LMFDB - Embedded newform 288.2.bf.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939466 + 1.05707i) q^{2} +(-0.494102 + 1.66008i) q^{3} +(-0.234807 - 1.98617i) q^{4} +(-0.0359748 - 0.273256i) q^{5} +(-1.29063 - 2.08189i) q^{6} +(-1.13217 - 4.22533i) q^{7} +(2.32012 + 1.61773i) q^{8} +(-2.51173 - 1.64050i) q^{9} +O(q^{10})$	\(q+(-0.939466 + 1.05707i) q^{2} +(-0.494102 + 1.66008i) q^{3} +(-0.234807 - 1.98617i) q^{4} +(-0.0359748 - 0.273256i) q^{5} +(-1.29063 - 2.08189i) q^{6} +(-1.13217 - 4.22533i) q^{7} +(2.32012 + 1.61773i) q^{8} +(-2.51173 - 1.64050i) q^{9} +(0.322648 + 0.218686i) q^{10} +(3.37509 - 2.58980i) q^{11} +(3.41322 + 0.591572i) q^{12} +(2.42190 - 3.15628i) q^{13} +(5.53013 + 2.77277i) q^{14} +(0.471401 + 0.0752951i) q^{15} +(-3.88973 + 0.932732i) q^{16} -1.15340 q^{17} +(4.09381 - 1.11389i) q^{18} +(-7.29638 + 3.02226i) q^{19} +(-0.534285 + 0.135614i) q^{20} +(7.57380 + 0.208246i) q^{21} +(-0.433178 + 6.00075i) q^{22} +(-3.36387 - 0.901347i) q^{23} +(-3.83194 + 3.05226i) q^{24} +(4.75625 - 1.27443i) q^{25} +(1.06113 + 5.52535i) q^{26} +(3.96440 - 3.35909i) q^{27} +(-8.12638 + 3.24083i) q^{28} +(8.61635 + 1.13436i) q^{29} +(-0.522458 + 0.427568i) q^{30} +(0.264668 - 0.152806i) q^{31} +(2.66831 - 4.98800i) q^{32} +(2.63163 + 6.88255i) q^{33} +(1.08358 - 1.21922i) q^{34} +(-1.11387 + 0.461379i) q^{35} +(-2.66853 + 5.37391i) q^{36} +(3.12198 - 7.53711i) q^{37} +(3.65995 - 10.5521i) q^{38} +(4.04301 + 5.58007i) q^{39} +(0.358588 - 0.692183i) q^{40} +(-0.968613 + 3.61491i) q^{41} +(-7.33546 + 7.81042i) q^{42} +(-2.90616 - 3.78738i) q^{43} +(-5.93627 - 6.09540i) q^{44} +(-0.357916 + 0.745360i) q^{45} +(4.11303 - 2.70907i) q^{46} +(-4.44564 - 2.56669i) q^{47} +(0.373515 - 6.91813i) q^{48} +(-10.5094 + 6.06763i) q^{49} +(-3.12117 + 6.22500i) q^{50} +(0.569895 - 1.91473i) q^{51} +(-6.83759 - 4.06919i) q^{52} +(-1.95684 + 4.72422i) q^{53} +(-0.173617 + 7.34642i) q^{54} +(-0.829095 - 0.829095i) q^{55} +(4.20867 - 11.6348i) q^{56} +(-1.41203 - 13.6059i) q^{57} +(-9.29388 + 8.04242i) q^{58} +(2.60929 - 0.343519i) q^{59} +(0.0388606 - 0.953962i) q^{60} +(1.02060 - 7.75221i) q^{61} +(-0.0871194 + 0.423330i) q^{62} +(-4.08793 + 12.4702i) q^{63} +(2.76590 + 7.50665i) q^{64} +(-0.949600 - 0.548252i) q^{65} +(-9.74768 - 3.68409i) q^{66} +(4.08265 - 5.32061i) q^{67} +(0.270825 + 2.29084i) q^{68} +(3.15840 - 5.13894i) q^{69} +(0.558729 - 1.61089i) q^{70} +(1.28366 + 1.28366i) q^{71} +(-3.17362 - 7.86944i) q^{72} +(1.49586 - 1.49586i) q^{73} +(5.03429 + 10.3810i) q^{74} +(-0.234412 + 8.52546i) q^{75} +(7.71595 + 13.7822i) q^{76} +(-14.7640 - 11.3288i) q^{77} +(-9.69682 - 0.968529i) q^{78} +(-0.601557 + 1.04193i) q^{79} +(0.394807 + 1.02934i) q^{80} +(3.61754 + 8.24096i) q^{81} +(-2.91125 - 4.41998i) q^{82} +(-13.1338 - 1.72910i) q^{83} +(-1.36477 - 15.0917i) q^{84} +(0.0414932 + 0.315172i) q^{85} +(6.73378 + 0.486093i) q^{86} +(-6.14049 + 13.7433i) q^{87} +(12.0202 - 0.548653i) q^{88} +(-5.53583 + 5.53583i) q^{89} +(-0.451650 - 1.07858i) q^{90} +(-16.0784 - 6.65988i) q^{91} +(-1.00037 + 6.89286i) q^{92} +(0.122897 + 0.514872i) q^{93} +(6.88971 - 2.28805i) q^{94} +(1.08833 + 1.88505i) q^{95} +(6.96206 + 6.89418i) q^{96} +(2.53281 - 4.38695i) q^{97} +(3.45934 - 16.8096i) q^{98} +(-12.7259 + 0.968040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.939466	+	1.05707i	−0.664303	+	0.747464i
$2$	−0.939466	+	1.05707i	−0.664303	+	0.747464i
$3$	−0.494102	+	1.66008i	−0.285270	+	0.958447i
$3$	−0.494102	+	1.66008i	−0.285270	+	0.958447i
$4$	−0.234807	−	1.98617i	−0.117403	−	0.993084i
$5$	−0.0359748	−	0.273256i	−0.0160884	−	0.122204i	0.981516	−	0.191380i	$-0.0612962\pi$
$5$	−0.0359748	−	0.273256i	−0.0160884	−	0.122204i	−0.997604	+	0.0691763i	$0.977963\pi$
$6$	−1.29063	−	2.08189i	−0.526899	−	0.849928i
$7$	−1.13217	−	4.22533i	−0.427922	−	1.59703i	−0.757459	−	0.652883i	$-0.773559\pi$
$7$	−1.13217	−	4.22533i	−0.427922	−	1.59703i	0.329537	−	0.944143i	$-0.393107\pi$
$8$	2.32012	+	1.61773i	0.820286	+	0.571954i
$9$	−2.51173	−	1.64050i	−0.837242	−	0.546832i
$10$	0.322648	+	0.218686i	0.102030	+	0.0691547i
$11$	3.37509	−	2.58980i	1.01763	−	0.780854i	0.0417412	−	0.999128i	$-0.486710\pi$
$11$	3.37509	−	2.58980i	1.01763	−	0.780854i	0.975887	+	0.218275i	$0.0700428\pi$
$12$	3.41322	+	0.591572i	0.985311	+	0.170772i
$13$	2.42190	−	3.15628i	0.671715	−	0.875396i	−0.325830	−	0.945428i	$-0.605644\pi$
$13$	2.42190	−	3.15628i	0.671715	−	0.875396i	0.997545	+	0.0700328i	$0.0223104\pi$
$14$	5.53013	+	2.77277i	1.47799	+	0.741053i
$15$	0.471401	+	0.0752951i	0.121715	+	0.0194411i
$16$	−3.88973	+	0.932732i	−0.972433	+	0.233183i
$17$	−1.15340			−0.279740			−0.139870	−	0.990170i	$-0.544668\pi$
$17$	−1.15340			−0.279740			−0.139870	+	0.990170i	$0.544668\pi$
$18$	4.09381	−	1.11389i	0.964920	−	0.262546i
$19$	−7.29638	+	3.02226i	−1.67390	+	0.693354i	−0.999007	−	0.0445583i	$-0.985812\pi$
$19$	−7.29638	+	3.02226i	−1.67390	+	0.693354i	−0.674897	+	0.737912i	$0.735812\pi$
$20$	−0.534285	+	0.135614i	−0.119470	+	0.0303243i
$21$	7.57380	+	0.208246i	1.65274	+	0.0454429i
$22$	−0.433178	+	6.00075i	−0.0923538	+	1.27936i
$23$	−3.36387	−	0.901347i	−0.701416	−	0.187944i	−0.109551	−	0.993981i	$-0.534941\pi$
$23$	−3.36387	−	0.901347i	−0.701416	−	0.187944i	−0.591865	+	0.806037i	$0.701608\pi$
$24$	−3.83194	+	3.05226i	−0.782191	+	0.623039i
$25$	4.75625	−	1.27443i	0.951251	−	0.254887i
$26$	1.06113	+	5.52535i	0.208104	+	1.08361i
$27$	3.96440	−	3.35909i	0.762950	−	0.646458i
$28$	−8.12638	+	3.24083i	−1.53574	+	0.612459i
$29$	8.61635	+	1.13436i	1.60002	+	0.210646i	0.877107	−	0.480296i	$-0.159471\pi$
$29$	8.61635	+	1.13436i	1.60002	+	0.210646i	0.722910	+	0.690942i	$0.242804\pi$
$30$	−0.522458	+	0.427568i	−0.0953873	+	0.0780629i
$31$	0.264668	−	0.152806i	0.0475358	−	0.0274448i	−0.476044	−	0.879422i	$-0.657930\pi$
$31$	0.264668	−	0.152806i	0.0475358	−	0.0274448i	0.523580	+	0.851977i	$0.324596\pi$
$32$	2.66831	−	4.98800i	0.471694	−	0.881762i
$33$	2.63163	+	6.88255i	0.458108	+	1.19810i
$34$	1.08358	−	1.21922i	0.185832	−	0.209095i
$35$	−1.11387	+	0.461379i	−0.188278	+	0.0779872i
$36$	−2.66853	+	5.37391i	−0.444755	+	0.895652i
$37$	3.12198	−	7.53711i	0.513250	−	1.23909i	−0.428733	−	0.903431i	$-0.641040\pi$
$37$	3.12198	−	7.53711i	0.513250	−	1.23909i	0.941982	−	0.335663i	$-0.108960\pi$
$38$	3.65995	−	10.5521i	0.593723	−	1.71178i
$39$	4.04301	+	5.58007i	0.647401	+	0.893527i
$40$	0.358588	−	0.692183i	0.0566978	−	0.109444i
$41$	−0.968613	+	3.61491i	−0.151272	+	0.564555i	0.848124	+	0.529798i	$0.177732\pi$
$41$	−0.968613	+	3.61491i	−0.151272	+	0.564555i	−0.999396	+	0.0347566i	$0.988934\pi$
$42$	−7.33546	+	7.81042i	−1.13189	+	1.20517i
$43$	−2.90616	−	3.78738i	−0.443185	−	0.577570i	0.517334	−	0.855784i	$-0.326924\pi$
$43$	−2.90616	−	3.78738i	−0.443185	−	0.577570i	−0.960519	+	0.278213i	$0.910258\pi$
$44$	−5.93627	−	6.09540i	−0.894927	−	0.918916i
$45$	−0.357916	+	0.745360i	−0.0533550	+	0.111112i
$46$	4.11303	−	2.70907i	0.606434	−	0.399431i
$47$	−4.44564	−	2.56669i	−0.648464	−	0.374391i	0.139404	−	0.990236i	$-0.455481\pi$
$47$	−4.44564	−	2.56669i	−0.648464	−	0.374391i	−0.787867	+	0.615845i	$0.788815\pi$
$48$	0.373515	−	6.91813i	0.0539122	−	0.998546i
$49$	−10.5094	+	6.06763i	−1.50135	+	0.866804i
$50$	−3.12117	+	6.22500i	−0.441400	+	0.880347i
$51$	0.569895	−	1.91473i	0.0798013	−	0.268116i
$52$	−6.83759	−	4.06919i	−0.948203	−	0.564295i
$53$	−1.95684	+	4.72422i	−0.268792	+	0.648922i	−0.999427	−	0.0338468i	$-0.989224\pi$
$53$	−1.95684	+	4.72422i	−0.268792	+	0.648922i	0.730635	+	0.682768i	$0.239224\pi$
$54$	−0.173617	+	7.34642i	−0.0236262	+	0.999721i
$55$	−0.829095	−	0.829095i	−0.111795	−	0.111795i
$56$	4.20867	−	11.6348i	0.562407	−	1.55477i
$57$	−1.41203	−	13.6059i	−0.187029	−	1.80214i
$58$	−9.29388	+	8.04242i	−1.22035	+	1.05602i
$59$	2.60929	−	0.343519i	0.339700	−	0.0447224i	0.0412536	−	0.999149i	$-0.486865\pi$
$59$	2.60929	−	0.343519i	0.339700	−	0.0447224i	0.298447	+	0.954426i	$0.403531\pi$
$60$	0.0388606	−	0.953962i	0.00501688	−	0.123156i
$61$	1.02060	−	7.75221i	0.130674	−	0.992568i	−0.792955	−	0.609280i	$-0.791458\pi$
$61$	1.02060	−	7.75221i	0.130674	−	0.992568i	0.923629	−	0.383288i	$-0.125208\pi$
$62$	−0.0871194	+	0.423330i	−0.0110642	+	0.0537629i
$63$	−4.08793	+	12.4702i	−0.515031	+	1.57110i
$64$	2.76590	+	7.50665i	0.345737	+	0.938331i
$65$	−0.949600	−	0.548252i	−0.117783	−	0.0680022i
$66$	−9.74768	−	3.68409i	−1.19986	−	0.453480i
$67$	4.08265	−	5.32061i	0.498774	−	0.650016i	−0.474339	−	0.880342i	$-0.657313\pi$
$67$	4.08265	−	5.32061i	0.498774	−	0.650016i	0.973113	+	0.230327i	$0.0739795\pi$
$68$	0.270825	+	2.29084i	0.0328424	+	0.277805i
$69$	3.15840	−	5.13894i	0.380227	−	0.618655i
$70$	0.558729	−	1.61089i	0.0667809	−	0.192538i
$71$	1.28366	+	1.28366i	0.152343	+	0.152343i	0.779164	−	0.626821i	$-0.215644\pi$
$71$	1.28366	+	1.28366i	0.152343	+	0.152343i	−0.626821	+	0.779164i	$0.715644\pi$
$72$	−3.17362	−	7.86944i	−0.374015	−	0.927423i
$73$	1.49586	−	1.49586i	0.175077	−	0.175077i	−0.614129	−	0.789206i	$-0.710492\pi$
$73$	1.49586	−	1.49586i	0.175077	−	0.175077i	0.789206	+	0.614129i	$0.210492\pi$
$74$	5.03429	+	10.3810i	0.585224	+	1.20677i
$75$	−0.234412	+	8.52546i	−0.0270676	+	0.984435i
$76$	7.71595	+	13.7822i	0.885081	+	1.58093i
$77$	−14.7640	−	11.3288i	−1.68251	−	1.29103i
$78$	−9.69682	−	0.968529i	−1.09795	−	0.109664i
$79$	−0.601557	+	1.04193i	−0.0676805	+	0.117226i	−0.897880	−	0.440240i	$-0.854893\pi$
$79$	−0.601557	+	1.04193i	−0.0676805	+	0.117226i	0.830199	+	0.557467i	$0.188227\pi$
$80$	0.394807	+	1.02934i	0.0441407	+	0.115083i
$81$	3.61754	+	8.24096i	0.401949	+	0.915662i
$82$	−2.91125	−	4.41998i	−0.321494	−	0.488105i
$83$	−13.1338	−	1.72910i	−1.44162	−	0.189793i	−0.631191	−	0.775627i	$-0.717434\pi$
$83$	−13.1338	−	1.72910i	−1.44162	−	0.189793i	−0.810431	+	0.585834i	$0.800767\pi$
$84$	−1.36477	−	15.0917i	−0.148908	−	1.64664i
$85$	0.0414932	+	0.315172i	0.00450057	+	0.0341852i
$86$	6.73378	+	0.486093i	0.726122	+	0.0524168i
$87$	−6.14049	+	13.7433i	−0.658330	+	1.47344i
$88$	12.0202	−	0.548653i	1.28136	−	0.0584866i
$89$	−5.53583	+	5.53583i	−0.586797	+	0.586797i	−0.936763	−	0.349965i	$-0.886193\pi$
$89$	−5.53583	+	5.53583i	−0.586797	+	0.586797i	0.349965	+	0.936763i	$0.386193\pi$
$90$	−0.451650	−	1.07858i	−0.0476081	−	0.113693i
$91$	−16.0784	−	6.65988i	−1.68547	−	0.698145i
$92$	−1.00037	+	6.89286i	−0.104295	+	0.718630i
$93$	0.122897	+	0.514872i	0.0127439	+	0.0533897i
$94$	6.88971	−	2.28805i	0.710620	−	0.235994i
$95$	1.08833	+	1.88505i	0.111661	+	0.193402i
$96$	6.96206	+	6.89418i	0.710562	+	0.703634i
$97$	2.53281	−	4.38695i	0.257167	−	0.445427i	−0.708315	−	0.705897i	$-0.750544\pi$
$97$	2.53281	−	4.38695i	0.257167	−	0.445427i	0.965482	+	0.260470i	$0.0838775\pi$
$98$	3.45934	−	16.8096i	0.349446	−	1.69802i
$99$	−12.7259	+	0.968040i	−1.27900	+	0.0972917i
$100$	−3.64804	−	9.14748i	−0.364804	−	0.914748i
$101$	1.91183	−	1.46700i	0.190235	−	0.145972i	−0.509253	−	0.860617i	$-0.670078\pi$
$101$	1.91183	−	1.46700i	0.190235	−	0.145972i	0.699488	+	0.714645i	$0.253412\pi$
$102$	1.48861	+	2.40124i	0.147394	+	0.237759i
$103$	9.47134	+	2.53784i	0.933239	+	0.250061i	0.693235	−	0.720711i	$-0.256185\pi$
$103$	9.47134	+	2.53784i	0.933239	+	0.250061i	0.240004	+	0.970772i	$0.422851\pi$
$104$	10.7251	−	3.40497i	1.05168	−	0.333885i
$105$	−0.215561	−	2.07707i	−0.0210366	−	0.202702i
$106$	−3.15546	−	6.50676i	−0.306486	−	0.631993i
$107$	15.4965	+	6.41887i	1.49811	+	0.620536i	0.973063	−	0.230539i	$-0.0740491\pi$
$107$	15.4965	+	6.41887i	1.49811	+	0.620536i	0.525043	+	0.851075i	$0.324049\pi$
$108$	−7.60259	−	7.08524i	−0.731560	−	0.681777i
$109$	7.19766	+	17.3767i	0.689411	+	1.66439i	0.745965	+	0.665986i	$0.231989\pi$
$109$	7.19766	+	17.3767i	0.689411	+	1.66439i	−0.0565538	+	0.998400i	$0.518011\pi$
$110$	1.65532	−	0.0975074i	0.157829	−	0.00929696i
$111$	10.9696	+	8.90683i	1.04119	+	0.845399i
$112$	8.34496	+	15.3794i	0.788525	+	1.45322i
$113$	−2.80113	−	4.85170i	−0.263508	−	0.456410i	0.703663	−	0.710534i	$-0.251546\pi$
$113$	−2.80113	−	4.85170i	−0.263508	−	0.456410i	−0.967172	+	0.254124i	$0.918213\pi$
$114$	15.7090	+	11.2896i	1.47128	+	1.05737i
$115$	−0.125283	+	0.951623i	−0.0116827	+	0.0887393i
$116$	0.229860	−	17.3799i	0.0213420	−	1.61368i
$117$	−11.2610	+	3.95460i	−1.04108	+	0.365603i
$118$	−2.08821	+	3.08093i	−0.192236	+	0.283623i
$119$	1.30585	+	4.87348i	0.119707	+	0.446751i
$120$	0.971899	+	0.937294i	0.0887219	+	0.0855628i
$121$	1.83718	−	6.85644i	0.167016	−	0.623313i
$122$	7.23583	+	8.36178i	0.655101	+	0.757040i
$123$	−5.52245	−	3.39411i	−0.497942	−	0.306037i
$124$	−0.365645	−	0.489796i	−0.0328359	−	0.0439849i
$125$	−1.04672	−	2.52699i	−0.0936211	−	0.226021i
$126$	−9.34145	−	16.0366i	−0.832202	−	1.42865i
$127$			4.34360i			0.385432i	0.981255	+	0.192716i	$0.0617296\pi$
$127$			4.34360i			0.385432i	−0.981255	+	0.192716i	$0.938270\pi$
$128$	−10.5335	−	4.12849i	−0.931043	−	0.364910i
$129$	7.72329	−	2.95310i	0.679998	−	0.260006i
$130$	1.47166	−	0.488732i	0.129073	−	0.0428647i
$131$	6.57249	+	5.04325i	0.574241	+	0.440631i	0.854616	−	0.519260i	$-0.173792\pi$
$131$	6.57249	+	5.04325i	0.574241	+	0.440631i	−0.280375	+	0.959890i	$0.590459\pi$
$132$	13.0520	−	6.84293i	1.13603	−	0.595601i
$133$	21.0308	+	27.4079i	1.82360	+	2.37657i
$134$	1.78876	+	9.31418i	0.154526	+	0.804623i
$135$	−1.06051	−	0.962453i	−0.0912741	−	0.0828348i
$136$	−2.67602	−	1.86588i	−0.229466	−	0.159998i
$137$	−19.6831	+	5.27408i	−1.68164	+	0.450595i	−0.968212	−	0.250130i	$-0.919527\pi$
$137$	−19.6831	+	5.27408i	−1.68164	+	0.450595i	−0.713431	+	0.700725i	$0.752860\pi$
$138$	2.46502	+	8.16652i	0.209836	+	0.695180i
$139$	3.24227	−	0.426853i	0.275006	−	0.0362052i	0.00823800	−	0.999966i	$-0.497378\pi$
$139$	3.24227	−	0.426853i	0.275006	−	0.0362052i	0.266768	+	0.963761i	$0.414044\pi$
$140$	1.17792	+	2.10399i	0.0995523	+	0.177820i
$141$	6.45751	−	6.11191i	0.543821	−	0.514716i
$142$	−2.56288	+	0.150968i	−0.215073	+	0.0126689i
$143$		−	16.9250i		−	1.41534i
$144$	11.3001	+	4.03832i	0.941674	+	0.336527i
$145$		−	2.39528i		−	0.198917i
$146$	0.175924	+	2.98654i	0.0145595	+	0.247168i
$147$	−4.88001	−	20.4445i	−0.402497	−	1.68624i
$148$	−15.7030	−	4.43100i	−1.29078	−	0.364226i
$149$	−0.328422	+	0.0432376i	−0.0269054	+	0.00354216i	−0.143967	−	0.989583i	$-0.545986\pi$
$149$	−0.328422	+	0.0432376i	−0.0269054	+	0.00354216i	0.117061	+	0.993125i	$0.462653\pi$
$150$	−8.79181	−	8.25717i	−0.717848	−	0.674195i
$151$	12.0319	−	3.22394i	0.979141	−	0.262360i	0.266458	−	0.963846i	$-0.414146\pi$
$151$	12.0319	−	3.22394i	0.979141	−	0.262360i	0.712683	+	0.701486i	$0.247480\pi$
$152$	−21.8177	−	4.79157i	−1.76965	−	0.388648i
$153$	2.89702	+	1.89214i	0.234210	+	0.152971i
$154$	25.8456	−	4.96357i	2.08270	−	0.399976i
$155$	−0.0512765	−	0.0668249i	−0.00411863	−	0.00536750i
$156$	10.1336	−	9.34035i	0.811341	−	0.747826i
$157$	0.0525391	+	0.0403147i	0.00419308	+	0.00321746i	0.610856	−	0.791742i	$-0.290825\pi$
$157$	0.0525391	+	0.0403147i	0.00419308	+	0.00321746i	−0.606663	+	0.794959i	$0.707492\pi$
$158$	−0.536251	−	1.61475i	−0.0426619	−	0.128462i
$159$	−6.87570	−	5.58275i	−0.545279	−	0.442741i
$160$	−1.45899	−	0.549687i	−0.115343	−	0.0434566i
$161$			15.2340i			1.20060i
$162$	−12.1099	−	3.91810i	−0.951440	−	0.307835i
$163$	−2.50860	−	6.05630i	−0.196489	−	0.474366i	0.794671	−	0.607041i	$-0.207643\pi$
$163$	−2.50860	−	6.05630i	−0.196489	−	0.474366i	−0.991160	+	0.132675i	$0.957643\pi$
$164$	7.40726	+	1.07502i	0.578410	+	0.0839451i
$165$	1.78602	−	0.966706i	0.139042	−	0.0752580i
$166$	14.1665	−	12.2590i	1.09954	−	0.951480i
$167$	−4.08001	+	15.2268i	−0.315721	+	1.17829i	0.607595	+	0.794247i	$0.292134\pi$
$167$	−4.08001	+	15.2268i	−0.315721	+	1.17829i	−0.923316	+	0.384040i	$0.874532\pi$
$168$	17.2352	+	12.7355i	1.32973	+	0.982566i
$169$	−0.731872	−	2.73138i	−0.0562978	−	0.210106i
$170$	−0.372141	−	0.252232i	−0.0285419	−	0.0193453i
$171$	23.2845	+	4.37860i	1.78061	+	0.334840i
$172$	−6.83999	+	6.66143i	−0.521545	+	0.507929i
$173$	0.525131	−	3.98877i	0.0399250	−	0.303260i	−0.959819	−	0.280621i	$-0.909460\pi$
$173$	0.525131	−	3.98877i	0.0399250	−	0.303260i	0.999744	−	0.0226395i	$-0.00720701\pi$
$174$	−8.75893	−	19.4024i	−0.664013	−	1.47089i
$175$	−10.7698	−	18.6539i	−0.814122	−	1.41010i
$176$	−10.7126	+	13.2217i	−0.807494	+	0.996622i
$177$	−0.718985	+	4.50136i	−0.0540422	+	0.338343i
$178$	−0.651052	−	11.0525i	−0.0487984	−	0.828421i
$179$	1.93617	+	4.67433i	0.144716	+	0.349376i	0.979572	−	0.201092i	$-0.0644491\pi$
$179$	1.93617	+	4.67433i	0.144716	+	0.349376i	−0.834856	+	0.550468i	$0.814449\pi$
$180$	1.56445	+	0.535866i	0.116607	+	0.0399411i
$181$	1.23891	+	0.513173i	0.0920875	+	0.0381439i	0.428252	−	0.903660i	$-0.359130\pi$
$181$	1.23891	+	0.513173i	0.0920875	+	0.0381439i	−0.336164	+	0.941803i	$0.609130\pi$
$182$	22.1451	−	10.7393i	1.64150	−	0.796048i
$183$	12.3650	+	5.52465i	0.914047	+	0.408394i
$184$	−6.34644	−	7.53307i	−0.467866	−	0.555345i
$185$	−2.17187	−	0.581951i	−0.159679	−	0.0427859i
$186$	−0.659715	−	0.353793i	−0.0483727	−	0.0259414i
$187$	−3.89282	+	2.98706i	−0.284671	+	0.218436i
$188$	−4.05402	+	9.43247i	−0.295670	+	0.687934i
$189$	−18.6817	−	12.9478i	−1.35889	−	0.941817i
$190$	−3.01509	−	0.620492i	−0.218738	−	0.0450152i
$191$	−0.154022	+	0.266773i	−0.0111446	+	0.0193030i	−0.871544	−	0.490317i	$-0.836881\pi$
$191$	−0.154022	+	0.266773i	−0.0111446	+	0.0193030i	0.860399	+	0.509620i	$0.170214\pi$
$192$	−13.8283	+	0.882560i	−0.997970	+	0.0636933i
$193$	0.732361	+	1.26849i	0.0527165	+	0.0913076i	0.891179	−	0.453651i	$-0.149879\pi$
$193$	0.732361	+	1.26849i	0.0527165	+	0.0913076i	−0.838463	+	0.544959i	$0.816545\pi$
$194$	2.25784	+	6.79875i	0.162103	+	0.488122i
$195$	1.37934	−	1.30552i	0.0987766	−	0.0934901i
$196$	14.5190	+	19.4488i	1.03707	+	1.38920i
$197$	11.3587	+	4.70492i	0.809273	+	0.335212i	0.748664	−	0.662950i	$-0.230696\pi$
$197$	11.3587	+	4.70492i	0.809273	+	0.335212i	0.0606093	+	0.998162i	$0.480696\pi$
$198$	10.9322	−	14.3616i	0.776920	−	1.02064i
$199$	0.751575	−	0.751575i	0.0532778	−	0.0532778i	−0.679966	−	0.733244i	$-0.738005\pi$
$199$	0.751575	−	0.751575i	0.0532778	−	0.0532778i	0.733244	+	0.679966i	$0.238005\pi$
$200$	13.0968	+	4.73750i	0.926081	+	0.334992i
$201$	6.81539	+	9.40644i	0.480720	+	0.663479i
$202$	−0.245375	+	3.39915i	−0.0172645	+	0.239163i
$203$	−4.96215	−	37.6913i	−0.348275	−	2.64541i
$204$	−3.93679	−	0.682317i	−0.275630	−	0.0477717i
$205$	1.02264	+	0.134633i	0.0714243	+	0.00940319i
$206$	−11.5807	+	7.62769i	−0.806865	+	0.531446i
$207$	6.97047	+	7.78236i	0.484481	+	0.540911i
$208$	−6.47658	+	14.5361i	−0.449070	+	1.00790i
$209$	−16.7989	+	29.0966i	−1.16200	+	2.01265i
$210$	2.39813	+	1.72348i	0.165487	+	0.118931i
$211$	17.5831	+	13.4920i	1.21047	+	0.928828i	0.998822	−	0.0485177i	$-0.0154497\pi$
$211$	17.5831	+	13.4920i	1.21047	+	0.928828i	0.211650	+	0.977346i	$0.432116\pi$
$212$	9.84258	+	2.77733i	0.675991	+	0.190748i
$213$	−2.76524	+	1.49672i	−0.189471	+	0.102554i
$214$	−21.3437	+	10.3507i	−1.45902	+	0.707556i
$215$	−0.930375	+	0.930375i	−0.0634510	+	0.0634510i
$216$	14.6320	−	1.38016i	0.995581	−	0.0939078i
$217$	−0.945308	−	0.945308i	−0.0641717	−	0.0641717i
$218$	−25.1304	−	8.71636i	−1.70204	−	0.590346i
$219$	1.74414	+	3.22235i	0.117858	+	0.217746i
$220$	−1.45205	+	1.84140i	−0.0978969	+	0.124147i
$221$	−2.79341	+	3.64045i	−0.187905	+	0.244883i
$222$	−19.7208	+	3.22804i	−1.32357	+	0.216652i
$223$	−15.0107	−	8.66641i	−1.00519	−	0.580346i	−0.0954089	−	0.995438i	$-0.530416\pi$
$223$	−15.0107	−	8.66641i	−1.00519	−	0.580346i	−0.909779	+	0.415093i	$0.863749\pi$
$224$	−24.0970	−	5.62719i	−1.61005	−	0.375983i
$225$	−14.0371	−	4.60159i	−0.935808	−	0.306773i
$226$	7.76017	+	1.59701i	0.516199	+	0.106232i
$227$	−2.97839	+	22.6231i	−0.197682	+	1.50155i	0.548694	+	0.836023i	$0.315125\pi$
$227$	−2.97839	+	22.6231i	−0.197682	+	1.50155i	−0.746377	+	0.665524i	$0.768208\pi$
$228$	−26.6920	+	5.99929i	−1.76772	+	0.397313i
$229$	3.98879	−	0.525134i	0.263587	−	0.0347019i	0.00242560	−	0.999997i	$-0.499228\pi$
$229$	3.98879	−	0.525134i	0.263587	−	0.0347019i	0.261161	+	0.965295i	$0.415895\pi$
$230$	−0.888235	−	1.02645i	−0.0585685	−	0.0676822i
$231$	26.1016	−	18.9118i	1.71736	−	1.24430i
$232$	18.1559	+	16.5708i	1.19199	+	1.08793i
$233$	1.18238	+	1.18238i	0.0774604	+	0.0774604i	0.744776	−	0.667315i	$-0.232557\pi$
$233$	1.18238	+	1.18238i	0.0774604	+	0.0774604i	−0.667315	+	0.744776i	$0.732557\pi$
$234$	6.39905	−	15.6189i	0.418319	−	1.02104i
$235$	−0.541432	+	1.30713i	−0.0353191	+	0.0852680i
$236$	−1.29497	−	5.10182i	−0.0842951	−	0.332100i
$237$	−1.43245	−	1.51345i	−0.0930478	−	0.0983092i
$238$	−6.37843	−	3.19810i	−0.413452	−	0.207302i
$239$	3.15768	−	1.82309i	0.204253	−	0.117926i	−0.394385	−	0.918945i	$-0.629042\pi$
$239$	3.15768	−	1.82309i	0.204253	−	0.117926i	0.598638	+	0.801020i	$0.295709\pi$
$240$	−1.90385	+	0.146813i	−0.122893	+	0.00947675i
$241$	−7.55215	−	4.36024i	−0.486477	−	0.280867i	0.236635	−	0.971599i	$-0.423955\pi$
$241$	−7.55215	−	4.36024i	−0.486477	−	0.280867i	−0.723112	+	0.690731i	$0.757289\pi$
$242$	5.52179	+	8.38342i	0.354954	+	0.538907i
$243$	−15.4681	+	1.93353i	−0.992278	+	0.124036i
$244$	−15.6368	−	0.206807i	−1.00105	−	0.0132395i
$245$	2.03609	+	2.65348i	0.130081	+	0.169525i
$246$	8.77598	−	2.64898i	0.559536	−	0.168893i
$247$	−8.13200	+	30.3491i	−0.517427	+	1.93106i
$248$	0.861261	+	0.0736331i	0.0546901	+	0.00467571i
$249$	9.35988	−	20.9488i	0.593158	−	1.32758i
$250$	3.65457	+	1.26757i	0.231135	+	0.0801682i
$251$	6.64923	−	16.0527i	0.419695	−	1.01323i	−0.562740	−	0.826634i	$-0.690253\pi$
$251$	6.64923	−	16.0527i	0.419695	−	1.01323i	0.982436	−	0.186601i	$-0.0597471\pi$
$252$	25.7278	+	5.19123i	1.62070	+	0.327017i
$253$	−13.6877	+	5.66962i	−0.860537	+	0.356446i
$254$	−4.59150	−	4.08066i	−0.288096	−	0.256044i
$255$	−0.543712	−	0.0868451i	−0.0340486	−	0.00543845i
$256$	14.2600	−	7.25615i	0.891251	−	0.453510i
$257$	12.2550	−	7.07545i	0.764448	−	0.441354i	−0.0664425	−	0.997790i	$-0.521165\pi$
$257$	12.2550	−	7.07545i	0.764448	−	0.441354i	0.830890	+	0.556436i	$0.187832\pi$
$258$	−4.13413	+	10.9384i	−0.257379	+	0.680997i
$259$	−35.3814	−	4.65806i	−2.19850	−	0.289437i
$260$	−0.865948	+	2.01480i	−0.0537038	+	0.124952i
$261$	−19.7810	−	16.9843i	−1.22441	−	1.05130i
$262$	−11.5057	+	2.20964i	−0.710825	+	0.136512i
$263$	18.5787	−	4.97815i	1.14561	−	0.306966i	0.364407	−	0.931240i	$-0.381272\pi$
$263$	18.5787	−	4.97815i	1.14561	−	0.306966i	0.781206	+	0.624274i	$0.214605\pi$
$264$	−5.02840	+	20.2256i	−0.309477	+	1.24480i
$265$	1.36132	+	0.364764i	0.0836250	+	0.0224073i
$266$	−48.7299	−	3.51768i	−2.98782	−	0.215683i
$267$	−6.45466	−	11.9252i	−0.395019	−	0.729810i
$268$	−11.5263	−	6.85951i	−0.704078	−	0.419011i
$269$	−0.959457	+	0.397420i	−0.0584991	+	0.0242311i	−0.411741	−	0.911301i	$-0.635079\pi$
$269$	−0.959457	+	0.397420i	−0.0584991	+	0.0242311i	0.353242	+	0.935532i	$0.385079\pi$
$270$	2.01370	−	0.216844i	0.122550	−	0.0131967i
$271$	−6.00379			−0.364704			−0.182352	−	0.983233i	$-0.558371\pi$
$271$	−6.00379			−0.364704			−0.182352	+	0.983233i	$0.558371\pi$
$272$	4.48640	−	1.07581i	0.272028	−	0.0652305i
$273$	19.0003	−	23.4007i	1.14995	−	1.41628i
$274$	12.9165	−	25.7613i	0.780317	−	1.55630i
$275$	12.7523	−	16.6191i	0.768991	−	1.00217i
$276$	−10.9484	−	5.06646i	−0.659017	−	0.304965i
$277$	15.2300	−	11.6864i	0.915085	−	0.702169i	−0.0397805	−	0.999208i	$-0.512666\pi$
$277$	15.2300	−	11.6864i	0.915085	−	0.702169i	0.954865	+	0.297039i	$0.0959992\pi$
$278$	−2.59479	+	3.82833i	−0.155625	+	0.229608i
$279$	−0.915452	−	0.0503798i	−0.0548067	−	0.00301616i
$280$	−3.33069	−	0.731482i	−0.199047	−	0.0437144i
$281$	0.487451	+	1.81919i	0.0290789	+	0.108524i	0.978940	−	0.204148i	$-0.0654425\pi$
$281$	0.487451	+	1.81919i	0.0290789	+	0.108524i	−0.949861	+	0.312672i	$0.898776\pi$
$282$	0.394121	+	12.5680i	0.0234695	+	0.748413i
$283$	−0.179222	−	1.36132i	−0.0106536	−	0.0809223i	0.985292	−	0.170879i	$-0.0546606\pi$
$283$	−0.179222	−	1.36132i	−0.0106536	−	0.0809223i	−0.995946	+	0.0899563i	$0.971327\pi$
$284$	2.24816	−	2.85099i	0.133404	−	0.169175i
$285$	−3.66708	+	0.875315i	−0.217219	+	0.0518492i
$286$	17.8909	+	15.9005i	1.05791	+	0.940213i
$287$	16.3709			0.966341
$288$	−14.8849	+	8.15115i	−0.877098	+	0.480311i
$289$	−15.6697			−0.921746
$290$	2.53198	+	2.25028i	0.148683	+	0.132141i
$291$	6.03122	+	6.37226i	0.353556	+	0.373548i
$292$	−3.32227	−	2.61979i	−0.194421	−	0.153312i
$293$	−1.37323	−	10.4307i	−0.0802247	−	0.609367i	−0.983580	−	0.180474i	$-0.942237\pi$
$293$	−1.37323	−	10.4307i	−0.0802247	−	0.609367i	0.903355	−	0.428893i	$-0.141096\pi$
$294$	26.1960	+	14.0484i	1.52778	+	0.819321i
$295$	−0.187737	−	0.700644i	−0.0109305	−	0.0407931i
$296$	19.4364	−	12.4365i	1.12972	−	0.722856i
$297$	4.68085	−	21.6043i	0.271611	−	1.25361i
$298$	0.262836	−	0.387787i	0.0152257	−	0.0224639i
$299$	−10.9919	+	8.43436i	−0.635676	+	0.487772i
$300$	16.9880	−	1.53625i	0.980805	−	0.0886957i
$301$	−12.7127	+	16.5675i	−0.732746	+	0.954933i
$302$	−7.89562	+	15.7474i	−0.454342	+	0.906159i
$303$	1.49070	+	3.89865i	0.0856384	+	0.223971i
$304$	25.5620	−	18.5613i	1.46608	−	1.06457i
$305$	−2.15505			−0.123398
$306$	−4.72178	+	1.28475i	−0.269926	+	0.0734445i
$307$	−0.406913	+	0.168549i	−0.0232238	+	0.00961960i	−0.394265	−	0.918997i	$-0.629001\pi$
$307$	−0.406913	+	0.168549i	−0.0232238	+	0.00961960i	0.371041	+	0.928616i	$0.379001\pi$
$308$	−19.0342	+	31.9838i	−1.08457	+	1.82245i
$309$	−8.89282	+	14.4692i	−0.505895	+	0.823126i
$310$	0.118811	+	0.00857667i	0.00674803	+	0.000487122i
$311$	−24.1516	−	6.47140i	−1.36951	−	0.366960i	−0.502211	−	0.864745i	$-0.667480\pi$
$311$	−24.1516	−	6.47140i	−1.36951	−	0.366960i	−0.867300	+	0.497785i	$0.834147\pi$
$312$	0.353218	+	19.4869i	0.0199970	+	1.10323i
$313$	−3.78761	+	1.01489i	−0.214089	+	0.0573649i	−0.364269	−	0.931294i	$-0.618681\pi$
$313$	−3.78761	+	1.01489i	−0.214089	+	0.0573649i	0.150181	+	0.988659i	$0.452014\pi$
$314$	−0.0919743	+	0.0176634i	−0.00519041	+	0.000996804i
$315$	3.55462	+	0.668437i	0.200280	+	0.0376622i
$316$	2.21069	+	0.950143i	0.124361	+	0.0534497i
$317$	−20.0706	−	2.64235i	−1.12728	−	0.148409i	−0.456258	−	0.889848i	$-0.650811\pi$
$317$	−20.0706	−	2.64235i	−1.12728	−	0.148409i	−0.671021	+	0.741439i	$0.734144\pi$
$318$	12.3609	−	2.02332i	0.693163	−	0.113462i
$319$	32.0188	−	18.4860i	1.79271	−	1.03502i
$320$	1.95173	−	1.02585i	0.109105	−	0.0573466i
$321$	−18.3127	+	22.5539i	−1.02212	+	1.25884i
$322$	−16.1034	−	14.3118i	−0.897408	−	0.797565i
$323$	8.41561	−	3.48586i	0.468257	−	0.193959i
$324$	15.5185	−	9.12008i	0.862139	−	0.506671i
$325$	7.49670	−	18.0986i	0.415842	−	1.00393i
$326$	8.75870	+	3.03791i	0.485099	+	0.168254i
$327$	−32.4031	+	3.36283i	−1.79189	+	0.185965i
$328$	−8.09525	+	6.82007i	−0.446985	+	0.376575i
$329$	−5.81189	+	21.6903i	−0.320420	+	1.19582i
$330$	−0.656028	+	2.79614i	−0.0361131	+	0.153923i
$331$	15.7341	+	20.5051i	0.864824	+	1.12706i	0.990841	+	0.135033i	$0.0431139\pi$
$331$	15.7341	+	20.5051i	0.864824	+	1.12706i	−0.126017	+	0.992028i	$0.540219\pi$
$332$	−0.350373	+	26.4920i	−0.0192292	+	1.45393i
$333$	−20.2062	+	13.8096i	−1.10729	+	0.756760i
$334$	−12.2628	−	18.6180i	−0.670992	−	1.01873i
$335$	−1.60076	−	0.924198i	−0.0874587	−	0.0504943i
$336$	−29.6543	+	6.25430i	−1.61777	+	0.341200i
$337$	−9.66811	+	5.58189i	−0.526656	+	0.304065i	−0.739654	−	0.672988i	$-0.765011\pi$
$337$	−9.66811	+	5.58189i	−0.526656	+	0.304065i	0.212998	+	0.977053i	$0.431677\pi$
$338$	3.57484	+	1.79240i	0.194446	+	0.0974936i
$339$	9.43826	−	2.25287i	0.512616	−	0.122359i
$340$	0.616242	−	0.156417i	0.0334204	−	0.00848290i
$341$	0.497542	−	1.20117i	0.0269434	−	0.0650471i
$342$	−26.5035	+	20.4999i	−1.43315	+	1.10851i
$343$	15.8842	+	15.8842i	0.857665	+	0.857665i
$344$	−0.615674	−	13.4886i	−0.0331949	−	0.727254i
$345$	−1.51787	−	0.678179i	−0.0817192	−	0.0365119i
$346$	3.72308	+	4.30241i	0.200154	+	0.231299i
$347$	19.2237	−	2.53085i	1.03198	−	0.135863i	0.404537	−	0.914522i	$-0.367433\pi$
$347$	19.2237	−	2.53085i	1.03198	−	0.135863i	0.627448	+	0.778658i	$0.284099\pi$
$348$	28.7384	+	8.96902i	1.54054	+	0.480790i
$349$	−1.33759	+	10.1600i	−0.0715998	+	0.543854i	0.917625	+	0.397448i	$0.130104\pi$
$349$	−1.33759	+	10.1600i	−0.0715998	+	0.543854i	−0.989225	+	0.146406i	$0.953229\pi$
$350$	29.8364	+	6.14020i	1.59482	+	0.328207i
$351$	−1.00085	−	20.6482i	−0.0534216	−	1.10212i
$352$	−3.91214	−	23.7453i	−0.208518	−	1.26563i
$353$	19.0016	+	10.9706i	1.01135	+	0.583905i	0.911588	−	0.411105i	$-0.134857\pi$
$353$	19.0016	+	10.9706i	1.01135	+	0.583905i	0.0997662	+	0.995011i	$0.468191\pi$
$354$	−4.08280	−	4.98889i	−0.216998	−	0.265157i
$355$	0.304589	−	0.396948i	0.0161659	−	0.0210678i
$356$	12.2950	+	9.69525i	0.651631	+	0.513847i
$357$	−8.73559	−	0.240190i	−0.462336	−	0.0127122i
$358$	−6.76008	−	2.34470i	−0.357281	−	0.123921i
$359$	−8.43702	−	8.43702i	−0.445289	−	0.445289i	0.448496	−	0.893785i	$-0.351960\pi$
$359$	−8.43702	−	8.43702i	−0.445289	−	0.445289i	−0.893785	+	0.448496i	$0.851960\pi$
$360$	−2.03620	+	1.15031i	−0.107317	+	0.0606267i
$361$	30.6680	−	30.6680i	1.61411	−	1.61411i
$362$	−1.70638	+	0.827509i	−0.0896851	+	0.0434929i
$363$	10.4745	+	6.43764i	0.549767	+	0.337888i
$364$	−9.45233	+	33.4981i	−0.495437	+	1.75578i
$365$	−0.462565	−	0.354939i	−0.0242118	−	0.0185784i
$366$	−17.4565	+	7.88048i	−0.912464	+	0.411919i
$367$	18.7762	−	32.5213i	0.980108	−	1.69760i	0.318179	−	0.948031i	$-0.396929\pi$
$367$	18.7762	−	32.5213i	0.980108	−	1.69760i	0.661929	−	0.749567i	$-0.269738\pi$
$368$	13.9253	+	0.368406i	0.725905	+	0.0192045i
$369$	8.36314	−	7.49067i	0.435368	−	0.389949i
$370$	2.65556	−	1.74910i	0.138056	−	0.0909315i
$371$	22.1769	+	2.91964i	1.15137	+	0.151580i
$372$	0.993765	−	0.364990i	0.0515243	−	0.0189239i
$373$	0.623568	+	4.73647i	0.0322872	+	0.245245i	0.999976	−	0.00690138i	$-0.00219680\pi$
$373$	0.623568	+	4.73647i	0.0322872	+	0.245245i	−0.967689	+	0.252147i	$0.918863\pi$
$374$	0.499625	−	6.92124i	0.0258350	−	0.357889i
$375$	4.71219	−	0.489038i	0.243337	−	0.0252538i
$376$	−6.16220	−	13.1469i	−0.317791	−	0.677999i
$377$	24.4483	−	24.4483i	1.25915	−	1.25915i
$378$	31.2376	−	7.58384i	1.60669	−	0.390071i
$379$	22.1286	+	9.16596i	1.13667	+	0.470824i	0.870043	−	0.492976i	$-0.164091\pi$
$379$	22.1286	+	9.16596i	1.13667	+	0.470824i	0.266626	+	0.963800i	$0.414091\pi$
$380$	3.48848	−	2.60424i	0.178955	−	0.133595i
$381$	−7.21072	−	2.14618i	−0.369416	−	0.109952i
$382$	−0.137301	−	0.413437i	−0.00702492	−	0.0211533i
$383$	4.35613	+	7.54503i	0.222588	+	0.385533i	0.955593	−	0.294690i	$-0.0952163\pi$
$383$	4.35613	+	7.54503i	0.222588	+	0.385533i	−0.733005	+	0.680223i	$0.761883\pi$
$384$	12.0583	−	15.4466i	0.615346	−	0.788257i
$385$	−2.56452	+	4.44189i	−0.130700	+	0.226379i
$386$	−2.02891	−	0.417541i	−0.103269	−	0.0212523i
$387$	1.08629	+	14.2804i	0.0552193	+	0.725914i
$388$	−9.30794	−	4.00049i	−0.472539	−	0.203094i
$389$	26.0391	−	19.9805i	1.32024	−	1.01305i	0.322447	−	0.946588i	$-0.395495\pi$
$389$	26.0391	−	19.9805i	1.32024	−	1.01305i	0.997789	−	0.0664648i	$-0.0211720\pi$
$390$	0.0841851	+	2.68455i	0.00426288	+	0.135938i
$391$	3.87988	+	1.03961i	0.196214	+	0.0525753i
$392$	−34.1989	−	2.92382i	−1.72731	−	0.147675i
$393$	−11.6197	+	8.41897i	−0.586135	+	0.424681i
$394$	−15.6446	+	7.58685i	−0.788161	+	0.382220i
$395$	0.306354	+	0.126896i	0.0154143	+	0.00638482i
$396$	4.91081	+	25.0484i	0.246778	+	1.25873i
$397$	8.96790	+	21.6504i	0.450086	+	1.08660i	0.972289	+	0.233783i	$0.0751104\pi$
$397$	8.96790	+	21.6504i	0.450086	+	1.08660i	−0.522203	+	0.852821i	$0.674890\pi$
$398$	0.0883905	+	1.50055i	0.00443061	+	0.0752158i
$399$	−55.8907	+	21.3705i	−2.79803	+	1.06987i
$400$	−17.3118	+	9.39352i	−0.865592	+	0.469676i
$401$	−8.65904	−	14.9979i	−0.432412	−	0.748959i	0.564669	−	0.825318i	$-0.309004\pi$
$401$	−8.65904	−	14.9979i	−0.432412	−	0.748959i	−0.997080	+	0.0763586i	$0.975671\pi$
$402$	−16.3461	−	1.63267i	−0.815270	−	0.0814301i
$403$	0.158700	−	1.20545i	0.00790543	−	0.0600477i
$404$	−3.36263	−	3.45276i	−0.167297	−	0.171781i
$405$	2.12175	−	1.28498i	0.105431	−	0.0638512i
$406$	44.5042	+	30.1643i	2.20871	+	1.49703i
$407$	−8.98266	−	33.5237i	−0.445254	−	1.66171i
$408$	4.41974	−	3.52046i	0.218810	−	0.174289i
$409$	−9.39934	+	35.0788i	−0.464767	+	1.73454i	0.192892	+	0.981220i	$0.438213\pi$
$409$	−9.39934	+	35.0788i	−0.464767	+	1.73454i	−0.657659	+	0.753315i	$0.728453\pi$
$410$	−1.10305	+	0.954523i	−0.0544759	+	0.0471405i
$411$	0.970084	−	35.2815i	0.0478507	−	1.74031i
$412$	2.81664	−	19.4076i	0.138766	−	0.956143i
$413$	−4.40565	−	10.6362i	−0.216788	−	0.523373i
$414$	−14.7750	+	0.0570345i	−0.726154	+	0.00280309i
$415$			3.65109i			0.179225i
$416$	−9.28117	−	20.5024i	−0.455047	−	1.00521i
$417$	−0.893402	+	5.59333i	−0.0437501	+	0.273907i
$418$	−14.9752	−	45.0929i	−0.732460	−	2.20557i
$419$	21.4741	+	16.4777i	1.04908	+	0.804988i	0.981256	−	0.192710i	$-0.0617275\pi$
$419$	21.4741	+	16.4777i	1.04908	+	0.804988i	0.0678245	+	0.997697i	$0.478394\pi$
$420$	−4.07480	+	0.915853i	−0.198830	+	0.0446890i
$421$	2.74337	+	3.57523i	0.133704	+	0.174246i	0.855407	−	0.517957i	$-0.173307\pi$
$421$	2.74337	+	3.57523i	0.133704	+	0.174246i	−0.721703	+	0.692203i	$0.756640\pi$
$422$	−30.7808	+	5.91136i	−1.49838	+	0.287761i
$423$	6.95559	+	13.7399i	0.338192	+	0.668057i
$424$	−12.1826	+	7.79512i	−0.591640	+	0.378564i
$425$	−5.48585	+	1.46993i	−0.266103	+	0.0713020i
$426$	1.01571	−	4.32919i	0.0492112	−	0.209750i
$427$	−33.9111	+	4.46449i	−1.64108	+	0.216052i
$428$	9.11027	−	32.2859i	0.440362	−	1.56060i
$429$	28.0968	+	8.36267i	1.35653	+	0.403753i
$430$	−0.109419	−	1.85753i	−0.00527663	−	0.0895780i
$431$		−	14.7412i		−	0.710058i	−0.934855	−	0.355029i	$-0.884471\pi$
$431$		−	14.7412i		−	0.710058i	0.934855	−	0.355029i	$-0.115529\pi$
$432$	−12.2873	+	16.7637i	−0.591175	+	0.806544i
$433$			7.45114i			0.358079i	0.983842	+	0.179039i	$0.0572990\pi$
$433$			7.45114i			0.358079i	−0.983842	+	0.179039i	$0.942701\pi$
$434$	1.88734	−	0.111175i	0.0905954	−	0.00533656i
$435$	3.97635	+	1.18351i	0.190651	+	0.0567450i
$436$	32.8230	−	18.3759i	1.57194	−	0.880048i
$437$	27.2682	−	3.58992i	1.30441	−	0.171729i
$438$	−5.04482	−	1.18361i	−0.241051	−	0.0565551i
$439$	−27.1089	+	7.26381i	−1.29384	+	0.346683i	−0.839117	−	0.543952i	$-0.816928\pi$
$439$	−27.1089	+	7.26381i	−1.29384	+	0.346683i	−0.454721	+	0.890634i	$0.650261\pi$
$440$	−0.582347	−	3.26485i	−0.0277623	−	0.155646i
$441$	36.3508	+	2.00048i	1.73099	+	0.0952610i
$442$	−1.22390	−	6.37292i	−0.0582150	−	0.303129i
$443$	7.54478	+	9.83254i	0.358463	+	0.467158i	0.937420	−	0.348200i	$-0.113207\pi$
$443$	7.54478	+	9.83254i	0.358463	+	0.467158i	−0.578957	+	0.815358i	$0.696540\pi$
$444$	15.1147	−	23.8789i	0.717313	−	1.13324i
$445$	1.71185	+	1.31355i	0.0811494	+	0.0622681i
$446$	23.2630	−	7.72557i	1.10154	−	0.365816i
$447$	0.0904963	−	0.566571i	0.00428033	−	0.0267979i
$448$	28.5866	−	20.1857i	1.35059	−	0.953684i
$449$		−	32.5738i		−	1.53725i	−0.639699	−	0.768625i	$-0.720941\pi$
$449$		−	32.5738i		−	1.53725i	0.639699	−	0.768625i	$-0.279059\pi$
$450$	18.0516	−	10.5152i	0.850961	−	0.495692i
$451$	6.09274	+	14.7092i	0.286896	+	0.692628i
$452$	−8.97858	+	6.70273i	−0.422317	+	0.315270i
$453$	−0.592992	+	21.5668i	−0.0278612	+	1.01330i
$454$	−21.1162	−	24.4020i	−0.991031	−	1.14524i
$455$	−1.24143	+	4.63309i	−0.0581993	+	0.217203i
$456$	18.7345	−	33.8515i	0.877325	−	1.58524i
$457$	1.79825	+	6.71116i	0.0841186	+	0.313935i	0.995146	−	0.0984112i	$-0.0313761\pi$
$457$	1.79825	+	6.71116i	0.0841186	+	0.313935i	−0.911027	+	0.412346i	$0.864709\pi$
$458$	−3.19223	+	4.70979i	−0.149163	+	0.220074i
$459$	−4.57253	+	3.87436i	−0.213427	+	0.180840i
$460$	1.91950	+	0.0253866i	0.0894972	+	0.00118366i
$461$	2.92515	−	22.2187i	0.136238	−	1.03483i	−0.777603	−	0.628756i	$-0.783565\pi$
$461$	2.92515	−	22.2187i	0.136238	−	1.03483i	0.913841	−	0.406073i	$-0.133102\pi$
$462$	−4.53043	+	45.3582i	−0.210775	+	2.11026i
$463$	−11.2083	−	19.4133i	−0.520892	−	0.902211i	−0.999705	−	0.0242943i	$-0.992266\pi$
$463$	−11.2083	−	19.4133i	−0.520892	−	0.902211i	0.478813	−	0.877917i	$-0.341067\pi$
$464$	−34.5734	+	3.62438i	−1.60503	+	0.168257i
$465$	0.136270	−	0.0521048i	0.00631939	−	0.00241630i
$466$	−2.36067	+	0.139056i	−0.109356	+	0.00644166i
$467$	11.6297	+	28.0767i	0.538160	+	1.29923i	0.926006	+	0.377509i	$0.123219\pi$
$467$	11.6297	+	28.0767i	0.538160	+	1.29923i	−0.387846	+	0.921724i	$0.626781\pi$
$468$	10.4987	+	21.4377i	0.485301	+	0.990960i
$469$	−27.1036	−	11.2267i	−1.25153	−	0.518400i
$470$	−0.873078	−	1.80034i	−0.0402721	−	0.0830435i
$471$	−0.0928853	+	0.0672996i	−0.00427993	+	0.00310100i
$472$	6.60958	+	3.42412i	0.304230	+	0.157608i
$473$	−19.6171	−	5.25639i	−0.901996	−	0.241689i
$474$	2.94557	−	0.0923703i	0.135294	−	0.00424271i
$475$	−30.8518	+	23.6734i	−1.41558	+	1.08621i
$476$	9.37294	−	3.73796i	0.429608	−	0.171329i
$477$	12.6651	−	8.65577i	0.579895	−	0.396320i
$478$	−1.03940	+	5.05063i	−0.0475409	+	0.231010i
$479$	−5.90948	+	10.2355i	−0.270011	+	0.467673i	−0.968864	−	0.247592i	$-0.920361\pi$
$479$	−5.90948	+	10.2355i	−0.270011	+	0.467673i	0.698853	+	0.715265i	$0.253694\pi$
$480$	1.63341	−	2.15044i	0.0745548	−	0.0981537i
$481$	−16.2282	−	28.1080i	−0.739940	−	1.28161i
$482$	11.7041	−	3.88688i	0.533106	−	0.177043i
$483$	−25.2896	−	7.52713i	−1.15072	−	0.342496i
$484$	−14.0494	−	2.03900i	−0.638610	−	0.0926820i
$485$	−1.28988	−	0.534284i	−0.0585702	−	0.0242606i
$486$	12.4879	−	18.1674i	0.566461	−	0.824089i
$487$	20.4135	−	20.4135i	0.925023	−	0.925023i	−0.0723556	−	0.997379i	$-0.523052\pi$
$487$	20.4135	−	20.4135i	0.925023	−	0.925023i	0.997379	+	0.0723556i	$0.0230516\pi$
$488$	14.9089	−	16.3350i	0.674893	−	0.739450i
$489$	11.2934	−	1.17205i	0.510707	−	0.0530018i
$490$	−4.71776	−	0.340562i	−0.213127	−	0.0153850i
$491$	2.75107	+	20.8964i	0.124154	+	0.943042i	0.934218	+	0.356701i	$0.116099\pi$
$491$	2.75107	+	20.8964i	0.124154	+	0.943042i	−0.810065	+	0.586341i	$0.800568\pi$
$492$	−5.44457	+	11.7655i	−0.245460	+	0.530429i
$493$	−9.93807	−	1.30837i	−0.447588	−	0.0589261i
$494$	−24.4414	−	37.1080i	−1.09967	−	1.66957i
$495$	0.722333	+	3.44259i	0.0324664	+	0.154733i
$496$	−0.886961	+	0.841240i	−0.0398257	+	0.0377728i
$497$	3.97058	−	6.87724i	0.178105	−	0.308486i
$498$	13.3511	+	29.5748i	0.598278	+	1.32528i
$499$	5.05697	+	3.88035i	0.226381	+	0.173708i	0.715724	−	0.698383i	$-0.246097\pi$
$499$	5.05697	+	3.88035i	0.226381	+	0.173708i	−0.489343	+	0.872091i	$0.662763\pi$
$500$	−4.77326	+	2.67231i	−0.213467	+	0.119509i
$501$	−23.2618	−	14.2968i	−1.03926	−	0.638732i
$502$	10.7221	+	22.1096i	0.478551	+	0.986802i
$503$	18.1626	−	18.1626i	0.809831	−	0.809831i	−0.174777	−	0.984608i	$-0.555921\pi$
$503$	18.1626	−	18.1626i	0.809831	−	0.809831i	0.984608	+	0.174777i	$0.0559206\pi$
$504$	−29.6579	+	22.3192i	−1.32107	+	0.994176i
$505$	−0.469644	−	0.469644i	−0.0208989	−	0.0208989i
$506$	6.86591	−	19.7953i	0.305227	−	0.880009i
$507$	4.89593	+	0.134616i	0.217436	+	0.00597852i
$508$	8.62712	−	1.01991i	0.382767	−	0.0452511i
$509$	16.9476	−	22.0865i	0.751187	−	0.978966i	−0.248759	−	0.968566i	$-0.580023\pi$
$509$	16.9476	−	22.0865i	0.751187	−	0.978966i	0.999946	−	0.0104008i	$-0.00331073\pi$
$510$	0.602601	−	0.493156i	0.0266836	−	0.0218373i
$511$	−8.01408	−	4.62693i	−0.354522	−	0.204683i
$512$	−5.72652	+	21.8908i	−0.253079	+	0.967446i
$513$	−18.7737	+	36.4907i	−0.828881	+	1.61110i
$514$	−4.03392	+	19.6016i	−0.177929	+	0.864590i
$515$	0.352749	−	2.67940i	0.0155440	−	0.118068i
$516$	−7.67884	−	14.6464i	−0.338042	−	0.644770i
$517$	−21.6517	+	2.85050i	−0.952240	+	0.125365i
$518$	38.1636	−	33.0247i	1.67681	−	1.45102i
$519$	6.36220	+	2.84262i	0.279270	+	0.124777i
$520$	−1.31626	−	2.80820i	−0.0577218	−	0.123148i
$521$	21.9162	+	21.9162i	0.960166	+	0.960166i	0.999236	−	0.0390706i	$-0.0124397\pi$
$521$	21.9162	+	21.9162i	0.960166	+	0.960166i	−0.0390706	+	0.999236i	$0.512440\pi$
$522$	36.5372	−	4.95378i	1.59919	−	0.216821i
$523$	−7.64461	+	18.4557i	−0.334276	+	0.807013i	0.663968	+	0.747761i	$0.268871\pi$
$523$	−7.64461	+	18.4557i	−0.334276	+	0.807013i	−0.998243	+	0.0592512i	$0.981129\pi$
$524$	8.47348	−	14.2383i	0.370165	−	0.622001i
$525$	36.2883	−	8.66184i	1.58375	−	0.378034i
$526$	−12.1918	+	24.3159i	−0.531588	+	1.06022i
$527$	−0.305267	+	0.176246i	−0.0132976	+	0.00767740i
$528$	−16.6559	−	24.3166i	−0.724856	−	1.05825i
$529$	−9.41538	−	5.43597i	−0.409364	−	0.236347i
$530$	−1.66449	+	1.09633i	−0.0723009	+	0.0476214i
$531$	−7.11736	−	3.41770i	−0.308867	−	0.148316i
$532$	49.4985	−	48.2063i	2.14603	−	2.09001i
$533$	9.06381	+	11.8122i	0.392597	+	0.511642i
$534$	18.6697	+	4.38027i	0.807918	+	0.189553i
$535$	1.19651	−	4.46543i	0.0517296	−	0.193057i
$536$	18.0795	−	5.73982i	0.780917	−	0.247922i
$537$	−8.71643	+	0.904603i	−0.376142	+	0.0390365i
$538$	0.481275	−	1.38758i	0.0207492	−	0.0598228i
$539$	−19.7564	+	47.6962i	−0.850968	+	2.05442i
$540$	−1.66258	+	2.33234i	−0.0715460	+	0.100368i
$541$	4.57741	−	1.89602i	0.196798	−	0.0815164i	−0.282108	−	0.959383i	$-0.591034\pi$
$541$	4.57741	−	1.89602i	0.196798	−	0.0815164i	0.478906	+	0.877866i	$0.341034\pi$
$542$	5.64036	−	6.34645i	0.242274	−	0.272603i
$543$	−1.46406	+	1.80313i	−0.0628287	+	0.0773797i
$544$	−3.07761	+	5.75314i	−0.131952	+	0.246664i
$545$	4.48934	−	2.59192i	0.192302	−	0.111026i
$546$	6.88614	+	42.0689i	0.294700	+	1.80038i
$547$	8.02793	+	1.05690i	0.343250	+	0.0451897i	0.300180	−	0.953882i	$-0.402953\pi$
$547$	8.02793	+	1.05690i	0.343250	+	0.0451897i	0.0430691	+	0.999072i	$0.486286\pi$
$548$	15.0969	+	37.8556i	0.644910	+	1.61711i
$549$	−15.2809	+	17.7971i	−0.652174	+	0.759563i
$550$	5.58726	+	29.0931i	0.238241	+	1.24054i
$551$	−66.2965	+	17.7641i	−2.82433	+	0.756776i
$552$	15.6413	−	6.81350i	0.665737	−	0.290002i
$553$	5.08356	+	1.36214i	0.216175	+	0.0579239i
$554$	−1.95471	+	27.0783i	−0.0830475	+	1.15045i
$555$	2.03921	−	3.31794i	0.0865597	−	0.140839i
$556$	−1.60911	−	6.33946i	−0.0682414	−	0.268853i
$557$	−37.1226	+	15.3767i	−1.57293	+	0.651530i	−0.987274	−	0.159027i	$-0.949164\pi$
$557$	−37.1226	+	15.3767i	−1.57293	+	0.651530i	−0.585659	+	0.810557i	$0.699164\pi$
$558$	0.913291	−	0.920370i	0.0386627	−	0.0389624i
$559$	−18.9925			−0.803297
$560$	3.90230	−	2.83358i	0.164902	−	0.119741i
$561$	−3.03531	−	7.93830i	−0.128151	−	0.335155i
$562$	−2.38096	−	1.19380i	−0.100435	−	0.0503573i
$563$	−8.95659	+	11.6725i	−0.377475	+	0.491936i	−0.942999	−	0.332797i	$-0.892008\pi$
$563$	−8.95659	+	11.6725i	−0.377475	+	0.491936i	0.565523	+	0.824732i	$0.308674\pi$
$564$	−13.6556	−	11.3906i	−0.575003	−	0.479631i
$565$	−1.22499	+	0.939964i	−0.0515355	+	0.0395446i
$566$	1.60739	+	1.08947i	0.0675637	+	0.0457937i
$567$	30.7251	−	24.6155i	1.29033	−	1.03375i
$568$	0.901630	+	5.05487i	0.0378316	+	0.212098i
$569$	2.05981	+	7.68733i	0.0863519	+	0.322270i	0.995567	−	0.0940576i	$-0.0299838\pi$
$569$	2.05981	+	7.68733i	0.0863519	+	0.322270i	−0.909215	+	0.416327i	$0.863317\pi$
$570$	2.51983	−	4.69870i	0.105544	−	0.196807i
$571$	1.07927	+	8.19790i	0.0451662	+	0.343072i	0.999076	+	0.0429781i	$0.0136846\pi$
$571$	1.07927	+	8.19790i	0.0451662	+	0.343072i	−0.953910	+	0.300094i	$0.902982\pi$
$572$	−33.6159	+	3.97410i	−1.40555	+	0.166166i
$573$	−0.366762	−	0.387501i	−0.0153217	−	0.0161881i
$574$	−15.3799	+	17.3052i	−0.641943	+	0.722305i
$575$	−17.1481			−0.715127
$576$	5.36746	−	23.3921i	0.223644	−	0.974671i
$577$	25.5467			1.06352			0.531762	−	0.846894i	$-0.321530\pi$
$577$	25.5467			1.06352			0.531762	+	0.846894i	$0.321530\pi$
$578$	14.7211	−	16.5640i	0.612318	−	0.688971i
$579$	−2.46765	+	0.589016i	−0.102552	+	0.0244786i
$580$	−4.75742	+	0.562427i	−0.197541	+	0.0233535i
$581$	7.56374	+	57.4523i	0.313797	+	2.38352i
$582$	−12.4021	+	0.388917i	−0.514082	+	0.0161211i
$583$	5.63028	+	21.0125i	0.233182	+	0.870248i
$584$	5.89047	−	1.05067i	0.243749	−	0.0434772i
$585$	1.48573	+	2.93487i	0.0614274	+	0.121342i
$586$	12.3161	+	8.34768i	0.508773	+	0.344839i
$587$	33.3140	−	25.5627i	1.37501	−	1.05509i	0.383716	−	0.923451i	$-0.374644\pi$
$587$	33.3140	−	25.5627i	1.37501	−	1.05509i	0.991298	−	0.131635i	$-0.0420227\pi$
$588$	−39.4604	+	14.4930i	−1.62732	+	0.597683i
$589$	−1.46930	+	1.91483i	−0.0605414	+	0.0788991i
$590$	0.917005	+	0.459780i	0.0377525	+	0.0189288i
$591$	−13.4229	+	16.5316i	−0.552144	+	0.680020i
$592$	−5.11354	+	32.2293i	−0.210165	+	1.32462i
$593$	41.0912			1.68741			0.843706	−	0.536805i	$-0.180369\pi$
$593$	41.0912			1.68741			0.843706	+	0.536805i	$0.180369\pi$
$594$	18.4398	+	25.2445i	0.756593	+	1.03579i
$595$	1.28473	−	0.532152i	0.0526688	−	0.0218161i
$596$	0.162993	+	0.642150i	0.00667646	+	0.0263035i
$597$	0.876320	+	1.61903i	0.0358654	+	0.0662625i
$598$	1.41076	−	19.5430i	0.0576901	−	0.799173i
$599$	−36.8825	−	9.88264i	−1.50698	−	0.403794i	−0.591548	−	0.806270i	$-0.701483\pi$
$599$	−36.8825	−	9.88264i	−1.50698	−	0.403794i	−0.915430	+	0.402476i	$0.868150\pi$
$600$	−14.3358	+	19.4009i	−0.585255	+	0.792037i
$601$	−23.7562	+	6.36547i	−0.969037	+	0.259653i	−0.708421	−	0.705790i	$-0.750592\pi$
$601$	−23.7562	+	6.36547i	−0.969037	+	0.259653i	−0.260616	+	0.965443i	$0.583926\pi$
$602$	−5.56991	−	29.0028i	−0.227012	−	1.18207i
$603$	−18.9829	+	6.66634i	−0.773045	+	0.271474i
$604$	−9.22845	−	23.1404i	−0.375500	−	0.941568i
$605$	−1.93965	−	0.255360i	−0.0788581	−	0.0103819i
$606$	−5.52161	−	2.08687i	−0.224300	−	0.0847732i
$607$	13.6412	−	7.87576i	0.553680	−	0.319667i	−0.196925	−	0.980419i	$-0.563096\pi$
$607$	13.6412	−	7.87576i	0.553680	−	0.319667i	0.750605	+	0.660751i	$0.229762\pi$
$608$	−4.39393	+	44.4586i	−0.178198	+	1.80304i
$609$	65.0223	+	10.3858i	2.63484	+	0.420852i
$610$	2.02460	−	2.27804i	0.0819735	−	0.0922353i
$611$	−18.8681	+	7.81543i	−0.763323	+	0.316179i
$612$	3.07788	−	6.19825i	0.124416	−	0.250549i
$613$	8.23942	−	19.8917i	0.332787	−	0.803419i	−0.665582	−	0.746325i	$-0.731817\pi$
$613$	8.23942	−	19.8917i	0.332787	−	0.803419i	0.998369	−	0.0570938i	$-0.0181834\pi$
$614$	0.204113	−	0.588483i	0.00823732	−	0.0237492i
$615$	−0.728791	+	1.63114i	−0.0293877	+	0.0657740i
$616$	−15.9272	−	50.1682i	−0.641726	−	2.02134i
$617$	3.46075	−	12.9157i	0.139325	−	0.519967i	−0.860618	−	0.509251i	$-0.829922\pi$
$617$	3.46075	−	12.9157i	0.139325	−	0.519967i	0.999943	−	0.0107155i	$-0.00341091\pi$
$618$	−6.94053	−	22.9937i	−0.279189	−	0.924943i
$619$	−6.04944	−	7.88379i	−0.243148	−	0.316876i	0.655798	−	0.754936i	$-0.272332\pi$
$619$	−6.04944	−	7.88379i	−0.243148	−	0.316876i	−0.898946	+	0.438060i	$0.855666\pi$
$620$	−0.120685	+	0.117535i	−0.00484684	+	0.00472031i
$621$	−16.3635	+	7.72625i	−0.656643	+	0.310044i
$622$	29.5304	−	19.4503i	1.18406	−	0.779888i
$623$	29.6583	+	17.1232i	1.18823	+	0.686027i
$624$	−20.9310	−	17.9339i	−0.837909	−	0.717932i
$625$	20.6688	−	11.9332i	0.826754	−	0.477327i
$626$	2.48552	−	4.95724i	0.0993415	−	0.198131i
$627$	−40.0022	−	42.2642i	−1.59753	−	1.68787i
$628$	0.0677352	−	0.113818i	0.00270293	−	0.00454182i
$629$	−3.60087	+	8.69328i	−0.143576	+	0.346624i
$630$	−4.04603	+	3.12952i	−0.161198	+	0.124683i
$631$	0.575635	+	0.575635i	0.0229157	+	0.0229157i	0.718472	−	0.695556i	$-0.244842\pi$
$631$	0.575635	+	0.575635i	0.0229157	+	0.0229157i	−0.695556	+	0.718472i	$0.744842\pi$
$632$	−3.08124	+	1.44424i	−0.122565	+	0.0574487i
$633$	−31.0857	+	22.5230i	−1.23554	+	0.895207i
$634$	21.6488	−	18.7337i	0.859785	−	0.744011i
$635$	1.18691	−	0.156260i	0.0471012	−	0.00620099i
$636$	−9.47382	+	14.9672i	−0.375661	+	0.593487i
$637$	−6.30168	+	47.8660i	−0.249682	+	1.89652i
$638$	−10.5394	+	51.2132i	−0.417261	+	2.02755i
$639$	−1.11837	−	5.33006i	−0.0442419	−	0.210854i
$640$	−0.749190	+	3.02687i	−0.0296143	+	0.119648i
$641$	19.6431	+	11.3409i	0.775856	+	0.447941i	0.834960	−	0.550311i	$-0.185491\pi$
$641$	19.6431	+	11.3409i	0.775856	+	0.447941i	−0.0591038	+	0.998252i	$0.518824\pi$
$642$	−6.63695	−	40.5465i	−0.261939	−	1.60024i
$643$	16.6031	−	21.6376i	0.654762	−	0.853302i	−0.341482	−	0.939888i	$-0.610929\pi$
$643$	16.6031	−	21.6376i	0.654762	−	0.853302i	0.996244	+	0.0865857i	$0.0275956\pi$
$644$	30.2572	−	3.57704i	1.19230	−	0.140955i
$645$	−1.08480	−	2.00420i	−0.0427138	−	0.0789151i
$646$	−4.22137	+	12.1708i	−0.166088	+	0.478852i
$647$	7.63475	+	7.63475i	0.300153	+	0.300153i	0.841074	−	0.540921i	$-0.181924\pi$
$647$	7.63475	+	7.63475i	0.300153	+	0.300153i	−0.540921	+	0.841074i	$0.681924\pi$
$648$	−4.93852	+	24.9722i	−0.194004	+	0.981001i
$649$	7.91694	−	7.91694i	0.310767	−	0.310767i
$650$	12.0887	+	24.9276i	0.474157	+	0.977742i
$651$	2.03636	−	1.10221i	0.0798114	−	0.0431989i
$652$	−11.4398	+	6.40457i	−0.448017	+	0.250822i
$653$	−7.56997	−	5.80864i	−0.296236	−	0.227310i	0.449940	−	0.893059i	$-0.351445\pi$
$653$	−7.56997	−	5.80864i	−0.296236	−	0.227310i	−0.746176	+	0.665749i	$0.768112\pi$
$654$	26.8868	−	37.4117i	1.05136	−	1.46291i
$655$	1.14165	−	1.97740i	0.0446080	−	0.0772634i
$656$	0.395900	−	14.9645i	0.0154573	−	0.584265i
$657$	−6.21114	+	1.30324i	−0.242320	+	0.0508441i
$658$	−17.4681	−	26.5209i	−0.680978	−	1.03389i
$659$	−41.0330	−	5.40210i	−1.59842	−	0.210436i	−0.721967	−	0.691927i	$-0.756762\pi$
$659$	−41.0330	−	5.40210i	−1.59842	−	0.210436i	−0.876451	+	0.481491i	$0.840095\pi$
$660$	−2.33941	−	3.32035i	−0.0910615	−	0.129244i
$661$	−4.52022	−	34.3345i	−0.175816	−	1.33546i	−0.820780	−	0.571245i	$-0.806461\pi$
$661$	−4.52022	−	34.3345i	−0.175816	−	1.33546i	0.644964	−	0.764213i	$-0.276873\pi$
$662$	−36.4570	−	2.63173i	−1.41694	−	0.102285i
$663$	−4.66320	−	6.43604i	−0.181104	−	0.249955i
$664$	−27.6748	−	25.2587i	−1.07399	−	0.980226i
$665$	6.73278	−	6.73278i	0.261086	−	0.261086i
$666$	4.38527	−	34.3330i	0.169926	−	1.33038i
$667$	−27.9619	−	11.5822i	−1.08269	−	0.448464i
$668$	31.2011	+	4.52824i	1.20720	+	0.175203i
$669$	21.8037	−	20.6368i	0.842981	−	0.797865i
$670$	2.48080	−	0.823865i	0.0958418	−	0.0318287i
$671$	−16.6320	−	28.8075i	−0.642073	−	1.11210i
$672$	21.2479	−	37.2224i	0.819657	−	1.43589i
$673$	−4.73187	+	8.19583i	−0.182400	+	0.315926i	−0.942697	−	0.333649i	$-0.891720\pi$
$673$	−4.73187	+	8.19583i	−0.182400	+	0.315926i	0.760297	+	0.649575i	$0.225053\pi$
$674$	3.18240	−	15.4639i	0.122582	−	0.595647i
$675$	14.5748	−	21.0291i	0.560983	−	0.809409i
$676$	−5.25314	+	2.09497i	−0.202044	+	0.0805757i
$677$	−34.8900	+	26.7721i	−1.34093	+	1.02893i	−0.345023	+	0.938594i	$0.612129\pi$
$677$	−34.8900	+	26.7721i	−1.34093	+	1.02893i	−0.995911	+	0.0903401i	$0.971205\pi$
$678$	−6.48548	+	12.0934i	−0.249073	+	0.464445i
$679$	−21.4039	−	5.73516i	−0.821406	−	0.220095i
$680$	−0.413594	+	0.798361i	−0.0158606	+	0.0306157i
$681$	−36.0845	−	16.1225i	−1.38276	−	0.617814i
$682$	0.802303	+	1.65440i	0.0307218	+	0.0633502i
$683$	−41.6351	−	17.2458i	−1.59312	−	0.659893i	−0.602702	−	0.797967i	$-0.705909\pi$
$683$	−41.6351	−	17.2458i	−1.59312	−	0.659893i	−0.990422	+	0.138073i	$0.955909\pi$
$684$	3.22927	−	47.2751i	0.123474	−	1.80761i
$685$	2.14927	+	5.18879i	0.0821193	+	0.198254i
$686$	−31.7134	+	1.86809i	−1.21082	+	0.0713240i
$687$	−1.09911	+	6.88118i	−0.0419335	+	0.262533i
$688$	14.8368	+	12.0212i	0.565647	+	0.458305i
$689$	10.1717	+	17.6179i	0.387511	+	0.671190i
$690$	2.14287	−	0.967369i	0.0815776	−	0.0368271i
$691$	0.242754	−	1.84390i	0.00923481	−	0.0701454i	−0.986207	−	0.165517i	$-0.947071\pi$
$691$	0.242754	−	1.84390i	0.00923481	−	0.0701454i	0.995442	+	0.0953718i	$0.0304040\pi$
$692$	−8.04567	−	0.106409i	−0.305850	−	0.00404507i
$693$	18.4982	+	52.6750i	0.702688	+	2.00096i
$694$	−15.3848	+	22.6986i	−0.583997	+	0.861625i
$695$	−0.233280	−	0.870612i	−0.00884881	−	0.0330242i
$696$	−36.4797	+	21.9525i	−1.38276	+	0.832108i
$697$	1.11719	−	4.16943i	0.0423168	−	0.157928i
$698$	−9.48328	−	10.9589i	−0.358947	−	0.414802i
$699$	−2.54706	+	1.37863i	−0.0963388	+	0.0521446i
$700$	−34.5209	+	25.7707i	−1.30477	+	0.974042i
$701$	7.60109	+	18.3507i	0.287089	+	0.693095i	0.999966	−	0.00819394i	$-0.00260824\pi$
$701$	7.60109	+	18.3507i	0.287089	+	0.693095i	−0.712877	+	0.701289i	$0.752608\pi$
$702$	22.7669	+	18.3403i	0.859281	+	0.692209i
$703$			64.4290i			2.42999i
$704$	28.7759	+	18.1725i	1.08453	+	0.684902i
$705$	−1.90242	−	1.54468i	−0.0716494	−	0.0581759i
$706$	−29.4481	+	9.77960i	−1.10829	+	0.368060i
$707$	−8.36310	−	6.41724i	−0.314527	−	0.241345i
$708$	9.10928	+	0.371076i	0.342348	+	0.0139459i
$709$	8.99999	+	11.7290i	0.338002	+	0.440492i	0.931170	−	0.364586i	$-0.118790\pi$
$709$	8.99999	+	11.7290i	0.338002	+	0.440492i	−0.593168	+	0.805079i	$0.702123\pi$
$710$	0.133452	+	0.694892i	0.00500836	+	0.0260788i
$711$	3.22023	−	1.63019i	0.120768	−	0.0611367i
$712$	−21.7993	+	3.88830i	−0.816962	+	0.145720i
$713$	−1.02804	+	0.275463i	−0.0385004	+	0.0103162i
$714$	8.46069	−	9.00851i	0.316633	−	0.337135i
$715$	−4.62485	+	0.608873i	−0.172960	+	0.0227706i
$716$	8.82939	−	4.94313i	0.329970	−	0.184733i
$717$	1.46625	+	6.14279i	0.0547582	+	0.229407i
$718$	16.8448	−	0.992252i	0.628644	−	0.0370305i
$719$			24.8313i			0.926052i	0.886345	+	0.463026i	$0.153236\pi$
$719$			24.8313i			0.926052i	−0.886345	+	0.463026i	$0.846764\pi$
$720$	0.696977	−	3.23309i	0.0259748	−	0.120490i
$721$		−	42.8929i		−	1.59741i
$722$	3.60678	+	61.2300i	0.134230	+	2.27874i
$723$	10.9699	−	10.3828i	0.407974	−	0.386139i
$724$	0.728344	−	2.58118i	0.0270687	−	0.0959288i
$725$	42.4272	−	5.58565i	1.57571	−	0.207446i
$726$	−16.6455	+	5.02434i	−0.617771	+	0.186471i
$727$	42.8686	−	11.4866i	1.58991	−	0.426014i	0.647933	−	0.761698i	$-0.275634\pi$
$727$	42.8686	−	11.4866i	1.58991	−	0.426014i	0.941975	+	0.335683i	$0.108967\pi$
$728$	−26.5298	−	41.4622i	−0.983261	−	1.53669i
$729$	4.43299	−	26.6336i	0.164185	−	0.986430i
$730$	0.809761	−	0.155512i	0.0299706	−	0.00575577i
$731$	3.35195	+	4.36835i	0.123976	+	0.161569i
$732$	8.06950	−	25.8562i	0.298257	−	0.955672i
$733$	−26.5577	−	20.3785i	−0.980932	−	0.752695i	−0.0119757	−	0.999928i	$-0.503812\pi$
$733$	−26.5577	−	20.3785i	−0.980932	−	0.752695i	−0.968956	+	0.247233i	$0.920479\pi$
$734$	16.7378	+	50.4004i	0.617803	+	1.86031i
$735$	−5.41103	+	2.06898i	−0.199589	+	0.0763154i
$736$	−13.4718	+	14.3739i	−0.496575	+	0.529830i
$737$		−	28.5308i		−	1.05094i
$738$	0.0612909	+	15.8777i	0.00225615	+	0.584466i
$739$	5.99085	+	14.4632i	0.220377	+	0.532037i	0.994941	−	0.100458i	$-0.0320309\pi$
$739$	5.99085	+	14.4632i	0.220377	+	0.532037i	−0.774564	+	0.632495i	$0.782031\pi$
$740$	−0.645883	+	4.45035i	−0.0237431	+	0.163598i
$741$	−46.3638	−	28.4953i	−1.70322	−	1.04680i
$742$	−23.9207	+	20.6997i	−0.878157	+	0.759909i
$743$	−4.89507	+	18.2686i	−0.179583	+	0.670211i	0.816143	+	0.577850i	$0.196108\pi$
$743$	−4.89507	+	18.2686i	−0.179583	+	0.670211i	−0.995726	+	0.0923613i	$0.970559\pi$
$744$	−0.547787	+	1.39338i	−0.0200829	+	0.0510837i
$745$	0.0236299	+	0.0881878i	0.000865731	+	0.00323095i
$746$	−5.59262	−	3.79060i	−0.204760	−	0.138784i
$747$	30.1519	+	25.8890i	1.10320	+	0.947228i
$748$	6.84687	+	7.03041i	0.250346	+	0.257057i
$749$	9.57710	−	72.7453i	0.349940	−	2.65806i
$750$	−3.91000	+	5.44057i	−0.142773	+	0.198661i
$751$	18.5526	+	32.1340i	0.676993	+	1.17259i	0.975882	+	0.218299i	$0.0700508\pi$
$751$	18.5526	+	32.1340i	0.676993	+	1.17259i	−0.298888	+	0.954288i	$0.596616\pi$
$752$	19.6864	+	5.83715i	0.717889	+	0.212859i
$753$	23.3633	+	18.9699i	0.851405	+	0.691301i
$754$	2.87529	+	48.8121i	0.104712	+	1.77763i
$755$	−1.31380	−	3.17180i	−0.0478142	−	0.115434i
$756$	−21.3300	+	40.1452i	−0.775765	+	1.46007i
$757$	−16.8701	−	6.98780i	−0.613152	−	0.253976i	0.0544233	−	0.998518i	$-0.482668\pi$
$757$	−16.8701	−	6.98780i	−0.613152	−	0.253976i	−0.667576	+	0.744542i	$0.732668\pi$
$758$	−30.4782	+	14.7804i	−1.10702	+	0.536849i
$759$	−2.64891	−	25.5240i	−0.0961495	−	0.926463i
$760$	−0.524438	+	6.13417i	−0.0190234	+	0.222510i
$761$	−8.68016	−	2.32584i	−0.314655	−	0.0843117i	0.0980351	−	0.995183i	$-0.468744\pi$
$761$	−8.68016	−	2.32584i	−0.314655	−	0.0843117i	−0.412691	+	0.910871i	$0.635411\pi$
$762$	9.04290	−	5.60599i	0.327590	−	0.203084i
$763$	65.2733	−	50.0860i	2.36305	−	1.81323i
$764$	0.566022	+	0.243273i	0.0204780	+	0.00880130i
$765$	0.412819	−	0.859695i	0.0149255	−	0.0310823i
$766$	−12.0681	−	2.48356i	−0.436038	−	0.0897346i
$767$	5.23519	−	9.06762i	0.189032	−	0.327413i
$768$	4.99989	+	27.2580i	0.180418	+	0.983590i
$769$	−17.3787	−	30.1008i	−0.626692	−	1.08546i	−0.988211	−	0.153098i	$-0.951075\pi$
$769$	−17.3787	−	30.1008i	−0.626692	−	1.08546i	0.361519	−	0.932365i	$-0.382258\pi$
$770$	−2.28611	−	6.88389i	−0.0823858	−	0.248078i
$771$	5.69057	+	23.8403i	0.204941	+	0.858588i
$772$	2.34746	−	1.75244i	0.0844871	−	0.0630717i
$773$	−29.3663	−	12.1639i	−1.05623	−	0.437506i	−0.214119	−	0.976807i	$-0.568688\pi$
$773$	−29.3663	−	12.1639i	−1.05623	−	0.437506i	−0.842113	+	0.539302i	$0.818688\pi$
$774$	−16.1160	−	12.2677i	−0.579277	−	0.440952i
$775$	1.06409	−	1.06409i	0.0382232	−	0.0382232i
$776$	12.9733	−	6.08084i	0.465715	−	0.218290i
$777$	25.2148	−	56.4344i	0.904575	−	2.02457i
$778$	−3.34200	+	46.2963i	−0.119817	+	1.65980i
$779$	−3.85784	−	29.3032i	−0.138221	−	1.04989i
$780$	−2.91686	−	2.43306i	−0.104440	−	0.0871174i
$781$	7.65691	+	1.00805i	0.273986	+	0.0360709i
$782$	−4.74396	+	3.12463i	−0.169644	+	0.111737i
$783$	37.9691	−	24.4461i	1.35691	−	0.873631i
$784$	35.2194	−	33.4040i	1.25784	−	1.19300i
$785$	0.00912613	−	0.0158069i	0.000325726	−	0.000564173i
$786$	2.01682	−	20.1922i	0.0719375	−	0.720231i
$787$	15.4542	+	11.8584i	0.550882	+	0.422706i	0.846335	−	0.532651i	$-0.178804\pi$
$787$	15.4542	+	11.8584i	0.550882	+	0.422706i	−0.295453	+	0.955357i	$0.595471\pi$
$788$	6.67767	−	23.6650i	0.237882	−	0.843032i
$789$	−0.915652	+	33.3019i	−0.0325981	+	1.18558i
$790$	−0.421947	+	0.204624i	−0.0150122	+	0.00728019i
$791$	−17.3287	+	17.3287i	−0.616137	+	0.616137i
$792$	−31.0915	−	18.3410i	−1.10479	−	0.651721i
$793$	−21.9964	−	21.9964i	−0.781114	−	0.781114i
$794$	−31.3111	−	10.8601i	−1.11119	−	0.385411i
$795$	−1.27817	+	2.07966i	−0.0453319	+	0.0737580i
$796$	−1.66923	−	1.31628i	−0.0591643	−	0.0466543i
$797$	−14.0150	+	18.2647i	−0.496437	+	0.646970i	−0.972627	−	0.232373i	$-0.925351\pi$
$797$	−14.0150	+	18.2647i	−0.496437	+	0.646970i	0.476190	+	0.879343i	$0.342018\pi$
$798$	29.9172	−	79.1574i	1.05906	−	2.80214i
$799$	5.12759	+	2.96041i	0.181401	+	0.104732i
$800$	6.33426	−	27.1248i	0.223950	−	0.959006i
$801$	22.9860	−	4.82298i	0.812171	−	0.170412i
$802$	23.9887	+	4.93678i	0.847072	+	0.174324i
$803$	1.17469	−	8.92264i	0.0414538	−	0.314873i
$804$	17.0825	−	15.7452i	0.602452	−	0.555290i
$805$	4.16277	−	0.548038i	0.146718	−	0.0193158i
$806$	1.12515	+	1.30024i	0.0396319	+	0.0457989i
$807$	−0.185679	−	1.78914i	−0.00653622	−	0.0629807i
$808$	6.80890	−	0.310787i	0.239536	−	0.0109334i
$809$	1.09445	+	1.09445i	0.0384787	+	0.0384787i	0.726084	−	0.687606i	$-0.241338\pi$
$809$	1.09445	+	1.09445i	0.0384787	+	0.0384787i	−0.687606	+	0.726084i	$0.741338\pi$
$810$	−0.634993	+	3.45004i	−0.0223114	+	0.121222i
$811$	−10.1605	+	24.5297i	−0.356784	+	0.861353i	0.638964	+	0.769237i	$0.279363\pi$
$811$	−10.1605	+	24.5297i	−0.356784	+	0.861353i	−0.995748	+	0.0921166i	$0.970637\pi$
$812$	−73.6961	+	18.7058i	−2.58622	+	0.656446i
$813$	2.96649	−	9.96677i	0.104039	−	0.349550i
$814$	43.8760	+	21.9991i	1.53785	+	0.771068i
$815$	−1.56467	+	0.903364i	−0.0548081	+	0.0316434i
$816$	−0.430811	+	7.97934i	−0.0150814	+	0.279333i
$817$	32.6509	+	18.8510i	1.14231	+	0.659513i
$818$	−28.2505	−	42.8911i	−0.987756	−	1.49965i
$819$	29.4590	+	43.1043i	1.02938	+	1.50619i
$820$	0.0272812	−	2.06275i	0.000952701	−	0.0720344i
$821$	−32.0240	−	41.7345i	−1.11765	−	1.45654i	−0.873512	−	0.486803i	$-0.838163\pi$
$821$	−32.0240	−	41.7345i	−1.11765	−	1.45654i	−0.244134	−	0.969742i	$-0.578504\pi$
$822$	36.3838	+	34.1712i	1.26903	+	1.19186i
$823$	3.00033	−	11.1974i	0.104585	−	0.390316i	−0.893713	−	0.448639i	$-0.851909\pi$
$823$	3.00033	−	11.1974i	0.104585	−	0.390316i	0.998298	+	0.0583234i	$0.0185754\pi$
$824$	17.8691	+	21.2102i	0.622500	+	0.738891i
$825$	21.2881	+	29.3813i	0.741155	+	1.02293i
$826$	15.3822	+	5.33524i	0.535215	+	0.185637i
$827$	−2.54477	+	6.14362i	−0.0884904	+	0.213635i	−0.961929	−	0.273300i	$-0.911885\pi$
$827$	−2.54477	+	6.14362i	−0.0884904	+	0.213635i	0.873439	+	0.486934i	$0.161885\pi$
$828$	13.8204	−	15.6719i	0.480291	−	0.544635i
$829$	39.6398	−	16.4193i	1.37675	−	0.570267i	0.433137	−	0.901328i	$-0.357407\pi$
$829$	39.6398	−	16.4193i	1.37675	−	0.570267i	0.943609	+	0.331061i	$0.107407\pi$
$830$	−3.85947	−	3.43008i	−0.133964	−	0.119060i
$831$	11.8752	+	31.0574i	0.411946	+	1.07737i
$832$	30.3919	+	9.45041i	1.05365	+	0.327634i
$833$	12.1216	−	6.99838i	0.419987	−	0.242480i
$834$	−5.07324	−	6.19913i	−0.175672	−	0.214658i
$835$	4.30759	+	0.567105i	0.149070	+	0.0196255i
$836$	61.7352	+	26.5334i	2.13516	+	0.917676i
$837$	0.535961	−	1.49483i	0.0185255	−	0.0516689i
$838$	−37.5923	+	7.21951i	−1.29861	+	0.249394i
$839$	40.8435	−	10.9440i	1.41008	−	0.377829i	0.528123	−	0.849168i	$-0.322896\pi$
$839$	40.8435	−	10.9440i	1.41008	−	0.377829i	0.881952	+	0.471339i	$0.156229\pi$
$840$	2.86002	−	5.16778i	0.0986800	−	0.178305i
$841$	44.9429	+	12.0424i	1.54976	+	0.415256i
$842$	−6.35658	−	0.458864i	−0.219062	−	0.0158135i
$843$	−3.26085	−	0.0896589i	−0.112310	−	0.00308802i
$844$	22.6688	−	38.0911i	0.780291	−	1.31115i
$845$	−0.720036	+	0.298249i	−0.0247700	+	0.0102601i
$846$	−21.0586	−	5.55560i	−0.724010	−	0.191005i
$847$	−31.0507			−1.06692
$848$	3.20514	−	20.2012i	0.110065	−	0.693710i
$849$	2.34846	+	0.375111i	0.0805989	+	0.0128738i
$850$	3.59994	−	7.17989i	0.123477	−	0.246268i
$851$	−17.2955	+	22.5399i	−0.592881	+	0.772658i
$852$	3.62204	+	5.14080i	0.124089	+	0.176121i
$853$	−5.39161	+	4.13713i	−0.184605	+	0.141653i	−0.696930	−	0.717139i	$-0.745451\pi$
$853$	−5.39161	+	4.13713i	−0.184605	+	0.141653i	0.512325	+	0.858792i	$0.328784\pi$
$854$	27.1391	−	40.0408i	0.928680	−	1.37017i
$855$	0.358821	−	6.52014i	0.0122714	−	0.222984i
$856$	25.5698	+	39.9618i	0.873957	+	1.36586i
$857$	7.18011	+	26.7966i	0.245268	+	0.915353i	0.973249	+	0.229755i	$0.0737925\pi$
$857$	7.18011	+	26.7966i	0.245268	+	0.915353i	−0.727980	+	0.685598i	$0.759541\pi$
$858$	−35.2360	+	21.8439i	−1.20294	+	0.745740i
$859$	7.00717	+	53.2247i	0.239081	+	1.81600i	0.517656	+	0.855589i	$0.326805\pi$
$859$	7.00717	+	53.2247i	0.239081	+	1.81600i	−0.278575	+	0.960415i	$0.589862\pi$
$860$	2.06634	+	1.62942i	0.0704616	+	0.0555629i
$861$	−8.08887	+	27.1769i	−0.275668	+	0.926187i
$862$	15.5825	+	13.8488i	0.530742	+	0.471693i
$863$	−20.8609			−0.710112			−0.355056	−	0.934845i	$-0.615538\pi$
$863$	−20.8609			−0.710112			−0.355056	+	0.934845i	$0.615538\pi$
$864$	−6.17692	−	28.7375i	−0.210143	−	0.977671i
$865$	−1.10884			−0.0377018
$866$	−7.87640	−	7.00009i	−0.267651	−	0.237873i
$867$	7.74242	−	26.0129i	0.262946	−	0.883445i
$868$	−1.65558	+	2.09951i	−0.0561939	+	0.0712619i
$869$	0.668073	+	5.07452i	0.0226628	+	0.172141i
$870$	−4.98670	+	3.09142i	−0.169065	+	0.104809i
$871$	−6.90558	−	25.7720i	−0.233987	−	0.873250i
$872$	−11.4114	+	51.9599i	−0.386438	+	1.75958i
$873$	−13.5585	+	6.86375i	−0.458885	+	0.232303i
$874$	−21.8227	+	32.1971i	−0.738165	+	1.08908i
$875$	−9.49233	+	7.28372i	−0.320899	+	0.246235i
$876$	5.99060	−	4.22078i	0.202404	−	0.142607i
$877$	8.59862	−	11.2059i	0.290355	−	0.378398i	−0.625286	−	0.780396i	$-0.715018\pi$
$877$	8.59862	−	11.2059i	0.290355	−	0.378398i	0.915640	+	0.401998i	$0.131684\pi$
$878$	17.7895	−	35.4802i	0.600367	−	1.19740i
$879$	17.9943	+	2.87416i	0.606932	+	0.0969430i
$880$	3.99828	+	2.45163i	0.134782	+	0.0826446i
$881$	−48.5122			−1.63442			−0.817209	−	0.576342i	$-0.804480\pi$
$881$	−48.5122			−1.63442			−0.817209	+	0.576342i	$0.804480\pi$
$882$	−36.2650	+	36.5460i	−1.22111	+	1.23057i
$883$	33.6646	−	13.9443i	1.13290	−	0.469264i	0.264137	−	0.964485i	$-0.414913\pi$
$883$	33.6646	−	13.9443i	1.13290	−	0.469264i	0.868767	+	0.495221i	$0.164913\pi$
$884$	7.88645	+	4.69339i	0.265250	+	0.157856i
$885$	1.25589	+	0.0345313i	0.0422162	+	0.00116076i
$886$	−17.4818	−	1.26196i	−0.587312	−	0.0423964i
$887$	−5.16895	−	1.38501i	−0.173556	−	0.0465043i	0.170994	−	0.985272i	$-0.445302\pi$
$887$	−5.16895	−	1.38501i	−0.173556	−	0.0465043i	−0.344551	+	0.938768i	$0.611969\pi$
$888$	11.0420	+	38.4108i	0.370545	+	1.28898i
$889$	18.3532	−	4.91771i	0.615545	−	0.164935i
$890$	−2.99674	+	0.575515i	−0.100451	+	0.0192913i
$891$	33.5520	+	18.4453i	1.12403	+	0.617940i
$892$	−13.6883	+	31.8486i	−0.458320	+	1.06637i
$893$	40.1943	+	5.29168i	1.34505	+	0.177079i
$894$	0.513889	+	0.627935i	0.0171870	+	0.0210013i
$895$	1.20763	−	0.697228i	0.0403668	−	0.0233058i
$896$	−5.51842	+	49.1819i	−0.184358	+	1.64305i
$897$	−8.57060	−	22.4148i	−0.286164	−	0.748409i
$898$	34.4328	+	30.6019i	1.14904	+	1.02120i
$899$	2.45381	−	1.01640i	0.0818392	−	0.0338989i
$900$	−5.84352	+	28.9606i	−0.194784	+	0.965352i
$901$	2.25701	−	5.44890i	0.0751918	−	0.181529i
$902$	−21.2726	−	7.37830i	−0.708300	−	0.245671i
$903$	−21.2220	−	29.2901i	−0.706223	−	0.974712i
$904$	1.34979	−	15.7880i	0.0448933	−	0.525101i
$905$	0.0956580	−	0.357000i	0.00317978	−	0.0118671i
$906$	−22.2406	−	20.8882i	−0.738896	−	0.693963i
$907$	−28.9894	−	37.7797i	−0.962577	−	1.25445i	−0.967082	−	0.254464i	$-0.918101\pi$
$907$	−28.9894	−	37.7797i	−0.962577	−	1.25445i	0.00450550	−	0.999990i	$-0.498566\pi$
$908$	45.6326	+	0.603521i	1.51437	+	0.0200285i
$909$	−7.20862	+	0.548350i	−0.239095	+	0.0181876i
$910$	−3.73123	−	5.66492i	−0.123689	−	0.187790i
$911$	28.9759	+	16.7292i	0.960015	+	0.554265i	0.896178	−	0.443696i	$-0.146333\pi$
$911$	28.9759	+	16.7292i	0.960015	+	0.554265i	0.0638371	+	0.997960i	$0.479666\pi$
$912$	18.1831	+	51.6061i	0.602101	+	1.70885i
$913$	−48.8058	+	28.1781i	−1.61524	+	0.932557i
$914$	−8.78359	−	4.40403i	−0.290535	−	0.145672i
$915$	1.06481	−	3.57755i	0.0352017	−	0.118270i
$916$	−1.97960	−	7.79911i	−0.0654079	−	0.257690i
$917$	13.8682	−	33.4808i	0.457968	−	1.10563i
$918$	0.200249	−	8.47333i	0.00660920	−	0.279662i
$919$	27.1244	+	27.1244i	0.894752	+	0.894752i	0.994966	−	0.100214i	$-0.0319529\pi$
$919$	27.1244	+	27.1244i	0.894752	+	0.894752i	−0.100214	+	0.994966i	$0.531953\pi$
$920$	−1.83014	+	2.00520i	−0.0603380	+	0.0661096i
$921$	−0.0787481	−	0.758789i	−0.00259484	−	0.0250029i
$922$	20.7387	+	23.9658i	0.682993	+	0.789272i
$923$	7.16051	−	0.942700i	0.235691	−	0.0310293i
$924$	−43.6908	−	47.4015i	−1.43732	−	1.55940i
$925$	5.24335	−	39.8272i	0.172400	−	1.30951i
$926$	31.0510	+	6.39016i	1.02040	+	0.209994i
$927$	−19.6261	−	21.9121i	−0.644606	−	0.719687i
$928$	28.6493	−	39.9515i	0.940458	−	1.31147i
$929$	−20.0830	−	11.5949i	−0.658901	−	0.380417i	0.132957	−	0.991122i	$-0.457553\pi$
$929$	−20.0830	−	11.5949i	−0.658901	−	0.380417i	−0.791858	+	0.610705i	$0.790886\pi$
$930$	−0.0729429	+	0.192999i	−0.00239189	+	0.00632867i
$931$	58.3429	−	76.0340i	1.91211	−	2.49191i
$932$	2.07078	−	2.62604i	0.0678306	−	0.0860188i
$933$	22.6764	−	36.8960i	0.742392	−	1.20792i
$934$	−40.6048	−	14.0836i	−1.32863	−	0.460829i
$935$	0.956275	+	0.956275i	0.0312735	+	0.0312735i
$936$	−32.5244	−	9.04216i	−1.06309	−	0.295552i
$937$	−26.6790	+	26.6790i	−0.871566	+	0.871566i	−0.992643	−	0.121077i	$-0.961365\pi$
$937$	−26.6790	+	26.6790i	−0.871566	+	0.871566i	0.121077	+	0.992643i	$0.461365\pi$
$938$	37.3303	−	18.1034i	1.21888	−	0.591097i
$939$	0.186673	−	6.78920i	0.00609183	−	0.221557i
$940$	2.72332	+	0.768452i	0.0888249	+	0.0250641i
$941$	35.6132	+	27.3269i	1.16096	+	0.890833i	0.995441	−	0.0953747i	$-0.0304049\pi$
$941$	35.6132	+	27.3269i	1.16096	+	0.890833i	0.165514	+	0.986207i	$0.447072\pi$
$942$	0.0161220	−	0.161412i	0.000525284	−	0.00525909i
$943$	6.51658	−	11.2870i	0.212209	−	0.367557i
$944$	−9.82902	+	3.76996i	−0.319907	+	0.122702i
$945$	−2.86600	+	5.57067i	−0.0932311	+	0.181214i
$946$	23.9860	−	15.7985i	0.779852	−	0.513654i
$947$	−20.8260	−	2.74180i	−0.676754	−	0.0890964i	−0.215688	−	0.976462i	$-0.569199\pi$
$947$	−20.8260	−	2.74180i	−0.676754	−	0.0890964i	−0.461066	+	0.887366i	$0.652533\pi$
$948$	−2.66962	+	3.20046i	−0.0867052	+	0.103946i
$949$	−1.09853	−	8.34418i	−0.0356599	−	0.270864i
$950$	3.95968	−	54.8529i	0.128469	−	1.77966i
$951$	14.3034	−	32.0132i	0.463821	−	1.03810i
$952$	−4.85426	+	13.4196i	−0.157328	+	0.434931i
$953$	−25.8235	+	25.8235i	−0.836506	+	0.836506i	−0.988397	−	0.151891i	$-0.951464\pi$
$953$	−25.8235	+	25.8235i	−0.836506	+	0.836506i	0.151891	+	0.988397i	$0.451464\pi$
$954$	−2.74866	+	21.5197i	−0.0889912	+	0.696727i
$955$	0.0784382	+	0.0324902i	0.00253820	+	0.00105136i
$956$	−4.36240	−	5.84361i	−0.141090	−	0.188996i
$957$	14.8678	+	62.2877i	0.480607	+	2.01347i
$958$	−5.26794	−	15.8627i	−0.170199	−	0.512500i
$959$	44.5695	+	77.1966i	1.43922	+	2.49281i
$960$	0.738634	+	3.74690i	0.0238393	+	0.120931i
$961$	−15.4533	+	26.7659i	−0.498494	+	0.863416i
$962$	44.9580	+	9.25216i	1.44950	+	0.298302i
$963$	−28.3929	−	41.5445i	−0.914949	−	1.33875i
$964$	−6.88687	+	16.0237i	−0.221811	+	0.516087i
$965$	0.320274	−	0.245755i	0.0103100	−	0.00791114i
$966$	31.7154	−	19.6615i	1.02043	−	0.632597i
$967$	−17.9959	−	4.82199i	−0.578710	−	0.155065i	−0.0424216	−	0.999100i	$-0.513507\pi$
$967$	−17.9959	−	4.82199i	−0.578710	−	0.155065i	−0.536288	+	0.844035i	$0.680174\pi$
$968$	15.3543	−	12.9357i	0.493507	−	0.415769i
$969$	1.62864	+	15.6930i	0.0523193	+	0.504130i
$970$	1.77657	−	0.861551i	0.0570423	−	0.0276627i
$971$	−24.4480	−	10.1267i	−0.784574	−	0.324981i	−0.0458142	−	0.998950i	$-0.514588\pi$
$971$	−24.4480	−	10.1267i	−0.784574	−	0.324981i	−0.738760	+	0.673969i	$0.764588\pi$
$972$	7.47233	+	30.2682i	0.239675	+	0.970853i
$973$	−5.47441	−	13.2164i	−0.175501	−	0.423698i
$974$	2.40077	+	40.7563i	0.0769255	+	1.30592i
$975$	26.3410	+	21.3877i	0.843589	+	0.684955i
$976$	3.26088	+	31.1059i	0.104378	+	0.995677i
$977$	−24.3835	−	42.2334i	−0.780096	−	1.35117i	−0.931885	−	0.362753i	$-0.881837\pi$
$977$	−24.3835	−	42.2334i	−0.780096	−	1.35117i	0.151789	−	0.988413i	$-0.451496\pi$
$978$	−9.37087	+	13.0391i	−0.299647	+	0.416944i
$979$	−4.34725	+	33.0206i	−0.138939	+	1.05534i
$980$	4.79218	−	4.66707i	0.153080	−	0.149084i
$981$	10.4278	−	55.4532i	0.332936	−	1.77049i
$982$	−24.6736	−	16.7234i	−0.787365	−	0.533665i
$983$	7.05891	+	26.3442i	0.225144	+	0.840250i	0.982347	+	0.187070i	$0.0598990\pi$
$983$	7.05891	+	26.3442i	0.225144	+	0.840250i	−0.757202	+	0.653180i	$0.773434\pi$
$984$	−7.32198	−	16.8086i	−0.233416	−	0.535838i
$985$	0.877020	−	3.27308i	0.0279442	−	0.104289i
$986$	10.7195	−	9.27609i	0.341379	−	0.295411i
$987$	−33.1359	−	20.3654i	−1.05473	−	0.648238i
$988$	62.1878	+	9.02537i	1.97846	+	0.287135i
$989$	6.36221	+	15.3597i	0.202306	+	0.488411i
$990$	−4.31768	−	2.47064i	−0.137225	−	0.0785220i
$991$		−	58.5226i		−	1.85903i	−0.368782	−	0.929516i	$-0.620225\pi$
$991$		−	58.5226i		−	1.85903i	0.368782	−	0.929516i	$-0.379775\pi$
$992$	−0.0559821	−	1.72790i	−0.00177743	−	0.0548608i
$993$	−41.8143	+	15.9882i	−1.32694	+	0.507372i
$994$	3.53952	+	10.6581i	0.112267	+	0.338055i
$995$	−0.232410	−	0.178334i	−0.00736789	−	0.00565358i
$996$	−43.8056	−	13.6714i	−1.38803	−	0.433194i
$997$	−8.50249	−	11.0807i	−0.269276	−	0.350928i	0.639068	−	0.769150i	$-0.279320\pi$
$997$	−8.50249	−	11.0807i	−0.269276	−	0.350928i	−0.908345	+	0.418222i	$0.862653\pi$
$998$	−8.85267	+	1.70013i	−0.280226	+	0.0538167i
$999$	−12.9411	−	40.3672i	−0.409438	−	1.27716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.13	✓	368
3.2	odd	2		864.2.bn.a.683.34		368
9.4	even	3		864.2.bn.a.395.18		368
9.5	odd	6	inner	288.2.bf.a.203.29	yes	368
32.3	odd	8	inner	288.2.bf.a.227.29	yes	368
96.35	even	8		864.2.bn.a.35.18		368
288.67	odd	24		864.2.bn.a.611.34		368
288.131	even	24	inner	288.2.bf.a.131.13	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.13	✓	368	1.1	even	1	trivial
288.2.bf.a.131.13	yes	368	288.131	even	24	inner
288.2.bf.a.203.29	yes	368	9.5	odd	6	inner
288.2.bf.a.227.29	yes	368	32.3	odd	8	inner
864.2.bn.a.35.18		368	96.35	even	8
864.2.bn.a.395.18		368	9.4	even	3
864.2.bn.a.611.34		368	288.67	odd	24
864.2.bn.a.683.34		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939466 + 1.05707i) q^{2} +(-0.494102 + 1.66008i) q^{3} +(-0.234807 - 1.98617i) q^{4} +(-0.0359748 - 0.273256i) q^{5} +(-1.29063 - 2.08189i) q^{6} +(-1.13217 - 4.22533i) q^{7} +(2.32012 + 1.61773i) q^{8} +(-2.51173 - 1.64050i) q^{9} +O(q^{10})\)	\(q+(-0.939466 + 1.05707i) q^{2} +(-0.494102 + 1.66008i) q^{3} +(-0.234807 - 1.98617i) q^{4} +(-0.0359748 - 0.273256i) q^{5} +(-1.29063 - 2.08189i) q^{6} +(-1.13217 - 4.22533i) q^{7} +(2.32012 + 1.61773i) q^{8} +(-2.51173 - 1.64050i) q^{9} +(0.322648 + 0.218686i) q^{10} +(3.37509 - 2.58980i) q^{11} +(3.41322 + 0.591572i) q^{12} +(2.42190 - 3.15628i) q^{13} +(5.53013 + 2.77277i) q^{14} +(0.471401 + 0.0752951i) q^{15} +(-3.88973 + 0.932732i) q^{16} -1.15340 q^{17} +(4.09381 - 1.11389i) q^{18} +(-7.29638 + 3.02226i) q^{19} +(-0.534285 + 0.135614i) q^{20} +(7.57380 + 0.208246i) q^{21} +(-0.433178 + 6.00075i) q^{22} +(-3.36387 - 0.901347i) q^{23} +(-3.83194 + 3.05226i) q^{24} +(4.75625 - 1.27443i) q^{25} +(1.06113 + 5.52535i) q^{26} +(3.96440 - 3.35909i) q^{27} +(-8.12638 + 3.24083i) q^{28} +(8.61635 + 1.13436i) q^{29} +(-0.522458 + 0.427568i) q^{30} +(0.264668 - 0.152806i) q^{31} +(2.66831 - 4.98800i) q^{32} +(2.63163 + 6.88255i) q^{33} +(1.08358 - 1.21922i) q^{34} +(-1.11387 + 0.461379i) q^{35} +(-2.66853 + 5.37391i) q^{36} +(3.12198 - 7.53711i) q^{37} +(3.65995 - 10.5521i) q^{38} +(4.04301 + 5.58007i) q^{39} +(0.358588 - 0.692183i) q^{40} +(-0.968613 + 3.61491i) q^{41} +(-7.33546 + 7.81042i) q^{42} +(-2.90616 - 3.78738i) q^{43} +(-5.93627 - 6.09540i) q^{44} +(-0.357916 + 0.745360i) q^{45} +(4.11303 - 2.70907i) q^{46} +(-4.44564 - 2.56669i) q^{47} +(0.373515 - 6.91813i) q^{48} +(-10.5094 + 6.06763i) q^{49} +(-3.12117 + 6.22500i) q^{50} +(0.569895 - 1.91473i) q^{51} +(-6.83759 - 4.06919i) q^{52} +(-1.95684 + 4.72422i) q^{53} +(-0.173617 + 7.34642i) q^{54} +(-0.829095 - 0.829095i) q^{55} +(4.20867 - 11.6348i) q^{56} +(-1.41203 - 13.6059i) q^{57} +(-9.29388 + 8.04242i) q^{58} +(2.60929 - 0.343519i) q^{59} +(0.0388606 - 0.953962i) q^{60} +(1.02060 - 7.75221i) q^{61} +(-0.0871194 + 0.423330i) q^{62} +(-4.08793 + 12.4702i) q^{63} +(2.76590 + 7.50665i) q^{64} +(-0.949600 - 0.548252i) q^{65} +(-9.74768 - 3.68409i) q^{66} +(4.08265 - 5.32061i) q^{67} +(0.270825 + 2.29084i) q^{68} +(3.15840 - 5.13894i) q^{69} +(0.558729 - 1.61089i) q^{70} +(1.28366 + 1.28366i) q^{71} +(-3.17362 - 7.86944i) q^{72} +(1.49586 - 1.49586i) q^{73} +(5.03429 + 10.3810i) q^{74} +(-0.234412 + 8.52546i) q^{75} +(7.71595 + 13.7822i) q^{76} +(-14.7640 - 11.3288i) q^{77} +(-9.69682 - 0.968529i) q^{78} +(-0.601557 + 1.04193i) q^{79} +(0.394807 + 1.02934i) q^{80} +(3.61754 + 8.24096i) q^{81} +(-2.91125 - 4.41998i) q^{82} +(-13.1338 - 1.72910i) q^{83} +(-1.36477 - 15.0917i) q^{84} +(0.0414932 + 0.315172i) q^{85} +(6.73378 + 0.486093i) q^{86} +(-6.14049 + 13.7433i) q^{87} +(12.0202 - 0.548653i) q^{88} +(-5.53583 + 5.53583i) q^{89} +(-0.451650 - 1.07858i) q^{90} +(-16.0784 - 6.65988i) q^{91} +(-1.00037 + 6.89286i) q^{92} +(0.122897 + 0.514872i) q^{93} +(6.88971 - 2.28805i) q^{94} +(1.08833 + 1.88505i) q^{95} +(6.96206 + 6.89418i) q^{96} +(2.53281 - 4.38695i) q^{97} +(3.45934 - 16.8096i) q^{98} +(-12.7259 + 0.968040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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