LMFDB - Embedded newform 26.5.f.b.11.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,5,Mod(7,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.7"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 494x^{6} + 90747x^{4} - 7343258x^{2} + 221087161 $ x^8 - 494x^6 + 90747x^4 - 7343258*x^2 + 221087161
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.1
Root			$-12.0941 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.11
Dual form			26.5.f.b.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.732051 + 2.73205i) q^{2} +(-4.74800 - 8.22378i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-19.2341 - 19.2341i) q^{5} +(25.9436 - 6.95155i) q^{6} +(-5.11403 - 19.0858i) q^{7} +(16.0000 - 16.0000i) q^{8} +(-4.58700 + 7.94492i) q^{9} +(66.6289 - 38.4682i) q^{10} +(-31.7929 - 8.51887i) q^{11} +75.9680i q^{12} +(-94.3282 + 140.225i) q^{13} +55.8871 q^{14} +(-66.8535 + 249.501i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-186.163 - 107.481i) q^{17} +(-18.3480 - 18.3480i) q^{18} +(407.726 - 109.250i) q^{19} +(56.3214 + 210.194i) q^{20} +(-132.676 + 132.676i) q^{21} +(46.5480 - 80.6235i) q^{22} +(833.208 - 481.053i) q^{23} +(-207.548 - 55.6124i) q^{24} +114.902i q^{25} +(-314.050 - 360.362i) q^{26} -682.060 q^{27} +(-40.9122 + 152.686i) q^{28} +(-772.393 - 1337.82i) q^{29} +(-632.708 - 365.294i) q^{30} +(750.040 + 750.040i) q^{31} +(-174.851 + 46.8513i) q^{32} +(80.8952 + 301.905i) q^{33} +(429.924 - 429.924i) q^{34} +(-268.735 + 465.462i) q^{35} +(63.5593 - 36.6960i) q^{36} +(680.735 + 182.402i) q^{37} +1193.90i q^{38} +(1601.05 + 109.944i) q^{39} -615.491 q^{40} +(146.998 - 548.605i) q^{41} +(-265.352 - 459.603i) q^{42} +(-141.756 - 81.8426i) q^{43} +(186.192 + 186.192i) q^{44} +(241.040 - 64.5865i) q^{45} +(704.310 + 2628.52i) q^{46} +(-1733.01 + 1733.01i) q^{47} +(303.872 - 526.322i) q^{48} +(1741.21 - 1005.29i) q^{49} +(-313.917 - 84.1139i) q^{50} +2041.28i q^{51} +(1214.43 - 594.198i) q^{52} -4534.85 q^{53} +(499.302 - 1863.42i) q^{54} +(447.654 + 775.360i) q^{55} +(-387.197 - 223.548i) q^{56} +(-2834.33 - 2834.33i) q^{57} +(4220.44 - 1130.86i) q^{58} +(-201.708 - 752.785i) q^{59} +(1461.18 - 1461.18i) q^{60} +(-1974.23 + 3419.47i) q^{61} +(-2598.22 + 1500.08i) q^{62} +(175.093 + 46.9161i) q^{63} -512.000i q^{64} +(4511.43 - 882.793i) q^{65} -884.039 q^{66} +(1784.27 - 6658.99i) q^{67} +(859.849 + 1489.30i) q^{68} +(-7912.14 - 4568.08i) q^{69} +(-1074.94 - 1074.94i) q^{70} +(5330.87 - 1428.40i) q^{71} +(53.7267 + 200.511i) q^{72} +(-2496.58 + 2496.58i) q^{73} +(-996.665 + 1726.27i) q^{74} +(944.926 - 545.554i) q^{75} +(-3261.81 - 873.998i) q^{76} +650.358i q^{77} +(-1472.42 + 4293.67i) q^{78} +6710.05 q^{79} +(450.571 - 1681.55i) q^{80} +(3609.97 + 6252.64i) q^{81} +(1391.21 + 803.214i) q^{82} +(1361.30 + 1361.30i) q^{83} +(1449.91 - 388.502i) q^{84} +(1513.37 + 5647.98i) q^{85} +(327.370 - 327.370i) q^{86} +(-7334.65 + 12704.0i) q^{87} +(-644.988 + 372.384i) q^{88} +(6033.51 + 1616.67i) q^{89} +705.815i q^{90} +(3158.71 + 1083.21i) q^{91} -7696.84 q^{92} +(2606.97 - 9729.36i) q^{93} +(-3466.01 - 6003.31i) q^{94} +(-9943.56 - 5740.92i) q^{95} +(1215.49 + 1215.49i) q^{96} +(-4670.76 + 1251.53i) q^{97} +(1471.85 + 5493.00i) q^{98} +(213.516 - 213.516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21}+ \cdots - 55296 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.732051	+	2.73205i	−0.183013	+	0.683013i
$2$	−0.732051	+	2.73205i	−0.183013	+	0.683013i
$3$	−4.74800	−	8.22378i	−0.527556	−	0.913753i	−0.999484	−	0.0321162i	$-0.989775\pi$
$3$	−4.74800	−	8.22378i	−0.527556	−	0.913753i	0.471929	−	0.881637i	$-0.343558\pi$
$4$	−6.92820	−	4.00000i	−0.433013	−	0.250000i
$5$	−19.2341	−	19.2341i	−0.769364	−	0.769364i	0.208630	−	0.977995i	$-0.433099\pi$
$5$	−19.2341	−	19.2341i	−0.769364	−	0.769364i	−0.977995	+	0.208630i	$0.933099\pi$
$6$	25.9436	−	6.95155i	0.720654	−	0.193099i
$7$	−5.11403	−	19.0858i	−0.104368	−	0.389506i	0.893905	−	0.448257i	$-0.147955\pi$
$7$	−5.11403	−	19.0858i	−0.104368	−	0.389506i	−0.998273	+	0.0587506i	$0.981288\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	−4.58700	+	7.94492i	−0.0566296	+	0.0980854i
$10$	66.6289	−	38.4682i	0.666289	−	0.384682i
$11$	−31.7929	−	8.51887i	−0.262751	−	0.0704039i	0.125038	−	0.992152i	$-0.460095\pi$
$11$	−31.7929	−	8.51887i	−0.262751	−	0.0704039i	−0.387789	+	0.921748i	$0.626761\pi$
$12$			75.9680i			0.527556i
$13$	−94.3282	+	140.225i	−0.558155	+	0.829737i
$13$	−94.3282	+	140.225i	−0.558155	+	0.829737i
$14$	55.8871			0.285138
$15$	−66.8535	+	249.501i	−0.297127	+	1.10889i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−186.163	−	107.481i	−0.644162	−	0.371907i	0.142054	−	0.989859i	$-0.454629\pi$
$17$	−186.163	−	107.481i	−0.644162	−	0.371907i	−0.786216	+	0.617952i	$0.787963\pi$
$18$	−18.3480	−	18.3480i	−0.0566296	−	0.0566296i
$19$	407.726	−	109.250i	1.12943	−	0.302631i	0.354739	−	0.934965i	$-0.384570\pi$
$19$	407.726	−	109.250i	1.12943	−	0.302631i	0.774695	+	0.632335i	$0.217903\pi$
$20$	56.3214	+	210.194i	0.140803	+	0.525486i
$21$	−132.676	+	132.676i	−0.300853	+	0.300853i
$22$	46.5480	−	80.6235i	0.0961735	−	0.166577i
$23$	833.208	−	481.053i	1.57506	−	0.909362i	0.579528	−	0.814952i	$-0.303237\pi$
$23$	833.208	−	481.053i	1.57506	−	0.909362i	0.995533	−	0.0944099i	$-0.0300964\pi$
$24$	−207.548	−	55.6124i	−0.360327	−	0.0965494i
$25$			114.902i			0.183843i
$26$	−314.050	−	360.362i	−0.464571	−	0.533079i
$27$	−682.060			−0.935610
$28$	−40.9122	+	152.686i	−0.0521839	+	0.194753i
$29$	−772.393	−	1337.82i	−0.918422	−	1.59075i	−0.801812	−	0.597576i	$-0.796130\pi$
$29$	−772.393	−	1337.82i	−0.918422	−	1.59075i	−0.116610	−	0.993178i	$-0.537203\pi$
$30$	−632.708	−	365.294i	−0.703009	−	0.405882i
$31$	750.040	+	750.040i	0.780479	+	0.780479i	0.979912	−	0.199432i	$-0.0639099\pi$
$31$	750.040	+	750.040i	0.780479	+	0.780479i	−0.199432	+	0.979912i	$0.563910\pi$
$32$	−174.851	+	46.8513i	−0.170753	+	0.0457532i
$33$	80.8952	+	301.905i	0.0742839	+	0.277231i
$34$	429.924	−	429.924i	0.371907	−	0.371907i
$35$	−268.735	+	465.462i	−0.219375	+	0.379969i
$36$	63.5593	−	36.6960i	0.0490427	−	0.0283148i
$37$	680.735	+	182.402i	0.497250	+	0.133238i	0.498723	−	0.866761i	$-0.333802\pi$
$37$	680.735	+	182.402i	0.497250	+	0.133238i	−0.00147363	+	0.999999i	$0.500469\pi$
$38$			1193.90i			0.826803i
$39$	1601.05	+	109.944i	1.05263	+	0.0722838i
$40$	−615.491			−0.384682
$41$	146.998	−	548.605i	0.0874470	−	0.326357i	−0.908319	−	0.418277i	$-0.862634\pi$
$41$	146.998	−	548.605i	0.0874470	−	0.326357i	0.995766	+	0.0919209i	$0.0293007\pi$
$42$	−265.352	−	459.603i	−0.150426	−	0.260546i
$43$	−141.756	−	81.8426i	−0.0766661	−	0.0442632i	0.461177	−	0.887308i	$-0.347427\pi$
$43$	−141.756	−	81.8426i	−0.0766661	−	0.0442632i	−0.537843	+	0.843045i	$0.680761\pi$
$44$	186.192	+	186.192i	0.0961735	+	0.0961735i
$45$	241.040	−	64.5865i	0.119032	−	0.0318946i
$46$	704.310	+	2628.52i	0.332850	+	1.24221i
$47$	−1733.01	+	1733.01i	−0.784521	+	0.784521i	−0.980590	−	0.196069i	$-0.937182\pi$
$47$	−1733.01	+	1733.01i	−0.784521	+	0.784521i	0.196069	+	0.980590i	$0.437182\pi$
$48$	303.872	−	526.322i	0.131889	−	0.228438i
$49$	1741.21	−	1005.29i	0.725203	−	0.418696i
$50$	−313.917	−	84.1139i	−0.125567	−	0.0336456i
$51$			2041.28i			0.784806i
$52$	1214.43	−	594.198i	0.449122	−	0.219748i
$53$	−4534.85			−1.61440			−0.807200	−	0.590278i	$-0.799018\pi$
$53$	−4534.85			−1.61440			−0.807200	+	0.590278i	$0.799018\pi$
$54$	499.302	−	1863.42i	0.171228	−	0.639033i
$55$	447.654	+	775.360i	0.147985	+	0.256317i
$56$	−387.197	−	223.548i	−0.123469	−	0.0712846i
$57$	−2834.33	−	2834.33i	−0.872369	−	0.872369i
$58$	4220.44	−	1130.86i	1.25459	−	0.336166i
$59$	−201.708	−	752.785i	−0.0579454	−	0.216255i	0.930882	−	0.365320i	$-0.119040\pi$
$59$	−201.708	−	752.785i	−0.0579454	−	0.216255i	−0.988827	+	0.149065i	$0.952374\pi$
$60$	1461.18	−	1461.18i	0.405882	−	0.405882i
$61$	−1974.23	+	3419.47i	−0.530564	+	0.918965i	0.468800	+	0.883305i	$0.344687\pi$
$61$	−1974.23	+	3419.47i	−0.530564	+	0.918965i	−0.999364	+	0.0356600i	$0.988647\pi$
$62$	−2598.22	+	1500.08i	−0.675915	+	0.390240i
$63$	175.093	+	46.9161i	0.0441152	+	0.0118206i
$64$		−	512.000i		−	0.125000i
$65$	4511.43	−	882.793i	1.06779	−	0.208945i
$66$	−884.039			−0.202947
$67$	1784.27	−	6658.99i	0.397476	−	1.48340i	−0.420045	−	0.907503i	$-0.637986\pi$
$67$	1784.27	−	6658.99i	0.397476	−	1.48340i	0.817522	−	0.575898i	$-0.195347\pi$
$68$	859.849	+	1489.30i	0.185953	+	0.322081i
$69$	−7912.14	−	4568.08i	−1.66186	−	0.959478i
$70$	−1074.94	−	1074.94i	−0.219375	−	0.219375i
$71$	5330.87	−	1428.40i	1.05750	−	0.283357i	0.312154	−	0.950032i	$-0.398950\pi$
$71$	5330.87	−	1428.40i	1.05750	−	0.283357i	0.745349	+	0.666675i	$0.232283\pi$
$72$	53.7267	+	200.511i	0.0103639	+	0.0386788i
$73$	−2496.58	+	2496.58i	−0.468489	+	0.468489i	−0.901425	−	0.432936i	$-0.857478\pi$
$73$	−2496.58	+	2496.58i	−0.468489	+	0.468489i	0.432936	+	0.901425i	$0.357478\pi$
$74$	−996.665	+	1726.27i	−0.182006	+	0.315244i
$75$	944.926	−	545.554i	0.167987	−	0.0969873i
$76$	−3261.81	−	873.998i	−0.564717	−	0.151315i
$77$			650.358i			0.109691i
$78$	−1472.42	+	4293.67i	−0.242016	+	0.705732i
$79$	6710.05			1.07516			0.537578	−	0.843214i	$-0.319339\pi$
$79$	6710.05			1.07516			0.537578	+	0.843214i	$0.319339\pi$
$80$	450.571	−	1681.55i	0.0704017	−	0.262743i
$81$	3609.97	+	6252.64i	0.550216	+	0.953002i
$82$	1391.21	+	803.214i	0.206902	+	0.119455i
$83$	1361.30	+	1361.30i	0.197605	+	0.197605i	0.798972	−	0.601368i	$-0.205377\pi$
$83$	1361.30	+	1361.30i	0.197605	+	0.197605i	−0.601368	+	0.798972i	$0.705377\pi$
$84$	1449.91	−	388.502i	0.205486	−	0.0550598i
$85$	1513.37	+	5647.98i	0.209463	+	0.781727i
$86$	327.370	−	327.370i	0.0442632	−	0.0442632i
$87$	−7334.65	+	12704.0i	−0.969038	+	1.67842i
$88$	−644.988	+	372.384i	−0.0832887	+	0.0480868i
$89$	6033.51	+	1616.67i	0.761711	+	0.204100i	0.618707	−	0.785622i	$-0.287657\pi$
$89$	6033.51	+	1616.67i	0.761711	+	0.204100i	0.143004	+	0.989722i	$0.454324\pi$
$90$			705.815i			0.0871376i
$91$	3158.71	+	1083.21i	0.381441	+	0.130807i
$92$	−7696.84			−0.909362
$93$	2606.97	−	9729.36i	0.301419	−	1.12491i
$94$	−3466.01	−	6003.31i	−0.392260	−	0.679415i
$95$	−9943.56	−	5740.92i	−1.10178	−	0.636113i
$96$	1215.49	+	1215.49i	0.131889	+	0.131889i
$97$	−4670.76	+	1251.53i	−0.496414	+	0.133014i	−0.498335	−	0.866984i	$-0.666055\pi$
$97$	−4670.76	+	1251.53i	−0.496414	+	0.133014i	0.00192128	+	0.999998i	$0.499388\pi$
$98$	1471.85	+	5493.00i	0.153253	+	0.571950i
$99$	213.516	−	213.516i	0.0217851	−	0.0217851i
$100$	459.607	−	796.063i	0.0459607	−	0.0796063i
$101$	7300.50	−	4214.95i	0.715665	−	0.413190i	−0.0974899	−	0.995237i	$-0.531081\pi$
$101$	7300.50	−	4214.95i	0.715665	−	0.413190i	0.813155	+	0.582047i	$0.197748\pi$
$102$	−5576.88	−	1494.32i	−0.536033	−	0.143629i
$103$		−	2398.45i		−	0.226076i	−0.993591	−	0.113038i	$-0.963942\pi$
$103$		−	2398.45i		−	0.226076i	0.993591	−	0.113038i	$-0.0360583\pi$
$104$	734.356	+	3752.86i	0.0678954	+	0.346973i
$105$	5103.81			0.462930
$106$	3319.74	−	12389.4i	0.295456	−	1.10266i
$107$	−4706.11	−	8151.21i	−0.411049	−	0.711959i	0.583955	−	0.811786i	$-0.301504\pi$
$107$	−4706.11	−	8151.21i	−0.411049	−	0.711959i	−0.995005	+	0.0998272i	$0.968171\pi$
$108$	4725.45	+	2728.24i	0.405131	+	0.233902i
$109$	14993.7	+	14993.7i	1.26199	+	1.26199i	0.950128	+	0.311860i	$0.100952\pi$
$109$	14993.7	+	14993.7i	1.26199	+	1.26199i	0.311860	+	0.950128i	$0.399048\pi$
$110$	−2446.03	+	655.412i	−0.202151	+	0.0541662i
$111$	−1732.09	−	6464.26i	−0.140580	−	0.524654i
$112$	894.194	−	894.194i	0.0712846	−	0.0712846i
$113$	8782.46	−	15211.7i	0.687795	−	1.19130i	−0.284754	−	0.958601i	$-0.591912\pi$
$113$	8782.46	−	15211.7i	0.687795	−	1.19130i	0.972550	−	0.232696i	$-0.0747547\pi$
$114$	9818.40	−	5668.65i	0.755494	−	0.436185i
$115$	−25278.6	−	6773.39i	−1.91143	−	0.512165i
$116$			12358.3i			0.918422i
$117$	−681.396	−	1392.64i	−0.0497769	−	0.101735i
$118$	2204.31			0.158310
$119$	−1099.32	+	4102.73i	−0.0776303	+	0.289720i
$120$	2922.35	+	5061.66i	0.202941	+	0.351504i
$121$	−11741.3	−	6778.82i	−0.801944	−	0.463003i
$122$	−7896.92	−	7896.92i	−0.530564	−	0.530564i
$123$	−5209.56	+	1395.90i	−0.344342	+	0.0922663i
$124$	−2196.27	−	8196.59i	−0.142838	−	0.533077i
$125$	−9811.28	+	9811.28i	−0.627922	+	0.627922i
$126$	−256.354	+	444.018i	−0.0161473	+	0.0279679i
$127$	−14061.3	+	8118.27i	−0.871800	+	0.503334i	−0.867946	−	0.496659i	$-0.834560\pi$
$127$	−14061.3	+	8118.27i	−0.871800	+	0.503334i	−0.00385399	+	0.999993i	$0.501227\pi$
$128$	1398.81	+	374.810i	0.0853766	+	0.0228766i
$129$			1554.35i			0.0934051i
$130$	−890.762	+	12971.7i	−0.0527078	+	0.767557i
$131$	9149.90			0.533180			0.266590	−	0.963810i	$-0.414103\pi$
$131$	9149.90			0.533180			0.266590	+	0.963810i	$0.414103\pi$
$132$	647.162	−	2415.24i	0.0371420	−	0.138616i
$133$	−4170.24	−	7223.07i	−0.235753	−	0.408337i
$134$	16886.5	+	9749.43i	0.940439	+	0.542962i
$135$	13118.8	+	13118.8i	0.719825	+	0.719825i
$136$	−4698.30	+	1258.91i	−0.254017	+	0.0680637i
$137$	3049.09	+	11379.4i	0.162454	+	0.606286i	0.998351	+	0.0574001i	$0.0182811\pi$
$137$	3049.09	+	11379.4i	0.162454	+	0.606286i	−0.835898	+	0.548886i	$0.815052\pi$
$138$	18272.3	−	18272.3i	0.959478	−	0.959478i
$139$	1013.40	−	1755.27i	0.0524509	−	0.0908476i	−0.838608	−	0.544736i	$-0.816630\pi$
$139$	1013.40	−	1755.27i	0.0524509	−	0.0908476i	0.891059	+	0.453888i	$0.149963\pi$
$140$	3723.70	−	2149.88i	0.189985	−	0.109688i
$141$	22480.2	+	6023.54i	1.13074	+	0.302980i
$142$			15609.9i			0.774145i
$143$	4193.53	−	3654.60i	0.205072	−	0.178718i
$144$	−587.136			−0.0283148
$145$	−10875.6	+	40588.1i	−0.517268	+	1.93047i
$146$	−4993.15	−	8648.39i	−0.234244	−	0.405723i
$147$	−16534.6	−	9546.23i	−0.765170	−	0.441771i
$148$	−3986.66	−	3986.66i	−0.182006	−	0.182006i
$149$	23213.0	−	6219.90i	1.04558	−	0.280163i	0.305157	−	0.952302i	$-0.401291\pi$
$149$	23213.0	−	6219.90i	1.04558	−	0.280163i	0.740425	+	0.672139i	$0.234624\pi$
$150$	798.746	+	2980.96i	0.0354998	+	0.132487i
$151$	−1109.89	+	1109.89i	−0.0486774	+	0.0486774i	−0.731026	−	0.682349i	$-0.760958\pi$
$151$	−1109.89	+	1109.89i	−0.0486774	+	0.0486774i	0.682349	+	0.731026i	$0.260958\pi$
$152$	4775.62	−	8271.61i	0.206701	−	0.358016i
$153$	1707.86	−	986.032i	0.0729573	−	0.0421219i
$154$	−1776.81	−	476.095i	−0.0749204	−	0.0200748i
$155$		−	28852.7i		−	1.20095i
$156$	−10652.6	−	7165.93i	−0.437732	−	0.294458i
$157$	−17982.1			−0.729525			−0.364762	−	0.931101i	$-0.618850\pi$
$157$	−17982.1			−0.729525			−0.364762	+	0.931101i	$0.618850\pi$
$158$	−4912.10	+	18332.2i	−0.196767	+	0.734345i
$159$	21531.5	+	37293.6i	0.851685	+	1.47516i
$160$	4264.25	+	2461.97i	0.166572	+	0.0961705i
$161$	−13442.3	−	13442.3i	−0.518588	−	0.518588i
$162$	−19725.2	+	5285.36i	−0.751609	+	0.201393i
$163$	−12052.9	−	44982.0i	−0.453645	−	1.69303i	−0.692041	−	0.721858i	$-0.743288\pi$
$163$	−12052.9	−	44982.0i	−0.453645	−	1.69303i	0.238397	−	0.971168i	$-0.423378\pi$
$164$	−3212.86	+	3212.86i	−0.119455	+	0.119455i
$165$	4250.93	−	7362.82i	0.156141	−	0.270443i
$166$	−4715.68	+	2722.60i	−0.171131	+	0.0988024i
$167$	16884.4	+	4524.16i	0.605415	+	0.162220i	0.548489	−	0.836158i	$-0.315203\pi$
$167$	16884.4	+	4524.16i	0.605415	+	0.162220i	0.0569261	+	0.998378i	$0.481870\pi$
$168$			4245.63i			0.150426i
$169$	−10765.4	−	26454.4i	−0.376926	−	0.926244i
$170$	−16538.4			−0.572264
$171$	−1002.26	+	3740.48i	−0.0342758	+	0.127919i
$172$	654.741	+	1134.04i	0.0221316	+	0.0383330i
$173$	27983.5	+	16156.3i	0.934995	+	0.539820i	0.888388	−	0.459094i	$-0.151826\pi$
$173$	27983.5	+	16156.3i	0.934995	+	0.539820i	0.0466071	+	0.998913i	$0.485159\pi$
$174$	−29338.6	−	29338.6i	−0.969038	−	0.969038i
$175$	2192.99	−	587.610i	0.0716079	−	0.0191873i
$176$	−545.208	−	2034.74i	−0.0176010	−	0.0656877i
$177$	−5233.02	+	5233.02i	−0.167034	+	0.167034i
$178$	−8833.68	+	15300.4i	−0.278806	+	0.482905i
$179$	−11550.5	+	6668.66i	−0.360490	+	0.208129i	−0.669296	−	0.742996i	$-0.733404\pi$
$179$	−11550.5	+	6668.66i	−0.360490	+	0.208129i	0.308806	+	0.951125i	$0.400071\pi$
$180$	−1928.32	−	516.692i	−0.0595161	−	0.0159473i
$181$		−	46226.0i		−	1.41101i	−0.708706	−	0.705504i	$-0.750721\pi$
$181$		−	46226.0i		−	1.41101i	0.708706	−	0.705504i	$-0.249279\pi$
$182$	−5271.73	+	7836.80i	−0.159151	+	0.236590i
$183$	37494.6			1.11961
$184$	5634.48	−	21028.2i	0.166425	−	0.621106i
$185$	−9584.98	−	16601.7i	−0.280058	−	0.485074i
$186$	24672.7	+	14244.8i	0.713165	+	0.411746i
$187$	5003.03	+	5003.03i	0.143070	+	0.143070i
$188$	18938.6	−	5074.60i	0.535838	−	0.143577i
$189$	3488.07	+	13017.7i	0.0976476	+	0.364426i
$190$	22963.7	−	22963.7i	0.636113	−	0.636113i
$191$	−5958.51	+	10320.4i	−0.163332	+	0.282899i	−0.936062	−	0.351836i	$-0.885557\pi$
$191$	−5958.51	+	10320.4i	−0.163332	+	0.282899i	0.772730	+	0.634735i	$0.218891\pi$
$192$	−4210.57	+	2430.98i	−0.114219	+	0.0659444i
$193$	40675.2	+	10898.9i	1.09198	+	0.292595i	0.759495	−	0.650513i	$-0.225446\pi$
$193$	40675.2	+	10898.9i	1.09198	+	0.292595i	0.332485	+	0.943108i	$0.392113\pi$
$194$		−	13676.9i		−	0.363400i
$195$	−28680.2	−	32909.5i	−0.754245	−	0.865470i
$196$	−16084.6			−0.418696
$197$	−14295.4	+	53351.2i	−0.368353	+	1.37471i	0.494465	+	0.869198i	$0.335364\pi$
$197$	−14295.4	+	53351.2i	−0.368353	+	1.37471i	−0.862818	+	0.505515i	$0.831303\pi$
$198$	427.031	+	739.640i	0.0108925	+	0.0188664i
$199$	58463.5	+	33753.9i	1.47631	+	0.852350i	0.999643	−	0.0267315i	$-0.00850991\pi$
$199$	58463.5	+	33753.9i	1.47631	+	0.852350i	0.476671	+	0.879082i	$0.341843\pi$
$200$	1838.43	+	1838.43i	0.0459607	+	0.0459607i
$201$	−63233.7	+	16943.4i	−1.56515	+	0.419381i
$202$	6171.11	+	23030.9i	0.151238	+	0.564427i
$203$	−21583.4	+	21583.4i	−0.523755	+	0.523755i
$204$	8165.12	−	14142.4i	0.196202	−	0.339831i
$205$	−13379.3	+	7724.55i	−0.318366	+	0.183808i
$206$	6552.67	+	1755.78i	0.154413	+	0.0413749i
$207$			8826.35i			0.205987i
$208$	−10790.6	−	740.985i	−0.249413	−	0.0171271i
$209$	−13893.5			−0.318066
$210$	−3736.25	+	13943.9i	−0.0847221	+	0.316187i
$211$	2183.67	+	3782.23i	0.0490481	+	0.0849538i	0.889507	−	0.456921i	$-0.151048\pi$
$211$	2183.67	+	3782.23i	0.0490481	+	0.0849538i	−0.840459	+	0.541875i	$0.817715\pi$
$212$	31418.3	+	18139.4i	0.699055	+	0.403600i
$213$	−37057.8	−	37057.8i	−0.816809	−	0.816809i
$214$	25714.6	−	6890.22i	0.561504	−	0.150455i
$215$	1152.37	+	4300.71i	0.0249296	+	0.0930386i
$216$	−10913.0	+	10913.0i	−0.233902	+	0.233902i
$217$	10479.4	−	18150.8i	0.222544	−	0.385458i
$218$	−51939.6	+	29987.4i	−1.09291	+	0.630994i
$219$	32385.0	+	8677.54i	0.675236	+	0.180929i
$220$		−	7162.47i		−	0.147985i
$221$	32632.0	−	15966.3i	0.668127	−	0.326903i
$222$	18928.7			0.384073
$223$	−5915.63	+	22077.4i	−0.118957	+	0.443955i	−0.999552	−	0.0299144i	$-0.990477\pi$
$223$	−5915.63	+	22077.4i	−0.118957	+	0.443955i	0.880595	+	0.473870i	$0.157143\pi$
$224$	1788.39	+	3097.58i	0.0356423	+	0.0617343i
$225$	−912.885	−	527.054i	−0.0180323	−	0.0104110i
$226$	35129.8	+	35129.8i	0.687795	+	0.687795i
$227$	−42663.3	+	11431.6i	−0.827946	+	0.221848i	−0.647818	−	0.761795i	$-0.724318\pi$
$227$	−42663.3	+	11431.6i	−0.827946	+	0.221848i	−0.180129	+	0.983643i	$0.557651\pi$
$228$	8299.49	+	30974.1i	0.159655	+	0.595839i
$229$	−10025.3	+	10025.3i	−0.191172	+	0.191172i	−0.796202	−	0.605030i	$-0.793161\pi$
$229$	−10025.3	+	10025.3i	−0.191172	+	0.191172i	0.605030	+	0.796202i	$0.293161\pi$
$230$	37010.5	−	64104.0i	0.699631	−	1.21180i
$231$	5348.40	−	3087.90i	0.100230	−	0.0578681i
$232$	−33763.5	−	9046.90i	−0.627294	−	0.168083i
$233$			3033.83i			0.0558829i	0.999610	+	0.0279415i	$0.00889520\pi$
$233$			3033.83i			0.0558829i	−0.999610	+	0.0279415i	$0.991105\pi$
$234$	4303.59	−	842.123i	0.0785958	−	0.0153796i
$235$	66665.7			1.20716
$236$	−1613.66	+	6022.28i	−0.0289727	+	0.108128i
$237$	−31859.3	−	55181.9i	−0.567204	−	0.982427i
$238$	−10404.1	−	6006.81i	−0.183675	−	0.106045i
$239$	−27446.8	−	27446.8i	−0.480503	−	0.480503i	0.424789	−	0.905292i	$-0.360348\pi$
$239$	−27446.8	−	27446.8i	−0.480503	−	0.480503i	−0.905292	+	0.424789i	$0.860348\pi$
$240$	−15968.0	+	4278.62i	−0.277223	+	0.0742816i
$241$	−15000.4	−	55982.4i	−0.258267	−	0.963867i	−0.966243	−	0.257631i	$-0.917058\pi$
$241$	−15000.4	−	55982.4i	−0.258267	−	0.963867i	0.707976	−	0.706236i	$-0.249608\pi$
$242$	27115.3	−	27115.3i	0.463003	−	0.463003i
$243$	6656.82	−	11529.9i	0.112734	−	0.195261i
$244$	27355.7	−	15793.8i	0.459482	−	0.265282i
$245$	−52826.5	−	14154.8i	−0.880075	−	0.235815i
$246$		−	15254.6i		−	0.252076i
$247$	−23140.4	+	67478.9i	−0.379296	+	1.10605i
$248$	24001.3			0.390240
$249$	4731.57	−	17658.5i	0.0763145	−	0.284810i
$250$	−19622.6	−	33987.3i	−0.313961	−	0.543797i
$251$	−48211.8	−	27835.1i	−0.765254	−	0.441820i	0.0659249	−	0.997825i	$-0.479000\pi$
$251$	−48211.8	−	27835.1i	−0.765254	−	0.441820i	−0.831179	+	0.556005i	$0.812334\pi$
$252$	−1025.42	−	1025.42i	−0.0161473	−	0.0161473i
$253$	−30588.1	+	8196.05i	−0.477872	+	0.128045i
$254$	−11886.0	−	44359.1i	−0.184233	−	0.687567i
$255$	39262.2	−	39262.2i	0.603802	−	0.603802i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	17277.8	−	9975.36i	0.261591	−	0.151030i	−0.363469	−	0.931606i	$-0.618408\pi$
$257$	17277.8	−	9975.36i	0.261591	−	0.151030i	0.625060	+	0.780577i	$0.285074\pi$
$258$	−4246.58	−	1137.87i	−0.0637969	−	0.0170943i
$259$		−	13925.2i		−	0.207588i
$260$	−34787.3	−	11929.6i	−0.514605	−	0.176473i
$261$	14171.9			0.208040
$262$	−6698.19	+	24998.0i	−0.0975787	+	0.364169i
$263$	59229.8	+	102589.i	0.856305	+	1.48316i	0.875429	+	0.483347i	$0.160579\pi$
$263$	59229.8	+	102589.i	0.856305	+	1.48316i	−0.0191233	+	0.999817i	$0.506087\pi$
$264$	6124.80	+	3536.16i	0.0878788	+	0.0507369i
$265$	87223.8	+	87223.8i	1.24206	+	1.24206i
$266$	22786.6	−	6105.65i	0.322045	−	0.0862917i
$267$	−15351.9	−	57294.2i	−0.215348	−	0.803690i
$268$	−38997.7	+	38997.7i	−0.542962	+	0.542962i
$269$	6430.00	−	11137.1i	0.0888600	−	0.153910i	−0.818170	−	0.574977i	$-0.805011\pi$
$269$	6430.00	−	11137.1i	0.0888600	−	0.153910i	0.907030	+	0.421067i	$0.138344\pi$
$270$	−45444.9	+	26237.6i	−0.623387	+	0.359912i
$271$	−15408.0	−	4128.56i	−0.209801	−	0.0562161i	0.152388	−	0.988321i	$-0.451304\pi$
$271$	−15408.0	−	4128.56i	−0.209801	−	0.0562161i	−0.362189	+	0.932105i	$0.617970\pi$
$272$		−	13757.6i		−	0.185953i
$273$	−6089.46	−	31119.6i	−0.0817060	−	0.417551i
$274$	−33321.1			−0.443832
$275$	978.833	−	3653.06i	0.0129433	−	0.0483049i
$276$	36544.6	+	63297.1i	0.479739	+	0.830932i
$277$	52769.8	+	30466.6i	0.687742	+	0.397068i	0.802766	−	0.596295i	$-0.203361\pi$
$277$	52769.8	+	30466.6i	0.687742	+	0.397068i	−0.115024	+	0.993363i	$0.536694\pi$
$278$	4053.62	+	4053.62i	0.0524509	+	0.0524509i
$279$	−9399.45	+	2518.57i	−0.120752	+	0.0323554i
$280$	3147.64	+	11747.1i	0.0401485	+	0.149836i
$281$	−30774.2	+	30774.2i	−0.389739	+	0.389739i	−0.874594	−	0.484855i	$-0.838872\pi$
$281$	−30774.2	+	30774.2i	−0.389739	+	0.389739i	0.484855	+	0.874594i	$0.338872\pi$
$282$	−32913.3	+	57007.4i	−0.413878	+	0.716858i
$283$	95997.5	−	55424.2i	1.19864	−	0.692033i	0.238385	−	0.971171i	$-0.423382\pi$
$283$	95997.5	−	55424.2i	1.19864	−	0.692033i	0.960251	+	0.279138i	$0.0900487\pi$
$284$	−42647.0	−	11427.2i	−0.528751	−	0.141678i
$285$			109032.i			1.34234i
$286$	6914.68	+	14132.3i	0.0845356	+	0.172775i
$287$	−11222.3			−0.136245
$288$	429.813	−	1604.09i	0.00518197	−	0.0193394i
$289$	−18656.1	−	32313.4i	−0.223371	−	0.386889i
$290$	−102927.	−	59425.2i	−1.22387	−	0.706601i
$291$	32469.0	+	32469.0i	0.383428	+	0.383428i
$292$	27283.1	−	7310.48i	0.319984	−	0.0857394i
$293$	−8755.66	−	32676.6i	−0.101989	−	0.380628i	0.895997	−	0.444060i	$-0.146462\pi$
$293$	−8755.66	−	32676.6i	−0.101989	−	0.380628i	−0.997986	+	0.0634315i	$0.979796\pi$
$294$	38184.9	−	38184.9i	0.441771	−	0.441771i
$295$	−10599.5	+	18358.8i	−0.121798	+	0.210960i
$296$	13810.2	−	7973.32i	0.157622	−	0.0910030i
$297$	21684.6	+	5810.38i	0.245832	+	0.0658706i
$298$			67972.3i			0.765419i
$299$	−11139.2	+	162214.i	−0.124598	+	1.81445i
$300$	−8728.86			−0.0969873
$301$	−837.090	+	3124.06i	−0.00923931	+	0.0344816i
$302$	−2219.78	−	3844.78i	−0.0243387	−	0.0421558i
$303$	−69325.6	−	40025.1i	−0.755106	−	0.435961i
$304$	19102.5	+	19102.5i	0.206701	+	0.206701i
$305$	103743.	−	27797.8i	1.11522	−	0.298821i
$306$	1443.65	+	5387.78i	0.0154177	+	0.0575396i
$307$	98055.5	−	98055.5i	1.04039	−	1.04039i	0.0412382	−	0.999149i	$-0.486870\pi$
$307$	98055.5	−	98055.5i	1.04039	−	1.04039i	0.999149	−	0.0412382i	$-0.0131302\pi$
$308$	2601.43	−	4505.81i	0.0274228	−	0.0474976i
$309$	−19724.3	+	11387.8i	−0.206578	+	0.119268i
$310$	78827.1	+	21121.7i	0.820261	+	0.219788i
$311$		−	68074.1i		−	0.703819i	−0.936034	−	0.351910i	$-0.885532\pi$
$311$		−	68074.1i		−	0.703819i	0.936034	−	0.351910i	$-0.114468\pi$
$312$	27376.0	−	23857.8i	0.281229	−	0.245087i
$313$	−55684.0			−0.568383			−0.284192	−	0.958767i	$-0.591725\pi$
$313$	−55684.0			−0.568383			−0.284192	+	0.958767i	$0.591725\pi$
$314$	13163.8	−	49127.9i	0.133512	−	0.498275i
$315$	−2465.37	−	4270.15i	−0.0248463	−	0.0430350i
$316$	−46488.6	−	26840.2i	−0.465556	−	0.268789i
$317$	−23137.2	−	23137.2i	−0.230246	−	0.230246i	0.582549	−	0.812795i	$-0.302055\pi$
$317$	−23137.2	−	23137.2i	−0.230246	−	0.230246i	−0.812795	+	0.582549i	$0.802055\pi$
$318$	−117650.	+	31524.2i	−1.16342	+	0.311738i
$319$	13159.8	+	49113.2i	0.129321	+	0.482633i
$320$	−9847.86	+	9847.86i	−0.0961705	+	0.0961705i
$321$	−44689.2	+	77403.9i	−0.433703	+	0.751195i
$322$	46565.6	−	26884.6i	0.449110	−	0.259294i
$323$	−87645.6	−	23484.6i	−0.840089	−	0.225101i
$324$		−	57759.5i		−	0.550216i
$325$	−16112.2	−	10838.5i	−0.152541	−	0.102613i
$326$	131716.			1.23938
$327$	52114.7	−	194495.i	0.487377	−	1.81891i
$328$	−6425.71	−	11129.7i	−0.0597274	−	0.103451i
$329$	41938.5	+	24213.2i	0.387454	+	0.223697i
$330$	17003.7	+	17003.7i	0.156141	+	0.156141i
$331$	74041.0	−	19839.2i	0.675797	−	0.181079i	0.0954323	−	0.995436i	$-0.469577\pi$
$331$	74041.0	−	19839.2i	0.675797	−	0.181079i	0.580365	+	0.814357i	$0.302910\pi$
$332$	−3986.16	−	14876.6i	−0.0361642	−	0.134967i
$333$	−4571.70	+	4571.70i	−0.0412277	+	0.0412277i
$334$	−24720.5	+	42817.2i	−0.221597	+	0.383818i
$335$	−162399.	+	93760.8i	−1.44708	+	0.835472i
$336$	−11599.3	−	3108.02i	−0.102743	−	0.0275299i
$337$		−	15606.4i		−	0.137418i	−0.997637	−	0.0687090i	$-0.978112\pi$
$337$		−	15606.4i		−	0.137418i	0.997637	−	0.0687090i	$-0.0218880\pi$
$338$	80155.7	−	10045.6i	0.701618	−	0.0879307i
$339$	−166796.			−1.45140
$340$	12107.0	−	45183.8i	0.104732	−	0.390863i
$341$	−17456.4	−	30235.4i	−0.150123	−	0.260020i
$342$	−9485.47	−	5476.44i	−0.0810973	−	0.0468216i
$343$	−61637.6	−	61637.6i	−0.523911	−	0.523911i
$344$	−3577.57	+	958.607i	−0.0302323	+	0.00810072i
$345$	64320.1	+	240046.i	0.540391	+	2.01677i
$346$	−64625.0	+	64625.0i	−0.539820	+	0.539820i
$347$	−3570.79	+	6184.79i	−0.0296555	+	0.0513649i	−0.880472	−	0.474098i	$-0.842774\pi$
$347$	−3570.79	+	6184.79i	−0.0296555	+	0.0513649i	0.850817	+	0.525463i	$0.176108\pi$
$348$	101632.	−	58677.2i	0.839211	−	0.484519i
$349$	−173668.	−	46534.1i	−1.42583	−	0.382050i	−0.538282	−	0.842765i	$-0.680927\pi$
$349$	−173668.	−	46534.1i	−1.42583	−	0.382050i	−0.887548	+	0.460714i	$0.847593\pi$
$350$			6421.53i			0.0524206i
$351$	64337.5	−	95642.1i	0.522215	−	0.776310i
$352$	5958.14			0.0480868
$353$	54339.4	−	202797.i	0.436079	−	1.62747i	−0.302391	−	0.953184i	$-0.597785\pi$
$353$	54339.4	−	202797.i	0.436079	−	1.62747i	0.738470	−	0.674286i	$-0.235549\pi$
$354$	−10466.0	−	18127.7i	−0.0835172	−	0.144656i
$355$	−130009.	−	75060.5i	−1.03161	−	0.595600i
$356$	−35334.7	−	35334.7i	−0.278806	−	0.278806i
$357$	38959.5	−	10439.2i	0.305687	−	0.0819085i
$358$	−9763.59	−	36438.2i	−0.0761805	−	0.284309i
$359$	−111995.	+	111995.i	−0.868976	+	0.868976i	−0.992359	−	0.123383i	$-0.960626\pi$
$359$	−111995.	+	111995.i	−0.868976	+	0.868976i	0.123383	+	0.992359i	$0.460626\pi$
$360$	2823.26	−	4890.03i	0.0217844	−	0.0377317i
$361$	41443.5	−	23927.4i	0.318011	−	0.183603i
$362$	126292.	+	33839.8i	0.963737	+	0.258232i
$363$			128743.i			0.977038i
$364$	−17551.4	−	20139.6i	−0.132467	−	0.152001i
$365$	96038.8			0.720877
$366$	−27447.9	+	102437.i	−0.204903	+	0.764707i
$367$	−29488.8	−	51076.1i	−0.218940	−	0.379215i	0.735544	−	0.677477i	$-0.236927\pi$
$367$	−29488.8	−	51076.1i	−0.218940	−	0.379215i	−0.954484	+	0.298262i	$0.903593\pi$
$368$	53325.3	+	30787.4i	0.393765	+	0.227341i
$369$	3684.34	+	3684.34i	0.0270587	+	0.0270587i
$370$	52373.3	−	14033.4i	0.382566	−	0.102508i
$371$	23191.3	+	86551.2i	0.168491	+	0.628818i
$372$	−56979.1	+	56979.1i	−0.411746	+	0.411746i
$373$	27999.8	−	48497.1i	0.201251	−	0.348577i	−0.747681	−	0.664058i	$-0.768833\pi$
$373$	27999.8	−	48497.1i	0.201251	−	0.348577i	0.948932	+	0.315482i	$0.102166\pi$
$374$	−17331.0	+	10006.1i	−0.123903	+	0.0715352i
$375$	127270.	+	34101.8i	0.905030	+	0.242502i
$376$			55456.2i			0.392260i
$377$	260456.	+	17885.4i	1.83253	+	0.125839i
$378$	−38118.3			−0.266778
$379$	−27378.2	+	102177.i	−0.190601	+	0.711334i	0.802760	+	0.596302i	$0.203364\pi$
$379$	−27378.2	+	102177.i	−0.190601	+	0.711334i	−0.993362	+	0.115032i	$0.963303\pi$
$380$	45927.3	+	79548.5i	0.318056	+	0.550890i
$381$	133526.	+	77091.1i	0.919846	+	0.531073i
$382$	−23834.0	−	23834.0i	−0.163332	−	0.163332i
$383$	190137.	−	50947.1i	1.29619	−	0.347314i	0.456183	−	0.889886i	$-0.349216\pi$
$383$	190137.	−	50947.1i	1.29619	−	0.347314i	0.840009	+	0.542572i	$0.182550\pi$
$384$	−3559.20	−	13283.1i	−0.0241373	−	0.0900818i
$385$	12509.1	−	12509.1i	0.0843923	−	0.0843923i
$386$	−59552.6	+	103148.i	−0.399692	+	0.692288i
$387$	1300.47	−	750.824i	0.00868314	−	0.00501322i
$388$	37366.1	+	10012.2i	0.248207	+	0.0665069i
$389$			178816.i			1.18170i	0.806780	+	0.590852i	$0.201208\pi$
$389$			178816.i			1.18170i	−0.806780	+	0.590852i	$0.798792\pi$
$390$	110906.	−	54264.2i	0.729163	−	0.356767i
$391$	−206816.			−1.35279
$392$	11774.8	−	43944.0i	0.0766267	−	0.285975i
$393$	−43443.7	−	75246.8i	−0.281282	−	0.487195i
$394$	−135293.	−	78111.6i	−0.871533	−	0.503180i
$395$	−129062.	−	129062.i	−0.827186	−	0.827186i
$396$	−2333.34	+	625.217i	−0.0148795	+	0.00398695i
$397$	65796.0	+	245554.i	0.417463	+	1.55799i	0.779850	+	0.625967i	$0.215295\pi$
$397$	65796.0	+	245554.i	0.417463	+	1.55799i	−0.362386	+	0.932028i	$0.618038\pi$
$398$	−135016.	+	135016.i	−0.852350	+	0.852350i
$399$	−39600.6	+	68590.2i	−0.248746	+	0.430840i
$400$	−6368.50	+	3676.86i	−0.0398031	+	0.0229804i
$401$	−42604.7	−	11415.9i	−0.264953	−	0.0709939i	0.123897	−	0.992295i	$-0.460461\pi$
$401$	−42604.7	−	11415.9i	−0.264953	−	0.0709939i	−0.388850	+	0.921301i	$0.627127\pi$
$402$		−	185161.i		−	1.14577i
$403$	−175925.	+	34424.8i	−1.08322	+	0.211964i
$404$	−67439.1			−0.413190
$405$	50829.6	−	189699.i	0.309889	−	1.15652i
$406$	−43166.8	−	74767.1i	−0.261877	−	0.453585i
$407$	−20088.6	−	11598.2i	−0.121272	−	0.0700166i
$408$	32660.5	+	32660.5i	0.196202	+	0.196202i
$409$	−116159.	+	31124.6i	−0.694392	+	0.186062i	−0.588717	−	0.808339i	$-0.700367\pi$
$409$	−116159.	+	31124.6i	−0.694392	+	0.186062i	−0.105675	+	0.994401i	$0.533700\pi$
$410$	−11309.5	−	42207.7i	−0.0672786	−	0.251087i
$411$	79104.3	−	79104.3i	0.468292	−	0.468292i
$412$	−9593.78	+	16616.9i	−0.0565191	+	0.0978940i
$413$	−13336.0	+	7699.52i	−0.0781851	+	0.0451402i
$414$	−24114.0	−	6461.34i	−0.140692	−	0.0376983i
$415$		−	52366.8i		−	0.304060i
$416$	9923.67	−	28938.0i	0.0573437	−	0.167218i
$417$	−19246.6			−0.110683
$418$	10170.7	−	37957.6i	0.0582102	−	0.217243i
$419$	80827.3	+	139997.i	0.460394	+	0.797427i	0.998980	−	0.0451439i	$-0.0143746\pi$
$419$	80827.3	+	139997.i	0.460394	+	0.797427i	−0.538586	+	0.842571i	$0.681041\pi$
$420$	−35360.2	−	20415.2i	−0.200455	−	0.115733i
$421$	80144.5	+	80144.5i	0.452178	+	0.452178i	0.896077	−	0.443899i	$-0.146405\pi$
$421$	80144.5	+	80144.5i	0.452178	+	0.452178i	−0.443899	+	0.896077i	$0.646405\pi$
$422$	−11931.8	+	3197.11i	−0.0670009	+	0.0179528i
$423$	−5819.29	−	21717.9i	−0.0325229	−	0.121377i
$424$	−72557.6	+	72557.6i	−0.403600	+	0.403600i
$425$	12349.8	−	21390.4i	0.0683724	−	0.118424i
$426$	128372.	−	74115.6i	0.707378	−	0.408405i
$427$	75359.5	+	20192.5i	0.413316	+	0.110748i
$428$			75297.7i			0.411049i
$429$	−49965.5	−	17134.6i	−0.271491	−	0.0931020i
$430$	−12593.4			−0.0681090
$431$	−22499.7	+	83970.1i	−0.121122	+	0.452033i	−0.999672	−	0.0256176i	$-0.991845\pi$
$431$	−22499.7	+	83970.1i	−0.121122	+	0.452033i	0.878550	+	0.477650i	$0.158511\pi$
$432$	−21825.9	−	37803.6i	−0.116951	−	0.202565i
$433$	−186500.	−	107676.i	−0.994725	−	0.574305i	−0.0880419	−	0.996117i	$-0.528061\pi$
$433$	−186500.	−	107676.i	−0.994725	−	0.574305i	−0.906683	+	0.421812i	$0.861394\pi$
$434$	41917.6	+	41917.6i	0.222544	+	0.222544i
$435$	385425.	−	103274.i	2.03686	−	0.545775i
$436$	−43904.5	−	163854.i	−0.230960	−	0.861954i
$437$	287165.	−	287165.i	1.50373	−	1.50373i
$438$	−47415.0	+	82125.1i	−0.247154	+	0.428083i
$439$	254975.	−	147210.i	1.32303	−	0.763850i	0.338816	−	0.940852i	$-0.389973\pi$
$439$	254975.	−	147210.i	1.32303	−	0.763850i	0.984210	+	0.177003i	$0.0566401\pi$
$440$	19568.2	+	5243.29i	0.101076	+	0.0270831i
$441$			18445.1i			0.0948424i
$442$	19732.4	+	100840.i	0.101003	+	0.516167i
$443$	−75284.4			−0.383617			−0.191808	−	0.981432i	$-0.561435\pi$
$443$	−75284.4			−0.383617			−0.191808	+	0.981432i	$0.561435\pi$
$444$	−13856.7	+	51714.1i	−0.0702902	+	0.262327i
$445$	−84953.9	−	147145.i	−0.429006	−	0.743060i
$446$	−55986.2	−	32323.6i	−0.281456	−	0.162499i
$447$	−161366.	−	161366.i	−0.807602	−	0.807602i
$448$	−9771.93	+	2618.38i	−0.0486883	+	0.0130460i
$449$	−36394.3	−	135825.i	−0.180526	−	0.673733i	−0.995544	−	0.0942974i	$-0.969940\pi$
$449$	−36394.3	−	135825.i	−0.180526	−	0.673733i	0.815018	−	0.579436i	$-0.196727\pi$
$450$	2108.22	−	2108.22i	0.0104110	−	0.0104110i
$451$	−9347.00	+	16189.5i	−0.0459535	+	0.0795939i
$452$	−121693.	+	70259.7i	−0.595648	+	0.343898i
$453$	14397.3	+	3857.74i	0.0701591	+	0.0187991i
$454$		−	124927.i		−	0.606099i
$455$	−39920.4	−	81589.7i	−0.192829	−	0.394105i
$456$	−90698.5			−0.436185
$457$	−50410.3	+	188134.i	−0.241372	+	0.900813i	0.733800	+	0.679365i	$0.237745\pi$
$457$	−50410.3	+	188134.i	−0.241372	+	0.900813i	−0.975172	+	0.221447i	$0.928922\pi$
$458$	−20050.5	−	34728.5i	−0.0955861	−	0.165560i
$459$	126974.	+	73308.5i	0.602684	+	0.347960i
$460$	148042.	+	148042.i	0.699631	+	0.699631i
$461$	−316815.	+	84890.4i	−1.49075	+	0.399445i	−0.909989	−	0.414632i	$-0.863910\pi$
$461$	−316815.	+	84890.4i	−1.49075	+	0.399445i	−0.580758	+	0.814076i	$0.697244\pi$
$462$	4521.00	+	16872.6i	0.0211812	+	0.0790493i
$463$	195600.	−	195600.i	0.912447	−	0.912447i	−0.0840177	−	0.996464i	$-0.526775\pi$
$463$	195600.	−	195600.i	0.912447	−	0.912447i	0.996464	+	0.0840177i	$0.0267752\pi$
$464$	49433.2	−	85620.8i	0.229606	−	0.397689i
$465$	−237278.	+	136993.i	−1.09737	+	0.633565i
$466$	−8288.57	−	2220.92i	−0.0381687	−	0.0102273i
$467$			213346.i			0.978252i	0.872213	+	0.489126i	$0.162684\pi$
$467$			213346.i			0.978252i	−0.872213	+	0.489126i	$0.837316\pi$
$468$	−849.725	+	12374.1i	−0.00387960	+	0.0564966i
$469$	−136217.			−0.619278
$470$	−48802.7	+	182134.i	−0.220926	+	0.824509i
$471$	85378.8	+	147880.i	0.384865	+	0.666606i
$472$	−15271.9	−	8817.23i	−0.0685502	−	0.0395775i
$473$	3809.61	+	3809.61i	0.0170278	+	0.0170278i
$474$	174082.	−	46645.3i	0.774816	−	0.207611i
$475$	12553.0	+	46848.4i	0.0556365	+	0.207638i
$476$	24027.2	−	24027.2i	0.106045	−	0.106045i
$477$	20801.4	−	36029.0i	0.0914229	−	0.158349i
$478$	95078.6	−	54893.6i	0.416128	−	0.240252i
$479$	−139412.	−	37355.3i	−0.607615	−	0.162810i	−0.0581239	−	0.998309i	$-0.518512\pi$
$479$	−139412.	−	37355.3i	−0.607615	−	0.162810i	−0.549491	+	0.835499i	$0.685179\pi$
$480$		−	46757.6i		−	0.202941i
$481$	−89790.0	+	78250.7i	−0.388095	+	0.338219i
$482$	163928.			0.705600
$483$	−46722.5	+	174371.i	−0.200277	+	0.747445i
$484$	54230.6	+	93930.1i	0.231501	+	0.400972i
$485$	113910.	+	65765.9i	0.484259	+	0.279587i
$486$	26627.3	+	26627.3i	0.112734	+	0.112734i
$487$	−77919.1	+	20878.3i	−0.328538	+	0.0880315i	−0.419318	−	0.907839i	$-0.637731\pi$
$487$	−77919.1	+	20878.3i	−0.328538	+	0.0880315i	0.0907798	+	0.995871i	$0.471064\pi$
$488$	23123.8	+	86299.2i	0.0971000	+	0.362382i
$489$	−312695.	+	312695.i	−1.30768	+	1.30768i
$490$	77343.4	−	133963.i	0.322130	−	0.557945i
$491$	282641.	−	163183.i	1.17239	−	0.676880i	0.218149	−	0.975915i	$-0.429998\pi$
$491$	282641.	−	163183.i	1.17239	−	0.676880i	0.954242	+	0.299035i	$0.0966648\pi$
$492$	41676.4	+	11167.2i	0.172171	+	0.0461331i
$493$			332071.i			1.36627i
$494$	−167416.	−	112619.i	−0.686029	−	0.461484i
$495$	−8213.56			−0.0335213
$496$	−17570.2	+	65572.8i	−0.0714188	+	0.266539i
$497$	−54524.4	−	94439.0i	−0.220738	−	0.382330i
$498$	44780.1	+	25853.8i	0.180562	+	0.104248i
$499$	321163.	+	321163.i	1.28981	+	1.28981i	0.934904	+	0.354902i	$0.115486\pi$
$499$	321163.	+	321163.i	1.28981	+	1.28981i	0.354902	+	0.934904i	$0.384514\pi$
$500$	107220.	−	28729.4i	0.428879	−	0.114918i
$501$	−42961.5	−	160334.i	−0.171161	−	0.638780i
$502$	111340.	−	111340.i	0.441820	−	0.441820i
$503$	−38564.6	+	66795.9i	−0.152424	+	0.264006i	−0.932118	−	0.362155i	$-0.882041\pi$
$503$	−38564.6	+	66795.9i	−0.152424	+	0.264006i	0.779694	+	0.626161i	$0.215375\pi$
$504$	3552.15	−	2050.83i	0.0139840	−	0.00807364i
$505$	−221489.	−	59347.9i	−0.868501	−	0.232714i
$506$		−	89568.1i		−	0.349826i
$507$	−166441.	+	214138.i	−0.647509	+	0.833062i
$508$	129892.			0.503334
$509$	94717.1	−	353489.i	0.365589	−	1.36440i	−0.501032	−	0.865429i	$-0.667046\pi$
$509$	94717.1	−	353489.i	0.365589	−	1.36440i	0.866621	−	0.498967i	$-0.166287\pi$
$510$	78524.4	+	136008.i	0.301901	+	0.522908i
$511$	60416.7	+	34881.6i	0.231374	+	0.133584i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−278093.	+	74514.9i	−1.05671	+	0.283145i
$514$	14604.9	+	54506.4i	0.0552807	+	0.206310i
$515$	−46131.9	+	46131.9i	−0.173935	+	0.173935i
$516$	6217.42	−	10768.9i	0.0233513	−	0.0404456i
$517$	69860.5	−	40334.0i	0.261367	−	0.150900i
$518$	38044.3	+	10193.9i	0.141785	+	0.0379912i
$519$		−	306840.i		−	1.13914i
$520$	58058.2	−	86307.6i	0.214712	−	0.319185i
$521$	384986.			1.41830			0.709152	−	0.705055i	$-0.249078\pi$
$521$	384986.			1.41830			0.709152	+	0.705055i	$0.249078\pi$
$522$	−10374.5	+	38718.3i	−0.0380739	+	0.142094i
$523$	−50951.0	−	88249.7i	−0.186273	−	0.322634i	0.757732	−	0.652566i	$-0.226307\pi$
$523$	−50951.0	−	88249.7i	−0.186273	−	0.322634i	−0.944005	+	0.329932i	$0.892974\pi$
$524$	−63392.4	−	36599.6i	−0.230874	−	0.133295i
$525$	−15244.7	−	15244.7i	−0.0553096	−	0.0553096i
$526$	−323638.	+	86718.4i	−1.16973	+	0.313430i
$527$	−59014.4	−	220245.i	−0.212489	−	0.793020i
$528$	−14144.6	+	14144.6i	−0.0507369	+	0.0507369i
$529$	322903.	−	559284.i	1.15388	−	1.99858i
$530$	−302152.	+	174448.i	−1.07566	+	0.621031i
$531$	6906.05	+	1850.47i	0.0244929	+	0.00656286i
$532$			66723.8i			0.235753i
$533$	63062.3	+	72361.9i	0.221981	+	0.254716i
$534$	167769.			0.588342
$535$	−66263.6	+	247299.i	−0.231509	+	0.864002i
$536$	−77995.5	−	135092.i	−0.271481	−	0.470219i
$537$	109683.	+	63325.6i	0.380357	+	0.219599i
$538$	25720.0	+	25720.0i	0.0888600	+	0.0888600i
$539$	−63922.1	+	17127.9i	−0.220026	+	0.0589557i
$540$	−38414.5	−	143365.i	−0.131737	−	0.491650i
$541$	−52761.7	+	52761.7i	−0.180270	+	0.180270i	−0.791474	−	0.611203i	$-0.790686\pi$
$541$	−52761.7	+	52761.7i	−0.180270	+	0.180270i	0.611203	+	0.791474i	$0.290686\pi$
$542$	22558.9	−	39073.2i	0.0767926	−	0.133009i
$543$	−380153.	+	219481.i	−1.28931	+	0.744385i
$544$	37586.4	+	10071.2i	0.127009	+	0.0340318i
$545$		−	576780.i		−	1.94186i
$546$	89478.2	+	6144.43i	0.300146	+	0.0206109i
$547$	414681.			1.38592			0.692961	−	0.720975i	$-0.256306\pi$
$547$	414681.			1.38592			0.692961	+	0.720975i	$0.256306\pi$
$548$	24392.8	−	91035.0i	0.0812269	−	0.303143i
$549$	−18111.6	−	31370.2i	−0.0600913	−	0.104081i
$550$	9263.78	+	5348.45i	0.0306241	+	0.0176808i
$551$	−461082.	−	461082.i	−1.51871	−	1.51871i
$552$	−199683.	+	53505.0i	−0.655336	+	0.175597i
$553$	−34315.4	−	128067.i	−0.112212	−	0.418780i
$554$	−121867.	+	121867.i	−0.397068	+	0.397068i
$555$	−91019.0	+	157649.i	−0.295492	+	0.511807i
$556$	−14042.1	+	8107.23i	−0.0454238	+	0.0262255i
$557$	224316.	+	60105.3i	0.723019	+	0.193732i	0.601518	−	0.798859i	$-0.294563\pi$
$557$	224316.	+	60105.3i	0.723019	+	0.193732i	0.121501	+	0.992591i	$0.461229\pi$
$558$		−	27523.5i		−	0.0883965i
$559$	24848.0	−	12157.7i	0.0795183	−	0.0389069i
$560$	−34398.0			−0.109688
$561$	17389.4	−	64898.2i	0.0552534	−	0.206209i
$562$	−61548.4	−	106605.i	−0.194870	−	0.337524i
$563$	414896.	+	239540.i	1.30895	+	0.755721i	0.981921	−	0.189293i	$-0.0606197\pi$
$563$	414896.	+	239540.i	1.30895	+	0.755721i	0.327027	+	0.945015i	$0.393953\pi$
$564$	−131653.	−	131653.i	−0.413878	−	0.413878i
$565$	−461505.	+	123660.i	−1.44571	+	0.387376i
$566$	81146.7	+	302843.i	0.253302	+	0.945334i
$567$	100875.	−	100875.i	0.313775	−	0.313775i
$568$	62439.5	−	108148.i	0.193536	−	0.335215i
$569$	−113561.	+	65564.7i	−0.350757	+	0.202510i	−0.665019	−	0.746827i	$-0.731576\pi$
$569$	−113561.	+	65564.7i	−0.350757	+	0.202510i	0.314262	+	0.949336i	$0.398243\pi$
$570$	−297880.	−	79816.6i	−0.916835	−	0.245665i
$571$			131069.i			0.402003i	0.979591	+	0.201002i	$0.0644196\pi$
$571$			131069.i			0.402003i	−0.979591	+	0.201002i	$0.935580\pi$
$572$	−43672.0	+	8545.70i	−0.133478	+	0.0261189i
$573$	113164.			0.344667
$574$	8215.31	−	30660.0i	0.0249345	−	0.0930567i
$575$	55273.8	+	95737.0i	0.167180	+	0.289564i
$576$	4067.80	+	2348.54i	0.0122607	+	0.00707870i
$577$	265150.	+	265150.i	0.796416	+	0.796416i	0.982528	−	0.186112i	$-0.0595888\pi$
$577$	265150.	+	265150.i	0.796416	+	0.796416i	−0.186112	+	0.982528i	$0.559589\pi$
$578$	101939.	−	27314.5i	0.305130	−	0.0817593i
$579$	−103496.	−	386251.i	−0.308720	−	1.15216i
$580$	237701.	−	237701.i	0.706601	−	0.706601i
$581$	19019.8	−	32943.2i	0.0563447	−	0.0975919i
$582$	−112476.	+	64938.1i	−0.332058	+	0.191714i
$583$	144176.	+	38631.8i	0.424185	+	0.113660i
$584$			79890.4i			0.234244i
$585$	−13680.2	+	39892.3i	−0.0399743	+	0.116568i
$586$	95683.6			0.278639
$587$	−145082.	+	541455.i	−0.421055	+	1.57140i	0.351335	+	0.936250i	$0.385728\pi$
$587$	−145082.	+	541455.i	−0.421055	+	1.57140i	−0.772390	+	0.635149i	$0.780939\pi$
$588$	76369.8	+	132276.i	0.220885	+	0.382585i
$589$	387753.	+	223869.i	1.11770	+	0.645303i
$590$	−42397.9	−	42397.9i	−0.121798	−	0.121798i
$591$	506623.	−	135749.i	1.45047	−	0.388653i
$592$	11673.7	+	43567.0i	0.0333094	+	0.124312i
$593$	−284953.	+	284953.i	−0.810335	+	0.810335i	−0.984684	−	0.174349i	$-0.944218\pi$
$593$	−284953.	+	284953.i	−0.810335	+	0.810335i	0.174349	+	0.984684i	$0.444218\pi$
$594$	−31748.5	+	54990.0i	−0.0899809	+	0.155851i
$595$	100057.	−	57767.8i	0.282626	−	0.163174i
$596$	−185704.	−	49759.2i	−0.522791	−	0.140081i
$597$		−	641054.i		−	1.79865i
$598$	−435022.	−	149181.i	−1.21649	−	0.417169i
$599$	−311888.			−0.869251			−0.434625	−	0.900611i	$-0.643119\pi$
$599$	−311888.			−0.869251			−0.434625	+	0.900611i	$0.643119\pi$
$600$	6389.97	−	23847.7i	0.0177499	−	0.0662436i
$601$	174272.	+	301847.i	0.482478	+	0.835677i	0.999798	−	0.0201155i	$-0.00640338\pi$
$601$	174272.	+	301847.i	0.482478	+	0.835677i	−0.517319	+	0.855792i	$0.673070\pi$
$602$	−7922.31	−	4573.95i	−0.0218604	−	0.0126211i
$603$	44720.7	+	44720.7i	0.122991	+	0.122991i
$604$	12129.1	−	3249.99i	0.0332473	−	0.00890857i
$605$	95448.1	+	356217.i	0.260769	+	0.973205i
$606$	160101.	−	160101.i	0.435961	−	0.435961i
$607$	−187866.	+	325393.i	−0.509882	+	0.883142i	0.490052	+	0.871693i	$0.336978\pi$
$607$	−187866.	+	325393.i	−0.509882	+	0.883142i	−0.999934	+	0.0114491i	$0.996356\pi$
$608$	−66172.9	+	38204.9i	−0.179008	+	0.103350i
$609$	279975.	+	75019.1i	0.754892	+	0.202273i
$610$			303780.i			0.816395i
$611$	−79540.3	−	406483.i	−0.213061	−	1.08883i
$612$	−15776.5			−0.0421219
$613$	102859.	−	383876.i	0.273730	−	1.02158i	−0.682957	−	0.730458i	$-0.739306\pi$
$613$	102859.	−	383876.i	0.273730	−	1.02158i	0.956688	−	0.291117i	$-0.0940268\pi$
$614$	196111.	+	339674.i	0.520194	+	0.901002i
$615$	127050.	+	73352.3i	0.335911	+	0.193938i
$616$	10405.7	+	10405.7i	0.0274228	+	0.0274228i
$617$	−529221.	+	141804.i	−1.39017	+	0.372494i	−0.874804	−	0.484478i	$-0.839010\pi$
$617$	−529221.	+	141804.i	−1.39017	+	0.372494i	−0.515363	+	0.856972i	$0.672343\pi$
$618$	−16672.9	−	62224.2i	−0.0436551	−	0.162923i
$619$	104044.	−	104044.i	0.271540	−	0.271540i	−0.558180	−	0.829720i	$-0.688500\pi$
$619$	104044.	−	104044.i	0.271540	−	0.271540i	0.829720	+	0.558180i	$0.188500\pi$
$620$	−115411.	+	199897.i	−0.300236	+	0.520025i
$621$	−568297.	+	328107.i	−1.47364	+	0.850808i
$622$	185982.	+	49833.7i	0.480717	+	0.128808i
$623$		−	123422.i		−	0.317993i
$624$	45140.0	+	92257.6i	0.115929	+	0.236937i
$625$	449236.			1.15004
$626$	40763.5	−	152131.i	0.104021	−	0.388213i
$627$	65966.1	+	114257.i	0.167798	+	0.290634i
$628$	124583.	+	71928.2i	0.315894	+	0.182381i
$629$	−107123.	−	107123.i	−0.270757	−	0.270757i
$630$	13471.0	−	3609.55i	0.0339406	−	0.00909437i
$631$	−101850.	−	380110.i	−0.255802	−	0.954664i	−0.967643	−	0.252324i	$-0.918805\pi$
$631$	−101850.	−	380110.i	−0.255802	−	0.954664i	0.711841	−	0.702340i	$-0.247862\pi$
$632$	107361.	−	107361.i	0.268789	−	0.268789i
$633$	20736.1	−	35916.0i	0.0517512	−	0.0896356i
$634$	80149.6	−	46274.4i	0.199399	−	0.115123i
$635$	426604.	+	114308.i	1.05798	+	0.283485i
$636$		−	344503.i		−	0.851685i
$637$	−23278.3	+	338990.i	−0.0573683	+	0.835425i
$638$	−143813.			−0.353312
$639$	−13104.2	+	48905.4i	−0.0320928	+	0.119772i
$640$	−19695.7	−	34114.0i	−0.0480853	−	0.0832861i
$641$	84097.8	+	48553.9i	0.204677	+	0.118170i	0.598835	−	0.800872i	$-0.295630\pi$
$641$	84097.8	+	48553.9i	0.204677	+	0.118170i	−0.394158	+	0.919043i	$0.628964\pi$
$642$	−178757.	−	178757.i	−0.433703	−	0.433703i
$643$	238628.	−	63940.1i	0.577164	−	0.154651i	0.0415838	−	0.999135i	$-0.486760\pi$
$643$	238628.	−	63940.1i	0.577164	−	0.154651i	0.535580	+	0.844484i	$0.320093\pi$
$644$	39361.8	+	146900.i	0.0949082	+	0.354202i
$645$	29896.6	−	29896.6i	0.0718626	−	0.0718626i
$646$	128322.	−	222260.i	0.307494	−	0.532595i
$647$	−95982.0	+	55415.2i	−0.229288	+	0.132379i	−0.610243	−	0.792214i	$-0.708928\pi$
$647$	−95982.0	+	55415.2i	−0.229288	+	0.132379i	0.380956	+	0.924593i	$0.375595\pi$
$648$	157802.	+	42282.9i	0.375804	+	0.100696i
$649$			25651.5i			0.0609009i
$650$	41406.2	−	36084.9i	0.0980028	−	0.0854081i
$651$	−199025.			−0.469618
$652$	−96423.1	+	359856.i	−0.226822	+	0.846513i
$653$	86718.6	+	150201.i	0.203370	+	0.352246i	0.949612	−	0.313428i	$-0.101477\pi$
$653$	86718.6	+	150201.i	0.203370	+	0.352246i	−0.746242	+	0.665674i	$0.768144\pi$
$654$	493219.	+	284760.i	1.15315	+	0.665769i
$655$	−175990.	−	175990.i	−0.410210	−	0.410210i
$656$	35110.7	−	9407.89i	0.0815891	−	0.0218617i
$657$	−8383.29	−	31286.9i	−0.0194216	−	0.0724822i
$658$	−96852.7	+	96852.7i	−0.223697	+	0.223697i
$659$	−49301.9	+	85393.3i	−0.113525	+	0.196632i	−0.917189	−	0.398452i	$-0.869548\pi$
$659$	−49301.9	+	85393.3i	−0.113525	+	0.196632i	0.803664	+	0.595083i	$0.202881\pi$
$660$	−58902.6	+	34007.4i	−0.135222	+	0.0780703i
$661$	−760411.	−	203751.i	−1.74039	−	0.466335i	−0.757853	−	0.652426i	$-0.773751\pi$
$661$	−760411.	−	203751.i	−1.74039	−	0.466335i	−0.982532	+	0.186091i	$0.940418\pi$
$662$			216807.i			0.494718i
$663$	−286240.	−	192550.i	−0.651182	−	0.438044i
$664$	43561.6			0.0988024
$665$	−58718.4	+	219140.i	−0.132779	+	0.495540i
$666$	−9143.40	−	15836.8i	−0.0206139	−	0.0357043i
$667$	−1.28713e6	−	743124.i	−2.89314	−	1.67036i
$668$	−98882.0	−	98882.0i	−0.221597	−	0.221597i
$669$	209647.	−	56174.9i	0.468422	−	0.125513i
$670$	−137275.	−	512319.i	−0.305804	−	1.14128i
$671$	91896.4	−	91896.4i	0.204105	−	0.204105i
$672$	16982.5	−	29414.6i	0.0376066	−	0.0651365i
$673$	426080.	−	245997.i	0.940721	−	0.543125i	0.0505345	−	0.998722i	$-0.483908\pi$
$673$	426080.	−	245997.i	0.940721	−	0.543125i	0.890186	+	0.455597i	$0.150574\pi$
$674$	42637.6	+	11424.7i	0.0938583	+	0.0251492i
$675$		−	78369.9i		−	0.172005i
$676$	−31233.1	+	226343.i	−0.0683473	+	0.495307i
$677$	−556471.			−1.21413			−0.607065	−	0.794652i	$-0.707653\pi$
$677$	−556471.			−1.21413			−0.607065	+	0.794652i	$0.707653\pi$
$678$	122103.	−	455696.i	0.265625	−	0.991325i
$679$	47772.8	+	82744.8i	0.103619	+	0.179474i
$680$	114582.	+	66153.7i	0.247797	+	0.143066i
$681$	296576.	+	296576.i	0.639502	+	0.639502i
$682$	95383.7	−	25558.0i	0.205072	−	0.0549488i
$683$	−121235.	−	452456.i	−0.259889	−	0.969918i	−0.965305	−	0.261125i	$-0.915907\pi$
$683$	−121235.	−	452456.i	−0.259889	−	0.969918i	0.705416	−	0.708793i	$-0.250760\pi$
$684$	21905.7	−	21905.7i	0.0468216	−	0.0468216i
$685$	160226.	−	277519.i	0.341468	−	0.591441i
$686$	213519.	−	123275.i	0.453720	−	0.261955i
$687$	130045.	+	34845.6i	0.275538	+	0.0738302i
$688$		−	10475.9i		−	0.0221316i
$689$	427764.	−	635901.i	0.901085	−	1.33953i
$690$	−702903.			−1.47638
$691$	−158812.	+	592695.i	−0.332604	+	1.24129i	0.573840	+	0.818968i	$0.305453\pi$
$691$	−158812.	+	592695.i	−0.332604	+	1.24129i	−0.906444	+	0.422327i	$0.861213\pi$
$692$	−129250.	−	223868.i	−0.269910	−	0.467497i
$693$	−5167.04	−	2983.19i	−0.0107591	−	0.00621176i
$694$	−14283.2	−	14283.2i	−0.0296555	−	0.0296555i
$695$	−53252.9	+	14269.1i	−0.110249	+	0.0295411i
$696$	85909.3	+	320618.i	0.177346	+	0.661865i
$697$	−86330.3	+	86330.3i	−0.177704	+	0.177704i
$698$	254267.	−	440403.i	0.521890	−	0.903941i
$699$	24949.5	−	14404.6i	0.0510632	−	0.0294813i
$700$	−17543.9	−	4700.88i	−0.0358040	−	0.00959364i
$701$			445654.i			0.906905i	0.891280	+	0.453453i	$0.149808\pi$
$701$			445654.i			0.906905i	−0.891280	+	0.453453i	$0.850192\pi$
$702$	214201.	+	245788.i	0.434657	+	0.498754i
$703$	297480.			0.601933
$704$	−4361.66	+	16277.9i	−0.00880049	+	0.0328439i
$705$	−316529.	−	548244.i	−0.636846	−	1.10305i
$706$	514274.	+	296916.i	1.03177	+	0.595695i
$707$	−117781.	−	117781.i	−0.235632	−	0.235632i
$708$	57187.5	−	15323.4i	0.114087	−	0.0305694i
$709$	128823.	+	480775.i	0.256273	+	0.956422i	0.967378	+	0.253337i	$0.0815282\pi$
$709$	128823.	+	480775.i	0.256273	+	0.956422i	−0.711105	+	0.703085i	$0.751805\pi$
$710$	300242.	−	300242.i	0.595600	−	0.595600i
$711$	−30779.0	+	53310.8i	−0.0608857	+	0.105457i
$712$	122403.	−	70669.4i	0.241453	−	0.139403i
$713$	985748.	+	264130.i	1.93904	+	0.519564i
$714$			114081.i			0.223778i
$715$	−150952.	−	10365.8i	−0.295275	−	0.0202764i
$716$	106699.			0.208129
$717$	−95399.0	+	356034.i	−0.185569	+	0.692553i
$718$	−223989.	−	387960.i	−0.434488	−	0.752555i
$719$	−53204.8	−	30717.8i	−0.102918	−	0.0594200i	0.447657	−	0.894205i	$-0.352258\pi$
$719$	−53204.8	−	30717.8i	−0.102918	−	0.0594200i	−0.550576	+	0.834785i	$0.685592\pi$
$720$	11293.0	+	11293.0i	0.0217844	+	0.0217844i
$721$	−45776.2	+	12265.7i	−0.0880582	+	0.0235951i
$722$	35032.1	+	130742.i	0.0672035	+	0.250807i
$723$	−389164.	+	389164.i	−0.744486	+	0.744486i
$724$	−184904.	+	320263.i	−0.352752	+	0.610984i
$725$	153718.	−	88749.3i	0.292449	−	0.168845i
$726$	−351733.	−	94246.7i	−0.667330	−	0.178810i
$727$			121549.i			0.229975i	0.993367	+	0.114988i	$0.0366828\pi$
$727$			121549.i			0.229975i	−0.993367	+	0.114988i	$0.963317\pi$
$728$	67870.8	−	33208.0i	0.128062	−	0.0626585i
$729$	458388.			0.862538
$730$	−70305.3	+	262383.i	−0.131930	+	0.492368i
$731$	17593.1	+	30472.1i	0.0329236	+	0.0570253i
$732$	−259770.	−	149978.i	−0.484805	−	0.279902i
$733$	450529.	+	450529.i	0.838522	+	0.838522i	0.988664	−	0.150142i	$-0.0479732\pi$
$733$	450529.	+	450529.i	0.838522	+	0.838522i	−0.150142	+	0.988664i	$0.547973\pi$
$734$	161130.	−	43174.6i	0.299077	−	0.0801376i
$735$	134414.	+	501641.i	0.248811	+	0.928577i
$736$	−123149.	+	123149.i	−0.227341	+	0.227341i
$737$	−113454.	+	196508.i	−0.208874	+	0.361781i
$738$	−12762.9	+	7368.69i	−0.0234335	+	0.0135294i
$739$	−653211.	−	175027.i	−1.19609	−	0.320492i	−0.394801	−	0.918767i	$-0.629186\pi$
$739$	−653211.	−	175027.i	−1.19609	−	0.320492i	−0.801291	+	0.598275i	$0.795853\pi$
$740$			153360.i			0.280058i
$741$	664802.	−	130088.i	1.21075	−	0.236919i
$742$	−253440.			−0.460327
$743$	−17244.2	+	64356.2i	−0.0312367	+	0.116577i	−0.979784	−	0.200059i	$-0.935887\pi$
$743$	−17244.2	+	64356.2i	−0.0312367	+	0.116577i	0.948547	+	0.316636i	$0.102553\pi$
$744$	−113958.	−	197381.i	−0.205873	−	0.356583i
$745$	−566115.	−	326847.i	−1.01998	−	0.588886i
$746$	111999.	+	111999.i	0.201251	+	0.201251i
$747$	−17059.7	+	4571.13i	−0.0305724	+	0.00819186i
$748$	−14649.9	−	54674.1i	−0.0261837	−	0.0977189i
$749$	−131505.	+	131505.i	−0.234412	+	0.234412i
$750$	−186336.	+	322743.i	−0.331264	+	0.573766i
$751$	741981.	−	428383.i	1.31557	−	0.759543i	0.332555	−	0.943084i	$-0.392089\pi$
$751$	741981.	−	428383.i	1.31557	−	0.759543i	0.983012	+	0.183540i	$0.0587558\pi$
$752$	−151509.	−	40596.8i	−0.267919	−	0.0717886i
$753$			528644.i			0.932338i
$754$	−239530.	+	698485.i	−0.421326	+	1.22861i
$755$	42695.6			0.0749012
$756$	27904.6	−	104141.i	0.0488238	−	0.182213i
$757$	−485289.	−	840544.i	−0.846853	−	1.46679i	−0.884002	−	0.467483i	$-0.845161\pi$
$757$	−485289.	−	840544.i	−0.846853	−	1.46679i	0.0371484	−	0.999310i	$-0.488173\pi$
$758$	−259110.	−	149597.i	−0.450968	−	0.260366i
$759$	212635.	+	212635.i	0.369106	+	0.369106i
$760$	−250952.	+	67242.3i	−0.434473	+	0.116417i
$761$	106461.	+	397319.i	0.183833	+	0.686073i	0.994877	+	0.101089i	$0.0322327\pi$
$761$	106461.	+	397319.i	0.183833	+	0.686073i	−0.811045	+	0.584984i	$0.801101\pi$
$762$	−308364.	+	308364.i	−0.531073	+	0.531073i
$763$	209488.	−	362844.i	0.359841	−	0.623263i
$764$	82563.6	−	47668.1i	0.141450	−	0.0816660i
$765$	−51814.5	−	13883.7i	−0.0885378	−	0.0237236i
$766$			556760.i			0.948879i
$767$	124586.	+	42724.2i	0.211777	+	0.0726246i
$768$	38895.6			0.0659444
$769$	39128.5	−	146030.i	0.0661669	−	0.246938i	−0.924919	−	0.380165i	$-0.875867\pi$
$769$	39128.5	−	146030.i	0.0661669	−	0.246938i	0.991086	+	0.133227i	$0.0425339\pi$
$770$	25018.1	+	43332.6i	0.0421962	+	0.0730859i
$771$	−164070.	−	94726.0i	−0.276008	−	0.159353i
$772$	−238210.	−	238210.i	−0.399692	−	0.399692i
$773$	258234.	−	69193.5i	0.432169	−	0.115799i	−0.0361751	−	0.999345i	$-0.511517\pi$
$773$	258234.	−	69193.5i	0.432169	−	0.115799i	0.468344	+	0.883546i	$0.344851\pi$
$774$	1099.28	+	4102.58i	0.00183496	+	0.00684818i
$775$	−86181.0	+	86181.0i	−0.143485	+	0.143485i
$776$	−54707.7	+	94756.6i	−0.0908501	+	0.157357i
$777$	−114518.	+	66116.7i	−0.189684	+	0.109514i
$778$	−488536.	−	130903.i	−0.807118	−	0.216267i
$779$		−	239740.i		−	0.395062i
$780$	67064.0	+	342724.i	0.110230	+	0.563321i
$781$	−181652.			−0.297809
$782$	151400.	−	565032.i	0.247578	−	0.923974i
$783$	526818.	+	912476.i	0.859285	+	1.48833i
$784$	111438.	+	64338.5i	0.181301	+	0.104674i
$785$	345869.	+	345869.i	0.561270	+	0.561270i
$786$	237381.	−	63606.0i	0.384238	−	0.102956i
$787$	118929.	+	443851.i	0.192017	+	0.716617i	0.993019	+	0.117955i	$0.0376340\pi$
$787$	118929.	+	443851.i	0.192017	+	0.716617i	−0.801002	+	0.598662i	$0.795699\pi$
$788$	312446.	−	312446.i	0.503180	−	0.503180i
$789$	562446.	−	974185.i	0.903497	−	1.56490i
$790$	447083.	−	258124.i	0.716365	−	0.413593i
$791$	−335240.	−	89827.4i	−0.535801	−	0.143567i
$792$		−	6832.50i		−	0.0108925i
$793$	−293271.	−	599390.i	−0.466361	−	0.953154i
$794$	−719032.			−1.14053
$795$	303170.	−	1.13145e6i	0.479681	−	1.79019i
$796$	−270031.	−	467708.i	−0.426175	−	0.738157i
$797$	−220514.	−	127314.i	−0.347153	−	0.200429i	0.316278	−	0.948667i	$-0.397567\pi$
$797$	−220514.	−	127314.i	−0.347153	−	0.200429i	−0.663430	+	0.748238i	$0.730900\pi$
$798$	−158402.	−	158402.i	−0.248746	−	0.248746i
$799$	508887.	−	136356.i	0.797127	−	0.213590i
$800$	−5383.29	−	20090.7i	−0.00841139	−	0.0313917i
$801$	−40520.1	+	40520.1i	−0.0631546	+	0.0631546i
$802$	62377.6	−	108041.i	0.0969794	−	0.167973i
$803$	100641.	−	58105.3i	0.156079	−	0.0901124i
$804$	505870.	+	135547.i	0.782576	+	0.209691i
$805$			517102.i			0.797966i
$806$	34735.6	−	505836.i	0.0534693	−	0.778645i
$807$	−122119.			−0.187514
$808$	49368.9	−	184247.i	0.0756189	−	0.282214i
$809$	−74499.9	−	129038.i	−0.113830	−	0.197160i	0.803481	−	0.595330i	$-0.202979\pi$
$809$	−74499.9	−	129038.i	−0.113830	−	0.197160i	−0.917312	+	0.398170i	$0.869645\pi$
$810$	481056.	+	277738.i	0.733205	+	0.423316i
$811$	129192.	+	129192.i	0.196424	+	0.196424i	0.798465	−	0.602041i	$-0.205646\pi$
$811$	129192.	+	129192.i	0.196424	+	0.196424i	−0.602041	+	0.798465i	$0.705646\pi$
$812$	235868.	−	63200.6i	0.357731	−	0.0958538i
$813$	39204.8	+	146314.i	0.0593142	+	0.221364i
$814$	46392.7	−	46392.7i	0.0700166	−	0.0700166i
$815$	−633362.	+	1.09702e6i	−0.953535	+	1.65157i
$816$	−113139.	+	65321.0i	−0.169916	+	0.0981008i
$817$	−66738.7	−	17882.6i	−0.0999847	−	0.0267908i
$818$		−	340136.i		−	0.508330i
$819$	−23095.1	+	20127.0i	−0.0344311	+	0.0300062i
$820$	123593.			0.183808
$821$	123564.	−	461148.i	0.183319	−	0.684155i	−0.811666	−	0.584122i	$-0.801439\pi$
$821$	123564.	−	461148.i	0.183319	−	0.684155i	0.994984	−	0.100032i	$-0.0318946\pi$
$822$	158209.	+	274025.i	0.234146	+	0.405553i
$823$	−917060.	−	529465.i	−1.35394	−	0.781695i	−0.365138	−	0.930953i	$-0.618978\pi$
$823$	−917060.	−	529465.i	−1.35394	−	0.781695i	−0.988798	+	0.149258i	$0.952312\pi$
$824$	−38375.1	−	38375.1i	−0.0565191	−	0.0565191i
$825$	−34689.4	+	9295.00i	−0.0509670	+	0.0136566i
$826$	−11272.9	−	42071.0i	−0.0165225	−	0.0616627i
$827$	114562.	−	114562.i	0.167506	−	0.167506i	−0.618376	−	0.785882i	$-0.712209\pi$
$827$	114562.	−	114562.i	0.167506	−	0.167506i	0.785882	+	0.618376i	$0.212209\pi$
$828$	35305.4	−	61150.8i	0.0514969	−	0.0891952i
$829$	362084.	−	209050.i	0.526867	−	0.304187i	−0.212873	−	0.977080i	$-0.568282\pi$
$829$	362084.	−	209050.i	0.526867	−	0.304187i	0.739740	+	0.672893i	$0.234949\pi$
$830$	143069.	+	38335.1i	0.207677	+	0.0556469i
$831$		−	578622.i		−	0.837902i
$832$	71795.4	+	48296.0i	0.103717	+	0.0697694i
$833$	−432198.			−0.622864
$834$	14089.5	−	52582.6i	0.0202564	−	0.0755979i
$835$	−237738.	−	411775.i	−0.340978	−	0.590591i
$836$	96256.7	+	55573.8i	0.137727	+	0.0795166i
$837$	−511572.	−	511572.i	−0.730224	−	0.730224i
$838$	−441649.	+	118339.i	−0.628911	+	0.168516i
$839$	34000.3	+	126891.i	0.0483013	+	0.180263i	0.985862	−	0.167558i	$-0.0535882\pi$
$839$	34000.3	+	126891.i	0.0483013	+	0.180263i	−0.937561	+	0.347821i	$0.886922\pi$
$840$	81660.9	−	81660.9i	0.115733	−	0.115733i
$841$	−839542.	+	1.45413e6i	−1.18700	+	2.05594i
$842$	−277629.	+	160289.i	−0.391598	+	0.226089i
$843$	399196.	+	106964.i	0.561734	+	0.150516i
$844$		−	34938.7i		−	0.0490481i
$845$	−301765.	+	715890.i	−0.422626	+	1.00261i
$846$	63594.4			0.0888543
$847$	−69334.1	+	258758.i	−0.0966452	+	0.360685i
$848$	−145115.	−	251347.i	−0.201800	−	0.349528i
$849$	−911593.	−	526308.i	−1.26469	−	0.730171i
$850$	49399.1	+	49399.1i	0.0683724	+	0.0683724i
$851$	654938.	−	175490.i	0.904360	−	0.242323i
$852$	108513.	+	404975.i	0.149486	+	0.557891i
$853$	−73320.6	+	73320.6i	−0.100769	+	0.100769i	−0.755694	−	0.654925i	$-0.772700\pi$
$853$	−73320.6	+	73320.6i	−0.100769	+	0.100769i	0.654925	+	0.755694i	$0.272700\pi$
$854$	−110334.	+	191104.i	−0.151284	+	0.262032i
$855$	91222.3	−	52667.2i	0.124787	−	0.0720457i
$856$	−205717.	−	55121.7i	−0.280752	−	0.0752273i
$857$		−	973943.i		−	1.32609i	−0.748581	−	0.663043i	$-0.769265\pi$
$857$		−	973943.i		−	1.32609i	0.748581	−	0.663043i	$-0.230735\pi$
$858$	83389.8	−	123965.i	0.113276	−	0.168393i
$859$	−220355.			−0.298632			−0.149316	−	0.988790i	$-0.547707\pi$
$859$	−220355.			−0.298632			−0.149316	+	0.988790i	$0.547707\pi$
$860$	9218.98	−	34405.7i	0.0124648	−	0.0465193i
$861$	53283.6	+	92289.9i	0.0718765	+	0.124494i
$862$	−212940.	−	122941.i	−0.286577	−	0.165455i
$863$	224496.	+	224496.i	0.301430	+	0.301430i	0.841573	−	0.540143i	$-0.181630\pi$
$863$	224496.	+	224496.i	0.301430	+	0.301430i	−0.540143	+	0.841573i	$0.681630\pi$
$864$	119259.	−	31955.3i	0.159758	−	0.0428071i
$865$	−227486.	−	848988.i	−0.304034	−	1.13467i
$866$	430703.	−	430703.i	0.574305	−	0.574305i
$867$	−177159.	+	306848.i	−0.235681	+	0.408211i
$868$	−145207.	+	83835.2i	−0.192729	+	0.111272i
$869$	−213332.	−	57162.0i	−0.282498	−	0.0756952i
$870$			1.12860e6i			1.49109i
$871$	765453.	+	878331.i	1.00898	+	1.15777i
$872$	479798.			0.630994
$873$	11481.5	−	42849.5i	0.0150650	−	0.0562235i
$874$	574331.	+	994770.i	0.751864	+	1.30227i
$875$	237431.	+	137081.i	0.310114	+	0.179045i
$876$	−189660.	−	189660.i	−0.247154	−	0.247154i
$877$	389692.	−	104418.i	0.506667	−	0.135761i	0.00357470	−	0.999994i	$-0.498862\pi$
$877$	389692.	−	104418.i	0.506667	−	0.135761i	0.503093	+	0.864233i	$0.332195\pi$
$878$	215530.	+	804370.i	0.279588	+	1.04344i
$879$	−227153.	+	227153.i	−0.293995	+	0.293995i
$880$	−28649.9	+	49623.1i	−0.0369962	+	0.0640794i
$881$	−339319.	+	195906.i	−0.437176	+	0.252403i	−0.702399	−	0.711784i	$-0.747888\pi$
$881$	−339319.	+	195906.i	−0.437176	+	0.252403i	0.265223	+	0.964187i	$0.414554\pi$
$882$	−50392.8	−	13502.7i	−0.0647786	−	0.0173574i
$883$			579331.i			0.743029i	0.928427	+	0.371514i	$0.121161\pi$
$883$			579331.i			0.743029i	−0.928427	+	0.371514i	$0.878839\pi$
$884$	−289946.	−	19910.5i	−0.371033	−	0.0254787i
$885$	201305.			0.257021
$886$	55112.0	−	205681.i	0.0702067	−	0.262015i
$887$	646770.	+	1.12024e6i	0.822059	+	1.42385i	0.904146	+	0.427223i	$0.140508\pi$
$887$	646770.	+	1.12024e6i	0.822059	+	1.42385i	−0.0820875	+	0.996625i	$0.526159\pi$
$888$	−131142.	−	75714.6i	−0.166309	−	0.0960183i
$889$	226853.	+	226853.i	0.287040	+	0.287040i
$890$	464197.	−	124381.i	0.586033	−	0.157027i
$891$	−61505.7	−	229542.i	−0.0774747	−	0.289139i
$892$	129295.	−	129295.i	0.162499	−	0.162499i
$893$	−517261.	+	895922.i	−0.648644	+	1.12349i
$894$	558989.	−	322732.i	0.699404	−	0.403801i
$895$	350428.	+	93897.0i	0.437475	+	0.117221i
$896$		−	28614.2i		−	0.0356423i
$897$	1.38690e6	−	678585.i	1.72369	−	0.843372i
$898$	397724.			0.493207
$899$	424096.	−	1.58275e6i	0.524741	−	1.95836i
$900$	4216.44	+	7303.08i	0.00520548	+	0.00901615i
$901$	844220.	+	487410.i	1.03993	+	0.600406i
$902$	−37388.0	−	37388.0i	−0.0459535	−	0.0459535i
$903$	29666.1	−	7949.01i	0.0363819	−	0.00974849i
$904$	−102867.	−	383906.i	−0.125875	−	0.469773i
$905$	−889117.	+	889117.i	−1.08558	+	1.08558i
$906$	−21079.1	+	36510.0i	−0.0256800	+	0.0444791i
$907$	−1.15385e6	+	666178.i	−1.40261	+	0.809797i	−0.994660	−	0.103208i	$-0.967089\pi$
$907$	−1.15385e6	+	666178.i	−1.40261	+	0.809797i	−0.407949	+	0.913005i	$0.633756\pi$
$908$	341306.	+	91452.7i	0.413973	+	0.110924i
$909$			77335.9i			0.0935951i
$910$	252131.	−	49336.7i	0.304469	−	0.0595782i
$911$	224303.			0.270271			0.135135	−	0.990827i	$-0.456853\pi$
$911$	224303.			0.270271			0.135135	+	0.990827i	$0.456853\pi$
$912$	66395.9	−	247793.i	0.0798273	−	0.297920i
$913$	−31682.9	−	54876.4i	−0.0380087	−	0.0658330i
$914$	−477088.	−	275447.i	−0.571092	−	0.329720i
$915$	−721175.	−	721175.i	−0.861387	−	0.861387i
$916$	109558.	−	29356.0i	0.130573	−	0.0349869i
$917$	−46792.8	−	174633.i	−0.0556469	−	0.207677i
$918$	−293234.	+	293234.i	−0.347960	+	0.347960i
$919$	580970.	−	1.00627e6i	0.687896	−	1.19147i	−0.284621	−	0.958640i	$-0.591868\pi$
$919$	580970.	−	1.00627e6i	0.687896	−	1.19147i	0.972517	−	0.232831i	$-0.0747990\pi$
$920$	−512832.	+	296084.i	−0.605898	+	0.349815i
$921$	−1.27195e6	−	340819.i	−1.49952	−	0.401795i
$922$		−	927699.i		−	1.09130i
$923$	−302553.	+	882262.i	−0.355139	+	1.03561i
$924$	−49406.4			−0.0578681
$925$	−20958.3	+	78217.6i	−0.0244948	+	0.0914158i
$926$	391201.	+	677579.i	0.456223	+	0.790202i
$927$	19055.4	+	11001.7i	0.0221748	+	0.0128026i
$928$	197733.	+	197733.i	0.229606	+	0.229606i
$929$	−939320.	+	251690.i	−1.08838	+	0.291632i	−0.758026	−	0.652224i	$-0.773836\pi$
$929$	−939320.	+	251690.i	−1.08838	+	0.291632i	−0.330358	+	0.943856i	$0.607169\pi$
$930$	−200571.	−	748542.i	−0.231901	−	0.865466i
$931$	600109.	−	600109.i	0.692359	−	0.692359i
$932$	12135.3	−	21019.0i	0.0139707	−	0.0241980i
$933$	−559826.	+	323216.i	−0.643117	+	0.371304i
$934$	−582872.	−	156180.i	−0.668158	−	0.179033i
$935$		−	192458.i		−	0.220146i
$936$	−33184.7	−	11380.0i	−0.0378779	−	0.0129894i
$937$	−237066.			−0.270016			−0.135008	−	0.990845i	$-0.543106\pi$
$937$	−237066.			−0.270016			−0.135008	+	0.990845i	$0.543106\pi$
$938$	99717.7	−	372152.i	0.113336	−	0.422974i
$939$	264387.	+	457932.i	0.299854	+	0.519362i
$940$	−461873.	−	266663.i	−0.522718	−	0.301791i
$941$	−488611.	−	488611.i	−0.551803	−	0.551803i	0.375158	−	0.926961i	$-0.377589\pi$
$941$	−488611.	−	488611.i	−0.551803	−	0.551803i	−0.926961	+	0.375158i	$0.877589\pi$
$942$	−466519.	+	125003.i	−0.525735	+	0.140870i
$943$	−141428.	−	527816.i	−0.159042	−	0.593553i
$944$	35268.9	−	35268.9i	0.0395775	−	0.0395775i
$945$	183293.	−	317473.i	0.205250	−	0.355503i
$946$	−13196.9	+	7619.22i	−0.0147465	+	0.00851389i
$947$	1.53497e6	+	411293.i	1.71159	+	0.458618i	0.975812	−	0.218610i	$-0.0701523\pi$
$947$	1.53497e6	+	411293.i	1.71159	+	0.458618i	0.735773	+	0.677228i	$0.236819\pi$
$948$			509749.i			0.567204i
$949$	−114586.	−	585581.i	−0.127233	−	0.650211i
$950$	−137182.			−0.152002
$951$	−80419.7	+	300131.i	−0.0889204	+	0.331856i
$952$	48054.5	+	83232.8i	0.0530224	+	0.0918376i
$953$	469282.	+	270940.i	0.516711	+	0.298323i	0.735588	−	0.677429i	$-0.236906\pi$
$953$	469282.	+	270940.i	0.516711	+	0.298323i	−0.218877	+	0.975753i	$0.570239\pi$
$954$	83205.4	+	83205.4i	0.0914229	+	0.0914229i
$955$	313111.	−	83897.9i	0.343314	−	0.0919908i
$956$	80369.8	+	299944.i	0.0879382	+	0.328190i
$957$	341413.	−	341413.i	0.372783	−	0.372783i
$958$	204113.	−	353534.i	0.222403	−	0.385213i
$959$	201591.	−	116389.i	0.219197	−	0.126553i
$960$	127744.	+	34229.0i	0.138611	+	0.0371408i
$961$			201600.i			0.218295i
$962$	−148054.	−	302594.i	−0.159982	−	0.326972i
$963$	86347.6			0.0931103
$964$	−120003.	+	447859.i	−0.129134	+	0.481934i
$965$	−572720.	−	991981.i	−0.615018	−	1.06524i
$966$	−442186.	−	255296.i	−0.473861	−	0.273584i
$967$	906789.	+	906789.i	0.969735	+	0.969735i	0.999555	−	0.0298202i	$-0.00949348\pi$
$967$	906789.	+	906789.i	0.969735	+	0.969735i	−0.0298202	+	0.999555i	$0.509493\pi$
$968$	−296321.	+	79399.1i	−0.316237	+	0.0847354i
$969$	223009.	+	832283.i	0.237507	+	0.886387i
$970$	−263064.	+	263064.i	−0.279587	+	0.279587i
$971$	56975.0	−	98683.6i	0.0604291	−	0.104666i	−0.834228	−	0.551419i	$-0.814086\pi$
$971$	56975.0	−	98683.6i	0.0604291	−	0.104666i	0.894657	+	0.446753i	$0.147420\pi$
$972$	−92239.6	+	53254.5i	−0.0976303	+	0.0563669i
$973$	−38683.3	−	10365.1i	−0.0408599	−	0.0109484i
$974$		−	228163.i		−	0.240507i
$975$	−12632.7	+	183964.i	−0.0132889	+	0.193519i
$976$	−252701.			−0.265282
$977$	114361.	−	426801.i	0.119809	−	0.447133i	−0.879793	−	0.475358i	$-0.842319\pi$
$977$	114361.	−	426801.i	0.119809	−	0.447133i	0.999602	+	0.0282246i	$0.00898535\pi$
$978$	−625390.	−	1.08321e6i	−0.653842	−	1.13249i
$979$	−178050.	−	102797.i	−0.185771	−	0.107255i
$980$	309374.	+	309374.i	0.322130	+	0.322130i
$981$	−187900.	+	50347.5i	−0.195249	+	0.0523167i
$982$	238916.	+	891648.i	0.247755	+	0.924636i
$983$	810.786	−	810.786i	0.000839072	−	0.000839072i	−0.706687	−	0.707526i	$-0.749811\pi$
$983$	810.786	−	810.786i	0.000839072	−	0.000839072i	0.707526	+	0.706687i	$0.249811\pi$
$984$	−61018.5	+	105687.i	−0.0630190	+	0.109152i
$985$	1.30112e6	−	751203.i	1.34105	−	0.774257i
$986$	−907234.	−	243093.i	−0.933180	−	0.250045i
$987$		−	459857.i		−	0.472050i
$988$	430237.	−	374946.i	0.440752	−	0.384109i
$989$	−157482.			−0.161005
$990$	6012.75	−	22439.9i	0.00613483	−	0.0228955i
$991$	−137486.	−	238132.i	−0.139994	−	0.242477i	0.787500	−	0.616315i	$-0.211375\pi$
$991$	−137486.	−	238132.i	−0.139994	−	0.242477i	−0.927494	+	0.373838i	$0.878042\pi$
$992$	−166286.	−	96005.2i	−0.168979	−	0.0975599i
$993$	−514700.	−	514700.i	−0.521982	−	0.521982i
$994$	297927.	−	79829.3i	0.301534	−	0.0807959i
$995$	−475267.	−	1.77372e6i	−0.480055	−	1.79159i
$996$	−103415.	+	103415.i	−0.104248	+	0.104248i
$997$	769228.	−	1.33234e6i	0.773864	−	1.34037i	−0.161567	−	0.986862i	$-0.551655\pi$
$997$	769228.	−	1.33234e6i	0.773864	−	1.34037i	0.935431	−	0.353510i	$-0.115012\pi$
$998$	−1.11254e6	+	642326.i	−1.11700	+	0.644903i
$999$	−464302.	−	124409.i	−0.465232	−	0.124658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.b.11.1	✓	8
3.2	odd	2		234.5.bb.a.37.2		8
13.2	odd	12		338.5.d.f.239.3		8
13.3	even	3		338.5.d.f.99.3		8
13.6	odd	12	inner	26.5.f.b.19.1	yes	8
13.10	even	6		338.5.d.g.99.3		8
13.11	odd	12		338.5.d.g.239.3		8
39.32	even	12		234.5.bb.a.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.b.11.1	✓	8	1.1	even	1	trivial
26.5.f.b.19.1	yes	8	13.6	odd	12	inner
234.5.bb.a.19.2		8	39.32	even	12
234.5.bb.a.37.2		8	3.2	odd	2
338.5.d.f.99.3		8	13.3	even	3
338.5.d.f.239.3		8	13.2	odd	12
338.5.d.g.99.3		8	13.10	even	6
338.5.d.g.239.3		8	13.11	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.732051 + 2.73205i) q^{2} +(-4.74800 - 8.22378i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-19.2341 - 19.2341i) q^{5} +(25.9436 - 6.95155i) q^{6} +(-5.11403 - 19.0858i) q^{7} +(16.0000 - 16.0000i) q^{8} +(-4.58700 + 7.94492i) q^{9} +(66.6289 - 38.4682i) q^{10} +(-31.7929 - 8.51887i) q^{11} +75.9680i q^{12} +(-94.3282 + 140.225i) q^{13} +55.8871 q^{14} +(-66.8535 + 249.501i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-186.163 - 107.481i) q^{17} +(-18.3480 - 18.3480i) q^{18} +(407.726 - 109.250i) q^{19} +(56.3214 + 210.194i) q^{20} +(-132.676 + 132.676i) q^{21} +(46.5480 - 80.6235i) q^{22} +(833.208 - 481.053i) q^{23} +(-207.548 - 55.6124i) q^{24} +114.902i q^{25} +(-314.050 - 360.362i) q^{26} -682.060 q^{27} +(-40.9122 + 152.686i) q^{28} +(-772.393 - 1337.82i) q^{29} +(-632.708 - 365.294i) q^{30} +(750.040 + 750.040i) q^{31} +(-174.851 + 46.8513i) q^{32} +(80.8952 + 301.905i) q^{33} +(429.924 - 429.924i) q^{34} +(-268.735 + 465.462i) q^{35} +(63.5593 - 36.6960i) q^{36} +(680.735 + 182.402i) q^{37} +1193.90i q^{38} +(1601.05 + 109.944i) q^{39} -615.491 q^{40} +(146.998 - 548.605i) q^{41} +(-265.352 - 459.603i) q^{42} +(-141.756 - 81.8426i) q^{43} +(186.192 + 186.192i) q^{44} +(241.040 - 64.5865i) q^{45} +(704.310 + 2628.52i) q^{46} +(-1733.01 + 1733.01i) q^{47} +(303.872 - 526.322i) q^{48} +(1741.21 - 1005.29i) q^{49} +(-313.917 - 84.1139i) q^{50} +2041.28i q^{51} +(1214.43 - 594.198i) q^{52} -4534.85 q^{53} +(499.302 - 1863.42i) q^{54} +(447.654 + 775.360i) q^{55} +(-387.197 - 223.548i) q^{56} +(-2834.33 - 2834.33i) q^{57} +(4220.44 - 1130.86i) q^{58} +(-201.708 - 752.785i) q^{59} +(1461.18 - 1461.18i) q^{60} +(-1974.23 + 3419.47i) q^{61} +(-2598.22 + 1500.08i) q^{62} +(175.093 + 46.9161i) q^{63} -512.000i q^{64} +(4511.43 - 882.793i) q^{65} -884.039 q^{66} +(1784.27 - 6658.99i) q^{67} +(859.849 + 1489.30i) q^{68} +(-7912.14 - 4568.08i) q^{69} +(-1074.94 - 1074.94i) q^{70} +(5330.87 - 1428.40i) q^{71} +(53.7267 + 200.511i) q^{72} +(-2496.58 + 2496.58i) q^{73} +(-996.665 + 1726.27i) q^{74} +(944.926 - 545.554i) q^{75} +(-3261.81 - 873.998i) q^{76} +650.358i q^{77} +(-1472.42 + 4293.67i) q^{78} +6710.05 q^{79} +(450.571 - 1681.55i) q^{80} +(3609.97 + 6252.64i) q^{81} +(1391.21 + 803.214i) q^{82} +(1361.30 + 1361.30i) q^{83} +(1449.91 - 388.502i) q^{84} +(1513.37 + 5647.98i) q^{85} +(327.370 - 327.370i) q^{86} +(-7334.65 + 12704.0i) q^{87} +(-644.988 + 372.384i) q^{88} +(6033.51 + 1616.67i) q^{89} +705.815i q^{90} +(3158.71 + 1083.21i) q^{91} -7696.84 q^{92} +(2606.97 - 9729.36i) q^{93} +(-3466.01 - 6003.31i) q^{94} +(-9943.56 - 5740.92i) q^{95} +(1215.49 + 1215.49i) q^{96} +(-4670.76 + 1251.53i) q^{97} +(1471.85 + 5493.00i) q^{98} +(213.516 - 213.516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21}+ \cdots - 55296 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Introduction

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