LMFDB - Embedded newform 27.3.f.a.14.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,3,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.735696713773$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.3
Character	$\chi$	$=$	27.14
Dual form			27.3.f.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.115908 - 0.0204377i) q^{2} +(2.32380 + 1.89736i) q^{3} +(-3.74575 + 1.36334i) q^{4} +(3.98394 - 4.74788i) q^{5} +(0.308125 + 0.172426i) q^{6} +(-7.49258 - 2.72708i) q^{7} +(-0.814011 + 0.469969i) q^{8} +(1.80008 + 8.81815i) q^{9} +(0.364735 - 0.631740i) q^{10} +(-7.35571 - 8.76619i) q^{11} +(-11.2911 - 3.93889i) q^{12} +(-1.43358 + 8.13025i) q^{13} +(-0.924186 - 0.162959i) q^{14} +(18.2663 - 3.47416i) q^{15} +(12.1295 - 10.1779i) q^{16} +(20.7128 + 11.9585i) q^{17} +(0.388867 + 0.985304i) q^{18} +(6.12102 + 10.6019i) q^{19} +(-8.44988 + 23.2159i) q^{20} +(-12.2370 - 20.5533i) q^{21} +(-1.03175 - 0.865739i) q^{22} +(-5.04566 - 13.8628i) q^{23} +(-2.78330 - 0.452353i) q^{24} +(-2.32934 - 13.2103i) q^{25} +0.971660i q^{26} +(-12.5481 + 23.9070i) q^{27} +31.7833 q^{28} +(-17.5228 + 3.08975i) q^{29} +(2.04621 - 0.776004i) q^{30} +(-12.2356 + 4.45339i) q^{31} +(3.61462 - 4.30774i) q^{32} +(-0.460606 - 34.3273i) q^{33} +(2.64519 + 0.962769i) q^{34} +(-42.7978 + 24.7093i) q^{35} +(-18.7648 - 30.5765i) q^{36} +(8.53500 - 14.7831i) q^{37} +(0.926154 + 1.10375i) q^{38} +(-18.7573 + 16.1730i) q^{39} +(-1.01161 + 5.73715i) q^{40} +(30.2688 + 5.33721i) q^{41} +(-1.83843 - 2.13219i) q^{42} +(-30.5116 + 25.6022i) q^{43} +(39.5040 + 22.8076i) q^{44} +(49.0389 + 26.5844i) q^{45} +(-0.868158 - 1.50369i) q^{46} +(19.9668 - 54.8583i) q^{47} +(47.4976 - 0.637327i) q^{48} +(11.1657 + 9.36910i) q^{49} +(-0.539978 - 1.48358i) q^{50} +(25.4428 + 67.0888i) q^{51} +(-5.71447 - 32.4084i) q^{52} -91.2612i q^{53} +(-0.965824 + 3.02747i) q^{54} -70.9255 q^{55} +(7.38068 - 1.30141i) q^{56} +(-5.89158 + 36.2505i) q^{57} +(-1.96789 + 0.716253i) q^{58} +(-13.2814 + 15.8282i) q^{59} +(-63.6845 + 37.9166i) q^{60} +(32.8508 + 11.9567i) q^{61} +(-1.32719 + 0.766252i) q^{62} +(10.5605 - 70.9797i) q^{63} +(-31.3370 + 54.2773i) q^{64} +(32.8901 + 39.1969i) q^{65} +(-0.754959 - 3.96939i) q^{66} +(8.95370 - 50.7790i) q^{67} +(-93.8886 - 16.5551i) q^{68} +(14.5776 - 41.7879i) q^{69} +(-4.45561 + 3.73870i) q^{70} +(2.28181 + 1.31740i) q^{71} +(-5.60955 - 6.33208i) q^{72} +(-34.5072 - 59.7683i) q^{73} +(0.687144 - 1.88791i) q^{74} +(19.6518 - 35.1177i) q^{75} +(-37.3819 - 31.3671i) q^{76} +(31.2072 + 85.7410i) q^{77} +(-1.84358 + 2.25794i) q^{78} +(26.2964 + 149.134i) q^{79} -98.1375i q^{80} +(-74.5194 + 31.7468i) q^{81} +3.61748 q^{82} +(53.2469 - 9.38886i) q^{83} +(73.8580 + 60.3042i) q^{84} +(139.296 - 50.6997i) q^{85} +(-3.01328 + 3.59109i) q^{86} +(-46.5819 - 26.0671i) q^{87} +(10.1075 + 3.67882i) q^{88} +(-141.225 + 81.5361i) q^{89} +(6.22733 + 2.07910i) q^{90} +(32.9130 - 57.0070i) q^{91} +(37.7996 + 45.0478i) q^{92} +(-36.8828 - 12.8665i) q^{93} +(1.19313 - 6.76659i) q^{94} +(74.7224 + 13.1756i) q^{95} +(16.5730 - 3.15209i) q^{96} +(43.6738 - 36.6467i) q^{97} +(1.48567 + 0.857754i) q^{98} +(64.0607 - 80.6436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.115908	−	0.0204377i	0.0579540	−	0.0102189i	−0.144596	−	0.989491i	$-0.546188\pi$
$2$	0.115908	−	0.0204377i	0.0579540	−	0.0102189i	0.202550	+	0.979272i	$0.435077\pi$
$3$	2.32380	+	1.89736i	0.774600	+	0.632452i
$3$	2.32380	+	1.89736i	0.774600	+	0.632452i
$4$	−3.74575	+	1.36334i	−0.936438	+	0.340836i
$5$	3.98394	−	4.74788i	0.796788	−	0.949575i	−0.202772	−	0.979226i	$-0.564995\pi$
$5$	3.98394	−	4.74788i	0.796788	−	0.949575i	0.999560	+	0.0296506i	$0.00943948\pi$
$6$	0.308125	+	0.172426i	0.0513541	+	0.0287376i
$7$	−7.49258	−	2.72708i	−1.07037	−	0.389582i	−0.254054	−	0.967190i	$-0.581764\pi$
$7$	−7.49258	−	2.72708i	−1.07037	−	0.389582i	−0.816315	+	0.577608i	$0.803986\pi$
$8$	−0.814011	+	0.469969i	−0.101751	+	0.0587462i
$9$	1.80008	+	8.81815i	0.200009	+	0.979794i
$10$	0.364735	−	0.631740i	0.0364735	−	0.0631740i
$11$	−7.35571	−	8.76619i	−0.668701	−	0.796927i	0.319906	−	0.947449i	$-0.396349\pi$
$11$	−7.35571	−	8.76619i	−0.668701	−	0.796927i	−0.988607	+	0.150523i	$0.951904\pi$
$12$	−11.2911	−	3.93889i	−0.940927	−	0.328241i
$13$	−1.43358	+	8.13025i	−0.110276	+	0.625403i	0.878706	+	0.477364i	$0.158408\pi$
$13$	−1.43358	+	8.13025i	−0.110276	+	0.625403i	−0.988981	+	0.148040i	$0.952704\pi$
$14$	−0.924186	−	0.162959i	−0.0660133	−	0.0116399i
$15$	18.2663	−	3.47416i	1.21775	−	0.231611i
$16$	12.1295	−	10.1779i	0.758095	−	0.636117i
$17$	20.7128	+	11.9585i	1.21840	+	0.703443i	0.964576	−	0.263807i	$-0.0849782\pi$
$17$	20.7128	+	11.9585i	1.21840	+	0.703443i	0.253824	+	0.967250i	$0.418311\pi$
$18$	0.388867	+	0.985304i	0.0216037	+	0.0547391i
$19$	6.12102	+	10.6019i	0.322159	+	0.557995i	0.980933	−	0.194345i	$-0.0622582\pi$
$19$	6.12102	+	10.6019i	0.322159	+	0.557995i	−0.658774	+	0.752341i	$0.728925\pi$
$20$	−8.44988	+	23.2159i	−0.422494	+	1.16079i
$21$	−12.2370	−	20.5533i	−0.582715	−	0.978727i
$22$	−1.03175	−	0.865739i	−0.0468976	−	0.0393518i
$23$	−5.04566	−	13.8628i	−0.219377	−	0.602732i	0.780368	−	0.625320i	$-0.215032\pi$
$23$	−5.04566	−	13.8628i	−0.219377	−	0.602732i	−0.999745	+	0.0225880i	$0.992809\pi$
$24$	−2.78330	−	0.452353i	−0.115971	−	0.0188481i
$25$	−2.32934	−	13.2103i	−0.0931735	−	0.528413i
$26$			0.971660i			0.0373715i
$27$	−12.5481	+	23.9070i	−0.464745	+	0.885444i
$28$	31.7833			1.13512
$29$	−17.5228	+	3.08975i	−0.604235	+	0.106543i	−0.467393	−	0.884050i	$-0.654807\pi$
$29$	−17.5228	+	3.08975i	−0.604235	+	0.106543i	−0.136843	+	0.990593i	$0.543695\pi$
$30$	2.04621	−	0.776004i	0.0682069	−	0.0258668i
$31$	−12.2356	+	4.45339i	−0.394697	+	0.143658i	−0.531741	−	0.846907i	$-0.678462\pi$
$31$	−12.2356	+	4.45339i	−0.394697	+	0.143658i	0.137044	+	0.990565i	$0.456240\pi$
$32$	3.61462	−	4.30774i	0.112957	−	0.134617i
$33$	−0.460606	−	34.3273i	−0.0139578	−	1.04022i
$34$	2.64519	+	0.962769i	0.0777996	+	0.0283167i
$35$	−42.7978	+	24.7093i	−1.22280	+	0.705981i
$36$	−18.7648	−	30.5765i	−0.521245	−	0.849346i
$37$	8.53500	−	14.7831i	0.230676	−	0.399542i	−0.727331	−	0.686286i	$-0.759240\pi$
$37$	8.53500	−	14.7831i	0.230676	−	0.399542i	0.958007	+	0.286744i	$0.0925730\pi$
$38$	0.926154	+	1.10375i	0.0243725	+	0.0290460i
$39$	−18.7573	+	16.1730i	−0.480957	+	0.414693i
$40$	−1.01161	+	5.73715i	−0.0252904	+	0.143429i
$41$	30.2688	+	5.33721i	0.738265	+	0.130176i	0.530121	−	0.847922i	$-0.322147\pi$
$41$	30.2688	+	5.33721i	0.738265	+	0.130176i	0.208144	+	0.978098i	$0.433258\pi$
$42$	−1.83843	−	2.13219i	−0.0437722	−	0.0507665i
$43$	−30.5116	+	25.6022i	−0.709571	+	0.595401i	−0.924479	−	0.381233i	$-0.875499\pi$
$43$	−30.5116	+	25.6022i	−0.709571	+	0.595401i	0.214908	+	0.976634i	$0.431055\pi$
$44$	39.5040	+	22.8076i	0.897818	+	0.518356i
$45$	49.0389	+	26.5844i	1.08975	+	0.590764i
$46$	−0.868158	−	1.50369i	−0.0188730	−	0.0326890i
$47$	19.9668	−	54.8583i	0.424825	−	1.16720i	−0.524089	−	0.851663i	$-0.675594\pi$
$47$	19.9668	−	54.8583i	0.424825	−	1.16720i	0.948914	−	0.315534i	$-0.102184\pi$
$48$	47.4976	−	0.637327i	0.989534	−	0.0132776i
$49$	11.1657	+	9.36910i	0.227871	+	0.191206i
$50$	−0.539978	−	1.48358i	−0.0107996	−	0.0296715i
$51$	25.4428	+	67.0888i	0.498878	+	1.31547i
$52$	−5.71447	−	32.4084i	−0.109894	−	0.623238i
$53$		−	91.2612i		−	1.72191i	−0.508681	−	0.860955i	$-0.669867\pi$
$53$		−	91.2612i		−	1.72191i	0.508681	−	0.860955i	$-0.330133\pi$
$54$	−0.965824	+	3.02747i	−0.0178856	+	0.0560642i
$55$	−70.9255			−1.28956
$56$	7.38068	−	1.30141i	0.131798	−	0.0232395i
$57$	−5.89158	+	36.2505i	−0.103361	+	0.635973i
$58$	−1.96789	+	0.716253i	−0.0339291	+	0.0123492i
$59$	−13.2814	+	15.8282i	−0.225109	+	0.268274i	−0.866764	−	0.498719i	$-0.833804\pi$
$59$	−13.2814	+	15.8282i	−0.225109	+	0.268274i	0.641655	+	0.766994i	$0.278248\pi$
$60$	−63.6845	+	37.9166i	−1.06141	+	0.631943i
$61$	32.8508	+	11.9567i	0.538538	+	0.196012i	0.596947	−	0.802281i	$-0.296380\pi$
$61$	32.8508	+	11.9567i	0.538538	+	0.196012i	−0.0584084	+	0.998293i	$0.518603\pi$
$62$	−1.32719	+	0.766252i	−0.0214063	+	0.0123589i
$63$	10.5605	−	70.9797i	0.167627	−	1.12666i
$64$	−31.3370	+	54.2773i	−0.489641	+	0.848083i
$65$	32.8901	+	39.1969i	0.506001	+	0.603029i
$66$	−0.754959	−	3.96939i	−0.0114388	−	0.0601423i
$67$	8.95370	−	50.7790i	0.133637	−	0.757895i	−0.842162	−	0.539225i	$-0.818717\pi$
$67$	8.95370	−	50.7790i	0.133637	−	0.757895i	0.975799	−	0.218670i	$-0.0701718\pi$
$68$	−93.8886	−	16.5551i	−1.38072	−	0.243457i
$69$	14.5776	−	41.7879i	0.211270	−	0.605621i
$70$	−4.45561	+	3.73870i	−0.0636516	+	0.0534100i
$71$	2.28181	+	1.31740i	0.0321381	+	0.0185549i	0.515983	−	0.856599i	$-0.327427\pi$
$71$	2.28181	+	1.31740i	0.0321381	+	0.0185549i	−0.483845	+	0.875154i	$0.660760\pi$
$72$	−5.60955	−	6.33208i	−0.0779104	−	0.0879456i
$73$	−34.5072	−	59.7683i	−0.472702	−	0.818743i	0.526810	−	0.849983i	$-0.323388\pi$
$73$	−34.5072	−	59.7683i	−0.472702	−	0.818743i	−0.999512	+	0.0312395i	$0.990055\pi$
$74$	0.687144	−	1.88791i	0.00928572	−	0.0255123i
$75$	19.6518	−	35.1177i	0.262024	−	0.468237i
$76$	−37.3819	−	31.3671i	−0.491867	−	0.412725i
$77$	31.2072	+	85.7410i	0.405288	+	1.11352i
$78$	−1.84358	+	2.25794i	−0.0236357	+	0.0289480i
$79$	26.2964	+	149.134i	0.332866	+	1.88778i	0.447360	+	0.894354i	$0.352364\pi$
$79$	26.2964	+	149.134i	0.332866	+	1.88778i	−0.114494	+	0.993424i	$0.536525\pi$
$80$		−	98.1375i		−	1.22672i
$81$	−74.5194	+	31.7468i	−0.919993	+	0.391936i
$82$	3.61748			0.0441157
$83$	53.2469	−	9.38886i	0.641529	−	0.113119i	0.156585	−	0.987664i	$-0.449951\pi$
$83$	53.2469	−	9.38886i	0.641529	−	0.113119i	0.484943	+	0.874546i	$0.338840\pi$
$84$	73.8580	+	60.3042i	0.879262	+	0.717908i
$85$	139.296	−	50.6997i	1.63878	−	0.596467i
$86$	−3.01328	+	3.59109i	−0.0350382	+	0.0417569i
$87$	−46.5819	−	26.0671i	−0.535424	−	0.299622i
$88$	10.1075	+	3.67882i	0.114858	+	0.0418047i
$89$	−141.225	+	81.5361i	−1.58679	+	0.916136i	−0.592962	+	0.805230i	$0.702042\pi$
$89$	−141.225	+	81.5361i	−1.58679	+	0.916136i	−0.993831	+	0.110906i	$0.964625\pi$
$90$	6.22733	+	2.07910i	0.0691925	+	0.0231011i
$91$	32.9130	−	57.0070i	0.361682	−	0.626451i
$92$	37.7996	+	45.0478i	0.410865	+	0.489650i
$93$	−36.8828	−	12.8665i	−0.396589	−	0.138349i
$94$	1.19313	−	6.76659i	0.0126929	−	0.0719850i
$95$	74.7224	+	13.1756i	0.786551	+	0.138690i
$96$	16.5730	−	3.15209i	0.172635	−	0.0328343i
$97$	43.6738	−	36.6467i	0.450246	−	0.377801i	−0.389281	−	0.921119i	$-0.627277\pi$
$97$	43.6738	−	36.6467i	0.450246	−	0.377801i	0.839527	+	0.543318i	$0.182832\pi$
$98$	1.48567	+	0.857754i	0.0151599	+	0.00875259i
$99$	64.0607	−	80.6436i	0.647078	−	0.814582i
$100$	26.7353	+	46.3070i	0.267353	+	0.463070i
$101$	−9.49911	+	26.0986i	−0.0940506	+	0.258402i	−0.977793	−	0.209571i	$-0.932793\pi$
$101$	−9.49911	+	26.0986i	−0.0940506	+	0.258402i	0.883743	+	0.467973i	$0.155016\pi$
$102$	4.32016	+	7.25614i	0.0423546	+	0.0711386i
$103$	62.8906	+	52.7715i	0.610589	+	0.512345i	0.894829	−	0.446408i	$-0.147297\pi$
$103$	62.8906	+	52.7715i	0.610589	+	0.512345i	−0.284241	+	0.958753i	$0.591742\pi$
$104$	−2.65401	−	7.29185i	−0.0255194	−	0.0701139i
$105$	−146.336	−	23.7832i	−1.39368	−	0.226506i
$106$	−1.86517	−	10.5779i	−0.0175960	−	0.0997916i
$107$			35.8639i			0.335177i	0.985857	+	0.167588i	$0.0535980\pi$
$107$			35.8639i			0.335177i	−0.985857	+	0.167588i	$0.946402\pi$
$108$	14.4087	−	106.657i	0.133414	−	0.987566i
$109$	1.41546			0.0129859			0.00649295	−	0.999979i	$-0.497933\pi$
$109$	1.41546			0.0129859			0.00649295	+	0.999979i	$0.497933\pi$
$110$	−8.22084	+	1.44956i	−0.0747349	+	0.0131778i
$111$	47.8823	−	18.1589i	0.431372	−	0.163594i
$112$	−118.637	+	43.1804i	−1.05926	+	0.385540i
$113$	−95.7961	+	114.165i	−0.847753	+	1.01031i	0.152006	+	0.988380i	$0.451427\pi$
$113$	−95.7961	+	114.165i	−0.847753	+	1.01031i	−0.999759	+	0.0219332i	$0.993018\pi$
$114$	0.0579947	+	4.32213i	0.000508725	+	0.0379134i
$115$	−85.9207	−	31.2726i	−0.747136	−	0.271935i
$116$	61.4238	−	35.4630i	0.529515	−	0.305716i
$117$	−74.2743	+	1.99359i	−0.634823	+	0.0170393i
$118$	−1.21593	+	2.10606i	−0.0103045	+	0.0178479i
$119$	−122.580	−	146.086i	−1.03009	−	1.22761i
$120$	−13.2362	+	11.4126i	−0.110302	+	0.0951050i
$121$	−1.72825	+	9.80142i	−0.0142831	+	0.0810035i
$122$	4.05204	+	0.714485i	0.0332135	+	0.00585643i
$123$	60.2121	+	69.8334i	0.489530	+	0.567751i
$124$	39.7600	−	33.3626i	0.320646	−	0.269054i
$125$	62.1878	+	35.9041i	0.497502	+	0.287233i
$126$	−0.226617	−	8.44295i	−0.00179855	−	0.0670075i
$127$	−8.57044	−	14.8444i	−0.0674838	−	0.116885i	0.830309	−	0.557303i	$-0.188164\pi$
$127$	−8.57044	−	14.8444i	−0.0674838	−	0.116885i	−0.897793	+	0.440417i	$0.854830\pi$
$128$	−10.2161	+	28.0685i	−0.0798133	+	0.219285i
$129$	−119.479	+	1.60318i	−0.926196	+	0.0124278i
$130$	4.61332	+	3.87104i	0.0354871	+	0.0297772i
$131$	−49.9104	−	137.128i	−0.380995	−	1.04678i	−0.970938	−	0.239331i	$-0.923072\pi$
$131$	−49.9104	−	137.128i	−0.380995	−	1.04678i	0.589943	−	0.807445i	$-0.299150\pi$
$132$	48.5252	+	127.954i	0.367615	+	0.969345i
$133$	−16.9500	−	96.1282i	−0.127444	−	0.722768i
$134$		−	6.06869i		−	0.0452887i
$135$	63.5165	+	154.821i	0.470493	+	1.14682i
$136$	−22.4806			−0.165298
$137$	85.6934	−	15.1101i	0.625499	−	0.110292i	0.148091	−	0.988974i	$-0.452687\pi$
$137$	85.6934	−	15.1101i	0.625499	−	0.110292i	0.477409	+	0.878681i	$0.341576\pi$
$138$	0.835617	−	5.14148i	0.00605519	−	0.0372571i
$139$	−34.6380	+	12.6072i	−0.249194	+	0.0906992i	−0.463597	−	0.886046i	$-0.653442\pi$
$139$	−34.6380	+	12.6072i	−0.249194	+	0.0906992i	0.214403	+	0.976745i	$0.431219\pi$
$140$	126.623	−	150.903i	0.904449	−	1.07788i
$141$	150.484	−	89.5955i	1.06727	−	0.635429i
$142$	0.291404	+	0.106062i	0.00205214	+	0.000746919i
$143$	81.8163	−	47.2367i	0.572142	−	0.330326i
$144$	111.584	+	88.6388i	0.774890	+	0.615548i
$145$	−55.1402	+	95.5056i	−0.380277	+	0.658659i
$146$	−5.22119	−	6.22237i	−0.0357616	−	0.0426190i
$147$	8.17024	+	42.9571i	0.0555798	+	0.292225i
$148$	−11.8156	+	67.0098i	−0.0798354	+	0.452769i
$149$	63.6158	+	11.2172i	0.426952	+	0.0752832i	0.382995	−	0.923750i	$-0.374893\pi$
$149$	63.6158	+	11.2172i	0.426952	+	0.0752832i	0.0439567	+	0.999033i	$0.486004\pi$
$150$	1.56007	−	4.47207i	0.0104005	−	0.0298138i
$151$	−118.320	+	99.2826i	−0.783579	+	0.657501i	−0.944147	−	0.329524i	$-0.893112\pi$
$151$	−118.320	+	99.2826i	−0.783579	+	0.657501i	0.160568	+	0.987025i	$0.448667\pi$
$152$	−9.96515	−	5.75338i	−0.0655602	−	0.0378512i
$153$	−68.1674	+	204.175i	−0.445538	+	1.33448i
$154$	5.36951	+	9.30027i	0.0348670	+	0.0603914i
$155$	−27.6018	+	75.8352i	−0.178076	+	0.489259i
$156$	48.2109	−	86.1529i	0.309044	−	0.552262i
$157$	−147.505	−	123.771i	−0.939522	−	0.788352i	0.0379802	−	0.999278i	$-0.487908\pi$
$157$	−147.505	−	123.771i	−0.939522	−	0.788352i	−0.977502	+	0.210926i	$0.932352\pi$
$158$	6.09594	+	16.7484i	0.0385819	+	0.106003i
$159$	173.155	−	212.073i	1.08902	−	1.33379i
$160$	−6.05217	−	34.3235i	−0.0378260	−	0.214522i
$161$			117.628i			0.730611i
$162$	−7.98857	+	5.20272i	−0.0493121	+	0.0321155i
$163$	171.309			1.05098			0.525488	−	0.850801i	$-0.323883\pi$
$163$	171.309			1.05098			0.525488	+	0.850801i	$0.323883\pi$
$164$	−120.656	+	21.2749i	−0.735708	+	0.129725i
$165$	−164.817	−	134.571i	−0.998889	−	0.815581i
$166$	5.97985	−	2.17649i	0.0360232	−	0.0131114i
$167$	101.164	−	120.563i	0.605773	−	0.721932i	−0.372782	−	0.927919i	$-0.621596\pi$
$167$	101.164	−	120.563i	0.605773	−	0.721932i	0.978555	+	0.205987i	$0.0660404\pi$
$168$	19.6205	+	10.9796i	0.116789	+	0.0653545i
$169$	94.7623	+	34.4907i	0.560724	+	0.204087i
$170$	15.1094	−	8.72340i	0.0888786	−	0.0513141i
$171$	−82.4709	+	73.0604i	−0.482286	+	0.427254i
$172$	79.3842	−	137.497i	0.461536	−	0.799404i
$173$	33.7496	+	40.2212i	0.195084	+	0.232492i	0.854715	−	0.519097i	$-0.173732\pi$
$173$	33.7496	+	40.2212i	0.195084	+	0.232492i	−0.659631	+	0.751590i	$0.729287\pi$
$174$	−5.93196	−	2.06936i	−0.0340917	−	0.0118929i
$175$	−18.5728	+	105.332i	−0.106130	+	0.601896i
$176$	−178.442	−	31.4642i	−1.01388	−	0.178774i
$177$	−60.8951	+	11.5819i	−0.344040	+	0.0654347i
$178$	−14.7027	+	12.3370i	−0.0825992	+	0.0693090i
$179$	−57.9711	−	33.4697i	−0.323861	−	0.186981i	0.329251	−	0.944242i	$-0.393204\pi$
$179$	−57.9711	−	33.4697i	−0.323861	−	0.186981i	−0.653112	+	0.757261i	$0.726537\pi$
$180$	−219.931	−	32.7218i	−1.22184	−	0.181788i
$181$	64.7294	+	112.115i	0.357621	+	0.619418i	0.987563	−	0.157225i	$-0.0502547\pi$
$181$	64.7294	+	112.115i	0.357621	+	0.619418i	−0.629942	+	0.776642i	$0.716921\pi$
$182$	2.64979	−	7.28024i	0.0145593	−	0.0400013i
$183$	53.6526	+	90.1147i	0.293184	+	0.492430i
$184$	10.6223	+	8.91320i	0.0577301	+	0.0484413i
$185$	−36.1852	−	99.4180i	−0.195596	−	0.537394i
$186$	−4.53797	−	0.737531i	−0.0243977	−	0.00396522i
$187$	−47.5265	−	269.536i	−0.254152	−	1.44137i
$188$			232.707i			1.23780i
$189$	159.214	−	144.905i	0.842402	−	0.766696i
$190$	8.93020			0.0470011
$191$	−267.225	+	47.1189i	−1.39908	+	0.246696i	−0.821766	−	0.569825i	$-0.807011\pi$
$191$	−267.225	+	47.1189i	−1.39908	+	0.246696i	−0.577315	+	0.816521i	$0.695900\pi$
$192$	−175.804	+	66.6721i	−0.915647	+	0.347250i
$193$	−194.971	+	70.9637i	−1.01021	+	0.367688i	−0.793515	−	0.608551i	$-0.791751\pi$
$193$	−194.971	+	70.9637i	−1.01021	+	0.367688i	−0.216699	+	0.976238i	$0.569529\pi$
$194$	4.31317	−	5.14024i	0.0222329	−	0.0264961i
$195$	2.05954	+	153.490i	0.0105617	+	0.787128i
$196$	−54.5971	−	19.8717i	−0.278557	−	0.101386i
$197$	154.871	−	89.4146i	0.786145	−	0.453881i	−0.0524583	−	0.998623i	$-0.516706\pi$
$197$	154.871	−	89.4146i	0.786145	−	0.453881i	0.838604	+	0.544742i	$0.183372\pi$
$198$	5.77698	−	10.6565i	0.0291767	−	0.0538207i
$199$	12.8040	−	22.1772i	0.0643418	−	0.111443i	−0.832060	−	0.554686i	$-0.812839\pi$
$199$	12.8040	−	22.1772i	0.0643418	−	0.111443i	0.896402	+	0.443242i	$0.146172\pi$
$200$	8.10456	+	9.65863i	0.0405228	+	0.0482932i
$201$	117.152	−	101.012i	0.582848	−	0.502546i
$202$	−0.567628	+	3.21918i	−0.00281004	+	0.0159365i
$203$	139.717	+	24.6359i	0.688262	+	0.121359i
$204$	−186.767	−	216.611i	−0.915526	−	1.06182i
$205$	145.930	−	122.450i	0.711853	−	0.597315i
$206$	8.36806	+	4.83130i	0.0406216	+	0.0234529i
$207$	113.162	−	69.4477i	0.546676	−	0.335496i
$208$	65.3600	+	113.207i	0.314231	+	0.544263i
$209$	47.9140	−	131.643i	0.229254	−	0.629869i
$210$	−17.4476	+	0.234113i	−0.0830838	+	0.00111482i
$211$	275.995	+	231.587i	1.30803	+	1.09757i	0.988697	+	0.149928i	$0.0479041\pi$
$211$	275.995	+	231.587i	1.30803	+	1.09757i	0.319335	+	0.947642i	$0.396540\pi$
$212$	124.420	+	341.842i	0.586888	+	1.61246i
$213$	2.80288	+	7.39077i	0.0131591	+	0.0346985i
$214$	0.732977	+	4.15692i	0.00342512	+	0.0194248i
$215$			246.863i			1.14820i
$216$	−1.02125	−	25.3578i	−0.00472800	−	0.117397i
$217$	103.821			0.478438
$218$	0.164064	−	0.0289288i	0.000752585	−	0.000132701i
$219$	33.2138	−	204.362i	0.151661	−	0.933159i
$220$	265.670	−	96.6958i	1.20759	−	0.439526i
$221$	−126.919	+	151.257i	−0.574296	+	0.684419i
$222$	5.17882	−	3.08337i	0.0233280	−	0.0138891i
$223$	−8.44446	−	3.07353i	−0.0378675	−	0.0137827i	0.323017	−	0.946393i	$-0.395303\pi$
$223$	−8.44446	−	3.07353i	−0.0378675	−	0.0137827i	−0.360884	+	0.932611i	$0.617525\pi$
$224$	−38.8304	+	22.4187i	−0.173350	+	0.100084i
$225$	112.298	−	44.3202i	0.499101	−	0.196978i
$226$	−8.77026	+	15.1905i	−0.0388065	+	0.0672148i
$227$	46.1393	+	54.9867i	0.203257	+	0.242232i	0.858038	−	0.513587i	$-0.171684\pi$
$227$	46.1393	+	54.9867i	0.203257	+	0.242232i	−0.654781	+	0.755819i	$0.727239\pi$
$228$	−27.3534	−	143.818i	−0.119971	−	0.630779i
$229$	9.36599	−	53.1172i	0.0408995	−	0.231953i	−0.957505	−	0.288416i	$-0.906871\pi$
$229$	9.36599	−	53.1172i	0.0408995	−	0.231953i	0.998405	+	0.0564635i	$0.0179825\pi$
$230$	−10.5980	−	1.86872i	−0.0460784	−	0.00812487i
$231$	−90.1620	+	258.456i	−0.390312	+	1.11886i
$232$	12.8117	−	10.7503i	0.0552228	−	0.0463374i
$233$	−314.078	−	181.333i	−1.34798	−	0.778254i	−0.360013	−	0.932947i	$-0.617228\pi$
$233$	−314.078	−	181.333i	−1.34798	−	0.778254i	−0.987962	+	0.154694i	$0.950561\pi$
$234$	−8.56824	+	1.74907i	−0.0366164	+	0.00747466i
$235$	−180.914	−	313.352i	−0.769846	−	1.33341i
$236$	28.1697	−	77.3957i	0.119363	−	0.327948i
$237$	−221.853	+	396.452i	−0.936091	+	1.67279i
$238$	−17.1937	−	14.4272i	−0.0722425	−	0.0606187i
$239$	−86.0424	−	236.399i	−0.360010	−	0.989119i	−0.979025	−	0.203740i	$-0.934690\pi$
$239$	−86.0424	−	236.399i	−0.360010	−	0.989119i	0.619015	−	0.785379i	$-0.287532\pi$
$240$	186.202	−	228.052i	0.775841	−	0.950216i
$241$	69.9633	+	396.781i	0.290304	+	1.64640i	0.685699	+	0.727885i	$0.259497\pi$
$241$	69.9633	+	396.781i	0.290304	+	1.64640i	−0.395395	+	0.918511i	$0.629392\pi$
$242$			1.17139i			0.00484043i
$243$	−233.403	−	67.6166i	−0.960507	−	0.278257i
$244$	−139.352			−0.571116
$245$	88.9667	−	15.6872i	0.363129	−	0.0640295i
$246$	8.40631	+	6.86365i	0.0341720	+	0.0279010i
$247$	−94.9711	+	34.5667i	−0.384499	+	0.139946i
$248$	7.86695	−	9.37547i	0.0317216	−	0.0378043i
$249$	141.549	+	79.2104i	0.568470	+	0.318114i
$250$	7.94186	+	2.89060i	0.0317674	+	0.0115624i
$251$	329.280	−	190.110i	1.31187	−	0.757409i	0.329465	−	0.944168i	$-0.393132\pi$
$251$	329.280	−	190.110i	1.31187	−	0.757409i	0.982406	+	0.186759i	$0.0597983\pi$
$252$	57.2126	+	280.270i	0.227034	+	1.11218i
$253$	−84.4099	+	146.202i	−0.333636	+	0.577875i
$254$	−1.29677	−	1.54543i	−0.00510539	−	0.00608437i
$255$	419.892	+	146.479i	1.64663	+	0.574426i
$256$	42.9224	−	243.425i	0.167666	−	0.950880i
$257$	−21.3590	−	3.76618i	−0.0831091	−	0.0146544i	0.131939	−	0.991258i	$-0.457880\pi$
$257$	−21.3590	−	3.76618i	−0.0831091	−	0.0146544i	−0.215048	+	0.976603i	$0.568991\pi$
$258$	−13.8158	+	2.62771i	−0.0535498	+	0.0101849i
$259$	−104.264	+	87.4877i	−0.402563	+	0.337790i
$260$	−176.637	−	101.981i	−0.679373	−	0.392236i
$261$	−58.7884	−	148.957i	−0.225243	−	0.570716i
$262$	−8.58759	−	14.8742i	−0.0327771	−	0.0567716i
$263$	−23.2155	+	63.7841i	−0.0882719	+	0.242525i	−0.975972	−	0.217898i	$-0.930080\pi$
$263$	−23.2155	+	63.7841i	−0.0882719	+	0.242525i	0.887700	+	0.460423i	$0.152302\pi$
$264$	16.5077	+	27.7263i	0.0625292	+	0.105024i
$265$	−433.297	−	363.579i	−1.63508	−	1.37200i
$266$	−3.92928	−	10.7956i	−0.0147717	−	0.0405850i
$267$	−482.881	−	78.4799i	−1.80854	−	0.293932i
$268$	35.6908	+	202.412i	0.133175	+	0.755270i
$269$		−	290.581i		−	1.08023i	−0.841592	−	0.540113i	$-0.818381\pi$
$269$		−	290.581i		−	1.08023i	0.841592	−	0.540113i	$-0.181619\pi$
$270$	10.5263	+	16.6469i	0.0389862	+	0.0616551i
$271$	−414.644			−1.53005			−0.765026	−	0.644000i	$-0.777274\pi$
$271$	−414.644			−1.53005			−0.765026	+	0.644000i	$0.777274\pi$
$272$	372.949	−	65.7609i	1.37114	−	0.241768i
$273$	184.646	−	70.0252i	0.676359	−	0.256503i
$274$	9.62374	−	3.50276i	0.0351231	−	0.0127838i
$275$	−98.6704	+	117.591i	−0.358801	+	0.427603i
$276$	2.36697	+	176.401i	0.00857597	+	0.639135i
$277$	−164.568	−	59.8978i	−0.594108	−	0.216238i	0.0274272	−	0.999624i	$-0.491269\pi$
$277$	−164.568	−	59.8978i	−0.594108	−	0.216238i	−0.621535	+	0.783386i	$0.713491\pi$
$278$	−3.75716	+	2.16919i	−0.0135149	+	0.00780286i
$279$	−61.2958	−	99.8788i	−0.219698	−	0.357989i
$280$	23.2253	−	40.2273i	0.0829474	−	0.143669i
$281$	241.214	+	287.468i	0.858414	+	1.02302i	0.999455	+	0.0330139i	$0.0105106\pi$
$281$	241.214	+	287.468i	0.858414	+	1.02302i	−0.141041	+	0.990004i	$0.545045\pi$
$282$	15.6112	−	13.4604i	0.0553590	−	0.0477319i
$283$	2.56593	−	14.5521i	0.00906688	−	0.0514208i	−0.979939	−	0.199299i	$-0.936133\pi$
$283$	2.56593	−	14.5521i	0.00906688	−	0.0514208i	0.989006	+	0.147879i	$0.0472445\pi$
$284$	−10.3431	−	1.82378i	−0.0364195	−	0.00642175i
$285$	148.641	+	172.392i	0.521547	+	0.604885i
$286$	8.51776	−	7.14725i	0.0297824	−	0.0249904i
$287$	−212.237	−	122.535i	−0.739501	−	0.426951i
$288$	44.4929	+	24.1200i	0.154489	+	0.0837499i
$289$	141.513	+	245.108i	0.489665	+	0.848125i
$290$	−4.43927	+	12.1968i	−0.0153078	+	0.0420579i
$291$	171.021	−	2.29477i	0.587701	−	0.00788582i
$292$	210.740	+	176.832i	0.721713	+	0.605589i
$293$	−45.4702	−	124.928i	−0.155188	−	0.426376i	0.837596	−	0.546290i	$-0.183960\pi$
$293$	−45.4702	−	124.928i	−0.155188	−	0.426376i	−0.992784	+	0.119914i	$0.961738\pi$
$294$	1.82494	+	4.81210i	0.00620729	+	0.0163677i
$295$	22.2379	+	126.117i	0.0753826	+	0.427516i
$296$			16.0448i			0.0542053i
$297$	301.874	−	65.8537i	1.01641	−	0.221730i
$298$	7.60284			0.0255129
$299$	119.942	−	21.1490i	0.401143	−	0.0707323i
$300$	−25.7332	+	158.335i	−0.0857774	+	0.527782i
$301$	298.430	−	108.620i	0.991461	−	0.360862i
$302$	−11.6852	+	13.9259i	−0.0386926	+	0.0461121i
$303$	−71.5924	+	42.6247i	−0.236278	+	0.140676i
$304$	182.150	+	66.2972i	0.599178	+	0.218083i
$305$	187.645	−	108.337i	0.615229	−	0.355203i
$306$	−3.72828	+	25.0587i	−0.0121839	+	0.0818912i
$307$	−35.2589	+	61.0701i	−0.114850	+	0.198926i	−0.917720	−	0.397229i	$-0.869972\pi$
$307$	−35.2589	+	61.0701i	−0.114850	+	0.198926i	0.802870	+	0.596154i	$0.203305\pi$
$308$	−233.789	−	278.619i	−0.759055	−	0.904606i
$309$	46.0189	+	241.956i	0.148928	+	0.783030i
$310$	−1.64937	+	9.35403i	−0.00532054	+	0.0301743i
$311$	60.0519	+	10.5888i	0.193093	+	0.0340475i	0.269358	−	0.963040i	$-0.413188\pi$
$311$	60.0519	+	10.5888i	0.193093	+	0.0340475i	−0.0762652	+	0.997088i	$0.524300\pi$
$312$	7.66783	−	21.9804i	0.0245764	−	0.0704500i
$313$	161.890	−	135.842i	0.517221	−	0.434000i	−0.346441	−	0.938072i	$-0.612610\pi$
$313$	161.890	−	135.842i	0.517221	−	0.434000i	0.863662	+	0.504072i	$0.168165\pi$
$314$	−19.6266	−	11.3314i	−0.0625051	−	0.0360874i
$315$	−294.930	−	332.919i	−0.936287	−	1.05688i
$316$	−301.821	−	522.770i	−0.955131	−	1.65433i
$317$	45.7588	−	125.721i	0.144349	−	0.396597i	−0.846357	−	0.532617i	$-0.821209\pi$
$317$	45.7588	−	125.721i	0.144349	−	0.396597i	0.990706	+	0.136020i	$0.0434310\pi$
$318$	15.7358	−	28.1198i	0.0494836	−	0.0884271i
$319$	155.978	+	130.881i	0.488960	+	0.410286i
$320$	132.857	+	365.022i	0.415178	+	1.14069i
$321$	−68.0466	+	83.3405i	−0.211983	+	0.259628i
$322$	2.40406	+	13.6341i	0.00746601	+	0.0423419i
$323$			292.794i			0.906482i
$324$	235.849	−	220.511i	0.727931	−	0.680590i
$325$	110.743			0.340746
$326$	19.8561	−	3.50117i	0.0609083	−	0.0107398i
$327$	3.28925	+	2.68564i	0.0100589	+	0.00821296i
$328$	−27.1475	+	9.88088i	−0.0827667	+	0.0301246i
$329$	−299.206	+	356.579i	−0.909439	+	1.08383i
$330$	−21.8539	−	12.2294i	−0.0662239	−	0.0370587i
$331$	82.8821	+	30.1666i	0.250399	+	0.0911378i	0.464170	−	0.885746i	$-0.346353\pi$
$331$	82.8821	+	30.1666i	0.250399	+	0.0911378i	−0.213771	+	0.976884i	$0.568575\pi$
$332$	−186.649	+	107.762i	−0.562197	+	0.324585i
$333$	145.723	+	48.6521i	0.437606	+	0.146103i
$334$	9.26171	−	16.0418i	0.0277297	−	0.0480292i
$335$	−205.421	−	244.812i	−0.613198	−	0.730781i
$336$	−357.618	−	124.754i	−1.06434	−	0.371293i
$337$	7.15157	−	40.5586i	0.0212213	−	0.120352i	−0.972357	−	0.233500i	$-0.924982\pi$
$337$	7.15157	−	40.5586i	0.0212213	−	0.120352i	0.993578	+	0.113148i	$0.0360934\pi$
$338$	11.6886	+	2.06102i	0.0345817	+	0.00609769i
$339$	−439.223	+	83.5381i	−1.29564	+	0.246425i
$340$	−452.648	+	379.817i	−1.33132	+	1.11711i
$341$	129.041	+	74.5018i	0.378419	+	0.218480i
$342$	−8.06585	+	10.1538i	−0.0235844	+	0.0296895i
$343$	137.240	+	237.706i	0.400116	+	0.693022i
$344$	12.8045	−	35.1800i	0.0372223	−	0.102267i
$345$	−140.327	−	235.693i	−0.406746	−	0.683169i
$346$	4.73388	+	3.97220i	0.0136817	+	0.0114803i
$347$	117.292	+	322.257i	0.338017	+	0.928695i	0.985956	+	0.167003i	$0.0534090\pi$
$347$	117.292	+	322.257i	0.338017	+	0.928695i	−0.647939	+	0.761692i	$0.724369\pi$
$348$	210.023	+	34.1338i	0.603513	+	0.0980856i
$349$	−102.322	−	580.297i	−0.293186	−	1.66274i	−0.674484	−	0.738289i	$-0.735634\pi$
$349$	−102.322	−	580.297i	−0.293186	−	1.66274i	0.381298	−	0.924452i	$-0.375477\pi$
$350$			12.5884i			0.0359668i
$351$	−176.381	−	136.292i	−0.502510	−	0.388296i
$352$	−64.3505			−0.182814
$353$	124.087	−	21.8798i	0.351521	−	0.0619826i	0.00490000	−	0.999988i	$-0.498440\pi$
$353$	124.087	−	21.8798i	0.351521	−	0.0619826i	0.346621	+	0.938005i	$0.387329\pi$
$354$	−6.82152	+	2.58700i	−0.0192698	+	0.00730790i
$355$	15.3454	−	5.58528i	0.0432266	−	0.0157332i
$356$	417.831	−	497.952i	1.17368	−	1.39874i
$357$	−7.67585	−	572.053i	−0.0215010	−	1.60239i
$358$	−7.40336	−	2.69460i	−0.0206798	−	0.00752683i
$359$	−298.332	+	172.242i	−0.831007	+	0.479782i	−0.854197	−	0.519949i	$-0.825951\pi$
$359$	−298.332	+	172.242i	−0.831007	+	0.479782i	0.0231901	+	0.999731i	$0.492618\pi$
$360$	−52.4120	+	1.40679i	−0.145589	+	0.00390775i
$361$	105.566	−	182.846i	0.292427	−	0.506499i
$362$	9.79402	+	11.6721i	0.0270553	+	0.0322433i
$363$	−22.6129	+	19.4974i	−0.0622945	+	0.0537119i
$364$	−45.5640	+	258.406i	−0.125176	+	0.709907i
$365$	−421.247	−	74.2772i	−1.15410	−	0.203499i
$366$	8.06051	+	9.34849i	0.0220232	+	0.0255423i
$367$	258.712	−	217.085i	0.704937	−	0.591513i	−0.218236	−	0.975896i	$-0.570030\pi$
$367$	258.712	−	217.085i	0.704937	−	0.591513i	0.923174	+	0.384383i	$0.125586\pi$
$368$	−202.296	−	116.795i	−0.549717	−	0.317379i
$369$	7.42214	+	276.523i	0.0201142	+	0.749384i
$370$	−6.22603	−	10.7838i	−0.0168271	−	0.0291454i
$371$	−248.876	+	683.782i	−0.670826	+	1.84308i
$372$	155.695	−	2.08913i	0.418535	−	0.00561594i
$373$	75.9155	+	63.7007i	0.203527	+	0.170779i	0.738854	−	0.673865i	$-0.235367\pi$
$373$	75.9155	+	63.7007i	0.203527	+	0.170779i	−0.535327	+	0.844645i	$0.679812\pi$
$374$	−11.0174	−	30.2701i	−0.0294583	−	0.0809360i
$375$	76.3890	+	201.426i	0.203704	+	0.537137i
$376$	9.52853	+	54.0390i	0.0253418	+	0.143721i
$377$		−	146.894i		−	0.389640i
$378$	15.4927	−	20.0497i	0.0409859	−	0.0530415i
$379$	599.859			1.58274			0.791370	−	0.611337i	$-0.209368\pi$
$379$	599.859			1.58274			0.791370	+	0.611337i	$0.209368\pi$
$380$	−297.854	+	52.5198i	−0.783827	+	0.138210i
$381$	8.24920	−	50.7567i	0.0216514	−	0.133220i
$382$	−30.0105	+	10.9229i	−0.0785614	+	0.0285940i
$383$	73.0625	−	87.0726i	0.190764	−	0.227343i	−0.662182	−	0.749343i	$-0.730369\pi$
$383$	73.0625	−	87.0726i	0.190764	−	0.227343i	0.852946	+	0.522000i	$0.174814\pi$
$384$	−76.9961	+	45.8420i	−0.200511	+	0.119380i
$385$	531.415	+	193.419i	1.38030	+	0.502388i
$386$	−21.1484	+	12.2100i	−0.0547886	+	0.0316322i
$387$	−280.688	−	222.969i	−0.725291	−	0.576148i
$388$	−113.629	+	196.812i	−0.292859	+	0.507247i
$389$	233.254	+	277.981i	0.599624	+	0.714604i	0.977425	−	0.211283i	$-0.0677640\pi$
$389$	233.254	+	277.981i	0.599624	+	0.714604i	−0.377801	+	0.925887i	$0.623320\pi$
$390$	3.37570	+	17.7486i	0.00865564	+	0.0455093i
$391$	61.2696	−	347.477i	0.156700	−	0.888688i
$392$	−13.4922	−	2.37903i	−0.0344188	−	0.00606896i
$393$	144.198	−	413.355i	0.366917	−	1.05179i
$394$	16.1233	−	13.5291i	0.0409221	−	0.0343378i
$395$	812.835	+	469.291i	2.05781	+	1.18808i
$396$	−130.011	+	389.408i	−0.328310	+	0.983353i
$397$	239.208	+	414.320i	0.602539	+	1.04363i	0.992435	+	0.122769i	$0.0391775\pi$
$397$	239.208	+	414.320i	0.602539	+	1.04363i	−0.389896	+	0.920859i	$0.627489\pi$
$398$	1.03084	−	2.83220i	0.00259004	−	0.00711609i
$399$	143.001	−	255.543i	0.358398	−	0.640458i
$400$	−162.707	−	136.527i	−0.406767	−	0.341318i
$401$	−218.214	−	599.538i	−0.544174	−	1.49511i	−0.841461	−	0.540319i	$-0.818304\pi$
$401$	−218.214	−	599.538i	−0.544174	−	1.49511i	0.297286	−	0.954788i	$-0.403919\pi$
$402$	11.5145	−	14.1024i	0.0286429	−	0.0350806i
$403$	−18.6665	−	105.863i	−0.0463188	−	0.262687i
$404$		−	110.709i		−	0.274033i
$405$	−146.151	+	480.286i	−0.360867	+	1.18589i
$406$	16.6978			0.0411277
$407$	−192.372	+	33.9204i	−0.472659	+	0.0833425i
$408$	−52.2404	−	42.6537i	−0.128040	−	0.104543i
$409$	−575.541	+	209.480i	−1.40719	+	0.512175i	−0.930304	−	0.366790i	$-0.880457\pi$
$409$	−575.541	+	209.480i	−1.40719	+	0.512175i	−0.476886	+	0.878965i	$0.658235\pi$
$410$	14.4118	−	17.1754i	0.0351508	−	0.0418911i
$411$	227.803	+	127.478i	0.554266	+	0.310166i
$412$	−307.518	−	111.928i	−0.746404	−	0.271669i
$413$	142.677	−	82.3746i	0.345465	−	0.199454i
$414$	11.6970	−	10.3623i	0.0282537	−	0.0250297i
$415$	167.555	−	290.214i	0.403748	−	0.699311i
$416$	29.8411	+	35.5632i	0.0717334	+	0.0854886i
$417$	−104.412	−	36.4239i	−0.250388	−	0.0873476i
$418$	2.86314	−	16.2377i	0.00684963	−	0.0388462i
$419$	516.661	+	91.1012i	1.23308	+	0.217425i	0.751948	−	0.659223i	$-0.229114\pi$
$419$	516.661	+	91.1012i	1.23308	+	0.217425i	0.481132	+	0.876648i	$0.340226\pi$
$420$	580.563	−	110.420i	1.38229	−	0.262905i
$421$	−282.105	+	236.715i	−0.670084	+	0.562267i	−0.913090	−	0.407757i	$-0.866311\pi$
$421$	−282.105	+	236.715i	−0.670084	+	0.562267i	0.243006	+	0.970025i	$0.421866\pi$
$422$	36.7231	+	21.2021i	0.0870217	+	0.0502420i
$423$	519.690	+	77.3205i	1.22858	+	0.182791i
$424$	42.8900	+	74.2876i	0.101156	+	0.175207i
$425$	109.729	−	301.478i	0.258186	−	0.709361i
$426$	0.475927	+	0.799365i	0.00111720	+	0.00187644i
$427$	−213.531	−	179.174i	−0.500072	−	0.419610i
$428$	−48.8948	−	134.337i	−0.114240	−	0.313872i
$429$	279.749	+	45.4661i	0.652097	+	0.105982i
$430$	5.04532	+	28.6134i	0.0117333	+	0.0665428i
$431$		−	178.021i		−	0.413043i	−0.978442	−	0.206521i	$-0.933786\pi$
$431$		−	178.021i		−	0.413043i	0.978442	−	0.206521i	$-0.0662143\pi$
$432$	91.1197	+	417.694i	0.210925	+	0.966883i
$433$	−710.746			−1.64144			−0.820722	−	0.571327i	$-0.806429\pi$
$433$	−710.746			−1.64144			−0.820722	+	0.571327i	$0.806429\pi$
$434$	12.0337	−	2.12186i	0.0277274	−	0.00488909i
$435$	−309.343	+	117.315i	−0.711133	+	0.269690i
$436$	−5.30198	+	1.92976i	−0.0121605	+	0.00442606i
$437$	116.088	−	138.348i	0.265648	−	0.316587i
$438$	−0.326945	−	24.3660i	−0.000746450	−	0.0556302i
$439$	−598.391	−	217.797i	−1.36308	−	0.496120i	−0.446073	−	0.894996i	$-0.647178\pi$
$439$	−598.391	−	217.797i	−1.36308	−	0.496120i	−0.917005	+	0.398877i	$0.869400\pi$
$440$	57.7341	−	33.3328i	0.131214	−	0.0757564i
$441$	−62.5190	+	115.326i	−0.141766	+	0.261509i
$442$	−11.6196	+	20.1258i	−0.0262888	+	0.0455335i
$443$	−207.534	−	247.329i	−0.468473	−	0.558305i	0.479134	−	0.877742i	$-0.340951\pi$
$443$	−207.534	−	247.329i	−0.468473	−	0.558305i	−0.947608	+	0.319437i	$0.896506\pi$
$444$	−154.599	+	133.299i	−0.348195	+	0.300223i
$445$	−175.507	+	995.352i	−0.394399	+	2.23675i
$446$	−1.04160	−	0.183662i	−0.00233542	−	0.000411798i
$447$	126.547	+	146.768i	0.283104	+	0.328341i
$448$	382.813	−	321.219i	0.854494	−	0.717006i
$449$	22.4287	+	12.9492i	0.0499526	+	0.0288401i	0.524768	−	0.851245i	$-0.324152\pi$
$449$	22.4287	+	12.9492i	0.0499526	+	0.0288401i	−0.474816	+	0.880085i	$0.657485\pi$
$450$	12.1104	−	7.43217i	0.0269120	−	0.0165159i
$451$	−175.862	−	304.602i	−0.389938	−	0.675392i
$452$	203.182	−	558.238i	0.449518	−	1.23504i
$453$	−463.327	+	6.21696i	−1.02280	+	0.0137240i
$454$	6.47172	+	5.43042i	0.0142549	+	0.0119613i
$455$	−139.539	−	383.380i	−0.306679	−	0.842593i
$456$	−12.2408	−	32.2771i	−0.0268438	−	0.0707832i
$457$	−68.6711	−	389.453i	−0.150265	−	0.852195i	−0.962988	−	0.269544i	$-0.913127\pi$
$457$	−68.6711	−	389.453i	−0.150265	−	0.852195i	0.812723	−	0.582650i	$-0.197984\pi$
$458$		−	6.34813i		−	0.0138605i
$459$	−545.800	+	345.124i	−1.18911	+	0.751903i
$460$	364.473			0.792332
$461$	−883.267	+	155.744i	−1.91598	+	0.337839i	−0.998238	−	0.0593356i	$-0.981102\pi$
$461$	−883.267	+	155.744i	−1.91598	+	0.337839i	−0.917743	+	0.397175i	$0.869991\pi$
$462$	−5.16825	+	31.7998i	−0.0111867	+	0.0688308i
$463$	279.650	−	101.784i	0.603997	−	0.219837i	−0.0218778	−	0.999761i	$-0.506964\pi$
$463$	279.650	−	101.784i	0.603997	−	0.219837i	0.625874	+	0.779924i	$0.284742\pi$
$464$	−181.096	+	215.822i	−0.390294	+	0.465134i
$465$	−208.027	+	123.855i	−0.447370	+	0.266356i
$466$	−40.1102	−	14.5989i	−0.0860734	−	0.0313282i
$467$	−684.460	+	395.173i	−1.46565	+	0.846196i	−0.999263	−	0.0383833i	$-0.987779\pi$
$467$	−684.460	+	395.173i	−1.46565	+	0.846196i	−0.466391	+	0.884579i	$0.654446\pi$
$468$	275.495	−	108.729i	0.588665	−	0.232326i
$469$	−205.565	+	356.048i	−0.438304	+	0.759165i
$470$	−27.3736	−	32.6226i	−0.0582416	−	0.0694097i
$471$	−107.934	−	567.489i	−0.229158	−	1.20486i
$472$	3.37246	−	19.1262i	0.00714505	−	0.0405216i
$473$	448.868	+	79.1476i	0.948982	+	0.167331i
$474$	−17.6120	+	50.4862i	−0.0371562	+	0.106511i
$475$	125.797	−	105.556i	0.264836	−	0.222223i
$476$	658.321	+	380.082i	1.38303	+	0.798491i
$477$	804.755	−	164.278i	1.68712	−	0.344398i
$478$	−14.8045	−	25.6421i	−0.0309717	−	0.0536445i
$479$	−0.369996	+	1.01656i	−0.000772435	+	0.00212225i	−0.940078	−	0.340959i	$-0.889248\pi$
$479$	−0.369996	+	1.01656i	−0.000772435	+	0.00212225i	0.939306	+	0.343081i	$0.111471\pi$
$480$	51.0599	−	91.2441i	0.106375	−	0.190092i
$481$	107.954	+	90.5844i	0.224437	+	0.188325i
$482$	16.2186	+	44.5603i	0.0336486	+	0.0924487i
$483$	−223.183	+	273.345i	−0.462076	+	0.565931i
$484$	−6.88908	−	39.0699i	−0.0142336	−	0.0807230i
$485$		−	353.356i		−	0.728569i
$486$	−28.4352	−	3.06708i	−0.0585087	−	0.00631086i
$487$	647.606			1.32979			0.664893	−	0.746939i	$-0.268477\pi$
$487$	647.606			1.32979			0.664893	+	0.746939i	$0.268477\pi$
$488$	−32.3602	+	5.70598i	−0.0663119	+	0.0116926i
$489$	398.088	+	325.034i	0.814086	+	0.664692i
$490$	9.99134	−	3.63655i	0.0203905	−	0.00742153i
$491$	200.752	−	239.247i	0.408863	−	0.487264i	−0.521838	−	0.853045i	$-0.674753\pi$
$491$	200.752	−	239.247i	0.408863	−	0.487264i	0.930701	+	0.365781i	$0.119198\pi$
$492$	−320.747	−	179.489i	−0.651924	−	0.364815i
$493$	−399.896	−	145.550i	−0.811147	−	0.295233i
$494$	−10.3015	+	5.94755i	−0.0208531	+	0.0120396i
$495$	−127.672	−	625.432i	−0.257923	−	1.26350i
$496$	−103.086	+	178.550i	−0.207834	+	0.359980i
$497$	−13.5040	−	16.0934i	−0.0271709	−	0.0323811i
$498$	18.0256	+	6.28819i	0.0361959	+	0.0126269i
$499$	7.96919	−	45.1955i	0.0159703	−	0.0905722i	−0.975781	−	0.218751i	$-0.929802\pi$
$499$	7.96919	−	45.1955i	0.0159703	−	0.0905722i	0.991751	+	0.128178i	$0.0409130\pi$
$500$	−281.890	−	49.7048i	−0.563779	−	0.0994095i
$501$	463.835	−	88.2192i	0.925819	−	0.176086i
$502$	34.2807	−	28.7650i	0.0682883	−	0.0573007i
$503$	493.829	+	285.113i	0.981768	+	0.566824i	0.902803	−	0.430053i	$-0.141505\pi$
$503$	493.829	+	285.113i	0.981768	+	0.566824i	0.0789646	+	0.996877i	$0.474839\pi$
$504$	24.7619	+	62.7413i	0.0491308	+	0.124487i
$505$	86.0690	+	149.076i	0.170434	+	0.295200i
$506$	−6.79575	+	18.6712i	−0.0134303	+	0.0368995i
$507$	154.768	+	259.947i	0.305261	+	0.512716i
$508$	52.3408	+	43.9192i	0.103033	+	0.0864551i
$509$	177.877	+	488.713i	0.349464	+	0.960144i	0.982540	+	0.186054i	$0.0595700\pi$
$509$	177.877	+	488.713i	0.349464	+	0.960144i	−0.633076	+	0.774090i	$0.718208\pi$
$510$	51.6625	+	8.39642i	0.101299	+	0.0164636i
$511$	95.5556	+	541.923i	0.186997	+	1.06051i
$512$		−	148.572i		−	0.290179i
$513$	−330.267	+	13.3010i	−0.643796	+	0.0259280i
$514$	−2.55266			−0.00496626
$515$	501.105	−	88.3583i	0.973020	−	0.171570i
$516$	445.354	−	168.896i	0.863090	−	0.327319i
$517$	−627.768	+	228.489i	−1.21425	+	0.441952i
$518$	−10.2970	+	12.2714i	−0.0198783	+	0.0236900i
$519$	2.11336	+	157.501i	0.00407199	+	0.303470i
$520$	−45.1942	−	16.4494i	−0.0869120	−	0.0316334i
$521$	−365.719	+	211.148i	−0.701956	+	0.405275i	−0.808076	−	0.589079i	$-0.799491\pi$
$521$	−365.719	+	211.148i	−0.701956	+	0.405275i	0.106119	+	0.994353i	$0.466157\pi$
$522$	−9.85839	−	16.0638i	−0.0188858	−	0.0307736i
$523$	500.529	−	866.942i	0.957035	−	1.65763i	0.227394	−	0.973803i	$-0.426979\pi$
$523$	500.529	−	866.942i	0.957035	−	1.65763i	0.729641	−	0.683831i	$-0.239687\pi$
$524$	373.904	+	445.602i	0.713558	+	0.850385i
$525$	−243.011	+	209.531i	−0.462879	+	0.399106i
$526$	−1.38726	+	7.86756i	−0.00263738	+	0.0149573i
$527$	−306.690	−	54.0777i	−0.581954	−	0.102614i
$528$	−354.966	−	411.685i	−0.672283	−	0.779707i
$529$	238.518	−	200.140i	0.450884	−	0.378337i
$530$	−57.6533	−	33.2862i	−0.108780	−	0.0628041i
$531$	−163.483	−	88.6255i	−0.307878	−	0.166903i
$532$	194.546	+	336.964i	0.365688	+	0.633391i
$533$	−86.7857	+	238.442i	−0.162825	+	0.447358i
$534$	−57.5737	+	0.772528i	−0.107816	+	0.00144668i
$535$	170.277	+	142.880i	0.318276	+	0.267065i
$536$	16.5761	+	45.5426i	0.0309257	+	0.0849675i
$537$	−71.2094	−	187.769i	−0.132606	−	0.349662i
$538$	−5.93881	−	33.6807i	−0.0110387	−	0.0626035i
$539$		−	166.797i		−	0.309456i
$540$	−448.991	−	493.327i	−0.831465	−	0.913568i
$541$	−192.818			−0.356410			−0.178205	−	0.983993i	$-0.557029\pi$
$541$	−192.818			−0.356410			−0.178205	+	0.983993i	$0.557029\pi$
$542$	−48.0606	+	8.47438i	−0.0886727	+	0.0156354i
$543$	−62.3031	+	383.346i	−0.114739	+	0.705979i
$544$	126.383	−	45.9997i	0.232322	−	0.0845583i
$545$	5.63912	−	6.72044i	0.0103470	−	0.0123311i
$546$	19.9708	−	11.8902i	0.0365765	−	0.0217770i
$547$	710.023	+	258.427i	1.29803	+	0.472444i	0.896355	−	0.443338i	$-0.146206\pi$
$547$	710.023	+	258.427i	1.29803	+	0.472444i	0.401676	+	0.915782i	$0.368428\pi$
$548$	−300.386	+	173.428i	−0.548150	+	0.316475i
$549$	−46.3019	+	311.207i	−0.0843386	+	0.566861i
$550$	−9.03341	+	15.6463i	−0.0164244	+	0.0284479i
$551$	−140.015	−	166.863i	−0.254110	−	0.302837i
$552$	7.77267	+	40.8668i	0.0140809	+	0.0740341i
$553$	209.673	−	1189.11i	0.379155	−	2.15030i
$554$	−20.2989	−	3.57925i	−0.0366407	−	0.00646074i
$555$	104.544	−	299.684i	0.188368	−	0.539970i
$556$	112.557	−	94.4468i	0.202441	−	0.169868i
$557$	−741.183	−	427.922i	−1.33067	−	0.768262i	−0.345267	−	0.938505i	$-0.612212\pi$
$557$	−741.183	−	427.922i	−1.33067	−	0.768262i	−0.985402	+	0.170242i	$0.945545\pi$
$558$	−9.14597	−	10.3240i	−0.0163906	−	0.0185018i
$559$	−164.412	−	284.769i	−0.294118	−	0.509427i
$560$	−267.629	+	735.303i	−0.477908	+	1.31304i
$561$	400.964	−	716.522i	0.714730	−	1.27722i
$562$	33.8339	+	28.3900i	0.0602026	+	0.0505160i
$563$	53.2716	+	146.362i	0.0946209	+	0.259969i	0.977970	−	0.208748i	$-0.0669388\pi$
$563$	53.2716	+	146.362i	0.0946209	+	0.259969i	−0.883349	+	0.468717i	$0.844717\pi$
$564$	−441.528	+	540.765i	−0.782851	+	0.958803i
$565$	160.397	+	909.656i	0.283888	+	1.61001i
$566$		−	1.73915i		−	0.00307270i
$567$	644.919	−	34.6455i	1.13742	−	0.0611031i
$568$	−2.47655			−0.00436013
$569$	626.354	−	110.443i	1.10080	−	0.194100i	0.406402	−	0.913694i	$-0.366783\pi$
$569$	626.354	−	110.443i	1.10080	−	0.194100i	0.694395	+	0.719594i	$0.255672\pi$
$570$	20.7520	+	16.9438i	0.0364070	+	0.0297259i
$571$	943.621	−	343.450i	1.65258	−	0.601488i	0.663406	−	0.748260i	$-0.269110\pi$
$571$	943.621	−	343.450i	1.65258	−	0.601488i	0.989170	+	0.146772i	$0.0468882\pi$
$572$	−242.064	+	288.481i	−0.423189	+	0.504337i
$573$	−710.377	−	397.525i	−1.23975	−	0.693761i
$574$	−27.1043	−	9.86516i	−0.0472200	−	0.0171867i
$575$	−171.380	+	98.9461i	−0.298052	+	0.172080i
$576$	−535.034	−	178.631i	−0.928879	−	0.310123i
$577$	−414.908	+	718.642i	−0.719079	+	1.24548i	0.242287	+	0.970205i	$0.422103\pi$
$577$	−414.908	+	718.642i	−0.719079	+	1.24548i	−0.961365	+	0.275276i	$0.911231\pi$
$578$	21.4120	+	25.5178i	0.0370450	+	0.0441485i
$579$	−587.718	−	205.024i	−1.01506	−	0.354101i
$580$	76.3346	−	432.915i	0.131611	−	0.746406i
$581$	−424.561	−	74.8615i	−0.730741	−	0.128849i
$582$	19.7758	−	3.76126i	0.0339791	−	0.00646265i
$583$	−800.013	+	671.291i	−1.37224	+	1.15144i
$584$	56.1785	+	32.4347i	0.0961961	+	0.0555388i
$585$	−286.439	+	360.587i	−0.489639	+	0.616389i
$586$	−7.82361	−	13.5509i	−0.0133509	−	0.0231244i
$587$	100.401	−	275.849i	0.171040	−	0.469930i	−0.824323	−	0.566120i	$-0.808444\pi$
$587$	100.401	−	275.849i	0.171040	−	0.469930i	0.995363	+	0.0961909i	$0.0306659\pi$
$588$	−89.1690	−	149.768i	−0.151648	−	0.254708i
$589$	−122.109	−	102.461i	−0.207316	−	0.173958i
$590$	5.15509	+	14.1635i	0.00873745	+	0.0240059i
$591$	529.540	+	86.0631i	0.896006	+	0.145623i
$592$	−46.9346	−	266.180i	−0.0792815	−	0.449628i
$593$		−	720.027i		−	1.21421i	−0.794621	−	0.607106i	$-0.792330\pi$
$593$		−	720.027i		−	1.21421i	0.794621	−	0.607106i	$-0.207670\pi$
$594$	33.6437	−	13.8026i	0.0566392	−	0.0232367i
$595$	−1181.95			−1.98647
$596$	−253.582	+	44.7134i	−0.425473	+	0.0750224i
$597$	71.8320	−	27.2416i	0.120322	−	0.0456308i
$598$	13.4700	−	4.90267i	0.0225250	−	0.00819844i
$599$	−297.913	+	355.039i	−0.497351	+	0.592719i	−0.955071	−	0.296377i	$-0.904222\pi$
$599$	−297.913	+	355.039i	−0.497351	+	0.592719i	0.457721	+	0.889096i	$0.348666\pi$
$600$	0.507498	+	37.8219i	0.000845830	+	0.0630366i
$601$	512.198	+	186.425i	0.852244	+	0.310191i	0.730955	−	0.682426i	$-0.239075\pi$
$601$	512.198	+	186.425i	0.852244	+	0.310191i	0.121289	+	0.992617i	$0.461297\pi$
$602$	32.3705	−	18.6891i	0.0537715	−	0.0310450i
$603$	463.894	−	12.4514i	0.769310	−	0.0206490i
$604$	307.843	−	533.199i	0.509674	−	0.882781i
$605$	39.6507	+	47.2538i	0.0655383	+	0.0781055i
$606$	−7.42698	+	6.40373i	−0.0122557	+	0.0105672i
$607$	−176.997	+	1003.80i	−0.291593	+	1.65371i	0.389142	+	0.921178i	$0.372771\pi$
$607$	−176.997	+	1003.80i	−0.291593	+	1.65371i	−0.680735	+	0.732529i	$0.738340\pi$
$608$	67.7954	+	11.9542i	0.111506	+	0.0196614i
$609$	277.932	+	322.342i	0.456374	+	0.529297i
$610$	19.5354	−	16.3921i	0.0320252	−	0.0268724i
$611$	417.387	+	240.979i	0.683122	+	0.394400i
$612$	−23.0222	−	857.724i	−0.0376179	−	1.40151i
$613$	−496.963	−	860.765i	−0.810706	−	1.40418i	−0.912370	−	0.409366i	$-0.865750\pi$
$613$	−496.963	−	860.765i	−0.810706	−	1.40418i	0.101664	−	0.994819i	$-0.467583\pi$
$614$	−2.83865	+	7.79913i	−0.00462321	+	0.0127022i
$615$	571.442	−	7.66765i	0.929174	−	0.0124677i
$616$	−65.6986	−	55.1277i	−0.106654	−	0.0894930i
$617$	323.050	+	887.573i	0.523582	+	1.43853i	0.866506	+	0.499166i	$0.166360\pi$
$617$	323.050	+	887.573i	0.523582	+	1.43853i	−0.342924	+	0.939363i	$0.611417\pi$
$618$	10.2790	+	27.1042i	0.0166327	+	0.0438579i
$619$	−81.4780	−	462.084i	−0.131628	−	0.746502i	−0.977148	−	0.212558i	$-0.931821\pi$
$619$	−81.4780	−	462.084i	−0.131628	−	0.746502i	0.845520	−	0.533944i	$-0.179291\pi$
$620$		−	321.691i		−	0.518856i
$621$	394.733	+	53.3260i	0.635640	+	0.0858712i
$622$	7.17691			0.0115384
$623$	1280.49	−	225.785i	2.05536	−	0.362416i
$624$	−62.9101	+	387.081i	−0.100817	+	0.620322i
$625$	733.350	−	266.917i	1.17336	−	0.427068i
$626$	15.9881	−	19.0539i	0.0255401	−	0.0304375i
$627$	361.115	−	215.001i	0.575942	−	0.342905i
$628$	721.260	+	262.517i	1.14850	+	0.418021i
$629$	353.568	−	204.132i	0.562111	−	0.324535i
$630$	−40.9889	−	32.5602i	−0.0650617	−	0.0516829i
$631$	−510.282	+	883.835i	−0.808689	+	1.40069i	0.105084	+	0.994463i	$0.466489\pi$
$631$	−510.282	+	883.835i	−0.808689	+	1.40069i	−0.913773	+	0.406226i	$0.866844\pi$
$632$	−91.4942	−	109.039i	−0.144769	−	0.172529i
$633$	201.953	+	1061.82i	0.319042	+	1.67744i
$634$	2.73436	−	15.5073i	0.00431286	−	0.0244595i
$635$	−104.624	−	18.4480i	−0.164762	−	0.0290520i
$636$	−359.468	+	1030.44i	−0.565201	+	1.62019i
$637$	−92.1800	+	77.3482i	−0.144710	+	0.121426i
$638$	20.7540	+	11.9823i	0.0325298	+	0.0187811i
$639$	−7.50959	+	22.4927i	−0.0117521	+	0.0351999i
$640$	92.5655	+	160.328i	0.144634	+	0.250513i
$641$	384.982	−	1057.73i	0.600596	−	1.65012i	−0.149473	−	0.988766i	$-0.547758\pi$
$641$	384.982	−	1057.73i	0.600596	−	1.65012i	0.750069	−	0.661359i	$-0.230020\pi$
$642$	−6.18386	+	11.0506i	−0.00963218	+	0.0172127i
$643$	−163.564	−	137.247i	−0.254377	−	0.213448i	0.506677	−	0.862136i	$-0.330874\pi$
$643$	−163.564	−	137.247i	−0.254377	−	0.213448i	−0.761054	+	0.648688i	$0.775318\pi$
$644$	−160.368	−	440.607i	−0.249018	−	0.684172i
$645$	−468.387	+	573.660i	−0.726181	+	0.889395i
$646$	5.98404	+	33.9371i	0.00926321	+	0.0525343i
$647$		−	267.943i		−	0.414132i	−0.978327	−	0.207066i	$-0.933609\pi$
$647$		−	267.943i		−	0.414132i	0.978327	−	0.207066i	$-0.0663914\pi$
$648$	45.7396	−	60.8641i	0.0705857	−	0.0939260i
$649$	236.447			0.364326
$650$	12.8360	−	2.26332i	0.0197476	−	0.00348204i
$651$	241.259	+	196.985i	0.370598	+	0.302589i
$652$	−641.682	+	233.553i	−0.984175	+	0.358210i
$653$	34.1737	−	40.7266i	0.0523333	−	0.0623684i	−0.739243	−	0.673439i	$-0.764816\pi$
$653$	34.1737	−	40.7266i	0.0523333	−	0.0623684i	0.791576	+	0.611071i	$0.209261\pi$
$654$	0.436139	+	0.244062i	0.000666879	+	0.000373184i
$655$	−849.906	−	309.340i	−1.29757	−	0.472275i
$656$	421.468	−	243.335i	0.642482	−	0.370937i
$657$	464.929	−	411.878i	0.707655	−	0.626907i
$658$	−27.3927	+	47.4455i	−0.0416302	+	0.0721056i
$659$	−322.292	−	384.092i	−0.489062	−	0.582841i	0.463917	−	0.885879i	$-0.346444\pi$
$659$	−322.292	−	384.092i	−0.489062	−	0.582841i	−0.952979	+	0.303038i	$0.901999\pi$
$660$	800.829	+	279.368i	1.21338	+	0.423285i
$661$	100.807	−	571.703i	0.152506	−	0.864906i	−0.808524	−	0.588463i	$-0.799733\pi$
$661$	100.807	−	571.703i	0.152506	−	0.864906i	0.961030	−	0.276443i	$-0.0891557\pi$
$662$	10.2232	+	1.80263i	0.0154430	+	0.00272301i
$663$	−581.923	+	110.679i	−0.877711	+	0.166936i
$664$	−38.9310	+	32.6670i	−0.0586311	+	0.0491973i
$665$	−523.933	−	302.493i	−0.787869	−	0.454876i
$666$	17.8848	+	2.66093i	0.0268540	+	0.00399539i
$667$	131.247	+	227.326i	0.196772	+	0.340819i
$668$	−214.568	+	589.519i	−0.321209	+	0.882514i
$669$	−13.7916	−	23.1644i	−0.0206153	−	0.0346254i
$670$	−28.8134	−	24.1773i	−0.0430050	−	0.0360855i
$671$	−136.826	−	375.927i	−0.203914	−	0.560249i
$672$	−132.770	−	21.5784i	−0.197575	−	0.0321107i
$673$	−20.6831	−	117.300i	−0.0307327	−	0.174294i	0.965578	−	0.260114i	$-0.0837601\pi$
$673$	−20.6831	−	117.300i	−0.0307327	−	0.174294i	−0.996311	+	0.0858201i	$0.972649\pi$
$674$		−	4.84723i		−	0.00719173i
$675$	345.048	+	110.077i	0.511183	+	0.163078i
$676$	−401.979			−0.594643
$677$	−460.585	+	81.2136i	−0.680333	+	0.119961i	−0.503127	−	0.864213i	$-0.667817\pi$
$677$	−460.585	+	81.2136i	−0.680333	+	0.119961i	−0.177206	+	0.984174i	$0.556706\pi$
$678$	−49.2022	+	18.6595i	−0.0725696	+	0.0275213i
$679$	−427.168	+	155.476i	−0.629113	+	0.228979i
$680$	−89.5613	+	106.735i	−0.131708	+	0.156963i
$681$	2.88919	+	215.321i	0.00424257	+	0.316183i
$682$	16.4795	+	5.99806i	0.0241635	+	0.00879480i
$683$	−271.489	+	156.744i	−0.397495	+	0.229494i	−0.685402	−	0.728164i	$-0.740374\pi$
$683$	−271.489	+	156.744i	−0.397495	+	0.229494i	0.287908	+	0.957658i	$0.407040\pi$
$684$	209.309	−	386.102i	0.306008	−	0.564477i
$685$	269.657	−	467.059i	0.393660	−	0.681839i
$686$	20.7654	+	24.7472i	0.0302702	+	0.0360747i
$687$	122.547	−	105.663i	0.178380	−	0.153803i
$688$	−109.514	+	621.086i	−0.159178	+	0.902741i
$689$	741.976	+	130.830i	1.07689	+	0.189884i
$690$	−21.0821	−	24.4508i	−0.0305537	−	0.0354359i
$691$	−515.245	+	432.342i	−0.745651	+	0.625675i	−0.934349	−	0.356360i	$-0.884018\pi$
$691$	−515.245	+	432.342i	−0.745651	+	0.625675i	0.188698	+	0.982035i	$0.439573\pi$
$692$	−181.253	−	104.646i	−0.261926	−	0.151223i
$693$	−699.901	+	429.530i	−1.00996	+	0.619813i
$694$	20.1813	+	34.9550i	0.0290797	+	0.0503675i
$695$	−78.1382	+	214.683i	−0.112429	+	0.308896i
$696$	50.1689	−	0.673170i	0.0720817	−	0.000967198i
$697$	563.127	+	472.520i	0.807930	+	0.677934i
$698$	−23.7199	−	65.1698i	−0.0339826	−	0.0933665i
$699$	−385.801	−	1017.30i	−0.551933	−	1.45536i
$700$	−74.0341	−	419.868i	−0.105763	−	0.599811i
$701$			906.580i			1.29327i	0.762801	+	0.646633i	$0.223824\pi$
$701$			906.580i			1.29327i	−0.762801	+	0.646633i	$0.776176\pi$
$702$	−23.2295	−	12.1925i	−0.0330904	−	0.0173682i
$703$	208.972			0.297257
$704$	706.311	−	124.542i	1.00328	−	0.176906i
$705$	174.133	−	1071.43i	0.246997	−	1.51975i
$706$	13.9355	−	5.07210i	0.0197386	−	0.00718428i
$707$	142.346	−	169.641i	0.201338	−	0.239945i
$708$	212.308	−	126.404i	0.299870	−	0.178537i
$709$	27.2901	+	9.93278i	0.0384910	+	0.0140096i	0.361194	−	0.932491i	$-0.382369\pi$
$709$	27.2901	+	9.93278i	0.0384910	+	0.0140096i	−0.322703	+	0.946500i	$0.604591\pi$
$710$	1.66451	−	0.961005i	0.00234438	−	0.00135353i
$711$	−1267.75	+	500.340i	−1.78306	+	0.703714i
$712$	76.6389	−	132.742i	0.107639	−	0.186436i
$713$	123.473	+	147.150i	0.173175	+	0.206381i
$714$	−12.5811	−	66.1486i	−0.0176206	−	0.0926451i
$715$	101.678	−	576.642i	0.142206	−	0.806492i
$716$	262.776	+	46.3345i	0.367006	+	0.0647130i
$717$	248.589	−	712.598i	0.346707	−	0.993860i
$718$	−31.0588	+	26.0614i	−0.0432574	+	0.0362973i
$719$	−837.314	−	483.423i	−1.16455	−	0.672355i	−0.212162	−	0.977234i	$-0.568051\pi$
$719$	−837.314	−	483.423i	−1.16455	−	0.672355i	−0.952391	+	0.304879i	$0.901384\pi$
$720$	865.391	−	176.656i	1.20193	−	0.245355i
$721$	−327.301	−	566.902i	−0.453955	−	0.786272i
$722$	8.49902	−	23.3509i	0.0117715	−	0.0323419i
$723$	−590.255	+	1054.79i	−0.816397	+	1.45890i
$724$	−395.311	−	331.705i	−0.546010	−	0.458156i
$725$	81.6331	+	224.285i	0.112597	+	0.309359i
$726$	−2.22253	+	2.72206i	−0.00306134	+	0.00374940i
$727$	152.352	+	864.032i	0.209563	+	1.18849i	0.890096	+	0.455773i	$0.150637\pi$
$727$	152.352	+	864.032i	0.209563	+	1.18849i	−0.680533	+	0.732717i	$0.738252\pi$
$728$			61.8725i			0.0849896i
$729$	−414.089	−	599.976i	−0.568024	−	0.823012i
$730$	−50.3440			−0.0689644
$731$	−938.145	+	165.420i	−1.28337	+	0.226293i
$732$	−323.827	−	264.401i	−0.442386	−	0.361203i
$733$	−34.0124	+	12.3795i	−0.0464017	+	0.0168888i	−0.365117	−	0.930962i	$-0.618971\pi$
$733$	−34.0124	+	12.3795i	−0.0464017	+	0.0168888i	0.318715	+	0.947851i	$0.396749\pi$
$734$	25.5501	−	30.4494i	0.0348094	−	0.0414842i
$735$	236.505	+	132.347i	0.321775	+	0.180065i
$736$	−77.9556	−	28.3735i	−0.105918	−	0.0385510i
$737$	−510.999	+	295.026i	−0.693350	+	0.400306i
$738$	6.51178	+	31.8995i	0.00882354	+	0.0432243i
$739$	237.815	−	411.907i	0.321806	−	0.557384i	−0.659055	−	0.752095i	$-0.729043\pi$
$739$	237.815	−	411.907i	0.321806	−	0.557384i	0.980861	+	0.194711i	$0.0623768\pi$
$740$	271.082	+	323.062i	0.366326	+	0.436571i
$741$	−286.279	−	99.8680i	−0.386342	−	0.134775i
$742$	−14.8718	+	84.3423i	−0.0200429	+	0.113669i
$743$	50.1096	+	8.83567i	0.0674422	+	0.0118919i	0.207267	−	0.978284i	$-0.433543\pi$
$743$	50.1096	+	8.83567i	0.0674422	+	0.0118919i	−0.139825	+	0.990176i	$0.544654\pi$
$744$	36.0698	−	6.86030i	0.0484809	−	0.00922083i
$745$	306.700	−	257.352i	0.411677	−	0.345438i
$746$	10.1011	+	5.83188i	0.0135404	+	0.00781754i
$747$	178.641	+	452.638i	0.239145	+	0.605941i
$748$	545.492	+	944.820i	0.729268	+	1.26313i
$749$	97.8037	−	268.713i	0.130579	−	0.358763i
$750$	12.9708	+	21.7857i	0.0172944	+	0.0290476i
$751$	36.1543	+	30.3371i	0.0481416	+	0.0403956i	0.666541	−	0.745468i	$-0.267774\pi$
$751$	36.1543	+	30.3371i	0.0481416	+	0.0403956i	−0.618399	+	0.785864i	$0.712219\pi$
$752$	−316.153	−	868.624i	−0.420417	−	1.15509i
$753$	1125.89	+	182.984i	1.49520	+	0.243006i
$754$	−3.00218	−	17.0262i	−0.00398167	−	0.0225812i
$755$			957.307i			1.26796i
$756$	−398.821	+	759.843i	−0.527541	+	1.00508i
$757$	973.584			1.28611			0.643054	−	0.765821i	$-0.277667\pi$
$757$	973.584			1.28611			0.643054	+	0.765821i	$0.277667\pi$
$758$	69.5284	−	12.2597i	0.0917262	−	0.0161738i
$759$	−473.549	+	179.589i	−0.623912	+	0.236613i
$760$	−67.0169	+	24.3922i	−0.0881801	+	0.0320949i
$761$	−10.4814	+	12.4913i	−0.0137733	+	0.0164143i	−0.772887	−	0.634544i	$-0.781188\pi$
$761$	−10.4814	+	12.4913i	−0.0137733	+	0.0164143i	0.759114	+	0.650958i	$0.225633\pi$
$762$	−0.0812023	−	6.05170i	−0.000106565	−	0.00794187i
$763$	−10.6055	−	3.86008i	−0.0138997	−	0.00505908i
$764$	936.718	−	540.814i	1.22607	−	0.707872i
$765$	697.822	+	1137.07i	0.912186	+	1.48637i
$766$	6.68897	−	11.5856i	0.00873234	−	0.0151249i
$767$	−109.647	−	130.672i	−0.142956	−	0.170368i
$768$	561.607	−	484.232i	0.731260	−	0.630511i
$769$	24.6634	−	139.873i	0.0320720	−	0.181890i	−0.964563	−	0.263851i	$-0.915007\pi$
$769$	24.6634	−	139.873i	0.0320720	−	0.181890i	0.996636	+	0.0819614i	$0.0261184\pi$
$770$	65.5484	+	11.5579i	0.0851277	+	0.0150103i
$771$	−42.4884	−	49.2775i	−0.0551081	−	0.0639138i
$772$	633.566	−	531.625i	0.820682	−	0.688634i
$773$	991.099	+	572.211i	1.28215	+	0.740248i	0.977240	−	0.212135i	$-0.0680416\pi$
$773$	991.099	+	572.211i	1.28215	+	0.740248i	0.304906	+	0.952382i	$0.401375\pi$
$774$	−37.0909	−	20.1073i	−0.0479211	−	0.0259784i
$775$	87.3317	+	151.263i	0.112686	+	0.195178i
$776$	−18.3281	+	50.3562i	−0.0236187	+	0.0648920i
$777$	−408.283	+	5.47838i	−0.525461	+	0.00705068i
$778$	32.7173	+	27.4531i	0.0420531	+	0.0352867i
$779$	128.691	+	353.577i	0.165201	+	0.453886i
$780$	−216.974	−	572.127i	−0.278172	−	0.733497i
$781$	−5.23571	−	29.6932i	−0.00670385	−	0.0380194i
$782$		−	41.5276i		−	0.0531043i
$783$	146.012	−	457.689i	0.186478	−	0.584532i
$784$	230.792			0.294377
$785$	−1175.30	+	207.237i	−1.49720	+	0.263997i
$786$	8.26571	−	50.8583i	0.0105162	−	0.0647052i
$787$	243.549	−	88.6445i	0.309465	−	0.112636i	−0.182619	−	0.983184i	$-0.558458\pi$
$787$	243.549	−	88.6445i	0.309465	−	0.112636i	0.492084	+	0.870548i	$0.336235\pi$
$788$	−458.205	+	546.067i	−0.581478	+	0.692978i
$789$	−174.969	+	104.173i	−0.221761	+	0.132032i
$790$	103.805	+	37.7821i	0.131399	+	0.0478254i
$791$	1029.10	−	594.150i	1.30101	−	0.751138i
$792$	−14.2461	+	95.7513i	−0.0179874	+	0.120898i
$793$	−144.305	+	249.944i	−0.181974	+	0.315188i
$794$	36.1939	+	43.1342i	0.0455842	+	0.0543252i
$795$	−317.056	−	1667.00i	−0.398812	−	2.09686i
$796$	−17.7256	+	100.527i	−0.0222683	+	0.126290i
$797$	−1045.29	−	184.314i	−1.31154	−	0.231259i	−0.526217	−	0.850350i	$-0.676390\pi$
$797$	−1045.29	−	184.314i	−1.31154	−	0.231259i	−0.785319	+	0.619091i	$0.787501\pi$
$798$	11.3523	−	32.5421i	0.0142259	−	0.0407795i
$799$	1069.59	−	897.495i	1.33866	−	1.12327i
$800$	−65.3263	−	37.7162i	−0.0816579	−	0.0471452i
$801$	−973.213	−	1098.57i	−1.21500	−	1.37149i
$802$	−37.5459	−	65.0315i	−0.0468154	−	0.0810866i
$803$	−270.115	+	742.135i	−0.336382	+	0.924203i
$804$	−301.110	+	538.084i	−0.374515	+	0.669259i
$805$	558.485	+	468.625i	0.693770	+	0.582142i
$806$	−4.32719	−	11.8888i	−0.00536872	−	0.0147504i
$807$	551.335	−	675.252i	0.683191	−	0.836743i
$808$	−4.53316	−	25.7088i	−0.00561035	−	0.0318179i
$809$			1471.80i			1.81928i	0.415398	+	0.909640i	$0.363642\pi$
$809$			1471.80i			1.81928i	−0.415398	+	0.909640i	$0.636358\pi$
$810$	−7.12412	+	58.6560i	−0.00879521	+	0.0724149i
$811$	128.574			0.158537			0.0792685	−	0.996853i	$-0.474742\pi$
$811$	128.574			0.158537			0.0792685	+	0.996853i	$0.474742\pi$
$812$	−556.933	+	98.2024i	−0.685878	+	0.120939i
$813$	−963.549	−	786.727i	−1.18518	−	0.967684i
$814$	−21.6042	+	7.86330i	−0.0265408	+	0.00966007i
$815$	682.486	−	813.355i	0.837406	−	0.997981i
$816$	991.430	+	554.801i	1.21499	+	0.679903i
$817$	−458.195	−	166.769i	−0.560826	−	0.204124i
$818$	−62.4285	+	36.0431i	−0.0763185	+	0.0440625i
$819$	561.943	+	187.614i	0.686133	+	0.229077i
$820$	−379.676	+	657.618i	−0.463020	+	0.801974i
$821$	956.042	+	1139.37i	1.16448	+	1.38778i	0.906806	+	0.421547i	$0.138513\pi$
$821$	956.042	+	1139.37i	1.16448	+	1.38778i	0.257678	+	0.966231i	$0.417043\pi$
$822$	29.0096	+	10.1200i	0.0352915	+	0.0123114i
$823$	−208.329	+	1181.49i	−0.253134	+	1.43559i	0.547685	+	0.836685i	$0.315509\pi$
$823$	−208.329	+	1181.49i	−0.253134	+	1.43559i	−0.800818	+	0.598907i	$0.795602\pi$
$824$	−75.9946	−	13.3999i	−0.0922265	−	0.0162620i
$825$	−452.402	+	86.0446i	−0.548366	+	0.104296i
$826$	14.8539	−	12.4639i	0.0179829	−	0.0150894i
$827$	−609.332	−	351.798i	−0.736798	−	0.425391i	0.0841057	−	0.996457i	$-0.473197\pi$
$827$	−609.332	−	351.798i	−0.736798	−	0.425391i	−0.820904	+	0.571066i	$0.806530\pi$
$828$	−329.196	+	414.412i	−0.397579	+	0.500498i
$829$	112.799	+	195.374i	0.136066	+	0.235674i	0.926004	−	0.377513i	$-0.123221\pi$
$829$	112.799	+	195.374i	0.136066	+	0.235674i	−0.789938	+	0.613187i	$0.789887\pi$
$830$	13.4897	−	37.0626i	0.0162526	−	0.0446538i
$831$	−268.775	−	451.434i	−0.323436	−	0.543242i
$832$	−396.363	−	332.588i	−0.476398	−	0.399746i
$833$	119.231	+	327.585i	0.143135	+	0.393260i
$834$	−12.8466	−	2.08789i	−0.0154036	−	0.00250346i
$835$	−169.385	−	960.629i	−0.202856	−	1.15045i
$836$			558.424i			0.667971i
$837$	47.0665	−	348.398i	0.0562324	−	0.416246i
$838$	61.7470			0.0736838
$839$	−703.465	+	124.040i	−0.838456	+	0.147842i	−0.576356	−	0.817198i	$-0.695526\pi$
$839$	−703.465	+	124.040i	−0.838456	+	0.147842i	−0.262100	+	0.965041i	$0.584415\pi$
$840$	130.296	−	49.4137i	0.155115	−	0.0588258i
$841$	−492.779	+	179.357i	−0.585944	+	0.213266i
$842$	−27.8604	+	33.2027i	−0.0330883	+	0.0394332i
$843$	15.1046	+	1125.69i	0.0179176	+	1.33533i
$844$	−1349.54	−	491.193i	−1.59898	−	0.581982i
$845$	541.285	−	312.511i	0.640574	−	0.369836i
$846$	61.8165	−	1.65922i	0.0730692	−	0.00196125i
$847$	39.6783	−	68.7249i	0.0468457	−	0.0811392i
$848$	−928.845	−	1106.95i	−1.09534	−	1.30537i
$849$	33.5732	−	28.9477i	0.0395444	−	0.0340962i
$850$	6.55696	−	37.1864i	0.00771407	−	0.0437487i
$851$	−248.000	−	43.7291i	−0.291422	−	0.0513855i
$852$	−20.5750	−	23.8627i	−0.0241491	−	0.0280079i
$853$	199.629	−	167.509i	0.234032	−	0.196376i	−0.518228	−	0.855242i	$-0.673408\pi$
$853$	199.629	−	167.509i	0.234032	−	0.196376i	0.752260	+	0.658866i	$0.228964\pi$
$854$	−28.4118	−	16.4036i	−0.0332691	−	0.0192079i
$855$	18.3225	+	682.630i	0.0214298	+	0.798397i
$856$	−16.8549	−	29.1936i	−0.0196904	−	0.0341047i
$857$	354.046	−	972.733i	0.413122	−	1.13504i	−0.542399	−	0.840121i	$-0.682484\pi$
$857$	354.046	−	972.733i	0.413122	−	1.13504i	0.955521	−	0.294923i	$-0.0952940\pi$
$858$	33.3544	−	0.447553i	0.0388746	−	0.000521623i
$859$	−427.947	−	359.090i	−0.498192	−	0.418033i	0.358759	−	0.933430i	$-0.383200\pi$
$859$	−427.947	−	359.090i	−0.498192	−	0.418033i	−0.856951	+	0.515397i	$0.827644\pi$
$860$	−336.559	−	924.688i	−0.391348	−	1.07522i
$861$	−260.703	−	687.435i	−0.302791	−	0.798415i
$862$	−3.63835	−	20.6341i	−0.00422083	−	0.0239375i
$863$		−	251.585i		−	0.291523i	−0.989320	−	0.145762i	$-0.953437\pi$
$863$		−	251.585i		−	0.291523i	0.989320	−	0.145762i	$-0.0465633\pi$
$864$	57.6283	+	140.469i	0.0666995	+	0.162580i
$865$	325.422			0.376210
$866$	−82.3811	+	14.5260i	−0.0951283	+	0.0167737i
$867$	−136.209	+	838.083i	−0.157104	+	0.966647i
$868$	−388.888	+	141.544i	−0.448028	+	0.163069i
$869$	1113.91	−	1327.51i	1.28183	−	1.52763i
$870$	−33.4576	+	19.9200i	−0.0384571	+	0.0228966i
$871$	400.010	+	145.592i	0.459253	+	0.167155i
$872$	−1.15220	+	0.665224i	−0.00132133	+	0.000762872i
$873$	401.772	+	319.155i	0.460220	+	0.365584i
$874$	10.6280	−	18.4083i	0.0121602	−	0.0210621i
$875$	−368.034	−	438.605i	−0.420610	−	0.501263i
$876$	154.205	+	810.771i	0.176033	+	0.925538i
$877$	−84.6067	+	479.828i	−0.0964729	+	0.547125i	0.897813	+	0.440376i	$0.145155\pi$
$877$	−84.6067	+	479.828i	−0.0964729	+	0.547125i	−0.994286	+	0.106748i	$0.965956\pi$
$878$	−73.8096	−	13.0146i	−0.0840656	−	0.0148230i
$879$	131.370	−	376.581i	0.149454	−	0.428420i
$880$	−860.293	+	721.871i	−0.977605	+	0.820308i
$881$	−53.6224	−	30.9589i	−0.0608654	−	0.0351407i	0.469258	−	0.883061i	$-0.344521\pi$
$881$	−53.6224	−	30.9589i	−0.0608654	−	0.0351407i	−0.530124	+	0.847920i	$0.677855\pi$
$882$	−4.88946	+	14.6449i	−0.00554361	+	0.0166042i
$883$	50.9265	+	88.2073i	0.0576744	+	0.0998950i	0.893421	−	0.449220i	$-0.148298\pi$
$883$	50.9265	+	88.2073i	0.0576744	+	0.0998950i	−0.835747	+	0.549115i	$0.814965\pi$
$884$	269.194	−	739.604i	0.304518	−	0.836657i
$885$	−187.613	+	335.264i	−0.211992	+	0.378830i
$886$	−29.1097	−	24.4259i	−0.0328551	−	0.0275687i
$887$	430.135	+	1181.79i	0.484933	+	1.33234i	0.905217	+	0.424950i	$0.139708\pi$
$887$	430.135	+	1181.79i	0.484933	+	1.33234i	−0.420284	+	0.907393i	$0.638070\pi$
$888$	−30.4426	+	37.2848i	−0.0342822	+	0.0419874i
$889$	23.7328	+	134.595i	0.0266961	+	0.151401i
$890$			118.956i			0.133659i
$891$	826.442	+	419.731i	0.927544	+	0.471079i
$892$	35.8212			0.0401582
$893$	703.820	−	124.102i	0.788152	−	0.138972i
$894$	17.6675	+	14.4253i	0.0197623	+	0.0161357i
$895$	−389.863	+	141.899i	−0.435602	+	0.158546i
$896$	153.090	−	182.446i	0.170859	−	0.203622i
$897$	318.847	+	178.426i	0.355460	+	0.198914i
$898$	2.86432	+	1.04253i	0.00318967	+	0.00116094i
$899$	200.642	−	115.841i	0.223184	−	0.128855i
$900$	−360.216	+	319.113i	−0.400240	+	0.354569i
$901$	1091.35	−	1890.27i	1.21127	−	2.09797i
$902$	−26.6092	−	31.7116i	−0.0295002	−	0.0351569i
$903$	899.581	+	313.817i	0.996213	+	0.347527i
$904$	24.3248	−	137.953i	0.0269080	−	0.152603i
$905$	790.184	+	139.331i	0.873132	+	0.153957i
$906$	−53.5763	+	10.1899i	−0.0591350	+	0.0112472i
$907$	−639.102	+	536.271i	−0.704633	+	0.591258i	−0.923088	−	0.384590i	$-0.874343\pi$
$907$	−639.102	+	536.271i	−0.704633	+	0.591258i	0.218454	+	0.975847i	$0.429899\pi$
$908$	−247.792	−	143.063i	−0.272899	−	0.157558i
$909$	−247.240	−	36.7849i	−0.271992	−	0.0404674i
$910$	−24.0091	−	41.5849i	−0.0263836	−	0.0456977i
$911$	−244.801	+	672.586i	−0.268717	+	0.738294i	0.729790	+	0.683671i	$0.239618\pi$
$911$	−244.801	+	672.586i	−0.268717	+	0.738294i	−0.998507	+	0.0546228i	$0.982604\pi$
$912$	297.491	+	499.665i	0.326196	+	0.547878i
$913$	−473.973	−	397.711i	−0.519138	−	0.435609i
$914$	−15.9191	−	43.7373i	−0.0174169	−	0.0478526i
$915$	641.602	+	104.276i	0.701205	+	0.113963i
$916$	37.3342	+	211.733i	0.0407579	+	0.231149i
$917$			1163.55i			1.26887i
$918$	−56.2090	+	51.1575i	−0.0612299	+	0.0557271i
$919$	−714.401			−0.777367			−0.388684	−	0.921371i	$-0.627070\pi$
$919$	−714.401			−0.777367			−0.388684	+	0.921371i	$0.627070\pi$
$920$	84.6375	−	14.9239i	0.0919973	−	0.0162216i
$921$	−197.806	+	75.0162i	−0.214773	+	0.0814508i
$922$	−99.1947	+	36.1039i	−0.107586	+	0.0391583i
$923$	−13.9819	+	16.6630i	−0.0151484	+	0.0180531i
$924$	−14.6396	−	1091.03i	−0.0158437	−	1.18077i
$925$	−215.170	−	78.3155i	−0.232616	−	0.0846654i
$926$	30.3335	−	17.5130i	0.0327576	−	0.0189126i
$927$	−352.138	+	649.572i	−0.379869	+	0.700725i
$928$	−50.0285	+	86.6520i	−0.0539101	+	0.0933749i
$929$	−207.867	−	247.726i	−0.223753	−	0.266659i	0.642476	−	0.766306i	$-0.277907\pi$
$929$	−207.867	−	247.726i	−0.223753	−	0.266659i	−0.866229	+	0.499647i	$0.833463\pi$
$930$	−21.5807	+	18.6074i	−0.0232051	+	0.0200080i
$931$	−30.9852	+	175.726i	−0.0332816	+	0.188750i
$932$	1423.68	+	251.033i	1.52755	+	0.269349i
$933$	119.458	+	138.546i	0.128036	+	0.148495i
$934$	−71.2580	+	59.7926i	−0.0762934	+	0.0640177i
$935$	−1469.07	−	848.166i	−1.57119	−	0.907129i
$936$	59.5231	−	36.5294i	0.0635931	−	0.0390272i
$937$	530.062	+	918.094i	0.565701	+	0.979823i	0.996984	+	0.0776063i	$0.0247277\pi$
$937$	530.062	+	918.094i	0.565701	+	0.979823i	−0.431283	+	0.902217i	$0.641939\pi$
$938$	−16.5498	+	45.4701i	−0.0176437	+	0.0484756i
$939$	633.941	−	8.50627i	0.675124	−	0.00905886i
$940$	1104.86	+	927.092i	1.17539	+	0.986268i
$941$	−444.757	−	1221.96i	−0.472643	−	1.29858i	−0.915620	−	0.402044i	$-0.868300\pi$
$941$	−444.757	−	1221.96i	−0.472643	−	1.29858i	0.442977	−	0.896533i	$-0.353922\pi$
$942$	−24.1086	−	63.5706i	−0.0255929	−	0.0674847i
$943$	−78.7374	−	446.542i	−0.0834967	−	0.473533i
$944$			327.165i			0.346573i
$945$	−53.6937	−	1333.22i	−0.0568187	−	1.41082i
$946$	53.6451			0.0567073
$947$	1618.54	−	285.392i	1.70912	−	0.301364i	0.768254	−	0.640145i	$-0.221126\pi$
$947$	1618.54	−	285.392i	1.70912	−	0.301364i	0.940865	+	0.338781i	$0.110015\pi$
$948$	290.508	−	1787.47i	0.306443	−	1.88552i
$949$	535.400	−	194.870i	0.564172	−	0.205342i
$950$	12.4235	−	14.8058i	0.0130774	−	0.0155851i
$951$	344.872	−	205.330i	0.362641	−	0.215910i
$952$	168.438	+	61.3063i	0.176930	+	0.0643974i
$953$	404.262	−	233.401i	0.424199	−	0.244912i	−0.272673	−	0.962107i	$-0.587908\pi$
$953$	404.262	−	233.401i	0.424199	−	0.244912i	0.696872	+	0.717195i	$0.254574\pi$
$954$	89.9201	−	35.4885i	0.0942559	−	0.0371997i
$955$	−840.892	+	1456.47i	−0.880515	+	1.52510i
$956$	644.587	+	768.189i	0.674254	+	0.803545i
$957$	114.134	+	600.087i	0.119262	+	0.627051i
$958$	−0.0221095	+	0.125389i	−2.30788e−5	+	0.000130886i
$959$	−683.271	−	120.479i	−0.712483	−	0.125630i
$960$	−383.843	+	1100.31i	−0.399836	+	1.14616i
$961$	−606.291	+	508.739i	−0.630896	+	0.529385i
$962$	14.3641	+	8.29312i	0.0149315	+	0.00862071i
$963$	−316.253	+	64.5581i	−0.328404	+	0.0670385i
$964$	−803.014	−	1390.86i	−0.833002	−	1.44280i
$965$	−439.827	+	1208.41i	−0.455779	+	1.25224i
$966$	−20.2821	+	36.2442i	−0.0209960	+	0.0375199i
$967$	−878.060	−	736.780i	−0.908025	−	0.761923i	0.0637176	−	0.997968i	$-0.479704\pi$
$967$	−878.060	−	736.780i	−0.908025	−	0.761923i	−0.971742	+	0.236045i	$0.924149\pi$
$968$	−3.19955	−	8.79069i	−0.00330532	−	0.00908129i
$969$	−555.534	+	680.394i	−0.573306	+	0.702161i
$970$	−7.22179	−	40.9568i	−0.00744515	−	0.0422235i
$971$		−	1439.65i		−	1.48264i	−0.671150	−	0.741322i	$-0.734199\pi$
$971$		−	1439.65i		−	1.48264i	0.671150	−	0.741322i	$-0.265801\pi$
$972$	966.455	−	64.9334i	0.994295	−	0.0668039i
$973$	293.908			0.302064
$974$	75.0627	−	13.2356i	0.0770665	−	0.0135889i
$975$	257.343	+	210.118i	0.263942	+	0.215506i
$976$	520.159	−	189.322i	0.532950	−	0.193978i
$977$	−885.175	+	1054.91i	−0.906013	+	1.07974i	0.0904659	+	0.995900i	$0.471164\pi$
$977$	−885.175	+	1054.91i	−0.906013	+	1.07974i	−0.996479	+	0.0838447i	$0.973280\pi$
$978$	52.7846	+	29.5381i	0.0539720	+	0.0302025i
$979$	1753.57	+	638.247i	1.79118	+	0.651937i
$980$	−311.860	+	180.053i	−0.318225	+	0.183727i
$981$	2.54795	+	12.4818i	0.00259730	+	0.0127235i
$982$	18.3791	−	31.8335i	0.0187160	−	0.0324170i
$983$	−792.551	−	944.525i	−0.806257	−	0.960860i	0.193538	−	0.981093i	$-0.438004\pi$
$983$	−792.551	−	944.525i	−0.806257	−	0.960860i	−0.999795	+	0.0202328i	$0.993559\pi$
$984$	−81.8329	−	28.5473i	−0.0831635	−	0.0290115i
$985$	192.466	−	1091.53i	0.195397	−	1.10815i
$986$	−49.3258	−	8.69747i	−0.0500262	−	0.00882097i
$987$	−1371.85	+	260.919i	−1.38992	+	0.264356i
$988$	308.612	−	258.956i	0.312361	−	0.262102i
$989$	508.871	+	293.797i	0.514531	+	0.297064i
$990$	−27.5806	−	69.8832i	−0.0278592	−	0.0705891i
$991$	25.7878	+	44.6657i	0.0260220	+	0.0450714i	0.878743	−	0.477295i	$-0.158383\pi$
$991$	25.7878	+	44.6657i	0.0260220	+	0.0450714i	−0.852721	+	0.522366i	$0.825049\pi$
$992$	−25.0430	+	68.8051i	−0.0252450	+	0.0693600i
$993$	135.365	+	227.358i	0.136319	+	0.228961i
$994$	−1.89413	−	1.58936i	−0.00190556	−	0.00159896i
$995$	−54.2842	−	149.145i	−0.0545570	−	0.149894i
$996$	−638.199	−	103.723i	−0.640762	−	0.104139i
$997$	−143.357	−	813.019i	−0.143789	−	0.815465i	−0.968332	−	0.249667i	$-0.919679\pi$
$997$	−143.357	−	813.019i	−0.143789	−	0.815465i	0.824543	−	0.565799i	$-0.191432\pi$
$998$		−	5.40139i		−	0.00541222i
$999$	246.320	+	389.546i	0.246567	+	0.389936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.14.3	yes	30
3.2	odd	2		81.3.f.a.71.3		30
4.3	odd	2		432.3.bc.a.257.1		30
9.2	odd	6		243.3.f.a.134.3		30
9.4	even	3		243.3.f.c.53.3		30
9.5	odd	6		243.3.f.b.53.3		30
9.7	even	3		243.3.f.d.134.3		30
27.2	odd	18	inner	27.3.f.a.2.3	✓	30
27.5	odd	18		729.3.b.a.728.16		30
27.7	even	9		243.3.f.a.107.3		30
27.11	odd	18		243.3.f.c.188.3		30
27.16	even	9		243.3.f.b.188.3		30
27.20	odd	18		243.3.f.d.107.3		30
27.22	even	9		729.3.b.a.728.15		30
27.25	even	9		81.3.f.a.8.3		30
108.83	even	18		432.3.bc.a.353.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.3	✓	30	27.2	odd	18	inner
27.3.f.a.14.3	yes	30	1.1	even	1	trivial
81.3.f.a.8.3		30	27.25	even	9
81.3.f.a.71.3		30	3.2	odd	2
243.3.f.a.107.3		30	27.7	even	9
243.3.f.a.134.3		30	9.2	odd	6
243.3.f.b.53.3		30	9.5	odd	6
243.3.f.b.188.3		30	27.16	even	9
243.3.f.c.53.3		30	9.4	even	3
243.3.f.c.188.3		30	27.11	odd	18
243.3.f.d.107.3		30	27.20	odd	18
243.3.f.d.134.3		30	9.7	even	3
432.3.bc.a.257.1		30	4.3	odd	2
432.3.bc.a.353.1		30	108.83	even	18
729.3.b.a.728.15		30	27.22	even	9
729.3.b.a.728.16		30	27.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.115908 - 0.0204377i) q^{2} +(2.32380 + 1.89736i) q^{3} +(-3.74575 + 1.36334i) q^{4} +(3.98394 - 4.74788i) q^{5} +(0.308125 + 0.172426i) q^{6} +(-7.49258 - 2.72708i) q^{7} +(-0.814011 + 0.469969i) q^{8} +(1.80008 + 8.81815i) q^{9} +(0.364735 - 0.631740i) q^{10} +(-7.35571 - 8.76619i) q^{11} +(-11.2911 - 3.93889i) q^{12} +(-1.43358 + 8.13025i) q^{13} +(-0.924186 - 0.162959i) q^{14} +(18.2663 - 3.47416i) q^{15} +(12.1295 - 10.1779i) q^{16} +(20.7128 + 11.9585i) q^{17} +(0.388867 + 0.985304i) q^{18} +(6.12102 + 10.6019i) q^{19} +(-8.44988 + 23.2159i) q^{20} +(-12.2370 - 20.5533i) q^{21} +(-1.03175 - 0.865739i) q^{22} +(-5.04566 - 13.8628i) q^{23} +(-2.78330 - 0.452353i) q^{24} +(-2.32934 - 13.2103i) q^{25} +0.971660i q^{26} +(-12.5481 + 23.9070i) q^{27} +31.7833 q^{28} +(-17.5228 + 3.08975i) q^{29} +(2.04621 - 0.776004i) q^{30} +(-12.2356 + 4.45339i) q^{31} +(3.61462 - 4.30774i) q^{32} +(-0.460606 - 34.3273i) q^{33} +(2.64519 + 0.962769i) q^{34} +(-42.7978 + 24.7093i) q^{35} +(-18.7648 - 30.5765i) q^{36} +(8.53500 - 14.7831i) q^{37} +(0.926154 + 1.10375i) q^{38} +(-18.7573 + 16.1730i) q^{39} +(-1.01161 + 5.73715i) q^{40} +(30.2688 + 5.33721i) q^{41} +(-1.83843 - 2.13219i) q^{42} +(-30.5116 + 25.6022i) q^{43} +(39.5040 + 22.8076i) q^{44} +(49.0389 + 26.5844i) q^{45} +(-0.868158 - 1.50369i) q^{46} +(19.9668 - 54.8583i) q^{47} +(47.4976 - 0.637327i) q^{48} +(11.1657 + 9.36910i) q^{49} +(-0.539978 - 1.48358i) q^{50} +(25.4428 + 67.0888i) q^{51} +(-5.71447 - 32.4084i) q^{52} -91.2612i q^{53} +(-0.965824 + 3.02747i) q^{54} -70.9255 q^{55} +(7.38068 - 1.30141i) q^{56} +(-5.89158 + 36.2505i) q^{57} +(-1.96789 + 0.716253i) q^{58} +(-13.2814 + 15.8282i) q^{59} +(-63.6845 + 37.9166i) q^{60} +(32.8508 + 11.9567i) q^{61} +(-1.32719 + 0.766252i) q^{62} +(10.5605 - 70.9797i) q^{63} +(-31.3370 + 54.2773i) q^{64} +(32.8901 + 39.1969i) q^{65} +(-0.754959 - 3.96939i) q^{66} +(8.95370 - 50.7790i) q^{67} +(-93.8886 - 16.5551i) q^{68} +(14.5776 - 41.7879i) q^{69} +(-4.45561 + 3.73870i) q^{70} +(2.28181 + 1.31740i) q^{71} +(-5.60955 - 6.33208i) q^{72} +(-34.5072 - 59.7683i) q^{73} +(0.687144 - 1.88791i) q^{74} +(19.6518 - 35.1177i) q^{75} +(-37.3819 - 31.3671i) q^{76} +(31.2072 + 85.7410i) q^{77} +(-1.84358 + 2.25794i) q^{78} +(26.2964 + 149.134i) q^{79} -98.1375i q^{80} +(-74.5194 + 31.7468i) q^{81} +3.61748 q^{82} +(53.2469 - 9.38886i) q^{83} +(73.8580 + 60.3042i) q^{84} +(139.296 - 50.6997i) q^{85} +(-3.01328 + 3.59109i) q^{86} +(-46.5819 - 26.0671i) q^{87} +(10.1075 + 3.67882i) q^{88} +(-141.225 + 81.5361i) q^{89} +(6.22733 + 2.07910i) q^{90} +(32.9130 - 57.0070i) q^{91} +(37.7996 + 45.0478i) q^{92} +(-36.8828 - 12.8665i) q^{93} +(1.19313 - 6.76659i) q^{94} +(74.7224 + 13.1756i) q^{95} +(16.5730 - 3.15209i) q^{96} +(43.6738 - 36.6467i) q^{97} +(1.48567 + 0.857754i) q^{98} +(64.0607 - 80.6436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

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