LMFDB - Embedded newform 27.5.f.a.2.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,5,Mod(2,27)] 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("27.2"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	27.2
Dual form			27.5.f.a.14.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.34334 + 1.29483i) q^{2} +(-4.72310 + 7.66109i) q^{3} +(37.2130 + 13.5444i) q^{4} +(-22.9421 - 27.3414i) q^{5} +(-44.6032 + 50.1424i) q^{6} +(14.0427 - 5.11111i) q^{7} +(152.408 + 87.9929i) q^{8} +(-36.3846 - 72.3682i) q^{9} +(-133.070 - 230.483i) q^{10} +(35.3079 - 42.0783i) q^{11} +(-279.526 + 221.121i) q^{12} +(-0.746352 - 4.23277i) q^{13} +(109.738 - 19.3498i) q^{14} +(317.823 - 46.6257i) q^{15} +(519.869 + 436.222i) q^{16} +(-309.675 + 178.791i) q^{17} +(-173.480 - 578.537i) q^{18} +(-273.006 + 472.860i) q^{19} +(-483.423 - 1328.19i) q^{20} +(-27.1682 + 131.722i) q^{21} +(313.762 - 263.278i) q^{22} +(130.510 - 358.573i) q^{23} +(-1393.96 + 752.014i) q^{24} +(-112.679 + 639.035i) q^{25} -32.0491i q^{26} +(726.268 + 63.0564i) q^{27} +591.797 q^{28} +(36.0636 + 6.35898i) q^{29} +(2394.25 + 69.1376i) q^{30} +(803.077 + 292.296i) q^{31} +(1442.80 + 1719.46i) q^{32} +(155.603 + 469.237i) q^{33} +(-2505.56 + 911.948i) q^{34} +(-461.914 - 266.686i) q^{35} +(-373.796 - 3185.85i) q^{36} +(245.703 + 425.571i) q^{37} +(-2617.05 + 3118.88i) q^{38} +(35.9528 + 14.2739i) q^{39} +(-1090.72 - 6185.80i) q^{40} +(2325.15 - 409.987i) q^{41} +(-370.064 + 932.105i) q^{42} +(444.443 + 372.932i) q^{43} +(1883.84 - 1087.63i) q^{44} +(-1143.91 + 2655.09i) q^{45} +(1422.67 - 2464.14i) q^{46} +(-1267.80 - 3483.25i) q^{47} +(-5797.33 + 1922.44i) q^{48} +(-1668.20 + 1399.79i) q^{49} +(-1654.88 + 4546.75i) q^{50} +(92.8928 - 3216.90i) q^{51} +(29.5565 - 167.623i) q^{52} +597.366i q^{53} +(5251.59 + 1403.44i) q^{54} -1960.52 q^{55} +(2589.96 + 456.680i) q^{56} +(-2333.19 - 4324.89i) q^{57} +(256.593 + 93.3924i) q^{58} +(-2190.28 - 2610.27i) q^{59} +(12458.7 + 2569.65i) q^{60} +(530.905 - 193.234i) q^{61} +(5518.80 + 3186.28i) q^{62} +(-880.819 - 830.277i) q^{63} +(2939.43 + 5091.23i) q^{64} +(-98.6069 + 117.515i) q^{65} +(535.064 + 3647.25i) q^{66} +(533.761 + 3027.11i) q^{67} +(-13945.6 + 2458.98i) q^{68} +(2130.65 + 2693.43i) q^{69} +(-3046.68 - 2556.47i) q^{70} +(1579.71 - 912.046i) q^{71} +(822.574 - 14231.1i) q^{72} +(2766.22 - 4791.24i) q^{73} +(1253.24 + 3443.25i) q^{74} +(-4363.51 - 3881.47i) q^{75} +(-16564.0 + 13898.9i) q^{76} +(280.750 - 771.353i) q^{77} +(245.531 + 151.371i) q^{78} +(-423.277 + 2400.52i) q^{79} -24221.8i q^{80} +(-3913.32 + 5266.18i) q^{81} +17605.3 q^{82} +(-5141.02 - 906.501i) q^{83} +(-2795.12 + 4533.81i) q^{84} +(11993.0 + 4365.10i) q^{85} +(2780.81 + 3314.04i) q^{86} +(-219.049 + 246.252i) q^{87} +(9083.80 - 3306.23i) q^{88} +(3582.86 + 2068.56i) q^{89} +(-11838.0 + 18016.1i) q^{90} +(-32.1149 - 55.6247i) q^{91} +(9713.34 - 11575.9i) q^{92} +(-6032.32 + 4771.90i) q^{93} +(-4799.67 - 27220.3i) q^{94} +(19192.0 - 3384.07i) q^{95} +(-19987.4 + 2932.22i) q^{96} +(-10080.0 - 8458.14i) q^{97} +(-14062.6 + 8119.07i) q^{98} +(-4329.79 - 1024.16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	7.34334	+	1.29483i	1.83584	+	0.323707i	0.980823	−	0.194900i	$-0.0624382\pi$
$2$	7.34334	+	1.29483i	1.83584	+	0.323707i	0.855013	+	0.518607i	$0.173549\pi$
$3$	−4.72310	+	7.66109i	−0.524789	+	0.851232i
$3$	−4.72310	+	7.66109i	−0.524789	+	0.851232i
$4$	37.2130	+	13.5444i	2.32581	+	0.846527i
$5$	−22.9421	−	27.3414i	−0.917686	−	1.09366i	−0.995316	−	0.0966730i	$-0.969180\pi$
$5$	−22.9421	−	27.3414i	−0.917686	−	1.09366i	0.0776305	−	0.996982i	$-0.475265\pi$
$6$	−44.6032	+	50.1424i	−1.23898	+	1.39284i
$7$	14.0427	−	5.11111i	0.286585	−	0.104308i	−0.194728	−	0.980857i	$-0.562382\pi$
$7$	14.0427	−	5.11111i	0.286585	−	0.104308i	0.481313	+	0.876549i	$0.340160\pi$
$8$	152.408	+	87.9929i	2.38138	+	1.37489i
$9$	−36.3846	−	72.3682i	−0.449193	−	0.893435i
$10$	−133.070	−	230.483i	−1.33070	−	2.30483i
$11$	35.3079	−	42.0783i	0.291801	−	0.347754i	−0.600150	−	0.799888i	$-0.704892\pi$
$11$	35.3079	−	42.0783i	0.291801	−	0.347754i	0.891950	+	0.452133i	$0.149337\pi$
$12$	−279.526	+	221.121i	−1.94115	+	1.53556i
$13$	−0.746352	−	4.23277i	−0.00441628	−	0.0250460i	0.982520	−	0.186157i	$-0.0596034\pi$
$13$	−0.746352	−	4.23277i	−0.00441628	−	0.0250460i	−0.986936	+	0.161111i	$0.948492\pi$
$14$	109.738	−	19.3498i	0.559888	−	0.0987234i
$15$	317.823	−	46.6257i	1.41255	−	0.207226i
$16$	519.869	+	436.222i	2.03074	+	1.70399i
$17$	−309.675	+	178.791i	−1.07154	+	0.618655i	−0.928602	−	0.371077i	$-0.878989\pi$
$17$	−309.675	+	178.791i	−1.07154	+	0.618655i	−0.142939	+	0.989731i	$0.545655\pi$
$18$	−173.480	−	578.537i	−0.535433	−	1.78561i
$19$	−273.006	+	472.860i	−0.756250	+	1.30986i	0.188501	+	0.982073i	$0.439637\pi$
$19$	−273.006	+	472.860i	−0.756250	+	1.30986i	−0.944751	+	0.327790i	$0.893696\pi$
$20$	−483.423	−	1328.19i	−1.20856	−	3.32048i
$21$	−27.1682	+	131.722i	−0.0616060	+	0.298690i
$22$	313.762	−	263.278i	0.648269	−	0.543962i
$23$	130.510	−	358.573i	0.246711	−	0.677832i	−0.753091	−	0.657917i	$-0.771438\pi$
$23$	130.510	−	358.573i	0.246711	−	0.677832i	0.999802	−	0.0199158i	$-0.00633981\pi$
$24$	−1393.96	+	752.014i	−2.42007	+	1.30558i
$25$	−112.679	+	639.035i	−0.180287	+	1.02246i
$26$		−	32.0491i		−	0.0474099i
$27$	726.268	+	63.0564i	0.996252	+	0.0864971i
$28$	591.797			0.754843
$29$	36.0636	+	6.35898i	0.0428818	+	0.00756122i	0.195048	−	0.980794i	$-0.437514\pi$
$29$	36.0636	+	6.35898i	0.0428818	+	0.00756122i	−0.152166	+	0.988355i	$0.548625\pi$
$30$	2394.25	+	69.1376i	2.66028	+	0.0768196i
$31$	803.077	+	292.296i	0.835668	+	0.304158i	0.724183	−	0.689608i	$-0.242217\pi$
$31$	803.077	+	292.296i	0.835668	+	0.304158i	0.111485	+	0.993766i	$0.464439\pi$
$32$	1442.80	+	1719.46i	1.40898	+	1.67916i
$33$	155.603	+	469.237i	0.142886	+	0.430888i
$34$	−2505.56	+	911.948i	−2.16744	+	0.788883i
$35$	−461.914	−	266.686i	−0.377072	−	0.217703i
$36$	−373.796	−	3185.85i	−0.288423	−	2.45822i
$37$	245.703	+	425.571i	0.179476	+	0.310862i	0.941701	−	0.336450i	$-0.109226\pi$
$37$	245.703	+	425.571i	0.179476	+	0.310862i	−0.762225	+	0.647312i	$0.775893\pi$
$38$	−2617.05	+	3118.88i	−1.81236	+	2.15989i
$39$	35.9528	+	14.2739i	0.0236376	+	0.00938458i
$40$	−1090.72	−	6185.80i	−0.681702	−	3.86612i
$41$	2325.15	−	409.987i	1.38320	−	0.243895i	0.567975	−	0.823046i	$-0.307727\pi$
$41$	2325.15	−	409.987i	1.38320	−	0.243895i	0.815220	+	0.579151i	$0.196616\pi$
$42$	−370.064	+	932.105i	−0.209787	+	0.528404i
$43$	444.443	+	372.932i	0.240369	+	0.201694i	0.755012	−	0.655711i	$-0.227631\pi$
$43$	444.443	+	372.932i	0.240369	+	0.201694i	−0.514643	+	0.857405i	$0.672075\pi$
$44$	1883.84	−	1087.63i	0.973057	−	0.561795i
$45$	−1143.91	+	2655.09i	−0.564892	+	1.31115i
$46$	1422.67	−	2464.14i	0.672340	−	1.16453i
$47$	−1267.80	−	3483.25i	−0.573925	−	1.57684i	−0.798247	−	0.602330i	$-0.794239\pi$
$47$	−1267.80	−	3483.25i	−0.573925	−	1.57684i	0.224323	−	0.974515i	$-0.427983\pi$
$48$	−5797.33	+	1922.44i	−2.51620	+	0.834393i
$49$	−1668.20	+	1399.79i	−0.694794	+	0.583001i
$50$	−1654.88	+	4546.75i	−0.661953	+	1.81870i
$51$	92.8928	−	3216.90i	0.0357143	−	1.23679i
$52$	29.5565	−	167.623i	0.0109307	−	0.0619908i
$53$			597.366i			0.212661i	0.994331	+	0.106331i	$0.0339102\pi$
$53$			597.366i			0.212661i	−0.994331	+	0.106331i	$0.966090\pi$
$54$	5251.59	+	1403.44i	1.80096	+	0.481289i
$55$	−1960.52			−0.648105
$56$	2589.96	+	456.680i	0.825880	+	0.145625i
$57$	−2333.19	−	4324.89i	−0.718126	−	1.33115i
$58$	256.593	+	93.3924i	0.0762763	+	0.0277623i
$59$	−2190.28	−	2610.27i	−0.629210	−	0.749863i	0.353415	−	0.935467i	$-0.385020\pi$
$59$	−2190.28	−	2610.27i	−0.629210	−	0.749863i	−0.982625	+	0.185604i	$0.940576\pi$
$60$	12458.7	+	2569.65i	3.46074	+	0.713791i
$61$	530.905	−	193.234i	0.142678	−	0.0519306i	−0.269694	−	0.962946i	$-0.586923\pi$
$61$	530.905	−	193.234i	0.142678	−	0.0519306i	0.412372	+	0.911015i	$0.364700\pi$
$62$	5518.80	+	3186.28i	1.43569	+	0.828897i
$63$	−880.819	−	830.277i	−0.221925	−	0.209190i
$64$	2939.43	+	5091.23i	0.717633	+	1.24298i
$65$	−98.6069	+	117.515i	−0.0233389	+	0.0278142i
$66$	535.064	+	3647.25i	0.122834	+	0.837292i
$67$	533.761	+	3027.11i	0.118904	+	0.674339i	0.984743	+	0.174016i	$0.0556743\pi$
$67$	533.761	+	3027.11i	0.118904	+	0.674339i	−0.865839	+	0.500323i	$0.833215\pi$
$68$	−13945.6	+	2458.98i	−3.01591	+	0.531787i
$69$	2130.65	+	2693.43i	0.447522	+	0.565727i
$70$	−3046.68	−	2556.47i	−0.621771	−	0.521728i
$71$	1579.71	−	912.046i	0.313372	−	0.180926i	−0.335062	−	0.942196i	$-0.608757\pi$
$71$	1579.71	−	912.046i	0.313372	−	0.180926i	0.648435	+	0.761270i	$0.275424\pi$
$72$	822.574	−	14231.1i	0.158676	−	2.74520i
$73$	2766.22	−	4791.24i	0.519088	−	0.899087i	−0.480666	−	0.876904i	$-0.659605\pi$
$73$	2766.22	−	4791.24i	0.519088	−	0.899087i	0.999754	−	0.0221832i	$-0.00706171\pi$
$74$	1253.24	+	3443.25i	0.228861	+	0.628790i
$75$	−4363.51	−	3881.47i	−0.775735	−	0.690039i
$76$	−16564.0	+	13898.9i	−2.86773	+	2.40631i
$77$	280.750	−	771.353i	0.0473520	−	0.130098i
$78$	245.531	+	151.371i	0.0403569	+	0.0248802i
$79$	−423.277	+	2400.52i	−0.0678220	+	0.384638i	0.931936	+	0.362624i	$0.118119\pi$
$79$	−423.277	+	2400.52i	−0.0678220	+	0.384638i	−0.999758	+	0.0220141i	$0.992992\pi$
$80$		−	24221.8i		−	3.78465i
$81$	−3913.32	+	5266.18i	−0.596451	+	0.802649i
$82$	17605.3			2.61827
$83$	−5141.02	−	906.501i	−0.746266	−	0.131587i	−0.212431	−	0.977176i	$-0.568138\pi$
$83$	−5141.02	−	906.501i	−0.746266	−	0.131587i	−0.533834	+	0.845589i	$0.679249\pi$
$84$	−2795.12	+	4533.81i	−0.396133	+	0.642547i
$85$	11993.0	+	4365.10i	1.65993	+	0.604166i
$86$	2780.81	+	3314.04i	0.375989	+	0.448086i
$87$	−219.049	+	246.252i	−0.0289402	+	0.0325343i
$88$	9083.80	−	3306.23i	1.17301	−	0.426941i
$89$	3582.86	+	2068.56i	0.452324	+	0.261149i	0.708811	−	0.705398i	$-0.249232\pi$
$89$	3582.86	+	2068.56i	0.452324	+	0.261149i	−0.256487	+	0.966548i	$0.582565\pi$
$90$	−11838.0	+	18016.1i	−1.46148	+	2.22420i
$91$	−32.1149	−	55.6247i	−0.00387815	−	0.00671715i
$92$	9713.34	−	11575.9i	1.14761	−	1.36766i
$93$	−6032.32	+	4771.90i	−0.697459	+	0.551729i
$94$	−4799.67	−	27220.3i	−0.543195	−	3.08061i
$95$	19192.0	−	3384.07i	2.12654	−	0.374966i
$96$	−19987.4	+	2932.22i	−2.16877	+	0.318167i
$97$	−10080.0	−	8458.14i	−1.07132	−	0.898942i	−0.0761458	−	0.997097i	$-0.524261\pi$
$97$	−10080.0	−	8458.14i	−1.07132	−	0.898942i	−0.995171	+	0.0981550i	$0.968706\pi$
$98$	−14062.6	+	8119.07i	−1.46425	+	0.845385i
$99$	−4329.79	−	1024.16i	−0.441771	−	0.104496i
$100$	−12848.5	+	22254.2i	−1.28485	+	2.22542i
$101$	5913.44	+	16247.1i	0.579693	+	1.59269i	0.788700	+	0.614778i	$0.210755\pi$
$101$	5913.44	+	16247.1i	0.579693	+	1.59269i	−0.209007	+	0.977914i	$0.567023\pi$
$102$	4847.48	−	23502.5i	0.465925	−	2.25899i
$103$	9925.23	−	8328.26i	0.935548	−	0.785018i	−0.0412568	−	0.999149i	$-0.513136\pi$
$103$	9925.23	−	8328.26i	0.935548	−	0.785018i	0.976805	+	0.214130i	$0.0686917\pi$
$104$	258.704	−	710.783i	0.0239186	−	0.0657159i
$105$	4224.77	−	2279.18i	0.383199	−	0.206728i
$106$	−773.487	+	4386.66i	−0.0688401	+	0.390411i
$107$			10732.5i			0.937422i	0.883352	+	0.468711i	$0.155281\pi$
$107$			10732.5i			0.937422i	−0.883352	+	0.468711i	$0.844719\pi$
$108$	26172.6	+	12183.4i	2.24387	+	1.04453i
$109$	−1507.97			−0.126923			−0.0634615	−	0.997984i	$-0.520214\pi$
$109$	−1507.97			−0.126923			−0.0634615	+	0.997984i	$0.520214\pi$
$110$	−14396.7	−	2538.53i	−1.18981	−	0.209796i
$111$	−4420.82	−	127.658i	−0.358803	−	0.0103610i
$112$	9529.92	+	3468.61i	0.759719	+	0.276515i
$113$	−22.4010	−	26.6964i	−0.00175432	−	0.00209072i	0.765167	−	0.643832i	$-0.222657\pi$
$113$	−22.4010	−	26.6964i	−0.00175432	−	0.00209072i	−0.766921	+	0.641742i	$0.778212\pi$
$114$	−11533.4	−	34780.3i	−0.887460	−	2.67623i
$115$	−12798.1	+	4658.12i	−0.967718	+	0.352220i
$116$	1255.91	+	725.098i	0.0933343	+	0.0538866i
$117$	−279.162	+	208.020i	−0.0203932	+	0.0151961i
$118$	−12704.1	−	22004.2i	−0.912389	−	1.58030i
$119$	−3434.85	+	4093.49i	−0.242557	+	0.289068i
$120$	52541.6	+	20860.0i	3.64872	+	1.44861i
$121$	2018.45	+	11447.2i	0.137863	+	0.781858i
$122$	4148.83	−	731.550i	0.278744	−	0.0491501i
$123$	−7840.98	+	19749.6i	−0.518275	+	1.30541i
$124$	25926.0	+	21754.5i	1.68613	+	1.41483i
$125$	738.531	−	426.391i	0.0472660	−	0.0272890i
$126$	−5393.09	−	7237.52i	−0.339701	−	0.455878i
$127$	9282.82	−	16078.3i	0.575536	−	0.996857i	−0.420447	−	0.907317i	$-0.638127\pi$
$127$	9282.82	−	16078.3i	0.575536	−	0.996857i	0.995983	−	0.0895403i	$-0.0285398\pi$
$128$	2709.79	+	7445.08i	0.165392	+	0.454412i
$129$	−4956.21	+	1643.52i	−0.297831	+	0.0987634i
$130$	−876.267	+	735.275i	−0.0518501	+	0.0435074i
$131$	9476.12	−	26035.4i	0.552189	−	1.51713i	−0.278525	−	0.960429i	$-0.589845\pi$
$131$	9476.12	−	26035.4i	0.552189	−	1.51713i	0.830714	−	0.556699i	$-0.187932\pi$
$132$	−565.092	+	19569.3i	−0.0324318	+	1.12312i
$133$	−1416.89	+	8035.58i	−0.0801001	+	0.454270i
$134$			22920.2i			1.27647i
$135$	−14938.1	−	21303.8i	−0.819648	−	1.16893i
$136$	−62929.5			−3.40233
$137$	−22228.3	−	3919.46i	−1.18431	−	0.208826i	−0.453406	−	0.891304i	$-0.649791\pi$
$137$	−22228.3	−	3919.46i	−1.18431	−	0.208826i	−0.730906	+	0.682478i	$0.760902\pi$
$138$	12158.6	+	22537.6i	0.638446	+	1.18345i
$139$	18170.5	+	6613.53i	0.940454	+	0.342297i	0.766345	−	0.642429i	$-0.222073\pi$
$139$	18170.5	+	6613.53i	0.940454	+	0.342297i	0.174109	+	0.984726i	$0.444295\pi$
$140$	−13577.1	−	16180.5i	−0.692709	−	0.825538i
$141$	32673.4	+	6739.02i	1.64345	+	0.338968i
$142$	12781.3	−	4652.01i	0.633867	−	0.230709i
$143$	−204.460	−	118.045i	−0.00999853	−	0.00577265i
$144$	12653.3	−	53493.7i	0.610212	−	2.57975i
$145$	−653.513	−	1131.92i	−0.0310826	−	0.0538367i
$146$	26517.1	−	31601.9i	1.24400	−	1.48254i
$147$	−2844.81	−	19391.6i	−0.131649	−	0.897384i
$148$	3379.25	+	19164.7i	0.154275	+	0.874940i
$149$	−25568.2	+	4508.36i	−1.15167	+	0.203070i	−0.716704	−	0.697377i	$-0.754350\pi$
$149$	−25568.2	+	4508.36i	−1.15167	+	0.203070i	−0.434965	+	0.900448i	$0.643239\pi$
$150$	−27016.9	−	34153.0i	−1.20075	−	1.51791i
$151$	−6349.86	−	5328.17i	−0.278491	−	0.233681i	0.492834	−	0.870123i	$-0.335961\pi$
$151$	−6349.86	−	5328.17i	−0.278491	−	0.233681i	−0.771325	+	0.636442i	$0.780405\pi$
$152$	−83216.7	+	48045.2i	−3.60183	+	2.07952i
$153$	24206.2	+	15905.4i	1.03406	+	0.679457i
$154$	3060.41	−	5300.79i	0.129044	−	0.223511i
$155$	−10432.5	−	28663.1i	−0.434237	−	1.19306i
$156$	1144.58	+	1018.14i	0.0470323	+	0.0418366i
$157$	−13957.3	+	11711.5i	−0.566241	+	0.475133i	−0.880396	−	0.474239i	$-0.842723\pi$
$157$	−13957.3	+	11711.5i	−0.566241	+	0.475133i	0.314155	+	0.949372i	$0.398279\pi$
$158$	−6216.54	+	17079.8i	−0.249020	+	0.684177i
$159$	−4576.47	−	2821.42i	−0.181024	−	0.111602i
$160$	13911.5	−	78896.1i	0.543419	−	3.08188i
$161$		−	5702.38i		−	0.219991i
$162$	−35555.6	+	33604.3i	−1.35481	+	1.28046i
$163$	−45051.0			−1.69562			−0.847811	−	0.530298i	$-0.822080\pi$
$163$	−45051.0			−1.69562			−0.847811	+	0.530298i	$0.822080\pi$
$164$	92079.0	+	16236.0i	3.42352	+	0.603659i
$165$	9259.72	−	15019.7i	0.340118	−	0.551688i
$166$	−36578.5	−	13313.5i	−1.32743	−	0.483143i
$167$	29417.7	+	35058.6i	1.05481	+	1.25708i	0.965315	+	0.261089i	$0.0840817\pi$
$167$	29417.7	+	35058.6i	1.05481	+	1.25708i	0.0894977	+	0.995987i	$0.471474\pi$
$168$	−15731.3	+	17685.0i	−0.557373	+	0.626593i
$169$	26821.2	−	9762.12i	0.939085	−	0.341799i
$170$	82416.8	+	47583.4i	2.85179	+	1.64648i
$171$	44153.3	+	2552.11i	1.50998	+	0.0872785i
$172$	11487.9	+	19897.6i	0.388315	+	0.672581i
$173$	−22596.5	+	26929.5i	−0.755004	+	0.899779i	−0.997521	−	0.0703680i	$-0.977583\pi$
$173$	−22596.5	+	26929.5i	−0.755004	+	0.899779i	0.242517	+	0.970147i	$0.422027\pi$
$174$	−1927.40	+	1524.68i	−0.0636611	+	0.0503595i
$175$	1683.86	+	9549.67i	0.0549833	+	0.311826i
$176$	36710.9	−	6473.12i	1.18514	−	0.208972i
$177$	30342.4	−	4451.34i	0.968510	−	0.142084i
$178$	23631.7	+	19829.4i	0.745857	+	0.625848i
$179$	−6494.87	+	3749.81i	−0.202705	+	0.117032i	−0.597917	−	0.801558i	$-0.704005\pi$
$179$	−6494.87	+	3749.81i	−0.202705	+	0.117032i	0.395212	+	0.918590i	$0.370671\pi$
$180$	−78529.8	+	83310.3i	−2.42376	+	2.57131i
$181$	−1045.63	+	1811.08i	−0.0319168	+	0.0552816i	−0.881543	−	0.472104i	$-0.843494\pi$
$181$	−1045.63	+	1811.08i	−0.0319168	+	0.0552816i	0.849626	+	0.527386i	$0.176828\pi$
$182$	−163.807	−	450.055i	−0.00494525	−	0.0135870i
$183$	−1027.14	+	4979.98i	−0.0306709	+	0.148705i
$184$	51442.7	−	43165.6i	1.51946	−	1.27498i
$185$	5998.73	−	16481.4i	0.175273	−	0.481559i
$186$	−50476.2	+	27230.9i	−1.45902	+	0.787111i
$187$	−3410.75	+	19343.3i	−0.0975365	+	0.553157i
$188$		−	146794.i		−	4.15329i
$189$	10521.0	−	2826.56i	0.294533	−	0.0791287i
$190$	145315.			4.02535
$191$	11234.8	+	1980.99i	0.307962	+	0.0543021i	0.325494	−	0.945544i	$-0.394470\pi$
$191$	11234.8	+	1980.99i	0.307962	+	0.0543021i	−0.0175312	+	0.999846i	$0.505581\pi$
$192$	−52887.6	−	1527.21i	−1.43467	−	0.0414282i
$193$	−26467.5	−	9633.39i	−0.710557	−	0.258622i	−0.0386453	−	0.999253i	$-0.512304\pi$
$193$	−26467.5	−	9633.39i	−0.710557	−	0.258622i	−0.671911	+	0.740631i	$0.734526\pi$
$194$	−63069.2	−	75162.9i	−1.67577	−	1.99710i
$195$	−434.564	−	1310.47i	−0.0114284	−	0.0344635i
$196$	−81038.1	+	29495.4i	−2.10949	+	0.767791i
$197$	−58133.9	−	33563.6i	−1.49795	−	0.864841i	−0.497951	−	0.867205i	$-0.665914\pi$
$197$	−58133.9	−	33563.6i	−1.49795	−	0.864841i	−0.999997	+	0.00236466i	$0.999247\pi$
$198$	−30469.0	−	13127.1i	−0.777192	−	0.334842i
$199$	10421.6	+	18050.8i	0.263165	+	0.455816i	0.967081	−	0.254468i	$-0.0819002\pi$
$199$	10421.6	+	18050.8i	0.263165	+	0.455816i	−0.703916	+	0.710283i	$0.748567\pi$
$200$	−73403.8	+	87479.2i	−1.83509	+	2.18698i
$201$	−25711.9	−	10208.1i	−0.636419	−	0.252671i
$202$	22387.3	+	126965.i	0.548654	+	3.11157i
$203$	538.930	−	95.0279i	0.0130780	−	0.00230600i
$204$	47027.9	−	118452.i	1.13004	−	2.84632i
$205$	−64553.6	−	54166.9i	−1.53608	−	1.28892i
$206$	83668.1	−	48305.8i	1.97163	−	1.13832i
$207$	−30697.9	+	3601.78i	−0.716420	+	0.0840575i
$208$	1458.42	−	2526.06i	0.0337098	−	0.0583871i
$209$	10257.9	+	28183.3i	0.234836	+	0.645208i
$210$	33975.1	−	11266.4i	0.770410	−	0.255475i
$211$	30301.2	−	25425.8i	0.680606	−	0.571096i	−0.235578	−	0.971856i	$-0.575698\pi$
$211$	30301.2	−	25425.8i	0.680606	−	0.571096i	0.916183	+	0.400760i	$0.131254\pi$
$212$	−8090.98	+	22229.8i	−0.180024	+	0.494611i
$213$	−473.863	+	16410.0i	−0.0104446	+	0.361700i
$214$	−13896.8	+	78812.7i	−0.303450	+	1.72095i
$215$		−	20707.5i		−	0.447972i
$216$	105141.	+	73516.7i	2.25353	+	1.57572i
$217$	12771.3			0.271216
$218$	−11073.6	−	1952.57i	−0.233010	−	0.0410859i
$219$	23640.9	+	43821.8i	0.492920	+	0.913696i
$220$	−72956.7	−	26554.1i	−1.50737	−	0.548638i
$221$	987.910	+	1177.34i	0.0202271	+	0.0241057i
$222$	−32298.3	−	6661.64i	−0.655350	−	0.135168i
$223$	52481.4	−	19101.7i	1.05535	−	0.384115i	0.244669	−	0.969607i	$-0.421321\pi$
$223$	52481.4	−	19101.7i	1.05535	−	0.384115i	0.810678	+	0.585492i	$0.199098\pi$
$224$	29049.1	+	16771.5i	0.578943	+	0.334253i
$225$	50345.6	−	15096.7i	0.994481	−	0.298206i
$226$	−129.931	−	225.047i	−0.00254387	−	0.00440611i
$227$	−7696.64	+	9172.50i	−0.149365	+	0.178006i	−0.835539	−	0.549431i	$-0.814844\pi$
$227$	−7696.64	+	9172.50i	−0.149365	+	0.178006i	0.686174	+	0.727438i	$0.259289\pi$
$228$	−28246.9	−	192544.i	−0.543377	−	3.70391i
$229$	−9076.93	−	51477.8i	−0.173088	−	0.981633i	−0.940327	−	0.340272i	$-0.889481\pi$
$229$	−9076.93	−	51477.8i	−0.173088	−	0.981633i	0.767239	−	0.641362i	$-0.221630\pi$
$230$	−100012.	+	17634.8i	−1.89059	+	0.333362i
$231$	4583.40	+	5794.03i	0.0858942	+	0.108582i
$232$	4936.84	+	4142.50i	0.0917219	+	0.0769638i
$233$	−23116.2	+	13346.2i	−0.425800	+	0.245836i	−0.697556	−	0.716531i	$-0.745729\pi$
$233$	−23116.2	+	13346.2i	−0.425800	+	0.245836i	0.271756	+	0.962366i	$0.412396\pi$
$234$	−2319.34	+	1166.09i	−0.0423577	+	0.0212962i
$235$	−66150.8	+	114577.i	−1.19784	+	2.07472i
$236$	−46152.2	−	126802.i	−0.828645	−	2.27668i
$237$	−16391.5	−	14580.7i	−0.291824	−	0.259586i
$238$	−30523.6	+	25612.4i	−0.538868	+	0.452164i
$239$	−1205.00	+	3310.71i	−0.0210956	+	0.0579596i	−0.949793	−	0.312878i	$-0.898707\pi$
$239$	−1205.00	+	3310.71i	−0.0210956	+	0.0579596i	0.928698	+	0.370837i	$0.120929\pi$
$240$	185565.	+	114402.i	3.22162	+	1.98614i
$241$	14955.3	−	84815.6i	0.257490	−	1.46030i	−0.532110	−	0.846675i	$-0.678601\pi$
$241$	14955.3	−	84815.6i	0.257490	−	1.46030i	0.789600	−	0.613622i	$-0.210288\pi$
$242$			86674.1i			1.47999i
$243$	−21861.7	−	54853.0i	−0.370230	−	0.928940i
$244$	22373.8			0.375803
$245$	76544.2	+	13496.8i	1.27520	+	0.224853i
$246$	−83151.4	+	134875.i	−1.37404	+	2.22876i
$247$	2205.27	+	802.652i	0.0361466	+	0.0131563i
$248$	96675.6	+	115213.i	1.57186	+	1.87327i
$249$	31226.4	−	35104.4i	0.503643	−	0.566190i
$250$	5975.39	−	2174.86i	0.0956063	−	0.0347978i
$251$	−11184.3	−	6457.26i	−0.177526	−	0.102495i	0.408604	−	0.912712i	$-0.366016\pi$
$251$	−11184.3	−	6457.26i	−0.177526	−	0.102495i	−0.586130	+	0.810217i	$0.699349\pi$
$252$	−21532.3	−	42827.3i	−0.339070	−	0.674403i
$253$	−10480.1	−	18152.1i	−0.163729	−	0.283587i
$254$	88985.6	−	106049.i	1.37928	−	1.64376i
$255$	−90085.7	+	71262.8i	−1.38540	+	1.09593i
$256$	−6074.84	−	34452.1i	−0.0926946	−	0.525697i
$257$	9408.96	−	1659.05i	0.142454	−	0.0251185i	−0.101966	−	0.994788i	$-0.532513\pi$
$257$	9408.96	−	1659.05i	0.142454	−	0.0251185i	0.244421	+	0.969669i	$0.421402\pi$
$258$	−38523.2	+	5651.50i	−0.578740	+	0.0849032i
$259$	5625.47	+	4720.33i	0.0838608	+	0.0703676i
$260$	−5261.14	+	3037.52i	−0.0778275	+	0.0449337i
$261$	−851.972	−	2841.23i	−0.0125067	−	0.0417085i
$262$	103298.	−	178917.i	1.50483	−	2.60645i
$263$	29073.3	+	79878.1i	0.420322	+	1.15483i	0.951523	+	0.307579i	$0.0995189\pi$
$263$	29073.3	+	79878.1i	0.420322	+	1.15483i	−0.531201	+	0.847246i	$0.678259\pi$
$264$	−17574.4	+	85207.5i	−0.252157	+	1.22256i
$265$	16332.8	−	13704.9i	0.232578	−	0.195156i
$266$	−20809.4	+	57173.4i	−0.294101	+	0.808036i
$267$	−32769.7	+	17678.6i	−0.459673	+	0.247984i
$268$	−21137.6	+	119877.i	−0.294297	+	1.66904i
$269$			14077.8i			0.194549i	0.995258	+	0.0972745i	$0.0310125\pi$
$269$			14077.8i			0.194549i	−0.995258	+	0.0972745i	$0.968988\pi$
$270$	−82110.7	−	175783.i	−1.12635	−	2.41130i
$271$	−18138.8			−0.246984			−0.123492	−	0.992346i	$-0.539409\pi$
$271$	−18138.8			−0.246984			−0.123492	+	0.992346i	$0.539409\pi$
$272$	−238983.	−	42139.2i	−3.23020	−	0.569572i
$273$	577.828	+	16.6856i	0.00775307	+	0.000223881i
$274$	−158155.	−	57563.8i	−2.10660	−	0.766741i
$275$	22911.0	+	27304.3i	0.302956	+	0.361049i
$276$	42807.0	+	129089.i	0.561949	+	1.69462i
$277$	136985.	−	49858.4i	1.78531	−	0.649799i	0.785798	−	0.618483i	$-0.212252\pi$
$277$	136985.	−	49858.4i	1.78531	−	0.649799i	0.999510	−	0.0313162i	$-0.00996987\pi$
$278$	124869.	+	72093.1i	1.61572	+	0.932834i
$279$	−8066.72	−	68752.4i	−0.103631	−	0.883241i
$280$	−46933.0	−	81290.3i	−0.598635	−	1.03687i
$281$	786.212	−	936.971i	0.00995696	−	0.0118662i	−0.761043	−	0.648701i	$-0.775312\pi$
$281$	786.212	−	936.971i	0.00995696	−	0.0118662i	0.771000	+	0.636835i	$0.219757\pi$
$282$	231206.	+	91793.4i	2.90738	+	1.15429i
$283$	18788.2	+	106553.i	0.234592	+	1.33044i	0.843472	+	0.537173i	$0.180508\pi$
$283$	18788.2	+	106553.i	0.234592	+	1.33044i	−0.608880	+	0.793262i	$0.708381\pi$
$284$	71138.9	−	12543.7i	0.882004	−	0.155521i
$285$	−64720.1	+	163015.i	−0.796800	+	2.00696i
$286$	−1348.57	−	1131.59i	−0.0164870	−	0.0138342i
$287$	30555.8	−	17641.4i	0.370963	−	0.214175i
$288$	71938.5	−	166975.i	0.867314	−	2.01310i
$289$	22172.1	−	38403.2i	0.265467	−	0.459803i
$290$	−3333.33	−	9158.24i	−0.0396353	−	0.108897i
$291$	112408.	−	37275.3i	1.32742	−	0.440185i
$292$	167834.	−	140829.i	1.96840	−	1.65169i
$293$	−36375.6	+	99941.2i	−0.423716	+	1.16415i	0.525848	+	0.850579i	$0.323748\pi$
$293$	−36375.6	+	99941.2i	−0.423716	+	1.16415i	−0.949564	+	0.313573i	$0.898474\pi$
$294$	4218.35	−	146082.i	0.0488031	−	1.69006i
$295$	−21118.8	+	119770.i	−0.242675	+	1.37628i
$296$			86480.6i			0.987041i
$297$	28296.3	−	28333.7i	0.320787	−	0.321211i
$298$	−193594.			−2.18001
$299$	−1615.17	−	284.797i	−0.0180665	−	0.00318562i
$300$	−109807.	−	203543.i	−1.22008	−	2.26158i
$301$	8147.25	+	2965.36i	0.0899246	+	0.0327299i
$302$	−39730.2	−	47348.6i	−0.435619	−	0.519150i
$303$	−152400.	−	31433.0i	−1.65997	−	0.342374i
$304$	−348199.	+	126734.i	−3.76774	+	1.37134i
$305$	−17463.4	−	10082.5i	−0.187728	−	0.108385i
$306$	157160.	+	148142.i	1.67841	+	1.58210i
$307$	37577.3	+	65085.9i	0.398703	+	0.690573i	0.993566	−	0.113253i	$-0.0361272\pi$
$307$	37577.3	+	65085.9i	0.398703	+	0.690573i	−0.594863	+	0.803827i	$0.702794\pi$
$308$	20895.1	−	24901.8i	0.220264	−	0.262500i
$309$	16925.7	+	115373.i	0.177267	+	1.20834i
$310$	−39495.8	−	223992.i	−0.410986	−	2.33082i
$311$	64675.3	−	11404.0i	0.668679	−	0.117906i	0.171005	−	0.985270i	$-0.445299\pi$
$311$	64675.3	−	11404.0i	0.668679	−	0.117906i	0.497674	+	0.867364i	$0.334187\pi$
$312$	4223.49	+	5339.05i	0.0433873	+	0.0548473i
$313$	−61767.7	−	51829.3i	−0.630483	−	0.529038i	0.270596	−	0.962693i	$-0.412779\pi$
$313$	−61767.7	−	51829.3i	−0.630483	−	0.529038i	−0.901079	+	0.433655i	$0.857224\pi$
$314$	−117658.	+	67929.6i	−1.19333	+	0.688969i
$315$	−2493.03	+	43131.1i	−0.0251250	+	0.434680i
$316$	−48265.2	+	83597.7i	−0.483348	+	0.837183i
$317$	11934.7	+	32790.3i	0.118766	+	0.326307i	0.984804	−	0.173672i	$-0.0555632\pi$
$317$	11934.7	+	32790.3i	0.118766	+	0.326307i	−0.866037	+	0.499979i	$0.833341\pi$
$318$	−29953.4	−	26644.4i	−0.296204	−	0.263483i
$319$	1540.90	−	1292.97i	0.0151424	−	0.0127060i
$320$	71764.7	−	197172.i	0.700827	−	1.92551i
$321$	−82223.0	−	50690.9i	−0.797964	−	0.491949i
$322$	7383.60	−	41874.5i	0.0712126	−	0.403867i
$323$		−	195244.i		−	1.87143i
$324$	−216954.	+	142967.i	−2.06670	+	1.36190i
$325$	2788.99			0.0264046
$326$	−330825.	−	58333.4i	−3.11289	−	0.548886i
$327$	7122.31	−	11552.7i	0.0666078	−	0.108041i
$328$	390448.	+	142112.i	3.62924	+	1.32094i
$329$	−35606.6	−	42434.2i	−0.328956	−	0.392035i
$330$	87445.2	−	98305.0i	0.802986	−	0.902709i
$331$	121557.	−	44243.1i	1.10949	−	0.403821i	0.278684	−	0.960383i	$-0.410102\pi$
$331$	121557.	−	44243.1i	1.10949	−	0.403821i	0.830806	+	0.556562i	$0.187880\pi$
$332$	−179035.	−	103366.i	−1.62428	−	0.937780i
$333$	21858.0	−	33265.3i	0.197116	−	0.299988i
$334$	170629.	+	295538.i	1.52954	+	2.64924i
$335$	70519.7	−	84042.1i	0.628378	−	0.748871i
$336$	−71584.1	+	56627.0i	−0.634071	+	0.501585i
$337$	−23137.5	−	131219.i	−0.203731	−	1.15541i	−0.899425	−	0.437076i	$-0.856014\pi$
$337$	−23137.5	−	131219.i	−0.203731	−	1.15541i	0.695694	−	0.718338i	$-0.255097\pi$
$338$	209598.	−	36957.7i	1.83465	−	0.323498i
$339$	310.326	−	45.5259i	0.00270034	−	0.000396150i
$340$	387174.	+	324877.i	3.34925	+	2.81036i
$341$	40654.3	−	23471.8i	0.349621	−	0.201854i
$342$	320928.	+	75912.0i	2.74382	+	0.649020i
$343$	−34211.6	+	59256.3i	−0.290794	+	0.503670i
$344$	34921.4	+	95945.7i	0.295103	+	0.810790i
$345$	24760.3	−	120048.i	0.208026	−	1.00859i
$346$	−200803.	+	168494.i	−1.67733	+	1.40745i
$347$	19826.7	−	54473.4i	0.164661	−	0.452403i	−0.829730	−	0.558165i	$-0.811506\pi$
$347$	19826.7	−	54473.4i	0.164661	−	0.452403i	0.994392	+	0.105761i	$0.0337280\pi$
$348$	−11486.8	+	6196.90i	−0.0948508	+	0.0511701i
$349$	−22672.5	+	128582.i	−0.186144	+	1.05568i	0.738332	+	0.674437i	$0.235614\pi$
$349$	−22672.5	+	128582.i	−0.186144	+	1.05568i	−0.924476	+	0.381239i	$0.875497\pi$
$350$			72306.8i			0.590260i
$351$	−275.148	−	3121.19i	−0.00223333	−	0.0253341i
$352$	123294.			0.995076
$353$	−27299.6	−	4813.66i	−0.219082	−	0.0386301i	0.0630294	−	0.998012i	$-0.479924\pi$
$353$	−27299.6	−	4813.66i	−0.219082	−	0.0386301i	−0.282112	+	0.959382i	$0.591035\pi$
$354$	228579.	+	6600.55i	1.82402	+	0.0526712i
$355$	−61178.5	−	22267.2i	−0.485448	−	0.176688i
$356$	105311.	+	125505.i	0.830951	+	0.990289i
$357$	−15137.5	−	45648.6i	−0.118773	−	0.358172i
$358$	−52549.4	+	19126.4i	−0.410017	+	0.149234i
$359$	19338.9	+	11165.3i	0.150053	+	0.0866329i	0.573146	−	0.819453i	$-0.305723\pi$
$359$	19338.9	+	11165.3i	0.150053	+	0.0866329i	−0.423094	+	0.906086i	$0.639056\pi$
$360$	−407970.	+	304002.i	−3.14791	+	2.34569i
$361$	−83904.2	−	145326.i	−0.643827	−	1.11514i
$362$	−10023.4	+	11945.5i	−0.0764891	+	0.0911562i
$363$	−97231.2	−	38602.7i	−0.737892	−	0.292957i
$364$	−441.689	−	2504.94i	−0.00333360	−	0.0189058i
$365$	−194462.	+	34288.9i	−1.45965	+	0.257376i
$366$	−13990.9	+	35239.7i	−0.104444	+	0.263069i
$367$	−149004.	−	125029.i	−1.10628	−	0.928278i	−0.108447	−	0.994102i	$-0.534588\pi$
$367$	−149004.	−	125029.i	−1.10628	−	0.928278i	−0.997831	+	0.0658243i	$0.979032\pi$
$368$	224265.	−	129480.i	1.65602	−	0.956106i
$369$	−114270.	−	153350.i	−0.839226	−	1.12624i
$370$	65391.3	−	113261.i	0.477657	−	0.827327i
$371$	3053.20	+	8388.61i	0.0221824	+	0.0609456i
$372$	−289114.	+	95872.6i	−2.08921	+	0.692801i
$373$	−130382.	+	109403.i	−0.937127	+	0.786343i	−0.977083	−	0.212858i	$-0.931723\pi$
$373$	−130382.	+	109403.i	−0.937127	+	0.786343i	0.0399560	+	0.999201i	$0.487278\pi$
$374$	−50092.7	+	137628.i	−0.358122	+	0.983932i
$375$	−221.536	+	7671.84i	−0.00157537	+	0.0545553i
$376$	113278.	−	642433.i	0.801256	−	4.54415i
$377$		−	157.395i		−	0.00110741i
$378$	80919.4	−	7133.44i	0.566329	−	0.0499247i
$379$	177096.			1.23290			0.616452	−	0.787392i	$-0.288569\pi$
$379$	177096.			1.23290			0.616452	+	0.787392i	$0.288569\pi$
$380$	760028.	+	134013.i	5.26335	+	0.928071i
$381$	79333.7	+	147056.i	0.546522	+	1.01305i
$382$	79935.8	+	29094.2i	0.547790	+	0.199379i
$383$	−29074.2	−	34649.2i	−0.198203	−	0.236209i	0.657784	−	0.753207i	$-0.271494\pi$
$383$	−29074.2	−	34649.2i	−0.198203	−	0.236209i	−0.855987	+	0.516998i	$0.827050\pi$
$384$	−69836.0	−	14403.9i	−0.473606	−	0.0976830i
$385$	−27530.9	+	10020.4i	−0.185737	+	0.0676027i
$386$	−181887.	−	105012.i	−1.22075	−	0.704799i
$387$	10817.5	−	45732.5i	0.0722280	−	0.305354i
$388$	−260547.	−	451281.i	−1.73071	−	2.99767i
$389$	−42121.3	+	50198.2i	−0.278357	+	0.331733i	−0.887050	−	0.461672i	$-0.847250\pi$
$389$	−42121.3	+	50198.2i	−0.278357	+	0.331733i	0.608693	+	0.793406i	$0.291694\pi$
$390$	−1494.31	−	10185.9i	−0.00982454	−	0.0669687i
$391$	23694.0	+	134375.i	0.154983	+	0.878954i
$392$	−377419.	+	66549.1i	−2.45613	+	0.433082i
$393$	154703.	+	195565.i	1.00165	+	1.26621i
$394$	−383438.	−	321742.i	−2.47003	−	2.07260i
$395$	75344.6	−	43500.2i	0.482901	−	0.278803i
$396$	−147253.	−	96756.9i	−0.939017	−	0.617009i
$397$	−111760.	+	193575.i	−0.709099	+	1.22820i	0.256093	+	0.966652i	$0.417565\pi$
$397$	−111760.	+	193575.i	−0.709099	+	1.22820i	−0.965192	+	0.261543i	$0.915769\pi$
$398$	53156.8	+	146047.i	0.335577	+	0.921991i
$399$	−54869.2	−	48807.8i	−0.344654	−	0.306580i
$400$	−337339.	+	283061.i	−2.10837	+	1.76913i
$401$	92421.2	−	253925.i	0.574755	−	1.57913i	−0.222144	−	0.975014i	$-0.571305\pi$
$401$	92421.2	−	253925.i	0.574755	−	1.57913i	0.796899	−	0.604113i	$-0.206472\pi$
$402$	−175594.	−	108254.i	−1.08657	−	0.669875i
$403$	637.845	−	3617.40i	0.00392740	−	0.0222734i
$404$			684696.i			4.19503i
$405$	233765.	−	13822.0i	1.42518	−	0.0842677i
$406$	4080.59			0.0247555
$407$	26582.5	+	4687.22i	0.160475	+	0.0282961i
$408$	297222.	−	482108.i	1.78550	−	2.89617i
$409$	194660.	+	70850.6i	1.16367	+	0.423542i	0.850408	−	0.526124i	$-0.176355\pi$
$409$	194660.	+	70850.6i	1.16367	+	0.423542i	0.313265	+	0.949666i	$0.398577\pi$
$410$	−403902.	−	481352.i	−2.40275	−	2.86349i
$411$	135014.	−	151781.i	0.799273	−	0.898535i
$412$	482149.	−	175488.i	2.84045	−	1.03384i
$413$	−44098.7	−	25460.4i	−0.258539	−	0.149268i
$414$	−230089.	−	13299.4i	−1.34244	−	0.0775945i
$415$	93161.1	+	161360.i	0.540927	+	0.936913i
$416$	6201.24	−	7390.35i	0.0358337	−	0.0427050i
$417$	−136488.	+	107970.i	−0.784915	+	0.620911i
$418$	38834.6	+	220242.i	0.222263	+	1.26051i
$419$	−86433.7	+	15240.6i	−0.492329	+	0.0868108i	−0.414300	−	0.910140i	$-0.635974\pi$
$419$	−86433.7	+	15240.6i	−0.492329	+	0.0868108i	−0.0780285	+	0.996951i	$0.524863\pi$
$420$	188087.	−	27593.0i	1.06625	−	0.156423i
$421$	212742.	+	178512.i	1.20030	+	1.00717i	0.999621	+	0.0275143i	$0.00875917\pi$
$421$	212742.	+	178512.i	1.20030	+	1.00717i	0.200679	+	0.979657i	$0.435685\pi$
$422$	255434.	−	147475.i	1.43435	−	0.828121i
$423$	−205948.	+	218485.i	−1.15101	+	1.22107i
$424$	−52564.0	+	91043.5i	−0.292386	+	0.506427i
$425$	−79359.9	−	218039.i	−0.439363	−	1.20714i
$426$	−24727.9	+	119891.i	−0.136260	+	0.660642i
$427$	6467.69	−	5427.03i	0.0354726	−	0.0297651i
$428$	−145366.	+	399390.i	−0.793553	+	2.18027i
$429$	1870.04	−	1008.85i	0.0101610	−	0.00548165i
$430$	26812.7	−	152062.i	0.145012	−	0.822404i
$431$		−	41851.0i		−	0.225295i	−0.993635	−	0.112647i	$-0.964067\pi$
$431$		−	41851.0i		−	0.225295i	0.993635	−	0.112647i	$-0.0359331\pi$
$432$	350057.	+	349595.i	1.87574	+	1.87326i
$433$	1012.86			0.00540225			0.00270113	−	0.999996i	$-0.499140\pi$
$433$	1012.86			0.00540225			0.00270113	+	0.999996i	$0.499140\pi$
$434$	93784.1	+	16536.7i	0.497909	+	0.0877947i
$435$	11758.3	+	339.539i	0.0621394	+	0.00179437i
$436$	−56116.2	−	20424.6i	−0.295199	−	0.107444i
$437$	133925.	+	159606.i	0.701292	+	0.835768i
$438$	116862.	+	352409.i	0.609151	+	1.83696i
$439$	−61671.4	+	22446.6i	−0.320004	+	0.116472i	−0.497028	−	0.867735i	$-0.665575\pi$
$439$	−61671.4	+	22446.6i	−0.320004	+	0.116472i	0.177024	+	0.984207i	$0.443353\pi$
$440$	−298799.	−	172512.i	−1.54338	−	0.891072i
$441$	161997.	+	69793.9i	0.832970	+	0.358873i
$442$	5730.10	+	9924.82i	0.0293304	+	0.0508017i
$443$	−11275.3	+	13437.4i	−0.0574540	+	0.0684710i	−0.794006	−	0.607910i	$-0.792008\pi$
$443$	−11275.3	+	13437.4i	−0.0574540	+	0.0684710i	0.736552	+	0.676381i	$0.236453\pi$
$444$	−162783.	−	64628.0i	−0.825739	−	0.327834i
$445$	−25641.0	−	145418.i	−0.129484	−	0.734339i
$446$	410122.	−	72315.6i	2.06179	−	0.363548i
$447$	86222.2	−	217174.i	0.431523	−	1.08691i
$448$	67299.2	+	56470.8i	0.335316	+	0.281363i
$449$	−310961.	+	179534.i	−1.54246	+	0.890540i	−0.543777	+	0.839230i	$0.683006\pi$
$449$	−310961.	+	179534.i	−1.54246	+	0.890540i	−0.998683	+	0.0513099i	$0.983660\pi$
$450$	389253.	−	45671.0i	1.92224	−	0.225536i
$451$	64844.6	−	112314.i	0.318802	−	0.552181i
$452$	−472.020	−	1296.86i	−0.00231038	−	0.00634772i
$453$	70810.6	−	23481.4i	0.345066	−	0.114427i
$454$	−68395.9	+	57391.0i	−0.331832	+	0.278440i
$455$	−784.071	+	2154.22i	−0.00378733	+	0.0104056i
$456$	24962.4	−	864453.i	0.120048	−	4.15731i
$457$	−60611.2	+	343743.i	−0.290215	+	1.64589i	0.395823	+	0.918327i	$0.370459\pi$
$457$	−60611.2	+	343743.i	−0.290215	+	1.64589i	−0.686038	+	0.727566i	$0.740652\pi$
$458$		−	389772.i		−	1.85815i
$459$	−236181.	+	110323.i	−1.12104	+	0.523651i
$460$	−539346.			−2.54890
$461$	92015.8	+	16224.9i	0.432973	+	0.0763447i	0.385887	−	0.922546i	$-0.373896\pi$
$461$	92015.8	+	16224.9i	0.432973	+	0.0763447i	0.0470857	+	0.998891i	$0.485007\pi$
$462$	26155.2	+	48482.3i	0.122539	+	0.227143i
$463$	−12089.8	−	4400.31i	−0.0563969	−	0.0205268i	0.313668	−	0.949533i	$-0.398442\pi$
$463$	−12089.8	−	4400.31i	−0.0563969	−	0.0205268i	−0.370065	+	0.929006i	$0.620664\pi$
$464$	15974.4	+	19037.6i	0.0741974	+	0.0884250i
$465$	268865.	+	55454.4i	1.24345	+	0.256466i
$466$	−187032.	+	68073.9i	−0.861277	+	0.313479i
$467$	104386.	+	60267.3i	0.478639	+	0.276342i	0.719849	−	0.694130i	$-0.244211\pi$
$467$	104386.	+	60267.3i	0.478639	+	0.276342i	−0.241210	+	0.970473i	$0.577544\pi$
$468$	−13206.0	+	3959.96i	−0.0602947	+	0.0180800i
$469$	22967.3	+	39780.5i	0.104415	+	0.180853i
$470$	−634126.	+	755721.i	−2.87065	+	3.42110i
$471$	−23801.6	−	162243.i	−0.107291	−	0.731347i
$472$	−104131.	−	590556.i	−0.467408	−	2.65080i
$473$	31384.6	−	5533.96i	0.140280	−	0.0247351i
$474$	−101489.	−	128295.i	−0.451711	−	0.571023i
$475$	−271412.	−	227742.i	−1.20294	−	1.00938i
$476$	−183265.	+	105808.i	−0.808846	+	0.466987i
$477$	43230.3	−	21734.9i	0.189999	−	0.0955260i
$478$	−13135.5	+	22751.4i	−0.0574899	+	0.0995754i
$479$	−51328.2	−	141023.i	−0.223710	−	0.614638i	0.776164	−	0.630531i	$-0.217163\pi$
$479$	−51328.2	−	141023.i	−0.223710	−	0.614638i	−0.999874	+	0.0158933i	$0.994941\pi$
$480$	538725.	+	479212.i	2.33822	+	2.07991i
$481$	1617.96	−	1357.63i	0.00699324	−	0.00586802i
$482$	219643.	−	603465.i	0.945418	−	2.59752i
$483$	43686.4	+	26932.9i	0.187263	+	0.115449i
$484$	−79933.1	+	453323.i	−0.341221	+	1.93516i
$485$			469650.i			1.99660i
$486$	−89512.7	−	431111.i	−0.378977	−	1.82523i
$487$	−88735.1			−0.374143			−0.187071	−	0.982346i	$-0.559900\pi$
$487$	−88735.1			−0.374143			−0.187071	+	0.982346i	$0.559900\pi$
$488$	97917.6	+	17265.5i	0.411170	+	0.0725003i
$489$	212780.	−	345140.i	0.889844	−	1.44337i
$490$	544614.	+	198223.i	2.26828	+	0.825586i
$491$	273525.	+	325975.i	1.13458	+	1.35214i	0.927504	+	0.373812i	$0.121950\pi$
$491$	273525.	+	325975.i	1.13458	+	1.35214i	0.207074	+	0.978325i	$0.433606\pi$
$492$	−559284.	+	628741.i	−2.31048	+	2.59742i
$493$	−12304.9	+	4478.63i	−0.0506274	+	0.0184269i
$494$	15154.8	+	8749.60i	0.0621005	+	0.0358537i
$495$	71332.7	+	141879.i	0.291124	+	0.579039i
$496$	289989.	+	502275.i	1.17874	+	2.04164i
$497$	17521.8	−	20881.6i	0.0709357	−	0.0845379i
$498$	274760.	−	217350.i	1.10789	−	0.876399i
$499$	−20429.8	−	115863.i	−0.0820472	−	0.465313i	−0.997955	−	0.0639235i	$-0.979639\pi$
$499$	−20429.8	−	115863.i	−0.0820472	−	0.465313i	0.915908	−	0.401389i	$-0.131472\pi$
$500$	33258.2	−	5864.32i	0.133033	−	0.0234573i
$501$	−407530.	+	59786.1i	−1.62362	+	0.238191i
$502$	−73769.1	−	61899.6i	−0.292730	−	0.245630i
$503$	225624.	−	130264.i	0.891764	−	0.514860i	0.0172448	−	0.999851i	$-0.494511\pi$
$503$	225624.	−	130264.i	0.891764	−	0.514860i	0.874519	+	0.484991i	$0.161177\pi$
$504$	−61185.6	−	204047.i	−0.240873	−	0.803283i
$505$	308550.	−	534424.i	1.20988	−	2.09557i
$506$	−53455.2	−	146867.i	−0.208780	−	0.573619i
$507$	−51890.8	+	251587.i	−0.201871	+	0.978752i
$508$	563213.	−	472592.i	2.18246	−	1.83130i
$509$	62362.0	−	171338.i	0.240705	−	0.661331i	−0.759240	−	0.650811i	$-0.774429\pi$
$509$	62362.0	−	171338.i	0.240705	−	0.661331i	0.999945	−	0.0105200i	$-0.00334869\pi$
$510$	−753803.	+	406662.i	−2.89813	+	1.56348i
$511$	14356.6	−	81420.2i	0.0549805	−	0.311810i
$512$		−	387626.i		−	1.47867i
$513$	−228092.	+	326209.i	−0.866715	+	1.23954i
$514$	71241.4			0.269654
$515$	−455412.	−	80301.5i	−1.71708	−	0.302767i
$516$	−206696.	−	5968.66i	−0.776306	−	0.0224170i
$517$	−191332.	−	69639.3i	−0.715826	−	0.260539i
$518$	35197.7	+	41947.0i	0.131176	+	0.156330i
$519$	−99583.6	−	300305.i	−0.369703	−	1.11488i
$520$	−25369.0	+	9233.57i	−0.0938203	+	0.0341478i
$521$	386241.	+	222996.i	1.42293	+	0.821528i	0.996548	−	0.0830166i	$-0.0264554\pi$
$521$	386241.	+	222996.i	1.42293	+	0.821528i	0.426380	+	0.904544i	$0.359789\pi$
$522$	−2577.42	−	21967.3i	−0.00945897	−	0.0806185i
$523$	−236571.	−	409752.i	−0.864883	−	1.49802i	−0.867163	−	0.498024i	$-0.834059\pi$
$523$	−236571.	−	409752.i	−0.864883	−	1.49802i	0.00227985	−	0.999997i	$-0.499274\pi$
$524$	705270.	−	840508.i	2.56858	−	3.06111i
$525$	−81113.9	−	32203.8i	−0.294291	−	0.116839i
$526$	110066.	+	624217.i	0.397817	+	2.25613i
$527$	−300953.	+	53066.2i	−1.08362	+	0.191072i
$528$	−123798.	+	311819.i	−0.444065	+	1.11850i
$529$	102829.	+	86283.5i	0.367454	+	0.308331i
$530$	137683.	−	79491.2i	0.490149	−	0.282988i
$531$	−109208.	+	253480.i	−0.387317	+	0.898991i
$532$	−161564.	+	279837.i	−0.570850	+	0.988741i
$533$	−3470.76	−	9535.85i	−0.0122172	−	0.0335664i
$534$	−263530.	+	87388.6i	−0.924159	+	0.306459i
$535$	293443.	−	246227.i	1.02522	−	0.860259i
$536$	−185015.	+	508323.i	−0.643986	+	1.76934i
$537$	1948.25	−	67468.5i	0.00675611	−	0.233966i
$538$	−18228.3	+	103378.i	−0.0629770	+	0.357160i
$539$			119618.i			0.411738i
$540$	−267343.	−	995107.i	−0.916816	−	3.41258i
$541$	22010.9			0.0752045			0.0376023	−	0.999293i	$-0.488028\pi$
$541$	22010.9			0.0752045			0.0376023	+	0.999293i	$0.488028\pi$
$542$	−133199.	−	23486.6i	−0.453422	−	0.0799506i
$543$	−8936.24	−	16564.6i	−0.0303079	−	0.0561798i
$544$	−754223.	−	274515.i	−2.54860	−	0.927615i
$545$	34596.1	+	41230.0i	0.116475	+	0.138810i
$546$	4221.59	+	870.717i	0.0141609	+	0.00292073i
$547$	129770.	−	47232.4i	0.433710	−	0.157858i	−0.115933	−	0.993257i	$-0.536986\pi$
$547$	129770.	−	47232.4i	0.433710	−	0.157858i	0.549643	+	0.835399i	$0.314764\pi$
$548$	−774097.	−	446925.i	−2.57771	−	1.48824i
$549$	−33300.8	−	31389.9i	−0.110487	−	0.104147i
$550$	132889.	+	230171.i	0.439303	+	0.760895i
$551$	−12852.5	+	15317.0i	−0.0423335	+	0.0504511i
$552$	87726.2	+	597983.i	0.287906	+	1.96250i
$553$	6325.41	+	35873.2i	0.0206842	+	0.117306i
$554$	1.07049e6	−	188755.i	3.48788	−	0.615007i
$555$	97932.7	+	123800.i	0.317937	+	0.401915i
$556$	586603.	+	492219.i	1.89756	+	1.59224i
$557$	−254021.	+	146659.i	−0.818765	+	0.472714i	−0.849990	−	0.526798i	$-0.823392\pi$
$557$	−254021.	+	146659.i	−0.818765	+	0.472714i	0.0312254	+	0.999512i	$0.490059\pi$
$558$	29785.9	−	515317.i	0.0956627	−	1.65503i
$559$	1246.82	−	2159.56i	0.00399008	−	0.00691102i
$560$	−123800.	−	340138.i	−0.394771	−	1.08463i
$561$	−132082.	−	117491.i	−0.419679	−	0.373317i
$562$	6986.64	−	5862.49i	0.0221205	−	0.0185613i
$563$	18682.7	−	51330.3i	0.0589417	−	0.161941i	−0.906727	−	0.421719i	$-0.861427\pi$
$563$	18682.7	−	51330.3i	0.0589417	−	0.161941i	0.965668	+	0.259778i	$0.0836493\pi$
$564$	1.12460e6	+	693322.i	3.53542	+	2.17960i
$565$	−215.991	+	1224.95i	−0.000676611	+	0.00383725i
$566$			806785.i			2.51840i
$567$	−28037.4	+	93952.6i	−0.0872109	+	0.292242i
$568$	321014.			0.995011
$569$	−115769.	−	20413.2i	−0.357576	−	0.0630504i	−0.00802559	−	0.999968i	$-0.502555\pi$
$569$	−115769.	−	20413.2i	−0.357576	−	0.0630504i	−0.349551	+	0.936917i	$0.613666\pi$
$570$	−686339.	+	1.11327e6i	−2.11246	+	3.42651i
$571$	−244279.	−	88910.4i	−0.749229	−	0.272697i	−0.0609476	−	0.998141i	$-0.519412\pi$
$571$	−244279.	−	88910.4i	−0.749229	−	0.272697i	−0.688281	+	0.725444i	$0.741634\pi$
$572$	−6009.72	−	7162.10i	−0.0183680	−	0.0218901i
$573$	−68239.6	+	76714.2i	−0.207839	+	0.233650i
$574$	247225.	−	89982.4i	0.750357	−	0.273108i
$575$	214435.	+	123804.i	0.648575	+	0.374455i
$576$	261494.	−	397964.i	0.788163	−	1.19949i
$577$	−251986.	−	436453.i	−0.756877	−	1.31095i	−0.944436	−	0.328696i	$-0.893391\pi$
$577$	−251986.	−	436453.i	−0.756877	−	1.31095i	0.187558	−	0.982253i	$-0.439943\pi$
$578$	212543.	−	253299.i	0.636196	−	0.758189i
$579$	198811.	−	157271.i	0.593039	−	0.469127i
$580$	−8988.00	−	50973.5i	−0.0267182	−	0.151526i
$581$	−76826.9	+	13546.7i	−0.227594	+	0.0401310i
$582$	873712.	−	128177.i	2.57942	−	0.378410i
$583$	25136.1	+	21091.7i	0.0739539	+	0.0620547i
$584$	843190.	−	486816.i	2.47229	−	1.42738i
$585$	12092.1	+	2860.26i	0.0353339	+	0.00835784i
$586$	−396526.	+	686802.i	−1.15472	+	2.00003i
$587$	70170.3	+	192791.i	0.203647	+	0.559514i	0.998906	−	0.0467544i	$-0.0148878\pi$
$587$	70170.3	+	192791.i	0.203647	+	0.559514i	−0.795260	+	0.606269i	$0.792666\pi$
$588$	156784.	−	760150.i	0.453468	−	2.19859i
$589$	−357460.	+	299945.i	−1.03038	+	0.864591i
$590$	−310165.	+	852170.i	−0.891022	+	2.44806i
$591$	531706.	−	286845.i	1.52229	−	0.821243i
$592$	−57909.6	+	328422.i	−0.165237	+	0.937106i
$593$			319505.i			0.908590i	0.890851	+	0.454295i	$0.150109\pi$
$593$			319505.i			0.908590i	−0.890851	+	0.454295i	$0.849891\pi$
$594$	244477.	−	171425.i	0.692890	−	0.485850i
$595$	190724.			0.538732
$596$	−1.01253e6	−	178537.i	−2.85047	−	0.502615i
$597$	−187511.	−	5414.65i	−0.526111	−	0.0151922i
$598$	−11492.0	−	4182.73i	−0.0321360	−	0.0116965i
$599$	−58679.5	−	69931.5i	−0.163543	−	0.194903i	0.678049	−	0.735017i	$-0.262826\pi$
$599$	−58679.5	−	69931.5i	−0.163543	−	0.194903i	−0.841592	+	0.540114i	$0.818381\pi$
$600$	−323493.	−	975526.i	−0.898591	−	2.70979i
$601$	−276168.	+	100517.i	−0.764581	+	0.278285i	−0.694728	−	0.719272i	$-0.744475\pi$
$601$	−276168.	+	100517.i	−0.764581	+	0.278285i	−0.0698533	+	0.997557i	$0.522253\pi$
$602$	55988.5	+	32324.9i	0.154492	+	0.0891959i
$603$	199646.	−	148767.i	0.549067	−	0.409141i
$604$	−164131.	−	284283.i	−0.449900	−	0.779249i
$605$	266674.	−	317810.i	0.728568	−	0.868274i
$606$	−1.07842e6	−	428156.i	−2.93660	−	1.16589i
$607$	93005.7	+	527462.i	0.252425	+	1.43157i	0.802597	+	0.596522i	$0.203451\pi$
$607$	93005.7	+	527462.i	0.252425	+	1.43157i	−0.550172	+	0.835051i	$0.685438\pi$
$608$	−1.20696e6	+	212819.i	−3.26501	+	0.575709i
$609$	−1817.40	+	4577.62i	−0.00490024	+	0.0123426i
$610$	−115185.	−	96651.3i	−0.309553	−	0.259745i
$611$	−13797.6	+	7966.04i	−0.0369590	+	0.0213383i
$612$	685357.	+	919748.i	1.82984	+	2.45565i
$613$	212960.	−	368858.i	0.566732	−	0.981608i	−0.430154	−	0.902755i	$-0.641541\pi$
$613$	212960.	−	368858.i	0.566732	−	0.981608i	0.996886	−	0.0788530i	$-0.0251258\pi$
$614$	191668.	+	526604.i	0.508409	+	1.39684i
$615$	719871.	−	238715.i	1.90329	−	0.631146i
$616$	110662.	−	92856.6i	0.291634	−	0.244710i
$617$	134093.	−	368417.i	0.352237	−	0.967763i	−0.629413	−	0.777071i	$-0.716705\pi$
$617$	134093.	−	368417.i	0.352237	−	0.967763i	0.981650	−	0.190692i	$-0.0610732\pi$
$618$	−25097.7	+	869142.i	−0.0657140	+	2.27569i
$619$	−969.457	+	5498.07i	−0.00253016	+	0.0143492i	−0.986047	−	0.166469i	$-0.946763\pi$
$619$	−969.457	+	5498.07i	−0.00253016	+	0.0143492i	0.983517	+	0.180818i	$0.0578746\pi$
$620$		−	1.20795e6i		−	3.14242i
$621$	117396.	−	252191.i	0.304417	−	0.653952i
$622$	489699.			1.26575
$623$	60885.5	+	10735.8i	0.156869	+	0.0276603i
$624$	12464.1	+	23103.9i	0.0320105	+	0.0593358i
$625$	352498.	+	128299.i	0.902396	+	0.328445i
$626$	−386472.	−	460579.i	−0.986209	−	1.17532i
$627$	−264364.	−	54526.0i	−0.672461	−	0.138698i
$628$	−678019.	+	246779.i	−1.71918	+	0.625732i
$629$	−152177.	−	87859.2i	−0.384633	−	0.222068i
$630$	−74154.6	+	313499.i	−0.186835	+	0.789868i
$631$	327793.	+	567755.i	0.823269	+	1.42594i	0.903235	+	0.429145i	$0.141185\pi$
$631$	327793.	+	567755.i	0.823269	+	1.42594i	−0.0799669	+	0.996798i	$0.525481\pi$
$632$	−275740.	+	328614.i	−0.690345	+	0.822721i
$633$	51673.2	+	352229.i	0.128961	+	0.879058i
$634$	45182.7	+	256244.i	0.112407	+	0.637492i
$635$	−652571.	+	115066.i	−1.61838	+	0.285364i
$636$	−132090.	−	166979.i	−0.326554	−	0.412808i
$637$	7170.04	+	6016.38i	0.0176703	+	0.0148271i
$638$	12989.6	−	7499.53i	0.0319119	−	0.0184244i
$639$	−123480.	−	81136.3i	−0.302410	−	0.198707i
$640$	141390.	−	244895.i	0.345192	−	0.597889i
$641$	58215.2	+	159945.i	0.141684	+	0.389273i	0.990156	−	0.139966i	$-0.0446995\pi$
$641$	58215.2	+	159945.i	0.141684	+	0.389273i	−0.848472	+	0.529240i	$0.822477\pi$
$642$	−538155.	−	478705.i	−1.30568	−	1.16144i
$643$	590812.	−	495750.i	1.42898	−	1.19906i	0.482675	−	0.875800i	$-0.339665\pi$
$643$	590812.	−	495750.i	1.42898	−	1.19906i	0.946310	−	0.323261i	$-0.104779\pi$
$644$	77235.4	−	212203.i	0.186228	−	0.511657i
$645$	158642.	+	97803.8i	0.381329	+	0.235091i
$646$	252808.	−	1.43375e6i	0.605796	−	3.43564i
$647$		−	205603.i		−	0.491159i	−0.969377	−	0.245579i	$-0.921022\pi$
$647$		−	205603.i		−	0.491159i	0.969377	−	0.245579i	$-0.0789782\pi$
$648$	−1.05981e6	+	458265.i	−2.52393	+	1.09136i
$649$	−187170.			−0.444372
$650$	20480.5	+	3611.26i	0.0484745	+	0.00854737i
$651$	−60320.2	+	97842.1i	−0.142331	+	0.230868i
$652$	−1.67648e6	−	610190.i	−3.94370	−	1.43539i
$653$	−240608.	−	286746.i	−0.564266	−	0.672467i	0.406177	−	0.913794i	$-0.366862\pi$
$653$	−240608.	−	286746.i	−0.564266	−	0.672467i	−0.970444	+	0.241328i	$0.922417\pi$
$654$	67260.3	−	75613.4i	0.157255	−	0.176784i
$655$	−929247.	+	338218.i	−2.16595	+	0.788342i
$656$	1.38762e6	+	801142.i	3.22450	+	1.86167i
$657$	−447381.	−	25859.1i	−1.03645	−	0.0599078i
$658$	−206526.	−	357714.i	−0.477005	−	0.826197i
$659$	−341921.	+	407485.i	−0.787326	+	0.938299i	−0.999240	−	0.0389896i	$-0.987586\pi$
$659$	−341921.	+	407485.i	−0.787326	+	0.938299i	0.211913	+	0.977288i	$0.432031\pi$
$660$	548015.	−	433511.i	1.25807	−	0.995203i
$661$	−63363.3	−	359351.i	−0.145022	−	0.822463i	−0.967349	−	0.253447i	$-0.918436\pi$
$661$	−63363.3	−	359351.i	−0.145022	−	0.822463i	0.822327	−	0.569015i	$-0.192676\pi$
$662$	949921.	−	167497.i	2.16756	−	0.382200i
$663$	−13685.7	+	2007.75i	−0.0311345	+	0.00456754i
$664$	−703769.	−	590532.i	−1.59622	−	1.33939i
$665$	252210.	−	145614.i	0.570322	−	0.329275i
$666$	203583.	−	215976.i	0.458980	−	0.486920i
$667$	6986.82	−	12101.5i	0.0157046	−	0.0272012i
$668$	619871.	+	1.70308e6i	1.38915	+	3.81665i
$669$	−101535.	+	492284.i	−0.226864	+	1.09993i
$670$	626670.	−	525839.i	1.39601	−	1.17139i
$671$	10614.2	−	29162.3i	0.0235745	−	0.0647703i
$672$	−265690.	+	143334.i	−0.588350	+	0.317403i
$673$	−41086.6	+	233014.i	−0.0907131	+	0.514459i	0.905264	+	0.424850i	$0.139673\pi$
$673$	−41086.6	+	233014.i	−0.0907131	+	0.514459i	−0.995977	+	0.0896096i	$0.971438\pi$
$674$		−	993546.i		−	2.18710i
$675$	−122130.	+	457005.i	−0.268050	+	1.00303i
$676$	1.13032e6			2.47348
$677$	469839.	+	82845.2i	1.02511	+	0.180755i	0.660832	−	0.750534i	$-0.270204\pi$
$677$	469839.	+	82845.2i	1.02511	+	0.180755i	0.364281	+	0.931289i	$0.381315\pi$
$678$	2337.78	+	67.5068i	0.00508562	+	0.000146855i
$679$	−184781.	−	67254.7i	−0.400791	−	0.145876i
$680$	1.44374e6	+	1.72058e6i	3.12227	+	3.72097i
$681$	−33919.3	−	102287.i	−0.0731397	−	0.220560i
$682$	328930.	−	119721.i	0.707188	−	0.257395i
$683$	−303490.	−	175220.i	−0.650584	−	0.375615i	0.138096	−	0.990419i	$-0.455902\pi$
$683$	−303490.	−	175220.i	−0.650584	−	0.375615i	−0.788680	+	0.614804i	$0.789235\pi$
$684$	1.60851e6	+	693003.i	3.43805	+	1.48123i
$685$	402803.	+	697674.i	0.858442	+	1.48687i
$686$	−327955.	+	390841.i	−0.696892	+	0.830524i
$687$	437248.	+	173596.i	0.926433	+	0.367812i
$688$	68371.0	+	387751.i	0.144442	+	0.819174i
$689$	2528.51	−	445.845i	0.00532632	−	0.000939173i
$690$	337265.	−	849493.i	0.708391	−	1.78427i
$691$	−93314.5	−	78300.2i	−0.195431	−	0.163986i	0.539821	−	0.841780i	$-0.318492\pi$
$691$	−93314.5	−	78300.2i	−0.195431	−	0.163986i	−0.735252	+	0.677794i	$0.762936\pi$
$692$	−1.20563e6	+	696071.i	−2.51769	+	1.45359i
$693$	−66036.5	+	7748.06i	−0.137505	+	0.0161334i
$694$	216128.	−	374345.i	0.448738	−	0.777236i
$695$	−236048.	−	648535.i	−0.488686	−	1.34265i
$696$	−55053.3	+	18256.1i	−0.113649	+	0.0376869i
$697$	−646740.	+	542680.i	−1.33126	+	1.11706i
$698$	−332985.	+	914868.i	−0.683460	+	1.87779i
$699$	6934.14	−	240131.i	0.0141918	−	0.491466i
$700$	−66683.2	+	378179.i	−0.136088	+	0.771794i
$701$		−	430379.i		−	0.875820i	−0.899019	−	0.437910i	$-0.855719\pi$
$701$		−	430379.i		−	0.875820i	0.899019	−	0.437910i	$-0.144281\pi$
$702$	2020.90	−	23276.2i	0.00410082	−	0.0472322i
$703$	−268314.			−0.542916
$704$	318015.	+	56074.7i	0.641656	+	0.113141i
$705$	−565345.	−	1.04794e6i	−1.13746	−	2.10843i
$706$	−194238.	−	70696.8i	−0.389695	−	0.141837i
$707$	166081.	+	197928.i	0.332262	+	0.395975i
$708$	1.18942e6	+	245323.i	2.37285	+	0.489409i
$709$	701376.	−	255280.i	1.39527	−	0.507837i	0.468500	−	0.883463i	$-0.344795\pi$
$709$	701376.	−	255280.i	1.39527	−	0.507837i	0.926771	+	0.375626i	$0.122572\pi$
$710$	−420423.	−	242731.i	−0.834007	−	0.481514i
$711$	189122.	−	56710.4i	0.374114	−	0.112182i
$712$	364038.	+	630532.i	0.718103	+	1.24379i
$713$	209619.	−	249815.i	0.412337	−	0.491404i
$714$	−52052.5	−	354814.i	−0.102105	−	0.695992i
$715$	1463.24	+	8298.42i	0.00286221	+	0.0162324i
$716$	−292483.	+	51572.6i	−0.570524	+	0.100599i
$717$	−19672.3	−	24868.4i	−0.0382663	−	0.0483738i
$718$	127555.	+	107031.i	0.247428	+	0.207617i
$719$	−41439.1	+	23924.9i	−0.0801590	+	0.0462798i	−0.539544	−	0.841958i	$-0.681403\pi$
$719$	−41439.1	+	23924.9i	−0.0801590	+	0.0462798i	0.459385	+	0.888237i	$0.348070\pi$
$720$	−1.75289e6	+	881301.i	−3.38134	+	1.70004i
$721$	96810.0	−	167680.i	0.186230	−	0.322560i
$722$	−427964.	−	1.17582e6i	−0.820981	−	2.25563i
$723$	579144.	+	515166.i	1.10792	+	0.985532i
$724$	−63441.0	+	53233.3i	−0.121030	+	0.101556i
$725$	−8127.22	+	22329.4i	−0.0154620	+	0.0424816i
$726$	−664018.	−	409371.i	−1.25982	−	0.776682i
$727$	48735.6	−	276393.i	0.0922098	−	0.522948i	−0.903357	−	0.428890i	$-0.858905\pi$
$727$	48735.6	−	276393.i	0.0922098	−	0.522948i	0.995567	−	0.0940583i	$-0.0299840\pi$
$728$		−	11303.6i		−	0.0213281i
$729$	523489.	+	91591.7i	0.985036	+	0.172346i
$730$	−1.47240e6			−2.76299
$731$	−204310.	−	36025.4i	−0.382344	−	0.0674176i
$732$	−105674.	+	171408.i	−0.197218	+	0.319896i
$733$	−440523.	−	160337.i	−0.819900	−	0.298419i	−0.102193	−	0.994765i	$-0.532586\pi$
$733$	−440523.	−	160337.i	−0.819900	−	0.298419i	−0.717707	+	0.696345i	$0.754808\pi$
$734$	−932293.	−	1.11106e6i	−1.73046	−	2.06228i
$735$	−464926.	+	522665.i	−0.860615	+	0.967495i
$736$	804851.	−	292942.i	1.48580	−	0.540787i
$737$	146221.	+	84421.0i	0.269201	+	0.155423i
$738$	−640561.	−	1.27406e6i	−1.17611	−	2.33925i
$739$	−23646.7	−	40957.4i	−0.0432995	−	0.0749969i	0.843563	−	0.537030i	$-0.180454\pi$
$739$	−23646.7	−	40957.4i	−0.0432995	−	0.0749969i	−0.886863	+	0.462033i	$0.847120\pi$
$740$	446462.	−	532072.i	0.815306	−	0.971644i
$741$	−16564.9	+	13103.8i	−0.0301684	+	0.0238649i
$742$	11558.9	+	65553.8i	0.0209947	+	0.119067i
$743$	556406.	−	98109.4i	1.00789	−	0.177719i	0.354756	−	0.934959i	$-0.384564\pi$
$743$	556406.	−	98109.4i	1.00789	−	0.177719i	0.653136	+	0.757240i	$0.273453\pi$
$744$	−1.33927e6	+	196476.i	−2.41948	+	0.354946i
$745$	709854.	+	595638.i	1.27896	+	1.07317i
$746$	−1.09909e6	+	634563.i	−1.97496	+	1.14024i
$747$	121452.	+	405029.i	0.217653	+	0.725847i
$748$	−388919.	+	673628.i	−0.695114	+	1.20397i
$749$	54855.2	+	150713.i	0.0977810	+	0.268651i
$750$	−11560.5	+	56050.1i	−0.0205521	+	0.0996447i
$751$	−243878.	+	204638.i	−0.432408	+	0.362833i	−0.832859	−	0.553485i	$-0.813298\pi$
$751$	−243878.	+	204638.i	−0.432408	+	0.362833i	0.400452	+	0.916318i	$0.368853\pi$
$752$	860380.	−	2.36387e6i	1.52144	−	4.18012i
$753$	102294.	−	55185.7i	0.180410	−	0.0973277i
$754$	203.800	−	1155.81i	0.000358477	−	0.00203302i
$755$			295854.i			0.519019i
$756$	429803.	+	37316.6i	0.752014	+	0.0652918i
$757$	55832.2			0.0974301			0.0487151	−	0.998813i	$-0.484487\pi$
$757$	55832.2			0.0974301			0.0487151	+	0.998813i	$0.484487\pi$
$758$	1.30047e6	+	229309.i	2.26341	+	0.399100i
$759$	188563.	+	5445.05i	0.327321	+	0.00945188i
$760$	3.22279e6	+	1.17300e6i	5.57963	+	2.03082i
$761$	−357987.	−	426632.i	−0.618156	−	0.736689i	0.362597	−	0.931946i	$-0.381890\pi$
$761$	−357987.	−	426632.i	−0.618156	−	0.736689i	−0.980752	+	0.195257i	$0.937446\pi$
$762$	392162.	+	1.18261e6i	0.675392	+	2.03671i
$763$	−21175.9	+	7707.41i	−0.0363742	+	0.0132391i
$764$	391249.	+	225887.i	0.670295	+	0.386995i
$765$	−120467.	−	1.02674e6i	−0.205847	−	1.75443i
$766$	−168637.	−	292087.i	−0.287405	−	0.497800i
$767$	−9413.97	+	11219.1i	−0.0160023	+	0.0190708i
$768$	292633.	+	116181.i	0.496136	+	0.196976i
$769$	57418.1	+	325634.i	0.0970948	+	0.550652i	0.994085	+	0.108602i	$0.0346374\pi$
$769$	57418.1	+	325634.i	0.0970948	+	0.550652i	−0.896991	+	0.442050i	$0.854251\pi$
$770$	−215143.	+	37935.6i	−0.362866	+	0.0639831i
$771$	−31729.3	+	79918.8i	−0.0533767	+	0.134444i
$772$	−854458.	−	716975.i	−1.43369	−	1.20301i
$773$	919517.	−	530884.i	1.53887	−	0.888465i	0.539961	−	0.841690i	$-0.318439\pi$
$773$	919517.	−	530884.i	1.53887	−	0.888465i	0.998905	−	0.0467747i	$-0.0148943\pi$
$774$	138653.	−	321823.i	0.231444	−	0.537198i
$775$	−277278.	+	480259.i	−0.461648	+	0.799598i
$776$	−792021.	−	2.17606e6i	−1.31527	−	3.61366i
$777$	−62732.5	+	20802.6i	−0.103908	+	0.0344569i
$778$	−374309.	+	314083.i	−0.618403	+	0.518901i
$779$	−440914.	+	1.21140e6i	−0.726573	+	1.99624i
$780$	1578.17	−	54652.6i	0.00259397	−	0.0898300i
$781$	17398.9	−	98673.9i	0.0285246	−	0.161771i
$782$			1.01744e6i			1.66378i
$783$	25790.8	+	6892.36i	0.0420671	+	0.0112420i
$784$	−1.47786e6			−2.40437
$785$	640420.	+	112923.i	1.03926	+	0.183250i
$786$	882814.	+	1.63642e6i	1.42897	+	2.64880i
$787$	375416.	+	136640.i	0.606127	+	0.220612i	0.626808	−	0.779174i	$-0.284361\pi$
$787$	375416.	+	136640.i	0.606127	+	0.220612i	−0.0206809	+	0.999786i	$0.506583\pi$
$788$	−1.70874e6	−	2.03639e6i	−2.75184	−	3.27951i
$789$	−749269.	−	154540.i	−1.20360	−	0.248248i
$790$	609606.	−	221879.i	0.976777	−	0.355518i
$791$	−451.018	−	260.395i	−0.000720843	−	0.000416179i
$792$	−569777.	−	537082.i	−0.908353	−	0.856230i
$793$	−1214.16	−	2102.98i	−0.00193076	−	0.00334418i
$794$	−1.07134e6	+	1.27677e6i	−1.69937	+	2.02522i
$795$	27852.6	+	189857.i	0.0440689	+	0.300394i
$796$	143332.	+	812878.i	0.226213	+	1.28292i
$797$	−969956.	+	171029.i	−1.52699	+	0.269249i	−0.873175	−	0.487407i	$-0.837943\pi$
$797$	−969956.	+	171029.i	−1.52699	+	0.269249i	−0.653813	+	0.756657i	$0.726832\pi$
$798$	−339726.	−	429459.i	−0.533486	−	0.674397i
$799$	1.01538e6	+	852006.i	1.59051	+	1.33459i
$800$	−1.26137e6	+	728251.i	−1.97089	+	1.13789i
$801$	19337.3	−	334549.i	0.0301392	−	0.521428i
$802$	1.00747e6	−	1.74499e6i	1.56633	−	2.71296i
$803$	−103938.	−	285566.i	−0.161191	−	0.442869i
$804$	−818556.	−	728130.i	−1.26630	−	1.12641i
$805$	−155911.	+	130825.i	−0.240594	+	0.201882i
$806$	9367.83	−	25737.9i	0.0144201	−	0.0396190i
$807$	−107851.	−	66490.7i	−0.165606	−	0.102097i
$808$	−528368.	+	2.99653e6i	−0.809309	+	4.58982i
$809$		−	321706.i		−	0.491544i	−0.969328	−	0.245772i	$-0.920959\pi$
$809$		−	321706.i		−	0.491544i	0.969328	−	0.245772i	$-0.0790414\pi$
$810$	1.73451e6	+	201186.i	2.64367	+	0.306639i
$811$	−183034.			−0.278285			−0.139143	−	0.990272i	$-0.544435\pi$
$811$	−183034.			−0.278285			−0.139143	+	0.990272i	$0.544435\pi$
$812$	21342.3	+	3763.23i	0.0323690	+	0.00570753i
$813$	85671.2	−	138963.i	0.129615	−	0.210241i
$814$	189135.	+	68839.7i	0.285446	+	0.103894i
$815$	1.03357e6	+	1.23176e6i	1.55605	+	1.85443i
$816$	1.45157e6	−	1.63184e6i	2.18001	−	2.45075i
$817$	−297680.	+	108347.i	−0.445970	+	0.162320i
$818$	1.33772e6	+	772332.i	1.99921	+	1.15424i
$819$	−2856.97	+	4347.99i	−0.00425930	+	0.00648217i
$820$	−1.66857e6	−	2.89006e6i	−2.48152	−	4.29812i
$821$	472182.	−	562724.i	0.700523	−	0.834851i	−0.292062	−	0.956399i	$-0.594341\pi$
$821$	472182.	−	562724.i	0.700523	−	0.834851i	0.992586	+	0.121548i	$0.0387858\pi$
$822$	1.18799e6	−	939763.i	1.75820	−	1.39083i
$823$	−188428.	−	1.06863e6i	−0.278192	−	1.57771i	−0.728635	−	0.684902i	$-0.759845\pi$
$823$	−188428.	−	1.06863e6i	−0.278192	−	1.57771i	0.450443	−	0.892805i	$-0.351266\pi$
$824$	2.24551e6	−	395945.i	3.30721	−	0.583150i
$825$	−317392.	+	46562.5i	−0.466324	+	0.0684114i
$826$	−290865.	−	244065.i	−0.426316	−	0.357722i
$827$	−126278.	+	72906.7i	−0.184636	+	0.106600i	−0.589469	−	0.807791i	$-0.700663\pi$
$827$	−126278.	+	72906.7i	−0.184636	+	0.106600i	0.404833	+	0.914391i	$0.367330\pi$
$828$	−1.19114e6	−	281752.i	−1.73742	−	0.410966i
$829$	−403873.	+	699529.i	−0.587673	+	1.01788i	0.406863	+	0.913489i	$0.366623\pi$
$829$	−403873.	+	699529.i	−0.587673	+	1.01788i	−0.994536	+	0.104391i	$0.966711\pi$
$830$	475181.	+	1.30555e6i	0.689767	+	1.89512i
$831$	−265024.	+	1.28494e6i	−0.383780	+	1.86072i
$832$	19356.2	−	16241.8i	0.0279623	−	0.0234632i
$833$	266331.	−	731739.i	0.383824	−	1.05455i
$834$	−1.14208e6	+	616129.i	−1.64197	+	0.885808i
$835$	283646.	−	1.60864e6i	0.406822	−	2.30720i
$836$			1.18772e6i			1.69943i
$837$	564818.	+	262925.i	0.806228	+	0.375301i
$838$	−654446.			−0.931936
$839$	−683160.	−	120459.i	−0.970506	−	0.171126i	−0.334148	−	0.942520i	$-0.608449\pi$
$839$	−683160.	−	120459.i	−0.970506	−	0.171126i	−0.636358	+	0.771394i	$0.719560\pi$
$840$	844441.	+	24384.5i	1.19677	+	0.0345585i
$841$	−663367.	−	241446.i	−0.937911	−	0.341372i
$842$	1.33110e6	+	1.58634e6i	1.87753	+	2.23755i
$843$	3464.86	+	10448.6i	0.00487563	+	0.0147030i
$844$	1.47198e6	−	535756.i	2.06641	−	0.752112i
$845$	−882246.	−	509365.i	−1.23559	−	0.713371i
$846$	−1.79525e6	+	1.33774e6i	−2.50833	+	1.86910i
$847$	86852.2	+	150432.i	0.121064	+	0.209689i
$848$	−260584.	+	310552.i	−0.362373	+	0.431859i
$849$	−905053.	−	359324.i	−1.25562	−	0.498506i
$850$	−300443.	−	1.70390e6i	−0.415838	−	2.35833i
$851$	184665.	−	32561.4i	0.254991	−	0.0449618i
$852$	−239898.	+	604247.i	−0.330481	+	0.832406i
$853$	573354.	+	481101.i	0.787998	+	0.661208i	0.945249	−	0.326350i	$-0.105819\pi$
$853$	573354.	+	481101.i	0.787998	+	0.661208i	−0.157251	+	0.987559i	$0.550263\pi$
$854$	54521.5	−	31478.0i	0.0747571	−	0.0431610i
$855$	−943193.	−	1.26576e6i	−1.29023	−	1.73149i
$856$	−944388.	+	1.63573e6i	−1.28885	+	2.23236i
$857$	−84810.3	−	233014.i	−0.115475	−	0.317264i	0.868469	−	0.495744i	$-0.165104\pi$
$857$	−84810.3	−	233014.i	−0.115475	−	0.317264i	−0.983944	+	0.178479i	$0.942882\pi$
$858$	15038.6	−	4986.93i	0.0204284	−	0.00677421i
$859$	842217.	−	706704.i	1.14140	−	0.957748i	0.141916	−	0.989879i	$-0.454674\pi$
$859$	842217.	−	706704.i	1.14140	−	0.957748i	0.999484	+	0.0321302i	$0.0102291\pi$
$860$	280472.	−	770590.i	0.379221	−	1.04190i
$861$	−9165.78	+	317413.i	−0.0123641	+	0.428173i
$862$	54189.9	−	307326.i	0.0729296	−	0.413604i
$863$		−	337849.i		−	0.453629i	−0.973938	−	0.226814i	$-0.927169\pi$
$863$		−	337849.i		−	0.453629i	0.973938	−	0.226814i	$-0.0728311\pi$
$864$	939434.	+	1.33977e6i	1.25846	+	1.79474i
$865$	1.25470e6			1.67691
$866$	7437.80	+	1311.48i	0.00991765	+	0.00174875i
$867$	189489.	+	351245.i	0.252085	+	0.467274i
$868$	475259.	+	172980.i	0.630799	+	0.229592i
$869$	86064.9	+	102568.i	0.113969	+	0.135823i
$870$	85905.8	+	17718.4i	0.113497	+	0.0234091i
$871$	12414.7	−	4518.58i	0.0163644	−	0.00595614i
$872$	−229827.	−	132691.i	−0.302252	−	0.174505i
$873$	−245343.	+	1.03722e6i	−0.321918	+	1.36095i
$874$	776796.	+	1.34545e6i	1.01691	+	1.76135i
$875$	8191.61	−	9762.38i	0.0106992	−	0.0127509i
$876$	286210.	+	1.95094e6i	0.372973	+	2.54236i
$877$	−53418.6	−	302952.i	−0.0694533	−	0.393889i	−0.999641	−	0.0268043i	$-0.991467\pi$
$877$	−53418.6	−	302952.i	−0.0694533	−	0.393889i	0.930187	−	0.367085i	$-0.119644\pi$
$878$	−481939.	+	84978.8i	−0.625177	+	0.110236i
$879$	−593853.	−	750710.i	−0.768601	−	0.971615i
$880$	−1.01921e6	−	855220.i	−1.31613	−	1.10436i
$881$	−1.14282e6	+	659808.i	−1.47240	+	0.850092i	−0.999518	−	0.0310333i	$-0.990120\pi$
$881$	−1.14282e6	+	659808.i	−1.47240	+	0.850092i	−0.472884	+	0.881125i	$0.656787\pi$
$882$	1.09923e6	+	722279.i	1.41303	+	0.928470i
$883$	−347184.	+	601340.i	−0.445285	+	0.771256i	−0.998072	−	0.0620666i	$-0.980231\pi$
$883$	−347184.	+	601340.i	−0.445285	+	0.771256i	0.552787	+	0.833322i	$0.313564\pi$
$884$	20816.6	+	57193.2i	0.0266383	+	0.0731880i
$885$	−817826.	−	727481.i	−1.04418	−	0.928827i
$886$	−100197.	+	84075.6i	−0.127641	+	0.107103i
$887$	196811.	−	540733.i	0.250150	−	0.687283i	−0.749529	−	0.661971i	$-0.769720\pi$
$887$	196811.	−	540733.i	0.250150	−	0.687283i	0.999680	−	0.0253113i	$-0.00805770\pi$
$888$	−662536.	−	408457.i	−0.840201	−	0.517988i
$889$	48177.4	−	273228.i	0.0609593	−	0.345717i
$890$		−	1.10105e6i		−	1.39004i
$891$	83421.0	+	350603.i	0.105080	+	0.441632i
$892$	2.21171e6			2.77971
$893$	1.99321e6	+	351456.i	2.49948	+	0.440726i
$894$	914362.	−	1.48314e6i	1.14405	−	1.85570i
$895$	251531.	+	91549.9i	0.314012	+	0.114291i
$896$	76105.3	+	90698.7i	0.0947979	+	0.112976i
$897$	9810.45	−	11028.8i	0.0121928	−	0.0137070i
$898$	−2.51596e6	+	915735.i	−3.11998	+	1.13558i
$899$	27103.1	+	15648.0i	0.0335352	+	0.0193615i
$900$	2.07799e6	+	120110.i	2.56542	+	0.148284i
$901$	−106804.	−	184990.i	−0.131564	−	0.227876i
$902$	621604.	−	740799.i	0.764013	−	0.910515i
$903$	−61198.2	+	48411.2i	−0.0750521	+	0.0593704i
$904$	−1064.99	−	6039.88i	−0.00130320	−	0.00739080i
$905$	73506.3	−	12961.1i	0.0897486	−	0.0158251i
$906$	550391.	−	80744.3i	0.670525	−	0.0983684i
$907$	−820336.	−	688344.i	−0.997189	−	0.836741i	−0.0105963	−	0.999944i	$-0.503373\pi$
$907$	−820336.	−	688344.i	−0.997189	−	0.836741i	−0.986592	+	0.163203i	$0.947817\pi$
$908$	−410651.	+	237090.i	−0.498083	+	0.287568i
$909$	960612.	−	1.01909e6i	1.16257	−	1.23334i
$910$	−8547.05	+	14803.9i	−0.0103213	+	0.0178770i
$911$	495638.	+	1.36175e6i	0.597211	+	1.64082i	0.756805	+	0.653641i	$0.226759\pi$
$911$	495638.	+	1.36175e6i	0.597211	+	1.64082i	−0.159594	+	0.987183i	$0.551019\pi$
$912$	673658.	−	3.26616e6i	0.809935	−	3.92689i
$913$	−219663.	+	184319.i	−0.263521	+	0.221120i
$914$	−890177.	+	2.44574e6i	−1.06558	+	2.92764i
$915$	159724.	−	86168.0i	0.190778	−	0.102921i
$916$	359458.	−	2.03859e6i	0.428408	−	2.42962i
$917$		−	414040.i		−	0.492384i
$918$	−1.87721e6	+	504327.i	−2.22755	+	0.598449i
$919$	−795804.			−0.942269			−0.471134	−	0.882061i	$-0.656155\pi$
$919$	−795804.			−0.942269			−0.471134	+	0.882061i	$0.656155\pi$
$920$	−2.36041e6	−	416204.i	−2.78877	−	0.491735i
$921$	−676110.	−	19523.7i	−0.797073	−	0.0230167i
$922$	654695.	+	238289.i	0.770153	+	0.280313i
$923$	−5039.50	−	6005.85i	−0.00591540	−	0.00704970i
$924$	92085.3	+	277693.i	0.107857	+	0.325253i
$925$	−299640.	+	109060.i	−0.350200	+	0.127462i
$926$	−83081.5	−	47967.2i	−0.0968908	−	0.0559399i
$927$	−963827.	−	415251.i	−1.12160	−	0.483227i
$928$	41098.4	+	71184.6i	0.0477232	+	0.0826590i
$929$	−709612.	+	845683.i	−0.822223	+	0.979887i	−0.999991	−	0.00418521i	$-0.998668\pi$
$929$	−709612.	+	845683.i	−0.822223	+	0.979887i	0.177768	+	0.984072i	$0.443112\pi$
$930$	1.90256e6	+	755355.i	2.19975	+	0.873343i
$931$	−206475.	−	1.17098e6i	−0.238214	−	1.35098i
$932$	−1.04099e6	+	183555.i	−1.19844	+	0.211317i
$933$	−218101.	+	549346.i	−0.250550	+	0.631077i
$934$	688506.	+	577725.i	0.789249	+	0.662258i
$935$	607124.	−	350523.i	0.694471	−	0.400953i
$936$	−60851.0	+	7139.64i	−0.0694569	+	0.00814938i
$937$	−88661.1	+	153565.i	−0.100984	+	0.174910i	−0.912090	−	0.409989i	$-0.865533\pi$
$937$	−88661.1	+	153565.i	−0.100984	+	0.174910i	0.811106	+	0.584899i	$0.198866\pi$
$938$	117148.	+	321861.i	0.133146	+	0.365816i
$939$	688804.	−	228413.i	0.781204	−	0.259054i
$940$	−4.01355e6	+	3.36777e6i	−4.54227	+	3.81142i
$941$	156015.	−	428647.i	0.176192	−	0.484084i	−0.819890	−	0.572522i	$-0.805965\pi$
$941$	156015.	−	428647.i	0.176192	−	0.484084i	0.996082	+	0.0884379i	$0.0281875\pi$
$942$	35293.5	−	1.22222e6i	0.0397734	−	1.37736i
$943$	156445.	−	887245.i	0.175930	−	0.997746i
$944$		−	2.31245e6i		−	2.59494i
$945$	−318657.	−	222812.i	−0.356828	−	0.249503i
$946$	237634.			0.265537
$947$	−924331.	−	162985.i	−1.03069	−	0.181738i	−0.367370	−	0.930075i	$-0.619742\pi$
$947$	−924331.	−	162985.i	−1.03069	−	0.181738i	−0.663319	+	0.748337i	$0.730853\pi$
$948$	−412489.	−	764605.i	−0.458982	−	0.850786i
$949$	−22344.8	−	8132.84i	−0.0248110	−	0.00903046i
$950$	−1.69819e6	−	2.02382e6i	−1.88165	−	2.24246i
$951$	−307578.	−	63439.1i	−0.340091	−	0.0701449i
$952$	−883697.	+	321639.i	−0.975056	+	0.354891i
$953$	−53349.3	−	30801.2i	−0.0587412	−	0.0339143i	0.470342	−	0.882484i	$-0.344131\pi$
$953$	−53349.3	−	30801.2i	−0.0587412	−	0.0339143i	−0.529083	+	0.848570i	$0.677464\pi$
$954$	345598.	−	103631.i	0.379730	−	0.113866i
$955$	−203587.	−	352623.i	−0.223225	−	0.386637i
$956$	−89683.3	+	106880.i	−0.0981287	+	0.116945i
$957$	2627.73	+	17911.8i	0.00286917	+	0.0195576i
$958$	−194320.	−	1.10204e6i	−0.211732	−	1.20079i
$959$	−332178.	+	58571.9i	−0.361188	+	0.0636872i
$960$	1.17160e6	+	1.48106e6i	1.27127	+	1.60705i
$961$	−147962.	−	124155.i	−0.160215	−	0.134436i
$962$	13639.2	−	7874.57i	0.0147380	−	0.00850896i
$963$	776695.	−	390500.i	0.837525	−	0.421083i
$964$	1.70531e6	−	2.95368e6i	1.83506	−	3.17841i
$965$	343832.	+	944670.i	0.369225	+	1.01444i
$966$	285931.	+	254344.i	0.306413	+	0.272563i
$967$	163927.	−	137551.i	0.175306	−	0.147099i	−0.550913	−	0.834563i	$-0.685720\pi$
$967$	163927.	−	137551.i	0.175306	−	0.147099i	0.726219	+	0.687463i	$0.241276\pi$
$968$	−699643.	+	1.92225e6i	−0.746665	+	2.05145i
$969$	1.49578e6	+	922159.i	1.59302	+	0.982106i
$970$	−608116.	+	3.44880e6i	−0.646313	+	3.66542i
$971$		−	597290.i		−	0.633500i	−0.948509	−	0.316750i	$-0.897408\pi$
$971$		−	597290.i		−	0.633500i	0.948509	−	0.316750i	$-0.102592\pi$
$972$	−70587.6	−	2.33735e6i	−0.0747129	−	2.47395i
$973$	288965.			0.305225
$974$	−651612.	−	114897.i	−0.686865	−	0.121113i
$975$	−13172.7	+	21366.7i	−0.0138569	+	0.0224765i
$976$	360294.	+	131136.i	0.378231	+	0.137665i
$977$	463336.	+	552182.i	0.485408	+	0.578487i	0.952043	−	0.305963i	$-0.0989784\pi$
$977$	463336.	+	552182.i	0.485408	+	0.578487i	−0.466635	+	0.884450i	$0.654534\pi$
$978$	2.00942e6	−	2.25897e6i	2.10084	−	2.36174i
$979$	213545.	−	77723.9i	0.222804	−	0.0810941i
$980$	2.66563e6	+	1.53900e6i	2.77554	+	1.60246i
$981$	54867.0	+	109129.i	0.0570129	+	0.113397i
$982$	1.58651e6	+	2.74791e6i	1.64520	+	2.84957i
$983$	217960.	−	259754.i	0.225564	−	0.268816i	−0.641379	−	0.767224i	$-0.721637\pi$
$983$	217960.	−	259754.i	0.225564	−	0.268816i	0.866943	+	0.498408i	$0.166082\pi$
$984$	−2.93286e6	+	2.32005e6i	−3.02901	+	2.39611i
$985$	416040.	+	2.35948e6i	0.428808	+	2.43189i
$986$	−96158.5	+	16955.3i	−0.0989085	+	0.0174402i
$987$	493266.	−	72363.9i	0.506345	−	0.0742827i
$988$	71193.3	+	59738.3i	0.0729332	+	0.0611982i
$989$	191728.	−	110694.i	0.196016	−	0.113170i
$990$	340111.	+	1.13423e6i	0.347017	+	1.15726i
$991$	−246687.	+	427275.i	−0.251188	+	0.435071i	−0.963853	−	0.266433i	$-0.914155\pi$
$991$	−246687.	+	427275.i	−0.251188	+	0.435071i	0.712665	+	0.701505i	$0.247488\pi$
$992$	656086.	+	1.80258e6i	0.666711	+	1.83177i
$993$	−235175.	+	1.14022e6i	−0.238502	+	1.15635i
$994$	155707.	−	130653.i	0.157592	−	0.132235i
$995$	254439.	−	699064.i	0.257002	−	0.706108i
$996$	1.63750e6	−	883396.i	1.65067	−	0.890506i
$997$	135947.	−	770996.i	0.136767	−	0.775643i	−0.836846	−	0.547438i	$-0.815603\pi$
$997$	135947.	−	770996.i	0.136767	−	0.775643i	0.973613	−	0.228205i	$-0.0732857\pi$
$998$		−	877277.i		−	0.880797i
$999$	151611.	+	324571.i	0.151915	+	0.325221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.2.11	✓	66
3.2	odd	2		81.5.f.a.8.1		66
27.13	even	9		81.5.f.a.71.1		66
27.14	odd	18	inner	27.5.f.a.14.11	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.11	✓	66	1.1	even	1	trivial
27.5.f.a.14.11	yes	66	27.14	odd	18	inner
81.5.f.a.8.1		66	3.2	odd	2
81.5.f.a.71.1		66	27.13	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.34334 + 1.29483i) q^{2} +(-4.72310 + 7.66109i) q^{3} +(37.2130 + 13.5444i) q^{4} +(-22.9421 - 27.3414i) q^{5} +(-44.6032 + 50.1424i) q^{6} +(14.0427 - 5.11111i) q^{7} +(152.408 + 87.9929i) q^{8} +(-36.3846 - 72.3682i) q^{9} +(-133.070 - 230.483i) q^{10} +(35.3079 - 42.0783i) q^{11} +(-279.526 + 221.121i) q^{12} +(-0.746352 - 4.23277i) q^{13} +(109.738 - 19.3498i) q^{14} +(317.823 - 46.6257i) q^{15} +(519.869 + 436.222i) q^{16} +(-309.675 + 178.791i) q^{17} +(-173.480 - 578.537i) q^{18} +(-273.006 + 472.860i) q^{19} +(-483.423 - 1328.19i) q^{20} +(-27.1682 + 131.722i) q^{21} +(313.762 - 263.278i) q^{22} +(130.510 - 358.573i) q^{23} +(-1393.96 + 752.014i) q^{24} +(-112.679 + 639.035i) q^{25} -32.0491i q^{26} +(726.268 + 63.0564i) q^{27} +591.797 q^{28} +(36.0636 + 6.35898i) q^{29} +(2394.25 + 69.1376i) q^{30} +(803.077 + 292.296i) q^{31} +(1442.80 + 1719.46i) q^{32} +(155.603 + 469.237i) q^{33} +(-2505.56 + 911.948i) q^{34} +(-461.914 - 266.686i) q^{35} +(-373.796 - 3185.85i) q^{36} +(245.703 + 425.571i) q^{37} +(-2617.05 + 3118.88i) q^{38} +(35.9528 + 14.2739i) q^{39} +(-1090.72 - 6185.80i) q^{40} +(2325.15 - 409.987i) q^{41} +(-370.064 + 932.105i) q^{42} +(444.443 + 372.932i) q^{43} +(1883.84 - 1087.63i) q^{44} +(-1143.91 + 2655.09i) q^{45} +(1422.67 - 2464.14i) q^{46} +(-1267.80 - 3483.25i) q^{47} +(-5797.33 + 1922.44i) q^{48} +(-1668.20 + 1399.79i) q^{49} +(-1654.88 + 4546.75i) q^{50} +(92.8928 - 3216.90i) q^{51} +(29.5565 - 167.623i) q^{52} +597.366i q^{53} +(5251.59 + 1403.44i) q^{54} -1960.52 q^{55} +(2589.96 + 456.680i) q^{56} +(-2333.19 - 4324.89i) q^{57} +(256.593 + 93.3924i) q^{58} +(-2190.28 - 2610.27i) q^{59} +(12458.7 + 2569.65i) q^{60} +(530.905 - 193.234i) q^{61} +(5518.80 + 3186.28i) q^{62} +(-880.819 - 830.277i) q^{63} +(2939.43 + 5091.23i) q^{64} +(-98.6069 + 117.515i) q^{65} +(535.064 + 3647.25i) q^{66} +(533.761 + 3027.11i) q^{67} +(-13945.6 + 2458.98i) q^{68} +(2130.65 + 2693.43i) q^{69} +(-3046.68 - 2556.47i) q^{70} +(1579.71 - 912.046i) q^{71} +(822.574 - 14231.1i) q^{72} +(2766.22 - 4791.24i) q^{73} +(1253.24 + 3443.25i) q^{74} +(-4363.51 - 3881.47i) q^{75} +(-16564.0 + 13898.9i) q^{76} +(280.750 - 771.353i) q^{77} +(245.531 + 151.371i) q^{78} +(-423.277 + 2400.52i) q^{79} -24221.8i q^{80} +(-3913.32 + 5266.18i) q^{81} +17605.3 q^{82} +(-5141.02 - 906.501i) q^{83} +(-2795.12 + 4533.81i) q^{84} +(11993.0 + 4365.10i) q^{85} +(2780.81 + 3314.04i) q^{86} +(-219.049 + 246.252i) q^{87} +(9083.80 - 3306.23i) q^{88} +(3582.86 + 2068.56i) q^{89} +(-11838.0 + 18016.1i) q^{90} +(-32.1149 - 55.6247i) q^{91} +(9713.34 - 11575.9i) q^{92} +(-6032.32 + 4771.90i) q^{93} +(-4799.67 - 27220.3i) q^{94} +(19192.0 - 3384.07i) q^{95} +(-19987.4 + 2932.22i) q^{96} +(-10080.0 - 8458.14i) q^{97} +(-14062.6 + 8119.07i) q^{98} +(-4329.79 - 1024.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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