LMFDB - Embedded newform 162.2.g.b.115.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			115.3
Character	$\chi$	$=$	162.115
Dual form			162.2.g.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396080 - 0.918216i) q^{2} +(0.178274 + 1.72285i) q^{3} +(-0.686242 - 0.727374i) q^{4} +(-0.253242 - 4.34800i) q^{5} +(1.65256 + 0.518693i) q^{6} +(3.96081 + 0.938728i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.93644 + 0.614278i) q^{9} +O(q^{10})$	\(q+(0.396080 - 0.918216i) q^{2} +(0.178274 + 1.72285i) q^{3} +(-0.686242 - 0.727374i) q^{4} +(-0.253242 - 4.34800i) q^{5} +(1.65256 + 0.518693i) q^{6} +(3.96081 + 0.938728i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.93644 + 0.614278i) q^{9} +(-4.09271 - 1.48962i) q^{10} +(1.14679 + 0.754256i) q^{11} +(1.13082 - 1.31196i) q^{12} +(0.410136 + 0.0479380i) q^{13} +(2.43075 - 3.26506i) q^{14} +(7.44581 - 1.21143i) q^{15} +(-0.0581448 + 0.998308i) q^{16} +(0.360116 - 0.302173i) q^{17} +(-0.599023 + 2.93959i) q^{18} +(0.227520 + 0.190912i) q^{19} +(-2.98883 + 3.16798i) q^{20} +(-0.911183 + 6.99123i) q^{21} +(1.14679 - 0.754256i) q^{22} +(-6.34530 + 1.50386i) q^{23} +(-0.756772 - 1.55798i) q^{24} +(-13.8748 + 1.62173i) q^{25} +(0.206464 - 0.357606i) q^{26} +(-1.58180 - 4.94954i) q^{27} +(-2.03526 - 3.52518i) q^{28} +(4.14206 + 5.56376i) q^{29} +(1.83678 - 7.31669i) q^{30} +(-2.61346 + 8.72957i) q^{31} +(0.893633 + 0.448799i) q^{32} +(-1.09503 + 2.11021i) q^{33} +(-0.134826 - 0.450349i) q^{34} +(3.07855 - 17.4593i) q^{35} +(2.46191 + 1.71434i) q^{36} +(-0.254225 - 1.44178i) q^{37} +(0.265415 - 0.133296i) q^{38} +(-0.00947370 + 0.715149i) q^{39} +(1.72507 + 3.99917i) q^{40} +(-1.98418 - 4.59985i) q^{41} +(6.05856 + 3.60575i) q^{42} +(-2.26969 + 1.13988i) q^{43} +(-0.238349 - 1.35175i) q^{44} +(3.41451 + 12.6121i) q^{45} +(-1.13237 + 6.42200i) q^{46} +(0.597351 + 1.99529i) q^{47} +(-1.73030 + 0.0777970i) q^{48} +(8.55134 + 4.29464i) q^{49} +(-4.00642 + 13.3824i) q^{50} +(0.584798 + 0.566557i) q^{51} +(-0.246583 - 0.331219i) q^{52} +(1.77553 + 3.07530i) q^{53} +(-5.17126 - 0.507978i) q^{54} +(2.98909 - 5.17725i) q^{55} +(-4.04300 + 0.472559i) q^{56} +(-0.288352 + 0.426018i) q^{57} +(6.74932 - 1.59962i) q^{58} +(4.66336 - 3.06714i) q^{59} +(-5.99079 - 4.58455i) q^{60} +(4.11569 - 4.36238i) q^{61} +(6.98049 + 5.85733i) q^{62} +(-12.2073 - 0.323481i) q^{63} +(0.766044 - 0.642788i) q^{64} +(0.104571 - 1.79541i) q^{65} +(1.50391 + 1.84129i) q^{66} +(2.81104 - 3.77588i) q^{67} +(-0.466919 - 0.0545750i) q^{68} +(-3.72213 - 10.6639i) q^{69} +(-14.8121 - 9.74204i) q^{70} +(-1.16819 - 0.425188i) q^{71} +(2.54925 - 1.58155i) q^{72} +(4.83702 - 1.76053i) q^{73} +(-1.42456 - 0.337627i) q^{74} +(-5.26750 - 23.6150i) q^{75} +(-0.0172694 - 0.296504i) q^{76} +(3.83417 + 4.06399i) q^{77} +(0.652909 + 0.291955i) q^{78} +(3.39340 - 7.86678i) q^{79} +4.35537 q^{80} +(8.24533 - 3.60758i) q^{81} -5.00955 q^{82} +(-3.65159 + 8.46534i) q^{83} +(5.71053 - 4.13490i) q^{84} +(-1.40504 - 1.48926i) q^{85} +(0.147679 + 2.53555i) q^{86} +(-8.84711 + 8.12803i) q^{87} +(-1.33560 - 0.316543i) q^{88} +(-10.4279 + 3.79543i) q^{89} +(12.9330 + 1.86013i) q^{90} +(1.57947 + 0.574879i) q^{91} +(5.44828 + 3.58339i) q^{92} +(-15.5057 - 2.94636i) q^{93} +(2.06871 + 0.241797i) q^{94} +(0.772467 - 1.03760i) q^{95} +(-0.613903 + 1.61961i) q^{96} +(-0.337750 + 5.79894i) q^{97} +(7.33042 - 6.15096i) q^{98} +(-3.83080 - 1.51038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	0.396080	−	0.918216i	0.280071	−	0.649277i
$2$	0.396080	−	0.918216i	0.280071	−	0.649277i
$3$	0.178274	+	1.72285i	0.102926	+	0.994689i
$3$	0.178274	+	1.72285i	0.102926	+	0.994689i
$4$	−0.686242	−	0.727374i	−0.343121	−	0.363687i
$5$	−0.253242	−	4.34800i	−0.113253	−	1.94448i	−0.283265	−	0.959042i	$-0.591418\pi$
$5$	−0.253242	−	4.34800i	−0.113253	−	1.94448i	0.170012	−	0.985442i	$-0.445619\pi$
$6$	1.65256	+	0.518693i	0.674655	+	0.211756i
$7$	3.96081	+	0.938728i	1.49704	+	0.354806i	0.895871	−	0.444314i	$-0.146552\pi$
$7$	3.96081	+	0.938728i	1.49704	+	0.354806i	0.601172	+	0.799119i	$0.294701\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	−2.93644	+	0.614278i	−0.978812	+	0.204759i
$10$	−4.09271	−	1.48962i	−1.29423	−	0.471060i
$11$	1.14679	+	0.754256i	0.345770	+	0.227417i	0.710501	−	0.703696i	$-0.248468\pi$
$11$	1.14679	+	0.754256i	0.345770	+	0.227417i	−0.364730	+	0.931113i	$0.618839\pi$
$12$	1.13082	−	1.31196i	0.326439	−	0.378731i
$13$	0.410136	+	0.0479380i	0.113751	+	0.0132956i	0.172778	−	0.984961i	$-0.444726\pi$
$13$	0.410136	+	0.0479380i	0.113751	+	0.0132956i	−0.0590268	+	0.998256i	$0.518800\pi$
$14$	2.43075	−	3.26506i	0.649645	−	0.872625i
$15$	7.44581	−	1.21143i	1.92250	−	0.312790i
$16$	−0.0581448	+	0.998308i	−0.0145362	+	0.249577i
$17$	0.360116	−	0.302173i	0.0873409	−	0.0732877i	−0.598072	−	0.801443i	$-0.704066\pi$
$17$	0.360116	−	0.302173i	0.0873409	−	0.0732877i	0.685413	+	0.728155i	$0.259622\pi$
$18$	−0.599023	+	2.93959i	−0.141191	+	0.692867i
$19$	0.227520	+	0.190912i	0.0521967	+	0.0437982i	0.668513	−	0.743701i	$-0.266931\pi$
$19$	0.227520	+	0.190912i	0.0521967	+	0.0437982i	−0.616316	+	0.787499i	$0.711376\pi$
$20$	−2.98883	+	3.16798i	−0.668324	+	0.708382i
$21$	−0.911183	+	6.99123i	−0.198836	+	1.52561i
$22$	1.14679	−	0.754256i	0.244497	−	0.160808i
$23$	−6.34530	+	1.50386i	−1.32309	+	0.313577i	−0.830661	−	0.556778i	$-0.812037\pi$
$23$	−6.34530	+	1.50386i	−1.32309	+	0.313577i	−0.492425	+	0.870355i	$0.663889\pi$
$24$	−0.756772	−	1.55798i	−0.154476	−	0.318021i
$25$	−13.8748	+	1.62173i	−2.77495	+	0.324345i
$26$	0.206464	−	0.357606i	0.0404909	−	0.0701323i
$27$	−1.58180	−	4.94954i	−0.304417	−	0.952539i
$28$	−2.03526	−	3.52518i	−0.384629	−	0.666196i
$29$	4.14206	+	5.56376i	0.769162	+	1.03316i	0.998213	+	0.0597496i	$0.0190302\pi$
$29$	4.14206	+	5.56376i	0.769162	+	1.03316i	−0.229051	+	0.973414i	$0.573562\pi$
$30$	1.83678	−	7.31669i	0.335348	−	1.33584i
$31$	−2.61346	+	8.72957i	−0.469392	+	1.56788i	0.315926	+	0.948784i	$0.397685\pi$
$31$	−2.61346	+	8.72957i	−0.469392	+	1.56788i	−0.785317	+	0.619094i	$0.787500\pi$
$32$	0.893633	+	0.448799i	0.157973	+	0.0793372i
$33$	−1.09503	+	2.11021i	−0.190620	+	0.367341i
$34$	−0.134826	−	0.450349i	−0.0231224	−	0.0772342i
$35$	3.07855	−	17.4593i	0.520369	−	2.95116i
$36$	2.46191	+	1.71434i	0.410319	+	0.285724i
$37$	−0.254225	−	1.44178i	−0.0417943	−	0.237027i	0.956754	−	0.290900i	$-0.0939547\pi$
$37$	−0.254225	−	1.44178i	−0.0417943	−	0.237027i	−0.998548	+	0.0538725i	$0.982844\pi$
$38$	0.265415	−	0.133296i	0.0430559	−	0.0216235i
$39$	−0.00947370	+	0.715149i	−0.00151701	+	0.114516i
$40$	1.72507	+	3.99917i	0.272758	+	0.632324i
$41$	−1.98418	−	4.59985i	−0.309877	−	0.718376i	0.690108	−	0.723706i	$-0.257563\pi$
$41$	−1.98418	−	4.59985i	−0.309877	−	0.718376i	−0.999986	+	0.00532951i	$0.998304\pi$
$42$	6.05856	+	3.60575i	0.934856	+	0.556379i
$43$	−2.26969	+	1.13988i	−0.346124	+	0.173830i	−0.613365	−	0.789800i	$-0.710184\pi$
$43$	−2.26969	+	1.13988i	−0.346124	+	0.173830i	0.267241	+	0.963630i	$0.413888\pi$
$44$	−0.238349	−	1.35175i	−0.0359325	−	0.203784i
$45$	3.41451	+	12.6121i	0.509005	+	1.88010i
$46$	−1.13237	+	6.42200i	−0.166959	+	0.946873i
$47$	0.597351	+	1.99529i	0.0871326	+	0.291043i	0.990439	−	0.137953i	$-0.0440524\pi$
$47$	0.597351	+	1.99529i	0.0871326	+	0.291043i	−0.903306	+	0.428997i	$0.858867\pi$
$48$	−1.73030	+	0.0777970i	−0.249748	+	0.0112290i
$49$	8.55134	+	4.29464i	1.22162	+	0.613521i
$50$	−4.00642	+	13.3824i	−0.566593	+	1.89255i
$51$	0.584798	+	0.566557i	0.0818882	+	0.0793338i
$52$	−0.246583	−	0.331219i	−0.0341950	−	0.0459318i
$53$	1.77553	+	3.07530i	0.243887	+	0.422425i	0.961818	−	0.273689i	$-0.0882439\pi$
$53$	1.77553	+	3.07530i	0.243887	+	0.422425i	−0.717931	+	0.696114i	$0.754911\pi$
$54$	−5.17126	−	0.507978i	−0.703720	−	0.0691271i
$55$	2.98909	−	5.17725i	0.403049	−	0.698101i
$56$	−4.04300	+	0.472559i	−0.540269	+	0.0631484i
$57$	−0.288352	+	0.426018i	−0.0381932	+	0.0564275i
$58$	6.74932	−	1.59962i	0.886229	−	0.210040i
$59$	4.66336	−	3.06714i	0.607118	−	0.399307i	−0.208397	−	0.978044i	$-0.566825\pi$
$59$	4.66336	−	3.06714i	0.607118	−	0.399307i	0.815514	+	0.578737i	$0.196454\pi$
$60$	−5.99079	−	4.58455i	−0.773407	−	0.591863i
$61$	4.11569	−	4.36238i	0.526960	−	0.558545i	−0.408144	−	0.912917i	$-0.633824\pi$
$61$	4.11569	−	4.36238i	0.526960	−	0.558545i	0.935104	+	0.354372i	$0.115305\pi$
$62$	6.98049	+	5.85733i	0.886524	+	0.743882i
$63$	−12.2073	−	0.323481i	−1.53797	−	0.0407548i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	0.104571	−	1.79541i	0.0129704	−	0.222693i
$66$	1.50391	+	1.84129i	0.185119	+	0.226647i
$67$	2.81104	−	3.77588i	0.343423	−	0.461297i	−0.596535	−	0.802587i	$-0.703456\pi$
$67$	2.81104	−	3.77588i	0.343423	−	0.461297i	0.939958	+	0.341290i	$0.110864\pi$
$68$	−0.466919	−	0.0545750i	−0.0566223	−	0.00661819i
$69$	−3.72213	−	10.6639i	−0.448092	−	1.28378i
$70$	−14.8121	−	9.74204i	−1.77038	−	1.16440i
$71$	−1.16819	−	0.425188i	−0.138639	−	0.0504605i	0.271769	−	0.962363i	$-0.412391\pi$
$71$	−1.16819	−	0.425188i	−0.138639	−	0.0504605i	−0.410408	+	0.911902i	$0.634614\pi$
$72$	2.54925	−	1.58155i	0.300432	−	0.186388i
$73$	4.83702	−	1.76053i	0.566131	−	0.206055i	−0.0430682	−	0.999072i	$-0.513713\pi$
$73$	4.83702	−	1.76053i	0.566131	−	0.206055i	0.609199	+	0.793017i	$0.291491\pi$
$74$	−1.42456	−	0.337627i	−0.165602	−	0.0392483i
$75$	−5.26750	−	23.6150i	−0.608238	−	2.72683i
$76$	−0.0172694	−	0.296504i	−0.00198093	−	0.0340113i
$77$	3.83417	+	4.06399i	0.436945	+	0.463134i
$78$	0.652909	+	0.291955i	0.0739274	+	0.0330574i
$79$	3.39340	−	7.86678i	0.381787	−	0.885081i	−0.613643	−	0.789584i	$-0.710296\pi$
$79$	3.39340	−	7.86678i	0.381787	−	0.885081i	0.995430	−	0.0954977i	$-0.0304443\pi$
$80$	4.35537			0.486945
$81$	8.24533	−	3.60758i	0.916147	−	0.400842i
$82$	−5.00955			−0.553213
$83$	−3.65159	+	8.46534i	−0.400814	+	0.929192i	0.591598	+	0.806233i	$0.298497\pi$
$83$	−3.65159	+	8.46534i	−0.400814	+	0.929192i	−0.992412	+	0.122958i	$0.960762\pi$
$84$	5.71053	−	4.13490i	0.623070	−	0.451155i
$85$	−1.40504	−	1.48926i	−0.152398	−	0.161533i
$86$	0.147679	+	2.53555i	0.0159246	+	0.273415i
$87$	−8.84711	+	8.12803i	−0.948510	+	0.871417i
$88$	−1.33560	−	0.316543i	−0.142376	−	0.0337436i
$89$	−10.4279	+	3.79543i	−1.10535	+	0.402315i	−0.829286	−	0.558824i	$-0.811253\pi$
$89$	−10.4279	+	3.79543i	−1.10535	+	0.402315i	−0.276065	+	0.961139i	$0.589031\pi$
$90$	12.9330	+	1.86013i	1.36326	+	0.196074i
$91$	1.57947	+	0.574879i	0.165573	+	0.0602637i
$92$	5.44828	+	3.58339i	0.568022	+	0.373594i
$93$	−15.5057	−	2.94636i	−1.60786	−	0.305523i
$94$	2.06871	+	0.241797i	0.213371	+	0.0249395i
$95$	0.772467	−	1.03760i	0.0792535	−	0.106456i
$96$	−0.613903	+	1.61961i	−0.0626563	+	0.165300i
$97$	−0.337750	+	5.79894i	−0.0342933	+	0.588793i	0.936766	+	0.349956i	$0.113803\pi$
$97$	−0.337750	+	5.79894i	−0.0342933	+	0.588793i	−0.971060	+	0.238838i	$0.923234\pi$
$98$	7.33042	−	6.15096i	0.740485	−	0.621340i
$99$	−3.83080	−	1.51038i	−0.385010	−	0.151799i
$100$	10.7010	+	8.97924i	1.07010	+	0.897924i
$101$	−0.717214	+	0.760202i	−0.0713655	+	0.0756430i	−0.762072	−	0.647492i	$-0.775818\pi$
$101$	−0.717214	+	0.760202i	−0.0713655	+	0.0756430i	0.690707	+	0.723135i	$0.257299\pi$
$102$	0.751848	−	0.312570i	0.0744441	−	0.0309490i
$103$	2.76671	−	1.81969i	0.272612	−	0.179300i	−0.405841	−	0.913944i	$-0.633021\pi$
$103$	2.76671	−	1.81969i	0.272612	−	0.179300i	0.678453	+	0.734644i	$0.262651\pi$
$104$	−0.401797	+	0.0952277i	−0.0393995	+	0.00933785i
$105$	30.6286	+	2.19135i	2.98905	+	0.213853i
$106$	3.52704	−	0.412252i	0.342577	−	0.0400415i
$107$	2.20473	−	3.81871i	0.213140	−	0.369169i	−0.739556	−	0.673095i	$-0.764964\pi$
$107$	2.20473	−	3.81871i	0.213140	−	0.369169i	0.952696	+	0.303926i	$0.0982977\pi$
$108$	−2.51467	+	4.54714i	−0.241974	+	0.437548i
$109$	−6.61618	−	11.4596i	−0.633715	−	1.09763i	−0.986786	−	0.162030i	$-0.948196\pi$
$109$	−6.61618	−	11.4596i	−0.633715	−	1.09763i	0.353071	−	0.935597i	$-0.385138\pi$
$110$	−3.56992	−	4.79523i	−0.340378	−	0.457208i
$111$	2.43865	−	0.695023i	0.231467	−	0.0659687i
$112$	−1.16744	+	3.89952i	−0.110313	+	0.368470i
$113$	−9.76552	−	4.90443i	−0.918663	−	0.461370i	−0.0743573	−	0.997232i	$-0.523691\pi$
$113$	−9.76552	−	4.90443i	−0.918663	−	0.461370i	−0.844306	+	0.535862i	$0.819987\pi$
$114$	0.276966	+	0.433507i	0.0259402	+	0.0406016i
$115$	8.14569	+	27.2085i	0.759589	+	2.53721i
$116$	1.20447	−	6.83091i	0.111833	−	0.634234i
$117$	−1.23379	+	0.111170i	−0.114063	+	0.0102777i
$118$	−0.969235	−	5.49680i	−0.0892253	−	0.506022i
$119$	1.71001	−	0.858798i	0.156756	−	0.0787259i
$120$	−6.58244	+	3.68499i	−0.600892	+	0.336392i
$121$	−3.61065	−	8.37043i	−0.328241	−	0.760948i
$122$	−2.37546	−	5.50694i	−0.215064	−	0.498575i
$123$	7.57114	−	4.23849i	0.682667	−	0.382171i
$124$	8.14313	−	4.08963i	0.731274	−	0.367260i
$125$	6.78343	+	38.4707i	0.606729	+	3.44093i
$126$	−5.13209	+	11.0808i	−0.457203	+	0.987157i
$127$	0.618189	−	3.50592i	0.0548554	−	0.311100i	−0.945018	−	0.327019i	$-0.893956\pi$
$127$	0.618189	−	3.50592i	0.0548554	−	0.311100i	0.999873	+	0.0159183i	$0.00506715\pi$
$128$	−0.286803	−	0.957990i	−0.0253501	−	0.0846751i
$129$	−2.36847	−	3.70712i	−0.208532	−	0.326394i
$130$	−1.60716	−	0.807144i	−0.140957	−	0.0707912i
$131$	2.37243	−	7.92448i	0.207281	−	0.692365i	−0.789613	−	0.613605i	$-0.789719\pi$
$131$	2.37243	−	7.92448i	0.207281	−	0.692365i	0.996894	−	0.0787602i	$-0.0250961\pi$
$132$	2.28637	−	0.651622i	0.199003	−	0.0567164i
$133$	0.721948	+	0.969745i	0.0626009	+	0.0840875i
$134$	−2.35368	−	4.07669i	−0.203327	−	0.352172i
$135$	−21.1200	+	8.13109i	−1.81772	+	0.699813i
$136$	−0.235049	+	0.407117i	−0.0201553	+	0.0349100i
$137$	−18.3333	+	2.14286i	−1.56632	+	0.183077i	−0.854563	−	0.519348i	$-0.826175\pi$
$137$	−18.3333	+	2.14286i	−1.56632	+	0.183077i	−0.711758	+	0.702425i	$0.752101\pi$
$138$	−11.2660	−	0.806037i	−0.959029	−	0.0686144i
$139$	12.4118	−	2.94165i	1.05275	−	0.249507i	0.332418	−	0.943132i	$-0.392136\pi$
$139$	12.4118	−	2.94165i	1.05275	−	0.249507i	0.720336	+	0.693625i	$0.243987\pi$
$140$	−14.8121	+	9.74204i	−1.25185	+	0.823353i
$141$	−3.33110	+	1.38485i	−0.280529	+	0.116626i
$142$	−0.853113	+	0.904247i	−0.0715916	+	0.0758827i
$143$	0.434182	+	0.364322i	0.0363081	+	0.0304662i
$144$	−0.442500	−	2.96719i	−0.0368750	−	0.247266i
$145$	23.1423	−	19.4187i	1.92186	−	1.61263i
$146$	0.299298	−	5.13874i	0.0247701	−	0.425286i
$147$	−5.87456	+	15.4983i	−0.484525	+	1.27828i
$148$	−0.874254	+	1.17433i	−0.0718632	+	0.0965291i
$149$	−6.17878	−	0.722195i	−0.506185	−	0.0591645i	−0.140832	−	0.990034i	$-0.544978\pi$
$149$	−6.17878	−	0.722195i	−0.506185	−	0.0591645i	−0.365353	+	0.930869i	$0.619052\pi$
$150$	−23.7701	−	4.51674i	−1.94082	−	0.368790i
$151$	15.9160	+	10.4681i	1.29523	+	0.851884i	0.994793	−	0.101919i	$-0.0324982\pi$
$151$	15.9160	+	10.4681i	1.29523	+	0.851884i	0.300434	+	0.953803i	$0.402869\pi$
$152$	−0.279095	−	0.101582i	−0.0226376	−	0.00823940i
$153$	−0.871839	+	1.10852i	−0.0704840	+	0.0896188i
$154$	5.25026	−	1.91094i	0.423078	−	0.153988i
$155$	38.6180	+	9.15263i	3.10187	+	0.735157i
$156$	0.526682	−	0.483874i	0.0421683	−	0.0387409i
$157$	0.673757	+	11.5680i	0.0537717	+	0.923224i	0.912060	+	0.410057i	$0.134491\pi$
$157$	0.673757	+	11.5680i	0.0537717	+	0.923224i	−0.858288	+	0.513168i	$0.828472\pi$
$158$	−5.87935	−	6.23174i	−0.467736	−	0.495771i
$159$	−4.98176	+	3.60722i	−0.395079	+	0.286071i
$160$	1.72507	−	3.99917i	0.136379	−	0.316162i
$161$	−26.5442			−2.09198
$162$	−0.0467284	−	8.99988i	−0.00367133	−	0.707097i
$163$	−8.76205			−0.686297			−0.343148	−	0.939281i	$-0.611493\pi$
$163$	−8.76205			−0.686297			−0.343148	+	0.939281i	$0.611493\pi$
$164$	−1.98418	+	4.59985i	−0.154939	+	0.359188i
$165$	9.45251	+	4.22679i	0.735877	+	0.329055i
$166$	6.32669	+	6.70590i	0.491046	+	0.520479i
$167$	−0.583365	−	10.0160i	−0.0451421	−	0.775060i	−0.942593	−	0.333945i	$-0.891620\pi$
$167$	−0.583365	−	10.0160i	−0.0451421	−	0.775060i	0.897450	−	0.441115i	$-0.145417\pi$
$168$	−1.53491	−	6.88125i	−0.118421	−	0.530900i
$169$	−12.4837	−	2.95868i	−0.960282	−	0.227591i
$170$	−1.92397	+	0.700268i	−0.147562	+	0.0537081i
$171$	−0.785371	−	0.420841i	−0.0600589	−	0.0321825i
$172$	2.38667	+	0.868678i	0.181982	+	0.0662360i
$173$	10.0925	+	6.63794i	0.767319	+	0.504674i	0.871805	−	0.489853i	$-0.162949\pi$
$173$	10.0925	+	6.63794i	0.767319	+	0.504674i	−0.104486	+	0.994526i	$0.533320\pi$
$174$	3.95913	+	11.3429i	0.300141	+	0.859904i
$175$	−56.4776	−	6.60128i	−4.26930	−	0.499010i
$176$	−0.819660	+	1.10099i	−0.0617842	+	0.0829906i
$177$	6.11558	+	7.48749i	0.459675	+	0.562794i
$178$	−0.645239	+	11.0783i	−0.0483627	+	0.830356i
$179$	10.0604	−	8.44166i	0.751948	−	0.630960i	−0.184069	−	0.982913i	$-0.558927\pi$
$179$	10.0604	−	8.44166i	0.751948	−	0.630960i	0.936017	+	0.351954i	$0.114483\pi$
$180$	6.83050	−	11.1385i	0.509116	−	0.830218i
$181$	−0.397081	−	0.333191i	−0.0295148	−	0.0247659i	0.627911	−	0.778285i	$-0.283910\pi$
$181$	−0.397081	−	0.333191i	−0.0295148	−	0.0247659i	−0.657426	+	0.753519i	$0.728355\pi$
$182$	1.15346	−	1.22259i	0.0855000	−	0.0906247i
$183$	8.24945	+	6.31303i	0.609817	+	0.466673i
$184$	5.44828	−	3.58339i	0.401652	−	0.264171i
$185$	−6.20448	+	1.47049i	−0.456163	+	0.108112i
$186$	−8.84688	+	13.0706i	−0.648684	+	0.958380i
$187$	0.640893	−	0.0749097i	0.0468668	−	0.00547794i
$188$	1.04139	−	1.80375i	0.0759515	−	0.131552i
$189$	−1.61893	−	21.0890i	−0.117760	−	1.53400i
$190$	−0.646786	−	1.12027i	−0.0469228	−	0.0812726i
$191$	−14.1730	−	19.0377i	−1.02552	−	1.37752i	−0.923874	−	0.382696i	$-0.874996\pi$
$191$	−14.1730	−	19.0377i	−1.02552	−	1.37752i	−0.101648	−	0.994820i	$-0.532412\pi$
$192$	1.24399	+	1.20519i	0.0897775	+	0.0869770i
$193$	0.705059	−	2.35506i	0.0507513	−	0.169521i	−0.928857	−	0.370439i	$-0.879207\pi$
$193$	0.705059	−	2.35506i	0.0507513	−	0.169521i	0.979608	+	0.200918i	$0.0643925\pi$
$194$	5.19091	+	2.60697i	0.372685	+	0.187170i
$195$	3.11187	−	0.139914i	0.222845	−	0.0100195i
$196$	−2.74447	−	9.16718i	−0.196034	−	0.654799i
$197$	0.961541	−	5.45317i	0.0685070	−	0.388522i	−0.931204	−	0.364497i	$-0.881241\pi$
$197$	0.961541	−	5.45317i	0.0685070	−	0.388522i	0.999711	−	0.0240249i	$-0.00764811\pi$
$198$	−2.90416	+	2.91927i	−0.206389	+	0.207464i
$199$	0.939417	+	5.32770i	0.0665935	+	0.377670i	0.999831	+	0.0184092i	$0.00586016\pi$
$199$	0.939417	+	5.32770i	0.0665935	+	0.377670i	−0.933237	+	0.359261i	$0.883029\pi$
$200$	12.4833	−	6.26937i	0.882706	−	0.443312i
$201$	7.00641	+	4.16986i	0.494194	+	0.294119i
$202$	0.413956	+	0.959658i	0.0291259	+	0.0675213i
$203$	11.1831	+	25.9252i	0.784897	+	1.81959i
$204$	0.0107853	−	0.814162i	0.000755125	−	0.0570027i
$205$	−19.4977	+	9.79210i	−1.36178	+	0.683910i
$206$	−0.575034	−	3.26118i	−0.0400645	−	0.227217i
$207$	17.7088	−	8.31378i	1.23085	−	0.577847i
$208$	−0.0717042	+	0.406655i	−0.00497179	+	0.0281964i
$209$	0.116921	+	0.390544i	0.00808762	+	0.0270145i
$210$	14.1435	−	27.2557i	0.975994	−	1.88082i
$211$	−9.52718	−	4.78473i	−0.655878	−	0.329394i	0.0895483	−	0.995982i	$-0.471458\pi$
$211$	−9.52718	−	4.78473i	−0.655878	−	0.329394i	−0.745426	+	0.666588i	$0.767754\pi$
$212$	1.01845	−	3.40187i	0.0699477	−	0.233642i
$213$	0.524278	−	2.08843i	0.0359229	−	0.143097i
$214$	−2.63315	−	3.53694i	−0.179999	−	0.241780i
$215$	5.53097	+	9.57993i	0.377209	+	0.653346i
$216$	3.17925	+	4.11004i	0.216320	+	0.279653i
$217$	−18.5461	+	32.1228i	−1.25899	+	2.18064i
$218$	−13.1429	+	1.53618i	−0.890149	+	0.104043i
$219$	3.89545	+	8.01962i	0.263230	+	0.541916i
$220$	−5.81703	+	1.37866i	−0.392184	+	0.0929494i
$221$	0.162182	−	0.106669i	0.0109095	−	0.00717532i
$222$	0.327720	−	2.51450i	0.0219951	−	0.168762i
$223$	−6.68089	+	7.08133i	−0.447386	+	0.474201i	−0.911338	−	0.411659i	$-0.864949\pi$
$223$	−6.68089	+	7.08133i	−0.447386	+	0.474201i	0.463952	+	0.885860i	$0.346431\pi$
$224$	3.11820	+	2.61648i	0.208344	+	0.174821i
$225$	39.7462	−	13.2851i	2.64974	−	0.885671i
$226$	−8.37125	+	7.02431i	−0.556847	+	0.467250i
$227$	0.417303	−	7.16481i	0.0276973	−	0.475545i	−0.955730	−	0.294244i	$-0.904932\pi$
$227$	0.417303	−	7.16481i	0.0276973	−	0.475545i	0.983428	−	0.181301i	$-0.0580308\pi$
$228$	0.507754	−	0.0826114i	0.0336268	−	0.00547107i
$229$	11.0280	−	14.8131i	0.728748	−	0.978879i	−0.271118	−	0.962546i	$-0.587393\pi$
$229$	11.0280	−	14.8131i	0.728748	−	0.978879i	0.999867	−	0.0163328i	$-0.00519912\pi$
$230$	28.2096	+	3.29723i	1.86009	+	0.217413i
$231$	−6.31811	+	7.33021i	−0.415701	+	0.482293i
$232$	−5.79518	−	3.81155i	−0.380473	−	0.250241i
$233$	20.2463	+	7.36906i	1.32638	+	0.482763i	0.905497	−	0.424352i	$-0.139498\pi$
$233$	20.2463	+	7.36906i	1.32638	+	0.482763i	0.420883	+	0.907115i	$0.361720\pi$
$234$	−0.386599	+	1.17691i	−0.0252728	+	0.0769373i
$235$	8.52425	−	3.10257i	0.556061	−	0.202389i
$236$	−5.43115	−	1.28721i	−0.353538	−	0.0837899i
$237$	14.1582	+	4.44388i	0.919677	+	0.288661i
$238$	−0.111263	−	1.91031i	−0.00721209	−	0.123827i
$239$	7.63560	+	8.09326i	0.493906	+	0.523510i	0.925596	−	0.378512i	$-0.123564\pi$
$239$	7.63560	+	8.09326i	0.493906	+	0.523510i	−0.431690	+	0.902022i	$0.642083\pi$
$240$	0.776447	+	7.50365i	0.0501194	+	0.484359i
$241$	10.3566	−	24.0094i	0.667129	−	1.54658i	−0.161556	−	0.986863i	$-0.551651\pi$
$241$	10.3566	−	24.0094i	0.667129	−	1.54658i	0.828685	−	0.559715i	$-0.189089\pi$
$242$	−9.11597			−0.585997
$243$	7.68524	+	13.5623i	0.493009	+	0.870024i
$244$	−5.99744			−0.383947
$245$	16.5075	−	38.2688i	1.05463	−	2.44490i
$246$	−0.893071	−	8.63072i	−0.0569401	−	0.550275i
$247$	0.0841622	+	0.0892067i	0.00535511	+	0.00567609i
$248$	−0.529838	−	9.09697i	−0.0336448	−	0.577658i
$249$	−15.2355	−	4.78200i	−0.965511	−	0.303047i
$250$	38.0112	+	9.00883i	2.40404	+	0.569768i
$251$	−15.2966	+	5.56752i	−0.965515	+	0.351419i	−0.776192	−	0.630496i	$-0.782851\pi$
$251$	−15.2966	+	5.56752i	−0.965515	+	0.351419i	−0.189323	+	0.981915i	$0.560629\pi$
$252$	8.14186	+	9.10125i	0.512889	+	0.573325i
$253$	−8.41103	−	3.06136i	−0.528797	−	0.192466i
$254$	−2.97434	−	1.95626i	−0.186627	−	0.122746i
$255$	2.31529	−	2.68618i	0.144989	−	0.168215i
$256$	−0.993238	−	0.116093i	−0.0620774	−	0.00725581i
$257$	11.9707	−	16.0794i	0.746710	−	1.00301i	−0.252661	−	0.967555i	$-0.581306\pi$
$257$	11.9707	−	16.0794i	0.746710	−	1.00301i	0.999371	−	0.0354509i	$-0.0112867\pi$
$258$	−4.34204	+	0.706449i	−0.270324	+	0.0439816i
$259$	0.346505	−	5.94926i	0.0215308	−	0.369669i
$260$	−1.37769	+	1.15602i	−0.0854410	+	0.0716935i
$261$	−15.5806	−	13.7932i	−0.964415	−	0.853781i
$262$	−6.33671	−	5.31714i	−0.391484	−	0.328494i
$263$	−22.1950	+	23.5253i	−1.36860	+	1.45063i	−0.629630	+	0.776895i	$0.716794\pi$
$263$	−22.1950	+	23.5253i	−1.36860	+	1.45063i	−0.738971	+	0.673738i	$0.764688\pi$
$264$	0.307255	−	2.35747i	0.0189102	−	0.145093i
$265$	12.9218	−	8.49878i	0.793778	−	0.522076i
$266$	1.17638	−	0.278808i	0.0721288	−	0.0170948i
$267$	−8.39798	−	17.2890i	−0.513948	−	1.05807i
$268$	−4.67552	+	0.546490i	−0.285603	+	0.0333822i
$269$	6.50632	−	11.2693i	0.396697	−	0.687100i	−0.596619	−	0.802525i	$-0.703490\pi$
$269$	6.50632	−	11.2693i	0.396697	−	0.687100i	0.993316	+	0.115425i	$0.0368229\pi$
$270$	−0.899107	+	22.6133i	−0.0547179	+	1.37620i
$271$	6.52939	+	11.3092i	0.396632	+	0.686987i	0.993308	−	0.115495i	$-0.0368455\pi$
$271$	6.52939	+	11.3092i	0.396632	+	0.686987i	−0.596676	+	0.802482i	$0.703512\pi$
$272$	0.280723	+	0.377076i	0.0170213	+	0.0228636i
$273$	−0.708854	+	2.82367i	−0.0429018	+	0.170896i
$274$	−5.29385	+	17.6827i	−0.319813	+	1.06825i
$275$	−17.1346	−	8.60534i	−1.03326	−	0.518922i
$276$	−5.20236	+	10.0254i	−0.313146	+	0.603458i
$277$	−6.54671	−	21.8675i	−0.393354	−	1.31389i	−0.893932	−	0.448202i	$-0.852064\pi$
$277$	−6.54671	−	21.8675i	−0.393354	−	1.31389i	0.500578	−	0.865691i	$-0.333121\pi$
$278$	2.21499	−	12.5618i	0.132846	−	0.753409i
$279$	2.31188	−	27.2392i	0.138409	−	1.63077i
$280$	3.07855	+	17.4593i	0.183978	+	1.04339i
$281$	−2.36917	+	1.18984i	−0.141333	+	0.0709799i	−0.518060	−	0.855344i	$-0.673346\pi$
$281$	−2.36917	+	1.18984i	−0.141333	+	0.0709799i	0.376727	+	0.926324i	$0.377049\pi$
$282$	−0.0477849	+	3.60718i	−0.00284555	+	0.214805i
$283$	4.81566	+	11.1640i	0.286262	+	0.663629i	0.999297	−	0.0374995i	$-0.0119393\pi$
$283$	4.81566	+	11.1640i	0.286262	+	0.663629i	−0.713035	+	0.701128i	$0.752680\pi$
$284$	0.492393	+	1.14150i	0.0292182	+	0.0677353i
$285$	1.92535	+	1.14587i	0.114048	+	0.0678755i
$286$	0.506497	−	0.254373i	0.0299498	−	0.0150414i
$287$	−3.54095	−	20.0817i	−0.209016	−	1.18539i
$288$	−2.89978	−	0.768932i	−0.170871	−	0.0453097i
$289$	−2.91364	+	16.5241i	−0.171391	+	0.972006i
$290$	−8.66435	−	28.9409i	−0.508788	−	1.69947i
$291$	−10.0509	+	0.451905i	−0.589196	+	0.0264911i
$292$	−4.59993	−	2.31017i	−0.269191	−	0.135193i
$293$	−7.17957	+	23.9814i	−0.419435	+	1.40101i	0.443763	+	0.896144i	$0.353643\pi$
$293$	−7.17957	+	23.9814i	−0.419435	+	1.40101i	−0.863198	+	0.504866i	$0.831542\pi$
$294$	11.9040	+	11.5327i	0.694256	+	0.672600i
$295$	−14.5169	−	19.4995i	−0.845205	−	1.13531i
$296$	0.732011	+	1.26788i	0.0425473	+	0.0736941i
$297$	1.91923	−	6.86916i	0.111365	−	0.398589i
$298$	−3.11042	+	5.38740i	−0.180182	+	0.312084i
$299$	−2.67453	+	0.312607i	−0.154672	+	0.0180785i
$300$	−13.5622	+	20.0371i	−0.783013	+	1.15684i
$301$	−10.0598	+	2.38422i	−0.579839	+	0.137424i
$302$	15.9160	−	10.4681i	0.915863	−	0.602373i
$303$	−1.43758	−	1.10013i	−0.0825866	−	0.0632008i
$304$	−0.203818	+	0.216035i	−0.0116898	+	0.0123904i
$305$	−20.0099	−	16.7903i	−1.14576	−	0.961409i
$306$	0.672546	+	1.23960i	0.0384469	+	0.0708632i
$307$	−12.9945	+	10.9037i	−0.741638	+	0.622308i	−0.933277	−	0.359158i	$-0.883064\pi$
$307$	−12.9945	+	10.9037i	−0.741638	+	0.622308i	0.191639	+	0.981465i	$0.438620\pi$
$308$	0.324867	−	5.57775i	0.0185110	−	0.317822i
$309$	3.62829	+	4.44223i	0.206406	+	0.252709i
$310$	23.6999	−	31.8345i	1.34606	−	1.80808i
$311$	21.9206	+	2.56215i	1.24300	+	0.145286i	0.712059	−	0.702119i	$-0.247763\pi$
$311$	21.9206	+	2.56215i	1.24300	+	0.145286i	0.530946	+	0.847406i	$0.321837\pi$
$312$	−0.235693	−	0.675261i	−0.0133435	−	0.0382291i
$313$	14.3553	+	9.44161i	0.811408	+	0.533671i	0.886078	−	0.463537i	$-0.153420\pi$
$313$	14.3553	+	9.44161i	0.811408	+	0.533671i	−0.0746699	+	0.997208i	$0.523790\pi$
$314$	10.8888	+	3.96318i	0.614488	+	0.223655i
$315$	1.68491	+	53.1592i	0.0949337	+	2.99518i
$316$	−8.05078	+	2.93024i	−0.452892	+	0.164839i
$317$	−7.84023	−	1.85817i	−0.440351	−	0.104365i	0.00445880	−	0.999990i	$-0.498581\pi$
$317$	−7.84023	−	1.85817i	−0.440351	−	0.104365i	−0.444810	+	0.895625i	$0.646729\pi$
$318$	1.33903	+	6.00308i	0.0750890	+	0.336636i
$319$	0.553582	+	9.50464i	0.0309947	+	0.532158i
$320$	−2.98883	−	3.16798i	−0.167081	−	0.177095i
$321$	6.97212	+	3.11766i	0.389146	+	0.174011i
$322$	−10.5136	+	24.3733i	−0.585901	+	1.35827i
$323$	0.139622			0.00776878
$324$	−8.28234	−	3.52176i	−0.460130	−	0.195654i
$325$	−5.76828			−0.319967
$326$	−3.47047	+	8.04546i	−0.192212	+	0.445597i
$327$	18.5636	−	13.4416i	1.02657	−	0.743324i
$328$	3.43777	+	3.64382i	0.189819	+	0.201196i
$329$	0.492955	+	8.46371i	0.0271775	+	0.466619i
$330$	7.62505	−	7.00531i	0.419745	−	0.385629i
$331$	9.75325	+	2.31156i	0.536087	+	0.127055i	0.489737	−	0.871870i	$-0.337093\pi$
$331$	9.75325	+	2.31156i	0.536087	+	0.127055i	0.0463502	+	0.998925i	$0.485241\pi$
$332$	8.66334	−	3.15320i	0.475462	−	0.173054i
$333$	1.63217	+	4.07753i	0.0894424	+	0.223448i
$334$	−9.42790	−	3.43147i	−0.515872	−	0.187762i
$335$	−17.1294	−	11.2662i	−0.935878	−	0.615537i
$336$	−6.92642	−	1.31614i	−0.377867	−	0.0718016i
$337$	−20.6739	−	2.41643i	−1.12618	−	0.131631i	−0.467455	−	0.884017i	$-0.654829\pi$
$337$	−20.6739	−	2.41643i	−1.12618	−	0.131631i	−0.658723	+	0.752386i	$0.728903\pi$
$338$	−7.66124	+	10.2908i	−0.416717	+	0.559747i
$339$	6.70867	−	17.6989i	0.364365	−	0.961271i
$340$	−0.119049	+	2.04398i	−0.00645631	+	0.110851i
$341$	−9.58143	+	8.03977i	−0.518863	+	0.435378i
$342$	−0.697492	+	0.554454i	−0.0377161	+	0.0299815i
$343$	8.01125	+	6.72224i	0.432567	+	0.362967i
$344$	1.74295	−	1.84742i	0.0939734	−	0.0996059i
$345$	−45.4241	+	18.8844i	−2.44555	+	1.01670i
$346$	10.0925	−	6.63794i	0.542576	−	0.356858i
$347$	13.8597	−	3.28480i	0.744026	−	0.176337i	0.158917	−	0.987292i	$-0.449200\pi$
$347$	13.8597	−	3.28480i	0.744026	−	0.176337i	0.585109	+	0.810955i	$0.301052\pi$
$348$	11.9834	+	0.857359i	0.642376	+	0.0459593i
$349$	34.8459	−	4.07290i	1.86526	−	0.218018i	0.892697	−	0.450658i	$-0.148811\pi$
$349$	34.8459	−	4.07290i	1.86526	−	0.218018i	0.972563	+	0.232641i	$0.0747366\pi$
$350$	−28.4310	+	49.2440i	−1.51970	+	2.63220i
$351$	−0.411481	−	2.10581i	−0.0219633	−	0.112400i
$352$	0.686300	+	1.18871i	0.0365799	+	0.0633583i
$353$	9.32601	+	12.5270i	0.496374	+	0.666746i	0.977751	−	0.209768i	$-0.0672708\pi$
$353$	9.32601	+	12.5270i	0.496374	+	0.666746i	−0.481378	+	0.876513i	$0.659863\pi$
$354$	9.29739	−	2.64978i	0.494151	−	0.140834i
$355$	−1.55288	+	5.18698i	−0.0824183	+	0.275296i
$356$	9.91673	+	4.98037i	0.525586	+	0.263959i
$357$	1.78443	+	2.79299i	0.0944421	+	0.147821i
$358$	−3.76656	−	12.5812i	−0.199069	−	0.664936i
$359$	−5.25256	+	29.7888i	−0.277220	+	1.57219i	0.454602	+	0.890695i	$0.349781\pi$
$359$	−5.25256	+	29.7888i	−0.277220	+	1.57219i	−0.731822	+	0.681496i	$0.761330\pi$
$360$	−7.52217	−	10.6836i	−0.396453	−	0.563077i
$361$	−3.28400	−	18.6245i	−0.172842	−	0.980236i
$362$	−0.463217	+	0.232636i	−0.0243461	+	0.0122271i
$363$	13.7773	−	7.71284i	0.723122	−	0.404819i
$364$	−0.665744	−	1.54337i	−0.0348945	−	0.0808945i
$365$	−8.87973	−	20.5855i	−0.464786	−	1.07750i
$366$	9.06417	−	5.07431i	0.473791	−	0.265239i
$367$	−12.6294	+	6.34275i	−0.659252	+	0.331089i	−0.746778	−	0.665073i	$-0.768400\pi$
$367$	−12.6294	+	6.34275i	−0.659252	+	0.331089i	0.0875260	+	0.996162i	$0.472104\pi$
$368$	−1.13237	−	6.42200i	−0.0590290	−	0.334770i
$369$	8.65202	+	12.2883i	0.450406	+	0.639705i
$370$	−1.10724	+	6.27949i	−0.0575628	+	0.326455i
$371$	4.14564	+	13.8474i	0.215231	+	0.718922i
$372$	8.49754	+	13.3003i	0.440577	+	0.689590i
$373$	1.85728	+	0.932761i	0.0961663	+	0.0482965i	0.496232	−	0.868190i	$-0.334716\pi$
$373$	1.85728	+	0.932761i	0.0961663	+	0.0482965i	−0.400066	+	0.916486i	$0.631013\pi$
$374$	0.185062	−	0.618149i	0.00956931	−	0.0319637i
$375$	−65.0701	+	18.5452i	−3.36021	+	0.957668i
$376$	−1.24376	−	1.67065i	−0.0641418	−	0.0861574i
$377$	1.43209	+	2.48046i	0.0737566	+	0.127750i
$378$	−20.0055	−	6.86641i	−1.02897	−	0.353170i
$379$	11.2910	−	19.5565i	0.579978	−	1.00455i	−0.415503	−	0.909592i	$-0.636395\pi$
$379$	11.2910	−	19.5565i	0.579978	−	1.00455i	0.995481	−	0.0949594i	$-0.0302721\pi$
$380$	−1.28482	+	0.150174i	−0.0659101	+	0.00770379i
$381$	6.15039	+	0.440034i	0.315094	+	0.0225436i
$382$	−23.0943	+	5.47345i	−1.18161	+	0.280046i
$383$	22.3115	−	14.6745i	1.14006	−	0.749831i	0.168287	−	0.985738i	$-0.446176\pi$
$383$	22.3115	−	14.6745i	1.14006	−	0.749831i	0.971776	+	0.235907i	$0.0758061\pi$
$384$	1.59934	−	0.664904i	0.0816162	−	0.0339307i
$385$	16.6992	−	17.7001i	0.851071	−	0.902083i
$386$	−1.88320	−	1.58019i	−0.0958521	−	0.0804295i
$387$	5.96459	−	4.74140i	0.303197	−	0.241019i
$388$	4.44978	−	3.73381i	0.225903	−	0.189555i
$389$	0.607370	−	10.4281i	0.0307949	−	0.528728i	−0.947271	−	0.320433i	$-0.896172\pi$
$389$	0.607370	−	10.4281i	0.0307949	−	0.528728i	0.978066	−	0.208295i	$-0.0667914\pi$
$390$	1.10408	−	2.91278i	0.0559071	−	0.147495i
$391$	−1.83061	+	2.45894i	−0.0925782	+	0.124354i
$392$	−9.50448	−	1.11091i	−0.480049	−	0.0561097i
$393$	14.0757	+	2.67463i	0.710023	+	0.134917i
$394$	−4.62634	−	3.04279i	−0.233072	−	0.153294i
$395$	−35.0641	−	12.7623i	−1.76427	−	0.642140i
$396$	1.53025	+	3.82291i	0.0768978	+	0.192108i
$397$	−31.9768	+	11.6386i	−1.60487	+	0.584124i	−0.980416	−	0.196938i	$-0.936900\pi$
$397$	−31.9768	+	11.6386i	−1.60487	+	0.584124i	−0.624453	+	0.781063i	$0.714678\pi$
$398$	5.26406	+	1.24761i	0.263863	+	0.0625368i
$399$	−1.54202	+	1.41669i	−0.0771977	+	0.0709232i
$400$	−0.812238	−	13.9456i	−0.0406119	−	0.697279i
$401$	16.6682	+	17.6673i	0.832370	+	0.882261i	0.994524	−	0.104504i	$-0.0333256\pi$
$401$	16.6682	+	17.6673i	0.832370	+	0.882261i	−0.162154	+	0.986765i	$0.551844\pi$
$402$	6.60393	−	4.78180i	0.329374	−	0.238495i
$403$	−1.49035	+	3.45503i	−0.0742398	+	0.172107i
$404$	1.04513			0.0519973
$405$	−17.7738	−	34.9371i	−0.883187	−	1.73604i
$406$	28.2343			1.40125
$407$	0.795929	−	1.84517i	0.0394528	−	0.0914618i
$408$	−0.743305	−	0.332376i	−0.0367991	−	0.0164551i
$409$	−17.7750	−	18.8404i	−0.878917	−	0.931598i	0.119204	−	0.992870i	$-0.461966\pi$
$409$	−17.7750	−	18.8404i	−0.878917	−	0.931598i	−0.998121	+	0.0612717i	$0.980484\pi$
$410$	1.26863	+	21.7815i	0.0626532	+	1.07571i
$411$	−6.96017	−	31.2036i	−0.343320	−	1.53916i
$412$	−3.22223	−	0.763682i	−0.158748	−	0.0376239i
$413$	21.3499	−	7.77071i	1.05056	−	0.382372i
$414$	−0.619754	−	19.5534i	−0.0304593	−	0.960997i
$415$	37.7320	+	13.7333i	1.85219	+	0.674143i
$416$	0.344996	+	0.226908i	0.0169148	+	0.0111251i
$417$	7.28072	+	20.8593i	0.356538	+	1.02148i
$418$	0.404914	+	0.0473277i	0.0198050	+	0.00231487i
$419$	−9.26854	+	12.4498i	−0.452798	+	0.608213i	−0.968639	−	0.248471i	$-0.920072\pi$
$419$	−9.26854	+	12.4498i	−0.452798	+	0.608213i	0.515841	+	0.856684i	$0.327479\pi$
$420$	−19.4247	−	23.7822i	−0.947828	−	1.16045i
$421$	1.84735	−	31.7178i	0.0900345	−	1.54583i	−0.586821	−	0.809716i	$-0.699621\pi$
$421$	1.84735	−	31.7178i	0.0900345	−	1.54583i	0.676856	−	0.736116i	$-0.263342\pi$
$422$	−8.16694	+	6.85287i	−0.397560	+	0.333593i
$423$	−2.97975	−	5.49211i	−0.144880	−	0.267035i
$424$	−2.72027	−	2.28257i	−0.132108	−	0.110852i
$425$	−4.50648	+	4.77659i	−0.218596	+	0.231699i
$426$	−1.70997	−	1.30858i	−0.0828483	−	0.0634011i
$427$	20.3965	−	13.4150i	0.987058	−	0.649198i
$428$	−4.29061	+	1.01689i	−0.207395	+	0.0491534i
$429$	−0.550270	+	0.812981i	−0.0265673	+	0.0392511i
$430$	10.9872	−	1.28421i	0.529847	−	0.0619303i
$431$	−7.53078	+	13.0437i	−0.362745	+	0.628293i	−0.988412	−	0.151798i	$-0.951494\pi$
$431$	−7.53078	+	13.0437i	−0.362745	+	0.628293i	0.625667	+	0.780091i	$0.284827\pi$
$432$	5.03314	−	1.29133i	0.242157	−	0.0621293i
$433$	11.3852	+	19.7198i	0.547138	+	0.947672i	0.998469	+	0.0553147i	$0.0176162\pi$
$433$	11.3852	+	19.7198i	0.547138	+	0.947672i	−0.451331	+	0.892357i	$0.649050\pi$
$434$	22.1499	+	29.7525i	1.06323	+	1.42817i
$435$	37.5811	+	36.4089i	1.80188	+	1.74567i
$436$	−3.79508	+	12.6765i	−0.181752	+	0.607092i
$437$	−1.73079	−	0.869234i	−0.0827948	−	0.0415811i
$438$	8.90665	−	0.400457i	0.425576	−	0.0191346i
$439$	9.77250	+	32.6424i	0.466416	+	1.55794i	0.790838	+	0.612026i	$0.209645\pi$
$439$	9.77250	+	32.6424i	0.466416	+	1.55794i	−0.324422	+	0.945913i	$0.605170\pi$
$440$	−1.03810	+	5.88735i	−0.0494894	+	0.280669i
$441$	−27.7486	−	7.35805i	−1.32136	−	0.350383i
$442$	−0.0337080	−	0.191167i	−0.00160332	−	0.00909291i
$443$	3.85187	−	1.93448i	0.183008	−	0.0919101i	−0.354936	−	0.934891i	$-0.615497\pi$
$443$	3.85187	−	1.93448i	0.183008	−	0.0919101i	0.537944	+	0.842980i	$0.319201\pi$
$444$	−2.17905	−	1.29686i	−0.103413	−	0.0615462i
$445$	19.1433	+	44.3792i	0.907480	+	2.10377i
$446$	3.85603	+	8.93927i	0.182588	+	0.423287i
$447$	0.142723	−	10.7739i	0.00675057	−	0.509586i
$448$	3.63756	−	1.82685i	0.171858	−	0.0863105i
$449$	−1.78444	−	10.1201i	−0.0842131	−	0.477596i	−0.997524	−	0.0703324i	$-0.977594\pi$
$449$	−1.78444	−	10.1201i	−0.0842131	−	0.477596i	0.913310	−	0.407264i	$-0.133517\pi$
$450$	3.54410	−	41.7575i	0.167070	−	1.96847i
$451$	1.19402	−	6.77165i	0.0562244	−	0.318865i
$452$	3.13415	+	10.4688i	0.147418	+	0.492411i
$453$	−15.1976	+	29.2871i	−0.714047	+	1.37603i
$454$	−6.41356	−	3.22101i	−0.301003	−	0.151169i
$455$	2.09959	−	7.01310i	0.0984301	−	0.328779i
$456$	0.125256	−	0.498948i	0.00586564	−	0.0233654i
$457$	0.725223	+	0.974143i	0.0339245	+	0.0455685i	0.818762	−	0.574133i	$-0.194661\pi$
$457$	0.725223	+	0.974143i	0.0339245	+	0.0455685i	−0.784837	+	0.619702i	$0.787254\pi$
$458$	−9.23370	−	15.9932i	−0.431462	−	0.747315i
$459$	−2.06525	−	1.30443i	−0.0963975	−	0.0608855i
$460$	14.2008	−	24.5966i	0.662117	−	1.14682i
$461$	37.2341	−	4.35204i	1.73416	−	0.202695i	0.810458	−	0.585796i	$-0.199218\pi$
$461$	37.2341	−	4.35204i	1.73416	−	0.202695i	0.923706	+	0.383102i	$0.125144\pi$
$462$	4.22824	+	8.70474i	0.196716	+	0.404981i
$463$	3.82971	−	0.907657i	0.177982	−	0.0421824i	−0.140659	−	0.990058i	$-0.544922\pi$
$463$	3.82971	−	0.907657i	0.177982	−	0.0421824i	0.318640	+	0.947876i	$0.396774\pi$
$464$	−5.79518	+	3.81155i	−0.269035	+	0.176947i
$465$	−8.88406	+	68.1648i	−0.411989	+	3.16107i
$466$	14.7855	−	15.6718i	0.684927	−	0.725981i
$467$	−13.9066	−	11.6690i	−0.643521	−	0.539978i	0.261576	−	0.965183i	$-0.415758\pi$
$467$	−13.9066	−	11.6690i	−0.643521	−	0.539978i	−0.905097	+	0.425204i	$0.860202\pi$
$468$	0.927537	+	0.821133i	0.0428754	+	0.0379569i
$469$	14.6785	−	12.3167i	0.677790	−	0.568733i
$470$	0.527450	−	9.05597i	0.0243295	−	0.417721i
$471$	−19.8098	+	3.22305i	−0.912786	+	0.148510i
$472$	−3.33310	+	4.47713i	−0.153418	+	0.206077i
$473$	−3.46262	−	0.404722i	−0.159211	−	0.0186091i
$474$	9.68824	−	11.2402i	0.444995	−	0.516279i
$475$	−3.46639	−	2.27988i	−0.159049	−	0.104608i
$476$	−1.79814	−	0.654471i	−0.0824178	−	0.0299976i
$477$	−7.10281	−	7.93977i	−0.325216	−	0.363537i
$478$	10.4557	−	3.80555i	0.478231	−	0.174062i
$479$	−9.66806	−	2.29137i	−0.441745	−	0.104696i	0.00372352	−	0.999993i	$-0.498815\pi$
$479$	−9.66806	−	2.29137i	−0.441745	−	0.104696i	−0.445469	+	0.895298i	$0.646963\pi$
$480$	7.19751	+	2.25910i	0.328520	+	0.103113i
$481$	−0.0351506	−	0.603513i	−0.00160273	−	0.0275178i
$482$	−17.9437	−	19.0192i	−0.817314	−	0.866303i
$483$	−4.73213	−	45.7317i	−0.215319	−	2.08087i
$484$	−3.61065	+	8.37043i	−0.164120	+	0.380474i
$485$	25.2993			1.14878
$486$	15.4971	−	1.68495i	0.702964	−	0.0764307i
$487$	−14.1362			−0.640573			−0.320287	−	0.947321i	$-0.603779\pi$
$487$	−14.1362			−0.640573			−0.320287	+	0.947321i	$0.603779\pi$
$488$	−2.37546	+	5.50694i	−0.107532	+	0.249288i
$489$	−1.56204	−	15.0957i	−0.0706380	−	0.682652i
$490$	−28.6007	−	30.3150i	−1.29205	−	1.36949i
$491$	−1.23323	−	21.1738i	−0.0556550	−	0.955560i	−0.904381	−	0.426726i	$-0.859667\pi$
$491$	−1.23323	−	21.1738i	−0.0556550	−	0.955560i	0.848726	−	0.528833i	$-0.177370\pi$
$492$	−8.27859	−	2.59842i	−0.373228	−	0.117146i
$493$	3.17284	+	0.751977i	0.142898	+	0.0338673i
$494$	0.115246	−	0.0419461i	0.00518516	−	0.00188724i
$495$	−5.59700	+	17.0388i	−0.251566	+	0.765837i
$496$	−8.56284	−	3.11662i	−0.384483	−	0.139940i
$497$	−4.22785	−	2.78070i	−0.189645	−	0.124732i
$498$	−10.4254	+	12.0954i	−0.467173	+	0.542009i
$499$	37.8455	+	4.42351i	1.69420	+	0.198023i	0.907715	−	0.419588i	$-0.137825\pi$
$499$	37.8455	+	4.42351i	1.69420	+	0.198023i	0.786483	+	0.617612i	$0.211900\pi$
$500$	23.3275	−	31.3343i	1.04324	−	1.40131i
$501$	17.1521	−	2.79064i	0.766298	−	0.124676i
$502$	−0.946501	+	16.2508i	−0.0422444	+	0.725309i
$503$	−19.7261	+	16.5522i	−0.879545	+	0.738026i	−0.966085	−	0.258223i	$-0.916863\pi$
$503$	−19.7261	+	16.5522i	−0.879545	+	0.738026i	0.0865408	+	0.996248i	$0.472419\pi$
$504$	11.5817	−	3.87117i	0.515892	−	0.172436i
$505$	3.48699	+	2.92593i	0.155169	+	0.130202i
$506$	−6.14243	+	6.51060i	−0.273064	+	0.289431i
$507$	2.87187	−	22.0350i	0.127544	−	0.978607i
$508$	−2.97434	+	1.95626i	−0.131965	+	0.0867948i
$509$	17.8731	−	4.23601i	0.792212	−	0.187758i	0.185463	−	0.982651i	$-0.440622\pi$
$509$	17.8731	−	4.23601i	0.792212	−	0.187758i	0.606749	+	0.794894i	$0.292473\pi$
$510$	−1.54945	−	3.18988i	−0.0686109	−	0.141250i
$511$	20.8112	−	2.43248i	0.920632	−	0.107606i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	0.585035	−	1.42810i	0.0258299	−	0.0630523i
$514$	−10.0230	−	17.3604i	−0.442097	−	0.765734i
$515$	−8.61267	−	11.5688i	−0.379520	−	0.509783i
$516$	−1.07112	+	4.26674i	−0.0471535	+	0.187833i
$517$	−0.819924	+	2.73874i	−0.0360602	+	0.120449i
$518$	−5.32546	−	2.67455i	−0.233987	−	0.117513i
$519$	−9.63697	+	18.5713i	−0.423016	+	0.815188i
$520$	0.515802	+	1.72290i	0.0226194	+	0.0755541i
$521$	−3.28343	+	18.6212i	−0.143850	+	0.815811i	0.824434	+	0.565958i	$0.191494\pi$
$521$	−3.28343	+	18.6212i	−0.143850	+	0.815811i	−0.968284	+	0.249853i	$0.919618\pi$
$522$	−18.8363	+	8.84314i	−0.824444	+	0.387054i
$523$	−6.18344	−	35.0680i	−0.270383	−	1.53342i	−0.753256	−	0.657728i	$-0.771518\pi$
$523$	−6.18344	−	35.0680i	−0.270383	−	1.53342i	0.482872	−	0.875691i	$-0.339593\pi$
$524$	−7.39212	+	3.71246i	−0.322926	+	0.162180i
$525$	1.30457	−	98.4793i	0.0569362	−	4.29799i
$526$	12.8103	+	29.6977i	0.558557	+	1.29488i
$527$	1.69669	+	3.93337i	0.0739091	+	0.171340i
$528$	−2.04297	−	1.21587i	−0.0889090	−	0.0529141i
$529$	17.4476	−	8.76254i	0.758593	−	0.380980i
$530$	−2.68567	−	15.2312i	−0.116658	−	0.661600i
$531$	−11.8096	+	11.8711i	−0.512492	+	0.515160i
$532$	0.209936	−	1.19061i	0.00910187	−	0.0516193i
$533$	−0.593277	−	1.98168i	−0.0256977	−	0.0858362i
$534$	−19.2013	+	0.863321i	−0.830923	+	0.0373596i
$535$	−17.1621	−	8.61912i	−0.741982	−	0.372637i
$536$	−1.35008	+	4.50960i	−0.0583148	+	0.194785i
$537$	16.3372	+	15.8276i	0.705004	+	0.683012i
$538$	−7.77061	−	10.4377i	−0.335015	−	0.450003i
$539$	6.56733	+	11.3750i	0.282875	+	0.489954i
$540$	20.4078	+	9.78224i	0.878210	+	0.420960i
$541$	−17.9602	+	31.1080i	−0.772169	+	1.33744i	0.164203	+	0.986427i	$0.447495\pi$
$541$	−17.9602	+	31.1080i	−0.772169	+	1.33744i	−0.936372	+	0.351010i	$0.885838\pi$
$542$	12.9705	−	1.51603i	0.557130	−	0.0651192i
$543$	0.503249	−	0.743511i	0.0215965	−	0.0319071i
$544$	0.457426	−	0.108412i	0.0196120	−	0.00464813i
$545$	−48.1506	+	31.6692i	−2.06255	+	1.35656i
$546$	2.31198	+	1.76928i	0.0989436	+	0.0757182i
$547$	−17.9951	+	19.0737i	−0.769415	+	0.815532i	−0.987036	−	0.160501i	$-0.948689\pi$
$547$	−17.9951	+	19.0737i	−0.769415	+	0.815532i	0.217621	+	0.976033i	$0.430170\pi$
$548$	14.1397	+	11.8646i	0.604020	+	0.506833i
$549$	−9.40576	+	15.3380i	−0.401428	+	0.654611i
$550$	−14.6882	+	12.3249i	−0.626309	+	0.525536i
$551$	−0.119785	+	2.05664i	−0.00510303	+	0.0876157i
$552$	7.14493	+	8.74775i	0.304108	+	0.372329i
$553$	20.8253	−	27.9733i	0.885584	−	1.18955i
$554$	−22.6722	−	2.65000i	−0.963248	−	0.112588i
$555$	−3.63953	−	10.4273i	−0.154489	−	0.442612i
$556$	−10.6572	−	7.00933i	−0.451964	−	0.297262i
$557$	18.3756	+	6.68818i	0.778600	+	0.283387i	0.700589	−	0.713565i	$-0.252921\pi$
$557$	18.3756	+	6.68818i	0.778600	+	0.283387i	0.0780115	+	0.996952i	$0.475143\pi$
$558$	−24.0958	−	12.9117i	−1.02006	−	0.546597i
$559$	−0.985523	+	0.358701i	−0.0416832	+	0.0151714i
$560$	17.2508	+	4.08850i	0.728978	+	0.172771i
$561$	0.243313	+	1.09081i	0.0102727	+	0.0460540i
$562$	0.154152	+	2.64668i	0.00650249	+	0.111643i
$563$	13.6682	+	14.4875i	0.576047	+	0.610574i	0.948230	−	0.317585i	$-0.102872\pi$
$563$	13.6682	+	14.4875i	0.576047	+	0.610574i	−0.372183	+	0.928159i	$0.621391\pi$
$564$	3.29325	+	1.47261i	0.138671	+	0.0620080i
$565$	−18.8514	+	43.7025i	−0.793085	+	1.83858i
$566$	12.1583			0.511052
$567$	36.0447	−	6.54879i	1.51373	−	0.275023i
$568$	1.24317			0.0521621
$569$	−0.603019	+	1.39796i	−0.0252799	+	0.0586054i	−0.930388	−	0.366575i	$-0.880530\pi$
$569$	−0.603019	+	1.39796i	−0.0252799	+	0.0586054i	0.905108	+	0.425181i	$0.139789\pi$
$570$	1.81475	−	1.31403i	0.0760114	−	0.0550387i
$571$	1.02010	+	1.08124i	0.0426897	+	0.0452484i	0.748367	−	0.663285i	$-0.230838\pi$
$571$	1.02010	+	1.08124i	0.0426897	+	0.0452484i	−0.705677	+	0.708534i	$0.749357\pi$
$572$	−0.0329556	−	0.565826i	−0.00137794	−	0.0236584i
$573$	30.2724	−	27.8119i	1.26465	−	1.16186i
$574$	−19.8419	−	4.70261i	−0.828184	−	0.196283i
$575$	85.6006	−	31.1561i	3.56979	−	1.29930i
$576$	−1.85459	+	2.35807i	−0.0772746	+	0.0982529i
$577$	−31.2779	−	11.3842i	−1.30211	−	0.473931i	−0.404430	−	0.914569i	$-0.632530\pi$
$577$	−31.2779	−	11.3842i	−1.30211	−	0.473931i	−0.897685	+	0.440638i	$0.854752\pi$
$578$	14.0187	+	9.22022i	0.583099	+	0.383510i
$579$	4.18311	+	0.794867i	0.173844	+	0.0330335i
$580$	−30.0058	−	3.50718i	−1.24592	−	0.145628i
$581$	−22.4099	+	30.1017i	−0.929719	+	1.24883i
$582$	−3.56602	+	9.40792i	−0.147816	+	0.389971i
$583$	−0.283408	+	4.86593i	−0.0117376	+	0.201526i
$584$	−3.94318	+	3.30872i	−0.163170	+	0.136916i
$585$	0.795815	+	5.33634i	0.0329029	+	0.220631i
$586$	19.1765	+	16.0910i	0.792172	+	0.664711i
$587$	−6.04447	+	6.40676i	−0.249482	+	0.264435i	−0.839997	−	0.542591i	$-0.817443\pi$
$587$	−6.04447	+	6.40676i	−0.249482	+	0.264435i	0.590515	+	0.807027i	$0.298925\pi$
$588$	15.3044	−	6.36259i	0.631144	−	0.262389i
$589$	−2.26120	+	1.48721i	−0.0931709	+	0.0612795i
$590$	−23.6546	+	5.60625i	−0.973846	+	0.230806i
$591$	9.56642	+	0.684437i	0.393510	+	0.0281540i
$592$	1.45412	−	0.169963i	0.0597641	−	0.00698542i
$593$	3.72036	−	6.44385i	0.152777	−	0.264617i	−0.779470	−	0.626439i	$-0.784512\pi$
$593$	3.72036	−	6.44385i	0.152777	−	0.264617i	0.932247	+	0.361822i	$0.117845\pi$
$594$	−5.54721	−	4.48300i	−0.227605	−	0.183940i
$595$	−4.16710	−	7.21762i	−0.170834	−	0.295894i
$596$	3.71483	+	4.98988i	0.152165	+	0.204393i
$597$	−9.01136	+	2.56826i	−0.368810	+	0.105112i
$598$	−0.772285	+	2.57961i	−0.0315811	+	0.105488i
$599$	21.6157	+	10.8558i	0.883192	+	0.443556i	0.831769	−	0.555121i	$-0.187328\pi$
$599$	21.6157	+	10.8558i	0.883192	+	0.443556i	0.0514226	+	0.998677i	$0.483624\pi$
$600$	13.0267	+	20.3893i	0.531811	+	0.832389i
$601$	−8.96408	−	29.9421i	−0.365652	−	1.22136i	−0.920940	−	0.389705i	$-0.872577\pi$
$601$	−8.96408	−	29.9421i	−0.365652	−	1.22136i	0.555287	−	0.831659i	$-0.312608\pi$
$602$	−1.79526	+	10.1814i	−0.0731694	+	0.414964i
$603$	−5.93499	+	12.8144i	−0.241692	+	0.521842i
$604$	−3.30799	−	18.7605i	−0.134600	−	0.763356i
$605$	−35.4802	+	17.8188i	−1.44248	+	0.724439i
$606$	−1.57955	+	0.884267i	−0.0641649	+	0.0359209i
$607$	11.5142	+	26.6928i	0.467345	+	1.08343i	0.975068	+	0.221907i	$0.0712283\pi$
$607$	11.5142	+	26.6928i	0.467345	+	1.08343i	−0.507723	+	0.861521i	$0.669512\pi$
$608$	0.117638	+	0.272716i	0.00477086	+	0.0110601i
$609$	−42.6717	+	23.8885i	−1.72914	+	0.968012i
$610$	−23.3426	+	11.7231i	−0.945115	+	0.474654i
$611$	0.149345	+	0.846976i	0.00604184	+	0.0342650i
$612$	1.40460	−	0.126562i	0.0567777	−	0.00511596i
$613$	−6.78846	+	38.4993i	−0.274183	+	1.55497i	0.467361	+	0.884067i	$0.345205\pi$
$613$	−6.78846	+	38.4993i	−0.274183	+	1.55497i	−0.741544	+	0.670904i	$0.765906\pi$
$614$	4.86509	+	16.2505i	0.196339	+	0.655818i
$615$	−20.3463	−	31.8459i	−0.820440	−	1.28415i
$616$	−4.99291	−	2.50753i	−0.201170	−	0.101031i
$617$	3.50668	−	11.7131i	0.141173	−	0.471552i	−0.857936	−	0.513757i	$-0.828253\pi$
$617$	3.50668	−	11.7131i	0.141173	−	0.471552i	0.999109	+	0.0422053i	$0.0134383\pi$
$618$	5.51602	−	1.57208i	0.221887	−	0.0632384i
$619$	−0.521047	−	0.699887i	−0.0209426	−	0.0281308i	0.791529	−	0.611132i	$-0.209286\pi$
$619$	−0.521047	−	0.699887i	−0.0209426	−	0.0281308i	−0.812471	+	0.583001i	$0.801878\pi$
$620$	−19.8439	−	34.3706i	−0.796950	−	1.38036i
$621$	17.4804	+	29.0275i	0.701465	+	1.16483i
$622$	11.0349	−	19.1131i	0.442460	−	0.766364i
$623$	−44.8656	+	5.24404i	−1.79750	+	0.210098i
$624$	−0.713388	−	0.0510399i	−0.0285584	−	0.00204323i
$625$	97.5895	−	23.1291i	3.90358	−	0.925166i
$626$	14.3553	−	9.44161i	0.573752	−	0.377363i
$627$	−0.652006	+	0.271062i	−0.0260386	+	0.0108252i
$628$	7.95187	−	8.42849i	0.317314	−	0.336334i
$629$	−0.527218	−	0.442388i	−0.0210215	−	0.0176392i
$630$	49.4790	+	19.5082i	1.97129	+	0.777224i
$631$	1.85524	−	1.55673i	0.0738560	−	0.0619725i	−0.605112	−	0.796140i	$-0.706872\pi$
$631$	1.85524	−	1.55673i	0.0738560	−	0.0619725i	0.678968	+	0.734168i	$0.262427\pi$
$632$	−0.498153	+	8.55296i	−0.0198155	+	0.340219i
$633$	6.54493	−	17.2669i	0.260138	−	0.686298i
$634$	−4.81156	+	6.46305i	−0.191091	+	0.256680i
$635$	−15.4003	−	1.80004i	−0.611142	−	0.0714323i
$636$	6.04249	+	1.14818i	0.239600	+	0.0455283i
$637$	3.30133	+	2.17132i	0.130804	+	0.0860309i
$638$	8.94658	+	3.25629i	0.354198	+	0.128918i
$639$	3.69151	+	0.530942i	0.146034	+	0.0210037i
$640$	−4.09271	+	1.48962i	−0.161778	+	0.0588825i
$641$	8.99703	+	2.13234i	0.355361	+	0.0842222i	0.404419	−	0.914574i	$-0.367474\pi$
$641$	8.99703	+	2.13234i	0.355361	+	0.0842222i	−0.0490577	+	0.998796i	$0.515622\pi$
$642$	5.62420	−	5.16707i	0.221969	−	0.203928i
$643$	−1.98692	−	34.1141i	−0.0783565	−	1.34533i	−0.776837	−	0.629701i	$-0.783177\pi$
$643$	−1.98692	−	34.1141i	−0.0783565	−	1.34533i	0.698481	−	0.715629i	$-0.253860\pi$
$644$	18.2157	+	19.3076i	0.717801	+	0.760824i
$645$	−15.5188	+	11.2369i	−0.611051	+	0.442452i
$646$	0.0553015	−	0.128203i	0.00217581	−	0.00504409i
$647$	10.2649			0.403555			0.201777	−	0.979431i	$-0.435328\pi$
$647$	10.2649			0.403555			0.201777	+	0.979431i	$0.435328\pi$
$648$	−6.51421	+	6.21008i	−0.255902	+	0.243955i
$649$	7.66130			0.300732
$650$	−2.28470	+	5.29653i	−0.0896132	+	0.207747i
$651$	−58.6491	−	26.2256i	−2.29864	−	1.02786i
$652$	6.01288	+	6.37329i	0.235483	+	0.249597i
$653$	−0.630450	−	10.8244i	−0.0246714	−	0.423592i	−0.987918	−	0.154975i	$-0.950470\pi$
$653$	−0.630450	−	10.8244i	−0.0246714	−	0.423592i	0.963247	−	0.268617i	$-0.0865666\pi$
$654$	−4.98965	−	22.3694i	−0.195111	−	0.874712i
$655$	−35.0564	−	8.30853i	−1.36977	−	0.324641i
$656$	4.70744	−	1.71337i	0.183795	−	0.0668958i
$657$	−13.1222	+	8.14097i	−0.511944	+	0.317609i
$658$	7.96676	+	2.89966i	0.310577	+	0.113041i
$659$	−17.8744	−	11.7562i	−0.696287	−	0.457955i	0.151386	−	0.988475i	$-0.451626\pi$
$659$	−17.8744	−	11.7562i	−0.696287	−	0.457955i	−0.847673	+	0.530520i	$0.821997\pi$
$660$	−3.41225	−	9.77611i	−0.132822	−	0.380534i
$661$	−30.8790	−	3.60924i	−1.20105	−	0.140383i	−0.508057	−	0.861324i	$-0.669636\pi$
$661$	−30.8790	−	3.60924i	−1.20105	−	0.140383i	−0.692997	+	0.720940i	$0.743710\pi$
$662$	5.98558	−	8.04003i	0.232636	−	0.312485i
$663$	0.212687	+	0.260399i	0.00826009	+	0.0101131i
$664$	0.536056	−	9.20373i	0.0208030	−	0.357174i
$665$	4.03362	−	3.38461i	0.156417	−	0.131250i
$666$	4.39053	+	0.116345i	0.170129	+	0.00450826i
$667$	−34.6498	−	29.0746i	−1.34164	−	1.12577i
$668$	−6.88504	+	7.29771i	−0.266390	+	0.282357i
$669$	−13.3911	−	10.2478i	−0.517730	−	0.396202i
$670$	−17.1294	+	11.2662i	−0.661766	+	0.435250i
$671$	8.01019	−	1.89845i	0.309230	−	0.0732888i
$672$	−3.95192	+	5.83865i	−0.152449	+	0.225231i
$673$	−46.5296	+	5.43853i	−1.79358	+	0.209640i	−0.946695	−	0.322130i	$-0.895601\pi$
$673$	−46.5296	+	5.43853i	−1.79358	+	0.209640i	−0.846889	+	0.531770i	$0.821527\pi$
$674$	−10.4073	+	18.0260i	−0.400875	+	0.694335i
$675$	29.9739	+	66.1084i	1.15370	+	2.54451i
$676$	6.41475	+	11.1107i	0.246721	+	0.427333i
$677$	1.76303	+	2.36817i	0.0677589	+	0.0910160i	0.834711	−	0.550689i	$-0.185635\pi$
$677$	1.76303	+	2.36817i	0.0677589	+	0.0910160i	−0.766952	+	0.641705i	$0.778227\pi$
$678$	−13.5942	−	13.1702i	−0.522083	−	0.505798i
$679$	−6.78139	+	22.6514i	−0.260246	+	0.869282i
$680$	1.82967	+	0.918893i	0.0701645	+	0.0352379i
$681$	12.4183	−	0.558345i	0.475870	−	0.0213958i
$682$	3.58724	+	11.9822i	0.137362	+	0.458823i
$683$	−0.0468507	+	0.265704i	−0.00179269	+	0.0101669i	−0.985691	−	0.168562i	$-0.946088\pi$
$683$	−0.0468507	+	0.265704i	−0.00179269	+	0.0101669i	0.983898	+	0.178729i	$0.0571986\pi$
$684$	0.232846	+	0.860057i	0.00890310	+	0.0328851i
$685$	13.9599	+	79.1705i	0.533380	+	3.02495i
$686$	9.34556	−	4.69352i	0.356815	−	0.179199i
$687$	27.4868	+	16.3588i	1.04869	+	0.624126i
$688$	−1.00598	−	2.33213i	−0.0383526	−	0.0889114i
$689$	0.580783	+	1.34641i	0.0221261	+	0.0512940i
$690$	−0.651612	+	49.1888i	−0.0248065	+	1.87259i
$691$	8.18392	−	4.11012i	0.311331	−	0.156356i	−0.286272	−	0.958148i	$-0.592416\pi$
$691$	8.18392	−	4.11012i	0.311331	−	0.156356i	0.597603	+	0.801792i	$0.296120\pi$
$692$	−2.09763	−	11.8963i	−0.0797399	−	0.452228i
$693$	−13.7552	−	9.57839i	−0.522518	−	0.363853i
$694$	2.47337	−	14.0272i	0.0938880	−	0.532465i
$695$	−15.9335	−	53.2215i	−0.604391	−	2.01881i
$696$	5.53361	−	10.6637i	0.209751	−	0.404208i
$697$	−2.10449	−	1.05691i	−0.0797131	−	0.0400334i
$698$	10.0620	−	33.6093i	0.380851	−	1.27213i
$699$	−9.08641	+	36.1951i	−0.343680	+	1.36903i
$700$	33.9557	+	45.6104i	1.28340	+	1.72391i
$701$	−14.3073	−	24.7809i	−0.540379	−	0.935964i	−0.998882	−	0.0472708i	$-0.984948\pi$
$701$	−14.3073	−	24.7809i	−0.540379	−	0.935964i	0.458503	−	0.888693i	$-0.348386\pi$
$702$	−2.09657	−	0.456240i	−0.0791299	−	0.0172197i
$703$	0.217412	−	0.376569i	0.00819985	−	0.0142026i
$704$	1.36332	−	0.159349i	0.0513820	−	0.00600570i
$705$	6.86492	+	14.1329i	0.258548	+	0.532276i
$706$	15.1963	−	3.60160i	0.571922	−	0.135548i
$707$	−3.55437	+	2.33774i	−0.133676	+	0.0879199i
$708$	1.24943	−	9.58654i	0.0469566	−	0.360284i
$709$	−29.7909	+	31.5765i	−1.11882	+	1.18588i	−0.138108	+	0.990417i	$0.544102\pi$
$709$	−29.7909	+	31.5765i	−1.11882	+	1.18588i	−0.980711	+	0.195462i	$0.937379\pi$
$710$	4.14771	+	3.48034i	0.155661	+	0.130615i
$711$	−5.13211	+	25.1848i	−0.192469	+	0.944503i
$712$	8.50087	−	7.13308i	0.318584	−	0.267323i
$713$	3.45511	−	59.3220i	0.129395	−	2.22163i
$714$	3.27134	−	0.532247i	0.122427	−	0.0199188i
$715$	1.47412	−	1.98009i	0.0551289	−	0.0740510i
$716$	−13.0441	−	1.52464i	−0.487481	−	0.0569783i
$717$	−12.5823	+	14.5978i	−0.469893	+	0.545166i
$718$	25.2721	+	16.6217i	0.943146	+	0.620317i
$719$	13.3534	+	4.86023i	0.497997	+	0.181256i	0.578793	−	0.815475i	$-0.303524\pi$
$719$	13.3534	+	4.86023i	0.497997	+	0.181256i	−0.0807961	+	0.996731i	$0.525746\pi$
$720$	−12.7893	+	2.67541i	−0.476628	+	0.0997065i
$721$	12.6666	−	4.61026i	0.471729	−	0.171695i
$722$	−18.4020	−	4.36136i	−0.684852	−	0.162313i
$723$	43.2109	+	13.5627i	1.60703	+	0.504402i
$724$	0.0301395	+	0.517476i	0.00112013	+	0.0192318i
$725$	−66.4931	−	70.4785i	−2.46949	−	2.61751i
$726$	−1.62514	−	15.7055i	−0.0603145	−	0.582884i
$727$	17.7226	−	41.0856i	0.657294	−	1.52378i	−0.183842	−	0.982956i	$-0.558853\pi$
$727$	17.7226	−	41.0856i	0.657294	−	1.52378i	0.841136	−	0.540824i	$-0.181887\pi$
$728$	−1.68083			−0.0622958
$729$	−21.9958	+	15.6583i	−0.814660	+	0.579939i
$730$	−22.4190			−0.829766
$731$	−0.472909	+	1.09633i	−0.0174912	+	0.0405491i
$732$	−1.06918	−	10.3327i	−0.0395182	−	0.381907i
$733$	−15.6207	−	16.5569i	−0.576962	−	0.611544i	0.371501	−	0.928433i	$-0.378843\pi$
$733$	−15.6207	−	16.5569i	−0.576962	−	0.611544i	−0.948463	+	0.316889i	$0.897362\pi$
$734$	0.821744	+	14.1088i	0.0303311	+	0.520765i
$735$	68.8743	+	21.6177i	2.54047	+	0.797382i
$736$	−6.34530	−	1.50386i	−0.233891	−	0.0554331i
$737$	6.07165	−	2.20990i	0.223652	−	0.0814027i
$738$	14.7102	−	3.07726i	0.541491	−	0.113275i
$739$	36.4063	+	13.2508i	1.33923	+	0.487439i	0.909569	−	0.415553i	$-0.136412\pi$
$739$	36.4063	+	13.2508i	1.33923	+	0.487439i	0.429658	+	0.902992i	$0.358634\pi$
$740$	5.32737	+	3.50387i	0.195838	+	0.128805i
$741$	−0.138686	+	0.160902i	−0.00509476	+	0.00591089i
$742$	14.3569	+	1.67808i	0.527059	+	0.0616044i
$743$	−16.2315	+	21.8027i	−0.595477	+	0.799865i	−0.993048	−	0.117707i	$-0.962446\pi$
$743$	−16.2315	+	21.8027i	−0.595477	+	0.799865i	0.397571	+	0.917571i	$0.369853\pi$
$744$	15.5783	−	2.53458i	0.571127	−	0.0929223i
$745$	−1.57538	+	27.0482i	−0.0577174	+	0.990969i
$746$	1.59211	−	1.33594i	0.0582912	−	0.0489121i
$747$	5.52260	−	27.1010i	0.202061	−	0.991575i
$748$	−0.494295	−	0.414763i	−0.0180732	−	0.0151652i
$749$	12.3173	−	13.0555i	0.450063	−	0.477039i
$750$	−8.74448	+	67.0938i	−0.319303	+	2.44992i
$751$	−29.9114	+	19.6731i	−1.09148	+	0.717880i	−0.961821	−	0.273678i	$-0.911760\pi$
$751$	−29.9114	+	19.6731i	−1.09148	+	0.717880i	−0.129662	+	0.991558i	$0.541389\pi$
$752$	−2.02665	+	0.480324i	−0.0739043	+	0.0175156i
$753$	−12.3190	−	25.3613i	−0.448929	−	0.924217i
$754$	2.84482	−	0.332512i	0.103602	−	0.0121094i
$755$	41.4848	−	71.8537i	1.50979	−	2.61503i
$756$	−14.2286	+	15.6497i	−0.517490	+	0.569175i
$757$	0.960884	+	1.66430i	0.0349239	+	0.0604900i	0.882959	−	0.469450i	$-0.155548\pi$
$757$	0.960884	+	1.66430i	0.0349239	+	0.0604900i	−0.848035	+	0.529940i	$0.822214\pi$
$758$	−13.4850	−	18.1135i	−0.489797	−	0.657911i
$759$	3.77481	−	15.0367i	0.137017	−	0.545798i
$760$	−0.371000	+	1.23923i	−0.0134576	+	0.0449515i
$761$	−23.9331	−	12.0197i	−0.867575	−	0.435713i	−0.0414109	−	0.999142i	$-0.513185\pi$
$761$	−23.9331	−	12.0197i	−0.867575	−	0.435713i	−0.826164	+	0.563430i	$0.809482\pi$
$762$	2.84009	−	5.47310i	0.102886	−	0.198269i
$763$	−15.4480	−	51.5999i	−0.559255	−	1.86804i
$764$	−4.12138	+	23.3735i	−0.149106	+	0.845624i
$765$	5.04064	+	3.51003i	0.182245	+	0.126905i
$766$	−4.63723	−	26.2990i	−0.167550	−	0.950222i
$767$	2.05964	−	1.03439i	0.0743694	−	0.0373497i
$768$	0.0229428	−	1.73190i	0.000827875	−	0.0624945i
$769$	5.21507	+	12.0899i	0.188060	+	0.435972i	0.985996	−	0.166770i	$-0.0533338\pi$
$769$	5.21507	+	12.0899i	0.188060	+	0.435972i	−0.797936	+	0.602743i	$0.794075\pi$
$770$	−9.63833	−	22.3442i	−0.347341	−	0.805228i
$771$	29.8365	+	17.7572i	1.07453	+	0.639509i
$772$	−2.19685	+	1.10330i	−0.0790664	+	0.0397086i
$773$	−0.743084	−	4.21424i	−0.0267269	−	0.151576i	0.968524	−	0.248921i	$-0.0800760\pi$
$773$	−0.743084	−	4.21424i	−0.0267269	−	0.151576i	−0.995251	+	0.0973454i	$0.968965\pi$
$774$	−1.99118	−	7.35476i	−0.0715715	−	0.264361i
$775$	22.1042	−	125.359i	0.794006	−	4.50303i
$776$	−1.66597	−	5.56474i	−0.0598050	−	0.199763i
$777$	10.3115	−	0.463619i	0.369922	−	0.0166322i
$778$	−9.33472	−	4.68807i	−0.334666	−	0.168076i
$779$	0.426726	−	1.42536i	0.0152890	−	0.0510689i
$780$	−2.23726	−	2.16747i	−0.0801068	−	0.0776080i
$781$	−1.01897	−	1.36872i	−0.0364617	−	0.0489766i
$782$	1.53277	+	2.65484i	0.0548118	+	0.0949368i
$783$	20.9861	−	29.3020i	0.749982	−	1.04717i
$784$	−4.78459	+	8.28716i	−0.170878	+	0.295970i
$785$	50.1269	−	5.85899i	1.78910	−	0.209116i
$786$	8.03097	−	11.8651i	0.286455	−	0.423215i
$787$	−26.4068	+	6.25853i	−0.941301	+	0.223092i	−0.672495	−	0.740102i	$-0.734777\pi$
$787$	−26.4068	+	6.25853i	−0.941301	+	0.223092i	−0.268806	+	0.963194i	$0.586629\pi$
$788$	−4.62634	+	3.04279i	−0.164807	+	0.108395i
$789$	−44.4874	−	34.0447i	−1.58379	−	1.21202i
$790$	−25.6067	+	27.1415i	−0.911046	+	0.965652i
$791$	−34.0754	−	28.5927i	−1.21158	−	1.01664i
$792$	4.11635	+	0.109079i	0.146268	+	0.00387596i
$793$	1.89712	−	1.59187i	0.0673686	−	0.0565289i
$794$	−1.97861	+	33.9714i	−0.0702182	+	1.20560i
$795$	16.9458	+	20.7472i	0.601004	+	0.735827i
$796$	3.23056	−	4.33939i	0.114504	−	0.153806i
$797$	9.63557	+	1.12624i	0.341309	+	0.0398934i	0.285021	−	0.958521i	$-0.407999\pi$
$797$	9.63557	+	1.12624i	0.341309	+	0.0398934i	0.0562882	+	0.998415i	$0.482073\pi$
$798$	0.690063	+	1.97703i	0.0244280	+	0.0699862i
$799$	0.818039	+	0.538032i	0.0289401	+	0.0190342i
$800$	−13.1268	−	4.77775i	−0.464101	−	0.168919i
$801$	28.2893	−	17.5507i	0.999554	−	0.620122i
$802$	22.8243	−	8.30737i	0.805954	−	0.293343i
$803$	6.87495	+	1.62939i	0.242612	+	0.0575000i
$804$	−1.77504	−	7.95781i	−0.0626010	−	0.280650i
$805$	6.72211	+	115.414i	0.236923	+	4.06781i
$806$	2.58216	+	2.73693i	0.0909528	+	0.0964043i
$807$	20.5752	+	9.20041i	0.724281	+	0.323870i
$808$	0.413956	−	0.959658i	0.0145629	−	0.0337607i
$809$	−4.47713			−0.157407			−0.0787037	−	0.996898i	$-0.525078\pi$
$809$	−4.47713			−0.157407			−0.0787037	+	0.996898i	$0.525078\pi$
$810$	−39.1196	+	2.48232i	−1.37452	+	0.0872199i
$811$	10.7641			0.377977			0.188989	−	0.981979i	$-0.439479\pi$
$811$	10.7641			0.377977			0.188989	+	0.981979i	$0.439479\pi$
$812$	11.1831	−	25.9252i	0.392448	−	0.909797i
$813$	−18.3201	+	13.2653i	−0.642515	+	0.465235i
$814$	−1.37901	−	1.46167i	−0.0483344	−	0.0512315i
$815$	2.21892	+	38.0974i	0.0777254	+	1.33449i
$816$	−0.599601	+	0.550867i	−0.0209902	+	0.0192842i
$817$	−0.734016	−	0.173965i	−0.0256800	−	0.00608626i
$818$	−24.3399	+	8.85899i	−0.851024	+	0.309747i
$819$	−4.99114	−	0.717864i	−0.174405	−	0.0250842i
$820$	20.5026	+	7.46235i	0.715983	+	0.260596i
$821$	42.2005	+	27.7557i	1.47281	+	0.968682i	0.995970	+	0.0896910i	$0.0285880\pi$
$821$	42.2005	+	27.7557i	1.47281	+	0.968682i	0.476839	+	0.878991i	$0.341782\pi$
$822$	−31.4084	−	5.96816i	−1.09549	−	0.208163i
$823$	−12.6456	−	1.47806i	−0.440799	−	0.0515220i	−0.107201	−	0.994237i	$-0.534189\pi$
$823$	−12.6456	−	1.47806i	−0.440799	−	0.0515220i	−0.333598	+	0.942715i	$0.608263\pi$
$824$	−1.97748	+	2.65622i	−0.0688889	+	0.0925339i
$825$	11.7711	−	31.0546i	0.409816	−	1.08118i
$826$	1.32105	−	22.6816i	0.0459653	−	0.789194i
$827$	20.3942	−	17.1128i	0.709176	−	0.595070i	−0.215192	−	0.976572i	$-0.569038\pi$
$827$	20.3942	−	17.1128i	0.709176	−	0.595070i	0.924368	+	0.381502i	$0.124593\pi$
$828$	−18.1997	−	7.17564i	−0.632484	−	0.249371i
$829$	−29.8261	−	25.0271i	−1.03590	−	0.869227i	−0.0443624	−	0.999016i	$-0.514126\pi$
$829$	−29.8261	−	25.0271i	−1.03590	−	0.869227i	−0.991542	+	0.129789i	$0.958570\pi$
$830$	27.5550	−	29.2066i	0.956450	−	1.01378i
$831$	36.5074	−	15.1774i	1.26643	−	0.526499i
$832$	0.344996	−	0.226908i	0.0119606	−	0.00786660i
$833$	4.37720	−	1.03741i	0.151661	−	0.0359443i
$834$	22.0371	+	1.57666i	0.763081	+	0.0545952i
$835$	−43.4018	+	5.07294i	−1.50198	+	0.175556i
$836$	0.203835	−	0.353053i	0.00704980	−	0.0122106i
$837$	47.3413	−	0.873000i	1.63636	−	0.0301753i
$838$	7.76054	+	13.4416i	0.268083	+	0.464334i
$839$	25.7303	+	34.5617i	0.888307	+	1.19320i	0.980314	+	0.197445i	$0.0632644\pi$
$839$	25.7303	+	34.5617i	0.888307	+	1.19320i	−0.0920069	+	0.995758i	$0.529328\pi$
$840$	−29.5310	+	8.41641i	−1.01891	+	0.290394i
$841$	−5.48141	+	18.3092i	−0.189014	+	0.631352i
$842$	−28.3921	−	14.2591i	−0.978457	−	0.491400i
$843$	−2.47228	−	3.86961i	−0.0851498	−	0.133276i
$844$	3.05766	+	10.2133i	0.105249	+	0.351556i
$845$	−9.70296	+	55.0282i	−0.333792	+	1.89303i
$846$	−6.22316	+	0.560739i	−0.213957	+	0.0192786i
$847$	−6.44353	−	36.5431i	−0.221402	−	1.25563i
$848$	−3.17334	+	1.59371i	−0.108973	+	0.0547282i
$849$	−18.3754	+	10.2869i	−0.630640	+	0.353046i
$850$	2.60102	+	6.02983i	0.0892141	+	0.206821i
$851$	3.78137	+	8.76621i	0.129624	+	0.300502i
$852$	−1.87885	+	1.05182i	−0.0643682	+	0.0360347i
$853$	1.16228	−	0.583719i	0.0397957	−	0.0199862i	−0.428790	−	0.903404i	$-0.641060\pi$
$853$	1.16228	−	0.583719i	0.0397957	−	0.0199862i	0.468586	+	0.883418i	$0.344764\pi$
$854$	−4.23923	−	24.0418i	−0.145063	−	0.822695i
$855$	−1.63092	+	3.52137i	−0.0557765	+	0.120428i
$856$	−0.765696	+	4.34248i	−0.0261710	+	0.148423i
$857$	10.9839	+	36.6889i	0.375204	+	1.25327i	0.912222	+	0.409697i	$0.134365\pi$
$857$	10.9839	+	36.6889i	0.375204	+	1.25327i	−0.537018	+	0.843571i	$0.680449\pi$
$858$	0.528541	+	0.827272i	0.0180441	+	0.0282426i
$859$	17.7121	+	8.89535i	0.604329	+	0.303505i	0.724529	−	0.689244i	$-0.242057\pi$
$859$	17.7121	+	8.89535i	0.604329	+	0.303505i	−0.120200	+	0.992750i	$0.538354\pi$
$860$	3.17260	−	10.5972i	0.108185	−	0.361363i
$861$	33.9666	−	9.68058i	1.15758	−	0.329913i
$862$	8.99414	+	12.0812i	0.306342	+	0.411488i
$863$	20.1970	+	34.9822i	0.687513	+	1.19081i	0.972640	+	0.232317i	$0.0746307\pi$
$863$	20.1970	+	34.9822i	0.687513	+	1.19081i	−0.285127	+	0.958490i	$0.592036\pi$
$864$	0.807801	−	5.13298i	0.0274819	−	0.174627i
$865$	26.3059	−	45.5632i	0.894428	−	1.54919i
$866$	22.6165	−	2.64348i	0.768539	−	0.0898293i
$867$	−28.9880	−	2.07397i	−0.984484	−	0.0704356i
$868$	36.0924	−	8.55406i	1.22506	−	0.290344i
$869$	9.82508	−	6.46206i	0.333293	−	0.219210i
$870$	48.3163	−	20.0868i	1.63808	−	0.681006i
$871$	1.33391	−	1.41387i	0.0451980	−	0.0479071i
$872$	10.1366	+	8.50560i	0.343268	+	0.288036i
$873$	−2.57038	−	17.2357i	−0.0869942	−	0.583340i
$874$	−1.48368	+	1.24495i	−0.0501861	+	0.0421111i
$875$	−9.24572	+	158.743i	−0.312562	+	5.36649i
$876$	3.16004	−	8.33684i	0.106768	−	0.281676i
$877$	23.5165	−	31.5881i	0.794096	−	1.06666i	−0.202088	−	0.979367i	$-0.564773\pi$
$877$	23.5165	−	31.5881i	0.794096	−	1.06666i	0.996183	−	0.0872880i	$-0.0278200\pi$
$878$	33.8435	+	3.95574i	1.14216	+	0.133500i
$879$	−42.5964	−	8.09408i	−1.43674	−	0.273007i
$880$	4.99469	+	3.28506i	0.168371	+	0.110739i
$881$	17.9904	+	6.54798i	0.606113	+	0.220607i	0.626801	−	0.779179i	$-0.284364\pi$
$881$	17.9904	+	6.54798i	0.606113	+	0.220607i	−0.0206888	+	0.999786i	$0.506586\pi$
$882$	−17.7469	+	22.5648i	−0.597570	+	0.759797i
$883$	−17.8413	+	6.49369i	−0.600406	+	0.218530i	−0.624300	−	0.781185i	$-0.714616\pi$
$883$	−17.8413	+	6.49369i	−0.600406	+	0.218530i	0.0238941	+	0.999714i	$0.492394\pi$
$884$	−0.188884	−	0.0447663i	−0.00635286	−	0.00150565i
$885$	31.0068	−	28.4867i	1.04228	−	0.957569i
$886$	−0.250625	−	4.30306i	−0.00841990	−	0.144564i
$887$	10.3544	+	10.9750i	0.347666	+	0.368504i	0.877483	−	0.479608i	$-0.159221\pi$
$887$	10.3544	+	10.9750i	0.347666	+	0.368504i	−0.529817	+	0.848112i	$0.677740\pi$
$888$	−2.05387	+	1.48718i	−0.0689235	+	0.0499064i
$889$	5.73963	−	13.3060i	0.192501	−	0.446268i
$890$	48.3319			1.62009
$891$	12.1767	+	2.08195i	0.407935	+	0.0697480i
$892$	9.73548			0.325968
$893$	−0.245016	+	0.568010i	−0.00819914	+	0.0190077i
$894$	−9.83621	−	4.39836i	−0.328972	−	0.147103i
$895$	−39.2520	−	41.6047i	−1.31205	−	1.39069i
$896$	−0.236680	−	4.06364i	−0.00790693	−	0.135757i
$897$	−1.01537	−	4.55208i	−0.0339023	−	0.151990i
$898$	−9.99921	−	2.36986i	−0.333678	−	0.0790831i
$899$	−59.3944	+	21.6178i	−1.98091	+	0.720993i
$900$	−36.9387	−	19.7936i	−1.23129	−	0.659785i
$901$	1.56867	+	0.570949i	0.0522599	+	0.0190211i
$902$	−5.74491	−	3.77849i	−0.191285	−	0.125810i
$903$	−5.90106	−	16.9065i	−0.196375	−	0.562615i
$904$	10.8540	+	1.26865i	0.360999	+	0.0421947i
$905$	−1.34815	+	1.81089i	−0.0448142	+	0.0601959i
$906$	20.8724	+	25.5547i	0.693440	+	0.848999i
$907$	−1.77884	+	30.5415i	−0.0590655	+	1.01411i	0.830416	+	0.557144i	$0.188103\pi$
$907$	−1.77884	+	30.5415i	−0.0590655	+	1.01411i	−0.889482	+	0.456971i	$0.848934\pi$
$908$	−5.49786	+	4.61325i	−0.182453	+	0.153096i
$909$	1.63908	−	2.67286i	0.0543648	−	0.0886530i
$910$	−5.60794	−	4.70562i	−0.185901	−	0.155990i
$911$	39.9071	−	42.2991i	1.32218	−	1.40143i	0.465976	−	0.884798i	$-0.345703\pi$
$911$	39.9071	−	42.2991i	1.32218	−	1.40143i	0.856207	−	0.516634i	$-0.172815\pi$
$912$	−0.408531	−	0.312635i	−0.0135278	−	0.0103524i
$913$	−10.5726	+	6.95374i	−0.349903	+	0.230135i
$914$	1.18172	−	0.280073i	0.0390878	−	0.00926399i
$915$	25.3599	−	37.4673i	0.838373	−	1.23863i
$916$	−18.3425	+	2.14393i	−0.606054	+	0.0708376i
$917$	16.8357	−	29.1603i	0.555963	−	0.962957i
$918$	−2.01575	+	1.37969i	−0.0665297	+	0.0455364i
$919$	14.1201	+	24.4567i	0.465779	+	0.806753i	0.999236	−	0.0390741i	$-0.0124409\pi$
$919$	14.1201	+	24.4567i	0.465779	+	0.806753i	−0.533457	+	0.845827i	$0.679108\pi$
$920$	−16.9603	−	22.7816i	−0.559165	−	0.751088i
$921$	−21.1021	−	20.4438i	−0.695337	−	0.673647i
$922$	10.7516	−	35.9127i	0.354084	−	1.18272i
$923$	−0.458736	−	0.230386i	−0.0150995	−	0.00758324i
$924$	9.66756	−	0.434668i	0.318039	−	0.0142995i
$925$	5.86549	+	19.5921i	0.192856	+	0.644184i
$926$	0.683444	−	3.87600i	0.0224594	−	0.127373i
$927$	−7.00647	+	7.04294i	−0.230123	+	0.231321i
$928$	1.20447	+	6.83091i	0.0395388	+	0.224236i
$929$	−42.7172	+	21.4534i	−1.40151	+	0.703863i	−0.979258	−	0.202617i	$-0.935055\pi$
$929$	−42.7172	+	21.4534i	−1.40151	+	0.703863i	−0.422249	+	0.906480i	$0.638759\pi$
$930$	59.0712	+	35.1562i	1.93702	+	1.15282i
$931$	1.12570	+	2.60967i	0.0368934	+	0.0855285i
$932$	−8.53381	−	19.7836i	−0.279534	−	0.648033i
$933$	−0.506343	+	38.2228i	−0.0165769	+	1.25136i
$934$	−16.2228	+	8.14741i	−0.530827	+	0.266591i
$935$	−0.488008	−	2.76763i	−0.0159596	−	0.0905112i
$936$	1.12136	−	0.526445i	0.0366527	−	0.0172074i
$937$	−0.665387	+	3.77360i	−0.0217372	+	0.123278i	−0.993745	−	0.111669i	$-0.964380\pi$
$937$	−0.665387	+	3.77360i	−0.0217372	+	0.123278i	0.972008	+	0.234947i	$0.0754916\pi$
$938$	−5.49555	−	18.3564i	−0.179436	−	0.599359i
$939$	−13.7073	+	26.4152i	−0.447322	+	0.862027i
$940$	−8.10642	−	4.07120i	−0.264402	−	0.132788i
$941$	3.57848	−	11.9529i	0.116655	−	0.389655i	−0.879642	−	0.475637i	$-0.842218\pi$
$941$	3.57848	−	11.9529i	0.116655	−	0.389655i	0.996297	+	0.0859821i	$0.0274028\pi$
$942$	−4.88680	+	19.4662i	−0.159221	+	0.634244i
$943$	19.5078	+	26.2035i	0.635261	+	0.853303i
$944$	2.79080	+	4.83381i	0.0908328	+	0.157327i
$945$	−91.2851	+	12.3797i	−2.96950	+	0.402712i
$946$	−1.74309	+	3.01913i	−0.0566729	+	0.0981603i
$947$	−22.3089	+	2.60754i	−0.724942	+	0.0847336i	−0.470557	−	0.882369i	$-0.655947\pi$
$947$	−22.3089	+	2.60754i	−0.724942	+	0.0847336i	−0.254385	+	0.967103i	$0.581873\pi$
$948$	−6.48361	−	13.3479i	−0.210578	−	0.433520i
$949$	2.06823	−	0.490180i	0.0671377	−	0.0159119i
$950$	−3.46639	+	2.27988i	−0.112465	+	0.0739692i
$951$	1.80364	−	13.8388i	0.0584872	−	0.448755i
$952$	−1.31315	+	1.39186i	−0.0425596	+	0.0451105i
$953$	0.608669	+	0.510734i	0.0197167	+	0.0165443i	0.652593	−	0.757709i	$-0.273681\pi$
$953$	0.608669	+	0.510734i	0.0197167	+	0.0165443i	−0.632876	+	0.774253i	$0.718126\pi$
$954$	−10.1037	+	3.37714i	−0.327119	+	0.109339i
$955$	−79.1865	+	66.4453i	−2.56241	+	2.15012i
$956$	0.646960	−	11.1079i	0.0209242	−	0.359254i
$957$	−16.2764	+	2.64817i	−0.526141	+	0.0856031i
$958$	−5.93330	+	7.96980i	−0.191696	+	0.257493i
$959$	−74.6262	−	8.72255i	−2.40981	−	0.281666i
$960$	4.92513	−	5.71408i	0.158958	−	0.184421i
$961$	−43.4751	−	28.5940i	−1.40242	−	0.922389i
$962$	−0.568078	−	0.206763i	−0.0183156	−	0.00666632i
$963$	−4.12831	+	12.5677i	−0.133033	+	0.404989i
$964$	−24.5709	+	8.94308i	−0.791376	+	0.288037i
$965$	−10.4184	−	2.46919i	−0.335379	−	0.0794862i
$966$	−43.8659	−	13.7683i	−1.41136	−	0.442988i
$967$	0.738478	+	12.6792i	0.0237479	+	0.407735i	0.989144	+	0.146948i	$0.0469450\pi$
$967$	0.738478	+	12.6792i	0.0237479	+	0.407735i	−0.965396	+	0.260787i	$0.916018\pi$
$968$	6.25576	+	6.63072i	0.201068	+	0.213119i
$969$	0.0248909	+	0.240548i	0.000799611	+	0.00772752i
$970$	10.0205	−	23.2302i	0.321740	−	0.745878i
$971$	−48.7638			−1.56490			−0.782452	−	0.622711i	$-0.786031\pi$
$971$	−48.7638			−1.56490			−0.782452	+	0.622711i	$0.786031\pi$
$972$	4.59095	−	14.8971i	0.147255	−	0.477824i
$973$	51.9221			1.66455
$974$	−5.59907	+	12.9801i	−0.179406	+	0.415909i
$975$	−1.02833	−	9.93789i	−0.0329330	−	0.318267i
$976$	4.11569	+	4.36238i	0.131740	+	0.139636i
$977$	−0.381457	−	6.54936i	−0.0122039	−	0.209532i	−0.998898	−	0.0469425i	$-0.985052\pi$
$977$	−0.381457	−	6.54936i	−0.0122039	−	0.209532i	0.986694	−	0.162590i	$-0.0519848\pi$
$978$	−14.4798	−	4.54482i	−0.463014	−	0.145327i
$979$	−14.8213	−	3.51271i	−0.473691	−	0.112267i
$980$	−39.1639	+	14.2545i	−1.25104	+	0.455343i
$981$	26.4673	+	29.5861i	0.845037	+	0.944612i
$982$	−19.9306	−	7.25413i	−0.636010	−	0.231489i
$983$	−7.49132	−	4.92712i	−0.238936	−	0.157151i	0.424394	−	0.905478i	$-0.360487\pi$
$983$	−7.49132	−	4.92712i	−0.238936	−	0.157151i	−0.663330	+	0.748327i	$0.730857\pi$
$984$	−5.66490	+	6.57236i	−0.180590	+	0.209519i
$985$	−23.9539	−	2.79981i	−0.763234	−	0.0892093i
$986$	1.94718	−	2.61551i	0.0620107	−	0.0832948i
$987$	−14.4938	+	2.35814i	−0.461344	+	0.0750605i
$988$	0.00713101	−	0.122435i	0.000226868	−	0.00389517i
$989$	12.6876	−	10.6462i	0.403443	−	0.338529i
$990$	13.4284	+	11.8880i	0.426784	+	0.377825i
$991$	−13.2357	−	11.1061i	−0.420446	−	0.352796i	0.407887	−	0.913032i	$-0.366266\pi$
$991$	−13.2357	−	11.1061i	−0.420446	−	0.352796i	−0.828333	+	0.560237i	$0.810710\pi$
$992$	−6.25330	+	6.62811i	−0.198542	+	0.210443i
$993$	−2.24373	+	17.2155i	−0.0712027	+	0.546317i
$994$	−4.22785	+	2.78070i	−0.134099	+	0.0881986i
$995$	22.9269	−	5.43378i	0.726832	−	0.172262i
$996$	6.97694	+	14.3635i	0.221073	+	0.455125i
$997$	12.5738	−	1.46966i	0.398216	−	0.0465447i	0.0853715	−	0.996349i	$-0.472792\pi$
$997$	12.5738	−	1.46966i	0.398216	−	0.0465447i	0.312844	+	0.949804i	$0.398718\pi$
$998$	19.0516	−	32.9983i	0.603067	−	1.04454i
$999$	−6.73402	+	3.53890i	−0.213055	+	0.111966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.115.3	yes	90
3.2	odd	2		486.2.g.b.181.5		90
81.31	even	27	inner	162.2.g.b.31.3	✓	90
81.50	odd	54		486.2.g.b.145.5		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.31.3	✓	90	81.31	even	27	inner
162.2.g.b.115.3	yes	90	1.1	even	1	trivial
486.2.g.b.145.5		90	81.50	odd	54
486.2.g.b.181.5		90	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396080 - 0.918216i) q^{2} +(0.178274 + 1.72285i) q^{3} +(-0.686242 - 0.727374i) q^{4} +(-0.253242 - 4.34800i) q^{5} +(1.65256 + 0.518693i) q^{6} +(3.96081 + 0.938728i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.93644 + 0.614278i) q^{9} +O(q^{10})\)	\(q+(0.396080 - 0.918216i) q^{2} +(0.178274 + 1.72285i) q^{3} +(-0.686242 - 0.727374i) q^{4} +(-0.253242 - 4.34800i) q^{5} +(1.65256 + 0.518693i) q^{6} +(3.96081 + 0.938728i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.93644 + 0.614278i) q^{9} +(-4.09271 - 1.48962i) q^{10} +(1.14679 + 0.754256i) q^{11} +(1.13082 - 1.31196i) q^{12} +(0.410136 + 0.0479380i) q^{13} +(2.43075 - 3.26506i) q^{14} +(7.44581 - 1.21143i) q^{15} +(-0.0581448 + 0.998308i) q^{16} +(0.360116 - 0.302173i) q^{17} +(-0.599023 + 2.93959i) q^{18} +(0.227520 + 0.190912i) q^{19} +(-2.98883 + 3.16798i) q^{20} +(-0.911183 + 6.99123i) q^{21} +(1.14679 - 0.754256i) q^{22} +(-6.34530 + 1.50386i) q^{23} +(-0.756772 - 1.55798i) q^{24} +(-13.8748 + 1.62173i) q^{25} +(0.206464 - 0.357606i) q^{26} +(-1.58180 - 4.94954i) q^{27} +(-2.03526 - 3.52518i) q^{28} +(4.14206 + 5.56376i) q^{29} +(1.83678 - 7.31669i) q^{30} +(-2.61346 + 8.72957i) q^{31} +(0.893633 + 0.448799i) q^{32} +(-1.09503 + 2.11021i) q^{33} +(-0.134826 - 0.450349i) q^{34} +(3.07855 - 17.4593i) q^{35} +(2.46191 + 1.71434i) q^{36} +(-0.254225 - 1.44178i) q^{37} +(0.265415 - 0.133296i) q^{38} +(-0.00947370 + 0.715149i) q^{39} +(1.72507 + 3.99917i) q^{40} +(-1.98418 - 4.59985i) q^{41} +(6.05856 + 3.60575i) q^{42} +(-2.26969 + 1.13988i) q^{43} +(-0.238349 - 1.35175i) q^{44} +(3.41451 + 12.6121i) q^{45} +(-1.13237 + 6.42200i) q^{46} +(0.597351 + 1.99529i) q^{47} +(-1.73030 + 0.0777970i) q^{48} +(8.55134 + 4.29464i) q^{49} +(-4.00642 + 13.3824i) q^{50} +(0.584798 + 0.566557i) q^{51} +(-0.246583 - 0.331219i) q^{52} +(1.77553 + 3.07530i) q^{53} +(-5.17126 - 0.507978i) q^{54} +(2.98909 - 5.17725i) q^{55} +(-4.04300 + 0.472559i) q^{56} +(-0.288352 + 0.426018i) q^{57} +(6.74932 - 1.59962i) q^{58} +(4.66336 - 3.06714i) q^{59} +(-5.99079 - 4.58455i) q^{60} +(4.11569 - 4.36238i) q^{61} +(6.98049 + 5.85733i) q^{62} +(-12.2073 - 0.323481i) q^{63} +(0.766044 - 0.642788i) q^{64} +(0.104571 - 1.79541i) q^{65} +(1.50391 + 1.84129i) q^{66} +(2.81104 - 3.77588i) q^{67} +(-0.466919 - 0.0545750i) q^{68} +(-3.72213 - 10.6639i) q^{69} +(-14.8121 - 9.74204i) q^{70} +(-1.16819 - 0.425188i) q^{71} +(2.54925 - 1.58155i) q^{72} +(4.83702 - 1.76053i) q^{73} +(-1.42456 - 0.337627i) q^{74} +(-5.26750 - 23.6150i) q^{75} +(-0.0172694 - 0.296504i) q^{76} +(3.83417 + 4.06399i) q^{77} +(0.652909 + 0.291955i) q^{78} +(3.39340 - 7.86678i) q^{79} +4.35537 q^{80} +(8.24533 - 3.60758i) q^{81} -5.00955 q^{82} +(-3.65159 + 8.46534i) q^{83} +(5.71053 - 4.13490i) q^{84} +(-1.40504 - 1.48926i) q^{85} +(0.147679 + 2.53555i) q^{86} +(-8.84711 + 8.12803i) q^{87} +(-1.33560 - 0.316543i) q^{88} +(-10.4279 + 3.79543i) q^{89} +(12.9330 + 1.86013i) q^{90} +(1.57947 + 0.574879i) q^{91} +(5.44828 + 3.58339i) q^{92} +(-15.5057 - 2.94636i) q^{93} +(2.06871 + 0.241797i) q^{94} +(0.772467 - 1.03760i) q^{95} +(-0.613903 + 1.61961i) q^{96} +(-0.337750 + 5.79894i) q^{97} +(7.33042 - 6.15096i) q^{98} +(-3.83080 - 1.51038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

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