LMFDB - Embedded newform 189.2.ba.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21351 + 0.213974i) q^{2} +(-1.60161 - 0.659440i) q^{3} +(-0.452565 + 0.164720i) q^{4} +(-0.378134 + 2.14451i) q^{5} +(2.08467 + 0.457534i) q^{6} +(-0.671624 - 2.55909i) q^{7} +(2.64823 - 1.52896i) q^{8} +(2.13028 + 2.11232i) q^{9} -2.68329i q^{10} +(-0.0432582 + 0.00762759i) q^{11} +(0.833453 + 0.0346227i) q^{12} +(2.80925 - 3.34793i) q^{13} +(1.36260 + 2.96176i) q^{14} +(2.01979 - 3.18529i) q^{15} +(-2.14863 + 1.80291i) q^{16} +4.53595 q^{17} +(-3.03710 - 2.10750i) q^{18} -6.99767i q^{19} +(-0.182113 - 1.03281i) q^{20} +(-0.611886 + 4.54154i) q^{21} +(0.0508621 - 0.0185123i) q^{22} +(0.167036 - 0.199066i) q^{23} +(-5.24967 + 0.702436i) q^{24} +(0.242545 + 0.0882792i) q^{25} +(-2.69268 + 4.66385i) q^{26} +(-2.01891 - 4.78790i) q^{27} +(0.725487 + 1.04752i) q^{28} +(2.65522 + 3.16437i) q^{29} +(-1.76947 + 4.29757i) q^{30} +(1.31493 + 3.61275i) q^{31} +(-1.70958 + 2.03739i) q^{32} +(0.0743125 + 0.0163098i) q^{33} +(-5.50442 + 0.970577i) q^{34} +(5.74194 - 0.472625i) q^{35} +(-1.31203 - 0.605064i) q^{36} +(-2.18902 - 3.79150i) q^{37} +(1.49732 + 8.49174i) q^{38} +(-6.70706 + 3.50953i) q^{39} +(2.27747 + 6.25730i) q^{40} +(-5.10519 - 4.28376i) q^{41} +(-0.229244 - 5.64213i) q^{42} +(9.15605 + 3.33253i) q^{43} +(0.0183207 - 0.0105775i) q^{44} +(-5.33542 + 3.76965i) q^{45} +(-0.160105 + 0.277310i) q^{46} +(-6.09518 - 2.21846i) q^{47} +(4.63016 - 1.47066i) q^{48} +(-6.09784 + 3.43749i) q^{49} +(-0.313220 - 0.0552292i) q^{50} +(-7.26480 - 2.99119i) q^{51} +(-0.719895 + 1.97790i) q^{52} +(7.32681 - 4.23013i) q^{53} +(3.47446 + 5.37817i) q^{54} -0.0956517i q^{55} +(-5.69135 - 5.75017i) q^{56} +(-4.61454 + 11.2075i) q^{57} +(-3.89923 - 3.27184i) q^{58} +(-7.98695 - 6.70185i) q^{59} +(-0.389406 + 1.77425i) q^{60} +(3.82219 - 10.5014i) q^{61} +(-2.36872 - 4.10274i) q^{62} +(3.97487 - 6.87025i) q^{63} +(4.44347 - 7.69631i) q^{64} +(6.11738 + 7.29041i) q^{65} +(-0.0936688 - 0.00389112i) q^{66} +(0.622290 - 3.52918i) q^{67} +(-2.05281 + 0.747162i) q^{68} +(-0.398798 + 0.208675i) q^{69} +(-6.86677 + 1.80216i) q^{70} +(5.14654 + 2.97136i) q^{71} +(8.87112 + 2.33682i) q^{72} +(5.45458 + 3.14920i) q^{73} +(3.46769 + 4.13263i) q^{74} +(-0.330247 - 0.301332i) q^{75} +(1.15266 + 3.16690i) q^{76} +(0.0485729 + 0.105579i) q^{77} +(7.38813 - 5.69399i) q^{78} +(1.77980 + 10.0937i) q^{79} +(-3.05389 - 5.28948i) q^{80} +(0.0761693 + 8.99968i) q^{81} +(7.11181 + 4.10601i) q^{82} +(9.64103 - 8.08979i) q^{83} +(-0.471165 - 2.15613i) q^{84} +(-1.71520 + 9.72737i) q^{85} +(-11.8240 - 2.08490i) q^{86} +(-2.16590 - 6.81902i) q^{87} +(-0.102895 + 0.0863395i) q^{88} +0.332132 q^{89} +(5.66798 - 5.71615i) q^{90} +(-10.4544 - 4.94055i) q^{91} +(-0.0428046 + 0.117605i) q^{92} +(0.276387 - 6.65332i) q^{93} +(7.87125 + 1.38791i) q^{94} +(15.0065 + 2.64606i) q^{95} +(4.08160 - 2.13574i) q^{96} +(-1.19363 + 3.27948i) q^{97} +(6.66425 - 5.47621i) q^{98} +(-0.108264 - 0.0751265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.21351	+	0.213974i	−0.858081	+	0.151303i	−0.585343	−	0.810786i	$-0.699040\pi$
$2$	−1.21351	+	0.213974i	−0.858081	+	0.151303i	−0.272738	+	0.962088i	$0.587929\pi$
$3$	−1.60161	−	0.659440i	−0.924687	−	0.380728i
$3$	−1.60161	−	0.659440i	−0.924687	−	0.380728i
$4$	−0.452565	+	0.164720i	−0.226282	+	0.0823601i
$5$	−0.378134	+	2.14451i	−0.169107	+	0.959052i	0.775622	+	0.631198i	$0.217436\pi$
$5$	−0.378134	+	2.14451i	−0.169107	+	0.959052i	−0.944728	+	0.327854i	$0.893675\pi$
$6$	2.08467	+	0.457534i	0.851061	+	0.186787i
$7$	−0.671624	−	2.55909i	−0.253850	−	0.967244i
$7$	−0.671624	−	2.55909i	−0.253850	−	0.967244i
$8$	2.64823	−	1.52896i	0.936291	−	0.540568i
$9$	2.13028	+	2.11232i	0.710093	+	0.704108i
$10$		−	2.68329i		−	0.848530i
$11$	−0.0432582	+	0.00762759i	−0.0130428	+	0.00229980i	−0.180166	−	0.983636i	$-0.557663\pi$
$11$	−0.0432582	+	0.00762759i	−0.0130428	+	0.00229980i	0.167123	+	0.985936i	$0.446552\pi$
$12$	0.833453	+	0.0346227i	0.240597	+	0.00999472i
$13$	2.80925	−	3.34793i	0.779145	−	0.928549i	−0.219750	−	0.975556i	$-0.570524\pi$
$13$	2.80925	−	3.34793i	0.779145	−	0.928549i	0.998895	+	0.0470077i	$0.0149685\pi$
$14$	1.36260	+	2.96176i	0.364171	+	0.791565i
$15$	2.01979	−	3.18529i	0.521509	−	0.822439i
$16$	−2.14863	+	1.80291i	−0.537157	+	0.450728i
$17$	4.53595			1.10013			0.550065	−	0.835122i	$-0.314603\pi$
$17$	4.53595			1.10013			0.550065	+	0.835122i	$0.314603\pi$
$18$	−3.03710	−	2.10750i	−0.715850	−	0.496743i
$19$		−	6.99767i		−	1.60538i	−0.596399	−	0.802688i	$-0.703402\pi$
$19$		−	6.99767i		−	1.60538i	0.596399	−	0.802688i	$-0.296598\pi$
$20$	−0.182113	−	1.03281i	−0.0407217	−	0.230944i
$21$	−0.611886	+	4.54154i	−0.133524	+	0.991046i
$22$	0.0508621	−	0.0185123i	0.0108438	−	0.00394684i
$23$	0.167036	−	0.199066i	0.0348295	−	0.0415082i	−0.748349	−	0.663306i	$-0.769153\pi$
$23$	0.167036	−	0.199066i	0.0348295	−	0.0415082i	0.783178	+	0.621798i	$0.213597\pi$
$24$	−5.24967	+	0.702436i	−1.07159	+	0.143384i
$25$	0.242545	+	0.0882792i	0.0485090	+	0.0176558i
$26$	−2.69268	+	4.66385i	−0.528077	+	0.914657i
$27$	−2.01891	−	4.78790i	−0.388540	−	0.921432i
$28$	0.725487	+	1.04752i	0.137104	+	0.197963i
$29$	2.65522	+	3.16437i	0.493062	+	0.587608i	0.953993	−	0.299828i	$-0.0969292\pi$
$29$	2.65522	+	3.16437i	0.493062	+	0.587608i	−0.460932	+	0.887436i	$0.652485\pi$
$30$	−1.76947	+	4.29757i	−0.323059	+	0.784625i
$31$	1.31493	+	3.61275i	0.236169	+	0.648869i	0.999994	+	0.00344562i	$0.00109678\pi$
$31$	1.31493	+	3.61275i	0.236169	+	0.648869i	−0.763825	+	0.645423i	$0.776681\pi$
$32$	−1.70958	+	2.03739i	−0.302213	+	0.360164i
$33$	0.0743125	+	0.0163098i	0.0129361	+	0.00283917i
$34$	−5.50442	+	0.970577i	−0.944000	+	0.166453i
$35$	5.74194	−	0.472625i	0.970565	−	0.0798881i
$36$	−1.31203	−	0.605064i	−0.218672	−	0.100844i
$37$	−2.18902	−	3.79150i	−0.359873	−	0.623319i	0.628066	−	0.778160i	$-0.283847\pi$
$37$	−2.18902	−	3.79150i	−0.359873	−	0.623319i	−0.987939	+	0.154841i	$0.950513\pi$
$38$	1.49732	+	8.49174i	0.242898	+	1.37754i
$39$	−6.70706	+	3.50953i	−1.07399	+	0.561975i
$40$	2.27747	+	6.25730i	0.360100	+	0.989365i
$41$	−5.10519	−	4.28376i	−0.797297	−	0.669012i	0.150243	−	0.988649i	$-0.451994\pi$
$41$	−5.10519	−	4.28376i	−0.797297	−	0.669012i	−0.947540	+	0.319638i	$0.896439\pi$
$42$	−0.229244	−	5.64213i	−0.0353732	−	0.870600i
$43$	9.15605	+	3.33253i	1.39628	+	0.508206i	0.927073	−	0.374880i	$-0.122316\pi$
$43$	9.15605	+	3.33253i	1.39628	+	0.508206i	0.469211	+	0.883086i	$0.344538\pi$
$44$	0.0183207	−	0.0105775i	0.00276195	−	0.00159461i
$45$	−5.33542	+	3.76965i	−0.795358	+	0.561946i
$46$	−0.160105	+	0.277310i	−0.0236062	+	0.0408872i
$47$	−6.09518	−	2.21846i	−0.889073	−	0.323596i	−0.143208	−	0.989693i	$-0.545742\pi$
$47$	−6.09518	−	2.21846i	−0.889073	−	0.323596i	−0.745866	+	0.666096i	$0.767964\pi$
$48$	4.63016	−	1.47066i	0.668307	−	0.212272i
$49$	−6.09784	+	3.43749i	−0.871120	+	0.491070i
$50$	−0.313220	−	0.0552292i	−0.0442960	−	0.00781059i
$51$	−7.26480	−	2.99119i	−1.01728	−	0.418850i
$52$	−0.719895	+	1.97790i	−0.0998315	+	0.274285i
$53$	7.32681	−	4.23013i	1.00641	−	0.581054i	0.0962747	−	0.995355i	$-0.469307\pi$
$53$	7.32681	−	4.23013i	1.00641	−	0.581054i	0.910140	+	0.414301i	$0.135974\pi$
$54$	3.47446	+	5.37817i	0.472814	+	0.731876i
$55$		−	0.0956517i		−	0.0128977i
$56$	−5.69135	−	5.75017i	−0.760538	−	0.768398i
$57$	−4.61454	+	11.2075i	−0.611211	+	1.48447i
$58$	−3.89923	−	3.27184i	−0.511993	−	0.429613i
$59$	−7.98695	−	6.70185i	−1.03981	−	0.872506i	−0.0478267	−	0.998856i	$-0.515230\pi$
$59$	−7.98695	−	6.70185i	−1.03981	−	0.872506i	−0.991986	+	0.126349i	$0.959674\pi$
$60$	−0.389406	+	1.77425i	−0.0502721	+	0.229055i
$61$	3.82219	−	10.5014i	0.489382	−	1.34457i	−0.411860	−	0.911247i	$-0.635121\pi$
$61$	3.82219	−	10.5014i	0.489382	−	1.34457i	0.901241	−	0.433318i	$-0.142657\pi$
$62$	−2.36872	−	4.10274i	−0.300828	−	0.521049i
$63$	3.97487	−	6.87025i	0.500787	−	0.865571i
$64$	4.44347	−	7.69631i	0.555434	−	0.962039i
$65$	6.11738	+	7.29041i	0.758768	+	0.904264i
$66$	−0.0936688	−	0.00389112i	−0.0115298	−	0.000478964i
$67$	0.622290	−	3.52918i	0.0760248	−	0.431158i	−0.922910	−	0.385016i	$-0.874196\pi$
$67$	0.622290	−	3.52918i	0.0760248	−	0.431158i	0.998935	−	0.0461425i	$-0.0146928\pi$
$68$	−2.05281	+	0.747162i	−0.248940	+	0.0906067i
$69$	−0.398798	+	0.208675i	−0.0480097	+	0.0251215i
$70$	−6.86677	+	1.80216i	−0.820736	+	0.215400i
$71$	5.14654	+	2.97136i	0.610782	+	0.352635i	0.773272	−	0.634075i	$-0.218619\pi$
$71$	5.14654	+	2.97136i	0.610782	+	0.352635i	−0.162489	+	0.986710i	$0.551952\pi$
$72$	8.87112	+	2.33682i	1.04547	+	0.275397i
$73$	5.45458	+	3.14920i	0.638410	+	0.368586i	0.784002	−	0.620759i	$-0.213175\pi$
$73$	5.45458	+	3.14920i	0.638410	+	0.368586i	−0.145592	+	0.989345i	$0.546509\pi$
$74$	3.46769	+	4.13263i	0.403110	+	0.480408i
$75$	−0.330247	−	0.301332i	−0.0381336	−	0.0347949i
$76$	1.15266	+	3.16690i	0.132219	+	0.363269i
$77$	0.0485729	+	0.105579i	0.00553540	+	0.0120318i
$78$	7.38813	−	5.69399i	0.836541	−	0.644717i
$79$	1.77980	+	10.0937i	0.200243	+	1.13563i	0.904752	+	0.425938i	$0.140056\pi$
$79$	1.77980	+	10.0937i	0.200243	+	1.13563i	−0.704510	+	0.709694i	$0.748833\pi$
$80$	−3.05389	−	5.28948i	−0.341435	−	0.591382i
$81$	0.0761693	+	8.99968i	0.00846326	+	0.999964i
$82$	7.11181	+	4.10601i	0.785368	+	0.453433i
$83$	9.64103	−	8.08979i	1.05824	−	0.887970i	0.0643051	−	0.997930i	$-0.479517\pi$
$83$	9.64103	−	8.08979i	1.05824	−	0.887970i	0.993936	+	0.109961i	$0.0350725\pi$
$84$	−0.471165	−	2.15613i	−0.0514083	−	0.235253i
$85$	−1.71520	+	9.72737i	−0.186039	+	1.05508i
$86$	−11.8240	−	2.08490i	−1.27502	−	0.224820i
$87$	−2.16590	−	6.81902i	−0.232209	−	0.731076i
$88$	−0.102895	+	0.0863395i	−0.0109687	+	0.00920382i
$89$	0.332132			0.0352060			0.0176030	−	0.999845i	$-0.494397\pi$
$89$	0.332132			0.0352060			0.0176030	+	0.999845i	$0.494397\pi$
$90$	5.66798	−	5.71615i	0.597457	−	0.602535i
$91$	−10.4544	−	4.94055i	−1.09592	−	0.517911i
$92$	−0.0428046	+	0.117605i	−0.00446269	+	0.0122611i
$93$	0.276387	−	6.65332i	0.0286600	−	0.689917i
$94$	7.87125	+	1.38791i	0.811858	+	0.143152i
$95$	15.0065	+	2.64606i	1.53964	+	0.271480i
$96$	4.08160	−	2.13574i	0.416577	−	0.217978i
$97$	−1.19363	+	3.27948i	−0.121195	+	0.332981i	−0.985424	−	0.170119i	$-0.945585\pi$
$97$	−1.19363	+	3.27948i	−0.121195	+	0.332981i	0.864228	+	0.503100i	$0.167807\pi$
$98$	6.66425	−	5.47621i	0.673191	−	0.553181i
$99$	−0.108264	−	0.0751265i	−0.0108809	−	0.00755049i
$100$	−0.124309			−0.0124309
$101$	−3.91229	+	3.28280i	−0.389288	+	0.326651i	−0.816336	−	0.577578i	$-0.803998\pi$
$101$	−3.91229	+	3.28280i	−0.389288	+	0.326651i	0.427048	+	0.904229i	$0.359554\pi$
$102$	9.45594	+	2.07535i	0.936278	+	0.205490i
$103$	4.71444	+	0.831282i	0.464527	+	0.0819087i	0.401013	−	0.916072i	$-0.368658\pi$
$103$	4.71444	+	0.831282i	0.464527	+	0.0819087i	0.0635140	+	0.997981i	$0.479769\pi$
$104$	2.32069	−	13.1613i	0.227563	−	1.29057i
$105$	−9.50798	−	3.02950i	−0.927884	−	0.295649i
$106$	−7.98601	+	6.70106i	−0.775670	+	0.650864i
$107$	−4.62564	−	2.67061i	−0.447177	−	0.258178i	0.259460	−	0.965754i	$-0.416455\pi$
$107$	−4.62564	−	2.67061i	−0.447177	−	0.258178i	−0.706637	+	0.707576i	$0.749789\pi$
$108$	1.70235	+	1.83428i	0.163809	+	0.176504i
$109$	−5.25793	−	9.10701i	−0.503619	−	0.872293i	−0.999991	−	0.00418370i	$-0.998668\pi$
$109$	−5.25793	−	9.10701i	−0.503619	−	0.872293i	0.496372	−	0.868110i	$-0.334665\pi$
$110$	0.0204670	+	0.116074i	0.00195145	+	0.0110672i
$111$	1.00569	+	7.51602i	0.0954554	+	0.713389i
$112$	6.05688	+	4.28764i	0.572321	+	0.405144i
$113$	−5.25570	−	14.4399i	−0.494415	−	1.35839i	−0.896602	−	0.442836i	$-0.853972\pi$
$113$	−5.25570	−	14.4399i	−0.494415	−	1.35839i	0.402188	−	0.915557i	$-0.368250\pi$
$114$	3.20167	−	14.5878i	0.299864	−	1.36627i
$115$	0.363736	+	0.433484i	0.0339186	+	0.0404226i
$116$	−1.72289	−	0.994713i	−0.159967	−	0.0923568i
$117$	13.0564	−	1.19798i	1.20706	−	0.110753i
$118$	11.1263	+	6.42375i	1.02426	+	0.591354i
$119$	−3.04645	−	11.6079i	−0.279268	−	1.06409i
$120$	0.478704	−	11.5236i	0.0436995	−	1.05195i
$121$	−10.3348	+	3.76156i	−0.939528	+	0.341960i
$122$	−2.39124	+	13.5614i	−0.216493	+	1.22779i
$123$	5.35162	+	10.2275i	0.482539	+	0.922179i
$124$	−1.19019	−	1.41841i	−0.106882	−	0.127377i
$125$	−5.72500	+	9.91599i	−0.512060	+	0.886913i
$126$	−3.35349	+	9.18764i	−0.298752	+	0.818500i
$127$	1.20135	+	2.08079i	0.106602	+	0.184640i	0.914392	−	0.404831i	$-0.132670\pi$
$127$	1.20135	+	2.08079i	0.106602	+	0.184640i	−0.807789	+	0.589471i	$0.799336\pi$
$128$	−1.92608	+	5.29187i	−0.170243	+	0.467740i
$129$	−12.4668	−	11.3753i	−1.09764	−	1.00154i
$130$	−8.98346	−	7.53802i	−0.787902	−	0.661128i
$131$	3.57730	+	3.00171i	0.312550	+	0.262260i	0.785545	−	0.618805i	$-0.212383\pi$
$131$	3.57730	+	3.00171i	0.312550	+	0.262260i	−0.472995	+	0.881065i	$0.656827\pi$
$132$	−0.0363178	+	0.00485952i	−0.00316106	+	0.000422967i
$133$	−17.9076	+	4.69981i	−1.55279	+	0.407525i
$134$			4.41585i			0.381471i
$135$	11.0311	−	2.51910i	0.949406	−	0.216810i
$136$	12.0122	−	6.93527i	1.03004	−	0.594694i
$137$	−6.14278	+	16.8771i	−0.524813	+	1.44191i	0.340292	+	0.940320i	$0.389474\pi$
$137$	−6.14278	+	16.8771i	−0.524813	+	1.44191i	−0.865104	+	0.501592i	$0.832748\pi$
$138$	0.439295	−	0.338562i	0.0373952	−	0.0288203i
$139$	14.2972	+	2.52097i	1.21267	+	0.213826i	0.743167	−	0.669106i	$-0.233323\pi$
$139$	14.2972	+	2.52097i	1.21267	+	0.213826i	0.469501	+	0.882932i	$0.344434\pi$
$140$	−2.52075	+	1.15971i	−0.213042	+	0.0980131i
$141$	8.29913	+	7.57251i	0.698913	+	0.637720i
$142$	−6.88118	−	2.50454i	−0.577455	−	0.210177i
$143$	−0.0959863	+	0.166253i	−0.00802678	+	0.0139028i
$144$	−8.38551	−	0.697893i	−0.698792	−	0.0581578i
$145$	−7.79003	+	4.49757i	−0.646927	+	0.373503i
$146$	−7.29303	−	2.65445i	−0.603576	−	0.219684i
$147$	12.0332	−	1.48434i	0.992478	−	0.122426i
$148$	1.61521	+	1.35532i	0.132770	+	0.111407i
$149$	6.37610	+	17.5182i	0.522351	+	1.43515i	0.867897	+	0.496745i	$0.165472\pi$
$149$	6.37610	+	17.5182i	0.522351	+	1.43515i	−0.345546	+	0.938402i	$0.612306\pi$
$150$	0.465235	+	0.295005i	0.0379863	+	0.0240871i
$151$	−1.11155	−	6.30392i	−0.0904567	−	0.513006i	−0.996045	−	0.0888482i	$-0.971681\pi$
$151$	−1.11155	−	6.30392i	−0.0904567	−	0.513006i	0.905588	−	0.424157i	$-0.139430\pi$
$152$	−10.6991	−	18.5315i	−0.867815	−	1.50310i
$153$	9.66283	+	9.58140i	0.781194	+	0.774610i
$154$	−0.0815348	−	0.117727i	−0.00657026	−	0.00948673i
$155$	−8.24478	+	1.45378i	−0.662237	+	0.116770i
$156$	2.45729	−	2.69308i	0.196741	−	0.215619i
$157$	11.2601	−	13.4193i	0.898655	−	1.07098i	−0.0984651	−	0.995141i	$-0.531393\pi$
$157$	11.2601	−	13.4193i	0.898655	−	1.07098i	0.997120	−	0.0758352i	$-0.0241623\pi$
$158$	−4.31960	−	11.8680i	−0.343649	−	0.944167i
$159$	−14.5242	+	1.94342i	−1.15184	+	0.154123i
$160$	−3.72275	−	4.43660i	−0.294309	−	0.350744i
$161$	−0.621613	−	0.293763i	−0.0489900	−	0.0231517i
$162$	−2.01813	−	10.9049i	−0.158560	−	0.856770i
$163$	−3.72087	+	6.44474i	−0.291441	+	0.504791i	−0.974151	−	0.225899i	$-0.927468\pi$
$163$	−3.72087	+	6.44474i	−0.291441	+	0.504791i	0.682710	+	0.730690i	$0.260801\pi$
$164$	3.01605	+	1.09775i	0.235514	+	0.0857202i
$165$	−0.0630765	+	0.153196i	−0.00491050	+	0.0119263i
$166$	−9.96848	+	11.8800i	−0.773704	+	0.922065i
$167$	−23.5674	+	8.57783i	−1.82370	+	0.663772i	−0.829210	+	0.558937i	$0.811209\pi$
$167$	−23.5674	+	8.57783i	−1.82370	+	0.663772i	−0.994490	+	0.104835i	$0.966569\pi$
$168$	5.32340	+	12.9626i	0.410710	+	1.00009i
$169$	−1.05934	−	6.00782i	−0.0814877	−	0.462140i
$170$		−	12.1713i		−	0.933493i
$171$	14.7814	−	14.9070i	1.13036	−	1.13997i
$172$	−4.69264			−0.357811
$173$	−2.47077	+	2.07322i	−0.187849	+	0.157624i	−0.731862	−	0.681452i	$-0.761349\pi$
$173$	−2.47077	+	2.07322i	−0.187849	+	0.157624i	0.544013	+	0.839077i	$0.316904\pi$
$174$	4.08744	+	7.81150i	0.309868	+	0.592188i
$175$	0.0630148	−	0.679984i	0.00476347	−	0.0514020i
$176$	0.0791938	−	0.0943796i	0.00596946	−	0.00711413i
$177$	8.37248	+	16.0006i	0.629314	+	1.20268i
$178$	−0.403046	+	0.0710679i	−0.0302096	+	0.00532676i
$179$			6.05400i			0.452497i	0.974070	+	0.226249i	$0.0726462\pi$
$179$			6.05400i			0.452497i	−0.974070	+	0.226249i	$0.927354\pi$
$180$	1.79369	−	2.58486i	0.133694	−	0.192664i
$181$	−20.8337	+	12.0283i	−1.54856	+	0.894059i	−0.550303	+	0.834965i	$0.685488\pi$
$181$	−20.8337	+	12.0283i	−1.54856	+	0.894059i	−0.998252	+	0.0590938i	$0.981179\pi$
$182$	13.7437	+	3.75843i	1.01875	+	0.278594i
$183$	−13.0467	+	14.2986i	−0.964438	+	1.05698i
$184$	0.137987	−	0.782564i	0.0101726	−	0.0576914i
$185$	8.95864	−	3.26068i	0.658652	−	0.239730i
$186$	1.08824	+	8.13300i	0.0797937	+	0.596341i
$187$	−0.196217	+	0.0345983i	−0.0143488	+	0.00253008i
$188$	3.12389			0.227833
$189$	−10.8967	+	8.38224i	−0.792618	+	0.609718i
$190$	−18.7768			−1.36221
$191$	6.41790	−	1.13165i	0.464383	−	0.0818832i	0.0634387	−	0.997986i	$-0.479793\pi$
$191$	6.41790	−	1.13165i	0.464383	−	0.0818832i	0.400944	+	0.916103i	$0.368682\pi$
$192$	−12.1919	+	9.39626i	−0.879878	+	0.678116i
$193$	19.1535	−	6.97130i	1.37870	−	0.501805i	0.456915	−	0.889510i	$-0.348954\pi$
$193$	19.1535	−	6.97130i	1.37870	−	0.501805i	0.921784	+	0.387705i	$0.126732\pi$
$194$	0.746760	−	4.23509i	0.0536143	−	0.304062i
$195$	−4.99004	−	15.7104i	−0.357344	−	1.12505i
$196$	2.19345	−	2.56012i	0.156675	−	0.182866i
$197$	−15.3673	+	8.87232i	−1.09487	+	0.632126i	−0.934870	−	0.354990i	$-0.884484\pi$
$197$	−15.3673	+	8.87232i	−1.09487	+	0.632126i	−0.160005	+	0.987116i	$0.551151\pi$
$198$	0.147454	+	0.0680010i	0.0104791	+	0.00483262i
$199$			11.1081i			0.787433i	0.919232	+	0.393716i	$0.128811\pi$
$199$			11.1081i			0.787433i	−0.919232	+	0.393716i	$0.871189\pi$
$200$	0.777290	−	0.137057i	0.0549627	−	0.00969141i
$201$	−3.32394	+	5.24199i	−0.234453	+	0.369742i
$202$	4.04517	−	4.82084i	0.284617	−	0.339193i
$203$	6.31457	−	8.92020i	0.443196	−	0.626075i
$204$	3.78050	+	0.157047i	0.264688	+	0.0109955i
$205$	11.1170	−	9.32827i	0.776445	−	0.651515i
$206$	−5.89889			−0.410995
$207$	0.776326	−	0.0712313i	0.0539584	−	0.00495092i
$208$			12.2583i			0.849958i
$209$	0.0533754	+	0.302707i	0.00369205	+	0.0209387i
$210$	12.1863	+	1.64187i	0.840932	+	0.113300i
$211$	−0.626599	+	0.228064i	−0.0431369	+	0.0157005i	−0.363498	−	0.931595i	$-0.618418\pi$
$211$	−0.626599	+	0.228064i	−0.0431369	+	0.0157005i	0.320362	+	0.947295i	$0.396196\pi$
$212$	−2.61907	+	3.12128i	−0.179878	+	0.214371i
$213$	−6.28330	−	8.15278i	−0.430525	−	0.558619i
$214$	6.18470	+	2.25105i	0.422777	+	0.153878i
$215$	−10.6088	+	18.3751i	−0.723517	+	1.25317i
$216$	−12.6670	−	9.59263i	−0.861883	−	0.652696i
$217$	8.36219	−	5.79144i	0.567663	−	0.393148i
$218$	8.32922	+	9.92638i	0.564126	+	0.672299i
$219$	−6.65937	−	8.64075i	−0.449999	−	0.583887i
$220$	0.0157558	+	0.0432886i	0.00106225	+	0.00291852i
$221$	12.7426	−	15.1860i	0.857160	−	1.02152i
$222$	−2.82865	−	8.90557i	−0.189846	−	0.597703i
$223$	−3.89164	+	0.686201i	−0.260604	+	0.0459514i	−0.302423	−	0.953174i	$-0.597796\pi$
$223$	−3.89164	+	0.686201i	−0.260604	+	0.0459514i	0.0418197	+	0.999125i	$0.486684\pi$
$224$	6.36206	+	3.00659i	0.425083	+	0.200886i
$225$	0.330214	+	0.700393i	0.0220143	+	0.0466929i
$226$	9.46762	+	16.3984i	0.629777	+	1.09081i
$227$	−0.687421	−	3.89856i	−0.0456257	−	0.258756i	0.953459	−	0.301521i	$-0.0974945\pi$
$227$	−0.687421	−	3.89856i	−0.0456257	−	0.258756i	−0.999085	+	0.0427649i	$0.986383\pi$
$228$	0.242278	−	5.83223i	0.0160453	−	0.386249i
$229$	−2.13581	−	5.86810i	−0.141138	−	0.387775i	0.848903	−	0.528548i	$-0.177263\pi$
$229$	−2.13581	−	5.86810i	−0.141138	−	0.387775i	−0.990042	+	0.140773i	$0.955041\pi$
$230$	−0.534152	−	0.448207i	−0.0352209	−	0.0295539i
$231$	−0.00817191	−	0.201126i	−0.000537672	−	0.0132331i
$232$	11.8698	+	4.32026i	0.779291	+	0.283639i
$233$	20.4315	−	11.7961i	1.33851	−	0.772789i	0.351923	−	0.936029i	$-0.385528\pi$
$233$	20.4315	−	11.7961i	1.33851	−	0.772789i	0.986586	+	0.163240i	$0.0521946\pi$
$234$	−15.5877	+	4.24749i	−1.01900	+	0.277667i
$235$	7.06230	−	12.2323i	0.460694	−	0.797945i
$236$	4.71854	+	1.71741i	0.307151	+	0.111794i
$237$	3.80567	−	17.3398i	0.247205	−	1.12634i
$238$	6.18069	+	13.4344i	0.400635	+	0.870824i
$239$	0.767685	+	0.135364i	0.0496574	+	0.00875594i	0.198422	−	0.980117i	$-0.436418\pi$
$239$	0.767685	+	0.135364i	0.0496574	+	0.00875594i	−0.148764	+	0.988873i	$0.547530\pi$
$240$	1.40302	+	10.4855i	0.0905646	+	0.676837i
$241$	4.98893	−	13.7070i	0.321365	−	0.882944i	−0.668850	−	0.743397i	$-0.733213\pi$
$241$	4.98893	−	13.7070i	0.321365	−	0.882944i	0.990216	−	0.139547i	$-0.0445645\pi$
$242$	11.7365	−	6.77608i	0.754451	−	0.435583i
$243$	5.81275	−	14.4642i	0.372888	−	0.927876i
$244$			5.38215i			0.344557i
$245$	−5.06591	−	14.3767i	−0.323649	−	0.918493i
$246$	−8.68265	−	11.2660i	−0.553586	−	0.718295i
$247$	−23.4277	−	19.6582i	−1.49067	−	1.25082i
$248$	9.00598	+	7.55692i	0.571881	+	0.479865i
$249$	−20.7759	+	6.59896i	−1.31662	+	0.418192i
$250$	4.82557	−	13.2582i	0.305196	−	0.838519i
$251$	4.52654	+	7.84019i	0.285712	+	0.494868i	0.972782	−	0.231724i	$-0.0744365\pi$
$251$	4.52654	+	7.84019i	0.285712	+	0.494868i	−0.687069	+	0.726592i	$0.741103\pi$
$252$	−0.667219	+	3.76398i	−0.0420308	+	0.237108i
$253$	−0.00570730	+	0.00988533i	−0.000358815	+	0.000621485i
$254$	−1.90308	−	2.26800i	−0.119410	−	0.142307i
$255$	9.16168	−	14.4483i	0.573727	−	0.904790i
$256$	−1.88141	+	10.6700i	−0.117588	+	0.666874i
$257$	11.3566	−	4.13346i	0.708405	−	0.257838i	0.0374099	−	0.999300i	$-0.488089\pi$
$257$	11.3566	−	4.13346i	0.708405	−	0.257838i	0.670995	+	0.741462i	$0.265867\pi$
$258$	17.5626	+	11.1364i	1.09340	+	0.693323i
$259$	−8.23258	+	8.14837i	−0.511547	+	0.506315i
$260$	−3.96939	−	2.29173i	−0.246171	−	0.142127i
$261$	−1.02781	+	12.3497i	−0.0636201	+	0.764425i
$262$	−4.98337	−	2.87715i	−0.307874	−	0.177751i
$263$	−4.57384	−	5.45089i	−0.282035	−	0.336116i	0.606365	−	0.795186i	$-0.292627\pi$
$263$	−4.57384	−	5.45089i	−0.282035	−	0.336116i	−0.888400	+	0.459070i	$0.848183\pi$
$264$	0.221734	−	0.0704285i	0.0136468	−	0.00433457i
$265$	6.30103	+	17.3119i	0.387069	+	1.06346i
$266$	20.7255	−	9.53504i	1.27076	−	0.584631i
$267$	−0.531945	−	0.219021i	−0.0325545	−	0.0134039i
$268$	0.299701	+	1.69969i	0.0183071	+	0.103825i
$269$	10.3782	+	17.9755i	0.632768	+	1.09599i	0.986983	+	0.160823i	$0.0514148\pi$
$269$	10.3782	+	17.9755i	0.632768	+	1.09599i	−0.354215	+	0.935164i	$0.615252\pi$
$270$	−12.8473	+	5.41733i	−0.781863	+	0.329688i
$271$	17.9167	+	10.3442i	1.08836	+	0.628367i	0.933141	−	0.359512i	$-0.117057\pi$
$271$	17.9167	+	10.3442i	1.08836	+	0.628367i	0.155224	+	0.987879i	$0.450390\pi$
$272$	−9.74606	+	8.17792i	−0.590942	+	0.495859i
$273$	13.4858	+	14.8069i	0.816199	+	0.896152i
$274$	3.84304	−	21.7950i	0.232167	−	1.31668i
$275$	−0.0111654	−	0.00196876i	−0.000673300	−	0.000118721i
$276$	0.146109	−	0.160129i	0.00879474	−	0.00963864i
$277$	−9.49475	+	7.96704i	−0.570484	+	0.478693i	−0.881806	−	0.471611i	$-0.843673\pi$
$277$	−9.49475	+	7.96704i	−0.570484	+	0.478693i	0.311322	+	0.950304i	$0.399228\pi$
$278$	−17.8892			−1.07292
$279$	−4.83013	+	10.4737i	−0.289172	+	0.627046i
$280$	14.4834	−	10.0308i	0.865546	−	0.599455i
$281$	−1.59337	+	4.37775i	−0.0950525	+	0.261155i	−0.978102	−	0.208125i	$-0.933264\pi$
$281$	−1.59337	+	4.37775i	−0.0950525	+	0.261155i	0.883050	+	0.469279i	$0.155486\pi$
$282$	−11.6914	−	7.41351i	−0.696212	−	0.441468i
$283$	−19.5994	−	3.45591i	−1.16507	−	0.205432i	−0.442522	−	0.896758i	$-0.645916\pi$
$283$	−19.5994	−	3.45591i	−1.16507	−	0.205432i	−0.722543	+	0.691325i	$0.757027\pi$
$284$	−2.81859	−	0.496993i	−0.167252	−	0.0294911i
$285$	−22.2896	−	14.1339i	−1.32032	−	0.837217i
$286$	0.0809064	−	0.222288i	0.00478409	−	0.0131442i
$287$	−7.53375	+	15.9417i	−0.444703	+	0.941009i
$288$	−7.94551	+	0.729035i	−0.468194	+	0.0429588i
$289$	3.57483			0.210284
$290$	8.49091	−	7.12472i	0.498603	−	0.418378i
$291$	4.07435	−	4.46530i	0.238843	−	0.261761i
$292$	−2.98729	−	0.526740i	−0.174818	−	0.0308251i
$293$	3.35078	−	19.0032i	0.195755	−	1.11018i	−0.715586	−	0.698525i	$-0.753840\pi$
$293$	3.35078	−	19.0032i	0.195755	−	1.11018i	0.911340	−	0.411654i	$-0.135049\pi$
$294$	−14.2847	+	4.37605i	−0.833103	+	0.255216i
$295$	17.3923	−	14.5939i	1.01262	−	0.849688i
$296$	−11.5941	−	6.69385i	−0.673892	−	0.389072i
$297$	0.123855	+	0.191716i	0.00718678	+	0.0111245i
$298$	−11.4859	−	19.8942i	−0.665361	−	1.15244i
$299$	−0.197213	−	1.11845i	−0.0114051	−	0.0646817i
$300$	0.199094	+	0.0819742i	0.0114947	+	0.00473278i
$301$	2.37880	−	25.6693i	0.137112	−	1.47956i
$302$	2.69776	+	7.41202i	0.155238	+	0.426514i
$303$	8.43076	−	2.67783i	0.484335	−	0.153837i
$304$	12.6162	+	15.0354i	0.723588	+	0.862339i
$305$	21.0750	+	12.1676i	1.20675	+	0.696717i
$306$	−13.7761	−	9.55952i	−0.787528	−	0.546481i
$307$	−3.69874	−	2.13547i	−0.211098	−	0.121878i	0.390723	−	0.920508i	$-0.372225\pi$
$307$	−3.69874	−	2.13547i	−0.211098	−	0.121878i	−0.601822	+	0.798630i	$0.705558\pi$
$308$	−0.0393733	−	0.0397802i	−0.00224350	−	0.00226669i
$309$	−7.00248	−	4.44027i	−0.398357	−	0.252598i
$310$	9.69405	−	3.52835i	0.550585	−	0.200397i
$311$	−4.10127	+	23.2594i	−0.232561	+	1.31892i	0.615127	+	0.788428i	$0.289105\pi$
$311$	−4.10127	+	23.2594i	−0.232561	+	1.31892i	−0.847689	+	0.530494i	$0.822006\pi$
$312$	−12.3959	+	19.5489i	−0.701781	+	1.10674i
$313$	0.887728	+	1.05795i	0.0501773	+	0.0597990i	0.790549	−	0.612398i	$-0.209795\pi$
$313$	0.887728	+	1.05795i	0.0501773	+	0.0597990i	−0.740372	+	0.672197i	$0.765351\pi$
$314$	−10.7929	+	18.6938i	−0.609077	+	1.05495i
$315$	13.2303	+	11.1220i	0.745441	+	0.626655i
$316$	−2.46811	−	4.27490i	−0.138842	−	0.240482i
$317$	2.88645	−	7.93046i	0.162119	−	0.445419i	−0.831860	−	0.554985i	$-0.812724\pi$
$317$	2.88645	−	7.93046i	0.162119	−	0.445419i	0.993979	+	0.109566i	$0.0349462\pi$
$318$	17.2094	−	5.46616i	0.965054	−	0.306527i
$319$	−0.138996	−	0.116632i	−0.00778230	−	0.00653013i
$320$	14.8246	+	12.4393i	0.828718	+	0.695377i
$321$	5.64733	+	7.32760i	0.315203	+	0.408987i
$322$	0.817191	+	0.223474i	0.0455403	+	0.0124537i
$323$		−	31.7411i		−	1.76612i
$324$	−1.51690	−	4.06039i	−0.0842722	−	0.225577i
$325$	0.976921	−	0.564026i	0.0541899	−	0.0312865i
$326$	3.13630	−	8.61692i	0.173704	−	0.477247i
$327$	2.41561	+	18.0531i	0.133584	+	0.998340i
$328$	−20.0694	−	3.53878i	−1.10815	−	0.195396i
$329$	−1.58357	+	17.0881i	−0.0873049	+	0.942096i
$330$	0.0437639	−	0.199402i	0.00240912	−	0.0109767i
$331$	22.3801	+	8.14567i	1.23012	+	0.447727i	0.873638	−	0.486576i	$-0.161754\pi$
$331$	22.3801	+	8.14567i	1.23012	+	0.447727i	0.356481	+	0.934303i	$0.383977\pi$
$332$	−3.03064	+	5.24923i	−0.166328	+	0.288089i
$333$	3.34565	−	12.7009i	0.183341	−	0.696004i
$334$	26.7638	−	15.4521i	1.46445	−	0.845501i
$335$	7.33304	+	2.66901i	0.400647	+	0.145823i
$336$	−6.87328	−	10.8613i	−0.374968	−	0.592530i
$337$	−4.78944	−	4.01882i	−0.260898	−	0.218919i	0.502950	−	0.864315i	$-0.332248\pi$
$337$	−4.78944	−	4.01882i	−0.260898	−	0.218919i	−0.763848	+	0.645396i	$0.776692\pi$
$338$	2.57104	+	7.06387i	0.139846	+	0.384224i
$339$	−1.10470	+	26.5929i	−0.0599992	+	1.44433i
$340$	−0.826055	−	4.68479i	−0.0447991	−	0.254069i
$341$	−0.0844382	−	0.146251i	−0.00457258	−	0.00791995i
$342$	−14.7476	+	21.2526i	−0.797459	+	1.14921i
$343$	12.8923	+	13.2962i	0.696118	+	0.717927i
$344$	29.3426	−	5.17390i	1.58205	−	0.278958i
$345$	−0.296705	−	0.934132i	−0.0159741	−	0.0502920i
$346$	2.55469	−	3.04456i	0.137341	−	0.163677i
$347$	−2.59393	−	7.12677i	−0.139250	−	0.382585i	0.850391	−	0.526151i	$-0.176365\pi$
$347$	−2.59393	−	7.12677i	−0.139250	−	0.382585i	−0.989641	+	0.143566i	$0.954143\pi$
$348$	2.10344	+	2.72928i	0.112756	+	0.146305i
$349$	8.81684	+	10.5075i	0.471954	+	0.562453i	0.948533	−	0.316678i	$-0.102568\pi$
$349$	8.81684	+	10.5075i	0.471954	+	0.562453i	−0.476578	+	0.879132i	$0.658123\pi$
$350$	0.0690302	+	0.838651i	0.00368982	+	0.0448278i
$351$	−21.7012	−	6.69121i	−1.15832	−	0.357151i
$352$	0.0584128	−	0.101174i	0.00311341	−	0.00539259i
$353$	−5.40349	−	1.96671i	−0.287599	−	0.104677i	0.194192	−	0.980963i	$-0.437791\pi$
$353$	−5.40349	−	1.96671i	−0.287599	−	0.104677i	−0.481791	+	0.876286i	$0.660014\pi$
$354$	−13.5838	−	17.6254i	−0.721971	−	0.936780i
$355$	−8.31818	+	9.91322i	−0.441483	+	0.526139i
$356$	−0.150312	+	0.0547089i	−0.00796649	+	0.00289957i
$357$	−2.77548	+	20.6002i	−0.146894	+	1.09028i
$358$	−1.29540	−	7.34659i	−0.0684641	−	0.388279i
$359$		−	26.9598i		−	1.42288i	−0.702745	−	0.711442i	$-0.748042\pi$
$359$		−	26.9598i		−	1.42288i	0.702745	−	0.711442i	$-0.251958\pi$
$360$	−8.36580	+	18.1405i	−0.440916	+	0.956090i
$361$	−29.9674			−1.57723
$362$	22.7081	−	19.0544i	1.19351	−	1.00148i
$363$	19.0328	+	0.790647i	0.998963	+	0.0414982i
$364$	5.54510	+	0.513870i	0.290642	+	0.0269341i
$365$	−8.81604	+	10.5066i	−0.461453	+	0.549938i
$366$	12.7727	−	20.1431i	0.667642	−	1.05290i
$367$	1.06672	−	0.188092i	0.0556825	−	0.00981833i	−0.145738	−	0.989323i	$-0.546555\pi$
$367$	1.06672	−	0.188092i	0.0556825	−	0.00981833i	0.201420	+	0.979505i	$0.435444\pi$
$368$			0.728871i			0.0379950i
$369$	−1.82678	−	19.9094i	−0.0950982	−	1.03644i
$370$	−10.1737	+	5.87379i	−0.528905	+	0.305364i
$371$	−15.7461	−	15.9089i	−0.817499	−	0.825947i
$372$	0.970852	+	3.05658i	0.0503364	+	0.158477i
$373$	2.74691	−	15.5785i	0.142230	−	0.806625i	−0.827320	−	0.561731i	$-0.810136\pi$
$373$	2.74691	−	15.5785i	0.142230	−	0.806625i	0.969550	−	0.244894i	$-0.0787532\pi$
$374$	0.230708	−	0.0839708i	0.0119296	−	0.00434203i
$375$	15.7082	−	12.1062i	0.811167	−	0.625162i
$376$	−19.5334	+	3.44426i	−1.00736	+	0.177624i
$377$	18.0532			0.929789
$378$	11.4297	−	12.5035i	0.587878	−	0.643113i
$379$	−35.6120			−1.82927			−0.914633	−	0.404284i	$-0.867521\pi$
$379$	−35.6120			−1.82927			−0.914633	+	0.404284i	$0.867521\pi$
$380$	−7.22730	+	1.27437i	−0.370753	+	0.0653737i
$381$	−0.551925	−	4.12482i	−0.0282760	−	0.211321i
$382$	−7.54604	+	2.74653i	−0.386089	+	0.140525i
$383$	−5.66579	+	32.1323i	−0.289509	+	1.64188i	0.399213	+	0.916858i	$0.369283\pi$
$383$	−5.66579	+	32.1323i	−0.289509	+	1.64188i	−0.688721	+	0.725026i	$0.741828\pi$
$384$	6.57450	−	7.20536i	0.335504	−	0.367697i
$385$	−0.244781	+	0.0642420i	−0.0124752	+	0.00327408i
$386$	−21.7513	+	12.5581i	−1.10711	+	0.639191i
$387$	12.4655	+	26.4398i	0.633659	+	1.34401i
$388$		−	1.68079i		−	0.0853294i
$389$	−10.9769	+	1.93553i	−0.556552	+	0.0981352i	−0.444848	−	0.895606i	$-0.646742\pi$
$389$	−10.9769	+	1.93553i	−0.556552	+	0.0981352i	−0.111705	+	0.993741i	$0.535631\pi$
$390$	9.41709	+	17.9970i	0.476853	+	0.911313i
$391$	0.757668	−	0.902954i	0.0383169	−	0.0456643i
$392$	−10.8927	+	18.4266i	−0.550165	+	0.930684i
$393$	−3.74997	−	7.16656i	−0.189161	−	0.361505i
$394$	16.7499	−	14.0548i	0.843849	−	0.708073i
$395$	−22.3190			−1.12299
$396$	0.0613713	+	0.0161664i	0.00308402	+	0.000812390i
$397$		−	14.3758i		−	0.721500i	−0.932663	−	0.360750i	$-0.882521\pi$
$397$		−	14.3758i		−	0.721500i	0.932663	−	0.360750i	$-0.117479\pi$
$398$	−2.37685	−	13.4798i	−0.119141	−	0.675681i
$399$	31.7802	+	4.28178i	1.59100	+	0.214357i
$400$	−0.680298	+	0.247608i	−0.0340149	+	0.0123804i
$401$	10.6855	−	12.7345i	0.533609	−	0.635930i	−0.430133	−	0.902765i	$-0.641533\pi$
$401$	10.6855	−	12.7345i	0.533609	−	0.635930i	0.963742	+	0.266835i	$0.0859779\pi$
$402$	2.91199	−	7.07245i	0.145237	−	0.352742i
$403$	15.7892	+	5.74680i	0.786516	+	0.286268i
$404$	1.22982	−	2.13012i	0.0611860	−	0.105977i
$405$	−19.3287	−	3.23974i	−0.960449	−	0.160984i
$406$	−5.75410	+	12.1759i	−0.285571	+	0.604280i
$407$	0.123613	+	0.147317i	0.00612728	+	0.00730221i
$408$	−23.8123	+	3.18621i	−1.17888	+	0.157741i
$409$	−0.284532	−	0.781744i	−0.0140692	−	0.0386548i	0.932459	−	0.361275i	$-0.117658\pi$
$409$	−0.284532	−	0.781744i	−0.0140692	−	0.0386548i	−0.946528	+	0.322620i	$0.895436\pi$
$410$	−11.4946	+	13.6987i	−0.567677	+	0.676531i
$411$	20.9678	−	22.9797i	1.03426	−	1.13351i
$412$	−2.27052	+	0.400353i	−0.111860	+	0.0197240i
$413$	−11.7864	+	24.9404i	−0.579969	+	1.22724i
$414$	−0.926838	+	0.252554i	−0.0455516	+	0.0124123i
$415$	13.7030	+	23.7343i	0.672653	+	1.16507i
$416$	2.01843	+	11.4471i	0.0989616	+	0.561239i
$417$	−21.2360	−	13.4657i	−1.03993	−	0.659419i
$418$	−0.129543	−	0.355916i	−0.00633616	−	0.0174084i
$419$	4.03215	+	3.38337i	0.196983	+	0.165289i	0.735944	−	0.677042i	$-0.236739\pi$
$419$	4.03215	+	3.38337i	0.196983	+	0.165289i	−0.538961	+	0.842331i	$0.681183\pi$
$420$	4.80200	−	0.195109i	0.234314	−	0.00952035i
$421$	25.6716	+	9.34372i	1.25116	+	0.455385i	0.880793	−	0.473501i	$-0.157010\pi$
$421$	25.6716	+	9.34372i	1.25116	+	0.455385i	0.370366	+	0.928886i	$0.379232\pi$
$422$	0.711584	−	0.410833i	0.0346394	−	0.0199991i
$423$	−8.29831	−	17.6009i	−0.403478	−	0.855787i
$424$	12.9354	−	22.4047i	0.628198	−	1.08807i
$425$	1.10017	+	0.400430i	0.0533662	+	0.0194237i
$426$	9.36933	+	8.54901i	0.453946	+	0.414201i
$427$	−29.4410	−	2.72833i	−1.42475	−	0.132033i
$428$	2.53330	+	0.446690i	0.122452	+	0.0215916i
$429$	0.263366	−	0.202975i	0.0127154	−	0.00979971i
$430$	8.94214	−	24.5683i	0.431228	−	1.18479i
$431$	−22.2979	+	12.8737i	−1.07405	+	0.620104i	−0.929285	−	0.369362i	$-0.879576\pi$
$431$	−22.2979	+	12.8737i	−1.07405	+	0.620104i	−0.144766	+	0.989466i	$0.546243\pi$
$432$	12.9701	+	6.64749i	0.624022	+	0.319827i
$433$			10.9555i			0.526489i	0.964729	+	0.263245i	$0.0847927\pi$
$433$			10.9555i			0.526489i	−0.964729	+	0.263245i	$0.915207\pi$
$434$	−8.90838	+	8.81726i	−0.427616	+	0.423242i
$435$	15.4424	−	2.06628i	0.740408	−	0.0990707i
$436$	3.87967	+	3.25543i	0.185802	+	0.155907i
$437$	−1.39300	−	1.16887i	−0.0666362	−	0.0559144i
$438$	9.93011	+	9.06069i	0.474479	+	0.432937i
$439$	−8.32770	+	22.8802i	−0.397459	+	1.09201i	0.566058	+	0.824365i	$0.308468\pi$
$439$	−8.32770	+	22.8802i	−0.397459	+	1.09201i	−0.963518	+	0.267645i	$0.913754\pi$
$440$	−0.146247	−	0.253308i	−0.00697207	−	0.0120760i
$441$	−20.2512	−	5.55781i	−0.964342	−	0.264658i
$442$	−12.2138	+	21.1550i	−0.580953	+	1.00624i
$443$	−21.0336	−	25.0669i	−0.999339	−	1.19097i	−0.981566	−	0.191123i	$-0.938787\pi$
$443$	−21.0336	−	25.0669i	−0.999339	−	1.19097i	−0.0177725	−	0.999842i	$-0.505657\pi$
$444$	−1.69318	−	3.23583i	−0.0803547	−	0.153566i
$445$	−0.125591	+	0.712260i	−0.00595357	+	0.0337644i
$446$	4.57571	−	1.66542i	0.216666	−	0.0788601i
$447$	1.34020	−	32.2619i	0.0633893	−	1.52594i
$448$	−22.6799	−	6.20219i	−1.07152	−	0.293026i
$449$	13.1832	+	7.61132i	0.622154	+	0.359201i	0.777707	−	0.628627i	$-0.216383\pi$
$449$	13.1832	+	7.61132i	0.622154	+	0.359201i	−0.155553	+	0.987827i	$0.549716\pi$
$450$	−0.550584	−	0.779276i	−0.0259548	−	0.0367354i
$451$	0.253516	+	0.146368i	0.0119376	+	0.00689218i
$452$	4.75709	+	5.66928i	0.223755	+	0.266661i
$453$	−2.37679	+	10.8294i	−0.111671	+	0.508809i
$454$	1.66838	+	4.58385i	0.0783011	+	0.215131i
$455$	14.5482	−	20.5513i	0.682030	−	0.963461i
$456$	4.91542	+	36.7355i	0.230185	+	1.72030i
$457$	−2.63572	−	14.9479i	−0.123294	−	0.699234i	−0.982307	−	0.187280i	$-0.940033\pi$
$457$	−2.63572	−	14.9479i	−0.123294	−	0.699234i	0.859013	−	0.511954i	$-0.171078\pi$
$458$	3.84745	+	6.66398i	0.179780	+	0.311387i
$459$	−9.15769	−	21.7177i	−0.427444	−	1.01369i
$460$	−0.236018	−	0.136265i	−0.0110044	−	0.00635339i
$461$	−1.36503	+	1.14540i	−0.0635760	+	0.0533466i	−0.674022	−	0.738711i	$-0.735435\pi$
$461$	−1.36503	+	1.14540i	−0.0635760	+	0.0533466i	0.610446	+	0.792058i	$0.290990\pi$
$462$	0.0529525	+	0.242320i	0.00246358	+	0.0112737i
$463$	−4.20119	+	23.8261i	−0.195246	+	1.10729i	0.716822	+	0.697256i	$0.245596\pi$
$463$	−4.20119	+	23.8261i	−0.195246	+	1.10729i	−0.912068	+	0.410038i	$0.865515\pi$
$464$	−11.4101	−	2.01192i	−0.529703	−	0.0934009i
$465$	14.1636	+	3.10856i	0.656820	+	0.144156i
$466$	−22.2697	+	18.6865i	−1.03162	+	0.865635i
$467$	−1.75046			−0.0810018			−0.0405009	−	0.999180i	$-0.512895\pi$
$467$	−1.75046			−0.0810018			−0.0405009	+	0.999180i	$0.512895\pi$
$468$	−5.71153	+	2.69282i	−0.264016	+	0.124475i
$469$	−9.44942	+	0.777791i	−0.436334	+	0.0359151i
$470$	−5.95278	+	16.3551i	−0.274581	+	0.754406i
$471$	−26.8835	+	14.0670i	−1.23873	+	0.648174i
$472$	−31.3981	−	5.53634i	−1.44522	−	0.254831i
$473$	−0.421493	−	0.0743206i	−0.0193803	−	0.00341727i
$474$	−0.907941	+	21.8564i	−0.0417031	+	1.00390i
$475$	0.617749	−	1.69725i	0.0283443	−	0.0778752i
$476$	3.29077	+	4.75151i	0.150832	+	0.217785i
$477$	24.5436	+	6.46523i	1.12377	+	0.296023i
$478$	−0.960557			−0.0439349
$479$	−11.3189	+	9.49769i	−0.517174	+	0.433961i	−0.863645	−	0.504100i	$-0.831824\pi$
$479$	−11.3189	+	9.49769i	−0.517174	+	0.433961i	0.346471	+	0.938061i	$0.387380\pi$
$480$	3.03671	+	9.56062i	0.138606	+	0.436380i
$481$	−18.8432	−	3.32256i	−0.859176	−	0.151496i
$482$	−3.12117	+	17.7010i	−0.142165	+	0.806260i
$483$	0.801860	+	0.880408i	0.0364859	+	0.0400600i
$484$	4.05757	−	3.40470i	0.184435	−	0.154759i
$485$	−6.58151	−	3.79984i	−0.298851	−	0.172542i
$486$	−3.95887	+	18.7962i	−0.179578	+	0.852612i
$487$	8.57754	+	14.8567i	0.388685	+	0.673223i	0.992273	−	0.124074i	$-0.0395960\pi$
$487$	8.57754	+	14.8567i	0.388685	+	0.673223i	−0.603588	+	0.797297i	$0.706263\pi$
$488$	−5.93412	−	33.6541i	−0.268625	−	1.52345i
$489$	10.2093	−	7.86824i	0.461680	−	0.355814i
$490$	9.22378	+	16.3623i	0.416688	+	0.739172i
$491$	−10.3608	−	28.4661i	−0.467577	−	1.28466i	−0.919672	−	0.392687i	$-0.871546\pi$
$491$	−10.3608	−	28.4661i	−0.467577	−	1.28466i	0.452096	−	0.891970i	$-0.350677\pi$
$492$	−4.10662	−	3.74707i	−0.185141	−	0.168931i
$493$	12.0439	+	14.3534i	0.542431	+	0.646445i
$494$	32.6361	+	18.8425i	1.46837	+	0.847763i
$495$	0.202047	−	0.203765i	0.00908136	−	0.00915854i
$496$	−9.33877	−	5.39174i	−0.419323	−	0.242096i
$497$	4.14742	−	15.1661i	0.186037	−	0.680292i
$498$	23.7997	−	12.4534i	1.06649	−	0.558051i
$499$	−12.0166	+	4.37367i	−0.537935	+	0.195792i	−0.596678	−	0.802481i	$-0.703513\pi$
$499$	−12.0166	+	4.37367i	−0.537935	+	0.195792i	0.0587428	+	0.998273i	$0.481291\pi$
$500$	0.957571	−	5.43065i	0.0428239	−	0.242866i
$501$	43.4022	+	1.80298i	1.93907	+	0.0805513i
$502$	−7.17059	−	8.54558i	−0.320039	−	0.381408i
$503$	−3.27645	+	5.67499i	−0.146090	+	0.253035i	−0.929779	−	0.368118i	$-0.880002\pi$
$503$	−3.27645	+	5.67499i	−0.146090	+	0.253035i	0.783689	+	0.621153i	$0.213336\pi$
$504$	0.0220611	−	24.2714i	0.000982679	−	1.08114i
$505$	−5.56062	−	9.63127i	−0.247444	−	0.428586i
$506$	0.00481065	−	0.0132172i	0.000213860	−	0.000587574i
$507$	−2.26515	+	10.3207i	−0.100599	+	0.458359i
$508$	−0.886436	−	0.743808i	−0.0393292	−	0.0330011i
$509$	9.37776	+	7.86888i	0.415662	+	0.348782i	0.826510	−	0.562922i	$-0.190323\pi$
$509$	9.37776	+	7.86888i	0.415662	+	0.348782i	−0.410848	+	0.911704i	$0.634767\pi$
$510$	−8.02621	+	19.4936i	−0.355407	+	0.863189i
$511$	4.39565	−	16.0738i	0.194452	−	0.711064i
$512$		−	24.6137i		−	1.08778i
$513$	−33.5042	+	14.1277i	−1.47924	+	0.623753i
$514$	−12.8969	+	7.44602i	−0.568857	+	0.328430i
$515$	−3.56538	+	9.79580i	−0.157109	+	0.431654i
$516$	7.51576	+	3.09452i	0.330863	+	0.136228i
$517$	0.280588	+	0.0494752i	0.0123402	+	0.00217592i
$518$	8.24677	−	11.6497i	0.362342	−	0.511858i
$519$	5.32437	−	1.69116i	0.233714	−	0.0742337i
$520$	27.3470	+	9.95348i	1.19924	+	0.436489i
$521$	19.5442	−	33.8516i	0.856249	−	1.48307i	−0.0192325	−	0.999815i	$-0.506122\pi$
$521$	19.5442	−	33.8516i	0.856249	−	1.48307i	0.875481	−	0.483252i	$-0.160544\pi$
$522$	−1.39525	−	15.2064i	−0.0610684	−	0.665564i
$523$	3.66206	−	2.11429i	0.160131	−	0.0924514i	−0.417793	−	0.908542i	$-0.637196\pi$
$523$	3.66206	−	2.11429i	0.160131	−	0.0924514i	0.577924	+	0.816091i	$0.303863\pi$
$524$	−2.11340	−	0.769215i	−0.0923244	−	0.0336033i
$525$	−0.549334	+	1.04751i	−0.0239749	+	0.0457172i
$526$	6.71675	+	5.63602i	0.292864	+	0.245742i
$527$	5.96447	+	16.3872i	0.259816	+	0.713840i
$528$	−0.189075	+	0.0989352i	−0.00822843	+	0.00430560i
$529$	3.98218	+	22.5841i	0.173138	+	0.981916i
$530$	−11.3507	−	19.6599i	−0.493042	−	0.853973i
$531$	−2.85795	−	31.1478i	−0.124024	−	1.35170i
$532$	7.33022	−	5.07672i	0.317805	−	0.220104i
$533$	−28.6835	+	5.05767i	−1.24242	+	0.219072i
$534$	0.692385	+	0.151962i	0.0299624	+	0.00657603i
$535$	7.47625	−	8.90985i	0.323227	−	0.385207i
$536$	−3.74800	−	10.2975i	−0.161889	−	0.444786i
$537$	3.99225	−	9.69612i	0.172278	−	0.418419i
$538$	−16.4403	−	19.5928i	−0.708792	−	0.844706i
$539$	0.237562	−	0.195211i	0.0102325	−	0.00840835i
$540$	−4.57734	+	2.95710i	−0.196977	+	0.127253i
$541$	−12.8174	+	22.2003i	−0.551061	+	0.954466i	0.447137	+	0.894465i	$0.352444\pi$
$541$	−12.8174	+	22.2003i	−0.551061	+	0.954466i	−0.998198	+	0.0600007i	$0.980890\pi$
$542$	−23.9555	−	8.71910i	−1.02898	−	0.374517i
$543$	41.2993	−	5.52608i	1.77232	−	0.237147i
$544$	−7.75455	+	9.24151i	−0.332474	+	0.396227i
$545$	21.5182	−	7.83200i	0.921740	−	0.335486i
$546$	−19.5335	−	15.0826i	−0.835955	−	0.645478i
$547$	2.11377	+	11.9878i	0.0903783	+	0.512561i	0.996066	+	0.0886153i	$0.0282442\pi$
$547$	2.11377	+	11.9878i	0.0903783	+	0.512561i	−0.905688	+	0.423946i	$0.860645\pi$
$548$		−	8.64984i		−	0.369503i
$549$	30.3247	−	14.2972i	1.29423	−	0.610188i
$550$	0.0139706			0.000595709
$551$	22.1432	−	18.5803i	0.943332	−	0.791549i
$552$	−0.737055	+	1.16236i	−0.0313712	+	0.0494735i
$553$	24.6353	−	11.3338i	1.04760	−	0.481964i
$554$	9.81722	−	11.6997i	0.417094	−	0.497073i
$555$	−16.4984	−	0.685366i	−0.700319	−	0.0290921i
$556$	−6.88565	+	1.21413i	−0.292016	+	0.0514904i
$557$		−	35.9805i		−	1.52454i	−0.647258	−	0.762271i	$-0.724084\pi$
$557$		−	35.9805i		−	1.52454i	0.647258	−	0.762271i	$-0.275916\pi$
$558$	3.62029	−	13.7435i	0.153259	−	0.581808i
$559$	36.8787	−	21.2919i	1.55980	−	0.900552i
$560$	−11.4852	+	11.3677i	−0.485337	+	0.480373i
$561$	0.337078	+	0.0739804i	0.0142314	+	0.00312346i
$562$	0.996844	−	5.65338i	0.0420493	−	0.238474i
$563$	−28.7430	+	10.4616i	−1.21137	+	0.440904i	−0.867180	−	0.497995i	$-0.834070\pi$
$563$	−28.7430	+	10.4616i	−1.21137	+	0.440904i	−0.344194	+	0.938899i	$0.611848\pi$
$564$	−5.00324	−	2.06002i	−0.210674	−	0.0867424i
$565$	32.9539	−	5.81065i	1.38638	−	0.244456i
$566$	24.5236			1.03080
$567$	22.9798	−	6.23933i	0.965061	−	0.262027i
$568$	18.1723			0.762493
$569$	25.1224	−	4.42976i	1.05319	−	0.185705i	0.379856	−	0.925046i	$-0.375974\pi$
$569$	25.1224	−	4.42976i	1.05319	−	0.185705i	0.673332	+	0.739340i	$0.264863\pi$
$570$	30.0730	+	12.3822i	1.25962	+	0.518631i
$571$	33.3922	−	12.1538i	1.39742	−	0.508619i	0.470008	−	0.882662i	$-0.344251\pi$
$571$	33.3922	−	12.1538i	1.39742	−	0.508619i	0.927411	+	0.374043i	$0.122029\pi$
$572$	0.0160548	−	0.0910512i	0.000671285	−	0.00380704i
$573$	−11.0252	−	2.41976i	−0.460584	−	0.101087i
$574$	5.73116	−	20.9574i	0.239214	−	0.874747i
$575$	0.0580872	−	0.0335367i	0.00242241	−	0.00139858i
$576$	25.7229	−	7.00924i	1.07179	−	0.292052i
$577$			12.7442i			0.530549i	0.964173	+	0.265275i	$0.0854626\pi$
$577$			12.7442i			0.530549i	−0.964173	+	0.265275i	$0.914537\pi$
$578$	−4.33809	+	0.764922i	−0.180441	+	0.0318166i
$579$	−35.2735	−	1.46531i	−1.46592	−	0.0608960i
$580$	2.78465	−	3.31862i	0.115626	−	0.137798i
$581$	−27.1776	−	19.2389i	−1.12752	−	0.798166i
$582$	−3.98880	+	6.29049i	−0.165341	+	0.260749i
$583$	−0.284679	+	0.238874i	−0.0117902	+	0.00989315i
$584$	19.2600			0.796983
$585$	−2.36799	+	28.4525i	−0.0979044	+	1.17637i
$586$			23.7776i			0.982242i
$587$	−3.09078	−	17.5287i	−0.127570	−	0.723487i	−0.979748	−	0.200234i	$-0.935830\pi$
$587$	−3.09078	−	17.5287i	−0.127570	−	0.723487i	0.852178	−	0.523252i	$-0.175281\pi$
$588$	−5.20128	+	2.65386i	−0.214497	+	0.109443i
$589$	25.2808	−	9.20147i	1.04168	−	0.379140i
$590$	−17.9830	+	21.4313i	−0.740348	+	0.882313i
$591$	30.4631	−	4.07613i	1.25308	−	0.167670i
$592$	11.5391	+	4.19990i	0.474256	+	0.172615i
$593$	−12.9163	+	22.3717i	−0.530408	+	0.918694i	0.468962	+	0.883218i	$0.344628\pi$
$593$	−12.9163	+	22.3717i	−0.530408	+	0.918694i	−0.999371	+	0.0354760i	$0.988705\pi$
$594$	−0.191321	−	0.206148i	−0.00785001	−	0.00845836i
$595$	26.0451	−	2.14380i	1.06775	−	0.0878873i
$596$	−5.77120	−	6.87785i	−0.236398	−	0.281728i
$597$	7.32513	−	17.7908i	0.299797	−	0.728129i
$598$	0.478640	+	1.31505i	0.0195731	+	0.0537765i
$599$	14.7106	−	17.5314i	0.601057	−	0.716312i	−0.376633	−	0.926362i	$-0.622918\pi$
$599$	14.7106	−	17.5314i	0.601057	−	0.716312i	0.977691	+	0.210050i	$0.0673628\pi$
$600$	−1.33529	−	0.293065i	−0.0545131	−	0.0119643i
$601$	−11.3373	+	1.99907i	−0.462457	+	0.0815436i	−0.400022	−	0.916505i	$-0.630998\pi$
$601$	−11.3373	+	1.99907i	−0.462457	+	0.0815436i	−0.0624345	+	0.998049i	$0.519886\pi$
$602$	2.60588	+	31.6590i	0.106208	+	1.29032i
$603$	8.78043	−	6.20366i	0.357567	−	0.252632i
$604$	1.54143	+	2.66984i	0.0627200	+	0.108634i
$605$	−4.15875	−	23.5854i	−0.169077	−	0.958884i
$606$	−9.65782	+	5.05354i	−0.392322	+	0.205286i
$607$	5.99762	+	16.4783i	0.243436	+	0.668834i	0.999891	+	0.0147883i	$0.00470745\pi$
$607$	5.99762	+	16.4783i	0.243436	+	0.668834i	−0.756455	+	0.654046i	$0.773070\pi$
$608$	14.2570	+	11.9631i	0.578198	+	0.485166i
$609$	−15.9958	+	10.1225i	−0.648182	+	0.410186i
$610$	−28.1783	−	10.2560i	−1.14090	−	0.415255i
$611$	−24.5501	+	14.1740i	−0.993192	+	0.573420i
$612$	−5.95131	−	2.74454i	−0.240567	−	0.110941i
$613$	−16.7170	+	28.9547i	−0.675193	+	1.16947i	0.301220	+	0.953555i	$0.402606\pi$
$613$	−16.7170	+	28.9547i	−0.675193	+	1.16947i	−0.976412	+	0.215914i	$0.930727\pi$
$614$	4.94540	+	1.79998i	0.199580	+	0.0726412i
$615$	−23.9565	+	7.60921i	−0.966019	+	0.306833i
$616$	0.290057	+	0.205331i	0.0116867	+	0.00827300i
$617$	−0.596187	−	0.105124i	−0.0240016	−	0.00423212i	0.161634	−	0.986851i	$-0.448323\pi$
$617$	−0.596187	−	0.105124i	−0.0240016	−	0.00423212i	−0.185636	+	0.982619i	$0.559435\pi$
$618$	9.44769	+	3.88996i	0.380042	+	0.156477i
$619$	−5.14679	+	14.1407i	−0.206867	+	0.568362i	−0.999125	−	0.0418239i	$-0.986683\pi$
$619$	−5.14679	+	14.1407i	−0.206867	+	0.568362i	0.792258	+	0.610186i	$0.208905\pi$
$620$	3.49183	−	2.01601i	0.140235	−	0.0809649i
$621$	−1.29034	−	0.397856i	−0.0517796	−	0.0159654i
$622$		−	29.1031i		−	1.16693i
$623$	−0.223068	−	0.849955i	−0.00893704	−	0.0340527i
$624$	8.08360	−	19.6329i	0.323603	−	0.785946i
$625$	−18.1115	−	15.1973i	−0.724458	−	0.607893i
$626$	−1.30364	−	1.09388i	−0.0521040	−	0.0437204i
$627$	0.114131	−	0.520014i	0.00455794	−	0.0207674i
$628$	−2.88551	+	7.92787i	−0.115144	+	0.316356i
$629$	−9.92930	−	17.1981i	−0.395907	−	0.685731i
$630$	−18.4349	−	10.6657i	−0.734463	−	0.424933i
$631$	−5.47505	+	9.48307i	−0.217958	+	0.377515i	−0.954184	−	0.299222i	$-0.903273\pi$
$631$	−5.47505	+	9.48307i	−0.217958	+	0.377515i	0.736225	+	0.676736i	$0.236606\pi$
$632$	20.1462	+	24.0093i	0.801372	+	0.955038i
$633$	1.15396	+	0.0479369i	0.0458657	+	0.00190532i
$634$	−1.80582	+	10.2413i	−0.0717183	+	0.406734i
$635$	−4.91654	+	1.78947i	−0.195107	+	0.0710131i
$636$	6.25301	−	3.27195i	0.247948	−	0.129741i
$637$	−5.62187	+	30.0719i	−0.222746	+	1.19149i
$638$	0.193630	+	0.111792i	0.00766587	+	0.00442589i
$639$	4.68710	+	17.2010i	0.185419	+	0.680461i
$640$	−10.6201	−	6.13154i	−0.419798	−	0.242370i
$641$	13.8457	+	16.5006i	0.546871	+	0.651735i	0.966713	−	0.255862i	$-0.0823592\pi$
$641$	13.8457	+	16.5006i	0.546871	+	0.651735i	−0.419843	+	0.907597i	$0.637915\pi$
$642$	−8.42101	−	7.68372i	−0.332351	−	0.303252i
$643$	14.9068	+	40.9562i	0.587868	+	1.61515i	0.774394	+	0.632703i	$0.218055\pi$
$643$	14.9068	+	40.9562i	0.587868	+	1.61515i	−0.186527	+	0.982450i	$0.559723\pi$
$644$	0.329709	+	0.0305545i	0.0129924	+	0.00120401i
$645$	29.1084	−	22.4337i	1.14614	−	0.883326i
$646$	6.79178	+	38.5181i	0.267219	+	1.51547i
$647$	−4.16497	−	7.21394i	−0.163742	−	0.283609i	0.772466	−	0.635056i	$-0.219023\pi$
$647$	−4.16497	−	7.21394i	−0.163742	−	0.283609i	−0.936208	+	0.351447i	$0.885690\pi$
$648$	13.9618	+	23.7168i	0.548473	+	0.931682i
$649$	0.396620	+	0.228989i	0.0155687	+	0.00898859i
$650$	−1.06482	+	0.893487i	−0.0417655	+	0.0350454i
$651$	−17.2120	+	3.76123i	−0.674593	+	0.147414i
$652$	0.622358	−	3.52957i	0.0243734	−	0.138228i
$653$	0.880334	+	0.155227i	0.0344501	+	0.00607449i	0.190847	−	0.981620i	$-0.438877\pi$
$653$	0.880334	+	0.155227i	0.0344501	+	0.00607449i	−0.156397	+	0.987694i	$0.549988\pi$
$654$	−6.79427	−	21.3908i	−0.265677	−	0.836445i
$655$	−7.78988	+	6.53648i	−0.304376	+	0.255402i
$656$	18.6924			0.729816
$657$	4.96763	+	18.2305i	0.193806	+	0.711240i
$658$	−1.73473	−	21.0754i	−0.0676270	−	0.821604i
$659$	−8.57287	+	23.5538i	−0.333951	+	0.917524i	0.653122	+	0.757253i	$0.273459\pi$
$659$	−8.57287	+	23.5538i	−0.333951	+	0.917524i	−0.987073	+	0.160271i	$0.948763\pi$
$660$	0.00331172	−	0.0797212i	0.000128909	−	0.00310314i
$661$	−6.90665	−	1.21783i	−0.268638	−	0.0473681i	0.0377066	−	0.999289i	$-0.487995\pi$
$661$	−6.90665	−	1.21783i	−0.268638	−	0.0473681i	−0.306344	+	0.951921i	$0.599106\pi$
$662$	−28.9014	−	5.09609i	−1.12328	−	0.198065i
$663$	−30.4229	+	15.9191i	−1.18153	+	0.618245i
$664$	13.1627	−	36.1644i	0.510814	−	1.40345i
$665$	−3.30727	−	40.1802i	−0.128251	−	1.55812i
$666$	−1.34232	+	16.1285i	−0.0520137	+	0.624968i
$667$	1.07344			0.0415636
$668$	9.25283	−	7.76405i	0.358003	−	0.300400i
$669$	6.68538	+	1.46728i	0.258472	+	0.0567283i
$670$	−9.46981	−	1.66978i	−0.365851	−	0.0645093i
$671$	−0.0852409	+	0.483425i	−0.00329069	+	0.0186624i
$672$	−8.20684	−	9.01076i	−0.316586	−	0.347598i
$673$	−15.9699	+	13.4003i	−0.615593	+	0.516543i	−0.896415	−	0.443216i	$-0.853837\pi$
$673$	−15.9699	+	13.4003i	−0.615593	+	0.516543i	0.280822	+	0.959760i	$0.409393\pi$
$674$	6.67196	+	3.85206i	0.256994	+	0.148376i
$675$	−0.0670055	−	1.33951i	−0.00257904	−	0.0515578i
$676$	1.46903	+	2.54443i	0.0565011	+	0.0978628i
$677$	1.52435	+	8.64503i	0.0585856	+	0.332255i	0.999987	−	0.00503198i	$-0.00160173\pi$
$677$	1.52435	+	8.64503i	0.0585856	+	0.332255i	−0.941402	+	0.337287i	$0.890491\pi$
$678$	−4.34963	−	32.5071i	−0.167047	−	1.24843i
$679$	9.19414	+	0.852031i	0.352839	+	0.0326979i
$680$	10.3305	+	28.3828i	0.396156	+	1.08843i
$681$	−1.46989	+	6.69727i	−0.0563262	+	0.256640i
$682$	0.133761	+	0.159410i	0.00512196	+	0.00610411i
$683$	−19.2647	−	11.1225i	−0.737142	−	0.425589i	0.0838871	−	0.996475i	$-0.473267\pi$
$683$	−19.2647	−	11.1225i	−0.737142	−	0.425589i	−0.821029	+	0.570886i	$0.806600\pi$
$684$	−4.23404	+	9.18117i	−0.161893	+	0.351051i
$685$	−33.8703	−	19.5550i	−1.29412	−	0.747160i
$686$	−18.4900	−	13.3764i	−0.705950	−	0.510715i
$687$	−0.448929	+	10.8068i	−0.0171277	+	0.412306i
$688$	−25.6812	+	9.34719i	−0.979086	+	0.356358i
$689$	6.42062	−	36.4131i	0.244606	−	1.38723i
$690$	0.559935	+	1.07009i	0.0213164	+	0.0407377i
$691$	−26.5759	−	31.6719i	−1.01099	−	1.20486i	−0.978683	−	0.205378i	$-0.934158\pi$
$691$	−26.5759	−	31.6719i	−1.01099	−	1.20486i	−0.0323116	−	0.999478i	$-0.510287\pi$
$692$	0.776683	−	1.34526i	0.0295251	−	0.0511389i
$693$	−0.119542	+	0.327513i	−0.00454104	+	0.0124412i
$694$	4.67271	+	8.09337i	0.177374	+	0.307220i
$695$	−10.8125	+	29.7071i	−0.410141	+	1.12685i
$696$	−16.1618	−	14.7468i	−0.612611	−	0.558975i
$697$	−23.1569	−	19.4309i	−0.877130	−	0.735999i
$698$	−12.9477	−	10.8644i	−0.490076	−	0.411222i
$699$	−40.5019	+	5.41939i	−1.53192	+	0.204980i
$700$	0.0834888	+	0.318117i	0.00315558	+	0.0120237i
$701$			2.77920i			0.104969i	0.998622	+	0.0524844i	$0.0167140\pi$
$701$			2.77920i			0.104969i	−0.998622	+	0.0524844i	$0.983286\pi$
$702$	27.7663	+	3.47635i	1.04797	+	0.131206i
$703$	−26.5317	+	15.3181i	−1.00066	+	0.577732i
$704$	−0.133512	+	0.366822i	−0.00503193	+	0.0138251i
$705$	−19.3775	+	14.9341i	−0.729798	+	0.562451i
$706$	6.97802	+	1.23041i	0.262621	+	0.0463072i
$707$	11.0286	+	7.80708i	0.414772	+	0.293616i
$708$	−6.42472	−	5.86221i	−0.241456	−	0.220315i
$709$	−6.12927	−	2.23087i	−0.230189	−	0.0837821i	0.224350	−	0.974509i	$-0.427974\pi$
$709$	−6.12927	−	2.23087i	−0.230189	−	0.0837821i	−0.454540	+	0.890726i	$0.650196\pi$
$710$	7.97301	−	13.8097i	0.299222	−	0.518268i
$711$	−17.5298	+	25.2619i	−0.657417	+	0.947397i
$712$	0.879563	−	0.507816i	0.0329630	−	0.0190312i
$713$	0.938818	+	0.341702i	0.0351590	+	0.0127968i
$714$	−1.03984	−	25.5924i	−0.0389150	−	0.957772i
$715$	−0.320235	−	0.268709i	−0.0119761	−	0.0100492i
$716$	−0.997216	−	2.73983i	−0.0372677	−	0.102392i
$717$	−1.14026	−	0.723041i	−0.0425839	−	0.0270025i
$718$	5.76871	+	32.7160i	0.215286	+	1.22095i
$719$	12.9225	+	22.3824i	0.481928	+	0.834724i	0.999785	−	0.0207432i	$-0.00660324\pi$
$719$	12.9225	+	22.3824i	0.481928	+	0.834724i	−0.517857	+	0.855467i	$0.673270\pi$
$720$	4.66748	−	17.7189i	0.173947	−	0.660343i
$721$	−1.03901	−	12.6230i	−0.0386947	−	0.470103i
$722$	36.3657	−	6.41226i	1.35339	−	0.238640i
$723$	−17.0292	+	18.6633i	−0.633323	+	0.694094i
$724$	7.44729	−	8.87533i	0.276776	−	0.329849i
$725$	0.364662	+	1.00190i	0.0135432	+	0.0372097i
$726$	−23.2657	+	3.11308i	−0.863470	+	0.115537i
$727$	0.704657	+	0.839777i	0.0261343	+	0.0311456i	0.778953	−	0.627082i	$-0.215751\pi$
$727$	0.704657	+	0.839777i	0.0261343	+	0.0311456i	−0.752819	+	0.658228i	$0.771306\pi$
$728$	−35.2395	+	2.90060i	−1.30606	+	0.107503i
$729$	−18.8480	+	19.3327i	−0.698073	+	0.716026i
$730$	8.45022	−	14.6362i	0.312757	−	0.541710i
$731$	41.5314	+	15.1162i	1.53609	+	0.559092i
$732$	3.54921	−	8.62008i	0.131182	−	0.318607i
$733$	−25.3107	+	30.1641i	−0.934872	+	1.11414i	0.0583953	+	0.998294i	$0.481402\pi$
$733$	−25.3107	+	30.1641i	−0.934872	+	1.11414i	−0.993267	+	0.115844i	$0.963043\pi$
$734$	−1.25423	+	0.456503i	−0.0462945	+	0.0168498i
$735$	−1.36697	+	26.3664i	−0.0504214	+	0.972541i
$736$	0.120015	+	0.680637i	0.00442380	+	0.0250886i
$737$			0.157413i			0.00579837i
$738$	6.47692	+	23.7694i	0.238419	+	0.874964i
$739$	36.8444			1.35534			0.677672	−	0.735364i	$-0.262989\pi$
$739$	36.8444			1.35534			0.677672	+	0.735364i	$0.262989\pi$
$740$	−3.51727	+	2.95134i	−0.129297	+	0.108493i
$741$	24.5586	+	46.9338i	0.902181	+	1.72416i
$742$	22.5122	+	15.9363i	0.826448	+	0.585040i
$743$	24.6431	−	29.3685i	0.904066	−	1.07742i	−0.0925892	−	0.995704i	$-0.529514\pi$
$743$	24.6431	−	29.3685i	0.904066	−	1.07742i	0.996655	−	0.0817197i	$-0.0260412\pi$
$744$	−9.44070	−	18.0421i	−0.346113	−	0.661456i
$745$	−39.9789	+	7.04936i	−1.46471	+	0.258269i
$746$			19.4924i			0.713669i
$747$	37.6263	+	3.13150i	1.37668	+	0.114575i
$748$	0.0831019	−	0.0479789i	0.00303851	−	0.00175428i
$749$	−3.72764	+	13.6310i	−0.136205	+	0.498068i
$750$	−16.4716	+	18.0521i	−0.601458	+	0.659171i
$751$	−4.91683	+	27.8847i	−0.179418	+	1.01753i	0.753503	+	0.657445i	$0.228363\pi$
$751$	−4.91683	+	27.8847i	−0.179418	+	1.01753i	−0.932920	+	0.360083i	$0.882748\pi$
$752$	17.0960	−	6.22242i	0.623426	−	0.226908i
$753$	−2.07959	−	15.5419i	−0.0757844	−	0.566377i
$754$	−21.9078	+	3.86293i	−0.797834	+	0.140680i
$755$	13.9391			0.507296
$756$	3.55074	−	5.58842i	0.129139	−	0.203249i
$757$	45.6205			1.65811			0.829053	−	0.559170i	$-0.188880\pi$
$757$	45.6205			1.65811			0.829053	+	0.559170i	$0.188880\pi$
$758$	43.2155	−	7.62006i	1.56966	−	0.276773i
$759$	0.0156596	−	0.0120688i	0.000568408	−	0.000438069i
$760$	43.7865	−	15.9370i	1.58830	−	0.578095i
$761$	2.23609	−	12.6815i	0.0810582	−	0.459704i	−0.917080	−	0.398704i	$-0.869460\pi$
$761$	2.23609	−	12.6815i	0.0810582	−	0.459704i	0.998138	−	0.0609997i	$-0.0194289\pi$
$762$	1.55237	+	4.88741i	0.0562365	+	0.177052i
$763$	−19.7743	+	19.5720i	−0.715876	+	0.708554i
$764$	−2.71811	+	1.56930i	−0.0983378	+	0.0567754i
$765$	−24.2012	+	17.0989i	−0.874996	+	0.618214i
$766$		−	40.2052i		−	1.45267i
$767$	−44.8746	+	7.91261i	−1.62033	+	0.285708i
$768$	10.0495	−	15.8484i	0.362629	−	0.571881i
$769$	29.5087	−	35.1671i	1.06411	−	1.26816i	0.102210	−	0.994763i	$-0.467409\pi$
$769$	29.5087	−	35.1671i	1.06411	−	1.26816i	0.961902	−	0.273396i	$-0.0881470\pi$
$770$	0.283298	−	0.130335i	0.0102093	−	0.00469695i
$771$	−20.9146	−	0.868817i	−0.753219	−	0.0312897i
$772$	−7.51989	+	6.30994i	−0.270647	+	0.227100i
$773$	−9.37848			−0.337320			−0.168660	−	0.985674i	$-0.553944\pi$
$773$	−9.37848			−0.337320			−0.168660	+	0.985674i	$0.553944\pi$
$774$	−20.7845	−	29.4176i	−0.747083	−	1.05739i
$775$			0.992336i			0.0356458i
$776$	1.85317	+	10.5098i	0.0665248	+	0.377281i
$777$	18.5587	−	7.62158i	0.665789	−	0.273423i
$778$	12.9065	−	4.69757i	0.462719	−	0.168416i
$779$	−29.9764	+	35.7245i	−1.07402	+	1.27996i
$780$	4.84614	+	6.28802i	0.173520	+	0.225147i
$781$	−0.245295	−	0.0892799i	−0.00877733	−	0.00319469i
$782$	−0.726229	+	1.25786i	−0.0259699	+	0.0449812i
$783$	9.79001	−	19.1015i	0.349866	−	0.682632i
$784$	6.90449	−	18.3798i	0.246589	−	0.656420i
$785$	24.5199	+	29.2217i	0.875153	+	1.04297i
$786$	6.08409	+	7.89430i	0.217012	+	0.281580i
$787$	5.12715	+	14.0867i	0.182763	+	0.502138i	0.996913	−	0.0785176i	$-0.0250187\pi$
$787$	5.12715	+	14.0867i	0.182763	+	0.502138i	−0.814150	+	0.580655i	$0.802796\pi$
$788$	5.49325	−	6.54660i	0.195689	−	0.233213i
$789$	3.73095	+	11.7463i	0.132825	+	0.418181i
$790$	27.0844	−	4.77571i	0.963619	−	0.169912i
$791$	−33.4231	+	23.1480i	−1.18839	+	0.823048i
$792$	−0.401573	−	0.0334214i	−0.0142693	−	0.00118758i
$793$	−24.4204	−	42.2974i	−0.867195	−	1.50203i
$794$	3.07605	+	17.4451i	0.109165	+	0.619105i
$795$	1.32442	−	31.8820i	0.0469723	−	1.13074i
$796$	−1.82973	−	5.02714i	−0.0648530	−	0.178182i
$797$	−4.80439	−	4.03136i	−0.170180	−	0.142798i	0.553720	−	0.832703i	$-0.313208\pi$
$797$	−4.80439	−	4.03136i	−0.170180	−	0.142798i	−0.723900	+	0.689905i	$0.757652\pi$
$798$	−39.4818	+	1.60418i	−1.39764	+	0.0567872i
$799$	−27.6474	−	10.0628i	−0.978096	−	0.355998i
$800$	−0.594509	+	0.343240i	−0.0210191	+	0.0121354i
$801$	0.707534	+	0.701571i	0.0249995	+	0.0247888i
$802$	−10.2421	+	17.7399i	−0.361661	+	0.626416i
$803$	−0.259976	−	0.0946235i	−0.00917436	−	0.00333919i
$804$	0.640839	−	2.91986i	0.0226007	−	0.102976i
$805$	0.865029	−	1.22197i	0.0304883	−	0.0430688i
$806$	−20.3900	−	3.59531i	−0.718208	−	0.126639i
$807$	−4.76796	−	35.6335i	−0.167840	−	1.25436i
$808$	−5.34139	+	14.6753i	−0.187909	+	0.516277i
$809$	−28.2350	+	16.3015i	−0.992691	+	0.573131i	−0.906078	−	0.423111i	$-0.860938\pi$
$809$	−28.2350	+	16.3015i	−0.992691	+	0.573131i	−0.0866137	+	0.996242i	$0.527605\pi$
$810$	24.1487	−	0.204384i	0.848500	−	0.00718133i
$811$		−	31.8026i		−	1.11674i	−0.829592	−	0.558371i	$-0.811427\pi$
$811$		−	31.8026i		−	1.11674i	0.829592	−	0.558371i	$-0.188573\pi$
$812$	−1.38842	+	5.07711i	−0.0487239	+	0.178171i
$813$	−21.8741	−	28.3824i	−0.767160	−	0.995414i
$814$	−0.181528	−	0.152320i	−0.00636255	−	0.00533881i
$815$	−12.4138	−	10.4164i	−0.434836	−	0.364871i
$816$	21.0022	−	6.67085i	0.735224	−	0.233526i
$817$	23.3199	−	64.0710i	0.815862	−	2.24156i
$818$	0.512555	+	0.887772i	0.0179211	+	0.0310402i
$819$	−11.8347	−	32.6078i	−0.413539	−	1.13941i
$820$	−3.49461	+	6.05284i	−0.122037	+	0.211374i
$821$	33.6677	+	40.1236i	1.17501	+	1.40032i	0.898308	+	0.439366i	$0.144797\pi$
$821$	33.6677	+	40.1236i	1.17501	+	1.40032i	0.276702	+	0.960956i	$0.410759\pi$
$822$	−20.5275	+	32.3727i	−0.715979	+	1.12913i
$823$	−4.25813	+	24.1490i	−0.148429	+	0.841783i	0.816121	+	0.577881i	$0.196120\pi$
$823$	−4.25813	+	24.1490i	−0.148429	+	0.841783i	−0.964550	+	0.263901i	$0.914991\pi$
$824$	13.7559	−	5.00674i	0.479210	−	0.174418i
$825$	0.0165843	+	0.0105161i	0.000577392	+	0.000366124i
$826$	8.96626	−	32.7874i	0.311976	−	1.14082i
$827$	42.0347	+	24.2687i	1.46169	+	0.843906i	0.999090	−	0.0426613i	$-0.0135836\pi$
$827$	42.0347	+	24.2687i	1.46169	+	0.843906i	0.462599	+	0.886568i	$0.346917\pi$
$828$	−0.339605	+	0.160113i	−0.0118021	+	0.00556432i
$829$	8.51992	+	4.91898i	0.295909	+	0.170843i	0.640604	−	0.767872i	$-0.278684\pi$
$829$	8.51992	+	4.91898i	0.295909	+	0.170843i	−0.344695	+	0.938715i	$0.612018\pi$
$830$	−21.7072	−	25.8697i	−0.753469	−	0.897950i
$831$	20.4606	−	6.49883i	0.709771	−	0.225442i
$832$	−13.2839	−	36.4973i	−0.460537	−	1.26532i
$833$	−27.6595	+	15.5923i	−0.958345	+	0.540240i
$834$	28.6514	+	11.7968i	0.992115	+	0.408491i
$835$	−9.48357	−	53.7840i	−0.328192	−	1.86127i
$836$	−0.0740177	−	0.128202i	−0.00255996	−	0.00443397i
$837$	14.6427	−	13.5896i	0.506127	−	0.469725i
$838$	−5.61701	−	3.24298i	−0.194036	−	0.112027i
$839$	−23.4091	+	19.6425i	−0.808170	+	0.678135i	−0.950170	−	0.311731i	$-0.899091\pi$
$839$	−23.4091	+	19.6425i	−0.808170	+	0.678135i	0.142000	+	0.989867i	$0.454647\pi$
$840$	−29.8113	+	6.51447i	−1.02859	+	0.224771i
$841$	2.07277	−	11.7553i	0.0714749	−	0.405354i
$842$	−33.1521	−	5.84561i	−1.14250	−	0.201453i
$843$	5.43881	−	5.96069i	0.187323	−	0.205297i
$844$	0.246010	−	0.206427i	0.00846802	−	0.00710551i
$845$	13.2844			0.456996
$846$	13.8362	+	19.5833i	0.475700	+	0.673287i
$847$	16.5673	+	23.9213i	0.569258	+	0.821946i
$848$	−8.11602	+	22.2986i	−0.278705	+	0.765736i
$849$	29.1116	+	18.4596i	0.999107	+	0.633533i
$850$	−1.42075	−	0.250517i	−0.0487314	−	0.00859265i
$851$	−1.12041	−	0.197558i	−0.0384070	−	0.00677220i
$852$	4.18653	+	2.65468i	0.143428	+	0.0909477i
$853$	−11.8148	+	32.4608i	−0.404530	+	1.11144i	0.555494	+	0.831520i	$0.312529\pi$
$853$	−11.8148	+	32.4608i	−0.404530	+	1.11144i	−0.960024	+	0.279917i	$0.909693\pi$
$854$	36.3108	−	2.98878i	1.24253	−	0.102274i
$855$	26.3788	+	37.3355i	0.902135	+	1.27685i
$856$	−16.3330			−0.558251
$857$	−4.91148	+	4.12122i	−0.167773	+	0.140778i	−0.722808	−	0.691048i	$-0.757149\pi$
$857$	−4.91148	+	4.12122i	−0.167773	+	0.140778i	0.555035	+	0.831827i	$0.312705\pi$
$858$	−0.276166	+	0.302665i	−0.00942815	+	0.0103328i
$859$	31.7647	+	5.60097i	1.08380	+	0.191103i	0.686894	−	0.726758i	$-0.258974\pi$
$859$	31.7647	+	5.60097i	1.08380	+	0.191103i	0.396903	+	0.917861i	$0.370085\pi$
$860$	1.77445	−	10.0634i	0.0605082	−	0.343159i
$861$	22.5787	−	20.5643i	0.769480	−	0.700828i
$862$	24.3040	−	20.3935i	0.827799	−	0.694606i
$863$	19.3990	+	11.2000i	0.660349	+	0.381253i	0.792410	−	0.609989i	$-0.208826\pi$
$863$	19.3990	+	11.2000i	0.660349	+	0.381253i	−0.132061	+	0.991242i	$0.542159\pi$
$864$	13.2063	+	4.07196i	0.449288	+	0.138531i
$865$	−3.51176	−	6.08254i	−0.119403	−	0.206813i
$866$	−2.34421	−	13.2946i	−0.0796593	−	0.451771i
$867$	−5.72547	−	2.35739i	−0.194447	−	0.0800610i
$868$	−2.83047	+	3.99842i	−0.0960724	+	0.135715i
$869$	−0.153982	−	0.423061i	−0.00522346	−	0.0143514i
$870$	−18.2974	+	5.81174i	−0.620340	+	0.197036i
$871$	−10.0673	−	11.9977i	−0.341117	−	0.406527i
$872$	−27.8484	−	16.0783i	−0.943067	−	0.544480i
$873$	−9.47010	+	4.46486i	−0.320514	+	0.151113i
$874$	1.94053	+	1.12036i	0.0656393	+	0.0378968i
$875$	29.2209	+	7.99094i	0.987847	+	0.270143i
$876$	4.43710	+	2.81357i	0.149916	+	0.0950616i
$877$	35.5949	−	12.9555i	1.20196	−	0.437476i	0.338049	−	0.941129i	$-0.390233\pi$
$877$	35.5949	−	12.9555i	1.20196	−	0.437476i	0.863906	+	0.503653i	$0.168011\pi$
$878$	5.20997	−	29.5472i	0.175828	−	0.997170i
$879$	−17.8981	+	28.2260i	−0.603688	+	0.952039i
$880$	0.172452	+	0.205520i	0.00581334	+	0.00692807i
$881$	0.0267134	−	0.0462690i	0.000899999	−	0.00155884i	−0.865575	−	0.500779i	$-0.833047\pi$
$881$	0.0267134	−	0.0462690i	0.000899999	−	0.00155884i	0.866475	+	0.499220i	$0.166380\pi$
$882$	25.7642	+	2.41122i	0.867527	+	0.0811900i
$883$	−11.1816	−	19.3670i	−0.376289	−	0.651752i	0.614230	−	0.789127i	$-0.289467\pi$
$883$	−11.1816	−	19.3670i	−0.376289	−	0.651752i	−0.990519	+	0.137375i	$0.956133\pi$
$884$	−3.26541	+	8.97163i	−0.109828	+	0.301749i
$885$	−37.4794	+	11.9044i	−1.25985	+	0.400163i
$886$	30.8882	+	25.9183i	1.03771	+	0.870742i
$887$	26.2348	+	22.0136i	0.880880	+	0.739146i	0.966360	−	0.257194i	$-0.0827979\pi$
$887$	26.2348	+	22.0136i	0.880880	+	0.739146i	−0.0854799	+	0.996340i	$0.527242\pi$
$888$	14.1550	+	18.3665i	0.475009	+	0.616339i
$889$	4.51807	−	4.47186i	0.151531	−	0.149981i
$890$		−	0.891207i		−	0.0298733i
$891$	−0.0719408	−	0.388729i	−0.00241011	−	0.0130229i
$892$	1.64819	−	0.951582i	0.0551854	−	0.0318613i
$893$	−15.5241	+	42.6521i	−0.519494	+	1.42730i
$894$	5.27688	+	39.4369i	0.176485	+	1.31897i
$895$	−12.9828	−	2.28923i	−0.433969	−	0.0765204i
$896$	14.8360	+	1.37486i	0.495635	+	0.0459310i
$897$	−0.421694	+	1.92137i	−0.0140800	+	0.0641526i
$898$	−17.6266	−	6.41555i	−0.588206	−	0.214090i
$899$	−7.94062	+	13.7536i	−0.264835	+	0.458707i
$900$	−0.264812	−	0.262580i	−0.00882708	−	0.00875268i
$901$	33.2340	−	19.1877i	1.10719	−	0.639234i
$902$	−0.338963	−	0.123373i	−0.0112862	−	0.00410786i
$903$	−20.7373	+	39.5434i	−0.690093	+	1.31592i
$904$	−35.9963	−	30.2045i	−1.19722	−	1.00459i
$905$	−17.9169	−	49.2263i	−0.595578	−	1.63634i
$906$	0.567044	−	13.6501i	0.0188388	−	0.453496i
$907$	−7.38437	−	41.8789i	−0.245194	−	1.39056i	−0.820041	−	0.572304i	$-0.806050\pi$
$907$	−7.38437	−	41.8789i	−0.245194	−	1.39056i	0.574847	−	0.818261i	$-0.305061\pi$
$908$	0.953274	+	1.65112i	0.0316355	+	0.0547943i
$909$	−15.2686	−	1.27075i	−0.506428	−	0.0421481i
$910$	−13.2569	+	28.0522i	−0.439463	+	0.929920i
$911$	−2.14751	+	0.378664i	−0.0711502	+	0.0125457i	−0.209110	−	0.977892i	$-0.567057\pi$
$911$	−2.14751	+	0.378664i	−0.0711502	+	0.0125457i	0.137960	+	0.990438i	$0.455946\pi$
$912$	−10.2912	−	32.4004i	−0.340776	−	1.07288i
$913$	−0.355348	+	0.423487i	−0.0117603	+	0.0140154i
$914$	6.39694	+	17.5755i	0.211592	+	0.581344i
$915$	−25.7300	−	33.3855i	−0.850607	−	1.10369i
$916$	1.93319	+	2.30388i	0.0638743	+	0.0761224i
$917$	5.27903	−	11.1706i	0.174329	−	0.368887i
$918$	15.7600	+	24.3951i	0.520156	+	0.805158i
$919$	−3.97906	+	6.89193i	−0.131257	+	0.227344i	−0.924161	−	0.382002i	$-0.875235\pi$
$919$	−3.97906	+	6.89193i	−0.131257	+	0.227344i	0.792904	+	0.609346i	$0.208568\pi$
$920$	1.62604	+	0.591829i	0.0536088	+	0.0195120i
$921$	4.51571	+	5.85928i	0.148798	+	0.193070i
$922$	1.41140	−	1.68204i	0.0464818	−	0.0553949i
$923$	24.4058	−	8.88299i	0.803327	−	0.292387i
$924$	0.0368278	+	0.0896765i	0.00121155	+	0.00295014i
$925$	−0.196226	−	1.11286i	−0.00645189	−	0.0365905i
$926$		−	29.8122i		−	0.979689i
$927$	8.28712	+	11.7293i	0.272185	+	0.385240i
$928$	−10.9864			−0.360645
$929$	10.0944	−	8.47023i	0.331187	−	0.277899i	−0.461996	−	0.886882i	$-0.652867\pi$
$929$	10.0944	−	8.47023i	0.331187	−	0.277899i	0.793183	+	0.608983i	$0.208422\pi$
$930$	−17.8528	−	0.741627i	−0.585415	−	0.0243189i
$931$	24.0544	+	42.6707i	0.788352	+	1.39848i
$932$	−7.30350	+	8.70398i	−0.239234	+	0.285108i
$933$	21.9068	−	34.5479i	0.717197	−	1.13105i
$934$	2.12420	−	0.374555i	0.0695061	−	0.0122558i
$935$		−	0.433871i		−	0.0141891i
$936$	32.7447	−	23.1352i	1.07029	−	0.756197i
$937$	0.326071	−	0.188257i	0.0106523	−	0.00615009i	−0.494664	−	0.869084i	$-0.664709\pi$
$937$	0.326071	−	0.188257i	0.0106523	−	0.00615009i	0.505317	+	0.862934i	$0.331376\pi$
$938$	11.3005	−	2.96579i	0.368976	−	0.0968365i
$939$	−0.724133	−	2.27983i	−0.0236312	−	0.0743993i
$940$	−1.18125	+	6.69920i	−0.0385281	+	0.218504i
$941$	5.15476	−	1.87618i	0.168040	−	0.0611617i	−0.256630	−	0.966510i	$-0.582612\pi$
$941$	5.15476	−	1.87618i	0.168040	−	0.0611617i	0.424670	+	0.905348i	$0.360390\pi$
$942$	29.6134	−	22.8228i	0.964856	−	0.743609i
$943$	−1.70550	+	0.300727i	−0.0555389	+	0.00979300i
$944$	29.2438			0.951805
$945$	−13.8554	−	26.5376i	−0.450715	−	0.863269i
$946$	0.527389			0.0171469
$947$	6.09611	−	1.07491i	0.198097	−	0.0349299i	−0.0737191	−	0.997279i	$-0.523487\pi$
$947$	6.09611	−	1.07491i	0.198097	−	0.0349299i	0.271816	+	0.962349i	$0.412376\pi$
$948$	1.13390	+	8.47427i	0.0368275	+	0.275231i
$949$	25.8666	−	9.41466i	0.839664	−	0.305613i
$950$	−0.386476	+	2.19181i	−0.0125389	+	0.0711118i
$951$	−9.85261	+	10.7980i	−0.319493	+	0.350150i
$952$	−25.8157	−	26.0825i	−0.836690	−	0.845337i
$953$	49.4334	−	28.5404i	1.60131	−	0.924514i	0.610079	−	0.792341i	$-0.291138\pi$
$953$	49.4334	−	28.5404i	1.60131	−	0.924514i	0.991227	−	0.132174i	$-0.0421957\pi$
$954$	−31.1672	−	2.59393i	−1.00908	−	0.0839816i
$955$			14.1911i			0.459214i
$956$	−0.369724	+	0.0651924i	−0.0119577	+	0.00210847i
$957$	0.145706	+	0.278458i	0.00471000	+	0.00900127i
$958$	11.7033	−	13.9475i	0.378118	−	0.450623i
$959$	47.3157	+	4.38479i	1.52790	+	0.141592i
$960$	−15.5401	−	29.6987i	−0.501556	−	0.958522i
$961$	12.4245	−	10.4254i	0.400789	−	0.336302i
$962$	23.5773			0.760164
$963$	−4.21269	−	15.4600i	−0.135752	−	0.498191i
$964$			7.02507i			0.226262i
$965$	7.70741	+	43.7109i	0.248110	+	1.40710i
$966$	−1.16145	−	0.896806i	−0.0373690	−	0.0288543i
$967$	−25.0313	+	9.11064i	−0.804951	+	0.292978i	−0.711537	−	0.702649i	$-0.752000\pi$
$967$	−25.0313	+	9.11064i	−0.804951	+	0.292978i	−0.0934147	+	0.995627i	$0.529778\pi$
$968$	−21.6177	+	25.7630i	−0.694819	+	0.828053i
$969$	−20.9313	+	50.8367i	−0.672411	+	1.63311i
$970$	8.79979	+	3.20286i	0.282544	+	0.102838i
$971$	−12.5356	+	21.7123i	−0.402287	+	0.696782i	−0.994002	−	0.109366i	$-0.965118\pi$
$971$	−12.5356	+	21.7123i	−0.402287	+	0.696782i	0.591714	+	0.806148i	$0.298451\pi$
$972$	−0.248110	+	7.50345i	−0.00795812	+	0.240673i
$973$	−3.15093	−	38.2808i	−0.101014	−	1.22723i
$974$	−13.5879	−	16.1934i	−0.435384	−	0.518870i
$975$	−1.93658	+	0.259126i	−0.0620203	+	0.00829867i
$976$	10.7206	+	29.4546i	0.343158	+	0.942820i
$977$	−3.20190	+	3.81588i	−0.102438	+	0.122081i	−0.814828	−	0.579703i	$-0.803168\pi$
$977$	−3.20190	+	3.81588i	−0.102438	+	0.122081i	0.712390	+	0.701784i	$0.247613\pi$
$978$	−10.7055	+	11.7327i	−0.342323	+	0.375171i
$979$	−0.0143674	+	0.00253337i	−0.000459186	+	8.09668e-5i
$980$	4.66079	+	5.67193i	0.148883	+	0.181183i
$981$	8.03610	−	30.5069i	0.256573	−	0.974011i
$982$	18.6640	+	32.3269i	0.595591	+	1.03159i
$983$	−3.72001	−	21.0972i	−0.118650	−	0.672896i	−0.984878	−	0.173248i	$-0.944574\pi$
$983$	−3.72001	−	21.0972i	−0.118650	−	0.672896i	0.866228	−	0.499648i	$-0.166537\pi$
$984$	29.8097	+	18.9023i	0.950297	+	0.602583i
$985$	−13.2158	−	36.3102i	−0.421091	−	1.15694i
$986$	−17.6867	−	14.8409i	−0.563259	−	0.472630i
$987$	13.8048	−	26.3241i	0.439412	−	0.837904i
$988$	13.8407	+	5.03759i	0.440330	+	0.160267i
$989$	2.19279	−	1.26601i	0.0697266	−	0.0402566i
$990$	−0.201586	+	0.290503i	−0.00640682	+	0.00923280i
$991$	−5.99208	+	10.3786i	−0.190345	+	0.329687i	−0.945364	−	0.326015i	$-0.894294\pi$
$991$	−5.99208	+	10.3786i	−0.190345	+	0.329687i	0.755020	+	0.655702i	$0.227627\pi$
$992$	−9.60857	−	3.49723i	−0.305072	−	0.111037i
$993$	−30.4724	−	27.8044i	−0.967013	−	0.882348i
$994$	−1.78777	+	19.2916i	−0.0567048	+	0.611893i
$995$	−23.8214	−	4.20035i	−0.755189	−	0.133160i
$996$	8.31544	−	6.40866i	0.263485	−	0.203066i
$997$	−17.2512	+	47.3974i	−0.546352	+	1.50109i	0.292249	+	0.956342i	$0.405596\pi$
$997$	−17.2512	+	47.3974i	−0.546352	+	1.50109i	−0.838601	+	0.544747i	$0.816626\pi$
$998$	13.6464	−	7.87873i	0.431968	−	0.249397i
$999$	−13.7339	+	18.1355i	−0.434521	+	0.573783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.8	✓	132
3.2	odd	2		567.2.ba.a.530.15		132
7.3	odd	6		189.2.bd.a.59.15	yes	132
21.17	even	6		567.2.bd.a.206.8		132
27.11	odd	18		189.2.bd.a.173.15	yes	132
27.16	even	9		567.2.bd.a.278.8		132
189.38	even	18	inner	189.2.ba.a.38.8	yes	132
189.178	odd	18		567.2.ba.a.521.15		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.8	✓	132	1.1	even	1	trivial
189.2.ba.a.38.8	yes	132	189.38	even	18	inner
189.2.bd.a.59.15	yes	132	7.3	odd	6
189.2.bd.a.173.15	yes	132	27.11	odd	18
567.2.ba.a.521.15		132	189.178	odd	18
567.2.ba.a.530.15		132	3.2	odd	2
567.2.bd.a.206.8		132	21.17	even	6
567.2.bd.a.278.8		132	27.16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21351 + 0.213974i) q^{2} +(-1.60161 - 0.659440i) q^{3} +(-0.452565 + 0.164720i) q^{4} +(-0.378134 + 2.14451i) q^{5} +(2.08467 + 0.457534i) q^{6} +(-0.671624 - 2.55909i) q^{7} +(2.64823 - 1.52896i) q^{8} +(2.13028 + 2.11232i) q^{9} -2.68329i q^{10} +(-0.0432582 + 0.00762759i) q^{11} +(0.833453 + 0.0346227i) q^{12} +(2.80925 - 3.34793i) q^{13} +(1.36260 + 2.96176i) q^{14} +(2.01979 - 3.18529i) q^{15} +(-2.14863 + 1.80291i) q^{16} +4.53595 q^{17} +(-3.03710 - 2.10750i) q^{18} -6.99767i q^{19} +(-0.182113 - 1.03281i) q^{20} +(-0.611886 + 4.54154i) q^{21} +(0.0508621 - 0.0185123i) q^{22} +(0.167036 - 0.199066i) q^{23} +(-5.24967 + 0.702436i) q^{24} +(0.242545 + 0.0882792i) q^{25} +(-2.69268 + 4.66385i) q^{26} +(-2.01891 - 4.78790i) q^{27} +(0.725487 + 1.04752i) q^{28} +(2.65522 + 3.16437i) q^{29} +(-1.76947 + 4.29757i) q^{30} +(1.31493 + 3.61275i) q^{31} +(-1.70958 + 2.03739i) q^{32} +(0.0743125 + 0.0163098i) q^{33} +(-5.50442 + 0.970577i) q^{34} +(5.74194 - 0.472625i) q^{35} +(-1.31203 - 0.605064i) q^{36} +(-2.18902 - 3.79150i) q^{37} +(1.49732 + 8.49174i) q^{38} +(-6.70706 + 3.50953i) q^{39} +(2.27747 + 6.25730i) q^{40} +(-5.10519 - 4.28376i) q^{41} +(-0.229244 - 5.64213i) q^{42} +(9.15605 + 3.33253i) q^{43} +(0.0183207 - 0.0105775i) q^{44} +(-5.33542 + 3.76965i) q^{45} +(-0.160105 + 0.277310i) q^{46} +(-6.09518 - 2.21846i) q^{47} +(4.63016 - 1.47066i) q^{48} +(-6.09784 + 3.43749i) q^{49} +(-0.313220 - 0.0552292i) q^{50} +(-7.26480 - 2.99119i) q^{51} +(-0.719895 + 1.97790i) q^{52} +(7.32681 - 4.23013i) q^{53} +(3.47446 + 5.37817i) q^{54} -0.0956517i q^{55} +(-5.69135 - 5.75017i) q^{56} +(-4.61454 + 11.2075i) q^{57} +(-3.89923 - 3.27184i) q^{58} +(-7.98695 - 6.70185i) q^{59} +(-0.389406 + 1.77425i) q^{60} +(3.82219 - 10.5014i) q^{61} +(-2.36872 - 4.10274i) q^{62} +(3.97487 - 6.87025i) q^{63} +(4.44347 - 7.69631i) q^{64} +(6.11738 + 7.29041i) q^{65} +(-0.0936688 - 0.00389112i) q^{66} +(0.622290 - 3.52918i) q^{67} +(-2.05281 + 0.747162i) q^{68} +(-0.398798 + 0.208675i) q^{69} +(-6.86677 + 1.80216i) q^{70} +(5.14654 + 2.97136i) q^{71} +(8.87112 + 2.33682i) q^{72} +(5.45458 + 3.14920i) q^{73} +(3.46769 + 4.13263i) q^{74} +(-0.330247 - 0.301332i) q^{75} +(1.15266 + 3.16690i) q^{76} +(0.0485729 + 0.105579i) q^{77} +(7.38813 - 5.69399i) q^{78} +(1.77980 + 10.0937i) q^{79} +(-3.05389 - 5.28948i) q^{80} +(0.0761693 + 8.99968i) q^{81} +(7.11181 + 4.10601i) q^{82} +(9.64103 - 8.08979i) q^{83} +(-0.471165 - 2.15613i) q^{84} +(-1.71520 + 9.72737i) q^{85} +(-11.8240 - 2.08490i) q^{86} +(-2.16590 - 6.81902i) q^{87} +(-0.102895 + 0.0863395i) q^{88} +0.332132 q^{89} +(5.66798 - 5.71615i) q^{90} +(-10.4544 - 4.94055i) q^{91} +(-0.0428046 + 0.117605i) q^{92} +(0.276387 - 6.65332i) q^{93} +(7.87125 + 1.38791i) q^{94} +(15.0065 + 2.64606i) q^{95} +(4.08160 - 2.13574i) q^{96} +(-1.19363 + 3.27948i) q^{97} +(6.66425 - 5.47621i) q^{98} +(-0.108264 - 0.0751265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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