LMFDB - Embedded newform 483.2.r.a.34.7

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			34.7
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.7

$q$-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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.33182	+	0.855909i	−0.941739	+	0.605219i	−0.918887	−	0.394520i	$-0.870911\pi$
$2$	−1.33182	+	0.855909i	−0.941739	+	0.605219i	−0.0228516	+	0.999739i	$0.507275\pi$
$3$	−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	−0.867532	+	0.497381i	$0.834295\pi$
$5$	−4.17306	+	1.22532i	−1.86625	+	0.547981i	−0.998719	+	0.0505996i	$0.983887\pi$
$6$	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	−0.344585	+	0.938755i	$0.611980\pi$
$11$	−3.50024	+	5.44647i	−1.05536	+	1.64217i	−0.710776	+	0.703419i	$0.751656\pi$
$12$	−0.273740	+	0.425947i	−0.0790219	+	0.122960i
$13$	−2.11393	−	1.83173i	−0.586299	−	0.508031i	0.310439	−	0.950593i	$-0.399524\pi$
$13$	−2.11393	−	1.83173i	−0.586299	−	0.508031i	−0.896738	+	0.442563i	$0.854069\pi$
$14$	−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	0.677392	−	0.735622i	$-0.263110\pi$
$17$	−1.32826	−	2.90849i	−0.322152	−	0.705414i	−0.999544	+	0.0302087i	$0.990383\pi$
$18$	−1.51901	+	0.446021i	−0.358034	+	0.105128i
$19$	−1.41547	+	3.09945i	−0.324731	+	0.711062i	−0.999640	−	0.0268395i	$-0.991456\pi$
$19$	−1.41547	+	3.09945i	−0.324731	+	0.711062i	0.674909	+	0.737901i	$0.264183\pi$
$20$	−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	0.873629	−	0.486593i	$-0.161761\pi$
$29$	−0.356601	−	0.780848i	−0.0662192	−	0.145000i	−0.939848	+	0.341594i	$0.889033\pi$
$30$	−5.20367	+	4.50901i	−0.950056	+	0.823228i
$31$	−1.03495	+	0.148803i	−0.185882	+	0.0267258i	−0.234627	−	0.972085i	$-0.575387\pi$
$31$	−1.03495	+	0.148803i	−0.185882	+	0.0267258i	0.0487450	+	0.998811i	$0.484478\pi$
$32$	−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	−0.968602	−	0.248618i	$-0.920024\pi$
$37$	−0.117697	+	0.400840i	−0.0193493	+	0.0658977i	0.949252	+	0.314515i	$0.101842\pi$
$38$	−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	−0.987385	−	0.158338i	$-0.949386\pi$
$41$	−1.55178	−	5.28489i	−0.242348	−	0.825362i	0.745037	−	0.667023i	$-0.232432\pi$
$42$	0.349482	+	4.17398i	0.0539263	+	0.644060i
$43$	5.78126	+	0.831220i	0.881634	+	0.126760i	0.568239	−	0.822863i	$-0.307625\pi$
$43$	5.78126	+	0.831220i	0.881634	+	0.126760i	0.313394	+	0.949623i	$0.398534\pi$
$44$	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
$49$	−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	−0.746975	−	0.664852i	$-0.768495\pi$
$53$	−1.42105	+	1.23135i	−0.195196	+	0.169138i	0.551779	+	0.833990i	$0.313949\pi$
$54$	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	0.834011	−	0.551749i	$-0.186039\pi$
$59$	3.12292	+	2.70603i	0.406570	+	0.352295i	−0.427440	+	0.904044i	$0.640585\pi$
$60$	0.620411	−	2.11293i	0.0800947	−	0.272777i
$61$	1.75024	+	12.1732i	0.224095	+	1.55861i	0.722315	+	0.691564i	$0.243078\pi$
$61$	1.75024	+	12.1732i	0.224095	+	1.55861i	−0.498220	+	0.867050i	$0.666013\pi$
$62$	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	0.572976	−	0.819572i	$-0.305789\pi$
$67$	−3.36055	−	5.22911i	−0.410556	−	0.638838i	−0.983532	+	0.180734i	$0.942153\pi$
$68$	−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	−0.786042	−	0.618173i	$-0.787873\pi$
$71$	−4.63663	+	2.97978i	−0.550267	+	0.353635i	0.235776	+	0.971807i	$0.424237\pi$
$72$	0.336531	−	2.34062i	0.0396606	−	0.275845i
$73$	7.75564	+	3.54188i	0.907729	+	0.414546i	0.813875	−	0.581040i	$-0.197354\pi$
$73$	7.75564	+	3.54188i	0.907729	+	0.414546i	0.0938541	+	0.995586i	$0.470081\pi$
$74$	−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	−0.996093	−	0.0883098i	$-0.971853\pi$
$79$	−10.8904	−	9.43656i	−1.22526	−	1.06170i	−0.229170	−	0.973386i	$-0.573601\pi$
$80$	−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	$-0.140715\pi$
$83$	13.0549	+	3.83325i	1.43296	+	0.420754i	0.529089	+	0.848566i	$0.322534\pi$
$84$	−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	−0.987721	−	0.156228i	$-0.950067\pi$
$89$	0.0377817	−	0.262778i	0.00400486	−	0.0278544i	0.991726	+	0.128374i	$0.0409756\pi$
$90$	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	$-0.740712\pi$
$97$	−8.56990	+	2.51635i	−0.870142	+	0.255497i	−0.183966	+	0.982933i	$0.558894\pi$
$98$	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	−0.975496	−	0.220017i	$-0.929389\pi$
$101$	−0.360852	+	1.22895i	−0.0359061	+	0.122285i	0.939590	+	0.342302i	$0.111207\pi$
$102$	−3.82560	−	3.31490i	−0.378790	−	0.328224i
$103$	−9.86187	−	6.33784i	−0.971719	−	0.624486i	−0.0445013	−	0.999009i	$-0.514170\pi$
$103$	−9.86187	−	6.33784i	−0.971719	−	0.624486i	−0.927217	+	0.374524i	$0.877806\pi$
$104$	−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	−0.358142	−	0.933667i	$-0.616590\pi$
$107$	−4.53829	+	0.652508i	−0.438733	+	0.0630803i	−0.0805907	+	0.996747i	$0.525681\pi$
$108$	−0.382655	+	0.331572i	−0.0368210	+	0.0319055i
$109$	−12.9396	+	5.90933i	−1.23939	+	0.566012i	−0.923797	−	0.382882i	$-0.874931\pi$
$109$	−12.9396	+	5.90933i	−1.23939	+	0.566012i	−0.315595	+	0.948894i	$0.602204\pi$
$110$	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	0.867701	−	0.497087i	$-0.165597\pi$
$113$	0.585494	+	0.911047i	0.0550787	+	0.0857041i	−0.812622	+	0.582791i	$0.801961\pi$
$114$			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	0.729048	−	0.684462i	$-0.239963\pi$
$127$	4.61254	+	2.96430i	0.409297	+	0.263039i	−0.319751	+	0.947501i	$0.603599\pi$
$128$	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	−0.233375	+	0.972387i	$0.574977\pi$
$131$	−14.0674	+	12.1895i	−1.22908	+	1.06500i	−0.995702	+	0.0926144i	$0.970478\pi$
$132$	−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	$-0.936299\pi$
$137$		−	4.65351i		−	0.397576i	0.980042	−	0.198788i	$-0.0637006\pi$
$138$	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	$0.954809\pi$
$140$	−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	−0.763957	−	0.645267i	$-0.776746\pi$
$149$	1.71328	−	2.66591i	0.140357	−	0.218400i	0.904315	+	0.426867i	$0.140383\pi$
$150$	11.9107	−	18.5334i	0.972507	−	1.51325i
$151$	0.812563	−	0.937747i	0.0661254	−	0.0763128i	−0.721723	−	0.692182i	$-0.756650\pi$
$151$	0.812563	−	0.937747i	0.0661254	−	0.0763128i	0.787848	+	0.615869i	$0.211195\pi$
$152$	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	−0.842496	−	0.538702i	$-0.818915\pi$
$157$	1.45781	−	3.19215i	0.116346	−	0.254761i	0.958842	+	0.283941i	$0.0916420\pi$
$158$	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	−0.564340	−	0.825542i	$-0.690869\pi$
$163$	−0.610728	+	0.392491i	−0.0478359	+	0.0307423i	0.516504	+	0.856285i	$0.327233\pi$
$164$	−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	$-0.395046\pi$
$167$	16.1645	−	7.38210i	1.25085	−	0.571244i	0.927070	+	0.374888i	$0.122319\pi$
$168$	−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	−0.388255	−	0.921552i	$-0.626922\pi$
$173$	8.04046	−	12.5112i	0.611305	−	0.951209i	0.999560	−	0.0296574i	$-0.00944164\pi$
$174$	−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	0.318674	−	0.947864i	$-0.396762\pi$
$179$	14.7065	−	4.31821i	1.09921	−	0.322758i	0.780540	+	0.625106i	$0.214944\pi$
$180$	−0.914797	+	2.00313i	−0.0681849	+	0.149304i
$181$	0.513903	−	3.57427i	0.0381981	−	0.265673i	−0.961768	−	0.273864i	$-0.911698\pi$
$181$	0.513903	−	3.57427i	0.0381981	−	0.265673i	0.999966	+	0.00819071i	$0.00260721\pi$
$182$	−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	−0.346058	−	0.938213i	$-0.612480\pi$
$191$	7.37112	−	6.38711i	0.533356	−	0.462155i	0.879414	+	0.476058i	$0.157935\pi$
$192$	5.02735	−	0.722824i	0.362818	−	0.0521653i
$193$	9.59490	+	2.81732i	0.690656	+	0.202795i	0.608181	−	0.793798i	$-0.291899\pi$
$193$	9.59490	+	2.81732i	0.690656	+	0.202795i	0.0824749	+	0.996593i	$0.473718\pi$
$194$	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	−0.761870	−	0.647731i	$-0.775718\pi$
$197$	−0.172731	+	0.199342i	−0.0123066	+	0.0142026i	0.749563	+	0.661933i	$0.230264\pi$
$198$	2.88765	−	9.83443i	0.205216	−	0.698902i
$199$	1.15318	+	8.02055i	0.0817469	+	0.568562i	0.988993	+	0.147962i	$0.0472713\pi$
$199$	1.15318	+	8.02055i	0.0817469	+	0.568562i	−0.907246	+	0.420600i	$0.861820\pi$
$200$	−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	−0.474262	−	0.880384i	$-0.657285\pi$
$211$	7.28708	−	15.9565i	0.501663	−	1.09849i	0.975925	−	0.218106i	$-0.0699877\pi$
$212$	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	−0.877142	−	0.480231i	$-0.840553\pi$
$223$	−7.86425	+	6.81441i	−0.526629	+	0.456327i	0.350513	+	0.936558i	$0.386007\pi$
$224$	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	−0.489487	−	0.872011i	$-0.662816\pi$
$227$	3.40271	−	23.6664i	0.225846	−	1.57079i	0.715333	−	0.698784i	$-0.246275\pi$
$228$	−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	−0.971415	−	0.237388i	$-0.923709\pi$
$233$	0.420239	−	2.92283i	0.0275308	−	0.191481i	0.998946	+	0.0459071i	$0.0146178\pi$
$234$	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	0.649980	−	0.759952i	$-0.274777\pi$
$239$	12.1500	+	3.56755i	0.785917	+	0.230766i	0.135937	+	0.990718i	$0.456596\pi$
$240$	15.6336	+	13.5466i	1.00914	+	0.874429i
$241$	14.0586	+	9.03494i	0.905597	+	0.581992i	0.908445	−	0.418004i	$-0.137270\pi$
$241$	14.0586	+	9.03494i	0.905597	+	0.581992i	−0.00284827	+	0.999996i	$0.500907\pi$
$242$	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	−0.422506	−	0.906360i	$-0.638849\pi$
$251$	3.58738	−	2.30547i	0.226433	−	0.145520i	0.648939	+	0.760840i	$0.275213\pi$
$252$	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	$-0.328551\pi$
$257$	3.20819	+	1.46513i	0.200121	+	0.0913923i	−0.312833	+	0.949808i	$0.601278\pi$
$258$	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	0.359983	−	0.932959i	$-0.382783\pi$
$263$	−8.30728	−	7.19830i	−0.512249	−	0.443866i	−0.872232	+	0.489093i	$0.837328\pi$
$264$	−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	−0.187524	−	0.982260i	$-0.560046\pi$
$269$	12.4330	−	10.7732i	0.758051	−	0.656855i	0.945575	+	0.325405i	$0.105501\pi$
$270$	−6.26322	+	2.86032i	−0.381167	+	0.174073i
$271$	6.49601	+	22.1234i	0.394604	+	1.34390i	0.882219	+	0.470840i	$0.156049\pi$
$271$	6.49601	+	22.1234i	0.394604	+	1.34390i	−0.487614	+	0.873059i	$0.662133\pi$
$272$	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	0.942540	+	0.334094i	$0.108430\pi$
$281$	5.53599	+	18.8539i	0.330250	+	1.12473i	−0.612290	+	0.790633i	$0.709752\pi$
$282$	−0.259878	−	0.569052i	−0.0154755	−	0.0338866i
$283$	−8.54684	−	9.86358i	−0.508057	−	0.586329i	0.442543	−	0.896747i	$-0.354076\pi$
$283$	−8.54684	−	9.86358i	−0.508057	−	0.586329i	−0.950600	+	0.310418i	$0.899531\pi$
$284$	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	−0.899926	−	0.436043i	$-0.856380\pi$
$293$	−10.9574	−	23.9934i	−0.640139	−	1.40171i	0.259787	−	0.965666i	$-0.416348\pi$
$294$	−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	−0.616988	−	0.786973i	$-0.711647\pi$
$307$	−17.2983	+	2.48712i	−0.987268	+	0.141948i	−0.370280	+	0.928920i	$0.620738\pi$
$308$	−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	0.272437	+	0.962174i	$0.412170\pi$
$311$	−12.6261	+	19.6466i	−0.715961	+	1.11406i	−0.988398	+	0.151884i	$0.951466\pi$
$312$	4.33148	−	4.99880i	0.245222	−	0.283001i
$313$	2.68097	+	0.787205i	0.151538	+	0.0444954i	0.356622	−	0.934249i	$-0.383929\pi$
$313$	2.68097	+	0.787205i	0.151538	+	0.0444954i	−0.205084	+	0.978744i	$0.565747\pi$
$314$	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	−0.547297	−	0.836938i	$-0.684343\pi$
$317$	−9.88559	+	2.90267i	−0.555230	+	0.163030i	−0.00793265	+	0.999969i	$0.502525\pi$
$318$	−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	−0.151559	−	0.988448i	$-0.548429\pi$
$331$	−14.7995	−	4.34552i	−0.813454	−	0.238852i	−0.661895	+	0.749597i	$0.730247\pi$
$332$	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	−0.514421	−	0.857538i	$-0.671993\pi$
$337$	−14.0694	+	2.02287i	−0.766408	+	0.110193i	−0.251987	+	0.967731i	$0.581084\pi$
$338$	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	0.264338	−	0.964430i	$-0.414847\pi$
$347$	23.3115	−	14.9814i	1.25142	−	0.804242i	0.987086	+	0.160188i	$0.0512102\pi$
$348$	0.430216	+	0.0618557i	0.0230620	+	0.00331581i
$349$	3.10426	+	1.41767i	0.166167	+	0.0758860i	0.496762	−	0.867887i	$-0.334522\pi$
$349$	3.10426	+	1.41767i	0.166167	+	0.0758860i	−0.330595	+	0.943773i	$0.607249\pi$
$350$	−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	−0.807247	−	0.590213i	$-0.799044\pi$
$353$	−26.5951	+	3.82380i	−1.41551	+	0.203520i	−0.608266	+	0.793733i	$0.708135\pi$
$354$	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	−0.890273	−	0.455428i	$-0.849486\pi$
$359$	1.98748	−	6.76873i	0.104895	−	0.357240i	0.995168	+	0.0981877i	$0.0313046\pi$
$360$	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	−0.919445	−	0.393218i	$-0.871362\pi$
$373$	−6.92472	−	23.5834i	−0.358548	−	1.22110i	0.560897	−	0.827886i	$-0.310456\pi$
$374$	−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	−0.472899	−	0.881116i	$-0.656793\pi$
$379$	10.2215	−	15.9049i	0.525042	−	0.816981i	0.997941	+	0.0641354i	$0.0204290\pi$
$380$	−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	−0.977489	−	0.210985i	$-0.932333\pi$
$383$	−1.93819	−	13.4804i	−0.0990367	−	0.688815i	0.878453	−	0.477830i	$-0.158576\pi$
$384$	−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	0.893464	−	0.449135i	$-0.148268\pi$
$389$	2.24367	+	3.49122i	0.113759	+	0.177012i	−0.779706	+	0.626146i	$0.784631\pi$
$390$	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	$-0.981022\pi$
$397$	−32.0170	+	14.6217i	−1.60689	+	0.733841i	−0.608665	+	0.793428i	$0.708295\pi$
$398$	−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	0.167930	−	0.985799i	$-0.446292\pi$
$401$	−15.6983	−	13.6027i	−0.783936	−	0.679285i	−0.951866	+	0.306514i	$0.900837\pi$
$402$	−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	−0.999831	−	0.0183874i	$-0.994147\pi$
$409$	−3.41095	−	11.6166i	−0.168661	−	0.574405i	0.831170	−	0.556018i	$-0.187671\pi$
$410$	−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	$-0.463922\pi$
$419$	15.2583	−	4.48023i	0.745415	−	0.218874i	0.632316	+	0.774710i	$0.282104\pi$
$420$	4.70620	+	3.43471i	0.229639	+	0.167597i
$421$	7.27680	−	6.30538i	0.354649	−	0.307305i	−0.459255	−	0.888305i	$-0.651884\pi$
$421$	7.27680	−	6.30538i	0.354649	−	0.307305i	0.813904	+	0.580999i	$0.197338\pi$
$422$	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	−0.874325	−	0.485341i	$-0.838696\pi$
$431$	−22.4233	+	10.2404i	−1.08009	+	0.493261i	−0.205765	+	0.978601i	$0.565968\pi$
$432$	−1.34000	−	4.56362i	−0.0644708	−	0.219567i
$433$	5.56393	−	12.1833i	0.267385	−	0.585492i	−0.727545	−	0.686060i	$-0.759339\pi$
$433$	5.56393	−	12.1833i	0.267385	−	0.585492i	0.994930	+	0.100568i	$0.0320660\pi$
$434$	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	−0.998135	−	0.0610467i	$-0.980556\pi$
$439$	−13.3891	−	20.8338i	−0.639025	−	0.994342i	0.359110	−	0.933295i	$-0.383080\pi$
$440$	−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	0.963370	−	0.268176i	$-0.0864207\pi$
$443$	2.73246	+	5.98326i	0.129823	+	0.284273i	−0.833547	+	0.552449i	$0.813693\pi$
$444$	−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	−0.0786118	−	0.996905i	$-0.525049\pi$
$449$	−21.5728	−	13.8640i	−1.01809	−	0.654284i	−0.939473	+	0.342622i	$0.888685\pi$
$450$	−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	0.699237	−	0.714890i	$-0.253523\pi$
$457$	24.9848	+	3.59228i	1.16874	+	0.168040i	0.469505	+	0.882930i	$0.344432\pi$
$458$	−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	$0.851268\pi$
$462$	−23.9568	−	12.7065i	−1.11457	−	0.591159i
$463$	−1.81269	+	12.6075i	−0.0842429	+	0.585922i	0.903352	+	0.428900i	$0.141099\pi$
$463$	−1.81269	+	12.6075i	−0.0842429	+	0.585922i	−0.987595	+	0.157022i	$0.949810\pi$
$464$	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	$-0.0989241\pi$
$467$	11.1057	+	12.8167i	0.513910	+	0.593084i	−0.438185	+	0.898885i	$0.644379\pi$
$468$	−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	0.318063	+	0.948070i	$0.396968\pi$
$479$	−13.2789	+	29.0767i	−0.606727	+	1.32855i	−0.924790	+	0.380478i	$0.875760\pi$
$480$	−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	0.527034	+	0.849844i	$0.323304\pi$
$487$	−10.1595	+	22.2461i	−0.460369	+	1.00807i	−0.987403	+	0.158223i	$0.949423\pi$
$488$	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	0.993655	+	0.112474i	$0.0358774\pi$
$491$	1.59403	+	11.0867i	0.0719375	+	0.500336i	−0.921717	+	0.387863i	$0.873213\pi$
$492$	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	0.992581	−	0.121581i	$-0.0387965\pi$
$499$	16.3288	+	18.8445i	0.730979	+	0.843594i	−0.261603	+	0.965176i	$0.584251\pi$
$500$	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	0.742696	+	0.669629i	$0.233547\pi$
$503$	−3.55640	+	24.7353i	−0.158572	+	1.10289i	−0.901268	+	0.433263i	$0.857362\pi$
$504$	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	−0.142281	−	0.989826i	$-0.545444\pi$
$509$	−12.5815	−	1.80895i	−0.557666	−	0.0801802i	−0.415384	+	0.909646i	$0.636353\pi$
$510$	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	0.956087	+	0.293084i	$0.0946817\pi$
$521$	2.76872	+	19.2568i	0.121300	+	0.843657i	−0.834787	+	0.550573i	$0.814409\pi$
$522$	0.889955	+	1.02706i	0.0389523	+	0.0449533i
$523$	−16.0829	−	35.2167i	−0.703257	−	1.53992i	−0.835977	−	0.548765i	$-0.815098\pi$
$523$	−16.0829	−	35.2167i	−0.703257	−	1.53992i	0.132720	−	0.991154i	$-0.457629\pi$
$524$	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	0.432364	−	0.901699i	$-0.357679\pi$
$541$	−4.84353	−	3.11275i	−0.208240	−	0.133827i	−0.640604	+	0.767872i	$0.721316\pi$
$542$	−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	−0.421829	−	0.906675i	$-0.638612\pi$
$547$	−6.70088	+	1.96756i	−0.286509	+	0.0841266i	0.135320	+	0.990802i	$0.456794\pi$
$548$	−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	0.999584	−	0.0288497i	$-0.00918443\pi$
$557$	3.37688	+	11.5006i	0.143083	+	0.487296i	−0.856501	+	0.516146i	$0.827366\pi$
$558$	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	−0.240821	−	0.970569i	$-0.577417\pi$
$563$	−29.0360	−	18.6603i	−1.22372	−	0.786439i	−0.982902	+	0.184130i	$0.941053\pi$
$564$	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	−0.516694	−	0.856170i	$-0.672838\pi$
$569$	−4.96173	+	2.26595i	−0.208007	+	0.0949934i	0.308688	+	0.951164i	$0.400110\pi$
$570$	−6.60979	−	22.5109i	−0.276853	−	0.942876i
$571$	12.6026	+	5.75540i	0.527401	+	0.240856i	0.661277	−	0.750142i	$-0.270015\pi$
$571$	12.6026	+	5.75540i	0.527401	+	0.240856i	−0.133876	+	0.990998i	$0.542742\pi$
$572$	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	$-0.340136\pi$
$577$	−12.3923	−	19.2828i	−0.515898	−	0.802752i	−0.997276	+	0.0737605i	$0.976500\pi$
$578$	−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	−0.553992	−	0.832522i	$-0.686896\pi$
$587$	10.5012	−	16.3403i	0.433433	−	0.674434i	0.987425	+	0.158087i	$0.0505327\pi$
$588$	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	−0.971060	−	0.238834i	$-0.923235\pi$
$593$	−6.89822	−	23.4932i	−0.283276	−	0.964749i	0.687785	−	0.725915i	$-0.258583\pi$
$594$	−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	0.583769	−	0.811920i	$-0.301577\pi$
$601$	22.4351	+	3.22568i	0.915147	+	0.131578i	0.331378	+	0.943498i	$0.392487\pi$
$602$	−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	−0.994007	−	0.109321i	$-0.965132\pi$
$607$	−2.43150	+	8.28094i	−0.0986917	+	0.336113i	0.895315	+	0.445434i	$0.146951\pi$
$608$	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	0.239351	−	0.970933i	$-0.423065\pi$
$613$	18.3847	−	2.64332i	0.742550	−	0.106763i	0.503199	+	0.864171i	$0.332156\pi$
$614$	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	−0.249463	−	0.968384i	$-0.580254\pi$
$617$	−28.4333	−	12.9851i	−1.14468	−	0.522759i	−0.895220	+	0.445625i	$0.852981\pi$
$618$	−18.3699	−	2.64120i	−0.738947	−	0.106245i
$619$	29.9926	−	19.2751i	1.20550	−	0.774730i	0.225604	−	0.974219i	$-0.427565\pi$
$619$	29.9926	−	19.2751i	1.20550	−	0.774730i	0.979900	+	0.199489i	$0.0639282\pi$
$620$		−	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	0.443257	−	0.896395i	$-0.353823\pi$
$631$	−9.56890	−	8.29150i	−0.380932	−	0.330080i	−0.824189	+	0.566315i	$0.808368\pi$
$632$	−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	0.822990	−	0.568056i	$-0.192304\pi$
$641$	36.7770	+	5.28773i	1.45260	+	0.208853i	0.629614	+	0.776908i	$0.283213\pi$
$642$	−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	−0.148184	−	0.988960i	$-0.547343\pi$
$647$	−14.4729	−	2.08089i	−0.568988	−	0.0818081i	−0.420804	+	0.907152i	$0.638252\pi$
$648$	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	−0.688276	−	0.725449i	$-0.741632\pi$
$653$	−42.4066	−	12.4517i	−1.65950	−	0.487273i	−0.971222	+	0.238176i	$0.923451\pi$
$654$	−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	−0.601191	−	0.799105i	$-0.705307\pi$
$659$	−24.4618	+	3.51708i	−0.952896	+	0.137006i	−0.351705	+	0.936111i	$0.614398\pi$
$660$	9.33641	+	10.7748i	0.363419	+	0.419408i
$661$	−4.23967	−	9.28358i	−0.164904	−	0.361090i	0.809083	−	0.587695i	$-0.199964\pi$
$661$	−4.23967	−	9.28358i	−0.164904	−	0.361090i	−0.973987	+	0.226605i	$0.927237\pi$
$662$	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	0.771999	+	0.635623i	$0.219257\pi$
$673$	19.3742	+	42.4235i	0.746819	+	1.63531i	−0.0251801	+	0.999683i	$0.508016\pi$
$674$	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	$-0.790895\pi$
$677$	−1.94393	+	2.24342i	−0.0747114	+	0.0862215i	0.717163	+	0.696905i	$0.245440\pi$
$678$	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	0.393804	−	0.919195i	$-0.371159\pi$
$683$	−14.9509	−	17.2542i	−0.572079	−	0.660214i	−0.965883	+	0.258980i	$0.916613\pi$
$684$	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	$-0.737820\pi$
$691$		−	38.5703i		−	1.46728i	0.679538	−	0.733641i	$-0.262180\pi$
$692$	−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	0.112484	+	0.993654i	$0.464119\pi$
$701$	−22.1900	+	34.5282i	−0.838103	+	1.30411i	−0.950586	+	0.310460i	$0.899517\pi$
$702$	−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	−0.516407	−	0.856343i	$-0.672731\pi$
$709$	−39.9875	−	18.2617i	−1.50176	−	0.685832i	−0.985356	+	0.170511i	$0.945458\pi$
$710$	−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	$-0.747734\pi$
$719$	−16.7217	+	7.63656i	−0.623615	+	0.284795i	0.0784392	+	0.996919i	$0.475006\pi$
$720$	−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	0.689009	−	0.724753i	$-0.258046\pi$
$727$	23.6414	+	6.94173i	0.876810	+	0.257455i	0.187801	+	0.982207i	$0.439864\pi$
$728$	−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	0.953063	+	0.302773i	$0.0979125\pi$
$733$	−1.26423	+	8.79290i	−0.0466953	+	0.324773i	−0.999758	+	0.0220000i	$0.992997\pi$
$734$	−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	0.697922	+	0.716174i	$0.254108\pi$
$739$	−4.71648	+	32.8039i	−0.173499	+	1.20671i	−0.871421	+	0.490536i	$0.836801\pi$
$740$	−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	−0.566948	−	0.823753i	$-0.691876\pi$
$743$	4.57214	−	3.96178i	0.167735	−	0.145344i	0.734684	+	0.678410i	$0.237331\pi$
$744$	−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	−0.353743	−	0.935343i	$-0.615091\pi$
$751$	−11.7740	+	1.69285i	−0.429640	+	0.0617730i	−0.0758974	+	0.997116i	$0.524182\pi$
$752$	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	0.775632	−	0.631185i	$-0.217431\pi$
$757$	−3.32153	−	5.16840i	−0.120723	−	0.187849i	−0.896355	+	0.443336i	$0.853795\pi$
$758$			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	$-0.0849252\pi$
$761$	8.94017	+	13.9112i	0.324081	+	0.504280i	−0.640539	+	0.767926i	$0.721289\pi$
$762$	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	0.211813	−	0.977310i	$-0.432063\pi$
$769$	31.8636	−	36.7726i	1.14903	−	1.32605i	0.937219	−	0.348742i	$-0.113391\pi$
$770$	−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	−0.119977	−	0.992777i	$-0.538282\pi$
$773$	−21.0647	−	6.18515i	−0.757644	−	0.222464i	−0.637667	+	0.770312i	$0.720100\pi$
$774$	−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	0.130067	−	0.991505i	$-0.458481\pi$
$787$	21.7565	−	6.38827i	0.775534	−	0.227717i	0.645467	+	0.763788i	$0.276663\pi$
$788$	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	0.907852	+	0.419290i	$0.137721\pi$
$797$	4.37307	+	30.4154i	0.154902	+	1.07737i	−0.752950	+	0.658077i	$0.771370\pi$
$798$	−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	−0.867024	−	0.498266i	$-0.833970\pi$
$809$	2.19920	−	4.81558i	0.0773198	−	0.169307i	0.944344	+	0.328959i	$0.106698\pi$
$810$	6.60654	−	1.93985i	0.232130	−	0.0681595i
$811$	−47.1596	+	21.5370i	−1.65600	+	0.756268i	−0.655997	+	0.754764i	$0.727752\pi$
$811$	−47.1596	+	21.5370i	−1.65600	+	0.756268i	−0.999999	+	0.00150447i	$0.999521\pi$
$812$	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	0.886199	−	0.463306i	$-0.153337\pi$
$821$	8.63861	+	9.96949i	0.301490	+	0.347938i	−0.584709	+	0.811243i	$0.698791\pi$
$822$	−3.06043	−	6.70140i	−0.106745	−	0.233738i
$823$	41.5367	−	12.1963i	1.44788	−	0.425135i	0.539038	−	0.842282i	$-0.318788\pi$
$823$	41.5367	−	12.1963i	1.44788	−	0.425135i	0.908839	+	0.417147i	$0.136970\pi$
$824$	−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	$-0.604380\pi$
$827$		−	54.4505i		−	1.89343i	0.322073	−	0.946715i	$-0.395620\pi$
$828$	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
$833$	−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	0.999975	+	0.00712672i	$0.00226853\pi$
$839$	41.1849	+	26.4679i	1.42186	+	0.913775i	0.421887	+	0.906648i	$0.361368\pi$
$840$	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	0.920488	+	0.390770i	$0.127791\pi$
$853$	26.0975	+	40.6085i	0.893560	+	1.39041i	−0.0269280	+	0.999637i	$0.508572\pi$
$854$	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	−0.198734	−	0.980053i	$-0.563683\pi$
$857$	12.0552	−	5.50542i	0.411798	−	0.188062i	0.610532	+	0.791992i	$0.290956\pi$
$858$	21.6670	−	18.7745i	0.739698	−	0.640952i
$859$	13.8413	−	1.99008i	0.472259	−	0.0679006i	0.0979235	−	0.995194i	$-0.468780\pi$
$859$	13.8413	−	1.99008i	0.472259	−	0.0679006i	0.374335	+	0.927293i	$0.377871\pi$
$860$	−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	0.501615	−	0.865091i	$-0.332739\pi$
$863$	−2.25968	−	1.45221i	−0.0769203	−	0.0494337i	−0.578536	+	0.815657i	$0.696376\pi$
$864$	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	−0.818639	−	0.574309i	$-0.805271\pi$
$877$	3.80959	−	26.4963i	0.128641	−	0.894717i	0.947280	−	0.320408i	$-0.103820\pi$
$878$	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	$-0.262537\pi$
$881$	−4.29800	−	4.96016i	−0.144803	−	0.167112i	−0.823518	+	0.567290i	$0.807992\pi$
$882$	10.1892	+	4.35765i	0.343090	+	0.146730i
$883$	−36.0483	−	10.5847i	−1.21312	−	0.356204i	−0.388265	−	0.921548i	$-0.626926\pi$
$883$	−36.0483	−	10.5847i	−1.21312	−	0.356204i	−0.824856	+	0.565343i	$0.808744\pi$
$884$	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	$-0.0307245\pi$
$887$	31.0216	+	26.8804i	1.04160	+	0.902555i	0.0462592	+	0.998929i	$0.485270\pi$
$888$	−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	0.469888	−	0.882726i	$-0.344294\pi$
$907$	−10.1487	−	8.79388i	−0.336981	−	0.291996i	−0.806869	+	0.590730i	$0.798840\pi$
$908$	−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	−0.906710	−	0.421754i	$-0.861415\pi$
$911$	2.53777	−	8.64287i	0.0840802	−	0.286351i	0.990791	+	0.135403i	$0.0432329\pi$
$912$	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	$0.0647640\pi$
$919$			12.2510i			0.404122i	−0.979373	+	0.202061i	$0.935236\pi$
$920$	−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	−0.856732	−	0.515762i	$-0.827509\pi$
$929$	4.35366	−	14.8272i	0.142839	−	0.486465i	0.999571	+	0.0292973i	$0.00932697\pi$
$930$	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	−0.994362	−	0.106040i	$-0.966183\pi$
$937$	−12.9584	−	28.3750i	−0.423333	−	0.926970i	0.571029	−	0.820930i	$-0.306544\pi$
$938$	−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	−0.0246157	−	0.999697i	$-0.507836\pi$
$941$	26.8264	−	17.2403i	0.874515	−	0.562017i	0.899131	+	0.437680i	$0.144200\pi$
$942$		−	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	0.347717	+	0.937600i	$0.386957\pi$
$947$	−18.1126	+	39.6610i	−0.588580	+	1.28881i	−0.936297	+	0.351210i	$0.885770\pi$
$948$	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	0.613673	−	0.789560i	$-0.289691\pi$
$953$	−2.48557	−	2.15376i	−0.0805156	−	0.0697671i	−0.694189	+	0.719793i	$0.744237\pi$
$954$	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	−0.689838	−	0.723963i	$-0.742318\pi$
$971$	−27.3830	+	8.04038i	−0.878763	+	0.258028i	−0.188925	+	0.981992i	$0.560500\pi$
$972$	−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	0.256399	+	0.966571i	$0.417464\pi$
$977$	−22.7969	+	35.4727i	−0.729337	+	1.13487i	−0.985736	+	0.168300i	$0.946172\pi$
$978$	−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	−0.907194	−	0.420712i	$-0.861780\pi$
$983$	−19.7856	−	43.3243i	−0.631061	−	1.38183i	0.276133	−	0.961120i	$-0.410947\pi$
$984$	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	−0.684688	−	0.728836i	$-0.740062\pi$
$991$	−9.63750	+	6.19365i	−0.306145	+	0.196748i	0.378543	+	0.925584i	$0.376425\pi$
$992$	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	−0.143896	−	0.989593i	$-0.545963\pi$
$997$	−0.0998935	+	0.0143625i	−0.00316366	+	0.000454866i	0.140733	+	0.990048i	$0.455054\pi$
$998$	−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.34.7	✓	320
7.6	odd	2	inner	483.2.r.a.34.8	yes	320
23.21	odd	22	inner	483.2.r.a.412.8	yes	320
161.90	even	22	inner	483.2.r.a.412.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.7	✓	320	1.1	even	1	trivial
483.2.r.a.34.8	yes	320	7.6	odd	2	inner
483.2.r.a.412.7	yes	320	161.90	even	22	inner
483.2.r.a.412.8	yes	320	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.33182 + 0.855909i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(0.210335 - 0.460569i) q^{4} +(-4.17306 + 1.22532i) q^{5} +(1.44007 - 0.657659i) q^{6} +(-0.894449 + 2.48997i) q^{7} +(-0.336531 - 2.34062i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(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

Groups

Database

Properties

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