LMFDB - Embedded newform 483.2.r.a.34.20

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			34.20
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.20

$q$-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} +(-1.80110 + 1.93805i) 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} +(-0.126238 + 0.703351i) 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} +(-2.05858 + 1.66200i) 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} +(-1.95540 - 4.70862i) 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} +(-1.28128 + 2.56549i) 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} +(-0.225050 + 0.678226i) 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} +(-0.512079 - 6.98124i) 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} +(-2.30655 - 1.59836i) 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} +(-2.27415 + 1.35212i) 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} +(2.95065 + 11.5168i) 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} +(-1.26539 - 4.93898i) 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} +(-1.13576 - 1.51146i) 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} - 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}+ \cdots + 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

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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	−0.457838	−	0.889036i	$-0.651376\pi$
$2$	0.227214	−	0.146021i	0.160664	−	0.103253i	0.618502	+	0.785783i	$0.287740\pi$
$3$	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	$-0.512987\pi$
$5$	1.03996	−	0.305361i	0.465086	−	0.136562i	0.505876	+	0.862606i	$0.331169\pi$
$6$	0.245682	−	0.112199i	0.100299	−	0.0458051i
$7$	−1.80110	+	1.93805i	−0.680752	+	0.732514i
$7$	−1.80110	+	1.93805i	−0.680752	+	0.732514i
$8$	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	−0.252575	−	0.967577i	$-0.581277\pi$
$11$	2.42939	−	3.78020i	0.732488	−	1.13977i	0.985063	−	0.172196i	$-0.0550862\pi$
$12$	−1.04184	+	1.62114i	−0.300754	+	0.467983i
$13$	2.38102	+	2.06316i	0.660375	+	0.572218i	0.919241	−	0.393695i	$-0.128803\pi$
$13$	2.38102	+	2.06316i	0.660375	+	0.572218i	−0.258866	+	0.965913i	$0.583349\pi$
$14$	−0.126238	+	0.703351i	−0.0337385	+	0.187978i
$15$	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	0.965290	+	0.261182i	$0.0841122\pi$
$17$	2.18750	+	4.78996i	0.530547	+	1.16174i	−0.434742	+	0.900555i	$0.643161\pi$
$18$	0.259149	−	0.0760930i	0.0610820	−	0.0179353i
$19$	−2.28938	+	5.01305i	−0.525221	+	1.15007i	0.442204	+	0.896914i	$0.354197\pi$
$19$	−2.28938	+	5.01305i	−0.525221	+	1.15007i	−0.967425	+	0.253158i	$0.918531\pi$
$20$	−0.297249	+	2.06741i	−0.0664669	+	0.462287i
$21$	−2.05858	+	1.66200i	−0.449219	+	0.362678i
$22$		−	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
$28$	−1.95540	−	4.70862i	−0.369535	−	0.889846i
$29$	−0.778025	−	1.70364i	−0.144476	−	0.316358i	0.823535	−	0.567265i	$-0.191998\pi$
$29$	−0.778025	−	1.70364i	−0.144476	−	0.316358i	−0.968011	+	0.250907i	$0.919271\pi$
$30$	0.221239	−	0.191705i	0.0403926	−	0.0350004i
$31$	6.66165	−	0.957801i	1.19647	−	0.172026i	0.484853	−	0.874596i	$-0.338873\pi$
$31$	6.66165	−	0.957801i	1.19647	−	0.172026i	0.711615	+	0.702569i	$0.247964\pi$
$32$	−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
$35$	−1.28128	+	2.56549i	−0.216575	+	0.433647i
$36$	−1.26195	+	1.45637i	−0.210325	+	0.242728i
$37$	2.08577	−	7.10348i	0.342899	−	1.16781i	−0.589921	−	0.807461i	$-0.700841\pi$
$37$	2.08577	−	7.10348i	0.342899	−	1.16781i	0.932819	−	0.360344i	$-0.117341\pi$
$38$	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	−0.726983	−	0.686655i	$-0.759078\pi$
$41$	−3.11602	−	10.6122i	−0.486640	−	1.65734i	0.240343	−	0.970688i	$-0.422740\pi$
$42$	−0.225050	+	0.678226i	−0.0347260	+	0.104653i
$43$	−1.39400	−	0.200427i	−0.212583	−	0.0305649i	0.0352003	−	0.999380i	$-0.488793\pi$
$43$	−1.39400	−	0.200427i	−0.212583	−	0.0305649i	−0.247784	+	0.968815i	$0.579702\pi$
$44$	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
$49$	−0.512079	−	6.98124i	−0.0731541	−	0.997321i
$50$	−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	−0.745376	−	0.666645i	$-0.767730\pi$
$53$	−1.39483	+	1.20863i	−0.191595	+	0.166018i	0.553781	+	0.832662i	$0.313184\pi$
$54$	0.267340	−	0.0384377i	0.0363804	−	0.00523071i
$55$	1.37215	−	4.67312i	0.185021	−	0.630123i
$56$	−2.30655	−	1.59836i	−0.308226	−	0.213590i
$57$	−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	0.992676	+	0.120808i	$0.0385486\pi$
$59$	9.62852	+	8.34316i	1.25353	+	1.08619i	0.260851	+	0.965379i	$0.415997\pi$
$60$	−0.588447	+	2.00407i	−0.0759682	+	0.258724i
$61$	−1.66120	−	11.5539i	−0.212695	−	1.47932i	−0.764106	−	0.645090i	$-0.776820\pi$
$61$	−1.66120	−	11.5539i	−0.212695	−	1.47932i	0.551412	−	0.834233i	$-0.314089\pi$
$62$	1.37376	−	1.19037i	0.174468	−	0.151177i
$63$	−2.27415	+	1.35212i	−0.286517	+	0.170351i
$64$	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	−0.993831	−	0.110907i	$-0.964625\pi$
$67$	−5.58129	−	8.68465i	−0.681863	−	1.06100i	0.311968	−	0.950093i	$-0.399012\pi$
$68$	−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	0.0785010	−	0.996914i	$-0.474987\pi$
$71$	8.57728	−	5.51229i	1.01794	−	0.654188i	0.939435	+	0.342726i	$0.111350\pi$
$72$	−0.150947	+	1.04986i	−0.0177893	+	0.123727i
$73$	12.5808	+	5.74545i	1.47247	+	0.672454i	0.980204	−	0.197992i	$-0.0634420\pi$
$73$	12.5808	+	5.74545i	1.47247	+	0.672454i	0.492265	+	0.870446i	$0.336169\pi$
$74$	−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
$77$	2.95065	+	11.5168i	0.336258	+	1.31246i
$78$	0.816458	+	0.239734i	0.0924456	+	0.0271445i
$79$	−6.67014	−	5.77971i	−0.750450	−	0.650268i	0.193221	−	0.981155i	$-0.438107\pi$
$79$	−6.67014	−	5.77971i	−0.750450	−	0.650268i	−0.943670	+	0.330887i	$0.892652\pi$
$80$	−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	$-0.396420\pi$
$83$	0.695752	+	0.204291i	0.0763688	+	0.0224239i	−0.243325	+	0.969945i	$0.578238\pi$
$84$	−1.26539	−	4.93898i	−0.138065	−	0.538887i
$85$	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	−0.688747	−	0.725002i	$-0.741839\pi$
$89$	1.66375	−	11.5717i	0.176358	−	1.22659i	0.865104	−	0.501592i	$-0.167252\pi$
$90$	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	$-0.457439\pi$
$97$	7.69464	−	2.25935i	0.781272	−	0.229402i	0.647963	+	0.761672i	$0.275621\pi$
$98$	−1.13576	−	1.51146i	−0.114729	−	0.152680i
$99$	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	−0.708058	−	0.706154i	$-0.750429\pi$
$101$	2.70718	−	9.21979i	0.269374	−	0.917404i	0.977432	−	0.211250i	$-0.0677533\pi$
$102$	1.07486	+	0.931371i	0.106427	+	0.0922195i
$103$	−8.38523	−	5.38886i	−0.826221	−	0.530980i	0.0578537	−	0.998325i	$-0.481574\pi$
$103$	−8.38523	−	5.38886i	−0.826221	−	0.530980i	−0.884075	+	0.467345i	$0.845211\pi$
$104$	−1.80662	+	2.81116i	−0.177154	+	0.275657i
$105$	−1.63334	+	2.35703i	−0.159398	+	0.230023i
$106$	−0.140439	+	0.478292i	−0.0136407	+	0.0464558i
$107$	−5.56322	+	0.799870i	−0.537816	+	0.0773263i	−0.405870	−	0.913931i	$-0.633032\pi$
$107$	−5.56322	+	0.799870i	−0.537816	+	0.0773263i	−0.131946	+	0.991257i	$0.542123\pi$
$108$	−1.45637	+	1.26195i	−0.140139	+	0.121431i
$109$	−2.82030	+	1.28799i	−0.270135	+	0.123367i	−0.545878	−	0.837865i	$-0.683804\pi$
$109$	−2.82030	+	1.28799i	−0.270135	+	0.123367i	0.275742	+	0.961232i	$0.411076\pi$
$110$	−0.370603	−	1.26216i	−0.0353356	−	0.120342i
$111$	3.07547	−	6.73434i	0.291911	−	0.639196i
$112$	9.43335	+	0.328320i	0.891368	+	0.0310233i
$113$	4.77648	+	7.43234i	0.449333	+	0.699176i	0.989843	−	0.142161i	$-0.0454052\pi$
$113$	4.77648	+	7.43234i	0.449333	+	0.699176i	−0.540510	+	0.841337i	$0.681769\pi$
$114$			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
$119$	−13.2231	−	4.38771i	−1.21216	−	0.402221i
$120$	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
$126$	−0.319281	+	0.639295i	−0.0284438	+	0.0569529i
$127$	−7.42569	−	4.77220i	−0.658924	−	0.423465i	0.167994	−	0.985788i	$-0.446271\pi$
$127$	−7.42569	−	4.77220i	−0.658924	−	0.423465i	−0.826917	+	0.562323i	$0.809908\pi$
$128$	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	−0.324439	+	0.945907i	$0.605175\pi$
$131$	−14.9580	+	12.9612i	−1.30689	+	1.13243i	−0.982451	+	0.186520i	$0.940279\pi$
$132$	3.59719	+	7.87675i	0.313095	+	0.685583i
$133$	−5.59214	−	13.4659i	−0.484900	−	1.16765i
$134$	−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	$0.0382805\pi$
$137$			2.80847i			0.239944i	−0.992777	+	0.119972i	$0.961719\pi$
$138$	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	$0.837522\pi$
$140$	−3.47137	−	4.29970i	−0.293385	−	0.363391i
$141$	−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
$147$	0.486668	−	6.98306i	0.0401397	−	0.575953i
$148$	10.7820	+	9.34269i	0.886278	+	0.767964i
$149$	−6.27446	+	9.76325i	−0.514024	+	0.799836i	−0.997129	−	0.0757260i	$-0.975873\pi$
$149$	−6.27446	+	9.76325i	−0.514024	+	0.799836i	0.483105	+	0.875562i	$0.339509\pi$
$150$	−0.558565	+	0.869144i	−0.0456066	+	0.0709653i
$151$	−5.69807	+	6.57593i	−0.463703	+	0.535141i	−0.938649	−	0.344873i	$-0.887922\pi$
$151$	−5.69807	+	6.57593i	−0.463703	+	0.535141i	0.474947	+	0.880015i	$0.342467\pi$
$152$	−5.60857	−	1.64683i	−0.454915	−	0.133575i
$153$	0.749405	+	5.21223i	0.0605858	+	0.421384i
$154$	2.35213	+	2.18591i	0.189540	+	0.176146i
$155$	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	−0.342171	−	0.939638i	$-0.611162\pi$
$157$	7.41817	−	16.2435i	0.592034	−	1.29637i	0.934205	−	0.356736i	$-0.116111\pi$
$158$	−2.35951	−	0.339246i	−0.187712	−	0.0269890i
$159$	−1.55264	+	0.997820i	−0.123132	+	0.0791323i
$160$	−3.34362			−0.264336
$161$	−8.77959	−	9.16072i	−0.691928	−	0.721966i
$162$	0.270089			0.0212202
$163$	−19.1315	+	12.2951i	−1.49849	+	0.963024i	−0.503404	+	0.864051i	$0.667919\pi$
$163$	−19.1315	+	12.2951i	−1.49849	+	0.963024i	−0.995090	+	0.0989727i	$0.968444\pi$
$164$	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	$-0.529630\pi$
$167$	7.73632	−	3.53306i	0.598654	−	0.273396i	0.691607	+	0.722274i	$0.256903\pi$
$168$	−2.05560	−	1.91035i	−0.158593	−	0.147386i
$169$	−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	$-0.697624\pi$
$173$	5.25864	−	8.18260i	0.399807	−	0.622112i	0.981538	+	0.191270i	$0.0612605\pi$
$174$	−0.382294	−	0.331259i	−0.0289816	−	0.0251127i
$175$	1.78788	−	9.96143i	0.135151	−	0.753013i
$176$	−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	0.659996	−	0.751269i	$-0.270558\pi$
$179$	21.6927	−	6.36954i	1.62139	−	0.476082i	0.961391	+	0.275187i	$0.0887399\pi$
$180$	−0.867666	+	1.89992i	−0.0646720	+	0.141612i
$181$	−1.43926	+	10.0103i	−0.106979	+	0.744058i	0.863757	+	0.503909i	$0.168105\pi$
$181$	−1.43926	+	10.0103i	−0.106979	+	0.744058i	−0.970736	+	0.240149i	$0.922804\pi$
$182$	−1.75170	+	1.41424i	−0.129845	+	0.104830i
$183$		−	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
$189$	−2.44343	+	1.01471i	−0.177734	+	0.0738092i
$190$	0.670198	+	1.46753i	0.0486212	+	0.106466i
$191$	14.4740	−	12.5418i	1.04730	−	0.907495i	0.0514701	−	0.998675i	$-0.483609\pi$
$191$	14.4740	−	12.5418i	1.04730	−	0.907495i	0.995834	+	0.0911800i	$0.0290639\pi$
$192$	6.23792	−	0.896878i	0.450183	−	0.0647266i
$193$	4.26226	+	1.25151i	0.306804	+	0.0900857i	0.431510	−	0.902108i	$-0.357981\pi$
$193$	4.26226	+	1.25151i	0.306804	+	0.0900857i	−0.124707	+	0.992194i	$0.539799\pi$
$194$	1.41841	−	1.63694i	0.101836	−	0.117525i
$195$	2.87269	+	1.84616i	0.205717	+	0.132206i
$196$	12.6474	+	4.69104i	0.903387	+	0.335074i
$197$	−1.25209	+	1.44499i	−0.0892079	+	0.102951i	−0.798598	−	0.601864i	$-0.794425\pi$
$197$	−1.25209	+	1.44499i	−0.0892079	+	0.102951i	0.709391	+	0.704816i	$0.248970\pi$
$198$	0.341926	−	1.16449i	0.0242996	−	0.0827570i
$199$	−1.29091	−	8.97847i	−0.0915102	−	0.636467i	−0.983024	−	0.183475i	$-0.941265\pi$
$199$	−1.29091	−	8.97847i	−0.0915102	−	0.636467i	0.891514	−	0.452993i	$-0.149644\pi$
$200$	−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
$203$	4.70304	+	1.56057i	0.330089	+	0.109531i
$204$	−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
$210$	−0.0269402	+	0.774053i	−0.00185905	+	0.0534147i
$211$	−7.86869	+	17.2300i	−0.541703	+	1.18616i	0.418847	+	0.908057i	$0.362434\pi$
$211$	−7.86869	+	17.2300i	−0.541703	+	1.18616i	−0.960550	+	0.278108i	$0.910293\pi$
$212$	−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
$217$	−10.1420	+	14.6357i	−0.688486	+	0.993537i
$218$	−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	$-0.997735\pi$
$223$	−16.9528	+	14.6897i	−1.13524	+	0.983695i	−0.135269	+	0.990809i	$0.543190\pi$
$224$	7.01552	−	4.17113i	0.468744	−	0.278695i
$225$	−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	0.875322	+	0.483541i	$0.160649\pi$
$227$	−1.51829	+	10.5599i	−0.100772	+	0.700888i	−0.976094	+	0.217347i	$0.930260\pi$
$228$	−5.74167	−	8.93422i	−0.380252	−	0.591683i
$229$	−3.49933			−0.231242			−0.115621	−	0.993293i	$-0.536886\pi$
$229$	−3.49933			−0.231242			−0.115621	+	0.993293i	$0.536886\pi$
$230$	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	−0.845917	−	0.533315i	$-0.820946\pi$
$233$	1.77046	−	12.3138i	0.115986	−	0.806704i	0.961904	−	0.273389i	$-0.0881447\pi$
$234$	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
$238$	−3.64517	+	0.933907i	−0.236281	+	0.0605362i
$239$	−10.9628	−	3.21897i	−0.709124	−	0.208218i	−0.0927711	−	0.995687i	$-0.529572\pi$
$239$	−10.9628	−	3.21897i	−0.709124	−	0.208218i	−0.616353	+	0.787470i	$0.711391\pi$
$240$	−2.92237	−	2.53225i	−0.188638	−	0.163456i
$241$	15.9870	+	10.2742i	1.02981	+	0.661821i	0.942447	−	0.334355i	$-0.108518\pi$
$241$	15.9870	+	10.2742i	1.02981	+	0.661821i	0.0873668	+	0.996176i	$0.472155\pi$
$242$	−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
$245$	−2.66435	−	7.10388i	−0.170219	−	0.453850i
$246$	−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	$-0.787965\pi$
$251$	−8.72513	+	5.60730i	−0.550725	+	0.353930i	0.235495	+	0.971875i	$0.424329\pi$
$252$	−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	$-0.0363213\pi$
$257$	24.9774	+	11.4068i	1.55805	+	0.711538i	0.564553	+	0.825397i	$0.309049\pi$
$258$	−0.364969	+	0.107165i	−0.0227220	+	0.00667177i
$259$	10.0102	+	16.8364i	0.622005	+	1.04616i
$260$	−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	0.497232	−	0.867618i	$-0.334350\pi$
$263$	−4.71585	−	4.08631i	−0.290792	−	0.251972i	−0.788023	+	0.615645i	$0.788895\pi$
$264$	4.00949	+	2.57674i	0.246767	+	0.158587i
$265$	−1.08151	+	1.68286i	−0.0664364	+	0.103377i
$266$	−3.23692	−	2.24307i	−0.198469	−	0.137532i
$267$	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	$-0.855672\pi$
$269$	−9.73091	+	8.43188i	−0.593304	+	0.514101i	0.305650	+	0.952144i	$0.401126\pi$
$270$	0.266287	−	0.121609i	0.0162057	−	0.00740090i
$271$	0.363936	+	1.23945i	0.0221076	+	0.0752915i	0.969808	−	0.243870i	$-0.0784170\pi$
$271$	0.363936	+	1.23945i	0.0221076	+	0.0752915i	−0.947700	+	0.319161i	$0.896599\pi$
$272$	7.80421	−	17.0888i	0.473199	−	1.03616i
$273$	−8.33049	−	0.289935i	−0.504184	−	0.0175477i
$274$	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
$280$	−2.88681	−	0.957905i	−0.172520	−	0.0572458i
$281$	−6.69105	−	22.7876i	−0.399155	−	1.35940i	−0.876805	−	0.480846i	$-0.840329\pi$
$281$	−6.69105	−	22.7876i	−0.399155	−	1.35940i	0.477650	−	0.878550i	$-0.341489\pi$
$282$	0.125610	+	0.275047i	0.00747995	+	0.0163788i
$283$	6.30384	+	7.27502i	0.374724	+	0.432455i	0.911519	−	0.411258i	$-0.134911\pi$
$283$	6.30384	+	7.27502i	0.374724	+	0.432455i	−0.536795	+	0.843713i	$0.680365\pi$
$284$	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
$287$	26.1792	+	13.0746i	1.54531	+	0.771769i
$288$	−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	$-0.156497\pi$
$293$	−0.898909	−	1.96834i	−0.0525148	−	0.114991i	−0.934071	+	0.357089i	$0.883769\pi$
$294$	−0.909098	−	1.65771i	−0.0530197	−	0.0966797i
$295$	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
$301$	2.89917	−	2.34066i	0.167106	−	0.134913i
$302$	−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	$-0.387563\pi$
$307$	16.5084	−	2.37356i	0.942187	−	0.135466i	0.596256	+	0.802794i	$0.296654\pi$
$308$	−22.5499	−	4.04728i	−1.28490	−	0.230615i
$309$	−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	$-0.972782\pi$
$311$	−8.90159	+	13.8511i	−0.504763	+	0.785426i	0.491584	+	0.870830i	$0.336418\pi$
$312$	−2.18830	+	2.52544i	−0.123888	+	0.142975i
$313$	−32.5568	−	9.55955i	−1.84022	−	0.540338i	−0.840224	−	0.542240i	$-0.817576\pi$
$313$	−32.5568	−	9.55955i	−1.84022	−	0.540338i	−0.999998	+	0.00190234i	$0.999394\pi$
$314$	−0.686392	−	4.77396i	−0.0387353	−	0.269410i
$315$	−1.95216	+	2.10059i	−0.109992	+	0.118355i
$316$	15.4709	−	7.06533i	0.870307	−	0.397456i
$317$	3.56166	−	1.04580i	0.200043	−	0.0587378i	−0.180176	−	0.983634i	$-0.557667\pi$
$317$	3.56166	−	1.04580i	0.200043	−	0.0587378i	0.380219	+	0.924897i	$0.375849\pi$
$318$	−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
$322$	−3.33250	−	0.799434i	−0.185713	−	0.0445507i
$323$	−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
$329$	−2.16970	−	2.01638i	−0.119619	−	0.111166i
$330$	−0.187207	−	1.30205i	−0.0103054	−	0.0716757i
$331$	−4.66719	−	1.37041i	−0.256532	−	0.0753246i	0.150938	−	0.988543i	$-0.451771\pi$
$331$	−4.66719	−	1.37041i	−0.256532	−	0.0753246i	−0.407470	+	0.913219i	$0.633589\pi$
$332$	−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
$336$	9.29061	+	1.66748i	0.506844	+	0.0909687i
$337$	−1.60868	+	0.231293i	−0.0876302	+	0.0125993i	−0.185990	−	0.982552i	$-0.559549\pi$
$337$	−1.60868	+	0.231293i	−0.0876302	+	0.0125993i	0.0983602	+	0.995151i	$0.468640\pi$
$338$	−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
$343$	14.4523	+	11.5815i	0.780351	+	0.625341i
$344$		−	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	0.0407812	−	0.999168i	$-0.487015\pi$
$347$	18.0057	−	11.5716i	0.966598	−	0.621195i	0.925816	+	0.377974i	$0.123379\pi$
$348$	3.57241	+	0.513636i	0.191502	+	0.0275338i
$349$	−23.7180	−	10.8316i	−1.26959	−	0.579804i	−0.337262	−	0.941411i	$-0.609501\pi$
$349$	−23.7180	−	10.8316i	−1.26959	−	0.579804i	−0.932331	+	0.361607i	$0.882228\pi$
$350$	−1.04835	−	2.52444i	−0.0560366	−	0.134937i
$351$	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	$-0.430327\pi$
$353$	13.1611	−	1.89228i	0.700495	−	0.100716i	0.483355	+	0.875424i	$0.339418\pi$
$354$	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
$357$	−12.4641	−	6.22489i	−0.659669	−	0.329456i
$358$	3.99878	−	4.61484i	0.211342	−	0.243902i
$359$	4.06200	−	13.8339i	0.214384	−	0.730125i	−0.780139	−	0.625606i	$-0.784852\pi$
$359$	4.06200	−	13.8339i	0.214384	−	0.730125i	0.994523	−	0.104518i	$-0.0333301\pi$
$360$	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
$364$	5.05882	−	15.2456i	0.265154	−	0.799087i
$365$	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	$-0.549266\pi$
$367$	−5.90645			−0.308314			−0.154157	+	0.988046i	$0.549266\pi$
$368$	13.5569	−	10.4381i	0.706702	−	0.544125i
$369$		−	11.0602i		−	0.575770i
$370$	−1.17172	−	1.82323i	−0.0609147	−	0.0947851i
$371$	0.169848	−	4.88011i	0.00881807	−	0.253363i
$372$	−5.38767	+	11.7973i	−0.279338	+	0.611664i
$373$	1.94395	+	6.62049i	0.100654	+	0.342796i	0.994387	−	0.105803i	$-0.0337413\pi$
$373$	1.94395	+	6.62049i	0.100654	+	0.342796i	−0.893733	+	0.448599i	$0.851923\pi$
$374$	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
$378$	−0.407012	+	0.587349i	−0.0209345	+	0.0302100i
$379$	2.26030	−	3.51710i	0.116104	−	0.180661i	−0.778338	−	0.627846i	$-0.783937\pi$
$379$	2.26030	−	3.51710i	0.116104	−	0.180661i	0.894442	+	0.447185i	$0.147573\pi$
$380$	−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	−0.495178	−	0.868792i	$-0.664897\pi$
$383$	−5.18273	−	36.0467i	−0.264825	−	1.84190i	0.230353	−	0.973107i	$-0.426012\pi$
$384$	5.94919	−	5.15500i	0.303593	−	0.263065i
$385$	6.58535	+	11.0760i	0.335621	+	0.564488i
$386$	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	0.826583	−	0.562814i	$-0.190281\pi$
$389$	−0.566956	−	0.882200i	−0.0287458	−	0.0447293i	−0.855329	+	0.518085i	$0.826645\pi$
$390$	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	$-0.617549\pi$
$397$	2.14138	−	0.977934i	0.107473	−	0.0490811i	0.468426	+	0.883503i	$0.344821\pi$
$398$	−1.60436	−	1.85153i	−0.0804194	−	0.0928089i
$399$	−3.61881	−	14.1247i	−0.181167	−	0.707121i
$400$	13.0942	+	3.84481i	0.654710	+	0.192240i
$401$	16.9334	+	14.6729i	0.845614	+	0.732728i	0.965596	−	0.260048i	$-0.0837383\pi$
$401$	16.9334	+	14.6729i	0.845614	+	0.732728i	−0.119982	+	0.992776i	$0.538284\pi$
$402$	−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
$406$	1.29647	−	0.332161i	0.0643428	−	0.0164849i
$407$	−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	$-0.127272\pi$
$409$	−1.29893	−	4.42376i	−0.0642281	−	0.218741i	−0.985353	+	0.170526i	$0.945453\pi$
$410$	−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	$-0.786938\pi$
$419$	−22.6903	+	6.66248i	−1.10849	+	0.325483i	−0.324273	+	0.945964i	$0.605120\pi$
$420$	−2.82413	−	4.74996i	−0.137803	−	0.231774i
$421$	0.466757	−	0.404448i	0.0227484	−	0.0197116i	−0.643412	−	0.765520i	$-0.722482\pi$
$421$	0.466757	−	0.404448i	0.0227484	−	0.0197116i	0.666161	+	0.745808i	$0.267936\pi$
$422$	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
$427$	25.3840	+	17.5902i	1.22842	+	0.851250i
$428$	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	−0.168655	−	0.985675i	$-0.553942\pi$
$431$	9.67073	−	4.41648i	0.465823	−	0.212734i	0.634478	+	0.772941i	$0.281215\pi$
$432$	−1.00512	−	3.42312i	−0.0483588	−	0.164695i
$433$	7.20625	−	15.7795i	0.346310	−	0.758314i	−0.653689	−	0.756764i	$-0.726779\pi$
$433$	7.20625	−	15.7795i	0.346310	−	0.758314i	0.999999	−	0.00154997i	$-0.000493372\pi$
$434$	−0.167282	+	4.80639i	−0.00802980	+	0.230714i
$435$	−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	$-0.0776603\pi$
$439$	7.28174	+	11.3306i	0.347538	+	0.540780i	−0.622847	+	0.782344i	$0.714024\pi$
$440$	5.11324	+	0.735172i	0.243764	+	0.0350480i
$441$	1.47551	−	6.84272i	0.0702623	−	0.325844i
$442$	1.26240	+	4.29932i	0.0600460	+	0.204498i
$443$	−2.45335	−	5.37209i	−0.116562	−	0.255236i	0.842354	−	0.538924i	$-0.181169\pi$
$443$	−2.45335	−	5.37209i	−0.116562	−	0.255236i	−0.958916	+	0.283689i	$0.908442\pi$
$444$	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
$448$	−7.44987	+	14.9168i	−0.351973	+	0.704754i
$449$	8.93655	+	5.74317i	0.421742	+	0.271037i	0.734252	−	0.678877i	$-0.237533\pi$
$449$	8.93655	+	5.74317i	0.421742	+	0.271037i	−0.312510	+	0.949915i	$0.601170\pi$
$450$	−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
$455$	−8.34376	+	3.46500i	−0.391161	+	0.162441i
$456$	−5.31712	−	2.42825i	−0.248997	−	0.113713i
$457$	−32.2218	−	4.63280i	−1.50727	−	0.216713i	−0.661374	−	0.750057i	$-0.730026\pi$
$457$	−32.2218	−	4.63280i	−1.50727	−	0.216713i	−0.845899	+	0.533344i	$0.820935\pi$
$458$	−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	$0.970049\pi$
$462$	2.01710	+	2.49841i	0.0938438	+	0.116236i
$463$	−4.02965	+	28.0268i	−0.187274	+	1.30252i	0.651755	+	0.758430i	$0.274033\pi$
$463$	−4.02965	+	28.0268i	−0.187274	+	1.30252i	−0.839028	+	0.544088i	$0.816876\pi$
$464$	−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	$-0.199240\pi$
$467$	2.48941	+	2.87293i	0.115196	+	0.132943i	−0.695223	+	0.718795i	$0.744694\pi$
$468$	−6.00945	+	0.864028i	−0.277787	+	0.0399397i
$469$	26.8837	+	4.82511i	1.24138	+	0.222803i
$470$	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
$476$	18.2767	−	19.6664i	0.837711	−	0.901408i
$477$	−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	$-0.936952\pi$
$479$	−4.15124	+	9.08995i	−0.189675	+	0.415330i	0.790773	+	0.612110i	$0.209679\pi$
$480$	−3.30958	−	0.475846i	−0.151061	−	0.0217193i
$481$	19.6219	−	12.6102i	0.894681	−	0.574977i
$482$	5.13272			0.233789
$483$	−7.38652	−	10.3169i	−0.336098	−	0.469437i
$484$	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	−0.629516	−	0.776987i	$-0.716747\pi$
$487$	8.16380	−	17.8762i	0.369937	−	0.810049i	0.999453	−	0.0330617i	$-0.0105258\pi$
$488$	11.8792	−	3.48805i	0.537746	−	0.157897i
$489$	−20.6865	+	9.44722i	−0.935477	+	0.427218i
$490$	−1.64269	−	1.22505i	−0.0742093	−	0.0553420i
$491$	4.89665	+	34.0570i	0.220983	+	1.53697i	0.734333	+	0.678790i	$0.237495\pi$
$491$	4.89665	+	34.0570i	0.220983	+	1.53697i	−0.513350	+	0.858180i	$0.671596\pi$
$492$	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
$497$	−4.76546	+	26.5514i	−0.213760	+	1.19099i
$498$	0.193855	−	0.0278722i	0.00868686	−	0.00124898i
$499$	8.97398	+	10.3565i	0.401731	+	0.463622i	0.920185	−	0.391483i	$-0.128038\pi$
$499$	8.97398	+	10.3565i	0.401731	+	0.463622i	−0.518455	+	0.855105i	$0.673492\pi$
$500$	−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	0.698302	+	0.715804i	$0.253939\pi$
$503$	−3.88849	+	27.0450i	−0.173379	+	1.20588i	−0.871681	+	0.490074i	$0.836970\pi$
$504$	−1.76281	−	2.18344i	−0.0785218	−	0.0972583i
$505$		−	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	$-0.439492\pi$
$509$	2.11143	+	0.303578i	0.0935875	+	0.0134558i	−0.0953620	+	0.995443i	$0.530401\pi$
$510$	1.40222	+	0.640373i	0.0620914	+	0.0283562i
$511$	−33.7942	+	14.0341i	−1.49497	+	0.620830i
$512$	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
$518$	4.73294	+	2.36376i	0.207953	+	0.103857i
$519$	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	−0.657968	−	0.753046i	$-0.728584\pi$
$521$	−5.45094	−	37.9121i	−0.238810	−	1.66096i	0.419158	−	0.907913i	$-0.362325\pi$
$522$	−0.331259	−	0.382294i	−0.0144988	−	0.0167325i
$523$	−6.97867	−	15.2812i	−0.305156	−	0.668199i	0.693476	−	0.720479i	$-0.256078\pi$
$523$	−6.97867	−	15.2812i	−0.305156	−	0.668199i	−0.998632	+	0.0522808i	$0.983351\pi$
$524$	−10.7455	−	36.5959i	−0.469420	−	1.59870i
$525$	3.18734	−	9.60559i	0.139107	−	0.419222i
$526$	−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
$532$	28.0812	+	0.977342i	1.21747	+	0.0423731i
$533$	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
$539$	−27.6345	−	15.0244i	−1.19030	−	0.647146i
$540$	−1.12922	+	1.75710i	−0.0485940	+	0.0756137i
$541$	−38.3527	−	24.6478i	−1.64891	−	1.05969i	−0.931955	−	0.362574i	$-0.881898\pi$
$541$	−38.3527	−	24.6478i	−1.64891	−	1.05969i	−0.716957	−	0.697117i	$-0.754466\pi$
$542$	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
$546$	−1.93514	+	1.15055i	−0.0828162	+	0.0492391i
$547$	11.3960	−	3.34618i	0.487260	−	0.143072i	−0.0288693	−	0.999583i	$-0.509191\pi$
$547$	11.3960	−	3.34618i	0.487260	−	0.143072i	0.516129	+	0.856511i	$0.327372\pi$
$548$	−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	0.985241	−	0.171171i	$-0.0547550\pi$
$557$	1.50719	+	5.13302i	0.0638617	+	0.217493i	−0.921380	+	0.388664i	$0.872937\pi$
$558$	1.65348	−	0.755118i	0.0699973	−	0.0319667i
$559$	−2.90563	−	3.35327i	−0.122895	−	0.141828i
$560$	9.91061	−	2.53914i	0.418800	−	0.107298i
$561$	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	$-0.224278\pi$
$563$	11.6071	+	7.45945i	0.489182	+	0.314378i	−0.272694	+	0.962101i	$0.587915\pi$
$564$	−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
$567$	−2.56297	+	0.656644i	−0.107635	+	0.0275764i
$568$	7.08184	+	8.17288i	0.297147	+	0.342926i
$569$	21.2851	−	9.72056i	0.892316	−	0.407507i	0.0841443	−	0.996454i	$-0.473184\pi$
$569$	21.2851	−	9.72056i	0.892316	−	0.407507i	0.808172	+	0.588946i	$0.200457\pi$
$570$	0.454525	+	1.54797i	0.0190380	+	0.0648373i
$571$	−43.2169	−	19.7365i	−1.80857	−	0.825946i	−0.949261	−	0.314489i	$-0.898167\pi$
$571$	−43.2169	−	19.7365i	−1.80857	−	0.825946i	−0.859309	−	0.511457i	$-0.829106\pi$
$572$	−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	$-0.0912525\pi$
$577$	7.29062	+	11.3444i	0.303513	+	0.472275i	−0.655676	+	0.755043i	$0.727616\pi$
$578$	−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
$581$	−1.64905	+	0.980454i	−0.0684140	+	0.0406761i
$582$	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	$-0.814199\pi$
$587$	0.327769	−	0.510018i	0.0135285	−	0.0210507i	0.847952	+	0.530073i	$0.177836\pi$
$588$	11.8511	+	6.44321i	0.488730	+	0.265713i
$589$	−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	0.993338	+	0.115235i	$0.0367622\pi$
$593$	5.35710	+	18.2446i	0.219990	+	0.749217i	−0.773348	+	0.633981i	$0.781420\pi$
$594$	0.504171	−	1.10398i	0.0206864	−	0.0452968i
$595$	−15.0914	−	0.525243i	−0.618687	−	0.0215329i
$596$	−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	$-0.488243\pi$
$601$	−5.12812	−	0.737313i	−0.209181	−	0.0300756i	−0.246108	+	0.969242i	$0.579152\pi$
$602$	0.316946	−	0.955170i	0.0129178	−	0.0389298i
$603$	−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	$-0.997129\pi$
$607$	−3.79079	+	12.9103i	−0.153864	+	0.524011i	0.846096	+	0.533031i	$0.178947\pi$
$608$	11.1333	−	12.8485i	0.451516	−	0.521077i
$609$	4.43308	+	2.21400i	0.179637	+	0.0897157i
$610$	−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	0.00670569	−	0.999978i	$-0.497865\pi$
$613$	7.30054	−	1.04966i	0.294866	−	0.0423953i	0.288160	+	0.957582i	$0.406956\pi$
$614$	3.40435	−	2.94989i	0.137389	−	0.119048i
$615$	−4.97991	−	10.9045i	−0.200809	−	0.439711i
$616$	−11.6456	+	4.83619i	−0.469215	+	0.194856i
$617$	33.3461	+	15.2286i	1.34246	+	0.613082i	0.951592	−	0.307363i	$-0.0994467\pi$
$617$	33.3461	+	15.2286i	1.34246	+	0.613082i	0.390871	+	0.920446i	$0.372174\pi$
$618$	−2.66473	−	0.383130i	−0.107191	−	0.0154117i
$619$	−11.1866	+	7.18916i	−0.449626	+	0.288957i	−0.745791	−	0.666180i	$-0.767928\pi$
$619$	−11.1866	+	7.18916i	−0.449626	+	0.288957i	0.296166	+	0.955137i	$0.404292\pi$
$620$			14.0571i			0.564546i
$621$	−2.24116	+	4.23995i	−0.0899346	+	0.170143i
$622$			4.44699i			0.178308i
$623$	19.4299	+	24.0662i	0.778442	+	0.964191i
$624$	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
$630$	−0.136825	+	0.762340i	−0.00545125	+	0.0303724i
$631$	5.37572	+	4.65809i	0.214004	+	0.185435i	0.755266	−	0.655419i	$-0.227508\pi$
$631$	5.37572	+	4.65809i	0.214004	+	0.185435i	−0.541262	+	0.840854i	$0.682053\pi$
$632$	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
$637$	13.1842	−	17.6790i	0.522376	−	0.700466i
$638$	−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	0.634045	−	0.773296i	$-0.281393\pi$
$641$	25.9394	+	3.72952i	1.02454	+	0.147307i	0.390499	+	0.920603i	$0.372302\pi$
$642$	−1.27704	+	0.820702i	−0.0504006	+	0.0323905i
$643$	−18.8578			−0.743678			−0.371839	−	0.928297i	$-0.621273\pi$
$643$	−18.8578			−0.743678			−0.371839	+	0.928297i	$0.621273\pi$
$644$	23.0862	−	8.05641i	0.909723	−	0.317467i
$645$	−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	$-0.368525\pi$
$647$	13.4429	+	1.93280i	0.528496	+	0.0759863i	0.127098	+	0.991890i	$0.459434\pi$
$648$	−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
$651$	−12.1217	+	13.0434i	−0.475086	+	0.511211i
$652$	−6.23685	−	43.3783i	−0.244254	−	1.69882i
$653$	−17.4593	−	5.12651i	−0.683235	−	0.200616i	−0.0783464	−	0.996926i	$-0.524964\pi$
$653$	−17.4593	−	5.12651i	−0.683235	−	0.200616i	−0.604888	+	0.796310i	$0.706782\pi$
$654$	−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
$658$	−0.787418	−	0.141326i	−0.0306968	−	0.00550947i
$659$	7.42513	−	1.06757i	0.289242	−	0.0415867i	0.00383348	−	0.999993i	$-0.498780\pi$
$659$	7.42513	−	1.06757i	0.289242	−	0.0415867i	0.285409	+	0.958406i	$0.407871\pi$
$660$	6.14621	+	7.09310i	0.239241	+	0.276099i
$661$	−7.89523	−	17.2882i	−0.307089	−	0.672431i	0.691671	−	0.722213i	$-0.256875\pi$
$661$	−7.89523	−	17.2882i	−0.307089	−	0.672431i	−0.998760	+	0.0497815i	$0.984148\pi$
$662$	−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
$665$	−9.92760	−	12.2965i	−0.384976	−	0.476837i
$666$		−	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
$672$	7.53772	−	3.13026i	0.290774	−	0.120753i
$673$	−3.26764	−	7.15514i	−0.125958	−	0.275810i	0.836138	−	0.548518i	$-0.184808\pi$
$673$	−3.26764	−	7.15514i	−0.125958	−	0.275810i	−0.962097	+	0.272708i	$0.912081\pi$
$674$	−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	$-0.755294\pi$
$677$	1.86548	−	2.15288i	0.0716963	−	0.0827420i	0.790465	+	0.612508i	$0.209839\pi$
$678$	2.00740	+	1.29008i	0.0770936	+	0.0495450i
$679$	−9.48008	+	18.9819i	−0.363812	+	0.728459i
$680$	−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	0.835634	−	0.549287i	$-0.185100\pi$
$683$	4.52163	+	5.21824i	0.173015	+	0.199670i	−0.662619	+	0.748957i	$0.730555\pi$
$684$	−4.41176	−	9.66041i	−0.168688	−	0.369375i
$685$	0.857599	+	2.92072i	0.0327672	+	0.111595i
$686$	4.97491	+	0.521126i	0.189943	+	0.0198967i
$687$	−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
$693$	−0.413528	+	11.8816i	−0.0157086	+	0.451344i
$694$	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
$700$	16.0302	+	11.1084i	0.605885	+	0.419857i
$701$	−20.2576	+	31.5215i	−0.765120	+	1.19055i	0.211877	+	0.977296i	$0.432042\pi$
$701$	−20.2576	+	31.5215i	−0.765120	+	1.19055i	−0.976997	+	0.213253i	$0.931594\pi$
$702$	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
$707$	12.9925	+	21.8524i	0.488634	+	0.821844i
$708$	−23.5568	+	6.91691i	−0.885320	+	0.259953i
$709$	−36.7527	−	16.7844i	−1.38027	−	0.630350i	−0.419519	−	0.907746i	$-0.637801\pi$
$709$	−36.7527	−	16.7844i	−1.38027	−	0.630350i	−0.960756	+	0.277396i	$0.910529\pi$
$710$	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	$-0.436073\pi$
$719$	28.7094	−	13.1112i	1.07068	−	0.488964i	0.871195	+	0.490937i	$0.163345\pi$
$720$	−2.53225	−	2.92237i	−0.0943712	−	0.108910i
$721$	25.5465	−	6.54512i	0.951402	−	0.243753i
$722$	−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	$-0.183165\pi$
$727$	33.7177	+	9.90040i	1.25052	+	0.367186i	0.411562	+	0.911382i	$0.364984\pi$
$728$	−2.19426	−	8.56450i	−0.0813247	−	0.317422i
$729$	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	0.747218	+	0.664579i	$0.231389\pi$
$733$	−4.24969	+	29.5572i	−0.156966	+	1.09172i	−0.904184	+	0.427143i	$0.859520\pi$
$734$	−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	−0.799392	−	0.600809i	$-0.794845\pi$
$739$	3.72120	−	25.8815i	0.136887	−	0.952067i	0.936279	−	0.351257i	$-0.114246\pi$
$740$	14.0658	+	6.42365i	0.517070	+	0.236138i
$741$	−16.6595	+	4.89168i	−0.612003	+	0.179700i
$742$	−0.674009	−	1.13363i	−0.0247436	−	0.0416168i
$743$	−7.25393	+	6.28557i	−0.266121	+	0.230595i	−0.777691	−	0.628646i	$-0.783609\pi$
$743$	−7.25393	+	6.28557i	−0.266121	+	0.230595i	0.511570	+	0.859241i	$0.329064\pi$
$744$	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
$749$	8.46972	−	12.2224i	0.309477	−	0.446598i
$750$	−0.727859	+	2.47886i	−0.0265777	+	0.0905152i
$751$	−23.5208	+	3.38177i	−0.858284	+	0.123403i	−0.557386	−	0.830254i	$-0.688196\pi$
$751$	−23.5208	+	3.38177i	−0.858284	+	0.123403i	−0.300898	+	0.953656i	$0.597287\pi$
$752$	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
$756$	0.177341	−	5.09541i	0.00644984	−	0.185318i
$757$	−5.87141	−	9.13609i	−0.213400	−	0.332057i	0.718007	−	0.696036i	$-0.245054\pi$
$757$	−5.87141	−	9.13609i	−0.213400	−	0.332057i	−0.931407	+	0.363979i	$0.881418\pi$
$758$		−	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	$-0.0137762\pi$
$761$	15.0257	+	23.3805i	0.544682	+	0.847541i	−0.454382	+	0.890807i	$0.650140\pi$
$762$	−2.35980	−	0.339287i	−0.0854864	−	0.0122911i
$763$	2.58345	−	7.78567i	0.0935273	−	0.281860i
$764$	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	$-0.880245\pi$
$769$	−12.0360	+	13.8903i	−0.434030	+	0.500897i	0.496030	+	0.868305i	$0.334791\pi$
$770$	3.11362	+	1.55503i	0.112207	+	0.0560393i
$771$	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	$-0.641823\pi$
$773$	−35.6254	−	10.4606i	−1.28136	−	0.376241i	−0.850402	+	0.526133i	$0.823641\pi$
$774$	−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
$777$	7.51227	+	18.0896i	0.269501	+	0.648962i
$778$	−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
$784$	−17.6267	+	17.6910i	−0.629525	+	0.631821i
$785$	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	$-0.698818\pi$
$787$	−17.9026	+	5.25668i	−0.638159	+	0.187380i	−0.0533816	+	0.998574i	$0.517000\pi$
$788$	−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
$791$	−23.0072	−	4.12934i	−0.818041	−	0.146822i
$792$	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	0.911700	+	0.410856i	$0.134770\pi$
$797$	4.31039	+	29.9794i	0.152682	+	1.06193i	−0.759018	+	0.651069i	$0.774321\pi$
$798$	−2.88475	−	2.68091i	−0.102119	−	0.0949030i
$799$	−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
$805$	−11.9278	−	6.84589i	−0.420399	−	0.241286i
$806$	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	−0.143582	+	0.989638i	$0.545862\pi$
$809$	−22.6825	+	49.6678i	−0.797475	+	1.74623i	−0.653892	+	0.756588i	$0.726865\pi$
$810$	0.280883	−	0.0824748i	0.00986924	−	0.00289787i
$811$	−17.4723	+	7.97932i	−0.613534	+	0.280192i	−0.697846	−	0.716248i	$-0.745858\pi$
$811$	−17.4723	+	7.97932i	−0.613534	+	0.280192i	0.0843118	+	0.996439i	$0.473131\pi$
$812$	−6.50044	+	6.99472i	−0.228121	+	0.245466i
$813$	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
$819$	−8.20443	−	1.47254i	−0.286686	−	0.0514546i
$820$	22.8660	−	3.28763i	0.798514	−	0.114809i
$821$	1.30591	+	1.50710i	0.0455766	+	0.0525981i	0.778080	−	0.628165i	$-0.216194\pi$
$821$	1.30591	+	1.50710i	0.0455766	+	0.0525981i	−0.732504	+	0.680763i	$0.761648\pi$
$822$	0.315109	+	0.689992i	0.0109907	+	0.0240662i
$823$	−7.99543	+	2.34767i	−0.278703	+	0.0818347i	−0.418097	−	0.908402i	$-0.637303\pi$
$823$	−7.99543	+	2.34767i	−0.278703	+	0.0818347i	0.139394	+	0.990237i	$0.455485\pi$
$824$	4.39182	−	9.61674i	0.152996	−	0.335015i
$825$	−2.44622	+	17.0138i	−0.0851664	+	0.592345i
$826$	−7.08365	+	5.71900i	−0.246472	+	0.198990i
$827$			47.9455i			1.66723i	0.552347	+	0.833614i	$0.313732\pi$
$827$			47.9455i			1.66723i	−0.552347	+	0.833614i	$0.686268\pi$
$828$	−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
$833$	32.3197	−	17.7243i	1.11981	−	0.614112i
$834$	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	$-0.424807\pi$
$839$	−16.0212	−	10.2962i	−0.553115	−	0.355465i	−0.787149	+	0.616763i	$0.788444\pi$
$840$	−2.72110	−	1.35899i	−0.0938869	−	0.0468896i
$841$	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
$847$	23.0818	+	7.65903i	0.793099	+	0.263167i
$848$	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	0.952837	+	0.303481i	$0.0981489\pi$
$853$	24.3308	+	37.8595i	0.833071	+	1.29628i	−0.119767	+	0.992802i	$0.538215\pi$
$854$	8.33614	+	0.290132i	0.285257	+	0.00992811i
$855$	−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	$-0.634024\pi$
$857$	0.391463	−	0.178775i	0.0133721	−	0.00610685i	0.422090	+	0.906554i	$0.361297\pi$
$858$	2.88973	−	2.50397i	0.0986538	−	0.0854840i
$859$	44.1198	−	6.34347i	1.50535	−	0.216436i	0.660249	−	0.751046i	$-0.270451\pi$
$859$	44.1198	−	6.34347i	1.50535	−	0.216436i	0.845099	+	0.534610i	$0.179542\pi$
$860$	0.828731	−	2.82240i	0.0282595	−	0.0962430i
$861$	24.0520	+	16.6672i	0.819690	+	0.568016i
$862$	1.55242	−	2.41562i	0.0528757	−	0.0822762i
$863$	−34.6908	−	22.2944i	−1.18089	−	0.758912i	−0.205340	−	0.978691i	$-0.565830\pi$
$863$	−34.6908	−	22.2944i	−1.18089	−	0.758912i	−0.975550	+	0.219779i	$0.929466\pi$
$864$	−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
$868$	−17.5361	−	29.4943i	−0.595214	−	1.00110i
$869$	−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	−0.659518	−	0.751689i	$-0.729240\pi$
$877$	5.48040	−	38.1171i	0.185060	−	1.28712i	0.844578	−	0.535433i	$-0.179851\pi$
$878$	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	$-0.436553\pi$
$881$	−23.7570	−	27.4171i	−0.800395	−	0.923705i	−0.998403	+	0.0564951i	$0.982007\pi$
$882$	−0.663928	−	1.77022i	−0.0223556	−	0.0596063i
$883$	−27.5009	−	8.07500i	−0.925480	−	0.271745i	−0.215937	−	0.976407i	$-0.569280\pi$
$883$	−27.5009	−	8.07500i	−0.925480	−	0.271745i	−0.709543	+	0.704662i	$0.751099\pi$
$884$	−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	$-0.217383\pi$
$887$	7.78761	+	6.74800i	0.261482	+	0.226576i	−0.514246	+	0.857643i	$0.671928\pi$
$888$	7.53434	+	2.21228i	0.252836	+	0.0742394i
$889$	22.6232	−	5.79615i	0.758757	−	0.194397i
$890$	−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
$903$	3.20277	−	1.90424i	0.106582	−	0.0633690i
$904$	−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	0.619812	−	0.784750i	$-0.287209\pi$
$907$	−2.07024	−	1.79388i	−0.0687413	−	0.0595647i	−0.688554	+	0.725185i	$0.741754\pi$
$908$	−17.2952	−	11.1149i	−0.573960	−	0.368862i
$909$	5.19503	−	8.08363i	0.172308	−	0.268117i
$910$	−1.38985	+	2.00566i	−0.0460732	+	0.0664870i
$911$	14.4023	−	49.0498i	0.477170	−	1.62509i	−0.271704	−	0.962381i	$-0.587587\pi$
$911$	14.4023	−	49.0498i	0.477170	−	1.62509i	0.748874	−	0.662712i	$-0.230595\pi$
$912$	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
$917$	1.82143	−	52.3339i	0.0601491	−	1.72822i
$918$	0.768923	+	1.19647i	0.0253782	+	0.0394893i
$919$			15.7075i			0.518142i	0.965858	+	0.259071i	$0.0834163\pi$
$919$			15.7075i			0.518142i	−0.965858	+	0.259071i	$0.916584\pi$
$920$	−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
$924$	−21.7444	−	7.21527i	−0.715339	−	0.237365i
$925$	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	0.543091	+	0.839674i	$0.317254\pi$
$929$	−11.2088	+	38.1736i	−0.367748	+	1.25244i	−0.910839	+	0.412762i	$0.864564\pi$
$930$	1.29020	−	1.48898i	0.0423075	−	0.0488254i
$931$	36.1697	+	13.4157i	1.18541	+	0.439681i
$932$	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	$-0.0539487\pi$
$937$	6.51140	+	14.2580i	0.212718	+	0.465788i	−0.772954	+	0.634463i	$0.781221\pi$
$938$	6.81292	−	2.82927i	0.222450	−	0.0923789i
$939$	−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	$-0.713403\pi$
$941$	−5.11296	+	3.28590i	−0.166678	+	0.107117i	0.454643	+	0.890674i	$0.349767\pi$
$942$		−	4.82305i		−	0.157144i
$943$	51.6731	−	11.9762i	1.68271	−	0.390000i
$944$		−	45.4529i		−	1.47937i
$945$	−2.23123	+	1.80139i	−0.0725820	+	0.0585993i
$946$	−0.243250	+	1.69184i	−0.00790872	+	0.0550064i
$947$	20.4952	−	44.8782i	0.666004	−	1.45835i	−0.210815	−	0.977526i	$-0.567612\pi$
$947$	20.4952	−	44.8782i	0.666004	−	1.45835i	0.876819	−	0.480820i	$-0.159661\pi$
$948$	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
$952$	2.61049	−	14.5447i	0.0846065	−	0.471397i
$953$	−22.2093	−	19.2445i	−0.719431	−	0.623391i	0.216208	−	0.976347i	$-0.430631\pi$
$953$	−22.2093	−	19.2445i	−0.719431	−	0.623391i	−0.935640	+	0.352956i	$0.885176\pi$
$954$	−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
$959$	−5.44297	−	5.05834i	−0.175763	−	0.163342i
$960$	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
$966$	−3.18481	−	1.26556i	−0.102470	−	0.0407188i
$967$	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	$-0.537418\pi$
$971$	10.0015	−	2.93670i	0.320963	−	0.0942431i	0.438245	+	0.898855i	$0.355600\pi$
$972$	−1.75291	+	0.800526i	−0.0562245	+	0.0256769i
$973$	−22.3266	−	20.7489i	−0.715757	−	0.665178i
$974$	−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	−0.912718	−	0.408591i	$-0.866020\pi$
$977$	−5.06030	+	7.87398i	−0.161893	+	0.251911i	0.750824	+	0.660502i	$0.229657\pi$
$978$	−3.32077	+	5.16721i	−0.106186	+	0.165229i
$979$	−39.7013	−	34.4014i	−1.26886	−	1.09947i
$980$	14.5853	+	1.01649i	0.465911	+	0.0324706i
$981$	−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	$-0.243726\pi$
$983$	−8.62034	−	18.8759i	−0.274946	−	0.602048i	−0.995852	+	0.0909847i	$0.970999\pi$
$984$	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
$987$	−1.86065	−	2.30463i	−0.0592252	−	0.0733573i
$988$		−	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	−0.962068	−	0.272811i	$-0.912046\pi$
$991$	−35.0553	+	22.5286i	−1.11357	+	0.715646i	−0.151499	+	0.988457i	$0.548410\pi$
$992$	−20.5505	−	2.95471i	−0.652478	−	0.0938122i
$993$	−4.42465	−	2.02067i	−0.140412	−	0.0641241i
$994$	2.79429	+	6.72870i	0.0886296	+	0.213421i
$995$	−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	$-0.947195\pi$
$997$	−59.5532	+	8.56246i	−1.88607	+	0.271176i	−0.899798	+	0.436307i	$0.856286\pi$
$998$	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.34.20	yes	320
7.6	odd	2	inner	483.2.r.a.34.19	✓	320
23.21	odd	22	inner	483.2.r.a.412.19	yes	320
161.90	even	22	inner	483.2.r.a.412.20	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.19	✓	320	7.6	odd	2	inner
483.2.r.a.34.20	yes	320	1.1	even	1	trivial
483.2.r.a.412.19	yes	320	23.21	odd	22	inner
483.2.r.a.412.20	yes	320	161.90	even	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+(0.227214 - 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} +(-1.80110 + 1.93805i) 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} +(-0.126238 + 0.703351i) 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} +(-2.05858 + 1.66200i) 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} +(-1.95540 - 4.70862i) 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} +(-1.28128 + 2.56549i) 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} +(-0.225050 + 0.678226i) 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} +(-0.512079 - 6.98124i) 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} +(-2.30655 - 1.59836i) 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} +(-2.27415 + 1.35212i) 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} +(2.95065 + 11.5168i) 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} +(-1.26539 - 4.93898i) 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} +(-1.13576 - 1.51146i) q^{98} +(3.39599 - 2.94264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49}+ \cdots + 44 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

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