LMFDB - Embedded newform 483.2.r.a.412.19

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			412.19
Character	$\chi$	$=$	483.412
Dual form			483.2.r.a.34.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.227214 + 0.146021i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(-0.800526 - 1.75291i) q^{4} +(-1.03996 - 0.305361i) q^{5} +(-0.245682 - 0.112199i) q^{6} +(-2.17465 - 1.50695i) q^{7} +(0.150947 - 1.04986i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.227214 + 0.146021i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(-0.800526 - 1.75291i) q^{4} +(-1.03996 - 0.305361i) q^{5} +(-0.245682 - 0.112199i) q^{6} +(-2.17465 - 1.50695i) q^{7} +(0.150947 - 1.04986i) q^{8} +(0.959493 - 0.281733i) q^{9} +(-0.191705 - 0.221239i) q^{10} +(2.42939 + 3.78020i) q^{11} +(1.04184 + 1.62114i) q^{12} +(-2.38102 + 2.06316i) q^{13} +(-0.274062 - 0.659945i) q^{14} +(1.07284 + 0.154251i) q^{15} +(-2.33630 + 2.69624i) q^{16} +(-2.18750 + 4.78996i) q^{17} +(0.259149 + 0.0760930i) q^{18} +(2.28938 + 5.01305i) q^{19} +(0.297249 + 2.06741i) q^{20} +(2.36697 + 1.18213i) q^{21} +1.21366i q^{22} +(-0.277290 - 4.78781i) q^{23} +1.06065i q^{24} +(-3.21799 - 2.06807i) q^{25} +(-0.842265 + 0.121099i) q^{26} +(-0.909632 + 0.415415i) q^{27} +(-0.900689 + 5.01831i) q^{28} +(-0.778025 + 1.70364i) q^{29} +(0.221239 + 0.191705i) q^{30} +(-6.66165 - 0.957801i) q^{31} +(-2.95993 + 0.869114i) q^{32} +(-2.94264 - 3.39599i) q^{33} +(-1.19647 + 0.768923i) q^{34} +(1.80139 + 2.23123i) q^{35} +(-1.26195 - 1.45637i) q^{36} +(2.08577 + 7.10348i) q^{37} +(-0.211833 + 1.47333i) q^{38} +(2.06316 - 2.38102i) q^{39} +(-0.477566 + 1.04572i) q^{40} +(3.11602 - 10.6122i) q^{41} +(0.365193 + 0.614225i) q^{42} +(-1.39400 + 0.200427i) q^{43} +(4.68155 - 7.28464i) q^{44} -1.08387 q^{45} +(0.636118 - 1.12835i) q^{46} +1.11953i q^{47} +(1.92881 - 3.00128i) q^{48} +(2.45818 + 6.55419i) q^{49} +(-0.429187 - 0.939789i) q^{50} +(1.48355 - 5.05252i) q^{51} +(5.52260 + 2.52209i) q^{52} +(-1.39483 - 1.20863i) q^{53} +(-0.267340 - 0.0384377i) q^{54} +(-1.37215 - 4.67312i) q^{55} +(-1.91035 + 2.05560i) q^{56} +(-2.97951 - 4.63621i) q^{57} +(-0.425546 + 0.273482i) q^{58} +(-9.62852 + 8.34316i) q^{59} +(-0.588447 - 2.00407i) q^{60} +(1.66120 - 11.5539i) q^{61} +(-1.37376 - 1.19037i) q^{62} +(-2.51112 - 0.833243i) q^{63} +(6.04679 + 1.77550i) q^{64} +(3.10618 - 1.41855i) q^{65} +(-0.172721 - 1.20130i) q^{66} +(-5.58129 + 8.68465i) q^{67} +10.1475 q^{68} +(0.955844 + 4.69961i) q^{69} +(0.0834932 + 0.770008i) q^{70} +(8.57728 + 5.51229i) q^{71} +(-0.150947 - 1.04986i) q^{72} +(-12.5808 + 5.74545i) q^{73} +(-0.563345 + 1.91858i) q^{74} +(3.47955 + 1.58906i) q^{75} +(6.95470 - 8.02616i) q^{76} +(0.413528 - 11.8816i) q^{77} +(0.816458 - 0.239734i) q^{78} +(-6.67014 + 5.77971i) q^{79} +(3.25300 - 2.09058i) q^{80} +(0.841254 - 0.540641i) q^{81} +(2.25761 - 1.95623i) q^{82} +(-0.695752 + 0.204291i) q^{83} +(0.177341 - 5.09541i) q^{84} +(3.73760 - 4.31342i) q^{85} +(-0.346003 - 0.158014i) q^{86} +(0.527653 - 1.79702i) q^{87} +(4.33539 - 1.97990i) q^{88} +(-1.66375 - 11.5717i) q^{89} +(-0.246270 - 0.158268i) q^{90} +(8.28696 - 0.898568i) q^{91} +(-8.17061 + 4.31883i) q^{92} +6.73016 q^{93} +(-0.163475 + 0.254371i) q^{94} +(-0.850087 - 5.91249i) q^{95} +(2.80611 - 1.28151i) q^{96} +(-7.69464 - 2.25935i) q^{97} +(-0.398519 + 1.84815i) q^{98} +(3.39599 + 2.94264i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.227214	+	0.146021i	0.160664	+	0.103253i	0.618502	−	0.785783i	$-0.287740\pi$
$2$	0.227214	+	0.146021i	0.160664	+	0.103253i	−0.457838	+	0.889036i	$0.651376\pi$
$3$	−0.989821	+	0.142315i	−0.571474	+	0.0821655i
$3$	−0.989821	+	0.142315i	−0.571474	+	0.0821655i
$4$	−0.800526	−	1.75291i	−0.400263	−	0.876454i
$5$	−1.03996	−	0.305361i	−0.465086	−	0.136562i	0.0407898	−	0.999168i	$-0.487013\pi$
$5$	−1.03996	−	0.305361i	−0.465086	−	0.136562i	−0.505876	+	0.862606i	$0.668831\pi$
$6$	−0.245682	−	0.112199i	−0.100299	−	0.0458051i
$7$	−2.17465	−	1.50695i	−0.821939	−	0.569575i
$7$	−2.17465	−	1.50695i	−0.821939	−	0.569575i
$8$	0.150947	−	1.04986i	0.0533678	−	0.371181i
$9$	0.959493	−	0.281733i	0.319831	−	0.0939109i
$10$	−0.191705	−	0.221239i	−0.0606224	−	0.0699620i
$11$	2.42939	+	3.78020i	0.732488	+	1.13977i	0.985063	+	0.172196i	$0.0550862\pi$
$11$	2.42939	+	3.78020i	0.732488	+	1.13977i	−0.252575	+	0.967577i	$0.581277\pi$
$12$	1.04184	+	1.62114i	0.300754	+	0.467983i
$13$	−2.38102	+	2.06316i	−0.660375	+	0.572218i	−0.919241	−	0.393695i	$-0.871197\pi$
$13$	−2.38102	+	2.06316i	−0.660375	+	0.572218i	0.258866	+	0.965913i	$0.416651\pi$
$14$	−0.274062	−	0.659945i	−0.0732462	−	0.176378i
$15$	1.07284	+	0.154251i	0.277005	+	0.0398274i
$16$	−2.33630	+	2.69624i	−0.584075	+	0.674059i
$17$	−2.18750	+	4.78996i	−0.530547	+	1.16174i	0.434742	+	0.900555i	$0.356839\pi$
$17$	−2.18750	+	4.78996i	−0.530547	+	1.16174i	−0.965290	+	0.261182i	$0.915888\pi$
$18$	0.259149	+	0.0760930i	0.0610820	+	0.0179353i
$19$	2.28938	+	5.01305i	0.525221	+	1.15007i	0.967425	+	0.253158i	$0.0814693\pi$
$19$	2.28938	+	5.01305i	0.525221	+	1.15007i	−0.442204	+	0.896914i	$0.645803\pi$
$20$	0.297249	+	2.06741i	0.0664669	+	0.462287i
$21$	2.36697	+	1.18213i	0.516516	+	0.257962i
$22$			1.21366i			0.258752i
$23$	−0.277290	−	4.78781i	−0.0578190	−	0.998327i
$23$	−0.277290	−	4.78781i	−0.0578190	−	0.998327i
$24$			1.06065i			0.216505i
$25$	−3.21799	−	2.06807i	−0.643597	−	0.413615i
$26$	−0.842265	+	0.121099i	−0.165182	+	0.0237495i
$27$	−0.909632	+	0.415415i	−0.175059	+	0.0799467i
$28$	−0.900689	+	5.01831i	−0.170214	+	0.948372i
$29$	−0.778025	+	1.70364i	−0.144476	+	0.316358i	−0.968011	−	0.250907i	$-0.919271\pi$
$29$	−0.778025	+	1.70364i	−0.144476	+	0.316358i	0.823535	+	0.567265i	$0.191998\pi$
$30$	0.221239	+	0.191705i	0.0403926	+	0.0350004i
$31$	−6.66165	−	0.957801i	−1.19647	−	0.172026i	−0.484853	−	0.874596i	$-0.661127\pi$
$31$	−6.66165	−	0.957801i	−1.19647	−	0.172026i	−0.711615	+	0.702569i	$0.752036\pi$
$32$	−2.95993	+	0.869114i	−0.523247	+	0.153639i
$33$	−2.94264	−	3.39599i	−0.512248	−	0.591165i
$34$	−1.19647	+	0.768923i	−0.205192	+	0.131869i
$35$	1.80139	+	2.23123i	0.304491	+	0.377147i
$36$	−1.26195	−	1.45637i	−0.210325	−	0.242728i
$37$	2.08577	+	7.10348i	0.342899	+	1.16781i	0.932819	+	0.360344i	$0.117341\pi$
$37$	2.08577	+	7.10348i	0.342899	+	1.16781i	−0.589921	+	0.807461i	$0.700841\pi$
$38$	−0.211833	+	1.47333i	−0.0343639	+	0.239006i
$39$	2.06316	−	2.38102i	0.330370	−	0.381268i
$40$	−0.477566	+	1.04572i	−0.0755098	+	0.165343i
$41$	3.11602	−	10.6122i	0.486640	−	1.65734i	−0.240343	−	0.970688i	$-0.577260\pi$
$41$	3.11602	−	10.6122i	0.486640	−	1.65734i	0.726983	−	0.686655i	$-0.240922\pi$
$42$	0.365193	+	0.614225i	0.0563504	+	0.0947770i
$43$	−1.39400	+	0.200427i	−0.212583	+	0.0305649i	−0.247784	−	0.968815i	$-0.579702\pi$
$43$	−1.39400	+	0.200427i	−0.212583	+	0.0305649i	0.0352003	+	0.999380i	$0.488793\pi$
$44$	4.68155	−	7.28464i	0.705771	−	1.09820i
$45$	−1.08387			−0.161574
$46$	0.636118	−	1.12835i	0.0937905	−	0.166365i
$47$			1.11953i			0.163300i	0.996661	+	0.0816498i	$0.0260189\pi$
$47$			1.11953i			0.163300i	−0.996661	+	0.0816498i	$0.973981\pi$
$48$	1.92881	−	3.00128i	0.278399	−	0.433198i
$49$	2.45818	+	6.55419i	0.351169	+	0.936312i
$50$	−0.429187	−	0.939789i	−0.0606963	−	0.132906i
$51$	1.48355	−	5.05252i	0.207739	−	0.707495i
$52$	5.52260	+	2.52209i	0.765847	+	0.349750i
$53$	−1.39483	−	1.20863i	−0.191595	−	0.166018i	0.553781	−	0.832662i	$-0.313184\pi$
$53$	−1.39483	−	1.20863i	−0.191595	−	0.166018i	−0.745376	+	0.666645i	$0.767730\pi$
$54$	−0.267340	−	0.0384377i	−0.0363804	−	0.00523071i
$55$	−1.37215	−	4.67312i	−0.185021	−	0.630123i
$56$	−1.91035	+	2.05560i	−0.255281	+	0.274691i
$57$	−2.97951	−	4.63621i	−0.394646	−	0.614081i
$58$	−0.425546	+	0.273482i	−0.0558769	+	0.0359099i
$59$	−9.62852	+	8.34316i	−1.25353	+	1.08619i	−0.260851	+	0.965379i	$0.584003\pi$
$59$	−9.62852	+	8.34316i	−1.25353	+	1.08619i	−0.992676	+	0.120808i	$0.961451\pi$
$60$	−0.588447	−	2.00407i	−0.0759682	−	0.258724i
$61$	1.66120	−	11.5539i	0.212695	−	1.47932i	−0.551412	−	0.834233i	$-0.685911\pi$
$61$	1.66120	−	11.5539i	0.212695	−	1.47932i	0.764106	−	0.645090i	$-0.223180\pi$
$62$	−1.37376	−	1.19037i	−0.174468	−	0.151177i
$63$	−2.51112	−	0.833243i	−0.316371	−	0.104979i
$64$	6.04679	+	1.77550i	0.755849	+	0.221937i
$65$	3.10618	−	1.41855i	0.385275	−	0.175949i
$66$	−0.172721	−	1.20130i	−0.0212605	−	0.147870i
$67$	−5.58129	+	8.68465i	−0.681863	+	1.06100i	0.311968	+	0.950093i	$0.399012\pi$
$67$	−5.58129	+	8.68465i	−0.681863	+	1.06100i	−0.993831	+	0.110907i	$0.964625\pi$
$68$	10.1475			1.23057
$69$	0.955844	+	4.69961i	0.115070	+	0.565767i
$70$	0.0834932	+	0.770008i	0.00997934	+	0.0920336i
$71$	8.57728	+	5.51229i	1.01794	+	0.654188i	0.939435	−	0.342726i	$-0.111350\pi$
$71$	8.57728	+	5.51229i	1.01794	+	0.654188i	0.0785010	+	0.996914i	$0.474987\pi$
$72$	−0.150947	−	1.04986i	−0.0177893	−	0.123727i
$73$	−12.5808	+	5.74545i	−1.47247	+	0.672454i	−0.980204	−	0.197992i	$-0.936558\pi$
$73$	−12.5808	+	5.74545i	−1.47247	+	0.672454i	−0.492265	+	0.870446i	$0.663831\pi$
$74$	−0.563345	+	1.91858i	−0.0654875	+	0.223030i
$75$	3.47955	+	1.58906i	0.401784	+	0.183488i
$76$	6.95470	−	8.02616i	0.797759	−	0.920663i
$77$	0.413528	−	11.8816i	0.0471259	−	1.35403i
$78$	0.816458	−	0.239734i	0.0924456	−	0.0271445i
$79$	−6.67014	+	5.77971i	−0.750450	+	0.650268i	−0.943670	−	0.330887i	$-0.892652\pi$
$79$	−6.67014	+	5.77971i	−0.750450	+	0.650268i	0.193221	+	0.981155i	$0.438107\pi$
$80$	3.25300	−	2.09058i	0.363696	−	0.233733i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	2.25761	−	1.95623i	0.249311	−	0.216029i
$83$	−0.695752	+	0.204291i	−0.0763688	+	0.0224239i	−0.319694	−	0.947521i	$-0.603580\pi$
$83$	−0.695752	+	0.204291i	−0.0763688	+	0.0224239i	0.243325	+	0.969945i	$0.421762\pi$
$84$	0.177341	−	5.09541i	0.0193495	−	0.555955i
$85$	3.73760	−	4.31342i	0.405399	−	0.467856i
$86$	−0.346003	−	0.158014i	−0.0373104	−	0.0170391i
$87$	0.527653	−	1.79702i	0.0565704	−	0.192661i
$88$	4.33539	−	1.97990i	0.462154	−	0.211059i
$89$	−1.66375	−	11.5717i	−0.176358	−	1.22659i	−0.865104	−	0.501592i	$-0.832748\pi$
$89$	−1.66375	−	11.5717i	−0.176358	−	1.22659i	0.688747	−	0.725002i	$-0.258161\pi$
$90$	−0.246270	−	0.158268i	−0.0259591	−	0.0166829i
$91$	8.28696	−	0.898568i	0.868709	−	0.0941955i
$92$	−8.17061	+	4.31883i	−0.851845	+	0.450269i
$93$	6.73016			0.697885
$94$	−0.163475	+	0.254371i	−0.0168611	+	0.0262364i
$95$	−0.850087	−	5.91249i	−0.0872171	−	0.606608i
$96$	2.80611	−	1.28151i	0.286398	−	0.130794i
$97$	−7.69464	−	2.25935i	−0.781272	−	0.229402i	−0.133310	−	0.991074i	$-0.542561\pi$
$97$	−7.69464	−	2.25935i	−0.781272	−	0.229402i	−0.647963	+	0.761672i	$0.724379\pi$
$98$	−0.398519	+	1.84815i	−0.0402565	+	0.186691i
$99$	3.39599	+	2.94264i	0.341309	+	0.295746i
$100$	−1.04906	+	7.29638i	−0.104906	+	0.729638i
$101$	−2.70718	−	9.21979i	−0.269374	−	0.917404i	−0.977432	−	0.211250i	$-0.932247\pi$
$101$	−2.70718	−	9.21979i	−0.269374	−	0.917404i	0.708058	−	0.706154i	$-0.249571\pi$
$102$	1.07486	−	0.931371i	0.106427	−	0.0922195i
$103$	8.38523	−	5.38886i	0.826221	−	0.530980i	−0.0578537	−	0.998325i	$-0.518426\pi$
$103$	8.38523	−	5.38886i	0.826221	−	0.530980i	0.884075	+	0.467345i	$0.154789\pi$
$104$	1.80662	+	2.81116i	0.177154	+	0.275657i
$105$	−2.10059	−	1.95216i	−0.204997	−	0.190511i
$106$	−0.140439	−	0.478292i	−0.0136407	−	0.0464558i
$107$	−5.56322	−	0.799870i	−0.537816	−	0.0773263i	−0.131946	−	0.991257i	$-0.542123\pi$
$107$	−5.56322	−	0.799870i	−0.537816	−	0.0773263i	−0.405870	+	0.913931i	$0.633032\pi$
$108$	1.45637	+	1.26195i	0.140139	+	0.121431i
$109$	−2.82030	−	1.28799i	−0.270135	−	0.123367i	0.275742	−	0.961232i	$-0.411076\pi$
$109$	−2.82030	−	1.28799i	−0.270135	−	0.123367i	−0.545878	+	0.837865i	$0.683804\pi$
$110$	0.370603	−	1.26216i	0.0353356	−	0.120342i
$111$	−3.07547	−	6.73434i	−0.291911	−	0.639196i
$112$	9.14374	−	2.34266i	0.864002	−	0.221361i
$113$	4.77648	−	7.43234i	0.449333	−	0.699176i	−0.540510	−	0.841337i	$-0.681769\pi$
$113$	4.77648	−	7.43234i	0.449333	−	0.699176i	0.989843	+	0.142161i	$0.0454052\pi$
$114$		−	1.48848i		−	0.139409i
$115$	−1.17364	+	5.06383i	−0.109442	+	0.472204i
$116$	3.60915			0.335101
$117$	−1.70331	+	2.65040i	−0.157471	+	0.245029i
$118$	−3.40601	+	0.489711i	−0.313549	+	0.0450815i
$119$	11.9753	−	7.12001i	1.09777	−	0.652691i
$120$	0.323883	−	1.10304i	0.0295663	−	0.100694i
$121$	−3.81843	+	8.36119i	−0.347130	+	0.760108i
$122$	2.06456	−	2.38263i	0.186917	−	0.215713i
$123$	−1.57403	+	10.9476i	−0.141925	+	0.987113i
$124$	3.65389	+	12.4440i	0.328129	+	1.11751i
$125$	6.26400	+	7.22904i	0.560269	+	0.646585i
$126$	−0.448889	−	0.556001i	−0.0399902	−	0.0495325i
$127$	−7.42569	+	4.77220i	−0.658924	+	0.423465i	−0.826917	−	0.562323i	$-0.809908\pi$
$127$	−7.42569	+	4.77220i	−0.658924	+	0.423465i	0.167994	+	0.985788i	$0.446271\pi$
$128$	5.15500	+	5.94919i	0.455642	+	0.525839i
$129$	1.35129	−	0.396774i	0.118974	−	0.0349340i
$130$	0.912905	+	0.131256i	0.0800671	+	0.0115119i
$131$	14.9580	+	12.9612i	1.30689	+	1.13243i	0.982451	+	0.186520i	$0.0597209\pi$
$131$	14.9580	+	12.9612i	1.30689	+	1.13243i	0.324439	+	0.945907i	$0.394825\pi$
$132$	−3.59719	+	7.87675i	−0.313095	+	0.685583i
$133$	2.57583	−	14.3516i	0.223353	−	1.24444i
$134$	−2.53629	+	1.15828i	−0.219102	+	0.100061i
$135$	1.07284	−	0.154251i	0.0923351	−	0.0132758i
$136$	4.69859	+	3.01960i	0.402901	+	0.258929i
$137$		−	2.80847i		−	0.239944i	−0.992777	−	0.119972i	$-0.961719\pi$
$137$		−	2.80847i		−	0.239944i	0.992777	−	0.119972i	$-0.0382805\pi$
$138$	−0.469063	+	1.20739i	−0.0399293	+	0.102780i
$139$			11.5201i			0.977123i	0.872529	+	0.488562i	$0.162478\pi$
$139$			11.5201i			0.977123i	−0.872529	+	0.488562i	$0.837522\pi$
$140$	2.46908	−	4.94383i	0.208676	−	0.417830i
$141$	−0.159325	−	1.10813i	−0.0134176	−	0.0933214i
$142$	1.14396	+	2.50493i	0.0959994	+	0.210209i
$143$	−13.5836	−	3.98850i	−1.13592	−	0.333535i
$144$	−1.48205	+	3.24523i	−0.123504	+	0.270436i
$145$	1.32934	−	1.53415i	0.110396	−	0.127404i
$146$	−3.69748	−	0.531618i	−0.306006	−	0.0439970i
$147$	−3.36592	−	6.13764i	−0.277616	−	0.506224i
$148$	10.7820	−	9.34269i	0.886278	−	0.767964i
$149$	−6.27446	−	9.76325i	−0.514024	−	0.799836i	0.483105	−	0.875562i	$-0.339509\pi$
$149$	−6.27446	−	9.76325i	−0.514024	−	0.799836i	−0.997129	+	0.0757260i	$0.975873\pi$
$150$	0.558565	+	0.869144i	0.0456066	+	0.0709653i
$151$	−5.69807	−	6.57593i	−0.463703	−	0.535141i	0.474947	−	0.880015i	$-0.342467\pi$
$151$	−5.69807	−	6.57593i	−0.463703	−	0.535141i	−0.938649	+	0.344873i	$0.887922\pi$
$152$	5.60857	−	1.64683i	0.454915	−	0.133575i
$153$	−0.749405	+	5.21223i	−0.0605858	+	0.421384i
$154$	1.82892	−	2.63927i	0.147379	−	0.212679i
$155$	6.63541	+	3.03029i	0.532969	+	0.243399i
$156$	−5.82532	−	1.71047i	−0.466399	−	0.136947i
$157$	−7.41817	−	16.2435i	−0.592034	−	1.29637i	−0.934205	−	0.356736i	$-0.883889\pi$
$157$	−7.41817	−	16.2435i	−0.592034	−	1.29637i	0.342171	−	0.939638i	$-0.388838\pi$
$158$	−2.35951	+	0.339246i	−0.187712	+	0.0269890i
$159$	1.55264	+	0.997820i	0.123132	+	0.0791323i
$160$	3.34362			0.264336
$161$	−6.61200	+	10.8297i	−0.521099	+	0.853497i
$162$	0.270089			0.0212202
$163$	−19.1315	−	12.2951i	−1.49849	−	0.963024i	−0.995090	−	0.0989727i	$-0.968444\pi$
$163$	−19.1315	−	12.2951i	−1.49849	−	0.963024i	−0.503404	−	0.864051i	$-0.667919\pi$
$164$	−21.0966	+	3.03324i	−1.64737	+	0.236856i
$165$	2.02324	+	4.43027i	0.157509	+	0.344896i
$166$	−0.187915	−	0.0551769i	−0.0145851	−	0.00428256i
$167$	−7.73632	−	3.53306i	−0.598654	−	0.273396i	0.0929524	−	0.995671i	$-0.470370\pi$
$167$	−7.73632	−	3.53306i	−0.598654	−	0.273396i	−0.691607	+	0.722274i	$0.743097\pi$
$168$	1.59836	−	2.30655i	0.123316	−	0.177954i
$169$	−0.437494	+	3.04284i	−0.0336534	+	0.234064i
$170$	1.47908	−	0.434298i	0.113441	−	0.0333091i
$171$	3.60899	+	4.16499i	0.275986	+	0.318505i
$172$	1.46727	+	2.28311i	0.111878	+	0.174085i
$173$	−5.25864	−	8.18260i	−0.399807	−	0.622112i	0.581731	−	0.813382i	$-0.302376\pi$
$173$	−5.25864	−	8.18260i	−0.399807	−	0.622112i	−0.981538	+	0.191270i	$0.938739\pi$
$174$	0.382294	−	0.331259i	0.0289816	−	0.0251127i
$175$	3.88149	+	9.34669i	0.293413	+	0.706543i
$176$	−15.8681	−	2.28149i	−1.19610	−	0.171974i
$177$	8.34316	−	9.62852i	0.627110	−	0.723724i
$178$	1.31168	−	2.87218i	0.0983148	−	0.215279i
$179$	21.6927	+	6.36954i	1.62139	+	0.476082i	0.961391	−	0.275187i	$-0.0887399\pi$
$179$	21.6927	+	6.36954i	1.62139	+	0.476082i	0.659996	+	0.751269i	$0.270558\pi$
$180$	0.867666	+	1.89992i	0.0646720	+	0.141612i
$181$	1.43926	+	10.0103i	0.106979	+	0.744058i	0.970736	+	0.240149i	$0.0771962\pi$
$181$	1.43926	+	10.0103i	0.106979	+	0.744058i	−0.863757	+	0.503909i	$0.831895\pi$
$182$	2.01412	+	1.00591i	0.149297	+	0.0745627i
$183$			11.6727i			0.862871i
$184$	−5.06838	−	0.431590i	−0.373646	−	0.0318172i
$185$		−	8.02429i		−	0.589957i
$186$	1.52918	+	0.982747i	0.112125	+	0.0720585i
$187$	−23.4213	+	3.36748i	−1.71274	+	0.246254i
$188$	1.96242	−	0.896209i	0.143124	−	0.0653628i
$189$	2.60414	+	0.467392i	0.189423	+	0.0339978i
$190$	0.670198	−	1.46753i	0.0486212	−	0.106466i
$191$	14.4740	+	12.5418i	1.04730	+	0.907495i	0.995834	−	0.0911800i	$-0.0290639\pi$
$191$	14.4740	+	12.5418i	1.04730	+	0.907495i	0.0514701	+	0.998675i	$0.483609\pi$
$192$	−6.23792	−	0.896878i	−0.450183	−	0.0647266i
$193$	4.26226	−	1.25151i	0.306804	−	0.0900857i	−0.124707	−	0.992194i	$-0.539799\pi$
$193$	4.26226	−	1.25151i	0.306804	−	0.0900857i	0.431510	+	0.902108i	$0.357981\pi$
$194$	−1.41841	−	1.63694i	−0.101836	−	0.117525i
$195$	−2.87269	+	1.84616i	−0.205717	+	0.132206i
$196$	9.52105	−	9.55576i	0.680075	−	0.682554i
$197$	−1.25209	−	1.44499i	−0.0892079	−	0.102951i	0.709391	−	0.704816i	$-0.248970\pi$
$197$	−1.25209	−	1.44499i	−0.0892079	−	0.102951i	−0.798598	+	0.601864i	$0.794425\pi$
$198$	0.341926	+	1.16449i	0.0242996	+	0.0827570i
$199$	1.29091	−	8.97847i	0.0915102	−	0.636467i	−0.891514	−	0.452993i	$-0.850356\pi$
$199$	1.29091	−	8.97847i	0.0915102	−	0.636467i	0.983024	−	0.183475i	$-0.0587345\pi$
$200$	−2.65693	+	3.06626i	−0.187873	+	0.216817i
$201$	4.28852	−	9.39055i	0.302489	−	0.662359i
$202$	0.731179	−	2.49017i	0.0514456	−	0.175208i
$203$	4.25924	−	2.53236i	0.298940	−	0.177737i
$204$	−10.0442	+	1.44414i	−0.703237	+	0.101110i
$205$	−6.48109	+	10.0848i	−0.452659	+	0.704351i
$206$	2.69213			0.187569
$207$	−1.61494	−	4.51575i	−0.112246	−	0.313866i
$208$		−	11.2399i		−	0.779350i
$209$	−13.3885	+	20.8330i	−0.926104	+	1.44105i
$210$	−0.192227	−	0.750288i	−0.0132649	−	0.0517748i
$211$	−7.86869	−	17.2300i	−0.541703	−	1.18616i	−0.960550	−	0.278108i	$-0.910293\pi$
$211$	−7.86869	−	17.2300i	−0.541703	−	1.18616i	0.418847	−	0.908057i	$-0.362434\pi$
$212$	−1.00201	+	3.41255i	−0.0688186	+	0.234375i
$213$	−9.27446	−	4.23550i	−0.635476	−	0.290212i
$214$	−1.14724	−	0.994089i	−0.0784237	−	0.0679546i
$215$	1.51092	+	0.217237i	0.103044	+	0.0148154i
$216$	0.298821	+	1.01769i	0.0203322	+	0.0692451i
$217$	13.0434	+	12.1217i	0.885443	+	0.822874i
$218$	−0.452736	−	0.704471i	−0.0306632	−	0.0477128i
$219$	11.6351	−	7.47740i	0.786224	−	0.505276i
$220$	−7.09310	+	6.14621i	−0.478217	+	0.414377i
$221$	−4.67399	−	15.9182i	−0.314407	−	1.07077i
$222$	0.284569	−	1.97922i	0.0190990	−	0.132836i
$223$	16.9528	+	14.6897i	1.13524	+	0.983695i	0.999975	−	0.00711417i	$-0.00226453\pi$
$223$	16.9528	+	14.6897i	1.13524	+	0.983695i	0.135269	+	0.990809i	$0.456810\pi$
$224$	7.74652	+	2.57046i	0.517586	+	0.171746i
$225$	−3.67028	−	1.07769i	−0.244685	−	0.0718461i
$226$	2.17056	−	0.991262i	0.144384	−	0.0659378i
$227$	1.51829	+	10.5599i	0.100772	+	0.700888i	0.976094	+	0.217347i	$0.0697404\pi$
$227$	1.51829	+	10.5599i	0.100772	+	0.700888i	−0.875322	+	0.483541i	$0.839351\pi$
$228$	−5.74167	+	8.93422i	−0.380252	+	0.591683i
$229$	3.49933			0.231242			0.115621	−	0.993293i	$-0.463114\pi$
$229$	3.49933			0.231242			0.115621	+	0.993293i	$0.463114\pi$
$230$	−1.00609	+	0.979194i	−0.0663399	+	0.0645661i
$231$	1.28161	+	11.8195i	0.0843235	+	0.777665i
$232$	1.67114	+	1.07398i	0.109716	+	0.0705100i
$233$	1.77046	+	12.3138i	0.115986	+	0.806704i	0.961904	+	0.273389i	$0.0881447\pi$
$233$	1.77046	+	12.3138i	0.115986	+	0.806704i	−0.845917	+	0.533315i	$0.820946\pi$
$234$	−0.774030	+	0.353487i	−0.0505999	+	0.0231082i
$235$	0.341860	−	1.16427i	0.0223005	−	0.0759484i
$236$	22.3327	+	10.1990i	1.45373	+	0.663898i
$237$	5.77971	−	6.67014i	0.375433	−	0.433272i
$238$	3.76063	+	0.130885i	0.243765	+	0.00848403i
$239$	−10.9628	+	3.21897i	−0.709124	+	0.208218i	−0.616353	−	0.787470i	$-0.711391\pi$
$239$	−10.9628	+	3.21897i	−0.709124	+	0.208218i	−0.0927711	+	0.995687i	$0.529572\pi$
$240$	−2.92237	+	2.53225i	−0.188638	+	0.163456i
$241$	−15.9870	+	10.2742i	−1.02981	+	0.661821i	−0.942447	−	0.334355i	$-0.891482\pi$
$241$	−15.9870	+	10.2742i	−1.02981	+	0.661821i	−0.0873668	+	0.996176i	$0.527845\pi$
$242$	−2.08851	+	1.34220i	−0.134255	+	0.0862801i
$243$	−0.755750	+	0.654861i	−0.0484814	+	0.0420093i
$244$	−21.5827	+	6.33726i	−1.38169	+	0.405702i
$245$	−0.555026	−	7.56676i	−0.0354593	−	0.483422i
$246$	−1.95623	+	2.25761i	−0.124724	+	0.143940i
$247$	−15.7938	−	7.21278i	−1.00493	−	0.458938i
$248$	−2.01111	+	6.84922i	−0.127706	+	0.434926i
$249$	0.659597	−	0.301228i	0.0418003	−	0.0190895i
$250$	0.367672	+	2.55721i	0.0232536	+	0.161732i
$251$	8.72513	+	5.60730i	0.550725	+	0.353930i	0.786221	−	0.617946i	$-0.212035\pi$
$251$	8.72513	+	5.60730i	0.550725	+	0.353930i	−0.235495	+	0.971875i	$0.575671\pi$
$252$	0.549617	+	5.06879i	0.0346226	+	0.319304i
$253$	17.4252	−	12.6797i	1.09551	−	0.797163i
$254$	−2.38406			−0.149589
$255$	−3.08569	+	4.80143i	−0.193233	+	0.300677i
$256$	−1.49118	−	10.3714i	−0.0931986	−	0.648210i
$257$	−24.9774	+	11.4068i	−1.55805	+	0.711538i	−0.993497	−	0.113859i	$-0.963679\pi$
$257$	−24.9774	+	11.4068i	−1.55805	+	0.711538i	−0.564553	+	0.825397i	$0.690951\pi$
$258$	0.364969	+	0.107165i	0.0227220	+	0.00667177i
$259$	6.16881	−	18.5907i	0.383311	−	1.15517i
$260$	−4.97316	−	4.30927i	−0.308422	−	0.267249i
$261$	−0.266540	+	1.85382i	−0.0164984	+	0.114749i
$262$	1.50606	+	5.12916i	0.0930445	+	0.316880i
$263$	−4.71585	+	4.08631i	−0.290792	+	0.251972i	−0.788023	−	0.615645i	$-0.788895\pi$
$263$	−4.71585	+	4.08631i	−0.290792	+	0.251972i	0.497232	+	0.867618i	$0.334350\pi$
$264$	−4.00949	+	2.57674i	−0.246767	+	0.158587i
$265$	1.08151	+	1.68286i	0.0664364	+	0.103377i
$266$	2.68091	−	2.88475i	0.164377	−	0.176876i
$267$	3.29364	+	11.2171i	0.201567	+	0.686476i
$268$	19.6914	+	2.83119i	1.20284	+	0.172942i
$269$	9.73091	+	8.43188i	0.593304	+	0.514101i	0.898954	−	0.438043i	$-0.144328\pi$
$269$	9.73091	+	8.43188i	0.593304	+	0.514101i	−0.305650	+	0.952144i	$0.598874\pi$
$270$	0.266287	+	0.121609i	0.0162057	+	0.00740090i
$271$	−0.363936	+	1.23945i	−0.0221076	+	0.0752915i	−0.969808	−	0.243870i	$-0.921583\pi$
$271$	−0.363936	+	1.23945i	−0.0221076	+	0.0752915i	0.947700	+	0.319161i	$0.103401\pi$
$272$	−7.80421	−	17.0888i	−0.473199	−	1.03616i
$273$	−8.07473	+	2.06878i	−0.488705	+	0.125208i
$274$	0.410097	−	0.638124i	0.0247749	−	0.0385505i
$275$		−	17.1888i		−	1.03652i
$276$	7.47281	−	5.43767i	0.449810	−	0.327309i
$277$	12.3157			0.739977			0.369988	−	0.929036i	$-0.379362\pi$
$277$	12.3157			0.739977			0.369988	+	0.929036i	$0.379362\pi$
$278$	−1.68218	+	2.61753i	−0.100891	+	0.156989i
$279$	−6.66165	+	0.957801i	−0.398823	+	0.0573421i
$280$	2.61439	−	1.55441i	0.156240	−	0.0928937i
$281$	−6.69105	+	22.7876i	−0.399155	+	1.35940i	0.477650	+	0.878550i	$0.341489\pi$
$281$	−6.69105	+	22.7876i	−0.399155	+	1.35940i	−0.876805	+	0.480846i	$0.840329\pi$
$282$	0.125610	−	0.275047i	0.00747995	−	0.0163788i
$283$	−6.30384	+	7.27502i	−0.374724	+	0.432455i	−0.911519	−	0.411258i	$-0.865089\pi$
$283$	−6.30384	+	7.27502i	−0.374724	+	0.432455i	0.536795	+	0.843713i	$0.319635\pi$
$284$	2.79619	−	19.4479i	0.165923	−	1.15402i
$285$	1.68287	+	5.73132i	0.0996845	+	0.339494i
$286$	−2.50397	−	2.88973i	−0.148063	−	0.170873i
$287$	−22.7683	+	18.3820i	−1.34397	+	1.08506i
$288$	−2.59517	+	1.66782i	−0.152922	+	0.0982771i
$289$	−7.02595	−	8.10838i	−0.413291	−	0.476963i
$290$	0.526063	−	0.154466i	0.0308915	−	0.00907056i
$291$	7.93786	+	1.14129i	0.465326	+	0.0669037i
$292$	20.1425	+	17.4536i	1.17875	+	1.02139i
$293$	0.898909	−	1.96834i	0.0525148	−	0.114991i	−0.881556	−	0.472080i	$-0.843503\pi$
$293$	0.898909	−	1.96834i	0.0525148	−	0.114991i	0.934071	+	0.357089i	$0.116231\pi$
$294$	0.131444	−	1.88605i	0.00766596	−	0.109997i
$295$	12.5610	−	5.73642i	0.731330	−	0.333987i
$296$	7.77250	−	1.11752i	0.451767	−	0.0649543i
$297$	−3.78020	−	2.42939i	−0.219349	−	0.140967i
$298$		−	3.13455i		−	0.181579i
$299$	10.5383	+	10.8278i	0.609443	+	0.626185i
$300$		−	7.37141i		−	0.425589i
$301$	3.33350	+	1.66484i	0.192140	+	0.0959597i
$302$	−0.334454	−	2.32618i	−0.0192457	−	0.133857i
$303$	3.99173	+	8.74068i	0.229319	+	0.502139i
$304$	−18.8651	−	5.53928i	−1.08199	−	0.317700i
$305$	−5.25570	+	11.5084i	−0.300940	+	0.658968i
$306$	−0.931371	+	1.07486i	−0.0532430	+	0.0614457i
$307$	−16.5084	−	2.37356i	−0.942187	−	0.135466i	−0.345931	−	0.938260i	$-0.612437\pi$
$307$	−16.5084	−	2.37356i	−0.942187	−	0.135466i	−0.596256	+	0.802794i	$0.703346\pi$
$308$	−21.1583	+	8.78664i	−1.20561	+	0.500665i
$309$	−7.53297	+	6.52735i	−0.428536	+	0.371328i
$310$	1.06517	+	1.65744i	0.0604975	+	0.0941360i
$311$	8.90159	+	13.8511i	0.504763	+	0.785426i	0.996346	−	0.0854041i	$-0.0272181\pi$
$311$	8.90159	+	13.8511i	0.504763	+	0.785426i	−0.491584	+	0.870830i	$0.663582\pi$
$312$	−2.18830	−	2.52544i	−0.123888	−	0.142975i
$313$	32.5568	−	9.55955i	1.84022	−	0.540338i	0.840224	−	0.542240i	$-0.182424\pi$
$313$	32.5568	−	9.55955i	1.84022	−	0.540338i	0.999998	+	0.00190234i	$0.000605534\pi$
$314$	0.686392	−	4.77396i	0.0387353	−	0.269410i
$315$	2.35703	+	1.63334i	0.132804	+	0.0920283i
$316$	15.4709	+	7.06533i	0.870307	+	0.397456i
$317$	3.56166	+	1.04580i	0.200043	+	0.0587378i	0.380219	−	0.924897i	$-0.375849\pi$
$317$	3.56166	+	1.04580i	0.200043	+	0.0587378i	−0.180176	+	0.983634i	$0.557667\pi$
$318$	0.207078	+	0.453437i	0.0116123	+	0.0254275i
$319$	−8.33022	+	1.19770i	−0.466403	+	0.0670586i
$320$	−5.74628	−	3.69291i	−0.321227	−	0.206440i
$321$	5.62042			0.313701
$322$	−3.08370	+	1.49515i	−0.171848	+	0.0833216i
$323$	−29.0204			−1.61474
$324$	−1.62114	−	1.04184i	−0.0900633	−	0.0578802i
$325$	11.9288	−	1.71511i	0.661693	−	0.0951371i
$326$	−2.55159	−	5.58721i	−0.141320	−	0.309447i
$327$	2.97489	+	0.873506i	0.164512	+	0.0483050i
$328$	−10.6709	−	4.87325i	−0.589204	−	0.269080i
$329$	1.68707	−	2.43457i	0.0930113	−	0.134222i
$330$	−0.187207	+	1.30205i	−0.0103054	+	0.0716757i
$331$	−4.66719	+	1.37041i	−0.256532	+	0.0753246i	−0.407470	−	0.913219i	$-0.633589\pi$
$331$	−4.66719	+	1.37041i	−0.256532	+	0.0753246i	0.150938	+	0.988543i	$0.451771\pi$
$332$	0.915072	+	1.05605i	0.0502211	+	0.0579582i
$333$	4.00256	+	6.22811i	0.219339	+	0.341298i
$334$	−1.24190	−	1.93243i	−0.0679535	−	0.105738i
$335$	8.45630	−	7.32742i	0.462017	−	0.400340i
$336$	−8.71727	+	3.62011i	−0.475566	+	0.197493i
$337$	−1.60868	−	0.231293i	−0.0876302	−	0.0125993i	0.0983602	−	0.995151i	$-0.468640\pi$
$337$	−1.60868	−	0.231293i	−0.0876302	−	0.0125993i	−0.185990	+	0.982552i	$0.559549\pi$
$338$	−0.543724	+	0.627491i	−0.0295747	+	0.0341310i
$339$	−3.67013	+	8.03645i	−0.199334	+	0.436480i
$340$	−10.5531	−	3.09866i	−0.572320	−	0.168048i
$341$	−12.5631	−	27.5093i	−0.680328	−	1.48971i
$342$	0.211833	+	1.47333i	0.0114546	+	0.0796687i
$343$	4.53118	−	17.9574i	0.244661	−	0.969609i
$344$			1.49376i			0.0805381i
$345$	0.441036	−	5.17931i	0.0237446	−	0.278845i
$346$		−	2.62707i		−	0.141232i
$347$	18.0057	+	11.5716i	0.966598	+	0.621195i	0.925816	−	0.377974i	$-0.123379\pi$
$347$	18.0057	+	11.5716i	0.966598	+	0.621195i	0.0407812	+	0.999168i	$0.487015\pi$
$348$	−3.57241	+	0.513636i	−0.191502	+	0.0275338i
$349$	23.7180	−	10.8316i	1.26959	−	0.579804i	0.337262	−	0.941411i	$-0.390499\pi$
$349$	23.7180	−	10.8316i	1.26959	−	0.579804i	0.932331	+	0.361607i	$0.117772\pi$
$350$	−0.482888	+	2.69048i	−0.0258115	+	0.143812i
$351$	1.30878	−	2.86583i	0.0698575	−	0.152967i
$352$	−10.4762	−	9.07771i	−0.558385	−	0.483844i
$353$	−13.1611	−	1.89228i	−0.700495	−	0.100716i	−0.217140	−	0.976140i	$-0.569673\pi$
$353$	−13.1611	−	1.89228i	−0.700495	−	0.100716i	−0.483355	+	0.875424i	$0.660582\pi$
$354$	3.30165	−	0.969452i	0.175481	−	0.0515258i
$355$	−7.23684	−	8.35175i	−0.384091	−	0.443265i
$356$	−18.9522	+	12.1798i	−1.00446	+	0.645530i
$357$	−10.8401	+	8.75181i	−0.573720	+	0.463195i
$358$	3.99878	+	4.61484i	0.211342	+	0.243902i
$359$	4.06200	+	13.8339i	0.214384	+	0.730125i	0.994523	+	0.104518i	$0.0333301\pi$
$359$	4.06200	+	13.8339i	0.214384	+	0.730125i	−0.780139	+	0.625606i	$0.784852\pi$
$360$	−0.163607	+	1.13791i	−0.00862283	+	0.0599731i
$361$	−7.44704	+	8.59434i	−0.391950	+	0.452334i
$362$	−1.13469	+	2.48463i	−0.0596382	+	0.130589i
$363$	2.58964	−	8.81950i	0.135921	−	0.462904i
$364$	−8.20903	−	13.8069i	−0.430270	−	0.723681i
$365$	14.8380	−	2.13338i	0.776657	−	0.111666i
$366$	−1.70446	+	2.65220i	−0.0890937	+	0.138633i
$367$	5.90645			0.308314			0.154157	−	0.988046i	$-0.450734\pi$
$367$	5.90645			0.308314			0.154157	+	0.988046i	$0.450734\pi$
$368$	13.5569	+	10.4381i	0.706702	+	0.544125i
$369$		−	11.0602i		−	0.575770i
$370$	1.17172	−	1.82323i	0.0609147	−	0.0947851i
$371$	1.21192	+	4.73028i	0.0629197	+	0.245584i
$372$	−5.38767	−	11.7973i	−0.279338	−	0.611664i
$373$	1.94395	−	6.62049i	0.100654	−	0.342796i	−0.893733	−	0.448599i	$-0.851923\pi$
$373$	1.94395	−	6.62049i	0.100654	−	0.342796i	0.994387	+	0.105803i	$0.0337413\pi$
$374$	−5.81336	−	2.65487i	−0.300602	−	0.137280i
$375$	−7.22904	−	6.26400i	−0.373306	−	0.323472i
$376$	1.17534	+	0.168989i	0.0606137	+	0.00871494i
$377$	−1.66239	−	5.66158i	−0.0856175	−	0.291586i
$378$	0.523447	+	0.486458i	0.0269232	+	0.0250207i
$379$	2.26030	+	3.51710i	0.116104	+	0.180661i	0.894442	−	0.447185i	$-0.147573\pi$
$379$	2.26030	+	3.51710i	0.116104	+	0.180661i	−0.778338	+	0.627846i	$0.783937\pi$
$380$	−9.68353	+	6.22322i	−0.496754	+	0.319245i
$381$	6.67096	−	5.78042i	0.341763	−	0.296140i
$382$	1.45732	+	4.96319i	0.0745632	+	0.253939i
$383$	5.18273	−	36.0467i	0.264825	−	1.84190i	−0.230353	−	0.973107i	$-0.573988\pi$
$383$	5.18273	−	36.0467i	0.264825	−	1.84190i	0.495178	−	0.868792i	$-0.335103\pi$
$384$	−5.94919	−	5.15500i	−0.303593	−	0.263065i
$385$	−4.05823	+	12.2301i	−0.206826	+	0.623306i
$386$	1.15119	+	0.338020i	0.0585940	+	0.0172048i
$387$	−1.28107	+	0.585044i	−0.0651203	+	0.0297395i
$388$	2.19933	+	15.2967i	0.111654	+	0.776571i
$389$	−0.566956	+	0.882200i	−0.0287458	+	0.0447293i	−0.855329	−	0.518085i	$-0.826645\pi$
$389$	−0.566956	+	0.882200i	−0.0287458	+	0.0447293i	0.826583	+	0.562814i	$0.190281\pi$
$390$	−0.922293			−0.0467021
$391$	23.5400	+	9.14514i	1.19047	+	0.462489i
$392$	7.25203	−	1.59141i	0.366283	−	0.0803782i
$393$	−16.6504	−	10.7005i	−0.839900	−	0.539771i
$394$	−0.0734928	−	0.511154i	−0.00370252	−	0.0257516i
$395$	8.70161	−	3.97389i	0.437826	−	0.199948i
$396$	2.43960	−	8.30851i	0.122594	−	0.417518i
$397$	−2.14138	−	0.977934i	−0.107473	−	0.0490811i	0.360953	−	0.932584i	$-0.382451\pi$
$397$	−2.14138	−	0.977934i	−0.107473	−	0.0490811i	−0.468426	+	0.883503i	$0.655179\pi$
$398$	1.60436	−	1.85153i	0.0804194	−	0.0928089i
$399$	−0.507169	+	14.5721i	−0.0253902	+	0.729518i
$400$	13.0942	−	3.84481i	0.654710	−	0.192240i
$401$	16.9334	−	14.6729i	0.845614	−	0.732728i	−0.119982	−	0.992776i	$-0.538284\pi$
$401$	16.9334	−	14.6729i	0.845614	−	0.732728i	0.965596	+	0.260048i	$0.0837383\pi$
$402$	2.34563	−	1.50745i	0.116990	−	0.0751846i
$403$	17.8376	−	11.4635i	0.888554	−	0.571039i
$404$	−13.9943	+	12.1261i	−0.696242	+	0.603297i
$405$	−1.03996	+	0.305361i	−0.0516763	+	0.0151735i
$406$	1.33754	+	0.0465517i	0.0663808	+	0.00231032i
$407$	−21.7854	+	25.1417i	−1.07986	+	1.24623i
$408$	−5.08050	−	2.32019i	−0.251522	−	0.114866i
$409$	1.29893	−	4.42376i	0.0642281	−	0.218741i	−0.921125	−	0.389267i	$-0.872728\pi$
$409$	1.29893	−	4.42376i	0.0642281	−	0.218741i	0.985353	+	0.170526i	$0.0545467\pi$
$410$	−2.94519	+	1.34502i	−0.145452	+	0.0664259i
$411$	0.399688	+	2.77989i	0.0197151	+	0.137122i
$412$	−16.1588	−	10.3846i	−0.796086	−	0.511613i
$413$	33.5114	−	3.63369i	1.64899	−	0.178802i
$414$	0.292459	−	1.26185i	0.0143736	−	0.0620168i
$415$	0.785941			0.0385803
$416$	5.25452	−	8.17619i	0.257624	−	0.400871i
$417$	−1.63948	−	11.4029i	−0.0802858	−	0.558400i
$418$	−6.08412	+	2.77852i	−0.297584	+	0.135902i
$419$	22.6903	+	6.66248i	1.10849	+	0.325483i	0.784222	−	0.620480i	$-0.213062\pi$
$419$	22.6903	+	6.66248i	1.10849	+	0.325483i	0.324273	+	0.945964i	$0.394880\pi$
$420$	−1.74037	+	5.24490i	−0.0849214	+	0.255925i
$421$	0.466757	+	0.404448i	0.0227484	+	0.0197116i	0.666161	−	0.745808i	$-0.267936\pi$
$421$	0.466757	+	0.404448i	0.0227484	+	0.0197116i	−0.643412	+	0.765520i	$0.722482\pi$
$422$	0.728078	−	5.06390i	0.0354423	−	0.246507i
$423$	0.315407	+	1.07418i	0.0153356	+	0.0522282i
$424$	−1.47943	+	1.28194i	−0.0718477	+	0.0622564i
$425$	16.9454	−	10.8901i	0.821970	−	0.528248i
$426$	−1.48881	−	2.31663i	−0.0721331	−	0.112241i
$427$	−21.0237	+	22.6223i	−1.01741	+	1.09477i
$428$	3.05140	+	10.3921i	0.147495	+	0.502322i
$429$	14.0129	+	2.01476i	0.676551	+	0.0972733i
$430$	0.311579	+	0.269985i	0.0150257	+	0.0130198i
$431$	9.67073	+	4.41648i	0.465823	+	0.212734i	0.634478	−	0.772941i	$-0.281215\pi$
$431$	9.67073	+	4.41648i	0.465823	+	0.212734i	−0.168655	+	0.985675i	$0.553942\pi$
$432$	1.00512	−	3.42312i	0.0483588	−	0.164695i
$433$	−7.20625	−	15.7795i	−0.346310	−	0.758314i	−0.999999	−	0.00154997i	$-0.999507\pi$
$433$	−7.20625	−	15.7795i	−0.346310	−	0.758314i	0.653689	−	0.756764i	$-0.273221\pi$
$434$	1.19361	+	4.65882i	0.0572951	+	0.223631i
$435$	−1.09748	+	1.70772i	−0.0526202	+	0.0818787i
$436$			5.97479i			0.286140i
$437$	23.3667	−	12.3512i	1.11778	−	0.590838i
$438$	3.73550			0.178489
$439$	−7.28174	+	11.3306i	−0.347538	+	0.540780i	−0.970385	−	0.241564i	$-0.922340\pi$
$439$	−7.28174	+	11.3306i	−0.347538	+	0.540780i	0.622847	+	0.782344i	$0.285976\pi$
$440$	−5.11324	+	0.735172i	−0.243764	+	0.0350480i
$441$	4.20513	+	5.59615i	0.200244	+	0.266483i
$442$	1.26240	−	4.29932i	0.0600460	−	0.204498i
$443$	−2.45335	+	5.37209i	−0.116562	+	0.255236i	−0.958916	−	0.283689i	$-0.908442\pi$
$443$	−2.45335	+	5.37209i	−0.116562	+	0.255236i	0.842354	+	0.538924i	$0.181169\pi$
$444$	−9.34269	+	10.7820i	−0.443384	+	0.511693i
$445$	−1.80329	+	12.5422i	−0.0854843	+	0.594556i
$446$	1.70690	+	5.81317i	0.0808241	+	0.275262i
$447$	7.60005	+	8.77092i	0.359470	+	0.414850i
$448$	−10.4740	−	12.9733i	−0.494852	−	0.612931i
$449$	8.93655	−	5.74317i	0.421742	−	0.271037i	−0.312510	−	0.949915i	$-0.601170\pi$
$449$	8.93655	−	5.74317i	0.421742	−	0.271037i	0.734252	+	0.678877i	$0.237533\pi$
$450$	−0.676572	−	0.780805i	−0.0318939	−	0.0368075i
$451$	47.6861	−	14.0019i	2.24545	−	0.659324i
$452$	−16.8519	−	2.42294i	−0.792647	−	0.113965i
$453$	6.57593	+	5.69807i	0.308964	+	0.267719i
$454$	−1.19700	+	2.62106i	−0.0561780	+	0.123013i
$455$	−8.89253	−	1.59604i	−0.416888	−	0.0748234i
$456$	−5.31712	+	2.42825i	−0.248997	+	0.113713i
$457$	−32.2218	+	4.63280i	−1.50727	+	0.216713i	−0.845899	−	0.533344i	$-0.820935\pi$
$457$	−32.2218	+	4.63280i	−1.50727	+	0.216713i	−0.661374	+	0.750057i	$0.730026\pi$
$458$	0.795095	+	0.510976i	0.0371523	+	0.0238764i
$459$		−	5.26583i		−	0.245788i
$460$	9.81595	−	1.99644i	0.457671	−	0.0930847i
$461$			4.03455i			0.187908i	0.995577	+	0.0939540i	$0.0299507\pi$
$461$			4.03455i			0.187908i	−0.995577	+	0.0939540i	$0.970049\pi$
$462$	−1.43470	+	2.87269i	−0.0667483	+	0.133650i
$463$	−4.02965	−	28.0268i	−0.187274	−	1.30252i	−0.839028	−	0.544088i	$-0.816876\pi$
$463$	−4.02965	−	28.0268i	−0.187274	−	1.30252i	0.651755	−	0.758430i	$-0.274033\pi$
$464$	−2.77571	−	6.07795i	−0.128859	−	0.282162i
$465$	−6.99913	−	2.05513i	−0.324577	−	0.0953043i
$466$	−1.39581	+	3.05639i	−0.0646594	+	0.141584i
$467$	−2.48941	+	2.87293i	−0.115196	+	0.132943i	−0.810419	−	0.585851i	$-0.800760\pi$
$467$	−2.48941	+	2.87293i	−0.115196	+	0.132943i	0.695223	+	0.718795i	$0.255306\pi$
$468$	6.00945	+	0.864028i	0.277787	+	0.0399397i
$469$	25.2247	−	10.4753i	1.16477	−	0.483705i
$470$	0.247683	−	0.214619i	0.0114248	−	0.00989961i
$471$	9.65436	+	15.0225i	0.444849	+	0.692199i
$472$	7.30575	+	11.3680i	0.336274	+	0.523253i
$473$	−4.14422	−	4.78269i	−0.190552	−	0.219908i
$474$	2.28721	−	0.671586i	0.105055	−	0.0308470i
$475$	3.00016	−	20.8665i	0.137657	−	0.957422i
$476$	−22.0673	−	15.2918i	−1.01145	−	0.700900i
$477$	−1.67884	−	0.766701i	−0.0768688	−	0.0351048i
$478$	−2.96093	−	0.869409i	−0.135430	−	0.0397658i
$479$	4.15124	+	9.08995i	0.189675	+	0.415330i	0.980448	−	0.196780i	$-0.0630483\pi$
$479$	4.15124	+	9.08995i	0.189675	+	0.415330i	−0.790773	+	0.612110i	$0.790321\pi$
$480$	−3.30958	+	0.475846i	−0.151061	+	0.0217193i
$481$	−19.6219	−	12.6102i	−0.894681	−	0.574977i
$482$	−5.13272			−0.233789
$483$	5.00348	−	11.6604i	0.227666	−	0.530567i
$484$	17.7131			0.805143
$485$	7.31224	+	4.69929i	0.332032	+	0.213384i
$486$	−0.267340	+	0.0384377i	−0.0121268	+	0.00174357i
$487$	8.16380	+	17.8762i	0.369937	+	0.810049i	0.999453	+	0.0330617i	$0.0105258\pi$
$487$	8.16380	+	17.8762i	0.369937	+	0.810049i	−0.629516	+	0.776987i	$0.716747\pi$
$488$	−11.8792	−	3.48805i	−0.537746	−	0.157897i
$489$	20.6865	+	9.44722i	0.935477	+	0.427218i
$490$	0.978798	−	1.80032i	0.0442176	−	0.0813300i
$491$	4.89665	−	34.0570i	0.220983	−	1.53697i	−0.513350	−	0.858180i	$-0.671596\pi$
$491$	4.89665	−	34.0570i	0.220983	−	1.53697i	0.734333	−	0.678790i	$-0.237495\pi$
$492$	20.4502	−	6.00472i	0.921967	−	0.270714i
$493$	−6.45843	−	7.45343i	−0.290873	−	0.335685i
$494$	−2.53534	−	3.94507i	−0.114071	−	0.177497i
$495$	−2.63314	−	4.09724i	−0.118351	−	0.184157i
$496$	18.1461	−	15.7237i	0.814784	−	0.706014i
$497$	−10.3458	−	24.9128i	−0.464073	−	1.11749i
$498$	0.193855	+	0.0278722i	0.00868686	+	0.00124898i
$499$	8.97398	−	10.3565i	0.401731	−	0.463622i	−0.518455	−	0.855105i	$-0.673492\pi$
$499$	8.97398	−	10.3565i	0.401731	−	0.463622i	0.920185	+	0.391483i	$0.128038\pi$
$500$	7.65735	−	16.7673i	0.342447	−	0.749854i
$501$	8.16038	+	2.39610i	0.364579	+	0.107050i
$502$	1.16368	+	2.54811i	0.0519377	+	0.113728i
$503$	3.88849	+	27.0450i	0.173379	+	1.20588i	0.871681	+	0.490074i	$0.163030\pi$
$503$	3.88849	+	27.0450i	0.173379	+	1.20588i	−0.698302	+	0.715804i	$0.746061\pi$
$504$	−1.25383	+	2.51054i	−0.0558502	+	0.111828i
$505$			10.4149i			0.463458i
$506$	5.81075	−	0.336534i	0.258319	−	0.0149608i
$507$		−	3.07413i		−	0.136527i
$508$	14.3097	+	9.19628i	0.634890	+	0.408019i
$509$	−2.11143	+	0.303578i	−0.0935875	+	0.0134558i	−0.188949	−	0.981987i	$-0.560508\pi$
$509$	−2.11143	+	0.303578i	−0.0935875	+	0.0134558i	0.0953620	+	0.995443i	$0.469599\pi$
$510$	−1.40222	+	0.640373i	−0.0620914	+	0.0283562i
$511$	36.0169	+	6.46433i	1.59329	+	0.285965i
$512$	7.71584	−	16.8953i	0.340995	−	0.746675i
$513$	−4.16499	−	3.60899i	−0.183889	−	0.159341i
$514$	−7.34085	−	1.05546i	−0.323791	−	0.0465541i
$515$	−10.3659	+	3.04370i	−0.456776	+	0.134122i
$516$	−1.77725	−	2.05106i	−0.0782391	−	0.0902928i
$517$	−4.23203	+	2.71976i	−0.186124	+	0.119615i
$518$	4.11628	−	3.32329i	0.180859	−	0.146017i
$519$	6.36962	+	7.35093i	0.279595	+	0.322670i
$520$	−1.02040	−	3.47518i	−0.0447477	−	0.152397i
$521$	5.45094	−	37.9121i	0.238810	−	1.66096i	−0.419158	−	0.907913i	$-0.637675\pi$
$521$	5.45094	−	37.9121i	0.238810	−	1.66096i	0.657968	−	0.753046i	$-0.271416\pi$
$522$	−0.331259	+	0.382294i	−0.0144988	+	0.0167325i
$523$	6.97867	−	15.2812i	0.305156	−	0.668199i	−0.693476	−	0.720479i	$-0.743922\pi$
$523$	6.97867	−	15.2812i	0.305156	−	0.668199i	0.998632	+	0.0522808i	$0.0166491\pi$
$524$	10.7455	−	36.5959i	0.469420	−	1.59870i
$525$	−5.17216	−	8.69916i	−0.225731	−	0.379662i
$526$	−1.66819	+	0.239850i	−0.0727367	+	0.0104580i
$527$	19.1602	−	29.8139i	0.834632	−	1.29871i
$528$	16.0313			0.697671
$529$	−22.8462	+	2.65522i	−0.993314	+	0.115444i
$530$			0.540291i			0.0234688i
$531$	−6.88796	+	10.7179i	−0.298912	+	0.465116i
$532$	−27.2191	+	6.97364i	−1.18010	+	0.302346i
$533$	14.4754	+	31.6966i	0.626997	+	1.37293i
$534$	−0.889577	+	3.02962i	−0.0384958	+	0.131105i
$535$	5.54130	+	2.53063i	0.239571	+	0.109409i
$536$	8.27518	+	7.17049i	0.357433	+	0.309718i
$537$	−22.3783	−	3.21752i	−0.965697	−	0.138846i
$538$	0.979761	+	3.33676i	0.0422405	+	0.143858i
$539$	−18.8043	+	25.2151i	−0.809957	+	1.08609i
$540$	−1.12922	−	1.75710i	−0.0485940	−	0.0756137i
$541$	−38.3527	+	24.6478i	−1.64891	+	1.05969i	−0.716957	+	0.697117i	$0.754466\pi$
$541$	−38.3527	+	24.6478i	−1.64891	+	1.05969i	−0.931955	+	0.362574i	$0.881898\pi$
$542$	−0.263678	+	0.228478i	−0.0113259	+	0.00981398i
$543$	−2.84922	−	9.70355i	−0.122272	−	0.416419i
$544$	2.31183	−	16.0791i	0.0991190	−	0.689388i
$545$	2.53971	+	2.20067i	0.108789	+	0.0942663i
$546$	−2.13677	−	0.709028i	−0.0914455	−	0.0303436i
$547$	11.3960	+	3.34618i	0.487260	+	0.143072i	0.516129	−	0.856511i	$-0.327372\pi$
$547$	11.3960	+	3.34618i	0.487260	+	0.143072i	−0.0288693	+	0.999583i	$0.509191\pi$
$548$	−4.92300	+	2.24826i	−0.210300	+	0.0960408i
$549$	−1.66120	−	11.5539i	−0.0708982	−	0.493108i
$550$	2.50993	−	3.90553i	0.107024	−	0.166532i
$551$	−10.3216			−0.439716
$552$	5.07821	−	0.294109i	0.216143	−	0.0125181i
$553$	23.2150	−	2.51723i	0.987201	−	0.107044i
$554$	2.79829	+	1.79835i	0.118888	+	0.0764046i
$555$	1.14198	+	7.94261i	0.0484741	+	0.337145i
$556$	20.1937	−	9.22215i	0.856403	−	0.391106i
$557$	1.50719	−	5.13302i	0.0638617	−	0.217493i	−0.921380	−	0.388664i	$-0.872937\pi$
$557$	1.50719	−	5.13302i	0.0638617	−	0.217493i	0.985241	+	0.171171i	$0.0547550\pi$
$558$	−1.65348	−	0.755118i	−0.0699973	−	0.0319667i
$559$	2.90563	−	3.35327i	0.122895	−	0.141828i
$560$	−10.2245	−	0.355855i	−0.432065	−	0.0150376i
$561$	22.7037	−	6.66640i	0.958550	−	0.281456i
$562$	−4.84778	+	4.20063i	−0.204491	+	0.177193i
$563$	−11.6071	+	7.45945i	−0.489182	+	0.314378i	−0.761876	−	0.647722i	$-0.775722\pi$
$563$	−11.6071	+	7.45945i	−0.489182	+	0.314378i	0.272694	+	0.962101i	$0.412085\pi$
$564$	−1.81491	+	1.16637i	−0.0764213	+	0.0491130i
$565$	−7.23692	+	6.27082i	−0.304459	+	0.263816i
$566$	−2.49463	+	0.732488i	−0.104857	+	0.0307888i
$567$	−2.64415	−	0.0920273i	−0.111044	−	0.00386478i
$568$	7.08184	−	8.17288i	0.297147	−	0.342926i
$569$	21.2851	+	9.72056i	0.892316	+	0.407507i	0.808172	−	0.588946i	$-0.200457\pi$
$569$	21.2851	+	9.72056i	0.892316	+	0.407507i	0.0841443	+	0.996454i	$0.473184\pi$
$570$	−0.454525	+	1.54797i	−0.0190380	+	0.0648373i
$571$	−43.2169	+	19.7365i	−1.80857	+	0.825946i	−0.859309	+	0.511457i	$0.829106\pi$
$571$	−43.2169	+	19.7365i	−1.80857	+	0.825946i	−0.949261	+	0.314489i	$0.898167\pi$
$572$	3.88254	+	27.0036i	0.162337	+	1.12908i
$573$	−16.1116	−	10.3543i	−0.673072	−	0.432557i
$574$	−7.85744	+	0.851994i	−0.327963	+	0.0355616i
$575$	−9.00923	+	15.9806i	−0.375711	+	0.666435i
$576$	6.30207			0.262586
$577$	−7.29062	+	11.3444i	−0.303513	+	0.472275i	−0.959188	−	0.282768i	$-0.908747\pi$
$577$	−7.29062	+	11.3444i	−0.303513	+	0.472275i	0.655676	+	0.755043i	$0.272384\pi$
$578$	−0.412395	−	2.86827i	−0.0171534	−	0.119304i
$579$	−4.04076	+	1.84535i	−0.167928	+	0.0766903i
$580$	−3.75339	−	1.10209i	−0.155851	−	0.0457620i
$581$	1.82087	+	0.604205i	0.0755426	+	0.0250667i
$582$	1.63694	+	1.41841i	0.0678532	+	0.0587952i
$583$	1.18027	−	8.20896i	0.0488818	−	0.339981i
$584$	4.13288	+	14.0753i	0.171020	+	0.582440i
$585$	2.58071	−	2.23620i	0.106699	−	0.0924554i
$586$	0.491664	−	0.315973i	0.0203104	−	0.0130527i
$587$	−0.327769	−	0.510018i	−0.0135285	−	0.0210507i	0.834423	−	0.551124i	$-0.185801\pi$
$587$	−0.327769	−	0.510018i	−0.0135285	−	0.0210507i	−0.847952	+	0.530073i	$0.822164\pi$
$588$	−8.06421	+	10.8135i	−0.332562	+	0.445941i
$589$	−10.4496	−	35.5880i	−0.430567	−	1.46638i
$590$	3.69167	+	0.530782i	0.151984	+	0.0218520i
$591$	1.44499	+	1.25209i	0.0594390	+	0.0515042i
$592$	−24.0257	−	10.9722i	−0.987448	−	0.450953i
$593$	−5.35710	+	18.2446i	−0.219990	+	0.749217i	0.773348	+	0.633981i	$0.218580\pi$
$593$	−5.35710	+	18.2446i	−0.219990	+	0.749217i	−0.993338	+	0.115235i	$0.963238\pi$
$594$	−0.504171	−	1.10398i	−0.0206864	−	0.0452968i
$595$	−14.6281	+	3.74777i	−0.599692	+	0.153644i
$596$	−12.0912	+	18.8143i	−0.495275	+	0.770663i
$597$			9.07080i			0.371243i
$598$	0.813352	+	3.99902i	0.0332605	+	0.163532i
$599$	−45.3081			−1.85124			−0.925620	−	0.378453i	$-0.876456\pi$
$599$	−45.3081			−1.85124			−0.925620	+	0.378453i	$0.876456\pi$
$600$	2.19351	−	3.41317i	0.0895498	−	0.139342i
$601$	5.12812	−	0.737313i	0.209181	−	0.0300756i	−0.0369278	−	0.999318i	$-0.511757\pi$
$601$	5.12812	−	0.737313i	0.209181	−	0.0300756i	0.246108	+	0.969242i	$0.420848\pi$
$602$	0.514314	+	0.865035i	0.0209619	+	0.0352562i
$603$	−2.90846	+	9.90529i	−0.118441	+	0.403375i
$604$	−6.96554	+	15.2524i	−0.283424	+	0.620611i
$605$	6.52421	−	7.52934i	0.265247	−	0.306111i
$606$	−0.369349	+	2.56888i	−0.0150038	+	0.104354i
$607$	3.79079	+	12.9103i	0.153864	+	0.524011i	0.999959	−	0.00901974i	$-0.00287111\pi$
$607$	3.79079	+	12.9103i	0.153864	+	0.524011i	−0.846096	+	0.533031i	$0.821053\pi$
$608$	−11.1333	−	12.8485i	−0.451516	−	0.521077i
$609$	−3.85549	+	3.11274i	−0.156232	+	0.126135i
$610$	−2.87463	+	1.84742i	−0.116391	+	0.0747997i
$611$	−2.30976	−	2.66561i	−0.0934429	−	0.107839i
$612$	9.73647	−	2.85889i	0.393574	−	0.115564i
$613$	7.30054	+	1.04966i	0.294866	+	0.0423953i	0.288160	−	0.957582i	$-0.406956\pi$
$613$	7.30054	+	1.04966i	0.294866	+	0.0423953i	0.00670569	+	0.999978i	$0.497865\pi$
$614$	−3.40435	−	2.94989i	−0.137389	−	0.119048i
$615$	4.97991	−	10.9045i	0.200809	−	0.439711i
$616$	−12.4116	−	2.22763i	−0.500076	−	0.0897539i
$617$	33.3461	−	15.2286i	1.34246	−	0.613082i	0.390871	−	0.920446i	$-0.372174\pi$
$617$	33.3461	−	15.2286i	1.34246	−	0.613082i	0.951592	+	0.307363i	$0.0994467\pi$
$618$	−2.66473	+	0.383130i	−0.107191	+	0.0154117i
$619$	11.1866	+	7.18916i	0.449626	+	0.288957i	0.745791	−	0.666180i	$-0.232072\pi$
$619$	11.1866	+	7.18916i	0.449626	+	0.288957i	−0.296166	+	0.955137i	$0.595708\pi$
$620$		−	14.0571i		−	0.564546i
$621$	2.24116	+	4.23995i	0.0899346	+	0.170143i
$622$			4.44699i			0.178308i
$623$	−13.8199	+	27.6715i	−0.553682	+	1.10863i
$624$	1.59961	+	11.1255i	0.0640357	+	0.445378i
$625$	3.63841	+	7.96701i	0.145537	+	0.318681i
$626$	8.79326	+	2.58193i	0.351449	+	0.103195i
$627$	10.2874	−	22.5263i	0.410840	−	0.899614i
$628$	−22.5350	+	26.0067i	−0.899243	+	1.03778i
$629$	−38.5881	−	5.54812i	−1.53861	−	0.221218i
$630$	0.297047	+	0.715295i	0.0118347	+	0.0284980i
$631$	5.37572	−	4.65809i	0.214004	−	0.185435i	−0.541262	−	0.840854i	$-0.682053\pi$
$631$	5.37572	−	4.65809i	0.214004	−	0.185435i	0.755266	+	0.655419i	$0.227508\pi$
$632$	5.06104	+	7.87514i	0.201318	+	0.313256i
$633$	10.2407	+	15.9348i	0.407031	+	0.633353i
$634$	0.656549	+	0.757698i	0.0260749	+	0.0300920i
$635$	9.17971	−	2.69541i	0.364286	−	0.106964i
$636$	0.506159	−	3.52041i	0.0200705	−	0.139594i
$637$	−19.3753	−	10.5340i	−0.767678	−	0.417372i
$638$	−2.06763	−	0.944255i	−0.0818582	−	0.0373834i
$639$	9.78283	+	2.87250i	0.387003	+	0.113634i
$640$	−3.54437	−	7.76108i	−0.140103	−	0.306784i
$641$	25.9394	−	3.72952i	1.02454	−	0.147307i	0.390499	−	0.920603i	$-0.372302\pi$
$641$	25.9394	−	3.72952i	1.02454	−	0.147307i	0.634045	+	0.773296i	$0.281393\pi$
$642$	1.27704	+	0.820702i	0.0504006	+	0.0323905i
$643$	18.8578			0.743678			0.371839	−	0.928297i	$-0.378727\pi$
$643$	18.8578			0.743678			0.371839	+	0.928297i	$0.378727\pi$
$644$	24.2765	+	2.92080i	0.956627	+	0.115096i
$645$	−1.52645			−0.0601040
$646$	−6.59382	−	4.23759i	−0.259430	−	0.166726i
$647$	−13.4429	+	1.93280i	−0.528496	+	0.0759863i	−0.401398	−	0.915904i	$-0.631475\pi$
$647$	−13.4429	+	1.93280i	−0.528496	+	0.0759863i	−0.127098	+	0.991890i	$0.540566\pi$
$648$	−0.440612	−	0.964806i	−0.0173089	−	0.0379011i
$649$	−54.9302	−	16.1290i	−2.15620	−	0.633117i
$650$	2.96084	+	1.35217i	0.116134	+	0.0530365i
$651$	−14.6357	−	10.1420i	−0.573619	−	0.397498i
$652$	−6.23685	+	43.3783i	−0.244254	+	1.69882i
$653$	−17.4593	+	5.12651i	−0.683235	+	0.200616i	−0.604888	−	0.796310i	$-0.706782\pi$
$653$	−17.4593	+	5.12651i	−0.683235	+	0.200616i	−0.0783464	+	0.996926i	$0.524964\pi$
$654$	0.548385	+	0.632870i	0.0214435	+	0.0247472i
$655$	−11.5980	−	18.0468i	−0.453171	−	0.705147i
$656$	21.3330	+	33.1948i	0.832913	+	1.29604i
$657$	−10.4525	+	9.05713i	−0.407790	+	0.353352i
$658$	0.738825	−	0.306819i	0.0288024	−	0.0119611i
$659$	7.42513	+	1.06757i	0.289242	+	0.0415867i	0.285409	−	0.958406i	$-0.407871\pi$
$659$	7.42513	+	1.06757i	0.289242	+	0.0415867i	0.00383348	+	0.999993i	$0.498780\pi$
$660$	6.14621	−	7.09310i	0.239241	−	0.276099i
$661$	7.89523	−	17.2882i	0.307089	−	0.672431i	−0.691671	−	0.722213i	$-0.743125\pi$
$661$	7.89523	−	17.2882i	0.307089	−	0.672431i	0.998760	+	0.0497815i	$0.0158525\pi$
$662$	−1.26056	−	0.370133i	−0.0489930	−	0.0143856i
$663$	6.89181	+	15.0909i	0.267656	+	0.586084i
$664$	0.109455	+	0.761279i	0.00424769	+	0.0295434i
$665$	−7.06120	+	14.1386i	−0.273822	+	0.548272i
$666$			1.99957i			0.0774818i
$667$	8.37243	+	3.25264i	0.324182	+	0.125943i
$668$			16.3894i			0.634123i
$669$	−18.8708	−	12.1275i	−0.729588	−	0.468878i
$670$	2.99135	−	0.430091i	0.115566	−	0.0166159i
$671$	47.7117	−	21.7892i	1.84189	−	0.841163i
$672$	−8.03348	−	1.44185i	−0.309898	−	0.0556207i
$673$	−3.26764	+	7.15514i	−0.125958	+	0.275810i	−0.962097	−	0.272708i	$-0.912081\pi$
$673$	−3.26764	+	7.15514i	−0.125958	+	0.275810i	0.836138	+	0.548518i	$0.184808\pi$
$674$	−0.331740	−	0.287454i	−0.0127781	−	0.0110723i
$675$	3.78629	+	0.544387i	0.145734	+	0.0209535i
$676$	5.68404	−	1.66898i	0.218617	−	0.0641917i
$677$	−1.86548	−	2.15288i	−0.0716963	−	0.0827420i	0.718768	−	0.695250i	$-0.244706\pi$
$677$	−1.86548	−	2.15288i	−0.0716963	−	0.0827420i	−0.790465	+	0.612508i	$0.790161\pi$
$678$	−2.00740	+	1.29008i	−0.0770936	+	0.0495450i
$679$	13.3284	+	16.5088i	0.511497	+	0.633548i
$680$	−3.96430	−	4.57505i	−0.152024	−	0.175445i
$681$	−3.00567	−	10.2364i	−0.115178	−	0.392259i
$682$	1.16244	−	8.08495i	0.0445122	−	0.309589i
$683$	4.52163	−	5.21824i	0.173015	−	0.199670i	−0.662619	−	0.748957i	$-0.730555\pi$
$683$	4.52163	−	5.21824i	0.173015	−	0.199670i	0.835634	+	0.549287i	$0.185100\pi$
$684$	4.41176	−	9.66041i	0.168688	−	0.369375i
$685$	−0.857599	+	2.92072i	−0.0327672	+	0.111595i
$686$	3.65171	−	3.41852i	0.139423	−	0.130520i
$687$	−3.46371	+	0.498006i	−0.132149	+	0.0190001i
$688$	2.71641	−	4.22682i	0.103562	−	0.161146i
$689$	5.81471			0.221523
$690$	0.856499	−	1.11241i	0.0326064	−	0.0423487i
$691$			1.87878i			0.0714722i	0.999361	+	0.0357361i	$0.0113776\pi$
$691$			1.87878i			0.0714722i	−0.999361	+	0.0357361i	$0.988622\pi$
$692$	−10.1337	+	15.7683i	−0.385224	+	0.599421i
$693$	−2.95065	−	11.5168i	−0.112086	−	0.437487i
$694$	2.40145	+	5.25844i	0.0911577	+	0.199608i
$695$	3.51780	−	11.9805i	0.133438	−	0.454447i
$696$	−1.80697	−	0.825217i	−0.0684931	−	0.0312798i
$697$	44.0156	+	38.1398i	1.66721	+	1.44465i
$698$	6.97069	+	1.00223i	0.263845	+	0.0379351i
$699$	−3.50487	−	11.9365i	−0.132566	−	0.451480i
$700$	13.2766	−	14.2862i	0.501810	−	0.539966i
$701$	−20.2576	−	31.5215i	−0.765120	−	1.19055i	−0.976997	−	0.213253i	$-0.931594\pi$
$701$	−20.2576	−	31.5215i	−0.765120	−	1.19055i	0.211877	−	0.977296i	$-0.432042\pi$
$702$	0.715845	−	0.460045i	0.0270178	−	0.0173633i
$703$	−30.8350	+	26.7187i	−1.16296	+	1.00771i
$704$	7.97826	+	27.1714i	0.300692	+	1.02406i
$705$	−0.172687	+	1.20107i	−0.00650379	+	0.0452348i
$706$	−2.71407	−	2.35175i	−0.102145	−	0.0885094i
$707$	−8.00665	+	24.1294i	−0.301121	+	0.907479i
$708$	−23.5568	−	6.91691i	−0.885320	−	0.259953i
$709$	−36.7527	+	16.7844i	−1.38027	+	0.630350i	−0.960756	−	0.277396i	$-0.910529\pi$
$709$	−36.7527	+	16.7844i	−1.38027	+	0.630350i	−0.419519	+	0.907746i	$0.637801\pi$
$710$	−0.424774	−	2.95437i	−0.0159415	−	0.110875i
$711$	−4.77162	+	7.42479i	−0.178950	+	0.278451i
$712$	−12.3998			−0.464701
$713$	−2.73856	+	32.1603i	−0.102560	+	1.20441i
$714$	−3.74097	+	0.405640i	−0.140002	+	0.0151807i
$715$	12.9085	+	8.29579i	0.482751	+	0.310245i
$716$	−6.20033	−	43.1242i	−0.231717	−	1.61163i
$717$	10.3931	−	4.74637i	0.388138	−	0.177256i
$718$	−1.09710	+	3.73639i	−0.0409435	+	0.139441i
$719$	−28.7094	−	13.1112i	−1.07068	−	0.488964i	−0.199486	−	0.979901i	$-0.563927\pi$
$719$	−28.7094	−	13.1112i	−1.07068	−	0.488964i	−0.871195	+	0.490937i	$0.836655\pi$
$720$	2.53225	−	2.92237i	0.0943712	−	0.108910i
$721$	−26.3557	−	0.917286i	−0.981537	−	0.0341615i
$722$	−2.94703	+	0.865325i	−0.109677	+	0.0322041i
$723$	14.3621	−	12.4448i	0.534133	−	0.462829i
$724$	16.3949	−	10.5364i	0.609312	−	0.391581i
$725$	6.02693	−	3.87327i	0.223834	−	0.143850i
$726$	1.87624	−	1.62577i	0.0696337	−	0.0603379i
$727$	−33.7177	+	9.90040i	−1.25052	+	0.367186i	−0.838958	−	0.544196i	$-0.816835\pi$
$727$	−33.7177	+	9.90040i	−1.25052	+	0.367186i	−0.411562	+	0.911382i	$0.635016\pi$
$728$	0.307521	−	8.83577i	0.0113975	−	0.327476i
$729$	0.654861	−	0.755750i	0.0242541	−	0.0279907i
$730$	3.68292	+	1.68193i	0.136311	+	0.0622511i
$731$	2.08934	−	7.11565i	0.0772772	−	0.263182i
$732$	20.4612	−	9.34430i	0.756267	−	0.345375i
$733$	4.24969	+	29.5572i	0.156966	+	1.09172i	0.904184	+	0.427143i	$0.140480\pi$
$733$	4.24969	+	29.5572i	0.156966	+	1.09172i	−0.747218	+	0.664579i	$0.768611\pi$
$734$	1.34202	+	0.862467i	0.0495350	+	0.0318342i
$735$	1.62624	+	7.41075i	0.0599847	+	0.273350i
$736$	4.98191	+	13.9306i	0.183636	+	0.513488i
$737$	−46.3888			−1.70875
$738$	1.61502	−	2.51303i	0.0594498	−	0.0925058i
$739$	3.72120	+	25.8815i	0.136887	+	0.952067i	0.936279	+	0.351257i	$0.114246\pi$
$739$	3.72120	+	25.8815i	0.136887	+	0.952067i	−0.799392	+	0.600809i	$0.794845\pi$
$740$	−14.0658	+	6.42365i	−0.517070	+	0.236138i
$741$	16.6595	+	4.89168i	0.612003	+	0.179700i
$742$	−0.415358	+	1.25175i	−0.0152483	+	0.0459532i
$743$	−7.25393	−	6.28557i	−0.266121	−	0.230595i	0.511570	−	0.859241i	$-0.329064\pi$
$743$	−7.25393	−	6.28557i	−0.266121	−	0.230595i	−0.777691	+	0.628646i	$0.783609\pi$
$744$	1.01590	−	7.06572i	0.0372446	−	0.259042i
$745$	3.54390	+	12.0694i	0.129838	+	0.442189i
$746$	1.40843	−	1.22041i	0.0515661	−	0.0446823i
$747$	−0.610014	+	0.392032i	−0.0223192	+	0.0143437i
$748$	24.6522	+	38.3596i	0.901376	+	1.40257i
$749$	10.8927	+	10.1229i	0.398009	+	0.369884i
$750$	−0.727859	−	2.47886i	−0.0265777	−	0.0905152i
$751$	−23.5208	−	3.38177i	−0.858284	−	0.123403i	−0.300898	−	0.953656i	$-0.597287\pi$
$751$	−23.5208	−	3.38177i	−0.858284	−	0.123403i	−0.557386	+	0.830254i	$0.688196\pi$
$752$	−3.01850	−	2.61555i	−0.110074	−	0.0953792i
$753$	−9.43432	−	4.30851i	−0.343806	−	0.157011i
$754$	0.448994	−	1.52913i	0.0163514	−	0.0556877i
$755$	3.91776	+	8.57870i	0.142582	+	0.312211i
$756$	−1.26539	−	4.93898i	−0.0460217	−	0.179629i
$757$	−5.87141	+	9.13609i	−0.213400	+	0.332057i	−0.931407	−	0.363979i	$-0.881418\pi$
$757$	−5.87141	+	9.13609i	−0.213400	+	0.332057i	0.718007	+	0.696036i	$0.245054\pi$
$758$			1.12918i			0.0410138i
$759$	−15.4434	+	15.0305i	−0.560559	+	0.545571i
$760$	−6.33559			−0.229816
$761$	−15.0257	+	23.3805i	−0.544682	+	0.847541i	−0.999064	−	0.0432657i	$-0.986224\pi$
$761$	−15.0257	+	23.3805i	−0.544682	+	0.847541i	0.454382	+	0.890807i	$0.349860\pi$
$762$	2.35980	−	0.339287i	0.0854864	−	0.0122911i
$763$	4.19221	+	7.05097i	0.151768	+	0.255262i
$764$	10.3978	−	35.4117i	0.376180	−	1.28115i
$765$	2.37097	−	5.19169i	0.0857225	−	0.187706i
$766$	6.44117	−	7.43351i	0.232729	−	0.268584i
$767$	5.71237	−	39.7304i	0.206262	−	1.43458i
$768$	2.95200	+	10.0536i	0.106521	+	0.362778i
$769$	12.0360	+	13.8903i	0.434030	+	0.500897i	0.930060	−	0.367408i	$-0.119755\pi$
$769$	12.0360	+	13.8903i	0.434030	+	0.500897i	−0.496030	+	0.868305i	$0.665209\pi$
$770$	−2.70795	+	2.18627i	−0.0975876	+	0.0787876i
$771$	23.0998	−	14.8454i	0.831921	−	0.534643i
$772$	−5.60583	−	6.46947i	−0.201758	−	0.232841i
$773$	35.6254	−	10.4606i	1.28136	−	0.376241i	0.430955	−	0.902373i	$-0.358177\pi$
$773$	35.6254	−	10.4606i	1.28136	−	0.376241i	0.850402	+	0.526133i	$0.176359\pi$
$774$	−0.376505	−	0.0541333i	−0.0135332	−	0.00194578i
$775$	19.4563	+	16.8590i	0.698891	+	0.605593i
$776$	−3.53348	+	7.73725i	−0.126845	+	0.277751i
$777$	−3.46028	+	19.2794i	−0.124137	+	0.691645i
$778$	−0.257640	+	0.117660i	−0.00923685	+	0.00421833i
$779$	60.3331	−	8.67459i	2.16166	−	0.310800i
$780$	5.53581	+	3.55765i	0.198214	+	0.127384i
$781$			45.8153i			1.63940i
$782$	4.01322	+	5.51524i	0.143513	+	0.197225i
$783$		−	1.87289i		−	0.0669315i
$784$	−23.4147	−	8.68472i	−0.836239	−	0.310169i
$785$	2.75449	+	19.1579i	0.0983120	+	0.683775i
$786$	−2.22068	−	4.86262i	−0.0792091	−	0.173444i
$787$	17.9026	+	5.25668i	0.638159	+	0.187380i	0.584777	−	0.811194i	$-0.301182\pi$
$787$	17.9026	+	5.25668i	0.638159	+	0.187380i	0.0533816	+	0.998574i	$0.483000\pi$
$788$	−1.53060	+	3.35156i	−0.0545255	+	0.119394i
$789$	4.08631	−	4.71585i	0.145476	−	0.167889i
$790$	2.55740	+	0.367698i	0.0909882	+	0.0130821i
$791$	−21.5873	+	8.96479i	−0.767558	+	0.318751i
$792$	3.60197	−	3.12112i	0.127990	−	0.110904i
$793$	19.8822	+	30.9373i	0.706038	+	1.09862i
$794$	−0.343751	−	0.534887i	−0.0121993	−	0.0189824i
$795$	−1.30999	−	1.51181i	−0.0464607	−	0.0536185i
$796$	−16.7718	+	4.92466i	−0.594462	+	0.174550i
$797$	−4.31039	+	29.9794i	−0.152682	+	1.06193i	0.759018	+	0.651069i	$0.225679\pi$
$797$	−4.31039	+	29.9794i	−0.152682	+	1.06193i	−0.911700	+	0.410856i	$0.865230\pi$
$798$	−2.24307	+	3.23692i	−0.0794040	+	0.114586i
$799$	−5.36248	−	2.44896i	−0.189711	−	0.0866381i
$800$	11.3224	+	3.32456i	0.400307	+	0.117541i
$801$	−4.85648	−	10.6342i	−0.171595	−	0.375741i
$802$	5.99005	−	0.861239i	0.211516	−	0.0304114i
$803$	−52.2825	−	33.5999i	−1.84501	−	1.18572i
$804$	−19.8939			−0.701602
$805$	10.1832	−	9.24342i	0.358911	−	0.325788i
$806$	5.72687			0.201720
$807$	−10.8318	−	6.96120i	−0.381299	−	0.245046i
$808$	−10.0881	+	1.45045i	−0.354899	+	0.0510268i
$809$	−22.6825	−	49.6678i	−0.797475	−	1.74623i	−0.653892	−	0.756588i	$-0.726865\pi$
$809$	−22.6825	−	49.6678i	−0.797475	−	1.74623i	−0.143582	−	0.989638i	$-0.545862\pi$
$810$	−0.280883	−	0.0824748i	−0.00986924	−	0.00289787i
$811$	17.4723	+	7.97932i	0.613534	+	0.280192i	0.697846	−	0.716248i	$-0.254142\pi$
$811$	17.4723	+	7.97932i	0.613534	+	0.280192i	−0.0843118	+	0.996439i	$0.526869\pi$
$812$	−7.84863	−	5.43882i	−0.275433	−	0.190865i
$813$	0.183839	−	1.27863i	0.00644753	−	0.0448436i
$814$	−8.62118	+	2.53141i	−0.302172	+	0.0887258i
$815$	16.1416	+	18.6285i	0.565417	+	0.652526i
$816$	10.1568	+	15.8042i	0.355558	+	0.553259i
$817$	−4.19616	−	6.52935i	−0.146805	−	0.228433i
$818$	0.941098	−	0.815466i	0.0329047	−	0.0285121i
$819$	7.69812	−	3.19688i	0.268994	−	0.111708i
$820$	22.8660	+	3.28763i	0.798514	+	0.114809i
$821$	1.30591	−	1.50710i	0.0455766	−	0.0525981i	−0.732504	−	0.680763i	$-0.761648\pi$
$821$	1.30591	−	1.50710i	0.0455766	−	0.0525981i	0.778080	+	0.628165i	$0.216194\pi$
$822$	−0.315109	+	0.689992i	−0.0109907	+	0.0240662i
$823$	−7.99543	−	2.34767i	−0.278703	−	0.0818347i	0.139394	−	0.990237i	$-0.455485\pi$
$823$	−7.99543	−	2.34767i	−0.278703	−	0.0818347i	−0.418097	+	0.908402i	$0.637303\pi$
$824$	−4.39182	−	9.61674i	−0.152996	−	0.335015i
$825$	2.44622	+	17.0138i	0.0851664	+	0.592345i
$826$	8.14484	+	4.06775i	0.283395	+	0.141535i
$827$		−	47.9455i		−	1.66723i	−0.552347	−	0.833614i	$-0.686268\pi$
$827$		−	47.9455i		−	1.66723i	0.552347	−	0.833614i	$-0.313732\pi$
$828$	−6.62289	+	6.44581i	−0.230161	+	0.224008i
$829$		−	32.2563i		−	1.12031i	−0.828389	−	0.560153i	$-0.810742\pi$
$829$		−	32.2563i		−	1.12031i	0.828389	−	0.560153i	$-0.189258\pi$
$830$	0.178576	+	0.114764i	0.00619848	+	0.00398352i
$831$	−12.1903	+	1.75270i	−0.422877	+	0.0608006i
$832$	−18.0606	+	8.24802i	−0.626140	+	0.285949i
$833$	−36.7716	−	2.56271i	−1.27406	−	0.0887926i
$834$	1.29255	−	2.83028i	0.0447572	−	0.0980047i
$835$	6.96664	+	6.03663i	0.241091	+	0.208906i
$836$	47.2361	+	6.79153i	1.63370	+	0.234890i
$837$	6.45754	−	1.89610i	0.223205	−	0.0655390i
$838$	4.18269	+	4.82708i	0.144489	+	0.166749i
$839$	16.0212	−	10.2962i	0.553115	−	0.355465i	−0.234034	−	0.972228i	$-0.575193\pi$
$839$	16.0212	−	10.2962i	0.553115	−	0.355465i	0.787149	+	0.616763i	$0.211556\pi$
$840$	−2.36657	+	1.91065i	−0.0816543	+	0.0659239i
$841$	16.6939	+	19.2658i	0.575652	+	0.664338i
$842$	0.0469957	+	0.160053i	0.00161958	+	0.00551577i
$843$	3.37993	−	23.5079i	0.116411	−	0.809656i
$844$	−23.9036	+	27.5862i	−0.822795	+	0.949556i
$845$	1.38414	−	3.03085i	0.0476160	−	0.104264i
$846$	−0.0851880	+	0.290124i	−0.00292882	+	0.00997466i
$847$	20.9037	−	12.4284i	0.718258	−	0.427046i
$848$	6.51749	−	0.937074i	0.223812	−	0.0321792i
$849$	5.20433	−	8.09810i	0.178612	−	0.277926i
$850$	5.44041			0.186604
$851$	33.4318	−	11.9560i	1.14603	−	0.409846i
$852$			19.6479i			0.673126i
$853$	−24.3308	+	37.8595i	−0.833071	+	1.29628i	0.119767	+	0.992802i	$0.461785\pi$
$853$	−24.3308	+	37.8595i	−0.833071	+	1.29628i	−0.952837	+	0.303481i	$0.901851\pi$
$854$	−8.08021	+	2.07018i	−0.276499	+	0.0708402i
$855$	−2.48139	−	5.43349i	−0.0848618	−	0.185821i
$856$	−1.67950	+	5.71985i	−0.0574042	+	0.195501i
$857$	−0.391463	−	0.178775i	−0.0133721	−	0.00610685i	0.408718	−	0.912661i	$-0.365976\pi$
$857$	−0.391463	−	0.178775i	−0.0133721	−	0.00610685i	−0.422090	+	0.906554i	$0.638703\pi$
$858$	2.88973	+	2.50397i	0.0986538	+	0.0854840i
$859$	−44.1198	−	6.34347i	−1.50535	−	0.216436i	−0.660249	−	0.751046i	$-0.729549\pi$
$859$	−44.1198	−	6.34347i	−1.50535	−	0.216436i	−0.845099	+	0.534610i	$0.820458\pi$
$860$	−0.828731	−	2.82240i	−0.0282595	−	0.0962430i
$861$	19.9205	−	21.4352i	0.678889	−	0.730510i
$862$	1.55242	+	2.41562i	0.0528757	+	0.0822762i
$863$	−34.6908	+	22.2944i	−1.18089	+	0.758912i	−0.975550	−	0.219779i	$-0.929466\pi$
$863$	−34.6908	+	22.2944i	−1.18089	+	0.758912i	−0.205340	+	0.978691i	$0.565830\pi$
$864$	2.33140	−	2.02017i	0.0793160	−	0.0687277i
$865$	2.97015	+	10.1154i	0.100988	+	0.343934i
$866$	0.666783	−	4.63758i	0.0226582	−	0.157591i
$867$	8.10838	+	7.02595i	0.275375	+	0.238614i
$868$	10.8066	−	32.5676i	0.366801	−	1.10542i
$869$	−38.0528	−	11.1733i	−1.29085	−	0.379029i
$870$	−0.498726	+	0.227760i	−0.0169084	+	0.00772180i
$871$	−4.62871	−	32.1934i	−0.156838	−	1.09083i
$872$	−1.77792	+	2.76650i	−0.0602079	+	0.0936854i
$873$	−8.01949			−0.271418
$874$	7.11277	+	0.605676i	0.240593	+	0.0204873i
$875$	−2.72816	−	25.1602i	−0.0922286	−	0.850569i
$876$	−22.4214	−	14.4093i	−0.757548	−	0.486846i
$877$	5.48040	+	38.1171i	0.185060	+	1.28712i	0.844578	+	0.535433i	$0.179851\pi$
$877$	5.48040	+	38.1171i	0.185060	+	1.28712i	−0.659518	+	0.751689i	$0.729240\pi$
$878$	−3.30902	+	1.51118i	−0.111674	+	0.0509998i
$879$	−0.609636	+	2.07623i	−0.0205625	+	0.0700295i
$880$	15.8056	+	7.21817i	0.532806	+	0.243324i
$881$	23.7570	−	27.4171i	0.800395	−	0.923705i	−0.198008	−	0.980200i	$-0.563447\pi$
$881$	23.7570	−	27.4171i	0.800395	−	0.923705i	0.998403	+	0.0564951i	$0.0179925\pi$
$882$	0.138307	+	1.88556i	0.00465704	+	0.0634901i
$883$	−27.5009	+	8.07500i	−0.925480	+	0.271745i	−0.709543	−	0.704662i	$-0.751099\pi$
$883$	−27.5009	+	8.07500i	−0.925480	+	0.271745i	−0.215937	+	0.976407i	$0.569280\pi$
$884$	−24.1614	+	20.9360i	−0.812636	+	0.704153i
$885$	−11.6168	+	7.46565i	−0.390494	+	0.250955i
$886$	−1.34187	+	0.862371i	−0.0450812	+	0.0289719i
$887$	−7.78761	+	6.74800i	−0.261482	+	0.226576i	−0.775728	−	0.631067i	$-0.782617\pi$
$887$	−7.78761	+	6.74800i	−0.261482	+	0.226576i	0.514246	+	0.857643i	$0.328072\pi$
$888$	−7.53434	+	2.21228i	−0.252836	+	0.0742394i
$889$	23.3398	+	0.812320i	0.782790	+	0.0272443i
$890$	−2.24116	+	2.58643i	−0.0751238	+	0.0866975i
$891$	4.08746	+	1.86668i	0.136935	+	0.0625362i
$892$	12.1785	−	41.4762i	0.407767	−	1.38873i
$893$	−5.61223	+	2.56302i	−0.187806	+	0.0857683i
$894$	0.446093	+	3.10264i	0.0149196	+	0.103768i
$895$	−20.6146	−	13.2482i	−0.689070	−	0.442839i
$896$	−2.24515	−	20.7057i	−0.0750053	−	0.691730i
$897$	−11.9719	−	9.21779i	−0.399731	−	0.307773i
$898$	2.86913			0.0957442
$899$	6.81468	−	10.6039i	0.227282	−	0.353658i
$900$	1.04906	+	7.29638i	0.0349687	+	0.243213i
$901$	8.84048	−	4.03731i	0.294519	−	0.134502i
$902$	12.8795	+	3.78177i	0.428841	+	0.125919i
$903$	−3.53650	−	1.17349i	−0.117687	−	0.0390512i
$904$	−7.08192	−	6.13652i	−0.235541	−	0.204097i
$905$	1.55997	−	10.8498i	0.0518551	−	0.360660i
$906$	0.662100	+	2.25491i	0.0219968	+	0.0749142i
$907$	−2.07024	+	1.79388i	−0.0687413	+	0.0595647i	−0.688554	−	0.725185i	$-0.741754\pi$
$907$	−2.07024	+	1.79388i	−0.0687413	+	0.0595647i	0.619812	+	0.784750i	$0.287209\pi$
$908$	17.2952	−	11.1149i	0.573960	−	0.368862i
$909$	−5.19503	−	8.08363i	−0.172308	−	0.268117i
$910$	−1.78745	−	1.66114i	−0.0592534	−	0.0550663i
$911$	14.4023	+	49.0498i	0.477170	+	1.62509i	0.748874	+	0.662712i	$0.230595\pi$
$911$	14.4023	+	49.0498i	0.477170	+	1.62509i	−0.271704	+	0.962381i	$0.587587\pi$
$912$	19.4614	+	2.79812i	0.644430	+	0.0926551i
$913$	−2.46251	−	2.13378i	−0.0814973	−	0.0706178i
$914$	−7.99772	−	3.65244i	−0.264541	−	0.120812i
$915$	3.56439	−	12.1392i	0.117835	−	0.401310i
$916$	−2.80130	−	6.13400i	−0.0925576	−	0.202673i
$917$	−12.9965	−	50.7271i	−0.429182	−	1.67516i
$918$	0.768923	−	1.19647i	0.0253782	−	0.0394893i
$919$		−	15.7075i		−	0.518142i	−0.965858	−	0.259071i	$-0.916584\pi$
$919$		−	15.7075i		−	0.518142i	0.965858	−	0.259071i	$-0.0834163\pi$
$920$	5.13915	+	1.99653i	0.169433	+	0.0658235i
$921$	16.6782			0.549566
$922$	−0.589131	+	0.916706i	−0.0194020	+	0.0301901i
$923$	−31.7954	+	4.57149i	−1.04656	+	0.150472i
$924$	19.6925	−	11.7083i	0.647836	−	0.385176i
$925$	7.97855	−	27.1724i	0.262333	−	0.893424i
$926$	3.17692	−	6.95649i	0.104400	−	0.228605i
$927$	6.52735	−	7.53297i	0.214386	−	0.247415i
$928$	0.822245	−	5.71884i	0.0269915	−	0.187730i
$929$	11.2088	+	38.1736i	0.367748	+	1.25244i	0.910839	+	0.412762i	$0.135436\pi$
$929$	11.2088	+	38.1736i	0.367748	+	1.25244i	−0.543091	+	0.839674i	$0.682746\pi$
$930$	−1.29020	−	1.48898i	−0.0423075	−	0.0488254i
$931$	−27.2287	+	27.3280i	−0.892386	+	0.895640i
$932$	20.1677	−	12.9610i	0.660613	−	0.424551i
$933$	−10.7822	−	12.4433i	−0.352994	−	0.407376i
$934$	−0.985137	+	0.289262i	−0.0322347	+	0.00946496i
$935$	25.3856	+	3.64990i	0.830199	+	0.119365i
$936$	2.52544	+	2.18830i	0.0825465	+	0.0715269i
$937$	−6.51140	+	14.2580i	−0.212718	+	0.465788i	−0.985672	−	0.168675i	$-0.946051\pi$
$937$	−6.51140	+	14.2580i	−0.212718	+	0.465788i	0.772954	+	0.634463i	$0.218779\pi$
$938$	7.26101	+	1.30321i	0.237081	+	0.0425513i
$939$	−30.8650	+	14.0956i	−1.00724	+	0.459992i
$940$	−2.31452	+	0.332778i	−0.0754913	+	0.0108540i
$941$	5.11296	+	3.28590i	0.166678	+	0.107117i	0.621320	−	0.783557i	$-0.286597\pi$
$941$	5.11296	+	3.28590i	0.166678	+	0.107117i	−0.454643	+	0.890674i	$0.650233\pi$
$942$			4.82305i			0.157144i
$943$	−51.6731	−	11.9762i	−1.68271	−	0.390000i
$944$		−	45.4529i		−	1.47937i
$945$	−2.56549	−	1.28128i	−0.0834554	−	0.0416799i
$946$	−0.243250	−	1.69184i	−0.00790872	−	0.0550064i
$947$	20.4952	+	44.8782i	0.666004	+	1.45835i	0.876819	+	0.480820i	$0.159661\pi$
$947$	20.4952	+	44.8782i	0.666004	+	1.45835i	−0.210815	+	0.977526i	$0.567612\pi$
$948$	−16.3190	−	4.79168i	−0.530015	−	0.155626i
$949$	18.1012	−	39.6362i	0.587591	−	1.28664i
$950$	3.72864	−	4.30308i	0.120973	−	0.139610i
$951$	−3.67424	−	0.528276i	−0.119145	−	0.0171305i
$952$	−5.66738	−	13.6471i	−0.183681	−	0.442306i
$953$	−22.2093	+	19.2445i	−0.719431	+	0.623391i	−0.935640	−	0.352956i	$-0.885176\pi$
$953$	−22.2093	+	19.2445i	−0.719431	+	0.623391i	0.216208	+	0.976347i	$0.430631\pi$
$954$	−0.269501	−	0.419351i	−0.00872541	−	0.0135770i
$955$	−11.2227	−	17.4629i	−0.363158	−	0.565085i
$956$	14.4186	+	16.6399i	0.466330	+	0.538173i
$957$	8.07498	−	2.37103i	0.261027	−	0.0766444i
$958$	−0.384108	+	2.67153i	−0.0124100	+	0.0863132i
$959$	−4.23224	+	6.10744i	−0.136666	+	0.197220i
$960$	6.21335	+	2.83754i	0.200535	+	0.0915812i
$961$	13.7160	+	4.02737i	0.442451	+	0.129915i
$962$	−2.61700	−	5.73043i	−0.0843754	−	0.184756i
$963$	−5.56322	+	0.799870i	−0.179272	+	0.0257754i
$964$	30.8078	+	19.7990i	0.992252	+	0.637682i
$965$	−4.81476			−0.154993
$966$	2.83953	−	1.91879i	0.0913603	−	0.0617361i
$967$	4.46220			0.143495			0.0717473	−	0.997423i	$-0.477142\pi$
$967$	4.46220			0.143495			0.0717473	+	0.997423i	$0.477142\pi$
$968$	8.20169	+	5.27090i	0.263612	+	0.169413i
$969$	28.7250	−	4.13003i	0.922779	−	0.132676i
$970$	0.975244	+	2.13549i	0.0313132	+	0.0685663i
$971$	−10.0015	−	2.93670i	−0.320963	−	0.0942431i	0.117283	−	0.993099i	$-0.462582\pi$
$971$	−10.0015	−	2.93670i	−0.320963	−	0.0942431i	−0.438245	+	0.898855i	$0.644400\pi$
$972$	1.75291	+	0.800526i	0.0562245	+	0.0256769i
$973$	17.3603	−	25.0522i	0.556545	−	0.803136i
$974$	−0.755384	+	5.25381i	−0.0242041	+	0.168343i
$975$	−11.5633	+	3.39530i	−0.370323	+	0.108737i
$976$	27.2710	+	31.4724i	0.872922	+	1.00741i
$977$	−5.06030	−	7.87398i	−0.161893	−	0.251911i	0.750824	−	0.660502i	$-0.229657\pi$
$977$	−5.06030	−	7.87398i	−0.161893	−	0.251911i	−0.912718	+	0.408591i	$0.866020\pi$
$978$	3.32077	+	5.16721i	0.106186	+	0.165229i
$979$	39.7013	−	34.4014i	1.26886	−	1.09947i
$980$	−12.8195	+	7.03030i	−0.409504	+	0.224575i
$981$	−3.06892	−	0.441244i	−0.0979831	−	0.0140878i
$982$	6.08563	−	7.02319i	0.194200	−	0.224119i
$983$	8.62034	−	18.8759i	0.274946	−	0.602048i	−0.720906	−	0.693033i	$-0.756274\pi$
$983$	8.62034	−	18.8759i	0.274946	−	0.602048i	0.995852	+	0.0909847i	$0.0290015\pi$
$984$	11.2559	+	3.30502i	0.358824	+	0.105360i
$985$	0.860887	+	1.88508i	0.0274302	+	0.0600637i
$986$	−0.379084	−	2.63659i	−0.0120725	−	0.0839661i
$987$	−1.32342	+	2.64989i	−0.0421251	+	0.0843468i
$988$			33.4591i			1.06448i
$989$	1.34615	+	6.61864i	0.0428051	+	0.210460i
$990$		−	1.31544i		−	0.0418075i
$991$	−35.0553	−	22.5286i	−1.11357	−	0.715646i	−0.151499	−	0.988457i	$-0.548410\pi$
$991$	−35.0553	−	22.5286i	−1.11357	−	0.715646i	−0.962068	+	0.272811i	$0.912046\pi$
$992$	20.5505	−	2.95471i	0.652478	−	0.0938122i
$993$	4.42465	−	2.02067i	0.140412	−	0.0641241i
$994$	1.28710	−	7.17125i	0.0408243	−	0.227458i
$995$	−4.08418	+	8.94310i	−0.129477	+	0.283515i
$996$	−1.05605	−	0.915072i	−0.0334622	−	0.0289952i
$997$	59.5532	+	8.56246i	1.88607	+	0.271176i	0.986272	−	0.165131i	$-0.0528047\pi$
$997$	59.5532	+	8.56246i	1.88607	+	0.271176i	0.899798	+	0.436307i	$0.143714\pi$
$998$	3.55129	−	1.04275i	0.112414	−	0.0330077i
$999$	−4.84818	−	5.59509i	−0.153390	−	0.177021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.412.19	yes	320
7.6	odd	2	inner	483.2.r.a.412.20	yes	320
23.11	odd	22	inner	483.2.r.a.34.20	yes	320
161.34	even	22	inner	483.2.r.a.34.19	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.19	✓	320	161.34	even	22	inner
483.2.r.a.34.20	yes	320	23.11	odd	22	inner
483.2.r.a.412.19	yes	320	1.1	even	1	trivial
483.2.r.a.412.20	yes	320	7.6	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.227214 + 0.146021i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(-0.800526 - 1.75291i) q^{4} +(-1.03996 - 0.305361i) q^{5} +(-0.245682 - 0.112199i) q^{6} +(-2.17465 - 1.50695i) q^{7} +(0.150947 - 1.04986i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.227214 + 0.146021i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(-0.800526 - 1.75291i) q^{4} +(-1.03996 - 0.305361i) q^{5} +(-0.245682 - 0.112199i) q^{6} +(-2.17465 - 1.50695i) q^{7} +(0.150947 - 1.04986i) q^{8} +(0.959493 - 0.281733i) q^{9} +(-0.191705 - 0.221239i) q^{10} +(2.42939 + 3.78020i) q^{11} +(1.04184 + 1.62114i) q^{12} +(-2.38102 + 2.06316i) q^{13} +(-0.274062 - 0.659945i) q^{14} +(1.07284 + 0.154251i) q^{15} +(-2.33630 + 2.69624i) q^{16} +(-2.18750 + 4.78996i) q^{17} +(0.259149 + 0.0760930i) q^{18} +(2.28938 + 5.01305i) q^{19} +(0.297249 + 2.06741i) q^{20} +(2.36697 + 1.18213i) q^{21} +1.21366i q^{22} +(-0.277290 - 4.78781i) q^{23} +1.06065i q^{24} +(-3.21799 - 2.06807i) q^{25} +(-0.842265 + 0.121099i) q^{26} +(-0.909632 + 0.415415i) q^{27} +(-0.900689 + 5.01831i) q^{28} +(-0.778025 + 1.70364i) q^{29} +(0.221239 + 0.191705i) q^{30} +(-6.66165 - 0.957801i) q^{31} +(-2.95993 + 0.869114i) q^{32} +(-2.94264 - 3.39599i) q^{33} +(-1.19647 + 0.768923i) q^{34} +(1.80139 + 2.23123i) q^{35} +(-1.26195 - 1.45637i) q^{36} +(2.08577 + 7.10348i) q^{37} +(-0.211833 + 1.47333i) q^{38} +(2.06316 - 2.38102i) q^{39} +(-0.477566 + 1.04572i) q^{40} +(3.11602 - 10.6122i) q^{41} +(0.365193 + 0.614225i) q^{42} +(-1.39400 + 0.200427i) q^{43} +(4.68155 - 7.28464i) q^{44} -1.08387 q^{45} +(0.636118 - 1.12835i) q^{46} +1.11953i q^{47} +(1.92881 - 3.00128i) q^{48} +(2.45818 + 6.55419i) q^{49} +(-0.429187 - 0.939789i) q^{50} +(1.48355 - 5.05252i) q^{51} +(5.52260 + 2.52209i) q^{52} +(-1.39483 - 1.20863i) q^{53} +(-0.267340 - 0.0384377i) q^{54} +(-1.37215 - 4.67312i) q^{55} +(-1.91035 + 2.05560i) q^{56} +(-2.97951 - 4.63621i) q^{57} +(-0.425546 + 0.273482i) q^{58} +(-9.62852 + 8.34316i) q^{59} +(-0.588447 - 2.00407i) q^{60} +(1.66120 - 11.5539i) q^{61} +(-1.37376 - 1.19037i) q^{62} +(-2.51112 - 0.833243i) q^{63} +(6.04679 + 1.77550i) q^{64} +(3.10618 - 1.41855i) q^{65} +(-0.172721 - 1.20130i) q^{66} +(-5.58129 + 8.68465i) q^{67} +10.1475 q^{68} +(0.955844 + 4.69961i) q^{69} +(0.0834932 + 0.770008i) q^{70} +(8.57728 + 5.51229i) q^{71} +(-0.150947 - 1.04986i) q^{72} +(-12.5808 + 5.74545i) q^{73} +(-0.563345 + 1.91858i) q^{74} +(3.47955 + 1.58906i) q^{75} +(6.95470 - 8.02616i) q^{76} +(0.413528 - 11.8816i) q^{77} +(0.816458 - 0.239734i) q^{78} +(-6.67014 + 5.77971i) q^{79} +(3.25300 - 2.09058i) q^{80} +(0.841254 - 0.540641i) q^{81} +(2.25761 - 1.95623i) q^{82} +(-0.695752 + 0.204291i) q^{83} +(0.177341 - 5.09541i) q^{84} +(3.73760 - 4.31342i) q^{85} +(-0.346003 - 0.158014i) q^{86} +(0.527653 - 1.79702i) q^{87} +(4.33539 - 1.97990i) q^{88} +(-1.66375 - 11.5717i) q^{89} +(-0.246270 - 0.158268i) q^{90} +(8.28696 - 0.898568i) q^{91} +(-8.17061 + 4.31883i) q^{92} +6.73016 q^{93} +(-0.163475 + 0.254371i) q^{94} +(-0.850087 - 5.91249i) q^{95} +(2.80611 - 1.28151i) q^{96} +(-7.69464 - 2.25935i) q^{97} +(-0.398519 + 1.84815i) q^{98} +(3.39599 + 2.94264i) 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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