LMFDB - Embedded newform 208.2.n.a.157.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(53,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("208.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (of order $4$, degree $2$, 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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.24
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40077 + 0.194546i) q^{2} +(0.902776 + 0.902776i) q^{3} +(1.92430 + 0.545027i) q^{4} +(-1.29480 + 1.29480i) q^{5} +(1.08895 + 1.44021i) q^{6} -3.20594i q^{7} +(2.58947 + 1.13782i) q^{8} -1.36999i q^{9} +O(q^{10})$	\(q+(1.40077 + 0.194546i) q^{2} +(0.902776 + 0.902776i) q^{3} +(1.92430 + 0.545027i) q^{4} +(-1.29480 + 1.29480i) q^{5} +(1.08895 + 1.44021i) q^{6} -3.20594i q^{7} +(2.58947 + 1.13782i) q^{8} -1.36999i q^{9} +(-2.06562 + 1.56182i) q^{10} +(-2.72143 + 2.72143i) q^{11} +(1.24518 + 2.22925i) q^{12} +(0.707107 + 0.707107i) q^{13} +(0.623701 - 4.49078i) q^{14} -2.33784 q^{15} +(3.40589 + 2.09760i) q^{16} -6.03671 q^{17} +(0.266526 - 1.91904i) q^{18} +(1.89947 + 1.89947i) q^{19} +(-3.19730 + 1.78589i) q^{20} +(2.89424 - 2.89424i) q^{21} +(-4.34154 + 3.28266i) q^{22} -8.67448i q^{23} +(1.31051 + 3.36491i) q^{24} +1.64697i q^{25} +(0.852928 + 1.12806i) q^{26} +(3.94512 - 3.94512i) q^{27} +(1.74732 - 6.16920i) q^{28} +(-6.82640 - 6.82640i) q^{29} +(-3.27477 - 0.454816i) q^{30} +5.23082 q^{31} +(4.36279 + 3.60085i) q^{32} -4.91369 q^{33} +(-8.45603 - 1.17442i) q^{34} +(4.15106 + 4.15106i) q^{35} +(0.746682 - 2.63628i) q^{36} +(-0.208536 + 0.208536i) q^{37} +(2.29118 + 3.03025i) q^{38} +1.27672i q^{39} +(-4.82611 + 1.87960i) q^{40} +9.29774i q^{41} +(4.61723 - 3.49110i) q^{42} +(0.0416722 - 0.0416722i) q^{43} +(-6.72012 + 3.75361i) q^{44} +(1.77387 + 1.77387i) q^{45} +(1.68758 - 12.1509i) q^{46} +2.16694 q^{47} +(1.18110 + 4.96842i) q^{48} -3.27803 q^{49} +(-0.320410 + 2.30702i) q^{50} +(-5.44980 - 5.44980i) q^{51} +(0.975296 + 1.74608i) q^{52} +(-6.38002 + 6.38002i) q^{53} +(6.29371 - 4.75870i) q^{54} -7.04745i q^{55} +(3.64778 - 8.30168i) q^{56} +3.42959i q^{57} +(-8.23415 - 10.8902i) q^{58} +(3.38796 - 3.38796i) q^{59} +(-4.49871 - 1.27418i) q^{60} +(1.72743 + 1.72743i) q^{61} +(7.32717 + 1.01763i) q^{62} -4.39210 q^{63} +(5.41072 + 5.89271i) q^{64} -1.83113 q^{65} +(-6.88295 - 0.955938i) q^{66} +(-1.56033 - 1.56033i) q^{67} +(-11.6165 - 3.29017i) q^{68} +(7.83111 - 7.83111i) q^{69} +(5.00710 + 6.62224i) q^{70} +9.73843i q^{71} +(1.55880 - 3.54755i) q^{72} +6.08728i q^{73} +(-0.332680 + 0.251540i) q^{74} +(-1.48684 + 1.48684i) q^{75} +(2.61989 + 4.69041i) q^{76} +(8.72475 + 8.72475i) q^{77} +(-0.248380 + 1.78839i) q^{78} -5.31445 q^{79} +(-7.12593 + 1.69399i) q^{80} +3.01316 q^{81} +(-1.80884 + 13.0240i) q^{82} +(9.71028 + 9.71028i) q^{83} +(7.14685 - 3.99196i) q^{84} +(7.81635 - 7.81635i) q^{85} +(0.0664803 - 0.0502660i) q^{86} -12.3254i q^{87} +(-10.1436 + 3.95057i) q^{88} -5.94615i q^{89} +(2.13968 + 2.82988i) q^{90} +(2.26694 - 2.26694i) q^{91} +(4.72783 - 16.6923i) q^{92} +(4.72226 + 4.72226i) q^{93} +(3.03538 + 0.421569i) q^{94} -4.91887 q^{95} +(0.687861 + 7.18938i) q^{96} -9.79055 q^{97} +(-4.59177 - 0.637727i) q^{98} +(3.72834 + 3.72834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 4 * q^4 - 12 * q^8	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.40077	+	0.194546i	0.990493	+	0.137565i
$2$	1.40077	+	0.194546i	0.990493	+	0.137565i
$3$	0.902776	+	0.902776i	0.521218	+	0.521218i	0.917939	−	0.396721i	$-0.129852\pi$
$3$	0.902776	+	0.902776i	0.521218	+	0.521218i	−0.396721	+	0.917939i	$0.629852\pi$
$4$	1.92430	+	0.545027i	0.962152	+	0.272513i
$5$	−1.29480	+	1.29480i	−0.579054	+	0.579054i	−0.934643	−	0.355589i	$-0.884280\pi$
$5$	−1.29480	+	1.29480i	−0.579054	+	0.579054i	0.355589	+	0.934643i	$0.384280\pi$
$6$	1.08895	+	1.44021i	0.444562	+	0.587964i
$7$		−	3.20594i		−	1.21173i	−0.795567	−	0.605865i	$-0.792827\pi$
$7$		−	3.20594i		−	1.21173i	0.795567	−	0.605865i	$-0.207173\pi$
$8$	2.58947	+	1.13782i	0.915516	+	0.402281i
$9$		−	1.36999i		−	0.456663i
$10$	−2.06562	+	1.56182i	−0.653206	+	0.493891i
$11$	−2.72143	+	2.72143i	−0.820543	+	0.820543i	−0.986186	−	0.165642i	$-0.947030\pi$
$11$	−2.72143	+	2.72143i	−0.820543	+	0.820543i	0.165642	+	0.986186i	$0.447030\pi$
$12$	1.24518	+	2.22925i	0.359452	+	0.643530i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	0.623701	−	4.49078i	0.166691	−	1.20021i
$15$	−2.33784			−0.603627
$16$	3.40589	+	2.09760i	0.851473	+	0.524399i
$17$	−6.03671			−1.46412			−0.732058	−	0.681242i	$-0.761440\pi$
$17$	−6.03671			−1.46412			−0.732058	+	0.681242i	$0.761440\pi$
$18$	0.266526	−	1.91904i	0.0628207	−	0.452322i
$19$	1.89947	+	1.89947i	0.435768	+	0.435768i	0.890585	−	0.454817i	$-0.150295\pi$
$19$	1.89947	+	1.89947i	0.435768	+	0.435768i	−0.454817	+	0.890585i	$0.650295\pi$
$20$	−3.19730	+	1.78589i	−0.714938	+	0.399338i
$21$	2.89424	−	2.89424i	0.631576	−	0.631576i
$22$	−4.34154	+	3.28266i	−0.925620	+	0.699865i
$23$		−	8.67448i		−	1.80875i	−0.426734	−	0.904377i	$-0.640336\pi$
$23$		−	8.67448i		−	1.80875i	0.426734	−	0.904377i	$-0.359664\pi$
$24$	1.31051	+	3.36491i	0.267508	+	0.686860i
$25$			1.64697i			0.329393i
$26$	0.852928	+	1.12806i	0.167273	+	0.221230i
$27$	3.94512	−	3.94512i	0.759239	−	0.759239i
$28$	1.74732	−	6.16920i	0.330213	−	1.16587i
$29$	−6.82640	−	6.82640i	−1.26763	−	1.26763i	−0.947309	−	0.320321i	$-0.896209\pi$
$29$	−6.82640	−	6.82640i	−1.26763	−	1.26763i	−0.320321	−	0.947309i	$-0.603791\pi$
$30$	−3.27477	−	0.454816i	−0.597888	−	0.0830377i
$31$	5.23082			0.939484			0.469742	−	0.882804i	$-0.344347\pi$
$31$	5.23082			0.939484			0.469742	+	0.882804i	$0.344347\pi$
$32$	4.36279	+	3.60085i	0.771239	+	0.636546i
$33$	−4.91369			−0.855364
$34$	−8.45603	−	1.17442i	−1.45020	−	0.201411i
$35$	4.15106	+	4.15106i	0.701657	+	0.701657i
$36$	0.746682	−	2.63628i	0.124447	−	0.439380i
$37$	−0.208536	+	0.208536i	−0.0342830	+	0.0342830i	−0.724041	−	0.689757i	$-0.757717\pi$
$37$	−0.208536	+	0.208536i	−0.0342830	+	0.0342830i	0.689757	+	0.724041i	$0.257717\pi$
$38$	2.29118	+	3.03025i	0.371678	+	0.491571i
$39$			1.27672i			0.204439i
$40$	−4.82611	+	1.87960i	−0.763075	+	0.297191i
$41$			9.29774i			1.45206i	0.687662	+	0.726031i	$0.258637\pi$
$41$			9.29774i			1.45206i	−0.687662	+	0.726031i	$0.741363\pi$
$42$	4.61723	−	3.49110i	0.712454	−	0.538689i
$43$	0.0416722	−	0.0416722i	0.00635495	−	0.00635495i	−0.703922	−	0.710277i	$-0.748570\pi$
$43$	0.0416722	−	0.0416722i	0.00635495	−	0.00635495i	0.710277	+	0.703922i	$0.248570\pi$
$44$	−6.72012	+	3.75361i	−1.01310	+	0.565878i
$45$	1.77387	+	1.77387i	0.264433	+	0.264433i
$46$	1.68758	−	12.1509i	0.248821	−	1.79156i
$47$	2.16694			0.316081			0.158040	−	0.987433i	$-0.449482\pi$
$47$	2.16694			0.316081			0.158040	+	0.987433i	$0.449482\pi$
$48$	1.18110	+	4.96842i	0.170477	+	0.717129i
$49$	−3.27803			−0.468290
$50$	−0.320410	+	2.30702i	−0.0453129	+	0.326262i
$51$	−5.44980	−	5.44980i	−0.763124	−	0.763124i
$52$	0.975296	+	1.74608i	0.135249	+	0.242138i
$53$	−6.38002	+	6.38002i	−0.876363	+	0.876363i	−0.993156	−	0.116793i	$-0.962739\pi$
$53$	−6.38002	+	6.38002i	−0.876363	+	0.876363i	0.116793	+	0.993156i	$0.462739\pi$
$54$	6.29371	−	4.75870i	0.856466	−	0.647577i
$55$		−	7.04745i		−	0.950278i
$56$	3.64778	−	8.30168i	0.487456	−	1.10936i
$57$			3.42959i			0.454260i
$58$	−8.23415	−	10.8902i	−1.08120	−	1.42996i
$59$	3.38796	−	3.38796i	0.441075	−	0.441075i	−0.451298	−	0.892373i	$-0.649039\pi$
$59$	3.38796	−	3.38796i	0.441075	−	0.441075i	0.892373	+	0.451298i	$0.149039\pi$
$60$	−4.49871	−	1.27418i	−0.580781	−	0.164496i
$61$	1.72743	+	1.72743i	0.221175	+	0.221175i	0.808993	−	0.587818i	$-0.200013\pi$
$61$	1.72743	+	1.72743i	0.221175	+	0.221175i	−0.587818	+	0.808993i	$0.700013\pi$
$62$	7.32717	+	1.01763i	0.930552	+	0.129240i
$63$	−4.39210			−0.553353
$64$	5.41072	+	5.89271i	0.676340	+	0.736589i
$65$	−1.83113			−0.227124
$66$	−6.88295	−	0.955938i	−0.847232	−	0.117668i
$67$	−1.56033	−	1.56033i	−0.190624	−	0.190624i	0.605342	−	0.795966i	$-0.293037\pi$
$67$	−1.56033	−	1.56033i	−0.190624	−	0.190624i	−0.795966	+	0.605342i	$0.793037\pi$
$68$	−11.6165	−	3.29017i	−1.40870	−	0.398992i
$69$	7.83111	−	7.83111i	0.942755	−	0.942755i
$70$	5.00710	+	6.62224i	0.598463	+	0.791509i
$71$			9.73843i			1.15574i	0.816129	+	0.577869i	$0.196116\pi$
$71$			9.73843i			1.15574i	−0.816129	+	0.577869i	$0.803884\pi$
$72$	1.55880	−	3.54755i	0.183707	−	0.418083i
$73$			6.08728i			0.712462i	0.934398	+	0.356231i	$0.115938\pi$
$73$			6.08728i			0.712462i	−0.934398	+	0.356231i	$0.884062\pi$
$74$	−0.332680	+	0.251540i	−0.0386732	+	0.0292410i
$75$	−1.48684	+	1.48684i	−0.171686	+	0.171686i
$76$	2.61989	+	4.69041i	0.300522	+	0.538027i
$77$	8.72475	+	8.72475i	0.994277	+	0.994277i
$78$	−0.248380	+	1.78839i	−0.0281235	+	0.202495i
$79$	−5.31445			−0.597922			−0.298961	−	0.954265i	$-0.596640\pi$
$79$	−5.31445			−0.597922			−0.298961	+	0.954265i	$0.596640\pi$
$80$	−7.12593	+	1.69399i	−0.796704	+	0.189393i
$81$	3.01316			0.334795
$82$	−1.80884	+	13.0240i	−0.199752	+	1.43826i
$83$	9.71028	+	9.71028i	1.06584	+	1.06584i	0.997674	+	0.0681682i	$0.0217155\pi$
$83$	9.71028	+	9.71028i	1.06584	+	1.06584i	0.0681682	+	0.997674i	$0.478285\pi$
$84$	7.14685	−	3.99196i	0.779785	−	0.435559i
$85$	7.81635	−	7.81635i	0.847802	−	0.847802i
$86$	0.0664803	−	0.0502660i	0.00716875	−	0.00542032i
$87$		−	12.3254i		−	1.32142i
$88$	−10.1436	+	3.95057i	−1.08131	+	0.421132i
$89$		−	5.94615i		−	0.630291i	−0.949043	−	0.315145i	$-0.897947\pi$
$89$		−	5.94615i		−	0.630291i	0.949043	−	0.315145i	$-0.102053\pi$
$90$	2.13968	+	2.82988i	0.225542	+	0.298295i
$91$	2.26694	−	2.26694i	0.237640	−	0.237640i
$92$	4.72783	−	16.6923i	0.492910	−	1.74030i
$93$	4.72226	+	4.72226i	0.489676	+	0.489676i
$94$	3.03538	+	0.421569i	0.313076	+	0.0434815i
$95$	−4.91887			−0.504666
$96$	0.687861	+	7.18938i	0.0702046	+	0.733763i
$97$	−9.79055			−0.994080			−0.497040	−	0.867728i	$-0.665580\pi$
$97$	−9.79055			−0.994080			−0.497040	+	0.867728i	$0.665580\pi$
$98$	−4.59177	−	0.637727i	−0.463838	−	0.0644202i
$99$	3.72834	+	3.72834i	0.374712	+	0.374712i
$100$	−0.897641	+	3.16926i	−0.0897641	+	0.316926i
$101$	−4.75506	+	4.75506i	−0.473146	+	0.473146i	−0.902931	−	0.429785i	$-0.858589\pi$
$101$	−4.75506	+	4.75506i	−0.473146	+	0.473146i	0.429785	+	0.902931i	$0.358589\pi$
$102$	−6.57367	−	8.69414i	−0.650890	−	0.860848i
$103$		−	2.88844i		−	0.284607i	−0.989823	−	0.142303i	$-0.954549\pi$
$103$		−	2.88844i		−	0.284607i	0.989823	−	0.142303i	$-0.0454509\pi$
$104$	1.02647	+	2.63559i	0.100654	+	0.258441i
$105$			7.49496i			0.731433i
$106$	−10.1781	+	7.69573i	−0.988588	+	0.747475i
$107$	3.70795	−	3.70795i	0.358461	−	0.358461i	−0.504785	−	0.863245i	$-0.668428\pi$
$107$	3.70795	−	3.70795i	0.358461	−	0.358461i	0.863245	+	0.504785i	$0.168428\pi$
$108$	9.74181	−	5.44142i	0.937407	−	0.523601i
$109$	2.76524	+	2.76524i	0.264862	+	0.264862i	0.827026	−	0.562164i	$-0.190031\pi$
$109$	2.76524	+	2.76524i	0.264862	+	0.264862i	−0.562164	+	0.827026i	$0.690031\pi$
$110$	1.37105	−	9.87184i	0.130725	−	0.941243i
$111$	−0.376522			−0.0357379
$112$	6.72476	−	10.9191i	0.635430	−	1.03176i
$113$	9.12934			0.858816			0.429408	−	0.903111i	$-0.358722\pi$
$113$	9.12934			0.858816			0.429408	+	0.903111i	$0.358722\pi$
$114$	−0.667211	+	4.80406i	−0.0624901	+	0.449941i
$115$	11.2317	+	11.2317i	1.04737	+	1.04737i
$116$	−9.41549	−	16.8566i	−0.874206	−	1.56510i
$117$	0.968729	−	0.968729i	0.0895591	−	0.0895591i
$118$	5.40487	−	4.08664i	0.497558	−	0.376206i
$119$			19.3533i			1.77411i
$120$	−6.05376	−	2.66004i	−0.552630	−	0.242827i
$121$		−	3.81241i		−	0.346583i
$122$	2.08367	+	2.75580i	0.188646	+	0.249498i
$123$	−8.39378	+	8.39378i	−0.756841	+	0.756841i
$124$	10.0657	+	2.85094i	0.903926	+	0.256022i
$125$	−8.60652	−	8.60652i	−0.769790	−	0.769790i
$126$	−6.15232	−	0.854465i	−0.548092	−	0.0761218i
$127$	12.7097			1.12780			0.563901	−	0.825842i	$-0.309300\pi$
$127$	12.7097			1.12780			0.563901	+	0.825842i	$0.309300\pi$
$128$	6.43277	+	9.30696i	0.568582	+	0.822627i
$129$	0.0752414			0.00662464
$130$	−2.56499	−	0.356238i	−0.224964	−	0.0312442i
$131$	6.39425	+	6.39425i	0.558668	+	0.558668i	0.928928	−	0.370260i	$-0.120731\pi$
$131$	6.39425	+	6.39425i	0.558668	+	0.558668i	−0.370260	+	0.928928i	$0.620731\pi$
$132$	−9.45544	−	2.67810i	−0.822990	−	0.233098i
$133$	6.08957	−	6.08957i	0.528033	−	0.528033i
$134$	−1.88210	−	2.48921i	−0.162589	−	0.215035i
$135$			10.2163i			0.879281i
$136$	−15.6319	−	6.86870i	−1.34042	−	0.588986i
$137$		−	19.8173i		−	1.69310i	−0.532306	−	0.846552i	$-0.678674\pi$
$137$		−	19.8173i		−	1.69310i	0.532306	−	0.846552i	$-0.321326\pi$
$138$	12.4931	−	9.44607i	1.06348	−	0.804103i
$139$	−7.81457	+	7.81457i	−0.662823	+	0.662823i	−0.956045	−	0.293221i	$-0.905273\pi$
$139$	−7.81457	+	7.81457i	−0.662823	+	0.662823i	0.293221	+	0.956045i	$0.405273\pi$
$140$	5.72546	+	10.2503i	0.483890	+	0.866312i
$141$	1.95626	+	1.95626i	0.164747	+	0.164747i
$142$	−1.89457	+	13.6413i	−0.158989	+	1.14475i
$143$	−3.84869			−0.321844
$144$	2.87368	−	4.66604i	0.239474	−	0.388836i
$145$	17.6777			1.46805
$146$	−1.18425	+	8.52687i	−0.0980096	+	0.705689i
$147$	−2.95933	−	2.95933i	−0.244081	−	0.244081i
$148$	−0.514943	+	0.287628i	−0.0423281	+	0.0236429i
$149$	6.86136	−	6.86136i	0.562104	−	0.562104i	−0.367800	−	0.929905i	$-0.619889\pi$
$149$	6.86136	−	6.86136i	0.562104	−	0.562104i	0.929905	+	0.367800i	$0.119889\pi$
$150$	−2.37198	+	1.79346i	−0.193671	+	0.146436i
$151$		−	12.0002i		−	0.976560i	−0.872687	−	0.488280i	$-0.837624\pi$
$151$		−	12.0002i		−	0.976560i	0.872687	−	0.488280i	$-0.162376\pi$
$152$	2.75736	+	7.07987i	0.223651	+	0.574253i
$153$			8.27023i			0.668608i
$154$	10.5240	+	13.9187i	0.848047	+	1.12160i
$155$	−6.77289	+	6.77289i	−0.544012	+	0.544012i
$156$	−0.695846	+	2.45679i	−0.0557123	+	0.196701i
$157$	1.81214	+	1.81214i	0.144625	+	0.144625i	0.775712	−	0.631087i	$-0.217391\pi$
$157$	1.81214	+	1.81214i	0.144625	+	0.144625i	−0.631087	+	0.775712i	$0.717391\pi$
$158$	−7.44431	−	1.03390i	−0.592237	−	0.0822529i
$159$	−11.5195			−0.913553
$160$	−10.3113	+	0.986563i	−0.815183	+	0.0779946i
$161$	−27.8098			−2.19172
$162$	4.22073	+	0.586197i	0.331612	+	0.0460560i
$163$	−13.8786	−	13.8786i	−1.08706	−	1.08706i	−0.995830	−	0.0912264i	$-0.970921\pi$
$163$	−13.8786	−	13.8786i	−1.08706	−	1.08706i	−0.0912264	−	0.995830i	$-0.529079\pi$
$164$	−5.06752	+	17.8917i	−0.395707	+	1.39711i
$165$	6.36227	−	6.36227i	0.495302	−	0.495302i
$166$	11.7128	+	15.4910i	0.909087	+	1.20233i
$167$			3.99276i			0.308969i	0.987995	+	0.154485i	$0.0493717\pi$
$167$			3.99276i			0.308969i	−0.987995	+	0.154485i	$0.950628\pi$
$168$	10.7877	−	4.20143i	0.832289	−	0.324147i
$169$			1.00000i			0.0769231i
$170$	12.4695	−	9.42826i	0.956370	−	0.723115i
$171$	2.60225	−	2.60225i	0.198999	−	0.198999i
$172$	0.102903	−	0.0574775i	0.00784624	−	0.00438262i
$173$	12.5447	+	12.5447i	0.953756	+	0.953756i	0.998977	−	0.0452212i	$-0.0143993\pi$
$173$	12.5447	+	12.5447i	0.953756	+	0.953756i	−0.0452212	+	0.998977i	$0.514399\pi$
$174$	2.39786	−	17.2651i	0.181781	−	1.30886i
$175$	5.28007			0.399136
$176$	−14.9774	+	3.56044i	−1.12896	+	0.268378i
$177$	6.11715			0.459793
$178$	1.15680	−	8.32918i	0.0867057	−	0.624299i
$179$	−6.56516	−	6.56516i	−0.490703	−	0.490703i	0.417825	−	0.908528i	$-0.362793\pi$
$179$	−6.56516	−	6.56516i	−0.490703	−	0.490703i	−0.908528	+	0.417825i	$0.862793\pi$
$180$	2.44666	+	4.38027i	0.182363	+	0.326486i
$181$	6.91102	−	6.91102i	0.513692	−	0.513692i	−0.401964	−	0.915656i	$-0.631672\pi$
$181$	6.91102	−	6.91102i	0.513692	−	0.513692i	0.915656	+	0.401964i	$0.131672\pi$
$182$	3.61648	−	2.73443i	0.268071	−	0.202690i
$183$			3.11897i			0.230561i
$184$	9.87001	−	22.4623i	0.727627	−	1.65594i
$185$		−	0.540025i		−	0.0397035i
$186$	5.69610	+	7.53349i	0.417658	+	0.552382i
$187$	16.4285	−	16.4285i	1.20137	−	1.20137i
$188$	4.16985	+	1.18104i	0.304118	+	0.0861363i
$189$	−12.6478	−	12.6478i	−0.919993	−	0.919993i
$190$	−6.89020	−	0.956946i	−0.499868	−	0.0694241i
$191$	−11.2566			−0.814502			−0.407251	−	0.913316i	$-0.633513\pi$
$191$	−11.2566			−0.814502			−0.407251	+	0.913316i	$0.633513\pi$
$192$	−0.435128	+	10.2045i	−0.0314027	+	0.736444i
$193$	−2.54609			−0.183272			−0.0916358	−	0.995793i	$-0.529210\pi$
$193$	−2.54609			−0.183272			−0.0916358	+	0.995793i	$0.529210\pi$
$194$	−13.7143	−	1.90471i	−0.984629	−	0.136750i
$195$	−1.65310	−	1.65310i	−0.118381	−	0.118381i
$196$	−6.30793	−	1.78662i	−0.450567	−	0.127615i
$197$	4.30038	−	4.30038i	0.306389	−	0.306389i	−0.537118	−	0.843507i	$-0.680487\pi$
$197$	4.30038	−	4.30038i	0.306389	−	0.306389i	0.843507	+	0.537118i	$0.180487\pi$
$198$	4.49721	+	5.94787i	0.319603	+	0.422697i
$199$		−	26.2885i		−	1.86354i	−0.363048	−	0.931771i	$-0.618264\pi$
$199$		−	26.2885i		−	1.86354i	0.363048	−	0.931771i	$-0.381736\pi$
$200$	−1.87395	+	4.26477i	−0.132509	+	0.301565i
$201$		−	2.81725i		−	0.198714i
$202$	−7.58581	+	5.73566i	−0.533736	+	0.403560i
$203$	−21.8850	+	21.8850i	−1.53603	+	1.53603i
$204$	−7.51678	−	13.4574i	−0.526280	−	0.942203i
$205$	−12.0387	−	12.0387i	−0.840823	−	0.840823i
$206$	0.561934	−	4.04604i	0.0391518	−	0.281901i
$207$	−11.8840			−0.825992
$208$	0.925105	+	3.89155i	0.0641445	+	0.269831i
$209$	−10.3385			−0.715132
$210$	−1.45811	+	10.4987i	−0.100619	+	0.724479i
$211$	−7.51991	−	7.51991i	−0.517692	−	0.517692i	0.399180	−	0.916872i	$-0.369295\pi$
$211$	−7.51991	−	7.51991i	−0.517692	−	0.517692i	−0.916872	+	0.399180i	$0.869295\pi$
$212$	−15.7544	+	8.79982i	−1.08202	+	0.604374i
$213$	−8.79162	+	8.79162i	−0.602392	+	0.602392i
$214$	5.91534	−	4.47261i	0.404364	−	0.305741i
$215$			0.107915i			0.00735972i
$216$	14.7046	−	5.72694i	1.00052	−	0.389669i
$217$		−	16.7697i		−	1.13840i
$218$	3.33550	+	4.41143i	0.225908	+	0.298780i
$219$	−5.49545	+	5.49545i	−0.371348	+	0.371348i
$220$	3.84105	−	13.5614i	0.258963	−	0.914311i
$221$	−4.26860	−	4.26860i	−0.287137	−	0.287137i
$222$	−0.527420	−	0.0732507i	−0.0353981	−	0.00491627i
$223$	−18.7318			−1.25438			−0.627188	−	0.778868i	$-0.715794\pi$
$223$	−18.7318			−1.25438			−0.627188	+	0.778868i	$0.715794\pi$
$224$	11.5441	−	13.9868i	0.771322	−	0.934534i
$225$	2.25633			0.150422
$226$	12.7881	+	1.77607i	0.850651	+	0.118143i
$227$	0.552713	+	0.552713i	0.0366849	+	0.0366849i	0.725211	−	0.688526i	$-0.241742\pi$
$227$	0.552713	+	0.552713i	0.0366849	+	0.0366849i	−0.688526	+	0.725211i	$0.741742\pi$
$228$	−1.86922	+	6.59957i	−0.123792	+	0.437067i
$229$	−14.9481	+	14.9481i	−0.987798	+	0.987798i	−0.999926	−	0.0121281i	$-0.996139\pi$
$229$	−14.9481	+	14.9481i	−0.987798	+	0.987798i	0.0121281	+	0.999926i	$0.496139\pi$
$230$	13.5480	+	17.9182i	0.893328	+	1.18149i
$231$			15.7530i			1.03647i
$232$	−9.90954	−	25.4440i	−0.650593	−	1.67048i
$233$		−	23.9526i		−	1.56919i	−0.620009	−	0.784595i	$-0.712871\pi$
$233$		−	23.9526i		−	1.56919i	0.620009	−	0.784595i	$-0.287129\pi$
$234$	1.54543	−	1.16850i	0.101028	−	0.0763874i
$235$	−2.80576	+	2.80576i	−0.183028	+	0.183028i
$236$	8.36600	−	4.67294i	0.544581	−	0.304183i
$237$	−4.79776	−	4.79776i	−0.311648	−	0.311648i
$238$	−3.76510	+	27.1095i	−0.244055	+	1.75725i
$239$	1.49140			0.0964709			0.0482354	−	0.998836i	$-0.484640\pi$
$239$	1.49140			0.0964709			0.0482354	+	0.998836i	$0.484640\pi$
$240$	−7.96242	−	4.90383i	−0.513972	−	0.316541i
$241$	−0.0970048			−0.00624863			−0.00312431	−	0.999995i	$-0.500995\pi$
$241$	−0.0970048			−0.00624863			−0.00312431	+	0.999995i	$0.500995\pi$
$242$	0.741689	−	5.34031i	0.0476776	−	0.343288i
$243$	−9.11516	−	9.11516i	−0.584738	−	0.584738i
$244$	2.38261	+	4.26560i	0.152531	+	0.273077i
$245$	4.24441	−	4.24441i	0.271165	−	0.271165i
$246$	−13.3907	+	10.1248i	−0.853761	+	0.645531i
$247$			2.68625i			0.170922i
$248$	13.5451	+	5.95174i	0.860113	+	0.377936i
$249$			17.5324i			1.11107i
$250$	−10.3814	−	13.7301i	−0.656576	−	0.868368i
$251$	7.32996	−	7.32996i	0.462663	−	0.462663i	−0.436864	−	0.899527i	$-0.643911\pi$
$251$	7.32996	−	7.32996i	0.462663	−	0.462663i	0.899527	+	0.436864i	$0.143911\pi$
$252$	−8.45174	−	2.39381i	−0.532410	−	0.150796i
$253$	23.6070	+	23.6070i	1.48416	+	1.48416i
$254$	17.8033	+	2.47261i	1.11708	+	0.155146i
$255$	14.1128			0.883780
$256$	7.20019	+	14.2884i	0.450012	+	0.893023i
$257$	28.9029			1.80291			0.901457	−	0.432869i	$-0.142499\pi$
$257$	28.9029			1.80291			0.901457	+	0.432869i	$0.142499\pi$
$258$	0.105396	+	0.0146379i	0.00656165	+	0.000911315i
$259$	0.668552	+	0.668552i	0.0415418	+	0.0415418i
$260$	−3.52365	−	0.998015i	−0.218527	−	0.0618942i
$261$	−9.35210	+	9.35210i	−0.578880	+	0.578880i
$262$	7.71289	+	10.2008i	0.476504	+	0.630210i
$263$			17.4287i			1.07470i	0.843360	+	0.537349i	$0.180574\pi$
$263$			17.4287i			1.07470i	−0.843360	+	0.537349i	$0.819426\pi$
$264$	−12.7239	−	5.59091i	−0.783100	−	0.344097i
$265$		−	16.5217i		−	1.01492i
$266$	9.71478	−	7.34538i	0.595651	−	0.450374i
$267$	5.36804	−	5.36804i	0.328519	−	0.328519i
$268$	−2.15212	−	3.85297i	−0.131462	−	0.235357i
$269$	−12.0262	−	12.0262i	−0.733248	−	0.733248i	0.238013	−	0.971262i	$-0.423504\pi$
$269$	−12.0262	−	12.0262i	−0.733248	−	0.733248i	−0.971262	+	0.238013i	$0.923504\pi$
$270$	−1.98754	+	14.3107i	−0.120958	+	0.870921i
$271$	1.79480			0.109026			0.0545131	−	0.998513i	$-0.482639\pi$
$271$	1.79480			0.109026			0.0545131	+	0.998513i	$0.482639\pi$
$272$	−20.5604	−	12.6626i	−1.24666	−	0.767781i
$273$	4.09308			0.247724
$274$	3.85537	−	27.7594i	0.232911	−	1.67701i
$275$	−4.48211	−	4.48211i	−0.270282	−	0.270282i
$276$	19.3376	−	10.8013i	1.16399	−	0.650160i
$277$	−1.31019	+	1.31019i	−0.0787215	+	0.0787215i	−0.745371	−	0.666650i	$-0.767728\pi$
$277$	−1.31019	+	1.31019i	−0.0787215	+	0.0787215i	0.666650	+	0.745371i	$0.267728\pi$
$278$	−12.4667	+	9.42611i	−0.747703	+	0.565341i
$279$		−	7.16618i		−	0.429028i
$280$	6.02588	+	15.4722i	0.360115	+	0.924642i
$281$			26.8404i			1.60116i	0.599225	+	0.800581i	$0.295475\pi$
$281$			26.8404i			1.60116i	−0.599225	+	0.800581i	$0.704525\pi$
$282$	2.35969	+	3.12085i	0.140517	+	0.185844i
$283$	1.50326	−	1.50326i	0.0893595	−	0.0893595i	−0.661014	−	0.750374i	$-0.729874\pi$
$283$	1.50326	−	1.50326i	0.0893595	−	0.0893595i	0.750374	+	0.661014i	$0.229874\pi$
$284$	−5.30771	+	18.7397i	−0.314954	+	1.11200i
$285$	−4.44064	−	4.44064i	−0.263041	−	0.263041i
$286$	−5.39112	−	0.748746i	−0.318784	−	0.0442743i
$287$	29.8080			1.75951
$288$	4.93312	−	5.97697i	0.290687	−	0.352197i
$289$	19.4418			1.14364
$290$	24.7623	+	3.43912i	1.45409	+	0.201952i
$291$	−8.83868	−	8.83868i	−0.518133	−	0.518133i
$292$	−3.31773	+	11.7138i	−0.194156	+	0.685497i
$293$	−4.58243	+	4.58243i	−0.267709	+	0.267709i	−0.828176	−	0.560468i	$-0.810621\pi$
$293$	−4.58243	+	4.58243i	−0.267709	+	0.267709i	0.560468	+	0.828176i	$0.310621\pi$
$294$	−3.56961	−	4.72106i	−0.208184	−	0.275338i
$295$			8.77350i			0.510813i
$296$	−0.777273	+	0.302721i	−0.0451781	+	0.0175953i
$297$			21.4728i			1.24598i
$298$	10.9460	−	8.27633i	0.634086	−	0.479435i
$299$	6.13378	−	6.13378i	0.354726	−	0.354726i
$300$	−3.67151	+	2.05077i	−0.211975	+	0.118401i
$301$	−0.133599	−	0.133599i	−0.00770049	−	0.00770049i
$302$	2.33458	−	16.8095i	0.134340	−	0.967276i
$303$	−8.58551			−0.493224
$304$	2.48507	+	10.4537i	0.142528	+	0.599560i
$305$	−4.47337			−0.256144
$306$	−1.60894	+	11.5847i	−0.0919769	+	0.662252i
$307$	13.7315	+	13.7315i	0.783699	+	0.783699i	0.980453	−	0.196754i	$-0.0630401\pi$
$307$	13.7315	+	13.7315i	0.783699	+	0.783699i	−0.196754	+	0.980453i	$0.563040\pi$
$308$	12.0338	+	21.5443i	0.685692	+	1.22760i
$309$	2.60762	−	2.60762i	0.148342	−	0.148342i
$310$	−10.8049	+	8.16961i	−0.613676	+	0.464003i
$311$			1.60913i			0.0912455i	0.998959	+	0.0456228i	$0.0145272\pi$
$311$			1.60913i			0.0912455i	−0.998959	+	0.0456228i	$0.985473\pi$
$312$	−1.45268	+	3.30603i	−0.0822417	+	0.187167i
$313$		−	14.3857i		−	0.813126i	−0.913623	−	0.406563i	$-0.866727\pi$
$313$		−	14.3857i		−	0.813126i	0.913623	−	0.406563i	$-0.133273\pi$
$314$	2.18585	+	2.89094i	0.123355	+	0.163145i
$315$	5.68691	−	5.68691i	0.320421	−	0.320421i
$316$	−10.2266	−	2.89652i	−0.575292	−	0.162942i
$317$	−12.4126	−	12.4126i	−0.697160	−	0.697160i	0.266637	−	0.963797i	$-0.414088\pi$
$317$	−12.4126	−	12.4126i	−0.697160	−	0.697160i	−0.963797	+	0.266637i	$0.914088\pi$
$318$	−16.1361	−	2.24106i	−0.904867	−	0.125673i
$319$	37.1552			2.08029
$320$	−14.6357	−	0.624081i	−0.818162	−	0.0348872i
$321$	6.69489			0.373673
$322$	−38.9551	−	5.41028i	−2.17089	−	0.301503i
$323$	−11.4665	−	11.4665i	−0.638015	−	0.638015i
$324$	5.79823	+	1.64225i	0.322124	+	0.0912362i
$325$	−1.16458	+	1.16458i	−0.0645994	+	0.0645994i
$326$	−16.7407	−	22.1407i	−0.927181	−	1.22626i
$327$			4.99279i			0.276102i
$328$	−10.5792	+	24.0762i	−0.584137	+	1.32939i
$329$		−	6.94708i		−	0.383005i
$330$	10.1498	−	7.67431i	0.558729	−	0.422457i
$331$	−17.1517	+	17.1517i	−0.942742	+	0.942742i	−0.998447	−	0.0557049i	$-0.982259\pi$
$331$	−17.1517	+	17.1517i	−0.942742	+	0.942742i	0.0557049	+	0.998447i	$0.482259\pi$
$332$	13.3932	+	23.9779i	0.735046	+	1.31596i
$333$	0.285692	+	0.285692i	0.0156558	+	0.0156558i
$334$	−0.776775	+	5.59294i	−0.0425032	+	0.306032i
$335$	4.04064			0.220764
$336$	15.9284	−	3.78653i	0.868967	−	0.206572i
$337$	30.8004			1.67781			0.838903	−	0.544281i	$-0.183198\pi$
$337$	30.8004			1.67781			0.838903	+	0.544281i	$0.183198\pi$
$338$	−0.194546	+	1.40077i	−0.0105819	+	0.0761918i
$339$	8.24175	+	8.24175i	0.447631	+	0.447631i
$340$	19.3012	−	10.7809i	1.04675	−	0.584677i
$341$	−14.2353	+	14.2353i	−0.770887	+	0.770887i
$342$	4.15141	−	3.13889i	0.224482	−	0.169732i
$343$		−	11.9324i		−	0.644289i
$344$	0.155325	−	0.0604935i	0.00837454	−	0.00326159i
$345$			20.2795i			1.09181i
$346$	15.1317	+	20.0127i	0.813485	+	1.07589i
$347$	22.1815	−	22.1815i	1.19076	−	1.19076i	0.213910	−	0.976853i	$-0.431380\pi$
$347$	22.1815	−	22.1815i	1.19076	−	1.19076i	0.976853	−	0.213910i	$-0.0686198\pi$
$348$	6.71768	−	23.7178i	0.360106	−	1.27141i
$349$	15.7484	+	15.7484i	0.842990	+	0.842990i	0.989247	−	0.146256i	$-0.0467224\pi$
$349$	15.7484	+	15.7484i	0.842990	+	0.842990i	−0.146256	+	0.989247i	$0.546722\pi$
$350$	7.39616	+	1.02722i	0.395341	+	0.0549070i
$351$	5.57925			0.297798
$352$	−21.6725	+	2.07357i	−1.15515	+	0.110522i
$353$	28.1232			1.49685			0.748424	−	0.663220i	$-0.230811\pi$
$353$	28.1232			1.49685			0.748424	+	0.663220i	$0.230811\pi$
$354$	8.56871	+	1.19006i	0.455422	+	0.0632512i
$355$	−12.6094	−	12.6094i	−0.669235	−	0.669235i
$356$	3.24081	−	11.4422i	0.171763	−	0.606436i
$357$	−17.4717	+	17.4717i	−0.924701	+	0.924701i
$358$	−7.91905	−	10.4735i	−0.418535	−	0.553541i
$359$		−	2.91495i		−	0.153845i	−0.997037	−	0.0769225i	$-0.975491\pi$
$359$		−	2.91495i		−	0.153845i	0.997037	−	0.0769225i	$-0.0245094\pi$
$360$	2.57504	+	6.61173i	0.135716	+	0.348469i
$361$		−	11.7841i		−	0.620213i
$362$	11.0252	−	8.33623i	0.579474	−	0.438142i
$363$	3.44176	−	3.44176i	0.180645	−	0.180645i
$364$	5.59782	−	3.12674i	0.293406	−	0.163886i
$365$	−7.88183	−	7.88183i	−0.412554	−	0.412554i
$366$	−0.606782	+	4.36895i	−0.0317170	+	0.228369i
$367$	−6.29896			−0.328803			−0.164402	−	0.986394i	$-0.552569\pi$
$367$	−6.29896			−0.328803			−0.164402	+	0.986394i	$0.552569\pi$
$368$	18.1955	−	29.5443i	0.948508	−	1.54010i
$369$	12.7378			0.663104
$370$	0.105060	−	0.756450i	0.00546179	−	0.0393260i
$371$	20.4539	+	20.4539i	1.06192	+	1.06192i
$372$	6.51331	+	11.6608i	0.337699	+	0.604586i
$373$	−12.7757	+	12.7757i	−0.661498	+	0.661498i	−0.955733	−	0.294235i	$-0.904935\pi$
$373$	−12.7757	+	12.7757i	−0.661498	+	0.661498i	0.294235	+	0.955733i	$0.404935\pi$
$374$	26.2086	−	19.8164i	1.35522	−	1.02468i
$375$		−	15.5395i		−	0.802457i
$376$	5.61123	+	2.46559i	0.289377	+	0.127153i
$377$		−	9.65398i		−	0.497205i
$378$	−15.2561	−	20.1772i	−0.784688	−	1.03781i
$379$	−17.8540	+	17.8540i	−0.917097	+	0.917097i	−0.996817	−	0.0797198i	$-0.974597\pi$
$379$	−17.8540	+	17.8540i	−0.917097	+	0.917097i	0.0797198	+	0.996817i	$0.474597\pi$
$380$	−9.46541	−	2.68092i	−0.485565	−	0.137528i
$381$	11.4740	+	11.4740i	0.587831	+	0.587831i
$382$	−15.7679	−	2.18993i	−0.806758	−	0.112047i
$383$	9.20840			0.470527			0.235264	−	0.971932i	$-0.424405\pi$
$383$	9.20840			0.470527			0.235264	+	0.971932i	$0.424405\pi$
$384$	−2.59475	+	14.2095i	−0.132413	+	0.725123i
$385$	−22.5937			−1.15148
$386$	−3.56648	−	0.495331i	−0.181529	−	0.0252117i
$387$	−0.0570905	−	0.0570905i	−0.00290208	−	0.00290208i
$388$	−18.8400	−	5.33612i	−0.956456	−	0.270900i
$389$	−19.1892	+	19.1892i	−0.972930	+	0.972930i	−0.999643	−	0.0267131i	$-0.991496\pi$
$389$	−19.1892	+	19.1892i	−0.972930	+	0.972930i	0.0267131	+	0.999643i	$0.491496\pi$
$390$	−1.99401	−	2.63721i	−0.100970	−	0.133540i
$391$			52.3653i			2.64823i
$392$	−8.48837	−	3.72982i	−0.428728	−	0.188384i
$393$			11.5452i			0.582376i
$394$	6.86045	−	5.18721i	0.345625	−	0.261328i
$395$	6.88117	−	6.88117i	0.346229	−	0.346229i
$396$	5.14241	+	9.20650i	0.258416	+	0.462644i
$397$	−15.2018	−	15.2018i	−0.762956	−	0.762956i	0.213900	−	0.976856i	$-0.431383\pi$
$397$	−15.2018	−	15.2018i	−0.762956	−	0.762956i	−0.976856	+	0.213900i	$0.931383\pi$
$398$	5.11431	−	36.8241i	0.256357	−	1.84582i
$399$	10.9950			0.550441
$400$	−3.45467	+	5.60939i	−0.172733	+	0.280470i
$401$	−18.1785			−0.907793			−0.453897	−	0.891054i	$-0.649966\pi$
$401$	−18.1785			−0.907793			−0.453897	+	0.891054i	$0.649966\pi$
$402$	0.548085	−	3.94632i	0.0273360	−	0.196825i
$403$	3.69875	+	3.69875i	0.184248	+	0.184248i
$404$	−11.7418	+	6.55854i	−0.584177	+	0.326300i
$405$	−3.90145	+	3.90145i	−0.193864	+	0.193864i
$406$	−34.9134	+	26.3982i	−1.73273	+	1.31012i
$407$		−	1.13503i		−	0.0562615i
$408$	−7.91120	−	20.3130i	−0.391663	−	1.00564i
$409$			5.29435i			0.261789i	0.991396	+	0.130894i	$0.0417849\pi$
$409$			5.29435i			0.261789i	−0.991396	+	0.130894i	$0.958215\pi$
$410$	−14.5214	−	19.2056i	−0.717161	−	0.948496i
$411$	17.8906	−	17.8906i	0.882477	−	0.882477i
$412$	1.57428	−	5.55824i	0.0775592	−	0.273835i
$413$	−10.8616	−	10.8616i	−0.534464	−	0.534464i
$414$	−16.6467	−	2.31197i	−0.818139	−	0.113627i
$415$	−25.1458			−1.23436
$416$	0.538773	+	5.63114i	0.0264155	+	0.276089i
$417$	−14.1096			−0.690951
$418$	−14.4819	−	2.01132i	−0.708334	−	0.0983769i
$419$	−1.93469	−	1.93469i	−0.0945158	−	0.0945158i	0.658268	−	0.752784i	$-0.271289\pi$
$419$	−1.93469	−	1.93469i	−0.0945158	−	0.0945158i	−0.752784	+	0.658268i	$0.771289\pi$
$420$	−4.08495	+	14.4226i	−0.199325	+	0.703749i
$421$	−7.75321	+	7.75321i	−0.377868	+	0.377868i	−0.870333	−	0.492464i	$-0.836096\pi$
$421$	−7.75321	+	7.75321i	−0.377868	+	0.377868i	0.492464	+	0.870333i	$0.336096\pi$
$422$	−9.07069	−	11.9966i	−0.441554	−	0.583987i
$423$		−	2.96869i		−	0.144343i
$424$	−23.7802	+	9.26156i	−1.15487	+	0.449781i
$425$		−	9.94226i		−	0.482270i
$426$	−14.0254	+	10.6047i	−0.679533	+	0.513797i
$427$	5.53804	−	5.53804i	0.268004	−	0.268004i
$428$	9.15615	−	5.11429i	0.442579	−	0.247208i
$429$	−3.47451	−	3.47451i	−0.167751	−	0.167751i
$430$	−0.0209943	+	0.151164i	−0.00101244	+	0.00728975i
$431$	−28.1933			−1.35802			−0.679011	−	0.734128i	$-0.737591\pi$
$431$	−28.1933			−1.35802			−0.679011	+	0.734128i	$0.737591\pi$
$432$	21.7119	−	5.16139i	1.04462	−	0.248327i
$433$	−28.5535			−1.37219			−0.686097	−	0.727511i	$-0.740677\pi$
$433$	−28.5535			−1.37219			−0.686097	+	0.727511i	$0.740677\pi$
$434$	3.26247	−	23.4905i	0.156604	−	1.12758i
$435$	15.9590	+	15.9590i	0.765175	+	0.765175i
$436$	3.81403	+	6.82829i	0.182659	+	0.327016i
$437$	16.4769	−	16.4769i	0.788196	−	0.788196i
$438$	−8.76697	+	6.62874i	−0.418902	+	0.316733i
$439$		−	0.436290i		−	0.0208230i	−0.999946	−	0.0104115i	$-0.996686\pi$
$439$		−	0.436290i		−	0.0208230i	0.999946	−	0.0104115i	$-0.00331414\pi$
$440$	8.01874	−	18.2492i	0.382278	−	0.869995i
$441$			4.49087i			0.213851i
$442$	−5.14888	−	6.80975i	−0.244907	−	0.323907i
$443$	22.4448	−	22.4448i	1.06638	−	1.06638i	0.0687507	−	0.997634i	$-0.478099\pi$
$443$	22.4448	−	22.4448i	1.06638	−	1.06638i	0.997634	−	0.0687507i	$-0.0219013\pi$
$444$	−0.724543	−	0.205215i	−0.0343853	−	0.00973906i
$445$	7.69910	+	7.69910i	0.364972	+	0.364972i
$446$	−26.2390	−	3.64420i	−1.24245	−	0.172558i
$447$	12.3885			0.585958
$448$	18.8917	−	17.3464i	0.892547	−	0.819542i
$449$	1.83048			0.0863856			0.0431928	−	0.999067i	$-0.486247\pi$
$449$	1.83048			0.0863856			0.0431928	+	0.999067i	$0.486247\pi$
$450$	3.16059	+	0.438959i	0.148992	+	0.0206927i
$451$	−25.3032	−	25.3032i	−1.19148	−	1.19148i
$452$	17.5676	+	4.97574i	0.826312	+	0.234039i
$453$	10.8335	−	10.8335i	0.509001	−	0.509001i
$454$	0.666696	+	0.881752i	0.0312896	+	0.0413827i
$455$			5.87048i			0.275213i
$456$	−3.90226	+	8.88082i	−0.182740	+	0.415882i
$457$		−	18.3262i		−	0.857264i	−0.903479	−	0.428632i	$-0.858996\pi$
$457$		−	18.3262i		−	0.857264i	0.903479	−	0.428632i	$-0.141004\pi$
$458$	−23.8469	+	18.0307i	−1.11429	+	0.842521i
$459$	−23.8156	+	23.8156i	−1.11161	+	1.11161i
$460$	15.4917	+	27.7349i	0.722304	+	1.29315i
$461$	−10.1809	−	10.1809i	−0.474171	−	0.474171i	0.429090	−	0.903262i	$-0.358834\pi$
$461$	−10.1809	−	10.1809i	−0.474171	−	0.474171i	−0.903262	+	0.429090i	$0.858834\pi$
$462$	−3.06468	+	22.0663i	−0.142582	+	1.02662i
$463$	28.8403			1.34032			0.670162	−	0.742215i	$-0.266225\pi$
$463$	28.8403			1.34032			0.670162	+	0.742215i	$0.266225\pi$
$464$	−8.93095	−	37.5690i	−0.414609	−	1.74410i
$465$	−12.2288			−0.567097
$466$	4.65988	−	33.5521i	0.215865	−	1.55427i
$467$	−11.4431	−	11.4431i	−0.529526	−	0.529526i	0.390905	−	0.920431i	$-0.372162\pi$
$467$	−11.4431	−	11.4431i	−0.529526	−	0.529526i	−0.920431	+	0.390905i	$0.872162\pi$
$468$	2.39211	−	1.33615i	0.110575	−	0.0617634i
$469$	−5.00231	+	5.00231i	−0.230985	+	0.230985i
$470$	−4.47607	+	3.38438i	−0.206466	+	0.156110i
$471$			3.27192i			0.150762i
$472$	12.6279	−	4.91814i	0.581248	−	0.226376i
$473$			0.226816i			0.0104290i
$474$	−5.78716	−	7.65393i	−0.265813	−	0.351557i
$475$	−3.12836	+	3.12836i	−0.143539	+	0.143539i
$476$	−10.5481	+	37.2416i	−0.483470	+	1.70697i
$477$	8.74057	+	8.74057i	0.400203	+	0.400203i
$478$	2.08911	+	0.290146i	0.0955537	+	0.0132710i
$479$	26.9400			1.23092			0.615459	−	0.788169i	$-0.288971\pi$
$479$	26.9400			1.23092			0.615459	+	0.788169i	$0.288971\pi$
$480$	−10.1995	−	8.41819i	−0.465540	−	0.384236i
$481$	−0.294914			−0.0134469
$482$	−0.135881	−	0.0188719i	−0.00618922	−	0.000859590i
$483$	−25.1061	−	25.1061i	−1.14237	−	1.14237i
$484$	2.07787	−	7.33624i	0.0944486	−	0.333466i
$485$	12.6768	−	12.6768i	0.575626	−	0.575626i
$486$	−10.9949	−	14.5415i	−0.498740	−	0.659618i
$487$		−	10.4127i		−	0.471844i	−0.971772	−	0.235922i	$-0.924189\pi$
$487$		−	10.4127i		−	0.471844i	0.971772	−	0.235922i	$-0.0758110\pi$
$488$	2.50763	+	6.43864i	0.113515	+	0.291464i
$489$		−	25.0586i		−	1.13319i
$490$	6.77117	−	5.11970i	0.305890	−	0.231285i
$491$	3.32818	−	3.32818i	0.150199	−	0.150199i	−0.628008	−	0.778207i	$-0.716130\pi$
$491$	3.32818	−	3.32818i	0.150199	−	0.150199i	0.778207	+	0.628008i	$0.216130\pi$
$492$	−20.7270	+	11.5773i	−0.934446	+	0.521947i
$493$	41.2090	+	41.2090i	1.85596	+	1.85596i
$494$	−0.522599	+	3.76282i	−0.0235128	+	0.169297i
$495$	−9.65493			−0.433957
$496$	17.8156	+	10.9721i	0.799945	+	0.492664i
$497$	31.2208			1.40044
$498$	−3.41086	+	24.5589i	−0.152844	+	1.10051i
$499$	12.7043	+	12.7043i	0.568720	+	0.568720i	0.931770	−	0.363049i	$-0.118264\pi$
$499$	12.7043	+	12.7043i	0.568720	+	0.568720i	−0.363049	+	0.931770i	$0.618264\pi$
$500$	−11.8708	−	21.2523i	−0.530877	−	0.950433i
$501$	−3.60457	+	3.60457i	−0.161040	+	0.161040i
$502$	11.6936	−	8.84156i	0.521910	−	0.394618i
$503$			4.37422i			0.195037i	0.995234	+	0.0975184i	$0.0310905\pi$
$503$			4.37422i			0.195037i	−0.995234	+	0.0975184i	$0.968910\pi$
$504$	−11.3732	−	4.99743i	−0.506604	−	0.222603i
$505$		−	12.3137i		−	0.547954i
$506$	28.4753	+	37.6606i	1.26588	+	1.67422i
$507$	−0.902776	+	0.902776i	−0.0400937	+	0.0400937i
$508$	24.4573	+	6.92712i	1.08512	+	0.307341i
$509$	−19.4429	−	19.4429i	−0.861791	−	0.861791i	0.129755	−	0.991546i	$-0.458581\pi$
$509$	−19.4429	−	19.4429i	−0.861791	−	0.861791i	−0.991546	+	0.129755i	$0.958581\pi$
$510$	19.7688	+	2.74559i	0.875378	+	0.121577i
$511$	19.5154			0.863312
$512$	7.30606	+	21.4155i	0.322885	+	0.946438i
$513$	14.9873			0.661704
$514$	40.4863	+	5.62293i	1.78577	+	0.248017i
$515$	3.73997	+	3.73997i	0.164803	+	0.164803i
$516$	0.144787	+	0.0410086i	0.00637391	+	0.00180530i
$517$	−5.89719	+	5.89719i	−0.259358	+	0.259358i
$518$	0.806423	+	1.06655i	0.0354322	+	0.0468615i
$519$			22.6501i			0.994230i
$520$	−4.74166	−	2.08350i	−0.207935	−	0.0913674i
$521$			36.9872i			1.62044i	0.586127	+	0.810219i	$0.300652\pi$
$521$			36.9872i			1.62044i	−0.586127	+	0.810219i	$0.699348\pi$
$522$	−14.9195	+	11.2807i	−0.653010	+	0.493743i
$523$	−1.80040	+	1.80040i	−0.0787260	+	0.0787260i	−0.745373	−	0.666647i	$-0.767729\pi$
$523$	−1.80040	+	1.80040i	−0.0787260	+	0.0787260i	0.666647	+	0.745373i	$0.267729\pi$
$524$	8.81944	+	15.7895i	0.385279	+	0.689768i
$525$	4.76672	+	4.76672i	0.208037	+	0.208037i
$526$	−3.39067	+	24.4135i	−0.147840	+	1.06448i
$527$	−31.5770			−1.37551
$528$	−16.7355	−	10.3069i	−0.728319	−	0.448552i
$529$	−52.2466			−2.27159
$530$	3.21424	−	23.1431i	0.139617	−	1.00527i
$531$	−4.64148	−	4.64148i	−0.201423	−	0.201423i
$532$	15.0372	−	8.39921i	0.651944	−	0.364152i
$533$	−6.57449	+	6.57449i	−0.284773	+	0.284773i
$534$	8.56372	−	6.47506i	0.370588	−	0.280203i
$535$			9.60213i			0.415136i
$536$	−2.26505	−	5.81580i	−0.0978352	−	0.251204i
$537$		−	11.8537i		−	0.511527i
$538$	−14.5062	−	19.1855i	−0.625408	−	0.827146i
$539$	8.92095	−	8.92095i	0.384253	−	0.384253i
$540$	−5.56817	+	19.6593i	−0.239616	+	0.846002i
$541$	13.6616	+	13.6616i	0.587357	+	0.587357i	0.936915	−	0.349558i	$-0.113668\pi$
$541$	13.6616	+	13.6616i	0.587357	+	0.587357i	−0.349558	+	0.936915i	$0.613668\pi$
$542$	2.51410	+	0.349170i	0.107990	+	0.0149981i
$543$	12.4782			0.535491
$544$	−26.3369	−	21.7373i	−1.12918	−	0.931977i
$545$	−7.16089			−0.306739
$546$	5.73346	+	0.796291i	0.245369	+	0.0340781i
$547$	−5.89436	−	5.89436i	−0.252025	−	0.252025i	0.569776	−	0.821800i	$-0.307030\pi$
$547$	−5.89436	−	5.89436i	−0.252025	−	0.252025i	−0.821800	+	0.569776i	$0.807030\pi$
$548$	10.8010	−	38.1345i	0.461394	−	1.62902i
$549$	2.36656	−	2.36656i	0.101003	−	0.101003i
$550$	−5.40643	−	7.15038i	−0.230531	−	0.304893i
$551$		−	25.9330i		−	1.10478i
$552$	29.1889	−	11.3680i	1.24236	−	0.483856i
$553$			17.0378i			0.724520i
$554$	−2.09016	+	1.58038i	−0.0888024	+	0.0671438i
$555$	0.487522	−	0.487522i	0.0206942	−	0.0206942i
$556$	−19.2968	+	10.7785i	−0.818365	+	0.457108i
$557$	9.07239	+	9.07239i	0.384409	+	0.384409i	0.872688	−	0.488278i	$-0.162375\pi$
$557$	9.07239	+	9.07239i	0.384409	+	0.384409i	−0.488278	+	0.872688i	$0.662375\pi$
$558$	1.39415	−	10.0382i	0.0590190	−	0.424949i
$559$	0.0589334			0.00249262
$560$	5.43081	+	22.8453i	0.229494	+	0.965390i
$561$	29.6625			1.25235
$562$	−5.22168	+	37.5971i	−0.220263	+	1.58594i
$563$	17.9168	+	17.9168i	0.755104	+	0.755104i	0.975427	−	0.220323i	$-0.0707110\pi$
$563$	17.9168	+	17.9168i	0.755104	+	0.755104i	−0.220323	+	0.975427i	$0.570711\pi$
$564$	2.69823	+	4.83066i	0.113616	+	0.203407i
$565$	−11.8207	+	11.8207i	−0.497301	+	0.497301i
$566$	2.39817	−	1.81327i	0.100803	−	0.0762173i
$567$		−	9.65999i		−	0.405681i
$568$	−11.0806	+	25.2174i	−0.464931	+	1.05810i
$569$			15.4121i			0.646109i	0.946380	+	0.323054i	$0.104710\pi$
$569$			15.4121i			0.646109i	−0.946380	+	0.323054i	$0.895290\pi$
$570$	−5.35640	−	7.08422i	−0.224355	−	0.296725i
$571$	15.6916	−	15.6916i	0.656673	−	0.656673i	−0.297919	−	0.954591i	$-0.596292\pi$
$571$	15.6916	−	15.6916i	0.656673	−	0.656673i	0.954591	+	0.297919i	$0.0962924\pi$
$572$	−7.40605	−	2.09764i	−0.309662	−	0.0877067i
$573$	−10.1622	−	10.1622i	−0.424533	−	0.424533i
$574$	41.7541	+	5.79901i	1.74278	+	0.242046i
$575$	14.2866			0.595792
$576$	8.07296	−	7.41264i	0.336373	−	0.308860i
$577$	−17.3626			−0.722815			−0.361407	−	0.932408i	$-0.617704\pi$
$577$	−17.3626			−0.722815			−0.361407	+	0.932408i	$0.617704\pi$
$578$	27.2335	+	3.78233i	1.13276	+	0.157324i
$579$	−2.29855	−	2.29855i	−0.0955244	−	0.0955244i
$580$	34.0172	+	9.63482i	1.41249	+	0.400064i
$581$	31.1306	−	31.1306i	1.29151	−	1.29151i
$582$	−10.6614	−	14.1005i	−0.441930	−	0.584483i
$583$		−	34.7256i		−	1.43819i
$584$	−6.92624	+	15.7628i	−0.286610	+	0.652271i
$585$			2.50863i			0.103719i
$586$	−7.31042	+	5.52744i	−0.301991	+	0.228336i
$587$	15.0345	−	15.0345i	0.620541	−	0.620541i	−0.325129	−	0.945670i	$-0.605408\pi$
$587$	15.0345	−	15.0345i	0.620541	−	0.620541i	0.945670	+	0.325129i	$0.105408\pi$
$588$	−4.08174	−	7.30757i	−0.168328	−	0.301359i
$589$	9.93577	+	9.93577i	0.409396	+	0.409396i
$590$	−1.70685	+	12.2896i	−0.0702698	+	0.505956i
$591$	7.76456			0.319391
$592$	−1.14767	+	0.272826i	−0.0471691	+	0.0112131i
$593$	−42.6498			−1.75142			−0.875709	−	0.482840i	$-0.839605\pi$
$593$	−42.6498			−1.75142			−0.875709	+	0.482840i	$0.839605\pi$
$594$	−4.17744	+	30.0784i	−0.171402	+	1.23413i
$595$	−25.0587	−	25.0587i	−1.02731	−	1.02731i
$596$	16.9430	−	9.46371i	0.694011	−	0.387649i
$597$	23.7326	−	23.7326i	0.971311	−	0.971311i
$598$	9.78531	−	7.39871i	0.400151	−	0.302556i
$599$			26.7066i			1.09120i	0.838045	+	0.545602i	$0.183699\pi$
$599$			26.7066i			1.09120i	−0.838045	+	0.545602i	$0.816301\pi$
$600$	−5.54190	+	2.15837i	−0.226247	+	0.0881153i
$601$			8.30933i			0.338944i	0.985535	+	0.169472i	$0.0542063\pi$
$601$			8.30933i			0.338944i	−0.985535	+	0.169472i	$0.945794\pi$
$602$	−0.161150	−	0.213132i	−0.00656797	−	0.00868660i
$603$	−2.13763	+	2.13763i	−0.0870512	+	0.0870512i
$604$	6.54042	−	23.0920i	0.266126	−	0.939599i
$605$	4.93633	+	4.93633i	0.200690	+	0.200690i
$606$	−12.0263	−	1.67027i	−0.488535	−	0.0678502i
$607$	−22.9913			−0.933190			−0.466595	−	0.884471i	$-0.654519\pi$
$607$	−22.9913			−0.933190			−0.466595	+	0.884471i	$0.654519\pi$
$608$	1.44728	+	15.1267i	0.0586950	+	0.613467i
$609$	−39.5145			−1.60121
$610$	−6.26615	−	0.870275i	−0.253709	−	0.0352364i
$611$	1.53226	+	1.53226i	0.0619886	+	0.0619886i
$612$	−4.50750	+	15.9144i	−0.182205	+	0.643303i
$613$	−6.71226	+	6.71226i	−0.271106	+	0.271106i	−0.829545	−	0.558440i	$-0.811400\pi$
$613$	−6.71226	+	6.71226i	−0.271106	+	0.271106i	0.558440	+	0.829545i	$0.311400\pi$
$614$	16.5633	+	21.9061i	0.668439	+	0.884057i
$615$		−	21.7366i		−	0.876504i
$616$	12.6653	+	32.5197i	0.510299	+	1.31026i
$617$			10.3150i			0.415266i	0.978207	+	0.207633i	$0.0665760\pi$
$617$			10.3150i			0.415266i	−0.978207	+	0.207633i	$0.933424\pi$
$618$	4.15997	−	3.14537i	0.167339	−	0.126525i
$619$	−6.94177	+	6.94177i	−0.279013	+	0.279013i	−0.832715	−	0.553702i	$-0.813215\pi$
$619$	−6.94177	+	6.94177i	−0.279013	+	0.279013i	0.553702	+	0.832715i	$0.313215\pi$
$620$	−16.7245	+	9.34169i	−0.671672	+	0.375171i
$621$	−34.2219	−	34.2219i	−1.37328	−	1.37328i
$622$	−0.313050	+	2.25402i	−0.0125522	+	0.0903780i
$623$	−19.0630			−0.763743
$624$	−2.67804	+	4.34836i	−0.107207	+	0.174074i
$625$	14.0527			0.562107
$626$	2.79867	−	20.1510i	0.111857	−	0.805396i
$627$	−9.33340	−	9.33340i	−0.372740	−	0.372740i
$628$	2.49945	+	4.47478i	0.0997388	+	0.178563i
$629$	1.25887	−	1.25887i	0.0501944	−	0.0501944i
$630$	9.07241	−	6.85968i	0.361453	−	0.273296i
$631$		−	11.6081i		−	0.462113i	−0.972940	−	0.231056i	$-0.925782\pi$
$631$		−	11.6081i		−	0.462113i	0.972940	−	0.231056i	$-0.0742182\pi$
$632$	−13.7616	−	6.04689i	−0.547407	−	0.240532i
$633$		−	13.5776i		−	0.539661i
$634$	−14.9723	−	19.8020i	−0.594628	−	0.786437i
$635$	−16.4565	+	16.4565i	−0.653058	+	0.653058i
$636$	−22.1669	−	6.27842i	−0.878977	−	0.248955i
$637$	−2.31792	−	2.31792i	−0.0918393	−	0.0918393i
$638$	52.0458	+	7.22838i	2.06051	+	0.286174i
$639$	13.3416			0.527784
$640$	−20.3799	−	3.72151i	−0.805585	−	0.147106i
$641$	27.0384			1.06795			0.533977	−	0.845499i	$-0.320697\pi$
$641$	27.0384			1.06795			0.533977	+	0.845499i	$0.320697\pi$
$642$	9.37800	+	1.30246i	0.370120	+	0.0514041i
$643$	−12.7661	−	12.7661i	−0.503444	−	0.503444i	0.409062	−	0.912507i	$-0.365856\pi$
$643$	−12.7661	−	12.7661i	−0.503444	−	0.503444i	−0.912507	+	0.409062i	$0.865856\pi$
$644$	−53.5146	−	15.1571i	−2.10877	−	0.597274i
$645$	−0.0974228	+	0.0974228i	−0.00383602	+	0.00383602i
$646$	−13.8312	−	18.2927i	−0.544181	−	0.719717i
$647$			10.0134i			0.393667i	0.980437	+	0.196833i	$0.0630658\pi$
$647$			10.0134i			0.393667i	−0.980437	+	0.196833i	$0.936934\pi$
$648$	7.80248	+	3.42843i	0.306510	+	0.134682i
$649$			18.4402i			0.723843i
$650$	−1.85787	+	1.40474i	−0.0728718	+	0.0550986i
$651$	15.1393	−	15.1393i	0.593355	−	0.593355i
$652$	−19.1424	−	34.2709i	−0.749676	−	1.34215i
$653$	9.13213	+	9.13213i	0.357368	+	0.357368i	0.862842	−	0.505474i	$-0.168682\pi$
$653$	9.13213	+	9.13213i	0.357368	+	0.357368i	−0.505474	+	0.862842i	$0.668682\pi$
$654$	−0.971325	+	6.99374i	−0.0379818	+	0.273477i
$655$	−16.5586			−0.646998
$656$	−19.5029	+	31.6671i	−0.761460	+	1.23639i
$657$	8.33951			0.325355
$658$	1.35152	−	9.73125i	0.0526879	−	0.379363i
$659$	26.5843	+	26.5843i	1.03558	+	1.03558i	0.999343	+	0.0362320i	$0.0115355\pi$
$659$	26.5843	+	26.5843i	1.03558	+	1.03558i	0.0362320	+	0.999343i	$0.488464\pi$
$660$	15.7105	−	8.77533i	0.611532	−	0.341579i
$661$	1.76639	−	1.76639i	0.0687044	−	0.0687044i	−0.671920	−	0.740624i	$-0.734530\pi$
$661$	1.76639	−	1.76639i	0.0687044	−	0.0687044i	0.740624	+	0.671920i	$0.234530\pi$
$662$	−27.3623	+	20.6888i	−1.06347	+	0.804092i
$663$		−	7.70718i		−	0.299322i
$664$	14.0959	+	36.1931i	0.547028	+	1.40456i
$665$			15.7696i			0.611519i
$666$	0.344608	+	0.455768i	0.0133533	+	0.0176607i
$667$	−59.2154	+	59.2154i	−2.29283	+	2.29283i
$668$	−2.17616	+	7.68329i	−0.0841983	+	0.297275i
$669$	−16.9107	−	16.9107i	−0.653804	−	0.653804i
$670$	5.65999	+	0.786088i	0.218665	+	0.0303692i
$671$	−9.40218			−0.362967
$672$	23.0487	−	2.20524i	0.889123	−	0.0850690i
$673$	39.1888			1.51062			0.755308	−	0.655370i	$-0.227487\pi$
$673$	39.1888			1.51062			0.755308	+	0.655370i	$0.227487\pi$
$674$	43.1442	+	5.99209i	1.66185	+	0.230807i
$675$	6.49749	+	6.49749i	0.250088	+	0.250088i
$676$	−0.545027	+	1.92430i	−0.0209626	+	0.0740117i
$677$	−13.8583	+	13.8583i	−0.532616	+	0.532616i	−0.921350	−	0.388734i	$-0.872913\pi$
$677$	−13.8583	+	13.8583i	−0.532616	+	0.532616i	0.388734	+	0.921350i	$0.372913\pi$
$678$	9.94139	+	13.1482i	0.381797	+	0.504953i
$679$			31.3879i			1.20456i
$680$	29.1338	−	11.3466i	1.11723	−	0.435122i
$681$			0.997953i			0.0382416i
$682$	−22.7098	+	17.1710i	−0.869605	+	0.657511i
$683$	−8.54143	+	8.54143i	−0.326829	+	0.326829i	−0.851379	−	0.524550i	$-0.824233\pi$
$683$	−8.54143	+	8.54143i	−0.326829	+	0.326829i	0.524550	+	0.851379i	$0.324233\pi$
$684$	6.42582	−	3.58922i	0.245697	−	0.137237i
$685$	25.6595	+	25.6595i	0.980399	+	0.980399i
$686$	2.32140	−	16.7145i	0.0886313	−	0.638163i
$687$	−26.9896			−1.02972
$688$	0.229343	−	0.0545196i	0.00874360	−	0.00207854i
$689$	−9.02271			−0.343738
$690$	−3.94529	+	28.4069i	−0.150195	+	1.08143i
$691$	−5.55830	−	5.55830i	−0.211448	−	0.211448i	0.593435	−	0.804882i	$-0.297772\pi$
$691$	−5.55830	−	5.55830i	−0.211448	−	0.211448i	−0.804882	+	0.593435i	$0.797772\pi$
$692$	17.3026	+	30.9770i	0.657747	+	1.17757i
$693$	11.9528	−	11.9528i	0.454050	−	0.454050i
$694$	35.3864	−	26.7558i	1.34325	−	1.01564i
$695$		−	20.2367i		−	0.767621i
$696$	14.0241	−	31.9163i	0.531583	−	1.20978i
$697$		−	56.1277i		−	2.12599i
$698$	18.9960	+	25.1236i	0.719010	+	0.950942i
$699$	21.6239	−	21.6239i	0.817890	−	0.817890i
$700$	10.1605	+	2.87778i	0.384029	+	0.108770i
$701$	−30.3550	−	30.3550i	−1.14649	−	1.14649i	−0.987238	−	0.159253i	$-0.949091\pi$
$701$	−30.3550	−	30.3550i	−1.14649	−	1.14649i	−0.159253	−	0.987238i	$-0.550909\pi$
$702$	7.81523	+	1.08542i	0.294967	+	0.0409665i
$703$	−0.792213			−0.0298789
$704$	−30.7616	−	1.31170i	−1.15937	−	0.0494366i
$705$	−5.06595			−0.190795
$706$	39.3941	+	5.47125i	1.48262	+	0.205913i
$707$	15.2444	+	15.2444i	0.573325	+	0.573325i
$708$	11.7713	+	3.33401i	0.442391	+	0.125300i
$709$	−33.0689	+	33.0689i	−1.24193	+	1.24193i	−0.282730	+	0.959199i	$0.591240\pi$
$709$	−33.0689	+	33.0689i	−1.24193	+	1.24193i	−0.959199	+	0.282730i	$0.908760\pi$
$710$	−15.2097	−	20.1159i	−0.570809	−	0.754935i
$711$			7.28074i			0.273049i
$712$	6.76566	−	15.3974i	0.253554	−	0.577042i
$713$		−	45.3747i		−	1.69929i
$714$	−27.8729	+	21.0748i	−1.04312	+	0.788703i
$715$	4.98330	−	4.98330i	0.186365	−	0.186365i
$716$	−9.05518	−	16.2116i	−0.338408	−	0.605854i
$717$	1.34640	+	1.34640i	0.0502824	+	0.0502824i
$718$	0.567090	−	4.08317i	0.0211636	−	0.152382i
$719$	−24.1360			−0.900121			−0.450060	−	0.892998i	$-0.648598\pi$
$719$	−24.1360			−0.900121			−0.450060	+	0.892998i	$0.648598\pi$
$720$	2.32074	+	9.76246i	0.0864891	+	0.363825i
$721$	−9.26017			−0.344867
$722$	2.29254	−	16.5067i	0.0853194	−	0.614317i
$723$	−0.0875736	−	0.0875736i	−0.00325690	−	0.00325690i
$724$	17.0656	−	9.53221i	0.634238	−	0.354262i
$725$	11.2428	−	11.2428i	0.417549	−	0.417549i
$726$	5.49068	−	4.15152i	0.203778	−	0.154078i
$727$		−	25.4413i		−	0.943564i	−0.881715	−	0.471782i	$-0.843611\pi$
$727$		−	25.4413i		−	0.943564i	0.881715	−	0.471782i	$-0.156389\pi$
$728$	8.44955	−	3.29080i	0.313161	−	0.121965i
$729$		−	25.4974i		−	0.944347i
$730$	−9.50724	−	12.5740i	−0.351879	−	0.465385i
$731$	−0.251563	+	0.251563i	−0.00930440	+	0.00930440i
$732$	−1.69992	+	6.00184i	−0.0628309	+	0.221835i
$733$	1.11861	+	1.11861i	0.0413170	+	0.0413170i	0.727463	−	0.686146i	$-0.240699\pi$
$733$	1.11861	+	1.11861i	0.0413170	+	0.0413170i	−0.686146	+	0.727463i	$0.740699\pi$
$734$	−8.82338	−	1.22544i	−0.325677	−	0.0452317i
$735$	7.66350			0.282673
$736$	31.2355	−	37.8449i	1.15135	−	1.39498i
$737$	8.49266			0.312831
$738$	17.8427	+	2.47809i	0.656800	+	0.0912196i
$739$	27.9487	+	27.9487i	1.02811	+	1.02811i	0.999593	+	0.0285153i	$0.00907792\pi$
$739$	27.9487	+	27.9487i	1.02811	+	1.02811i	0.0285153	+	0.999593i	$0.490922\pi$
$740$	0.294328	−	1.03917i	0.0108197	−	0.0382008i
$741$	−2.42508	+	2.42508i	−0.0890877	+	0.0890877i
$742$	24.6720	+	32.6305i	0.905738	+	1.19790i
$743$		−	6.84243i		−	0.251024i	−0.992092	−	0.125512i	$-0.959943\pi$
$743$		−	6.84243i		−	0.251024i	0.992092	−	0.125512i	$-0.0400574\pi$
$744$	6.85507	+	17.6013i	0.251319	+	0.645293i
$745$			17.7682i			0.650977i
$746$	−20.3812	+	15.4103i	−0.746208	+	0.564211i
$747$	13.3030	−	13.3030i	0.486731	−	0.486731i
$748$	40.5674	−	22.6595i	1.48329	−	0.828512i
$749$	−11.8874	−	11.8874i	−0.434358	−	0.434358i
$750$	3.02315	−	21.7673i	0.110390	−	0.794828i
$751$	−23.3074			−0.850500			−0.425250	−	0.905076i	$-0.639814\pi$
$751$	−23.3074			−0.850500			−0.425250	+	0.905076i	$0.639814\pi$
$752$	7.38037	+	4.54536i	0.269134	+	0.165752i
$753$	13.2346			0.482297
$754$	1.87814	−	13.5230i	0.0683979	−	0.492478i
$755$	15.5379	+	15.5379i	0.565481	+	0.565481i
$756$	−17.4448	−	31.2316i	−0.634463	−	1.13588i
$757$	10.0617	−	10.0617i	0.365700	−	0.365700i	−0.500206	−	0.865906i	$-0.666742\pi$
$757$	10.0617	−	10.0617i	0.365700	−	0.365700i	0.865906	+	0.500206i	$0.166742\pi$
$758$	−28.4827	+	21.5359i	−1.03454	+	0.782218i
$759$			42.6237i			1.54714i
$760$	−12.7373	−	5.59680i	−0.462030	−	0.203017i
$761$			10.4743i			0.379695i	0.981814	+	0.189847i	$0.0607993\pi$
$761$			10.4743i			0.379695i	−0.981814	+	0.189847i	$0.939201\pi$
$762$	13.8402	+	18.3046i	0.501378	+	0.663107i
$763$	8.86519	−	8.86519i	0.320941	−	0.320941i
$764$	−21.6612	−	6.13517i	−0.783675	−	0.221963i
$765$	−10.7083	−	10.7083i	−0.387160	−	0.387160i
$766$	12.8988	+	1.79145i	0.466054	+	0.0647279i
$767$	4.79131			0.173004
$768$	−6.39903	+	19.3994i	−0.230905	+	0.700014i
$769$	39.4816			1.42374			0.711871	−	0.702310i	$-0.247848\pi$
$769$	39.4816			1.42374			0.711871	+	0.702310i	$0.247848\pi$
$770$	−31.6485	−	4.39550i	−1.14053	−	0.158403i
$771$	26.0928	+	26.0928i	0.939711	+	0.939711i
$772$	−4.89945	−	1.38769i	−0.176335	−	0.0499440i
$773$	22.4954	−	22.4954i	0.809104	−	0.809104i	−0.175394	−	0.984498i	$-0.556120\pi$
$773$	22.4954	−	22.4954i	0.809104	−	0.809104i	0.984498	+	0.175394i	$0.0561199\pi$
$774$	−0.0688639	−	0.0910773i	−0.00247526	−	0.00327371i
$775$			8.61499i			0.309460i
$776$	−25.3524	−	11.1399i	−0.910097	−	0.399899i
$777$			1.20711i			0.0433047i
$778$	−30.6128	+	23.1464i	−1.09752	+	0.829839i
$779$	−17.6607	+	17.6607i	−0.632762	+	0.632762i
$780$	−2.28008	−	4.08205i	−0.0816400	−	0.146161i
$781$	−26.5025	−	26.5025i	−0.948334	−	0.948334i
$782$	−10.1874	+	73.3517i	−0.364302	+	2.62305i
$783$	−53.8619			−1.92487
$784$	−11.1646	−	6.87599i	−0.398737	−	0.245571i
$785$	−4.69274			−0.167491
$786$	−2.24606	+	16.1721i	−0.0801143	+	0.576839i
$787$	16.2640	+	16.2640i	0.579750	+	0.579750i	0.934834	−	0.355085i	$-0.115548\pi$
$787$	16.2640	+	16.2640i	0.579750	+	0.579750i	−0.355085	+	0.934834i	$0.615548\pi$
$788$	10.6191	−	5.93141i	0.378288	−	0.211298i
$789$	−15.7342	+	15.7342i	−0.560152	+	0.560152i
$790$	10.9776	−	8.30022i	0.390566	−	0.295308i
$791$		−	29.2681i		−	1.04065i
$792$	5.41224	+	13.8966i	0.192316	+	0.493795i
$793$			2.44296i			0.0867520i
$794$	−18.3367	−	24.2516i	−0.650747	−	0.860658i
$795$	14.9154	−	14.9154i	0.528996	−	0.528996i
$796$	14.3279	−	50.5870i	0.507840	−	1.79301i
$797$	27.5649	+	27.5649i	0.976398	+	0.976398i	0.999728	−	0.0233299i	$-0.00742683\pi$
$797$	27.5649	+	27.5649i	0.976398	+	0.976398i	−0.0233299	+	0.999728i	$0.507427\pi$
$798$	15.4015	+	2.13904i	0.545207	+	0.0757211i
$799$	−13.0812			−0.462779
$800$	−5.93047	+	7.18536i	−0.209674	+	0.254041i
$801$	−8.14617			−0.287831
$802$	−25.4639	−	3.53656i	−0.899163	−	0.124880i
$803$	−16.5661	−	16.5661i	−0.584606	−	0.584606i
$804$	1.53548	−	5.42125i	0.0541522	−	0.191193i
$805$	36.0083	−	36.0083i	1.26913	−	1.26913i
$806$	4.46152	+	5.90067i	0.157150	+	0.207842i
$807$		−	21.7139i		−	0.764365i
$808$	−17.7235	+	6.90268i	−0.623510	+	0.242835i
$809$		−	5.17865i		−	0.182072i	−0.995848	−	0.0910358i	$-0.970982\pi$
$809$		−	5.17865i		−	0.182072i	0.995848	−	0.0910358i	$-0.0290178\pi$
$810$	−6.22403	+	4.70601i	−0.218690	+	0.165352i
$811$	−32.6428	+	32.6428i	−1.14625	+	1.14625i	−0.158960	+	0.987285i	$0.550814\pi$
$811$	−32.6428	+	32.6428i	−1.14625	+	1.14625i	−0.987285	+	0.158960i	$0.949186\pi$
$812$	−54.0413	+	30.1855i	−1.89648	+	1.05930i
$813$	1.62030	+	1.62030i	0.0568264	+	0.0568264i
$814$	0.220816	−	1.58992i	0.00773958	−	0.0557266i
$815$	35.9401			1.25893
$816$	−7.12995	−	29.9929i	−0.249598	−	1.04996i
$817$	0.158310			0.00553857
$818$	−1.02999	+	7.41616i	−0.0360129	+	0.259300i
$819$	−3.10569	−	3.10569i	−0.108521	−	0.108521i
$820$	−16.6048	−	29.7276i	−0.579864	−	1.03813i
$821$	12.1496	−	12.1496i	0.424025	−	0.424025i	−0.462562	−	0.886587i	$-0.653070\pi$
$821$	12.1496	−	12.1496i	0.424025	−	0.424025i	0.886587	+	0.462562i	$0.153070\pi$
$822$	28.5411	−	21.5800i	0.995484	−	0.752689i
$823$		−	27.6976i		−	0.965476i	−0.875765	−	0.482738i	$-0.839642\pi$
$823$		−	27.6976i		−	0.965476i	0.875765	−	0.482738i	$-0.160358\pi$
$824$	3.28653	−	7.47954i	0.114492	−	0.260562i
$825$		−	8.09269i		−	0.281751i
$826$	−13.1015	−	17.3277i	−0.455860	−	0.602907i
$827$	−21.8635	+	21.8635i	−0.760269	+	0.760269i	−0.976371	−	0.216102i	$-0.930666\pi$
$827$	−21.8635	+	21.8635i	−0.760269	+	0.760269i	0.216102	+	0.976371i	$0.430666\pi$
$828$	−22.8683	−	6.47707i	−0.794730	−	0.225094i
$829$	14.7756	+	14.7756i	0.513178	+	0.513178i	0.915499	−	0.402320i	$-0.131796\pi$
$829$	14.7756	+	14.7756i	0.513178	+	0.513178i	−0.402320	+	0.915499i	$0.631796\pi$
$830$	−35.2235	−	4.89201i	−1.22262	−	0.169804i
$831$	−2.36561			−0.0820622
$832$	−0.340818	+	7.99274i	−0.0118157	+	0.277098i
$833$	19.7885			0.685632
$834$	−19.7643	−	2.74497i	−0.684382	−	0.0950504i
$835$	−5.16984	−	5.16984i	−0.178910	−	0.178910i
$836$	−19.8945	−	5.63479i	−0.688066	−	0.194883i
$837$	20.6362	−	20.6362i	0.713293	−	0.713293i
$838$	−2.33367	−	3.08644i	−0.0806152	−	0.106619i
$839$		−	0.625398i		−	0.0215912i	−0.999942	−	0.0107956i	$-0.996564\pi$
$839$		−	0.625398i		−	0.0215912i	0.999942	−	0.0107956i	$-0.00343641\pi$
$840$	−8.52792	+	19.4080i	−0.294241	+	0.669639i
$841$			64.1994i			2.21377i
$842$	−12.3688	+	9.35210i	−0.426257	+	0.322295i
$843$	−24.2308	+	24.2308i	−0.834554	+	0.834554i
$844$	−10.3720	−	18.5692i	−0.357021	−	0.639177i
$845$	−1.29480	−	1.29480i	−0.0445426	−	0.0445426i
$846$	0.577546	−	4.15844i	0.0198564	−	0.142970i
$847$	−12.2224			−0.419965
$848$	−35.1124	+	8.34696i	−1.20576	+	0.286636i
$849$	2.71421			0.0931516
$850$	1.93422	−	13.9268i	0.0663433	−	0.477685i
$851$	1.80894	+	1.80894i	0.0620096	+	0.0620096i
$852$	−21.7094	+	12.1261i	−0.743753	+	0.415433i
$853$	14.2267	−	14.2267i	0.487114	−	0.487114i	−0.420280	−	0.907394i	$-0.638068\pi$
$853$	14.2267	−	14.2267i	0.487114	−	0.487114i	0.907394	+	0.420280i	$0.138068\pi$
$854$	8.83491	−	6.68011i	0.302324	−	0.228589i
$855$			6.73881i			0.230462i
$856$	13.8206	−	5.38264i	0.472379	−	0.183975i
$857$			36.8671i			1.25936i	0.776857	+	0.629678i	$0.216813\pi$
$857$			36.8671i			1.25936i	−0.776857	+	0.629678i	$0.783187\pi$
$858$	−4.19103	−	5.54293i	−0.143079	−	0.189232i
$859$	−11.0958	+	11.0958i	−0.378584	+	0.378584i	−0.870591	−	0.492007i	$-0.836263\pi$
$859$	−11.0958	+	11.0958i	−0.378584	+	0.378584i	0.492007	+	0.870591i	$0.336263\pi$
$860$	−0.0588164	+	0.207661i	−0.00200562	+	0.00708117i
$861$	26.9099	+	26.9099i	0.917088	+	0.917088i
$862$	−39.4922	−	5.48488i	−1.34511	−	0.186816i
$863$	5.79818			0.197372			0.0986862	−	0.995119i	$-0.468536\pi$
$863$	5.79818			0.197372			0.0986862	+	0.995119i	$0.468536\pi$
$864$	31.4175	−	3.00595i	1.06885	−	0.102264i
$865$	−32.4858			−1.10455
$866$	−39.9968	−	5.55496i	−1.35915	−	0.188765i
$867$	17.5516	+	17.5516i	0.596085	+	0.596085i
$868$	9.13993	−	32.2700i	0.310230	−	1.09531i
$869$	14.4629	−	14.4629i	0.490621	−	0.490621i
$870$	19.2501	+	25.4596i	0.652640	+	0.863162i
$871$		−	2.20664i		−	0.0747690i
$872$	4.01416	+	10.3069i	0.135937	+	0.349034i
$873$			13.4130i			0.453960i
$874$	26.2858	−	19.8748i	0.889131	−	0.672275i
$875$	−27.5920	+	27.5920i	−0.932778	+	0.932778i
$876$	−13.5701	+	7.57975i	−0.458491	+	0.256096i
$877$	−11.4174	−	11.4174i	−0.385537	−	0.385537i	0.487555	−	0.873092i	$-0.337889\pi$
$877$	−11.4174	−	11.4174i	−0.385537	−	0.385537i	−0.873092	+	0.487555i	$0.837889\pi$
$878$	0.0848783	−	0.611141i	0.00286450	−	0.0206250i
$879$	−8.27382			−0.279069
$880$	14.7827	−	24.0028i	0.498324	−	0.809136i
$881$	21.6667			0.729971			0.364985	−	0.931013i	$-0.381074\pi$
$881$	21.6667			0.729971			0.364985	+	0.931013i	$0.381074\pi$
$882$	−0.873680	+	6.29067i	−0.0294183	+	0.211818i
$883$	3.37331	+	3.37331i	0.113521	+	0.113521i	0.761585	−	0.648064i	$-0.224421\pi$
$883$	3.37331	+	3.37331i	0.113521	+	0.113521i	−0.648064	+	0.761585i	$0.724421\pi$
$884$	−5.88758	−	10.5406i	−0.198021	−	0.354518i
$885$	−7.92050	+	7.92050i	−0.266245	+	0.266245i
$886$	35.8065	−	27.0734i	1.20294	−	0.909549i
$887$			10.0852i			0.338628i	0.985562	+	0.169314i	$0.0541552\pi$
$887$			10.0852i			0.338628i	−0.985562	+	0.169314i	$0.945845\pi$
$888$	−0.974993	−	0.428415i	−0.0327186	−	0.0143767i
$889$		−	40.7465i		−	1.36659i
$890$	9.28683	+	12.2825i	0.311295	+	0.411710i
$891$	−8.20011	+	8.20011i	−0.274714	+	0.274714i
$892$	−36.0457	−	10.2094i	−1.20690	−	0.341834i
$893$	4.11603	+	4.11603i	0.137738	+	0.137738i
$894$	17.3535	+	2.41014i	0.580387	+	0.0806071i
$895$	17.0012			0.568287
$896$	29.8375	−	20.6231i	0.996802	−	0.688968i
$897$	11.0749			0.369779
$898$	2.56407	+	0.356111i	0.0855643	+	0.0118836i
$899$	−35.7077	−	35.7077i	−1.19092	−	1.19092i
$900$	4.34186	+	1.22976i	0.144729	+	0.0409920i
$901$	38.5143	−	38.5143i	1.28310	−	1.28310i
$902$	−30.5213	−	40.3665i	−1.01625	−	1.34406i
$903$		−	0.241219i		−	0.00802727i
$904$	23.6402	+	10.3876i	0.786260	+	0.345485i
$905$			17.8968i			0.594910i
$906$	17.2828	−	13.0676i	0.574182	−	0.434141i
$907$	14.1727	−	14.1727i	0.470597	−	0.470597i	−0.431511	−	0.902108i	$-0.642019\pi$
$907$	14.1727	−	14.1727i	0.470597	−	0.470597i	0.902108	+	0.431511i	$0.142019\pi$
$908$	0.762345	+	1.36483i	0.0252993	+	0.0452936i
$909$	6.51438	+	6.51438i	0.216068	+	0.216068i
$910$	−1.14208	+	8.22319i	−0.0378595	+	0.272596i
$911$	5.12861			0.169919			0.0849593	−	0.996384i	$-0.472924\pi$
$911$	5.12861			0.169919			0.0849593	+	0.996384i	$0.472924\pi$
$912$	−7.19388	+	11.6808i	−0.238213	+	0.386790i
$913$	−52.8518			−1.74914
$914$	3.56529	−	25.6708i	0.117929	−	0.849114i
$915$	−4.03845	−	4.03845i	−0.133507	−	0.133507i
$916$	−36.9118	+	20.6176i	−1.21960	+	0.681224i
$917$	20.4996	−	20.4996i	0.676955	−	0.676955i
$918$	−37.9933	+	28.7269i	−1.25397	+	0.948128i
$919$			1.74928i			0.0577034i	0.999584	+	0.0288517i	$0.00918506\pi$
$919$			1.74928i			0.0577034i	−0.999584	+	0.0288517i	$0.990815\pi$
$920$	16.3046	+	41.8640i	0.537546	+	1.38022i
$921$			24.7930i			0.816956i
$922$	−12.2804	−	16.2417i	−0.404434	−	0.534892i
$923$	−6.88611	+	6.88611i	−0.226659	+	0.226659i
$924$	−8.58581	+	30.3135i	−0.282452	+	0.997242i
$925$	−0.343451	−	0.343451i	−0.0112926	−	0.0112926i
$926$	40.3986	+	5.61076i	1.32758	+	0.184381i
$927$	−3.95714			−0.129969
$928$	−5.20130	−	54.3629i	−0.170741	−	1.78455i
$929$	−28.8593			−0.946844			−0.473422	−	0.880836i	$-0.656981\pi$
$929$	−28.8593			−0.946844			−0.473422	+	0.880836i	$0.656981\pi$
$930$	−17.1297	−	2.37906i	−0.561706	−	0.0780125i
$931$	−6.22652	−	6.22652i	−0.204066	−	0.204066i
$932$	13.0548	−	46.0921i	0.427625	−	1.50980i
$933$	−1.45269	+	1.45269i	−0.0475588	+	0.0475588i
$934$	−13.8030	−	18.2554i	−0.451647	−	0.597335i
$935$			42.5434i			1.39132i
$936$	3.61074	−	1.40626i	0.118021	−	0.0459649i
$937$			12.4959i			0.408223i	0.978948	+	0.204111i	$0.0654304\pi$
$937$			12.4959i			0.408223i	−0.978948	+	0.204111i	$0.934570\pi$
$938$	−7.98026	+	6.03390i	−0.260565	+	0.197014i
$939$	12.9870	−	12.9870i	0.423816	−	0.423816i
$940$	−6.92836	+	3.86992i	−0.225978	+	0.126223i
$941$	−3.93712	−	3.93712i	−0.128347	−	0.128347i	0.640015	−	0.768362i	$-0.278928\pi$
$941$	−3.93712	−	3.93712i	−0.128347	−	0.128347i	−0.768362	+	0.640015i	$0.778928\pi$
$942$	−0.636538	+	4.58320i	−0.0207395	+	0.149329i
$943$	80.6530			2.62642
$944$	18.6456	−	4.43246i	0.606863	−	0.144264i
$945$	32.7529			1.06545
$946$	−0.0441262	+	0.317717i	−0.00143467	+	0.0103299i
$947$	31.9342	+	31.9342i	1.03772	+	1.03772i	0.999260	+	0.0384618i	$0.0122458\pi$
$947$	31.9342	+	31.9342i	1.03772	+	1.03772i	0.0384618	+	0.999260i	$0.487754\pi$
$948$	−6.61743	−	11.8472i	−0.214924	−	0.384781i
$949$	−4.30436	+	4.30436i	−0.139725	+	0.139725i
$950$	−4.99072	+	3.77350i	−0.161920	+	0.122428i
$951$		−	22.4116i		−	0.726745i
$952$	−22.0206	+	50.1148i	−0.713692	+	1.62423i
$953$		−	28.7558i		−	0.931492i	−0.884918	−	0.465746i	$-0.845786\pi$
$953$		−	28.7558i		−	0.931492i	0.884918	−	0.465746i	$-0.154214\pi$
$954$	10.5431	+	13.9439i	0.341344	+	0.451452i
$955$	14.5751	−	14.5751i	0.471640	−	0.471640i
$956$	2.86991	+	0.812855i	0.0928196	+	0.0262896i
$957$	33.5428	+	33.5428i	1.08429	+	1.08429i
$958$	37.7367	+	5.24105i	1.21922	+	0.169331i
$959$	−63.5329			−2.05159
$960$	−12.6494	−	13.7762i	−0.408257	−	0.444625i
$961$	−3.63849			−0.117371
$962$	−0.413106	−	0.0573742i	−0.0133191	−	0.00184982i
$963$	−5.07985	−	5.07985i	−0.163696	−	0.163696i
$964$	−0.186667	−	0.0528702i	−0.00601213	−	0.00170284i
$965$	3.29669	−	3.29669i	0.106124	−	0.106124i
$966$	−30.2835	−	40.0521i	−0.974356	−	1.28865i
$967$			5.77351i			0.185664i	0.995682	+	0.0928318i	$0.0295919\pi$
$967$			5.77351i			0.185664i	−0.995682	+	0.0928318i	$0.970408\pi$
$968$	4.33785	−	9.87214i	0.139424	−	0.317302i
$969$		−	20.7034i		−	0.665090i
$970$	20.2236	−	15.2911i	0.649339	−	0.490968i
$971$	−17.9091	+	17.9091i	−0.574729	+	0.574729i	−0.933446	−	0.358717i	$-0.883214\pi$
$971$	−17.9091	+	17.9091i	−0.574729	+	0.574729i	0.358717	+	0.933446i	$0.383214\pi$
$972$	−12.5723	−	22.5084i	−0.403258	−	0.721956i
$973$	25.0530	+	25.0530i	0.803163	+	0.803163i
$974$	2.02575	−	14.5858i	0.0649091	−	0.467358i
$975$	−2.10271			−0.0673407
$976$	2.25999	+	9.50690i	0.0723406	+	0.304308i
$977$	−3.82926			−0.122509			−0.0612544	−	0.998122i	$-0.519510\pi$
$977$	−3.82926			−0.122509			−0.0612544	+	0.998122i	$0.519510\pi$
$978$	4.87503	−	35.1012i	0.155886	−	1.12241i
$979$	16.1821	+	16.1821i	0.517181	+	0.517181i
$980$	10.4809	−	5.85422i	0.334799	−	0.187006i
$981$	3.78835	−	3.78835i	0.120953	−	0.120953i
$982$	5.30949	−	4.01453i	0.169433	−	0.128109i
$983$		−	42.4136i		−	1.35279i	−0.736541	−	0.676393i	$-0.763542\pi$
$983$		−	42.4136i		−	1.35279i	0.736541	−	0.676393i	$-0.236458\pi$
$984$	−31.2861	+	12.1848i	−0.997363	+	0.388438i
$985$			11.1363i			0.354832i
$986$	49.7072	+	65.7412i	1.58300	+	2.09363i
$987$	6.27166	−	6.27166i	0.199629	−	0.199629i
$988$	−1.46408	+	5.16916i	−0.0465786	+	0.164453i
$989$	−0.361485	−	0.361485i	−0.0114946	−	0.0114946i
$990$	−13.5243	−	1.87833i	−0.429831	−	0.0596971i
$991$	59.1239			1.87813			0.939066	−	0.343736i	$-0.111693\pi$
$991$	59.1239			1.87813			0.939066	+	0.343736i	$0.111693\pi$
$992$	22.8210	+	18.8354i	0.724566	+	0.598024i
$993$	−30.9683			−0.982749
$994$	43.7331	+	6.07387i	1.38713	+	0.192651i
$995$	34.0384	+	34.0384i	1.07909	+	1.07909i
$996$	−9.55565	+	33.7377i	−0.302782	+	1.06902i
$997$	−35.9832	+	35.9832i	−1.13960	+	1.13960i	−0.151079	+	0.988522i	$0.548275\pi$
$997$	−35.9832	+	35.9832i	−1.13960	+	1.13960i	−0.988522	+	0.151079i	$0.951725\pi$
$998$	15.3242	+	20.2673i	0.485078	+	0.641549i
$999$			1.64540i			0.0520581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.24	yes	48
4.3	odd	2		832.2.n.a.209.8		48
8.3	odd	2		1664.2.n.a.417.17		48
8.5	even	2		1664.2.n.b.417.8		48
16.3	odd	4		1664.2.n.a.1249.17		48
16.5	even	4	inner	208.2.n.a.53.24	✓	48
16.11	odd	4		832.2.n.a.625.8		48
16.13	even	4		1664.2.n.b.1249.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.24	✓	48	16.5	even	4	inner
208.2.n.a.157.24	yes	48	1.1	even	1	trivial
832.2.n.a.209.8		48	4.3	odd	2
832.2.n.a.625.8		48	16.11	odd	4
1664.2.n.a.417.17		48	8.3	odd	2
1664.2.n.a.1249.17		48	16.3	odd	4
1664.2.n.b.417.8		48	8.5	even	2
1664.2.n.b.1249.8		48	16.13	even	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40077 + 0.194546i) q^{2} +(0.902776 + 0.902776i) q^{3} +(1.92430 + 0.545027i) q^{4} +(-1.29480 + 1.29480i) q^{5} +(1.08895 + 1.44021i) q^{6} -3.20594i q^{7} +(2.58947 + 1.13782i) q^{8} -1.36999i q^{9} +O(q^{10})\)	\(q+(1.40077 + 0.194546i) q^{2} +(0.902776 + 0.902776i) q^{3} +(1.92430 + 0.545027i) q^{4} +(-1.29480 + 1.29480i) q^{5} +(1.08895 + 1.44021i) q^{6} -3.20594i q^{7} +(2.58947 + 1.13782i) q^{8} -1.36999i q^{9} +(-2.06562 + 1.56182i) q^{10} +(-2.72143 + 2.72143i) q^{11} +(1.24518 + 2.22925i) q^{12} +(0.707107 + 0.707107i) q^{13} +(0.623701 - 4.49078i) q^{14} -2.33784 q^{15} +(3.40589 + 2.09760i) q^{16} -6.03671 q^{17} +(0.266526 - 1.91904i) q^{18} +(1.89947 + 1.89947i) q^{19} +(-3.19730 + 1.78589i) q^{20} +(2.89424 - 2.89424i) q^{21} +(-4.34154 + 3.28266i) q^{22} -8.67448i q^{23} +(1.31051 + 3.36491i) q^{24} +1.64697i q^{25} +(0.852928 + 1.12806i) q^{26} +(3.94512 - 3.94512i) q^{27} +(1.74732 - 6.16920i) q^{28} +(-6.82640 - 6.82640i) q^{29} +(-3.27477 - 0.454816i) q^{30} +5.23082 q^{31} +(4.36279 + 3.60085i) q^{32} -4.91369 q^{33} +(-8.45603 - 1.17442i) q^{34} +(4.15106 + 4.15106i) q^{35} +(0.746682 - 2.63628i) q^{36} +(-0.208536 + 0.208536i) q^{37} +(2.29118 + 3.03025i) q^{38} +1.27672i q^{39} +(-4.82611 + 1.87960i) q^{40} +9.29774i q^{41} +(4.61723 - 3.49110i) q^{42} +(0.0416722 - 0.0416722i) q^{43} +(-6.72012 + 3.75361i) q^{44} +(1.77387 + 1.77387i) q^{45} +(1.68758 - 12.1509i) q^{46} +2.16694 q^{47} +(1.18110 + 4.96842i) q^{48} -3.27803 q^{49} +(-0.320410 + 2.30702i) q^{50} +(-5.44980 - 5.44980i) q^{51} +(0.975296 + 1.74608i) q^{52} +(-6.38002 + 6.38002i) q^{53} +(6.29371 - 4.75870i) q^{54} -7.04745i q^{55} +(3.64778 - 8.30168i) q^{56} +3.42959i q^{57} +(-8.23415 - 10.8902i) q^{58} +(3.38796 - 3.38796i) q^{59} +(-4.49871 - 1.27418i) q^{60} +(1.72743 + 1.72743i) q^{61} +(7.32717 + 1.01763i) q^{62} -4.39210 q^{63} +(5.41072 + 5.89271i) q^{64} -1.83113 q^{65} +(-6.88295 - 0.955938i) q^{66} +(-1.56033 - 1.56033i) q^{67} +(-11.6165 - 3.29017i) q^{68} +(7.83111 - 7.83111i) q^{69} +(5.00710 + 6.62224i) q^{70} +9.73843i q^{71} +(1.55880 - 3.54755i) q^{72} +6.08728i q^{73} +(-0.332680 + 0.251540i) q^{74} +(-1.48684 + 1.48684i) q^{75} +(2.61989 + 4.69041i) q^{76} +(8.72475 + 8.72475i) q^{77} +(-0.248380 + 1.78839i) q^{78} -5.31445 q^{79} +(-7.12593 + 1.69399i) q^{80} +3.01316 q^{81} +(-1.80884 + 13.0240i) q^{82} +(9.71028 + 9.71028i) q^{83} +(7.14685 - 3.99196i) q^{84} +(7.81635 - 7.81635i) q^{85} +(0.0664803 - 0.0502660i) q^{86} -12.3254i q^{87} +(-10.1436 + 3.95057i) q^{88} -5.94615i q^{89} +(2.13968 + 2.82988i) q^{90} +(2.26694 - 2.26694i) q^{91} +(4.72783 - 16.6923i) q^{92} +(4.72226 + 4.72226i) q^{93} +(3.03538 + 0.421569i) q^{94} -4.91887 q^{95} +(0.687861 + 7.18938i) q^{96} -9.79055 q^{97} +(-4.59177 - 0.637727i) q^{98} +(3.72834 + 3.72834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 4 * q^4 - 12 * q^8	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

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