LMFDB - Embedded newform 165.2.d.c.164.10

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			164.10
Root			$0.473307 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	165.164
Dual form			165.2.d.c.164.5

$q$-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} +(-3.27024 - 2.07498i) 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} +(3.12486 - 4.92489i) q^{30} +3.46410 q^{31} -1.50597i q^{32} +(4.62692 - 3.40464i) 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} +(6.68240 + 0.587860i) 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} +(0.876258 + 0.555989i) 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} +(5.12730 + 6.96801i) 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} +(0.326152 - 8.65411i) 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} +(-0.885300 + 10.0635i) 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} +(-4.40622 + 8.92106i) 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	$0.178725\pi$
$2$			1.50597i			1.06488i	−0.846467	+	0.532441i	$0.821275\pi$
$3$	−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
$15$	−3.27024	−	2.07498i	−0.844372	−	0.535757i
$16$	−4.46410			−1.11603
$17$		−	4.11439i		−	0.997886i	−0.866635	−	0.498943i	$-0.833722\pi$
$17$		−	4.11439i		−	0.997886i	0.866635	−	0.498943i	$-0.166278\pi$
$18$	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	$-0.312516\pi$
$23$	5.32844			1.11106			0.555529	+	0.831497i	$0.312516\pi$
$24$	−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	$-0.187769\pi$
$29$	8.95015			1.66200			0.831000	+	0.556272i	$0.187769\pi$
$30$	3.12486	−	4.92489i	0.570518	−	0.899157i
$31$	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
$33$	4.62692	−	3.40464i	0.805444	−	0.592672i
$34$	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	$-0.440037\pi$
$41$	2.39818			0.374533			0.187267	+	0.982309i	$0.440037\pi$
$42$	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
$45$	6.68240	+	0.587860i	0.996153	+	0.0876330i
$46$			8.02448i			1.18315i
$47$	−3.07638			−0.448736			−0.224368	−	0.974505i	$-0.572032\pi$
$47$	−3.07638			−0.448736			−0.224368	+	0.974505i	$0.572032\pi$
$48$	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	$-0.600110\pi$
$53$	−4.50413			−0.618690			−0.309345	+	0.950950i	$0.600110\pi$
$54$	−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	$0.103312\pi$
$59$			4.89898i			0.637793i	−0.947790	+	0.318896i	$0.896688\pi$
$60$	0.876258	+	0.555989i	0.113124	+	0.0717778i
$61$		−	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
$66$	5.12730	+	6.96801i	0.631126	+	0.857703i
$67$		−	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	$-0.707885\pi$
$71$		−	13.3843i		−	1.58842i	0.607644	−	0.794210i	$-0.292115\pi$
$72$	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
$75$	0.326152	−	8.65411i	0.0376608	−	0.999291i
$76$		−	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	$0.171139\pi$
$83$			9.33123i			1.02424i	−0.858915	+	0.512118i	$0.828861\pi$
$84$	−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	$0.0787693\pi$
$89$			4.62158i			0.489886i	−0.969537	+	0.244943i	$0.921231\pi$
$90$	−0.885300	+	10.0635i	−0.0933189	+	1.06079i
$91$	−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
$99$	−4.40622	+	8.92106i	−0.442841	+	0.896600i
$100$	0.660254	−	1.16575i	0.0660254	−	0.116575i
$101$	−8.95015			−0.890573			−0.445286	−	0.895388i	$-0.646898\pi$
$101$	−8.95015			−0.890573			−0.445286	+	0.895388i	$0.646898\pi$
$102$	−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
$105$	6.96484	+	4.41921i	0.679699	+	0.431271i
$106$		−	6.78309i		−	0.658832i
$107$		−	1.10245i		−	0.106578i	−0.998579	−	0.0532888i	$-0.983030\pi$
$107$		−	1.10245i		−	0.106578i	0.998579	−	0.0532888i	$-0.0169704\pi$
$108$	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	$-0.332871\pi$
$113$	10.6569			1.00252			0.501258	+	0.865298i	$0.332871\pi$
$114$	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
$120$	5.41241	−	8.53015i	0.494083	−	0.778693i
$121$	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	$0.5\pi$
$132$	−1.23978	+	0.912272i	−0.107909	+	0.0794030i
$133$		−	9.86707i		−	0.855583i
$134$	18.5429			1.60186
$135$	−10.7469	+	4.41645i	−0.924942	+	0.380108i
$136$	10.7321			0.920266
$137$	2.25207			0.192407			0.0962034	−	0.995362i	$-0.469330\pi$
$137$	2.25207			0.192407			0.0962034	+	0.995362i	$0.469330\pi$
$138$	−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	$-0.281004\pi$
$149$	15.5021			1.26998			0.634991	+	0.772519i	$0.281004\pi$
$150$	13.0328	+	0.491176i	1.06413	+	0.0401044i
$151$		−	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
$165$	11.7873	+	5.10479i	0.917642	+	0.397407i
$166$	−14.0526			−1.09069
$167$			13.1502i			1.01759i	0.860886	+	0.508797i	$0.169910\pi$
$167$			13.1502i			1.01759i	−0.860886	+	0.508797i	$0.830090\pi$
$168$	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	$-0.813470\pi$
$173$		−	14.5481i		−	1.10607i	0.833158	−	0.553034i	$-0.186530\pi$
$174$	−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	$-0.743238\pi$
$179$		−	19.3185i		−	1.44393i	0.691928	−	0.721967i	$-0.256762\pi$
$180$	−1.79054	−	0.157517i	−0.133459	−	0.0117406i
$181$	−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	$0.111932\pi$
$191$			9.52056i			0.688883i	−0.938808	+	0.344442i	$0.888068\pi$
$192$	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
$195$	−6.96484	−	4.41921i	−0.498763	−	0.316466i
$196$	0.660254			0.0471610
$197$		−	7.93338i		−	0.565230i	−0.959233	−	0.282615i	$-0.908798\pi$
$197$		−	7.93338i		−	0.565230i	0.959233	−	0.282615i	$-0.0912019\pi$
$198$	−13.4349	−	6.63563i	−0.954774	−	0.471574i
$199$	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
$210$	−6.65521	+	10.4889i	−0.459253	+	0.723799i
$211$			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
$225$	6.38894	+	13.5713i	0.425929	+	0.904757i
$226$			16.0490i			1.06756i
$227$		−	9.33123i		−	0.619335i	−0.950845	−	0.309668i	$-0.899782\pi$
$227$		−	9.33123i		−	0.619335i	0.950845	−	0.309668i	$-0.100218\pi$
$228$	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
$231$	−9.85425	+	7.25109i	−0.648362	+	0.477087i
$232$			23.3457i			1.53272i
$233$		−	10.1383i		−	0.664180i	−0.943248	−	0.332090i	$-0.892246\pi$
$233$		−	10.1383i		−	0.664180i	0.943248	−	0.332090i	$-0.107754\pi$
$234$	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	$-0.674872\pi$
$239$	−16.1447			−1.04431			−0.522157	+	0.852849i	$0.674872\pi$
$240$	14.5987	+	9.26291i	0.942341	+	0.597918i
$241$			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	$0.179909\pi$
$251$			16.9706i			1.07117i	−0.844481	+	0.535586i	$0.820091\pi$
$252$	0.988427	−	1.39785i	0.0622651	−	0.0880561i
$253$	−17.4559	+	2.75821i	−1.09744	+	0.173407i
$254$		−	16.0368i		−	1.00624i
$255$	−8.53727	+	13.4550i	−0.534624	+	0.842587i
$256$	6.32051			0.395032
$257$	−29.7186			−1.85379			−0.926897	−	0.375315i	$-0.877535\pi$
$257$	−29.7186			−1.85379			−0.926897	+	0.375315i	$0.877535\pi$
$258$	−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	$0.156980\pi$
$263$			15.3551i			0.946837i	−0.880838	+	0.473418i	$0.843020\pi$
$264$	8.88074	+	12.0689i	0.546572	+	0.742792i
$265$	−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	$0.0832870\pi$
$269$			8.48528i			0.517357i	−0.965964	+	0.258678i	$0.916713\pi$
$270$	−6.65105	−	16.1845i	−0.404770	−	0.984955i
$271$			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	$-0.556401\pi$
$281$	−5.90937			−0.352523			−0.176262	+	0.984343i	$0.556401\pi$
$282$	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
$285$	9.61324	−	15.1508i	0.569439	−	0.897457i
$286$	−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	$0.0383480\pi$
$293$			4.11439i			0.240365i	−0.992752	+	0.120183i	$0.961652\pi$
$294$	2.95469	+	5.70801i	0.172321	+	0.332898i
$295$	−9.46410	+	5.51641i	−0.551021	+	0.321178i
$296$	3.04078			0.176742
$297$	−0.325577	−	17.2306i	−0.0188919	−	0.999822i
$298$			23.3457i			1.35238i
$299$	11.3483			0.656291
$300$	−0.0873923	+	2.31886i	−0.00504559	+	0.133880i
$301$	−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	$-0.863189\pi$
$311$		−	14.6969i		−	0.833387i	0.909047	−	0.416693i	$-0.136811\pi$
$312$	−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
$315$	−14.2319	−	1.25200i	−0.801879	−	0.0705424i
$316$			3.72417i			0.209501i
$317$	22.9624			1.28970			0.644848	−	0.764311i	$-0.276921\pi$
$317$	22.9624			1.28970			0.644848	+	0.764311i	$0.276921\pi$
$318$	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
$330$	−7.68766	+	17.7514i	−0.423192	+	0.977181i
$331$	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
$345$	−17.4253	−	11.0564i	−0.938146	−	0.595257i
$346$	21.9090			1.17783
$347$		−	27.4029i		−	1.47106i	−0.677490	−	0.735532i	$-0.736932\pi$
$347$		−	27.4029i		−	1.47106i	0.677490	−	0.735532i	$-0.263068\pi$
$348$	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	$-0.486030\pi$
$353$	1.64863			0.0877475			0.0438738	+	0.999037i	$0.486030\pi$
$354$	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	$-0.514752\pi$
$359$	−1.75559			−0.0926566			−0.0463283	+	0.998926i	$0.514752\pi$
$360$	−1.53339	+	17.4305i	−0.0808165	+	0.918667i
$361$	−2.46410			−0.129690
$362$		−	14.2527i		−	0.749103i
$363$	−13.3953	+	13.5486i	−0.703073	+	0.711118i
$364$	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
$375$	17.0857	−	9.11473i	0.882303	−	0.470683i
$376$		−	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	$-0.679601\pi$
$383$	−20.9312			−1.06953			−0.534767	+	0.844999i	$0.679601\pi$
$384$	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	$0.177828\pi$
$389$			20.9086i			1.06011i	−0.847964	+	0.530054i	$0.822172\pi$
$390$	6.65521	−	10.4889i	0.337000	−	0.531124i
$391$		−	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
$396$	1.18064	−	2.39039i	0.0593295	−	0.120122i
$397$			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	$0.222115\pi$
$401$			25.7332i			1.28506i	−0.766262	+	0.642528i	$0.777885\pi$
$402$	−28.5225	+	14.7643i	−1.42257	+	0.736377i
$403$	7.37772			0.367511
$404$	2.39818			0.119314
$405$	13.0142	−	15.3503i	0.646681	−	0.762760i
$406$		−	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	$0.00962991\pi$
$419$			1.23835i			0.0604973i	−0.999542	+	0.0302486i	$0.990370\pi$
$420$	−1.86622	−	1.18412i	−0.0910624	−	0.0577794i
$421$	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
$429$	9.85425	−	7.25109i	0.475768	−	0.350086i
$430$	−27.6603	+	16.1225i	−1.33390	+	0.777498i
$431$	−19.6559			−0.946791			−0.473395	−	0.880850i	$-0.656972\pi$
$431$	−19.6559			−0.946791			−0.473395	+	0.880850i	$0.656972\pi$
$432$	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
$435$	−29.2691	−	18.5714i	−1.40335	−	0.890428i
$436$		−	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	$-0.194954\pi$
$443$	34.4436			1.63646			0.818232	+	0.574888i	$0.194954\pi$
$444$	−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	$0.121062\pi$
$449$			15.7322i			0.742449i	−0.928543	+	0.371225i	$0.878938\pi$
$450$	−20.4381	+	9.62155i	−0.963459	+	0.453564i
$451$	−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	$-0.642126\pi$
$461$	−18.5429			−0.863628			−0.431814	+	0.901963i	$0.642126\pi$
$462$	−10.9199	−	14.8402i	−0.508041	−	0.690430i
$463$			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
$465$	−11.3284	−	7.18793i	−0.525344	−	0.333332i
$466$	15.2679			0.707274
$467$	−4.12157			−0.190723			−0.0953616	−	0.995443i	$-0.530401\pi$
$467$	−4.12157			−0.190723			−0.0953616	+	0.995443i	$0.530401\pi$
$468$	−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	$-0.688671\pi$
$479$	−24.4523			−1.11725			−0.558626	+	0.829420i	$0.688671\pi$
$480$	−3.12486	+	4.92489i	−0.142630	+	0.224789i
$481$		−	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	$-0.353726\pi$
$491$	19.6559			0.887058			0.443529	+	0.896260i	$0.353726\pi$
$492$	0.988427	−	0.511648i	0.0445617	−	0.0230669i
$493$		−	36.8244i		−	1.65849i
$494$	−14.8595			−0.668561
$495$	−22.1957	+	1.53324i	−0.997623	+	0.0689142i
$496$	−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	$0.194972\pi$
$503$			25.7888i			1.14987i	−0.818201	+	0.574933i	$0.805028\pi$
$504$	−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	$-0.699255\pi$
$509$		−	36.5665i		−	1.62078i	0.585890	−	0.810390i	$-0.300745\pi$
$510$	−20.2629	−	12.8569i	−0.897256	−	0.569312i
$511$	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	$-0.843177\pi$
$521$		−	21.5921i		−	0.945969i	0.881071	−	0.472984i	$-0.156823\pi$
$522$	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
$525$	−0.694628	+	18.4312i	−0.0303160	+	0.804404i
$526$	−23.1244			−1.00827
$527$		−	14.2527i		−	0.620856i
$528$	−20.6550	+	15.1987i	−0.898896	+	0.661437i
$529$	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
$540$	2.87961	−	1.18338i	0.123919	−	0.0509248i
$541$			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
$555$	−2.41891	+	3.81230i	−0.102677	+	0.161823i
$556$			4.63294i			0.196480i
$557$			4.11439i			0.174332i	0.996194	+	0.0871661i	$0.0277811\pi$
$557$			4.11439i			0.174332i	−0.996194	+	0.0871661i	$0.972219\pi$
$558$	12.7786	+	9.03583i	0.540961	+	0.382517i
$559$	20.2487			0.856429
$560$	10.7057	+	18.3671i	0.452400	+	0.776150i
$561$	−14.0080	−	19.0370i	−0.591420	−	0.803741i
$562$		−	8.89934i		−	0.375396i
$563$		−	33.4268i		−	1.40877i	−0.709818	−	0.704385i	$-0.751223\pi$
$563$		−	33.4268i		−	1.40877i	0.709818	−	0.704385i	$-0.248777\pi$
$564$	−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	$-0.483992\pi$
$569$	2.39818			0.100537			0.0502686	+	0.998736i	$0.483992\pi$
$570$	22.8167	+	14.4773i	0.955686	+	0.606386i
$571$			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
$585$	14.2319	+	1.25200i	0.588418	+	0.0517640i
$586$	−6.19615			−0.255961
$587$	−8.62570			−0.356021			−0.178010	−	0.984029i	$-0.556966\pi$
$587$	−8.62570			−0.356021			−0.178010	+	0.984029i	$0.556966\pi$
$588$	−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	$0.0775757\pi$
$593$			11.7524i			0.482612i	−0.970449	+	0.241306i	$0.922424\pi$
$594$	25.9488	−	0.490310i	1.06469	−	0.0201177i
$595$	−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	$-0.880094\pi$
$599$		−	18.0058i		−	0.735699i	0.929885	−	0.367849i	$-0.119906\pi$
$600$	22.5735	+	0.850742i	0.921561	+	0.0347314i
$601$			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
$615$	−7.84264	−	4.97618i	−0.316246	−	0.200659i
$616$	2.87564	+	18.1991i	0.115863	+	0.733263i
$617$	−11.0986			−0.446814			−0.223407	−	0.974725i	$-0.571718\pi$
$617$	−11.0986			−0.446814			−0.223407	+	0.974725i	$0.571718\pi$
$618$	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
$627$	15.7735	+	21.4362i	0.629933	+	0.856081i
$628$		−	2.33151i		−	0.0930373i
$629$	−4.79637			−0.191244
$630$	1.88548	−	21.4329i	0.0751194	−	0.853906i
$631$	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	$-0.979185\pi$
$641$		−	3.30890i		−	0.130694i	0.997863	−	0.0653469i	$-0.0208154\pi$
$642$	−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
$645$	−31.0918	−	19.7278i	−1.22424	−	0.776782i
$646$			28.7064i			1.12944i
$647$	11.9229			0.468739			0.234370	−	0.972148i	$-0.424697\pi$
$647$	11.9229			0.468739			0.234370	+	0.972148i	$0.424697\pi$
$648$	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	$-0.386400\pi$
$653$	17.8548			0.698713			0.349357	+	0.936990i	$0.386400\pi$
$654$	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	$-0.636931\pi$
$659$	−21.4115			−0.834073			−0.417036	+	0.908890i	$0.636931\pi$
$660$	−3.15841	−	1.36782i	−0.122941	−	0.0532424i
$661$	−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
$675$	−20.6332	−	15.7883i	−0.794174	−	0.607691i
$676$	2.26795			0.0872288
$677$		−	13.9573i		−	0.536421i	−0.963360	−	0.268211i	$-0.913568\pi$
$677$		−	13.9573i		−	0.536421i	0.963360	−	0.268211i	$-0.0864323\pi$
$678$	−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	$-0.450951\pi$
$683$	8.02226			0.306963			0.153482	+	0.988152i	$0.450951\pi$
$684$	−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
$690$	16.6506	−	26.2420i	0.633878	−	0.999015i
$691$	−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
$693$	9.38420	−	18.9998i	0.356476	−	0.721741i
$694$	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	$-0.616903\pi$
$701$	−19.0133			−0.718122			−0.359061	+	0.933314i	$0.616903\pi$
$702$	−16.5079	−	2.28966i	−0.623051	−	0.0864177i
$703$	5.40087			0.203698
$704$	21.8189	−	3.44760i	0.822329	−	0.129936i
$705$	10.0605	+	6.38342i	0.378900	+	0.240413i
$706$			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	$-0.961390\pi$
$719$		−	6.48906i		−	0.242001i	0.992652	−	0.121001i	$-0.0386103\pi$
$720$	−29.8309	−	2.62427i	−1.11173	−	0.0978007i
$721$		−	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
$726$	−20.4038	−	20.1730i	−0.757257	−	0.748690i
$727$		−	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
$735$	8.05820	+	5.11296i	0.297231	+	0.188594i
$736$		−	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	$0.114401\pi$
$743$			19.1741i			0.703430i	−0.936107	+	0.351715i	$0.885599\pi$
$744$	−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
$750$	13.7265	+	25.7306i	0.501222	+	0.939548i
$751$	−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
$759$	24.6543	−	18.1415i	0.894894	−	0.658493i
$760$	−13.6077	−	23.3457i	−0.493603	−	0.846839i
$761$	49.5471			1.79608			0.898040	−	0.439913i	$-0.144991\pi$
$761$	49.5471			1.79608			0.898040	+	0.439913i	$0.144991\pi$
$762$	12.7689	+	24.6677i	0.462569	+	0.893615i
$763$		−	26.9573i		−	0.975921i
$764$		−	2.55103i		−	0.0922929i
$765$	2.41869	−	27.4940i	0.0874478	−	0.994047i
$766$		−	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	$-0.660489\pi$
$773$	−26.8631			−0.966198			−0.483099	+	0.875566i	$0.660489\pi$
$774$	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
$780$	1.86622	+	1.18412i	0.0668215	+	0.0423985i
$781$	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
$792$	−23.2699	−	11.4933i	−0.826858	−	0.408395i
$793$		−	7.22319i		−	0.256503i
$794$	−7.83714			−0.278130
$795$	14.7296	+	9.34597i	0.522405	+	0.331467i
$796$	−2.92820			−0.103787
$797$	−35.2679			−1.24925			−0.624627	−	0.780923i	$-0.714749\pi$
$797$	−35.2679			−1.24925			−0.624627	+	0.780923i	$0.714749\pi$
$798$	−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	$-0.456979\pi$
$809$	7.66496			0.269486			0.134743	+	0.990881i	$0.456979\pi$
$810$	23.1170	+	19.5990i	0.812250	+	0.688639i
$811$		−	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	$-0.759477\pi$
$821$	−41.7100			−1.45569			−0.727844	+	0.685743i	$0.759477\pi$
$822$	−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
$825$	3.41123	+	28.5195i	0.118764	+	0.992923i
$826$	15.7128			0.546719
$827$			40.0415i			1.39238i	0.717859	+	0.696189i	$0.245122\pi$
$827$			40.0415i			1.39238i	−0.717859	+	0.696189i	$0.754878\pi$
$828$	−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	$0.167153\pi$
$839$			29.0421i			1.00265i	−0.865260	+	0.501323i	$0.832847\pi$
$840$	−11.5272	+	18.1672i	−0.397725	+	0.626829i
$841$	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
$855$	−2.72352	+	30.9591i	−0.0931424	+	1.05878i
$856$	2.87564			0.0982875
$857$		−	34.8246i		−	1.18959i	−0.803879	−	0.594793i	$-0.797234\pi$
$857$		−	34.8246i		−	1.18959i	0.803879	−	0.594793i	$-0.202766\pi$
$858$	10.9199	+	14.8402i	0.372800	+	0.506637i
$859$	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	$-0.522348\pi$
$863$	−4.12157			−0.140300			−0.0701499	+	0.997536i	$0.522348\pi$
$864$	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
$870$	27.9679	−	44.0785i	0.948201	−	1.49440i
$871$		−	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	$0.0314726\pi$
$881$			5.85993i			0.197426i	−0.995116	+	0.0987130i	$0.968527\pi$
$882$	−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
$885$	10.1653	−	16.0208i	0.341702	−	0.538535i
$886$			51.8711i			1.74264i
$887$		−	9.33123i		−	0.313312i	−0.987653	−	0.156656i	$-0.949929\pi$
$887$		−	9.33123i		−	0.313312i	0.987653	−	0.156656i	$-0.0500714\pi$
$888$	−4.67729	+	2.42114i	−0.156960	+	0.0812482i
$889$	22.6795			0.760646
$890$	−7.83714	−	13.4456i	−0.262702	−	0.450698i
$891$	14.2202	+	26.2447i	0.476396	+	0.879231i
$892$			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
$900$	−1.71191	−	3.63643i	−0.0570637	−	0.121214i
$901$			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	$-0.656004\pi$
$911$		−	53.2596i		−	1.76457i	0.470715	−	0.882285i	$-0.343996\pi$
$912$	16.4675	+	31.8127i	0.545292	+	1.05342i
$913$	−4.83020	−	30.5689i	−0.159856	−	1.01168i
$914$			4.92619i			0.162944i
$915$	−7.03738	+	11.0912i	−0.232649	+	0.366663i
$916$	−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
$924$	2.64044	−	1.94292i	0.0868641	−	0.0639175i
$925$	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	$-0.960610\pi$
$929$		−	7.52433i		−	0.246865i	0.992353	−	0.123433i	$-0.0393903\pi$
$930$	10.8248	−	17.0603i	0.354960	−	0.559430i
$931$		−	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	$-0.375780\pi$
$941$	23.3393			0.760838			0.380419	+	0.924814i	$0.375780\pi$
$942$	20.1563	−	10.4337i	0.656728	−	0.339947i
$943$	12.7786			0.416128
$944$		−	21.8695i		−	0.711793i
$945$	22.8883	−	9.40601i	0.744556	−	0.305977i
$946$	−7.41154	−	46.9055i	−0.240970	−	1.52503i
$947$	−39.5512			−1.28524			−0.642620	−	0.766185i	$-0.722153\pi$
$947$	−39.5512			−1.28524			−0.642620	+	0.766185i	$0.722153\pi$
$948$	−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	$-0.822819\pi$
$953$		−	32.6197i		−	1.05666i	0.849040	−	0.528328i	$-0.177181\pi$
$954$	−16.6151	−	11.7487i	−0.537934	−	0.380377i
$955$	−18.3923	+	10.7205i	−0.595161	+	0.346906i
$956$	4.32596			0.139912
$957$	41.4116	−	30.4721i	1.33865	−	0.985022i
$958$		−	36.8244i		−	1.18974i
$959$	−4.79637			−0.154883
$960$	21.7806	+	13.8199i	0.702967	+	0.446035i
$961$	−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	$-0.930714\pi$
$971$		−	13.4586i		−	0.431907i	0.976404	−	0.215953i	$-0.0692859\pi$
$972$	−3.04679	−	2.85722i	−0.0977257	−	0.0916454i
$973$			36.8244i			1.18054i
$974$	48.2619			1.54641
$975$	0.694628	−	18.4312i	0.0222459	−	0.590271i
$976$			15.1402i			0.484626i
$977$	20.2686			0.648449			0.324225	−	0.945980i	$-0.394897\pi$
$977$	20.2686			0.648449			0.324225	+	0.945980i	$0.394897\pi$
$978$	−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	$-0.582051\pi$
$983$	−15.9853			−0.509853			−0.254926	+	0.966960i	$0.582051\pi$
$984$	−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
$990$	−2.30902	−	33.4261i	−0.0733855	−	1.06235i
$991$	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.164.10	yes	16
3.2	odd	2	inner	165.2.d.c.164.8	yes	16
5.2	odd	4		825.2.f.f.626.8		16
5.3	odd	4		825.2.f.f.626.9		16
5.4	even	2	inner	165.2.d.c.164.7	yes	16
11.10	odd	2	inner	165.2.d.c.164.6	yes	16
15.2	even	4		825.2.f.f.626.11		16
15.8	even	4		825.2.f.f.626.6		16
15.14	odd	2	inner	165.2.d.c.164.9	yes	16
33.32	even	2	inner	165.2.d.c.164.12	yes	16
55.32	even	4		825.2.f.f.626.12		16
55.43	even	4		825.2.f.f.626.5		16
55.54	odd	2	inner	165.2.d.c.164.11	yes	16
165.32	odd	4		825.2.f.f.626.7		16
165.98	odd	4		825.2.f.f.626.10		16
165.164	even	2	inner	165.2.d.c.164.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.d.c.164.5	✓	16	165.164	even	2	inner
165.2.d.c.164.6	yes	16	11.10	odd	2	inner
165.2.d.c.164.7	yes	16	5.4	even	2	inner
165.2.d.c.164.8	yes	16	3.2	odd	2	inner
165.2.d.c.164.9	yes	16	15.14	odd	2	inner
165.2.d.c.164.10	yes	16	1.1	even	1	trivial
165.2.d.c.164.11	yes	16	55.54	odd	2	inner
165.2.d.c.164.12	yes	16	33.32	even	2	inner
825.2.f.f.626.5		16	55.43	even	4
825.2.f.f.626.6		16	15.8	even	4
825.2.f.f.626.7		16	165.32	odd	4
825.2.f.f.626.8		16	5.2	odd	4
825.2.f.f.626.9		16	5.3	odd	4
825.2.f.f.626.10		16	165.98	odd	4
825.2.f.f.626.11		16	15.2	even	4
825.2.f.f.626.12		16	55.32	even	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} +(-3.27024 - 2.07498i) 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} +(3.12486 - 4.92489i) q^{30} +3.46410 q^{31} -1.50597i q^{32} +(4.62692 - 3.40464i) 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} +(6.68240 + 0.587860i) 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} +(0.876258 + 0.555989i) 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} +(5.12730 + 6.96801i) 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} +(0.326152 - 8.65411i) 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} +(-0.885300 + 10.0635i) 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} +(-4.40622 + 8.92106i) 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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