LMFDB - Embedded newform 483.2.r.a.412.8

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			412.8
Character	$\chi$	$=$	483.412
Dual form			483.2.r.a.34.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33182 - 0.855909i) q^{2} +(0.989821 - 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(4.17306 + 1.22532i) q^{5} +(-1.44007 - 0.657659i) q^{6} +(-2.59192 - 0.530984i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-1.33182 - 0.855909i) q^{2} +(0.989821 - 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(4.17306 + 1.22532i) q^{5} +(-1.44007 - 0.657659i) q^{6} +(-2.59192 - 0.530984i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +(-4.50901 - 5.20367i) q^{10} +(-3.50024 - 5.44647i) q^{11} +(0.273740 + 0.425947i) q^{12} +(2.11393 - 1.83173i) q^{13} +(2.99750 + 2.92562i) q^{14} +(4.30497 + 0.618961i) q^{15} +(3.11470 - 3.59456i) q^{16} +(1.32826 - 2.90849i) q^{17} +(-1.51901 - 0.446021i) q^{18} +(1.41547 + 3.09945i) q^{19} +(0.313395 + 2.17971i) q^{20} +(-2.64111 - 0.156711i) q^{21} +10.2496i q^{22} +(3.53817 - 3.23750i) q^{23} +2.36469i q^{24} +(11.7068 + 7.52349i) q^{25} +(-4.38317 + 0.630205i) q^{26} +(0.909632 - 0.415415i) q^{27} +(-0.300616 - 1.30544i) q^{28} +(-0.356601 + 0.780848i) q^{29} +(-5.20367 - 4.50901i) q^{30} +(1.03495 + 0.148803i) q^{31} +(-2.68703 + 0.788982i) q^{32} +(-4.23972 - 4.89290i) q^{33} +(-4.25842 + 2.73672i) q^{34} +(-10.1656 - 5.39177i) q^{35} +(0.331572 + 0.382655i) q^{36} +(-0.117697 - 0.400840i) q^{37} +(0.767692 - 5.33942i) q^{38} +(1.83173 - 2.11393i) q^{39} +(-4.27238 + 9.35522i) q^{40} +(1.55178 - 5.28489i) q^{41} +(3.38335 + 2.46926i) q^{42} +(5.78126 - 0.831220i) q^{43} +(1.77226 - 2.75768i) q^{44} +4.34924 q^{45} +(-7.48320 + 1.28342i) q^{46} -0.395155i q^{47} +(2.57144 - 4.00124i) q^{48} +(6.43611 + 2.75254i) q^{49} +(-9.15191 - 20.0399i) q^{50} +(0.900823 - 3.06792i) q^{51} +(1.28827 + 0.588334i) q^{52} +(-1.42105 - 1.23135i) q^{53} +(-1.56702 - 0.225304i) q^{54} +(-7.93303 - 27.0174i) q^{55} +(2.11510 - 5.88802i) q^{56} +(1.84216 + 2.86646i) q^{57} +(1.14326 - 0.734730i) q^{58} +(-3.12292 + 2.70603i) q^{59} +(0.620411 + 2.11293i) q^{60} +(-1.75024 + 12.1732i) q^{61} +(-1.25100 - 1.08400i) q^{62} +(-2.63653 + 0.220753i) q^{63} +(-4.87331 - 1.43093i) q^{64} +(11.0660 - 5.05369i) q^{65} +(1.45867 + 10.1453i) q^{66} +(-3.36055 + 5.22911i) q^{67} +1.61894 q^{68} +(3.04141 - 3.70808i) q^{69} +(8.92392 + 15.8817i) q^{70} +(-4.63663 - 2.97978i) q^{71} +(0.336531 + 2.34062i) q^{72} +(-7.75564 + 3.54188i) q^{73} +(-0.186331 + 0.634585i) q^{74} +(12.6583 + 5.78087i) q^{75} +(-1.12979 + 1.30384i) q^{76} +(6.18034 + 15.9754i) q^{77} +(-4.24887 + 1.24758i) q^{78} +(-10.8904 + 9.43656i) q^{79} +(17.4024 - 11.1838i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-6.59008 + 5.71034i) q^{82} +(-13.0549 + 3.83325i) q^{83} +(-0.483340 - 1.24937i) q^{84} +(9.10678 - 10.5098i) q^{85} +(-8.41105 - 3.84120i) q^{86} +(-0.241845 + 0.823649i) q^{87} +(13.9261 - 6.35983i) q^{88} +(-0.0377817 - 0.262778i) q^{89} +(-5.79240 - 3.72255i) q^{90} +(-6.45176 + 3.62524i) q^{91} +(2.23529 + 0.948611i) q^{92} +1.04559 q^{93} +(-0.338217 + 0.526276i) q^{94} +(2.10903 + 14.6686i) q^{95} +(-2.54739 + 1.16336i) q^{96} +(8.56990 + 2.51635i) q^{97} +(-6.21582 - 9.17461i) q^{98} +(-4.89290 - 4.23972i) 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 $

$2$	−1.33182	−	0.855909i	−0.941739	−	0.605219i	−0.0228516	−	0.999739i	$-0.507275\pi$
$2$	−1.33182	−	0.855909i	−0.941739	−	0.605219i	−0.918887	+	0.394520i	$0.870911\pi$
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i
$4$	0.210335	+	0.460569i	0.105167	+	0.230285i
$5$	4.17306	+	1.22532i	1.86625	+	0.547981i	0.998719	+	0.0505996i	$0.0161132\pi$
$5$	4.17306	+	1.22532i	1.86625	+	0.547981i	0.867532	+	0.497381i	$0.165705\pi$
$6$	−1.44007	−	0.657659i	−0.587907	−	0.268488i
$7$	−2.59192	−	0.530984i	−0.979654	−	0.200693i
$7$	−2.59192	−	0.530984i	−0.979654	−	0.200693i
$8$	−0.336531	+	2.34062i	−0.118982	+	0.827536i
$9$	0.959493	−	0.281733i	0.319831	−	0.0939109i
$10$	−4.50901	−	5.20367i	−1.42587	−	1.64555i
$11$	−3.50024	−	5.44647i	−1.05536	−	1.64217i	−0.710776	−	0.703419i	$-0.751656\pi$
$11$	−3.50024	−	5.44647i	−1.05536	−	1.64217i	−0.344585	−	0.938755i	$-0.611980\pi$
$12$	0.273740	+	0.425947i	0.0790219	+	0.122960i
$13$	2.11393	−	1.83173i	0.586299	−	0.508031i	−0.310439	−	0.950593i	$-0.600476\pi$
$13$	2.11393	−	1.83173i	0.586299	−	0.508031i	0.896738	+	0.442563i	$0.145931\pi$
$14$	2.99750	+	2.92562i	0.801115	+	0.781906i
$15$	4.30497	+	0.618961i	1.11154	+	0.159815i
$16$	3.11470	−	3.59456i	0.778676	−	0.898640i
$17$	1.32826	−	2.90849i	0.322152	−	0.705414i	−0.677392	−	0.735622i	$-0.736890\pi$
$17$	1.32826	−	2.90849i	0.322152	−	0.705414i	0.999544	+	0.0302087i	$0.00961718\pi$
$18$	−1.51901	−	0.446021i	−0.358034	−	0.105128i
$19$	1.41547	+	3.09945i	0.324731	+	0.711062i	0.999640	−	0.0268395i	$-0.00854430\pi$
$19$	1.41547	+	3.09945i	0.324731	+	0.711062i	−0.674909	+	0.737901i	$0.735817\pi$
$20$	0.313395	+	2.17971i	0.0700773	+	0.487399i
$21$	−2.64111	−	0.156711i	−0.576337	−	0.0341971i
$22$			10.2496i			2.18522i
$23$	3.53817	−	3.23750i	0.737758	−	0.675065i
$23$	3.53817	−	3.23750i	0.737758	−	0.675065i
$24$			2.36469i			0.482691i
$25$	11.7068	+	7.52349i	2.34136	+	1.50470i
$26$	−4.38317	+	0.630205i	−0.859610	+	0.123593i
$27$	0.909632	−	0.415415i	0.175059	−	0.0799467i
$28$	−0.300616	−	1.30544i	−0.0568112	−	0.246706i
$29$	−0.356601	+	0.780848i	−0.0662192	+	0.145000i	−0.939848	−	0.341594i	$-0.889033\pi$
$29$	−0.356601	+	0.780848i	−0.0662192	+	0.145000i	0.873629	+	0.486593i	$0.161761\pi$
$30$	−5.20367	−	4.50901i	−0.950056	−	0.823228i
$31$	1.03495	+	0.148803i	0.185882	+	0.0267258i	0.234627	−	0.972085i	$-0.424613\pi$
$31$	1.03495	+	0.148803i	0.185882	+	0.0267258i	−0.0487450	+	0.998811i	$0.515522\pi$
$32$	−2.68703	+	0.788982i	−0.475004	+	0.139474i
$33$	−4.23972	−	4.89290i	−0.738041	−	0.851745i
$34$	−4.25842	+	2.73672i	−0.730312	+	0.469343i
$35$	−10.1656	−	5.39177i	−1.71830	−	0.911376i
$36$	0.331572	+	0.382655i	0.0552620	+	0.0637758i
$37$	−0.117697	−	0.400840i	−0.0193493	−	0.0658977i	0.949252	−	0.314515i	$-0.101842\pi$
$37$	−0.117697	−	0.400840i	−0.0193493	−	0.0658977i	−0.968602	+	0.248618i	$0.920024\pi$
$38$	0.767692	−	5.33942i	0.124536	−	0.866168i
$39$	1.83173	−	2.11393i	0.293312	−	0.338500i
$40$	−4.27238	+	9.35522i	−0.675523	+	1.47919i
$41$	1.55178	−	5.28489i	0.242348	−	0.825362i	−0.745037	−	0.667023i	$-0.767568\pi$
$41$	1.55178	−	5.28489i	0.242348	−	0.825362i	0.987385	−	0.158338i	$-0.0506137\pi$
$42$	3.38335	+	2.46926i	0.522062	+	0.381015i
$43$	5.78126	−	0.831220i	0.881634	−	0.126760i	0.313394	−	0.949623i	$-0.398534\pi$
$43$	5.78126	−	0.831220i	0.881634	−	0.126760i	0.568239	+	0.822863i	$0.307625\pi$
$44$	1.77226	−	2.75768i	0.267178	−	0.415737i
$45$	4.34924			0.648346
$46$	−7.48320	+	1.28342i	−1.10334	+	0.189230i
$47$		−	0.395155i		−	0.0576393i	−0.999585	−	0.0288197i	$-0.990825\pi$
$47$		−	0.395155i		−	0.0576393i	0.999585	−	0.0288197i	$-0.00917485\pi$
$48$	2.57144	−	4.00124i	0.371156	−	0.577529i
$49$	6.43611	+	2.75254i	0.919444	+	0.393220i
$50$	−9.15191	−	20.0399i	−1.29427	−	2.83407i
$51$	0.900823	−	3.06792i	0.126140	−	0.429595i
$52$	1.28827	+	0.588334i	0.178651	+	0.0815872i
$53$	−1.42105	−	1.23135i	−0.195196	−	0.169138i	0.551779	−	0.833990i	$-0.313949\pi$
$53$	−1.42105	−	1.23135i	−0.195196	−	0.169138i	−0.746975	+	0.664852i	$0.768495\pi$
$54$	−1.56702	−	0.225304i	−0.213245	−	0.0306600i
$55$	−7.93303	−	27.0174i	−1.06969	−	3.64303i
$56$	2.11510	−	5.88802i	0.282642	−	0.786820i
$57$	1.84216	+	2.86646i	0.244000	+	0.379671i
$58$	1.14326	−	0.734730i	0.150118	−	0.0964748i
$59$	−3.12292	+	2.70603i	−0.406570	+	0.352295i	−0.834011	−	0.551749i	$-0.813961\pi$
$59$	−3.12292	+	2.70603i	−0.406570	+	0.352295i	0.427440	+	0.904044i	$0.359415\pi$
$60$	0.620411	+	2.11293i	0.0800947	+	0.272777i
$61$	−1.75024	+	12.1732i	−0.224095	+	1.55861i	0.498220	+	0.867050i	$0.333987\pi$
$61$	−1.75024	+	12.1732i	−0.224095	+	1.55861i	−0.722315	+	0.691564i	$0.756922\pi$
$62$	−1.25100	−	1.08400i	−0.158878	−	0.137668i
$63$	−2.63653	+	0.220753i	−0.332171	+	0.0278122i
$64$	−4.87331	−	1.43093i	−0.609164	−	0.178867i
$65$	11.0660	−	5.05369i	1.37257	−	0.626833i
$66$	1.45867	+	10.1453i	0.179550	+	1.24880i
$67$	−3.36055	+	5.22911i	−0.410556	+	0.638838i	−0.983532	−	0.180734i	$-0.942153\pi$
$67$	−3.36055	+	5.22911i	−0.410556	+	0.638838i	0.572976	+	0.819572i	$0.305789\pi$
$68$	1.61894			0.196326
$69$	3.04141	−	3.70808i	0.366142	−	0.446400i
$70$	8.92392	+	15.8817i	1.06661	+	1.89823i
$71$	−4.63663	−	2.97978i	−0.550267	−	0.353635i	0.235776	−	0.971807i	$-0.424237\pi$
$71$	−4.63663	−	2.97978i	−0.550267	−	0.353635i	−0.786042	+	0.618173i	$0.787873\pi$
$72$	0.336531	+	2.34062i	0.0396606	+	0.275845i
$73$	−7.75564	+	3.54188i	−0.907729	+	0.414546i	−0.813875	−	0.581040i	$-0.802646\pi$
$73$	−7.75564	+	3.54188i	−0.907729	+	0.414546i	−0.0938541	+	0.995586i	$0.529919\pi$
$74$	−0.186331	+	0.634585i	−0.0216605	+	0.0737690i
$75$	12.6583	+	5.78087i	1.46166	+	0.667517i
$76$	−1.12979	+	1.30384i	−0.129595	+	0.149561i
$77$	6.18034	+	15.9754i	0.704316	+	1.82057i
$78$	−4.24887	+	1.24758i	−0.481089	+	0.141261i
$79$	−10.8904	+	9.43656i	−1.22526	+	1.06170i	−0.229170	+	0.973386i	$0.573601\pi$
$79$	−10.8904	+	9.43656i	−1.22526	+	1.06170i	−0.996093	+	0.0883098i	$0.971853\pi$
$80$	17.4024	−	11.1838i	1.94564	−	1.25039i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	−6.59008	+	5.71034i	−0.727753	+	0.630602i
$83$	−13.0549	+	3.83325i	−1.43296	+	0.420754i	−0.903868	−	0.427812i	$-0.859285\pi$
$83$	−13.0549	+	3.83325i	−1.43296	+	0.420754i	−0.529089	+	0.848566i	$0.677466\pi$
$84$	−0.483340	−	1.24937i	−0.0527368	−	0.136318i
$85$	9.10678	−	10.5098i	0.987769	−	1.13995i
$86$	−8.41105	−	3.84120i	−0.906987	−	0.414207i
$87$	−0.241845	+	0.823649i	−0.0259285	+	0.0883045i
$88$	13.9261	−	6.35983i	1.48453	−	0.677960i
$89$	−0.0377817	−	0.262778i	−0.00400486	−	0.0278544i	0.987721	−	0.156228i	$-0.0499334\pi$
$89$	−0.0377817	−	0.262778i	−0.00400486	−	0.0278544i	−0.991726	+	0.128374i	$0.959024\pi$
$90$	−5.79240	−	3.72255i	−0.610573	−	0.392391i
$91$	−6.45176	+	3.62524i	−0.676328	+	0.380028i
$92$	2.23529	+	0.948611i	0.233045	+	0.0988995i
$93$	1.04559			0.108423
$94$	−0.338217	+	0.526276i	−0.0348844	+	0.0542812i
$95$	2.10903	+	14.6686i	0.216381	+	1.50497i
$96$	−2.54739	+	1.16336i	−0.259992	+	0.118734i
$97$	8.56990	+	2.51635i	0.870142	+	0.255497i	0.686176	−	0.727436i	$-0.259288\pi$
$97$	8.56990	+	2.51635i	0.870142	+	0.255497i	0.183966	+	0.982933i	$0.441106\pi$
$98$	−6.21582	−	9.17461i	−0.627893	−	0.926776i
$99$	−4.89290	−	4.23972i	−0.491755	−	0.426108i
$100$	−1.00274	+	6.97424i	−0.100274	+	0.697424i
$101$	0.360852	+	1.22895i	0.0359061	+	0.122285i	0.975496	−	0.220017i	$-0.0706114\pi$
$101$	0.360852	+	1.22895i	0.0359061	+	0.122285i	−0.939590	+	0.342302i	$0.888793\pi$
$102$	−3.82560	+	3.31490i	−0.378790	+	0.328224i
$103$	9.86187	−	6.33784i	0.971719	−	0.624486i	0.0445013	−	0.999009i	$-0.485830\pi$
$103$	9.86187	−	6.33784i	0.971719	−	0.624486i	0.927217	+	0.374524i	$0.122194\pi$
$104$	3.57599	+	5.56435i	0.350655	+	0.545629i
$105$	−10.8295	−	3.89017i	−1.05685	−	0.379642i
$106$	0.838661	+	2.85622i	0.0814580	+	0.277420i
$107$	−4.53829	−	0.652508i	−0.438733	−	0.0630803i	−0.0805907	−	0.996747i	$-0.525681\pi$
$107$	−4.53829	−	0.652508i	−0.438733	−	0.0630803i	−0.358142	+	0.933667i	$0.616590\pi$
$108$	0.382655	+	0.331572i	0.0368210	+	0.0319055i
$109$	−12.9396	−	5.90933i	−1.23939	−	0.566012i	−0.315595	−	0.948894i	$-0.602204\pi$
$109$	−12.9396	−	5.90933i	−1.23939	−	0.566012i	−0.923797	+	0.382882i	$0.874931\pi$
$110$	−12.5591	+	42.7723i	−1.19746	+	4.07818i
$111$	−0.173545	−	0.380010i	−0.0164721	−	0.0360689i
$112$	−9.98172	+	7.66296i	−0.943184	+	0.724081i
$113$	0.585494	−	0.911047i	0.0550787	−	0.0857041i	−0.812622	−	0.582791i	$-0.801961\pi$
$113$	0.585494	−	0.911047i	0.0550787	−	0.0857041i	0.867701	+	0.497087i	$0.165597\pi$
$114$		−	5.39432i		−	0.505225i
$115$	18.7320	−	9.17489i	1.74677	−	0.855563i
$116$	−0.434640			−0.0403553
$117$	1.51224	−	2.35310i	0.139807	−	0.217544i
$118$	6.47529	−	0.931006i	0.596099	−	0.0857060i
$119$	−4.98712	+	6.83330i	−0.457169	+	0.626408i
$120$	−2.89751	+	9.86802i	−0.264505	+	0.900823i
$121$	−12.8429	+	28.1219i	−1.16753	+	2.55654i
$122$	12.7501	−	14.7144i	1.15434	−	1.33218i
$123$	0.783871	−	5.45194i	0.0706793	−	0.491585i
$124$	0.149152	+	0.507964i	0.0133942	+	0.0456165i
$125$	25.3937	+	29.3059i	2.27128	+	2.62120i
$126$	3.70032	+	1.96262i	0.329651	+	0.174844i
$127$	4.61254	−	2.96430i	0.409297	−	0.263039i	−0.319751	−	0.947501i	$-0.603599\pi$
$127$	4.61254	−	2.96430i	0.409297	−	0.263039i	0.729048	+	0.684462i	$0.239963\pi$
$128$	8.93345	+	10.3098i	0.789613	+	0.911262i
$129$	5.60412	−	1.64552i	0.493415	−	0.144880i
$130$	−19.0635	−	2.74091i	−1.67198	−	0.240394i
$131$	14.0674	+	12.1895i	1.22908	+	1.06500i	0.995702	+	0.0926144i	$0.0295224\pi$
$131$	14.0674	+	12.1895i	1.22908	+	1.06500i	0.233375	+	0.972387i	$0.425023\pi$
$132$	1.36176	−	2.98183i	0.118526	−	0.259535i
$133$	−2.02303	−	8.78511i	−0.175419	−	0.761766i
$134$	8.95129	−	4.08792i	0.773274	−	0.353142i
$135$	4.30497	−	0.618961i	0.370513	−	0.0532717i
$136$	6.36069	+	4.08777i	0.545425	+	0.350523i
$137$			4.65351i			0.397576i	0.980042	+	0.198788i	$0.0637006\pi$
$137$			4.65351i			0.397576i	−0.980042	+	0.198788i	$0.936299\pi$
$138$	−7.22438	+	2.33532i	−0.614980	+	0.198796i
$139$			3.33641i			0.282990i	0.989939	+	0.141495i	$0.0451910\pi$
$139$			3.33641i			0.282990i	−0.989939	+	0.141495i	$0.954809\pi$
$140$	0.345097	−	5.81605i	0.0291660	−	0.491546i
$141$	−0.0562365	−	0.391133i	−0.00473597	−	0.0329394i
$142$	3.62473	+	7.93706i	0.304181	+	0.666063i
$143$	−17.3757	−	5.10197i	−1.45303	−	0.426649i
$144$	1.97583	−	4.32647i	0.164653	−	0.360539i
$145$	−2.44491	+	2.82158i	−0.203039	+	0.234319i
$146$	13.3606	+	1.92097i	1.10574	+	0.158981i
$147$	6.76233	+	1.80857i	0.557747	+	0.149168i
$148$	0.159859	−	0.138518i	0.0131403	−	0.0113861i
$149$	1.71328	+	2.66591i	0.140357	+	0.218400i	0.904315	−	0.426867i	$-0.140383\pi$
$149$	1.71328	+	2.66591i	0.140357	+	0.218400i	−0.763957	+	0.645267i	$0.776746\pi$
$150$	−11.9107	−	18.5334i	−0.972507	−	1.51325i
$151$	0.812563	+	0.937747i	0.0661254	+	0.0763128i	0.787848	−	0.615869i	$-0.211195\pi$
$151$	0.812563	+	0.937747i	0.0661254	+	0.0763128i	−0.721723	+	0.692182i	$0.756650\pi$
$152$	−7.73099	+	2.27002i	−0.627066	+	0.184123i
$153$	0.455043	−	3.16490i	0.0367881	−	0.255867i
$154$	5.44238	−	26.5662i	0.438560	−	2.14076i
$155$	4.13657	+	1.88911i	0.332258	+	0.151737i
$156$	1.35889	+	0.399005i	0.108798	+	0.0319460i
$157$	−1.45781	−	3.19215i	−0.116346	−	0.254761i	0.842496	−	0.538702i	$-0.181085\pi$
$157$	−1.45781	−	3.19215i	−0.116346	−	0.254761i	−0.958842	+	0.283941i	$0.908358\pi$
$158$	22.5809	−	3.24664i	1.79644	−	0.258289i
$159$	−1.58182	−	1.01658i	−0.125447	−	0.0806197i
$160$	−12.1799			−0.962905
$161$	−10.8897	+	6.51263i	−0.858229	+	0.513267i
$162$	−1.58314			−0.124383
$163$	−0.610728	−	0.392491i	−0.0478359	−	0.0307423i	0.516504	−	0.856285i	$-0.327233\pi$
$163$	−0.610728	−	0.392491i	−0.0478359	−	0.0307423i	−0.564340	+	0.825542i	$0.690869\pi$
$164$	2.76045	−	0.396893i	0.215555	−	0.0309921i
$165$	−11.6973	−	25.6134i	−0.910630	−	1.99400i
$166$	20.6676	+	6.06857i	1.60412	+	0.471012i
$167$	−16.1645	−	7.38210i	−1.25085	−	0.571244i	−0.323780	−	0.946132i	$-0.604954\pi$
$167$	−16.1645	−	7.38210i	−1.25085	−	0.571244i	−0.927070	+	0.374888i	$0.877681\pi$
$168$	1.25562	−	6.12910i	0.0968728	−	0.472870i
$169$	−0.736630	+	5.12338i	−0.0566639	+	0.394106i
$170$	−21.1240	+	6.20257i	−1.62014	+	0.475715i
$171$	2.23135	+	2.57511i	0.170635	+	0.196924i
$172$	1.59883	+	2.48784i	0.121910	+	0.189696i
$173$	−8.04046	−	12.5112i	−0.611305	−	0.951209i	−0.999560	−	0.0296574i	$-0.990558\pi$
$173$	−8.04046	−	12.5112i	−0.611305	−	0.951209i	0.388255	−	0.921552i	$-0.373078\pi$
$174$	1.02706	−	0.889955i	0.0778615	−	0.0674673i
$175$	−26.3482	−	25.7164i	−1.99174	−	1.94398i
$176$	−30.4799	−	4.38234i	−2.29751	−	0.330332i
$177$	−2.70603	+	3.12292i	−0.203398	+	0.234733i
$178$	−0.174595	+	0.382310i	−0.0130865	+	0.0286554i
$179$	14.7065	+	4.31821i	1.09921	+	0.322758i	0.780540	−	0.625106i	$-0.214944\pi$
$179$	14.7065	+	4.31821i	1.09921	+	0.322758i	0.318674	+	0.947864i	$0.396762\pi$
$180$	0.914797	+	2.00313i	0.0681849	+	0.149304i
$181$	−0.513903	−	3.57427i	−0.0381981	−	0.265673i	0.961768	−	0.273864i	$-0.0883019\pi$
$181$	−0.513903	−	3.57427i	−0.0381981	−	0.265673i	−0.999966	+	0.00819071i	$0.997393\pi$
$182$	11.6955	+	0.693954i	0.866925	+	0.0514393i
$183$			12.2983i			0.909120i
$184$	6.38706	+	9.37103i	0.470861	+	0.690842i
$185$		−	1.81695i		−	0.133585i
$186$	−1.39254	−	0.894930i	−0.102106	−	0.0656195i
$187$	−20.4903	+	2.94606i	−1.49840	+	0.215437i
$188$	0.181996	−	0.0831149i	0.0132734	−	0.00606178i
$189$	−2.57827	+	0.593723i	−0.187542	+	0.0431870i
$190$	9.74614	−	21.3411i	0.707059	−	1.54824i
$191$	7.37112	+	6.38711i	0.533356	+	0.462155i	0.879414	−	0.476058i	$-0.157935\pi$
$191$	7.37112	+	6.38711i	0.533356	+	0.462155i	−0.346058	+	0.938213i	$0.612480\pi$
$192$	−5.02735	−	0.722824i	−0.362818	−	0.0521653i
$193$	9.59490	−	2.81732i	0.690656	−	0.202795i	0.0824749	−	0.996593i	$-0.473718\pi$
$193$	9.59490	−	2.81732i	0.690656	−	0.202795i	0.608181	+	0.793798i	$0.291899\pi$
$194$	−9.25980	−	10.6864i	−0.664815	−	0.767238i
$195$	10.2342	−	6.57711i	0.732885	−	0.470996i
$196$	0.0860040	+	3.54323i	0.00614314	+	0.253088i
$197$	−0.172731	−	0.199342i	−0.0123066	−	0.0142026i	0.749563	−	0.661933i	$-0.230264\pi$
$197$	−0.172731	−	0.199342i	−0.0123066	−	0.0142026i	−0.761870	+	0.647731i	$0.775718\pi$
$198$	2.88765	+	9.83443i	0.205216	+	0.698902i
$199$	−1.15318	+	8.02055i	−0.0817469	+	0.568562i	0.907246	+	0.420600i	$0.138180\pi$
$199$	−1.15318	+	8.02055i	−0.0817469	+	0.568562i	−0.988993	+	0.147962i	$0.952729\pi$
$200$	−21.5494	+	24.8693i	−1.52377	+	1.75852i
$201$	−2.58216	+	5.65414i	−0.182132	+	0.398813i
$202$	0.571278	−	1.94560i	0.0401950	−	0.136892i
$203$	1.33890	−	1.83455i	0.0939724	−	0.128760i
$204$	1.60246	−	0.230400i	0.112195	−	0.0161312i
$205$	12.9514	−	20.1528i	0.904565	−	1.40753i
$206$	−18.5588			−1.29306
$207$	2.48274	−	4.10317i	0.172562	−	0.285190i
$208$		−	13.3039i		−	0.922463i
$209$	11.9266	−	18.5581i	0.824978	−	1.28369i
$210$	11.0933	+	14.4501i	0.765510	+	0.997149i
$211$	7.28708	+	15.9565i	0.501663	+	1.09849i	0.975925	+	0.218106i	$0.0699877\pi$
$211$	7.28708	+	15.9565i	0.501663	+	1.09849i	−0.474262	+	0.880384i	$0.657285\pi$
$212$	0.268224	−	0.913486i	0.0184217	−	0.0627385i
$213$	−5.01350	−	2.28959i	−0.343519	−	0.156880i
$214$	5.48570	+	4.75339i	0.374995	+	0.324935i
$215$	25.1441	+	3.61517i	1.71481	+	0.246553i
$216$	0.666211	+	2.26891i	0.0453299	+	0.154380i
$217$	−2.60349	−	0.935227i	−0.176737	−	0.0634874i
$218$	12.1754	+	18.9453i	0.824623	+	1.28314i
$219$	−7.17264	+	4.60957i	−0.484682	+	0.311486i
$220$	10.7748	−	9.33641i	0.726436	−	0.629461i
$221$	−2.51972	−	8.58138i	−0.169495	−	0.577246i
$222$	−0.0941235	+	0.654643i	−0.00631715	+	0.0439368i
$223$	7.86425	+	6.81441i	0.526629	+	0.456327i	0.877142	−	0.480231i	$-0.159447\pi$
$223$	7.86425	+	6.81441i	0.526629	+	0.456327i	−0.350513	+	0.936558i	$0.613993\pi$
$224$	7.38350	−	0.618211i	0.493331	−	0.0413059i
$225$	13.3522	+	3.92056i	0.890146	+	0.261370i
$226$	−1.55955	+	0.712221i	−0.103739	+	0.0473762i
$227$	−3.40271	−	23.6664i	−0.225846	−	1.57079i	−0.715333	−	0.698784i	$-0.753725\pi$
$227$	−3.40271	−	23.6664i	−0.225846	−	1.57079i	0.489487	−	0.872011i	$-0.337184\pi$
$228$	−0.932731	+	1.45136i	−0.0617716	+	0.0961185i
$229$	−1.72356			−0.113896			−0.0569479	−	0.998377i	$-0.518137\pi$
$229$	−1.72356			−0.113896			−0.0569479	+	0.998377i	$0.518137\pi$
$230$	−32.8005	−	3.81355i	−2.16280	−	0.251458i
$231$	8.39097	+	14.9332i	0.552086	+	0.982535i
$232$	−1.70766	−	1.09745i	−0.112114	−	0.0720510i
$233$	0.420239	+	2.92283i	0.0275308	+	0.191481i	0.998946	−	0.0459071i	$-0.0146178\pi$
$233$	0.420239	+	2.92283i	0.0275308	+	0.191481i	−0.971415	+	0.237388i	$0.923709\pi$
$234$	−4.02807	+	1.83956i	−0.263323	+	0.120256i
$235$	0.484193	−	1.64901i	0.0315852	−	0.107569i
$236$	−1.90317	−	0.869150i	−0.123886	−	0.0565769i
$237$	−9.43656	+	10.8904i	−0.612971	+	0.707406i
$238$	12.4906	−	4.83220i	0.809647	−	0.313225i
$239$	12.1500	−	3.56755i	0.785917	−	0.230766i	0.135937	−	0.990718i	$-0.456596\pi$
$239$	12.1500	−	3.56755i	0.785917	−	0.230766i	0.649980	+	0.759952i	$0.274777\pi$
$240$	15.6336	−	13.5466i	1.00914	−	0.874429i
$241$	−14.0586	+	9.03494i	−0.905597	+	0.581992i	−0.908445	−	0.418004i	$-0.862730\pi$
$241$	−14.0586	+	9.03494i	−0.905597	+	0.581992i	0.00284827	+	0.999996i	$0.499093\pi$
$242$	41.1742	−	26.4610i	2.64678	−	1.70098i
$243$	0.755750	−	0.654861i	0.0484814	−	0.0420093i
$244$	−5.97472	+	1.75434i	−0.382492	+	0.112310i
$245$	23.4856	+	19.3728i	1.50044	+	1.23768i
$246$	−5.71034	+	6.59008i	−0.364078	+	0.420168i
$247$	8.66956	+	3.95925i	0.551631	+	0.251921i
$248$	−0.696584	+	2.37235i	−0.0442331	+	0.150644i
$249$	−12.3765	+	5.65214i	−0.784326	+	0.358190i
$250$	−8.73668	−	60.7649i	−0.552556	−	3.84311i
$251$	−3.58738	−	2.30547i	−0.226433	−	0.145520i	0.422506	−	0.906360i	$-0.361151\pi$
$251$	−3.58738	−	2.30547i	−0.226433	−	0.145520i	−0.648939	+	0.760840i	$0.724787\pi$
$252$	−0.656225	−	1.16787i	−0.0413383	−	0.0735689i
$253$	−30.0174	−	7.93852i	−1.88718	−	0.499090i
$254$	−8.68024			−0.544647
$255$	7.51839	−	11.6988i	0.470820	−	0.732610i
$256$	−1.62790	−	11.3223i	−0.101743	−	0.707641i
$257$	−3.20819	+	1.46513i	−0.200121	+	0.0913923i	−0.512955	−	0.858416i	$-0.671449\pi$
$257$	−3.20819	+	1.46513i	−0.200121	+	0.0913923i	0.312833	+	0.949808i	$0.398722\pi$
$258$	−8.87209	−	2.60508i	−0.552352	−	0.162185i
$259$	0.0922222	+	1.10144i	0.00573041	+	0.0684402i
$260$	4.65514	+	4.03370i	0.288700	+	0.250160i
$261$	−0.122166	+	0.849684i	−0.00756189	+	0.0525941i
$262$	−8.30219	−	28.2747i	−0.512911	−	1.74681i
$263$	−8.30728	+	7.19830i	−0.512249	+	0.443866i	−0.872232	−	0.489093i	$-0.837328\pi$
$263$	−8.30728	+	7.19830i	−0.512249	+	0.443866i	0.359983	+	0.932959i	$0.382783\pi$
$264$	12.8792	−	8.27699i	0.792663	−	0.509413i
$265$	−4.42133	−	6.87973i	−0.271600	−	0.422618i
$266$	−4.82495	+	13.4317i	−0.295836	+	0.823551i
$267$	−0.0747943	−	0.254726i	−0.00457734	−	0.0155890i
$268$	−3.11521	−	0.447899i	−0.190292	−	0.0273598i
$269$	−12.4330	−	10.7732i	−0.758051	−	0.656855i	0.187524	−	0.982260i	$-0.439954\pi$
$269$	−12.4330	−	10.7732i	−0.758051	−	0.656855i	−0.945575	+	0.325405i	$0.894499\pi$
$270$	−6.26322	−	2.86032i	−0.381167	−	0.174073i
$271$	−6.49601	+	22.1234i	−0.394604	+	1.34390i	0.487614	+	0.873059i	$0.337867\pi$
$271$	−6.49601	+	22.1234i	−0.394604	+	1.34390i	−0.882219	+	0.470840i	$0.843951\pi$
$272$	−6.31761	−	13.8336i	−0.383061	−	0.838787i
$273$	−5.87017	+	4.50652i	−0.355279	+	0.272747i
$274$	3.98298	−	6.19764i	0.240621	−	0.374413i
$275$		−	90.0947i		−	5.43291i
$276$	2.34754	+	0.620840i	0.141305	+	0.0373702i
$277$	−16.3155			−0.980303			−0.490151	−	0.871637i	$-0.663058\pi$
$277$	−16.3155			−0.980303			−0.490151	+	0.871637i	$0.663058\pi$
$278$	2.85566	−	4.44349i	0.171271	−	0.266503i
$279$	1.03495	−	0.148803i	0.0619607	−	0.00890861i
$280$	16.0412	−	21.9794i	0.958643	−	1.31352i
$281$	5.53599	−	18.8539i	0.330250	−	1.12473i	−0.612290	−	0.790633i	$-0.709752\pi$
$281$	5.53599	−	18.8539i	0.330250	−	1.12473i	0.942540	−	0.334094i	$-0.108430\pi$
$282$	−0.259878	+	0.569052i	−0.0154755	+	0.0338866i
$283$	8.54684	−	9.86358i	0.508057	−	0.586329i	−0.442543	−	0.896747i	$-0.645924\pi$
$283$	8.54684	−	9.86358i	0.508057	−	0.586329i	0.950600	+	0.310418i	$0.100469\pi$
$284$	0.397150	−	2.76224i	0.0235665	−	0.163909i
$285$	4.17512	+	14.2191i	0.247313	+	0.842269i
$286$	18.7745	+	21.6670i	1.11016	+	1.28119i
$287$	−6.82830	+	12.8741i	−0.403062	+	0.759931i
$288$	−2.35590	+	1.51405i	−0.138823	+	0.0892160i
$289$	4.43758	+	5.12124i	0.261034	+	0.301249i
$290$	5.67119	−	1.66521i	0.333024	−	0.0977846i
$291$	8.84079	+	1.27111i	0.518256	+	0.0745140i
$292$	−3.26256	−	2.82703i	−0.190927	−	0.165439i
$293$	10.9574	−	23.9934i	0.640139	−	1.40171i	−0.259787	−	0.965666i	$-0.583652\pi$
$293$	10.9574	−	23.9934i	0.640139	−	1.40171i	0.899926	−	0.436043i	$-0.143620\pi$
$294$	−7.45823	−	8.19662i	−0.434973	−	0.478037i
$295$	−16.3479	+	7.46585i	−0.951813	+	0.434678i
$296$	0.977824	−	0.140590i	0.0568349	−	0.00817162i
$297$	−5.44647	−	3.50024i	−0.316036	−	0.203104i
$298$		−	5.01692i		−	0.290623i
$299$	1.54921	−	13.3248i	0.0895931	−	0.770594i
$300$			7.04595i			0.406798i
$301$	−15.4259	−	0.915303i	−0.889136	−	0.0527572i
$302$	−0.279561	−	1.94439i	−0.0160869	−	0.111887i
$303$	0.532077	+	1.16509i	0.0305670	+	0.0669324i
$304$	15.5499	+	4.56587i	0.891849	+	0.261870i
$305$	−22.2199	+	48.6548i	−1.27231	+	2.78597i
$306$	−3.31490	+	3.82560i	−0.189500	+	0.218695i
$307$	17.2983	+	2.48712i	0.987268	+	0.141948i	0.616988	−	0.786973i	$-0.288353\pi$
$307$	17.2983	+	2.48712i	0.987268	+	0.141948i	0.370280	+	0.928920i	$0.379262\pi$
$308$	−6.05783	+	6.20666i	−0.345177	+	0.353657i
$309$	8.85952	−	7.67682i	0.504000	−	0.436719i
$310$	−3.89227	−	6.05648i	−0.221066	−	0.343985i
$311$	12.6261	+	19.6466i	0.715961	+	1.11406i	0.988398	+	0.151884i	$0.0485340\pi$
$311$	12.6261	+	19.6466i	0.715961	+	1.11406i	−0.272437	+	0.962174i	$0.587830\pi$
$312$	4.33148	+	4.99880i	0.245222	+	0.283001i
$313$	−2.68097	+	0.787205i	−0.151538	+	0.0444954i	−0.356622	−	0.934249i	$-0.616071\pi$
$313$	−2.68097	+	0.787205i	−0.151538	+	0.0444954i	0.205084	+	0.978744i	$0.434253\pi$
$314$	−0.790654	+	5.49912i	−0.0446192	+	0.310333i
$315$	−11.2729	−	2.30938i	−0.635155	−	0.130119i
$316$	−6.63681	−	3.03093i	−0.373350	−	0.170503i
$317$	−9.88559	−	2.90267i	−0.555230	−	0.163030i	−0.00793265	−	0.999969i	$-0.502525\pi$
$317$	−9.88559	−	2.90267i	−0.555230	−	0.163030i	−0.547297	+	0.836938i	$0.684343\pi$
$318$	1.23661	+	2.70779i	0.0693455	+	0.151845i
$319$	5.50105	−	0.790932i	0.308000	−	0.0442837i
$320$	−18.5833	−	11.9427i	−1.03884	−	0.667620i
$321$	−4.58496			−0.255907
$322$	20.0773	+	0.646947i	1.11887	+	0.0360529i
$323$	10.8948			0.606205
$324$	0.425947	+	0.273740i	0.0236637	+	0.0152078i
$325$	38.5283	−	5.53954i	2.13717	−	0.307278i
$326$	0.477444	+	1.04546i	0.0264432	+	0.0579024i
$327$	−13.6489	−	4.00768i	−0.754787	−	0.221625i
$328$	11.8477	+	5.41068i	0.654181	+	0.298755i
$329$	−0.209821	+	1.02421i	−0.0115678	+	0.0564666i
$330$	−6.34411	+	44.1243i	−0.349232	+	2.42896i
$331$	−14.7995	+	4.34552i	−0.813454	+	0.238852i	−0.661895	−	0.749597i	$-0.730247\pi$
$331$	−14.7995	+	4.34552i	−0.813454	+	0.238852i	−0.151559	+	0.988448i	$0.548429\pi$
$332$	−4.51137	−	5.20640i	−0.247594	−	0.285738i
$333$	−0.225859	−	0.351444i	−0.0123770	−	0.0192590i
$334$	15.2099	+	23.6670i	0.832247	+	1.29500i
$335$	−20.4311	+	17.7037i	−1.11627	+	0.967255i
$336$	−8.78957	+	9.00551i	−0.479510	+	0.491291i
$337$	−14.0694	−	2.02287i	−0.766408	−	0.110193i	−0.251987	−	0.967731i	$-0.581084\pi$
$337$	−14.0694	−	2.02287i	−0.766408	−	0.110193i	−0.514421	+	0.857538i	$0.671993\pi$
$338$	5.36620	−	6.19293i	0.291883	−	0.336851i
$339$	0.449879	−	0.985098i	0.0244341	−	0.0535032i
$340$	6.75595	+	1.98373i	0.366393	+	0.107583i
$341$	−2.81211	−	6.15766i	−0.152284	−	0.333456i
$342$	−0.767692	−	5.33942i	−0.0415120	−	0.288723i
$343$	−15.2203	−	10.5518i	−0.821821	−	0.569746i
$344$			13.8115i			0.744666i
$345$	17.2356	−	11.7473i	0.927932	−	0.632456i
$346$			23.5446i			1.26576i
$347$	23.3115	+	14.9814i	1.25142	+	0.804242i	0.987086	−	0.160188i	$-0.0512102\pi$
$347$	23.3115	+	14.9814i	1.25142	+	0.804242i	0.264338	+	0.964430i	$0.414847\pi$
$348$	−0.430216	+	0.0618557i	−0.0230620	+	0.00331581i
$349$	−3.10426	+	1.41767i	−0.166167	+	0.0758860i	−0.496762	−	0.867887i	$-0.665478\pi$
$349$	−3.10426	+	1.41767i	−0.166167	+	0.0758860i	0.330595	+	0.943773i	$0.392751\pi$
$350$	13.0802	+	56.8013i	0.699164	+	3.03616i
$351$	1.16197	−	2.54436i	0.0620214	−	0.135808i
$352$	13.7024	+	11.8732i	0.730341	+	0.632844i
$353$	26.5951	+	3.82380i	1.41551	+	0.203520i	0.807247	−	0.590213i	$-0.200956\pi$
$353$	26.5951	+	3.82380i	1.41551	+	0.203520i	0.608266	+	0.793733i	$0.291865\pi$
$354$	6.27688	−	1.84306i	0.333613	−	0.0979575i
$355$	−15.6978	−	18.1162i	−0.833151	−	0.961507i
$356$	0.113080	−	0.0726724i	0.00599325	−	0.00385163i
$357$	−3.96388	+	7.47349i	−0.209791	+	0.395539i
$358$	−15.8904	−	18.3385i	−0.839833	−	0.969219i
$359$	1.98748	+	6.76873i	0.104895	+	0.357240i	0.995168	−	0.0981877i	$-0.0313046\pi$
$359$	1.98748	+	6.76873i	0.104895	+	0.357240i	−0.890273	+	0.455428i	$0.849486\pi$
$360$	−1.46365	+	10.1799i	−0.0771413	+	0.536530i
$361$	4.83934	−	5.58490i	0.254702	−	0.293942i
$362$	−2.37482	+	5.20014i	−0.124818	+	0.273313i
$363$	−8.70997	+	29.6634i	−0.457155	+	1.55693i
$364$	−3.02670	−	2.20897i	−0.158642	−	0.115781i
$365$	−36.7047	+	5.27734i	−1.92121	+	0.276229i
$366$	10.5263	−	16.3792i	0.550217	−	0.856154i
$367$	−9.90430			−0.517000			−0.258500	−	0.966011i	$-0.583228\pi$
$367$	−9.90430			−0.517000			−0.258500	+	0.966011i	$0.583228\pi$
$368$	−0.617041	−	22.8020i	−0.0321655	−	1.18864i
$369$		−	5.50801i		−	0.286735i
$370$	−1.55514	+	2.41985i	−0.0808480	+	0.125802i
$371$	3.02942	+	3.94610i	0.157280	+	0.204872i
$372$	0.219924	+	0.481567i	0.0114025	+	0.0249681i
$373$	−6.92472	+	23.5834i	−0.358548	+	1.22110i	0.560897	+	0.827886i	$0.310456\pi$
$373$	−6.92472	+	23.5834i	−0.358548	+	1.22110i	−0.919445	+	0.393218i	$0.871362\pi$
$374$	29.8109	+	13.6142i	1.54149	+	0.703973i
$375$	29.3059	+	25.3937i	1.51335	+	1.31133i
$376$	0.924910	+	0.132982i	0.0476986	+	0.00685802i
$377$	0.676473	+	2.30385i	0.0348401	+	0.118655i
$378$	3.94197	+	1.41604i	0.202753	+	0.0728330i
$379$	10.2215	+	15.9049i	0.525042	+	0.816981i	0.997941	−	0.0641354i	$-0.0204290\pi$
$379$	10.2215	+	15.9049i	0.525042	+	0.816981i	−0.472899	+	0.881116i	$0.656793\pi$
$380$	−6.31230	+	4.05667i	−0.323814	+	0.208103i
$381$	4.14373	−	3.59056i	0.212290	−	0.183950i
$382$	−4.35022	−	14.8155i	−0.222577	−	0.758027i
$383$	1.93819	−	13.4804i	0.0990367	−	0.688815i	−0.878453	−	0.477830i	$-0.841424\pi$
$383$	1.93819	−	13.4804i	0.0990367	−	0.688815i	0.977489	−	0.210985i	$-0.0676673\pi$
$384$	10.3098	+	8.93345i	0.526117	+	0.455883i
$385$	6.21596	+	74.2393i	0.316795	+	3.78358i
$386$	−15.1901	−	4.46020i	−0.773153	−	0.227018i
$387$	5.31290	−	2.42632i	0.270070	−	0.123337i
$388$	0.643596	+	4.47631i	0.0326736	+	0.227250i
$389$	2.24367	−	3.49122i	0.113759	−	0.177012i	−0.779706	−	0.626146i	$-0.784631\pi$
$389$	2.24367	−	3.49122i	0.113759	−	0.177012i	0.893464	+	0.449135i	$0.148268\pi$
$390$	−19.2595			−0.975242
$391$	−4.71662	−	14.5910i	−0.238530	−	0.737898i
$392$	−8.60861	+	14.1382i	−0.434801	+	0.714087i
$393$	15.6590	+	10.0634i	0.789892	+	0.507632i
$394$	0.0594279	+	0.413330i	0.00299394	+	0.0208233i
$395$	−57.0091	+	26.0352i	−2.86844	+	1.30997i
$396$	0.923538	−	3.14528i	0.0464095	−	0.158056i
$397$	32.0170	+	14.6217i	1.60689	+	0.733841i	0.998223	−	0.0595865i	$-0.0189782\pi$
$397$	32.0170	+	14.6217i	1.60689	+	0.733841i	0.608665	+	0.793428i	$0.291705\pi$
$398$	8.40069	−	9.69491i	0.421089	−	0.485962i
$399$	−3.25269	−	8.40779i	−0.162838	−	0.420916i
$400$	63.5068	−	18.6473i	3.17534	−	0.932364i
$401$	−15.6983	+	13.6027i	−0.783936	+	0.679285i	−0.951866	−	0.306514i	$-0.900837\pi$
$401$	−15.6983	+	13.6027i	−0.783936	+	0.679285i	0.167930	+	0.985799i	$0.446292\pi$
$402$	8.27841	−	5.32021i	0.412889	−	0.265348i
$403$	2.46038	−	1.58119i	0.122560	−	0.0787645i
$404$	−0.490116	+	0.424688i	−0.0243842	+	0.0211290i
$405$	4.17306	−	1.22532i	0.207361	−	0.0608868i
$406$	−3.35338	+	1.29731i	−0.166425	+	0.0643844i
$407$	−1.77120	+	2.04407i	−0.0877949	+	0.101321i
$408$	6.87770	+	3.14094i	0.340497	+	0.155500i
$409$	3.41095	−	11.6166i	0.168661	−	0.574405i	−0.831170	−	0.556018i	$-0.812329\pi$
$409$	3.41095	−	11.6166i	0.168661	−	0.574405i	0.999831	−	0.0183874i	$-0.00585321\pi$
$410$	−34.4979	+	15.7546i	−1.70373	+	0.778066i
$411$	0.662264	+	4.60615i	0.0326671	+	0.227204i
$412$	4.99331	+	3.20900i	0.246003	+	0.158096i
$413$	9.53123	−	5.35559i	0.469001	−	0.263531i
$414$	−6.81850	+	3.33969i	−0.335111	+	0.164137i
$415$	−59.1757			−2.90482
$416$	−4.23498	+	6.58976i	−0.207637	+	0.323090i
$417$	0.474820	+	3.30245i	0.0232520	+	0.161721i
$418$	−31.7681	+	14.5080i	−1.55383	+	0.709610i
$419$	−15.2583	−	4.48023i	−0.745415	−	0.218874i	−0.113098	−	0.993584i	$-0.536078\pi$
$419$	−15.2583	−	4.48023i	−0.745415	−	0.218874i	−0.632316	+	0.774710i	$0.717896\pi$
$420$	−0.486126	−	5.80596i	−0.0237205	−	0.283302i
$421$	7.27680	+	6.30538i	0.354649	+	0.307305i	0.813904	−	0.580999i	$-0.197338\pi$
$421$	7.27680	+	6.30538i	0.354649	+	0.307305i	−0.459255	+	0.888305i	$0.651884\pi$
$422$	3.95221	−	27.4882i	0.192391	−	1.33811i
$423$	−0.111328	−	0.379149i	−0.00541296	−	0.0184348i
$424$	3.36034	−	2.91175i	0.163193	−	0.141407i
$425$	37.4317	−	24.0559i	1.81571	−	1.16688i
$426$	4.71740	+	7.34042i	0.228559	+	0.355645i
$427$	11.0002	−	30.6225i	0.532339	−	1.48193i
$428$	−0.654036	−	2.22744i	−0.0316140	−	0.107667i
$429$	−17.9250	−	2.57722i	−0.865425	−	0.124429i
$430$	−30.3931	−	26.3358i	−1.46569	−	1.27003i
$431$	−22.4233	−	10.2404i	−1.08009	−	0.493261i	−0.205765	−	0.978601i	$-0.565968\pi$
$431$	−22.4233	−	10.2404i	−1.08009	−	0.493261i	−0.874325	+	0.485341i	$0.838696\pi$
$432$	1.34000	−	4.56362i	0.0644708	−	0.219567i
$433$	−5.56393	−	12.1833i	−0.267385	−	0.585492i	0.727545	−	0.686060i	$-0.240661\pi$
$433$	−5.56393	−	12.1833i	−0.267385	−	0.585492i	−0.994930	+	0.100568i	$0.967934\pi$
$434$	2.66691	+	3.47391i	0.128016	+	0.166753i
$435$	−2.01847	+	3.14080i	−0.0967783	+	0.150590i
$436$		−	7.20254i		−	0.344939i
$437$	15.0426	+	6.38377i	0.719586	+	0.305377i
$438$	13.4980			0.644961
$439$	13.3891	−	20.8338i	0.639025	−	0.994342i	−0.359110	−	0.933295i	$-0.616920\pi$
$439$	13.3891	−	20.8338i	0.639025	−	0.994342i	0.998135	−	0.0610467i	$-0.0194439\pi$
$440$	65.9073	−	9.47604i	3.14201	−	0.451752i
$441$	6.95088	+	0.827780i	0.330994	+	0.0394181i
$442$	−3.98906	+	13.5855i	−0.189740	+	0.646196i
$443$	2.73246	−	5.98326i	0.129823	−	0.284273i	−0.833547	−	0.552449i	$-0.813693\pi$
$443$	2.73246	−	5.98326i	0.129823	−	0.284273i	0.963370	+	0.268176i	$0.0864207\pi$
$444$	0.138518	−	0.159859i	0.00657379	−	0.00758656i
$445$	0.164322	−	1.14288i	0.00778960	−	0.0541779i
$446$	−4.64125	−	15.8066i	−0.219770	−	0.748466i
$447$	2.07524	+	2.39495i	0.0981554	+	0.113277i
$448$	11.8714	+	6.29652i	0.560872	+	0.297482i
$449$	−21.5728	+	13.8640i	−1.01809	+	0.654284i	−0.939473	−	0.342622i	$-0.888685\pi$
$449$	−21.5728	+	13.8640i	−1.01809	+	0.654284i	−0.0786118	+	0.996905i	$0.525049\pi$
$450$	−14.4271	−	16.6497i	−0.680099	−	0.784876i
$451$	−34.2156	+	10.0466i	−1.61115	+	0.473077i
$452$	0.542750	+	0.0780357i	0.0255288	+	0.00367049i
$453$	0.937747	+	0.812563i	0.0440592	+	0.0381775i
$454$	−15.7245	+	34.4318i	−0.737986	+	1.61596i
$455$	−31.3657	+	7.22287i	−1.47045	+	0.338613i
$456$	−7.32924	+	3.34715i	−0.343223	+	0.156745i
$457$	24.9848	−	3.59228i	1.16874	−	0.168040i	0.469505	−	0.882930i	$-0.344432\pi$
$457$	24.9848	−	3.59228i	1.16874	−	0.168040i	0.699237	+	0.714890i	$0.253523\pi$
$458$	2.29547	+	1.47521i	0.107260	+	0.0689319i
$459$		−	3.19744i		−	0.149244i
$460$	8.16566	+	6.69757i	0.380726	+	0.312276i
$461$			19.3427i			0.900878i	0.892807	+	0.450439i	$0.148732\pi$
$461$			19.3427i			0.900878i	−0.892807	+	0.450439i	$0.851268\pi$
$462$	1.60622	−	27.0703i	0.0747283	−	1.25942i
$463$	−1.81269	−	12.6075i	−0.0842429	−	0.585922i	−0.987595	−	0.157022i	$-0.949810\pi$
$463$	−1.81269	−	12.6075i	−0.0842429	−	0.585922i	0.903352	−	0.428900i	$-0.141099\pi$
$464$	1.69610	+	3.71393i	0.0787393	+	0.172415i
$465$	4.36332	+	1.28119i	0.202344	+	0.0594136i
$466$	1.94199	−	4.25237i	0.0899610	−	0.196987i
$467$	−11.1057	+	12.8167i	−0.513910	+	0.593084i	−0.952096	−	0.305800i	$-0.901076\pi$
$467$	−11.1057	+	12.8167i	−0.513910	+	0.593084i	0.438185	+	0.898885i	$0.355621\pi$
$468$	1.40184	+	0.201554i	0.0648001	+	0.00931685i
$469$	11.4869	−	11.7691i	0.530413	−	0.543444i
$470$	−2.05626	+	1.78176i	−0.0948481	+	0.0821864i
$471$	−1.89726	−	2.95219i	−0.0874211	−	0.136030i
$472$	−5.28284	−	8.22026i	−0.243162	−	0.378368i
$473$	−24.7630	−	28.5780i	−1.13860	−	1.31402i
$474$	21.8890	−	6.42718i	1.00539	−	0.295210i
$475$	−6.74807	+	46.9338i	−0.309622	+	2.15347i
$476$	−4.19617	−	0.859633i	−0.192331	−	0.0394012i
$477$	−1.71040	−	0.781112i	−0.0783136	−	0.0357646i
$478$	−19.2351	−	5.64793i	−0.879792	−	0.258330i
$479$	13.2789	+	29.0767i	0.606727	+	1.32855i	0.924790	+	0.380478i	$0.124240\pi$
$479$	13.2789	+	29.0767i	0.606727	+	1.32855i	−0.318063	+	0.948070i	$0.603032\pi$
$480$	−12.0559	+	1.73338i	−0.550275	+	0.0791176i
$481$	−0.983034	−	0.631758i	−0.0448225	−	0.0288057i
$482$	26.4567			1.20507
$483$	−9.85202	+	7.99610i	−0.448282	+	0.363835i
$484$	−15.6534			−0.711518
$485$	32.6794	+	21.0018i	1.48390	+	0.953642i
$486$	−1.56702	+	0.225304i	−0.0710816	+	0.0102200i
$487$	−10.1595	−	22.2461i	−0.460369	−	1.00807i	−0.987403	−	0.158223i	$-0.949423\pi$
$487$	−10.1595	−	22.2461i	−0.460369	−	1.00807i	0.527034	−	0.849844i	$-0.323304\pi$
$488$	−27.9038	−	8.19330i	−1.26315	−	0.370893i
$489$	−0.660370	−	0.301581i	−0.0298629	−	0.0136379i
$490$	−14.6972	−	45.9026i	−0.663950	−	2.07367i
$491$	1.59403	−	11.0867i	0.0719375	−	0.500336i	−0.921717	−	0.387863i	$-0.873213\pi$
$491$	1.59403	−	11.0867i	0.0719375	−	0.500336i	0.993655	−	0.112474i	$-0.0358774\pi$
$492$	2.67587	−	0.785707i	0.120638	−	0.0354224i
$493$	1.79743	+	2.07434i	0.0809522	+	0.0934238i
$494$	−8.15753	−	12.6934i	−0.367025	−	0.571101i
$495$	−15.2234	−	23.6880i	−0.684239	−	1.06470i
$496$	3.75844	−	3.25671i	0.168759	−	0.146230i
$497$	10.4356	+	10.1853i	0.468099	+	0.456875i
$498$	21.3209	+	3.06549i	0.955413	+	0.137368i
$499$	16.3288	−	18.8445i	0.730979	−	0.843594i	−0.261603	−	0.965176i	$-0.584251\pi$
$499$	16.3288	−	18.8445i	0.730979	−	0.843594i	0.992581	+	0.121581i	$0.0387965\pi$
$500$	−8.15622	+	17.8596i	−0.364757	+	0.798707i
$501$	−17.0506	−	5.00651i	−0.761764	−	0.223674i
$502$	2.80447	+	6.14094i	0.125170	+	0.274084i
$503$	3.55640	+	24.7353i	0.158572	+	1.10289i	0.901268	+	0.433263i	$0.142638\pi$
$503$	3.55640	+	24.7353i	0.158572	+	1.10289i	−0.742696	+	0.669629i	$0.766453\pi$
$504$	0.370573	−	6.24541i	0.0165066	−	0.278193i
$505$			5.57064i			0.247890i
$506$	33.1831	+	36.2648i	1.47517	+	1.61217i
$507$			5.17606i			0.229877i
$508$	2.33544	+	1.50090i	0.103618	+	0.0665916i
$509$	12.5815	−	1.80895i	0.557666	−	0.0801802i	0.142281	−	0.989826i	$-0.454556\pi$
$509$	12.5815	−	1.80895i	0.557666	−	0.0801802i	0.415384	+	0.909646i	$0.363647\pi$
$510$	−20.0263	+	9.14569i	−0.886778	+	0.404978i
$511$	21.9827	−	5.06216i	0.972457	−	0.223937i
$512$	3.81122	−	8.34542i	0.168434	−	0.368819i
$513$	2.57511	+	2.23135i	0.113694	+	0.0985164i
$514$	5.52674	+	0.794626i	0.243774	+	0.0350494i
$515$	48.9201	−	14.3642i	2.15568	−	0.632964i
$516$	1.93662	+	2.23497i	0.0852548	+	0.0983893i
$517$	−2.15220	+	1.38314i	−0.0946538	+	0.0608303i
$518$	0.819910	−	1.54585i	0.0360248	−	0.0679210i
$519$	−9.73915	−	11.2396i	−0.427501	−	0.493363i
$520$	8.10472	+	27.6021i	0.355415	+	1.21043i
$521$	−2.76872	+	19.2568i	−0.121300	+	0.843657i	0.834787	+	0.550573i	$0.185591\pi$
$521$	−2.76872	+	19.2568i	−0.121300	+	0.843657i	−0.956087	+	0.293084i	$0.905318\pi$
$522$	0.889955	−	1.02706i	0.0389523	−	0.0449533i
$523$	16.0829	−	35.2167i	0.703257	−	1.53992i	−0.132720	−	0.991154i	$-0.542371\pi$
$523$	16.0829	−	35.2167i	0.703257	−	1.53992i	0.835977	−	0.548765i	$-0.184902\pi$
$524$	−2.65523	+	9.04290i	−0.115994	+	0.395041i
$525$	−29.7398	−	21.7049i	−1.29795	−	0.947281i
$526$	17.2249	−	2.47657i	0.751041	−	0.107983i
$527$	1.80748	−	2.81249i	0.0787350	−	0.122514i
$528$	−30.7933			−1.34011
$529$	2.03722	−	22.9096i	0.0885750	−	0.996070i
$530$			12.9468i			0.562374i
$531$	−2.23405	+	3.47625i	−0.0969494	+	0.150856i
$532$	3.62064	−	2.77956i	0.156975	−	0.120509i
$533$	−6.40014	−	14.0143i	−0.277221	−	0.607029i
$534$	−0.118410	+	0.403266i	−0.00512409	+	0.0174510i
$535$	−18.1390	−	8.28382i	−0.784219	−	0.358141i
$536$	−11.1085	−	9.62554i	−0.479812	−	0.415760i
$537$	15.1713	+	2.18131i	0.654691	+	0.0941304i
$538$	7.33757	+	24.9895i	0.316345	+	1.07737i
$539$	−7.53628	−	44.6887i	−0.324610	−	1.92488i
$540$	1.19056	+	1.85255i	0.0512335	+	0.0797209i
$541$	−4.84353	+	3.11275i	−0.208240	+	0.133827i	−0.640604	−	0.767872i	$-0.721316\pi$
$541$	−4.84353	+	3.11275i	−0.208240	+	0.133827i	0.432364	+	0.901699i	$0.357679\pi$
$542$	27.5871	−	23.9044i	1.18497	−	1.02678i
$543$	−1.01734	−	3.46475i	−0.0436584	−	0.148687i
$544$	−1.27433	+	8.86318i	−0.0546366	+	0.380006i
$545$	−46.7571	−	40.5153i	−2.00285	−	1.73548i
$546$	11.6752	−	0.977547i	0.499651	−	0.0418351i
$547$	−6.70088	−	1.96756i	−0.286509	−	0.0841266i	0.135320	−	0.990802i	$-0.456794\pi$
$547$	−6.70088	−	1.96756i	−0.286509	−	0.0841266i	−0.421829	+	0.906675i	$0.638612\pi$
$548$	−2.14326	+	0.978796i	−0.0915557	+	0.0418121i
$549$	1.75024	+	12.1732i	0.0746983	+	0.519538i
$550$	−77.1128	+	119.990i	−3.28810	+	5.11639i
$551$	−2.92495			−0.124607
$552$	7.65569	+	8.36668i	0.325848	+	0.356109i
$553$	33.2377	−	18.6762i	1.41341	−	0.794193i
$554$	21.7293	+	13.9646i	0.923189	+	0.593298i
$555$	−0.258579	−	1.79845i	−0.0109761	−	0.0763401i
$556$	−1.53665	+	0.701762i	−0.0651683	+	0.0297614i
$557$	3.37688	−	11.5006i	0.143083	−	0.487296i	−0.856501	−	0.516146i	$-0.827366\pi$
$557$	3.37688	−	11.5006i	0.143083	−	0.487296i	0.999584	+	0.0288497i	$0.00918443\pi$
$558$	−1.50573	−	0.687642i	−0.0637425	−	0.0291102i
$559$	10.6986	−	12.3469i	0.452503	−	0.522216i
$560$	−51.0440	+	19.7472i	−2.15700	+	0.834471i
$561$	−19.8625	+	5.83214i	−0.838593	+	0.246233i
$562$	−23.5101	+	20.3716i	−0.991715	+	0.859326i
$563$	29.0360	−	18.6603i	1.22372	−	0.786439i	0.240821	−	0.970569i	$-0.422583\pi$
$563$	29.0360	−	18.6603i	1.22372	−	0.786439i	0.982902	+	0.184130i	$0.0589469\pi$
$564$	0.168315	−	0.108170i	0.00708736	−	0.00455477i
$565$	3.55963	−	3.08444i	0.149755	−	0.129763i
$566$	−19.8252	+	5.82120i	−0.833315	+	0.244683i
$567$	−2.46753	+	0.954606i	−0.103627	+	0.0400897i
$568$	8.53492	−	9.84982i	0.358117	−	0.413289i
$569$	−4.96173	−	2.26595i	−0.208007	−	0.0949934i	0.308688	−	0.951164i	$-0.400110\pi$
$569$	−4.96173	−	2.26595i	−0.208007	−	0.0949934i	−0.516694	+	0.856170i	$0.672838\pi$
$570$	6.60979	−	22.5109i	0.276853	−	0.942876i
$571$	12.6026	−	5.75540i	0.527401	−	0.240856i	−0.133876	−	0.990998i	$-0.542742\pi$
$571$	12.6026	−	5.75540i	0.527401	−	0.240856i	0.661277	+	0.750142i	$0.270015\pi$
$572$	−1.30491	−	9.07585i	−0.0545610	−	0.379480i
$573$	8.20508	+	5.27308i	0.342772	+	0.220286i
$574$	20.1131	−	11.3015i	0.839504	−	0.471716i
$575$	65.7778	−	11.2813i	2.74312	−	0.470464i
$576$	−5.07905			−0.211627
$577$	12.3923	−	19.2828i	0.515898	−	0.802752i	−0.481378	−	0.876513i	$-0.659864\pi$
$577$	12.3923	−	19.2828i	0.515898	−	0.802752i	0.997276	+	0.0737605i	$0.0235001\pi$
$578$	−1.52674	−	10.6187i	−0.0635042	−	0.441681i
$579$	9.09629	−	4.15414i	0.378029	−	0.172640i
$580$	−1.81378	−	0.532574i	−0.0753131	−	0.0221139i
$581$	35.8726	−	3.00356i	1.48824	−	0.124609i
$582$	−10.6864	−	9.25980i	−0.442965	−	0.383831i
$583$	−1.73249	+	12.0497i	−0.0717522	+	0.499048i
$584$	−5.68020	−	19.3450i	−0.235048	−	0.800502i
$585$	9.19399	−	7.96664i	0.380125	−	0.329380i
$586$	−35.1295	+	22.5763i	−1.45118	+	0.932620i
$587$	−10.5012	−	16.3403i	−0.433433	−	0.674434i	0.553992	−	0.832522i	$-0.313104\pi$
$587$	−10.5012	−	16.3403i	−0.433433	−	0.674434i	−0.987425	+	0.158087i	$0.949467\pi$
$588$	0.589383	+	3.49492i	0.0243057	+	0.144128i
$589$	1.00373	+	3.41839i	0.0413580	+	0.140852i
$590$	28.1626	+	4.04917i	1.15943	+	0.166702i
$591$	−0.199342	−	0.172731i	−0.00819985	−	0.00710521i
$592$	−1.80744	−	0.825428i	−0.0742851	−	0.0339249i
$593$	6.89822	−	23.4932i	0.283276	−	0.964749i	−0.687785	−	0.725915i	$-0.741417\pi$
$593$	6.89822	−	23.4932i	0.283276	−	0.964749i	0.971060	−	0.238834i	$-0.0767652\pi$
$594$	4.25784	+	9.32337i	0.174701	+	0.382543i
$595$	−29.1846	+	22.4050i	−1.19645	+	0.918514i
$596$	−0.867474	+	1.34982i	−0.0355331	+	0.0552906i
$597$			8.10303i			0.331635i
$598$	−13.4681	+	16.4203i	−0.550751	+	0.671475i
$599$	−34.5820			−1.41298			−0.706491	−	0.707722i	$-0.749723\pi$
$599$	−34.5820			−1.41298			−0.706491	+	0.707722i	$0.749723\pi$
$600$	−17.7908	+	27.6830i	−0.726305	+	1.13015i
$601$	−22.4351	+	3.22568i	−0.915147	+	0.131578i	−0.583769	−	0.811920i	$-0.698423\pi$
$601$	−22.4351	+	3.22568i	−0.915147	+	0.131578i	−0.331378	+	0.943498i	$0.607513\pi$
$602$	19.7612	+	14.4222i	0.805405	+	0.587806i
$603$	−1.75121	+	5.96407i	−0.0713148	+	0.242876i
$604$	−0.260987	+	0.571482i	−0.0106194	+	0.0232533i
$605$	−88.0525	+	101.618i	−3.57984	+	4.13136i
$606$	0.288576	−	2.00709i	0.0117226	−	0.0815326i
$607$	2.43150	+	8.28094i	0.0986917	+	0.336113i	0.994007	−	0.109321i	$-0.0348676\pi$
$607$	2.43150	+	8.28094i	0.0986917	+	0.336113i	−0.895315	+	0.445434i	$0.853049\pi$
$608$	−6.24881	−	7.21152i	−0.253423	−	0.292466i
$609$	1.06419	−	2.00642i	0.0431231	−	0.0813042i
$610$	71.2370	−	45.7812i	2.88430	−	1.85363i
$611$	−0.723818	−	0.835331i	−0.0292826	−	0.0337939i
$612$	1.55336	−	0.456109i	0.0627910	−	0.0184371i
$613$	18.3847	+	2.64332i	0.742550	+	0.106763i	0.503199	−	0.864171i	$-0.332156\pi$
$613$	18.3847	+	2.64332i	0.742550	+	0.106763i	0.239351	+	0.970933i	$0.423065\pi$
$614$	−20.9095	−	18.1182i	−0.843839	−	0.731191i
$615$	9.95153	−	21.7908i	0.401284	−	0.878690i
$616$	−39.4723	+	9.08965i	−1.59038	+	0.366232i
$617$	−28.4333	+	12.9851i	−1.14468	+	0.522759i	−0.895220	−	0.445625i	$-0.852981\pi$
$617$	−28.4333	+	12.9851i	−1.14468	+	0.522759i	−0.249463	+	0.968384i	$0.580254\pi$
$618$	−18.3699	+	2.64120i	−0.738947	+	0.106245i
$619$	−29.9926	−	19.2751i	−1.20550	−	0.774730i	−0.225604	−	0.974219i	$-0.572435\pi$
$619$	−29.9926	−	19.2751i	−1.20550	−	0.774730i	−0.979900	+	0.199489i	$0.936072\pi$
$620$			2.30252i			0.0924716i
$621$	1.87352	−	4.41474i	0.0751819	−	0.177157i
$622$		−	36.9726i		−	1.48246i
$623$	−0.0416036	+	0.701161i	−0.00166681	+	0.0280914i
$624$	−1.89335	−	13.1685i	−0.0757946	−	0.527163i
$625$	41.1561	+	90.1194i	1.64625	+	3.60477i
$626$	4.24435	+	1.24625i	0.169638	+	0.0498103i
$627$	9.16408	−	20.0665i	0.365978	−	0.801381i
$628$	1.16358	−	1.34284i	0.0464318	−	0.0535852i
$629$	−1.32217	−	0.190100i	−0.0527185	−	0.00757978i
$630$	13.0368	+	12.7242i	0.519400	+	0.506946i
$631$	−9.56890	+	8.29150i	−0.380932	+	0.330080i	−0.824189	−	0.566315i	$-0.808368\pi$
$631$	−9.56890	+	8.29150i	−0.380932	+	0.330080i	0.443257	+	0.896395i	$0.353823\pi$
$632$	−18.4225	−	28.6660i	−0.732808	−	1.14027i
$633$	9.48375	+	14.7570i	0.376945	+	0.586538i
$634$	10.6814	+	12.3270i	0.424213	+	0.489567i
$635$	22.8806	−	6.71836i	0.907991	−	0.266610i
$636$	0.135491	−	0.942360i	0.00537256	−	0.0373670i
$637$	18.6474	−	5.97055i	0.738837	−	0.236562i
$638$	−8.00338	−	3.65502i	−0.316857	−	0.144704i
$639$	−5.28831	−	1.55279i	−0.209202	−	0.0614274i
$640$	24.6471	+	53.9696i	0.974262	+	2.13334i
$641$	36.7770	−	5.28773i	1.45260	−	0.208853i	0.629614	−	0.776908i	$-0.283213\pi$
$641$	36.7770	−	5.28773i	1.45260	−	0.208853i	0.822990	+	0.568056i	$0.192304\pi$
$642$	6.10634	+	3.92431i	0.240998	+	0.154880i
$643$	−13.5856			−0.535762			−0.267881	−	0.963452i	$-0.586323\pi$
$643$	−13.5856			−0.535762			−0.267881	+	0.963452i	$0.586323\pi$
$644$	−5.29000	−	3.64563i	−0.208455	−	0.143658i
$645$	25.4026			1.00023
$646$	−14.5100	−	9.32499i	−0.570887	−	0.366887i
$647$	14.4729	−	2.08089i	0.568988	−	0.0818081i	0.148184	−	0.988960i	$-0.452657\pi$
$647$	14.4729	−	2.08089i	0.568988	−	0.0818081i	0.420804	+	0.907152i	$0.361748\pi$
$648$	0.982329	+	2.15100i	0.0385895	+	0.0844993i
$649$	25.6693	+	7.53718i	1.00761	+	0.295860i
$650$	−56.0542	−	25.5991i	−2.19862	−	1.00408i
$651$	−2.71009	−	0.555192i	−0.106217	−	0.0217597i
$652$	0.0523119	−	0.363837i	0.00204869	−	0.0142490i
$653$	−42.4066	+	12.4517i	−1.65950	+	0.487273i	−0.971222	−	0.238176i	$-0.923451\pi$
$653$	−42.4066	+	12.4517i	−1.65950	+	0.487273i	−0.688276	+	0.725449i	$0.741632\pi$
$654$	14.7477	+	17.0197i	0.576680	+	0.665525i
$655$	43.7682	+	68.1047i	1.71017	+	2.66107i
$656$	−14.1635	−	22.0389i	−0.552992	−	0.860473i
$657$	−6.44362	+	5.58343i	−0.251390	+	0.217830i
$658$	1.15608	−	1.18448i	0.0450685	−	0.0461757i
$659$	−24.4618	−	3.51708i	−0.952896	−	0.137006i	−0.351705	−	0.936111i	$-0.614398\pi$
$659$	−24.4618	−	3.51708i	−0.952896	−	0.137006i	−0.601191	+	0.799105i	$0.705307\pi$
$660$	9.33641	−	10.7748i	0.363419	−	0.419408i
$661$	4.23967	−	9.28358i	0.164904	−	0.361090i	−0.809083	−	0.587695i	$-0.800036\pi$
$661$	4.23967	−	9.28358i	0.164904	−	0.361090i	0.973987	+	0.226605i	$0.0727628\pi$
$662$	23.4296	+	6.87956i	0.910618	+	0.267382i
$663$	−3.71533	−	8.13544i	−0.144291	−	0.315954i
$664$	−4.57884	−	31.8465i	−0.177693	−	1.23589i
$665$	2.32237	−	39.1397i	0.0900575	−	1.51777i
$666$			0.661375i			0.0256278i
$667$	1.26628	+	3.91726i	0.0490305	+	0.151677i
$668$		−	8.99760i		−	0.348128i
$669$	8.75399	+	5.62585i	0.338449	+	0.217508i
$670$	42.3633	−	6.09093i	1.63664	−	0.235313i
$671$	72.4271	−	33.0763i	2.79602	−	1.27690i
$672$	7.22037	−	1.66270i	0.278532	−	0.0641400i
$673$	19.3742	−	42.4235i	0.746819	−	1.63531i	−0.0251801	−	0.999683i	$-0.508016\pi$
$673$	19.3742	−	42.4235i	0.746819	−	1.63531i	0.771999	−	0.635623i	$-0.219257\pi$
$674$	17.0065	+	14.7362i	0.655066	+	0.567618i
$675$	13.7742	+	1.98044i	0.530171	+	0.0762270i
$676$	−2.51461	+	0.738356i	−0.0967157	+	0.0283983i
$677$	1.94393	+	2.24342i	0.0747114	+	0.0862215i	0.791875	−	0.610684i	$-0.209105\pi$
$677$	1.94393	+	2.24342i	0.0747114	+	0.0862215i	−0.717163	+	0.696905i	$0.754560\pi$
$678$	−1.44231	+	0.926918i	−0.0553917	+	0.0355981i
$679$	−20.8764	−	11.0727i	−0.801162	−	0.424930i
$680$	21.5347	+	24.8524i	0.825820	+	0.953047i
$681$	−6.73616	−	22.9413i	−0.258130	−	0.879111i
$682$	−1.52517	+	10.6078i	−0.0584019	+	0.406194i
$683$	−14.9509	+	17.2542i	−0.572079	+	0.660214i	−0.965883	−	0.258980i	$-0.916613\pi$
$683$	−14.9509	+	17.2542i	−0.572079	+	0.660214i	0.393804	+	0.919195i	$0.371159\pi$
$684$	−0.716687	+	1.56933i	−0.0274032	+	0.0600047i
$685$	−5.70205	+	19.4194i	−0.217864	+	0.741978i
$686$	11.2393	+	27.0804i	0.429120	+	1.03393i
$687$	−1.70601	+	0.245288i	−0.0650884	+	0.00935830i
$688$	15.0190	−	23.3701i	0.572596	−	0.890976i
$689$	−5.25949			−0.200371
$690$	−33.0093	+	0.893260i	−1.25664	+	0.0340058i
$691$		−	38.5703i		−	1.46728i	−0.679538	−	0.733641i	$-0.737820\pi$
$691$		−	38.5703i		−	1.46728i	0.679538	−	0.733641i	$-0.262180\pi$
$692$	4.07109	−	6.33473i	0.154759	−	0.240810i
$693$	10.4308	+	13.5871i	0.396233	+	0.516131i
$694$	−18.2240	−	39.9050i	−0.691773	−	1.51477i
$695$	−4.08817	+	13.9230i	−0.155073	+	0.528131i
$696$	−1.84647	−	0.843253i	−0.0699901	−	0.0319634i
$697$	−13.3099	−	11.5331i	−0.504148	−	0.436847i
$698$	5.34771	+	0.768884i	0.202414	+	0.0291027i
$699$	0.831924	+	2.83327i	0.0314662	+	0.107164i
$700$	6.30224	−	17.5442i	0.238202	−	0.663109i
$701$	−22.1900	−	34.5282i	−0.838103	−	1.30411i	−0.950586	−	0.310460i	$-0.899517\pi$
$701$	−22.1900	−	34.5282i	−0.838103	−	1.30411i	0.112484	−	0.993654i	$-0.464119\pi$
$702$	−3.72527	+	2.39409i	−0.140601	+	0.0903590i
$703$	1.07578	−	0.932173i	0.0405740	−	0.0351576i
$704$	9.26420	+	31.5510i	0.349158	+	1.18912i
$705$	0.244586	−	1.70113i	0.00921164	−	0.0640683i
$706$	−32.1470	−	27.8556i	−1.20987	−	1.04836i
$707$	−0.282747	−	3.37695i	−0.0106338	−	0.127003i
$708$	−2.00749	−	0.589454i	−0.0754463	−	0.0221530i
$709$	−39.9875	+	18.2617i	−1.50176	+	0.685832i	−0.985356	−	0.170511i	$-0.945458\pi$
$709$	−39.9875	+	18.2617i	−1.50176	+	0.685832i	−0.516407	+	0.856343i	$0.672731\pi$
$710$	5.40079	+	37.5633i	0.202688	+	1.40973i
$711$	−7.79065	+	12.1225i	−0.292172	+	0.454629i
$712$	0.627779			0.0235270
$713$	4.14357	−	2.82415i	0.155178	−	0.105765i
$714$	11.6758	−	6.56062i	0.436956	−	0.245525i
$715$	−66.2585	−	42.5817i	−2.47793	−	1.59247i
$716$	1.10445	+	7.68162i	0.0412752	+	0.287076i
$717$	11.5186	−	5.26036i	0.430170	−	0.196452i
$718$	3.14645	−	10.7158i	0.117425	−	0.399911i
$719$	16.7217	+	7.63656i	0.623615	+	0.284795i	0.702054	−	0.712123i	$-0.252266\pi$
$719$	16.7217	+	7.63656i	0.623615	+	0.284795i	−0.0784392	+	0.996919i	$0.524994\pi$
$720$	13.5466	−	15.6336i	0.504852	−	0.582630i
$721$	−28.9265	+	11.1907i	−1.07728	+	0.416763i
$722$	−11.2253	+	3.29604i	−0.417762	+	0.122666i
$723$	−12.6297	+	10.9437i	−0.469705	+	0.407002i
$724$	1.53811	−	0.988481i	0.0571633	−	0.0367366i
$725$	−10.0494	+	6.45833i	−0.373224	+	0.239856i
$726$	36.9893	−	32.0514i	1.37280	−	1.18954i
$727$	−23.6414	+	6.94173i	−0.876810	+	0.257455i	−0.689009	−	0.724753i	$-0.741954\pi$
$727$	−23.6414	+	6.94173i	−0.876810	+	0.257455i	−0.187801	+	0.982207i	$0.560136\pi$
$728$	−6.31410	−	16.3212i	−0.234016	−	0.604902i
$729$	0.654861	−	0.755750i	0.0242541	−	0.0279907i
$730$	53.4010	+	24.3874i	1.97646	+	0.902619i
$731$	5.26145	−	17.9188i	0.194602	−	0.662752i
$732$	−5.66424	+	2.58677i	−0.209356	+	0.0956098i
$733$	1.26423	+	8.79290i	0.0466953	+	0.324773i	0.999758	+	0.0220000i	$0.00700338\pi$
$733$	1.26423	+	8.79290i	0.0466953	+	0.324773i	−0.953063	+	0.302773i	$0.902088\pi$
$734$	13.1908	+	8.47718i	0.486879	+	0.312898i
$735$	26.0036	+	15.8333i	0.959155	+	0.584020i
$736$	−6.95282	+	11.4908i	−0.256284	+	0.423556i
$737$	40.2429			1.48237
$738$	−4.71435	+	7.33567i	−0.173538	+	0.270030i
$739$	−4.71648	−	32.8039i	−0.173499	−	1.20671i	−0.871421	−	0.490536i	$-0.836801\pi$
$739$	−4.71648	−	32.8039i	−0.173499	−	1.20671i	0.697922	−	0.716174i	$-0.254108\pi$
$740$	0.836830	−	0.382167i	0.0307625	−	0.0140488i
$741$	9.14477	+	2.68515i	0.335942	+	0.0986414i
$742$	−0.657137	−	7.84841i	−0.0241243	−	0.288124i
$743$	4.57214	+	3.96178i	0.167735	+	0.145344i	0.734684	−	0.678410i	$-0.237331\pi$
$743$	4.57214	+	3.96178i	0.167735	+	0.145344i	−0.566948	+	0.823753i	$0.691876\pi$
$744$	−0.351874	+	2.44734i	−0.0129003	+	0.0897237i
$745$	3.88302	+	13.2243i	0.142263	+	0.484502i
$746$	29.4077	−	25.4820i	1.07669	−	0.932961i
$747$	−11.4461	+	7.35596i	−0.418791	+	0.269140i
$748$	−5.66668	−	8.81753i	−0.207194	−	0.322401i
$749$	11.4164	+	4.10101i	0.417147	+	0.149848i
$750$	−17.2955	−	58.9031i	−0.631543	−	2.15084i
$751$	−11.7740	−	1.69285i	−0.429640	−	0.0617730i	−0.0758974	−	0.997116i	$-0.524182\pi$
$751$	−11.7740	−	1.69285i	−0.429640	−	0.0617730i	−0.353743	+	0.935343i	$0.615091\pi$
$752$	−1.42041	−	1.23079i	−0.0517970	−	0.0448824i
$753$	−3.87897	−	1.77147i	−0.141357	−	0.0645558i
$754$	1.07095	−	3.64732i	0.0390017	−	0.132828i
$755$	2.24183	+	4.90893i	0.0815887	+	0.178654i
$756$	−0.815751	−	1.06259i	−0.0296686	−	0.0386461i
$757$	−3.32153	+	5.16840i	−0.120723	+	0.187849i	−0.896355	−	0.443336i	$-0.853795\pi$
$757$	−3.32153	+	5.16840i	−0.120723	+	0.187849i	0.775632	+	0.631185i	$0.217431\pi$
$758$		−	29.9311i		−	1.08715i
$759$	−30.8416	−	3.58580i	−1.11948	−	0.130156i
$760$	−35.0434			−1.27116
$761$	−8.94017	+	13.9112i	−0.324081	+	0.504280i	−0.964619	−	0.263646i	$-0.915075\pi$
$761$	−8.94017	+	13.9112i	−0.324081	+	0.504280i	0.640539	+	0.767926i	$0.278711\pi$
$762$	−8.59189	+	1.23533i	−0.311251	+	0.0447512i
$763$	30.4008	+	22.1873i	1.10058	+	0.803233i
$764$	−1.39130	+	4.73834i	−0.0503356	+	0.171427i
$765$	5.77694	−	12.6497i	0.208866	−	0.457352i
$766$	−14.1193	+	16.2945i	−0.510151	+	0.588745i
$767$	−1.64493	+	11.4407i	−0.0593948	+	0.413100i
$768$	−3.22265	−	10.9753i	−0.116287	−	0.396039i
$769$	−31.8636	−	36.7726i	−1.14903	−	1.32605i	−0.937219	−	0.348742i	$-0.886609\pi$
$769$	−31.8636	−	36.7726i	−1.14903	−	1.32605i	−0.211813	−	0.977310i	$-0.567937\pi$
$770$	55.2635	−	104.194i	1.99156	−	3.75488i
$771$	−2.96702	+	1.90679i	−0.106855	+	0.0686713i
$772$	3.31571	+	3.82654i	0.119335	+	0.137720i
$773$	21.0647	−	6.18515i	0.757644	−	0.222464i	0.119977	−	0.992777i	$-0.461718\pi$
$773$	21.0647	−	6.18515i	0.757644	−	0.222464i	0.637667	+	0.770312i	$0.279900\pi$
$774$	−9.15253	−	1.31594i	−0.328981	−	0.0473003i
$775$	10.9964	+	9.52843i	0.395002	+	0.342271i
$776$	−8.77387	+	19.2121i	−0.314964	+	0.689674i
$777$	0.248035	+	1.07711i	0.00889820	+	0.0386409i
$778$	−5.97633	+	2.72930i	−0.214262	+	0.0978501i
$779$	18.5767	−	2.67093i	0.665581	−	0.0956961i
$780$	5.18182	+	3.33015i	0.185539	+	0.119239i
$781$			35.6832i			1.27685i
$782$	−6.20686	+	23.4696i	−0.221957	+	0.839270i
$783$			0.858421i			0.0306775i
$784$	29.9407	−	14.5616i	1.06931	−	0.520059i
$785$	−2.17211	−	15.1073i	−0.0775258	−	0.539204i
$786$	−12.2416	−	26.8053i	−0.436643	−	0.956115i
$787$	−21.7565	−	6.38827i	−0.775534	−	0.227717i	−0.130067	−	0.991505i	$-0.541519\pi$
$787$	−21.7565	−	6.38827i	−0.775534	−	0.227717i	−0.645467	+	0.763788i	$0.723337\pi$
$788$	0.0554796	−	0.121483i	0.00197638	−	0.00432766i
$789$	−7.19830	+	8.30728i	−0.256266	+	0.295747i
$790$	98.2095	+	14.1204i	3.49414	+	0.502381i
$791$	−2.00131	+	2.05047i	−0.0711583	+	0.0729065i
$792$	11.5702	−	10.0256i	0.411130	−	0.356246i
$793$	18.5981	+	28.9392i	0.660437	+	1.02766i
$794$	−30.1261	−	46.8771i	−1.06913	−	1.66361i
$795$	−5.35542	−	6.18048i	−0.189937	−	0.219199i
$796$	−3.93657	+	1.15588i	−0.139528	+	0.0409692i
$797$	−4.37307	+	30.4154i	−0.154902	+	1.07737i	0.752950	+	0.658077i	$0.228630\pi$
$797$	−4.37307	+	30.4154i	−0.154902	+	1.07737i	−0.907852	+	0.419290i	$0.862279\pi$
$798$	−2.86430	+	13.9817i	−0.101395	+	0.494946i
$799$	−1.14931	−	0.524871i	−0.0406596	−	0.0185686i
$800$	−37.3924	−	10.9794i	−1.32202	−	0.388180i
$801$	−0.110284	−	0.241489i	−0.00389671	−	0.00853260i
$802$	32.5500	−	4.67998i	1.14938	−	0.165256i
$803$	46.4373	+	29.8435i	1.63874	+	1.05315i
$804$	−3.14724			−0.110995
$805$	−53.4235	+	13.8342i	−1.88293	+	0.487592i
$806$	−4.63013			−0.163089
$807$	−13.8396	−	8.89417i	−0.487177	−	0.313090i
$808$	−2.99795	+	0.431040i	−0.105467	+	0.0151639i
$809$	2.19920	+	4.81558i	0.0773198	+	0.169307i	0.944344	−	0.328959i	$-0.106698\pi$
$809$	2.19920	+	4.81558i	0.0773198	+	0.169307i	−0.867024	+	0.498266i	$0.833970\pi$
$810$	−6.60654	−	1.93985i	−0.232130	−	0.0681595i
$811$	47.1596	+	21.5370i	1.65600	+	0.756268i	0.999999	+	0.00150447i	$0.000478888\pi$
$811$	47.1596	+	21.5370i	1.65600	+	0.756268i	0.655997	+	0.754764i	$0.272248\pi$
$812$	1.12655	+	0.230787i	0.0395342	+	0.00809904i
$813$	−3.28140	+	22.8227i	−0.115084	+	0.800426i
$814$	4.10845	−	1.20635i	0.144001	−	0.0422826i
$815$	−2.06768	−	2.38623i	−0.0724277	−	0.0835860i
$816$	−8.22203	−	12.7937i	−0.287829	−	0.447870i
$817$	10.7595	+	16.7421i	0.376428	+	0.585733i
$818$	−14.4855	+	12.5518i	−0.506475	+	0.438863i
$819$	−5.16907	+	5.29606i	−0.180622	+	0.185059i
$820$	12.0059	+	1.72618i	0.419263	+	0.0602809i
$821$	8.63861	−	9.96949i	0.301490	−	0.347938i	−0.584709	−	0.811243i	$-0.698791\pi$
$821$	8.63861	−	9.96949i	0.301490	−	0.347938i	0.886199	+	0.463306i	$0.153337\pi$
$822$	3.06043	−	6.70140i	0.106745	−	0.233738i
$823$	41.5367	+	12.1963i	1.44788	+	0.425135i	0.908839	−	0.417147i	$-0.136970\pi$
$823$	41.5367	+	12.1963i	1.44788	+	0.425135i	0.539038	+	0.842282i	$0.318788\pi$
$824$	11.5157	+	25.2158i	0.401167	+	0.878434i
$825$	−12.8218	−	89.1777i	−0.446398	−	3.10477i
$826$	−17.2778	−	1.02518i	−0.601171	−	0.0356707i
$827$			54.4505i			1.89343i	0.322073	+	0.946715i	$0.395620\pi$
$827$			54.4505i			1.89343i	−0.322073	+	0.946715i	$0.604380\pi$
$828$	2.41200	+	0.280431i	0.0838228	+	0.00974567i
$829$			32.8025i			1.13928i	0.821895	+	0.569639i	$0.192917\pi$
$829$			32.8025i			1.13928i	−0.821895	+	0.569639i	$0.807083\pi$
$830$	78.8114	+	50.6490i	2.73558	+	1.75805i
$831$	−16.1494	+	2.32194i	−0.560217	+	0.0805471i
$832$	−12.9229	+	5.90170i	−0.448022	+	0.204605i
$833$	16.5546	−	15.0633i	0.573583	−	0.521912i
$834$	2.19422	−	4.80467i	0.0759795	−	0.166372i
$835$	−58.4102	−	50.6128i	−2.02137	−	1.75153i
$836$	11.0559	+	1.58959i	0.382375	+	0.0549773i
$837$	1.00324	−	0.294577i	0.0346769	−	0.0101821i
$838$	16.4866	+	19.0265i	0.569520	+	0.657261i
$839$	−41.1849	+	26.4679i	−1.42186	+	0.913775i	−0.421887	+	0.906648i	$0.638632\pi$
$839$	−41.1849	+	26.4679i	−1.42186	+	0.913775i	−0.999975	+	0.00712672i	$0.997731\pi$
$840$	12.7499	−	24.0386i	0.439913	−	0.829410i
$841$	18.5084	+	21.3598i	0.638221	+	0.736546i
$842$	−4.29455	−	14.6259i	−0.148000	−	0.504042i
$843$	2.79646	−	19.4498i	0.0963152	−	0.669887i
$844$	−5.81634	+	6.71241i	−0.200207	+	0.231051i
$845$	−9.35179	+	20.4776i	−0.321711	+	0.704450i
$846$	−0.176248	+	0.600245i	−0.00605952	+	0.0206368i
$847$	48.2200	−	66.0705i	1.65686	−	2.27021i
$848$	−8.85229	+	1.27277i	−0.303989	+	0.0437070i
$849$	7.05611	−	10.9795i	0.242165	−	0.376816i
$850$	−70.4420			−2.41614
$851$	−1.71415	−	1.03719i	−0.0587603	−	0.0355545i
$852$		−	2.79064i		−	0.0956059i
$853$	−26.0975	+	40.6085i	−0.893560	+	1.39041i	0.0269280	+	0.999637i	$0.491428\pi$
$853$	−26.0975	+	40.6085i	−0.893560	+	1.39041i	−0.920488	+	0.390770i	$0.872209\pi$
$854$	−40.8604	+	31.3685i	−1.39822	+	1.07341i
$855$	6.15622	+	13.4802i	0.210538	+	0.461014i
$856$	3.05455	−	10.4028i	0.104402	−	0.355562i
$857$	−12.0552	−	5.50542i	−0.411798	−	0.188062i	0.198734	−	0.980053i	$-0.436317\pi$
$857$	−12.0552	−	5.50542i	−0.411798	−	0.188062i	−0.610532	+	0.791992i	$0.709044\pi$
$858$	21.6670	+	18.7745i	0.739698	+	0.640952i
$859$	−13.8413	−	1.99008i	−0.472259	−	0.0679006i	−0.0979235	−	0.995194i	$-0.531220\pi$
$859$	−13.8413	−	1.99008i	−0.472259	−	0.0679006i	−0.374335	+	0.927293i	$0.622129\pi$
$860$	3.62364	+	12.3410i	0.123565	+	0.420824i
$861$	−4.92663	+	13.7148i	−0.167899	+	0.467398i
$862$	21.0989	+	32.8306i	0.718633	+	1.11821i
$863$	−2.25968	+	1.45221i	−0.0769203	+	0.0494337i	−0.578536	−	0.815657i	$-0.696376\pi$
$863$	−2.25968	+	1.45221i	−0.0769203	+	0.0494337i	0.501615	+	0.865091i	$0.332739\pi$
$864$	−2.11645	+	1.83392i	−0.0720031	+	0.0623911i
$865$	−18.2231	−	62.0622i	−0.619605	−	2.11018i
$866$	−3.01765	+	20.9882i	−0.102544	+	0.713208i
$867$	5.12124	+	4.43758i	0.173926	+	0.150708i
$868$	−0.116868	−	1.39580i	−0.00396677	−	0.0473765i
$869$	89.5149	+	26.2839i	3.03658	+	0.891622i
$870$	5.37648	−	2.45536i	0.182280	−	0.0832444i
$871$	2.47437	+	17.2096i	0.0838407	+	0.583125i
$872$	18.1861	−	28.2982i	0.615860	−	0.958297i
$873$	8.93170			0.302292
$874$	−14.5701	−	21.3771i	−0.492842	−	0.723093i
$875$	−50.2576	−	89.4423i	−1.69902	−	3.02370i
$876$	−3.63168	−	2.33394i	−0.122703	−	0.0788566i
$877$	3.80959	+	26.4963i	0.128641	+	0.894717i	0.947280	+	0.320408i	$0.103820\pi$
$877$	3.80959	+	26.4963i	0.128641	+	0.894717i	−0.818639	+	0.574309i	$0.805271\pi$
$878$	−35.6636	+	16.2870i	−1.20359	+	0.549661i
$879$	7.43127	−	25.3086i	0.250650	−	0.853637i
$880$	−121.825	−	55.6355i	−4.10671	−	1.87547i
$881$	4.29800	−	4.96016i	0.144803	−	0.167112i	−0.678715	−	0.734402i	$-0.737463\pi$
$881$	4.29800	−	4.96016i	0.144803	−	0.167112i	0.823518	+	0.567290i	$0.192008\pi$
$882$	−8.54882	−	7.05178i	−0.287854	−	0.237446i
$883$	−36.0483	+	10.5847i	−1.21312	+	0.356204i	−0.824856	−	0.565343i	$-0.808744\pi$
$883$	−36.0483	+	10.5847i	−1.21312	+	0.356204i	−0.388265	+	0.921548i	$0.626926\pi$
$884$	3.42233	−	2.96547i	0.115105	−	0.0997395i
$885$	−15.1190	+	9.71641i	−0.508220	+	0.326613i
$886$	−8.76028	+	5.62989i	−0.294307	+	0.189140i
$887$	−31.0216	+	26.8804i	−1.04160	+	0.902555i	−0.995345	−	0.0963741i	$-0.969275\pi$
$887$	−31.0216	+	26.8804i	−1.04160	+	0.902555i	−0.0462592	+	0.998929i	$0.514730\pi$
$888$	0.947864	−	0.278318i	0.0318082	−	0.00933974i
$889$	−13.5293	+	5.23404i	−0.453759	+	0.175544i
$890$	−1.19705	+	1.38147i	−0.0401252	+	0.0463070i
$891$	−5.88917	−	2.68949i	−0.197295	−	0.0901015i
$892$	−1.48438	+	5.05534i	−0.0497007	+	0.169265i
$893$	1.22476	−	0.559330i	0.0409851	−	0.0187173i
$894$	−0.713983	−	4.96586i	−0.0238792	−	0.166083i
$895$	56.0799	+	36.0404i	1.87454	+	1.20470i
$896$	−17.6805	−	31.4656i	−0.590664	−	1.05119i
$897$	−0.362877	−	13.4097i	−0.0121161	−	0.447735i
$898$	40.5975			1.35476
$899$	−0.485256	+	0.755073i	−0.0161842	+	0.0251831i
$900$	1.00274	+	6.97424i	0.0334248	+	0.232475i
$901$	−5.46889	+	2.49756i	−0.182195	+	0.0832057i
$902$	54.1681	+	15.9052i	1.80360	+	0.529585i
$903$	−15.3992	+	1.28935i	−0.512453	+	0.0429070i
$904$	1.93538	+	1.67702i	0.0643699	+	0.0557768i
$905$	2.23509	−	15.5454i	0.0742967	−	0.516745i
$906$	−0.553431	−	1.88481i	−0.0183865	−	0.0626187i
$907$	−10.1487	+	8.79388i	−0.336981	+	0.291996i	−0.806869	−	0.590730i	$-0.798840\pi$
$907$	−10.1487	+	8.79388i	−0.336981	+	0.291996i	0.469888	+	0.882726i	$0.344294\pi$
$908$	10.1843	−	6.54505i	0.337978	−	0.217205i
$909$	0.692470	+	1.07750i	0.0229678	+	0.0357386i
$910$	47.9556	+	17.2266i	1.58971	+	0.571057i
$911$	2.53777	+	8.64287i	0.0840802	+	0.286351i	0.990791	−	0.135403i	$-0.0432329\pi$
$911$	2.53777	+	8.64287i	0.0840802	+	0.286351i	−0.906710	+	0.421754i	$0.861415\pi$
$912$	16.0414	+	2.30641i	0.531185	+	0.0763728i
$913$	66.5728	+	57.6857i	2.20324	+	1.90912i
$914$	−36.3500	−	16.6005i	−1.20235	−	0.549095i
$915$	−15.0694	+	51.3218i	−0.498180	+	1.69665i
$916$	−0.362524	−	0.793816i	−0.0119781	−	0.0262284i
$917$	−29.9892	−	39.0638i	−0.990332	−	1.29000i
$918$	−2.73672	+	4.25842i	−0.0903251	+	0.140549i
$919$		−	12.2510i		−	0.404122i	−0.979373	−	0.202061i	$-0.935236\pi$
$919$		−	12.2510i		−	0.404122i	0.979373	−	0.202061i	$-0.0647640\pi$
$920$	15.1711	+	46.9321i	0.500176	+	1.54731i
$921$	17.4762			0.575861
$922$	16.5556	−	25.7610i	0.545228	−	0.848392i
$923$	−15.2597	+	2.19401i	−0.502278	+	0.0722167i
$924$	−5.11287	+	7.00560i	−0.168201	+	0.230467i
$925$	1.63786	−	5.57804i	0.0538525	−	0.183405i
$926$	−8.37673	+	18.3425i	−0.275276	+	0.602771i
$927$	7.67682	−	8.85952i	0.252140	−	0.290985i
$928$	0.342122	−	2.37951i	0.0112307	−	0.0781113i
$929$	−4.35366	−	14.8272i	−0.142839	−	0.486465i	0.856732	−	0.515762i	$-0.172491\pi$
$929$	−4.35366	−	14.8272i	−0.142839	−	0.486465i	−0.999571	+	0.0292973i	$0.990673\pi$
$930$	−4.71458	−	5.44091i	−0.154597	−	0.178414i
$931$	0.578773	+	23.8445i	0.0189685	+	0.781472i
$932$	−1.25777	+	0.808322i	−0.0411997	+	0.0264775i
$933$	15.2936	+	17.6498i	0.500690	+	0.577827i
$934$	25.7607	−	7.56402i	0.842915	−	0.247502i
$935$	−89.1171	−	12.8131i	−2.91444	−	0.419033i
$936$	4.99880	+	4.33148i	0.163391	+	0.141579i
$937$	12.9584	−	28.3750i	0.423333	−	0.926970i	−0.571029	−	0.820930i	$-0.693456\pi$
$937$	12.9584	−	28.3750i	0.423333	−	0.926970i	0.994362	−	0.106040i	$-0.0338171\pi$
$938$	−25.3717	+	5.84256i	−0.828414	+	0.190766i
$939$	−2.54165	+	1.16073i	−0.0829437	+	0.0378791i
$940$	0.861325	−	0.123840i	0.0280933	−	0.00403921i
$941$	−26.8264	−	17.2403i	−0.874515	−	0.562017i	0.0246157	−	0.999697i	$-0.492164\pi$
$941$	−26.8264	−	17.2403i	−0.874515	−	0.562017i	−0.899131	+	0.437680i	$0.855800\pi$
$942$			5.55567i			0.181014i
$943$	−11.6194	−	23.7227i	−0.378378	−	0.772518i
$944$			19.6540i			0.639684i
$945$	−11.4868	−	0.681573i	−0.373666	−	0.0221716i
$946$	8.51968	+	59.2556i	0.276999	+	1.92657i
$947$	−18.1126	−	39.6610i	−0.588580	−	1.28881i	−0.936297	−	0.351210i	$-0.885770\pi$
$947$	−18.1126	−	39.6610i	−0.588580	−	1.28881i	0.347717	−	0.937600i	$-0.386957\pi$
$948$	−7.00061	−	2.05556i	−0.227369	−	0.0667616i
$949$	−9.90711	+	21.6935i	−0.321598	+	0.704202i
$950$	49.1583	−	56.7317i	1.59491	−	1.84062i
$951$	−10.1981	−	1.46626i	−0.330695	−	0.0475467i
$952$	−14.3159	−	13.9726i	−0.463980	−	0.452855i
$953$	−2.48557	+	2.15376i	−0.0805156	+	0.0697671i	−0.694189	−	0.719793i	$-0.744237\pi$
$953$	−2.48557	+	2.15376i	−0.0805156	+	0.0697671i	0.613673	+	0.789560i	$0.289691\pi$
$954$	1.60938	+	2.50424i	0.0521056	+	0.0810779i
$955$	22.9339	+	35.6858i	0.742123	+	1.15477i
$956$	4.19867	+	4.84552i	0.135795	+	0.156715i
$957$	5.33250	−	1.56576i	0.172375	−	0.0506139i
$958$	7.20191	−	50.0904i	0.232683	−	1.61835i
$959$	2.47094	−	12.0615i	0.0797909	−	0.389487i
$960$	−20.0938	−	9.17651i	−0.648523	−	0.296171i
$961$	−28.6953	−	8.42570i	−0.925655	−	0.271797i
$962$	0.768498	+	1.68278i	0.0247774	+	0.0542549i
$963$	−4.53829	+	0.652508i	−0.146244	+	0.0210268i
$964$	−7.11824	−	4.57461i	−0.229263	−	0.147338i
$965$	43.4923			1.40007
$966$	19.9651	−	2.21694i	0.642365	−	0.0713289i
$967$	31.2149			1.00380			0.501902	−	0.864925i	$-0.332634\pi$
$967$	31.2149			1.00380			0.501902	+	0.864925i	$0.332634\pi$
$968$	−61.5009	−	39.5242i	−1.97671	−	1.27036i
$969$	10.7839	−	1.55050i	0.346430	−	0.0498092i
$970$	−25.5475	−	55.9412i	−0.820281	−	1.79616i
$971$	27.3830	+	8.04038i	0.878763	+	0.258028i	0.689838	−	0.723963i	$-0.257682\pi$
$971$	27.3830	+	8.04038i	0.878763	+	0.258028i	0.188925	+	0.981992i	$0.439500\pi$
$972$	0.460569	+	0.210335i	0.0147728	+	0.00674649i
$973$	1.77158	−	8.64770i	0.0567942	−	0.277233i
$974$	−5.51007	+	38.3234i	−0.176554	+	1.22796i
$975$	37.3478	−	10.9663i	1.19609	−	0.351203i
$976$	38.3057	+	44.2071i	1.22614	+	1.41504i
$977$	−22.7969	−	35.4727i	−0.729337	−	1.13487i	−0.985736	−	0.168300i	$-0.946172\pi$
$977$	−22.7969	−	35.4727i	−0.729337	−	1.13487i	0.256399	−	0.966571i	$-0.417464\pi$
$978$	0.621368	+	0.966867i	0.0198692	+	0.0309170i
$979$	−1.29897	+	1.12556i	−0.0415152	+	0.0359731i
$980$	−3.98270	+	14.8915i	−0.127223	+	0.475692i
$981$	−14.0803	−	2.02445i	−0.449551	−	0.0646356i
$982$	−11.6122	+	13.4012i	−0.370559	+	0.427648i
$983$	19.7856	−	43.3243i	0.631061	−	1.38183i	−0.276133	−	0.961120i	$-0.589053\pi$
$983$	19.7856	−	43.3243i	0.631061	−	1.38183i	0.907194	−	0.420712i	$-0.138220\pi$
$984$	12.4972	+	3.66949i	0.398395	+	0.116979i
$985$	−0.476560	−	1.04352i	−0.0151845	−	0.0332493i
$986$	−0.618403	−	4.30109i	−0.0196940	−	0.136975i
$987$	−0.0619251	+	1.04365i	−0.00197110	+	0.0332197i
$988$			4.82570i			0.153526i
$989$	17.7640	−	21.6578i	0.564862	−	0.688678i
$990$			44.5780i			1.41678i
$991$	−9.63750	−	6.19365i	−0.306145	−	0.196748i	0.378543	−	0.925584i	$-0.376425\pi$
$991$	−9.63750	−	6.19365i	−0.306145	−	0.196748i	−0.684688	+	0.728836i	$0.740062\pi$
$992$	−2.89834	+	0.416718i	−0.0920223	+	0.0132308i
$993$	−14.0304	+	6.40748i	−0.445242	+	0.203335i
$994$	−5.18057	−	22.4969i	−0.164318	−	0.713559i
$995$	−14.6401	+	32.0573i	−0.464121	+	1.01628i
$996$	−5.20640	−	4.51137i	−0.164971	−	0.142948i
$997$	0.0998935	+	0.0143625i	0.00316366	+	0.000454866i	0.143896	−	0.989593i	$-0.454037\pi$
$997$	0.0998935	+	0.0143625i	0.00316366	+	0.000454866i	−0.140733	+	0.990048i	$0.544946\pi$
$998$	−37.8762	+	11.1215i	−1.19895	+	0.352044i
$999$	−0.273576	−	0.315724i	−0.00865556	−	0.00998905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.412.8	yes	320
7.6	odd	2	inner	483.2.r.a.412.7	yes	320
23.11	odd	22	inner	483.2.r.a.34.7	✓	320
161.34	even	22	inner	483.2.r.a.34.8	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.7	✓	320	23.11	odd	22	inner
483.2.r.a.34.8	yes	320	161.34	even	22	inner
483.2.r.a.412.7	yes	320	7.6	odd	2	inner
483.2.r.a.412.8	yes	320	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.33182 - 0.855909i) q^{2} +(0.989821 - 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(4.17306 + 1.22532i) q^{5} +(-1.44007 - 0.657659i) q^{6} +(-2.59192 - 0.530984i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-1.33182 - 0.855909i) q^{2} +(0.989821 - 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(4.17306 + 1.22532i) q^{5} +(-1.44007 - 0.657659i) q^{6} +(-2.59192 - 0.530984i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +(-4.50901 - 5.20367i) q^{10} +(-3.50024 - 5.44647i) q^{11} +(0.273740 + 0.425947i) q^{12} +(2.11393 - 1.83173i) q^{13} +(2.99750 + 2.92562i) q^{14} +(4.30497 + 0.618961i) q^{15} +(3.11470 - 3.59456i) q^{16} +(1.32826 - 2.90849i) q^{17} +(-1.51901 - 0.446021i) q^{18} +(1.41547 + 3.09945i) q^{19} +(0.313395 + 2.17971i) q^{20} +(-2.64111 - 0.156711i) q^{21} +10.2496i q^{22} +(3.53817 - 3.23750i) q^{23} +2.36469i q^{24} +(11.7068 + 7.52349i) q^{25} +(-4.38317 + 0.630205i) q^{26} +(0.909632 - 0.415415i) q^{27} +(-0.300616 - 1.30544i) q^{28} +(-0.356601 + 0.780848i) q^{29} +(-5.20367 - 4.50901i) q^{30} +(1.03495 + 0.148803i) q^{31} +(-2.68703 + 0.788982i) q^{32} +(-4.23972 - 4.89290i) q^{33} +(-4.25842 + 2.73672i) q^{34} +(-10.1656 - 5.39177i) q^{35} +(0.331572 + 0.382655i) q^{36} +(-0.117697 - 0.400840i) q^{37} +(0.767692 - 5.33942i) q^{38} +(1.83173 - 2.11393i) q^{39} +(-4.27238 + 9.35522i) q^{40} +(1.55178 - 5.28489i) q^{41} +(3.38335 + 2.46926i) q^{42} +(5.78126 - 0.831220i) q^{43} +(1.77226 - 2.75768i) q^{44} +4.34924 q^{45} +(-7.48320 + 1.28342i) q^{46} -0.395155i q^{47} +(2.57144 - 4.00124i) q^{48} +(6.43611 + 2.75254i) q^{49} +(-9.15191 - 20.0399i) q^{50} +(0.900823 - 3.06792i) q^{51} +(1.28827 + 0.588334i) q^{52} +(-1.42105 - 1.23135i) q^{53} +(-1.56702 - 0.225304i) q^{54} +(-7.93303 - 27.0174i) q^{55} +(2.11510 - 5.88802i) q^{56} +(1.84216 + 2.86646i) q^{57} +(1.14326 - 0.734730i) q^{58} +(-3.12292 + 2.70603i) q^{59} +(0.620411 + 2.11293i) q^{60} +(-1.75024 + 12.1732i) q^{61} +(-1.25100 - 1.08400i) q^{62} +(-2.63653 + 0.220753i) q^{63} +(-4.87331 - 1.43093i) q^{64} +(11.0660 - 5.05369i) q^{65} +(1.45867 + 10.1453i) q^{66} +(-3.36055 + 5.22911i) q^{67} +1.61894 q^{68} +(3.04141 - 3.70808i) q^{69} +(8.92392 + 15.8817i) q^{70} +(-4.63663 - 2.97978i) q^{71} +(0.336531 + 2.34062i) q^{72} +(-7.75564 + 3.54188i) q^{73} +(-0.186331 + 0.634585i) q^{74} +(12.6583 + 5.78087i) q^{75} +(-1.12979 + 1.30384i) q^{76} +(6.18034 + 15.9754i) q^{77} +(-4.24887 + 1.24758i) q^{78} +(-10.8904 + 9.43656i) q^{79} +(17.4024 - 11.1838i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-6.59008 + 5.71034i) q^{82} +(-13.0549 + 3.83325i) q^{83} +(-0.483340 - 1.24937i) q^{84} +(9.10678 - 10.5098i) q^{85} +(-8.41105 - 3.84120i) q^{86} +(-0.241845 + 0.823649i) q^{87} +(13.9261 - 6.35983i) q^{88} +(-0.0377817 - 0.262778i) q^{89} +(-5.79240 - 3.72255i) q^{90} +(-6.45176 + 3.62524i) q^{91} +(2.23529 + 0.948611i) q^{92} +1.04559 q^{93} +(-0.338217 + 0.526276i) q^{94} +(2.10903 + 14.6686i) q^{95} +(-2.54739 + 1.16336i) q^{96} +(8.56990 + 2.51635i) q^{97} +(-6.21582 - 9.17461i) q^{98} +(-4.89290 - 4.23972i) 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

Fields

Representations

Groups

Database

Properties

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