LMFDB - Embedded newform 338.3.d.g.239.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(99,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.2
Root			$-4.71318 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.239
Dual form			338.3.d.g.99.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -3.84716 q^{3} -2.00000i q^{4} +(3.77418 - 3.77418i) q^{5} +(-3.84716 + 3.84716i) q^{6} +(7.25532 + 7.25532i) q^{7} +(-2.00000 - 2.00000i) q^{8} +5.80063 q^{9} -7.54837i q^{10} +(7.40816 + 7.40816i) q^{11} +7.69432i q^{12} +14.5106 q^{14} +(-14.5199 + 14.5199i) q^{15} -4.00000 q^{16} -4.88811i q^{17} +(5.80063 - 5.80063i) q^{18} +(18.6785 - 18.6785i) q^{19} +(-7.54837 - 7.54837i) q^{20} +(-27.9124 - 27.9124i) q^{21} +14.8163 q^{22} -19.9590i q^{23} +(7.69432 + 7.69432i) q^{24} -3.48892i q^{25} +12.3085 q^{27} +(14.5106 - 14.5106i) q^{28} +14.3044 q^{29} +29.0398i q^{30} +(19.0056 - 19.0056i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-28.5004 - 28.5004i) q^{33} +(-4.88811 - 4.88811i) q^{34} +54.7658 q^{35} -11.6013i q^{36} +(-42.9072 - 42.9072i) q^{37} -37.3569i q^{38} -15.0967 q^{40} +(3.54099 - 3.54099i) q^{41} -55.8247 q^{42} +11.9728i q^{43} +(14.8163 - 14.8163i) q^{44} +(21.8926 - 21.8926i) q^{45} +(-19.9590 - 19.9590i) q^{46} +(-7.59168 - 7.59168i) q^{47} +15.3886 q^{48} +56.2792i q^{49} +(-3.48892 - 3.48892i) q^{50} +18.8053i q^{51} +77.0450 q^{53} +(12.3085 - 12.3085i) q^{54} +55.9195 q^{55} -29.0213i q^{56} +(-71.8590 + 71.8590i) q^{57} +(14.3044 - 14.3044i) q^{58} +(44.4819 + 44.4819i) q^{59} +(29.0398 + 29.0398i) q^{60} -56.2764 q^{61} -38.0112i q^{62} +(42.0854 + 42.0854i) q^{63} +8.00000i q^{64} -57.0007 q^{66} +(-4.32207 + 4.32207i) q^{67} -9.77622 q^{68} +76.7856i q^{69} +(54.7658 - 54.7658i) q^{70} +(-40.4291 + 40.4291i) q^{71} +(-11.6013 - 11.6013i) q^{72} +(12.7990 + 12.7990i) q^{73} -85.8143 q^{74} +13.4224i q^{75} +(-37.3569 - 37.3569i) q^{76} +107.497i q^{77} +7.98532 q^{79} +(-15.0967 + 15.0967i) q^{80} -99.5584 q^{81} -7.08199i q^{82} +(-35.8343 + 35.8343i) q^{83} +(-55.8247 + 55.8247i) q^{84} +(-18.4486 - 18.4486i) q^{85} +(11.9728 + 11.9728i) q^{86} -55.0312 q^{87} -29.6326i q^{88} +(57.2867 + 57.2867i) q^{89} -43.7853i q^{90} -39.9181 q^{92} +(-73.1175 + 73.1175i) q^{93} -15.1834 q^{94} -140.992i q^{95} +(15.3886 - 15.3886i) q^{96} +(-38.7928 + 38.7928i) q^{97} +(56.2792 + 56.2792i) q^{98} +(42.9720 + 42.9720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} + 84 q^{9} + 42 q^{11} + 20 q^{14} + 60 q^{15} - 32 q^{16} + 84 q^{18} + 22 q^{19} - 12 q^{20} - 102 q^{21} + 84 q^{22} + 72 q^{27} + 20 q^{28} + 12 q^{29}+ \cdots + 252 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 + 84 * q^9 + 42 * q^11 + 20 * q^14 + 60 * q^15 - 32 * q^16 + 84 * q^18 + 22 * q^19 - 12 * q^20 - 102 * q^21 + 84 * q^22 + 72 * q^27 + 20 * q^28 + 12 * q^29 + 32 * q^31 - 32 * q^32 + 54 * q^33 - 60 * q^34 + 156 * q^35 + 32 * q^37 - 24 * q^40 - 12 * q^41 - 204 * q^42 + 84 * q^44 - 102 * q^45 - 108 * q^46 + 60 * q^47 - 88 * q^50 - 132 * q^53 + 72 * q^54 + 324 * q^55 - 294 * q^57 + 12 * q^58 + 234 * q^59 - 120 * q^60 - 72 * q^61 - 156 * q^63 + 108 * q^66 - 14 * q^67 - 120 * q^68 + 156 * q^70 + 162 * q^71 - 168 * q^72 + 166 * q^73 + 64 * q^74 - 44 * q^76 - 96 * q^79 - 24 * q^80 + 24 * q^81 - 240 * q^83 - 204 * q^84 - 234 * q^85 + 132 * q^86 - 720 * q^87 + 210 * q^89 - 216 * q^92 - 444 * q^93 + 120 * q^94 + 146 * q^97 - 16 * q^98 + 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	−3.84716			−1.28239			−0.641193	−	0.767380i	$-0.721560\pi$
$3$	−3.84716			−1.28239			−0.641193	+	0.767380i	$0.721560\pi$
$4$		−	2.00000i		−	0.500000i
$5$	3.77418	−	3.77418i	0.754837	−	0.754837i	−0.220541	−	0.975378i	$-0.570782\pi$
$5$	3.77418	−	3.77418i	0.754837	−	0.754837i	0.975378	+	0.220541i	$0.0707823\pi$
$6$	−3.84716	+	3.84716i	−0.641193	+	0.641193i
$7$	7.25532	+	7.25532i	1.03647	+	1.03647i	0.999309	+	0.0371646i	$0.0118326\pi$
$7$	7.25532	+	7.25532i	1.03647	+	1.03647i	0.0371646	+	0.999309i	$0.488167\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	5.80063			0.644514
$10$		−	7.54837i		−	0.754837i
$11$	7.40816	+	7.40816i	0.673469	+	0.673469i	0.958514	−	0.285045i	$-0.0920086\pi$
$11$	7.40816	+	7.40816i	0.673469	+	0.673469i	−0.285045	+	0.958514i	$0.592009\pi$
$12$			7.69432i			0.641193i
$13$		0			0
$13$		0			0
$14$	14.5106			1.03647
$15$	−14.5199	+	14.5199i	−0.967992	+	0.967992i
$16$	−4.00000			−0.250000
$17$		−	4.88811i		−	0.287536i	−0.989611	−	0.143768i	$-0.954078\pi$
$17$		−	4.88811i		−	0.287536i	0.989611	−	0.143768i	$-0.0459219\pi$
$18$	5.80063	−	5.80063i	0.322257	−	0.322257i
$19$	18.6785	−	18.6785i	0.983077	−	0.983077i	−0.0167821	−	0.999859i	$-0.505342\pi$
$19$	18.6785	−	18.6785i	0.983077	−	0.983077i	0.999859	+	0.0167821i	$0.00534217\pi$
$20$	−7.54837	−	7.54837i	−0.377418	−	0.377418i
$21$	−27.9124	−	27.9124i	−1.32916	−	1.32916i
$22$	14.8163			0.673469
$23$		−	19.9590i		−	0.867785i	−0.900965	−	0.433892i	$-0.857140\pi$
$23$		−	19.9590i		−	0.867785i	0.900965	−	0.433892i	$-0.142860\pi$
$24$	7.69432	+	7.69432i	0.320597	+	0.320597i
$25$		−	3.48892i		−	0.139557i
$26$		0			0
$27$	12.3085			0.455870
$28$	14.5106	−	14.5106i	0.518237	−	0.518237i
$29$	14.3044			0.493254			0.246627	−	0.969110i	$-0.420678\pi$
$29$	14.3044			0.493254			0.246627	+	0.969110i	$0.420678\pi$
$30$			29.0398i			0.967992i
$31$	19.0056	−	19.0056i	0.613083	−	0.613083i	−0.330665	−	0.943748i	$-0.607273\pi$
$31$	19.0056	−	19.0056i	0.613083	−	0.613083i	0.943748	+	0.330665i	$0.107273\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−28.5004	−	28.5004i	−0.863647	−	0.863647i
$34$	−4.88811	−	4.88811i	−0.143768	−	0.143768i
$35$	54.7658			1.56474
$36$		−	11.6013i		−	0.322257i
$37$	−42.9072	−	42.9072i	−1.15965	−	1.15965i	−0.984550	−	0.175103i	$-0.943974\pi$
$37$	−42.9072	−	42.9072i	−1.15965	−	1.15965i	−0.175103	−	0.984550i	$-0.556026\pi$
$38$		−	37.3569i		−	0.983077i
$39$		0			0
$40$	−15.0967			−0.377418
$41$	3.54099	−	3.54099i	0.0863657	−	0.0863657i	−0.662604	−	0.748970i	$-0.730549\pi$
$41$	3.54099	−	3.54099i	0.0863657	−	0.0863657i	0.748970	+	0.662604i	$0.230549\pi$
$42$	−55.8247			−1.32916
$43$			11.9728i			0.278438i	0.990262	+	0.139219i	$0.0444592\pi$
$43$			11.9728i			0.278438i	−0.990262	+	0.139219i	$0.955541\pi$
$44$	14.8163	−	14.8163i	0.336734	−	0.336734i
$45$	21.8926	−	21.8926i	0.486503	−	0.486503i
$46$	−19.9590	−	19.9590i	−0.433892	−	0.433892i
$47$	−7.59168	−	7.59168i	−0.161525	−	0.161525i	0.621717	−	0.783242i	$-0.286435\pi$
$47$	−7.59168	−	7.59168i	−0.161525	−	0.161525i	−0.783242	+	0.621717i	$0.786435\pi$
$48$	15.3886			0.320597
$49$			56.2792i			1.14856i
$50$	−3.48892	−	3.48892i	−0.0697783	−	0.0697783i
$51$			18.8053i			0.368732i
$52$		0			0
$53$	77.0450			1.45368			0.726840	−	0.686807i	$-0.240988\pi$
$53$	77.0450			1.45368			0.726840	+	0.686807i	$0.240988\pi$
$54$	12.3085	−	12.3085i	0.227935	−	0.227935i
$55$	55.9195			1.01672
$56$		−	29.0213i		−	0.518237i
$57$	−71.8590	+	71.8590i	−1.26068	+	1.26068i
$58$	14.3044	−	14.3044i	0.246627	−	0.246627i
$59$	44.4819	+	44.4819i	0.753930	+	0.753930i	0.975210	−	0.221280i	$-0.0710236\pi$
$59$	44.4819	+	44.4819i	0.753930	+	0.753930i	−0.221280	+	0.975210i	$0.571024\pi$
$60$	29.0398	+	29.0398i	0.483996	+	0.483996i
$61$	−56.2764			−0.922564			−0.461282	−	0.887254i	$-0.652610\pi$
$61$	−56.2764			−0.922564			−0.461282	+	0.887254i	$0.652610\pi$
$62$		−	38.0112i		−	0.613083i
$63$	42.0854	+	42.0854i	0.668022	+	0.668022i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−57.0007			−0.863647
$67$	−4.32207	+	4.32207i	−0.0645085	+	0.0645085i	−0.738625	−	0.674117i	$-0.764525\pi$
$67$	−4.32207	+	4.32207i	−0.0645085	+	0.0645085i	0.674117	+	0.738625i	$0.264525\pi$
$68$	−9.77622			−0.143768
$69$			76.7856i			1.11283i
$70$	54.7658	−	54.7658i	0.782368	−	0.782368i
$71$	−40.4291	+	40.4291i	−0.569424	+	0.569424i	−0.931967	−	0.362543i	$-0.881909\pi$
$71$	−40.4291	+	40.4291i	−0.569424	+	0.569424i	0.362543	+	0.931967i	$0.381909\pi$
$72$	−11.6013	−	11.6013i	−0.161129	−	0.161129i
$73$	12.7990	+	12.7990i	0.175329	+	0.175329i	0.789316	−	0.613987i	$-0.210435\pi$
$73$	12.7990	+	12.7990i	0.175329	+	0.175329i	−0.613987	+	0.789316i	$0.710435\pi$
$74$	−85.8143			−1.15965
$75$			13.4224i			0.178966i
$76$	−37.3569	−	37.3569i	−0.491539	−	0.491539i
$77$			107.497i			1.39607i
$78$		0			0
$79$	7.98532			0.101080			0.0505400	−	0.998722i	$-0.483906\pi$
$79$	7.98532			0.101080			0.0505400	+	0.998722i	$0.483906\pi$
$80$	−15.0967	+	15.0967i	−0.188709	+	0.188709i
$81$	−99.5584			−1.22912
$82$		−	7.08199i		−	0.0863657i
$83$	−35.8343	+	35.8343i	−0.431738	+	0.431738i	−0.889219	−	0.457481i	$-0.848752\pi$
$83$	−35.8343	+	35.8343i	−0.431738	+	0.431738i	0.457481	+	0.889219i	$0.348752\pi$
$84$	−55.8247	+	55.8247i	−0.664580	+	0.664580i
$85$	−18.4486	−	18.4486i	−0.217043	−	0.217043i
$86$	11.9728	+	11.9728i	0.139219	+	0.139219i
$87$	−55.0312			−0.632542
$88$		−	29.6326i		−	0.336734i
$89$	57.2867	+	57.2867i	0.643671	+	0.643671i	0.951456	−	0.307785i	$-0.0995877\pi$
$89$	57.2867	+	57.2867i	0.643671	+	0.643671i	−0.307785	+	0.951456i	$0.599588\pi$
$90$		−	43.7853i		−	0.486503i
$91$		0			0
$92$	−39.9181			−0.433892
$93$	−73.1175	+	73.1175i	−0.786209	+	0.786209i
$94$	−15.1834			−0.161525
$95$		−	140.992i		−	1.48413i
$96$	15.3886	−	15.3886i	0.160298	−	0.160298i
$97$	−38.7928	+	38.7928i	−0.399926	+	0.399926i	−0.878207	−	0.478281i	$-0.841260\pi$
$97$	−38.7928	+	38.7928i	−0.399926	+	0.399926i	0.478281	+	0.878207i	$0.341260\pi$
$98$	56.2792	+	56.2792i	0.574278	+	0.574278i
$99$	42.9720	+	42.9720i	0.434060	+	0.434060i
$100$	−6.97783			−0.0697783
$101$			14.0635i			0.139242i	0.997573	+	0.0696212i	$0.0221791\pi$
$101$			14.0635i			0.139242i	−0.997573	+	0.0696212i	$0.977821\pi$
$102$	18.8053	+	18.8053i	0.184366	+	0.184366i
$103$		−	80.8399i		−	0.784853i	−0.919783	−	0.392426i	$-0.871636\pi$
$103$		−	80.8399i		−	0.784853i	0.919783	−	0.392426i	$-0.128364\pi$
$104$		0			0
$105$	−210.693			−2.00660
$106$	77.0450	−	77.0450i	0.726840	−	0.726840i
$107$	162.705			1.52061			0.760304	−	0.649568i	$-0.225050\pi$
$107$	162.705			1.52061			0.760304	+	0.649568i	$0.225050\pi$
$108$		−	24.6170i		−	0.227935i
$109$	−62.6738	+	62.6738i	−0.574989	+	0.574989i	−0.933518	−	0.358530i	$-0.883278\pi$
$109$	−62.6738	+	62.6738i	−0.574989	+	0.574989i	0.358530	+	0.933518i	$0.383278\pi$
$110$	55.9195	−	55.9195i	0.508359	−	0.508359i
$111$	165.071	+	165.071i	1.48712	+	1.48712i
$112$	−29.0213	−	29.0213i	−0.259118	−	0.259118i
$113$	−69.8809			−0.618415			−0.309208	−	0.950995i	$-0.600064\pi$
$113$	−69.8809			−0.618415			−0.309208	+	0.950995i	$0.600064\pi$
$114$			143.718i			1.26068i
$115$	−75.3291	−	75.3291i	−0.655036	−	0.655036i
$116$		−	28.6087i		−	0.246627i
$117$		0			0
$118$	88.9637			0.753930
$119$	35.4648	−	35.4648i	0.298024	−	0.298024i
$120$	58.0795			0.483996
$121$		−	11.2384i		−	0.0928793i
$122$	−56.2764	+	56.2764i	−0.461282	+	0.461282i
$123$	−13.6228	+	13.6228i	−0.110754	+	0.110754i
$124$	−38.0112	−	38.0112i	−0.306542	−	0.306542i
$125$	81.1868	+	81.1868i	0.649494	+	0.649494i
$126$	84.1708			0.668022
$127$			82.7908i			0.651896i	0.945388	+	0.325948i	$0.105683\pi$
$127$			82.7908i			0.651896i	−0.945388	+	0.325948i	$0.894317\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	46.0614i		−	0.357065i
$130$		0			0
$131$	47.8506			0.365272			0.182636	−	0.983181i	$-0.441537\pi$
$131$	47.8506			0.365272			0.182636	+	0.983181i	$0.441537\pi$
$132$	−57.0007	+	57.0007i	−0.431824	+	0.431824i
$133$	271.036			2.03787
$134$			8.64414i			0.0645085i
$135$	46.4545	−	46.4545i	0.344107	−	0.344107i
$136$	−9.77622	+	9.77622i	−0.0718840	+	0.0718840i
$137$	−136.082	−	136.082i	−0.993298	−	0.993298i	0.00667939	−	0.999978i	$-0.497874\pi$
$137$	−136.082	−	136.082i	−0.993298	−	0.993298i	−0.999978	+	0.00667939i	$0.997874\pi$
$138$	76.7856	+	76.7856i	0.556417	+	0.556417i
$139$	193.093			1.38916			0.694578	−	0.719417i	$-0.255591\pi$
$139$	193.093			1.38916			0.694578	+	0.719417i	$0.255591\pi$
$140$		−	109.532i		−	0.782368i
$141$	29.2064	+	29.2064i	0.207137	+	0.207137i
$142$			80.8582i			0.569424i
$143$		0			0
$144$	−23.2025			−0.161129
$145$	53.9873	−	53.9873i	0.372326	−	0.372326i
$146$	25.5980			0.175329
$147$		−	216.515i		−	1.47289i
$148$	−85.8143	+	85.8143i	−0.579827	+	0.579827i
$149$	95.0866	−	95.0866i	0.638165	−	0.638165i	−0.311938	−	0.950103i	$-0.600978\pi$
$149$	95.0866	−	95.0866i	0.638165	−	0.638165i	0.950103	+	0.311938i	$0.100978\pi$
$150$	13.4224	+	13.4224i	0.0894828	+	0.0894828i
$151$	26.5821	+	26.5821i	0.176041	+	0.176041i	0.789627	−	0.613587i	$-0.210274\pi$
$151$	26.5821	+	26.5821i	0.176041	+	0.176041i	−0.613587	+	0.789627i	$0.710274\pi$
$152$	−74.7139			−0.491539
$153$		−	28.3541i		−	0.185321i
$154$	107.497	+	107.497i	0.698033	+	0.698033i
$155$		−	143.461i		−	0.925555i
$156$		0			0
$157$	−251.005			−1.59876			−0.799380	−	0.600826i	$-0.794838\pi$
$157$	−251.005			−1.59876			−0.799380	+	0.600826i	$0.794838\pi$
$158$	7.98532	−	7.98532i	0.0505400	−	0.0505400i
$159$	−296.404			−1.86418
$160$			30.1935i			0.188709i
$161$	144.809	−	144.809i	0.899436	−	0.899436i
$162$	−99.5584	+	99.5584i	−0.614558	+	0.614558i
$163$	−85.9701	−	85.9701i	−0.527424	−	0.527424i	0.392380	−	0.919803i	$-0.371652\pi$
$163$	−85.9701	−	85.9701i	−0.527424	−	0.527424i	−0.919803	+	0.392380i	$0.871652\pi$
$164$	−7.08199	−	7.08199i	−0.0431829	−	0.0431829i
$165$	−215.131			−1.30383
$166$			71.6686i			0.431738i
$167$	−43.7710	−	43.7710i	−0.262102	−	0.262102i	0.563806	−	0.825907i	$-0.309337\pi$
$167$	−43.7710	−	43.7710i	−0.262102	−	0.262102i	−0.825907	+	0.563806i	$0.809337\pi$
$168$			111.649i			0.664580i
$169$		0			0
$170$	−36.8973			−0.217043
$171$	108.347	−	108.347i	0.633607	−	0.633607i
$172$	23.9457			0.139219
$173$			310.835i			1.79674i	0.439244	+	0.898368i	$0.355246\pi$
$173$			310.835i			1.79674i	−0.439244	+	0.898368i	$0.644754\pi$
$174$	−55.0312	+	55.0312i	−0.316271	+	0.316271i
$175$	25.3132	−	25.3132i	0.144647	−	0.144647i
$176$	−29.6326	−	29.6326i	−0.168367	−	0.168367i
$177$	−171.129	−	171.129i	−0.966829	−	0.966829i
$178$	114.573			0.643671
$179$		−	63.3403i		−	0.353856i	−0.984224	−	0.176928i	$-0.943384\pi$
$179$		−	63.3403i		−	0.353856i	0.984224	−	0.176928i	$-0.0566160\pi$
$180$	−43.7853	−	43.7853i	−0.243251	−	0.243251i
$181$			186.504i			1.03041i	0.857067	+	0.515205i	$0.172284\pi$
$181$			186.504i			1.03041i	−0.857067	+	0.515205i	$0.827716\pi$
$182$		0			0
$183$	216.504			1.18308
$184$	−39.9181	+	39.9181i	−0.216946	+	0.216946i
$185$	−323.879			−1.75070
$186$			146.235i			0.786209i
$187$	36.2119	−	36.2119i	0.193647	−	0.193647i
$188$	−15.1834	+	15.1834i	−0.0807625	+	0.0807625i
$189$	89.3020	+	89.3020i	0.472497	+	0.472497i
$190$	−140.992	−	140.992i	−0.742063	−	0.742063i
$191$	−182.691			−0.956500			−0.478250	−	0.878224i	$-0.658729\pi$
$191$	−182.691			−0.956500			−0.478250	+	0.878224i	$0.658729\pi$
$192$		−	30.7773i		−	0.160298i
$193$	−64.4548	−	64.4548i	−0.333963	−	0.333963i	0.520126	−	0.854089i	$-0.325885\pi$
$193$	−64.4548	−	64.4548i	−0.333963	−	0.333963i	−0.854089	+	0.520126i	$0.825885\pi$
$194$			77.5856i			0.399926i
$195$		0			0
$196$	112.558			0.574278
$197$	−152.596	+	152.596i	−0.774600	+	0.774600i	−0.978907	−	0.204307i	$-0.934506\pi$
$197$	−152.596	+	152.596i	−0.774600	+	0.774600i	0.204307	+	0.978907i	$0.434506\pi$
$198$	85.9439			0.434060
$199$			78.4893i			0.394418i	0.980361	+	0.197209i	$0.0631878\pi$
$199$			78.4893i			0.394418i	−0.980361	+	0.197209i	$0.936812\pi$
$200$	−6.97783	+	6.97783i	−0.0348892	+	0.0348892i
$201$	16.6277	−	16.6277i	0.0827248	−	0.0827248i
$202$	14.0635	+	14.0635i	0.0696212	+	0.0696212i
$203$	103.783	+	103.783i	0.511245	+	0.511245i
$204$	37.6107			0.184366
$205$		−	26.7287i		−	0.130384i
$206$	−80.8399	−	80.8399i	−0.392426	−	0.392426i
$207$		−	115.775i		−	0.559300i
$208$		0			0
$209$	276.746			1.32414
$210$	−210.693	+	210.693i	−1.00330	+	1.00330i
$211$	−132.398			−0.627478			−0.313739	−	0.949509i	$-0.601582\pi$
$211$	−132.398			−0.627478			−0.313739	+	0.949509i	$0.601582\pi$
$212$		−	154.090i		−	0.726840i
$213$	155.537	−	155.537i	0.730221	−	0.730221i
$214$	162.705	−	162.705i	0.760304	−	0.760304i
$215$	45.1876	+	45.1876i	0.210175	+	0.210175i
$216$	−24.6170	−	24.6170i	−0.113968	−	0.113968i
$217$	275.783			1.27089
$218$			125.348i			0.574989i
$219$	−49.2398	−	49.2398i	−0.224839	−	0.224839i
$220$		−	111.839i		−	0.508359i
$221$		0			0
$222$	330.141			1.48712
$223$	84.4985	−	84.4985i	0.378917	−	0.378917i	−0.491794	−	0.870711i	$-0.663659\pi$
$223$	84.4985	−	84.4985i	0.378917	−	0.378917i	0.870711	+	0.491794i	$0.163659\pi$
$224$	−58.0425			−0.259118
$225$		−	20.2379i		−	0.0899462i
$226$	−69.8809	+	69.8809i	−0.309208	+	0.309208i
$227$	−299.942	+	299.942i	−1.32133	+	1.32133i	−0.408632	+	0.912699i	$0.633994\pi$
$227$	−299.942	+	299.942i	−1.32133	+	1.32133i	−0.912699	+	0.408632i	$0.866006\pi$
$228$	143.718	+	143.718i	0.630342	+	0.630342i
$229$	−158.206	−	158.206i	−0.690856	−	0.690856i	0.271564	−	0.962420i	$-0.412459\pi$
$229$	−158.206	−	158.206i	−0.690856	−	0.690856i	−0.962420	+	0.271564i	$0.912459\pi$
$230$	−150.658			−0.655036
$231$		−	413.558i		−	1.79030i
$232$	−28.6087	−	28.6087i	−0.123314	−	0.123314i
$233$			163.030i			0.699701i	0.936806	+	0.349850i	$0.113768\pi$
$233$			163.030i			0.699701i	−0.936806	+	0.349850i	$0.886232\pi$
$234$		0			0
$235$	−57.3048			−0.243850
$236$	88.9637	−	88.9637i	0.376965	−	0.376965i
$237$	−30.7208			−0.129624
$238$		−	70.9296i		−	0.298024i
$239$	−185.455	+	185.455i	−0.775962	+	0.775962i	−0.979142	−	0.203179i	$-0.934873\pi$
$239$	−185.455	+	185.455i	−0.775962	+	0.775962i	0.203179	+	0.979142i	$0.434873\pi$
$240$	58.0795	−	58.0795i	0.241998	−	0.241998i
$241$	−321.239	−	321.239i	−1.33294	−	1.33294i	−0.902728	−	0.430212i	$-0.858439\pi$
$241$	−321.239	−	321.239i	−1.33294	−	1.33294i	−0.430212	−	0.902728i	$-0.641561\pi$
$242$	−11.2384	−	11.2384i	−0.0464397	−	0.0464397i
$243$	272.240			1.12033
$244$			112.553i			0.461282i
$245$	212.408	+	212.408i	0.866972	+	0.866972i
$246$			27.2455i			0.110754i
$247$		0			0
$248$	−76.0223			−0.306542
$249$	137.860	−	137.860i	0.553655	−	0.553655i
$250$	162.374			0.649494
$251$			438.996i			1.74899i	0.485035	+	0.874495i	$0.338807\pi$
$251$			438.996i			1.74899i	−0.485035	+	0.874495i	$0.661193\pi$
$252$	84.1708	−	84.1708i	0.334011	−	0.334011i
$253$	147.860	−	147.860i	0.584426	−	0.584426i
$254$	82.7908	+	82.7908i	0.325948	+	0.325948i
$255$	70.9748	+	70.9748i	0.278333	+	0.278333i
$256$	16.0000			0.0625000
$257$		−	437.208i		−	1.70120i	−0.525815	−	0.850599i	$-0.676240\pi$
$257$		−	437.208i		−	1.70120i	0.525815	−	0.850599i	$-0.323760\pi$
$258$	−46.0614	−	46.0614i	−0.178532	−	0.178532i
$259$		−	622.610i		−	2.40390i
$260$		0			0
$261$	82.9743			0.317909
$262$	47.8506	−	47.8506i	0.182636	−	0.182636i
$263$	−287.959			−1.09490			−0.547451	−	0.836838i	$-0.684402\pi$
$263$	−287.959			−1.09490			−0.547451	+	0.836838i	$0.684402\pi$
$264$			114.001i			0.431824i
$265$	290.782	−	290.782i	1.09729	−	1.09729i
$266$	271.036	−	271.036i	1.01893	−	1.01893i
$267$	−220.391	−	220.391i	−0.825435	−	0.825435i
$268$	8.64414	+	8.64414i	0.0322542	+	0.0322542i
$269$	343.400			1.27658			0.638290	−	0.769796i	$-0.279642\pi$
$269$	343.400			1.27658			0.638290	+	0.769796i	$0.279642\pi$
$270$		−	92.9090i		−	0.344107i
$271$	5.87429	+	5.87429i	0.0216764	+	0.0216764i	0.717862	−	0.696186i	$-0.245121\pi$
$271$	5.87429	+	5.87429i	0.0216764	+	0.0216764i	−0.696186	+	0.717862i	$0.745121\pi$
$272$			19.5524i			0.0718840i
$273$		0			0
$274$	−272.164			−0.993298
$275$	25.8464	−	25.8464i	0.0939871	−	0.0939871i
$276$	153.571			0.556417
$277$		−	444.247i		−	1.60378i	−0.597471	−	0.801891i	$-0.703828\pi$
$277$		−	444.247i		−	1.60378i	0.597471	−	0.801891i	$-0.296172\pi$
$278$	193.093	−	193.093i	0.694578	−	0.694578i
$279$	110.244	−	110.244i	0.395141	−	0.395141i
$280$	−109.532	−	109.532i	−0.391184	−	0.391184i
$281$	−163.678	−	163.678i	−0.582486	−	0.582486i	0.353100	−	0.935586i	$-0.385128\pi$
$281$	−163.678	−	163.678i	−0.582486	−	0.582486i	−0.935586	+	0.353100i	$0.885128\pi$
$282$	58.4128			0.207137
$283$			464.139i			1.64007i	0.572315	+	0.820034i	$0.306045\pi$
$283$			464.139i			1.64007i	−0.572315	+	0.820034i	$0.693955\pi$
$284$	80.8582	+	80.8582i	0.284712	+	0.284712i
$285$			542.418i			1.90322i
$286$		0			0
$287$	51.3821			0.179032
$288$	−23.2025	+	23.2025i	−0.0805643	+	0.0805643i
$289$	265.106			0.917323
$290$		−	107.975i		−	0.372326i
$291$	149.242	−	149.242i	0.512859	−	0.512859i
$292$	25.5980	−	25.5980i	0.0876644	−	0.0876644i
$293$	44.9476	+	44.9476i	0.153405	+	0.153405i	0.779637	−	0.626232i	$-0.215404\pi$
$293$	44.9476	+	44.9476i	0.153405	+	0.153405i	−0.626232	+	0.779637i	$0.715404\pi$
$294$	−216.515	−	216.515i	−0.736446	−	0.736446i
$295$	335.765			1.13819
$296$			171.629i			0.579827i
$297$	91.1832	+	91.1832i	0.307014	+	0.307014i
$298$		−	190.173i		−	0.638165i
$299$		0			0
$300$	26.8448			0.0894828
$301$	−86.8667	+	86.8667i	−0.288594	+	0.288594i
$302$	53.1643			0.176041
$303$		−	54.1045i		−	0.178563i
$304$	−74.7139	+	74.7139i	−0.245769	+	0.245769i
$305$	−212.397	+	212.397i	−0.696385	+	0.696385i
$306$	−28.3541	−	28.3541i	−0.0926605	−	0.0926605i
$307$	67.1395	+	67.1395i	0.218695	+	0.218695i	0.807948	−	0.589253i	$-0.200578\pi$
$307$	67.1395	+	67.1395i	0.218695	+	0.218695i	−0.589253	+	0.807948i	$0.700578\pi$
$308$	214.994			0.698033
$309$			311.004i			1.00648i
$310$	−143.461	−	143.461i	−0.462778	−	0.462778i
$311$			331.141i			1.06476i	0.846505	+	0.532381i	$0.178703\pi$
$311$			331.141i			1.06476i	−0.846505	+	0.532381i	$0.821297\pi$
$312$		0			0
$313$	−391.075			−1.24944			−0.624721	−	0.780848i	$-0.714787\pi$
$313$	−391.075			−1.24944			−0.624721	+	0.780848i	$0.714787\pi$
$314$	−251.005	+	251.005i	−0.799380	+	0.799380i
$315$	317.676			1.00849
$316$		−	15.9706i		−	0.0505400i
$317$	−322.964	+	322.964i	−1.01881	+	1.01881i	−0.0189927	+	0.999820i	$0.506046\pi$
$317$	−322.964	+	322.964i	−1.01881	+	1.01881i	−0.999820	+	0.0189927i	$0.993954\pi$
$318$	−296.404	+	296.404i	−0.932089	+	0.932089i
$319$	105.969	+	105.969i	0.332191	+	0.332191i
$320$	30.1935	+	30.1935i	0.0943546	+	0.0943546i
$321$	−625.952			−1.95001
$322$		−	289.618i		−	0.899436i
$323$	−91.3024	−	91.3024i	−0.282670	−	0.282670i
$324$			199.117i			0.614558i
$325$		0			0
$326$	−171.940			−0.527424
$327$	241.116	−	241.116i	0.737357	−	0.737357i
$328$	−14.1640			−0.0431829
$329$		−	110.160i		−	0.334833i
$330$	−215.131	+	215.131i	−0.651913	+	0.651913i
$331$	346.516	−	346.516i	1.04688	−	1.04688i	0.0480317	−	0.998846i	$-0.484705\pi$
$331$	346.516	−	346.516i	1.04688	−	1.04688i	0.998846	−	0.0480317i	$-0.0152948\pi$
$332$	71.6686	+	71.6686i	0.215869	+	0.215869i
$333$	−248.889	−	248.889i	−0.747413	−	0.747413i
$334$	−87.5419			−0.262102
$335$			32.6246i			0.0973867i
$336$	111.649	+	111.649i	0.332290	+	0.332290i
$337$		−	498.500i		−	1.47923i	−0.673031	−	0.739614i	$-0.735008\pi$
$337$		−	498.500i		−	1.47923i	0.673031	−	0.739614i	$-0.264992\pi$
$338$		0			0
$339$	268.843			0.793047
$340$	−36.8973	+	36.8973i	−0.108521	+	0.108521i
$341$	281.593			0.825785
$342$		−	216.694i		−	0.633607i
$343$	−52.8131	+	52.8131i	−0.153974	+	0.153974i
$344$	23.9457	−	23.9457i	0.0696095	−	0.0696095i
$345$	289.803	+	289.803i	0.840009	+	0.840009i
$346$	310.835	+	310.835i	0.898368	+	0.898368i
$347$	−234.625			−0.676153			−0.338076	−	0.941119i	$-0.609776\pi$
$347$	−234.625			−0.676153			−0.338076	+	0.941119i	$0.609776\pi$
$348$			110.062i			0.316271i
$349$	125.061	+	125.061i	0.358341	+	0.358341i	0.863201	−	0.504860i	$-0.168456\pi$
$349$	125.061	+	125.061i	0.358341	+	0.358341i	−0.504860	+	0.863201i	$0.668456\pi$
$350$		−	50.6264i		−	0.144647i
$351$		0			0
$352$	−59.2653			−0.168367
$353$	−159.033	+	159.033i	−0.450518	+	0.450518i	−0.895526	−	0.445009i	$-0.853201\pi$
$353$	−159.033	+	159.033i	−0.450518	+	0.450518i	0.445009	+	0.895526i	$0.353201\pi$
$354$	−342.258			−0.966829
$355$			305.174i			0.859644i
$356$	114.573	−	114.573i	0.321836	−	0.321836i
$357$	−136.439	+	136.439i	−0.382181	+	0.382181i
$358$	−63.3403	−	63.3403i	−0.176928	−	0.176928i
$359$	290.278	+	290.278i	0.808574	+	0.808574i	0.984418	−	0.175844i	$-0.0562653\pi$
$359$	290.278	+	290.278i	0.808574	+	0.808574i	−0.175844	+	0.984418i	$0.556265\pi$
$360$	−87.5705			−0.243251
$361$		−	336.770i		−	0.932881i
$362$	186.504	+	186.504i	0.515205	+	0.515205i
$363$			43.2359i			0.119107i
$364$		0			0
$365$	96.6115			0.264689
$366$	216.504	−	216.504i	0.591542	−	0.591542i
$367$	−220.744			−0.601481			−0.300741	−	0.953706i	$-0.597234\pi$
$367$	−220.744			−0.601481			−0.300741	+	0.953706i	$0.597234\pi$
$368$			79.8362i			0.216946i
$369$	20.5400	−	20.5400i	0.0556639	−	0.0556639i
$370$	−323.879	+	323.879i	−0.875349	+	0.875349i
$371$	558.986	+	558.986i	1.50670	+	1.50670i
$372$	146.235	+	146.235i	0.393105	+	0.393105i
$373$	−62.1593			−0.166647			−0.0833235	−	0.996523i	$-0.526553\pi$
$373$	−62.1593			−0.166647			−0.0833235	+	0.996523i	$0.526553\pi$
$374$		−	72.4238i		−	0.193647i
$375$	−312.338	−	312.338i	−0.832902	−	0.832902i
$376$			30.3667i			0.0807625i
$377$		0			0
$378$	178.604			0.472497
$379$	−102.724	+	102.724i	−0.271038	+	0.271038i	−0.829518	−	0.558480i	$-0.811385\pi$
$379$	−102.724	+	102.724i	−0.271038	+	0.271038i	0.558480	+	0.829518i	$0.311385\pi$
$380$	−281.984			−0.742063
$381$		−	318.509i		−	0.835982i
$382$	−182.691	+	182.691i	−0.478250	+	0.478250i
$383$	−355.526	+	355.526i	−0.928265	+	0.928265i	−0.997594	−	0.0693288i	$-0.977914\pi$
$383$	−355.526	+	355.526i	−0.928265	+	0.928265i	0.0693288	+	0.997594i	$0.477914\pi$
$384$	−30.7773	−	30.7773i	−0.0801491	−	0.0801491i
$385$	405.714	+	405.714i	1.05380	+	1.05380i
$386$	−128.910			−0.333963
$387$			69.4499i			0.179457i
$388$	77.5856	+	77.5856i	0.199963	+	0.199963i
$389$		−	284.973i		−	0.732579i	−0.930501	−	0.366289i	$-0.880628\pi$
$389$		−	284.973i		−	0.732579i	0.930501	−	0.366289i	$-0.119372\pi$
$390$		0			0
$391$	−97.5621			−0.249519
$392$	112.558	−	112.558i	0.287139	−	0.287139i
$393$	−184.089			−0.468420
$394$			305.193i			0.774600i
$395$	30.1380	−	30.1380i	0.0762988	−	0.0762988i
$396$	85.9439	−	85.9439i	0.217030	−	0.217030i
$397$	−209.336	−	209.336i	−0.527294	−	0.527294i	0.392471	−	0.919764i	$-0.371620\pi$
$397$	−209.336	−	209.336i	−0.527294	−	0.527294i	−0.919764	+	0.392471i	$0.871620\pi$
$398$	78.4893	+	78.4893i	0.197209	+	0.197209i
$399$	−1042.72			−2.61333
$400$			13.9557i			0.0348892i
$401$	171.024	+	171.024i	0.426494	+	0.426494i	0.887432	−	0.460938i	$-0.152487\pi$
$401$	171.024	+	171.024i	0.426494	+	0.426494i	−0.460938	+	0.887432i	$0.652487\pi$
$402$		−	33.2554i		−	0.0827248i
$403$		0			0
$404$	28.1270			0.0696212
$405$	−375.752	+	375.752i	−0.927782	+	0.927782i
$406$	207.565			0.511245
$407$		−	635.726i		−	1.56198i
$408$	37.6107	−	37.6107i	0.0921830	−	0.0921830i
$409$	137.980	−	137.980i	0.337361	−	0.337361i	−0.518013	−	0.855373i	$-0.673328\pi$
$409$	137.980	−	137.980i	0.337361	−	0.337361i	0.855373	+	0.518013i	$0.173328\pi$
$410$	−26.7287	−	26.7287i	−0.0651920	−	0.0651920i
$411$	523.529	+	523.529i	1.27379	+	1.27379i
$412$	−161.680			−0.392426
$413$			645.460i			1.56286i
$414$	−115.775	−	115.775i	−0.279650	−	0.279650i
$415$			270.490i			0.651784i
$416$		0			0
$417$	−742.859			−1.78144
$418$	276.746	−	276.746i	0.662072	−	0.662072i
$419$	47.9110			0.114346			0.0571730	−	0.998364i	$-0.481791\pi$
$419$	47.9110			0.114346			0.0571730	+	0.998364i	$0.481791\pi$
$420$			421.385i			1.00330i
$421$	−477.018	+	477.018i	−1.13306	+	1.13306i	−0.143394	+	0.989666i	$0.545802\pi$
$421$	−477.018	+	477.018i	−1.13306	+	1.13306i	−0.989666	+	0.143394i	$0.954198\pi$
$422$	−132.398	+	132.398i	−0.313739	+	0.313739i
$423$	−44.0365	−	44.0365i	−0.104105	−	0.104105i
$424$	−154.090	−	154.090i	−0.363420	−	0.363420i
$425$	−17.0542			−0.0401276
$426$		−	311.074i		−	0.730221i
$427$	−408.303	−	408.303i	−0.956214	−	0.956214i
$428$		−	325.410i		−	0.760304i
$429$		0			0
$430$	90.3753			0.210175
$431$	55.0595	−	55.0595i	0.127748	−	0.127748i	−0.640342	−	0.768090i	$-0.721207\pi$
$431$	55.0595	−	55.0595i	0.127748	−	0.127748i	0.768090	+	0.640342i	$0.221207\pi$
$432$	−49.2340			−0.113968
$433$			497.603i			1.14920i	0.818435	+	0.574599i	$0.194842\pi$
$433$			497.603i			1.14920i	−0.818435	+	0.574599i	$0.805158\pi$
$434$	275.783	−	275.783i	0.635445	−	0.635445i
$435$	−207.698	+	207.698i	−0.477466	+	0.477466i
$436$	125.348	+	125.348i	0.287494	+	0.287494i
$437$	−372.804	−	372.804i	−0.853099	−	0.853099i
$438$	−98.4795			−0.224839
$439$			167.510i			0.381572i	0.981632	+	0.190786i	$0.0611037\pi$
$439$			167.510i			0.381572i	−0.981632	+	0.190786i	$0.938896\pi$
$440$	−111.839	−	111.839i	−0.254179	−	0.254179i
$441$			326.455i			0.740260i
$442$		0			0
$443$	−443.835			−1.00188			−0.500942	−	0.865481i	$-0.667013\pi$
$443$	−443.835			−1.00188			−0.500942	+	0.865481i	$0.667013\pi$
$444$	330.141	−	330.141i	0.743562	−	0.743562i
$445$	432.421			0.971733
$446$		−	168.997i		−	0.378917i
$447$	−365.813	+	365.813i	−0.818374	+	0.818374i
$448$	−58.0425	+	58.0425i	−0.129559	+	0.129559i
$449$	−181.585	−	181.585i	−0.404421	−	0.404421i	0.475366	−	0.879788i	$-0.342315\pi$
$449$	−181.585	−	181.585i	−0.404421	−	0.404421i	−0.879788	+	0.475366i	$0.842315\pi$
$450$	−20.2379	−	20.2379i	−0.0449731	−	0.0449731i
$451$	52.4645			0.116329
$452$			139.762i			0.309208i
$453$	−102.266	−	102.266i	−0.225752	−	0.225752i
$454$			599.884i			1.32133i
$455$		0			0
$456$	287.436			0.630342
$457$	61.5957	−	61.5957i	0.134783	−	0.134783i	−0.636497	−	0.771279i	$-0.719617\pi$
$457$	61.5957	−	61.5957i	0.134783	−	0.134783i	0.771279	+	0.636497i	$0.219617\pi$
$458$	−316.412			−0.690856
$459$		−	60.1653i		−	0.131079i
$460$	−150.658	+	150.658i	−0.327518	+	0.327518i
$461$	349.897	−	349.897i	0.758996	−	0.758996i	−0.217144	−	0.976140i	$-0.569674\pi$
$461$	349.897	−	349.897i	0.758996	−	0.758996i	0.976140	+	0.217144i	$0.0696741\pi$
$462$	−413.558	−	413.558i	−0.895148	−	0.895148i
$463$	−399.472	−	399.472i	−0.862789	−	0.862789i	0.128872	−	0.991661i	$-0.458864\pi$
$463$	−399.472	−	399.472i	−0.862789	−	0.862789i	−0.991661	+	0.128872i	$0.958864\pi$
$464$	−57.2175			−0.123314
$465$			551.917i			1.18692i
$466$	163.030	+	163.030i	0.349850	+	0.349850i
$467$			409.816i			0.877550i	0.898597	+	0.438775i	$0.144587\pi$
$467$			409.816i			0.877550i	−0.898597	+	0.438775i	$0.855413\pi$
$468$		0			0
$469$	−62.7159			−0.133723
$470$	−57.3048	+	57.3048i	−0.121925	+	0.121925i
$471$	965.657			2.05023
$472$		−	177.927i		−	0.376965i
$473$	−88.6966	+	88.6966i	−0.187519	+	0.187519i
$474$	−30.7208	+	30.7208i	−0.0648118	+	0.0648118i
$475$	−65.1676	−	65.1676i	−0.137195	−	0.137195i
$476$	−70.9296	−	70.9296i	−0.149012	−	0.149012i
$477$	446.909			0.936917
$478$			370.910i			0.775962i
$479$	376.568	+	376.568i	0.786153	+	0.786153i	0.980861	−	0.194708i	$-0.0623759\pi$
$479$	376.568	+	376.568i	0.786153	+	0.786153i	−0.194708	+	0.980861i	$0.562376\pi$
$480$		−	116.159i		−	0.241998i
$481$		0			0
$482$	−642.477			−1.33294
$483$	−557.104	+	557.104i	−1.15342	+	1.15342i
$484$	−22.4768			−0.0464397
$485$			292.822i			0.603757i
$486$	272.240	−	272.240i	0.560165	−	0.560165i
$487$	476.048	−	476.048i	0.977512	−	0.977512i	−0.0222407	−	0.999753i	$-0.507080\pi$
$487$	476.048	−	476.048i	0.977512	−	0.977512i	0.999753	+	0.0222407i	$0.00708003\pi$
$488$	112.553	+	112.553i	0.230641	+	0.230641i
$489$	330.740	+	330.740i	0.676361	+	0.676361i
$490$	424.816			0.866972
$491$			117.456i			0.239219i	0.992821	+	0.119609i	$0.0381642\pi$
$491$			117.456i			0.239219i	−0.992821	+	0.119609i	$0.961836\pi$
$492$	27.2455	+	27.2455i	0.0553771	+	0.0553771i
$493$		−	69.9214i		−	0.141828i
$494$		0			0
$495$	324.368			0.655289
$496$	−76.0223	+	76.0223i	−0.153271	+	0.153271i
$497$	−586.652			−1.18039
$498$		−	275.720i		−	0.553655i
$499$	155.387	−	155.387i	0.311396	−	0.311396i	−0.534054	−	0.845450i	$-0.679332\pi$
$499$	155.387	−	155.387i	0.311396	−	0.311396i	0.845450	+	0.534054i	$0.179332\pi$
$500$	162.374	−	162.374i	0.324747	−	0.324747i
$501$	168.394	+	168.394i	0.336116	+	0.336116i
$502$	438.996	+	438.996i	0.874495	+	0.874495i
$503$	325.036			0.646196			0.323098	−	0.946366i	$-0.395276\pi$
$503$	325.036			0.646196			0.323098	+	0.946366i	$0.395276\pi$
$504$		−	168.342i		−	0.334011i
$505$	53.0782	+	53.0782i	0.105105	+	0.105105i
$506$		−	295.720i		−	0.584426i
$507$		0			0
$508$	165.582			0.325948
$509$	410.842	−	410.842i	0.807154	−	0.807154i	−0.177048	−	0.984202i	$-0.556655\pi$
$509$	410.842	−	410.842i	0.807154	−	0.807154i	0.984202	+	0.177048i	$0.0566547\pi$
$510$	141.950			0.278333
$511$			185.722i			0.363447i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	229.904	−	229.904i	0.448155	−	0.448155i
$514$	−437.208	−	437.208i	−0.850599	−	0.850599i
$515$	−305.104	−	305.104i	−0.592436	−	0.592436i
$516$	−92.1227			−0.178532
$517$		−	112.481i		−	0.217564i
$518$	−622.610	−	622.610i	−1.20195	−	1.20195i
$519$		−	1195.83i		−	2.30411i
$520$		0			0
$521$	400.067			0.767883			0.383942	−	0.923357i	$-0.374566\pi$
$521$	400.067			0.767883			0.383942	+	0.923357i	$0.374566\pi$
$522$	82.9743	−	82.9743i	0.158955	−	0.158955i
$523$	468.671			0.896120			0.448060	−	0.894004i	$-0.352115\pi$
$523$	468.671			0.896120			0.448060	+	0.894004i	$0.352115\pi$
$524$		−	95.7013i		−	0.182636i
$525$	−97.3839	+	97.3839i	−0.185493	+	0.185493i
$526$	−287.959	+	287.959i	−0.547451	+	0.547451i
$527$	−92.9014	−	92.9014i	−0.176283	−	0.176283i
$528$	114.001	+	114.001i	0.215912	+	0.215912i
$529$	130.636			0.246950
$530$		−	581.564i		−	1.09729i
$531$	258.023	+	258.023i	0.485918	+	0.485918i
$532$		−	542.073i		−	1.01893i
$533$		0			0
$534$	−440.782			−0.825435
$535$	614.079	−	614.079i	1.14781	−	1.14781i
$536$	17.2883			0.0322542
$537$			243.680i			0.453781i
$538$	343.400	−	343.400i	0.638290	−	0.638290i
$539$	−416.925	+	416.925i	−0.773516	+	0.773516i
$540$	−92.9090	−	92.9090i	−0.172054	−	0.172054i
$541$	155.599	+	155.599i	0.287614	+	0.287614i	0.836136	−	0.548522i	$-0.184809\pi$
$541$	155.599	+	155.599i	0.287614	+	0.287614i	−0.548522	+	0.836136i	$0.684809\pi$
$542$	11.7486			0.0216764
$543$		−	717.511i		−	1.32138i
$544$	19.5524	+	19.5524i	0.0359420	+	0.0359420i
$545$			473.085i			0.868045i
$546$		0			0
$547$	858.888			1.57018			0.785090	−	0.619382i	$-0.212617\pi$
$547$	858.888			1.57018			0.785090	+	0.619382i	$0.212617\pi$
$548$	−272.164	+	272.164i	−0.496649	+	0.496649i
$549$	−326.439			−0.594606
$550$		−	51.6929i		−	0.0939871i
$551$	267.184	−	267.184i	0.484907	−	0.484907i
$552$	153.571	−	153.571i	0.278209	−	0.278209i
$553$	57.9360	+	57.9360i	0.104767	+	0.104767i
$554$	−444.247	−	444.247i	−0.801891	−	0.801891i
$555$	1246.01			2.24507
$556$		−	386.186i		−	0.694578i
$557$	−377.023	−	377.023i	−0.676881	−	0.676881i	0.282412	−	0.959293i	$-0.408865\pi$
$557$	−377.023	−	377.023i	−0.676881	−	0.676881i	−0.959293	+	0.282412i	$0.908865\pi$
$558$		−	220.489i		−	0.395141i
$559$		0			0
$560$	−219.063			−0.391184
$561$	−139.313	+	139.313i	−0.248330	+	0.248330i
$562$	−327.357			−0.582486
$563$		−	434.624i		−	0.771979i	−0.922503	−	0.385990i	$-0.873860\pi$
$563$		−	434.624i		−	0.771979i	0.922503	−	0.385990i	$-0.126140\pi$
$564$	58.4128	−	58.4128i	0.103569	−	0.103569i
$565$	−263.743	+	263.743i	−0.466803	+	0.466803i
$566$	464.139	+	464.139i	0.820034	+	0.820034i
$567$	−722.327	−	722.327i	−1.27395	−	1.27395i
$568$	161.716			0.284712
$569$		−	332.271i		−	0.583955i	−0.956425	−	0.291978i	$-0.905687\pi$
$569$		−	332.271i		−	0.583955i	0.956425	−	0.291978i	$-0.0943133\pi$
$570$	542.418	+	542.418i	0.951611	+	0.951611i
$571$			555.806i			0.973391i	0.873572	+	0.486696i	$0.161798\pi$
$571$			555.806i			0.973391i	−0.873572	+	0.486696i	$0.838202\pi$
$572$		0			0
$573$	702.843			1.22660
$574$	51.3821	−	51.3821i	0.0895158	−	0.0895158i
$575$	−69.6354			−0.121105
$576$			46.4050i			0.0805643i
$577$	287.753	−	287.753i	0.498705	−	0.498705i	−0.412330	−	0.911035i	$-0.635285\pi$
$577$	287.753	−	287.753i	0.498705	−	0.498705i	0.911035	+	0.412330i	$0.135285\pi$
$578$	265.106	−	265.106i	0.458662	−	0.458662i
$579$	247.968	+	247.968i	0.428269	+	0.428269i
$580$	−107.975	−	107.975i	−0.186163	−	0.186163i
$581$	−519.978			−0.894971
$582$		−	298.484i		−	0.512859i
$583$	570.762	+	570.762i	0.979008	+	0.979008i
$584$		−	51.1960i		−	0.0876644i
$585$		0			0
$586$	89.8951			0.153405
$587$	−473.776	+	473.776i	−0.807114	+	0.807114i	−0.984196	−	0.177082i	$-0.943334\pi$
$587$	−473.776	+	473.776i	−0.807114	+	0.807114i	0.177082	+	0.984196i	$0.443334\pi$
$588$	−433.030			−0.736446
$589$		−	709.990i		−	1.20542i
$590$	335.765	−	335.765i	0.569094	−	0.569094i
$591$	587.062	−	587.062i	0.993337	−	0.993337i
$592$	171.629	+	171.629i	0.289913	+	0.289913i
$593$	−69.0570	−	69.0570i	−0.116454	−	0.116454i	0.646479	−	0.762932i	$-0.276241\pi$
$593$	−69.0570	−	69.0570i	−0.116454	−	0.116454i	−0.762932	+	0.646479i	$0.776241\pi$
$594$	182.366			0.307014
$595$		−	267.701i		−	0.449918i
$596$	−190.173	−	190.173i	−0.319082	−	0.319082i
$597$		−	301.961i		−	0.505797i
$598$		0			0
$599$	461.140			0.769850			0.384925	−	0.922948i	$-0.374227\pi$
$599$	461.140			0.769850			0.384925	+	0.922948i	$0.374227\pi$
$600$	26.8448	−	26.8448i	0.0447414	−	0.0447414i
$601$	176.162			0.293115			0.146558	−	0.989202i	$-0.453181\pi$
$601$	176.162			0.293115			0.146558	+	0.989202i	$0.453181\pi$
$602$			173.733i			0.288594i
$603$	−25.0707	+	25.0707i	−0.0415766	+	0.0415766i
$604$	53.1643	−	53.1643i	0.0880203	−	0.0880203i
$605$	−42.4158	−	42.4158i	−0.0701087	−	0.0701087i
$606$	−54.1045	−	54.1045i	−0.0892813	−	0.0892813i
$607$	−315.414			−0.519628			−0.259814	−	0.965659i	$-0.583661\pi$
$607$	−315.414			−0.519628			−0.259814	+	0.965659i	$0.583661\pi$
$608$			149.428i			0.245769i
$609$	−399.269	−	399.269i	−0.655613	−	0.655613i
$610$			424.795i			0.696385i
$611$		0			0
$612$	−56.7082			−0.0926605
$613$	−638.354	+	638.354i	−1.04136	+	1.04136i	−0.0422542	+	0.999107i	$0.513454\pi$
$613$	−638.354	+	638.354i	−1.04136	+	1.04136i	−0.999107	+	0.0422542i	$0.986546\pi$
$614$	134.279			0.218695
$615$			102.830i			0.167203i
$616$	214.994	−	214.994i	0.349016	−	0.349016i
$617$	−483.018	+	483.018i	−0.782849	+	0.782849i	−0.980311	−	0.197461i	$-0.936730\pi$
$617$	−483.018	+	483.018i	−0.782849	+	0.782849i	0.197461	+	0.980311i	$0.436730\pi$
$618$	311.004	+	311.004i	0.503242	+	0.503242i
$619$	−413.378	−	413.378i	−0.667816	−	0.667816i	0.289394	−	0.957210i	$-0.406546\pi$
$619$	−413.378	−	413.378i	−0.667816	−	0.667816i	−0.957210	+	0.289394i	$0.906546\pi$
$620$	−286.922			−0.462778
$621$		−	245.666i		−	0.395597i
$622$	331.141	+	331.141i	0.532381	+	0.532381i
$623$			831.267i			1.33430i
$624$		0			0
$625$	700.050			1.12008
$626$	−391.075	+	391.075i	−0.624721	+	0.624721i
$627$	−1064.69			−1.69806
$628$			502.010i			0.799380i
$629$	−209.735	+	209.735i	−0.333442	+	0.333442i
$630$	317.676	−	317.676i	0.504247	−	0.504247i
$631$	1.18650	+	1.18650i	0.00188035	+	0.00188035i	0.708046	−	0.706166i	$-0.249577\pi$
$631$	1.18650	+	1.18650i	0.00188035	+	0.00188035i	−0.706166	+	0.708046i	$0.749577\pi$
$632$	−15.9706	−	15.9706i	−0.0252700	−	0.0252700i
$633$	509.356			0.804670
$634$			645.927i			1.01881i
$635$	312.468	+	312.468i	0.492075	+	0.492075i
$636$			592.809i			0.932089i
$637$		0			0
$638$	211.938			0.332191
$639$	−234.514	+	234.514i	−0.367002	+	0.367002i
$640$	60.3869			0.0943546
$641$			1227.53i			1.91502i	0.288406	+	0.957508i	$0.406875\pi$
$641$			1227.53i			1.91502i	−0.288406	+	0.957508i	$0.593125\pi$
$642$	−625.952	+	625.952i	−0.975003	+	0.975003i
$643$	−426.567	+	426.567i	−0.663401	+	0.663401i	−0.956180	−	0.292779i	$-0.905420\pi$
$643$	−426.567	+	426.567i	−0.663401	+	0.663401i	0.292779	+	0.956180i	$0.405420\pi$
$644$	−289.618	−	289.618i	−0.449718	−	0.449718i
$645$	−173.844	−	173.844i	−0.269526	−	0.269526i
$646$	−182.605			−0.282670
$647$			876.797i			1.35517i	0.735443	+	0.677587i	$0.236974\pi$
$647$			876.797i			1.35517i	−0.735443	+	0.677587i	$0.763026\pi$
$648$	199.117	+	199.117i	0.307279	+	0.307279i
$649$			659.057i			1.01550i
$650$		0			0
$651$	−1060.98			−1.62977
$652$	−171.940	+	171.940i	−0.263712	+	0.263712i
$653$	150.361			0.230261			0.115131	−	0.993350i	$-0.463271\pi$
$653$	150.361			0.230261			0.115131	+	0.993350i	$0.463271\pi$
$654$		−	482.232i		−	0.737357i
$655$	180.597	−	180.597i	0.275721	−	0.275721i
$656$	−14.1640	+	14.1640i	−0.0215914	+	0.0215914i
$657$	74.2422	+	74.2422i	0.113002	+	0.113002i
$658$	−110.160	−	110.160i	−0.167416	−	0.167416i
$659$	873.541			1.32556			0.662778	−	0.748816i	$-0.269377\pi$
$659$	873.541			1.32556			0.662778	+	0.748816i	$0.269377\pi$
$660$			430.262i			0.651913i
$661$	−336.481	−	336.481i	−0.509048	−	0.509048i	0.405186	−	0.914234i	$-0.367207\pi$
$661$	−336.481	−	336.481i	−0.509048	−	0.509048i	−0.914234	+	0.405186i	$0.867207\pi$
$662$		−	693.033i		−	1.04688i
$663$		0			0
$664$	143.337			0.215869
$665$	1022.94	−	1022.94i	1.53826	−	1.53826i
$666$	−497.777			−0.747413
$667$		−	285.502i		−	0.428038i
$668$	−87.5419	+	87.5419i	−0.131051	+	0.131051i
$669$	−325.079	+	325.079i	−0.485918	+	0.485918i
$670$	32.6246	+	32.6246i	0.0486934	+	0.0486934i
$671$	−416.905	−	416.905i	−0.621318	−	0.621318i
$672$	223.299			0.332290
$673$		−	1105.76i		−	1.64302i	−0.570191	−	0.821512i	$-0.693131\pi$
$673$		−	1105.76i		−	1.64302i	0.570191	−	0.821512i	$-0.306869\pi$
$674$	−498.500	−	498.500i	−0.739614	−	0.739614i
$675$		−	42.9433i		−	0.0636197i
$676$		0			0
$677$	474.341			0.700651			0.350326	−	0.936628i	$-0.386071\pi$
$677$	474.341			0.700651			0.350326	+	0.936628i	$0.386071\pi$
$678$	268.843	−	268.843i	0.396524	−	0.396524i
$679$	−562.908			−0.829025
$680$			73.7945i			0.108521i
$681$	1153.93	−	1153.93i	1.69446	−	1.69446i
$682$	281.593	−	281.593i	0.412892	−	0.412892i
$683$	−741.412	−	741.412i	−1.08552	−	1.08552i	−0.995983	−	0.0895398i	$-0.971460\pi$
$683$	−741.412	−	741.412i	−1.08552	−	1.08552i	−0.0895398	−	0.995983i	$-0.528540\pi$
$684$	−216.694	−	216.694i	−0.316804	−	0.316804i
$685$	−1027.20			−1.49956
$686$			105.626i			0.153974i
$687$	608.644	+	608.644i	0.885945	+	0.885945i
$688$		−	47.8913i		−	0.0696095i
$689$		0			0
$690$	579.606			0.840009
$691$	−286.793	+	286.793i	−0.415040	+	0.415040i	−0.883490	−	0.468450i	$-0.844813\pi$
$691$	−286.793	+	286.793i	−0.415040	+	0.415040i	0.468450	+	0.883490i	$0.344813\pi$
$692$	621.671			0.898368
$693$			623.550i			0.899784i
$694$	−234.625	+	234.625i	−0.338076	+	0.338076i
$695$	728.768	−	728.768i	1.04859	−	1.04859i
$696$	110.062	+	110.062i	0.158136	+	0.158136i
$697$	−17.3088	−	17.3088i	−0.0248333	−	0.0248333i
$698$	250.122			0.358341
$699$		−	627.203i		−	0.897287i
$700$	−50.6264	−	50.6264i	−0.0723234	−	0.0723234i
$701$		−	322.739i		−	0.460398i	−0.973144	−	0.230199i	$-0.926062\pi$
$701$		−	322.739i		−	0.460398i	0.973144	−	0.230199i	$-0.0739378\pi$
$702$		0			0
$703$	−1602.88			−2.28006
$704$	−59.2653	+	59.2653i	−0.0841836	+	0.0841836i
$705$	220.460			0.312710
$706$			318.065i			0.450518i
$707$	−102.035	+	102.035i	−0.144321	+	0.144321i
$708$	−342.258	+	342.258i	−0.483415	+	0.483415i
$709$	68.9061	+	68.9061i	0.0971877	+	0.0971877i	0.754029	−	0.656841i	$-0.228108\pi$
$709$	68.9061	+	68.9061i	0.0971877	+	0.0971877i	−0.656841	+	0.754029i	$0.728108\pi$
$710$	305.174	+	305.174i	0.429822	+	0.429822i
$711$	46.3198			0.0651475
$712$		−	229.147i		−	0.321836i
$713$	−379.333	−	379.333i	−0.532024	−	0.532024i
$714$			272.877i			0.382181i
$715$		0			0
$716$	−126.681			−0.176928
$717$	713.475	−	713.475i	0.995083	−	0.995083i
$718$	580.556			0.808574
$719$		−	892.454i		−	1.24124i	−0.784110	−	0.620622i	$-0.786880\pi$
$719$		−	892.454i		−	1.24124i	0.784110	−	0.620622i	$-0.213120\pi$
$720$	−87.5705	+	87.5705i	−0.121626	+	0.121626i
$721$	586.519	−	586.519i	0.813479	−	0.813479i
$722$	−336.770	−	336.770i	−0.466440	−	0.466440i
$723$	1235.86	+	1235.86i	1.70934	+	1.70934i
$724$	373.008			0.515205
$725$		−	49.9067i		−	0.0688369i
$726$	43.2359	+	43.2359i	0.0595536	+	0.0595536i
$727$		−	1093.66i		−	1.50435i	−0.658964	−	0.752175i	$-0.729005\pi$
$727$		−	1093.66i		−	1.50435i	0.658964	−	0.752175i	$-0.270995\pi$
$728$		0			0
$729$	−151.327			−0.207581
$730$	96.6115	−	96.6115i	0.132345	−	0.132345i
$731$	58.5245			0.0800609
$732$		−	433.009i		−	0.591542i
$733$	136.804	−	136.804i	0.186636	−	0.186636i	−0.607604	−	0.794240i	$-0.707869\pi$
$733$	136.804	−	136.804i	0.186636	−	0.186636i	0.794240	+	0.607604i	$0.207869\pi$
$734$	−220.744	+	220.744i	−0.300741	+	0.300741i
$735$	−817.168	−	817.168i	−1.11179	−	1.11179i
$736$	79.8362	+	79.8362i	0.108473	+	0.108473i
$737$	−64.0371			−0.0868889
$738$		−	41.0800i		−	0.0556639i
$739$	−568.031	−	568.031i	−0.768649	−	0.768649i	0.209220	−	0.977869i	$-0.432908\pi$
$739$	−568.031	−	568.031i	−0.768649	−	0.768649i	−0.977869	+	0.209220i	$0.932908\pi$
$740$			647.758i			0.875349i
$741$		0			0
$742$	1117.97			1.50670
$743$	505.313	−	505.313i	0.680098	−	0.680098i	−0.279924	−	0.960022i	$-0.590309\pi$
$743$	505.313	−	505.313i	0.680098	−	0.680098i	0.960022	+	0.279924i	$0.0903093\pi$
$744$	292.470			0.393105
$745$		−	717.748i		−	0.963421i
$746$	−62.1593	+	62.1593i	−0.0833235	+	0.0833235i
$747$	−207.861	+	207.861i	−0.278261	+	0.278261i
$748$	−72.4238	−	72.4238i	−0.0968233	−	0.0968233i
$749$	1180.48	+	1180.48i	1.57607	+	1.57607i
$750$	−624.677			−0.832902
$751$		−	24.3942i		−	0.0324823i	−0.999868	−	0.0162412i	$-0.994830\pi$
$751$		−	24.3942i		−	0.0324823i	0.999868	−	0.0162412i	$-0.00516995\pi$
$752$	30.3667	+	30.3667i	0.0403813	+	0.0403813i
$753$		−	1688.89i		−	2.24288i
$754$		0			0
$755$	200.652			0.265764
$756$	178.604	−	178.604i	0.236249	−	0.236249i
$757$	−1025.22			−1.35433			−0.677163	−	0.735833i	$-0.736791\pi$
$757$	−1025.22			−1.35433			−0.677163	+	0.735833i	$0.736791\pi$
$758$			205.447i			0.271038i
$759$	−568.840	+	568.840i	−0.749460	+	0.749460i
$760$	−281.984	+	281.984i	−0.371031	+	0.371031i
$761$	−272.647	−	272.647i	−0.358275	−	0.358275i	0.504902	−	0.863177i	$-0.331529\pi$
$761$	−272.647	−	272.647i	−0.358275	−	0.358275i	−0.863177	+	0.504902i	$0.831529\pi$
$762$	−318.509	−	318.509i	−0.417991	−	0.417991i
$763$	−909.436			−1.19192
$764$			365.383i			0.478250i
$765$	−107.014	−	107.014i	−0.139887	−	0.139887i
$766$			711.051i			0.928265i
$767$		0			0
$768$	−61.5545			−0.0801491
$769$	171.616	−	171.616i	0.223168	−	0.223168i	−0.586663	−	0.809831i	$-0.699559\pi$
$769$	171.616	−	171.616i	0.223168	−	0.223168i	0.809831	+	0.586663i	$0.199559\pi$
$770$	811.427			1.05380
$771$			1682.01i			2.18159i
$772$	−128.910	+	128.910i	−0.166981	+	0.166981i
$773$	367.857	−	367.857i	0.475883	−	0.475883i	−0.427929	−	0.903812i	$-0.640757\pi$
$773$	367.857	−	367.857i	0.475883	−	0.475883i	0.903812	+	0.427929i	$0.140757\pi$
$774$	69.4499	+	69.4499i	0.0897286	+	0.0897286i
$775$	−66.3089	−	66.3089i	−0.0855598	−	0.0855598i
$776$	155.171			0.199963
$777$			2395.28i			3.08273i
$778$	−284.973	−	284.973i	−0.366289	−	0.366289i
$779$		−	132.281i		−	0.169808i
$780$		0			0
$781$	−599.010			−0.766978
$782$	−97.5621	+	97.5621i	−0.124760	+	0.124760i
$783$	176.065			0.224860
$784$		−	225.117i		−	0.287139i
$785$	−947.340	+	947.340i	−1.20680	+	1.20680i
$786$	−184.089	+	184.089i	−0.234210	+	0.234210i
$787$	1028.17	+	1028.17i	1.30644	+	1.30644i	0.923965	+	0.382478i	$0.124929\pi$
$787$	1028.17	+	1028.17i	1.30644	+	1.30644i	0.382478	+	0.923965i	$0.375071\pi$
$788$	305.193	+	305.193i	0.387300	+	0.387300i
$789$	1107.83			1.40409
$790$		−	60.2761i		−	0.0762988i
$791$	−507.008	−	507.008i	−0.640971	−	0.640971i
$792$		−	171.888i		−	0.217030i
$793$		0			0
$794$	−418.671			−0.527294
$795$	−1118.68	+	1118.68i	−1.40715	+	1.40715i
$796$	156.979			0.197209
$797$			472.216i			0.592491i	0.955112	+	0.296246i	$0.0957347\pi$
$797$			472.216i			0.592491i	−0.955112	+	0.296246i	$0.904265\pi$
$798$	−1042.72	+	1042.72i	−1.30667	+	1.30667i
$799$	−37.1090	+	37.1090i	−0.0464443	+	0.0464443i
$800$	13.9557	+	13.9557i	0.0174446	+	0.0174446i
$801$	332.299	+	332.299i	0.414855	+	0.414855i
$802$	342.048			0.426494
$803$			189.634i			0.236157i
$804$	−33.2554	−	33.2554i	−0.0413624	−	0.0413624i
$805$		−	1093.07i		−	1.35785i
$806$		0			0
$807$	−1321.11			−1.63707
$808$	28.1270	−	28.1270i	0.0348106	−	0.0348106i
$809$	954.431			1.17977			0.589883	−	0.807489i	$-0.299174\pi$
$809$	954.431			1.17977			0.589883	+	0.807489i	$0.299174\pi$
$810$			751.503i			0.927782i
$811$	643.215	−	643.215i	0.793114	−	0.793114i	−0.188885	−	0.981999i	$-0.560487\pi$
$811$	643.215	−	643.215i	0.793114	−	0.793114i	0.981999	+	0.188885i	$0.0604875\pi$
$812$	207.565	−	207.565i	0.255622	−	0.255622i
$813$	−22.5993	−	22.5993i	−0.0277975	−	0.0277975i
$814$	−635.726	−	635.726i	−0.780990	−	0.780990i
$815$	−648.934			−0.796238
$816$		−	75.2214i		−	0.0921830i
$817$	223.634	+	223.634i	0.273726	+	0.273726i
$818$		−	275.961i		−	0.337361i
$819$		0			0
$820$	−53.4574			−0.0651920
$821$	609.239	−	609.239i	0.742069	−	0.742069i	−0.230907	−	0.972976i	$-0.574169\pi$
$821$	609.239	−	609.239i	0.742069	−	0.742069i	0.972976	+	0.230907i	$0.0741692\pi$
$822$	1047.06			1.27379
$823$		−	747.037i		−	0.907700i	−0.891078	−	0.453850i	$-0.850050\pi$
$823$		−	747.037i		−	0.907700i	0.891078	−	0.453850i	$-0.149950\pi$
$824$	−161.680	+	161.680i	−0.196213	+	0.196213i
$825$	−99.4354	+	99.4354i	−0.120528	+	0.120528i
$826$	645.460	+	645.460i	0.781428	+	0.781428i
$827$	−1064.80	−	1064.80i	−1.28755	−	1.28755i	−0.936273	−	0.351272i	$-0.885749\pi$
$827$	−1064.80	−	1064.80i	−1.28755	−	1.28755i	−0.351272	−	0.936273i	$-0.614251\pi$
$828$	−231.550			−0.279650
$829$		−	127.571i		−	0.153886i	−0.997036	−	0.0769429i	$-0.975484\pi$
$829$		−	127.571i		−	0.153886i	0.997036	−	0.0769429i	$-0.0245159\pi$
$830$	270.490	+	270.490i	0.325892	+	0.325892i
$831$			1709.09i			2.05667i
$832$		0			0
$833$	275.099			0.330251
$834$	−742.859	+	742.859i	−0.890718	+	0.890718i
$835$	−330.399			−0.395688
$836$		−	553.492i		−	0.662072i
$837$	233.930	−	233.930i	0.279486	−	0.279486i
$838$	47.9110	−	47.9110i	0.0571730	−	0.0571730i
$839$	−335.660	−	335.660i	−0.400071	−	0.400071i	0.478187	−	0.878258i	$-0.341294\pi$
$839$	−335.660	−	335.660i	−0.400071	−	0.400071i	−0.878258	+	0.478187i	$0.841294\pi$
$840$	421.385	+	421.385i	0.501649	+	0.501649i
$841$	−636.385			−0.756700
$842$			954.036i			1.13306i
$843$	629.697	+	629.697i	0.746972	+	0.746972i
$844$			264.796i			0.313739i
$845$		0			0
$846$	−88.0730			−0.104105
$847$	81.5381	−	81.5381i	0.0962670	−	0.0962670i
$848$	−308.180			−0.363420
$849$		−	1785.62i		−	2.10320i
$850$	−17.0542	+	17.0542i	−0.0200638	+	0.0200638i
$851$	−856.386	+	856.386i	−1.00633	+	1.00633i
$852$	−311.074	−	311.074i	−0.365111	−	0.365111i
$853$	425.319	+	425.319i	0.498616	+	0.498616i	0.911007	−	0.412391i	$-0.135306\pi$
$853$	425.319	+	425.319i	0.498616	+	0.498616i	−0.412391	+	0.911007i	$0.635306\pi$
$854$	−816.606			−0.956214
$855$		−	817.841i		−	0.956540i
$856$	−325.410	−	325.410i	−0.380152	−	0.380152i
$857$		−	48.5237i		−	0.0566204i	−0.999599	−	0.0283102i	$-0.990987\pi$
$857$		−	48.5237i		−	0.0566204i	0.999599	−	0.0283102i	$-0.00901262\pi$
$858$		0			0
$859$	165.922			0.193157			0.0965787	−	0.995325i	$-0.469210\pi$
$859$	165.922			0.193157			0.0965787	+	0.995325i	$0.469210\pi$
$860$	90.3753	−	90.3753i	0.105088	−	0.105088i
$861$	−197.675			−0.229588
$862$		−	110.119i		−	0.127748i
$863$	376.277	−	376.277i	0.436010	−	0.436010i	−0.454657	−	0.890667i	$-0.650238\pi$
$863$	376.277	−	376.277i	0.436010	−	0.436010i	0.890667	+	0.454657i	$0.150238\pi$
$864$	−49.2340	+	49.2340i	−0.0569838	+	0.0569838i
$865$	1173.15	+	1173.15i	1.35624	+	1.35624i
$866$	497.603	+	497.603i	0.574599	+	0.574599i
$867$	−1019.91			−1.17636
$868$		−	551.566i		−	0.635445i
$869$	59.1565	+	59.1565i	0.0680742	+	0.0680742i
$870$			415.395i			0.477466i
$871$		0			0
$872$	250.695			0.287494
$873$	−225.023	+	225.023i	−0.257758	+	0.257758i
$874$	−745.609			−0.853099
$875$			1178.07i			1.34637i
$876$	−98.4795	+	98.4795i	−0.112420	+	0.112420i
$877$	−903.857	+	903.857i	−1.03062	+	1.03062i	−0.0311071	+	0.999516i	$0.509903\pi$
$877$	−903.857	+	903.857i	−1.03062	+	1.03062i	−0.999516	+	0.0311071i	$0.990097\pi$
$878$	167.510	+	167.510i	0.190786	+	0.190786i
$879$	−172.920	−	172.920i	−0.196724	−	0.196724i
$880$	−223.678			−0.254179
$881$		−	1248.35i		−	1.41697i	−0.705727	−	0.708484i	$-0.749379\pi$
$881$		−	1248.35i		−	1.41697i	0.705727	−	0.708484i	$-0.250621\pi$
$882$	326.455	+	326.455i	0.370130	+	0.370130i
$883$			1217.43i			1.37874i	0.724408	+	0.689371i	$0.242113\pi$
$883$			1217.43i			1.37874i	−0.724408	+	0.689371i	$0.757887\pi$
$884$		0			0
$885$	−1291.74			−1.45960
$886$	−443.835	+	443.835i	−0.500942	+	0.500942i
$887$	−31.0970			−0.0350587			−0.0175293	−	0.999846i	$-0.505580\pi$
$887$	−31.0970			−0.0350587			−0.0175293	+	0.999846i	$0.505580\pi$
$888$		−	660.283i		−	0.743562i
$889$	−600.673	+	600.673i	−0.675673	+	0.675673i
$890$	432.421	−	432.421i	0.485867	−	0.485867i
$891$	−737.544	−	737.544i	−0.827771	−	0.827771i
$892$	−168.997	−	168.997i	−0.189459	−	0.189459i
$893$	−283.602			−0.317583
$894$			731.626i			0.818374i
$895$	−239.058	−	239.058i	−0.267104	−	0.267104i
$896$			116.085i			0.129559i
$897$		0			0
$898$	−363.170			−0.404421
$899$	271.863	−	271.863i	0.302406	−	0.302406i
$900$	−40.4758			−0.0449731
$901$		−	376.605i		−	0.417985i
$902$	52.4645	−	52.4645i	0.0581646	−	0.0581646i
$903$	334.190	−	334.190i	0.370088	−	0.370088i
$904$	139.762	+	139.762i	0.154604	+	0.154604i
$905$	703.901	+	703.901i	0.777791	+	0.777791i
$906$	−204.531			−0.225752
$907$			1539.44i			1.69728i	0.528968	+	0.848642i	$0.322579\pi$
$907$			1539.44i			1.69728i	−0.528968	+	0.848642i	$0.677421\pi$
$908$	599.884	+	599.884i	0.660666	+	0.660666i
$909$			81.5771i			0.0897438i
$910$		0			0
$911$	−148.518			−0.163027			−0.0815136	−	0.996672i	$-0.525975\pi$
$911$	−148.518			−0.163027			−0.0815136	+	0.996672i	$0.525975\pi$
$912$	287.436	−	287.436i	0.315171	−	0.315171i
$913$	−530.932			−0.581525
$914$		−	123.191i		−	0.134783i
$915$	817.127	−	817.127i	0.893035	−	0.893035i
$916$	−316.412	+	316.412i	−0.345428	+	0.345428i
$917$	347.171	+	347.171i	0.378595	+	0.378595i
$918$	−60.1653	−	60.1653i	−0.0655395	−	0.0655395i
$919$	−1750.17			−1.90442			−0.952212	−	0.305438i	$-0.901197\pi$
$919$	−1750.17			−1.90442			−0.952212	+	0.305438i	$0.901197\pi$
$920$			301.316i			0.327518i
$921$	−258.296	−	258.296i	−0.280452	−	0.280452i
$922$		−	699.794i		−	0.758996i
$923$		0			0
$924$	−827.116			−0.895148
$925$	−149.700	+	149.700i	−0.161837	+	0.161837i
$926$	−798.943			−0.862789
$927$		−	468.922i		−	0.505849i
$928$	−57.2175	+	57.2175i	−0.0616568	+	0.0616568i
$929$	−696.265	+	696.265i	−0.749478	+	0.749478i	−0.974381	−	0.224903i	$-0.927793\pi$
$929$	−696.265	+	696.265i	−0.749478	+	0.749478i	0.224903	+	0.974381i	$0.427793\pi$
$930$	551.917	+	551.917i	0.593460	+	0.593460i
$931$	1051.21	+	1051.21i	1.12912	+	1.12912i
$932$	326.061			0.349850
$933$		−	1273.95i		−	1.36544i
$934$	409.816	+	409.816i	0.438775	+	0.438775i
$935$		−	273.341i		−	0.292343i
$936$		0			0
$937$	835.853			0.892052			0.446026	−	0.895020i	$-0.352839\pi$
$937$	835.853			0.892052			0.446026	+	0.895020i	$0.352839\pi$
$938$	−62.7159	+	62.7159i	−0.0668613	+	0.0668613i
$939$	1504.53			1.60227
$940$			114.610i			0.121925i
$941$	759.883	−	759.883i	0.807527	−	0.807527i	−0.176732	−	0.984259i	$-0.556553\pi$
$941$	759.883	−	759.883i	0.807527	−	0.807527i	0.984259	+	0.176732i	$0.0565525\pi$
$942$	965.657	−	965.657i	1.02511	−	1.02511i
$943$	−70.6749	−	70.6749i	−0.0749468	−	0.0749468i
$944$	−177.927	−	177.927i	−0.188482	−	0.188482i
$945$	674.084			0.713317
$946$			177.393i			0.187519i
$947$	816.039	+	816.039i	0.861709	+	0.861709i	0.991537	−	0.129827i	$-0.0414423\pi$
$947$	816.039	+	816.039i	0.861709	+	0.861709i	−0.129827	+	0.991537i	$0.541442\pi$
$948$			61.4415i			0.0648118i
$949$		0			0
$950$	−130.335			−0.137195
$951$	1242.49	−	1242.49i	1.30651	−	1.30651i
$952$	−141.859			−0.149012
$953$		−	1628.14i		−	1.70844i	−0.519914	−	0.854219i	$-0.674036\pi$
$953$		−	1628.14i		−	1.70844i	0.519914	−	0.854219i	$-0.325964\pi$
$954$	446.909	−	446.909i	0.468458	−	0.468458i
$955$	−689.511	+	689.511i	−0.722001	+	0.722001i
$956$	370.910	+	370.910i	0.387981	+	0.387981i
$957$	−407.680	−	407.680i	−0.425998	−	0.425998i
$958$	753.135			0.786153
$959$		−	1974.63i		−	2.05906i
$960$	−116.159	−	116.159i	−0.120999	−	0.120999i
$961$			238.576i			0.248258i
$962$		0			0
$963$	943.791			0.980053
$964$	−642.477	+	642.477i	−0.666470	+	0.666470i
$965$	−486.529			−0.504175
$966$			1114.21i			1.15342i
$967$	−1097.29	+	1097.29i	−1.13473	+	1.13473i	−0.145354	+	0.989380i	$0.546432\pi$
$967$	−1097.29	+	1097.29i	−1.13473	+	1.13473i	−0.989380	+	0.145354i	$0.953568\pi$
$968$	−22.4768	+	22.4768i	−0.0232198	+	0.0232198i
$969$	351.255	+	351.255i	0.362492	+	0.362492i
$970$	292.822	+	292.822i	0.301879	+	0.301879i
$971$	1289.79			1.32831			0.664157	−	0.747593i	$-0.268791\pi$
$971$	1289.79			1.32831			0.664157	+	0.747593i	$0.268791\pi$
$972$		−	544.481i		−	0.560165i
$973$	1400.95	+	1400.95i	1.43982	+	1.43982i
$974$		−	952.097i		−	0.977512i
$975$		0			0
$976$	225.106			0.230641
$977$	−1105.01	+	1105.01i	−1.13102	+	1.13102i	−0.141012	+	0.990008i	$0.545036\pi$
$977$	−1105.01	+	1105.01i	−1.13102	+	1.13102i	−0.990008	+	0.141012i	$0.954964\pi$
$978$	661.481			0.676361
$979$			848.778i			0.866985i
$980$	424.816	−	424.816i	0.433486	−	0.433486i
$981$	−363.547	+	363.547i	−0.370588	+	0.370588i
$982$	117.456	+	117.456i	0.119609	+	0.119609i
$983$	79.2765	+	79.2765i	0.0806475	+	0.0806475i	0.746280	−	0.665632i	$-0.231838\pi$
$983$	79.2765	+	79.2765i	0.0806475	+	0.0806475i	−0.665632	+	0.746280i	$0.731838\pi$
$984$	54.4911			0.0553771
$985$			1151.85i			1.16939i
$986$	−69.9214	−	69.9214i	−0.0709142	−	0.0709142i
$987$			423.803i			0.429385i
$988$		0			0
$989$	238.966			0.241624
$990$	324.368	−	324.368i	0.327645	−	0.327645i
$991$	−203.185			−0.205030			−0.102515	−	0.994731i	$-0.532689\pi$
$991$	−203.185			−0.205030			−0.102515	+	0.994731i	$0.532689\pi$
$992$			152.045i			0.153271i
$993$	−1333.10	+	1333.10i	−1.34250	+	1.34250i
$994$	−586.652	+	586.652i	−0.590193	+	0.590193i
$995$	296.233	+	296.233i	0.297721	+	0.297721i
$996$	−275.720	−	275.720i	−0.276828	−	0.276828i
$997$	1972.04			1.97798			0.988989	−	0.147987i	$-0.0472792\pi$
$997$	1972.04			1.97798			0.988989	+	0.147987i	$0.0472792\pi$
$998$		−	310.774i		−	0.311396i
$999$	−528.123	−	528.123i	−0.528651	−	0.528651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.d.g.239.2		8
13.2	odd	12		338.3.f.i.319.2		8
13.3	even	3		338.3.f.h.19.2		8
13.4	even	6		338.3.f.i.249.2		8
13.5	odd	4		338.3.d.f.99.2		8
13.6	odd	12		338.3.f.j.89.2		8
13.7	odd	12		338.3.f.h.89.2		8
13.8	odd	4	inner	338.3.d.g.99.2		8
13.9	even	3		26.3.f.b.15.2	yes	8
13.10	even	6		338.3.f.j.19.2		8
13.11	odd	12		26.3.f.b.7.2	✓	8
13.12	even	2		338.3.d.f.239.2		8
39.11	even	12		234.3.bb.f.163.1		8
39.35	odd	6		234.3.bb.f.145.1		8
52.11	even	12		208.3.bd.f.33.1		8
52.35	odd	6		208.3.bd.f.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.7.2	✓	8	13.11	odd	12
26.3.f.b.15.2	yes	8	13.9	even	3
208.3.bd.f.33.1		8	52.11	even	12
208.3.bd.f.145.1		8	52.35	odd	6
234.3.bb.f.145.1		8	39.35	odd	6
234.3.bb.f.163.1		8	39.11	even	12
338.3.d.f.99.2		8	13.5	odd	4
338.3.d.f.239.2		8	13.12	even	2
338.3.d.g.99.2		8	13.8	odd	4	inner
338.3.d.g.239.2		8	1.1	even	1	trivial
338.3.f.h.19.2		8	13.3	even	3
338.3.f.h.89.2		8	13.7	odd	12
338.3.f.i.249.2		8	13.4	even	6
338.3.f.i.319.2		8	13.2	odd	12
338.3.f.j.19.2		8	13.10	even	6
338.3.f.j.89.2		8	13.6	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -3.84716 q^{3} -2.00000i q^{4} +(3.77418 - 3.77418i) q^{5} +(-3.84716 + 3.84716i) q^{6} +(7.25532 + 7.25532i) q^{7} +(-2.00000 - 2.00000i) q^{8} +5.80063 q^{9} -7.54837i q^{10} +(7.40816 + 7.40816i) q^{11} +7.69432i q^{12} +14.5106 q^{14} +(-14.5199 + 14.5199i) q^{15} -4.00000 q^{16} -4.88811i q^{17} +(5.80063 - 5.80063i) q^{18} +(18.6785 - 18.6785i) q^{19} +(-7.54837 - 7.54837i) q^{20} +(-27.9124 - 27.9124i) q^{21} +14.8163 q^{22} -19.9590i q^{23} +(7.69432 + 7.69432i) q^{24} -3.48892i q^{25} +12.3085 q^{27} +(14.5106 - 14.5106i) q^{28} +14.3044 q^{29} +29.0398i q^{30} +(19.0056 - 19.0056i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-28.5004 - 28.5004i) q^{33} +(-4.88811 - 4.88811i) q^{34} +54.7658 q^{35} -11.6013i q^{36} +(-42.9072 - 42.9072i) q^{37} -37.3569i q^{38} -15.0967 q^{40} +(3.54099 - 3.54099i) q^{41} -55.8247 q^{42} +11.9728i q^{43} +(14.8163 - 14.8163i) q^{44} +(21.8926 - 21.8926i) q^{45} +(-19.9590 - 19.9590i) q^{46} +(-7.59168 - 7.59168i) q^{47} +15.3886 q^{48} +56.2792i q^{49} +(-3.48892 - 3.48892i) q^{50} +18.8053i q^{51} +77.0450 q^{53} +(12.3085 - 12.3085i) q^{54} +55.9195 q^{55} -29.0213i q^{56} +(-71.8590 + 71.8590i) q^{57} +(14.3044 - 14.3044i) q^{58} +(44.4819 + 44.4819i) q^{59} +(29.0398 + 29.0398i) q^{60} -56.2764 q^{61} -38.0112i q^{62} +(42.0854 + 42.0854i) q^{63} +8.00000i q^{64} -57.0007 q^{66} +(-4.32207 + 4.32207i) q^{67} -9.77622 q^{68} +76.7856i q^{69} +(54.7658 - 54.7658i) q^{70} +(-40.4291 + 40.4291i) q^{71} +(-11.6013 - 11.6013i) q^{72} +(12.7990 + 12.7990i) q^{73} -85.8143 q^{74} +13.4224i q^{75} +(-37.3569 - 37.3569i) q^{76} +107.497i q^{77} +7.98532 q^{79} +(-15.0967 + 15.0967i) q^{80} -99.5584 q^{81} -7.08199i q^{82} +(-35.8343 + 35.8343i) q^{83} +(-55.8247 + 55.8247i) q^{84} +(-18.4486 - 18.4486i) q^{85} +(11.9728 + 11.9728i) q^{86} -55.0312 q^{87} -29.6326i q^{88} +(57.2867 + 57.2867i) q^{89} -43.7853i q^{90} -39.9181 q^{92} +(-73.1175 + 73.1175i) q^{93} -15.1834 q^{94} -140.992i q^{95} +(15.3886 - 15.3886i) q^{96} +(-38.7928 + 38.7928i) q^{97} +(56.2792 + 56.2792i) q^{98} +(42.9720 + 42.9720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} + 84 q^{9} + 42 q^{11} + 20 q^{14} + 60 q^{15} - 32 q^{16} + 84 q^{18} + 22 q^{19} - 12 q^{20} - 102 q^{21} + 84 q^{22} + 72 q^{27} + 20 q^{28} + 12 q^{29}+ \cdots + 252 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 + 84 * q^9 + 42 * q^11 + 20 * q^14 + 60 * q^15 - 32 * q^16 + 84 * q^18 + 22 * q^19 - 12 * q^20 - 102 * q^21 + 84 * q^22 + 72 * q^27 + 20 * q^28 + 12 * q^29 + 32 * q^31 - 32 * q^32 + 54 * q^33 - 60 * q^34 + 156 * q^35 + 32 * q^37 - 24 * q^40 - 12 * q^41 - 204 * q^42 + 84 * q^44 - 102 * q^45 - 108 * q^46 + 60 * q^47 - 88 * q^50 - 132 * q^53 + 72 * q^54 + 324 * q^55 - 294 * q^57 + 12 * q^58 + 234 * q^59 - 120 * q^60 - 72 * q^61 - 156 * q^63 + 108 * q^66 - 14 * q^67 - 120 * q^68 + 156 * q^70 + 162 * q^71 - 168 * q^72 + 166 * q^73 + 64 * q^74 - 44 * q^76 - 96 * q^79 - 24 * q^80 + 24 * q^81 - 240 * q^83 - 204 * q^84 - 234 * q^85 + 132 * q^86 - 720 * q^87 + 210 * q^89 - 216 * q^92 - 444 * q^93 + 120 * q^94 + 146 * q^97 - 16 * q^98 + 252 * q^99

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