LMFDB - Embedded newform 165.2.d.c.164.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(164,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("165.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.d (of order $2$, degree $1$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24x^{14} + 244x^{12} - 1224x^{10} + 2880x^{8} - 2208x^{6} + 3976x^{4} + 432x^{2} + 2116 $ x^16 - 24x^14 + 244x^12 - 1224x^10 + 2880x^8 - 2208x^6 + 3976x^4 + 432*x^2 + 2116
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			164.8
Root			$-2.60307 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	165.164
Dual form			165.2.d.c.164.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50597i q^{2} +(1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(-1.12603 - 1.93185i) q^{5} +(1.19909 - 2.31647i) q^{6} -2.12976 q^{7} -2.60842i q^{8} +(1.73205 + 2.44949i) q^{9} +O(q^{10})$	\(q-1.50597i q^{2} +(1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(-1.12603 - 1.93185i) q^{5} +(1.19909 - 2.31647i) q^{6} -2.12976 q^{7} -2.60842i q^{8} +(1.73205 + 2.44949i) q^{9} +(-2.90931 + 1.69577i) q^{10} +(3.27598 - 0.517638i) q^{11} +(-0.412157 - 0.213348i) q^{12} +2.12976 q^{13} +3.20736i q^{14} +(-0.193862 - 3.86813i) q^{15} -4.46410 q^{16} +4.11439i q^{17} +(3.68886 - 2.60842i) q^{18} +4.63294i q^{19} +(0.301719 + 0.517638i) q^{20} +(-3.27598 - 1.69577i) q^{21} +(-0.779548 - 4.93353i) q^{22} -5.32844 q^{23} +(2.07689 - 4.01224i) q^{24} +(-2.46410 + 4.35066i) q^{25} -3.20736i q^{26} +(0.713876 + 5.14688i) q^{27} +0.570669 q^{28} -8.95015 q^{29} +(-5.82529 + 0.291950i) q^{30} +3.46410 q^{31} +1.50597i q^{32} +(5.45123 + 1.81219i) q^{33} +6.19615 q^{34} +(2.39818 + 4.11439i) q^{35} +(-0.464102 - 0.656339i) q^{36} -1.16575i q^{37} +6.97707 q^{38} +(3.27598 + 1.69577i) q^{39} +(-5.03908 + 2.93716i) q^{40} -2.39818 q^{41} +(-2.55378 + 4.93353i) q^{42} +9.50749 q^{43} +(-0.877796 + 0.138701i) q^{44} +(2.78171 - 6.10427i) q^{45} +8.02448i q^{46} +3.07638 q^{47} +(-6.86663 - 3.55443i) q^{48} -2.46410 q^{49} +(6.55196 + 3.71087i) q^{50} +(-3.27598 + 6.32871i) q^{51} -0.570669 q^{52} +4.50413 q^{53} +(7.75105 - 1.07508i) q^{54} +(-4.68886 - 5.74583i) q^{55} +5.55532i q^{56} +(-3.68886 + 7.12633i) q^{57} +13.4787i q^{58} -4.89898i q^{59} +(0.0519451 + 1.03646i) q^{60} -3.39154i q^{61} -5.21684i q^{62} +(-3.68886 - 5.21684i) q^{63} -6.66025 q^{64} +(-2.39818 - 4.11439i) q^{65} +(2.72911 - 8.20940i) q^{66} -12.3129i q^{67} -1.10245i q^{68} +(-8.19615 - 4.24264i) q^{69} +(6.19615 - 3.61160i) q^{70} +13.3843i q^{71} +(6.38929 - 4.51791i) q^{72} -2.12976 q^{73} -1.75559 q^{74} +(-7.25436 + 4.73015i) q^{75} -1.24139i q^{76} +(-6.97707 + 1.10245i) q^{77} +(2.55378 - 4.93353i) q^{78} -13.8988i q^{79} +(5.02672 + 8.62398i) q^{80} +(-3.00000 + 8.48528i) q^{81} +3.61160i q^{82} -9.33123i q^{83} +(0.877796 + 0.454381i) q^{84} +(7.94839 - 4.63294i) q^{85} -14.3180i q^{86} +(-13.7670 - 7.12633i) q^{87} +(-1.35022 - 8.54513i) q^{88} -4.62158i q^{89} +(-9.19286 - 4.18917i) q^{90} -4.53590 q^{91} +1.42775 q^{92} +(5.32844 + 2.75821i) q^{93} -4.63294i q^{94} +(8.95015 - 5.21684i) q^{95} +(-1.19909 + 2.31647i) q^{96} +1.16575i q^{97} +3.71087i q^{98} +(6.94211 + 7.12791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4}+O(q^{10}) $ 16 * q - 32 * q^4	$ 16 q - 32 q^{4} - 16 q^{16} + 16 q^{25} + 16 q^{34} + 48 q^{36} + 48 q^{45} + 16 q^{49} - 16 q^{55} - 48 q^{60} + 32 q^{64} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 48 q^{81} - 128 q^{91} + 48 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 - 16 * q^16 + 16 * q^25 + 16 * q^34 + 48 * q^36 + 48 * q^45 + 16 * q^49 - 16 * q^55 - 48 * q^60 + 32 * q^64 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 48 * q^81 - 128 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.50597i		−	1.06488i	−0.846467	−	0.532441i	$-0.821275\pi$
$2$		−	1.50597i		−	1.06488i	0.846467	−	0.532441i	$-0.178725\pi$
$3$	1.53819	+	0.796225i	0.888074	+	0.459701i
$3$	1.53819	+	0.796225i	0.888074	+	0.459701i
$4$	−0.267949			−0.133975
$5$	−1.12603	−	1.93185i	−0.503577	−	0.863950i
$5$	−1.12603	−	1.93185i	−0.503577	−	0.863950i
$6$	1.19909	−	2.31647i	0.489527	−	0.945694i
$7$	−2.12976			−0.804975			−0.402488	−	0.915425i	$-0.631854\pi$
$7$	−2.12976			−0.804975			−0.402488	+	0.915425i	$0.631854\pi$
$8$		−	2.60842i		−	0.922215i
$9$	1.73205	+	2.44949i	0.577350	+	0.816497i
$10$	−2.90931	+	1.69577i	−0.920006	+	0.536250i
$11$	3.27598	−	0.517638i	0.987745	−	0.156074i
$11$	3.27598	−	0.517638i	0.987745	−	0.156074i
$12$	−0.412157	−	0.213348i	−0.118979	−	0.0615882i
$13$	2.12976			0.590690			0.295345	−	0.955391i	$-0.404565\pi$
$13$	2.12976			0.590690			0.295345	+	0.955391i	$0.404565\pi$
$14$			3.20736i			0.857204i
$15$	−0.193862	−	3.86813i	−0.0500549	−	0.998746i
$16$	−4.46410			−1.11603
$17$			4.11439i			0.997886i	0.866635	+	0.498943i	$0.166278\pi$
$17$			4.11439i			0.997886i	−0.866635	+	0.498943i	$0.833722\pi$
$18$	3.68886	−	2.60842i	0.869473	−	0.614810i
$19$			4.63294i			1.06287i	0.847100	+	0.531434i	$0.178347\pi$
$19$			4.63294i			1.06287i	−0.847100	+	0.531434i	$0.821653\pi$
$20$	0.301719	+	0.517638i	0.0674665	+	0.115747i
$21$	−3.27598	−	1.69577i	−0.714878	−	0.370048i
$22$	−0.779548	−	4.93353i	−0.166200	−	1.05183i
$23$	−5.32844			−1.11106			−0.555529	−	0.831497i	$-0.687484\pi$
$23$	−5.32844			−1.11106			−0.555529	+	0.831497i	$0.687484\pi$
$24$	2.07689	−	4.01224i	0.423943	−	0.818995i
$25$	−2.46410	+	4.35066i	−0.492820	+	0.870131i
$26$		−	3.20736i		−	0.629016i
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$	0.570669			0.107846
$29$	−8.95015			−1.66200			−0.831000	−	0.556272i	$-0.812231\pi$
$29$	−8.95015			−1.66200			−0.831000	+	0.556272i	$0.812231\pi$
$30$	−5.82529	+	0.291950i	−1.06355	+	0.0533026i
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$			1.50597i			0.266221i
$33$	5.45123	+	1.81219i	0.948938	+	0.315462i
$34$	6.19615			1.06263
$35$	2.39818	+	4.11439i	0.405367	+	0.695459i
$36$	−0.464102	−	0.656339i	−0.0773503	−	0.109390i
$37$		−	1.16575i		−	0.191649i	−0.995398	−	0.0958244i	$-0.969451\pi$
$37$		−	1.16575i		−	0.191649i	0.995398	−	0.0958244i	$-0.0305487\pi$
$38$	6.97707			1.13183
$39$	3.27598	+	1.69577i	0.524577	+	0.271541i
$40$	−5.03908	+	2.93716i	−0.796748	+	0.464406i
$41$	−2.39818			−0.374533			−0.187267	−	0.982309i	$-0.559963\pi$
$41$	−2.39818			−0.374533			−0.187267	+	0.982309i	$0.559963\pi$
$42$	−2.55378	+	4.93353i	−0.394058	+	0.761261i
$43$	9.50749			1.44988			0.724939	−	0.688813i	$-0.241868\pi$
$43$	9.50749			1.44988			0.724939	+	0.688813i	$0.241868\pi$
$44$	−0.877796	+	0.138701i	−0.132333	+	0.0209099i
$45$	2.78171	−	6.10427i	0.414672	−	0.909971i
$46$			8.02448i			1.18315i
$47$	3.07638			0.448736			0.224368	−	0.974505i	$-0.427968\pi$
$47$	3.07638			0.448736			0.224368	+	0.974505i	$0.427968\pi$
$48$	−6.86663	−	3.55443i	−0.991113	−	0.513038i
$49$	−2.46410			−0.352015
$50$	6.55196	+	3.71087i	0.926587	+	0.524796i
$51$	−3.27598	+	6.32871i	−0.458729	+	0.886197i
$52$	−0.570669			−0.0791375
$53$	4.50413			0.618690			0.309345	−	0.950950i	$-0.399890\pi$
$53$	4.50413			0.618690			0.309345	+	0.950950i	$0.399890\pi$
$54$	7.75105	−	1.07508i	1.05478	−	0.146299i
$55$	−4.68886	−	5.74583i	−0.632246	−	0.774768i
$56$			5.55532i			0.742361i
$57$	−3.68886	+	7.12633i	−0.488602	+	0.943906i
$58$			13.4787i			1.76984i
$59$		−	4.89898i		−	0.637793i	−0.947790	−	0.318896i	$-0.896688\pi$
$59$		−	4.89898i		−	0.637793i	0.947790	−	0.318896i	$-0.103312\pi$
$60$	0.0519451	+	1.03646i	0.00670609	+	0.133807i
$61$		−	3.39154i		−	0.434243i	−0.976145	−	0.217121i	$-0.930333\pi$
$61$		−	3.39154i		−	0.434243i	0.976145	−	0.217121i	$-0.0696668\pi$
$62$		−	5.21684i		−	0.662539i
$63$	−3.68886	−	5.21684i	−0.464753	−	0.657260i
$64$	−6.66025			−0.832532
$65$	−2.39818	−	4.11439i	−0.297458	−	0.510327i
$66$	2.72911	−	8.20940i	0.335930	−	1.01051i
$67$		−	12.3129i		−	1.50426i	−0.659014	−	0.752131i	$-0.729026\pi$
$67$		−	12.3129i		−	1.50426i	0.659014	−	0.752131i	$-0.270974\pi$
$68$		−	1.10245i		−	0.133691i
$69$	−8.19615	−	4.24264i	−0.986701	−	0.510754i
$70$	6.19615	−	3.61160i	0.740582	−	0.431668i
$71$			13.3843i			1.58842i	0.607644	+	0.794210i	$0.292115\pi$
$71$			13.3843i			1.58842i	−0.607644	+	0.794210i	$0.707885\pi$
$72$	6.38929	−	4.51791i	0.752986	−	0.532441i
$73$	−2.12976			−0.249270			−0.124635	−	0.992203i	$-0.539776\pi$
$73$	−2.12976			−0.249270			−0.124635	+	0.992203i	$0.539776\pi$
$74$	−1.75559			−0.204084
$75$	−7.25436	+	4.73015i	−0.837661	+	0.546191i
$76$		−	1.24139i		−	0.142397i
$77$	−6.97707	+	1.10245i	−0.795111	+	0.125636i
$78$	2.55378	−	4.93353i	0.289159	−	0.558613i
$79$		−	13.8988i		−	1.56374i	−0.623443	−	0.781869i	$-0.714266\pi$
$79$		−	13.8988i		−	1.56374i	0.623443	−	0.781869i	$-0.285734\pi$
$80$	5.02672	+	8.62398i	0.562005	+	0.964191i
$81$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$82$			3.61160i			0.398834i
$83$		−	9.33123i		−	1.02424i	−0.858915	−	0.512118i	$-0.828861\pi$
$83$		−	9.33123i		−	1.02424i	0.858915	−	0.512118i	$-0.171139\pi$
$84$	0.877796	+	0.454381i	0.0957754	+	0.0495770i
$85$	7.94839	−	4.63294i	0.862124	−	0.502513i
$86$		−	14.3180i		−	1.54395i
$87$	−13.7670	−	7.12633i	−1.47598	−	0.764023i
$88$	−1.35022	−	8.54513i	−0.143934	−	0.910914i
$89$		−	4.62158i		−	0.489886i	−0.969537	−	0.244943i	$-0.921231\pi$
$89$		−	4.62158i		−	0.489886i	0.969537	−	0.244943i	$-0.0787693\pi$
$90$	−9.19286	−	4.18917i	−0.969012	−	0.441577i
$91$	−4.53590			−0.475491
$92$	1.42775			0.148853
$93$	5.32844	+	2.75821i	0.552534	+	0.286013i
$94$		−	4.63294i		−	0.477851i
$95$	8.95015	−	5.21684i	0.918266	−	0.535236i
$96$	−1.19909	+	2.31647i	−0.122382	+	0.236424i
$97$			1.16575i			0.118364i	0.998247	+	0.0591822i	$0.0188493\pi$
$97$			1.16575i			0.118364i	−0.998247	+	0.0591822i	$0.981151\pi$
$98$			3.71087i			0.374854i
$99$	6.94211	+	7.12791i	0.697709	+	0.716382i
$100$	0.660254	−	1.16575i	0.0660254	−	0.116575i
$101$	8.95015			0.890573			0.445286	−	0.895388i	$-0.353102\pi$
$101$	8.95015			0.890573			0.445286	+	0.895388i	$0.353102\pi$
$102$	9.53085	+	4.93353i	0.943695	+	0.488493i
$103$			5.94311i			0.585592i	0.956175	+	0.292796i	$0.0945856\pi$
$103$			5.94311i			0.585592i	−0.956175	+	0.292796i	$0.905414\pi$
$104$		−	5.55532i		−	0.544744i
$105$	0.412880	+	8.23820i	0.0402930	+	0.803966i
$106$		−	6.78309i		−	0.658832i
$107$			1.10245i			0.106578i	0.998579	+	0.0532888i	$0.0169704\pi$
$107$			1.10245i			0.106578i	−0.998579	+	0.0532888i	$0.983030\pi$
$108$	−0.191282	−	1.37910i	−0.0184062	−	0.132704i
$109$			12.6574i			1.21236i	0.795327	+	0.606180i	$0.207299\pi$
$109$			12.6574i			1.21236i	−0.795327	+	0.606180i	$0.792701\pi$
$110$	−8.65306	+	7.06129i	−0.825037	+	0.673268i
$111$	0.928203	−	1.79315i	0.0881012	−	0.170198i
$112$	9.50749			0.898373
$113$	−10.6569			−1.00252			−0.501258	−	0.865298i	$-0.667129\pi$
$113$	−10.6569			−1.00252			−0.501258	+	0.865298i	$0.667129\pi$
$114$	10.7321	+	5.55532i	1.00515	+	0.520303i
$115$	6.00000	+	10.2938i	0.559503	+	0.959898i
$116$	2.39818			0.222666
$117$	3.68886	+	5.21684i	0.341035	+	0.482297i
$118$	−7.37772			−0.679174
$119$		−	8.76268i		−	0.803274i
$120$	−10.0897	+	0.505673i	−0.921059	+	0.0461614i
$121$	10.4641	−	3.39154i	0.951282	−	0.308322i
$122$	−5.10757			−0.462418
$123$	−3.68886	−	1.90949i	−0.332613	−	0.172173i
$124$	−0.928203			−0.0833551
$125$	11.1795	−	0.138701i	0.999923	−	0.0124058i
$126$	−7.85641	+	5.55532i	−0.699904	+	0.494907i
$127$	−10.6488			−0.944930			−0.472465	−	0.881349i	$-0.656636\pi$
$127$	−10.6488			−0.944930			−0.472465	+	0.881349i	$0.656636\pi$
$128$			13.0421i			1.15277i
$129$	14.6243	+	7.57010i	1.28760	+	0.666510i
$130$	−6.19615	+	3.61160i	−0.543439	+	0.316758i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−1.46065	−	0.485576i	−0.127134	−	0.0422639i
$133$		−	9.86707i		−	0.855583i
$134$	−18.5429			−1.60186
$135$	9.13916	−	7.17466i	0.786574	−	0.617496i
$136$	10.7321			0.920266
$137$	−2.25207			−0.192407			−0.0962034	−	0.995362i	$-0.530670\pi$
$137$	−2.25207			−0.192407			−0.0962034	+	0.995362i	$0.530670\pi$
$138$	−6.38929	+	12.3432i	−0.543893	+	1.05072i
$139$		−	17.2904i		−	1.46655i	−0.679933	−	0.733274i	$-0.737991\pi$
$139$		−	17.2904i		−	1.46655i	0.679933	−	0.733274i	$-0.262009\pi$
$140$	−0.642592	−	1.10245i	−0.0543089	−	0.0931738i
$141$	4.73205	+	2.44949i	0.398511	+	0.206284i
$142$	20.1563			1.69148
$143$	6.97707	−	1.10245i	0.583452	−	0.0921913i
$144$	−7.73205	−	10.9348i	−0.644338	−	0.911231i
$145$	10.0782	+	17.2904i	0.836945	+	1.43589i
$146$			3.20736i			0.265443i
$147$	−3.79025	−	1.96198i	−0.312615	−	0.161821i
$148$			0.312363i			0.0256761i
$149$	−15.5021			−1.26998			−0.634991	−	0.772519i	$-0.718996\pi$
$149$	−15.5021			−1.26998			−0.634991	+	0.772519i	$0.718996\pi$
$150$	7.12347	+	10.9249i	0.581629	+	0.892010i
$151$		−	10.5073i		−	0.855069i	−0.903999	−	0.427535i	$-0.859382\pi$
$151$		−	10.5073i		−	0.855069i	0.903999	−	0.427535i	$-0.140618\pi$
$152$	12.0846			0.980194
$153$	−10.0782	+	7.12633i	−0.814771	+	0.576130i
$154$	1.66025	+	10.5073i	0.133787	+	0.846700i
$155$	−3.90069	−	6.69213i	−0.313311	−	0.537525i
$156$	−0.877796	−	0.454381i	−0.0702800	−	0.0363796i
$157$			8.70131i			0.694440i	0.937784	+	0.347220i	$0.112874\pi$
$157$			8.70131i			0.694440i	−0.937784	+	0.347220i	$0.887126\pi$
$158$	−20.9312			−1.66520
$159$	6.92820	+	3.58630i	0.549442	+	0.284412i
$160$	2.90931	−	1.69577i	0.230001	−	0.134063i
$161$	11.3483			0.894374
$162$	12.7786	+	4.51791i	1.00398	+	0.354961i
$163$		−	5.94311i		−	0.465500i	−0.972537	−	0.232750i	$-0.925228\pi$
$163$		−	5.94311i		−	0.465500i	0.972537	−	0.232750i	$-0.0747724\pi$
$164$	0.642592			0.0501780
$165$	−2.63738	−	12.5716i	−0.205320	−	0.978695i
$166$	−14.0526			−1.09069
$167$		−	13.1502i		−	1.01759i	−0.860886	−	0.508797i	$-0.830090\pi$
$167$		−	13.1502i		−	1.01759i	0.860886	−	0.508797i	$-0.169910\pi$
$168$	−4.42328	+	8.54513i	−0.341264	+	0.659271i
$169$	−8.46410			−0.651085
$170$	−6.97707	−	11.9700i	−0.535117	−	0.918061i
$171$	−11.3483	+	8.02448i	−0.867829	+	0.613647i
$172$	−2.54752			−0.194247
$173$			14.5481i			1.10607i	0.833158	+	0.553034i	$0.186530\pi$
$173$			14.5481i			1.10607i	−0.833158	+	0.553034i	$0.813470\pi$
$174$	−10.7321	+	20.7327i	−0.813595	+	1.57174i
$175$	5.24796	−	9.26587i	0.396708	−	0.700434i
$176$	−14.6243	+	2.31079i	−1.10235	+	0.174182i
$177$	3.90069	−	7.53556i	0.293194	−	0.566407i
$178$	−6.95996			−0.521671
$179$			19.3185i			1.44393i	0.691928	+	0.721967i	$0.256762\pi$
$179$			19.3185i			1.44393i	−0.691928	+	0.721967i	$0.743238\pi$
$180$	−0.745356	+	1.63563i	−0.0555555	+	0.121913i
$181$	−9.46410			−0.703461			−0.351731	−	0.936101i	$-0.614407\pi$
$181$	−9.46410			−0.703461			−0.351731	+	0.936101i	$0.614407\pi$
$182$			6.83093i			0.506342i
$183$	2.70043	−	5.21684i	0.199622	−	0.385640i
$184$			13.8988i			1.02463i
$185$	−2.25207	+	1.31268i	−0.165575	+	0.0965100i
$186$	4.15378	−	8.02448i	0.304570	−	0.588384i
$187$	2.12976	+	13.4787i	0.155744	+	0.985657i
$188$	−0.824313			−0.0601192
$189$	−1.52039	−	10.9616i	−0.110592	−	0.797342i
$190$	−7.85641	−	13.4787i	−0.569964	−	0.977845i
$191$		−	9.52056i		−	0.688883i	−0.938808	−	0.344442i	$-0.888068\pi$
$191$		−	9.52056i		−	0.688883i	0.938808	−	0.344442i	$-0.111932\pi$
$192$	−10.2447	−	5.30306i	−0.739350	−	0.382716i
$193$	−10.6488			−0.766519			−0.383260	−	0.923641i	$-0.625199\pi$
$193$	−10.6488			−0.766519			−0.383260	+	0.923641i	$0.625199\pi$
$194$	1.75559			0.126044
$195$	−0.412880	−	8.23820i	−0.0295670	−	0.589950i
$196$	0.660254			0.0471610
$197$			7.93338i			0.565230i	0.959233	+	0.282615i	$0.0912019\pi$
$197$			7.93338i			0.565230i	−0.959233	+	0.282615i	$0.908798\pi$
$198$	10.7344	−	10.4546i	0.762862	−	0.742978i
$199$	10.9282			0.774680			0.387340	−	0.921937i	$-0.373394\pi$
$199$	10.9282			0.774680			0.387340	+	0.921937i	$0.373394\pi$
$200$	11.3483	+	6.42741i	0.802448	+	0.454486i
$201$	9.80385	−	18.9396i	0.691510	−	1.33589i
$202$		−	13.4787i		−	0.948355i
$203$	19.0617			1.33787
$204$	0.877796	−	1.69577i	0.0614580	−	0.118728i
$205$	2.70043	+	4.63294i	0.188606	+	0.323578i
$206$	8.95015			0.623586
$207$	−9.22913	−	13.0520i	−0.641469	−	0.907174i
$208$	−9.50749			−0.659226
$209$	2.39818	+	15.1774i	0.165886	+	1.04984i
$210$	12.4065	−	0.621785i	0.856130	−	0.0429073i
$211$			1.24139i			0.0854609i	0.999087	+	0.0427305i	$0.0136057\pi$
$211$			1.24139i			0.0854609i	−0.999087	+	0.0427305i	$0.986394\pi$
$212$	−1.20688			−0.0828887
$213$	−10.6569	+	20.5875i	−0.730198	+	1.41063i
$214$	1.66025			0.113493
$215$	−10.7057	−	18.3671i	−0.730125	−	1.25262i
$216$	13.4252	−	1.86209i	0.913470	−	0.126699i
$217$	−7.37772			−0.500832
$218$	19.0617			1.29102
$219$	−3.27598	−	1.69577i	−0.221370	−	0.114590i
$220$	1.25638	+	1.53959i	0.0847049	+	0.103799i
$221$			8.76268i			0.589442i
$222$	−2.70043	−	1.39785i	−0.181241	−	0.0938174i
$223$		−	12.6253i		−	0.845451i	−0.906258	−	0.422725i	$-0.861074\pi$
$223$		−	12.6253i		−	0.845451i	0.906258	−	0.422725i	$-0.138926\pi$
$224$		−	3.20736i		−	0.214301i
$225$	−14.9248	+	1.49976i	−0.994989	+	0.0999843i
$226$			16.0490i			1.06756i
$227$			9.33123i			0.619335i	0.950845	+	0.309668i	$0.100218\pi$
$227$			9.33123i			0.619335i	−0.950845	+	0.309668i	$0.899782\pi$
$228$	0.988427	−	1.90949i	0.0654602	−	0.126459i
$229$	21.3205			1.40890			0.704449	−	0.709754i	$-0.251194\pi$
$229$	21.3205			1.40890			0.704449	+	0.709754i	$0.251194\pi$
$230$	15.5021	−	9.03583i	1.02218	−	0.595805i
$231$	−11.6098	−	3.85955i	−0.763872	−	0.253939i
$232$			23.3457i			1.53272i
$233$			10.1383i			0.664180i	0.943248	+	0.332090i	$0.107754\pi$
$233$			10.1383i			0.664180i	−0.943248	+	0.332090i	$0.892246\pi$
$234$	7.85641	−	5.55532i	0.513589	−	0.363163i
$235$	−3.46410	−	5.94311i	−0.225973	−	0.387685i
$236$			1.31268i			0.0854480i
$237$	11.0666	−	21.3790i	0.718852	−	1.38872i
$238$	−13.1963			−0.855392
$239$	16.1447			1.04431			0.522157	−	0.852849i	$-0.325128\pi$
$239$	16.1447			1.04431			0.522157	+	0.852849i	$0.325128\pi$
$240$	0.865419	+	17.2677i	0.0558625	+	1.11463i
$241$			12.6574i			0.815336i	0.913130	+	0.407668i	$0.133658\pi$
$241$			12.6574i			0.815336i	−0.913130	+	0.407668i	$0.866342\pi$
$242$	−5.10757	−	15.7586i	−0.328327	−	1.01300i
$243$	−11.3708	+	10.6633i	−0.729435	+	0.684050i
$244$			0.908762i			0.0581775i
$245$	2.77466	+	4.76028i	0.177266	+	0.304123i
$246$	−2.87564	+	5.55532i	−0.183344	+	0.354194i
$247$			9.86707i			0.627826i
$248$		−	9.03583i		−	0.573776i
$249$	7.42976	−	14.3532i	0.470842	−	0.909597i
$250$	−0.208879	−	16.8360i	−0.0132107	−	1.06480i
$251$		−	16.9706i		−	1.07117i	−0.844481	−	0.535586i	$-0.820091\pi$
$251$		−	16.9706i		−	1.07117i	0.844481	−	0.535586i	$-0.179909\pi$
$252$	0.988427	+	1.39785i	0.0622651	+	0.0880561i
$253$	−17.4559	+	2.75821i	−1.09744	+	0.173407i
$254$			16.0368i			1.00624i
$255$	15.9150	−	0.797623i	0.996635	−	0.0499491i
$256$	6.32051			0.395032
$257$	29.7186			1.85379			0.926897	−	0.375315i	$-0.122465\pi$
$257$	29.7186			1.85379			0.926897	+	0.375315i	$0.122465\pi$
$258$	11.4004	−	22.0238i	0.709755	−	1.37114i
$259$			2.48278i			0.154273i
$260$	0.642592	+	1.10245i	0.0398518	+	0.0683709i
$261$	−15.5021	−	21.9233i	−0.959556	−	1.35702i
$262$		0			0
$263$		−	15.3551i		−	0.946837i	−0.880838	−	0.473418i	$-0.843020\pi$
$263$		−	15.3551i		−	0.946837i	0.880838	−	0.473418i	$-0.156980\pi$
$264$	4.72696	−	14.2191i	0.290924	−	0.875125i
$265$	−5.07180	−	8.70131i	−0.311558	−	0.534517i
$266$	−14.8595			−0.911095
$267$	3.67982	−	7.10886i	0.225201	−	0.435055i
$268$			3.29923i			0.201533i
$269$		−	8.48528i		−	0.517357i	−0.965964	−	0.258678i	$-0.916713\pi$
$269$		−	8.48528i		−	0.517357i	0.965964	−	0.258678i	$-0.0832870\pi$
$270$	−10.8048	−	13.7633i	−0.657561	−	0.837609i
$271$			24.0734i			1.46236i	0.682186	+	0.731179i	$0.261029\pi$
$271$			24.0734i			1.46236i	−0.682186	+	0.731179i	$0.738971\pi$
$272$		−	18.3671i		−	1.11367i
$273$	−6.97707	−	3.61160i	−0.422271	−	0.218584i
$274$			3.39154i			0.204891i
$275$	−5.82028	+	15.5282i	−0.350976	+	0.936384i
$276$	2.19615	+	1.13681i	0.132193	+	0.0684280i
$277$	−16.8852			−1.01453			−0.507267	−	0.861789i	$-0.669344\pi$
$277$	−16.8852			−1.01453			−0.507267	+	0.861789i	$0.669344\pi$
$278$	−26.0388			−1.56170
$279$	6.00000	+	8.48528i	0.359211	+	0.508001i
$280$	10.7321	−	6.25547i	0.641363	−	0.373836i
$281$	5.90937			0.352523			0.176262	−	0.984343i	$-0.443599\pi$
$281$	5.90937			0.352523			0.176262	+	0.984343i	$0.443599\pi$
$282$	3.68886	−	7.12633i	0.219668	−	0.424367i
$283$	25.4043			1.51013			0.755063	−	0.655652i	$-0.227606\pi$
$283$	25.4043			1.51013			0.755063	+	0.655652i	$0.227606\pi$
$284$		−	3.58630i		−	0.212808i
$285$	17.9208	−	0.898149i	1.06154	−	0.0532018i
$286$	−1.66025	−	10.5073i	−0.0981729	−	0.621308i
$287$	5.10757			0.301490
$288$	−3.68886	+	2.60842i	−0.217368	+	0.153703i
$289$	0.0717968			0.00422334
$290$	26.0388	−	15.1774i	1.52905	−	0.891248i
$291$	−0.928203	+	1.79315i	−0.0544122	+	0.105116i
$292$	0.570669			0.0333959
$293$		−	4.11439i		−	0.240365i	−0.992752	−	0.120183i	$-0.961652\pi$
$293$		−	4.11439i		−	0.240365i	0.992752	−	0.120183i	$-0.0383480\pi$
$294$	−2.95469	+	5.70801i	−0.172321	+	0.332898i
$295$	−9.46410	+	5.51641i	−0.551021	+	0.321178i
$296$	−3.04078			−0.176742
$297$	5.00287	+	16.4916i	0.290296	+	0.956937i
$298$			23.3457i			1.35238i
$299$	−11.3483			−0.656291
$300$	1.94380	−	1.26744i	0.112225	−	0.0731757i
$301$	−20.2487			−1.16712
$302$	−15.8236			−0.910548
$303$	13.7670	+	7.12633i	0.790894	+	0.409397i
$304$		−	20.6819i		−	1.18619i
$305$	−6.55196	+	3.81899i	−0.375164	+	0.218675i
$306$	10.7321	+	15.1774i	0.613511	+	0.867635i
$307$	−9.50749			−0.542621			−0.271310	−	0.962492i	$-0.587457\pi$
$307$	−9.50749			−0.542621			−0.271310	+	0.962492i	$0.587457\pi$
$308$	1.86950	−	0.295400i	0.106525	−	0.0168320i
$309$	−4.73205	+	9.14162i	−0.269197	+	0.520049i
$310$	−10.0782	+	5.87433i	−0.572401	+	0.333639i
$311$			14.6969i			0.833387i	0.909047	+	0.416693i	$0.136811\pi$
$311$			14.6969i			0.833387i	−0.909047	+	0.416693i	$0.863189\pi$
$312$	4.42328	−	8.54513i	0.250419	−	0.483773i
$313$		−	30.4546i		−	1.72140i	−0.509117	−	0.860698i	$-0.670028\pi$
$313$		−	30.4546i		−	1.72140i	0.509117	−	0.860698i	$-0.329972\pi$
$314$	13.1039			0.739497
$315$	−5.92438	+	13.0007i	−0.333801	+	0.732504i
$316$			3.72417i			0.209501i
$317$	−22.9624			−1.28970			−0.644848	−	0.764311i	$-0.723079\pi$
$317$	−22.9624			−1.28970			−0.644848	+	0.764311i	$0.723079\pi$
$318$	5.40087	−	10.4337i	0.302866	−	0.585091i
$319$	−29.3205	+	4.63294i	−1.64163	+	0.259395i
$320$	7.49966	+	12.8666i	0.419244	+	0.719266i
$321$	−0.877796	+	1.69577i	−0.0489938	+	0.0946488i
$322$		−	17.0903i		−	0.952403i
$323$	−19.0617			−1.06062
$324$	0.803848	−	2.27362i	0.0446582	−	0.126312i
$325$	−5.24796	+	9.26587i	−0.291104	+	0.513978i
$326$	−8.95015			−0.495703
$327$	−10.0782	+	19.4695i	−0.557323	+	1.07667i
$328$			6.25547i			0.345400i
$329$	−6.55196			−0.361221
$330$	−18.9324	+	3.97182i	−1.04220	+	0.218641i
$331$	8.53590			0.469175			0.234588	−	0.972095i	$-0.424626\pi$
$331$	8.53590			0.469175			0.234588	+	0.972095i	$0.424626\pi$
$332$			2.50029i			0.137222i
$333$	2.85550	−	2.01915i	0.156481	−	0.110649i
$334$	−19.8038			−1.08362
$335$	−23.7867	+	13.8647i	−1.29961	+	0.757511i
$336$	14.6243	+	7.57010i	0.797822	+	0.412983i
$337$	16.8852			0.919796			0.459898	−	0.887972i	$-0.347886\pi$
$337$	16.8852			0.919796			0.459898	+	0.887972i	$0.347886\pi$
$338$			12.7467i			0.693329i
$339$	−16.3923	−	8.48528i	−0.890308	−	0.460857i
$340$	−2.12976	+	1.24139i	−0.115503	+	0.0673239i
$341$	11.3483	−	1.79315i	0.614547	−	0.0971046i
$342$	12.0846	+	17.0903i	0.653462	+	0.924135i
$343$	20.1563			1.08834
$344$		−	24.7995i		−	1.33710i
$345$	1.03298	+	20.6111i	0.0556139	+	1.10966i
$346$	21.9090			1.17783
$347$			27.4029i			1.47106i	0.677490	+	0.735532i	$0.263068\pi$
$347$			27.4029i			1.47106i	−0.677490	+	0.735532i	$0.736932\pi$
$348$	3.68886	+	1.90949i	0.197744	+	0.102360i
$349$			25.3148i			1.35507i	0.735490	+	0.677536i	$0.236952\pi$
$349$			25.3148i			1.35507i	−0.735490	+	0.677536i	$0.763048\pi$
$350$	−13.9541	−	7.90327i	−0.745880	−	0.422448i
$351$	1.52039	+	10.9616i	0.0811523	+	0.585089i
$352$	0.779548	+	4.93353i	0.0415501	+	0.262958i
$353$	−1.64863			−0.0877475			−0.0438738	−	0.999037i	$-0.513970\pi$
$353$	−1.64863			−0.0877475			−0.0438738	+	0.999037i	$0.513970\pi$
$354$	−11.3483	−	5.87433i	−0.603157	−	0.312217i
$355$	25.8564	−	15.0711i	1.37232	−	0.799892i
$356$			1.23835i			0.0656323i
$357$	6.97707	−	13.4787i	0.369266	−	0.713366i
$358$	29.0931			1.53762
$359$	1.75559			0.0926566			0.0463283	−	0.998926i	$-0.485248\pi$
$359$	1.75559			0.0926566			0.0463283	+	0.998926i	$0.485248\pi$
$360$	−15.9225	−	7.25585i	−0.839189	−	0.382417i
$361$	−2.46410			−0.129690
$362$			14.2527i			0.749103i
$363$	18.7962	+	3.11494i	0.986545	+	0.163492i
$364$	1.21539			0.0637038
$365$	2.39818	+	4.11439i	0.125527	+	0.215357i
$366$	−7.85641	−	4.06678i	−0.410661	−	0.212574i
$367$			14.9568i			0.780738i	0.920659	+	0.390369i	$0.127652\pi$
$367$			14.9568i			0.780738i	−0.920659	+	0.390369i	$0.872348\pi$
$368$	23.7867			1.23997
$369$	−4.15378	−	5.87433i	−0.216237	−	0.305805i
$370$	1.97685	+	3.39154i	0.102772	+	0.176318i
$371$	−9.59274			−0.498030
$372$	−1.42775	−	0.739059i	−0.0740255	−	0.0383184i
$373$	−9.50749			−0.492279			−0.246140	−	0.969234i	$-0.579162\pi$
$373$	−9.50749			−0.492279			−0.246140	+	0.969234i	$0.579162\pi$
$374$	20.2985	−	3.20736i	1.04961	−	0.165849i
$375$	17.3066	+	8.68804i	0.893708	+	0.448648i
$376$		−	8.02448i		−	0.413831i
$377$	−19.0617			−0.981728
$378$	−16.5079	+	2.28966i	−0.849076	+	0.117767i
$379$	−2.92820			−0.150412			−0.0752058	−	0.997168i	$-0.523961\pi$
$379$	−2.92820			−0.150412			−0.0752058	+	0.997168i	$0.523961\pi$
$380$	−2.39818	+	1.39785i	−0.123024	+	0.0717081i
$381$	−16.3799	−	8.47886i	−0.839168	−	0.434385i
$382$	−14.3377			−0.733580
$383$	20.9312			1.06953			0.534767	−	0.844999i	$-0.320399\pi$
$383$	20.9312			1.06953			0.534767	+	0.844999i	$0.320399\pi$
$384$	−10.3844	+	20.0612i	−0.529929	+	1.02374i
$385$	9.98617	+	12.2373i	0.508942	+	0.623669i
$386$			16.0368i			0.816253i
$387$	16.4675	+	23.2885i	0.837088	+	1.18382i
$388$		−	0.312363i		−	0.0158578i
$389$		−	20.9086i		−	1.06011i	−0.847964	−	0.530054i	$-0.822172\pi$
$389$		−	20.9086i		−	1.06011i	0.847964	−	0.530054i	$-0.177828\pi$
$390$	−12.4065	+	0.621785i	−0.628227	+	0.0314853i
$391$		−	21.9233i		−	1.10871i
$392$			6.42741i			0.324633i
$393$		0			0
$394$	11.9474			0.601903
$395$	−26.8504	+	15.6505i	−1.35099	+	0.787463i
$396$	−1.86013	−	1.90992i	−0.0934752	−	0.0959769i
$397$			5.20405i			0.261184i	0.991436	+	0.130592i	$0.0416877\pi$
$397$			5.20405i			0.261184i	−0.991436	+	0.130592i	$0.958312\pi$
$398$		−	16.4576i		−	0.824943i
$399$	7.85641	−	15.1774i	0.393312	−	0.759821i
$400$	11.0000	−	19.4218i	0.550000	−	0.971088i
$401$		−	25.7332i		−	1.28506i	−0.766262	−	0.642528i	$-0.777885\pi$
$401$		−	25.7332i		−	1.28506i	0.766262	−	0.642528i	$-0.222115\pi$
$402$	−28.5225	−	14.7643i	−1.42257	−	0.736377i
$403$	7.37772			0.367511
$404$	−2.39818			−0.119314
$405$	19.7704	−	3.75915i	0.982399	−	0.186794i
$406$		−	28.7064i		−	1.42467i
$407$	−0.603439	−	3.81899i	−0.0299114	−	0.189300i
$408$	16.5079	+	8.54513i	0.817264	+	0.423047i
$409$		−	19.4405i		−	0.961271i	−0.876920	−	0.480636i	$-0.840406\pi$
$409$		−	19.4405i		−	0.961271i	0.876920	−	0.480636i	$-0.159594\pi$
$410$	6.97707	−	4.06678i	0.344573	−	0.200844i
$411$	−3.46410	−	1.79315i	−0.170872	−	0.0884496i
$412$		−	1.59245i		−	0.0784544i
$413$			10.4337i			0.513408i
$414$	−19.6559	+	13.8988i	−0.966034	+	0.683089i
$415$	−18.0265	+	10.5073i	−0.884888	+	0.515781i
$416$			3.20736i			0.157254i
$417$	13.7670	−	26.5958i	0.674174	−	1.30240i
$418$	22.8567	−	3.61160i	1.11796	−	0.176649i
$419$		−	1.23835i		−	0.0604973i	−0.999542	−	0.0302486i	$-0.990370\pi$
$419$		−	1.23835i		−	0.0604973i	0.999542	−	0.0302486i	$-0.00962991\pi$
$420$	−0.110631	−	2.20742i	−0.00539823	−	0.107711i
$421$	8.78461			0.428136			0.214068	−	0.976819i	$-0.431329\pi$
$421$	8.78461			0.428136			0.214068	+	0.976819i	$0.431329\pi$
$422$	1.86950			0.0910058
$423$	5.32844	+	7.53556i	0.259078	+	0.366391i
$424$		−	11.7487i		−	0.570565i
$425$	−17.9003	−	10.1383i	−0.868292	−	0.491779i
$426$	31.0042	+	16.0490i	1.50216	+	0.777575i
$427$			7.22319i			0.349555i
$428$		−	0.295400i		−	0.0142787i
$429$	11.6098	+	3.85955i	0.560529	+	0.186341i
$430$	−27.6603	+	16.1225i	−1.33390	+	0.777498i
$431$	19.6559			0.946791			0.473395	−	0.880850i	$-0.343028\pi$
$431$	19.6559			0.946791			0.473395	+	0.880850i	$0.343028\pi$
$432$	−3.18682	−	22.9762i	−0.153326	−	1.10544i
$433$			37.6778i			1.81068i	0.424689	+	0.905339i	$0.360383\pi$
$433$			37.6778i			1.81068i	−0.424689	+	0.905339i	$0.639617\pi$
$434$			11.1106i			0.533328i
$435$	1.73509	+	34.6203i	0.0831913	+	1.65992i
$436$		−	3.39154i		−	0.162426i
$437$		−	24.6863i		−	1.18091i
$438$	−2.55378	+	4.93353i	−0.122025	+	0.235733i
$439$		−	8.02448i		−	0.382988i	−0.981494	−	0.191494i	$-0.938667\pi$
$439$		−	8.02448i		−	0.382988i	0.981494	−	0.191494i	$-0.0613332\pi$
$440$	−14.9875	+	12.2305i	−0.714503	+	0.583067i
$441$	−4.26795	−	6.03579i	−0.203236	−	0.287419i
$442$	13.1963			0.627686
$443$	−34.4436			−1.63646			−0.818232	−	0.574888i	$-0.805046\pi$
$443$	−34.4436			−1.63646			−0.818232	+	0.574888i	$0.805046\pi$
$444$	−0.248711	+	0.480473i	−0.0118033	+	0.0228023i
$445$	−8.92820	+	5.20405i	−0.423237	+	0.246695i
$446$	−19.0133			−0.900306
$447$	−23.8452	−	12.3432i	−1.12784	−	0.583812i
$448$	14.1848			0.670168
$449$		−	15.7322i		−	0.742449i	−0.928543	−	0.371225i	$-0.878938\pi$
$449$		−	15.7322i		−	0.742449i	0.928543	−	0.371225i	$-0.121062\pi$
$450$	2.25860	+	22.4764i	0.106472	+	1.05955i
$451$	−7.85641	+	1.24139i	−0.369944	+	0.0584548i
$452$	2.85550			0.134312
$453$	8.36615	−	16.1622i	0.393076	−	0.759364i
$454$	14.0526			0.659519
$455$	5.10757	+	8.76268i	0.239447	+	0.410801i
$456$	18.5885	+	9.62209i	0.870484	+	0.450596i
$457$	3.27110			0.153016			0.0765079	−	0.997069i	$-0.475623\pi$
$457$	3.27110			0.153016			0.0765079	+	0.997069i	$0.475623\pi$
$458$		−	32.1081i		−	1.50031i
$459$	−21.1763	+	2.93716i	−0.988424	+	0.137095i
$460$	−1.60770	−	2.75821i	−0.0749592	−	0.128602i
$461$	18.5429			0.863628			0.431814	−	0.901963i	$-0.357874\pi$
$461$	18.5429			0.863628			0.431814	+	0.901963i	$0.357874\pi$
$462$	−5.81236	+	17.4841i	−0.270416	+	0.813434i
$463$			7.10886i			0.330377i	0.986262	+	0.165188i	$0.0528232\pi$
$463$			7.10886i			0.330377i	−0.986262	+	0.165188i	$0.947177\pi$
$464$	39.9544			1.85483
$465$	−0.671557	−	13.3996i	−0.0311427	−	0.621391i
$466$	15.2679			0.707274
$467$	4.12157			0.190723			0.0953616	−	0.995443i	$-0.469599\pi$
$467$	4.12157			0.190723			0.0953616	+	0.995443i	$0.469599\pi$
$468$	−0.988427	−	1.39785i	−0.0456901	−	0.0646155i
$469$			26.2236i			1.21089i
$470$	−8.95015	+	5.21684i	−0.412839	+	0.240635i
$471$	−6.92820	+	13.3843i	−0.319235	+	0.616714i
$472$	−12.7786			−0.588182
$473$	31.1463	−	4.92144i	1.43211	−	0.226288i
$474$	−32.1962	−	16.6660i	−1.47882	−	0.765493i
$475$	−20.1563	−	11.4160i	−0.924835	−	0.523803i
$476$			2.34795i			0.107618i
$477$	7.80138	+	11.0328i	0.357201	+	0.505158i
$478$		−	24.3135i		−	1.11207i
$479$	24.4523			1.11725			0.558626	−	0.829420i	$-0.311329\pi$
$479$	24.4523			1.11725			0.558626	+	0.829420i	$0.311329\pi$
$480$	5.82529	−	0.291950i	0.265887	−	0.0133256i
$481$		−	2.48278i		−	0.113205i
$482$	19.0617			0.868237
$483$	17.4559	+	9.03583i	0.794270	+	0.411144i
$484$	−2.80385	+	0.908762i	−0.127448	+	0.0413074i
$485$	2.25207	−	1.31268i	0.102261	−	0.0596056i
$486$	16.0586	+	17.1240i	0.728433	+	0.776762i
$487$		−	32.0470i		−	1.45219i	−0.687594	−	0.726095i	$-0.741333\pi$
$487$		−	32.0470i		−	1.45219i	0.687594	−	0.726095i	$-0.258667\pi$
$488$	−8.84657			−0.400465
$489$	4.73205	−	9.14162i	0.213991	−	0.413398i
$490$	7.16884	−	4.17856i	0.323855	−	0.188768i
$491$	−19.6559			−0.887058			−0.443529	−	0.896260i	$-0.646274\pi$
$491$	−19.6559			−0.887058			−0.443529	+	0.896260i	$0.646274\pi$
$492$	0.988427	+	0.511648i	0.0445617	+	0.0230669i
$493$		−	36.8244i		−	1.65849i
$494$	14.8595			0.668561
$495$	5.95301	−	21.4374i	0.267568	−	0.963539i
$496$	−15.4641			−0.694359
$497$		−	28.5053i		−	1.27864i
$498$	−21.6155	−	11.1890i	−0.968613	−	0.501391i
$499$	2.92820			0.131084			0.0655422	−	0.997850i	$-0.479122\pi$
$499$	2.92820			0.131084			0.0655422	+	0.997850i	$0.479122\pi$
$500$	−2.99553	+	0.0371647i	−0.133964	+	0.00166206i
$501$	10.4705	−	20.2275i	0.467789	−	0.903699i
$502$	−25.5572			−1.14067
$503$		−	25.7888i		−	1.14987i	−0.818201	−	0.574933i	$-0.805028\pi$
$503$		−	25.7888i		−	1.14987i	0.818201	−	0.574933i	$-0.194972\pi$
$504$	−13.6077	+	9.62209i	−0.606135	+	0.428602i
$505$	−10.0782	−	17.2904i	−0.448472	−	0.769411i
$506$	4.15378	+	26.2880i	0.184658	+	1.16865i
$507$	−13.0194	−	6.73933i	−0.578211	−	0.299304i
$508$	2.85334			0.126597
$509$			36.5665i			1.62078i	0.585890	+	0.810390i	$0.300745\pi$
$509$			36.5665i			1.62078i	−0.585890	+	0.810390i	$0.699255\pi$
$510$	−1.20120	−	23.9675i	−0.0531899	−	1.06130i
$511$	4.53590			0.200656
$512$			16.5657i			0.732107i
$513$	−23.8452	+	3.30734i	−1.05279	+	0.146023i
$514$		−	44.7553i		−	1.97407i
$515$	11.4812	−	6.69213i	0.505922	−	0.294891i
$516$	−3.91857	−	2.02840i	−0.172506	−	0.0892954i
$517$	10.0782	−	1.59245i	0.443237	−	0.0700359i
$518$	3.73900			0.164282
$519$	−11.5835	+	22.3777i	−0.508461	+	0.982271i
$520$	−10.7321	+	6.25547i	−0.470632	+	0.274320i
$521$			21.5921i			0.945969i	0.881071	+	0.472984i	$0.156823\pi$
$521$			21.5921i			0.945969i	−0.881071	+	0.472984i	$0.843177\pi$
$522$	−33.0158	+	23.3457i	−1.44506	+	1.02181i
$523$	3.27110			0.143035			0.0715177	−	0.997439i	$-0.477216\pi$
$523$	3.27110			0.143035			0.0715177	+	0.997439i	$0.477216\pi$
$524$		0			0
$525$	15.4501	−	10.0741i	0.674296	−	0.439670i
$526$	−23.1244			−1.00827
$527$			14.2527i			0.620856i
$528$	−24.3349	−	8.08982i	−1.05904	−	0.352064i
$529$	5.39230			0.234448
$530$	−13.1039	+	7.63798i	−0.569198	+	0.331773i
$531$	12.0000	−	8.48528i	0.520756	−	0.368230i
$532$			2.64387i			0.114626i
$533$	−5.10757			−0.221233
$534$	−10.7057	−	5.54170i	−0.463283	−	0.239813i
$535$	2.12976	−	1.24139i	0.0920778	−	0.0536700i
$536$	−32.1172			−1.38725
$537$	−15.3819	+	29.7155i	−0.663778	+	1.28232i
$538$	−12.7786			−0.550924
$539$	−8.07235	+	1.27551i	−0.347701	+	0.0549402i
$540$	−2.44883	+	1.92244i	−0.105381	+	0.0827288i
$541$			6.78309i			0.291628i	0.989312	+	0.145814i	$0.0465801\pi$
$541$			6.78309i			0.291628i	−0.989312	+	0.145814i	$0.953420\pi$
$542$	36.2539			1.55724
$543$	−14.5576	−	7.53556i	−0.624725	−	0.323382i
$544$	−6.19615			−0.265658
$545$	24.4523	−	14.2527i	1.04742	−	0.610517i
$546$	−5.43896	+	10.5073i	−0.232766	+	0.449669i
$547$	25.4043			1.08621			0.543104	−	0.839665i	$-0.317249\pi$
$547$	25.4043			1.08621			0.543104	+	0.839665i	$0.317249\pi$
$548$	0.603439			0.0257776
$549$	8.30755	−	5.87433i	0.354558	−	0.250710i
$550$	23.3850	+	8.76518i	0.997139	+	0.373749i
$551$		−	41.4655i		−	1.76649i
$552$	−11.0666	+	21.3790i	−0.471025	+	0.909951i
$553$			29.6012i			1.25877i
$554$			25.4286i			1.08036i
$555$	−4.50929	+	0.225995i	−0.191409	+	0.00959297i
$556$			4.63294i			0.196480i
$557$		−	4.11439i		−	0.174332i	−0.996194	−	0.0871661i	$-0.972219\pi$
$557$		−	4.11439i		−	0.174332i	0.996194	−	0.0871661i	$-0.0277811\pi$
$558$	12.7786	−	9.03583i	0.540961	−	0.382517i
$559$	20.2487			0.856429
$560$	−10.7057	−	18.3671i	−0.452400	−	0.776150i
$561$	−7.45607	+	22.4285i	−0.314796	+	0.946932i
$562$		−	8.89934i		−	0.375396i
$563$			33.4268i			1.40877i	0.709818	+	0.704385i	$0.248777\pi$
$563$			33.4268i			1.40877i	−0.709818	+	0.704385i	$0.751223\pi$
$564$	−1.26795	−	0.656339i	−0.0533903	−	0.0276368i
$565$	12.0000	+	20.5875i	0.504844	+	0.866124i
$566$		−	38.2581i		−	1.60811i
$567$	6.38929	−	18.0717i	0.268325	−	0.758938i
$568$	34.9118			1.46486
$569$	−2.39818			−0.100537			−0.0502686	−	0.998736i	$-0.516008\pi$
$569$	−2.39818			−0.100537			−0.0502686	+	0.998736i	$0.516008\pi$
$570$	−1.35259	−	26.9882i	−0.0566536	−	1.13041i
$571$			7.11572i			0.297784i	0.988853	+	0.148892i	$0.0475706\pi$
$571$			7.11572i			0.297784i	−0.988853	+	0.148892i	$0.952429\pi$
$572$	−1.86950	+	0.295400i	−0.0781677	+	0.0123513i
$573$	7.58051	−	14.6444i	0.316680	−	0.611779i
$574$		−	7.69185i		−	0.321052i
$575$	13.1298	−	23.1822i	0.547552	−	0.966765i
$576$	−11.5359	−	16.3142i	−0.480662	−	0.679759i
$577$		−	35.6586i		−	1.48449i	−0.670129	−	0.742244i	$-0.733761\pi$
$577$		−	35.6586i		−	1.48449i	0.670129	−	0.742244i	$-0.266239\pi$
$578$		−	0.108124i		−	0.00449736i
$579$	−16.3799	−	8.47886i	−0.680726	−	0.352369i
$580$	−2.70043	−	4.63294i	−0.112129	−	0.192372i
$581$			19.8733i			0.824484i
$582$	2.70043	+	1.39785i	0.111937	+	0.0579426i
$583$	14.7554	−	2.33151i	0.611108	−	0.0965612i
$584$			5.55532i			0.229881i
$585$	5.92438	−	13.0007i	0.244943	−	0.537511i
$586$	−6.19615			−0.255961
$587$	8.62570			0.356021			0.178010	−	0.984029i	$-0.443034\pi$
$587$	8.62570			0.356021			0.178010	+	0.984029i	$0.443034\pi$
$588$	1.01560	+	0.525711i	0.0418825	+	0.0216800i
$589$			16.0490i			0.661286i
$590$	8.30755	+	14.2527i	0.342017	+	0.586773i
$591$	−6.31676	+	12.2030i	−0.259837	+	0.501966i
$592$			5.20405i			0.213885i
$593$		−	11.7524i		−	0.482612i	−0.970449	−	0.241306i	$-0.922424\pi$
$593$		−	11.7524i		−	0.482612i	0.970449	−	0.241306i	$-0.0775757\pi$
$594$	24.8358	−	7.53417i	1.01903	−	0.309131i
$595$	−16.9282	+	9.86707i	−0.693989	+	0.404510i
$596$	4.15378			0.170145
$597$	16.8096	+	8.70131i	0.687973	+	0.356121i
$598$			17.0903i			0.698873i
$599$			18.0058i			0.735699i	0.929885	+	0.367849i	$0.119906\pi$
$599$			18.0058i			0.735699i	−0.929885	+	0.367849i	$0.880094\pi$
$600$	12.3382	+	18.9224i	0.503705	+	0.772504i
$601$			3.39154i			0.138344i	0.997605	+	0.0691720i	$0.0220357\pi$
$601$			3.39154i			0.138344i	−0.997605	+	0.0691720i	$0.977964\pi$
$602$			30.4940i			1.24284i
$603$	30.1603	−	21.3266i	1.22822	−	0.868486i
$604$			2.81541i			0.114558i
$605$	−18.3349	−	16.3961i	−0.745419	−	0.666596i
$606$	10.7321	−	20.7327i	0.435960	−	0.842210i
$607$	−30.8051			−1.25034			−0.625171	−	0.780488i	$-0.714971\pi$
$607$	−30.8051			−1.25034			−0.625171	+	0.780488i	$0.714971\pi$
$608$	−6.97707			−0.282958
$609$	29.3205	+	15.1774i	1.18813	+	0.615020i
$610$	5.75129	+	9.86707i	0.232863	+	0.399506i
$611$	6.55196			0.265064
$612$	2.70043	−	1.90949i	0.109159	−	0.0771868i
$613$	−45.5606			−1.84017			−0.920087	−	0.391714i	$-0.871882\pi$
$613$	−45.5606			−1.84017			−0.920087	+	0.391714i	$0.871882\pi$
$614$			14.3180i			0.577827i
$615$	0.464916	+	9.27649i	0.0187472	+	0.374064i
$616$	2.87564	+	18.1991i	0.115863	+	0.733263i
$617$	11.0986			0.446814			0.223407	−	0.974725i	$-0.428282\pi$
$617$	11.0986			0.446814			0.223407	+	0.974725i	$0.428282\pi$
$618$	13.7670	+	7.12633i	0.553791	+	0.286663i
$619$	1.60770			0.0646187			0.0323094	−	0.999478i	$-0.489714\pi$
$619$	1.60770			0.0646187			0.0323094	+	0.999478i	$0.489714\pi$
$620$	1.04519	+	1.79315i	0.0419757	+	0.0720147i
$621$	−3.80385	−	27.4249i	−0.152643	−	1.10052i
$622$	22.1332			0.887459
$623$			9.84287i			0.394346i
$624$	−14.6243	−	7.57010i	−0.585441	−	0.303047i
$625$	−12.8564	−	21.4409i	−0.514256	−	0.857637i
$626$	−45.8637			−1.83308
$627$	−8.39578	+	25.2552i	−0.335295	+	1.00860i
$628$		−	2.33151i		−	0.0930373i
$629$	4.79637			0.191244
$630$	19.5786	+	8.92194i	0.780031	+	0.355459i
$631$	38.6410			1.53827			0.769137	−	0.639084i	$-0.220686\pi$
$631$	38.6410			1.53827			0.769137	+	0.639084i	$0.220686\pi$
$632$	−36.2539			−1.44210
$633$	−0.988427	+	1.90949i	−0.0392865	+	0.0758956i
$634$			34.5807i			1.37338i
$635$	11.9909	+	20.5719i	0.475845	+	0.816373i
$636$	−1.85641	−	0.960947i	−0.0736113	−	0.0381040i
$637$	−5.24796			−0.207932
$638$	6.97707	+	44.1558i	0.276225	+	1.74815i
$639$	−32.7846	+	23.1822i	−1.29694	+	0.917074i
$640$	25.1954	−	14.6858i	0.995935	−	0.580508i
$641$			3.30890i			0.130694i	0.997863	+	0.0653469i	$0.0208154\pi$
$641$			3.30890i			0.130694i	−0.997863	+	0.0653469i	$0.979185\pi$
$642$	2.55378	+	1.32194i	0.100790	+	0.0521727i
$643$			29.7155i			1.17187i	0.810359	+	0.585933i	$0.199272\pi$
$643$			29.7155i			1.17187i	−0.810359	+	0.585933i	$0.800728\pi$
$644$	−3.04078			−0.119823
$645$	−1.84314	−	36.7762i	−0.0725735	−	1.44806i
$646$			28.7064i			1.12944i
$647$	−11.9229			−0.468739			−0.234370	−	0.972148i	$-0.575303\pi$
$647$	−11.9229			−0.468739			−0.234370	+	0.972148i	$0.575303\pi$
$648$	22.1332	+	7.82526i	0.869473	+	0.307405i
$649$	−2.53590	−	16.0490i	−0.0995427	−	0.629977i
$650$	13.9541	+	7.90327i	0.547326	+	0.309992i
$651$	−11.3483	−	5.87433i	−0.444776	−	0.230233i
$652$			1.59245i			0.0623652i
$653$	−17.8548			−0.698713			−0.349357	−	0.936990i	$-0.613600\pi$
$653$	−17.8548			−0.698713			−0.349357	+	0.936990i	$0.613600\pi$
$654$	29.3205	+	15.1774i	1.14652	+	0.593484i
$655$		0			0
$656$	10.7057			0.417989
$657$	−3.68886	−	5.21684i	−0.143916	−	0.203528i
$658$			9.86707i			0.384658i
$659$	21.4115			0.834073			0.417036	−	0.908890i	$-0.363069\pi$
$659$	21.4115			0.834073			0.417036	+	0.908890i	$0.363069\pi$
$660$	0.706683	+	3.36854i	0.0275076	+	0.131120i
$661$	−4.53590			−0.176426			−0.0882130	−	0.996102i	$-0.528116\pi$
$661$	−4.53590			−0.176426			−0.0882130	+	0.996102i	$0.528116\pi$
$662$		−	12.8548i		−	0.499617i
$663$	−6.97707	+	13.4787i	−0.270967	+	0.523468i
$664$	−24.3397			−0.944565
$665$	−19.0617	+	11.1106i	−0.739181	+	0.430852i
$666$	−3.04078	−	4.30031i	−0.117828	−	0.166634i
$667$	47.6903			1.84658
$668$			3.52359i			0.136332i
$669$	10.0526	−	19.4201i	0.388654	−	0.750823i
$670$	20.8799	+	35.8221i	0.806661	+	1.38393i
$671$	−1.75559	−	11.1106i	−0.0677739	−	0.428921i
$672$	2.55378	−	4.93353i	0.0985144	−	0.190315i
$673$	−49.8201			−1.92042			−0.960212	−	0.279272i	$-0.909907\pi$
$673$	−49.8201			−1.92042			−0.960212	+	0.279272i	$0.909907\pi$
$674$		−	25.4286i		−	0.979475i
$675$	−24.1514	−	9.57661i	−0.929587	−	0.368604i
$676$	2.26795			0.0872288
$677$			13.9573i			0.536421i	0.963360	+	0.268211i	$0.0864323\pi$
$677$			13.9573i			0.536421i	−0.963360	+	0.268211i	$0.913568\pi$
$678$	−12.7786	+	24.6863i	−0.490759	+	0.948073i
$679$		−	2.48278i		−	0.0952805i
$680$	−12.0846	−	20.7327i	−0.463425	−	0.795064i
$681$	−7.42976	+	14.3532i	−0.284709	+	0.550015i
$682$	−2.70043	−	17.0903i	−0.103405	−	0.654420i
$683$	−8.02226			−0.306963			−0.153482	−	0.988152i	$-0.549049\pi$
$683$	−8.02226			−0.306963			−0.153482	+	0.988152i	$0.549049\pi$
$684$	3.04078	−	2.15015i	0.116267	−	0.0822132i
$685$	2.53590	+	4.35066i	0.0968917	+	0.166230i
$686$		−	30.3548i		−	1.15895i
$687$	32.7950	+	16.9759i	1.25121	+	0.647672i
$688$	−42.4424			−1.61810
$689$	9.59274			0.365454
$690$	31.0397	−	1.55564i	1.18166	−	0.0592222i
$691$	−29.8564			−1.13579			−0.567896	−	0.823101i	$-0.692242\pi$
$691$	−29.8564			−1.13579			−0.567896	+	0.823101i	$0.692242\pi$
$692$		−	3.89814i		−	0.148185i
$693$	−14.7851	−	15.1808i	−0.561638	−	0.576670i
$694$	41.2679			1.56651
$695$	−33.4024	+	19.4695i	−1.26703	+	0.738520i
$696$	−18.5885	+	35.9101i	−0.704594	+	1.36117i
$697$		−	9.86707i		−	0.373742i
$698$	38.1234			1.44299
$699$	−8.07235	+	15.5946i	−0.305324	+	0.589841i
$700$	−1.40619	+	2.48278i	−0.0531488	+	0.0938404i
$701$	19.0133			0.718122			0.359061	−	0.933314i	$-0.383097\pi$
$701$	19.0133			0.718122			0.359061	+	0.933314i	$0.383097\pi$
$702$	16.5079	−	2.28966i	0.623051	−	0.0864177i
$703$	5.40087			0.203698
$704$	−21.8189	+	3.44760i	−0.822329	+	0.129936i
$705$	−0.596392	−	11.8998i	−0.0224614	−	0.448173i
$706$			2.48278i			0.0934408i
$707$	−19.0617			−0.716889
$708$	−1.04519	+	2.01915i	−0.0392805	+	0.0758842i
$709$	−29.0718			−1.09181			−0.545907	−	0.837846i	$-0.683815\pi$
$709$	−29.0718			−1.09181			−0.545907	+	0.837846i	$0.683815\pi$
$710$	−22.6967	−	38.9390i	−0.851791	−	1.46135i
$711$	34.0450	−	24.0734i	1.27679	−	0.902825i
$712$	−12.0550			−0.451781
$713$	−18.4583			−0.691268
$714$	−20.2985	−	10.5073i	−0.759651	−	0.393225i
$715$	−9.98617	−	12.2373i	−0.373462	−	0.457648i
$716$		−	5.17638i		−	0.193450i
$717$	24.8336	+	12.8548i	0.927428	+	0.480072i
$718$		−	2.64387i		−	0.0986684i
$719$			6.48906i			0.242001i	0.992652	+	0.121001i	$0.0386103\pi$
$719$			6.48906i			0.242001i	−0.992652	+	0.121001i	$0.961390\pi$
$720$	−12.4178	+	27.2501i	−0.462785	+	1.01555i
$721$		−	12.6574i		−	0.471387i
$722$			3.71087i			0.138104i
$723$	−10.0782	+	19.4695i	−0.374811	+	0.724079i
$724$	2.53590			0.0942459
$725$	22.0541	−	38.9390i	0.819068	−	1.44616i
$726$	4.69102	−	28.3065i	0.174100	−	1.05055i
$727$		−	31.7347i		−	1.17697i	−0.808507	−	0.588487i	$-0.799724\pi$
$727$		−	31.7347i		−	1.17697i	0.808507	−	0.588487i	$-0.200276\pi$
$728$			11.8315i			0.438505i
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	6.19615	−	3.61160i	0.229330	−	0.133671i
$731$			39.1175i			1.44681i
$732$	−0.723579	+	1.39785i	−0.0267442	+	0.0516659i
$733$	−2.12976			−0.0786647			−0.0393323	−	0.999226i	$-0.512523\pi$
$733$	−2.12976			−0.0786647			−0.0393323	+	0.999226i	$0.512523\pi$
$734$	22.5245			0.831394
$735$	0.477695	+	9.53146i	0.0176201	+	0.351573i
$736$		−	8.02448i		−	0.295786i
$737$	−6.37363	−	40.3369i	−0.234776	−	1.48583i
$738$	−8.84657	+	6.25547i	−0.325647	+	0.230267i
$739$			42.6052i			1.56726i	0.621230	+	0.783629i	$0.286633\pi$
$739$			42.6052i			1.56726i	−0.621230	+	0.783629i	$0.713367\pi$
$740$	0.603439	−	0.351731i	0.0221829	−	0.0129299i
$741$	−7.85641	+	15.1774i	−0.288612	+	0.557556i
$742$			14.4464i			0.530344i
$743$		−	19.1741i		−	0.703430i	−0.936107	−	0.351715i	$-0.885599\pi$
$743$		−	19.1741i		−	0.703430i	0.936107	−	0.351715i	$-0.114401\pi$
$744$	7.19455	−	13.8988i	0.263765	−	0.509555i
$745$	17.4559	+	29.9478i	0.639534	+	1.09720i
$746$			14.3180i			0.524219i
$747$	22.8567	−	16.1622i	0.836285	−	0.591342i
$748$	−0.570669	−	3.61160i	−0.0208657	−	0.132053i
$749$		−	2.34795i		−	0.0857924i
$750$	13.0839	−	26.0632i	0.477758	−	0.951694i
$751$	−31.7128			−1.15722			−0.578608	−	0.815605i	$-0.696404\pi$
$751$	−31.7128			−1.15722			−0.578608	+	0.815605i	$0.696404\pi$
$752$	−13.7333			−0.500801
$753$	13.5124	−	26.1039i	0.492419	−	0.951280i
$754$			28.7064i			1.04542i
$755$	−20.2985	+	11.8315i	−0.738737	+	0.430593i
$756$	0.407387	+	2.93716i	0.0148165	+	0.106824i
$757$		−	7.84792i		−	0.285237i	−0.989778	−	0.142619i	$-0.954448\pi$
$757$		−	7.84792i		−	0.285237i	0.989778	−	0.142619i	$-0.0455523\pi$
$758$			4.40979i			0.160171i
$759$	−29.0466	−	9.65617i	−1.05432	−	0.350497i
$760$	−13.6077	−	23.3457i	−0.493603	−	0.846839i
$761$	−49.5471			−1.79608			−0.898040	−	0.439913i	$-0.855009\pi$
$761$	−49.5471			−1.79608			−0.898040	+	0.439913i	$0.855009\pi$
$762$	−12.7689	+	24.6677i	−0.462569	+	0.893615i
$763$		−	26.9573i		−	0.975921i
$764$			2.55103i			0.0922929i
$765$	25.1153	+	11.4450i	0.908047	+	0.413796i
$766$		−	31.5218i		−	1.13893i
$767$		−	10.4337i		−	0.376738i
$768$	9.72214	+	5.03255i	0.350817	+	0.181596i
$769$		−	43.8466i		−	1.58115i	−0.612366	−	0.790574i	$-0.709782\pi$
$769$		−	43.8466i		−	1.58115i	0.612366	−	0.790574i	$-0.290218\pi$
$770$	18.4290	−	15.0389i	0.664134	−	0.541964i
$771$	45.7128	+	23.6627i	1.64631	+	0.852191i
$772$	2.85334			0.102694
$773$	26.8631			0.966198			0.483099	−	0.875566i	$-0.339511\pi$
$773$	26.8631			0.966198			0.483099	+	0.875566i	$0.339511\pi$
$774$	35.0718	−	24.7995i	1.26063	−	0.891400i
$775$	−8.53590	+	15.0711i	−0.306619	+	0.541370i
$776$	3.04078			0.109157
$777$	−1.97685	+	3.81899i	−0.0709193	+	0.137005i
$778$	−31.4877			−1.12889
$779$		−	11.1106i		−	0.398080i
$780$	0.110631	+	2.20742i	0.00396122	+	0.0790383i
$781$	6.92820	+	43.8466i	0.247911	+	1.56895i
$782$	−33.0158			−1.18064
$783$	−6.38929	−	46.0653i	−0.228335	−	1.64624i
$784$	11.0000			0.392857
$785$	16.8096	−	9.79796i	0.599962	−	0.349704i
$786$		0			0
$787$	22.2861			0.794413			0.397206	−	0.917729i	$-0.369980\pi$
$787$	22.2861			0.794413			0.397206	+	0.917729i	$0.369980\pi$
$788$		−	2.12574i		−	0.0757264i
$789$	12.2261	−	23.6191i	0.435262	−	0.840861i
$790$	23.5692	+	40.4360i	0.838555	+	1.43865i
$791$	22.6967			0.807000
$792$	18.5926	−	18.1079i	0.660658	−	0.643438i
$793$		−	7.22319i		−	0.256503i
$794$	7.83714			0.278130
$795$	−0.873179	−	17.4226i	−0.0309685	−	0.617914i
$796$	−2.92820			−0.103787
$797$	35.2679			1.24925			0.624627	−	0.780923i	$-0.285251\pi$
$797$	35.2679			1.24925			0.624627	+	0.780923i	$0.285251\pi$
$798$	−22.8567	−	11.8315i	−0.809120	−	0.418831i
$799$			12.6574i			0.447787i
$800$	−6.55196	−	3.71087i	−0.231647	−	0.131199i
$801$	11.3205	−	8.00481i	0.399990	−	0.282836i
$802$	−38.7535			−1.36843
$803$	−6.97707	+	1.10245i	−0.246215	+	0.0389045i
$804$	−2.62693	+	5.07484i	−0.0926448	+	0.178976i
$805$	−12.7786	−	21.9233i	−0.450386	−	0.772694i
$806$		−	11.1106i		−	0.391355i
$807$	6.75620	−	13.0520i	0.237829	−	0.459451i
$808$		−	23.3457i		−	0.821300i
$809$	−7.66496			−0.269486			−0.134743	−	0.990881i	$-0.543021\pi$
$809$	−7.66496			−0.269486			−0.134743	+	0.990881i	$0.543021\pi$
$810$	−5.66117	−	29.7737i	−0.198913	−	1.04614i
$811$		−	36.7309i		−	1.28980i	−0.764269	−	0.644898i	$-0.776900\pi$
$811$		−	36.7309i		−	1.28980i	0.764269	−	0.644898i	$-0.223100\pi$
$812$	−5.10757			−0.179241
$813$	−19.1679	+	37.0295i	−0.672247	+	1.29868i
$814$	−5.75129	+	0.908762i	−0.201583	+	0.0318521i
$815$	−11.4812	+	6.69213i	−0.402169	+	0.234415i
$816$	14.6243	−	28.2520i	0.511953	−	0.989018i
$817$			44.0476i			1.54103i
$818$	−29.2768			−1.02364
$819$	−7.85641	−	11.1106i	−0.274525	−	0.388237i
$820$	−0.723579	−	1.24139i	−0.0252685	−	0.0433513i
$821$	41.7100			1.45569			0.727844	−	0.685743i	$-0.240523\pi$
$821$	41.7100			1.45569			0.727844	+	0.685743i	$0.240523\pi$
$822$	−2.70043	+	5.21684i	−0.0941884	+	0.181958i
$823$			22.4923i			0.784034i	0.919958	+	0.392017i	$0.128222\pi$
$823$			22.4923i			0.784034i	−0.919958	+	0.392017i	$0.871778\pi$
$824$	15.5021			0.540042
$825$	−21.3166	+	19.2510i	−0.742150	+	0.670234i
$826$	15.7128			0.546719
$827$		−	40.0415i		−	1.39238i	−0.717859	−	0.696189i	$-0.754878\pi$
$827$		−	40.0415i		−	1.39238i	0.717859	−	0.696189i	$-0.245122\pi$
$828$	2.47294	+	3.49726i	0.0859406	+	0.121538i
$829$	−44.1051			−1.53183			−0.765917	−	0.642939i	$-0.777715\pi$
$829$	−44.1051			−1.53183			−0.765917	+	0.642939i	$0.777715\pi$
$830$	15.8236	+	27.1475i	0.549246	+	0.942302i
$831$	−25.9726	−	13.4444i	−0.900981	−	0.466382i
$832$	−14.1848			−0.491769
$833$		−	10.1383i		−	0.351270i
$834$	−40.0526	−	20.7327i	−1.38691	−	0.717916i
$835$	−25.4043	+	14.8076i	−0.879151	+	0.512437i
$836$	−0.642592	−	4.06678i	−0.0222245	−	0.140652i
$837$	2.47294	+	17.8293i	0.0854773	+	0.616271i
$838$	−1.86492			−0.0644225
$839$		−	29.0421i		−	1.00265i	−0.865260	−	0.501323i	$-0.832847\pi$
$839$		−	29.0421i		−	1.00265i	0.865260	−	0.501323i	$-0.167153\pi$
$840$	21.4887	−	1.07696i	0.741430	−	0.0371588i
$841$	51.1051			1.76225
$842$		−	13.2294i		−	0.455914i
$843$	9.08973	+	4.70519i	0.313067	+	0.162055i
$844$		−	0.332630i		−	0.0114496i
$845$	9.53085	+	16.3514i	0.327871	+	0.562505i
$846$	11.3483	−	8.02448i	0.390164	−	0.275887i
$847$	−22.2861	+	7.22319i	−0.765759	+	0.248192i
$848$	−20.1069			−0.690474
$849$	39.0766	+	20.2275i	1.34110	+	0.694207i
$850$	−15.2679	+	26.9573i	−0.523686	+	0.924629i
$851$			6.21166i			0.212933i
$852$	2.85550	−	5.51641i	0.0978280	−	0.188989i
$853$	−29.6638			−1.01567			−0.507835	−	0.861455i	$-0.669554\pi$
$853$	−29.6638			−1.01567			−0.507835	+	0.861455i	$0.669554\pi$
$854$	10.8779			0.372235
$855$	28.2807	+	12.8875i	0.967179	+	0.440742i
$856$	2.87564			0.0982875
$857$			34.8246i			1.18959i	0.803879	+	0.594793i	$0.202766\pi$
$857$			34.8246i			1.18959i	−0.803879	+	0.594793i	$0.797234\pi$
$858$	5.81236	−	17.4841i	0.198431	−	0.596897i
$859$	39.4641			1.34650			0.673249	−	0.739416i	$-0.264898\pi$
$859$	39.4641			1.34650			0.673249	+	0.739416i	$0.264898\pi$
$860$	2.86859	+	4.92144i	0.0978182	+	0.167820i
$861$	7.85641	+	4.06678i	0.267746	+	0.138595i
$862$		−	29.6012i		−	1.00822i
$863$	4.12157			0.140300			0.0701499	−	0.997536i	$-0.477652\pi$
$863$	4.12157			0.140300			0.0701499	+	0.997536i	$0.477652\pi$
$864$	−7.75105	+	1.07508i	−0.263696	+	0.0365749i
$865$	28.1047	−	16.3816i	0.955589	−	0.556991i
$866$	56.7417			1.92816
$867$	0.110437	+	0.0571664i	0.00375064	+	0.00194147i
$868$	1.97685			0.0670988
$869$	−7.19455	−	45.5322i	−0.244059	−	1.54458i
$870$	52.1372	−	2.61300i	1.76762	−	0.0885889i
$871$		−	26.2236i		−	0.888553i
$872$	33.0158			1.11806
$873$	−2.85550	+	2.01915i	−0.0966442	+	0.0683377i
$874$	−37.1769			−1.25753
$875$	−23.8097	+	0.295400i	−0.804914	+	0.00998634i
$876$	0.877796	+	0.454381i	0.0296580	+	0.0153521i
$877$	44.4192			1.49993			0.749966	−	0.661477i	$-0.230070\pi$
$877$	44.4192			1.49993			0.749966	+	0.661477i	$0.230070\pi$
$878$	−12.0846			−0.407837
$879$	3.27598	−	6.32871i	0.110496	−	0.213462i
$880$	20.9316	+	25.6500i	0.705602	+	0.864661i
$881$		−	5.85993i		−	0.197426i	−0.995116	−	0.0987130i	$-0.968527\pi$
$881$		−	5.85993i		−	0.197426i	0.995116	−	0.0987130i	$-0.0314726\pi$
$882$	−9.08973	+	6.42741i	−0.306067	+	0.216422i
$883$			15.8102i			0.532055i	0.963965	+	0.266027i	$0.0857111\pi$
$883$			15.8102i			0.532055i	−0.963965	+	0.266027i	$0.914289\pi$
$884$		−	2.34795i		−	0.0789702i
$885$	−18.9499	+	0.949725i	−0.636993	+	0.0319247i
$886$			51.8711i			1.74264i
$887$			9.33123i			0.313312i	0.987653	+	0.156656i	$0.0500714\pi$
$887$			9.33123i			0.313312i	−0.987653	+	0.156656i	$0.949929\pi$
$888$	−4.67729	−	2.42114i	−0.156960	−	0.0812482i
$889$	22.6795			0.760646
$890$	7.83714	+	13.4456i	0.262702	+	0.450698i
$891$	−5.43564	+	29.3505i	−0.182101	+	0.983280i
$892$			3.38293i			0.113269i
$893$			14.2527i			0.476947i
$894$	−18.5885	+	35.9101i	−0.621691	+	1.20101i
$895$	37.3205	−	21.7533i	1.24749	−	0.727132i
$896$		−	27.7766i		−	0.927951i
$897$	−17.4559	−	9.03583i	−0.582835	−	0.301697i
$898$	−23.6923			−0.790621
$899$	−31.0042			−1.03405
$900$	3.99910	−	0.401861i	0.133303	−	0.0133954i
$901$			18.5317i			0.617382i
$902$	1.86950	+	11.8315i	0.0622475	+	0.393947i
$903$	−31.1463	−	16.1225i	−1.03649	−	0.536524i
$904$			27.7976i			0.924535i
$905$	10.6569	+	18.2832i	0.354247	+	0.607755i
$906$	−24.3397	−	12.5992i	−0.808634	−	0.418580i
$907$			38.7292i			1.28598i	0.765874	+	0.642991i	$0.222307\pi$
$907$			38.7292i			1.28598i	−0.765874	+	0.642991i	$0.777693\pi$
$908$		−	2.50029i		−	0.0829752i
$909$	15.5021	+	21.9233i	0.514172	+	0.727150i
$910$	13.1963	−	7.69185i	0.437455	−	0.254982i
$911$			53.2596i			1.76457i	0.470715	+	0.882285i	$0.343996\pi$
$911$			53.2596i			1.76457i	−0.470715	+	0.882285i	$0.656004\pi$
$912$	16.4675	−	31.8127i	0.545292	−	1.05342i
$913$	−4.83020	−	30.5689i	−0.159856	−	1.01168i
$914$		−	4.92619i		−	0.162944i
$915$	−13.1189	+	0.657491i	−0.433699	+	0.0217360i
$916$	−5.71281			−0.188757
$917$		0			0
$918$	4.42328	+	31.8909i	0.145990	+	1.05256i
$919$		−	24.0734i		−	0.794110i	−0.917795	−	0.397055i	$-0.870032\pi$
$919$		−	24.0734i		−	0.794110i	0.917795	−	0.397055i	$-0.129968\pi$
$920$	26.8504	−	15.6505i	0.885233	−	0.515982i
$921$	−14.6243	−	7.57010i	−0.481887	−	0.249443i
$922$		−	27.9250i		−	0.919663i
$923$			28.5053i			0.938264i
$924$	3.11085	+	1.03416i	0.102339	+	0.0340214i
$925$	5.07180	+	2.87254i	0.166760	+	0.0944485i
$926$	10.7057			0.351812
$927$	−14.5576	+	10.2938i	−0.478134	+	0.338091i
$928$		−	13.4787i		−	0.442459i
$929$			7.52433i			0.246865i	0.992353	+	0.123433i	$0.0393903\pi$
$929$			7.52433i			0.246865i	−0.992353	+	0.123433i	$0.960610\pi$
$930$	−20.1794	+	1.01135i	−0.661708	+	0.0331633i
$931$		−	11.4160i		−	0.374145i
$932$		−	2.71654i		−	0.0889833i
$933$	−11.7021	+	22.6067i	−0.383109	+	0.740109i
$934$		−	6.20696i		−	0.203098i
$935$	23.6406	−	19.2918i	0.773130	−	0.630909i
$936$	13.6077	−	9.62209i	0.444781	−	0.314508i
$937$	59.1747			1.93315			0.966576	−	0.256379i	$-0.0825295\pi$
$937$	59.1747			1.93315			0.966576	+	0.256379i	$0.0825295\pi$
$938$	39.4920			1.28946
$939$	24.2487	−	46.8449i	0.791327	−	1.52873i
$940$	0.928203	+	1.59245i	0.0302747	+	0.0519400i
$941$	−23.3393			−0.760838			−0.380419	−	0.924814i	$-0.624220\pi$
$941$	−23.3393			−0.760838			−0.380419	+	0.924814i	$0.624220\pi$
$942$	20.1563	+	10.4337i	0.656728	+	0.339947i
$943$	12.7786			0.416128
$944$			21.8695i			0.711793i
$945$	−19.4643	+	15.2803i	−0.633173	+	0.497069i
$946$	−7.41154	−	46.9055i	−0.240970	−	1.52503i
$947$	39.5512			1.28524			0.642620	−	0.766185i	$-0.277847\pi$
$947$	39.5512			1.28524			0.642620	+	0.766185i	$0.277847\pi$
$948$	−2.96528	+	5.72848i	−0.0963079	+	0.186053i
$949$	−4.53590			−0.147241
$950$	−17.1922	+	30.3548i	−0.557789	+	0.984841i
$951$	−35.3205	−	18.2832i	−1.14535	−	0.592875i
$952$	−22.8567			−0.740791
$953$			32.6197i			1.05666i	0.849040	+	0.528328i	$0.177181\pi$
$953$			32.6197i			1.05666i	−0.849040	+	0.528328i	$0.822819\pi$
$954$	16.6151	−	11.7487i	0.537934	−	0.380377i
$955$	−18.3923	+	10.7205i	−0.595161	+	0.346906i
$956$	−4.32596			−0.139912
$957$	−48.7893	−	16.2194i	−1.57714	−	0.524299i
$958$		−	36.8244i		−	1.18974i
$959$	4.79637			0.154883
$960$	1.29117	+	25.7627i	0.0416723	+	0.831488i
$961$	−19.0000			−0.612903
$962$	−3.73900			−0.120550
$963$	−2.70043	+	1.90949i	−0.0870203	+	0.0615326i
$964$		−	3.39154i		−	0.109234i
$965$	11.9909	+	20.5719i	0.386001	+	0.662234i
$966$	13.6077	−	26.2880i	0.437820	−	0.845804i
$967$	9.50749			0.305740			0.152870	−	0.988246i	$-0.451148\pi$
$967$	9.50749			0.305740			0.152870	+	0.988246i	$0.451148\pi$
$968$	−8.84657	−	27.2948i	−0.284339	−	0.877287i
$969$	−29.3205	−	15.1774i	−0.941910	−	0.487569i
$970$	−1.97685	−	3.39154i	−0.0634730	−	0.108896i
$971$			13.4586i			0.431907i	0.976404	+	0.215953i	$0.0692859\pi$
$971$			13.4586i			0.431907i	−0.976404	+	0.215953i	$0.930714\pi$
$972$	3.04679	−	2.85722i	0.0977257	−	0.0916454i
$973$			36.8244i			1.18054i
$974$	−48.2619			−1.54641
$975$	−15.4501	+	10.0741i	−0.494798	+	0.322630i
$976$			15.1402i			0.484626i
$977$	−20.2686			−0.648449			−0.324225	−	0.945980i	$-0.605103\pi$
$977$	−20.2686			−0.648449			−0.324225	+	0.945980i	$0.605103\pi$
$978$	−13.7670	−	7.12633i	−0.440221	−	0.227875i
$979$	−2.39230	−	15.1402i	−0.0764584	−	0.483883i
$980$	−0.743468	−	1.27551i	−0.0237492	−	0.0407448i
$981$	−31.0042	+	21.9233i	−0.989888	+	0.699957i
$982$			29.6012i			0.944612i
$983$	15.9853			0.509853			0.254926	−	0.966960i	$-0.417949\pi$
$983$	15.9853			0.509853			0.254926	+	0.966960i	$0.417949\pi$
$984$	−4.98076	+	9.62209i	−0.158781	+	0.306741i
$985$	15.3261	−	8.93324i	0.488331	−	0.284637i
$986$	−55.4565			−1.76609
$987$	−10.0782	−	5.21684i	−0.320791	−	0.166054i
$988$		−	2.64387i		−	0.0841128i
$989$	−50.6601			−1.61090
$990$	−32.2841	−	8.96506i	−1.02606	−	0.284928i
$991$	0.248711			0.00790058			0.00395029	−	0.999992i	$-0.498743\pi$
$991$	0.248711			0.00790058			0.00395029	+	0.999992i	$0.498743\pi$
$992$			5.21684i			0.165635i
$993$	13.1298	+	6.79650i	0.416662	+	0.215680i
$994$	−42.9282			−1.36160
$995$	−12.3055	−	21.1117i	−0.390111	−	0.669285i
$996$	−1.99080	+	3.84593i	−0.0630808	+	0.121863i
$997$	−40.1597			−1.27187			−0.635935	−	0.771742i	$-0.719386\pi$
$997$	−40.1597			−1.27187			−0.635935	+	0.771742i	$0.719386\pi$
$998$		−	4.40979i		−	0.139589i
$999$	6.00000	−	0.832204i	0.189832	−	0.0263298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.d.c.164.8	yes	16
3.2	odd	2	inner	165.2.d.c.164.10	yes	16
5.2	odd	4		825.2.f.f.626.11		16
5.3	odd	4		825.2.f.f.626.6		16
5.4	even	2	inner	165.2.d.c.164.9	yes	16
11.10	odd	2	inner	165.2.d.c.164.12	yes	16
15.2	even	4		825.2.f.f.626.8		16
15.8	even	4		825.2.f.f.626.9		16
15.14	odd	2	inner	165.2.d.c.164.7	yes	16
33.32	even	2	inner	165.2.d.c.164.6	yes	16
55.32	even	4		825.2.f.f.626.7		16
55.43	even	4		825.2.f.f.626.10		16
55.54	odd	2	inner	165.2.d.c.164.5	✓	16
165.32	odd	4		825.2.f.f.626.12		16
165.98	odd	4		825.2.f.f.626.5		16
165.164	even	2	inner	165.2.d.c.164.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.d.c.164.5	✓	16	55.54	odd	2	inner
165.2.d.c.164.6	yes	16	33.32	even	2	inner
165.2.d.c.164.7	yes	16	15.14	odd	2	inner
165.2.d.c.164.8	yes	16	1.1	even	1	trivial
165.2.d.c.164.9	yes	16	5.4	even	2	inner
165.2.d.c.164.10	yes	16	3.2	odd	2	inner
165.2.d.c.164.11	yes	16	165.164	even	2	inner
165.2.d.c.164.12	yes	16	11.10	odd	2	inner
825.2.f.f.626.5		16	165.98	odd	4
825.2.f.f.626.6		16	5.3	odd	4
825.2.f.f.626.7		16	55.32	even	4
825.2.f.f.626.8		16	15.2	even	4
825.2.f.f.626.9		16	15.8	even	4
825.2.f.f.626.10		16	55.43	even	4
825.2.f.f.626.11		16	5.2	odd	4
825.2.f.f.626.12		16	165.32	odd	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.50597i q^{2} +(1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(-1.12603 - 1.93185i) q^{5} +(1.19909 - 2.31647i) q^{6} -2.12976 q^{7} -2.60842i q^{8} +(1.73205 + 2.44949i) q^{9} +O(q^{10})\)	\(q-1.50597i q^{2} +(1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(-1.12603 - 1.93185i) q^{5} +(1.19909 - 2.31647i) q^{6} -2.12976 q^{7} -2.60842i q^{8} +(1.73205 + 2.44949i) q^{9} +(-2.90931 + 1.69577i) q^{10} +(3.27598 - 0.517638i) q^{11} +(-0.412157 - 0.213348i) q^{12} +2.12976 q^{13} +3.20736i q^{14} +(-0.193862 - 3.86813i) q^{15} -4.46410 q^{16} +4.11439i q^{17} +(3.68886 - 2.60842i) q^{18} +4.63294i q^{19} +(0.301719 + 0.517638i) q^{20} +(-3.27598 - 1.69577i) q^{21} +(-0.779548 - 4.93353i) q^{22} -5.32844 q^{23} +(2.07689 - 4.01224i) q^{24} +(-2.46410 + 4.35066i) q^{25} -3.20736i q^{26} +(0.713876 + 5.14688i) q^{27} +0.570669 q^{28} -8.95015 q^{29} +(-5.82529 + 0.291950i) q^{30} +3.46410 q^{31} +1.50597i q^{32} +(5.45123 + 1.81219i) q^{33} +6.19615 q^{34} +(2.39818 + 4.11439i) q^{35} +(-0.464102 - 0.656339i) q^{36} -1.16575i q^{37} +6.97707 q^{38} +(3.27598 + 1.69577i) q^{39} +(-5.03908 + 2.93716i) q^{40} -2.39818 q^{41} +(-2.55378 + 4.93353i) q^{42} +9.50749 q^{43} +(-0.877796 + 0.138701i) q^{44} +(2.78171 - 6.10427i) q^{45} +8.02448i q^{46} +3.07638 q^{47} +(-6.86663 - 3.55443i) q^{48} -2.46410 q^{49} +(6.55196 + 3.71087i) q^{50} +(-3.27598 + 6.32871i) q^{51} -0.570669 q^{52} +4.50413 q^{53} +(7.75105 - 1.07508i) q^{54} +(-4.68886 - 5.74583i) q^{55} +5.55532i q^{56} +(-3.68886 + 7.12633i) q^{57} +13.4787i q^{58} -4.89898i q^{59} +(0.0519451 + 1.03646i) q^{60} -3.39154i q^{61} -5.21684i q^{62} +(-3.68886 - 5.21684i) q^{63} -6.66025 q^{64} +(-2.39818 - 4.11439i) q^{65} +(2.72911 - 8.20940i) q^{66} -12.3129i q^{67} -1.10245i q^{68} +(-8.19615 - 4.24264i) q^{69} +(6.19615 - 3.61160i) q^{70} +13.3843i q^{71} +(6.38929 - 4.51791i) q^{72} -2.12976 q^{73} -1.75559 q^{74} +(-7.25436 + 4.73015i) q^{75} -1.24139i q^{76} +(-6.97707 + 1.10245i) q^{77} +(2.55378 - 4.93353i) q^{78} -13.8988i q^{79} +(5.02672 + 8.62398i) q^{80} +(-3.00000 + 8.48528i) q^{81} +3.61160i q^{82} -9.33123i q^{83} +(0.877796 + 0.454381i) q^{84} +(7.94839 - 4.63294i) q^{85} -14.3180i q^{86} +(-13.7670 - 7.12633i) q^{87} +(-1.35022 - 8.54513i) q^{88} -4.62158i q^{89} +(-9.19286 - 4.18917i) q^{90} -4.53590 q^{91} +1.42775 q^{92} +(5.32844 + 2.75821i) q^{93} -4.63294i q^{94} +(8.95015 - 5.21684i) q^{95} +(-1.19909 + 2.31647i) q^{96} +1.16575i q^{97} +3.71087i q^{98} +(6.94211 + 7.12791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 16 * q - 32 * q^4	\( 16 q - 32 q^{4} - 16 q^{16} + 16 q^{25} + 16 q^{34} + 48 q^{36} + 48 q^{45} + 16 q^{49} - 16 q^{55} - 48 q^{60} + 32 q^{64} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 48 q^{81} - 128 q^{91} + 48 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 - 16 * q^16 + 16 * q^25 + 16 * q^34 + 48 * q^36 + 48 * q^45 + 16 * q^49 - 16 * q^55 - 48 * q^60 + 32 * q^64 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 48 * q^81 - 128 * q^91 + 48 * q^99

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