LMFDB - Embedded newform 483.2.r.a.412.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			412.7
Character	$\chi$	$=$	483.412
Dual form			483.2.r.a.34.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33182 - 0.855909i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(-4.17306 - 1.22532i) q^{5} +(1.44007 + 0.657659i) q^{6} +(-0.894449 - 2.48997i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(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} +(-0.894449 - 2.48997i) 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} +(-0.939945 + 4.08176i) 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} +(1.23970 + 2.33733i) 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} +(0.958671 - 0.935683i) 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} +(0.681573 + 11.4868i) 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} +(0.349482 - 4.17398i) 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} +(-5.39992 + 4.45430i) 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} +(6.12910 - 1.25562i) 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} +(-1.55972 - 2.13712i) 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} +(-10.4308 + 13.5871i) 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} +(-0.815751 + 1.06259i) 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} +(11.0042 - 1.31049i) 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	$-0.983887\pi$
$5$	−4.17306	−	1.22532i	−1.86625	−	0.547981i	−0.867532	−	0.497381i	$-0.834295\pi$
$6$	1.44007	+	0.657659i	0.587907	+	0.268488i
$7$	−0.894449	−	2.48997i	−0.338070	−	0.941121i
$7$	−0.894449	−	2.48997i	−0.338070	−	0.941121i
$8$	−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	−0.896738	−	0.442563i	$-0.854069\pi$
$13$	−2.11393	+	1.83173i	−0.586299	+	0.508031i	0.310439	+	0.950593i	$0.399524\pi$
$14$	−0.939945	+	4.08176i	−0.251211	+	1.09090i
$15$	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	−0.999544	−	0.0302087i	$-0.990383\pi$
$17$	−1.32826	+	2.90849i	−0.322152	+	0.705414i	0.677392	+	0.735622i	$0.263110\pi$
$18$	−1.51901	−	0.446021i	−0.358034	−	0.105128i
$19$	−1.41547	−	3.09945i	−0.324731	−	0.711062i	0.674909	−	0.737901i	$-0.264183\pi$
$19$	−1.41547	−	3.09945i	−0.324731	−	0.711062i	−0.999640	+	0.0268395i	$0.991456\pi$
$20$	−0.313395	−	2.17971i	−0.0700773	−	0.487399i
$21$	1.23970	+	2.33733i	0.270526	+	0.510048i
$22$			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
$28$	0.958671	−	0.935683i	0.181172	−	0.176828i
$29$	−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	0.0487450	−	0.998811i	$-0.484478\pi$
$31$	−1.03495	−	0.148803i	−0.185882	−	0.0267258i	−0.234627	+	0.972085i	$0.575387\pi$
$32$	−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
$35$	0.681573	+	11.4868i	0.115207	+	1.94162i
$36$	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	$0.232432\pi$
$41$	−1.55178	+	5.28489i	−0.242348	+	0.825362i	−0.987385	+	0.158338i	$0.949386\pi$
$42$	0.349482	−	4.17398i	0.0539263	−	0.644060i
$43$	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	$0.00917485\pi$
$47$			0.395155i			0.0576393i	−0.999585	+	0.0288197i	$0.990825\pi$
$48$	−2.57144	+	4.00124i	−0.371156	+	0.577529i
$49$	−5.39992	+	4.45430i	−0.771418	+	0.636329i
$50$	−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
$56$	6.12910	−	1.25562i	0.819035	−	0.167789i
$57$	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	−0.427440	−	0.904044i	$-0.640585\pi$
$59$	3.12292	−	2.70603i	0.406570	−	0.352295i	0.834011	+	0.551749i	$0.186039\pi$
$60$	0.620411	+	2.11293i	0.0800947	+	0.272777i
$61$	1.75024	−	12.1732i	0.224095	−	1.55861i	−0.498220	−	0.867050i	$-0.666013\pi$
$61$	1.75024	−	12.1732i	0.224095	−	1.55861i	0.722315	−	0.691564i	$-0.243078\pi$
$62$	1.25100	+	1.08400i	0.158878	+	0.137668i
$63$	−1.55972	−	2.13712i	−0.196507	−	0.269251i
$64$	−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	0.0938541	−	0.995586i	$-0.470081\pi$
$73$	7.75564	−	3.54188i	0.907729	−	0.414546i	0.813875	+	0.581040i	$0.197354\pi$
$74$	−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
$77$	−10.4308	+	13.5871i	−1.18870	+	1.54839i
$78$	−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	0.529089	−	0.848566i	$-0.322534\pi$
$83$	13.0549	−	3.83325i	1.43296	−	0.420754i	0.903868	+	0.427812i	$0.140715\pi$
$84$	−0.815751	+	1.06259i	−0.0890057	+	0.115938i
$85$	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	0.991726	−	0.128374i	$-0.0409756\pi$
$89$	0.0377817	+	0.262778i	0.00400486	+	0.0278544i	−0.987721	+	0.156228i	$0.950067\pi$
$90$	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	−0.183966	−	0.982933i	$-0.558894\pi$
$97$	−8.56990	−	2.51635i	−0.870142	−	0.255497i	−0.686176	+	0.727436i	$0.740712\pi$
$98$	11.0042	−	1.31049i	1.11159	−	0.132379i
$99$	−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	0.939590	−	0.342302i	$-0.111207\pi$
$101$	−0.360852	−	1.22895i	−0.0359061	−	0.122285i	−0.975496	+	0.220017i	$0.929389\pi$
$102$	−3.82560	+	3.31490i	−0.378790	+	0.328224i
$103$	−9.86187	+	6.33784i	−0.971719	+	0.624486i	−0.927217	−	0.374524i	$-0.877806\pi$
$103$	−9.86187	+	6.33784i	−0.971719	+	0.624486i	−0.0445013	+	0.999009i	$0.514170\pi$
$104$	−3.57599	−	5.56435i	−0.350655	−	0.545629i
$105$	−2.30938	−	11.2729i	−0.225372	−	1.10012i
$106$	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
$112$	−11.7363	−	4.54038i	−1.10898	−	0.429025i
$113$	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
$119$	8.43013	+	0.705844i	0.772789	+	0.0647046i
$120$	−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
$126$	0.248095	+	4.18123i	0.0221020	+	0.372494i
$127$	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	$-0.970478\pi$
$131$	−14.0674	−	12.1895i	−1.22908	−	1.06500i	−0.233375	−	0.972387i	$-0.574977\pi$
$132$	−1.36176	+	2.98183i	−0.118526	+	0.259535i
$133$	−6.45147	+	6.29678i	−0.559413	+	0.546000i
$134$	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	$-0.954809\pi$
$139$		−	3.33641i		−	0.282990i	0.989939	−	0.141495i	$-0.0451910\pi$
$140$	−5.14711	+	2.72999i	−0.435010	+	0.230726i
$141$	−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
$147$	4.71105	−	5.17746i	0.388561	−	0.427029i
$148$	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
$154$	25.5212	−	9.16775i	2.05656	−	0.738758i
$155$	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	0.958842	−	0.283941i	$-0.0916420\pi$
$157$	1.45781	+	3.19215i	0.116346	+	0.254761i	−0.842496	+	0.538702i	$0.818915\pi$
$158$	22.5809	−	3.24664i	1.79644	−	0.258289i
$159$	1.58182	+	1.01658i	0.125447	+	0.0806197i
$160$	12.1799			0.962905
$161$	−11.2260	−	5.91416i	−0.884732	−	0.466101i
$162$	−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	0.927070	−	0.374888i	$-0.122319\pi$
$167$	16.1645	+	7.38210i	1.25085	+	0.571244i	0.323780	+	0.946132i	$0.395046\pi$
$168$	−5.88802	+	2.11510i	−0.454271	+	0.163183i
$169$	−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	$0.00944164\pi$
$173$	8.04046	+	12.5112i	0.611305	+	0.951209i	−0.388255	+	0.921552i	$0.626922\pi$
$174$	−1.02706	+	0.889955i	−0.0778615	+	0.0674673i
$175$	8.26217	−	35.8789i	0.624562	−	2.71219i
$176$	−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	0.999966	−	0.00819071i	$-0.00260721\pi$
$181$	0.513903	+	3.57427i	0.0381981	+	0.265673i	−0.961768	+	0.273864i	$0.911698\pi$
$182$	−5.48971	−	10.3503i	−0.406924	−	0.767214i
$183$			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
$189$	1.84799	+	1.89339i	0.134422	+	0.137724i
$190$	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
$196$	−3.18731	−	1.55014i	−0.227665	−	0.110724i
$197$	−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	$-0.861820\pi$
$199$	1.15318	−	8.02055i	0.0817469	−	0.568562i	0.988993	−	0.147962i	$-0.0472713\pi$
$200$	−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
$203$	2.26325	+	0.189499i	0.158849	+	0.0133002i
$204$	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
$210$	−6.57289	+	16.9901i	−0.453572	+	1.17243i
$211$	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
$217$	0.555192	+	2.71009i	0.0376889	+	0.183973i
$218$	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	0.350513	−	0.936558i	$-0.386007\pi$
$223$	−7.86425	−	6.81441i	−0.526629	−	0.456327i	−0.877142	+	0.480231i	$0.840553\pi$
$224$	4.36795	+	5.98492i	0.291846	+	0.399884i
$225$	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	$0.246275\pi$
$227$	3.40271	+	23.6664i	0.225846	+	1.57079i	−0.489487	+	0.872011i	$0.662816\pi$
$228$	−0.932731	+	1.45136i	−0.0617716	+	0.0961185i
$229$	1.72356			0.113896			0.0569479	−	0.998377i	$-0.481863\pi$
$229$	1.72356			0.113896			0.0569479	+	0.998377i	$0.481863\pi$
$230$	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
$238$	−10.6233	−	8.15548i	−0.688605	−	0.528642i
$239$	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	−0.00284827	−	0.999996i	$-0.500907\pi$
$241$	14.0586	−	9.03494i	0.905597	−	0.581992i	0.908445	+	0.418004i	$0.137270\pi$
$242$	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
$245$	27.9922	−	11.9715i	1.78836	−	0.764828i
$246$	−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	0.648939	−	0.760840i	$-0.275213\pi$
$251$	3.58738	+	2.30547i	0.226433	+	0.145520i	−0.422506	+	0.906360i	$0.638849\pi$
$252$	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	−0.312833	−	0.949808i	$-0.601278\pi$
$257$	3.20819	−	1.46513i	0.200121	−	0.0913923i	0.512955	+	0.858416i	$0.328551\pi$
$258$	8.87209	+	2.60508i	0.552352	+	0.162185i
$259$	−0.892806	+	0.651593i	−0.0554763	+	0.0404880i
$260$	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
$266$	13.9817	−	2.86430i	0.857271	−	0.175622i
$267$	−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	0.945575	−	0.325405i	$-0.105501\pi$
$269$	12.4330	+	10.7732i	0.758051	+	0.656855i	−0.187524	+	0.982260i	$0.560046\pi$
$270$	−6.26322	−	2.86032i	−0.381167	−	0.174073i
$271$	6.49601	−	22.1234i	0.394604	−	1.34390i	−0.487614	−	0.873059i	$-0.662133\pi$
$271$	6.49601	−	22.1234i	0.394604	−	1.34390i	0.882219	−	0.470840i	$-0.156049\pi$
$272$	6.31761	+	13.8336i	0.383061	+	0.838787i
$273$	−6.90202	−	2.67016i	−0.417729	−	0.161605i
$274$	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
$280$	−27.1157	−	2.27036i	−1.62047	−	0.135680i
$281$	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	−0.950600	−	0.310418i	$-0.899531\pi$
$283$	−8.54684	+	9.86358i	−0.508057	+	0.586329i	0.442543	+	0.896747i	$0.354076\pi$
$284$	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
$287$	14.5472	−	0.863164i	0.858696	−	0.0509510i
$288$	−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	$0.416348\pi$
$293$	−10.9574	+	23.9934i	−0.640139	+	1.40171i	−0.899926	+	0.436043i	$0.856380\pi$
$294$	−10.7057	+	2.86321i	−0.624369	+	0.166986i
$295$	−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
$301$	−7.24075	−	13.6517i	−0.417350	−	0.786871i
$302$	−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	−0.370280	−	0.928920i	$-0.620738\pi$
$307$	−17.2983	−	2.48712i	−0.987268	−	0.141948i	−0.616988	+	0.786973i	$0.711647\pi$
$308$	−8.45175	−	1.94626i	−0.481583	−	0.110899i
$309$	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	$-0.951466\pi$
$311$	−12.6261	−	19.6466i	−0.715961	−	1.11406i	0.272437	−	0.962174i	$-0.412170\pi$
$312$	4.33148	+	4.99880i	0.245222	+	0.283001i
$313$	2.68097	−	0.787205i	0.151538	−	0.0444954i	−0.205084	−	0.978744i	$-0.565747\pi$
$313$	2.68097	−	0.787205i	0.151538	−	0.0444954i	0.356622	+	0.934249i	$0.383929\pi$
$314$	0.790654	−	5.49912i	0.0446192	−	0.310333i
$315$	3.89017	+	10.8295i	0.219186	+	0.610172i
$316$	−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
$322$	9.88901	+	17.4850i	0.551093	+	0.974402i
$323$	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
$329$	0.983926	−	0.353446i	0.0542456	−	0.0194861i
$330$	−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
$336$	12.2630	+	2.82391i	0.669002	+	0.154057i
$337$	−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
$343$	15.9210	+	9.46151i	0.859656	+	0.510874i
$344$			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	−0.330595	−	0.943773i	$-0.607249\pi$
$349$	3.10426	−	1.41767i	0.166167	−	0.0758860i	0.496762	+	0.867887i	$0.334522\pi$
$350$	−41.7128	+	40.7126i	−2.22964	+	2.17618i
$351$	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	−0.608266	−	0.793733i	$-0.708135\pi$
$353$	−26.5951	−	3.82380i	−1.41551	−	0.203520i	−0.807247	+	0.590213i	$0.799044\pi$
$354$	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
$357$	−8.44478	+	0.501074i	−0.446945	+	0.0265196i
$358$	−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
$364$	−0.312643	+	3.73400i	−0.0163869	+	0.195715i
$365$	−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	$-0.416772\pi$
$367$	9.90430			0.517000			0.258500	+	0.966011i	$0.416772\pi$
$368$	−0.617041	−	22.8020i	−0.0321655	−	1.18864i
$369$			5.50801i			0.286735i
$370$	1.55514	−	2.41985i	0.0808480	−	0.125802i
$371$	−1.79496	+	4.63975i	−0.0931897	+	0.240884i
$372$	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
$378$	−0.840621	−	4.10337i	−0.0432369	−	0.211054i
$379$	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	$0.158576\pi$
$383$	−1.93819	+	13.4804i	−0.0990367	+	0.688815i	−0.977489	+	0.210985i	$0.932333\pi$
$384$	−10.3098	−	8.93345i	−0.526117	−	0.455883i
$385$	60.1769	−	43.9187i	3.06690	−	2.23830i
$386$	−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	−0.608665	−	0.793428i	$-0.708295\pi$
$397$	−32.0170	−	14.6217i	−1.60689	−	0.733841i	−0.998223	+	0.0595865i	$0.981022\pi$
$398$	−8.40069	+	9.69491i	−0.421089	+	0.485962i
$399$	5.48968	−	7.15082i	0.274828	−	0.357989i
$400$	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
$406$	−2.85205	−	2.18951i	−0.141545	−	0.108664i
$407$	−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	$0.187671\pi$
$409$	−3.41095	+	11.6166i	−0.168661	+	0.574405i	−0.999831	+	0.0183874i	$0.994147\pi$
$410$	−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	0.632316	−	0.774710i	$-0.282104\pi$
$419$	15.2583	+	4.48023i	0.745415	+	0.218874i	0.113098	+	0.993584i	$0.463922\pi$
$420$	4.70620	−	3.43471i	0.229639	−	0.167597i
$421$	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
$427$	−31.8763	+	6.53023i	−1.54260	+	0.316020i
$428$	−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	0.994930	−	0.100568i	$-0.0320660\pi$
$433$	5.56393	+	12.1833i	0.267385	+	0.585492i	−0.727545	+	0.686060i	$0.759339\pi$
$434$	1.58017	−	4.08454i	0.0758507	−	0.196064i
$435$	−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	$0.383080\pi$
$439$	−13.3891	+	20.8338i	−0.639025	+	0.994342i	−0.998135	+	0.0610467i	$0.980556\pi$
$440$	−65.9073	+	9.47604i	−3.14201	+	0.451752i
$441$	−3.92627	+	5.79521i	−0.186965	+	0.275962i
$442$	−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
$448$	0.795942	+	13.4143i	0.0376047	+	0.633766i
$449$	−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
$455$	−22.4815	−	23.0338i	−1.05395	−	1.07984i
$456$	−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	$-0.851268\pi$
$461$		−	19.3427i		−	0.900878i	0.892807	−	0.450439i	$-0.148732\pi$
$462$	−23.9568	+	12.7065i	−1.11457	+	0.591159i
$463$	−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	−0.438185	−	0.898885i	$-0.644379\pi$
$467$	11.1057	−	12.8167i	0.513910	−	0.593084i	0.952096	+	0.305800i	$0.0989241\pi$
$468$	−1.40184	−	0.201554i	−0.0648001	−	0.00931685i
$469$	16.0262	+	3.69050i	0.740020	+	0.170411i
$470$	−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
$476$	1.44806	+	4.03112i	0.0663718	+	0.184766i
$477$	−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	$-0.875760\pi$
$479$	−13.2789	−	29.0767i	−0.606727	−	1.32855i	0.318063	−	0.948070i	$-0.396968\pi$
$480$	−12.0559	+	1.73338i	−0.550275	+	0.0791176i
$481$	0.983034	+	0.631758i	0.0448225	+	0.0288057i
$482$	−26.4567			−1.20507
$483$	11.9534	+	4.25634i	0.543898	+	0.193670i
$484$	−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
$490$	−47.5270	−	8.01494i	−2.14705	−	0.362078i
$491$	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
$497$	−3.27234	+	14.2103i	−0.146785	+	0.637421i
$498$	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	$-0.857362\pi$
$503$	−3.55640	−	24.7353i	−0.158572	−	1.10289i	0.742696	−	0.669629i	$-0.233547\pi$
$504$	5.52708	−	2.93152i	0.246196	−	0.130580i
$505$			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	−0.415384	−	0.909646i	$-0.636353\pi$
$509$	−12.5815	+	1.80895i	−0.557666	+	0.0801802i	−0.142281	+	0.989826i	$0.545444\pi$
$510$	20.0263	−	9.14569i	0.886778	−	0.404978i
$511$	−15.7562	−	16.1433i	−0.697014	−	0.714138i
$512$	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
$518$	1.74676	−	0.103645i	0.0767483	−	0.00455388i
$519$	−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	$-0.814409\pi$
$521$	2.76872	−	19.2568i	0.121300	−	0.843657i	0.956087	−	0.293084i	$-0.0946817\pi$
$522$	0.889955	−	1.02706i	0.0389523	−	0.0449533i
$523$	−16.0829	+	35.2167i	−0.703257	+	1.53992i	0.132720	+	0.991154i	$0.457629\pi$
$523$	−16.0829	+	35.2167i	−0.703257	+	1.53992i	−0.835977	+	0.548765i	$0.815098\pi$
$524$	2.65523	−	9.04290i	0.115994	−	0.395041i
$525$	−3.07197	+	36.6896i	−0.134072	+	1.60126i
$526$	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
$532$	−4.25707	−	1.64692i	−0.184567	−	0.0714029i
$533$	−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
$539$	43.1613	+	13.8194i	1.85909	+	0.595245i
$540$	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
$546$	6.90683	+	9.46367i	0.295585	+	0.405008i
$547$	−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
$560$	43.4129	+	33.3280i	1.83453	+	1.40837i
$561$	−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	−0.982902	−	0.184130i	$-0.941053\pi$
$563$	−29.0360	+	18.6603i	−1.22372	+	0.786439i	−0.240821	+	0.970569i	$0.577417\pi$
$564$	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
$567$	−2.09864	−	1.61112i	−0.0881345	−	0.0676608i
$568$	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	−0.997276	−	0.0737605i	$-0.976500\pi$
$577$	−12.3923	+	19.2828i	−0.515898	+	0.802752i	0.481378	+	0.876513i	$0.340136\pi$
$578$	−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
$581$	−21.2216	−	29.0776i	−0.880420	−	1.20634i
$582$	−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	0.987425	−	0.158087i	$-0.0505327\pi$
$587$	10.5012	+	16.3403i	0.433433	+	0.674434i	−0.553992	+	0.832522i	$0.686896\pi$
$588$	3.37547	+	1.08076i	0.139202	+	0.0445699i
$589$	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	$0.258583\pi$
$593$	−6.89822	+	23.4932i	−0.283276	+	0.964749i	−0.971060	+	0.238834i	$0.923235\pi$
$594$	−4.25784	−	9.32337i	−0.174701	−	0.382543i
$595$	−34.3146	−	13.2752i	−1.40676	−	0.544229i
$596$	−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	0.331378	−	0.943498i	$-0.392487\pi$
$601$	22.4351	−	3.22568i	0.915147	−	0.131578i	0.583769	+	0.811920i	$0.301577\pi$
$602$	−2.04122	+	24.3790i	−0.0831941	+	0.993615i
$603$	−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	0.895315	−	0.445434i	$-0.146951\pi$
$607$	−2.43150	−	8.28094i	−0.0986917	−	0.336113i	−0.994007	+	0.109321i	$0.965132\pi$
$608$	6.24881	+	7.21152i	0.253423	+	0.292466i
$609$	−2.26718	+	0.134524i	−0.0918709	+	0.00545119i
$610$	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
$616$	−28.2920	−	28.9870i	−1.13992	−	1.16792i
$617$	−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	0.979900	−	0.199489i	$-0.0639282\pi$
$619$	29.9926	+	19.2751i	1.20550	+	0.774730i	0.225604	+	0.974219i	$0.427565\pi$
$620$			2.30252i			0.0924716i
$621$	−1.87352	+	4.41474i	−0.0751819	+	0.177157i
$622$			36.9726i			1.48246i
$623$	0.620515	−	0.329117i	0.0248604	−	0.0131858i
$624$	−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
$630$	4.08804	−	17.7526i	0.162872	−	0.707279i
$631$	−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
$637$	3.25597	−	19.3073i	0.129006	−	0.764983i
$638$	−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	$-0.413677\pi$
$643$	13.5856			0.535762			0.267881	+	0.963452i	$0.413677\pi$
$644$	0.362663	−	6.41430i	0.0142909	−	0.252759i
$645$	25.4026			1.00023
$646$	−14.5100	−	9.32499i	−0.570887	−	0.366887i
$647$	−14.4729	+	2.08089i	−0.568988	+	0.0818081i	−0.420804	−	0.907152i	$-0.638252\pi$
$647$	−14.4729	+	2.08089i	−0.568988	+	0.0818081i	−0.148184	+	0.988960i	$0.547343\pi$
$648$	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
$651$	−0.935227	−	2.60349i	−0.0366544	−	0.102039i
$652$	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
$658$	−1.61293	−	0.371424i	−0.0628786	−	0.0144796i
$659$	−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	−0.973987	−	0.226605i	$-0.927237\pi$
$661$	−4.23967	+	9.28358i	−0.164904	+	0.361090i	0.809083	+	0.587695i	$0.199964\pi$
$662$	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
$665$	34.6380	−	18.3717i	1.34320	−	0.712425i
$666$			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
$672$	−5.17524	−	5.30238i	−0.199639	−	0.204544i
$673$	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	0.717163	−	0.696905i	$-0.245440\pi$
$677$	−1.94393	−	2.24342i	−0.0747114	−	0.0862215i	−0.791875	+	0.610684i	$0.790895\pi$
$678$	1.44231	−	0.926918i	0.0553917	−	0.0355981i
$679$	1.39969	+	23.5896i	0.0537153	+	0.905285i
$680$	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
$686$	−13.1058	−	26.2280i	−0.500381	−	1.00139i
$687$	−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	$0.262180\pi$
$691$			38.5703i			1.46728i	−0.679538	+	0.733641i	$0.737820\pi$
$692$	−4.07109	+	6.33473i	−0.154759	+	0.240810i
$693$	−6.18034	+	15.9754i	−0.234772	+	0.606855i
$694$	−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
$700$	18.2626	−	3.74129i	0.690260	−	0.141408i
$701$	−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
$707$	−2.73729	+	1.99774i	−0.102946	+	0.0751329i
$708$	−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	0.0784392	−	0.996919i	$-0.475006\pi$
$719$	−16.7217	−	7.63656i	−0.623615	−	0.284795i	−0.702054	+	0.712123i	$0.747734\pi$
$720$	−13.5466	+	15.6336i	−0.504852	+	0.582630i
$721$	24.6020	+	18.8869i	0.916225	+	0.703385i
$722$	−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	0.187801	−	0.982207i	$-0.439864\pi$
$727$	23.6414	−	6.94173i	0.876810	−	0.257455i	0.689009	+	0.724753i	$0.258046\pi$
$728$	−10.6565	+	13.8811i	−0.394958	+	0.514469i
$729$	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	$-0.992997\pi$
$733$	−1.26423	−	8.79290i	−0.0466953	−	0.324773i	0.953063	−	0.302773i	$-0.0979125\pi$
$734$	−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
$742$	6.36176	−	4.64298i	0.233548	−	0.170449i
$743$	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
$749$	2.43454	+	11.8839i	0.0889562	+	0.434226i
$750$	−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
$756$	−0.483340	+	1.24937i	−0.0175789	+	0.0454393i
$757$	−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	−0.640539	−	0.767926i	$-0.721289\pi$
$761$	8.94017	−	13.9112i	0.324081	−	0.504280i	0.964619	+	0.263646i	$0.0849252\pi$
$762$	8.59189	−	1.23533i	0.311251	−	0.0447512i
$763$	−3.14024	+	37.5049i	−0.113684	+	1.35777i
$764$	−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	$0.113391\pi$
$769$	31.8636	+	36.7726i	1.14903	+	1.32605i	0.211813	+	0.977310i	$0.432063\pi$
$770$	−117.735	+	6.98586i	−4.24288	+	0.251753i
$771$	−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	−0.637667	−	0.770312i	$-0.720100\pi$
$773$	−21.0647	+	6.18515i	−0.757644	+	0.222464i	−0.119977	+	0.992777i	$0.538282\pi$
$774$	−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
$777$	0.790987	−	0.772021i	0.0283765	−	0.0276961i
$778$	−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
$784$	−0.807900	+	33.2842i	−0.0288536	+	1.18872i
$785$	−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	0.645467	−	0.763788i	$-0.276663\pi$
$787$	21.7565	+	6.38827i	0.775534	+	0.227717i	0.130067	+	0.991505i	$0.458481\pi$
$788$	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
$791$	−2.79218	−	0.642980i	−0.0992784	−	0.0228617i
$792$	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	$-0.771370\pi$
$797$	4.37307	−	30.4154i	0.154902	−	1.07737i	0.907852	−	0.419290i	$-0.137721\pi$
$798$	−13.4317	+	4.82495i	−0.475478	+	0.170801i
$799$	−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
$805$	39.6000	+	38.4356i	1.39572	+	1.35468i
$806$	−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	$-0.999521\pi$
$811$	−47.1596	−	21.5370i	−1.65600	−	0.756268i	−0.655997	−	0.754764i	$-0.727752\pi$
$812$	0.388763	+	1.08224i	0.0136429	+	0.0379792i
$813$	−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
$819$	7.21177	+	1.66072i	0.252000	+	0.0580302i
$820$	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
$826$	8.10999	+	15.2905i	0.282183	+	0.532026i
$827$			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	$-0.807083\pi$
$829$		−	32.8025i		−	1.13928i	0.821895	−	0.569639i	$-0.192917\pi$
$830$	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
$833$	−5.78279	−	21.6221i	−0.200362	−	0.749163i
$834$	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	$-0.361368\pi$
$839$	41.1849	−	26.4679i	1.42186	−	0.913775i	0.999975	−	0.00712672i	$-0.00226853\pi$
$840$	27.1628	−	1.61171i	0.937205	−	0.0556093i
$841$	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
$847$	81.5101	+	6.82474i	2.80072	+	0.234501i
$848$	−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	$-0.508572\pi$
$853$	26.0975	−	40.6085i	0.893560	−	1.39041i	0.920488	−	0.390770i	$-0.127791\pi$
$854$	48.0428	+	18.5862i	1.64399	+	0.636005i
$855$	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	0.610532	−	0.791992i	$-0.290956\pi$
$857$	12.0552	+	5.50542i	0.411798	+	0.188062i	−0.198734	+	0.980053i	$0.563683\pi$
$858$	21.6670	+	18.7745i	0.739698	+	0.640952i
$859$	13.8413	+	1.99008i	0.472259	+	0.0679006i	0.374335	−	0.927293i	$-0.377871\pi$
$859$	13.8413	+	1.99008i	0.472259	+	0.0679006i	0.0979235	+	0.995194i	$0.468780\pi$
$860$	−3.62364	−	12.3410i	−0.123565	−	0.420824i
$861$	−14.2763	+	2.92466i	−0.486536	+	0.0996723i
$862$	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
$868$	−1.13141	+	0.825731i	−0.0384025	+	0.0280271i
$869$	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	−0.823518	−	0.567290i	$-0.807992\pi$
$881$	−4.29800	+	4.96016i	−0.144803	+	0.167112i	0.678715	+	0.734402i	$0.262537\pi$
$882$	10.1892	−	4.35765i	0.343090	−	0.146730i
$883$	−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	0.0462592	−	0.998929i	$-0.485270\pi$
$887$	31.0216	−	26.8804i	1.04160	−	0.902555i	0.995345	+	0.0963741i	$0.0307245\pi$
$888$	−0.947864	+	0.278318i	−0.0318082	+	0.00933974i
$889$	−11.5067	−	8.83368i	−0.385922	−	0.296272i
$890$	−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
$903$	9.10989	+	12.4823i	0.303158	+	0.415384i
$904$	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
$910$	10.2265	+	49.9191i	0.339005	+	1.65480i
$911$	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
$917$	−17.7689	+	45.9304i	−0.586781	+	1.51675i
$918$	−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
$924$	8.64270	+	0.723642i	0.284324	+	0.0238061i
$925$	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	0.999571	−	0.0292973i	$-0.00932697\pi$
$929$	4.35366	+	14.8272i	0.142839	+	0.486465i	−0.856732	+	0.515762i	$0.827509\pi$
$930$	4.71458	+	5.44091i	0.154597	+	0.178414i
$931$	21.4493	+	10.4318i	0.702973	+	0.341890i
$932$	−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	$0.306544\pi$
$937$	−12.9584	+	28.3750i	−0.423333	+	0.926970i	−0.994362	+	0.106040i	$0.966183\pi$
$938$	−18.1853	−	18.6320i	−0.593770	−	0.608357i
$939$	−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	0.899131	−	0.437680i	$-0.144200\pi$
$941$	26.8264	+	17.2403i	0.874515	+	0.562017i	−0.0246157	+	0.999697i	$0.507836\pi$
$942$			5.55567i			0.181014i
$943$	11.6194	+	23.7227i	0.378378	+	0.772518i
$944$		−	19.6540i		−	0.639684i
$945$	−5.39177	−	10.1656i	−0.175394	−	0.330688i
$946$	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
$952$	−4.48912	+	19.4942i	−0.145493	+	0.631812i
$953$	−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
$959$	11.5871	−	4.16233i	0.374168	−	0.134409i
$960$	−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
$966$	−12.2767	−	15.8997i	−0.394997	−	0.511564i
$967$	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	−0.188925	−	0.981992i	$-0.560500\pi$
$971$	−27.3830	−	8.04038i	−0.878763	−	0.258028i	−0.689838	+	0.723963i	$0.742318\pi$
$972$	−0.460569	−	0.210335i	−0.0147728	−	0.00674649i
$973$	−8.30756	+	2.98424i	−0.266328	+	0.0956704i
$974$	−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
$980$	11.4014	+	10.3743i	0.364205	+	0.331396i
$981$	−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	$0.410947\pi$
$983$	−19.7856	+	43.3243i	−0.631061	+	1.38183i	−0.907194	+	0.420712i	$0.861780\pi$
$984$	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
$987$	−0.923610	+	0.489876i	−0.0293988	+	0.0155929i
$988$			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
$994$	16.5209	−	16.1248i	0.524012	−	0.511447i
$995$	−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	0.140733	−	0.990048i	$-0.455054\pi$
$997$	−0.0998935	−	0.0143625i	−0.00316366	−	0.000454866i	−0.143896	+	0.989593i	$0.545963\pi$
$998$	−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.412.7	yes	320
7.6	odd	2	inner	483.2.r.a.412.8	yes	320
23.11	odd	22	inner	483.2.r.a.34.8	yes	320
161.34	even	22	inner	483.2.r.a.34.7	✓	320

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33182 - 0.855909i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(0.210335 + 0.460569i) q^{4} +(-4.17306 - 1.22532i) q^{5} +(1.44007 + 0.657659i) q^{6} +(-0.894449 - 2.48997i) q^{7} +(-0.336531 + 2.34062i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(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} +(-0.894449 - 2.48997i) 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} +(-0.939945 + 4.08176i) 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} +(1.23970 + 2.33733i) 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} +(0.958671 - 0.935683i) 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} +(0.681573 + 11.4868i) 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} +(0.349482 - 4.17398i) 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} +(-5.39992 + 4.45430i) 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} +(6.12910 - 1.25562i) 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} +(-1.55972 - 2.13712i) 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} +(-10.4308 + 13.5871i) 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} +(-0.815751 + 1.06259i) 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} +(11.0042 - 1.31049i) 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

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Database

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