27.1700	−	17.4611i	−1.04423	−	0.671086i	−0.946029	+	0.324081i	$0.894945\pi$
$678$	1.17867	−	8.19781i	0.0452665	−	0.314835i
$679$	−11.1423	+	4.12847i	−0.427602	+	0.158436i
$680$	−1.31727	−	0.846557i	−0.0505149	−	0.0324640i
$681$	6.40427	−	5.54933i	0.245412	−	0.212651i
$682$	13.9382	+	30.5204i	0.533722	+	1.16869i
$683$	−11.4207	+	7.33962i	−0.437000	+	0.280843i	−0.740587	−	0.671961i	$-0.765452\pi$
$683$	−11.4207	+	7.33962i	−0.437000	+	0.280843i	0.303586	+	0.952804i	$0.401816\pi$
$684$	8.26520	+	2.42688i	0.316028	+	0.0927942i
$685$	14.3288	+	12.4160i	0.547475	+	0.474390i
$686$	33.3175	−	7.02196i	1.27207	−	0.268100i
$687$	10.0223	+	4.57704i	0.382375	+	0.174625i
$688$	13.3941	−	1.92578i	0.510645	−	0.0734196i
$689$	−44.0296			−1.67740
$690$	14.6141	+	11.8576i	0.556350	+	0.451413i
$691$			26.0617i			0.991433i	0.868484	+	0.495716i	$0.165094\pi$
$691$			26.0617i			0.991433i	−0.868484	+	0.495716i	$0.834906\pi$
$692$	6.08562	−	0.874979i	0.231340	−	0.0332617i
$693$	1.02777	+	14.8200i	0.0390419	+	0.562964i
$694$	31.7590	−	9.32527i	1.20555	−	0.353983i
$695$	35.5869	+	30.8362i	1.34989	+	1.16969i
$696$	0.756303	−	2.57573i	0.0286676	−	0.0976328i
$697$	−1.90143	−	2.95869i	−0.0720220	−	0.112068i
$698$	−45.1361	+	20.6130i	−1.70843	+	0.780212i
$699$	4.55036	−	3.94291i	0.172110	−	0.149134i
$700$	0.119192	−	1.61742i	0.00450504	−	0.0611326i
$701$	30.3527	+	4.36406i	1.14640	+	0.164828i	0.689226	−	0.724547i	$-0.257951\pi$
$701$	30.3527	+	4.36406i	1.14640	+	0.164828i	0.457179	+	0.889375i	$0.348860\pi$
$702$	−1.34455	+	9.35153i	−0.0507466	+	0.352951i
$703$	22.1818	−	34.5156i	0.836604	−	1.30178i
$704$	10.6514	−	9.22949i	0.401440	−	0.347849i
$705$	−7.07259	−	15.4868i	−0.266369	−	0.583267i
$706$	−27.6450	−	43.0165i	−1.04043	−	1.61895i
$707$	25.0133	−	5.38476i	0.940724	−	0.202515i
$708$	−0.0756475	+	0.0873019i	−0.00284301	+	0.00328101i
$709$	−9.23064	−	31.4367i	−0.346664	−	1.18063i	−0.929742	−	0.368213i	$-0.879970\pi$
$709$	−9.23064	−	31.4367i	−0.346664	−	1.18063i	0.583077	−	0.812417i	$-0.301848\pi$
$710$	2.67388	−	5.85498i	0.100349	−	0.219733i
$711$	0.946007	−	0.136015i	0.0354780	−	0.00510097i
$712$	6.30898			0.236439
$713$	−11.4441	+	10.5836i	−0.428587	+	0.396361i
$714$	−2.75112	+	1.49452i	−0.102958	+	0.0559310i
$715$	−8.76470	−	60.9598i	−0.327781	−	2.27977i
$716$	−5.58849	+	12.2371i	−0.208852	+	0.457321i
$717$	−5.77524	−	19.6687i	−0.215680	−	0.734540i
$718$	3.15563	+	2.73437i	0.117767	+	0.102046i
$719$	−2.83374	+	9.65084i	−0.105681	+	0.359916i	−0.995306	−	0.0967751i	$-0.969147\pi$
$719$	−2.83374	+	9.65084i	−0.105681	+	0.359916i	0.889626	+	0.456691i	$0.150965\pi$
$720$	−8.71865	+	5.60314i	−0.324925	+	0.208817i
$721$	25.1763	−	33.4805i	0.937613	−	1.24688i
$722$	−24.0319	−	27.7343i	−0.894375	−	1.03216i
$723$	7.73680	−	12.0387i	0.287735	−	0.447724i
$724$	4.07589	−	28.3484i	0.151479	−	1.05356i
$725$	0.148884	−	1.03551i	0.00552941	−	0.0384579i
$726$	−20.4029	+	31.7475i	−0.757222	+	1.17826i
$727$	−14.4772	−	16.7075i	−0.536928	−	0.619648i	0.420859	−	0.907126i	$-0.361729\pi$
$727$	−14.4772	−	16.7075i	−0.536928	−	0.619648i	−0.957787	+	0.287478i	$0.907183\pi$
$728$	−12.3852	−	9.31328i	−0.459027	−	0.345173i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	10.9104	−	37.1573i	0.403811	−	1.37525i
$731$	−1.35565	−	1.17468i	−0.0501405	−	0.0434470i
$732$	−2.60428	−	8.86938i	−0.0962571	−	0.327822i
$733$	19.1486	−	41.9297i	0.707271	−	1.54871i	−0.123655	−	0.992325i	$-0.539462\pi$
$733$	19.1486	−	41.9297i	0.707271	−	1.54871i	0.830926	−	0.556383i	$-0.187811\pi$
$734$	2.07135	+	14.4066i	0.0764551	+	0.531757i
$735$	−12.5342	−	8.13198i	−0.462331	−	0.299953i
$736$	27.3625	+	16.3589i	1.00860	+	0.602997i
$737$	4.72071			0.173890
$738$	−9.94351	+	1.42966i	−0.366026	+	0.0526266i
$739$	−3.48450	+	7.63000i	−0.128180	+	0.280674i	−0.962831	−	0.270104i	$-0.912942\pi$
$739$	−3.48450	+	7.63000i	−0.128180	+	0.280674i	0.834651	+	0.550778i	$0.185669\pi$
$740$	−5.45498	−	18.5780i	−0.200529	−	0.682940i
$741$	21.0052	−	24.2413i	0.771644	−	0.890525i
$742$	−40.7433	+	8.77102i	−1.49573	+	0.321994i
$743$	−2.91544	−	4.53651i	−0.106957	−	0.166428i	0.783649	−	0.621203i	$-0.213356\pi$
$743$	−2.91544	−	4.53651i	−0.106957	−	0.166428i	−0.890606	+	0.454775i	$0.849720\pi$
$744$	−1.53892	−	3.36977i	−0.0564197	−	0.123542i
$745$	−30.7957	+	26.6846i	−1.12827	+	0.977649i
$746$	22.9759	−	35.7512i	0.841208	−	1.30894i
$747$	−1.58130	+	10.9982i	−0.0578568	+	0.402403i
$748$	−4.93681	−	0.709806i	−0.180508	−	0.0259531i
$749$	36.3788	+	2.68086i	1.32925	+	0.0979563i
$750$	−16.1457	+	13.9903i	−0.589556	+	0.510853i
$751$	−18.7006	+	8.54029i	−0.682396	+	0.311640i	−0.726282	−	0.687397i	$-0.758753\pi$
$751$	−18.7006	+	8.54029i	−0.682396	+	0.311640i	0.0438862	+	0.999037i	$0.486026\pi$
$752$	−20.9392	−	32.5820i	−0.763574	−	1.18814i
$753$	0.201045	−	0.684698i	0.00732650	−	0.0249518i
$754$	16.8171	+	14.5721i	0.612441	+	0.530684i
$755$	17.9292	−	5.26450i	0.652512	−	0.191595i
$756$	0.252613	+	3.64255i	0.00918744	+	0.132478i
$757$	−48.0312	+	6.90584i	−1.74572	+	0.250997i	−0.939970	−	0.341256i	$-0.889148\pi$
$757$	−48.0312	+	6.90584i	−1.74572	+	0.250997i	−0.805752	+	0.592253i	$0.798239\pi$
$758$			34.3093i			1.24617i
$759$	−26.0691	−	6.74669i	−0.946248	−	0.244889i
$760$	15.1848			0.550811
$761$	−34.7064	+	4.99002i	−1.25810	+	0.180888i	−0.738931	−	0.673781i	$-0.764669\pi$
$761$	−34.7064	+	4.99002i	−1.25810	+	0.180888i	−0.519173	+	0.854669i	$0.673760\pi$
$762$	−1.62864	−	0.743775i	−0.0589994	−	0.0269441i
$763$	15.4220	−	15.3555i	0.558313	−	0.555906i
$764$	19.0992	+	16.5495i	0.690984	+	0.598741i
$765$	1.31819	+	0.387055i	0.0476592	+	0.0139940i
$766$	−36.8275	+	23.6676i	−1.33063	+	0.855145i
$767$	0.178687	+	0.391270i	0.00645202	+	0.0141279i
$768$	−15.8544	+	13.7379i	−0.572095	+	0.495723i
$769$	17.8264	+	11.4563i	0.642836	+	0.413126i	0.821042	−	0.570868i	$-0.193393\pi$
$769$	17.8264	+	11.4563i	0.642836	+	0.413126i	−0.178206	+	0.983993i	$0.557029\pi$
$770$	−20.2541	−	54.6638i	−0.729908	−	1.96995i
$771$	1.17084	−	8.14335i	0.0421667	−	0.293276i
$772$	−23.4232	−	15.0532i	−0.843019	−	0.541775i
$773$	−10.0365	−	11.5828i	−0.360989	−	0.416603i	0.545982	−	0.837797i	$-0.316157\pi$
$773$	−10.0365	−	11.5828i	−0.360989	−	0.416603i	−0.906971	+	0.421194i	$0.861611\pi$
$774$	−4.66064	+	2.12844i	−0.167523	+	0.0765053i
$775$	−0.780519	−	1.21451i	−0.0280371	−	0.0436265i
$776$	4.91150	+	1.44215i	0.176313	+	0.0517701i
$777$	16.9855	+	3.73342i	0.609352	+	0.133936i
$778$	−10.6615	−	36.3096i	−0.382232	−	1.30176i
$779$	31.0242	+	14.1683i	1.11156	+	0.507631i
$780$	−2.15425	−	14.9831i	−0.0771344	−	0.536481i
$781$			9.20987i			0.329555i
$782$	−0.988957	−	5.58833i	−0.0353650	−	0.199838i
$783$			2.35530i			0.0841716i
$784$	−30.8561	−	14.2529i	−1.10200	−	0.509033i
$785$	−11.4201	+	25.0066i	−0.407602	+	0.892524i
$786$	25.9785	−	7.62799i	0.926624	−	0.272081i
$787$	7.01944	−	8.10087i	0.250216	−	0.288765i	−0.616722	−	0.787181i	$-0.711540\pi$
$787$	7.01944	−	8.10087i	0.250216	−	0.288765i	0.866938	+	0.498417i	$0.166085\pi$
$788$	34.8731	+	10.2397i	1.24230	+	0.364773i
$789$	−23.0258	+	14.7978i	−0.819739	+	0.526814i
$790$	−3.41153	+	1.55799i	−0.121377	+	0.0554309i
$791$	−11.1582	−	4.18926i	−0.396739	−	0.148953i
$792$	3.45988	−	5.38367i	0.122941	−	0.191300i
$793$	−34.0701	−	4.89854i	−1.20987	−	0.173952i
$794$	−47.4312	−	6.81958i	−1.68327	−	0.242018i
$795$	15.3848	+	9.88722i	0.545643	+	0.350664i
$796$	−18.6681	−	21.5442i	−0.661674	−	0.763613i
$797$	12.8046	+	28.0381i	0.453561	+	0.993160i	0.988908	+	0.148528i	$0.0474534\pi$
$797$	12.8046	+	28.0381i	0.453561	+	0.993160i	−0.535347	+	0.844632i	$0.679819\pi$
$798$	14.6083	−	26.6163i	0.517128	−	0.942206i
$799$	−1.44644	+	4.92613i	−0.0511715	+	0.174274i
$800$	−1.93353	+	2.23142i	−0.0683607	+	0.0788925i
$801$	−5.31115	+	1.55949i	−0.187660	+	0.0551020i
$802$	−11.3981	−	5.20533i	−0.402480	−	0.183807i
$803$	7.88581	+	54.8470i	0.278284	+	1.93551i
$804$	1.16029			0.0409202
$805$	21.1812	−	16.8774i	0.746538	−	0.594850i
$806$	30.7078			1.08164
$807$	0.401922	+	2.79543i	0.0141483	+	0.0984037i
$808$	−10.0262	−	4.57882i	−0.352721	−	0.161082i
$809$	−7.82715	+	2.29826i	−0.275188	+	0.0808025i	−0.416415	−	0.909175i	$-0.636714\pi$
$809$	−7.82715	+	2.29826i	−0.275188	+	0.0808025i	0.141227	+	0.989977i	$0.454895\pi$
$810$	2.56977	−	2.96568i	0.0902926	−	0.104203i
$811$	4.35065	−	14.8170i	0.152772	−	0.520294i	−0.847167	−	0.531327i	$-0.821694\pi$
$811$	4.35065	−	14.8170i	0.152772	−	0.520294i	0.999939	+	0.0110327i	$0.00351189\pi$
$812$	7.53904	+	4.13779i	0.264568	+	0.145208i
$813$	12.1210	+	26.5413i	0.425103	+	0.930846i
$814$	44.4351	+	51.2808i	1.55745	+	1.79739i
$815$	15.5702	+	10.0063i	0.545399	+	0.350506i
$816$	3.09348	+	0.444775i	0.108294	+	0.0155703i
$817$	17.2182	+	2.47560i	0.602389	+	0.0866105i
$818$	−3.25368	+	5.06282i	−0.113762	+	0.177018i
$819$	12.7285	+	4.77883i	0.444770	+	0.166986i
$820$	14.6409	−	6.68628i	0.511283	−	0.233495i
$821$	−3.30484	+	2.12389i	−0.115340	+	0.0741244i	−0.597039	−	0.802212i	$-0.703656\pi$
$821$	−3.30484	+	2.12389i	−0.115340	+	0.0741244i	0.481699	+	0.876337i	$0.340020\pi$
$822$	−15.6694	−	4.60095i	−0.546533	−	0.160476i
$823$	18.1982	−	21.0019i	0.634351	−	0.732080i	−0.344015	−	0.938964i	$-0.611787\pi$
$823$	18.1982	−	21.0019i	0.634351	−	0.732080i	0.978365	+	0.206885i	$0.0663325\pi$
$824$	−17.3148	+	5.08408i	−0.603189	+	0.177112i
$825$	1.03603	−	2.26859i	0.0360700	−	0.0789823i
$826$	0.243294	+	0.326470i	0.00846527	+	0.0113593i
$827$			22.4121i			0.779344i	0.920954	+	0.389672i	$0.127412\pi$
$827$			22.4121i			0.779344i	−0.920954	+	0.389672i	$0.872588\pi$
$828$	−6.40744	−	1.65825i	−0.222674	−	0.0576281i
$829$			3.50587i			0.121764i	0.998145	+	0.0608820i	$0.0193913\pi$
$829$			3.50587i			0.121764i	−0.998145	+	0.0608820i	$0.980609\pi$
$830$	−6.20527	−	43.1586i	−0.215388	−	1.49806i
$831$	18.9536	+	8.65582i	0.657493	+	0.300267i
$832$	−3.63404	−	12.3764i	−0.125988	−	0.429074i
$833$	1.25068	+	4.32851i	0.0433334	+	0.149974i
$834$	−38.9164	−	11.4269i	−1.34757	−	0.395681i
$835$	3.05220	+	4.74932i	0.105626	+	0.164357i
$836$	43.9964	−	20.0925i	1.52165	−	0.694913i
$837$	2.12849	+	2.45641i	0.0735715	+	0.0849060i
$838$	0.474145	+	0.304714i	0.0163791	+	0.0105262i
$839$	−4.82213	+	33.5386i	−0.166478	+	1.15788i	0.719614	+	0.694374i	$0.244319\pi$
$839$	−4.82213	+	33.5386i	−0.166478	+	1.15788i	−0.886093	+	0.463508i	$0.846590\pi$
$840$	2.23627	+	6.03545i	0.0771586	+	0.208243i
$841$	−19.7295	−	12.6794i	−0.680329	−	0.437221i
$842$	42.8119	−	37.0967i	1.47539	−	1.27844i
$843$	12.5754	+	27.5362i	0.433119	+	0.948399i
$844$	−15.5693	+	10.0058i	−0.535916	+	0.344413i
$845$	−27.4582	−	8.06246i	−0.944591	−	0.277357i
$846$	11.0829	+	9.60337i	0.381037	+	0.330171i
$847$	38.3190	+	38.4849i	1.31666	+	1.32236i
$848$	37.8431	+	17.2823i	1.29954	+	0.593478i
$849$	−18.9668	+	2.72702i	−0.650940	+	0.0935911i
$850$	0.525612			0.0180283
$851$	−16.1762	+	27.0570i	−0.554515	+	0.927501i
$852$			2.26366i			0.0775518i
$853$	47.8989	−	6.88683i	1.64003	−	0.235801i	0.740308	−	0.672267i	$-0.234679\pi$
$853$	47.8989	−	6.88683i	1.64003	−	0.235801i	0.899720	+	0.436467i	$0.143770\pi$
$854$	−32.5030	+	2.25410i	−1.11223	+	0.0771337i
$855$	−12.7832	+	3.75348i	−0.437176	+	0.128366i
$856$	−11.8758	−	10.2905i	−0.405908	−	0.351721i
$857$	15.8569	−	54.0035i	0.541660	−	1.84472i	0.00649045	−	0.999979i	$-0.497934\pi$
$857$	15.8569	−	54.0035i	0.541660	−	1.84472i	0.535169	−	0.844745i	$-0.320248\pi$
$858$	28.6797	+	44.6264i	0.979108	+	1.52352i
$859$	−16.7239	+	7.63757i	−0.570614	+	0.260591i	−0.679759	−	0.733435i	$-0.737916\pi$
$859$	−16.7239	+	7.63757i	−0.570614	+	0.260591i	0.109146	+	0.994026i	$0.465189\pi$
$860$	6.20407	−	5.37586i	0.211557	−	0.183315i
$861$	−1.06248	+	14.4176i	−0.0362091	+	0.491351i
$862$	47.3644	+	6.80997i	1.61324	+	0.231949i
$863$	−7.41921	+	51.6017i	−0.252553	+	1.75654i	0.330216	+	0.943905i	$0.392878\pi$
$863$	−7.41921	+	51.6017i	−0.252553	+	1.75654i	−0.582769	+	0.812638i	$0.698031\pi$
$864$	3.59385	−	5.59214i	0.122265	−	0.190249i
$865$	−7.18640	+	6.22705i	−0.244345	+	0.211726i
$866$	29.1832	+	63.9022i	0.991685	+	2.17149i
$867$	8.96691	+	13.9528i	0.304532	+	0.473862i
$868$	11.6020	−	2.49763i	0.393798	−	0.0847750i
$869$	3.51420	−	4.05560i	0.119211	−	0.137577i
$870$	−2.60393	−	8.86818i	−0.0882816	−	0.300659i
$871$	1.79479	−	3.93004i	0.0608141	−	0.133164i
$872$	−9.27979	+	1.33423i	−0.314253	+	0.0451828i
$873$	−4.49118			−0.152004
$874$	37.3670	+	40.4051i	1.26396	+	1.36672i
$875$	14.6759	+	27.0154i	0.496134	+	0.913287i
$876$	1.93823	+	13.4807i	0.0654866	+	0.455470i
$877$	6.17680	−	13.5253i	0.208576	−	0.456717i	−0.776213	−	0.630470i	$-0.782862\pi$
$877$	6.17680	−	13.5253i	0.208576	−	0.456717i	0.984789	+	0.173753i	$0.0555894\pi$
$878$	−4.11724	−	14.0220i	−0.138950	−	0.473221i
$879$	−12.8468	−	11.1318i	−0.433312	−	0.375467i
$880$	−16.3945	+	55.8347i	−0.552660	+	1.88219i
$881$	−0.160025	+	0.102842i	−0.00539138	+	0.00346483i	−0.543334	−	0.839517i	$-0.682838\pi$
$881$	−0.160025	+	0.102842i	−0.00539138	+	0.00346483i	0.537942	+	0.842982i	$0.319202\pi$
$882$	12.7304	+	1.88653i	0.428656	+	0.0635228i
$883$	−27.7992	−	32.0820i	−0.935518	−	1.07965i	−0.996672	−	0.0815168i	$-0.974024\pi$
$883$	−27.7992	−	32.0820i	−0.935518	−	1.07965i	0.0611541	−	0.998128i	$-0.480522\pi$
$884$	−2.46787	+	3.84008i	−0.0830034	+	0.129156i
$885$	0.0254262	−	0.176843i	0.000854692	−	0.00594452i
$886$	−3.60831	+	25.0964i	−0.121224	+	0.843129i
$887$	2.87853	−	4.47907i	0.0966514	−	0.150393i	−0.789560	−	0.613673i	$-0.789691\pi$
$887$	2.87853	−	4.47907i	0.0966514	−	0.150393i	0.886212	+	0.463280i	$0.153328\pi$
$888$	−4.90609	−	5.66193i	−0.164638	−	0.190002i
$889$	−1.54855	+	2.05933i	−0.0519366	+	0.0690677i
$890$	18.2734	−	11.7436i	0.612526	−	0.393647i
$891$	−1.58189	+	5.38743i	−0.0529954	+	0.180486i
$892$	−22.3304	−	19.3494i	−0.747676	−	0.647865i
$893$	−14.0269	−	47.7714i	−0.469394	−	1.59861i
$894$	14.5805	−	31.9269i	0.487646	−	1.06779i
$895$	−2.96107	−	20.5947i	−0.0989775	−	0.688404i
$896$	10.9625	+	20.1798i	0.366230	+	0.674158i
$897$	−15.5280	+	19.1377i	−0.518465	+	0.638990i
$898$	−6.65709			−0.222150
$899$	7.57751	−	1.08948i	0.252724	−	0.0363363i
$900$	0.254643	−	0.557590i	0.00848809	−	0.0185863i
$901$	−1.55371	−	5.29146i	−0.0517617	−	0.176284i
$902$	−36.9379	+	42.6286i	−1.22990	+	1.41938i
$903$	1.55176	+	7.20824i	0.0516392	+	0.239875i
$904$	2.77587	+	4.31934i	0.0923242	+	0.143659i
$905$	18.4010	+	40.2925i	0.611668	+	1.33937i
$906$	−12.1640	+	10.5402i	−0.404122	+	0.350173i
$907$	−3.11407	+	4.84559i	−0.103401	+	0.160895i	−0.889099	−	0.457716i	$-0.848668\pi$
$907$	−3.11407	+	4.84559i	−0.103401	+	0.160895i	0.785698	+	0.618611i	$0.212304\pi$
$908$	1.66433	−	11.5757i	0.0552328	−	0.384152i
$909$	9.57231	+	1.37629i	0.317494	+	0.0456487i
$910$	−53.2086	−	3.92110i	−1.76385	−	0.129983i
$911$	15.6807	−	13.5874i	0.519526	−	0.450172i	−0.355200	−	0.934791i	$-0.615587\pi$
$911$	15.6807	−	13.5874i	0.519526	−	0.450172i	0.874726	+	0.484619i	$0.161042\pi$
$912$	−27.5688	+	12.5903i	−0.912895	+	0.416905i
$913$	33.7297	+	52.4845i	1.11629	+	1.73698i
$914$	0.912922	−	3.10913i	0.0301968	−	0.102841i
$915$	10.8048	+	9.36238i	0.357194	+	0.309511i
$916$	14.5896	−	4.28388i	0.482052	−	0.141543i
$917$	−2.69568	−	38.8703i	−0.0890191	−	1.28361i
$918$	−1.17131	+	0.168409i	−0.0386589	+	0.00555831i
$919$			14.5751i			0.480789i	0.970675	+	0.240394i	$0.0772768\pi$
$919$			14.5751i			0.480789i	−0.970675	+	0.240394i	$0.922723\pi$
$920$	−11.6609	+	0.377423i	−0.384449	+	0.0124433i
$921$	−13.3854			−0.441065
$922$	−69.8826	+	10.0476i	−2.30146	+	0.330900i
$923$	7.66731	+	3.50154i	0.252372	+	0.115255i
$924$	14.4654	+	14.5281i	0.475878	+	0.477938i
$925$	−2.20650	−	1.91194i	−0.0725493	−	0.0628643i
$926$	−63.8811	−	18.7572i	−2.09926	−	0.616399i
$927$	13.3196	−	8.55998i	0.437472	−	0.281146i
$928$	−6.50400	−	14.2418i	−0.213504	−	0.467509i
$929$	−16.3619	+	14.1776i	−0.536816	+	0.465153i	−0.880577	−	0.473904i	$-0.842844\pi$
$929$	−16.3619	+	14.1776i	−0.536816	+	0.465153i	0.343761	+	0.939057i	$0.388299\pi$
$930$	−10.7299	−	6.89569i	−0.351848	−	0.226119i
$931$	−32.8970	−	28.7552i	−1.07816	−	0.942414i
$932$	1.18254	−	8.22475i	0.0387354	−	0.269410i
$933$	−8.63973	−	5.55242i	−0.282852	−	0.181778i
$934$	−11.5974	−	13.3841i	−0.379479	−	0.437942i
$935$	7.01683	−	3.20448i	0.229475	−	0.104798i
$936$	−3.16653	−	4.92722i	−0.103501	−	0.161051i
$937$	29.6950	+	8.71925i	0.970095	+	0.284846i	0.728130	−	0.685439i	$-0.240390\pi$
$937$	29.6950	+	8.71925i	0.970095	+	0.284846i	0.241965	+	0.970285i	$0.422208\pi$
$938$	0.877933	−	3.99423i	0.0286655	−	0.130416i
$939$	−2.40261	−	8.18252i	−0.0784061	−	0.267027i
$940$	−21.3727	−	9.76059i	−0.697101	−	0.318355i
$941$	4.64839	+	32.3303i	0.151533	+	1.05394i	0.913651	+	0.406499i	$0.133251\pi$
$941$	4.64839	+	32.3303i	0.151533	+	1.05394i	−0.762118	+	0.647438i	$0.775840\pi$
$942$		−	23.6792i		−	0.771511i
$943$	−24.1766	−	10.1092i	−0.787299	−	0.329199i
$944$		−	0.406431i		−	0.0132282i
$945$	−3.37446	−	4.52811i	−0.109771	−	0.147299i
$946$	−11.9509	+	26.1689i	−0.388558	+	0.850824i
$947$	9.20304	−	2.70226i	0.299059	−	0.0878116i	−0.128761	−	0.991676i	$-0.541100\pi$
$947$	9.20304	−	2.70226i	0.299059	−	0.0878116i	0.427820	+	0.903864i	$0.359282\pi$
$948$	0.863743	−	0.996813i	0.0280531	−	0.0323750i
$949$	48.6588	+	14.2875i	1.57953	+	0.463793i
$950$	−4.28799	+	2.75573i	−0.139121	+	0.0894075i
$951$	−18.2522	+	8.33552i	−0.591869	+	0.270298i
$952$	0.682217	−	1.81710i	0.0221108	−	0.0588924i
$953$	11.4347	−	17.7927i	0.370406	−	0.576362i	−0.605151	−	0.796111i	$-0.706887\pi$
$953$	11.4347	−	17.7927i	0.370406	−	0.576362i	0.975557	+	0.219748i	$0.0705236\pi$
$954$	−15.5920	−	2.24179i	−0.504808	−	0.0725805i
$955$	−38.6882	−	5.56253i	−1.25192	−	0.179999i
$956$	−23.7990	−	15.2947i	−0.769714	−	0.494665i
$957$	8.66035	+	9.99458i	0.279949	+	0.323079i
$958$	7.03818	+	15.4115i	0.227393	+	0.497922i
$959$	−11.3076	+	20.6025i	−0.365143	+	0.665288i
$960$	−1.50942	+	5.14061i	−0.0487163	+	0.165912i
$961$	−13.3824	+	15.4442i	−0.431692	+	0.498199i
$962$	59.5857	−	17.4959i	1.92112	−	0.564092i
$963$	12.5412	+	5.72739i	0.404136	+	0.184563i
$964$	−2.81061	−	19.5482i	−0.0905237	−	0.629606i
$965$	43.0630			1.38625
$966$	−10.5566	+	20.8026i	−0.339654	+	0.669312i
$967$	−49.0288			−1.57666			−0.788329	−	0.615253i	$-0.789054\pi$
$967$	−49.0288			−1.57666			−0.788329	+	0.615253i	$0.789054\pi$
$968$	−3.32953	−	23.1574i	−0.107015	−	0.744306i
$969$	3.65453	+	1.66897i	0.117400	+	0.0536149i
$970$	16.9102	−	4.96528i	0.542953	−	0.159425i
$971$	−10.4048	+	12.0078i	−0.333906	+	0.385348i	−0.897730	−	0.440547i	$-0.854784\pi$
$971$	−10.4048	+	12.0078i	−0.333906	+	0.385348i	0.563823	+	0.825896i	$0.309330\pi$
$972$	−0.388808	+	1.32416i	−0.0124710	+	0.0424724i
$973$	−28.0836	+	51.1682i	−0.900319	+	1.64038i
$974$	5.64595	+	12.3629i	0.180908	+	0.396133i
$975$	−1.49473	−	1.72501i	−0.0478698	−	0.0552447i
$976$	27.3602	+	17.5833i	0.875778	+	0.562829i
$977$	−34.1177	−	4.90538i	−1.09152	−	0.156937i	−0.427033	−	0.904236i	$-0.640441\pi$
$977$	−34.1177	−	4.90538i	−1.09152	−	0.156937i	−0.664488	+	0.747299i	$0.731350\pi$
$978$	−15.7798	−	2.26879i	−0.504582	−	0.0725480i
$979$	−16.8033	+	26.1465i	−0.537037	+	0.835646i
$980$	−20.4222	+	2.84627i	−0.652363	+	0.0909208i
$981$	7.48230	−	3.41705i	0.238892	−	0.109098i
$982$	14.3371	−	9.21389i	0.457515	−	0.294027i
$983$	−44.6834	−	13.1202i	−1.42518	−	0.418470i	−0.523926	−	0.851764i	$-0.675533\pi$
$983$	−44.6834	−	13.1202i	−1.42518	−	0.418470i	−0.901253	+	0.433294i	$0.857351\pi$
$984$	4.07832	−	4.70664i	0.130012	−	0.150042i
$985$	−53.9358	+	15.8370i	−1.71854	+	0.504608i
$986$	−1.15783	+	2.53528i	−0.0368727	+	0.0807399i
$987$	16.9218	−	12.6105i	0.538626	−	0.401398i
$988$		−	44.2665i		−	1.40830i
$989$	−13.2839	−	1.47313i	−0.422405	−	0.0468429i
$990$		−	22.0336i		−	0.700274i
$991$	−2.54093	−	17.6725i	−0.0807152	−	0.561387i	−0.989546	−	0.144221i	$-0.953932\pi$
$991$	−2.54093	−	17.6725i	−0.0807152	−	0.561387i	0.908830	−	0.417166i	$-0.136977\pi$
$992$	−19.6535	−	8.97546i	−0.624000	−	0.284971i
$993$	2.55244	+	8.69280i	0.0809991	+	0.275858i
$994$	7.79255	+	1.71280i	0.247165	+	0.0543268i
$995$	42.3038	+	12.4215i	1.34112	+	0.393788i
$996$	8.29032	+	12.9000i	0.262689	+	0.408752i
$997$	36.1054	−	16.4888i	1.14347	−	0.522206i	0.248633	−	0.968598i	$-0.420019\pi$
$997$	36.1054	−	16.4888i	1.14347	−	0.522206i	0.894837	+	0.446392i	$0.147291\pi$
$998$	−12.2663	−	14.1561i	−0.388284	−	0.448104i
$999$	5.52970	+	3.55372i	0.174952	+	0.112435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.7	✓	320
7.6	odd	2	inner	483.2.r.a.181.8	yes	320
23.15	odd	22	inner	483.2.r.a.475.8	yes	320
161.153	even	22	inner	483.2.r.a.475.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.7	✓	320	1.1	even	1	trivial
483.2.r.a.181.8	yes	320	7.6	odd	2	inner
483.2.r.a.475.7	yes	320	161.153	even	22	inner
483.2.r.a.475.8	yes	320	23.15	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261645 - 1.81978i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-1.32416 + 0.388808i) q^{4} +(1.39776 - 1.61310i) q^{5} +(-0.517964 + 1.76402i) q^{6} +(2.31938 + 1.27299i) q^{7} +(-0.473472 - 1.03676i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.261645 - 1.81978i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-1.32416 + 0.388808i) q^{4} +(1.39776 - 1.61310i) q^{5} +(-0.517964 + 1.76402i) q^{6} +(2.31938 + 1.27299i) q^{7} +(-0.473472 - 1.03676i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-3.30121 - 2.12156i) q^{10} +(5.55772 + 0.799079i) q^{11} +(1.36601 + 0.196403i) q^{12} +(2.77826 - 4.32305i) q^{13} +(1.70970 - 4.55383i) q^{14} +(-1.94155 + 0.886678i) q^{15} +(-4.08475 + 2.62511i) q^{16} +(0.617581 + 0.181338i) q^{17} +(1.20396 - 1.38944i) q^{18} +(-5.98902 + 1.75853i) q^{19} +(-1.22367 + 2.67946i) q^{20} +(-1.58096 - 2.12145i) q^{21} -10.3229i q^{22} +(4.55545 - 1.49929i) q^{23} +1.13976i q^{24} +(0.0632123 + 0.439651i) q^{25} +(-8.59392 - 3.92471i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-3.56617 - 0.783844i) q^{28} +(-2.25990 - 0.663565i) q^{29} +(2.12156 + 3.30121i) q^{30} +(-2.95658 + 1.35022i) q^{31} +(4.35312 + 5.02377i) q^{32} +(-4.72353 - 3.03563i) q^{33} +(0.168409 - 1.17131i) q^{34} +(5.29539 - 1.96206i) q^{35} +(-1.16098 - 0.746117i) q^{36} +(-4.96767 + 4.30451i) q^{37} +(4.76714 + 10.4386i) q^{38} +(-4.32305 + 2.77826i) q^{39} +(-2.33420 - 0.685382i) q^{40} +(-4.12951 - 3.57824i) q^{41} +(-3.44693 + 3.43207i) q^{42} +(-2.53503 - 1.15771i) q^{43} +(-7.66999 + 1.10278i) q^{44} +2.13444 q^{45} +(-3.92030 - 7.89764i) q^{46} +7.97650i q^{47} +(4.80613 - 0.691017i) q^{48} +(3.75901 + 5.90507i) q^{49} +(0.783529 - 0.230065i) q^{50} +(-0.486441 - 0.421503i) q^{51} +(-1.99801 + 6.80461i) q^{52} +(-4.63224 - 7.20790i) q^{53} +(-1.67235 + 0.763738i) q^{54} +(9.05735 - 7.84824i) q^{55} +(0.221621 - 3.00736i) q^{56} +(6.17832 + 0.888309i) q^{57} +(-0.616253 + 4.28613i) q^{58} +(-0.0452540 + 0.0704165i) q^{59} +(2.22618 - 1.92899i) q^{60} +(-2.78250 - 6.09283i) q^{61} +(3.23068 + 5.02704i) q^{62} +(0.556809 + 2.58650i) q^{63} +(1.64376 - 1.89700i) q^{64} +(-3.09018 - 10.5242i) q^{65} +(-4.28829 + 9.39004i) q^{66} +(0.832194 - 0.119651i) q^{67} -0.888280 q^{68} +(-4.76661 - 0.528597i) q^{69} +(-4.95603 - 9.12308i) q^{70} +(0.233434 + 1.62357i) q^{71} +(0.473472 - 1.03676i) q^{72} +(2.78031 + 9.46888i) q^{73} +(9.13303 + 7.91382i) q^{74} +(0.125138 - 0.426180i) q^{75} +(7.24667 - 4.65715i) q^{76} +(11.8732 + 8.92827i) q^{77} +(6.18692 + 7.14009i) q^{78} +(0.516710 - 0.804016i) q^{79} +(-1.47493 + 10.2584i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-5.43115 + 8.45103i) q^{82} +(7.27635 + 8.39735i) q^{83} +(2.91828 + 2.19445i) q^{84} +(1.15575 - 0.742753i) q^{85} +(-1.44350 + 4.91611i) q^{86} +(1.78002 + 1.54240i) q^{87} +(-1.80297 - 6.14035i) q^{88} +(-2.29948 + 5.03515i) q^{89} +(-0.558465 - 3.88421i) q^{90} +(11.9470 - 6.49010i) q^{91} +(-5.44920 + 3.75650i) q^{92} +3.25030 q^{93} +(14.5155 - 2.08701i) q^{94} +(-5.53452 + 12.1189i) q^{95} +(-1.87279 - 6.37813i) q^{96} +(-2.94110 + 3.39421i) q^{97} +(9.76241 - 8.38561i) q^{98} +(3.03563 + 4.72353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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