LMFDB - Embedded newform 155.2.q.a.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(41,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("155.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.q (of order $15$, degree $8$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			111.4
Character	$\chi$	$=$	155.111
Dual form			155.2.q.a.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19242 - 0.866342i) q^{2} +(-2.65459 + 1.18190i) q^{3} +(0.0532763 - 0.163968i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.14145 + 3.70910i) q^{6} +(2.31407 + 2.57003i) q^{7} +(0.832401 + 2.56187i) q^{8} +(3.64256 - 4.04548i) q^{9} +O(q^{10})$	\(q+(1.19242 - 0.866342i) q^{2} +(-2.65459 + 1.18190i) q^{3} +(0.0532763 - 0.163968i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.14145 + 3.70910i) q^{6} +(2.31407 + 2.57003i) q^{7} +(0.832401 + 2.56187i) q^{8} +(3.64256 - 4.04548i) q^{9} +(1.34648 + 0.599493i) q^{10} +(-2.60914 + 0.554589i) q^{11} +(0.0523664 + 0.498233i) q^{12} +(0.147324 - 1.40170i) q^{13} +(4.98586 + 1.05978i) q^{14} +(-2.35085 - 1.70799i) q^{15} +(3.49098 + 2.53634i) q^{16} +(-2.60755 - 0.554253i) q^{17} +(0.838689 - 7.97960i) q^{18} +(-0.482893 - 4.59442i) q^{19} +(0.168638 - 0.0358451i) q^{20} +(-9.18042 - 4.08739i) q^{21} +(-2.63071 + 2.92170i) q^{22} +(2.45950 + 7.56957i) q^{23} +(-5.23755 - 5.81689i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.03868 - 1.79904i) q^{26} +(-2.19433 + 6.75345i) q^{27} +(0.544687 - 0.242510i) q^{28} +(7.61531 - 5.53285i) q^{29} -4.28290 q^{30} +(1.63570 - 5.32207i) q^{31} +0.972630 q^{32} +(6.27071 - 4.55594i) q^{33} +(-3.58946 + 1.59813i) q^{34} +(-1.06868 + 3.28906i) q^{35} +(-0.469264 - 0.812790i) q^{36} +(4.77065 - 8.26300i) q^{37} +(-4.55615 - 5.06012i) q^{38} +(1.26558 + 3.89505i) q^{39} +(-1.80244 + 2.00181i) q^{40} +(-0.186553 - 0.0830590i) q^{41} +(-14.4880 + 3.07951i) q^{42} +(0.336657 + 3.20308i) q^{43} +(-0.0480705 + 0.457360i) q^{44} +(5.32477 + 1.13181i) q^{45} +(9.49058 + 6.89531i) q^{46} +(4.52897 + 3.29049i) q^{47} +(-12.2648 - 2.60697i) q^{48} +(-0.518459 + 4.93281i) q^{49} +(0.154065 + 1.46583i) q^{50} +(7.57705 - 1.61055i) q^{51} +(-0.221984 - 0.0988335i) q^{52} +(-2.59976 + 2.88732i) q^{53} +(3.23424 + 9.95396i) q^{54} +(-1.78486 - 1.98228i) q^{55} +(-4.65785 + 8.06763i) q^{56} +(6.71202 + 11.6256i) q^{57} +(4.28729 - 13.1949i) q^{58} +(-9.59361 + 4.27135i) q^{59} +(-0.405300 + 0.294467i) q^{60} -1.40790 q^{61} +(-2.66030 - 7.76321i) q^{62} +18.8261 q^{63} +(-5.82218 + 4.23006i) q^{64} +(1.28757 - 0.573261i) q^{65} +(3.53030 - 10.8652i) q^{66} +(-2.34549 - 4.06251i) q^{67} +(-0.229800 + 0.398025i) q^{68} +(-15.4754 - 17.1872i) q^{69} +(1.57514 + 4.84777i) q^{70} +(6.37569 - 7.08092i) q^{71} +(13.3960 + 5.96430i) q^{72} +(1.49789 - 0.318386i) q^{73} +(-1.46998 - 13.9860i) q^{74} +(0.303740 - 2.88989i) q^{75} +(-0.779063 - 0.165595i) q^{76} +(-7.46303 - 5.42221i) q^{77} +(4.88354 + 3.54810i) q^{78} +(9.67493 + 2.05647i) q^{79} +(-0.451049 + 4.29145i) q^{80} +(-0.449782 - 4.27939i) q^{81} +(-0.294407 + 0.0625781i) q^{82} +(-6.38388 - 2.84228i) q^{83} +(-1.15930 + 1.28753i) q^{84} +(-0.823780 - 2.53533i) q^{85} +(3.17639 + 3.52774i) q^{86} +(-13.6763 + 23.6880i) q^{87} +(-3.59263 - 6.22262i) q^{88} +(-4.05038 + 12.4658i) q^{89} +(7.32988 - 3.26347i) q^{90} +(3.94332 - 2.86499i) q^{91} +1.37220 q^{92} +(1.94804 + 16.0612i) q^{93} +8.25112 q^{94} +(3.73744 - 2.71541i) q^{95} +(-2.58193 + 1.14955i) q^{96} +(4.59828 - 14.1521i) q^{97} +(3.65528 + 6.33113i) q^{98} +(-7.26037 + 12.5753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9} - q^{10} - 28 q^{11} - 13 q^{12} - 6 q^{13} - 6 q^{14} - 2 q^{15} + 8 q^{16} - 10 q^{17} - 27 q^{18} - 13 q^{19} - 5 q^{20} - 8 q^{21} + 2 q^{22} - 12 q^{23} - 82 q^{24} - 20 q^{25} + 32 q^{26} - q^{27} + 22 q^{28} + 42 q^{29} + 8 q^{30} - 10 q^{31} + 4 q^{32} + 13 q^{33} + 32 q^{34} + 8 q^{35} - 13 q^{36} + 12 q^{37} + 30 q^{38} + 37 q^{39} + 44 q^{40} + 36 q^{41} - 64 q^{42} - 78 q^{43} - 56 q^{44} - 2 q^{45} + 18 q^{46} - 4 q^{47} - 41 q^{48} - 31 q^{49} + q^{50} - 2 q^{51} + 49 q^{52} - 11 q^{53} + 22 q^{54} - 17 q^{55} + 9 q^{56} + 38 q^{57} + 11 q^{58} - q^{59} - 11 q^{60} - 100 q^{61} - 35 q^{62} + 110 q^{63} + 17 q^{64} + 6 q^{65} - 40 q^{66} + 30 q^{67} - 34 q^{68} + 8 q^{69} + 18 q^{70} - 2 q^{71} + 151 q^{72} - 23 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} + 36 q^{77} - 2 q^{78} - 67 q^{79} - 41 q^{80} - 83 q^{81} + 2 q^{82} + 26 q^{84} - 5 q^{85} - 5 q^{86} - 46 q^{87} + 70 q^{88} + 20 q^{89} - 33 q^{90} + 19 q^{91} - 10 q^{92} - 67 q^{93} + 130 q^{94} + 4 q^{95} + 46 q^{96} - 18 q^{97} - 65 q^{98} + 53 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9 - q^10 - 28 * q^11 - 13 * q^12 - 6 * q^13 - 6 * q^14 - 2 * q^15 + 8 * q^16 - 10 * q^17 - 27 * q^18 - 13 * q^19 - 5 * q^20 - 8 * q^21 + 2 * q^22 - 12 * q^23 - 82 * q^24 - 20 * q^25 + 32 * q^26 - q^27 + 22 * q^28 + 42 * q^29 + 8 * q^30 - 10 * q^31 + 4 * q^32 + 13 * q^33 + 32 * q^34 + 8 * q^35 - 13 * q^36 + 12 * q^37 + 30 * q^38 + 37 * q^39 + 44 * q^40 + 36 * q^41 - 64 * q^42 - 78 * q^43 - 56 * q^44 - 2 * q^45 + 18 * q^46 - 4 * q^47 - 41 * q^48 - 31 * q^49 + q^50 - 2 * q^51 + 49 * q^52 - 11 * q^53 + 22 * q^54 - 17 * q^55 + 9 * q^56 + 38 * q^57 + 11 * q^58 - q^59 - 11 * q^60 - 100 * q^61 - 35 * q^62 + 110 * q^63 + 17 * q^64 + 6 * q^65 - 40 * q^66 + 30 * q^67 - 34 * q^68 + 8 * q^69 + 18 * q^70 - 2 * q^71 + 151 * q^72 - 23 * q^73 - 2 * q^74 - q^75 + 2 * q^76 + 36 * q^77 - 2 * q^78 - 67 * q^79 - 41 * q^80 - 83 * q^81 + 2 * q^82 + 26 * q^84 - 5 * q^85 - 5 * q^86 - 46 * q^87 + 70 * q^88 + 20 * q^89 - 33 * q^90 + 19 * q^91 - 10 * q^92 - 67 * q^93 + 130 * q^94 + 4 * q^95 + 46 * q^96 - 18 * q^97 - 65 * q^98 + 53 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	1.19242	−	0.866342i	0.843166	−	0.612596i	−0.0800872	−	0.996788i	$-0.525520\pi$
$2$	1.19242	−	0.866342i	0.843166	−	0.612596i	0.923253	+	0.384192i	$0.125520\pi$
$3$	−2.65459	+	1.18190i	−1.53263	+	0.682370i	−0.987735	−	0.156137i	$-0.950096\pi$
$3$	−2.65459	+	1.18190i	−1.53263	+	0.682370i	−0.544892	+	0.838506i	$0.683429\pi$
$4$	0.0532763	−	0.163968i	0.0266381	−	0.0819838i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.14145	+	3.70910i	−0.874242	+	1.51423i
$7$	2.31407	+	2.57003i	0.874636	+	0.971381i	0.999785	−	0.0207568i	$-0.00660757\pi$
$7$	2.31407	+	2.57003i	0.874636	+	0.971381i	−0.125149	+	0.992138i	$0.539941\pi$
$8$	0.832401	+	2.56187i	0.294298	+	0.905757i
$9$	3.64256	−	4.04548i	1.21419	−	1.34849i
$10$	1.34648	+	0.599493i	0.425795	+	0.189576i
$11$	−2.60914	+	0.554589i	−0.786684	+	0.167215i	−0.583702	−	0.811968i	$-0.698397\pi$
$11$	−2.60914	+	0.554589i	−0.786684	+	0.167215i	−0.202982	+	0.979183i	$0.565063\pi$
$12$	0.0523664	+	0.498233i	0.0151169	+	0.143828i
$13$	0.147324	−	1.40170i	0.0408604	−	0.388760i	−0.954911	−	0.296893i	$-0.904050\pi$
$13$	0.147324	−	1.40170i	0.0408604	−	0.388760i	0.995771	−	0.0918678i	$-0.0292837\pi$
$14$	4.98586	+	1.05978i	1.33253	+	0.283237i
$15$	−2.35085	−	1.70799i	−0.606987	−	0.441002i
$16$	3.49098	+	2.53634i	0.872745	+	0.634086i
$17$	−2.60755	−	0.554253i	−0.632425	−	0.134426i	−0.119464	−	0.992838i	$-0.538118\pi$
$17$	−2.60755	−	0.554253i	−0.632425	−	0.134426i	−0.512960	+	0.858412i	$0.671451\pi$
$18$	0.838689	−	7.97960i	0.197681	−	1.88081i
$19$	−0.482893	−	4.59442i	−0.110783	−	1.05403i	−0.898794	−	0.438371i	$-0.855556\pi$
$19$	−0.482893	−	4.59442i	−0.110783	−	1.05403i	0.788011	−	0.615661i	$-0.211111\pi$
$20$	0.168638	−	0.0358451i	0.0377086	−	0.00801522i
$21$	−9.18042	−	4.08739i	−2.00333	−	0.891941i
$22$	−2.63071	+	2.92170i	−0.560870	+	0.622909i
$23$	2.45950	+	7.56957i	0.512842	+	1.57836i	0.787175	+	0.616730i	$0.211543\pi$
$23$	2.45950	+	7.56957i	0.512842	+	1.57836i	−0.274333	+	0.961635i	$0.588457\pi$
$24$	−5.23755	−	5.81689i	−1.06911	−	1.18737i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.03868	−	1.79904i	−0.203701	−	0.352821i
$27$	−2.19433	+	6.75345i	−0.422299	+	1.29970i
$28$	0.544687	−	0.242510i	0.102936	−	0.0458301i
$29$	7.61531	−	5.53285i	1.41413	−	1.02742i	0.421422	−	0.906865i	$-0.361531\pi$
$29$	7.61531	−	5.53285i	1.41413	−	1.02742i	0.992706	−	0.120560i	$-0.0384690\pi$
$30$	−4.28290			−0.781946
$31$	1.63570	−	5.32207i	0.293781	−	0.955873i
$31$	1.63570	−	5.32207i	0.293781	−	0.955873i
$32$	0.972630			0.171938
$33$	6.27071	−	4.55594i	1.09159	−	0.793087i
$34$	−3.58946	+	1.59813i	−0.615588	+	0.274077i
$35$	−1.06868	+	3.28906i	−0.180640	+	0.555952i
$36$	−0.469264	−	0.812790i	−0.0782107	−	0.135465i
$37$	4.77065	−	8.26300i	0.784290	−	1.35843i	−0.145133	−	0.989412i	$-0.546361\pi$
$37$	4.77065	−	8.26300i	0.784290	−	1.35843i	0.929423	−	0.369017i	$-0.120306\pi$
$38$	−4.55615	−	5.06012i	−0.739105	−	0.820859i
$39$	1.26558	+	3.89505i	0.202655	+	0.623707i
$40$	−1.80244	+	2.00181i	−0.284991	+	0.316515i
$41$	−0.186553	−	0.0830590i	−0.0291348	−	0.0129716i	0.392118	−	0.919915i	$-0.371743\pi$
$41$	−0.186553	−	0.0830590i	−0.0291348	−	0.0129716i	−0.421252	+	0.906943i	$0.638409\pi$
$42$	−14.4880	+	3.07951i	−2.23554	+	0.475179i
$43$	0.336657	+	3.20308i	0.0513397	+	0.488465i	0.989736	+	0.142905i	$0.0456443\pi$
$43$	0.336657	+	3.20308i	0.0513397	+	0.488465i	−0.938397	+	0.345560i	$0.887689\pi$
$44$	−0.0480705	+	0.457360i	−0.00724690	+	0.0689496i
$45$	5.32477	+	1.13181i	0.793769	+	0.168721i
$46$	9.49058	+	6.89531i	1.39931	+	1.01666i
$47$	4.52897	+	3.29049i	0.660619	+	0.479968i	0.866872	−	0.498531i	$-0.166127\pi$
$47$	4.52897	+	3.29049i	0.660619	+	0.479968i	−0.206253	+	0.978499i	$0.566127\pi$
$48$	−12.2648	−	2.60697i	−1.77027	−	0.376283i
$49$	−0.518459	+	4.93281i	−0.0740656	+	0.704687i
$50$	0.154065	+	1.46583i	0.0217881	+	0.207300i
$51$	7.57705	−	1.61055i	1.06100	−	0.225522i
$52$	−0.221984	−	0.0988335i	−0.0307836	−	0.0137057i
$53$	−2.59976	+	2.88732i	−0.357104	+	0.396604i	−0.894751	−	0.446566i	$-0.852647\pi$
$53$	−2.59976	+	2.88732i	−0.357104	+	0.396604i	0.537647	+	0.843170i	$0.319313\pi$
$54$	3.23424	+	9.95396i	0.440124	+	1.35456i
$55$	−1.78486	−	1.98228i	−0.240670	−	0.267291i
$56$	−4.65785	+	8.06763i	−0.622431	+	1.07808i
$57$	6.71202	+	11.6256i	0.889029	+	1.53984i
$58$	4.28729	−	13.1949i	0.562949	−	1.73258i
$59$	−9.59361	+	4.27135i	−1.24898	+	0.556083i	−0.921354	−	0.388724i	$-0.872916\pi$
$59$	−9.59361	+	4.27135i	−1.24898	+	0.556083i	−0.327628	+	0.944807i	$0.606249\pi$
$60$	−0.405300	+	0.294467i	−0.0523240	+	0.0380156i
$61$	−1.40790			−0.180264			−0.0901318	−	0.995930i	$-0.528729\pi$
$61$	−1.40790			−0.180264			−0.0901318	+	0.995930i	$0.528729\pi$
$62$	−2.66030	−	7.76321i	−0.337858	−	0.985928i
$63$	18.8261			2.37187
$64$	−5.82218	+	4.23006i	−0.727772	+	0.528757i
$65$	1.28757	−	0.573261i	0.159703	−	0.0711043i
$66$	3.53030	−	10.8652i	0.434550	−	1.33741i
$67$	−2.34549	−	4.06251i	−0.286547	−	0.496314i	0.686436	−	0.727190i	$-0.259174\pi$
$67$	−2.34549	−	4.06251i	−0.286547	−	0.496314i	−0.972983	+	0.230876i	$0.925841\pi$
$68$	−0.229800	+	0.398025i	−0.0278674	+	0.0482677i
$69$	−15.4754	−	17.1872i	−1.86302	−	2.06910i
$70$	1.57514	+	4.84777i	0.188265	+	0.579419i
$71$	6.37569	−	7.08092i	0.756655	−	0.840350i	−0.234630	−	0.972085i	$-0.575388\pi$
$71$	6.37569	−	7.08092i	0.756655	−	0.840350i	0.991285	+	0.131735i	$0.0420546\pi$
$72$	13.3960	+	5.96430i	1.57874	+	0.702900i
$73$	1.49789	−	0.318386i	0.175315	−	0.0372643i	−0.119418	−	0.992844i	$-0.538103\pi$
$73$	1.49789	−	0.318386i	0.175315	−	0.0372643i	0.294732	+	0.955580i	$0.404769\pi$
$74$	−1.46998	−	13.9860i	−0.170882	−	1.62583i
$75$	0.303740	−	2.88989i	0.0350728	−	0.333696i
$76$	−0.779063	−	0.165595i	−0.0893646	−	0.0189950i
$77$	−7.46303	−	5.42221i	−0.850491	−	0.617918i
$78$	4.88354	+	3.54810i	0.552952	+	0.401743i
$79$	9.67493	+	2.05647i	1.08851	+	0.231371i	0.717012	−	0.697061i	$-0.245509\pi$
$79$	9.67493	+	2.05647i	1.08851	+	0.231371i	0.371503	+	0.928432i	$0.378843\pi$
$80$	−0.451049	+	4.29145i	−0.0504289	+	0.479799i
$81$	−0.449782	−	4.27939i	−0.0499758	−	0.475488i
$82$	−0.294407	+	0.0625781i	−0.0325118	+	0.00691060i
$83$	−6.38388	−	2.84228i	−0.700721	−	0.311981i	0.0252743	−	0.999681i	$-0.491954\pi$
$83$	−6.38388	−	2.84228i	−0.700721	−	0.311981i	−0.725996	+	0.687699i	$0.758621\pi$
$84$	−1.15930	+	1.28753i	−0.126490	+	0.140481i
$85$	−0.823780	−	2.53533i	−0.0893515	−	0.274996i
$86$	3.17639	+	3.52774i	0.342519	+	0.380406i
$87$	−13.6763	+	23.6880i	−1.46625	+	2.53962i
$88$	−3.59263	−	6.22262i	−0.382976	−	0.663333i
$89$	−4.05038	+	12.4658i	−0.429339	+	1.32137i	0.469438	+	0.882965i	$0.344457\pi$
$89$	−4.05038	+	12.4658i	−0.429339	+	1.32137i	−0.898777	+	0.438405i	$0.855543\pi$
$90$	7.32988	−	3.26347i	0.772637	−	0.344000i
$91$	3.94332	−	2.86499i	0.413373	−	0.300333i
$92$	1.37220			0.143061
$93$	1.94804	+	16.0612i	0.202002	+	1.66546i
$94$	8.25112			0.851038
$95$	3.73744	−	2.71541i	0.383453	−	0.278595i
$96$	−2.58193	+	1.14955i	−0.263517	+	0.117326i
$97$	4.59828	−	14.1521i	0.466885	−	1.43692i	−0.389712	−	0.920937i	$-0.627425\pi$
$97$	4.59828	−	14.1521i	0.466885	−	1.43692i	0.856596	−	0.515987i	$-0.172575\pi$
$98$	3.65528	+	6.33113i	0.369239	+	0.639540i
$99$	−7.26037	+	12.5753i	−0.729694	+	1.26387i
$100$	0.115362	+	0.128122i	0.0115362	+	0.0128122i
$101$	−2.78162	−	8.56095i	−0.276782	−	0.851847i	−0.988742	−	0.149627i	$-0.952193\pi$
$101$	−2.78162	−	8.56095i	−0.276782	−	0.851847i	0.711961	−	0.702219i	$-0.247807\pi$
$102$	7.63971	−	8.48476i	0.756444	−	0.840117i
$103$	1.95724	+	0.871417i	0.192852	+	0.0858633i	0.500891	−	0.865511i	$-0.333006\pi$
$103$	1.95724	+	0.871417i	0.192852	+	0.0858633i	−0.308038	+	0.951374i	$0.599673\pi$
$104$	3.71359	−	0.789348i	0.364148	−	0.0774020i
$105$	−1.05043	−	9.99417i	−0.102511	−	0.975331i
$106$	−0.598587	+	5.69517i	−0.0581399	+	0.553164i
$107$	−6.08566	−	1.29355i	−0.588323	−	0.125052i	−0.0958743	−	0.995393i	$-0.530565\pi$
$107$	−6.08566	−	1.29355i	−0.588323	−	0.125052i	−0.492449	+	0.870342i	$0.663898\pi$
$108$	0.990441	+	0.719597i	0.0953052	+	0.0692433i
$109$	11.8039	+	8.57606i	1.13061	+	0.821437i	0.985784	−	0.168020i	$-0.0537372\pi$
$109$	11.8039	+	8.57606i	1.13061	+	0.821437i	0.144828	+	0.989457i	$0.453737\pi$
$110$	−3.84563	−	0.817413i	−0.366666	−	0.0779373i
$111$	−2.89807	+	27.5733i	−0.275073	+	2.61714i
$112$	1.55987	+	14.8412i	0.147394	+	1.40236i
$113$	−11.0728	+	2.35359i	−1.04164	+	0.221407i	−0.696808	−	0.717258i	$-0.745397\pi$
$113$	−11.0728	+	2.35359i	−1.04164	+	0.221407i	−0.344831	+	0.938665i	$0.612064\pi$
$114$	18.0752	+	8.04762i	1.69290	+	0.753728i
$115$	−5.32569	+	5.91478i	−0.496623	+	0.551556i
$116$	−0.501492	−	1.54343i	−0.0465624	−	0.143304i
$117$	−5.13389	−	5.70176i	−0.474628	−	0.527128i
$118$	−7.73914	+	13.4046i	−0.712445	+	1.23399i
$119$	−4.60961	−	7.98408i	−0.422562	−	0.731899i
$120$	2.41880	−	7.44430i	0.220805	−	0.679568i
$121$	−3.54898	+	1.58011i	−0.322634	+	0.143646i
$122$	−1.67881	+	1.21973i	−0.151992	+	0.110429i
$123$	0.593390			0.0535042
$124$	−0.785503	−	0.551742i	−0.0705403	−	0.0495479i
$125$	−1.00000			−0.0894427
$126$	22.4486	−	16.3099i	1.99988	−	1.45300i
$127$	−5.98285	+	2.66374i	−0.530892	+	0.236368i	−0.654634	−	0.755946i	$-0.727177\pi$
$127$	−5.98285	+	2.66374i	−0.530892	+	0.236368i	0.123742	+	0.992314i	$0.460511\pi$
$128$	−3.87890	+	11.9380i	−0.342850	+	1.05518i
$129$	−4.67940	−	8.10495i	−0.411998	−	0.713601i
$130$	1.03868	−	1.79904i	0.0910979	−	0.157786i
$131$	−0.867294	−	0.963228i	−0.0757759	−	0.0841576i	0.704065	−	0.710136i	$-0.251367\pi$
$131$	−0.867294	−	0.963228i	−0.0757759	−	0.0841576i	−0.779840	+	0.625978i	$0.784700\pi$
$132$	−0.412946	−	1.27092i	−0.0359423	−	0.110619i
$133$	10.6904	−	11.8729i	0.926972	−	1.02951i
$134$	−6.31632	−	2.81221i	−0.545647	−	0.242938i
$135$	−6.94582	+	1.47638i	−0.597801	+	0.127067i
$136$	−0.750609	−	7.14156i	−0.0643642	−	0.612384i
$137$	−0.106890	+	1.01699i	−0.00913224	+	0.0868875i	−0.998139	−	0.0609850i	$-0.980576\pi$
$137$	−0.106890	+	1.01699i	−0.00913224	+	0.0868875i	0.989006	+	0.147872i	$0.0472425\pi$
$138$	−33.3432	−	7.08731i	−2.83836	−	0.603312i
$139$	−5.63093	−	4.09111i	−0.477609	−	0.347004i	0.322790	−	0.946471i	$-0.395379\pi$
$139$	−5.63093	−	4.09111i	−0.477609	−	0.347004i	−0.800399	+	0.599467i	$0.795379\pi$
$140$	0.482363	+	0.350458i	0.0407671	+	0.0296191i
$141$	−15.9116	−	3.38211i	−1.34000	−	0.284825i
$142$	1.46798	−	13.9669i	0.123190	−	1.17208i
$143$	0.392976	+	3.73892i	0.0328623	+	0.312664i
$144$	22.9768	−	4.88388i	1.91474	−	0.406990i
$145$	8.59925	+	3.82863i	0.714128	+	0.317950i
$146$	1.51028	−	1.67733i	0.124991	−	0.138817i
$147$	−4.45379	−	13.7073i	−0.367342	−	1.13056i
$148$	−1.10070	−	1.22245i	−0.0904771	−	0.100485i
$149$	10.3942	−	18.0033i	0.851527	−	1.47489i	−0.0283025	−	0.999599i	$-0.509010\pi$
$149$	10.3942	−	18.0033i	0.851527	−	1.47489i	0.879830	−	0.475289i	$-0.157656\pi$
$150$	−2.14145	−	3.70910i	−0.174848	−	0.302846i
$151$	0.0452157	−	0.139160i	0.00367960	−	0.0113246i	−0.949200	−	0.314674i	$-0.898105\pi$
$151$	0.0452157	−	0.139160i	0.00367960	−	0.0113246i	0.952879	+	0.303349i	$0.0981049\pi$
$152$	11.3683	−	5.06151i	0.922094	−	0.410543i
$153$	−11.7404	+	8.52989i	−0.949154	+	0.689601i
$154$	−13.5965			−1.09564
$155$	5.42690	−	1.24448i	0.435899	−	0.0999588i
$156$	0.706087			0.0565322
$157$	−0.335891	+	0.244039i	−0.0268070	+	0.0194764i	−0.601108	−	0.799168i	$-0.705274\pi$
$157$	−0.335891	+	0.244039i	−0.0268070	+	0.0194764i	0.574301	+	0.818644i	$0.305274\pi$
$158$	13.3182	−	5.92963i	1.05954	−	0.471736i
$159$	3.48876	−	10.7373i	0.276677	−	0.851524i
$160$	0.486315	+	0.842323i	0.0384466	+	0.0665915i
$161$	−13.7626	+	23.8375i	−1.08464	+	1.87866i
$162$	−4.24374	−	4.71315i	−0.333420	−	0.370300i
$163$	−3.25720	−	10.0246i	−0.255124	−	0.785191i	−0.993805	−	0.111136i	$-0.964551\pi$
$163$	−3.25720	−	10.0246i	−0.255124	−	0.785191i	0.738681	−	0.674055i	$-0.235449\pi$
$164$	−0.0235578	+	0.0261636i	−0.00183956	+	0.00204304i
$165$	7.08092	+	3.15263i	0.551249	+	0.245432i
$166$	−10.0746	+	2.14143i	−0.781943	+	0.166207i
$167$	−1.53630	−	14.6169i	−0.118882	−	1.13109i	−0.877508	−	0.479563i	$-0.840795\pi$
$167$	−1.53630	−	14.6169i	−0.118882	−	1.13109i	0.758625	−	0.651527i	$-0.225871\pi$
$168$	2.82955	−	26.9214i	0.218304	−	2.07703i
$169$	10.7729	+	2.28984i	0.828682	+	0.176142i
$170$	−3.17875	−	2.30950i	−0.243799	−	0.177131i
$171$	−20.3456	−	14.7819i	−1.55587	−	1.13040i
$172$	0.543136	+	0.115447i	0.0414137	+	0.00880276i
$173$	−1.82928	+	17.4044i	−0.139078	+	1.32323i	0.672981	+	0.739659i	$0.265013\pi$
$173$	−1.82928	+	17.4044i	−0.139078	+	1.32323i	−0.812059	+	0.583575i	$0.801653\pi$
$174$	4.21407	+	40.0942i	0.319468	+	3.03954i
$175$	−3.38275	+	0.719025i	−0.255712	+	0.0543532i
$176$	−10.5151	−	4.68161i	−0.792603	−	0.352890i
$177$	20.4188	−	22.6774i	1.53477	−	1.70453i
$178$	5.96989	+	18.3734i	0.447462	+	1.37715i
$179$	−9.50956	−	10.5614i	−0.710778	−	0.789399i	0.274275	−	0.961651i	$-0.411562\pi$
$179$	−9.50956	−	10.5614i	−0.710778	−	0.789399i	−0.985053	+	0.172252i	$0.944896\pi$
$180$	0.469264	−	0.812790i	0.0349769	−	0.0605818i
$181$	10.6424	+	18.4332i	0.791044	+	1.37013i	0.925321	+	0.379185i	$0.123796\pi$
$181$	10.6424	+	18.4332i	0.791044	+	1.37013i	−0.134277	+	0.990944i	$0.542871\pi$
$182$	2.22002	−	6.83253i	0.164559	−	0.506461i
$183$	3.73741	−	1.66400i	0.276277	−	0.123006i
$184$	−17.3449	+	12.6018i	−1.27869	+	0.929020i
$185$	9.54129			0.701490
$186$	16.2373	+	17.4639i	1.19058	+	1.28052i
$187$	7.11084			0.519996
$188$	0.780821	−	0.567299i	0.0569472	−	0.0413746i
$189$	−22.4344	+	9.98844i	−1.63186	+	0.726552i
$190$	2.10411	−	6.47580i	0.152648	−	0.469804i
$191$	−6.87683	−	11.9110i	−0.497590	−	0.861851i	0.502406	−	0.864632i	$-0.332448\pi$
$191$	−6.87683	−	11.9110i	−0.497590	−	0.861851i	−0.999996	+	0.00278081i	$0.999115\pi$
$192$	10.4560	−	18.1103i	0.754596	−	1.30700i
$193$	−13.6531	−	15.1633i	−0.982773	−	1.09148i	−0.995799	−	0.0915648i	$-0.970813\pi$
$193$	−13.6531	−	15.1633i	−0.982773	−	1.09148i	0.0130261	−	0.999915i	$-0.495854\pi$
$194$	−6.77745	−	20.8588i	−0.486592	−	1.49758i
$195$	−2.74042	+	3.04355i	−0.196246	+	0.217953i
$196$	0.781199	+	0.347812i	0.0557999	+	0.0248437i
$197$	−15.0118	+	3.19085i	−1.06954	+	0.227338i	−0.708859	−	0.705350i	$-0.750790\pi$
$197$	−15.0118	+	3.19085i	−1.06954	+	0.227338i	−0.360684	+	0.932688i	$0.617457\pi$
$198$	2.23714	+	21.2850i	0.158987	+	1.51266i
$199$	−1.55425	+	14.7877i	−0.110178	+	1.04827i	0.790106	+	0.612971i	$0.210026\pi$
$199$	−1.55425	+	14.7877i	−0.110178	+	1.04827i	−0.900284	+	0.435304i	$0.856641\pi$
$200$	−2.63484	−	0.560053i	−0.186312	−	0.0396017i
$201$	11.0278	+	8.01215i	0.777839	+	0.565133i
$202$	−10.7336	−	7.79839i	−0.755211	−	0.548693i
$203$	31.8420	+	6.76822i	2.23487	+	0.475036i
$204$	0.139599	−	1.32819i	0.00977387	−	0.0929922i
$205$	−0.0213456	−	0.203090i	−0.00149084	−	0.0141844i
$206$	3.08879	−	0.656542i	0.215206	−	0.0457434i
$207$	39.5814	+	17.6228i	2.75110	+	1.22487i
$208$	4.06949	−	4.51963i	0.282168	−	0.313380i
$209$	3.80795	+	11.7197i	0.263401	+	0.810666i
$210$	−9.91091	−	11.0072i	−0.683918	−	0.759568i
$211$	−4.43407	+	7.68004i	−0.305254	+	0.528716i	−0.977318	−	0.211777i	$-0.932075\pi$
$211$	−4.43407	+	7.68004i	−0.305254	+	0.528716i	0.672064	+	0.740493i	$0.265408\pi$
$212$	0.334922	+	0.580102i	0.0230025	+	0.0398415i
$213$	−8.55589	+	26.3323i	−0.586240	+	1.80426i
$214$	−8.37730	+	3.72981i	−0.572660	+	0.254965i
$215$	−2.60562	+	1.89309i	−0.177702	+	0.129108i
$216$	−19.1280			−1.30150
$217$	17.4630	−	8.11183i	1.18547	−	0.550667i
$218$	21.5050			1.45650
$219$	−3.59998	+	2.61554i	−0.243264	+	0.176742i
$220$	−0.420121	+	0.187050i	−0.0283245	+	0.0126109i
$221$	−1.16105	+	3.57334i	−0.0781006	+	0.240369i
$222$	20.4322	+	35.3896i	1.37132	+	2.37519i
$223$	10.8379	−	18.7719i	0.725762	−	1.25706i	−0.232897	−	0.972501i	$-0.574821\pi$
$223$	10.8379	−	18.7719i	0.725762	−	1.25706i	0.958659	−	0.284556i	$-0.0918461\pi$
$224$	2.25073	+	2.49969i	0.150383	+	0.167018i
$225$	1.68220	+	5.17729i	0.112147	+	0.345153i
$226$	−11.1643	+	12.3993i	−0.742641	+	0.824787i
$227$	−2.91760	−	1.29900i	−0.193648	−	0.0862176i	0.307622	−	0.951509i	$-0.400467\pi$
$227$	−2.91760	−	1.29900i	−0.193648	−	0.0862176i	−0.501270	+	0.865291i	$0.667134\pi$
$228$	2.26381	−	0.481187i	0.149924	−	0.0318674i
$229$	0.902887	+	8.59039i	0.0596644	+	0.567669i	0.982991	+	0.183653i	$0.0587924\pi$
$229$	0.902887	+	8.59039i	0.0596644	+	0.567669i	−0.923327	+	0.384016i	$0.874541\pi$
$230$	−1.22622	+	11.6667i	−0.0808548	+	0.769282i
$231$	26.2198	+	5.57319i	1.72513	+	0.366689i
$232$	20.5134	+	14.9039i	1.34677	+	0.978487i
$233$	−6.01820	−	4.37248i	−0.394265	−	0.286451i	0.372936	−	0.927857i	$-0.378351\pi$
$233$	−6.01820	−	4.37248i	−0.394265	−	0.286451i	−0.767201	+	0.641407i	$0.778351\pi$
$234$	−11.0614	−	2.35118i	−0.723107	−	0.153701i
$235$	−0.585163	+	5.56745i	−0.0381718	+	0.363181i
$236$	0.189251	+	1.80060i	0.0123192	+	0.117209i
$237$	−28.1135	+	5.97571i	−1.82617	+	0.388164i
$238$	−12.4135	−	5.52685i	−0.804648	−	0.358253i
$239$	−16.4005	+	18.2146i	−1.06086	+	1.17820i	−0.0774117	+	0.996999i	$0.524666\pi$
$239$	−16.4005	+	18.2146i	−1.06086	+	1.17820i	−0.983446	+	0.181202i	$0.942001\pi$
$240$	−3.87471	−	11.9251i	−0.250111	−	0.769764i
$241$	−5.04341	−	5.60127i	−0.324874	−	0.360810i	0.558478	−	0.829519i	$-0.311386\pi$
$241$	−5.04341	−	5.60127i	−0.324874	−	0.360810i	−0.883352	+	0.468710i	$0.844719\pi$
$242$	−2.86295	+	4.95877i	−0.184037	+	0.318762i
$243$	−4.39970	−	7.62050i	−0.282241	−	0.488855i
$244$	−0.0750079	+	0.230851i	−0.00480189	+	0.0147787i
$245$	−4.53117	+	2.01741i	−0.289486	+	0.128887i
$246$	0.707568	−	0.514078i	0.0451129	−	0.0327764i
$247$	−6.51112			−0.414293
$248$	14.9960	−	0.239648i	0.952247	−	0.0152177i
$249$	20.3059			1.28683
$250$	−1.19242	+	0.866342i	−0.0754151	+	0.0547923i
$251$	8.88229	−	3.95465i	0.560645	−	0.249615i	−0.106792	−	0.994281i	$-0.534058\pi$
$251$	8.88229	−	3.95465i	0.560645	−	0.249615i	0.667437	+	0.744666i	$0.267391\pi$
$252$	1.00299	−	3.08688i	0.0631822	−	0.194455i
$253$	−10.6152	−	18.3860i	−0.667370	−	1.15592i
$254$	−4.82634	+	8.35947i	−0.302832	+	0.524520i
$255$	5.18330	+	5.75664i	0.324591	+	0.360495i
$256$	1.26940	+	3.90682i	0.0793376	+	0.244176i
$257$	−1.73157	+	1.92310i	−0.108012	+	0.119960i	−0.794727	−	0.606968i	$-0.792386\pi$
$257$	−1.73157	+	1.92310i	−0.108012	+	0.119960i	0.686714	+	0.726928i	$0.259052\pi$
$258$	−12.6015	−	5.61053i	−0.784532	−	0.349296i
$259$	32.2758	−	6.86043i	2.00552	−	0.426286i
$260$	−0.0253995	−	0.241660i	−0.00157521	−	0.0149871i
$261$	5.35625	−	50.9613i	0.331544	−	3.15443i
$262$	−1.86866	−	0.397196i	−0.115446	−	0.0245389i
$263$	11.0846	+	8.05344i	0.683506	+	0.496596i	0.874519	−	0.484991i	$-0.161177\pi$
$263$	11.0846	+	8.05344i	0.683506	+	0.496596i	−0.191013	+	0.981588i	$0.561177\pi$
$264$	16.8915	+	12.2724i	1.03960	+	0.755312i
$265$	−3.80037	−	0.807794i	−0.233455	−	0.0496224i
$266$	2.46143	−	23.4189i	0.150920	−	1.43591i
$267$	−3.98121	−	37.8787i	−0.243646	−	2.31814i
$268$	−0.791078	+	0.168149i	−0.0483228	+	0.0102713i
$269$	18.5821	+	8.27330i	1.13297	+	0.504432i	0.885582	−	0.464484i	$-0.153760\pi$
$269$	18.5821	+	8.27330i	1.13297	+	0.504432i	0.247391	+	0.968916i	$0.420427\pi$
$270$	−7.00327	+	7.77792i	−0.426205	+	0.473349i
$271$	−8.58819	−	26.4317i	−0.521696	−	1.60561i	−0.770759	−	0.637127i	$-0.780123\pi$
$271$	−8.58819	−	26.4317i	−0.521696	−	1.60561i	0.249064	−	0.968487i	$-0.419877\pi$
$272$	−7.69714	−	8.54854i	−0.466708	−	0.518331i
$273$	−7.08177	+	12.2660i	−0.428608	+	0.742371i
$274$	0.753605	+	1.30528i	0.0455269	+	0.0788549i
$275$	0.824280	−	2.53687i	0.0497059	−	0.152979i
$276$	−3.64262	+	1.62180i	−0.219260	+	0.0976207i
$277$	−4.12746	+	2.99878i	−0.247995	+	0.180179i	−0.704838	−	0.709368i	$-0.748980\pi$
$277$	−4.12746	+	2.99878i	−0.247995	+	0.180179i	0.456843	+	0.889548i	$0.348980\pi$
$278$	−10.2587			−0.615277
$279$	−15.5722	−	26.0032i	−0.932282	−	1.55677i
$280$	−9.31570			−0.556720
$281$	3.96958	−	2.88407i	0.236805	−	0.172049i	−0.463053	−	0.886330i	$-0.653246\pi$
$281$	3.96958	−	2.88407i	0.236805	−	0.172049i	0.699859	+	0.714281i	$0.253246\pi$
$282$	−21.9033	+	9.75198i	−1.30432	+	0.580722i
$283$	−4.75911	+	14.6470i	−0.282899	+	0.870675i	0.704121	+	0.710080i	$0.251341\pi$
$283$	−4.75911	+	14.6470i	−0.282899	+	0.870675i	−0.987020	+	0.160595i	$0.948659\pi$
$284$	−0.821367	−	1.42265i	−0.0487392	−	0.0844188i
$285$	−6.71202	+	11.6256i	−0.397586	+	0.688639i
$286$	3.70777	+	4.11790i	0.219245	+	0.243496i
$287$	−0.218233	−	0.671653i	−0.0128819	−	0.0396464i
$288$	3.54287	−	3.93475i	0.208765	−	0.231858i
$289$	−9.03814	−	4.02404i	−0.531655	−	0.236708i
$290$	13.5708	−	2.88456i	0.796904	−	0.169387i
$291$	4.51976	+	43.0026i	0.264953	+	2.52086i
$292$	0.0275970	−	0.262568i	0.00161499	−	0.0153656i
$293$	14.5297	+	3.08839i	0.848835	+	0.180426i	0.611738	−	0.791060i	$-0.290471\pi$
$293$	14.5297	+	3.08839i	0.848835	+	0.180426i	0.237097	+	0.971486i	$0.423804\pi$
$294$	−17.1860	−	12.4864i	−1.00231	−	0.728220i
$295$	−8.49590	−	6.17264i	−0.494651	−	0.359385i
$296$	25.1398	+	5.34363i	1.46122	+	0.310592i
$297$	1.97991	−	18.8376i	0.114886	−	1.09307i
$298$	−3.20278	−	30.4724i	−0.185532	−	1.76522i
$299$	10.9726	−	2.33229i	0.634561	−	0.134880i
$300$	−0.457666	−	0.203766i	−0.0264234	−	0.0117644i
$301$	−7.45296	+	8.27735i	−0.429582	+	0.477099i
$302$	−0.0666438	−	0.205108i	−0.00383492	−	0.0118027i
$303$	17.5022	+	19.4382i	1.00548	+	1.11670i
$304$	9.96727	−	17.2638i	0.571662	−	0.990148i
$305$	−0.703952	−	1.21928i	−0.0403082	−	0.0698158i
$306$	−6.60964	+	20.3424i	−0.377848	+	1.16290i
$307$	−20.5708	+	9.15872i	−1.17404	+	0.522716i	−0.898671	−	0.438623i	$-0.855466\pi$
$307$	−20.5708	+	9.15872i	−1.17404	+	0.522716i	−0.275368	+	0.961339i	$0.588800\pi$
$308$	−1.28667	+	0.934819i	−0.0733147	+	0.0532663i
$309$	−6.22558			−0.354161
$310$	5.39299	−	6.18549i	0.306301	−	0.351312i
$311$	9.55538			0.541836			0.270918	−	0.962602i	$-0.412673\pi$
$311$	9.55538			0.541836			0.270918	+	0.962602i	$0.412673\pi$
$312$	−8.92513	+	6.48448i	−0.505286	+	0.367112i
$313$	12.5416	−	5.58387i	0.708892	−	0.315619i	−0.0204285	−	0.999791i	$-0.506503\pi$
$313$	12.5416	−	5.58387i	0.708892	−	0.315619i	0.729320	+	0.684172i	$0.239836\pi$
$314$	−0.189101	+	0.581992i	−0.0106716	+	0.0328437i
$315$	9.41307	+	16.3039i	0.530367	+	0.918622i
$316$	0.852639	−	1.47681i	0.0479647	−	0.0830772i
$317$	19.9984	+	22.2105i	1.12322	+	1.24746i	0.965619	+	0.259961i	$0.0837097\pi$
$317$	19.9984	+	22.2105i	1.12322	+	1.24746i	0.157602	+	0.987503i	$0.449624\pi$
$318$	−5.14212	−	15.8258i	−0.288356	−	0.887467i
$319$	−16.8009	+	18.6593i	−0.940672	+	1.04472i
$320$	−6.57443	−	2.92712i	−0.367522	−	0.163631i
$321$	17.6838	−	3.75880i	0.987011	−	0.209796i
$322$	4.24068	+	40.3473i	0.236324	+	2.24847i
$323$	−1.28730	+	12.2478i	−0.0716273	+	0.681488i
$324$	−0.725644	−	0.154240i	−0.0403136	−	0.00856891i
$325$	1.14024	+	0.828434i	0.0632493	+	0.0459533i
$326$	−12.5687	−	9.13170i	−0.696116	−	0.505758i
$327$	−41.4706	−	8.81485i	−2.29333	−	0.487462i
$328$	0.0574987	−	0.547064i	0.00317483	−	0.0302065i
$329$	2.02368	+	19.2540i	0.111569	+	1.06151i
$330$	11.1747	−	2.37525i	0.615145	−	0.130753i
$331$	−12.5135	−	5.57139i	−0.687807	−	0.306231i	0.0329126	−	0.999458i	$-0.489522\pi$
$331$	−12.5135	−	5.57139i	−0.687807	−	0.306231i	−0.720719	+	0.693227i	$0.756188\pi$
$332$	−0.806151	+	0.895322i	−0.0442433	+	0.0491372i
$333$	−16.0504	−	49.3980i	−0.879556	−	2.70700i
$334$	−14.4951	−	16.0985i	−0.793139	−	0.880870i
$335$	2.34549	−	4.06251i	0.128148	−	0.221958i
$336$	−21.6816	−	37.5537i	−1.18283	−	2.04872i
$337$	−3.05961	+	9.41650i	−0.166667	+	0.512950i	−0.999155	−	0.0410937i	$-0.986916\pi$
$337$	−3.05961	+	9.41650i	−0.166667	+	0.512950i	0.832488	+	0.554043i	$0.186916\pi$
$338$	14.8295	−	6.60254i	0.806621	−	0.359131i
$339$	26.6119	−	19.3347i	1.44536	−	1.05012i
$340$	−0.459600			−0.0249253
$341$	−1.31621	+	14.7932i	−0.0712766	+	0.801094i
$342$	−37.0666			−2.00433
$343$	5.70765	−	4.14685i	0.308184	−	0.223909i
$344$	−7.92562	+	3.52871i	−0.427321	+	0.190256i
$345$	7.14684	−	21.9957i	0.384773	−	1.18421i
$346$	12.8969	+	22.3381i	0.693343	+	1.20090i
$347$	11.0224	−	19.0913i	0.591711	−	1.02487i	−0.402291	−	0.915512i	$-0.631786\pi$
$347$	11.0224	−	19.0913i	0.591711	−	1.02487i	0.994002	−	0.109362i	$-0.0348808\pi$
$348$	3.15544	+	3.50447i	0.169149	+	0.187859i
$349$	−5.14640	−	15.8390i	−0.275480	−	0.847842i	−0.989092	−	0.147300i	$-0.952942\pi$
$349$	−5.14640	−	15.8390i	−0.275480	−	0.847842i	0.713611	−	0.700542i	$-0.247058\pi$
$350$	−3.41072	+	3.78799i	−0.182311	+	0.202477i
$351$	9.14300	+	4.07073i	0.488017	+	0.217279i
$352$	−2.53772	+	0.539410i	−0.135261	+	0.0287507i
$353$	0.910253	+	8.66048i	0.0484479	+	0.460951i	0.991672	+	0.128793i	$0.0411102\pi$
$353$	0.910253	+	8.66048i	0.0484479	+	0.460951i	−0.943224	+	0.332158i	$0.892223\pi$
$354$	4.70137	−	44.7305i	0.249875	−	2.37740i
$355$	9.32010	+	1.98105i	0.494659	+	0.105143i
$356$	1.82819	+	1.32826i	0.0968941	+	0.0703977i
$357$	21.6730	+	15.7463i	1.14706	+	0.833385i
$358$	−20.4892	−	4.35511i	−1.08289	−	0.230175i
$359$	1.51620	−	14.4256i	0.0800218	−	0.761357i	−0.878770	−	0.477246i	$-0.841635\pi$
$359$	1.51620	−	14.4256i	0.0800218	−	0.761357i	0.958792	−	0.284111i	$-0.0916983\pi$
$360$	1.53278	+	14.5835i	0.0807848	+	0.768616i
$361$	−2.29072	+	0.486908i	−0.120564	+	0.0256267i
$362$	28.6596	+	12.7601i	1.50632	+	0.670656i
$363$	7.55355	−	8.38907i	0.396459	−	0.440312i
$364$	−0.259680	−	0.799213i	−0.0136109	−	0.0418901i
$365$	1.02467	+	1.13802i	0.0536339	+	0.0595665i
$366$	3.01495	−	5.22205i	0.157594	−	0.272961i
$367$	−7.19340	−	12.4593i	−0.375493	−	0.650372i	0.614908	−	0.788599i	$-0.289193\pi$
$367$	−7.19340	−	12.4593i	−0.375493	−	0.650372i	−0.990401	+	0.138227i	$0.955860\pi$
$368$	−10.6130	+	32.6634i	−0.553239	+	1.70270i
$369$	−1.01555	+	0.452150i	−0.0528672	+	0.0235380i
$370$	11.3772	−	8.26602i	0.591472	−	0.429730i
$371$	−13.4365			−0.697590
$372$	2.73729	+	0.536264i	0.141922	+	0.0278040i
$373$	−18.6605			−0.966203			−0.483102	−	0.875564i	$-0.660490\pi$
$373$	−18.6605			−0.966203			−0.483102	+	0.875564i	$0.660490\pi$
$374$	8.47909	−	6.16042i	0.438443	−	0.318548i
$375$	2.65459	−	1.18190i	0.137082	−	0.0610330i
$376$	−4.65988	+	14.3416i	−0.240315	+	0.739614i
$377$	−6.63345	−	11.4895i	−0.341640	−	0.591738i
$378$	−18.0978	+	31.3463i	−0.930849	+	1.61228i
$379$	8.57853	+	9.52743i	0.440650	+	0.489391i	0.922029	−	0.387121i	$-0.126531\pi$
$379$	8.57853	+	9.52743i	0.440650	+	0.489391i	−0.481379	+	0.876513i	$0.659864\pi$
$380$	−0.246122	−	0.757485i	−0.0126258	−	0.0388582i
$381$	12.7337	−	14.1422i	0.652369	−	0.724529i
$382$	−18.5191	−	8.24521i	−0.947517	−	0.421862i
$383$	−27.3143	+	5.80583i	−1.39570	+	0.296664i	−0.843535	−	0.537074i	$-0.819530\pi$
$383$	−27.3143	+	5.80583i	−1.39570	+	0.296664i	−0.552160	+	0.833738i	$0.686196\pi$
$384$	−3.81266	−	36.2751i	−0.194564	−	1.85115i
$385$	0.964255	−	9.17428i	0.0491430	−	0.467564i
$386$	−29.4168	−	6.25274i	−1.49728	−	0.318256i
$387$	14.1843	+	10.3055i	0.721026	+	0.523856i
$388$	−2.07550	−	1.50794i	−0.105367	−	0.0765540i
$389$	−3.79125	−	0.805855i	−0.192224	−	0.0408585i	0.110794	−	0.993843i	$-0.464661\pi$
$389$	−3.79125	−	0.805855i	−0.192224	−	0.0408585i	−0.303018	+	0.952985i	$0.597994\pi$
$390$	−0.630974	+	6.00332i	−0.0319506	+	0.303990i
$391$	−2.21783	−	21.1012i	−0.112160	−	1.06714i
$392$	−13.0688	+	2.77785i	−0.660072	+	0.140303i
$393$	3.44075	+	1.53192i	0.173563	+	0.0772751i
$394$	−15.1359	+	16.8101i	−0.762536	+	0.846882i
$395$	3.05651	+	9.40697i	0.153790	+	0.473316i
$396$	1.67514	+	1.86043i	0.0841789	+	0.0934901i
$397$	−13.7741	+	23.8574i	−0.691300	+	1.19737i	0.280112	+	0.959967i	$0.409628\pi$
$397$	−13.7741	+	23.8574i	−0.691300	+	1.19737i	−0.971412	+	0.237399i	$0.923705\pi$
$398$	10.9579	+	18.9797i	0.549270	+	0.951364i
$399$	−14.3460	+	44.1525i	−0.718199	+	2.21039i
$400$	−3.94203	+	1.75510i	−0.197101	+	0.0877552i
$401$	9.00271	−	6.54085i	0.449574	−	0.326635i	−0.339854	−	0.940478i	$-0.610378\pi$
$401$	9.00271	−	6.54085i	0.449574	−	0.326635i	0.789427	+	0.613844i	$0.210378\pi$
$402$	20.0910			1.00205
$403$	−7.21895	−	3.07683i	−0.359602	−	0.153268i
$404$	−1.55191			−0.0772105
$405$	3.48117	−	2.52922i	0.172981	−	0.125678i
$406$	43.8325	−	19.5155i	2.17537	−	0.968537i
$407$	−7.86470	+	24.2050i	−0.389839	+	1.19980i
$408$	10.4332	+	18.0708i	0.516519	+	0.894636i
$409$	1.26897	−	2.19793i	0.0627468	−	0.108681i	−0.832946	−	0.553355i	$-0.813347\pi$
$409$	1.26897	−	2.19793i	0.0627468	−	0.108681i	0.895692	+	0.444674i	$0.146681\pi$
$410$	−0.201398	−	0.223675i	−0.00994633	−	0.0110465i
$411$	−0.918232	−	2.82603i	−0.0452930	−	0.139398i
$412$	0.247158	−	0.274497i	0.0121766	−	0.0135235i
$413$	−33.1778	−	14.7717i	−1.63257	−	0.726868i
$414$	62.4649	−	13.2773i	3.06998	−	0.652545i
$415$	−0.730447	−	6.94974i	−0.0358562	−	0.341149i
$416$	0.143292	−	1.36333i	0.00702547	−	0.0668429i
$417$	19.7831	+	4.20502i	0.968782	+	0.205921i
$418$	14.6939	+	10.6757i	0.718702	+	0.522167i
$419$	−14.6114	−	10.6158i	−0.713812	−	0.518615i	0.170589	−	0.985342i	$-0.445433\pi$
$419$	−14.6114	−	10.6158i	−0.713812	−	0.518615i	−0.884401	+	0.466727i	$0.845433\pi$
$420$	−1.69468	−	0.360216i	−0.0826920	−	0.0175767i
$421$	0.184868	−	1.75890i	0.00900991	−	0.0857236i	−0.989093	−	0.147293i	$-0.952944\pi$
$421$	0.184868	−	1.75890i	0.00900991	−	0.0857236i	0.998103	+	0.0615695i	$0.0196106\pi$
$422$	1.36627	+	12.9992i	0.0665092	+	0.632793i
$423$	29.8087	−	6.33603i	1.44935	−	0.308068i
$424$	−9.56098	−	4.25682i	−0.464322	−	0.206730i
$425$	1.78377	−	1.98108i	0.0865257	−	0.0960965i
$426$	12.6106	+	38.8114i	0.610986	+	1.88042i
$427$	−3.25799	−	3.61836i	−0.157665	−	0.175105i
$428$	−0.536321	+	0.928935i	−0.0259240	+	0.0449018i
$429$	−5.46221	−	9.46083i	−0.263718	−	0.456773i
$430$	−1.46692	+	4.51471i	−0.0707410	+	0.217719i
$431$	0.267400	−	0.119054i	0.0128802	−	0.00573463i	−0.400286	−	0.916390i	$-0.631089\pi$
$431$	0.267400	−	0.119054i	0.0128802	−	0.00573463i	0.413167	+	0.910655i	$0.364423\pi$
$432$	−24.7894	+	18.0106i	−1.19268	+	0.866534i
$433$	4.00282			0.192363			0.0961816	−	0.995364i	$-0.469337\pi$
$433$	4.00282			0.192363			0.0961816	+	0.995364i	$0.469337\pi$
$434$	13.7956	−	24.8016i	0.662210	−	1.19052i
$435$	−27.3525			−1.31145
$436$	2.03506	−	1.47856i	0.0974619	−	0.0708102i
$437$	33.5901	−	14.9553i	1.60683	−	0.715408i
$438$	−2.02673	+	6.23762i	−0.0968407	+	0.298045i
$439$	2.03306	+	3.52136i	0.0970325	+	0.168065i	0.910455	−	0.413608i	$-0.135732\pi$
$439$	2.03306	+	3.52136i	0.0970325	+	0.168065i	−0.813423	+	0.581673i	$0.802398\pi$
$440$	3.59263	−	6.22262i	0.171272	−	0.296652i
$441$	18.0670	+	20.0655i	0.860335	+	0.955499i
$442$	1.71128	+	5.26678i	0.0813973	+	0.250515i
$443$	6.08691	−	6.76020i	0.289198	−	0.321187i	−0.580986	−	0.813913i	$-0.697333\pi$
$443$	6.08691	−	6.76020i	0.289198	−	0.321187i	0.870184	+	0.492726i	$0.164000\pi$
$444$	4.36673	+	1.94419i	0.207236	+	0.0922673i
$445$	−12.8209	+	2.72516i	−0.607768	+	0.129185i
$446$	−3.33950	−	31.7733i	−0.158130	−	1.50451i
$447$	−6.31427	+	60.0763i	−0.298655	+	2.84151i
$448$	−24.3443	−	5.17454i	−1.15016	−	0.244474i
$449$	4.30026	+	3.12433i	0.202942	+	0.147446i	0.684615	−	0.728905i	$-0.259971\pi$
$449$	4.30026	+	3.12433i	0.202942	+	0.147446i	−0.481673	+	0.876351i	$0.659971\pi$
$450$	6.49119	+	4.71612i	0.305998	+	0.222320i
$451$	0.532807	+	0.113252i	0.0250889	+	0.00533281i
$452$	−0.204004	+	1.94097i	−0.00959553	+	0.0912953i
$453$	0.0444435	+	0.422852i	0.00208814	+	0.0198673i
$454$	−4.60437	+	0.978690i	−0.216094	+	0.0459322i
$455$	4.45282	+	1.98252i	0.208751	+	0.0929421i
$456$	−24.1961	+	26.8725i	−1.13308	+	1.25842i
$457$	−1.92806	−	5.93396i	−0.0901909	−	0.277579i	0.895780	−	0.444498i	$-0.146618\pi$
$457$	−1.92806	−	5.93396i	−0.0901909	−	0.277579i	−0.985971	+	0.166919i	$0.946618\pi$
$458$	8.51883	+	9.46112i	0.398059	+	0.442089i
$459$	9.46494	−	16.3938i	0.441786	−	0.765195i
$460$	0.686098	+	1.18836i	0.0319895	+	0.0554074i
$461$	8.34338	−	25.6783i	0.388590	−	1.19596i	−0.545252	−	0.838272i	$-0.683566\pi$
$461$	8.34338	−	25.6783i	0.388590	−	1.19596i	0.933842	−	0.357685i	$-0.116434\pi$
$462$	36.0932	−	16.0697i	1.67921	−	0.747631i
$463$	11.9020	−	8.64731i	0.553133	−	0.401875i	−0.275806	−	0.961213i	$-0.588945\pi$
$463$	11.9020	−	8.64731i	0.553133	−	0.401875i	0.828939	+	0.559339i	$0.188945\pi$
$464$	40.6181			1.88565
$465$	−12.9353	+	9.71763i	−0.599862	+	0.450644i
$466$	−10.9643			−0.507910
$467$	−22.9234	+	16.6548i	−1.06077	+	0.770694i	−0.974230	−	0.225555i	$-0.927581\pi$
$467$	−22.9234	+	16.6548i	−1.06077	+	0.770694i	−0.0865383	+	0.996249i	$0.527581\pi$
$468$	−1.20842	+	0.538022i	−0.0558591	+	0.0248701i
$469$	5.01315	−	15.4289i	0.231486	−	0.712440i
$470$	4.12556	+	7.14568i	0.190298	+	0.329605i
$471$	0.603222	−	1.04481i	0.0277950	−	0.0481424i
$472$	−18.9284	−	21.0221i	−0.871249	−	0.967620i
$473$	−2.65477	−	8.17055i	−0.122067	−	0.375682i
$474$	−28.3460	+	31.4814i	−1.30198	+	1.44599i
$475$	4.22033	+	1.87901i	0.193642	+	0.0862150i
$476$	−1.55471	+	0.330464i	−0.0712601	+	0.0151468i
$477$	2.21082	+	21.0345i	0.101226	+	0.963104i
$478$	−3.77616	+	35.9277i	−0.172717	+	1.64330i
$479$	5.96591	+	1.26809i	0.272589	+	0.0579407i	0.342178	−	0.939635i	$-0.388835\pi$
$479$	5.96591	+	1.26809i	0.272589	+	0.0579407i	−0.0695887	+	0.997576i	$0.522169\pi$
$480$	−2.28651	−	1.66124i	−0.104364	−	0.0758251i
$481$	−10.8794	−	7.90434i	−0.496057	−	0.360407i
$482$	−10.8665	−	2.30974i	−0.494953	−	0.105206i
$483$	8.36049	−	79.5447i	0.380415	−	3.61941i
$484$	0.0700099	+	0.666099i	0.00318227	+	0.0302772i
$485$	14.5552	−	3.09380i	0.660917	−	0.140482i
$486$	−11.8482	−	5.27517i	−0.537447	−	0.239287i
$487$	−14.4759	+	16.0771i	−0.655966	+	0.728524i	−0.975731	−	0.218973i	$-0.929729\pi$
$487$	−14.4759	+	16.0771i	−0.655966	+	0.728524i	0.319765	+	0.947497i	$0.396396\pi$
$488$	−1.17194	−	3.60686i	−0.0530513	−	0.163275i
$489$	20.4947	+	22.7616i	0.926800	+	1.02932i
$490$	−3.65528	+	6.33113i	−0.165129	+	0.286011i
$491$	0.338579	+	0.586436i	0.0152798	+	0.0264655i	0.873564	−	0.486709i	$-0.161803\pi$
$491$	0.338579	+	0.586436i	0.0152798	+	0.0264655i	−0.858284	+	0.513174i	$0.828469\pi$
$492$	0.0316136	−	0.0972967i	0.00142525	−	0.00438647i
$493$	−22.9239	+	10.2064i	−1.03244	+	0.459673i
$494$	−7.76397	+	5.64086i	−0.349318	+	0.253794i
$495$	−14.5207			−0.652658
$496$	19.2088	−	14.4305i	0.862501	−	0.647951i
$497$	32.9520			1.47810
$498$	24.2130	−	17.5918i	1.08501	−	0.788308i
$499$	28.0667	−	12.4961i	1.25644	−	0.559402i	0.332919	−	0.942955i	$-0.391966\pi$
$499$	28.0667	−	12.4961i	1.25644	−	0.559402i	0.923519	+	0.383553i	$0.125300\pi$
$500$	−0.0532763	+	0.163968i	−0.00238259	+	0.00733285i
$501$	21.3539	+	36.9861i	0.954024	+	1.65242i
$502$	7.16532	−	12.4107i	0.319804	−	0.553916i
$503$	9.85750	+	10.9479i	0.439524	+	0.488141i	0.921684	−	0.387942i	$-0.126814\pi$
$503$	9.85750	+	10.9479i	0.439524	+	0.488141i	−0.482159	+	0.876083i	$0.660147\pi$
$504$	15.6709	+	48.2301i	0.698037	+	2.14834i
$505$	6.02319	−	6.68943i	0.268029	−	0.297676i
$506$	−28.5863	−	12.7274i	−1.27082	−	0.565804i
$507$	−31.3039	+	6.65385i	−1.39026	+	0.295508i
$508$	0.118022	+	1.12291i	0.00523639	+	0.0498209i
$509$	−2.93549	+	27.9294i	−0.130114	+	1.23795i	0.713368	+	0.700789i	$0.247169\pi$
$509$	−2.93549	+	27.9294i	−0.130114	+	1.23795i	−0.843482	+	0.537158i	$0.819498\pi$
$510$	11.1679	+	2.37381i	0.494522	+	0.105114i
$511$	4.28448	+	3.11286i	0.189534	+	0.137705i
$512$	−15.4119	−	11.1974i	−0.681117	−	0.494860i
$513$	32.0878	+	6.82048i	1.41671	+	0.301131i
$514$	−0.398689	+	3.79327i	−0.0175854	+	0.167314i
$515$	0.223948	+	2.13072i	0.00986834	+	0.0938909i
$516$	−1.57825	+	0.335467i	−0.0694786	+	0.0147681i
$517$	−13.6416	−	6.07362i	−0.599956	−	0.267118i
$518$	32.5427	−	36.1424i	1.42985	−	1.58800i
$519$	−15.7143	−	48.3636i	−0.689781	−	2.12293i
$520$	2.54039	+	2.82139i	0.111404	+	0.123726i
$521$	−0.658209	+	1.14005i	−0.0288366	+	0.0499465i	−0.880084	−	0.474819i	$-0.842514\pi$
$521$	−0.658209	+	1.14005i	−0.0288366	+	0.0499465i	0.851247	+	0.524765i	$0.175847\pi$
$522$	−37.7630	−	65.4075i	−1.65284	−	2.86281i
$523$	−6.38431	+	19.6489i	−0.279167	+	0.859186i	0.708920	+	0.705289i	$0.249183\pi$
$523$	−6.38431	+	19.6489i	−0.279167	+	0.859186i	−0.988087	+	0.153898i	$0.950817\pi$
$524$	−0.204144	+	0.0908909i	−0.00891809	+	0.00397059i
$525$	8.12999	−	5.90678i	0.354822	−	0.257793i
$526$	20.1945			0.880522
$527$	−7.21495	+	12.9710i	−0.314288	+	0.565026i
$528$	33.4464			1.45557
$529$	−32.6418	+	23.7157i	−1.41921	+	1.03112i
$530$	−5.23146	+	2.32919i	−0.227240	+	0.101174i
$531$	−17.6657	+	54.3694i	−0.766625	+	2.35943i
$532$	−1.37722	−	2.38541i	−0.0597100	−	0.103421i
$533$	−0.143907	+	0.249255i	−0.00623331	+	0.0107964i
$534$	−37.5631	−	41.7181i	−1.62552	−	1.80532i
$535$	−1.92259	−	5.91711i	−0.0831206	−	0.255819i
$536$	8.45521	−	9.39046i	0.365210	−	0.405606i
$537$	37.7265	+	16.7969i	1.62802	+	0.724841i
$538$	29.3252	−	6.23326i	1.26430	−	0.268735i
$539$	−1.38295	−	13.1579i	−0.0595679	−	0.566751i
$540$	−0.127969	+	1.21755i	−0.00550692	+	0.0523948i
$541$	−44.1743	−	9.38953i	−1.89920	−	0.403688i	−0.899737	−	0.436432i	$-0.856242\pi$
$541$	−44.1743	−	9.38953i	−1.89920	−	0.403688i	−0.999464	+	0.0327444i	$0.989575\pi$
$542$	−33.1396	−	24.0773i	−1.42347	−	1.03421i
$543$	−50.0374	−	36.3543i	−2.14731	−	1.56011i
$544$	−2.53619	−	0.539083i	−0.108738	−	0.0231130i
$545$	−1.52512	+	14.5105i	−0.0653289	+	0.621563i
$546$	2.18211	+	20.7614i	0.0933857	+	0.888506i
$547$	38.9863	−	8.28680i	1.66694	−	0.354318i	0.724647	−	0.689120i	$-0.242003\pi$
$547$	38.9863	−	8.28680i	1.66694	−	0.354318i	0.942288	+	0.334802i	$0.108670\pi$
$548$	0.161059	+	0.0717080i	0.00688009	+	0.00306322i
$549$	−5.12838	+	5.69564i	−0.218874	+	0.243084i
$550$	−1.21491	−	3.73912i	−0.0518041	−	0.159436i
$551$	−29.0976	−	32.3162i	−1.23960	−	1.37672i
$552$	31.1496	−	53.9526i	1.32581	−	2.29638i
$553$	17.1033	+	29.6237i	0.727304	+	1.25973i
$554$	−2.32369	+	7.15159i	−0.0987242	+	0.303842i
$555$	−25.3282	+	11.2768i	−1.07512	+	0.478675i
$556$	−0.970804	+	0.705331i	−0.0411713	+	0.0299127i
$557$	−19.9182			−0.843963			−0.421982	−	0.906604i	$-0.638665\pi$
$557$	−19.9182			−0.843963			−0.421982	+	0.906604i	$0.638665\pi$
$558$	−41.0962	−	17.5158i	−1.73974	−	0.741504i
$559$	4.53934			0.191993
$560$	−12.0729	+	8.77149i	−0.510174	+	0.370663i
$561$	−18.8764	+	8.40430i	−0.796961	+	0.354830i
$562$	2.23481	−	6.87803i	0.0942697	−	0.290132i
$563$	−16.2792	−	28.1963i	−0.686085	−	1.18833i	−0.973095	−	0.230406i	$-0.925994\pi$
$563$	−16.2792	−	28.1963i	−0.686085	−	1.18833i	0.287010	−	0.957928i	$-0.407339\pi$
$564$	−1.40227	+	2.42880i	−0.0590461	+	0.102271i
$565$	−7.57465	−	8.41251i	−0.318668	−	0.353917i
$566$	7.01449	+	21.5884i	0.294841	+	0.907427i
$567$	9.95735	−	11.0588i	0.418170	−	0.464424i
$568$	23.4475	+	10.4395i	0.983835	+	0.438032i
$569$	−3.17999	+	0.675928i	−0.133312	+	0.0283364i	−0.274084	−	0.961706i	$-0.588375\pi$
$569$	−3.17999	+	0.675928i	−0.133312	+	0.0283364i	0.140772	+	0.990042i	$0.455041\pi$
$570$	2.06818	+	19.6774i	0.0866266	+	0.824197i
$571$	−0.840471	+	7.99655i	−0.0351726	+	0.334645i	0.962759	+	0.270361i	$0.0871431\pi$
$571$	−0.840471	+	7.99655i	−0.0351726	+	0.334645i	−0.997932	+	0.0642841i	$0.979524\pi$
$572$	0.633998	+	0.134760i	0.0265088	+	0.00563461i
$573$	32.3328	+	23.4911i	1.35072	+	0.981356i
$574$	−0.842106	−	0.611826i	−0.0351488	−	0.0255371i
$575$	−7.78519	−	1.65479i	−0.324665	−	0.0690096i
$576$	−4.09504	+	38.9617i	−0.170627	+	1.62341i
$577$	2.69618	+	25.6525i	0.112244	+	1.06793i	0.895143	+	0.445779i	$0.147073\pi$
$577$	2.69618	+	25.6525i	0.112244	+	1.06793i	−0.782900	+	0.622148i	$0.786260\pi$
$578$	−14.2634	+	3.03178i	−0.593280	+	0.126106i
$579$	54.1649	+	24.1158i	2.25102	+	1.00222i
$580$	1.08591	−	1.20602i	0.0450898	−	0.0500773i
$581$	−7.46796	−	22.9840i	−0.309823	−	0.953537i
$582$	42.6444	+	47.3614i	1.76767	+	1.96319i
$583$	5.18184	−	8.97522i	0.214610	−	0.371715i
$584$	2.06251	+	3.57237i	0.0853472	+	0.147826i
$585$	2.37093	−	7.29696i	0.0980257	−	0.301692i
$586$	20.0011	−	8.90506i	0.826237	−	0.367864i
$587$	−1.55298	+	1.12831i	−0.0640983	+	0.0465701i	−0.619373	−	0.785097i	$-0.712613\pi$
$587$	−1.55298	+	1.12831i	−0.0640983	+	0.0465701i	0.555275	+	0.831667i	$0.312613\pi$
$588$	−2.48484			−0.102473
$589$	−25.2417	−	4.94511i	−1.04007	−	0.203760i
$590$	−15.4783			−0.637230
$591$	36.0788	−	26.2128i	1.48408	−	1.07825i
$592$	37.6121	−	16.7460i	1.54585	−	0.688255i
$593$	−3.79186	+	11.6701i	−0.155713	+	0.479235i	−0.998232	−	0.0594306i	$-0.981071\pi$
$593$	−3.79186	+	11.6701i	−0.155713	+	0.479235i	0.842519	+	0.538666i	$0.181071\pi$
$594$	−13.9589	−	24.1776i	−0.572742	−	0.992018i
$595$	4.60961	−	7.98408i	0.188976	−	0.327315i
$596$	−2.39819	−	2.66346i	−0.0982338	−	0.109100i
$597$	−13.3517	−	41.0923i	−0.546449	−	1.68180i
$598$	11.0633	−	12.2871i	0.452413	−	0.502456i
$599$	−1.61046	−	0.717023i	−0.0658016	−	0.0292968i	0.373572	−	0.927601i	$-0.378133\pi$
$599$	−1.61046	−	0.717023i	−0.0658016	−	0.0292968i	−0.439374	+	0.898304i	$0.644800\pi$
$600$	7.65635	−	1.62741i	0.312569	−	0.0664386i
$601$	0.814152	+	7.74614i	0.0332099	+	0.315971i	0.998498	+	0.0547846i	$0.0174472\pi$
$601$	0.814152	+	7.74614i	0.0332099	+	0.315971i	−0.965288	+	0.261187i	$0.915886\pi$
$602$	−1.71602	+	16.3269i	−0.0699399	+	0.665434i
$603$	−24.9784	−	5.30931i	−1.01720	−	0.216212i
$604$	−0.0204087	−	0.0148278i	−0.000830419	−	0.000603335i
$605$	−3.14290	−	2.28345i	−0.127777	−	0.0928355i
$606$	37.7101	+	8.01553i	1.53187	+	0.325609i
$607$	−0.179668	+	1.70943i	−0.00729252	+	0.0693837i	−0.997563	−	0.0697730i	$-0.977772\pi$
$607$	−0.179668	+	1.70943i	−0.00729252	+	0.0693837i	0.990270	+	0.139157i	$0.0444392\pi$
$608$	−0.469677	−	4.46867i	−0.0190479	−	0.181229i
$609$	−92.5266	+	19.6671i	−3.74937	+	0.796953i
$610$	−1.89572	−	0.844028i	−0.0767554	−	0.0341737i
$611$	5.27950	−	5.86348i	0.213586	−	0.237211i
$612$	0.773141	+	2.37948i	0.0312524	+	0.0961849i
$613$	14.2554	+	15.8323i	0.575772	+	0.639459i	0.958734	−	0.284305i	$-0.0917628\pi$
$613$	14.2554	+	15.8323i	0.575772	+	0.639459i	−0.382962	+	0.923764i	$0.625096\pi$
$614$	−16.5944	+	28.7424i	−0.669696	+	1.15995i
$615$	0.296695	+	0.513891i	0.0119639	+	0.0207221i
$616$	7.67874	−	23.6327i	0.309385	−	0.952190i
$617$	13.0889	−	5.82757i	0.526941	−	0.234609i	−0.125984	−	0.992032i	$-0.540209\pi$
$617$	13.0889	−	5.82757i	0.526941	−	0.234609i	0.652924	+	0.757423i	$0.273542\pi$
$618$	−7.42349	+	5.39348i	−0.298617	+	0.216958i
$619$	−9.19099			−0.369417			−0.184709	−	0.982793i	$-0.559134\pi$
$619$	−9.19099			−0.369417			−0.184709	+	0.982793i	$0.559134\pi$
$620$	0.0850713	−	0.956137i	0.00341655	−	0.0383994i
$621$	−56.5177			−2.26798
$622$	11.3940	−	8.27822i	0.456857	−	0.331926i
$623$	−41.4103	+	18.4371i	−1.65907	+	0.738666i
$624$	−5.46108	+	16.8075i	−0.218618	+	0.672837i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.1172	−	17.5236i	0.404367	−	0.700384i
$627$	−23.9600	−	26.6103i	−0.956870	−	1.06271i
$628$	0.0221194	+	0.0680766i	0.000882661	+	0.00271655i
$629$	−17.0195	+	18.9021i	−0.678612	+	0.753675i
$630$	25.3491	+	11.2861i	1.00993	+	0.449650i
$631$	16.6459	−	3.53821i	0.662665	−	0.140854i	0.135712	−	0.990748i	$-0.456668\pi$
$631$	16.6459	−	3.53821i	0.662665	−	0.140854i	0.526953	+	0.849895i	$0.323334\pi$
$632$	2.78502	+	26.4977i	0.110782	+	1.05402i
$633$	2.69361	−	25.6280i	0.107061	−	1.01862i
$634$	43.0883	+	9.15869i	1.71125	+	0.363738i
$635$	−5.29829	−	3.84943i	−0.210256	−	0.152760i
$636$	−1.57470	−	1.14409i	−0.0624410	−	0.0453660i
$637$	6.83792	+	1.45344i	0.270928	+	0.0575875i
$638$	−3.86837	+	36.8050i	−0.153150	+	1.45713i
$639$	−5.42184	−	51.5854i	−0.214485	−	2.04069i
$640$	−12.2781	+	2.60979i	−0.485335	+	0.103161i
$641$	3.54414	+	1.57795i	0.139985	+	0.0623254i	0.475534	−	0.879698i	$-0.342255\pi$
$641$	3.54414	+	1.57795i	0.139985	+	0.0623254i	−0.335549	+	0.942023i	$0.608922\pi$
$642$	17.8300	−	19.8022i	0.703694	−	0.781532i
$643$	6.83125	+	21.0244i	0.269398	+	0.829123i	0.990647	+	0.136447i	$0.0435683\pi$
$643$	6.83125	+	21.0244i	0.269398	+	0.829123i	−0.721249	+	0.692676i	$0.756432\pi$
$644$	3.17536	+	3.52659i	0.125127	+	0.138967i
$645$	4.67940	−	8.10495i	0.184251	−	0.319132i
$646$	9.07582	+	15.7198i	0.357083	+	0.618486i
$647$	11.7127	−	36.0479i	0.460472	−	1.41719i	−0.404117	−	0.914707i	$-0.632421\pi$
$647$	11.7127	−	36.0479i	0.460472	−	1.41719i	0.864589	−	0.502480i	$-0.167579\pi$
$648$	10.5888	−	4.71445i	0.415969	−	0.185201i
$649$	22.6622	−	16.4650i	0.889569	−	0.646310i
$650$	2.07735			0.0814804
$651$	−36.7698	+	42.1731i	−1.44112	+	1.65289i
$652$	−1.81725			−0.0711689
$653$	−5.18775	+	3.76912i	−0.203012	+	0.147497i	−0.684647	−	0.728875i	$-0.740043\pi$
$653$	−5.18775	+	3.76912i	−0.203012	+	0.147497i	0.481634	+	0.876372i	$0.340043\pi$
$654$	−57.0869	+	25.4167i	−2.23228	+	0.993873i
$655$	0.400533	−	1.23271i	0.0156501	−	0.0481661i
$656$	−0.440588	−	0.763121i	−0.0172021	−	0.0297949i
$657$	4.16813	−	7.21941i	0.162614	−	0.281656i
$658$	19.0936	+	21.2056i	0.744348	+	0.826682i
$659$	3.69830	+	11.3822i	0.144065	+	0.443387i	0.996890	−	0.0788106i	$-0.0251122\pi$
$659$	3.69830	+	11.3822i	0.144065	+	0.443387i	−0.852824	+	0.522198i	$0.825112\pi$
$660$	0.894173	−	0.993080i	0.0348056	−	0.0386556i
$661$	9.01893	+	4.01548i	0.350796	+	0.156184i	0.574567	−	0.818457i	$-0.305170\pi$
$661$	9.01893	+	4.01548i	0.350796	+	0.156184i	−0.223772	+	0.974642i	$0.571837\pi$
$662$	−19.7481	+	4.19759i	−0.767531	+	0.163144i
$663$	−1.14122	−	10.8580i	−0.0443214	−	0.421690i
$664$	1.96761	−	18.7206i	0.0763581	−	0.726499i
$665$	15.6274	+	3.32170i	0.606004	+	0.128810i
$666$	−61.9343	−	44.9979i	−2.39991	−	1.74363i
$667$	60.6112	+	44.0366i	2.34687	+	1.70510i
$668$	−2.47855	−	0.526831i	−0.0958978	−	0.0203837i
$669$	−6.58383	+	62.6409i	−0.254545	+	2.42184i
$670$	−0.722717	−	6.87619i	−0.0279210	−	0.265651i
$671$	3.67341	−	0.780808i	0.141811	−	0.0301428i
$672$	−8.92915	−	3.97552i	−0.344450	−	0.153359i
$673$	−6.82356	+	7.57833i	−0.263029	+	0.292123i	−0.860164	−	0.510018i	$-0.829639\pi$
$673$	−6.82356	+	7.57833i	−0.263029	+	0.292123i	0.597135	+	0.802141i	$0.296306\pi$
$674$	4.50958	+	13.8791i	0.173703	+	0.534601i
$675$	−4.75149	−	5.27707i	−0.182885	−	0.203114i
$676$	0.949399	−	1.64441i	0.0365153	−	0.0632464i
$677$	−12.4018	−	21.4806i	−0.476641	−	0.825566i	0.523001	−	0.852332i	$-0.324812\pi$
$677$	−12.4018	−	21.4806i	−0.476641	−	0.825566i	−0.999642	+	0.0267663i	$0.991479\pi$
$678$	14.9821	−	46.1101i	0.575383	−	1.77085i
$679$	47.0120	−	20.9311i	1.80415	−	0.803262i
$680$	5.80947	−	4.22083i	0.222783	−	0.161861i
$681$	9.28031			0.355622
$682$	11.2465	+	18.7799i	0.430649	+	0.719119i
$683$	−27.4082			−1.04875			−0.524373	−	0.851489i	$-0.675700\pi$
$683$	−27.4082			−1.04875			−0.524373	+	0.851489i	$0.675700\pi$
$684$	−3.50769	+	2.54849i	−0.134120	+	0.0974439i
$685$	−0.934186	+	0.415926i	−0.0356934	+	0.0158917i
$686$	3.21331	−	9.88955i	0.122685	−	0.377585i
$687$	−12.5498	−	21.7368i	−0.478803	−	0.829312i
$688$	−6.94884	+	12.0357i	−0.264922	+	0.458859i
$689$	3.66414	+	4.06944i	0.139593	+	0.155033i
$690$	−10.5338	−	32.4197i	−0.401015	−	1.23420i
$691$	10.0242	−	11.1330i	0.381339	−	0.423520i	−0.521666	−	0.853150i	$-0.674689\pi$
$691$	10.0242	−	11.1330i	0.381339	−	0.423520i	0.903005	+	0.429630i	$0.141356\pi$
$692$	2.75630	+	1.22719i	0.104779	+	0.0466506i
$693$	−49.1200	+	10.4408i	−1.86591	+	0.396612i
$694$	−3.39633	−	32.3139i	−0.128923	−	1.22662i
$695$	0.727540	−	6.92209i	0.0275972	−	0.262570i
$696$	−72.0696	−	15.3189i	−2.73179	−	0.580660i
$697$	0.440412	+	0.319978i	0.0166818	+	0.0121200i
$698$	−19.8586	−	14.4281i	−0.751660	−	0.546113i
$699$	21.1437	+	4.49423i	0.799727	+	0.169987i
$700$	−0.0623234	+	0.592968i	−0.00235560	+	0.0224121i
$701$	4.23920	+	40.3333i	0.160113	+	1.52337i	0.719517	+	0.694474i	$0.244363\pi$
$701$	4.23920	+	40.3333i	0.160113	+	1.52337i	−0.559405	+	0.828895i	$0.688970\pi$
$702$	14.4289	−	3.06696i	0.544584	−	0.115755i
$703$	−40.2674	−	17.9282i	−1.51872	−	0.676176i
$704$	12.8449	−	14.2657i	0.484111	−	0.537659i
$705$	−5.02680	−	15.4709i	−0.189320	−	0.582668i
$706$	8.58834	+	9.53832i	0.323226	+	0.358979i
$707$	15.5651	−	26.9595i	0.585385	−	1.01392i
$708$	−2.63051	−	4.55618i	−0.0988607	−	0.171232i
$709$	12.6179	−	38.8338i	0.473874	−	1.45844i	−0.373595	−	0.927592i	$-0.621875\pi$
$709$	12.6179	−	38.8338i	0.473874	−	1.45844i	0.847470	−	0.530844i	$-0.178125\pi$
$710$	12.8297	−	5.71215i	0.481490	−	0.214373i
$711$	43.5609	−	31.6489i	1.63366	−	1.18693i
$712$	−35.3072			−1.32319
$713$	44.3088	−	0.708091i	1.65938	−	0.0265182i
$714$	39.4849			1.47769
$715$	−3.04151	+	2.20979i	−0.113746	+	0.0826414i
$716$	−2.23837	+	0.996585i	−0.0836517	+	0.0372441i
$717$	22.0087	−	67.7358i	0.821930	−	2.52964i
$718$	−10.6896	−	18.5149i	−0.398932	−	0.690971i
$719$	−3.15103	+	5.45775i	−0.117514	+	0.203540i	−0.918782	−	0.394766i	$-0.870826\pi$
$719$	−3.15103	+	5.45775i	−0.117514	+	0.203540i	0.801268	+	0.598305i	$0.204159\pi$
$720$	15.7180	+	17.4566i	0.585774	+	0.650568i
$721$	2.28960	+	7.04668i	0.0852693	+	0.262432i
$722$	−2.30967	+	2.56514i	−0.0859569	+	0.0954648i
$723$	20.0083	+	8.90827i	0.744117	+	0.331302i
$724$	3.58943	−	0.762958i	0.133400	−	0.0283551i
$725$	0.983931	+	9.36148i	0.0365423	+	0.347677i
$726$	1.73918	−	16.5472i	0.0645471	−	0.614125i
$727$	31.6478	+	6.72695i	1.17375	+	0.249489i	0.753208	−	0.657783i	$-0.228506\pi$
$727$	31.6478	+	6.72695i	1.17375	+	0.249489i	0.420545	+	0.907272i	$0.361839\pi$
$728$	10.6222	+	7.71745i	0.393683	+	0.286028i
$729$	31.1296	+	22.6170i	1.15295	+	0.837665i
$730$	2.20775	+	0.469272i	0.0817125	+	0.0173685i
$731$	0.897462	−	8.53878i	0.0331938	−	0.315818i
$732$	−0.0737269	−	0.701465i	−0.00272503	−	0.0259269i
$733$	−20.1402	+	4.28094i	−0.743897	+	0.158120i	−0.564242	−	0.825610i	$-0.690831\pi$
$733$	−20.1402	+	4.28094i	−0.743897	+	0.158120i	−0.179655	+	0.983730i	$0.557498\pi$
$734$	−19.3716	−	8.62478i	−0.715018	−	0.318346i
$735$	9.64401	−	10.7108i	0.355725	−	0.395072i
$736$	2.39219	+	7.36239i	0.0881772	+	0.271381i
$737$	8.37272	+	9.29885i	0.308413	+	0.342527i
$738$	−0.819238	+	1.41896i	−0.0301566	+	0.0522327i
$739$	18.6769	+	32.3494i	0.687041	+	1.18999i	0.972791	+	0.231686i	$0.0744243\pi$
$739$	18.6769	+	32.3494i	0.687041	+	1.18999i	−0.285749	+	0.958304i	$0.592242\pi$
$740$	0.508325	−	1.56446i	0.0186864	−	0.0575108i
$741$	17.2844	−	7.69549i	0.634957	−	0.282701i
$742$	−16.0219	+	11.6406i	−0.588184	+	0.427341i
$743$	6.28553			0.230594			0.115297	−	0.993331i	$-0.463218\pi$
$743$	6.28553			0.230594			0.115297	+	0.993331i	$0.463218\pi$
$744$	−39.5250	+	18.3599i	−1.44906	+	0.673108i
$745$	20.7884			0.761629
$746$	−22.2511	+	16.1664i	−0.814670	+	0.591892i
$747$	−34.7521	+	15.4726i	−1.27151	+	0.566113i
$748$	0.378839	−	1.16595i	0.0138517	−	0.0426313i
$749$	−10.7582	−	18.6337i	−0.393095	−	0.680860i
$750$	2.14145	−	3.70910i	0.0781946	−	0.135437i
$751$	2.94353	+	3.26912i	0.107411	+	0.119292i	0.794453	−	0.607326i	$-0.207758\pi$
$751$	2.94353	+	3.26912i	0.107411	+	0.119292i	−0.687042	+	0.726618i	$0.741091\pi$
$752$	7.46473	+	22.9741i	0.272211	+	0.837779i
$753$	−18.9048	+	20.9959i	−0.688930	+	0.765135i
$754$	−17.8637	−	7.95341i	−0.650556	−	0.289646i
$755$	0.143124	−	0.0304219i	0.00520880	−	0.00110716i
$756$	0.442558	+	4.21066i	0.0160957	+	0.153140i
$757$	0.191273	−	1.81984i	0.00695192	−	0.0661431i	−0.990496	−	0.137542i	$-0.956080\pi$
$757$	0.191273	−	1.81984i	0.00695192	−	0.0661431i	0.997448	+	0.0713991i	$0.0227464\pi$
$758$	18.4832	+	3.92872i	0.671340	+	0.142698i
$759$	49.9093	+	36.2613i	1.81159	+	1.31620i
$760$	10.0676	+	7.31451i	0.365189	+	0.265325i
$761$	17.5931	+	3.73953i	0.637750	+	0.135558i	0.515429	−	0.856933i	$-0.327633\pi$
$761$	17.5931	+	3.73953i	0.637750	+	0.135558i	0.122322	+	0.992491i	$0.460966\pi$
$762$	2.93190	−	27.8952i	0.106212	−	1.01054i
$763$	5.27435	+	50.1821i	0.190944	+	1.81671i
$764$	−2.31939	+	0.493002i	−0.0839126	+	0.0178362i
$765$	−13.2573	−	5.90253i	−0.479319	−	0.213406i
$766$	−27.5402	+	30.5865i	−0.995067	+	1.10513i
$767$	4.57376	+	14.0766i	0.165149	+	0.508277i
$768$	−7.98720	−	8.87069i	−0.288213	−	0.320093i
$769$	9.46486	−	16.3936i	0.341311	−	0.591169i	−0.643365	−	0.765560i	$-0.722462\pi$
$769$	9.46486	−	16.3936i	0.341311	−	0.591169i	0.984677	+	0.174391i	$0.0557956\pi$
$770$	−6.79826	−	11.7749i	−0.244992	−	0.424339i
$771$	2.32369	−	7.15159i	0.0836857	−	0.257558i
$772$	−3.21368	+	1.43082i	−0.115663	+	0.0514964i
$773$	16.9967	−	12.3488i	0.611328	−	0.444156i	−0.238554	−	0.971129i	$-0.576673\pi$
$773$	16.9967	−	12.3488i	0.611328	−	0.444156i	0.849882	+	0.526973i	$0.176673\pi$
$774$	25.8416			0.928857
$775$	3.79120	+	4.07760i	0.136184	+	0.146472i
$776$	40.0833			1.43891
$777$	−77.5706	+	56.3583i	−2.78283	+	2.02184i
$778$	−5.21889	+	2.32360i	−0.187106	+	0.0833051i
$779$	−0.291523	+	0.897214i	−0.0104449	+	0.0321460i
$780$	0.353043	+	0.611489i	0.0126410	+	0.0218948i
$781$	−12.7080	+	22.0110i	−0.454729	+	0.787614i
$782$	−20.9255	−	23.2401i	−0.748293	−	0.831063i
$783$	20.6553	+	63.5705i	0.738161	+	2.27183i
$784$	−14.3212	+	15.9053i	−0.511473	+	0.568048i
$785$	−0.379289	−	0.168870i	−0.0135374	−	0.00602724i
$786$	5.42997	−	1.15418i	0.193681	−	0.0411681i
$787$	2.46680	+	23.4700i	0.0879318	+	0.836615i	0.946237	+	0.323475i	$0.104851\pi$
$787$	2.46680	+	23.4700i	0.0879318	+	0.836615i	−0.858305	+	0.513140i	$0.828482\pi$
$788$	−0.276575	+	2.63144i	−0.00985258	+	0.0937410i
$789$	−38.9434	−	8.27768i	−1.38642	−	0.294693i
$790$	11.7943	+	8.56905i	0.419622	+	0.304873i
$791$	−31.6719	−	23.0110i	−1.12612	−	0.818178i
$792$	−38.2598	−	8.13238i	−1.35950	−	0.288972i
$793$	−0.207418	+	1.97345i	−0.00736564	+	0.0700794i
$794$	4.24421	+	40.3810i	0.150621	+	1.43307i
$795$	11.0432	−	2.34730i	0.391661	−	0.0832500i
$796$	2.34190	+	1.04268i	0.0830065	+	0.0369569i
$797$	16.5101	−	18.3363i	0.584818	−	0.649506i	−0.376022	−	0.926611i	$-0.622708\pi$
$797$	16.5101	−	18.3363i	0.584818	−	0.649506i	0.960840	+	0.277105i	$0.0893749\pi$
$798$	21.1447	+	65.0767i	0.748514	+	2.30369i
$799$	−9.98578	−	11.0903i	−0.353271	−	0.392348i
$800$	−0.486315	+	0.842323i	−0.0171938	+	0.0297806i
$801$	35.6763	+	61.7931i	1.26056	+	2.18335i
$802$	5.06837	−	15.5988i	0.178970	−	0.550814i
$803$	−3.73162	+	1.66143i	−0.131686	+	0.0586304i
$804$	1.90125	−	1.38134i	0.0670520	−	0.0487161i
$805$	−27.5252			−0.970135
$806$	−11.2736	+	2.58522i	−0.397095	+	0.0910604i
$807$	−59.1061			−2.08063
$808$	19.6166	−	14.2523i	0.690110	−	0.501394i
$809$	−11.3204	+	5.04018i	−0.398005	+	0.177203i	−0.595972	−	0.803005i	$-0.703233\pi$
$809$	−11.3204	+	5.04018i	−0.398005	+	0.177203i	0.197966	+	0.980209i	$0.436566\pi$
$810$	1.95984	−	6.03177i	0.0688618	−	0.211935i
$811$	27.1897	+	47.0939i	0.954758	+	1.65369i	0.734921	+	0.678153i	$0.237219\pi$
$811$	27.1897	+	47.0939i	0.954758	+	1.65369i	0.219837	+	0.975537i	$0.429447\pi$
$812$	2.80619	−	4.86046i	0.0984779	−	0.170569i
$813$	54.0378	+	60.0150i	1.89519	+	2.10482i
$814$	11.5918	+	35.6760i	0.406294	+	1.25044i
$815$	7.05299	−	7.83314i	0.247056	−	0.274383i
$816$	30.5362	+	13.5956i	1.06898	+	0.475942i
$817$	14.5537	−	3.09349i	0.509170	−	0.108227i
$818$	−0.391010	−	3.72021i	−0.0136713	−	0.130074i
$819$	2.77355	−	26.3885i	0.0969155	−	0.922090i
$820$	−0.0344373	−	0.00731987i	−0.00120260	−	0.000255621i
$821$	−19.9227	−	14.4747i	−0.695306	−	0.505169i	0.183094	−	0.983095i	$-0.441389\pi$
$821$	−19.9227	−	14.4747i	−0.695306	−	0.505169i	−0.878400	+	0.477926i	$0.841389\pi$
$822$	−3.54322	−	2.57430i	−0.123584	−	0.0897890i
$823$	−9.35942	−	1.98941i	−0.326249	−	0.0693463i	0.0418757	−	0.999123i	$-0.486667\pi$
$823$	−9.35942	−	1.98941i	−0.326249	−	0.0693463i	−0.368124	+	0.929777i	$0.620000\pi$
$824$	−0.603251	+	5.73955i	−0.0210152	+	0.199947i
$825$	0.810203	+	7.70857i	0.0282077	+	0.268378i
$826$	−52.3591	+	11.1293i	−1.82181	+	0.387237i
$827$	−36.2730	−	16.1498i	−1.26134	−	0.561583i	−0.336405	−	0.941718i	$-0.609211\pi$
$827$	−36.2730	−	16.1498i	−1.26134	−	0.561583i	−0.924931	+	0.380135i	$0.875878\pi$
$828$	4.99831	−	5.55119i	0.173703	−	0.192917i
$829$	13.6971	+	42.1553i	0.475720	+	1.46411i	0.844985	+	0.534790i	$0.179609\pi$
$829$	13.6971	+	42.1553i	0.475720	+	1.46411i	−0.369265	+	0.929324i	$0.620391\pi$
$830$	−6.89185	−	7.65417i	−0.239219	−	0.265680i
$831$	7.41246	−	12.8388i	0.257136	−	0.445372i
$832$	5.07151	+	8.78411i	0.175823	+	0.304534i
$833$	4.08593	−	12.5752i	0.141569	−	0.435705i
$834$	27.2327	−	12.1248i	0.942990	−	0.419846i
$835$	11.8905	−	8.63892i	0.411486	−	0.298962i
$836$	2.12452			0.0734780
$837$	32.3531	+	22.7250i	1.11829	+	0.785491i
$838$	−26.6197			−0.919564
$839$	40.2618	−	29.2519i	1.38999	−	1.00989i	0.394124	−	0.919057i	$-0.371048\pi$
$839$	40.2618	−	29.2519i	1.38999	−	1.00989i	0.995866	−	0.0908299i	$-0.0289520\pi$
$840$	24.7293	−	11.0102i	0.853244	−	0.379889i
$841$	18.4191	−	56.6881i	0.635141	−	1.95476i
$842$	−1.30337	−	2.25750i	−0.0449171	−	0.0777986i
$843$	−7.12893	+	12.3477i	−0.245533	+	0.425276i
$844$	1.02305	+	1.13621i	0.0352147	+	0.0391099i
$845$	3.40337	+	10.4745i	0.117080	+	0.360334i
$846$	30.0552	−	33.3797i	1.03332	−	1.14762i
$847$	−12.2735	−	5.46452i	−0.421723	−	0.187763i
$848$	−16.3989	+	3.48570i	−0.563142	+	0.119700i
$849$	−4.67783	−	44.5066i	−0.160543	−	1.52746i
$850$	0.410709	−	3.90763i	0.0140872	−	0.134031i
$851$	74.2808	+	15.7889i	2.54631	+	0.541235i
$852$	3.86182	+	2.80578i	0.132304	+	0.0961243i
$853$	19.0016	+	13.8055i	0.650602	+	0.472690i	0.863476	−	0.504390i	$-0.168282\pi$
$853$	19.0016	+	13.8055i	0.650602	+	0.472690i	−0.212874	+	0.977080i	$0.568282\pi$
$854$	−7.01961	−	1.49206i	−0.240206	−	0.0510574i
$855$	2.62874	−	25.0108i	0.0899009	−	0.855350i
$856$	−1.75181	−	16.6674i	−0.0598758	−	0.569680i
$857$	25.4293	−	5.40517i	0.868649	−	0.184637i	0.248033	−	0.968752i	$-0.420216\pi$
$857$	25.4293	−	5.40517i	0.868649	−	0.184637i	0.620616	+	0.784114i	$0.286883\pi$
$858$	−14.7096	−	6.54911i	−0.502176	−	0.223583i
$859$	9.55279	−	10.6095i	0.325937	−	0.361990i	−0.557798	−	0.829976i	$-0.688354\pi$
$859$	9.55279	−	10.6095i	0.325937	−	0.361990i	0.883736	+	0.467987i	$0.155020\pi$
$860$	0.171588	+	0.528093i	0.00585110	+	0.0180078i
$861$	1.37314	+	1.52503i	0.0467967	+	0.0519730i
$862$	0.215711	−	0.373622i	0.00734713	−	0.0127256i
$863$	−19.9369	−	34.5317i	−0.678659	−	1.17547i	−0.975385	−	0.220509i	$-0.929228\pi$
$863$	−19.9369	−	34.5317i	−0.678659	−	1.17547i	0.296726	−	0.954963i	$-0.404105\pi$
$864$	−2.13427	+	6.56861i	−0.0726094	+	0.223469i
$865$	−15.9873	+	7.11801i	−0.543585	+	0.242020i
$866$	4.77303	−	3.46781i	0.162194	−	0.117841i
$867$	28.7485			0.976351
$868$	−0.399712	−	3.29554i	−0.0135671	−	0.111858i
$869$	−26.3837			−0.895006
$870$	−32.6156	+	23.6966i	−1.10577	+	0.803391i
$871$	−6.03994	+	2.68916i	−0.204656	+	0.0911186i
$872$	−12.1451	+	37.3788i	−0.411285	+	1.26581i
$873$	−40.5023	−	70.1520i	−1.37079	−	2.37429i
$874$	27.0970	−	46.9334i	0.916571	−	1.58755i
$875$	−2.31407	−	2.57003i	−0.0782298	−	0.0868830i
$876$	0.237070	+	0.729626i	0.00800984	+	0.0246518i
$877$	9.37786	−	10.4152i	0.316668	−	0.351695i	−0.563706	−	0.825975i	$-0.690625\pi$
$877$	9.37786	−	10.4152i	0.316668	−	0.351695i	0.880374	+	0.474280i	$0.157292\pi$
$878$	5.47495	+	2.43761i	0.184771	+	0.0822652i
$879$	−42.2206	+	8.97426i	−1.42407	+	0.302694i
$880$	−1.20314	−	11.4471i	−0.0405579	−	0.385882i
$881$	−5.27580	+	50.1959i	−0.177746	+	1.69114i	0.434656	+	0.900597i	$0.356870\pi$
$881$	−5.27580	+	50.1959i	−0.177746	+	1.69114i	−0.612402	+	0.790546i	$0.709797\pi$
$882$	38.9270	+	8.27419i	1.31074	+	0.278606i
$883$	−13.0718	−	9.49725i	−0.439903	−	0.319608i	0.345694	−	0.938347i	$-0.387644\pi$
$883$	−13.0718	−	9.49725i	−0.439903	−	0.319608i	−0.785596	+	0.618739i	$0.787644\pi$
$884$	0.524056	+	0.380749i	0.0176259	+	0.0128060i
$885$	29.8486	+	6.34451i	1.00335	+	0.213268i
$886$	1.40149	−	13.3343i	0.0470841	−	0.447975i
$887$	−0.334472	−	3.18229i	−0.0112305	−	0.106851i	0.987471	−	0.157803i	$-0.0504411\pi$
$887$	−0.334472	−	3.18229i	−0.0112305	−	0.106851i	−0.998701	+	0.0509521i	$0.983774\pi$
$888$	−73.0515	+	15.5276i	−2.45145	+	0.521071i
$889$	−20.6906	−	9.21205i	−0.693941	−	0.308962i
$890$	−12.9269	+	14.3568i	−0.433311	+	0.481241i
$891$	3.54685	+	10.9161i	0.118824	+	0.365702i
$892$	−2.50057	−	2.77717i	−0.0837253	−	0.0929864i
$893$	12.9309	−	22.3970i	0.432716	−	0.749486i
$894$	44.5173	+	77.1063i	1.48888	+	2.57882i
$895$	4.39169	−	13.5162i	0.146798	−	0.451798i
$896$	−39.6572	+	17.6565i	−1.32485	+	0.589863i
$897$	−26.3711	+	19.1598i	−0.880507	+	0.639726i
$898$	7.83444			0.261439
$899$	−16.9898	−	49.5794i	−0.566643	−	1.65356i
$900$	0.938529			0.0312843
$901$	8.37931	−	6.08793i	0.279155	−	0.202818i
$902$	0.733443	−	0.326550i	0.0244210	−	0.0108729i
$903$	10.0016	−	30.7816i	0.332831	−	1.02435i
$904$	−15.2466	−	26.4078i	−0.507093	−	0.878312i
$905$	−10.6424	+	18.4332i	−0.353766	+	0.612740i
$906$	0.419329	+	0.465712i	0.0139313	+	0.0154723i
$907$	−10.4771	−	32.2453i	−0.347887	−	1.07069i	−0.960020	−	0.279932i	$-0.909688\pi$
$907$	−10.4771	−	32.2453i	−0.347887	−	1.07069i	0.612132	−	0.790755i	$-0.290312\pi$
$908$	−0.368433	+	0.409186i	−0.0122269	+	0.0135793i
$909$	−44.7654	−	19.9308i	−1.48477	−	0.661064i
$910$	7.02715	−	1.49367i	0.232948	−	0.0495146i
$911$	−1.46263	−	13.9160i	−0.0484592	−	0.461058i	−0.991664	−	0.128848i	$-0.958872\pi$
$911$	−1.46263	−	13.9160i	−0.0484592	−	0.461058i	0.943205	−	0.332211i	$-0.107794\pi$
$912$	−6.05491	+	57.6086i	−0.200498	+	1.90761i
$913$	18.2327	+	3.87548i	0.603414	+	0.128260i
$914$	−7.43989	−	5.40540i	−0.246090	−	0.178795i
$915$	3.30977	+	2.40469i	0.109418	+	0.0794965i
$916$	1.45665	+	0.309620i	0.0481290	+	0.0102301i
$917$	0.468549	−	4.45795i	0.0154729	−	0.147214i
$918$	−2.91644	−	27.7481i	−0.0962569	−	0.915823i
$919$	−38.5472	+	8.19345i	−1.27155	+	0.270277i	−0.793779	−	0.608206i	$-0.791890\pi$
$919$	−38.5472	+	8.19345i	−1.27155	+	0.270277i	−0.477774	+	0.878483i	$0.658556\pi$
$920$	−19.5860	−	8.72024i	−0.645731	−	0.287498i
$921$	43.7824	−	48.6253i	1.44268	−	1.60226i
$922$	−12.2974	−	37.8475i	−0.404993	−	1.24644i
$923$	−8.98600	−	9.97996i	−0.295778	−	0.328494i
$924$	2.31071	−	4.00227i	0.0760169	−	0.131665i
$925$	4.77065	+	8.26300i	0.156858	+	0.271686i
$926$	6.70062	−	20.6224i	0.220196	−	0.677694i
$927$	10.6547	−	4.74376i	0.349945	−	0.155805i
$928$	7.40689	−	5.38142i	0.243143	−	0.176654i
$929$	−12.8728			−0.422342			−0.211171	−	0.977449i	$-0.567728\pi$
$929$	−12.8728			−0.422342			−0.211171	+	0.977449i	$0.567728\pi$
$930$	−7.00554	+	22.7939i	−0.229721	+	0.747441i
$931$	22.9138			0.750968
$932$	−1.03757	+	0.753840i	−0.0339868	+	0.0246929i
$933$	−25.3656	+	11.2935i	−0.830432	+	0.369732i
$934$	−12.9055	+	39.7190i	−0.422280	+	1.29965i
$935$	3.55542	+	6.15817i	0.116275	+	0.201394i
$936$	10.3337	−	17.8985i	0.337768	−	0.585031i
$937$	−19.1562	−	21.2751i	−0.625805	−	0.695026i	0.343983	−	0.938976i	$-0.388224\pi$
$937$	−19.1562	−	21.2751i	−0.625805	−	0.695026i	−0.969788	+	0.243949i	$0.921557\pi$
$938$	−7.38893	−	22.7408i	−0.241257	−	0.742513i
$939$	−26.6932	+	29.6458i	−0.871098	+	0.967453i
$940$	0.881706	+	0.392561i	0.0287581	+	0.0128039i
$941$	19.8694	−	4.22338i	0.647725	−	0.137678i	0.127678	−	0.991816i	$-0.459248\pi$
$941$	19.8694	−	4.22338i	0.647725	−	0.137678i	0.520047	+	0.854137i	$0.325914\pi$
$942$	−0.185871	−	1.76845i	−0.00605601	−	0.0576191i
$943$	0.169892	−	1.61641i	0.00553244	−	0.0526377i
$944$	−44.3247	−	9.42151i	−1.44265	−	0.306644i
$945$	−19.8675	−	14.4345i	−0.646288	−	0.469556i
$946$	−10.2441	−	7.44277i	−0.333064	−	0.241985i
$947$	46.6903	+	9.92432i	1.51723	+	0.322497i	0.889864	−	0.456227i	$-0.150799\pi$
$947$	46.6903	+	9.92432i	1.51723	+	0.322497i	0.627367	+	0.778724i	$0.284133\pi$
$948$	−0.517960	+	4.92806i	−0.0168226	+	0.160056i
$949$	−0.225605	−	2.14649i	−0.00732346	−	0.0696780i
$950$	6.66026	−	1.41568i	0.216087	−	0.0459308i
$951$	−79.3380	−	35.3236i	−2.57271	−	1.14544i
$952$	16.6171	−	18.4552i	0.538563	−	0.598135i
$953$	−3.01620	−	9.28292i	−0.0977044	−	0.300703i	0.890245	−	0.455483i	$-0.150533\pi$
$953$	−3.01620	−	9.28292i	−0.0977044	−	0.300703i	−0.987949	+	0.154779i	$0.950533\pi$
$954$	20.8593	+	23.1666i	0.675344	+	0.750046i
$955$	6.87683	−	11.9110i	0.222529	−	0.385431i
$956$	2.11284	+	3.65955i	0.0683341	+	0.118358i
$957$	22.5461	−	69.3898i	0.728813	−	2.24305i
$958$	8.21246	−	3.65642i	0.265332	−	0.118134i
$959$	−2.86105	+	2.07868i	−0.0923882	+	0.0671240i
$960$	20.9120			0.674931
$961$	−25.6490	−	17.4107i	−0.827386	−	0.561634i
$962$	−19.8206			−0.639042
$963$	−27.4004	+	19.9076i	−0.882966	+	0.641512i
$964$	−1.18712	+	0.528540i	−0.0382346	+	0.0170231i
$965$	6.30526	−	19.4056i	0.202974	−	0.624689i
$966$	−58.9437	−	102.094i	−1.89648	−	3.28481i
$967$	−21.4730	+	37.1923i	−0.690525	+	1.19602i	0.281141	+	0.959666i	$0.409287\pi$
$967$	−21.4730	+	37.1923i	−0.690525	+	1.19602i	−0.971666	+	0.236358i	$0.924046\pi$
$968$	−7.00220	−	7.77673i	−0.225059	−	0.249954i
$969$	−11.0585	−	34.0344i	−0.355249	−	1.09334i
$970$	14.6756	−	16.2989i	0.471204	−	0.523325i
$971$	17.8152	+	7.93183i	0.571717	+	0.254545i	0.672170	−	0.740397i	$-0.265363\pi$
$971$	17.8152	+	7.93183i	0.571717	+	0.254545i	−0.100453	+	0.994942i	$0.532029\pi$
$972$	−1.48391	+	0.315416i	−0.0475966	+	0.0101170i
$973$	−2.51607	−	23.9388i	−0.0806614	−	0.767442i
$974$	−3.33304	+	31.7117i	−0.106797	+	1.01611i
$975$	−4.00600	−	0.851501i	−0.128295	−	0.0272699i
$976$	−4.91496	−	3.57093i	−0.157324	−	0.114303i
$977$	8.91987	+	6.48067i	0.285372	+	0.207335i	0.721257	−	0.692667i	$-0.243565\pi$
$977$	8.91987	+	6.48067i	0.285372	+	0.207335i	−0.435885	+	0.900002i	$0.643565\pi$
$978$	44.1575	+	9.38597i	1.41200	+	0.300130i
$979$	3.65460	−	34.7712i	0.116802	−	1.11129i
$980$	0.0893853	+	0.850444i	0.00285531	+	0.0271664i
$981$	77.6908	−	16.5137i	2.48048	−	0.527241i
$982$	0.911781	+	0.405951i	0.0290961	+	0.0129544i
$983$	−27.6386	+	30.6958i	−0.881535	+	0.979044i	−0.999903	−	0.0139261i	$-0.995567\pi$
$983$	−27.6386	+	30.6958i	−0.881535	+	0.979044i	0.118368	+	0.992970i	$0.462234\pi$
$984$	0.493939	+	1.52019i	0.0157462	+	0.0484618i
$985$	−10.2692	−	11.4051i	−0.327205	−	0.363398i
$986$	−18.4927	+	32.0302i	−0.588926	+	1.02005i
$987$	−28.1284	−	48.7198i	−0.895336	−	1.55077i
$988$	−0.346888	+	1.06761i	−0.0110360	+	0.0339653i
$989$	−23.4179	+	10.4263i	−0.744646	+	0.331538i
$990$	−17.3148	+	12.5799i	−0.550299	+	0.399816i
$991$	−19.5359			−0.620579			−0.310290	−	0.950642i	$-0.600426\pi$
$991$	−19.5359			−0.620579			−0.310290	+	0.950642i	$0.600426\pi$
$992$	1.59093	−	5.17641i	0.0505122	−	0.164351i
$993$	39.8031			1.26311
$994$	39.2925	−	28.5477i	1.24628	−	0.905477i
$995$	−13.5837	+	6.04784i	−0.430632	+	0.191730i
$996$	1.08182	−	3.32950i	0.0342788	−	0.105499i
$997$	−2.63337	−	4.56114i	−0.0833998	−	0.144453i	0.821308	−	0.570484i	$-0.193245\pi$
$997$	−2.63337	−	4.56114i	−0.0833998	−	0.144453i	−0.904708	+	0.426032i	$0.859911\pi$
$998$	22.6413	−	39.2159i	0.716698	−	1.24136i
$999$	45.3354	+	50.3501i	1.43435	+	1.59301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.q.a.111.4	yes	40
5.2	odd	4		775.2.ck.c.49.8		80
5.3	odd	4		775.2.ck.c.49.3		80
5.4	even	2		775.2.bl.c.576.2		40
31.9	even	15		4805.2.a.x.1.6		20
31.19	even	15	inner	155.2.q.a.81.4	✓	40
31.22	odd	30		4805.2.a.y.1.6		20
155.19	even	30		775.2.bl.c.701.2		40
155.112	odd	60		775.2.ck.c.174.3		80
155.143	odd	60		775.2.ck.c.174.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.4	✓	40	31.19	even	15	inner
155.2.q.a.111.4	yes	40	1.1	even	1	trivial
775.2.bl.c.576.2		40	5.4	even	2
775.2.bl.c.701.2		40	155.19	even	30
775.2.ck.c.49.3		80	5.3	odd	4
775.2.ck.c.49.8		80	5.2	odd	4
775.2.ck.c.174.3		80	155.112	odd	60
775.2.ck.c.174.8		80	155.143	odd	60
4805.2.a.x.1.6		20	31.9	even	15
4805.2.a.y.1.6		20	31.22	odd	30

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19242 - 0.866342i) q^{2} +(-2.65459 + 1.18190i) q^{3} +(0.0532763 - 0.163968i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.14145 + 3.70910i) q^{6} +(2.31407 + 2.57003i) q^{7} +(0.832401 + 2.56187i) q^{8} +(3.64256 - 4.04548i) q^{9} +O(q^{10})\)	\(q+(1.19242 - 0.866342i) q^{2} +(-2.65459 + 1.18190i) q^{3} +(0.0532763 - 0.163968i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.14145 + 3.70910i) q^{6} +(2.31407 + 2.57003i) q^{7} +(0.832401 + 2.56187i) q^{8} +(3.64256 - 4.04548i) q^{9} +(1.34648 + 0.599493i) q^{10} +(-2.60914 + 0.554589i) q^{11} +(0.0523664 + 0.498233i) q^{12} +(0.147324 - 1.40170i) q^{13} +(4.98586 + 1.05978i) q^{14} +(-2.35085 - 1.70799i) q^{15} +(3.49098 + 2.53634i) q^{16} +(-2.60755 - 0.554253i) q^{17} +(0.838689 - 7.97960i) q^{18} +(-0.482893 - 4.59442i) q^{19} +(0.168638 - 0.0358451i) q^{20} +(-9.18042 - 4.08739i) q^{21} +(-2.63071 + 2.92170i) q^{22} +(2.45950 + 7.56957i) q^{23} +(-5.23755 - 5.81689i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.03868 - 1.79904i) q^{26} +(-2.19433 + 6.75345i) q^{27} +(0.544687 - 0.242510i) q^{28} +(7.61531 - 5.53285i) q^{29} -4.28290 q^{30} +(1.63570 - 5.32207i) q^{31} +0.972630 q^{32} +(6.27071 - 4.55594i) q^{33} +(-3.58946 + 1.59813i) q^{34} +(-1.06868 + 3.28906i) q^{35} +(-0.469264 - 0.812790i) q^{36} +(4.77065 - 8.26300i) q^{37} +(-4.55615 - 5.06012i) q^{38} +(1.26558 + 3.89505i) q^{39} +(-1.80244 + 2.00181i) q^{40} +(-0.186553 - 0.0830590i) q^{41} +(-14.4880 + 3.07951i) q^{42} +(0.336657 + 3.20308i) q^{43} +(-0.0480705 + 0.457360i) q^{44} +(5.32477 + 1.13181i) q^{45} +(9.49058 + 6.89531i) q^{46} +(4.52897 + 3.29049i) q^{47} +(-12.2648 - 2.60697i) q^{48} +(-0.518459 + 4.93281i) q^{49} +(0.154065 + 1.46583i) q^{50} +(7.57705 - 1.61055i) q^{51} +(-0.221984 - 0.0988335i) q^{52} +(-2.59976 + 2.88732i) q^{53} +(3.23424 + 9.95396i) q^{54} +(-1.78486 - 1.98228i) q^{55} +(-4.65785 + 8.06763i) q^{56} +(6.71202 + 11.6256i) q^{57} +(4.28729 - 13.1949i) q^{58} +(-9.59361 + 4.27135i) q^{59} +(-0.405300 + 0.294467i) q^{60} -1.40790 q^{61} +(-2.66030 - 7.76321i) q^{62} +18.8261 q^{63} +(-5.82218 + 4.23006i) q^{64} +(1.28757 - 0.573261i) q^{65} +(3.53030 - 10.8652i) q^{66} +(-2.34549 - 4.06251i) q^{67} +(-0.229800 + 0.398025i) q^{68} +(-15.4754 - 17.1872i) q^{69} +(1.57514 + 4.84777i) q^{70} +(6.37569 - 7.08092i) q^{71} +(13.3960 + 5.96430i) q^{72} +(1.49789 - 0.318386i) q^{73} +(-1.46998 - 13.9860i) q^{74} +(0.303740 - 2.88989i) q^{75} +(-0.779063 - 0.165595i) q^{76} +(-7.46303 - 5.42221i) q^{77} +(4.88354 + 3.54810i) q^{78} +(9.67493 + 2.05647i) q^{79} +(-0.451049 + 4.29145i) q^{80} +(-0.449782 - 4.27939i) q^{81} +(-0.294407 + 0.0625781i) q^{82} +(-6.38388 - 2.84228i) q^{83} +(-1.15930 + 1.28753i) q^{84} +(-0.823780 - 2.53533i) q^{85} +(3.17639 + 3.52774i) q^{86} +(-13.6763 + 23.6880i) q^{87} +(-3.59263 - 6.22262i) q^{88} +(-4.05038 + 12.4658i) q^{89} +(7.32988 - 3.26347i) q^{90} +(3.94332 - 2.86499i) q^{91} +1.37220 q^{92} +(1.94804 + 16.0612i) q^{93} +8.25112 q^{94} +(3.73744 - 2.71541i) q^{95} +(-2.58193 + 1.14955i) q^{96} +(4.59828 - 14.1521i) q^{97} +(3.65528 + 6.33113i) q^{98} +(-7.26037 + 12.5753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9} - q^{10} - 28 q^{11} - 13 q^{12} - 6 q^{13} - 6 q^{14} - 2 q^{15} + 8 q^{16} - 10 q^{17} - 27 q^{18} - 13 q^{19} - 5 q^{20} - 8 q^{21} + 2 q^{22} - 12 q^{23} - 82 q^{24} - 20 q^{25} + 32 q^{26} - q^{27} + 22 q^{28} + 42 q^{29} + 8 q^{30} - 10 q^{31} + 4 q^{32} + 13 q^{33} + 32 q^{34} + 8 q^{35} - 13 q^{36} + 12 q^{37} + 30 q^{38} + 37 q^{39} + 44 q^{40} + 36 q^{41} - 64 q^{42} - 78 q^{43} - 56 q^{44} - 2 q^{45} + 18 q^{46} - 4 q^{47} - 41 q^{48} - 31 q^{49} + q^{50} - 2 q^{51} + 49 q^{52} - 11 q^{53} + 22 q^{54} - 17 q^{55} + 9 q^{56} + 38 q^{57} + 11 q^{58} - q^{59} - 11 q^{60} - 100 q^{61} - 35 q^{62} + 110 q^{63} + 17 q^{64} + 6 q^{65} - 40 q^{66} + 30 q^{67} - 34 q^{68} + 8 q^{69} + 18 q^{70} - 2 q^{71} + 151 q^{72} - 23 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} + 36 q^{77} - 2 q^{78} - 67 q^{79} - 41 q^{80} - 83 q^{81} + 2 q^{82} + 26 q^{84} - 5 q^{85} - 5 q^{86} - 46 q^{87} + 70 q^{88} + 20 q^{89} - 33 q^{90} + 19 q^{91} - 10 q^{92} - 67 q^{93} + 130 q^{94} + 4 q^{95} + 46 q^{96} - 18 q^{97} - 65 q^{98} + 53 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9 - q^10 - 28 * q^11 - 13 * q^12 - 6 * q^13 - 6 * q^14 - 2 * q^15 + 8 * q^16 - 10 * q^17 - 27 * q^18 - 13 * q^19 - 5 * q^20 - 8 * q^21 + 2 * q^22 - 12 * q^23 - 82 * q^24 - 20 * q^25 + 32 * q^26 - q^27 + 22 * q^28 + 42 * q^29 + 8 * q^30 - 10 * q^31 + 4 * q^32 + 13 * q^33 + 32 * q^34 + 8 * q^35 - 13 * q^36 + 12 * q^37 + 30 * q^38 + 37 * q^39 + 44 * q^40 + 36 * q^41 - 64 * q^42 - 78 * q^43 - 56 * q^44 - 2 * q^45 + 18 * q^46 - 4 * q^47 - 41 * q^48 - 31 * q^49 + q^50 - 2 * q^51 + 49 * q^52 - 11 * q^53 + 22 * q^54 - 17 * q^55 + 9 * q^56 + 38 * q^57 + 11 * q^58 - q^59 - 11 * q^60 - 100 * q^61 - 35 * q^62 + 110 * q^63 + 17 * q^64 + 6 * q^65 - 40 * q^66 + 30 * q^67 - 34 * q^68 + 8 * q^69 + 18 * q^70 - 2 * q^71 + 151 * q^72 - 23 * q^73 - 2 * q^74 - q^75 + 2 * q^76 + 36 * q^77 - 2 * q^78 - 67 * q^79 - 41 * q^80 - 83 * q^81 + 2 * q^82 + 26 * q^84 - 5 * q^85 - 5 * q^86 - 46 * q^87 + 70 * q^88 + 20 * q^89 - 33 * q^90 + 19 * q^91 - 10 * q^92 - 67 * q^93 + 130 * q^94 + 4 * q^95 + 46 * q^96 - 18 * q^97 - 65 * q^98 + 53 * q^99

Introduction

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