LMFDB - Embedded newform 324.2.p.a.59.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			59.35
Character	$\chi$	$=$	324.59
Dual form			324.2.p.a.11.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.627654 + 1.26730i) q^{2} +(-1.64246 - 0.549842i) q^{3} +(-1.21210 + 1.59085i) q^{4} +(-0.0995817 - 0.851976i) q^{5} +(-0.334081 - 2.42660i) q^{6} +(2.18215 - 4.34501i) q^{7} +(-2.77687 - 0.537591i) q^{8} +(2.39535 + 1.80619i) q^{9} +O(q^{10})$	\(q+(0.627654 + 1.26730i) q^{2} +(-1.64246 - 0.549842i) q^{3} +(-1.21210 + 1.59085i) q^{4} +(-0.0995817 - 0.851976i) q^{5} +(-0.334081 - 2.42660i) q^{6} +(2.18215 - 4.34501i) q^{7} +(-2.77687 - 0.537591i) q^{8} +(2.39535 + 1.80619i) q^{9} +(1.01721 - 0.660946i) q^{10} +(-1.18262 - 2.74163i) q^{11} +(2.86554 - 1.94645i) q^{12} +(-0.988870 - 0.234367i) q^{13} +(6.87607 + 0.0382718i) q^{14} +(-0.304893 + 1.45409i) q^{15} +(-1.06162 - 3.85655i) q^{16} +(3.36460 + 0.593269i) q^{17} +(-0.785532 + 4.16929i) q^{18} +(4.15287 - 0.732262i) q^{19} +(1.47607 + 0.874261i) q^{20} +(-5.97316 + 5.93667i) q^{21} +(2.73219 - 3.21954i) q^{22} +(0.229993 - 0.115507i) q^{23} +(4.26530 + 2.40981i) q^{24} +(4.14928 - 0.983397i) q^{25} +(-0.323656 - 1.40030i) q^{26} +(-2.94114 - 4.28365i) q^{27} +(4.26729 + 8.73806i) q^{28} +(-5.02900 - 1.50558i) q^{29} +(-2.03414 + 0.526274i) q^{30} +(-1.05850 + 1.60937i) q^{31} +(4.22107 - 3.76597i) q^{32} +(0.434949 + 5.15328i) q^{33} +(1.35995 + 4.63632i) q^{34} +(-3.91915 - 1.42645i) q^{35} +(-5.77678 + 1.62136i) q^{36} +(6.03610 - 2.19696i) q^{37} +(3.53456 + 4.80332i) q^{38} +(1.49532 + 0.928660i) q^{39} +(-0.181489 + 2.41936i) q^{40} +(-1.06233 - 1.00226i) q^{41} +(-11.2726 - 3.84361i) q^{42} +(-10.2861 - 7.65769i) q^{43} +(5.79499 + 1.44175i) q^{44} +(1.30029 - 2.22064i) q^{45} +(0.290738 + 0.218972i) q^{46} +(-7.35304 + 4.83617i) q^{47} +(-0.376820 + 6.91795i) q^{48} +(-9.93725 - 13.3480i) q^{49} +(3.85057 + 4.64115i) q^{50} +(-5.20001 - 2.82442i) q^{51} +(1.57145 - 1.28907i) q^{52} +(-1.29597 - 0.748231i) q^{53} +(3.58265 - 6.41596i) q^{54} +(-2.21804 + 1.28058i) q^{55} +(-8.39537 + 10.8924i) q^{56} +(-7.22354 - 1.08071i) q^{57} +(-1.24844 - 7.31824i) q^{58} +(-3.76029 + 8.71733i) q^{59} +(-1.94368 - 2.24754i) q^{60} +(0.438061 + 7.52121i) q^{61} +(-2.70394 - 0.331310i) q^{62} +(13.0749 - 6.46645i) q^{63} +(7.42199 + 2.98564i) q^{64} +(-0.101201 + 0.865832i) q^{65} +(-6.25775 + 3.78569i) q^{66} +(11.2877 - 3.37931i) q^{67} +(-5.02203 + 4.63347i) q^{68} +(-0.441264 + 0.0632554i) q^{69} +(-0.652124 - 5.86205i) q^{70} +(10.9032 + 9.14888i) q^{71} +(-5.68057 - 6.30326i) q^{72} +(4.25462 - 3.57005i) q^{73} +(6.57279 + 6.27062i) q^{74} +(-7.35574 - 0.666258i) q^{75} +(-3.86877 + 7.49417i) q^{76} +(-14.4931 - 0.844126i) q^{77} +(-0.238351 + 2.47789i) q^{78} +(-1.01905 + 0.961422i) q^{79} +(-3.17997 + 1.28852i) q^{80} +(2.47538 + 8.65289i) q^{81} +(0.603385 - 1.97536i) q^{82} +(11.1449 + 11.8129i) q^{83} +(-2.20429 - 16.6983i) q^{84} +(0.170399 - 2.92563i) q^{85} +(3.24851 - 17.8419i) q^{86} +(7.43209 + 5.23801i) q^{87} +(1.81012 + 8.24892i) q^{88} +(0.274740 + 0.327422i) q^{89} +(3.63035 + 0.254070i) q^{90} +(-3.17619 + 3.78523i) q^{91} +(-0.0950203 + 0.505890i) q^{92} +(2.62345 - 2.06132i) q^{93} +(-10.7440 - 6.28307i) q^{94} +(-1.03742 - 3.46522i) q^{95} +(-9.00363 + 3.86453i) q^{96} +(4.40766 + 0.515182i) q^{97} +(10.6788 - 20.9714i) q^{98} +(2.11910 - 8.70320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{41}{54}\right)$

Coefficient data

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

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

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

$2$	0.627654	+	1.26730i	0.443818	+	0.896117i
$2$	0.627654	+	1.26730i	0.443818	+	0.896117i
$3$	−1.64246	−	0.549842i	−0.948275	−	0.317451i
$3$	−1.64246	−	0.549842i	−0.948275	−	0.317451i
$4$	−1.21210	+	1.59085i	−0.606050	+	0.795426i
$5$	−0.0995817	−	0.851976i	−0.0445343	−	0.381015i	−0.997064	−	0.0765701i	$-0.975603\pi$
$5$	−0.0995817	−	0.851976i	−0.0445343	−	0.381015i	0.952530	−	0.304445i	$-0.0984710\pi$
$6$	−0.334081	−	2.42660i	−0.136388	−	0.990655i
$7$	2.18215	−	4.34501i	0.824774	−	1.64226i	0.0597894	−	0.998211i	$-0.480957\pi$
$7$	2.18215	−	4.34501i	0.824774	−	1.64226i	0.764984	−	0.644049i	$-0.222747\pi$
$8$	−2.77687	−	0.537591i	−0.981771	−	0.190067i
$9$	2.39535	+	1.80619i	0.798449	+	0.602062i
$10$	1.01721	−	0.660946i	0.321669	−	0.209009i
$11$	−1.18262	−	2.74163i	−0.356575	−	0.826633i	−0.998220	−	0.0596320i	$-0.981007\pi$
$11$	−1.18262	−	2.74163i	−0.356575	−	0.826633i	0.641646	−	0.767001i	$-0.278252\pi$
$12$	2.86554	−	1.94645i	0.827211	−	0.561891i
$13$	−0.988870	−	0.234367i	−0.274263	−	0.0650016i	0.0911826	−	0.995834i	$-0.470935\pi$
$13$	−0.988870	−	0.234367i	−0.274263	−	0.0650016i	−0.365446	+	0.930833i	$0.619083\pi$
$14$	6.87607	+	0.0382718i	1.83771	+	0.0102286i
$15$	−0.304893	+	1.45409i	−0.0787231	+	0.375444i
$16$	−1.06162	−	3.85655i	−0.265406	−	0.964137i
$17$	3.36460	+	0.593269i	0.816034	+	0.143889i	0.566060	−	0.824364i	$-0.308467\pi$
$17$	3.36460	+	0.593269i	0.816034	+	0.143889i	0.249974	+	0.968253i	$0.419578\pi$
$18$	−0.785532	+	4.16929i	−0.185152	+	0.982710i
$19$	4.15287	−	0.732262i	0.952733	−	0.167992i	0.324385	−	0.945925i	$-0.394843\pi$
$19$	4.15287	−	0.732262i	0.952733	−	0.167992i	0.628348	+	0.777933i	$0.283732\pi$
$20$	1.47607	+	0.874261i	0.330059	+	0.195491i
$21$	−5.97316	+	5.93667i	−1.30345	+	1.29549i
$22$	2.73219	−	3.21954i	0.582505	−	0.686408i
$23$	0.229993	−	0.115507i	0.0479568	−	0.0240848i	−0.424659	−	0.905353i	$-0.639606\pi$
$23$	0.229993	−	0.115507i	0.0479568	−	0.0240848i	0.472616	+	0.881268i	$0.343310\pi$
$24$	4.26530	+	2.40981i	0.870651	+	0.491901i
$25$	4.14928	−	0.983397i	0.829856	−	0.196679i
$26$	−0.323656	−	1.40030i	−0.0634741	−	0.274621i
$27$	−2.94114	−	4.28365i	−0.566023	−	0.824389i
$28$	4.26729	+	8.73806i	0.806442	+	1.65134i
$29$	−5.02900	−	1.50558i	−0.933861	−	0.279580i	−0.216501	−	0.976282i	$-0.569465\pi$
$29$	−5.02900	−	1.50558i	−0.933861	−	0.279580i	−0.717360	+	0.696703i	$0.754650\pi$
$30$	−2.03414	+	0.526274i	−0.371381	+	0.0960840i
$31$	−1.05850	+	1.60937i	−0.190113	+	0.289052i	−0.917949	−	0.396699i	$-0.870156\pi$
$31$	−1.05850	+	1.60937i	−0.190113	+	0.289052i	0.727836	+	0.685751i	$0.240526\pi$
$32$	4.22107	−	3.76597i	0.746187	−	0.665736i
$33$	0.434949	+	5.15328i	0.0757148	+	0.897070i
$34$	1.35995	+	4.63632i	0.233230	+	0.795123i
$35$	−3.91915	−	1.42645i	−0.662456	−	0.241114i
$36$	−5.77678	+	1.62136i	−0.962797	+	0.270227i
$37$	6.03610	−	2.19696i	0.992328	−	0.361178i	0.205707	−	0.978614i	$-0.434051\pi$
$37$	6.03610	−	2.19696i	0.992328	−	0.361178i	0.786621	+	0.617436i	$0.211828\pi$
$38$	3.53456	+	4.80332i	0.573381	+	0.779202i
$39$	1.49532	+	0.928660i	0.239442	+	0.148705i
$40$	−0.181489	+	2.41936i	−0.0286960	+	0.382534i
$41$	−1.06233	−	1.00226i	−0.165908	−	0.156526i	0.598810	−	0.800891i	$-0.295640\pi$
$41$	−1.06233	−	1.00226i	−0.165908	−	0.156526i	−0.764718	+	0.644365i	$0.777122\pi$
$42$	−11.2726	−	3.84361i	−1.73940	−	0.593082i
$43$	−10.2861	−	7.65769i	−1.56861	−	1.16779i	−0.909472	−	0.415765i	$-0.863514\pi$
$43$	−10.2861	−	7.65769i	−1.56861	−	1.16779i	−0.659138	−	0.752022i	$-0.729079\pi$
$44$	5.79499	+	1.44175i	0.873628	+	0.217353i
$45$	1.30029	−	2.22064i	0.193836	−	0.331034i
$46$	0.290738	+	0.218972i	0.0428669	+	0.0322856i
$47$	−7.35304	+	4.83617i	−1.07255	+	0.705428i	−0.957646	−	0.287949i	$-0.907027\pi$
$47$	−7.35304	+	4.83617i	−1.07255	+	0.705428i	−0.114905	+	0.993377i	$0.536656\pi$
$48$	−0.376820	+	6.91795i	−0.0543892	+	0.998520i
$49$	−9.93725	−	13.3480i	−1.41961	−	1.90686i
$50$	3.85057	+	4.64115i	0.544553	+	0.656358i
$51$	−5.20001	−	2.82442i	−0.728147	−	0.395497i
$52$	1.57145	−	1.28907i	0.217921	−	0.178762i
$53$	−1.29597	−	0.748231i	−0.178016	−	0.102777i	0.408344	−	0.912828i	$-0.366106\pi$
$53$	−1.29597	−	0.748231i	−0.178016	−	0.102777i	−0.586360	+	0.810051i	$0.699440\pi$
$54$	3.58265	−	6.41596i	0.487537	−	0.873102i
$55$	−2.21804	+	1.28058i	−0.299080	+	0.172674i
$56$	−8.39537	+	10.8924i	−1.12188	+	1.45556i
$57$	−7.22354	−	1.08071i	−0.956782	−	0.143143i
$58$	−1.24844	−	7.31824i	−0.163929	−	0.960931i
$59$	−3.76029	+	8.71733i	−0.489548	+	1.13490i	0.477113	+	0.878842i	$0.341683\pi$
$59$	−3.76029	+	8.71733i	−0.489548	+	1.13490i	−0.966661	+	0.256058i	$0.917576\pi$
$60$	−1.94368	−	2.24754i	−0.250928	−	0.290157i
$61$	0.438061	+	7.52121i	0.0560879	+	0.962993i	0.902561	+	0.430562i	$0.141684\pi$
$61$	0.438061	+	7.52121i	0.0560879	+	0.962993i	−0.846473	+	0.532431i	$0.821278\pi$
$62$	−2.70394	−	0.331310i	−0.343400	−	0.0420764i
$63$	13.0749	−	6.46645i	1.64728	−	0.814696i
$64$	7.42199	+	2.98564i	0.927749	+	0.373205i
$65$	−0.101201	+	0.865832i	−0.0125525	+	0.107393i
$66$	−6.25775	+	3.78569i	−0.770276	+	0.465986i
$67$	11.2877	−	3.37931i	1.37901	−	0.412848i	0.490394	−	0.871501i	$-0.336853\pi$
$67$	11.2877	−	3.37931i	1.37901	−	0.412848i	0.888616	+	0.458652i	$0.151668\pi$
$68$	−5.02203	+	4.63347i	−0.609011	+	0.561891i
$69$	−0.441264	+	0.0632554i	−0.0531220	+	0.00761506i
$70$	−0.652124	−	5.86205i	−0.0779437	−	0.700649i
$71$	10.9032	+	9.14888i	1.29397	+	1.08577i	0.991153	+	0.132724i	$0.0423725\pi$
$71$	10.9032	+	9.14888i	1.29397	+	1.08577i	0.302820	+	0.953048i	$0.402072\pi$
$72$	−5.68057	−	6.30326i	−0.669462	−	0.742846i
$73$	4.25462	−	3.57005i	0.497966	−	0.417843i	−0.358905	−	0.933374i	$-0.616850\pi$
$73$	4.25462	−	3.57005i	0.497966	−	0.417843i	0.856871	+	0.515531i	$0.172405\pi$
$74$	6.57279	+	6.27062i	0.764071	+	0.728944i
$75$	−7.35574	−	0.666258i	−0.849367	−	0.0769328i
$76$	−3.86877	+	7.49417i	−0.443778	+	0.859640i
$77$	−14.4931	−	0.844126i	−1.65164	−	0.0961971i
$78$	−0.238351	+	2.47789i	−0.0269879	+	0.280566i
$79$	−1.01905	+	0.961422i	−0.114652	+	0.108168i	−0.741433	−	0.671027i	$-0.765853\pi$
$79$	−1.01905	+	0.961422i	−0.114652	+	0.108168i	0.626781	+	0.779195i	$0.284372\pi$
$80$	−3.17997	+	1.28852i	−0.355531	+	0.144061i
$81$	2.47538	+	8.65289i	0.275042	+	0.961432i
$82$	0.603385	−	1.97536i	0.0666328	−	0.218142i
$83$	11.1449	+	11.8129i	1.22331	+	1.29663i	0.941441	+	0.337177i	$0.109472\pi$
$83$	11.1449	+	11.8129i	1.22331	+	1.29663i	0.281867	+	0.959454i	$0.409046\pi$
$84$	−2.20429	−	16.6983i	−0.240508	−	1.82193i
$85$	0.170399	−	2.92563i	0.0184823	−	0.317329i
$86$	3.24851	−	17.8419i	0.350295	−	1.92394i
$87$	7.43209	+	5.23801i	0.796804	+	0.561574i
$88$	1.81012	+	8.24892i	0.192959	+	0.879338i
$89$	0.274740	+	0.327422i	0.0291224	+	0.0347067i	0.780409	−	0.625269i	$-0.215011\pi$
$89$	0.274740	+	0.327422i	0.0291224	+	0.0347067i	−0.751287	+	0.659976i	$0.770566\pi$
$90$	3.63035	+	0.254070i	0.382673	+	0.0267813i
$91$	−3.17619	+	3.78523i	−0.332955	+	0.396800i
$92$	−0.0950203	+	0.505890i	−0.00990655	+	0.0527427i
$93$	2.62345	−	2.06132i	0.272039	−	0.213749i
$94$	−10.7440	−	6.28307i	−1.10816	−	0.648049i
$95$	−1.03742	−	3.46522i	−0.106437	−	0.355524i
$96$	−9.00363	+	3.86453i	−0.918929	+	0.394422i
$97$	4.40766	+	0.515182i	0.447530	+	0.0523088i	0.336873	−	0.941550i	$-0.390631\pi$
$97$	4.40766	+	0.515182i	0.447530	+	0.0523088i	0.110657	+	0.993859i	$0.464705\pi$
$98$	10.6788	−	20.9714i	1.07872	−	2.11843i
$99$	2.11910	−	8.70320i	0.212978	−	0.874705i
$100$	−3.46490	+	7.79287i	−0.346490	+	0.779287i
$101$	−7.72019	+	0.449650i	−0.768188	+	0.0447418i	−0.437763	−	0.899090i	$-0.644229\pi$
$101$	−7.72019	+	0.449650i	−0.768188	+	0.0447418i	−0.330425	+	0.943832i	$0.607192\pi$
$102$	0.315579	−	8.36273i	0.0312469	−	0.828034i
$103$	−1.29985	−	0.560699i	−0.128078	−	0.0552473i	0.331077	−	0.943604i	$-0.392588\pi$
$103$	−1.29985	−	0.560699i	−0.128078	−	0.0552473i	−0.459154	+	0.888357i	$0.651847\pi$
$104$	2.61997	+	1.18241i	0.256909	+	0.115945i
$105$	5.65271	+	4.49780i	0.551648	+	0.438940i
$106$	0.134810	−	2.11202i	0.0130939	−	0.205137i
$107$	0.299682	+	0.519064i	0.0289713	+	0.0501798i	0.880148	−	0.474700i	$-0.157444\pi$
$107$	0.299682	+	0.519064i	0.0289713	+	0.0501798i	−0.851176	+	0.524880i	$0.824110\pi$
$108$	10.3796	+	0.513293i	0.998779	+	0.0493916i
$109$	−2.69384	+	4.66586i	−0.258023	+	0.446908i	−0.965712	−	0.259615i	$-0.916404\pi$
$109$	−2.69384	+	4.66586i	−0.258023	+	0.446908i	0.707689	+	0.706524i	$0.249738\pi$
$110$	−3.01504	−	2.00715i	−0.287473	−	0.191375i
$111$	−11.1220	+	0.289517i	−1.05566	+	0.0274798i
$112$	−19.0734	−	3.80279i	−1.80226	−	0.359330i
$113$	9.77100	−	7.27424i	0.919178	−	0.684303i	−0.0298299	−	0.999555i	$-0.509497\pi$
$113$	9.77100	−	7.27424i	0.919178	−	0.684303i	0.949008	+	0.315252i	$0.102089\pi$
$114$	−3.16430	−	9.83271i	−0.296364	−	0.920918i
$115$	−0.121312	−	0.184446i	−0.0113124	−	0.0171997i
$116$	8.49081	−	6.17547i	0.788352	−	0.573378i
$117$	−1.94538	−	2.34747i	−0.179850	−	0.217024i
$118$	−13.4076	+	0.706051i	−1.23427	+	0.0649973i
$119$	9.91980	−	13.3246i	0.909347	−	1.22146i
$120$	1.62835	−	3.87391i	0.148648	−	0.353638i
$121$	1.43071	−	1.51647i	0.130065	−	0.137861i
$122$	−9.25669	+	5.27588i	−0.838061	+	0.477655i
$123$	1.19375	+	2.23028i	0.107637	+	0.201098i
$124$	−1.27727	−	3.63465i	−0.114702	−	0.326401i
$125$	−2.71791	−	7.46738i	−0.243097	−	0.667903i
$126$	16.4014	+	12.5111i	1.46116	+	1.11458i
$127$	−2.82779	+	7.76928i	−0.250926	+	0.689412i	0.748723	+	0.662884i	$0.230668\pi$
$127$	−2.82779	+	7.76928i	−0.250926	+	0.689412i	−0.999648	+	0.0265287i	$0.991555\pi$
$128$	0.874740	+	11.2798i	0.0773168	+	0.997007i
$129$	12.6839	+	18.2332i	1.11676	+	1.60534i
$130$	−1.16079	+	0.415191i	−0.101808	+	0.0364146i
$131$	−12.3604	−	8.12955i	−1.07993	−	0.710282i	−0.120639	−	0.992696i	$-0.538494\pi$
$131$	−12.3604	−	8.12955i	−1.07993	−	0.710282i	−0.959292	+	0.282415i	$0.908865\pi$
$132$	−8.72530	−	5.55435i	−0.759440	−	0.483444i
$133$	5.88047	−	19.6421i	0.509902	−	1.70319i
$134$	11.3674	+	12.1838i	0.981990	+	1.05252i
$135$	−3.35668	+	2.93236i	−0.288897	+	0.252377i
$136$	−9.02410	−	3.45621i	−0.773810	−	0.296367i
$137$	3.37481	+	14.2394i	0.288330	+	1.21656i	0.903647	+	0.428278i	$0.140880\pi$
$137$	3.37481	+	14.2394i	0.288330	+	1.21656i	−0.615317	+	0.788279i	$0.710972\pi$
$138$	−0.357125	−	0.519512i	−0.0304005	−	0.0442238i
$139$	8.65834	+	17.2402i	0.734390	+	1.46229i	0.881010	+	0.473098i	$0.156865\pi$
$139$	8.65834	+	17.2402i	0.734390	+	1.46229i	−0.146619	+	0.989193i	$0.546839\pi$
$140$	7.01967	−	4.50578i	0.593271	−	0.380808i
$141$	14.7362	−	3.90020i	1.24101	−	0.328456i
$142$	−4.75094	+	19.5600i	−0.398690	+	1.64144i
$143$	0.526916	+	2.98829i	0.0440629	+	0.249893i
$144$	4.42269	−	11.1553i	0.368558	−	0.929605i
$145$	−0.781924	+	4.43451i	−0.0649353	+	0.368266i
$146$	7.19476	+	3.15113i	0.595442	+	0.260789i
$147$	8.98221	+	27.3875i	0.740840	+	2.25889i
$148$	−3.82132	+	12.2655i	−0.314111	+	1.00822i
$149$	0.943304	−	3.98011i	0.0772785	−	0.326063i	−0.920651	−	0.390388i	$-0.872341\pi$
$149$	0.943304	−	3.98011i	0.0772785	−	0.326063i	0.997929	+	0.0643242i	$0.0204892\pi$
$150$	−3.77251	−	9.74011i	−0.308024	−	0.795276i
$151$	−6.84900	+	2.95437i	−0.557364	+	0.240423i	−0.656079	−	0.754693i	$-0.727786\pi$
$151$	−6.84900	+	2.95437i	−0.557364	+	0.240423i	0.0987150	+	0.995116i	$0.468527\pi$
$152$	−11.9256	−	0.199148i	−0.967295	−	0.0161531i
$153$	6.98782	+	7.49817i	0.564932	+	0.606191i
$154$	−8.02688	−	18.8969i	−0.646824	−	1.52276i
$155$	1.47656	+	0.741554i	0.118600	+	0.0595631i
$156$	−3.28983	+	1.25320i	−0.263398	+	0.100336i
$157$	13.9280	−	1.62795i	1.11157	−	0.129924i	0.459571	−	0.888141i	$-0.348003\pi$
$157$	13.9280	−	1.62795i	1.11157	−	0.129924i	0.652002	+	0.758217i	$0.273929\pi$
$158$	−1.85802	−	0.687999i	−0.147816	−	0.0547343i
$159$	1.71718	+	1.94152i	0.136181	+	0.153973i
$160$	−3.62886	−	3.22123i	−0.286886	−	0.254661i
$161$		−	1.25137i		−	0.0986221i
$162$	−9.41213	+	8.56807i	−0.739487	+	0.673171i
$163$			3.76444i			0.294854i	0.989073	+	0.147427i	$0.0470992\pi$
$163$			3.76444i			0.294854i	−0.989073	+	0.147427i	$0.952901\pi$
$164$	2.88210	−	0.475174i	0.225054	−	0.0371049i
$165$	4.34715	−	0.883738i	0.338425	−	0.0687989i
$166$	−7.97533	+	21.5383i	−0.619006	+	1.67170i
$167$	−2.11735	+	0.247483i	−0.163845	+	0.0191508i	−0.197620	−	0.980279i	$-0.563321\pi$
$167$	−2.11735	+	0.247483i	−0.163845	+	0.0191508i	0.0337746	+	0.999429i	$0.489247\pi$
$168$	19.7782	−	13.2742i	1.52592	−	1.02413i
$169$	−10.6943	−	5.37087i	−0.822637	−	0.413144i
$170$	3.81461	−	1.62034i	0.292567	−	0.124274i
$171$	11.2702	+	5.74683i	0.861850	+	0.439471i
$172$	24.6500	−	7.08172i	1.87955	−	0.539976i
$173$	−6.14942	+	2.65260i	−0.467532	+	0.201673i	−0.616795	−	0.787124i	$-0.711569\pi$
$173$	−6.14942	+	2.65260i	−0.467532	+	0.201673i	0.149263	+	0.988798i	$0.452310\pi$
$174$	−1.97335	+	12.7064i	−0.149600	+	0.963266i
$175$	4.78146	−	20.1746i	0.361445	−	1.52505i
$176$	−9.31773	+	7.47143i	−0.702351	+	0.563180i
$177$	10.9693	−	12.2503i	0.824502	−	0.920789i
$178$	−0.242501	+	0.553686i	−0.0181762	+	0.0415005i
$179$	2.05657	−	11.6634i	0.153716	−	0.871764i	−0.806235	−	0.591595i	$-0.798498\pi$
$179$	2.05657	−	11.6634i	0.153716	−	0.871764i	0.959951	−	0.280169i	$-0.0903905\pi$
$180$	1.95662	+	4.76022i	0.145838	+	0.354806i
$181$	2.89975	+	16.4453i	0.215537	+	1.22237i	0.879973	+	0.475024i	$0.157561\pi$
$181$	2.89975	+	16.4453i	0.215537	+	1.22237i	−0.664436	+	0.747345i	$0.731328\pi$
$182$	−6.79057	−	1.64937i	−0.503351	−	0.122259i
$183$	3.41598	−	12.5942i	0.252517	−	0.930987i
$184$	−0.700755	+	0.197105i	−0.0516603	+	0.0145308i
$185$	−2.47284	−	4.92383i	−0.181807	−	0.362007i
$186$	4.25894	+	2.03090i	0.312280	+	0.148913i
$187$	−2.35253	−	9.92610i	−0.172034	−	0.725868i
$188$	1.21899	−	17.5595i	0.0889042	−	1.28066i
$189$	−25.0305	+	3.43175i	−1.82070	+	0.249623i
$190$	3.74034	−	3.48968i	0.271352	−	0.253168i
$191$	6.36285	−	21.2534i	0.460400	−	1.53784i	−0.341206	−	0.939989i	$-0.610835\pi$
$191$	6.36285	−	21.2534i	0.460400	−	1.53784i	0.801606	−	0.597853i	$-0.203979\pi$
$192$	−10.5487	−	8.98472i	−0.761286	−	0.648416i
$193$	19.5885	+	12.8835i	1.41001	+	0.927377i	0.999882	+	0.0153475i	$0.00488546\pi$
$193$	19.5885	+	12.8835i	1.41001	+	0.927377i	0.410125	+	0.912029i	$0.365485\pi$
$194$	2.11360	+	5.90918i	0.151747	+	0.424255i
$195$	0.642290	−	1.36645i	0.0459953	−	0.0978535i
$196$	33.2797	+	0.370478i	2.37712	+	0.0264627i
$197$	−6.78334	+	18.6371i	−0.483293	+	1.32784i	0.423361	+	0.905961i	$0.360850\pi$
$197$	−6.78334	+	18.6371i	−0.483293	+	1.32784i	−0.906654	+	0.421875i	$0.861372\pi$
$198$	12.3596	−	2.77706i	0.878361	−	0.197357i
$199$	5.74801	+	15.7925i	0.407465	+	1.11950i	0.958518	+	0.285031i	$0.0920040\pi$
$199$	5.74801	+	15.7925i	0.407465	+	1.11950i	−0.551053	+	0.834470i	$0.685774\pi$
$200$	−12.0507	+	0.500148i	−0.852111	+	0.0353658i
$201$	−20.3976	−	0.656062i	−1.43874	−	0.0462751i
$202$	−5.41545	−	9.50158i	−0.381030	−	0.668529i
$203$	−17.5158	+	18.5656i	−1.22937	+	1.30305i
$204$	10.7962	−	4.84897i	0.755883	−	0.339496i
$205$	−0.748110	+	1.00489i	−0.0522503	+	0.0701843i
$206$	−0.105280	−	1.99922i	−0.00733518	−	0.139292i
$207$	0.759539	+	0.138731i	0.0527916	+	0.00964249i
$208$	0.145961	+	4.06243i	0.0101206	+	0.281679i
$209$	−6.91887	−	10.5196i	−0.478589	−	0.727659i
$210$	−2.15212	+	9.98675i	−0.148510	+	0.689151i
$211$	−8.19483	+	6.10082i	−0.564155	+	0.419998i	−0.841094	−	0.540890i	$-0.818088\pi$
$211$	−8.19483	+	6.10082i	−0.564155	+	0.419998i	0.276938	+	0.960888i	$0.410680\pi$
$212$	2.76118	−	1.15477i	0.189638	−	0.0793100i
$213$	−12.8776	−	21.0217i	−0.882362	−	1.44038i
$214$	−0.469714	+	0.705580i	−0.0321090	+	0.0482324i
$215$	−5.49986	+	9.52604i	−0.375088	+	0.649671i
$216$	5.86431	+	13.4763i	0.399016	+	0.916944i
$217$	4.68294	+	8.11110i	0.317899	+	0.550617i
$218$	−7.60384	−	0.485353i	−0.514997	−	0.0328723i
$219$	−8.95101	+	3.52429i	−0.604853	+	0.238150i
$220$	0.651264	−	5.08076i	0.0439082	−	0.342545i
$221$	−3.18811	−	1.37521i	−0.214455	−	0.0925070i
$222$	−7.34769	−	13.9132i	−0.493145	−	0.933795i
$223$	−11.8409	+	0.689655i	−0.792926	+	0.0461827i	−0.449826	−	0.893116i	$-0.648514\pi$
$223$	−11.8409	+	0.689655i	−0.792926	+	0.0461827i	−0.343100	+	0.939299i	$0.611477\pi$
$224$	−7.15219	−	26.5585i	−0.477876	−	1.77452i
$225$	11.7152	+	5.13879i	0.781011	+	0.342586i
$226$	15.3514	+	7.81708i	1.02116	+	0.519985i
$227$	26.0909	+	3.04959i	1.73172	+	0.202409i	0.922737	−	0.385429i	$-0.125947\pi$
$227$	26.0909	+	3.04959i	1.73172	+	0.202409i	0.808979	+	0.587838i	$0.200021\pi$
$228$	10.4749	−	10.1817i	0.693718	−	0.674297i
$229$	−4.65431	−	15.5465i	−0.307565	−	1.02734i	−0.962416	−	0.271581i	$-0.912453\pi$
$229$	−4.65431	−	15.5465i	−0.307565	−	1.02734i	0.654850	−	0.755759i	$-0.272732\pi$
$230$	0.157606	−	0.269507i	0.0103923	−	0.0177708i
$231$	23.3402	+	9.35535i	1.53567	+	0.615537i
$232$	13.1555	+	6.88435i	0.863699	+	0.451980i
$233$	10.1380	−	12.0820i	0.664160	−	0.791515i	−0.323816	−	0.946120i	$-0.604966\pi$
$233$	10.1380	−	12.0820i	0.664160	−	0.791515i	0.987976	+	0.154605i	$0.0494104\pi$
$234$	1.75393	−	3.93878i	0.114658	−	0.257486i
$235$	4.85252	+	5.78301i	0.316544	+	0.377242i
$236$	−9.31014	−	16.5484i	−0.606038	−	1.07721i
$237$	2.20237	−	1.01878i	0.143060	−	0.0661769i
$238$	23.1125	+	4.20813i	1.49816	+	0.272772i
$239$	0.864990	−	14.8513i	0.0559516	−	0.960651i	−0.847185	−	0.531298i	$-0.821704\pi$
$239$	0.864990	−	14.8513i	0.0559516	−	0.960651i	0.903137	−	0.429353i	$-0.141259\pi$
$240$	5.93145	−	0.367860i	0.382873	−	0.0237452i
$241$	−3.15657	−	3.34577i	−0.203333	−	0.215520i	0.617681	−	0.786429i	$-0.288072\pi$
$241$	−3.15657	−	3.34577i	−0.203333	−	0.215520i	−0.821013	+	0.570909i	$0.806591\pi$
$242$	2.81981	+	0.861326i	0.181264	+	0.0553681i
$243$	0.692015	−	15.5731i	0.0443928	−	0.999014i
$244$	−12.4961	−	8.41958i	−0.799982	−	0.539008i
$245$	−10.3826	+	9.79551i	−0.663322	+	0.625812i
$246$	−2.07717	+	2.91269i	−0.132436	+	0.185706i
$247$	−4.27826	−	0.249180i	−0.272219	−	0.0158550i
$248$	3.80451	−	3.89998i	0.241586	−	0.247649i
$249$	−11.8098	−	25.5301i	−0.748414	−	1.61790i
$250$	7.75751	−	8.13134i	0.490628	−	0.514271i
$251$	−10.3085	+	8.64982i	−0.650664	+	0.545972i	−0.907272	−	0.420544i	$-0.861839\pi$
$251$	−10.3085	+	8.64982i	−0.650664	+	0.545972i	0.256608	+	0.966515i	$0.417395\pi$
$252$	−5.56094	+	28.6382i	−0.350306	+	1.80404i
$253$	−0.588672	−	0.493955i	−0.0370095	−	0.0310547i
$254$	−11.6209	+	1.29276i	−0.729159	+	0.0811153i
$255$	−1.88851	+	4.71154i	−0.118263	+	0.295048i
$256$	−13.7459	+	8.18840i	−0.859120	+	0.511775i
$257$	5.09789	−	1.52621i	0.317997	−	0.0952022i	−0.123827	−	0.992304i	$-0.539517\pi$
$257$	5.09789	−	1.52621i	0.317997	−	0.0952022i	0.441824	+	0.897102i	$0.354332\pi$
$258$	−15.1458	+	27.5185i	−0.942935	+	1.71322i
$259$	3.62583	−	31.0210i	0.225298	−	1.92755i
$260$	−1.25475	−	1.21047i	−0.0778160	−	0.0750703i
$261$	−9.32683	−	12.6897i	−0.577316	−	0.785473i
$262$	2.54454	−	20.7669i	0.157202	−	1.28298i
$263$	0.0130587	+	0.224209i	0.000805232	+	0.0138253i	0.998687	−	0.0512308i	$-0.0163144\pi$
$263$	0.0130587	+	0.224209i	0.000805232	+	0.0138253i	−0.997882	+	0.0650561i	$0.979277\pi$
$264$	1.56256	−	14.5438i	0.0961690	−	0.895109i
$265$	−0.508419	+	1.17865i	−0.0312319	+	0.0724038i
$266$	28.5834	−	4.87615i	1.75256	−	0.298976i
$267$	−0.271219	−	0.688842i	−0.0165983	−	0.0421564i
$268$	−8.30583	+	22.0531i	−0.507359	+	1.34711i
$269$	13.2369	−	7.64234i	0.807069	−	0.465962i	−0.0388679	−	0.999244i	$-0.512375\pi$
$269$	13.2369	−	7.64234i	0.807069	−	0.465962i	0.845937	+	0.533283i	$0.179042\pi$
$270$	−5.82301	−	2.41342i	−0.354377	−	0.146876i
$271$	−19.6077	−	11.3205i	−1.19108	−	0.687672i	−0.232531	−	0.972589i	$-0.574701\pi$
$271$	−19.6077	−	11.3205i	−1.19108	−	0.687672i	−0.958552	+	0.284917i	$0.908034\pi$
$272$	−1.28396	−	13.6056i	−0.0778516	−	0.824958i
$273$	7.29804	−	4.47069i	0.441697	−	0.270578i
$274$	−15.9274	+	13.2143i	−0.962212	+	0.798308i
$275$	−7.60315	−	10.2128i	−0.458487	−	0.615855i
$276$	0.434227	−	0.778658i	0.0261374	−	0.0468697i
$277$	3.37953	−	2.22275i	0.203056	−	0.133552i	−0.443909	−	0.896072i	$-0.646409\pi$
$277$	3.37953	−	2.22275i	0.203056	−	0.133552i	0.646965	+	0.762520i	$0.276038\pi$
$278$	−16.4140	+	21.7936i	−0.984448	+	1.30709i
$279$	−5.44231	+	1.94316i	−0.325823	+	0.116334i
$280$	10.1161	+	6.06797i	0.604553	+	0.362630i
$281$	10.2264	+	7.61324i	0.610053	+	0.454168i	0.857323	−	0.514779i	$-0.172126\pi$
$281$	10.2264	+	7.61324i	0.610053	+	0.454168i	−0.247270	+	0.968947i	$0.579533\pi$
$282$	14.1920	+	16.2272i	0.845119	+	0.966316i
$283$	2.01507	+	1.90112i	0.119783	+	0.113010i	0.743803	−	0.668399i	$-0.233020\pi$
$283$	2.01507	+	1.90112i	0.119783	+	0.113010i	−0.624020	+	0.781409i	$0.714501\pi$
$284$	−27.7703	+	6.25603i	−1.64786	+	0.371227i
$285$	−0.201405	+	6.26190i	−0.0119302	+	0.370923i
$286$	−3.45634	+	2.54337i	−0.204377	+	0.150393i
$287$	−6.67298	+	2.42877i	−0.393894	+	0.143366i
$288$	16.9130	−	1.39677i	0.996607	−	0.0823052i
$289$	−5.00624	−	1.82212i	−0.294485	−	0.107184i
$290$	−6.11064	+	1.79241i	−0.358829	+	0.105254i
$291$	−6.95613	−	3.26968i	−0.407776	−	0.191672i
$292$	0.522394	+	11.0957i	0.0305708	+	0.649329i
$293$	−1.10057	+	1.67333i	−0.0642958	+	0.0977571i	−0.866205	−	0.499689i	$-0.833448\pi$
$293$	−1.10057	+	1.67333i	−0.0642958	+	0.0977571i	0.801909	+	0.597446i	$0.203818\pi$
$294$	−29.0705	+	28.5731i	−1.69543	+	1.66641i
$295$	7.80141	+	2.33559i	0.454216	+	0.135983i
$296$	−17.9425	+	2.85571i	−1.04289	+	0.165985i
$297$	−8.26593	+	13.1295i	−0.479638	+	0.761850i
$298$	5.63607	−	1.30268i	0.326488	−	0.0754624i
$299$	−0.254504	+	0.0603186i	−0.0147183	+	0.00348831i
$300$	9.97581	−	10.8943i	0.575954	−	0.628984i
$301$	−55.7184	+	27.9829i	−3.21156	+	1.61291i
$302$	−8.04288	−	6.82542i	−0.462816	−	0.392759i
$303$	12.9273	+	3.50635i	0.742656	+	0.201435i
$304$	−7.23278	−	15.2383i	−0.414828	−	0.873978i
$305$	6.36427	−	1.12219i	0.364417	−	0.0642565i
$306$	−5.11651	+	13.5619i	−0.292491	+	0.775284i
$307$	11.3892	+	2.00822i	0.650016	+	0.114615i	0.488927	−	0.872325i	$-0.337388\pi$
$307$	11.3892	+	2.00822i	0.650016	+	0.114615i	0.161088	+	0.986940i	$0.448500\pi$
$308$	18.9100	−	22.0332i	1.07749	−	1.25546i
$309$	1.82665	+	1.63563i	0.103914	+	0.0930480i
$310$	−0.0130058	+	2.33668i	−0.000738682	+	0.132714i
$311$	−23.3420	−	5.53216i	−1.32361	−	0.313700i	−0.492741	−	0.870176i	$-0.664005\pi$
$311$	−23.3420	−	5.53216i	−1.32361	−	0.313700i	−0.830864	+	0.556476i	$0.812153\pi$
$312$	−3.65305	−	3.38264i	−0.206813	−	0.191504i
$313$	11.5049	+	26.6714i	0.650295	+	1.50755i	0.849496	+	0.527595i	$0.176906\pi$
$313$	11.5049	+	26.6714i	0.650295	+	1.50755i	−0.199201	+	0.979959i	$0.563835\pi$
$314$	10.8050	+	16.6291i	0.609764	+	0.938436i
$315$	−6.81128	−	10.4956i	−0.383772	−	0.591358i
$316$	−0.294292	−	2.78649i	−0.0165552	−	0.156753i
$317$	14.0937	−	28.0629i	0.791581	−	1.57617i	−0.0255214	−	0.999674i	$-0.508125\pi$
$317$	14.0937	−	28.0629i	0.791581	−	1.57617i	0.817102	−	0.576493i	$-0.195579\pi$
$318$	−1.38270	+	3.39478i	−0.0775378	+	0.190370i
$319$	1.81966	+	15.5682i	0.101881	+	0.871652i
$320$	1.80460	−	6.62067i	0.100880	−	0.370107i
$321$	−0.206812	−	1.01732i	−0.0115431	−	0.0567813i
$322$	1.58587	−	0.785430i	0.0883769	−	0.0437703i
$323$	14.4071			0.801635
$324$	−16.7659	−	6.55022i	−0.931438	−	0.363901i
$325$	−4.33357			−0.240383
$326$	−4.77068	+	2.36277i	−0.264224	+	0.130862i
$327$	6.99000	−	6.18230i	0.386548	−	0.341882i
$328$	2.41115	+	3.35424i	0.133133	+	0.185207i
$329$	4.96780	+	42.5022i	0.273884	+	2.34322i
$330$	3.84847	+	4.95447i	0.211851	+	0.272735i
$331$	−2.62039	+	5.21763i	−0.144030	+	0.286787i	−0.954068	−	0.299590i	$-0.903150\pi$
$331$	−2.62039	+	5.21763i	−0.144030	+	0.286787i	0.810038	+	0.586377i	$0.199446\pi$
$332$	−32.3012	+	3.41145i	−1.77276	+	0.187228i
$333$	18.4267	+	5.63984i	1.00978	+	0.309061i
$334$	−1.64260	−	2.52799i	−0.0898790	−	0.138325i
$335$	−4.00314	−	9.28031i	−0.218715	−	0.507038i
$336$	29.2363	+	16.7333i	1.59497	+	0.912874i
$337$	21.0923	+	4.99898i	1.14897	+	0.272312i	0.760619	−	0.649198i	$-0.224896\pi$
$337$	21.0923	+	4.99898i	1.14897	+	0.272312i	0.388354	+	0.921510i	$0.373044\pi$
$338$	0.0941977	−	16.9239i	0.00512368	−	0.920540i
$339$	−20.0481	+	6.57514i	−1.08887	+	0.357112i
$340$	4.44771	+	3.81724i	0.241211	+	0.207019i
$341$	5.66413	+	0.998738i	0.306730	+	0.0540847i
$342$	−0.209199	+	17.8897i	−0.0113122	+	0.967364i
$343$	−46.1637	+	8.13990i	−2.49260	+	0.439513i
$344$	24.4463	+	26.7941i	1.31806	+	1.44464i
$345$	0.0978339	+	0.369647i	0.00526720	+	0.0199011i
$346$	−7.22135	−	6.12825i	−0.388222	−	0.329457i
$347$	0.159249	−	0.0799779i	0.00854894	−	0.00429344i	−0.444520	−	0.895769i	$-0.646626\pi$
$347$	0.159249	−	0.0799779i	0.00854894	−	0.00429344i	0.453069	+	0.891476i	$0.350329\pi$
$348$	−17.3414	+	5.47436i	−0.929594	+	0.293457i
$349$	−10.9478	+	2.59468i	−0.586023	+	0.138890i	−0.512923	−	0.858435i	$-0.671437\pi$
$349$	−10.9478	+	2.59468i	−0.586023	+	0.138890i	−0.0730999	+	0.997325i	$0.523289\pi$
$350$	28.5684	−	6.60310i	1.52704	−	0.352951i
$351$	1.90447	+	4.92528i	0.101653	+	0.262892i
$352$	−15.3169	−	7.11890i	−0.816391	−	0.379438i
$353$	−22.2292	−	6.65497i	−1.18314	−	0.354209i	−0.365981	−	0.930622i	$-0.619266\pi$
$353$	−22.2292	−	6.65497i	−1.18314	−	0.354209i	−0.817158	+	0.576414i	$0.804452\pi$
$354$	22.4097	+	6.21242i	1.19106	+	0.330187i
$355$	6.70886	−	10.2003i	0.356069	−	0.541377i
$356$	−0.853893	+	0.0402018i	−0.0452562	+	0.00213069i
$357$	−23.6193	+	16.4308i	−1.25007	+	0.869610i
$358$	16.0719	−	4.71429i	0.849424	−	0.249158i
$359$	10.2837	+	3.74296i	0.542753	+	0.197546i	0.598824	−	0.800881i	$-0.295635\pi$
$359$	10.2837	+	3.74296i	0.542753	+	0.197546i	−0.0560705	+	0.998427i	$0.517857\pi$
$360$	−4.80454	+	5.46740i	−0.253222	+	0.288157i
$361$	−1.14408	+	0.416410i	−0.0602146	+	0.0219163i
$362$	−19.0211	+	13.9968i	−0.999727	+	0.735656i
$363$	−3.18370	+	1.70407i	−0.167101	+	0.0894404i
$364$	−2.17189	−	9.64092i	−0.113838	−	0.505322i
$365$	−3.46528	−	3.26932i	−0.181381	−	0.171124i
$366$	18.1046	−	3.57570i	0.946344	−	0.186905i
$367$	−3.68725	−	2.74506i	−0.192473	−	0.143291i	0.496609	−	0.867975i	$-0.334578\pi$
$367$	−3.68725	−	2.74506i	−0.192473	−	0.143291i	−0.689082	+	0.724684i	$0.741986\pi$
$368$	−0.689623	−	0.764354i	−0.0359491	−	0.0398447i
$369$	−0.734387	−	4.31952i	−0.0382307	−	0.224865i
$370$	4.68788	−	6.22429i	0.243712	−	0.323586i
$371$	−6.07908	+	3.99827i	−0.315610	+	0.207580i
$372$	0.0993765	+	6.67205i	0.00515243	+	0.345930i
$373$	−13.2197	−	17.7572i	−0.684491	−	0.919431i	0.315070	−	0.949069i	$-0.397972\pi$
$373$	−13.2197	−	17.7572i	−0.684491	−	0.919431i	−0.999561	+	0.0296375i	$0.990565\pi$
$374$	11.1028	−	9.21152i	0.574111	−	0.476316i
$375$	0.358168	+	13.7593i	0.0184957	+	0.710527i
$376$	23.0183	−	9.47647i	1.18708	−	0.488712i
$377$	4.62017	+	2.66746i	0.237951	+	0.137381i
$378$	−20.0596	−	29.5672i	−1.03175	−	1.52077i
$379$	26.2848	−	15.1756i	1.35016	−	0.779516i	0.361889	−	0.932221i	$-0.382132\pi$
$379$	26.2848	−	15.1756i	1.35016	−	0.779516i	0.988272	+	0.152705i	$0.0487985\pi$
$380$	6.77011	+	2.54982i	0.347299	+	0.130803i
$381$	8.91640	−	11.2059i	0.456801	−	0.574095i
$382$	30.9281	−	5.27614i	1.58242	−	0.269951i
$383$	10.8397	−	25.1293i	0.553884	−	1.28405i	−0.379509	−	0.925188i	$-0.623907\pi$
$383$	10.8397	−	25.1293i	0.553884	−	1.28405i	0.933392	−	0.358858i	$-0.116834\pi$
$384$	4.76541	−	19.0077i	0.243184	−	0.969980i
$385$	0.724071	+	12.4318i	0.0369021	+	0.633584i
$386$	−4.03253	+	32.9109i	−0.205250	+	1.67512i
$387$	−10.8075	−	36.9214i	−0.549375	−	1.87682i
$388$	−6.16211	+	6.38748i	−0.312834	+	0.324275i
$389$	1.88769	−	16.1502i	0.0957097	−	0.818848i	−0.857073	−	0.515195i	$-0.827719\pi$
$389$	1.88769	−	16.1502i	0.0957097	−	0.818848i	0.952783	−	0.303653i	$-0.0982065\pi$
$390$	2.13484	−	0.0436832i	0.108102	−	0.00221199i
$391$	0.842359	−	0.252186i	0.0425999	−	0.0127536i
$392$	20.4186	+	42.4079i	1.03130	+	2.14192i
$393$	15.8315	+	20.1487i	0.798591	+	1.01637i
$394$	−27.8764	+	3.10110i	−1.40439	+	0.156231i
$395$	0.920586	+	0.772464i	0.0463197	+	0.0388669i
$396$	11.2769	+	13.9203i	0.566688	+	0.699523i
$397$	−21.0002	+	17.6212i	−1.05397	+	0.884384i	−0.993505	−	0.113787i	$-0.963702\pi$
$397$	−21.0002	+	17.6212i	−1.05397	+	0.884384i	−0.0604624	+	0.998170i	$0.519258\pi$
$398$	−16.4061	+	17.1967i	−0.822364	+	0.861992i
$399$	−20.4585	+	29.0281i	−1.02421	+	1.45322i
$400$	−8.19749	−	14.9579i	−0.409874	−	0.747895i
$401$	−20.5193	−	1.19511i	−1.02468	−	0.0596810i	−0.462438	−	0.886651i	$-0.653025\pi$
$401$	−20.5193	−	1.19511i	−1.02468	−	0.0596810i	−0.562246	+	0.826970i	$0.690062\pi$
$402$	−11.9712	−	26.2617i	−0.597071	−	1.30982i
$403$	1.42391	−	1.34339i	0.0709298	−	0.0669188i
$404$	8.64232	−	12.8267i	0.429972	−	0.638152i
$405$	7.12555	−	2.97063i	0.354071	−	0.147612i
$406$	−34.5221	−	10.5450i	−1.71330	−	0.523338i
$407$	−13.1617	−	13.9506i	−0.652401	−	0.691504i
$408$	12.9214	+	10.6385i	0.639702	+	0.526685i
$409$	0.467881	−	8.03320i	0.0231352	−	0.397216i	−0.966785	−	0.255591i	$-0.917730\pi$
$409$	0.467881	−	8.03320i	0.0231352	−	0.397216i	0.989920	−	0.141626i	$-0.0452329\pi$
$410$	−1.74305	−	0.317360i	−0.0860830	−	0.0156733i
$411$	2.28646	−	25.2433i	0.112783	−	1.24516i
$412$	2.46753	−	1.38824i	0.121567	−	0.0683936i
$413$	29.6714	+	35.3610i	1.46003	+	1.74000i
$414$	0.300914	+	1.04964i	0.0147891	+	0.0515870i
$415$	8.95445	−	10.6715i	0.439557	−	0.523843i
$416$	−5.05671	+	2.73478i	−0.247926	+	0.134084i
$417$	−4.74160	−	33.0770i	−0.232197	−	1.61979i
$418$	8.98888	−	15.3710i	0.439661	−	0.751819i
$419$	−2.65150	−	8.85662i	−0.129534	−	0.432674i	0.868476	−	0.495732i	$-0.165100\pi$
$419$	−2.65150	−	8.85662i	−0.129534	−	0.432674i	−0.998010	+	0.0630574i	$0.979915\pi$
$420$	−14.0070	+	3.54085i	−0.683472	+	0.172776i
$421$	−9.23921	−	1.07991i	−0.450291	−	0.0526315i	−0.112075	−	0.993700i	$-0.535750\pi$
$421$	−9.23921	−	1.07991i	−0.450291	−	0.0526315i	−0.338217	+	0.941068i	$0.609824\pi$
$422$	−12.8751	−	6.55610i	−0.626750	−	0.319146i
$423$	−26.3481	−	1.69666i	−1.28109	−	0.0824942i
$424$	3.19651	+	2.77444i	0.155236	+	0.134739i
$425$	14.5441	−	0.847095i	0.705491	−	0.0410902i
$426$	18.5581	−	29.5142i	0.899144	−	1.42997i
$427$	33.6357	+	14.5090i	1.62774	+	0.702140i
$428$	−1.18900	−	0.152409i	−0.0574724	−	0.00736695i
$429$	0.777648	−	5.19786i	0.0375452	−	0.250955i
$430$	−15.5244	−	0.990921i	−0.748652	−	0.0477864i
$431$	13.3316	+	23.0910i	0.642160	+	1.11225i	0.984950	+	0.172842i	$0.0552950\pi$
$431$	13.3316	+	23.0910i	0.642160	+	1.11225i	−0.342789	+	0.939412i	$0.611372\pi$
$432$	−13.3977	+	15.8903i	−0.644598	+	0.764522i
$433$	0.376793	−	0.652624i	0.0181075	−	0.0313631i	−0.856830	−	0.515600i	$-0.827569\pi$
$433$	0.376793	−	0.652624i	0.0181075	−	0.0313631i	0.874937	+	0.484236i	$0.160903\pi$
$434$	−7.33993	+	11.0257i	−0.352328	+	0.529249i
$435$	3.72256	−	6.85357i	0.178483	−	0.328604i
$436$	−4.15749	−	9.94099i	−0.199108	−	0.476087i
$437$	0.870548	−	0.648099i	0.0416440	−	0.0310028i
$438$	−10.0845	−	9.13158i	−0.481855	−	0.436324i
$439$	20.8919	+	31.7645i	0.997114	+	1.51604i	0.849907	+	0.526933i	$0.176658\pi$
$439$	20.8919	+	31.7645i	0.997114	+	1.51604i	0.147208	+	0.989106i	$0.452971\pi$
$440$	6.84762	−	2.36362i	0.326448	−	0.112681i
$441$	0.305895	−	49.9217i	0.0145664	−	2.37722i
$442$	−0.258217	−	4.90345i	−0.0122821	−	0.233233i
$443$	8.19085	−	11.0022i	0.389159	−	0.522731i	−0.563767	−	0.825934i	$-0.690648\pi$
$443$	8.19085	−	11.0022i	0.389159	−	0.522731i	0.952926	+	0.303203i	$0.0980559\pi$
$444$	13.0204	−	18.0444i	0.617923	−	0.856351i
$445$	0.251597	−	0.266677i	0.0119268	−	0.0126417i
$446$	−8.30600	−	14.5731i	−0.393300	−	0.690058i
$447$	−3.73777	+	6.01850i	−0.176791	+	0.284665i
$448$	29.1685	−	25.7335i	1.37808	−	1.21580i
$449$	−4.83012	−	13.2707i	−0.227948	−	0.626281i	0.772009	−	0.635612i	$-0.219252\pi$
$449$	−4.83012	−	13.2707i	−0.227948	−	0.626281i	−0.999956	+	0.00933083i	$0.997030\pi$
$450$	0.840671	+	18.0720i	0.0396296	+	0.851923i
$451$	−1.49148	+	4.09782i	−0.0702312	+	0.192959i
$452$	−0.271196	+	24.3613i	−0.0127560	+	1.14586i
$453$	12.8736	−	1.08657i	0.604856	−	0.0510513i
$454$	12.5113	+	34.9791i	0.587186	+	1.64165i
$455$	3.54121	+	2.32909i	0.166015	+	0.109190i
$456$	19.4778	+	6.88430i	0.912134	+	0.322387i
$457$	0.941483	−	3.14477i	0.0440407	−	0.147106i	−0.933141	−	0.359510i	$-0.882944\pi$
$457$	0.941483	−	3.14477i	0.0440407	−	0.147106i	0.977182	+	0.212403i	$0.0681291\pi$
$458$	16.7808	−	15.6562i	0.784113	−	0.731567i
$459$	−7.35440	−	16.1576i	−0.343274	−	0.754174i
$460$	0.440469	+	0.0305776i	0.0205370	+	0.00142569i
$461$	0.749830	+	3.16378i	0.0349231	+	0.147352i	0.987713	−	0.156278i	$-0.0499495\pi$
$461$	0.749830	+	3.16378i	0.0349231	+	0.147352i	−0.952790	+	0.303630i	$0.901801\pi$
$462$	2.79351	+	35.4509i	0.129966	+	1.64933i
$463$	−8.96437	−	17.8495i	−0.416610	−	0.829538i	−0.999851	−	0.0172393i	$-0.994512\pi$
$463$	−8.96437	−	17.8495i	−0.416610	−	0.829538i	0.583242	−	0.812299i	$-0.301784\pi$
$464$	−0.467454	+	20.9929i	−0.0217010	+	0.974572i
$465$	−2.01745	−	2.02985i	−0.0935568	−	0.0941318i
$466$	21.6746	+	5.26456i	1.00406	+	0.243876i
$467$	1.81723	+	10.3060i	0.0840913	+	0.476905i	0.997549	+	0.0699716i	$0.0222909\pi$
$467$	1.81723	+	10.3060i	0.0840913	+	0.476905i	−0.913458	+	0.406934i	$0.866598\pi$
$468$	6.09248	−	0.249434i	0.281625	−	0.0115301i
$469$	9.94824	−	56.4193i	0.459367	−	2.60520i
$470$	−4.28311	+	9.77934i	−0.197565	+	0.451087i
$471$	−23.7712	−	4.98435i	−1.09532	−	0.229667i
$472$	15.1282	−	22.1854i	0.696331	−	1.02116i
$473$	−8.83002	+	37.2568i	−0.406005	+	1.71307i
$474$	2.67343	+	2.15163i	0.122795	+	0.0988275i
$475$	16.5113	−	7.12227i	0.757590	−	0.326792i
$476$	9.17368	+	31.9317i	0.420475	+	1.46359i
$477$	−1.75286	−	4.13304i	−0.0802581	−	0.189239i
$478$	19.3640	−	8.22528i	0.885688	−	0.376216i
$479$	6.60239	+	3.31584i	0.301671	+	0.151505i	0.593195	−	0.805059i	$-0.297866\pi$
$479$	6.60239	+	3.31584i	0.301671	+	0.151505i	−0.291525	+	0.956563i	$0.594163\pi$
$480$	4.18909	+	7.28604i	0.191205	+	0.332561i
$481$	−6.48381	+	0.757849i	−0.295636	+	0.0345549i
$482$	2.25886	−	6.10031i	0.102888	−	0.277861i
$483$	−0.688058	+	2.05533i	−0.0313077	+	0.0935208i
$484$	0.678307	+	4.11416i	0.0308321	+	0.187007i
$485$		−	3.80652i		−	0.172845i
$486$	20.1701	−	8.89752i	0.914936	−	0.403600i
$487$			26.8863i			1.21833i	0.793042	+	0.609167i	$0.208496\pi$
$487$			26.8863i			1.21833i	−0.793042	+	0.609167i	$0.791504\pi$
$488$	2.82690	−	21.1209i	0.127968	−	0.956099i
$489$	2.06985	−	6.18295i	0.0936019	−	0.279603i
$490$	−18.9306	−	7.00973i	−0.855196	−	0.316667i
$491$	30.2800	−	3.53922i	1.36652	−	0.159723i	0.598998	−	0.800750i	$-0.295566\pi$
$491$	30.2800	−	3.53922i	1.36652	−	0.159723i	0.767518	+	0.641027i	$0.221492\pi$
$492$	−4.99500	−	0.804243i	−0.225192	−	0.0362581i
$493$	−16.0273	−	8.04923i	−0.721835	−	0.362519i
$494$	−2.36948	−	5.57824i	−0.106608	−	0.250977i
$495$	−7.62594	−	0.938745i	−0.342761	−	0.0421934i
$496$	7.33036	+	2.37362i	0.329143	+	0.106579i
$497$	63.5444	−	27.4104i	2.85035	−	1.22952i
$498$	24.9418	−	30.9906i	1.11767	−	1.38872i
$499$	1.89229	−	7.98419i	0.0847104	−	0.357421i	−0.914138	−	0.405404i	$-0.867131\pi$
$499$	1.89229	−	7.98419i	0.0847104	−	0.357421i	0.998848	+	0.0479823i	$0.0152791\pi$
$500$	15.1739	+	4.72744i	0.678597	+	0.211417i
$501$	3.61374	+	0.757728i	0.161450	+	0.0338528i
$502$	−17.4321	−	7.63482i	−0.778031	−	0.340759i
$503$	3.28407	−	18.6249i	0.146430	−	0.830443i	−0.819779	−	0.572680i	$-0.805904\pi$
$503$	3.28407	−	18.6249i	0.146430	−	0.830443i	0.966208	−	0.257763i	$-0.0829853\pi$
$504$	−39.7836	+	10.9275i	−1.77210	+	0.486750i
$505$	1.15188	+	6.53264i	0.0512580	+	0.290699i
$506$	0.256506	−	1.05606i	0.0114031	−	0.0469475i
$507$	14.6118	+	14.7016i	0.648933	+	0.652921i
$508$	−8.93222	−	13.9157i	−0.396303	−	0.617411i
$509$	10.7082	+	21.3217i	0.474632	+	0.945070i	0.995795	+	0.0916124i	$0.0292021\pi$
$509$	10.7082	+	21.3217i	0.474632	+	0.945070i	−0.521163	+	0.853457i	$0.674502\pi$
$510$	−7.15627	+	0.563909i	−0.316885	+	0.0249703i
$511$	−6.22770	−	26.2767i	−0.275497	−	1.16241i
$512$	−19.0048	−	12.2807i	−0.839903	−	0.542736i
$513$	−15.3509	−	15.6357i	−0.677760	−	0.690335i
$514$	5.13387	+	5.50262i	0.226445	+	0.242710i
$515$	−0.348261	+	1.16327i	−0.0153462	+	0.0512599i
$516$	−44.3805	−	1.92218i	−1.95374	−	0.0846192i
$517$	21.9549	+	14.4399i	0.965574	+	0.635068i
$518$	41.5887	−	14.8754i	1.82730	−	0.653589i
$519$	11.5587	−	0.975580i	0.507370	−	0.0428232i
$520$	0.746486	−	2.34990i	0.0327356	−	0.103050i
$521$	2.50986	−	6.89579i	0.109959	−	0.302110i	−0.872493	−	0.488627i	$-0.837498\pi$
$521$	2.50986	−	6.89579i	0.109959	−	0.302110i	0.982452	+	0.186517i	$0.0597200\pi$
$522$	10.2276	−	19.7846i	0.447652	−	0.865950i
$523$	3.63628	+	9.99061i	0.159004	+	0.436859i	0.993455	−	0.114222i	$-0.0364377\pi$
$523$	3.63628	+	9.99061i	0.159004	+	0.436859i	−0.834452	+	0.551081i	$0.814215\pi$
$524$	27.9149	−	9.80970i	1.21947	−	0.428539i
$525$	−18.9462	+	30.5069i	−0.826880	+	1.33143i
$526$	−0.275943	+	0.157275i	−0.0120317	+	0.00685750i
$527$	−4.51623	+	4.78692i	−0.196730	+	0.208521i
$528$	19.4121	−	7.14824i	0.844803	−	0.311087i
$529$	−13.6951	+	18.3957i	−0.595439	+	0.799813i
$530$	−1.81281	+	0.0954633i	−0.0787435	+	0.00414666i
$531$	−24.7523	+	14.0893i	−1.07416	+	0.611421i
$532$	24.1200	+	33.1632i	1.04574	+	1.43781i
$533$	0.815612	+	1.24008i	0.0353281	+	0.0537137i
$534$	0.702738	−	0.776070i	0.0304104	−	0.0335838i
$535$	0.412387	−	0.307011i	0.0178291	−	0.0132732i
$536$	−33.1611	+	3.31574i	−1.43234	+	0.143218i
$537$	−9.79087	+	18.0259i	−0.422507	+	0.777874i
$538$	17.9933	+	11.9784i	0.775748	+	0.516426i
$539$	−24.8434	+	43.0300i	−1.07008	+	1.85343i
$540$	−0.596307	−	8.89430i	−0.0256610	−	0.382750i
$541$	−4.02963	−	6.97953i	−0.173248	−	0.300074i	0.766306	−	0.642476i	$-0.222093\pi$
$541$	−4.02963	−	6.97953i	−0.173248	−	0.300074i	−0.939553	+	0.342402i	$0.888759\pi$
$542$	2.03964	−	31.9542i	0.0876099	−	1.37255i
$543$	4.27960	−	28.6051i	0.183655	−	1.22756i
$544$	16.4364	−	10.1667i	0.704706	−	0.435895i
$545$	4.24346	+	1.83045i	0.181770	+	0.0784078i
$546$	10.2463	+	6.44276i	0.438503	+	0.275725i
$547$	−15.5365	+	0.904898i	−0.664292	+	0.0386906i	−0.386978	−	0.922089i	$-0.626481\pi$
$547$	−15.5365	+	0.904898i	−0.664292	+	0.0386906i	−0.277314	+	0.960779i	$0.589444\pi$
$548$	−26.7435	−	11.8908i	−1.14242	−	0.507951i
$549$	−12.5354	+	18.8071i	−0.534998	+	0.802669i
$550$	8.17054	−	16.0456i	0.348393	−	0.684186i
$551$	−21.9872	−	2.56994i	−0.936688	−	0.109483i
$552$	1.25934	+	0.0615679i	0.0536010	+	0.00262050i
$553$	1.95368	+	6.52573i	0.0830788	+	0.277502i
$554$	4.93806	+	2.88776i	0.209798	+	0.122689i
$555$	1.35421	+	9.44686i	0.0574831	+	0.400997i
$556$	−37.9213	−	7.12268i	−1.60822	−	0.302069i
$557$	−11.1741	+	13.3168i	−0.473464	+	0.564252i	−0.948932	−	0.315481i	$-0.897834\pi$
$557$	−11.1741	+	13.3168i	−0.473464	+	0.564252i	0.475468	+	0.879733i	$0.342279\pi$
$558$	−5.87846	−	5.67741i	−0.248855	−	0.240344i
$559$	8.37688	+	9.98317i	0.354304	+	0.422243i
$560$	−1.34053	+	16.6287i	−0.0566476	+	0.702692i
$561$	−1.59385	+	17.5967i	−0.0672925	+	0.742935i
$562$	−3.22965	+	17.7383i	−0.136235	+	0.748247i
$563$	−2.49102	+	42.7692i	−0.104984	+	1.80251i	0.376879	+	0.926262i	$0.376997\pi$
$563$	−2.49102	+	42.7692i	−0.104984	+	1.80251i	−0.481864	+	0.876246i	$0.660040\pi$
$564$	−11.6571	+	28.1705i	−0.490853	+	1.18619i
$565$	−7.17049	−	7.60027i	−0.301665	−	0.319746i
$566$	−1.14452	+	3.74694i	−0.0481079	+	0.157496i
$567$	42.9985	+	8.12633i	1.80577	+	0.341274i
$568$	−25.3584	−	31.2667i	−1.06402	−	1.31192i
$569$	−19.7435	+	18.6270i	−0.827691	+	0.780886i	−0.978187	−	0.207724i	$-0.933394\pi$
$569$	−19.7435	+	18.6270i	−0.827691	+	0.780886i	0.150496	+	0.988611i	$0.451913\pi$
$570$	−8.06212	+	3.67507i	−0.337685	+	0.153932i
$571$	0.648733	+	0.0377844i	0.0271486	+	0.00158123i	0.0717138	−	0.997425i	$-0.477153\pi$
$571$	0.648733	+	0.0377844i	0.0271486	+	0.00158123i	−0.0445651	+	0.999006i	$0.514190\pi$
$572$	−5.39260	−	2.78386i	−0.225476	−	0.116399i
$573$	−22.1367	+	31.4093i	−0.924775	+	1.31214i
$574$	−7.26630	−	6.93225i	−0.303290	−	0.289346i
$575$	0.840715	−	0.705444i	0.0350602	−	0.0294190i
$576$	12.3856	+	20.5571i	0.516068	+	0.856548i
$577$	−22.0651	−	18.5148i	−0.918580	−	0.770780i	0.0551516	−	0.998478i	$-0.482436\pi$
$577$	−22.0651	−	18.5148i	−0.918580	−	0.770780i	−0.973732	+	0.227698i	$0.926880\pi$
$578$	−0.833010	−	7.48807i	−0.0346486	−	0.311463i
$579$	−25.0893	−	31.9312i	−1.04268	−	1.32702i
$580$	−6.10688	−	6.61900i	−0.253575	−	0.274839i
$581$	75.6468	−	22.6472i	3.13836	−	0.939562i
$582$	−0.222377	−	10.8677i	−0.00921780	−	0.450482i
$583$	−0.518723	+	4.43796i	−0.0214833	+	0.183801i
$584$	−13.7337	+	7.62631i	−0.568307	+	0.315579i
$585$	−1.80627	+	1.89118i	−0.0746799	+	0.0781907i
$586$	−2.81139	−	0.344476i	−0.116137	−	0.0142302i
$587$	0.379590	+	6.51731i	0.0156673	+	0.268998i	0.997040	+	0.0768843i	$0.0244972\pi$
$587$	0.379590	+	6.51731i	0.0156673	+	0.268998i	−0.981373	+	0.192114i	$0.938466\pi$
$588$	−54.4569	−	18.9071i	−2.24576	−	0.779715i
$589$	−3.21733	+	7.45862i	−0.132568	+	0.307327i
$590$	1.93669	+	11.3527i	0.0797324	+	0.467382i
$591$	21.3888	−	26.8809i	0.879818	−	1.10573i
$592$	−14.8807	−	20.9461i	−0.611594	−	0.860881i
$593$	−22.4463	+	12.9594i	−0.921757	+	0.532177i	−0.884195	−	0.467118i	$-0.845292\pi$
$593$	−22.4463	+	12.9594i	−0.921757	+	0.532177i	−0.0375620	+	0.999294i	$0.511959\pi$
$594$	−21.8271	−	2.23464i	−0.895579	−	0.0916884i
$595$	−12.3401	−	7.12454i	−0.505894	−	0.292078i
$596$	5.18839	+	6.32495i	0.212525	+	0.259080i
$597$	−0.757477	−	29.0991i	−0.0310015	−	1.19095i
$598$	−0.236182	−	0.284674i	−0.00965821	−	0.0116412i
$599$	16.6981	+	22.4294i	0.682265	+	0.916441i	0.999491	−	0.0319094i	$-0.0101588\pi$
$599$	16.6981	+	22.4294i	0.682265	+	0.916441i	−0.317226	+	0.948350i	$0.602751\pi$
$600$	20.0677	+	5.80449i	0.819262	+	0.236967i
$601$	−7.52423	+	4.94877i	−0.306920	+	0.201864i	−0.693620	−	0.720341i	$-0.743985\pi$
$601$	−7.52423	+	4.94877i	−0.306920	+	0.201864i	0.386700	+	0.922206i	$0.373615\pi$
$602$	−70.4346	−	53.0485i	−2.87070	−	2.16209i
$603$	33.1416	+	12.2930i	1.34963	+	0.500611i
$604$	3.60171	−	14.4767i	0.146552	−	0.589050i
$605$	−1.43447	−	1.06792i	−0.0583193	−	0.0434171i
$606$	3.67029	+	18.5836i	0.149095	+	0.754907i
$607$	11.9070	+	11.2337i	0.483292	+	0.455962i	0.888911	−	0.458080i	$-0.151463\pi$
$607$	11.9070	+	11.2337i	0.483292	+	0.455962i	−0.405619	+	0.914042i	$0.632944\pi$
$608$	14.7719	−	18.7305i	0.599078	−	0.759622i
$609$	38.9771	−	20.8624i	1.57943	−	0.845388i
$610$	5.41671	+	7.36109i	0.219316	+	0.298042i
$611$	8.40464	−	3.05904i	0.340015	−	0.123755i
$612$	−20.3984	+	2.02805i	−0.824558	+	0.0819790i
$613$	12.8699	+	4.68426i	0.519811	+	0.189196i	0.588583	−	0.808437i	$-0.299686\pi$
$613$	12.8699	+	4.68426i	0.519811	+	0.189196i	−0.0687723	+	0.997632i	$0.521908\pi$
$614$	4.60345	+	15.6940i	0.185780	+	0.633358i
$615$	1.78127	−	1.23914i	0.0718277	−	0.0499671i
$616$	39.7916	+	10.1354i	1.60325	+	0.408366i
$617$	14.0049	−	21.2934i	0.563817	−	0.857242i	−0.435255	−	0.900307i	$-0.643342\pi$
$617$	14.0049	−	21.2934i	0.563817	−	0.857242i	0.999072	+	0.0430651i	$0.0137123\pi$
$618$	−0.926338	+	3.34153i	−0.0372628	+	0.134416i
$619$	−8.98345	−	2.68947i	−0.361075	−	0.108099i	0.101127	−	0.994874i	$-0.467755\pi$
$619$	−8.98345	−	2.68947i	−0.361075	−	0.108099i	−0.462202	+	0.886775i	$0.652940\pi$
$620$	−2.96944	+	1.45014i	−0.119255	+	0.0582392i
$621$	−1.17123	−	0.645487i	−0.0469999	−	0.0259025i
$622$	−7.63981	−	33.0537i	−0.306328	−	1.32533i
$623$	2.02218	−	0.479265i	0.0810168	−	0.0192013i
$624$	1.99396	−	6.75264i	0.0798224	−	0.270322i
$625$	12.9619	−	6.50969i	0.518474	−	0.260388i
$626$	−26.5795	+	31.3205i	−1.06233	+	1.25182i
$627$	5.57983	+	21.0824i	0.222837	+	0.841949i
$628$	−14.2923	+	24.1306i	−0.570324	+	0.962915i
$629$	21.6124	−	3.81085i	0.861743	−	0.151949i
$630$	9.02590	−	15.2195i	0.359601	−	0.606360i
$631$	−31.8098	−	5.60893i	−1.26633	−	0.223288i	−0.500164	−	0.865931i	$-0.666727\pi$
$631$	−31.8098	−	5.60893i	−1.26633	−	0.223288i	−0.766166	+	0.642643i	$0.777838\pi$
$632$	3.34661	−	2.12191i	0.133121	−	0.0844050i
$633$	16.8142	−	5.51450i	0.668303	−	0.219182i
$634$	44.4100	+	0.247184i	1.76375	+	0.00981693i
$635$	6.90083	+	1.63553i	0.273851	+	0.0649039i
$636$	−5.17006	+	0.378455i	−0.205006	+	0.0150067i
$637$	6.69832	+	15.5284i	0.265397	+	0.615259i
$638$	−18.5875	+	12.0775i	−0.735885	+	0.478153i
$639$	9.59239	+	41.6080i	0.379469	+	1.64599i
$640$	9.52304	−	1.86852i	0.376431	−	0.0738598i
$641$	−12.7743	+	25.4358i	−0.504556	+	1.00465i	0.486808	+	0.873509i	$0.338161\pi$
$641$	−12.7743	+	25.4358i	−0.504556	+	1.00465i	−0.991363	+	0.131144i	$0.958135\pi$
$642$	1.15944	−	0.900618i	0.0457596	−	0.0355445i
$643$	0.0171490	+	0.146719i	0.000676289	+	0.00578602i	0.993572	−	0.113199i	$-0.0361099\pi$
$643$	0.0171490	+	0.146719i	0.000676289	+	0.00578602i	−0.992896	+	0.118985i	$0.962036\pi$
$644$	1.99075	+	1.51679i	0.0784466	+	0.0597700i
$645$	14.2711	−	12.6221i	0.561925	−	0.496994i
$646$	9.04270	+	18.2582i	0.355780	+	0.718358i
$647$	−7.90215			−0.310665			−0.155333	−	0.987862i	$-0.549645\pi$
$647$	−7.90215			−0.310665			−0.155333	+	0.987862i	$0.549645\pi$
$648$	−2.22208	−	25.3587i	−0.0872915	−	0.996183i
$649$	28.3467			1.11271
$650$	−2.71999	−	5.49194i	−0.106687	−	0.215412i
$651$	−3.23172	−	15.8970i	−0.126661	−	0.623054i
$652$	−5.98868	−	4.56289i	−0.234535	−	0.178696i
$653$	−1.33409	−	11.4138i	−0.0522069	−	0.446658i	−0.993908	−	0.110209i	$-0.964848\pi$
$653$	−1.33409	−	11.4138i	−0.0522069	−	0.446658i	0.941702	−	0.336449i	$-0.109226\pi$
$654$	12.2221	+	4.97809i	0.477923	+	0.194659i
$655$	−5.69531	+	11.3403i	−0.222534	+	0.443102i
$656$	−2.73746	+	5.16095i	−0.106880	+	0.201501i
$657$	16.6395	−	0.866871i	0.649168	−	0.0338199i
$658$	−50.7451	+	32.9724i	−1.97825	+	1.28540i
$659$	17.6178	+	40.8427i	0.686292	+	1.59100i	0.801728	+	0.597689i	$0.203914\pi$
$659$	17.6178	+	40.8427i	0.686292	+	1.59100i	−0.115436	+	0.993315i	$0.536827\pi$
$660$	−3.86329	+	7.98686i	−0.150378	+	0.310888i
$661$	18.0637	+	4.28118i	0.702597	+	0.166519i	0.566360	−	0.824158i	$-0.308351\pi$
$661$	18.0637	+	4.28118i	0.702597	+	0.166519i	0.136237	+	0.990676i	$0.456499\pi$
$662$	−8.25701	−	0.0459581i	−0.320918	−	0.00178621i
$663$	4.48019	+	4.01169i	0.173996	+	0.155801i
$664$	−24.5973	−	38.7942i	−0.954561	−	1.50551i
$665$	−17.3202	−	3.05402i	−0.671649	−	0.118430i
$666$	4.41820	+	26.8920i	0.171202	+	1.04204i
$667$	−1.33054	+	0.234610i	−0.0515186	+	0.00908413i
$668$	2.17273	−	3.66837i	0.0840656	−	0.141933i
$669$	19.8274	+	5.37790i	0.766572	+	0.207922i
$670$	9.24836	−	10.8980i	0.357295	−	0.421027i
$671$	20.1023	−	10.0958i	0.776042	−	0.389743i
$672$	−2.85580	+	47.5539i	−0.110165	+	1.83443i
$673$	−13.4757	+	3.19381i	−0.519451	+	0.123112i	−0.481974	−	0.876185i	$-0.660080\pi$
$673$	−13.4757	+	3.19381i	−0.519451	+	0.123112i	−0.0374769	+	0.999297i	$0.511932\pi$
$674$	6.90349	+	29.8680i	0.265912	+	1.15047i
$675$	−16.4162	−	14.8818i	−0.631858	−	0.572799i
$676$	21.5068	−	10.5030i	0.827185	−	0.403961i
$677$	15.1561	+	4.53745i	0.582497	+	0.174388i	0.564476	−	0.825449i	$-0.309078\pi$
$677$	15.1561	+	4.53745i	0.582497	+	0.174388i	0.0180210	+	0.999838i	$0.494263\pi$
$678$	−20.9160	−	21.2801i	−0.803273	−	0.817258i
$679$	11.8566	−	18.0271i	0.455016	−	0.691818i
$680$	−2.04597	+	8.03249i	−0.0784593	+	0.308032i
$681$	−41.1765	−	19.3547i	−1.57789	−	0.741675i
$682$	2.28941	+	7.80501i	0.0876660	+	0.298869i
$683$	1.74086	+	0.633622i	0.0666122	+	0.0242449i	0.375111	−	0.926980i	$-0.377604\pi$
$683$	1.74086	+	0.633622i	0.0666122	+	0.0242449i	−0.308499	+	0.951225i	$0.599827\pi$
$684$	−22.8029	+	10.9634i	−0.871892	+	0.419197i
$685$	11.7956	−	4.29324i	0.450686	−	0.164036i
$686$	−39.2905	−	53.3942i	−1.50012	−	2.03860i
$687$	−0.903592	+	28.0936i	−0.0344742	+	1.07184i
$688$	−18.6123	+	47.7983i	−0.709588	+	1.82229i
$689$	1.10619	+	1.04364i	0.0421425	+	0.0397594i
$690$	−0.407048	+	0.355996i	−0.0154961	+	0.0135525i
$691$	23.1114	+	17.2058i	0.879199	+	0.654540i	0.939092	−	0.343665i	$-0.111669\pi$
$691$	23.1114	+	17.2058i	0.879199	+	0.654540i	−0.0598930	+	0.998205i	$0.519076\pi$
$692$	3.23382	−	12.9980i	0.122931	−	0.494111i
$693$	−33.1913	−	28.1992i	−1.26083	−	1.07120i
$694$	0.201309	+	0.151618i	0.00764160	+	0.00575534i
$695$	13.8260	−	9.09350i	0.524450	−	0.344936i
$696$	−17.8220	−	18.5407i	−0.675542	−	0.702783i
$697$	−2.97971	−	4.00244i	−0.112864	−	0.151603i
$698$	−10.1597	−	12.2456i	−0.384549	−	0.463503i
$699$	−23.2944	+	14.2698i	−0.881074	+	0.539735i
$700$	26.2992	+	32.0602i	0.994015	+	1.21176i
$701$	−40.7519	−	23.5281i	−1.53918	−	0.888646i	−0.998887	−	0.0471682i	$-0.984980\pi$
$701$	−40.7519	−	23.5281i	−1.53918	−	0.888646i	−0.540292	−	0.841477i	$-0.681686\pi$
$702$	−5.04647	+	5.50490i	−0.190467	+	0.207769i
$703$	23.4583	−	13.5437i	0.884748	−	0.510810i
$704$	−0.591904	−	23.8793i	−0.0223082	−	0.899984i
$705$	−4.79033	−	12.1665i	−0.180414	−	0.458217i
$706$	−5.51837	−	32.3481i	−0.207687	−	1.21743i
$707$	−14.8929	+	34.5255i	−0.560103	+	1.29847i
$708$	6.19254	+	32.2991i	0.232730	+	1.21387i
$709$	1.21777	+	20.9083i	0.0457342	+	0.785226i	0.940731	+	0.339154i	$0.110141\pi$
$709$	1.21777	+	20.9083i	0.0457342	+	0.785226i	−0.894997	+	0.446073i	$0.852822\pi$
$710$	17.1377	+	2.09987i	0.643167	+	0.0788066i
$711$	−4.17748	+	0.462349i	−0.156668	+	0.0173394i
$712$	−0.586897	−	1.05691i	−0.0219949	−	0.0396092i
$713$	−0.0575543	+	0.492409i	−0.00215543	+	0.0184409i
$714$	−35.6475	−	19.6199i	−1.33407	−	0.734256i
$715$	2.49348	−	0.746498i	0.0932507	−	0.0279174i
$716$	16.0620	+	17.4089i	0.600265	+	0.650602i
$717$	−9.58659	+	23.9171i	−0.358018	+	0.893199i
$718$	1.71115	+	15.3818i	0.0638596	+	0.574045i
$719$	−16.9652	−	14.2355i	−0.632696	−	0.530895i	0.269070	−	0.963121i	$-0.413284\pi$
$719$	−16.9652	−	14.2355i	−0.632696	−	0.530895i	−0.901765	+	0.432226i	$0.857728\pi$
$720$	−9.94443	−	2.65717i	−0.370607	−	0.0990267i
$721$	−5.27270	+	4.42432i	−0.196365	+	0.164770i
$722$	−1.24580	−	1.18853i	−0.0463640	−	0.0442325i
$723$	3.34489	+	7.23091i	0.124398	+	0.268920i
$724$	−29.6768	−	15.3203i	−1.10293	−	0.569374i
$725$	−22.3473	−	1.30158i	−0.829958	−	0.0483395i
$726$	−4.15783	−	2.96514i	−0.154312	−	0.110047i
$727$	−3.92928	+	3.70708i	−0.145729	+	0.137488i	−0.755654	−	0.654971i	$-0.772681\pi$
$727$	−3.92928	+	3.70708i	−0.145729	+	0.137488i	0.609925	+	0.792459i	$0.291199\pi$
$728$	10.8548	−	8.80360i	0.402304	−	0.326283i
$729$	−9.69935	+	25.1977i	−0.359235	+	0.933247i
$730$	1.96822	−	6.44355i	0.0728470	−	0.238487i
$731$	−30.0654	−	31.8674i	−1.11201	−	1.17866i
$732$	15.8949	+	20.6997i	0.587493	+	0.765083i
$733$	−1.43663	+	24.6661i	−0.0530633	+	0.911061i	0.861788	+	0.507269i	$0.169345\pi$
$733$	−1.43663	+	24.6661i	−0.0530633	+	0.911061i	−0.914851	+	0.403792i	$0.867692\pi$
$734$	1.16449	−	6.39580i	0.0429823	−	0.236073i
$735$	22.4390	−	10.3799i	0.827677	−	0.382869i
$736$	0.535821	−	1.35371i	0.0197506	−	0.0498984i
$737$	−22.6139	−	26.9502i	−0.832994	−	0.992724i
$738$	5.01319	−	3.64186i	0.184538	−	0.134059i
$739$	12.4550	−	14.8432i	0.458163	−	0.546017i	−0.486663	−	0.873590i	$-0.661786\pi$
$739$	12.4550	−	14.8432i	0.458163	−	0.546017i	0.944826	+	0.327572i	$0.106231\pi$
$740$	10.8304	+	2.03426i	0.398134	+	0.0747807i
$741$	6.88987	+	2.76164i	0.253106	+	0.101451i
$742$	−8.88257	−	5.19448i	−0.326089	−	0.190696i
$743$	−13.1581	−	43.9511i	−0.482723	−	1.61241i	−0.758836	−	0.651282i	$-0.774231\pi$
$743$	−13.1581	−	43.9511i	−0.482723	−	1.61241i	0.276112	−	0.961125i	$-0.410954\pi$
$744$	−8.39312	+	4.31368i	−0.307707	+	0.158147i
$745$	−3.48489	−	0.407326i	−0.127677	−	0.0149233i
$746$	14.2063	−	27.8987i	0.520128	−	1.02144i
$747$	5.35958	+	48.4256i	0.196097	+	1.77180i
$748$	18.6425	+	8.28891i	0.681636	+	0.303072i
$749$	2.90929	−	0.169447i	0.106303	−	0.00619145i
$750$	−17.2124	+	9.08998i	−0.628506	+	0.331919i
$751$	5.15459	+	2.22347i	0.188094	+	0.0811357i	0.488044	−	0.872819i	$-0.337711\pi$
$751$	5.15459	+	2.22347i	0.188094	+	0.0811357i	−0.299950	+	0.953955i	$0.596970\pi$
$752$	26.4571	+	23.2231i	0.964790	+	0.846861i
$753$	21.6873	−	8.53896i	0.790328	−	0.311177i
$754$	−0.480600	+	7.52938i	−0.0175024	+	0.274204i
$755$	3.19909	+	5.54098i	0.116427	+	0.201657i
$756$	24.8801	−	43.9795i	0.904881	−	1.59952i
$757$	−6.95433	+	12.0453i	−0.252759	+	0.437792i	−0.964285	−	0.264868i	$-0.914671\pi$
$757$	−6.95433	+	12.0453i	−0.252759	+	0.437792i	0.711525	+	0.702661i	$0.248005\pi$
$758$	35.7298	+	23.7858i	1.29776	+	0.863939i
$759$	0.695273	+	1.13498i	0.0252368	+	0.0411971i
$760$	1.01790	+	10.1802i	0.0369232	+	0.369273i
$761$	−27.7346	+	20.6477i	−1.00538	+	0.748477i	−0.968032	−	0.250825i	$-0.919298\pi$
$761$	−27.7346	+	20.6477i	−1.00538	+	0.748477i	−0.0373470	+	0.999302i	$0.511891\pi$
$762$	19.7977	+	4.26634i	0.717193	+	0.154553i
$763$	14.3949	+	21.8863i	0.521129	+	0.792339i
$764$	26.0986	+	35.8836i	0.944214	+	1.29822i
$765$	5.69240	−	6.70013i	0.205809	−	0.242244i
$766$	38.6499	−	2.03532i	1.39648	−	0.0735391i
$767$	5.76149	−	7.73903i	0.208035	−	0.279440i
$768$	27.0794	−	5.89103i	0.977145	−	0.212574i
$769$	20.4555	−	21.6815i	0.737642	−	0.781855i	−0.244569	−	0.969632i	$-0.578647\pi$
$769$	20.4555	−	21.6815i	0.737642	−	0.781855i	0.982212	+	0.187776i	$0.0601281\pi$
$770$	−15.3004	+	8.72049i	−0.551387	+	0.314265i
$771$	−9.21225	−	0.296299i	−0.331771	−	0.0106710i
$772$	−44.2390	+	15.5462i	−1.59220	+	0.559520i
$773$	−11.8317	−	32.5074i	−0.425558	−	1.16921i	−0.948482	−	0.316831i	$-0.897381\pi$
$773$	−11.8317	−	32.5074i	−0.425558	−	1.16921i	0.522924	−	0.852379i	$-0.324841\pi$
$774$	40.0071	−	36.8702i	1.43803	−	1.32527i
$775$	−2.80937	+	7.71867i	−0.100915	+	0.277263i
$776$	−11.9625	−	3.80011i	−0.429430	−	0.136416i
$777$	−23.0119	+	48.9571i	−0.825549	+	1.75633i
$778$	21.6520	−	7.74448i	0.776261	−	0.277653i
$779$	−5.14563	−	3.38434i	−0.184361	−	0.121256i
$780$	1.39530	+	2.67806i	0.0499597	+	0.0958901i
$781$	12.1885	−	40.7123i	0.436137	−	1.45680i
$782$	0.848305	+	0.909237i	0.0303353	+	0.0325142i
$783$	8.34161	+	25.9706i	0.298105	+	0.928114i
$784$	−40.9277	+	52.4940i	−1.46170	+	1.87479i
$785$	−2.77394	−	11.7042i	−0.0990062	−	0.417740i
$786$	−15.5978	+	32.7096i	−0.556355	+	1.16671i
$787$	−6.32420	−	12.5925i	−0.225434	−	0.448875i	0.752273	−	0.658852i	$-0.228958\pi$
$787$	−6.32420	−	12.5925i	−0.225434	−	0.448875i	−0.977706	+	0.209977i	$0.932661\pi$
$788$	−21.4267	−	33.3813i	−0.763296	−	1.18916i
$789$	0.101831	−	0.375434i	0.00362528	−	0.0133658i
$790$	−0.401134	+	1.65150i	−0.0142717	+	0.0587577i
$791$	−10.2849	−	58.3285i	−0.365689	−	2.07392i
$792$	−10.5632	+	23.0284i	−0.375348	+	0.818280i
$793$	1.32954	−	7.54017i	0.0472132	−	0.267759i
$794$	−35.5122	−	15.5535i	−1.26028	−	0.551972i
$795$	1.48313	−	1.65633i	0.0526011	−	0.0587440i
$796$	−32.0907	−	9.99789i	−1.13743	−	0.354366i
$797$	3.44546	−	14.5376i	0.122045	−	0.514946i	−0.877340	−	0.479869i	$-0.840684\pi$
$797$	3.44546	−	14.5376i	0.122045	−	0.514946i	0.999385	−	0.0350773i	$-0.0111677\pi$
$798$	−49.6282	−	7.70749i	−1.75682	−	0.272842i
$799$	−27.6091	+	11.9094i	−0.976741	+	0.421325i
$800$	13.8110	−	19.7771i	0.488291	−	0.699225i
$801$	0.0667117	+	1.28052i	0.00235714	+	0.0452450i
$802$	−11.3644	−	26.7542i	−0.401292	−	0.944724i
$803$	−14.8194	−	7.44258i	−0.522965	−	0.262643i
$804$	25.7677	−	31.6544i	0.908757	−	1.11637i
$805$	−1.06614	+	0.124614i	−0.0375765	+	0.00439206i
$806$	2.59619	+	0.961335i	0.0914470	+	0.0338616i
$807$	−25.9432	+	5.27402i	−0.913243	+	0.185654i
$808$	21.6797	+	2.90169i	0.762688	+	0.102081i
$809$			26.6441i			0.936755i	0.883528	+	0.468378i	$0.155161\pi$
$809$			26.6441i			0.936755i	−0.883528	+	0.468378i	$0.844839\pi$
$810$	8.23706	+	7.16568i	0.289421	+	0.251776i
$811$		−	1.86982i		−	0.0656584i	−0.999461	−	0.0328292i	$-0.989548\pi$
$811$		−	1.86982i		−	0.0656584i	0.999461	−	0.0328292i	$-0.0104517\pi$
$812$	−8.30431	−	50.3685i	−0.291424	−	1.76759i
$813$	25.9804	+	29.3746i	0.911171	+	1.03021i
$814$	9.41859	−	25.4360i	0.330121	−	0.891530i
$815$	3.20722	−	0.374870i	0.112344	−	0.0131311i
$816$	−5.37205	+	23.0525i	−0.188059	+	0.807000i
$817$	−48.3241	−	24.2693i	−1.69065	−	0.849074i
$818$	10.4741	−	4.44913i	0.366220	−	0.155560i
$819$	−14.4449	+	3.33016i	−0.504746	+	0.116365i
$820$	−0.691841	−	2.40816i	−0.0241601	−	0.0840965i
$821$	−13.9910	+	6.03513i	−0.488289	+	0.210627i	−0.625967	−	0.779850i	$-0.715295\pi$
$821$	−13.9910	+	6.03513i	−0.488289	+	0.210627i	0.137678	+	0.990477i	$0.456036\pi$
$822$	33.4260	−	12.9464i	1.16586	−	0.451559i
$823$	−2.52951	+	10.6728i	−0.0881732	+	0.372032i	−0.999186	−	0.0403467i	$-0.987154\pi$
$823$	−2.52951	+	10.6728i	−0.0881732	+	0.372032i	0.911013	+	0.412379i	$0.135302\pi$
$824$	3.30807	+	2.25577i	0.115242	+	0.0785835i
$825$	6.87244	+	20.9547i	0.239268	+	0.729547i
$826$	−26.1896	+	59.7970i	−0.911254	+	2.08061i
$827$	−1.85203	+	10.5034i	−0.0644013	+	0.365238i	0.935527	+	0.353256i	$0.114925\pi$
$827$	−1.85203	+	10.5034i	−0.0644013	+	0.365238i	−0.999928	+	0.0119826i	$0.996186\pi$
$828$	−1.14134	+	1.04016i	−0.0396643	+	0.0361480i
$829$	4.85967	+	27.5605i	0.168783	+	0.957217i	0.945078	+	0.326846i	$0.105986\pi$
$829$	4.85967	+	27.5605i	0.168783	+	0.957217i	−0.776294	+	0.630371i	$0.782903\pi$
$830$	19.1443	+	4.64997i	0.664508	+	0.161403i
$831$	−6.77290	+	1.79257i	−0.234949	+	0.0621836i
$832$	−6.63965	−	4.69188i	−0.230189	−	0.162662i
$833$	−25.5158	−	50.8062i	−0.884071	−	1.76033i
$834$	38.9424	−	26.7699i	1.34846	−	0.926967i
$835$	0.421699	+	1.77929i	0.0145935	+	0.0615747i
$836$	25.1216	+	1.74395i	0.868847	+	0.0603159i
$837$	10.0072	−	0.199147i	0.345900	−	0.00688351i
$838$	9.55978	−	8.91914i	0.330237	−	0.308107i
$839$	−8.78708	+	29.3509i	−0.303364	+	1.01330i	0.661366	+	0.750063i	$0.269977\pi$
$839$	−8.78708	+	29.3509i	−0.303364	+	1.01330i	−0.964730	+	0.263242i	$0.915208\pi$
$840$	−13.2789	−	15.5287i	−0.458164	−	0.535789i
$841$	−1.20511	−	0.792614i	−0.0415555	−	0.0273315i
$842$	−4.43046	−	12.3867i	−0.152684	−	0.426872i
$843$	−12.6103	−	18.1273i	−0.434322	−	0.624338i
$844$	0.227449	−	20.4316i	0.00782912	−	0.703284i
$845$	−3.51090	+	9.64611i	−0.120779	+	0.331836i
$846$	−14.3873	−	34.4559i	−0.494646	−	1.18462i
$847$	−3.46704	−	9.52561i	−0.119129	−	0.327304i
$848$	−1.50975	+	5.79232i	−0.0518451	+	0.198909i
$849$	−2.26435	−	4.23048i	−0.0777125	−	0.145190i
$850$	10.2022	+	17.9000i	0.349931	+	0.613965i
$851$	1.13450	−	1.20249i	0.0388900	−	0.0412210i
$852$	49.0514	+	4.99400i	1.68047	+	0.171092i
$853$	3.14314	−	4.22197i	0.107619	−	0.144557i	−0.745051	−	0.667008i	$-0.767575\pi$
$853$	3.14314	−	4.22197i	0.107619	−	0.144557i	0.852670	+	0.522451i	$0.174982\pi$
$854$	2.72429	+	51.7331i	0.0932231	+	1.77027i
$855$	3.77386	−	10.1742i	0.129063	−	0.347950i
$856$	−0.553133	−	1.60248i	−0.0189057	−	0.0547716i
$857$	−2.28433	−	3.47315i	−0.0780311	−	0.118641i	0.794364	−	0.607442i	$-0.207804\pi$
$857$	−2.28433	−	3.47315i	−0.0780311	−	0.118641i	−0.872395	+	0.488802i	$0.837434\pi$
$858$	7.07535	−	2.27694i	0.241548	−	0.0777336i
$859$	20.1776	−	15.0217i	0.688451	−	0.512533i	−0.195150	−	0.980773i	$-0.562519\pi$
$859$	20.1776	−	15.0217i	0.688451	−	0.512533i	0.883601	+	0.468241i	$0.155112\pi$
$860$	−8.48814	−	20.2960i	−0.289443	−	0.692088i
$861$	12.2955	−	0.320065i	0.419031	−	0.0109078i
$862$	−20.8956	+	31.3883i	−0.711707	+	1.06909i
$863$	14.1650	−	24.5345i	0.482183	−	0.835165i	−0.517608	−	0.855618i	$-0.673177\pi$
$863$	14.1650	−	24.5345i	0.482183	−	0.835165i	0.999791	+	0.0204526i	$0.00651072\pi$
$864$	−28.5469	−	7.00534i	−0.971185	−	0.238326i
$865$	2.87232	+	4.97500i	0.0976618	+	0.169155i
$866$	1.06357	+	0.0678875i	0.0361415	+	0.00230691i
$867$	7.22067	+	5.74540i	0.245227	+	0.195124i
$868$	−18.5798	−	2.38160i	−0.630638	−	0.0808366i
$869$	3.84101	+	1.65685i	0.130297	+	0.0562049i
$870$	11.0220	+	0.415930i	0.373681	+	0.0141014i
$871$	−11.9541	+	0.696244i	−0.405048	+	0.0235913i
$872$	9.98875	−	11.5083i	0.338262	−	0.389720i
$873$	9.62736	+	9.19510i	0.325837	+	0.311207i
$874$	1.36774	+	0.696464i	0.0462645	+	0.0235582i
$875$	−38.3767	−	4.48560i	−1.29737	−	0.151641i
$876$	5.24289	−	18.5115i	0.177141	−	0.625447i
$877$	−4.05142	−	13.5327i	−0.136807	−	0.456967i	0.861940	−	0.507010i	$-0.169249\pi$
$877$	−4.05142	−	13.5327i	−0.136807	−	0.456967i	−0.998747	+	0.0500432i	$0.984064\pi$
$878$	−27.1424	+	46.4134i	−0.916010	+	1.56638i
$879$	2.72771	−	2.14324i	0.0920032	−	0.0722897i
$880$	7.29335	+	7.19446i	0.245859	+	0.242525i
$881$	34.4944	−	41.1089i	1.16215	−	1.38499i	0.253549	−	0.967323i	$-0.418402\pi$
$881$	34.4944	−	41.1089i	1.16215	−	1.38499i	0.908599	−	0.417670i	$-0.137153\pi$
$882$	63.4578	−	30.9459i	2.13674	−	1.04200i
$883$	8.81822	+	10.5091i	0.296757	+	0.353661i	0.893734	−	0.448597i	$-0.148076\pi$
$883$	8.81822	+	10.5091i	0.296757	+	0.353661i	−0.596977	+	0.802258i	$0.703632\pi$
$884$	6.05207	−	3.40491i	0.203553	−	0.114519i
$885$	−11.5293	−	8.12565i	−0.387553	−	0.273141i
$886$	19.0841	+	3.47468i	0.641144	+	0.116734i
$887$	1.22517	−	21.0354i	0.0411373	−	0.706301i	−0.913189	−	0.407536i	$-0.866388\pi$
$887$	1.22517	−	21.0354i	0.0411373	−	0.706301i	0.954327	−	0.298765i	$-0.0965747\pi$
$888$	31.0400	+	5.17515i	1.04164	+	0.173667i
$889$	27.5870	+	29.2405i	0.925237	+	0.980694i
$890$	0.495876	+	0.151468i	0.0166218	+	0.00507721i
$891$	20.7956	−	17.0197i	0.696679	−	0.570181i
$892$	13.2552	−	19.6731i	0.443818	−	0.658703i
$893$	−26.9948	+	25.4683i	−0.903347	+	0.852264i
$894$	−9.97328	−	0.959341i	−0.333556	−	0.0320852i
$895$	−10.1417	−	0.590689i	−0.339001	−	0.0197446i
$896$	50.9198	+	20.8135i	1.70111	+	0.695331i
$897$	0.451178	+	0.0408662i	0.0150644	+	0.00136448i
$898$	13.7863	−	14.4506i	0.460054	−	0.482223i
$899$	7.74625	−	6.49988i	0.258352	−	0.216783i
$900$	−22.3750	+	12.4084i	−0.745834	+	0.413612i
$901$	−3.91653	−	3.28635i	−0.130478	−	0.109484i
$902$	−6.12930	+	0.681853i	−0.204083	+	0.0227032i
$903$	106.901	−	15.3244i	3.55746	−	0.509963i
$904$	−31.0433	+	14.9468i	−1.03249	+	0.497123i
$905$	13.7222	−	4.10817i	0.456142	−	0.136560i
$906$	9.45720	+	15.6328i	0.314194	+	0.519365i
$907$	−1.39165	+	11.9063i	−0.0462088	+	0.395342i	0.950265	+	0.311442i	$0.100812\pi$
$907$	−1.39165	+	11.9063i	−0.0462088	+	0.395342i	−0.996474	+	0.0839004i	$0.973262\pi$
$908$	−36.4763	+	37.8104i	−1.21051	+	1.25478i
$909$	−19.3047	−	12.8670i	−0.640296	−	0.426773i
$910$	−0.729004	+	5.94965i	−0.0241662	+	0.197229i
$911$	−0.231841	−	3.98055i	−0.00768122	−	0.131881i	−0.999969	−	0.00792287i	$-0.997478\pi$
$911$	−0.231841	−	3.98055i	−0.00768122	−	0.131881i	0.992287	−	0.123959i	$-0.0395590\pi$
$912$	3.50087	+	29.0052i	0.115925	+	0.960459i
$913$	19.2063	−	44.5253i	0.635637	−	1.47357i
$914$	4.57630	−	0.780687i	0.151370	−	0.0258228i
$915$	−11.0701	−	1.65619i	−0.365966	−	0.0547519i
$916$	30.3736	+	11.4396i	1.00357	+	0.377974i
$917$	−62.2951	+	35.9661i	−2.05717	+	1.18771i
$918$	15.8606	−	19.4616i	0.523477	−	0.642330i
$919$	−29.1917	−	16.8538i	−0.962945	−	0.555957i	−0.0658671	−	0.997828i	$-0.520981\pi$
$919$	−29.1917	−	16.8538i	−0.962945	−	0.555957i	−0.897078	+	0.441872i	$0.854315\pi$
$920$	0.237711	+	0.577398i	0.00783710	+	0.0190363i
$921$	−17.6021	−	9.56068i	−0.580008	−	0.315035i
$922$	−3.53883	+	2.93602i	−0.116545	+	0.0966926i
$923$	−8.63767	−	11.6024i	−0.284312	−	0.381898i
$924$	−43.1736	+	25.7911i	−1.42031	+	0.848466i
$925$	22.8850	−	15.0517i	0.752453	−	0.494896i
$926$	16.9942	−	22.5639i	0.558464	−	0.741495i
$927$	−2.10086	−	3.69083i	−0.0690011	−	0.121223i
$928$	−26.8977	+	12.5839i	−0.882962	+	0.413086i
$929$	20.3365	+	15.1399i	0.667217	+	0.496725i	0.876669	−	0.481094i	$-0.159760\pi$
$929$	20.3365	+	15.1399i	0.667217	+	0.496725i	−0.209452	+	0.977819i	$0.567168\pi$
$930$	1.30617	−	3.83075i	0.0428309	−	0.125615i
$931$	−51.0423	−	48.1559i	−1.67284	−	1.57825i
$932$	6.93237	+	30.7726i	0.227077	+	1.00799i
$933$	35.2965	+	21.9208i	1.15556	+	0.717654i
$934$	−11.9202	+	8.77158i	−0.390042	+	0.287015i
$935$	−8.22253	+	2.99275i	−0.268905	+	0.0978735i
$936$	4.14008	+	7.56444i	0.135323	+	0.247252i
$937$	−53.9398	−	19.6325i	−1.76214	−	0.641365i	−0.762155	−	0.647395i	$-0.775859\pi$
$937$	−53.9398	−	19.6325i	−1.76214	−	0.641365i	−0.999982	+	0.00602953i	$0.998081\pi$
$938$	77.7442	−	22.8044i	2.53844	−	0.744589i
$939$	−4.23130	−	50.1325i	−0.138083	−	1.63601i
$940$	−15.0817	+	0.710054i	−0.491910	+	0.0231594i
$941$	−10.3655	+	15.7600i	−0.337907	+	0.513762i	−0.963970	−	0.266010i	$-0.914295\pi$
$941$	−10.3655	+	15.7600i	−0.337907	+	0.513762i	0.626064	+	0.779772i	$0.284665\pi$
$942$	−8.60345	−	33.2537i	−0.280315	−	1.08347i
$943$	−0.360096	−	0.107806i	−0.0117263	−	0.00351064i
$944$	37.6108	+	5.24722i	1.22413	+	0.170782i
$945$	5.41635	+	20.9837i	0.176194	+	0.682598i
$946$	−52.7577	+	12.1941i	−1.71530	+	0.396464i
$947$	4.46785	−	1.05890i	0.145186	−	0.0344096i	−0.157380	−	0.987538i	$-0.550305\pi$
$947$	4.46785	−	1.05890i	0.145186	−	0.0344096i	0.302566	+	0.953128i	$0.402157\pi$
$948$	−1.04877	+	4.73852i	−0.0340625	+	0.153900i
$949$	−5.04397	+	2.53318i	−0.163734	+	0.0822304i
$950$	19.3894	+	16.4544i	0.629076	+	0.533853i
$951$	−38.5785	+	38.3428i	−1.25099	+	1.24335i
$952$	−34.7092	+	31.6679i	−1.12493	+	1.02636i
$953$	−38.9599	+	6.86967i	−1.26203	+	0.222531i	−0.764335	−	0.644820i	$-0.776933\pi$
$953$	−38.9599	+	6.86967i	−1.26203	+	0.222531i	−0.497699	+	0.867350i	$0.665821\pi$
$954$	4.13762	−	4.81552i	0.133960	−	0.155908i
$955$	−18.7410	−	3.30454i	−0.606444	−	0.106933i
$956$	22.5778	+	19.3774i	0.730218	+	0.626709i
$957$	5.57133	−	26.5707i	0.180096	−	0.858908i
$958$	−0.0581553	+	10.4484i	−0.00187891	+	0.337573i
$959$	69.2349	+	16.4090i	2.23571	+	0.529873i
$960$	−6.60430	+	9.88194i	−0.213153	+	0.318938i
$961$	10.8088	+	25.0576i	0.348671	+	0.808311i
$962$	−5.03001	−	7.74127i	−0.162174	−	0.249589i
$963$	−0.219685	+	1.78462i	−0.00707924	+	0.0575086i
$964$	9.14871	−	0.966228i	0.294660	−	0.0311201i
$965$	9.02580	−	17.9718i	0.290551	−	0.578534i
$966$	−3.03658	+	0.418060i	−0.0977005	+	0.0134509i
$967$	−1.00970	−	8.63856i	−0.0324699	−	0.277797i	−0.999713	−	0.0239465i	$-0.992377\pi$
$967$	−1.00970	−	8.63856i	−0.0324699	−	0.277797i	0.967243	−	0.253851i	$-0.0816972\pi$
$968$	−4.78814	+	3.44189i	−0.153897	+	0.110626i
$969$	−23.6631	−	7.92165i	−0.760170	−	0.254480i
$970$	4.82401	−	2.38918i	0.154890	−	0.0767119i
$971$	10.3740			0.332917			0.166459	−	0.986048i	$-0.446767\pi$
$971$	10.3740			0.332917			0.166459	+	0.986048i	$0.446767\pi$
$972$	23.9357	+	19.9770i	0.767738	+	0.640764i
$973$	93.8025			3.00717
$974$	−34.0730	+	16.8753i	−1.09177	+	0.540719i
$975$	7.11772	+	2.38278i	0.227949	+	0.0763101i
$976$	28.5409	−	9.67409i	0.913571	−	0.309660i
$977$	1.58378	+	13.5501i	0.0506697	+	0.433507i	0.994634	+	0.103459i	$0.0329910\pi$
$977$	1.58378	+	13.5501i	0.0506697	+	0.433507i	−0.943964	+	0.330048i	$0.892935\pi$
$978$	9.13480	−	1.25763i	0.292099	−	0.0402146i
$979$	0.572757	−	1.14045i	0.0183054	−	0.0364491i
$980$	−2.99841	−	28.3904i	−0.0957807	−	0.906898i
$981$	−14.8801	+	6.31078i	−0.475085	+	0.201488i
$982$	23.4906	+	36.1524i	0.749615	+	1.15367i
$983$	4.06415	+	9.42175i	0.129626	+	0.300507i	0.970652	−	0.240487i	$-0.0773073\pi$
$983$	4.06415	+	9.42175i	0.129626	+	0.300507i	−0.841026	+	0.540994i	$0.818048\pi$
$984$	−2.11591	−	6.83495i	−0.0674528	−	0.217890i
$985$	16.5538	+	3.92333i	0.527449	+	0.125008i
$986$	0.141172	−	25.3636i	0.00449584	−	0.807741i
$987$	15.2101	−	72.5397i	0.484143	−	2.30897i
$988$	5.58210	−	6.50405i	0.177590	−	0.206922i
$989$	−3.25024	−	0.573104i	−0.103351	−	0.0182237i
$990$	−3.59678	−	10.2536i	−0.114313	−	0.325880i
$991$	24.5213	−	4.32377i	0.778944	−	0.137349i	0.229981	−	0.973195i	$-0.426134\pi$
$991$	24.5213	−	4.32377i	0.778944	−	0.137349i	0.548964	+	0.835846i	$0.315023\pi$
$992$	1.59285	+	10.7796i	0.0505729	+	0.342252i
$993$	7.17277	−	7.12895i	0.227621	−	0.226230i
$994$	74.6211	+	63.3256i	2.36684	+	2.00857i
$995$	12.8824	−	6.46981i	0.408401	−	0.205107i
$996$	54.9292	+	12.1574i	1.74050	+	0.385222i
$997$	54.2664	−	12.8614i	1.71863	−	0.407324i	0.751124	−	0.660161i	$-0.229512\pi$
$997$	54.2664	−	12.8614i	1.71863	−	0.407324i	0.967509	+	0.252837i	$0.0813637\pi$
$998$	11.3061	−	2.61321i	0.357887	−	0.0827198i
$999$	−27.1640	−	19.3950i	−0.859432	−	0.613629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.59.35	yes	936
3.2	odd	2		972.2.p.a.287.18		936
4.3	odd	2	inner	324.2.p.a.59.10	yes	936
12.11	even	2		972.2.p.a.287.43		936
81.11	odd	54	inner	324.2.p.a.11.10	✓	936
81.70	even	27		972.2.p.a.359.43		936
324.11	even	54	inner	324.2.p.a.11.35	yes	936
324.151	odd	54		972.2.p.a.359.18		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.10	✓	936	81.11	odd	54	inner
324.2.p.a.11.35	yes	936	324.11	even	54	inner
324.2.p.a.59.10	yes	936	4.3	odd	2	inner
324.2.p.a.59.35	yes	936	1.1	even	1	trivial
972.2.p.a.287.18		936	3.2	odd	2
972.2.p.a.287.43		936	12.11	even	2
972.2.p.a.359.18		936	324.151	odd	54
972.2.p.a.359.43		936	81.70	even	27

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627654 + 1.26730i) q^{2} +(-1.64246 - 0.549842i) q^{3} +(-1.21210 + 1.59085i) q^{4} +(-0.0995817 - 0.851976i) q^{5} +(-0.334081 - 2.42660i) q^{6} +(2.18215 - 4.34501i) q^{7} +(-2.77687 - 0.537591i) q^{8} +(2.39535 + 1.80619i) q^{9} +O(q^{10})\)	\(q+(0.627654 + 1.26730i) q^{2} +(-1.64246 - 0.549842i) q^{3} +(-1.21210 + 1.59085i) q^{4} +(-0.0995817 - 0.851976i) q^{5} +(-0.334081 - 2.42660i) q^{6} +(2.18215 - 4.34501i) q^{7} +(-2.77687 - 0.537591i) q^{8} +(2.39535 + 1.80619i) q^{9} +(1.01721 - 0.660946i) q^{10} +(-1.18262 - 2.74163i) q^{11} +(2.86554 - 1.94645i) q^{12} +(-0.988870 - 0.234367i) q^{13} +(6.87607 + 0.0382718i) q^{14} +(-0.304893 + 1.45409i) q^{15} +(-1.06162 - 3.85655i) q^{16} +(3.36460 + 0.593269i) q^{17} +(-0.785532 + 4.16929i) q^{18} +(4.15287 - 0.732262i) q^{19} +(1.47607 + 0.874261i) q^{20} +(-5.97316 + 5.93667i) q^{21} +(2.73219 - 3.21954i) q^{22} +(0.229993 - 0.115507i) q^{23} +(4.26530 + 2.40981i) q^{24} +(4.14928 - 0.983397i) q^{25} +(-0.323656 - 1.40030i) q^{26} +(-2.94114 - 4.28365i) q^{27} +(4.26729 + 8.73806i) q^{28} +(-5.02900 - 1.50558i) q^{29} +(-2.03414 + 0.526274i) q^{30} +(-1.05850 + 1.60937i) q^{31} +(4.22107 - 3.76597i) q^{32} +(0.434949 + 5.15328i) q^{33} +(1.35995 + 4.63632i) q^{34} +(-3.91915 - 1.42645i) q^{35} +(-5.77678 + 1.62136i) q^{36} +(6.03610 - 2.19696i) q^{37} +(3.53456 + 4.80332i) q^{38} +(1.49532 + 0.928660i) q^{39} +(-0.181489 + 2.41936i) q^{40} +(-1.06233 - 1.00226i) q^{41} +(-11.2726 - 3.84361i) q^{42} +(-10.2861 - 7.65769i) q^{43} +(5.79499 + 1.44175i) q^{44} +(1.30029 - 2.22064i) q^{45} +(0.290738 + 0.218972i) q^{46} +(-7.35304 + 4.83617i) q^{47} +(-0.376820 + 6.91795i) q^{48} +(-9.93725 - 13.3480i) q^{49} +(3.85057 + 4.64115i) q^{50} +(-5.20001 - 2.82442i) q^{51} +(1.57145 - 1.28907i) q^{52} +(-1.29597 - 0.748231i) q^{53} +(3.58265 - 6.41596i) q^{54} +(-2.21804 + 1.28058i) q^{55} +(-8.39537 + 10.8924i) q^{56} +(-7.22354 - 1.08071i) q^{57} +(-1.24844 - 7.31824i) q^{58} +(-3.76029 + 8.71733i) q^{59} +(-1.94368 - 2.24754i) q^{60} +(0.438061 + 7.52121i) q^{61} +(-2.70394 - 0.331310i) q^{62} +(13.0749 - 6.46645i) q^{63} +(7.42199 + 2.98564i) q^{64} +(-0.101201 + 0.865832i) q^{65} +(-6.25775 + 3.78569i) q^{66} +(11.2877 - 3.37931i) q^{67} +(-5.02203 + 4.63347i) q^{68} +(-0.441264 + 0.0632554i) q^{69} +(-0.652124 - 5.86205i) q^{70} +(10.9032 + 9.14888i) q^{71} +(-5.68057 - 6.30326i) q^{72} +(4.25462 - 3.57005i) q^{73} +(6.57279 + 6.27062i) q^{74} +(-7.35574 - 0.666258i) q^{75} +(-3.86877 + 7.49417i) q^{76} +(-14.4931 - 0.844126i) q^{77} +(-0.238351 + 2.47789i) q^{78} +(-1.01905 + 0.961422i) q^{79} +(-3.17997 + 1.28852i) q^{80} +(2.47538 + 8.65289i) q^{81} +(0.603385 - 1.97536i) q^{82} +(11.1449 + 11.8129i) q^{83} +(-2.20429 - 16.6983i) q^{84} +(0.170399 - 2.92563i) q^{85} +(3.24851 - 17.8419i) q^{86} +(7.43209 + 5.23801i) q^{87} +(1.81012 + 8.24892i) q^{88} +(0.274740 + 0.327422i) q^{89} +(3.63035 + 0.254070i) q^{90} +(-3.17619 + 3.78523i) q^{91} +(-0.0950203 + 0.505890i) q^{92} +(2.62345 - 2.06132i) q^{93} +(-10.7440 - 6.28307i) q^{94} +(-1.03742 - 3.46522i) q^{95} +(-9.00363 + 3.86453i) q^{96} +(4.40766 + 0.515182i) q^{97} +(10.6788 - 20.9714i) q^{98} +(2.11910 - 8.70320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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