LMFDB - Embedded newform 33.3.c.a.10.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,3,Mod(10,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.10"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	33.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.899184872389$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.39744.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 12x^{2} + 4x + 22 $ x^4 - 2x^3 + 12x^2 + 4*x + 22
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.4
Root			$-0.366025 + 1.29224i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.3.c.a.10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.53045i q^{2} -1.73205 q^{3} -8.46410 q^{4} +6.19615 q^{5} -6.11492i q^{6} +2.58447i q^{7} -15.7603i q^{8} +3.00000 q^{9} +21.8752i q^{10} +(6.73205 + 8.69940i) q^{11} +14.6603 q^{12} -23.7672i q^{13} -9.12436 q^{14} -10.7321 q^{15} +21.7846 q^{16} -12.2298i q^{17} +10.5914i q^{18} -3.27698i q^{19} -52.4449 q^{20} -4.47644i q^{21} +(-30.7128 + 23.7672i) q^{22} -14.3397 q^{23} +27.2976i q^{24} +13.3923 q^{25} +83.9090 q^{26} -5.19615 q^{27} -21.8752i q^{28} +38.5815i q^{29} -37.8890i q^{30} -11.1769 q^{31} +13.8683i q^{32} +(-11.6603 - 15.0678i) q^{33} +43.1769 q^{34} +16.0138i q^{35} -25.3923 q^{36} -12.5359 q^{37} +11.5692 q^{38} +41.1660i q^{39} -97.6532i q^{40} +1.38501i q^{41} +15.8038 q^{42} -23.9527i q^{43} +(-56.9808 - 73.6326i) q^{44} +18.5885 q^{45} -50.6258i q^{46} +19.8038 q^{47} -37.7321 q^{48} +42.3205 q^{49} +47.2809i q^{50} +21.1827i q^{51} +201.168i q^{52} -12.0526 q^{53} -18.3448i q^{54} +(41.7128 + 53.9028i) q^{55} +40.7321 q^{56} +5.67589i q^{57} -136.210 q^{58} -62.7461 q^{59} +90.8372 q^{60} +21.3683i q^{61} -39.4596i q^{62} +7.75341i q^{63} +38.1769 q^{64} -147.265i q^{65} +(53.1962 - 41.1660i) q^{66} -34.0000 q^{67} +103.515i q^{68} +24.8372 q^{69} -56.5359 q^{70} -69.2679 q^{71} -47.2809i q^{72} +39.9665i q^{73} -44.2574i q^{74} -23.1962 q^{75} +27.7367i q^{76} +(-22.4833 + 17.3988i) q^{77} -145.335 q^{78} -97.6532i q^{79} +134.981 q^{80} +9.00000 q^{81} -4.88973 q^{82} +71.9941i q^{83} +37.8890i q^{84} -75.7780i q^{85} +84.5641 q^{86} -66.8251i q^{87} +(137.105 - 106.099i) q^{88} +107.177 q^{89} +65.6257i q^{90} +61.4256 q^{91} +121.373 q^{92} +19.3590 q^{93} +69.9166i q^{94} -20.3047i q^{95} -24.0207i q^{96} -166.746 q^{97} +149.411i q^{98} +(20.1962 + 26.0982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 20 q^{4} + 4 q^{5} + 12 q^{9} + 20 q^{11} + 24 q^{12} + 12 q^{14} - 36 q^{15} + 4 q^{16} - 92 q^{20} - 12 q^{22} - 92 q^{23} + 12 q^{25} + 204 q^{26} + 80 q^{31} - 12 q^{33} + 48 q^{34} - 60 q^{36}+ \cdots + 60 q^{99}+O(q^{100}) $ 4 * q - 20 * q^4 + 4 * q^5 + 12 * q^9 + 20 * q^11 + 24 * q^12 + 12 * q^14 - 36 * q^15 + 4 * q^16 - 92 * q^20 - 12 * q^22 - 92 * q^23 + 12 * q^25 + 204 * q^26 + 80 * q^31 - 12 * q^33 + 48 * q^34 - 60 * q^36 - 64 * q^37 - 120 * q^38 + 84 * q^42 - 124 * q^44 + 12 * q^45 + 100 * q^47 - 144 * q^48 + 100 * q^49 + 28 * q^53 + 56 * q^55 + 156 * q^56 - 240 * q^58 + 40 * q^59 + 204 * q^60 + 28 * q^64 + 192 * q^66 - 136 * q^67 - 60 * q^69 - 240 * q^70 - 284 * q^71 - 72 * q^75 - 180 * q^77 - 228 * q^78 + 436 * q^80 + 36 * q^81 + 216 * q^82 - 216 * q^86 + 396 * q^88 + 304 * q^89 + 24 * q^91 + 340 * q^92 + 216 * q^93 - 376 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

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 $

$2$			3.53045i			1.76523i	0.470100	+	0.882613i	$0.344218\pi$
$2$			3.53045i			1.76523i	−0.470100	+	0.882613i	$0.655782\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−8.46410			−2.11603
$5$	6.19615			1.23923			0.619615	−	0.784906i	$-0.287289\pi$
$5$	6.19615			1.23923			0.619615	+	0.784906i	$0.287289\pi$
$6$		−	6.11492i		−	1.01915i
$7$			2.58447i			0.369210i	0.982813	+	0.184605i	$0.0591006\pi$
$7$			2.58447i			0.369210i	−0.982813	+	0.184605i	$0.940899\pi$
$8$		−	15.7603i		−	1.97004i
$9$	3.00000			0.333333
$10$			21.8752i			2.18752i
$11$	6.73205	+	8.69940i	0.612005	+	0.790854i
$11$	6.73205	+	8.69940i	0.612005	+	0.790854i
$12$	14.6603			1.22169
$13$		−	23.7672i		−	1.82825i	−0.405437	−	0.914123i	$-0.632881\pi$
$13$		−	23.7672i		−	1.82825i	0.405437	−	0.914123i	$-0.367119\pi$
$14$	−9.12436			−0.651740
$15$	−10.7321			−0.715470
$16$	21.7846			1.36154
$17$		−	12.2298i		−	0.719403i	−0.933067	−	0.359701i	$-0.882879\pi$
$17$		−	12.2298i		−	0.719403i	0.933067	−	0.359701i	$-0.117121\pi$
$18$			10.5914i			0.588409i
$19$		−	3.27698i		−	0.172473i	−0.996275	−	0.0862363i	$-0.972516\pi$
$19$		−	3.27698i		−	0.172473i	0.996275	−	0.0862363i	$-0.0274840\pi$
$20$	−52.4449			−2.62224
$21$		−	4.47644i		−	0.213164i
$22$	−30.7128	+	23.7672i	−1.39604	+	1.08033i
$23$	−14.3397			−0.623467			−0.311734	−	0.950170i	$-0.600910\pi$
$23$	−14.3397			−0.623467			−0.311734	+	0.950170i	$0.600910\pi$
$24$			27.2976i			1.13740i
$25$	13.3923			0.535692
$26$	83.9090			3.22727
$27$	−5.19615			−0.192450
$28$		−	21.8752i		−	0.781258i
$29$			38.5815i			1.33040i	0.746667	+	0.665198i	$0.231653\pi$
$29$			38.5815i			1.33040i	−0.746667	+	0.665198i	$0.768347\pi$
$30$		−	37.8890i		−	1.26297i
$31$	−11.1769			−0.360546			−0.180273	−	0.983617i	$-0.557698\pi$
$31$	−11.1769			−0.360546			−0.180273	+	0.983617i	$0.557698\pi$
$32$			13.8683i			0.433386i
$33$	−11.6603	−	15.0678i	−0.353341	−	0.456600i
$34$	43.1769			1.26991
$35$			16.0138i			0.457537i
$36$	−25.3923			−0.705342
$37$	−12.5359			−0.338808			−0.169404	−	0.985547i	$-0.554184\pi$
$37$	−12.5359			−0.338808			−0.169404	+	0.985547i	$0.554184\pi$
$38$	11.5692			0.304453
$39$			41.1660i			1.05554i
$40$		−	97.6532i		−	2.44133i
$41$			1.38501i			0.0337808i	0.999857	+	0.0168904i	$0.00537664\pi$
$41$			1.38501i			0.0337808i	−0.999857	+	0.0168904i	$0.994623\pi$
$42$	15.8038			0.376282
$43$		−	23.9527i		−	0.557041i	−0.960430	−	0.278520i	$-0.910156\pi$
$43$		−	23.9527i		−	0.557041i	0.960430	−	0.278520i	$-0.0898440\pi$
$44$	−56.9808	−	73.6326i	−1.29502	−	1.67347i
$45$	18.5885			0.413077
$46$		−	50.6258i		−	1.10056i
$47$	19.8038			0.421358			0.210679	−	0.977555i	$-0.432432\pi$
$47$	19.8038			0.421358			0.210679	+	0.977555i	$0.432432\pi$
$48$	−37.7321			−0.786084
$49$	42.3205			0.863684
$50$			47.2809i			0.945618i
$51$			21.1827i			0.415347i
$52$			201.168i			3.86861i
$53$	−12.0526			−0.227407			−0.113703	−	0.993515i	$-0.536271\pi$
$53$	−12.0526			−0.227407			−0.113703	+	0.993515i	$0.536271\pi$
$54$		−	18.3448i		−	0.339718i
$55$	41.7128	+	53.9028i	0.758415	+	0.980051i
$56$	40.7321			0.727358
$57$			5.67589i			0.0995771i
$58$	−136.210			−2.34845
$59$	−62.7461			−1.06349			−0.531747	−	0.846903i	$-0.678464\pi$
$59$	−62.7461			−1.06349			−0.531747	+	0.846903i	$0.678464\pi$
$60$	90.8372			1.51395
$61$			21.3683i			0.350300i	0.984542	+	0.175150i	$0.0560410\pi$
$61$			21.3683i			0.350300i	−0.984542	+	0.175150i	$0.943959\pi$
$62$		−	39.4596i		−	0.636445i
$63$			7.75341i			0.123070i
$64$	38.1769			0.596514
$65$		−	147.265i		−	2.26562i
$66$	53.1962	−	41.1660i	0.806002	−	0.623727i
$67$	−34.0000			−0.507463			−0.253731	−	0.967275i	$-0.581658\pi$
$67$	−34.0000			−0.507463			−0.253731	+	0.967275i	$0.581658\pi$
$68$			103.515i			1.52227i
$69$	24.8372			0.359959
$70$	−56.5359			−0.807656
$71$	−69.2679			−0.975605			−0.487802	−	0.872954i	$-0.662201\pi$
$71$	−69.2679			−0.975605			−0.487802	+	0.872954i	$0.662201\pi$
$72$		−	47.2809i		−	0.656679i
$73$			39.9665i			0.547487i	0.961803	+	0.273743i	$0.0882619\pi$
$73$			39.9665i			0.547487i	−0.961803	+	0.273743i	$0.911738\pi$
$74$		−	44.2574i		−	0.598073i
$75$	−23.1962			−0.309282
$76$			27.7367i			0.364956i
$77$	−22.4833	+	17.3988i	−0.291991	+	0.225958i
$78$	−145.335			−1.86326
$79$		−	97.6532i		−	1.23612i	−0.786132	−	0.618058i	$-0.787919\pi$
$79$		−	97.6532i		−	1.23612i	0.786132	−	0.618058i	$-0.212081\pi$
$80$	134.981			1.68726
$81$	9.00000			0.111111
$82$	−4.88973			−0.0596308
$83$			71.9941i			0.867399i	0.901058	+	0.433699i	$0.142792\pi$
$83$			71.9941i			0.867399i	−0.901058	+	0.433699i	$0.857208\pi$
$84$			37.8890i			0.451060i
$85$		−	75.7780i		−	0.891506i
$86$	84.5641			0.983303
$87$		−	66.8251i		−	0.768105i
$88$	137.105	−	106.099i	1.55801	−	1.20567i
$89$	107.177			1.20423			0.602117	−	0.798407i	$-0.294324\pi$
$89$	107.177			1.20423			0.602117	+	0.798407i	$0.294324\pi$
$90$			65.6257i			0.729174i
$91$	61.4256			0.675007
$92$	121.373			1.31927
$93$	19.3590			0.208161
$94$			69.9166i			0.743793i
$95$		−	20.3047i		−	0.213733i
$96$		−	24.0207i		−	0.250215i
$97$	−166.746			−1.71903			−0.859516	−	0.511109i	$-0.829235\pi$
$97$	−166.746			−1.71903			−0.859516	+	0.511109i	$0.829235\pi$
$98$			149.411i			1.52460i
$99$	20.1962	+	26.0982i	0.204002	+	0.263618i
$100$	−113.354			−1.13354
$101$		−	92.6699i		−	0.917523i	−0.888559	−	0.458762i	$-0.848293\pi$
$101$		−	92.6699i		−	0.917523i	0.888559	−	0.458762i	$-0.151707\pi$
$102$	−74.7846			−0.733182
$103$	140.746			1.36647			0.683234	−	0.730200i	$-0.260573\pi$
$103$	140.746			1.36647			0.683234	+	0.730200i	$0.260573\pi$
$104$	−374.578			−3.60171
$105$		−	27.7367i		−	0.264159i
$106$		−	42.5510i		−	0.401425i
$107$			74.8999i			0.700000i	0.936750	+	0.350000i	$0.113818\pi$
$107$			74.8999i			0.700000i	−0.936750	+	0.350000i	$0.886182\pi$
$108$	43.9808			0.407229
$109$			153.634i			1.40948i	0.709465	+	0.704741i	$0.248937\pi$
$109$			153.634i			1.40948i	−0.709465	+	0.704741i	$0.751063\pi$
$110$	−190.301	+	147.265i	−1.73001	+	1.33877i
$111$	21.7128			0.195611
$112$			56.3017i			0.502694i
$113$	166.315			1.47182			0.735909	−	0.677081i	$-0.236755\pi$
$113$	166.315			1.47182			0.735909	+	0.677081i	$0.236755\pi$
$114$	−20.0385			−0.175776
$115$	−88.8513			−0.772620
$116$		−	326.558i		−	2.81515i
$117$		−	71.3016i		−	0.609415i
$118$		−	221.522i		−	1.87731i
$119$	31.6077			0.265611
$120$			169.140i			1.40950i
$121$	−30.3590	+	117.130i	−0.250901	+	0.968013i
$122$	−75.4397			−0.618358
$123$		−	2.39891i		−	0.0195034i
$124$	94.6025			0.762924
$125$	−71.9230			−0.575384
$126$	−27.3731			−0.217247
$127$		−	190.323i		−	1.49861i	−0.662227	−	0.749304i	$-0.730388\pi$
$127$		−	190.323i		−	1.49861i	0.662227	−	0.749304i	$-0.269612\pi$
$128$			190.255i			1.48637i
$129$			41.4874i			0.321608i
$130$	519.913			3.99933
$131$			99.2238i			0.757434i	0.925513	+	0.378717i	$0.123635\pi$
$131$			99.2238i			0.757434i	−0.925513	+	0.378717i	$0.876365\pi$
$132$	98.6936	+	127.535i	0.747679	+	0.966177i
$133$	8.46926			0.0636786
$134$		−	120.035i		−	0.895787i
$135$	−32.1962			−0.238490
$136$	−192.746			−1.41725
$137$	−29.2154			−0.213251			−0.106626	−	0.994299i	$-0.534005\pi$
$137$	−29.2154			−0.213251			−0.106626	+	0.994299i	$0.534005\pi$
$138$			87.6865i			0.635409i
$139$			171.354i			1.23276i	0.787449	+	0.616380i	$0.211402\pi$
$139$			171.354i			1.23276i	−0.787449	+	0.616380i	$0.788598\pi$
$140$		−	135.542i		−	0.968159i
$141$	−34.3013			−0.243271
$142$		−	244.547i		−	1.72216i
$143$	206.760	−	160.002i	1.44588	−	1.11889i
$144$	65.3538			0.453846
$145$			239.057i			1.64867i
$146$	−141.100			−0.966438
$147$	−73.3013			−0.498648
$148$	106.105			0.716926
$149$			164.293i			1.10264i	0.834295	+	0.551318i	$0.185875\pi$
$149$			164.293i			1.10264i	−0.834295	+	0.551318i	$0.814125\pi$
$150$		−	81.8929i		−	0.545953i
$151$		−	229.547i		−	1.52018i	−0.649817	−	0.760091i	$-0.725154\pi$
$151$		−	229.547i		−	1.52018i	0.649817	−	0.760091i	$-0.274846\pi$
$152$	−51.6462			−0.339777
$153$		−	36.6895i		−	0.239801i
$154$	−61.4256	−	79.3764i	−0.398868	−	0.515431i
$155$	−69.2539			−0.446799
$156$		−	348.433i		−	2.23355i
$157$	−106.862			−0.680647			−0.340323	−	0.940308i	$-0.610537\pi$
$157$	−106.862			−0.680647			−0.340323	+	0.940308i	$0.610537\pi$
$158$	344.760			2.18203
$159$	20.8756			0.131293
$160$			85.9303i			0.537065i
$161$		−	37.0607i		−	0.230190i
$162$			31.7741i			0.196136i
$163$	−118.067			−0.724335			−0.362168	−	0.932113i	$-0.617963\pi$
$163$	−118.067			−0.724335			−0.362168	+	0.932113i	$0.617963\pi$
$164$		−	11.7229i		−	0.0714811i
$165$	−72.2487	−	93.3624i	−0.437871	−	0.565832i
$166$	−254.172			−1.53116
$167$			1.38501i			0.00829350i	0.999991	+	0.00414675i	$0.00131995\pi$
$167$			1.38501i			0.00829350i	−0.999991	+	0.00414675i	$0.998680\pi$
$168$	−70.5500			−0.419940
$169$	−395.879			−2.34248
$170$	267.531			1.57371
$171$		−	9.83093i		−	0.0574908i
$172$			202.738i			1.17871i
$173$			67.8390i			0.392133i	0.980591	+	0.196067i	$0.0628169\pi$
$173$			67.8390i			0.392133i	−0.980591	+	0.196067i	$0.937183\pi$
$174$	235.923			1.35588
$175$			34.6120i			0.197783i
$176$	146.655	+	189.513i	0.833268	+	1.07678i
$177$	108.679			0.614008
$178$			378.383i			2.12575i
$179$	−136.603			−0.763143			−0.381571	−	0.924339i	$-0.624617\pi$
$179$	−136.603			−0.763143			−0.381571	+	0.924339i	$0.624617\pi$
$180$	−157.335			−0.874081
$181$	172.172			0.951225			0.475613	−	0.879655i	$-0.342226\pi$
$181$	172.172			0.951225			0.475613	+	0.879655i	$0.342226\pi$
$182$			216.860i			1.19154i
$183$		−	37.0109i		−	0.202246i
$184$			225.999i			1.22825i
$185$	−77.6743			−0.419861
$186$			68.3460i			0.367452i
$187$	106.392	−	82.3320i	0.568943	−	0.440278i
$188$	−167.622			−0.891605
$189$		−	13.4293i		−	0.0710545i
$190$	71.6846			0.377288
$191$	137.765			0.721285			0.360642	−	0.932704i	$-0.382558\pi$
$191$	137.765			0.721285			0.360642	+	0.932704i	$0.382558\pi$
$192$	−66.1244			−0.344398
$193$		−	106.421i		−	0.551402i	−0.961243	−	0.275701i	$-0.911090\pi$
$193$		−	106.421i		−	0.551402i	0.961243	−	0.275701i	$-0.0889099\pi$
$194$		−	588.689i		−	3.03448i
$195$			255.071i			1.30805i
$196$	−358.205			−1.82758
$197$			33.4126i			0.169607i	0.996398	+	0.0848035i	$0.0270262\pi$
$197$			33.4126i			0.169607i	−0.996398	+	0.0848035i	$0.972974\pi$
$198$	−92.1384	+	71.3016i	−0.465346	+	0.360109i
$199$	334.056			1.67868			0.839338	−	0.543611i	$-0.182943\pi$
$199$	334.056			1.67868			0.839338	+	0.543611i	$0.182943\pi$
$200$		−	211.067i		−	1.05533i
$201$	58.8897			0.292984
$202$	327.167			1.61964
$203$	−99.7128			−0.491196
$204$		−	179.293i		−	0.878886i
$205$			8.58176i			0.0418622i
$206$			496.898i			2.41212i
$207$	−43.0192			−0.207822
$208$		−	517.759i		−	2.48923i
$209$	28.5077	−	22.0608i	0.136401	−	0.105554i
$210$	97.9230			0.466300
$211$			31.1495i			0.147628i	0.997272	+	0.0738140i	$0.0235171\pi$
$211$			31.1495i			0.147628i	−0.997272	+	0.0738140i	$0.976483\pi$
$212$	102.014			0.481199
$213$	119.976			0.563266
$214$	−264.431			−1.23566
$215$		−	148.415i		−	0.690302i
$216$			81.8929i			0.379134i
$217$		−	28.8864i		−	0.133117i
$218$	−542.396			−2.48806
$219$		−	69.2241i		−	0.316092i
$220$	−353.061	−	456.239i	−1.60482	−	2.07381i
$221$	−290.669			−1.31525
$222$			76.6561i			0.345298i
$223$	137.713			0.617546			0.308773	−	0.951136i	$-0.400082\pi$
$223$	137.713			0.617546			0.308773	+	0.951136i	$0.400082\pi$
$224$	−35.8423			−0.160010
$225$	40.1769			0.178564
$226$			587.169i			2.59809i
$227$		−	329.835i		−	1.45302i	−0.687158	−	0.726508i	$-0.741142\pi$
$227$		−	329.835i		−	1.45302i	0.687158	−	0.726508i	$-0.258858\pi$
$228$		−	48.0413i		−	0.210708i
$229$	299.282			1.30691			0.653454	−	0.756966i	$-0.273319\pi$
$229$	299.282			1.30691			0.653454	+	0.756966i	$0.273319\pi$
$230$		−	313.685i		−	1.36385i
$231$	38.9423	−	30.1356i	0.168581	−	0.130457i
$232$	608.056			2.62093
$233$			146.115i			0.627105i	0.949571	+	0.313552i	$0.101519\pi$
$233$			146.115i			0.627105i	−0.949571	+	0.313552i	$0.898481\pi$
$234$	251.727			1.07576
$235$	122.708			0.522160
$236$	531.090			2.25038
$237$			169.140i			0.713672i
$238$			111.589i			0.468863i
$239$			63.4123i			0.265324i	0.991161	+	0.132662i	$0.0423524\pi$
$239$			63.4123i			0.265324i	−0.991161	+	0.132662i	$0.957648\pi$
$240$	−233.794			−0.974140
$241$			351.018i			1.45650i	0.685309	+	0.728252i	$0.259667\pi$
$241$			351.018i			1.45650i	−0.685309	+	0.728252i	$0.740333\pi$
$242$	−413.520	−	107.181i	−1.70876	−	0.442897i
$243$	−15.5885			−0.0641500
$244$		−	180.863i		−	0.741243i
$245$	262.224			1.07030
$246$	8.46926			0.0344279
$247$	−77.8846			−0.315322
$248$			176.152i			0.710289i
$249$		−	124.697i		−	0.500793i
$250$		−	253.921i		−	1.01568i
$251$	65.7231			0.261845			0.130923	−	0.991393i	$-0.458206\pi$
$251$	65.7231			0.261845			0.130923	+	0.991393i	$0.458206\pi$
$252$		−	65.6257i		−	0.260419i
$253$	−96.5359	−	124.747i	−0.381565	−	0.493072i
$254$	671.927			2.64538
$255$			131.251i			0.514711i
$256$	−518.979			−2.02726
$257$	−206.182			−0.802265			−0.401132	−	0.916020i	$-0.631383\pi$
$257$	−206.182			−0.802265			−0.401132	+	0.916020i	$0.631383\pi$
$258$	−146.469			−0.567710
$259$		−	32.3987i		−	0.125091i
$260$			1246.47i			4.79410i
$261$			115.745i			0.443466i
$262$	−350.305			−1.33704
$263$			18.2769i			0.0694937i	0.999396	+	0.0347469i	$0.0110625\pi$
$263$			18.2769i			0.0694937i	−0.999396	+	0.0347469i	$0.988937\pi$
$264$	−237.473	+	183.769i	−0.899519	+	0.696095i
$265$	−74.6795			−0.281809
$266$			29.9003i			0.112407i
$267$	−185.636			−0.695265
$268$	287.779			1.07380
$269$	−172.130			−0.639887			−0.319943	−	0.947437i	$-0.603664\pi$
$269$	−172.130			−0.639887			−0.319943	+	0.947437i	$0.603664\pi$
$270$		−	113.667i		−	0.420989i
$271$		−	425.967i		−	1.57183i	−0.618332	−	0.785917i	$-0.712191\pi$
$271$		−	425.967i		−	1.57183i	0.618332	−	0.785917i	$-0.287809\pi$
$272$		−	266.422i		−	0.979494i
$273$	−106.392			−0.389715
$274$		−	103.144i		−	0.376436i
$275$	90.1577	+	116.505i	0.327846	+	0.423654i
$276$	−210.224			−0.761682
$277$		−	261.439i		−	0.943824i	−0.881646	−	0.471912i	$-0.843564\pi$
$277$		−	261.439i		−	0.943824i	0.881646	−	0.471912i	$-0.156436\pi$
$278$	−604.956			−2.17610
$279$	−33.5307			−0.120182
$280$	252.382			0.901364
$281$		−	329.192i		−	1.17150i	−0.810491	−	0.585751i	$-0.800800\pi$
$281$		−	329.192i		−	1.17150i	0.810491	−	0.585751i	$-0.199200\pi$
$282$		−	121.099i		−	0.429429i
$283$		−	231.353i		−	0.817503i	−0.912646	−	0.408751i	$-0.865964\pi$
$283$		−	231.353i		−	0.817503i	0.912646	−	0.408751i	$-0.134036\pi$
$284$	586.291			2.06440
$285$			35.1687i			0.123399i
$286$	564.879	+	729.957i	1.97510	+	2.55230i
$287$	−3.57953			−0.0124722
$288$			41.6050i			0.144462i
$289$	139.431			0.482459
$290$	−843.979			−2.91027
$291$	288.813			0.992484
$292$		−	338.281i		−	1.15850i
$293$		−	199.733i		−	0.681683i	−0.940121	−	0.340842i	$-0.889288\pi$
$293$		−	199.733i		−	0.681683i	0.940121	−	0.340842i	$-0.110712\pi$
$294$		−	258.787i		−	0.880227i
$295$	−388.785			−1.31791
$296$			197.570i			0.667465i
$297$	−34.9808	−	45.2034i	−0.117780	−	0.152200i
$298$	−580.028			−1.94640
$299$			340.815i			1.13985i
$300$	196.335			0.654449
$301$	61.9052			0.205665
$302$	810.406			2.68346
$303$			160.509i			0.529732i
$304$		−	71.3877i		−	0.234828i
$305$			132.401i			0.434102i
$306$	129.531			0.423303
$307$			426.289i			1.38856i	0.719704	+	0.694281i	$0.244278\pi$
$307$			426.289i			1.38856i	−0.719704	+	0.694281i	$0.755722\pi$
$308$	190.301	−	147.265i	0.617861	−	0.478134i
$309$	−243.779			−0.788930
$310$		−	244.498i		−	0.788702i
$311$	−301.611			−0.969812			−0.484906	−	0.874566i	$-0.661146\pi$
$311$	−301.611			−0.969812			−0.484906	+	0.874566i	$0.661146\pi$
$312$	648.788			2.07945
$313$	260.697			0.832899			0.416449	−	0.909159i	$-0.363274\pi$
$313$	260.697			0.832899			0.416449	+	0.909159i	$0.363274\pi$
$314$		−	377.270i		−	1.20150i
$315$			48.0413i			0.152512i
$316$			826.547i			2.61565i
$317$	451.191			1.42332			0.711658	−	0.702526i	$-0.247945\pi$
$317$	451.191			1.42332			0.711658	+	0.702526i	$0.247945\pi$
$318$			73.7005i			0.231763i
$319$	−335.636	+	259.733i	−1.05215	+	0.814209i
$320$	236.550			0.739219
$321$		−	129.731i		−	0.404145i
$322$	130.841			0.406338
$323$	−40.0770			−0.124077
$324$	−76.1769			−0.235114
$325$		−	318.297i		−	0.979377i
$326$		−	416.829i		−	1.27862i
$327$		−	266.101i		−	0.813765i
$328$	21.8282			0.0665495
$329$			51.1825i			0.155570i
$330$	329.611	−	255.071i	0.998823	−	0.772942i
$331$	229.569			0.693563			0.346781	−	0.937946i	$-0.387275\pi$
$331$	229.569			0.693563			0.346781	+	0.937946i	$0.387275\pi$
$332$		−	609.365i		−	1.83544i
$333$	−37.6077			−0.112936
$334$	−4.88973			−0.0146399
$335$	−210.669			−0.628863
$336$		−	97.5174i		−	0.290230i
$337$			178.143i			0.528614i	0.964439	+	0.264307i	$0.0851432\pi$
$337$			178.143i			0.528614i	−0.964439	+	0.264307i	$0.914857\pi$
$338$		−	1397.63i		−	4.13501i
$339$	−288.067			−0.849754
$340$			641.393i			1.88645i
$341$	−75.2436	−	97.2324i	−0.220656	−	0.285139i
$342$	34.7077			0.101484
$343$			236.015i			0.688091i
$344$	−377.503			−1.09739
$345$	153.895			0.446072
$346$	−239.503			−0.692204
$347$			574.839i			1.65660i	0.560287	+	0.828299i	$0.310691\pi$
$347$			574.839i			1.65660i	−0.560287	+	0.828299i	$0.689309\pi$
$348$			565.615i			1.62533i
$349$		−	182.619i		−	0.523265i	−0.965168	−	0.261632i	$-0.915739\pi$
$349$		−	182.619i		−	0.523265i	0.965168	−	0.261632i	$-0.0842608\pi$
$350$	−122.196			−0.349132
$351$			123.498i			0.351846i
$352$	−120.646	+	93.3624i	−0.342745	+	0.265234i
$353$	−195.990			−0.555212			−0.277606	−	0.960695i	$-0.589541\pi$
$353$	−195.990			−0.555212			−0.277606	+	0.960695i	$0.589541\pi$
$354$			383.688i			1.08386i
$355$	−429.195			−1.20900
$356$	−907.156			−2.54819
$357$	−54.7461			−0.153351
$358$		−	482.269i		−	1.34712i
$359$			707.105i			1.96965i	0.173548	+	0.984825i	$0.444477\pi$
$359$			707.105i			1.96965i	−0.173548	+	0.984825i	$0.555523\pi$
$360$		−	292.960i		−	0.813777i
$361$	350.261			0.970253
$362$			607.844i			1.67913i
$363$	52.5833	−	202.874i	0.144858	−	0.558882i
$364$	−519.913			−1.42833
$365$			247.639i			0.678462i
$366$	130.665			0.357009
$367$	359.415			0.979333			0.489667	−	0.871910i	$-0.337118\pi$
$367$	359.415			0.979333			0.489667	+	0.871910i	$0.337118\pi$
$368$	−312.386			−0.848874
$369$			4.15504i			0.0112603i
$370$		−	274.226i		−	0.741150i
$371$		−	31.1495i		−	0.0839609i
$372$	−163.856			−0.440474
$373$		−	363.804i		−	0.975346i	−0.873026	−	0.487673i	$-0.837846\pi$
$373$		−	363.804i		−	0.975346i	0.873026	−	0.487673i	$-0.162154\pi$
$374$	290.669	+	375.613i	0.777190	+	1.00431i
$375$	124.574			0.332198
$376$		−	312.115i		−	0.830092i
$377$	916.974			2.43229
$378$	47.4115			0.125427
$379$	−266.046			−0.701968			−0.350984	−	0.936381i	$-0.614153\pi$
$379$	−266.046			−0.701968			−0.350984	+	0.936381i	$0.614153\pi$
$380$			171.861i			0.452265i
$381$			329.649i			0.865221i
$382$			486.374i			1.27323i
$383$	331.258			0.864902			0.432451	−	0.901657i	$-0.357649\pi$
$383$	331.258			0.864902			0.432451	+	0.901657i	$0.357649\pi$
$384$		−	329.532i		−	0.858155i
$385$	−139.310	+	107.806i	−0.361845	+	0.280014i
$386$	375.713			0.973349
$387$		−	71.8582i		−	0.185680i
$388$	1411.36			3.63752
$389$	421.027			1.08233			0.541166	−	0.840916i	$-0.317983\pi$
$389$	421.027			1.08233			0.541166	+	0.840916i	$0.317983\pi$
$390$	−900.515			−2.30901
$391$			175.373i			0.448524i
$392$		−	666.984i		−	1.70149i
$393$		−	171.861i		−	0.437305i
$394$	−117.962			−0.299395
$395$		−	605.074i		−	1.53183i
$396$	−170.942	−	220.898i	−0.431672	−	0.557823i
$397$	−421.797			−1.06246			−0.531231	−	0.847227i	$-0.678270\pi$
$397$	−421.797			−1.06246			−0.531231	+	0.847227i	$0.678270\pi$
$398$			1179.37i			2.96324i
$399$	−14.6692			−0.0367649
$400$	291.746			0.729365
$401$	−353.531			−0.881623			−0.440811	−	0.897600i	$-0.645309\pi$
$401$	−353.531			−0.881623			−0.440811	+	0.897600i	$0.645309\pi$
$402$			207.907i			0.517183i
$403$			265.644i			0.659166i
$404$			784.367i			1.94150i
$405$	55.7654			0.137692
$406$		−	352.031i		−	0.867073i
$407$	−84.3923	−	109.055i	−0.207352	−	0.267948i
$408$	333.846			0.818250
$409$		−	625.515i		−	1.52938i	−0.644401	−	0.764688i	$-0.722893\pi$
$409$		−	625.515i		−	1.52938i	0.644401	−	0.764688i	$-0.277107\pi$
$410$	−30.2975			−0.0738963
$411$	50.6025			0.123121
$412$	−1191.29			−2.89148
$413$		−	162.166i		−	0.392653i
$414$		−	151.877i		−	0.366854i
$415$			446.086i			1.07491i
$416$	329.611			0.792335
$417$		−	296.793i		−	0.711735i
$418$	77.8846	+	100.645i	0.186327	+	0.240778i
$419$	100.631			0.240169			0.120084	−	0.992764i	$-0.461683\pi$
$419$	100.631			0.240169			0.120084	+	0.992764i	$0.461683\pi$
$420$			234.766i			0.558967i
$421$	−25.7616			−0.0611914			−0.0305957	−	0.999532i	$-0.509740\pi$
$421$	−25.7616			−0.0611914			−0.0305957	+	0.999532i	$0.509740\pi$
$422$	−109.972			−0.260597
$423$	59.4115			0.140453
$424$			189.952i			0.448000i
$425$		−	163.786i		−	0.385379i
$426$			423.568i			0.994292i
$427$	−55.2257			−0.129334
$428$		−	633.961i		−	1.48122i
$429$	−358.119	+	277.131i	−0.834777	+	0.645994i
$430$	523.972			1.21854
$431$		−	850.178i		−	1.97257i	−0.165047	−	0.986286i	$-0.552778\pi$
$431$		−	850.178i		−	1.97257i	0.165047	−	0.986286i	$-0.447222\pi$
$432$	−113.196			−0.262028
$433$	−502.631			−1.16081			−0.580405	−	0.814328i	$-0.697106\pi$
$433$	−502.631			−1.16081			−0.580405	+	0.814328i	$0.697106\pi$
$434$	101.982			0.234982
$435$		−	414.059i		−	0.951859i
$436$		−	1300.37i		−	2.98250i
$437$			46.9910i			0.107531i
$438$	244.392			0.557973
$439$		−	141.132i		−	0.321485i	−0.986996	−	0.160743i	$-0.948611\pi$
$439$		−	141.132i		−	0.321485i	0.986996	−	0.160743i	$-0.0513889\pi$
$440$	849.524	−	657.407i	1.93074	−	1.49411i
$441$	126.962			0.287895
$442$		−	1026.19i		−	2.32171i
$443$	−871.538			−1.96736			−0.983678	−	0.179940i	$-0.942410\pi$
$443$	−871.538			−1.96736			−0.983678	+	0.179940i	$0.942410\pi$
$444$	−183.779			−0.413918
$445$	664.084			1.49232
$446$			486.189i			1.09011i
$447$		−	284.564i		−	0.636607i
$448$			98.6671i			0.220239i
$449$	−122.364			−0.272526			−0.136263	−	0.990673i	$-0.543509\pi$
$449$	−122.364			−0.272526			−0.136263	+	0.990673i	$0.543509\pi$
$450$			141.843i			0.315206i
$451$	−12.0488	+	9.32398i	−0.0267157	+	0.0206740i
$452$	−1407.71			−3.11440
$453$			397.588i			0.877677i
$454$	1164.47			2.56490
$455$	380.603			0.836489
$456$	89.4538			0.196171
$457$			581.864i			1.27323i	0.771184	+	0.636613i	$0.219665\pi$
$457$			581.864i			1.27323i	−0.771184	+	0.636613i	$0.780335\pi$
$458$			1056.60i			2.30699i
$459$			63.5482i			0.138449i
$460$	752.046			1.63488
$461$		−	54.4595i		−	0.118133i	−0.998254	−	0.0590667i	$-0.981188\pi$
$461$		−	54.4595i		−	0.118133i	0.998254	−	0.0590667i	$-0.0188124\pi$
$462$	106.392	+	137.484i	0.230286	+	0.297584i
$463$	356.382			0.769724			0.384862	−	0.922974i	$-0.374249\pi$
$463$	356.382			0.769724			0.384862	+	0.922974i	$0.374249\pi$
$464$			840.483i			1.81139i
$465$	119.951			0.257960
$466$	−515.854			−1.10698
$467$	298.613			0.639428			0.319714	−	0.947514i	$-0.396413\pi$
$467$	298.613			0.639428			0.319714	+	0.947514i	$0.396413\pi$
$468$			603.504i			1.28954i
$469$		−	87.8720i		−	0.187360i
$470$			433.214i			0.921731i
$471$	185.090			0.392972
$472$			988.898i			2.09512i
$473$	208.374	−	161.251i	0.440538	−	0.340911i
$474$	−597.142			−1.25979
$475$		−	43.8863i		−	0.0923922i
$476$	−267.531			−0.562039
$477$	−36.1577			−0.0758023
$478$	−223.874			−0.468356
$479$		−	333.755i		−	0.696774i	−0.937351	−	0.348387i	$-0.886730\pi$
$479$		−	333.755i		−	0.696774i	0.937351	−	0.348387i	$-0.113270\pi$
$480$		−	148.836i		−	0.310074i
$481$			297.943i			0.619424i
$482$	−1239.25			−2.57106
$483$			64.1909i			0.132901i
$484$	256.962	−	991.396i	0.530912	−	2.04834i
$485$	−1033.18			−2.13028
$486$		−	55.0343i		−	0.113239i
$487$	−709.251			−1.45637			−0.728184	−	0.685382i	$-0.759635\pi$
$487$	−709.251			−1.45637			−0.728184	+	0.685382i	$0.759635\pi$
$488$	336.771			0.690104
$489$	204.497			0.418195
$490$			925.771i			1.88933i
$491$			31.9912i			0.0651551i	0.999469	+	0.0325776i	$0.0103716\pi$
$491$			31.9912i			0.0651551i	−0.999469	+	0.0325776i	$0.989628\pi$
$492$			20.3047i			0.0412696i
$493$	471.846			0.957091
$494$		−	274.968i		−	0.556615i
$495$	125.138	+	161.708i	0.252805	+	0.326684i
$496$	−243.485			−0.490897
$497$		−	179.021i		−	0.360203i
$498$	440.238			0.884013
$499$	27.6922			0.0554954			0.0277477	−	0.999615i	$-0.491167\pi$
$499$	27.6922			0.0554954			0.0277477	+	0.999615i	$0.491167\pi$
$500$	608.764			1.21753
$501$		−	2.39891i		−	0.00478825i
$502$			232.032i			0.462216i
$503$		−	69.6946i		−	0.138558i	−0.997597	−	0.0692789i	$-0.977930\pi$
$503$		−	69.6946i		−	0.138558i	0.997597	−	0.0692789i	$-0.0220698\pi$
$504$	122.196			0.242453
$505$		−	574.197i		−	1.13702i
$506$	440.414	−	340.815i	0.870383	−	0.673548i
$507$	685.683			1.35243
$508$			1610.91i			3.17109i
$509$	−252.732			−0.496527			−0.248263	−	0.968693i	$-0.579860\pi$
$509$	−252.732			−0.496527			−0.248263	+	0.968693i	$0.579860\pi$
$510$	−463.377			−0.908582
$511$	−103.292			−0.202138
$512$		−	1071.21i		−	2.09221i
$513$			17.0277i			0.0331924i
$514$		−	727.916i		−	1.41618i
$515$	872.084			1.69337
$516$		−	351.153i		−	0.680530i
$517$	133.321	+	172.282i	0.257873	+	0.333233i
$518$	114.382			0.220815
$519$		−	117.501i		−	0.226398i
$520$	−2320.94			−4.46335
$521$	−611.864			−1.17440			−0.587201	−	0.809441i	$-0.699770\pi$
$521$	−611.864			−1.17440			−0.587201	+	0.809441i	$0.699770\pi$
$522$	−408.631			−0.782817
$523$		−	6.31868i		−	0.0120816i	−0.999982	−	0.00604080i	$-0.998077\pi$
$523$		−	6.31868i		−	0.0120816i	0.999982	−	0.00604080i	$-0.00192286\pi$
$524$		−	839.840i		−	1.60275i
$525$		−	59.9498i		−	0.114190i
$526$	−64.5256			−0.122672
$527$			136.692i			0.259378i
$528$	−254.014	−	328.246i	−0.481087	−	0.621678i
$529$	−323.372			−0.611289
$530$		−	263.652i		−	0.497457i
$531$	−188.238			−0.354498
$532$	−71.6846			−0.134746
$533$	32.9179			0.0617597
$534$		−	655.379i		−	1.22730i
$535$			464.091i			0.867461i
$536$			535.850i			0.999721i
$537$	236.603			0.440601
$538$		−	607.695i		−	1.12955i
$539$	284.904	+	368.163i	0.528578	+	0.683048i
$540$	272.512			0.504651
$541$			427.018i			0.789311i	0.918829	+	0.394656i	$0.129136\pi$
$541$			427.018i			0.789311i	−0.918829	+	0.394656i	$0.870864\pi$
$542$	1503.86			2.77464
$543$	−298.210			−0.549190
$544$	169.608			0.311779
$545$			951.937i			1.74667i
$546$		−	375.613i		−	0.687936i
$547$			783.217i			1.43184i	0.698182	+	0.715921i	$0.253993\pi$
$547$			783.217i			1.43184i	−0.698182	+	0.715921i	$0.746007\pi$
$548$	247.282			0.451245
$549$			64.1048i			0.116767i
$550$	−411.315	+	318.297i	−0.747846	+	0.578723i
$551$	126.431			0.229457
$552$		−	391.441i		−	0.709133i
$553$	252.382			0.456387
$554$	922.999			1.66606
$555$	134.536			0.242407
$556$		−	1450.36i		−	2.60855i
$557$			508.385i			0.912720i	0.889795	+	0.456360i	$0.150847\pi$
$557$			508.385i			0.912720i	−0.889795	+	0.456360i	$0.849153\pi$
$558$		−	118.379i		−	0.212148i
$559$	−569.290			−1.01841
$560$			348.854i			0.622953i
$561$	−184.277	+	142.603i	−0.328479	+	0.254195i
$562$	1162.20			2.06797
$563$		−	670.786i		−	1.19145i	−0.803189	−	0.595725i	$-0.796865\pi$
$563$		−	670.786i		−	1.19145i	0.803189	−	0.595725i	$-0.203135\pi$
$564$	290.329			0.514769
$565$	1030.52			1.82392
$566$	816.782			1.44308
$567$			23.2602i			0.0410234i
$568$			1091.68i			1.92198i
$569$		−	756.359i		−	1.32928i	−0.747165	−	0.664639i	$-0.768586\pi$
$569$		−	756.359i		−	1.32928i	0.747165	−	0.664639i	$-0.231414\pi$
$570$	−124.161			−0.217827
$571$		−	647.983i		−	1.13482i	−0.823435	−	0.567411i	$-0.807945\pi$
$571$		−	647.983i		−	1.13482i	0.823435	−	0.567411i	$-0.192055\pi$
$572$	−1750.04	+	1354.27i	−3.05951	+	2.36761i
$573$	−238.617			−0.416434
$574$		−	12.6374i		−	0.0220163i
$575$	−192.042			−0.333987
$576$	114.531			0.198838
$577$	78.3257			0.135746			0.0678732	−	0.997694i	$-0.478379\pi$
$577$	78.3257			0.135746			0.0678732	+	0.997694i	$0.478379\pi$
$578$			492.254i			0.851650i
$579$			184.326i			0.318352i
$580$		−	2023.40i		−	3.48862i
$581$	−186.067			−0.320252
$582$			1019.64i			1.75196i
$583$	−81.1384	−	104.850i	−0.139174	−	0.179846i
$584$	629.885			1.07857
$585$		−	441.795i		−	0.755206i
$586$	705.149			1.20333
$587$	190.515			0.324558			0.162279	−	0.986745i	$-0.448116\pi$
$587$	190.515			0.324558			0.162279	+	0.986745i	$0.448116\pi$
$588$	620.429			1.05515
$589$			36.6265i			0.0621842i
$590$		−	1372.59i		−	2.32642i
$591$		−	57.8723i		−	0.0979226i
$592$	−273.090			−0.461300
$593$			770.010i			1.29850i	0.760575	+	0.649250i	$0.224917\pi$
$593$			770.010i			1.29850i	−0.760575	+	0.649250i	$0.775083\pi$
$594$	159.588	−	123.498i	0.268667	−	0.207909i
$595$	195.846			0.329153
$596$		−	1390.59i		−	2.33321i
$597$	−578.603			−0.969183
$598$	−1203.23			−2.01210
$599$	−891.517			−1.48834			−0.744171	−	0.667989i	$-0.767155\pi$
$599$	−891.517			−1.48834			−0.744171	+	0.667989i	$0.767155\pi$
$600$			365.578i			0.609297i
$601$		−	75.5063i		−	0.125635i	−0.998025	−	0.0628173i	$-0.979991\pi$
$601$		−	75.5063i		−	0.125635i	0.998025	−	0.0628173i	$-0.0200085\pi$
$602$			218.553i			0.363046i
$603$	−102.000			−0.169154
$604$			1942.91i			3.21674i
$605$	−188.109	+	725.753i	−0.310924	+	1.19959i
$606$	−566.669			−0.935098
$607$			442.017i			0.728200i	0.931360	+	0.364100i	$0.118623\pi$
$607$			442.017i			0.728200i	−0.931360	+	0.364100i	$0.881377\pi$
$608$	45.4462			0.0747471
$609$	172.708			0.283592
$610$	−467.436			−0.766288
$611$		−	470.682i		−	0.770347i
$612$			310.544i			0.507425i
$613$		−	544.346i		−	0.888003i	−0.896026	−	0.444002i	$-0.853558\pi$
$613$		−	544.346i		−	0.888003i	0.896026	−	0.444002i	$-0.146442\pi$
$614$	−1504.99			−2.45113
$615$		−	14.8640i		−	0.0241692i
$616$	274.210	+	354.344i	0.445146	+	0.575234i
$617$	406.946			0.659556			0.329778	−	0.944059i	$-0.393026\pi$
$617$	406.946			0.659556			0.329778	+	0.944059i	$0.393026\pi$
$618$		−	860.652i		−	1.39264i
$619$	−218.939			−0.353697			−0.176849	−	0.984238i	$-0.556590\pi$
$619$	−218.939			−0.353697			−0.176849	+	0.984238i	$0.556590\pi$
$620$	586.172			0.945438
$621$	74.5115			0.119986
$622$		−	1064.83i		−	1.71194i
$623$			276.996i			0.444616i
$624$			896.785i			1.43716i
$625$	−780.454			−1.24873
$626$			920.380i			1.47026i
$627$	−49.3768	+	38.2104i	−0.0787509	+	0.0609416i
$628$	904.487			1.44027
$629$			153.312i			0.243740i
$630$	−169.608			−0.269219
$631$	185.664			0.294238			0.147119	−	0.989119i	$-0.453000\pi$
$631$	185.664			0.294238			0.147119	+	0.989119i	$0.453000\pi$
$632$	−1539.04			−2.43520
$633$		−	53.9525i		−	0.0852330i
$634$			1592.91i			2.51247i
$635$		−	1179.27i		−	1.85712i
$636$	−176.694			−0.277820
$637$		−	1005.84i		−	1.57903i
$638$	−916.974	−	1184.95i	−1.43726	−	1.85728i
$639$	−207.804			−0.325202
$640$			1178.85i			1.84195i
$641$	375.618			0.585988			0.292994	−	0.956114i	$-0.405348\pi$
$641$	375.618			0.585988			0.292994	+	0.956114i	$0.405348\pi$
$642$	458.008			0.713407
$643$	−454.764			−0.707253			−0.353627	−	0.935387i	$-0.615052\pi$
$643$	−454.764			−0.707253			−0.353627	+	0.935387i	$0.615052\pi$
$644$			313.685i			0.487089i
$645$			257.062i			0.398546i
$646$		−	141.490i		−	0.219024i
$647$	724.273			1.11943			0.559716	−	0.828684i	$-0.310910\pi$
$647$	724.273			1.11943			0.559716	+	0.828684i	$0.310910\pi$
$648$		−	141.843i		−	0.218893i
$649$	−422.410	−	545.853i	−0.650863	−	0.841069i
$650$	1123.73			1.72882
$651$			50.0327i			0.0768552i
$652$	999.328			1.53271
$653$	−336.865			−0.515873			−0.257937	−	0.966162i	$-0.583043\pi$
$653$	−336.865			−0.515873			−0.257937	+	0.966162i	$0.583043\pi$
$654$	939.458			1.43648
$655$			614.806i			0.938635i
$656$			30.1720i			0.0459939i
$657$			119.900i			0.182496i
$658$	−180.697			−0.274616
$659$		−	41.1163i		−	0.0623919i	−0.999513	−	0.0311960i	$-0.990068\pi$
$659$		−	41.1163i		−	0.0623919i	0.999513	−	0.0311960i	$-0.00993159\pi$
$660$	611.520	+	790.229i	0.926546	+	1.19732i
$661$	−831.969			−1.25865			−0.629326	−	0.777141i	$-0.716669\pi$
$661$	−831.969			−1.25865			−0.629326	+	0.777141i	$0.716669\pi$
$662$			810.483i			1.22430i
$663$	503.454			0.759357
$664$	1134.65			1.70881
$665$	52.4768			0.0789125
$666$		−	132.772i		−	0.199358i
$667$		−	553.249i		−	0.829459i
$668$		−	11.7229i		−	0.0175493i
$669$	−238.526			−0.356540
$670$		−	743.758i		−	1.11009i
$671$	−185.891	+	143.852i	−0.277036	+	0.214385i
$672$	62.0807			0.0923820
$673$			682.274i			1.01378i	0.862011	+	0.506890i	$0.169205\pi$
$673$			682.274i			1.01378i	−0.862011	+	0.506890i	$0.830795\pi$
$674$	−628.925			−0.933124
$675$	−69.5885			−0.103094
$676$	3350.76			4.95675
$677$		−	483.554i		−	0.714261i	−0.934055	−	0.357130i	$-0.883755\pi$
$677$		−	483.554i		−	0.714261i	0.934055	−	0.357130i	$-0.116245\pi$
$678$		−	1017.01i		−	1.50001i
$679$		−	430.951i		−	0.634684i
$680$	−1194.28			−1.75630
$681$			571.291i			0.838900i
$682$	343.274	−	265.644i	0.503335	−	0.389507i
$683$	875.097			1.28126			0.640628	−	0.767852i	$-0.278674\pi$
$683$	875.097			1.28126			0.640628	+	0.767852i	$0.278674\pi$
$684$			83.2100i			0.121652i
$685$	−181.023			−0.264267
$686$	−833.241			−1.21464
$687$	−518.372			−0.754544
$688$		−	521.801i		−	0.758432i
$689$			286.455i			0.415755i
$690$			543.319i			0.787418i
$691$	845.615			1.22376			0.611878	−	0.790952i	$-0.290414\pi$
$691$	845.615			1.22376			0.611878	+	0.790952i	$0.290414\pi$
$692$		−	574.197i		−	0.829764i
$693$	−67.4500	+	52.1964i	−0.0973305	+	0.0753194i
$694$	−2029.44			−2.92427
$695$			1061.73i			1.52767i
$696$	−1053.18			−1.51320
$697$	16.9385			0.0243020
$698$	644.729			0.923681
$699$		−	253.079i		−	0.362059i
$700$		−	292.960i		−	0.418514i
$701$			842.982i			1.20254i	0.799045	+	0.601271i	$0.205339\pi$
$701$			842.982i			1.20254i	−0.799045	+	0.601271i	$0.794661\pi$
$702$	−436.004			−0.621088
$703$			41.0799i			0.0584351i
$704$	257.009	+	332.116i	0.365070	+	0.471756i
$705$	−212.536			−0.301469
$706$		−	691.932i		−	0.980074i
$707$	239.503			0.338759
$708$	−919.874			−1.29926
$709$	1227.03			1.73065			0.865325	−	0.501212i	$-0.167112\pi$
$709$	1227.03			1.73065			0.865325	+	0.501212i	$0.167112\pi$
$710$		−	1515.25i		−	2.13416i
$711$		−	292.960i		−	0.412039i
$712$		−	1689.14i		−	2.37239i
$713$	160.274			0.224788
$714$		−	193.279i		−	0.270698i
$715$	1281.12	−	991.396i	1.79177	−	1.38657i
$716$	1156.22			1.61483
$717$		−	109.833i		−	0.153185i
$718$	−2496.40			−3.47688
$719$	343.986			0.478423			0.239211	−	0.970968i	$-0.423111\pi$
$719$	343.986			0.478423			0.239211	+	0.970968i	$0.423111\pi$
$720$	404.942			0.562420
$721$			363.754i			0.504514i
$722$			1236.58i			1.71272i
$723$		−	607.980i		−	0.840913i
$724$	−1457.28			−2.01282
$725$			516.695i			0.712683i
$726$	716.238	+	185.643i	0.986554	+	0.255706i
$727$	205.138			0.282171			0.141086	−	0.989997i	$-0.454941\pi$
$727$	205.138			0.282171			0.141086	+	0.989997i	$0.454941\pi$
$728$		−	968.086i		−	1.32979i
$729$	27.0000			0.0370370
$730$	−874.277			−1.19764
$731$	−292.939			−0.400737
$732$			313.264i			0.427957i
$733$		−	849.486i		−	1.15892i	−0.815002	−	0.579458i	$-0.803264\pi$
$733$		−	849.486i		−	1.15892i	0.815002	−	0.579458i	$-0.196736\pi$
$734$			1268.90i			1.72875i
$735$	−454.186			−0.617940
$736$		−	198.868i		−	0.270202i
$737$	−228.890	−	295.779i	−0.310570	−	0.401329i
$738$	−14.6692			−0.0198769
$739$		−	1206.77i		−	1.63298i	−0.577360	−	0.816490i	$-0.695917\pi$
$739$		−	1206.77i		−	1.63298i	0.577360	−	0.816490i	$-0.304083\pi$
$740$	657.443			0.888437
$741$	134.900			0.182051
$742$	109.972			0.148210
$743$		−	229.932i		−	0.309464i	−0.987956	−	0.154732i	$-0.950549\pi$
$743$		−	229.932i		−	0.309464i	0.987956	−	0.154732i	$-0.0494514\pi$
$744$		−	305.103i		−	0.410085i
$745$			1017.98i			1.36642i
$746$	1284.39			1.72171
$747$			215.982i			0.289133i
$748$	−900.515	+	696.866i	−1.20390	+	0.931639i
$749$	−193.577			−0.258447
$750$			439.804i			0.586405i
$751$	616.269			0.820598			0.410299	−	0.911951i	$-0.365424\pi$
$751$	616.269			0.820598			0.410299	+	0.911951i	$0.365424\pi$
$752$	431.419			0.573696
$753$	−113.836			−0.151176
$754$			3237.33i			4.29355i
$755$		−	1422.31i		−	1.88386i
$756$			113.667i			0.150353i
$757$	85.4181			0.112838			0.0564188	−	0.998407i	$-0.482032\pi$
$757$	85.4181			0.112838			0.0564188	+	0.998407i	$0.482032\pi$
$758$		−	939.263i		−	1.23913i
$759$	167.205	+	216.068i	0.220297	+	0.284675i
$760$	−320.008			−0.421063
$761$		−	439.940i		−	0.578108i	−0.957313	−	0.289054i	$-0.906659\pi$
$761$		−	439.940i		−	0.578108i	0.957313	−	0.289054i	$-0.0933406\pi$
$762$	−1163.81			−1.52731
$763$	−397.061			−0.520395
$764$	−1166.06			−1.52626
$765$		−	227.334i		−	0.297169i
$766$			1169.49i			1.52675i
$767$			1491.30i			1.94433i
$768$	898.899			1.17044
$769$			928.726i			1.20771i	0.797095	+	0.603853i	$0.206369\pi$
$769$			928.726i			1.20771i	−0.797095	+	0.603853i	$0.793631\pi$
$770$	−380.603	−	491.828i	−0.494289	−	0.638738i
$771$	357.118			0.463188
$772$			900.754i			1.16678i
$773$	929.734			1.20276			0.601381	−	0.798963i	$-0.294618\pi$
$773$	929.734			1.20276			0.601381	+	0.798963i	$0.294618\pi$
$774$	253.692			0.327768
$775$	−149.685			−0.193141
$776$			2627.97i			3.38656i
$777$			56.1161i			0.0722215i
$778$			1486.42i			1.91056i
$779$	4.53866			0.00582627
$780$		−	2158.94i		−	2.76788i
$781$	−466.315	−	602.589i	−0.597075	−	0.771561i
$782$	−619.146			−0.791747
$783$		−	200.475i		−	0.256035i
$784$	921.936			1.17594
$785$	−662.131			−0.843478
$786$	606.746			0.771942
$787$			250.644i			0.318480i	0.987240	+	0.159240i	$0.0509044\pi$
$787$			250.644i			0.318480i	−0.987240	+	0.159240i	$0.949096\pi$
$788$		−	282.807i		−	0.358893i
$789$		−	31.6564i		−	0.0401222i
$790$	2136.19			2.70403
$791$			429.837i			0.543410i
$792$	411.315	−	318.297i	0.519338	−	0.401891i
$793$	507.864			0.640434
$794$		−	1489.14i		−	1.87549i
$795$	129.349			0.162703
$796$	−2827.49			−3.55212
$797$	872.319			1.09450			0.547252	−	0.836968i	$-0.315674\pi$
$797$	872.319			1.09450			0.547252	+	0.836968i	$0.315674\pi$
$798$		−	51.7889i		−	0.0648983i
$799$		−	242.198i		−	0.303127i
$800$			185.729i			0.232161i
$801$	321.531			0.401412
$802$		−	1248.12i		−	1.55626i
$803$	−347.685	+	269.057i	−0.432982	+	0.335064i
$804$	−498.449			−0.619961
$805$		−	229.634i		−	0.285259i
$806$	−937.843			−1.16358
$807$	298.137			0.369439
$808$	−1460.50			−1.80756
$809$		−	963.696i		−	1.19122i	−0.803274	−	0.595609i	$-0.796911\pi$
$809$		−	963.696i		−	1.19122i	0.803274	−	0.595609i	$-0.203089\pi$
$810$			196.877i			0.243058i
$811$			583.285i			0.719217i	0.933103	+	0.359609i	$0.117090\pi$
$811$			583.285i			0.719217i	−0.933103	+	0.359609i	$0.882910\pi$
$812$	843.979			1.03938
$813$			737.797i			0.907499i
$814$	385.013	−	297.943i	0.472989	−	0.366023i
$815$	−731.559			−0.897618
$816$			461.457i			0.565511i
$817$	−78.4926			−0.0960742
$818$	2208.35			2.69970
$819$	184.277			0.225002
$820$		−	72.6369i		−	0.0885815i
$821$		−	211.927i		−	0.258132i	−0.991636	−	0.129066i	$-0.958802\pi$
$821$		−	211.927i		−	0.258132i	0.991636	−	0.129066i	$-0.0411980\pi$
$822$			178.650i			0.217336i
$823$	−1049.19			−1.27484			−0.637421	−	0.770516i	$-0.719999\pi$
$823$	−1049.19			−1.27484			−0.637421	+	0.770516i	$0.719999\pi$
$824$		−	2218.20i		−	2.69199i
$825$	−156.158	−	201.793i	−0.189282	−	0.244597i
$826$	572.518			0.693121
$827$			1226.67i			1.48328i	0.670800	+	0.741638i	$0.265951\pi$
$827$			1226.67i			1.48328i	−0.670800	+	0.741638i	$0.734049\pi$
$828$	364.119			0.439757
$829$	579.395			0.698908			0.349454	−	0.936954i	$-0.386367\pi$
$829$	579.395			0.698908			0.349454	+	0.936954i	$0.386367\pi$
$830$	−1574.89			−1.89745
$831$			452.826i			0.544917i
$832$		−	907.358i		−	1.09057i
$833$		−	517.573i		−	0.621337i
$834$	1047.82			1.25637
$835$			8.58176i			0.0102776i
$836$	−241.292	+	186.725i	−0.288627	+	0.223355i
$837$	58.0770			0.0693870
$838$			355.272i			0.423952i
$839$	−1198.03			−1.42793			−0.713964	−	0.700182i	$-0.753102\pi$
$839$	−1198.03			−1.42793			−0.713964	+	0.700182i	$0.753102\pi$
$840$	−437.138			−0.520403
$841$	−647.533			−0.769956
$842$		−	90.9501i		−	0.108017i
$843$			570.177i			0.676367i
$844$		−	263.652i		−	0.312384i
$845$	−2452.93			−2.90287
$846$			209.750i			0.247931i
$847$	−302.718	−	78.4619i	−0.357400	−	0.0926351i
$848$	−262.560			−0.309623
$849$			400.716i			0.471985i
$850$	578.238			0.680280
$851$	179.762			0.211236
$852$	−1015.49			−1.19188
$853$		−	1015.06i		−	1.18999i	−0.803728	−	0.594997i	$-0.797153\pi$
$853$		−	1015.06i		−	1.18999i	0.803728	−	0.594997i	$-0.202847\pi$
$854$		−	194.972i		−	0.228304i
$855$		−	60.9140i		−	0.0712444i
$856$	1180.45			1.37903
$857$		−	1574.17i		−	1.83684i	−0.395603	−	0.918422i	$-0.629464\pi$
$857$		−	1574.17i		−	1.83684i	0.395603	−	0.918422i	$-0.370536\pi$
$858$	−978.400	−	1264.32i	−1.14033	−	1.47357i
$859$	99.9230			0.116325			0.0581624	−	0.998307i	$-0.481476\pi$
$859$	99.9230			0.116325			0.0581624	+	0.998307i	$0.481476\pi$
$860$			1256.20i			1.46070i
$861$	6.19993			0.00720084
$862$	3001.51			3.48204
$863$	−1405.55			−1.62868			−0.814339	−	0.580389i	$-0.802900\pi$
$863$	−1405.55			−1.62868			−0.814339	+	0.580389i	$0.802900\pi$
$864$		−	72.0620i		−	0.0834051i
$865$			420.341i			0.485943i
$866$		−	1774.51i		−	2.04909i
$867$	−241.501			−0.278548
$868$			244.498i			0.281679i
$869$	849.524	−	657.407i	0.977588	−	0.756509i
$870$	1461.82			1.68025
$871$			808.085i			0.927766i
$872$	2421.31			2.77673
$873$	−500.238			−0.573011
$874$	−165.900			−0.189817
$875$		−	185.883i		−	0.212438i
$876$			585.919i			0.668858i
$877$			1231.05i			1.40370i	0.712324	+	0.701851i	$0.247643\pi$
$877$			1231.05i			1.40370i	−0.712324	+	0.701851i	$0.752357\pi$
$878$	498.260			0.567494
$879$			345.948i			0.393570i
$880$	908.697	+	1174.25i	1.03261	+	1.33438i
$881$	419.359			0.476003			0.238002	−	0.971265i	$-0.423508\pi$
$881$	419.359			0.476003			0.238002	+	0.971265i	$0.423508\pi$
$882$			448.232i			0.508199i
$883$	867.856			0.982850			0.491425	−	0.870920i	$-0.336476\pi$
$883$	867.856			0.982850			0.491425	+	0.870920i	$0.336476\pi$
$884$	2460.25			2.78309
$885$	673.395			0.760898
$886$		−	3076.93i		−	3.47283i
$887$		−	484.124i		−	0.545800i	−0.962042	−	0.272900i	$-0.912017\pi$
$887$		−	484.124i		−	0.545800i	0.962042	−	0.272900i	$-0.0879828\pi$
$888$		−	342.201i		−	0.385361i
$889$	491.885			0.553301
$890$			2344.52i			2.63429i
$891$	60.5885	+	78.2946i	0.0680005	+	0.0878727i
$892$	−1165.62			−1.30674
$893$		−	64.8968i		−	0.0726728i
$894$	1004.64			1.12376
$895$	−846.410			−0.945710
$896$	−491.709			−0.548782
$897$		−	590.310i		−	0.658093i
$898$		−	432.001i		−	0.481070i
$899$		−	431.222i		−	0.479669i
$900$	−340.061			−0.377846
$901$			147.401i			0.163597i
$902$	−32.9179	−	42.5377i	−0.0364943	−	0.0471593i
$903$	−107.223			−0.118741
$904$		−	2621.18i		−	2.89954i
$905$	1066.80			1.17879
$906$	−1403.67			−1.54930
$907$	−794.610			−0.876086			−0.438043	−	0.898954i	$-0.644328\pi$
$907$	−794.610			−0.876086			−0.438043	+	0.898954i	$0.644328\pi$
$908$			2791.76i			3.07462i
$909$		−	278.010i		−	0.305841i
$910$			1343.70i			1.47659i
$911$	256.042			0.281056			0.140528	−	0.990077i	$-0.455120\pi$
$911$	256.042			0.281056			0.140528	+	0.990077i	$0.455120\pi$
$912$			123.647i			0.135578i
$913$	−626.305	+	484.668i	−0.685986	+	0.530852i
$914$	−2054.24			−2.24753
$915$		−	229.325i		−	0.250629i
$916$	−2533.15			−2.76545
$917$	−256.441			−0.279652
$918$	−224.354			−0.244394
$919$			546.682i			0.594866i	0.954743	+	0.297433i	$0.0961305\pi$
$919$			546.682i			0.594866i	−0.954743	+	0.297433i	$0.903870\pi$
$920$			1400.32i			1.52209i
$921$		−	738.354i		−	0.801687i
$922$	192.267			0.208532
$923$			1646.30i			1.78365i
$924$	−329.611	+	255.071i	−0.356722	+	0.276051i
$925$	−167.885			−0.181497
$926$			1258.19i			1.35874i
$927$	422.238			0.455489
$928$	−535.061			−0.576575
$929$	1434.55			1.54419			0.772096	−	0.635506i	$-0.219209\pi$
$929$	1434.55			1.54419			0.772096	+	0.635506i	$0.219209\pi$
$930$			423.482i			0.455357i
$931$		−	138.683i		−	0.148962i
$932$		−	1236.74i		−	1.32697i
$933$	522.406			0.559921
$934$			1054.24i			1.12874i
$935$	659.223	−	510.141i	0.705051	−	0.545606i
$936$	−1123.73			−1.20057
$937$			377.432i			0.402809i	0.979508	+	0.201405i	$0.0645506\pi$
$937$			377.432i			0.402809i	−0.979508	+	0.201405i	$0.935449\pi$
$938$	310.228			0.330734
$939$	−451.541			−0.480874
$940$	−1038.61			−1.10490
$941$			721.127i			0.766341i	0.923678	+	0.383171i	$0.125168\pi$
$941$			721.127i			0.766341i	−0.923678	+	0.383171i	$0.874832\pi$
$942$			653.450i			0.693684i
$943$		−	19.8607i		−	0.0210612i
$944$	−1366.90			−1.44799
$945$		−	83.2100i		−	0.0880529i
$946$	569.290	+	735.656i	0.601786	+	0.777649i
$947$	−1526.20			−1.61162			−0.805808	−	0.592177i	$-0.798269\pi$
$947$	−1526.20			−1.61162			−0.805808	+	0.592177i	$0.798269\pi$
$948$		−	1431.62i		−	1.51015i
$949$	949.892			1.00094
$950$	154.939			0.163093
$951$	−781.486			−0.821752
$952$		−	498.147i		−	0.523264i
$953$			252.264i			0.264705i	0.991203	+	0.132353i	$0.0422532\pi$
$953$			252.264i			0.264705i	−0.991203	+	0.132353i	$0.957747\pi$
$954$		−	127.653i		−	0.133808i
$955$	853.615			0.893838
$956$		−	536.728i		−	0.561431i
$957$	581.338	−	449.870i	0.607459	−	0.470084i
$958$	1178.31			1.22996
$959$		−	75.5063i		−	0.0787345i
$960$	−409.717			−0.426788
$961$	−836.077			−0.870007
$962$	−1051.87			−1.09342
$963$			224.700i			0.233333i
$964$		−	2971.05i		−	3.08200i
$965$		−	659.398i		−	0.683314i
$966$	−226.623			−0.234600
$967$		−	39.6815i		−	0.0410357i	−0.999789	−	0.0205179i	$-0.993469\pi$
$967$		−	39.6815i		−	0.0410357i	0.999789	−	0.0205179i	$-0.00653149\pi$
$968$	1846.00	+	478.467i	1.90702	+	0.494284i
$969$	69.4153			0.0716360
$970$		−	3647.61i		−	3.76042i
$971$	−790.585			−0.814196			−0.407098	−	0.913384i	$-0.633459\pi$
$971$	−790.585			−0.814196			−0.407098	+	0.913384i	$0.633459\pi$
$972$	131.942			0.135743
$973$	−442.859			−0.455148
$974$		−	2503.98i		−	2.57082i
$975$			551.307i			0.565443i
$976$			465.500i			0.476946i
$977$	−309.474			−0.316760			−0.158380	−	0.987378i	$-0.550627\pi$
$977$	−309.474			−0.316760			−0.158380	+	0.987378i	$0.550627\pi$
$978$			721.969i			0.738209i
$979$	721.520	+	932.374i	0.736997	+	0.952374i
$980$	−2219.49			−2.26479
$981$			460.901i			0.469827i
$982$	−112.943			−0.115014
$983$	529.604			0.538763			0.269381	−	0.963034i	$-0.413181\pi$
$983$	529.604			0.538763			0.269381	+	0.963034i	$0.413181\pi$
$984$	−37.8076			−0.0384224
$985$			207.029i			0.210182i
$986$			1665.83i			1.68948i
$987$		−	88.6506i		−	0.0898183i
$988$	659.223			0.667230
$989$			343.476i			0.347297i
$990$	−570.904	+	441.795i	−0.576671	+	0.446258i
$991$	1038.56			1.04799			0.523997	−	0.851720i	$-0.324440\pi$
$991$	1038.56			1.04799			0.523997	+	0.851720i	$0.324440\pi$
$992$		−	155.005i		−	0.156255i
$993$	−397.626			−0.400429
$994$	632.025			0.635840
$995$	2069.86			2.08027
$996$			1055.45i			1.05969i
$997$		−	1105.88i		−	1.10921i	−0.832115	−	0.554603i	$-0.812870\pi$
$997$		−	1105.88i		−	1.10921i	0.832115	−	0.554603i	$-0.187130\pi$
$998$			97.7660i			0.0979619i
$999$	65.1384			0.0652036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.3.c.a.10.4	yes	4
3.2	odd	2		99.3.c.b.10.1		4
4.3	odd	2		528.3.j.c.241.3		4
5.2	odd	4		825.3.h.a.274.2		8
5.3	odd	4		825.3.h.a.274.7		8
5.4	even	2		825.3.b.a.76.1		4
8.3	odd	2		2112.3.j.d.769.1		4
8.5	even	2		2112.3.j.a.769.4		4
11.2	odd	10		363.3.g.e.40.1		16
11.3	even	5		363.3.g.e.112.4		16
11.4	even	5		363.3.g.e.94.1		16
11.5	even	5		363.3.g.e.118.1		16
11.6	odd	10		363.3.g.e.118.4		16
11.7	odd	10		363.3.g.e.94.4		16
11.8	odd	10		363.3.g.e.112.1		16
11.9	even	5		363.3.g.e.40.4		16
11.10	odd	2	inner	33.3.c.a.10.1	✓	4
12.11	even	2		1584.3.j.f.1297.1		4
33.32	even	2		99.3.c.b.10.4		4
44.43	even	2		528.3.j.c.241.4		4
55.32	even	4		825.3.h.a.274.8		8
55.43	even	4		825.3.h.a.274.1		8
55.54	odd	2		825.3.b.a.76.4		4
88.21	odd	2		2112.3.j.a.769.3		4
88.43	even	2		2112.3.j.d.769.2		4
132.131	odd	2		1584.3.j.f.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.c.a.10.1	✓	4	11.10	odd	2	inner
33.3.c.a.10.4	yes	4	1.1	even	1	trivial
99.3.c.b.10.1		4	3.2	odd	2
99.3.c.b.10.4		4	33.32	even	2
363.3.g.e.40.1		16	11.2	odd	10
363.3.g.e.40.4		16	11.9	even	5
363.3.g.e.94.1		16	11.4	even	5
363.3.g.e.94.4		16	11.7	odd	10
363.3.g.e.112.1		16	11.8	odd	10
363.3.g.e.112.4		16	11.3	even	5
363.3.g.e.118.1		16	11.5	even	5
363.3.g.e.118.4		16	11.6	odd	10
528.3.j.c.241.3		4	4.3	odd	2
528.3.j.c.241.4		4	44.43	even	2
825.3.b.a.76.1		4	5.4	even	2
825.3.b.a.76.4		4	55.54	odd	2
825.3.h.a.274.1		8	55.43	even	4
825.3.h.a.274.2		8	5.2	odd	4
825.3.h.a.274.7		8	5.3	odd	4
825.3.h.a.274.8		8	55.32	even	4
1584.3.j.f.1297.1		4	12.11	even	2
1584.3.j.f.1297.2		4	132.131	odd	2
2112.3.j.a.769.3		4	88.21	odd	2
2112.3.j.a.769.4		4	8.5	even	2
2112.3.j.d.769.1		4	8.3	odd	2
2112.3.j.d.769.2		4	88.43	even	2

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.53045i q^{2} -1.73205 q^{3} -8.46410 q^{4} +6.19615 q^{5} -6.11492i q^{6} +2.58447i q^{7} -15.7603i q^{8} +3.00000 q^{9} +21.8752i q^{10} +(6.73205 + 8.69940i) q^{11} +14.6603 q^{12} -23.7672i q^{13} -9.12436 q^{14} -10.7321 q^{15} +21.7846 q^{16} -12.2298i q^{17} +10.5914i q^{18} -3.27698i q^{19} -52.4449 q^{20} -4.47644i q^{21} +(-30.7128 + 23.7672i) q^{22} -14.3397 q^{23} +27.2976i q^{24} +13.3923 q^{25} +83.9090 q^{26} -5.19615 q^{27} -21.8752i q^{28} +38.5815i q^{29} -37.8890i q^{30} -11.1769 q^{31} +13.8683i q^{32} +(-11.6603 - 15.0678i) q^{33} +43.1769 q^{34} +16.0138i q^{35} -25.3923 q^{36} -12.5359 q^{37} +11.5692 q^{38} +41.1660i q^{39} -97.6532i q^{40} +1.38501i q^{41} +15.8038 q^{42} -23.9527i q^{43} +(-56.9808 - 73.6326i) q^{44} +18.5885 q^{45} -50.6258i q^{46} +19.8038 q^{47} -37.7321 q^{48} +42.3205 q^{49} +47.2809i q^{50} +21.1827i q^{51} +201.168i q^{52} -12.0526 q^{53} -18.3448i q^{54} +(41.7128 + 53.9028i) q^{55} +40.7321 q^{56} +5.67589i q^{57} -136.210 q^{58} -62.7461 q^{59} +90.8372 q^{60} +21.3683i q^{61} -39.4596i q^{62} +7.75341i q^{63} +38.1769 q^{64} -147.265i q^{65} +(53.1962 - 41.1660i) q^{66} -34.0000 q^{67} +103.515i q^{68} +24.8372 q^{69} -56.5359 q^{70} -69.2679 q^{71} -47.2809i q^{72} +39.9665i q^{73} -44.2574i q^{74} -23.1962 q^{75} +27.7367i q^{76} +(-22.4833 + 17.3988i) q^{77} -145.335 q^{78} -97.6532i q^{79} +134.981 q^{80} +9.00000 q^{81} -4.88973 q^{82} +71.9941i q^{83} +37.8890i q^{84} -75.7780i q^{85} +84.5641 q^{86} -66.8251i q^{87} +(137.105 - 106.099i) q^{88} +107.177 q^{89} +65.6257i q^{90} +61.4256 q^{91} +121.373 q^{92} +19.3590 q^{93} +69.9166i q^{94} -20.3047i q^{95} -24.0207i q^{96} -166.746 q^{97} +149.411i q^{98} +(20.1962 + 26.0982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 20 q^{4} + 4 q^{5} + 12 q^{9} + 20 q^{11} + 24 q^{12} + 12 q^{14} - 36 q^{15} + 4 q^{16} - 92 q^{20} - 12 q^{22} - 92 q^{23} + 12 q^{25} + 204 q^{26} + 80 q^{31} - 12 q^{33} + 48 q^{34} - 60 q^{36}+ \cdots + 60 q^{99}+O(q^{100}) \) 4 * q - 20 * q^4 + 4 * q^5 + 12 * q^9 + 20 * q^11 + 24 * q^12 + 12 * q^14 - 36 * q^15 + 4 * q^16 - 92 * q^20 - 12 * q^22 - 92 * q^23 + 12 * q^25 + 204 * q^26 + 80 * q^31 - 12 * q^33 + 48 * q^34 - 60 * q^36 - 64 * q^37 - 120 * q^38 + 84 * q^42 - 124 * q^44 + 12 * q^45 + 100 * q^47 - 144 * q^48 + 100 * q^49 + 28 * q^53 + 56 * q^55 + 156 * q^56 - 240 * q^58 + 40 * q^59 + 204 * q^60 + 28 * q^64 + 192 * q^66 - 136 * q^67 - 60 * q^69 - 240 * q^70 - 284 * q^71 - 72 * q^75 - 180 * q^77 - 228 * q^78 + 436 * q^80 + 36 * q^81 + 216 * q^82 - 216 * q^86 + 396 * q^88 + 304 * q^89 + 24 * q^91 + 340 * q^92 + 216 * q^93 - 376 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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