LMFDB - Embedded newform 342.2.bb.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(53,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

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

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

chi := DirichletCharacter("342.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	342.89
Dual form			342.2.bb.a.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.92710 + 0.692454i) q^{5} +(-2.50404 + 4.33713i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.92710 + 0.692454i) q^{5} +(-2.50404 + 4.33713i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.56323 + 3.05474i) q^{10} +(-2.02419 + 1.16867i) q^{11} +(-0.706340 - 1.94065i) q^{13} +(0.869644 + 4.93200i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-2.08230 - 2.48159i) q^{17} +(3.25836 + 2.89536i) q^{19} +3.98768i q^{20} +(-0.799415 + 2.19638i) q^{22} +(0.0315583 + 0.00556458i) q^{23} +(10.2442 - 3.72857i) q^{25} +(-1.78852 - 1.03260i) q^{26} +(3.83641 + 3.21913i) q^{28} +(0.785032 + 0.658720i) q^{29} +(-5.59541 - 3.23051i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.19026 - 0.562530i) q^{34} +(6.83036 - 18.7663i) q^{35} +8.00812i q^{37} +(4.35715 + 0.123539i) q^{38} +(2.56323 + 3.05474i) q^{40} +(-5.39082 - 1.96210i) q^{41} +(0.852842 + 4.83671i) q^{43} +(0.799415 + 2.19638i) q^{44} +(0.0277519 - 0.0160226i) q^{46} +(0.996549 - 1.18764i) q^{47} +(-9.04044 - 15.6585i) q^{49} +(5.45080 - 9.44107i) q^{50} +(-2.03382 + 0.358618i) q^{52} +(-2.46843 + 13.9991i) q^{53} +(7.13995 - 5.99113i) q^{55} +5.00808 q^{56} +1.02479 q^{58} +(-1.23268 + 1.03435i) q^{59} +(0.304819 - 1.72872i) q^{61} +(-6.36286 + 1.12194i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(4.11768 + 7.13203i) q^{65} +(-2.98171 + 3.55346i) q^{67} +(-2.80547 + 1.61974i) q^{68} +(-6.83036 - 18.7663i) q^{70} +(2.43294 + 13.7979i) q^{71} +(-5.33798 - 1.94287i) q^{73} +(5.14752 + 6.13457i) q^{74} +(3.41718 - 2.70608i) q^{76} -11.7056i q^{77} +(3.77857 - 10.3815i) q^{79} +(3.92710 + 0.692454i) q^{80} +(-5.39082 + 1.96210i) q^{82} +(6.97592 + 4.02755i) q^{83} +(9.89577 + 8.30354i) q^{85} +(3.76229 + 3.15694i) q^{86} +(2.02419 + 1.16867i) q^{88} +(7.45714 - 2.71418i) q^{89} +(10.1856 + 1.79599i) q^{91} +(0.0109601 - 0.0301126i) q^{92} -1.55035i q^{94} +(-14.8008 - 9.11409i) q^{95} +(-7.98070 - 9.51103i) q^{97} +(-16.9905 - 6.18402i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{8}+O(q^{10}) $ 24 * q - 12 * q^8	$ 24 q - 12 q^{8} - 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} - 36 q^{26} + 12 q^{29} + 12 q^{34} + 48 q^{35} + 12 q^{38} + 12 q^{41} - 12 q^{44} - 36 q^{46} - 60 q^{47} - 36 q^{49} + 24 q^{50} + 48 q^{53} - 60 q^{55} - 24 q^{58} - 24 q^{59} - 60 q^{61} - 24 q^{62} - 12 q^{64} + 24 q^{65} - 48 q^{70} + 36 q^{71} + 24 q^{79} + 12 q^{82} - 72 q^{83} + 36 q^{86} + 120 q^{89} - 24 q^{91} - 12 q^{95}+O(q^{100}) $ 24 * q - 12 * q^8 - 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 - 36 * q^26 + 12 * q^29 + 12 * q^34 + 48 * q^35 + 12 * q^38 + 12 * q^41 - 12 * q^44 - 36 * q^46 - 60 * q^47 - 36 * q^49 + 24 * q^50 + 48 * q^53 - 60 * q^55 - 24 * q^58 - 24 * q^59 - 60 * q^61 - 24 * q^62 - 12 * q^64 + 24 * q^65 - 48 * q^70 + 36 * q^71 + 24 * q^79 + 12 * q^82 - 72 * q^83 + 36 * q^86 + 120 * q^89 - 24 * q^91 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−3.92710	+	0.692454i	−1.75625	+	0.309675i	−0.956733	−	0.290966i	$-0.906023\pi$
$5$	−3.92710	+	0.692454i	−1.75625	+	0.309675i	−0.799519	+	0.600641i	$0.794912\pi$
$6$		0			0
$7$	−2.50404	+	4.33713i	−0.946438	+	1.63928i	−0.193593	+	0.981082i	$0.562014\pi$
$7$	−2.50404	+	4.33713i	−0.946438	+	1.63928i	−0.752846	+	0.658197i	$0.771319\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−2.56323	+	3.05474i	−0.810565	+	0.965994i
$11$	−2.02419	+	1.16867i	−0.610316	+	0.352366i	−0.773089	−	0.634297i	$-0.781290\pi$
$11$	−2.02419	+	1.16867i	−0.610316	+	0.352366i	0.162773	+	0.986664i	$0.447956\pi$
$12$		0			0
$13$	−0.706340	−	1.94065i	−0.195903	−	0.538240i	0.802380	−	0.596814i	$-0.203567\pi$
$13$	−0.706340	−	1.94065i	−0.195903	−	0.538240i	−0.998283	+	0.0585737i	$0.981345\pi$
$14$	0.869644	+	4.93200i	0.232422	+	1.31813i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.08230	−	2.48159i	−0.505031	−	0.601873i	0.451943	−	0.892047i	$-0.350731\pi$
$17$	−2.08230	−	2.48159i	−0.505031	−	0.601873i	−0.956974	+	0.290174i	$0.906287\pi$
$18$		0			0
$19$	3.25836	+	2.89536i	0.747519	+	0.664241i
$19$	3.25836	+	2.89536i	0.747519	+	0.664241i
$20$			3.98768i			0.891673i
$21$		0			0
$22$	−0.799415	+	2.19638i	−0.170436	+	0.468269i
$23$	0.0315583	+	0.00556458i	0.00658036	+	0.00116029i	0.176937	−	0.984222i	$-0.443381\pi$
$23$	0.0315583	+	0.00556458i	0.00658036	+	0.00116029i	−0.170357	+	0.985382i	$0.554492\pi$
$24$		0			0
$25$	10.2442	−	3.72857i	2.04883	−	0.745714i
$26$	−1.78852	−	1.03260i	−0.350757	−	0.202509i
$27$		0			0
$28$	3.83641	+	3.21913i	0.725014	+	0.608359i
$29$	0.785032	+	0.658720i	0.145777	+	0.122321i	0.712760	−	0.701408i	$-0.247445\pi$
$29$	0.785032	+	0.658720i	0.145777	+	0.122321i	−0.566983	+	0.823730i	$0.691889\pi$
$30$		0			0
$31$	−5.59541	−	3.23051i	−1.00496	−	0.580217i	−0.0952513	−	0.995453i	$-0.530365\pi$
$31$	−5.59541	−	3.23051i	−1.00496	−	0.580217i	−0.909713	+	0.415237i	$0.863699\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$		0			0
$34$	−3.19026	−	0.562530i	−0.547126	−	0.0964730i
$35$	6.83036	−	18.7663i	1.15454	−	3.17208i
$36$		0			0
$37$			8.00812i			1.31653i	0.752788	+	0.658263i	$0.228709\pi$
$37$			8.00812i			1.31653i	−0.752788	+	0.658263i	$0.771291\pi$
$38$	4.35715	+	0.123539i	0.706823	+	0.0200407i
$39$		0			0
$40$	2.56323	+	3.05474i	0.405283	+	0.482997i
$41$	−5.39082	−	1.96210i	−0.841905	−	0.306428i	−0.115169	−	0.993346i	$-0.536741\pi$
$41$	−5.39082	−	1.96210i	−0.841905	−	0.306428i	−0.726735	+	0.686918i	$0.758963\pi$
$42$		0			0
$43$	0.852842	+	4.83671i	0.130057	+	0.737591i	0.978175	+	0.207783i	$0.0666248\pi$
$43$	0.852842	+	4.83671i	0.130057	+	0.737591i	−0.848118	+	0.529808i	$0.822264\pi$
$44$	0.799415	+	2.19638i	0.120516	+	0.331116i
$45$		0			0
$46$	0.0277519	−	0.0160226i	0.00409179	−	0.00236240i
$47$	0.996549	−	1.18764i	0.145362	−	0.173235i	−0.688451	−	0.725283i	$-0.741709\pi$
$47$	0.996549	−	1.18764i	0.145362	−	0.173235i	0.833813	+	0.552048i	$0.186153\pi$
$48$		0			0
$49$	−9.04044	−	15.6585i	−1.29149	−	2.23693i
$50$	5.45080	−	9.44107i	0.770860	−	1.33517i
$51$		0			0
$52$	−2.03382	+	0.358618i	−0.282041	+	0.0497314i
$53$	−2.46843	+	13.9991i	−0.339064	+	1.92293i	0.0436161	+	0.999048i	$0.486112\pi$
$53$	−2.46843	+	13.9991i	−0.339064	+	1.92293i	−0.382680	+	0.923881i	$0.624999\pi$
$54$		0			0
$55$	7.13995	−	5.99113i	0.962751	−	0.807844i
$56$	5.00808			0.669233
$57$		0			0
$58$	1.02479			0.134561
$59$	−1.23268	+	1.03435i	−0.160482	+	0.134660i	−0.719492	−	0.694500i	$-0.755626\pi$
$59$	−1.23268	+	1.03435i	−0.160482	+	0.134660i	0.559011	+	0.829160i	$0.311181\pi$
$60$		0			0
$61$	0.304819	−	1.72872i	0.0390281	−	0.221339i	−0.959056	−	0.283218i	$-0.908598\pi$
$61$	0.304819	−	1.72872i	0.0390281	−	0.221339i	0.998084	+	0.0618785i	$0.0197091\pi$
$62$	−6.36286	+	1.12194i	−0.808084	+	0.142487i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	4.11768	+	7.13203i	0.510735	+	0.884620i
$66$		0			0
$67$	−2.98171	+	3.55346i	−0.364274	+	0.434125i	−0.916785	−	0.399381i	$-0.869225\pi$
$67$	−2.98171	+	3.55346i	−0.364274	+	0.434125i	0.552511	+	0.833505i	$0.313670\pi$
$68$	−2.80547	+	1.61974i	−0.340213	+	0.196422i
$69$		0			0
$70$	−6.83036	−	18.7663i	−0.816384	−	2.24300i
$71$	2.43294	+	13.7979i	0.288737	+	1.63751i	0.691623	+	0.722259i	$0.256896\pi$
$71$	2.43294	+	13.7979i	0.288737	+	1.63751i	−0.402886	+	0.915250i	$0.631993\pi$
$72$		0			0
$73$	−5.33798	−	1.94287i	−0.624764	−	0.227395i	0.0101870	−	0.999948i	$-0.496757\pi$
$73$	−5.33798	−	1.94287i	−0.624764	−	0.227395i	−0.634951	+	0.772553i	$0.718980\pi$
$74$	5.14752	+	6.13457i	0.598387	+	0.713130i
$75$		0			0
$76$	3.41718	−	2.70608i	0.391977	−	0.310409i
$77$		−	11.7056i		−	1.33397i
$78$		0			0
$79$	3.77857	−	10.3815i	0.425122	−	1.16801i	−0.523617	−	0.851954i	$-0.675418\pi$
$79$	3.77857	−	10.3815i	0.425122	−	1.16801i	0.948739	−	0.316060i	$-0.102360\pi$
$80$	3.92710	+	0.692454i	0.439063	+	0.0774187i
$81$		0			0
$82$	−5.39082	+	1.96210i	−0.595316	+	0.216677i
$83$	6.97592	+	4.02755i	0.765707	+	0.442081i	0.831341	−	0.555763i	$-0.187574\pi$
$83$	6.97592	+	4.02755i	0.765707	+	0.442081i	−0.0656343	+	0.997844i	$0.520907\pi$
$84$		0			0
$85$	9.89577	+	8.30354i	1.07335	+	0.900645i
$86$	3.76229	+	3.15694i	0.405698	+	0.340421i
$87$		0			0
$88$	2.02419	+	1.16867i	0.215779	+	0.124580i
$89$	7.45714	−	2.71418i	0.790456	−	0.287702i	0.0849302	−	0.996387i	$-0.472933\pi$
$89$	7.45714	−	2.71418i	0.790456	−	0.287702i	0.705525	+	0.708685i	$0.250711\pi$
$90$		0			0
$91$	10.1856	+	1.79599i	1.06774	+	0.188271i
$92$	0.0109601	−	0.0301126i	0.00114267	−	0.00313945i
$93$		0			0
$94$		−	1.55035i		−	0.159907i
$95$	−14.8008	−	9.11409i	−1.51853	−	0.935086i
$96$		0			0
$97$	−7.98070	−	9.51103i	−0.810317	−	0.965698i	0.189552	−	0.981871i	$-0.439296\pi$
$97$	−7.98070	−	9.51103i	−0.810317	−	0.965698i	−0.999869	+	0.0161722i	$0.994852\pi$
$98$	−16.9905	−	6.18402i	−1.71630	−	0.624681i
$99$		0			0
$100$	−1.89304	−	10.7360i	−0.189304	−	1.07360i
$101$	0.400217	+	1.09959i	0.0398231	+	0.109413i	0.958010	−	0.286734i	$-0.0925694\pi$
$101$	0.400217	+	1.09959i	0.0398231	+	0.109413i	−0.918187	+	0.396147i	$0.870347\pi$
$102$		0			0
$103$	1.51184	−	0.872859i	0.148966	−	0.0860053i	−0.423665	−	0.905819i	$-0.639256\pi$
$103$	1.51184	−	0.872859i	0.148966	−	0.0860053i	0.572630	+	0.819814i	$0.305923\pi$
$104$	−1.32748	+	1.58203i	−0.130171	+	0.155131i
$105$		0			0
$106$	7.10755	+	12.3106i	0.690346	+	1.19571i
$107$	3.96843	−	6.87351i	0.383642	−	0.664488i	−0.607938	−	0.793985i	$-0.708003\pi$
$107$	3.96843	−	6.87351i	0.383642	−	0.664488i	0.991580	+	0.129497i	$0.0413363\pi$
$108$		0			0
$109$	−16.0271	+	2.82600i	−1.53511	+	0.270682i	−0.876352	−	0.481671i	$-0.840030\pi$
$109$	−16.0271	+	2.82600i	−1.53511	+	0.270682i	−0.658761	+	0.752352i	$0.728919\pi$
$110$	1.61850	−	9.17894i	0.154317	−	0.875178i
$111$		0			0
$112$	3.83641	−	3.21913i	0.362507	−	0.304179i
$113$	10.0738			0.947667			0.473834	−	0.880614i	$-0.342870\pi$
$113$	10.0738			0.947667			0.473834	+	0.880614i	$0.342870\pi$
$114$		0			0
$115$	−0.127786			−0.0119161
$116$	0.785032	−	0.658720i	0.0728884	−	0.0611607i
$117$		0			0
$118$	−0.279427	+	1.58471i	−0.0257233	+	0.145884i
$119$	15.9771	−	2.81719i	1.46462	−	0.258252i
$120$		0			0
$121$	−2.76844	+	4.79507i	−0.251676	+	0.435916i
$122$	−0.877692	−	1.52021i	−0.0794625	−	0.137633i
$123$		0			0
$124$	−4.15306	+	4.94943i	−0.372956	+	0.444472i
$125$	−20.3808	+	11.7669i	−1.82291	+	1.05246i
$126$		0			0
$127$	0.186220	+	0.511636i	0.0165244	+	0.0454004i	0.947681	−	0.319220i	$-0.103421\pi$
$127$	0.186220	+	0.511636i	0.0165244	+	0.0454004i	−0.931156	+	0.364621i	$0.881199\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$		0			0
$130$	7.73871	+	2.81666i	0.678729	+	0.247037i
$131$	6.17180	+	7.35526i	0.539232	+	0.642632i	0.965015	−	0.262193i	$-0.0844458\pi$
$131$	6.17180	+	7.35526i	0.539232	+	0.642632i	−0.425783	+	0.904825i	$0.640001\pi$
$132$		0			0
$133$	−20.7166	+	6.88182i	−1.79636	+	0.596730i
$134$			4.63872i			0.400724i
$135$		0			0
$136$	−1.10797	+	3.04411i	−0.0950074	+	0.261031i
$137$	−10.3988	−	1.83360i	−0.888433	−	0.156655i	−0.289238	−	0.957257i	$-0.593402\pi$
$137$	−10.3988	−	1.83360i	−0.888433	−	0.156655i	−0.599196	+	0.800603i	$0.704513\pi$
$138$		0			0
$139$	8.25070	−	3.00301i	0.699816	−	0.254712i	0.0324834	−	0.999472i	$-0.489658\pi$
$139$	8.25070	−	3.00301i	0.699816	−	0.254712i	0.667332	+	0.744760i	$0.267436\pi$
$140$	−17.2951	−	9.98532i	−1.46170	−	0.843913i
$141$		0			0
$142$	10.7329	+	9.00594i	0.900681	+	0.755762i
$143$	3.69774	+	3.10277i	0.309221	+	0.259467i
$144$		0			0
$145$	−3.53903	−	2.04326i	−0.293901	−	0.169684i
$146$	−5.33798	+	1.94287i	−0.441775	+	0.160793i
$147$		0			0
$148$	7.88646	+	1.39059i	0.648263	+	0.114306i
$149$	−1.70895	+	4.69529i	−0.140002	+	0.384653i	−0.989802	−	0.142453i	$-0.954501\pi$
$149$	−1.70895	+	4.69529i	−0.140002	+	0.384653i	0.849799	+	0.527107i	$0.176723\pi$
$150$		0			0
$151$		−	0.775944i		−	0.0631454i	−0.999501	−	0.0315727i	$-0.989948\pi$
$151$		−	0.775944i		−	0.0631454i	0.999501	−	0.0315727i	$-0.0100516\pi$
$152$	0.878273	−	4.26950i	0.0712374	−	0.346302i
$153$		0			0
$154$	−7.52419	−	8.96698i	−0.606316	−	0.722579i
$155$	24.2107	+	8.81197i	1.94465	+	0.707795i
$156$		0			0
$157$	−0.0711800	−	0.403682i	−0.00568078	−	0.0322173i	0.981836	−	0.189734i	$-0.0607624\pi$
$157$	−0.0711800	−	0.403682i	−0.00568078	−	0.0322173i	−0.987516	+	0.157516i	$0.949651\pi$
$158$	−3.77857	−	10.3815i	−0.300607	−	0.825911i
$159$		0			0
$160$	3.45343	−	1.99384i	0.273018	−	0.157627i
$161$	−0.103157	+	0.122938i	−0.00812995	+	0.00968890i
$162$		0			0
$163$	5.58055	+	9.66580i	0.437103	+	0.757084i	0.997465	−	0.0711637i	$-0.0226713\pi$
$163$	5.58055	+	9.66580i	0.437103	+	0.757084i	−0.560362	+	0.828248i	$0.689338\pi$
$164$	−2.86840	+	4.96821i	−0.223984	+	0.387952i
$165$		0			0
$166$	7.93272	−	1.39875i	0.615699	−	0.108564i
$167$	−3.31449	+	18.7974i	−0.256483	+	1.45459i	0.535753	+	0.844375i	$0.320028\pi$
$167$	−3.31449	+	18.7974i	−0.256483	+	1.45459i	−0.792236	+	0.610214i	$0.791083\pi$
$168$		0			0
$169$	6.69136	−	5.61472i	0.514720	−	0.431901i
$170$	12.9180			0.990766
$171$		0			0
$172$	4.91132			0.374485
$173$	−13.8073	+	11.5857i	−1.04975	+	0.880847i	−0.993068	−	0.117545i	$-0.962498\pi$
$173$	−13.8073	+	11.5857i	−1.04975	+	0.880847i	−0.0566854	+	0.998392i	$0.518053\pi$
$174$		0			0
$175$	−9.48052	+	53.7667i	−0.716660	+	4.06438i
$176$	2.30182	−	0.405874i	0.173507	−	0.0305939i
$177$		0			0
$178$	3.96786	−	6.87254i	0.297404	−	0.515119i
$179$	−4.43515	−	7.68190i	−0.331499	−	0.574172i	0.651307	−	0.758814i	$-0.274221\pi$
$179$	−4.43515	−	7.68190i	−0.331499	−	0.574172i	−0.982806	+	0.184642i	$0.940888\pi$
$180$		0			0
$181$	0.0867092	−	0.103336i	0.00644504	−	0.00768090i	−0.762812	−	0.646620i	$-0.776182\pi$
$181$	0.0867092	−	0.103336i	0.00644504	−	0.00768090i	0.769257	+	0.638939i	$0.220626\pi$
$182$	8.95703	−	5.17134i	0.663939	−	0.383325i
$183$		0			0
$184$	−0.0109601	−	0.0301126i	−0.000807988	−	0.00221993i
$185$	−5.54525	−	31.4487i	−0.407695	−	2.31215i
$186$		0			0
$187$	7.11511	+	2.58969i	0.520309	+	0.189377i
$188$	−0.996549	−	1.18764i	−0.0726808	−	0.0866176i
$189$		0			0
$190$	−17.1965	+	2.53197i	−1.24757	+	0.183689i
$191$		−	9.83242i		−	0.711449i	−0.934591	−	0.355724i	$-0.884234\pi$
$191$		−	9.83242i		−	0.711449i	0.934591	−	0.355724i	$-0.115766\pi$
$192$		0			0
$193$	−5.13511	+	14.1086i	−0.369633	+	1.01556i	0.605868	+	0.795565i	$0.292826\pi$
$193$	−5.13511	+	14.1086i	−0.369633	+	1.01556i	−0.975501	+	0.219993i	$0.929396\pi$
$194$	−12.2271	−	2.15597i	−0.877858	−	0.154790i
$195$		0			0
$196$	−16.9905	+	6.18402i	−1.21360	+	0.441716i
$197$	−0.994125	−	0.573958i	−0.0708285	−	0.0408928i	0.464168	−	0.885747i	$-0.346354\pi$
$197$	−0.994125	−	0.573958i	−0.0708285	−	0.0408928i	−0.534996	+	0.844855i	$0.679687\pi$
$198$		0			0
$199$	4.65010	+	3.90189i	0.329637	+	0.276598i	0.792552	−	0.609805i	$-0.208752\pi$
$199$	4.65010	+	3.90189i	0.329637	+	0.276598i	−0.462915	+	0.886403i	$0.653197\pi$
$200$	−8.35112	−	7.00742i	−0.590513	−	0.495499i
$201$		0			0
$202$	1.01338	+	0.585078i	0.0713015	+	0.0411659i
$203$	−4.82271	+	1.75532i	−0.338488	+	0.123199i
$204$		0			0
$205$	22.5289	+	3.97246i	1.57349	+	0.277449i
$206$	0.597071	−	1.64044i	0.0415999	−	0.114295i
$207$		0			0
$208$			2.06520i			0.143196i
$209$	−9.97925	−	2.05282i	−0.690279	−	0.141996i
$210$		0			0
$211$	−6.33447	−	7.54912i	−0.436083	−	0.519703i	0.502584	−	0.864528i	$-0.332383\pi$
$211$	−6.33447	−	7.54912i	−0.436083	−	0.519703i	−0.938667	+	0.344825i	$0.887938\pi$
$212$	13.3578	+	4.86185i	0.917419	+	0.333913i
$213$		0			0
$214$	−1.37822	−	7.81627i	−0.0942132	−	0.534309i
$215$	−6.69839	−	18.4037i	−0.456827	−	1.25512i
$216$		0			0
$217$	28.0222	−	16.1787i	1.90227	−	1.09828i
$218$	−10.4609	+	12.4668i	−0.708503	+	0.844361i
$219$		0			0
$220$	−4.66027	−	8.07183i	−0.314195	−	0.544202i
$221$	−3.34509	+	5.79386i	−0.225015	+	0.389737i
$222$		0			0
$223$	−10.3861	+	1.83135i	−0.695506	+	0.122637i	−0.510215	−	0.860047i	$-0.670434\pi$
$223$	−10.3861	+	1.83135i	−0.695506	+	0.122637i	−0.185292	+	0.982684i	$0.559323\pi$
$224$	0.869644	−	4.93200i	0.0581055	−	0.329533i
$225$		0			0
$226$	7.71701	−	6.47534i	0.513328	−	0.430733i
$227$	0.696829			0.0462502			0.0231251	−	0.999733i	$-0.492638\pi$
$227$	0.696829			0.0462502			0.0231251	+	0.999733i	$0.492638\pi$
$228$		0			0
$229$	−13.6612			−0.902761			−0.451380	−	0.892332i	$-0.649068\pi$
$229$	−13.6612			−0.902761			−0.451380	+	0.892332i	$0.649068\pi$
$230$	−0.0978896	+	0.0821391i	−0.00645465	+	0.00541609i
$231$		0			0
$232$	0.177952	−	1.00922i	0.0116831	−	0.0662584i
$233$	−16.3878	+	2.88962i	−1.07360	+	0.189305i	−0.682385	−	0.730993i	$-0.739057\pi$
$233$	−16.3878	+	2.88962i	−1.07360	+	0.189305i	−0.391217	+	0.920298i	$0.627946\pi$
$234$		0			0
$235$	−3.09116	+	5.35405i	−0.201645	+	0.349260i
$236$	0.804578	+	1.39357i	0.0523735	+	0.0907136i
$237$		0			0
$238$	10.4283	−	12.4280i	0.675967	−	0.805586i
$239$	23.7756	−	13.7269i	1.53792	−	0.887917i	0.538956	−	0.842334i	$-0.318819\pi$
$239$	23.7756	−	13.7269i	1.53792	−	0.887917i	0.998961	−	0.0455831i	$-0.0145146\pi$
$240$		0			0
$241$	9.17958	+	25.2207i	0.591308	+	1.62461i	0.768079	+	0.640355i	$0.221213\pi$
$241$	9.17958	+	25.2207i	0.591308	+	1.62461i	−0.176771	+	0.984252i	$0.556565\pi$
$242$	0.961468	+	5.45275i	0.0618055	+	0.350516i
$243$		0			0
$244$	−1.64952	−	0.600377i	−0.105600	−	0.0384352i
$245$	46.3455	+	55.2324i	2.96090	+	3.52867i
$246$		0			0
$247$	3.31737	−	8.36845i	0.211079	−	0.532472i
$248$			6.46102i			0.410275i
$249$		0			0
$250$	−8.04901	+	22.1145i	−0.509064	+	1.39864i
$251$	−16.5498	−	2.91817i	−1.04461	−	0.184193i	−0.375092	−	0.926987i	$-0.622389\pi$
$251$	−16.5498	−	2.91817i	−1.04461	−	0.184193i	−0.669520	+	0.742794i	$0.733500\pi$
$252$		0			0
$253$	−0.0703831	+	0.0256174i	−0.00442495	+	0.00161055i
$254$	0.471526	+	0.272236i	0.0295862	+	0.0170816i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.137338	+	0.115240i	0.00856692	+	0.00718850i	0.647061	−	0.762438i	$-0.275998\pi$
$257$	0.137338	+	0.115240i	0.00856692	+	0.00718850i	−0.638494	+	0.769627i	$0.720442\pi$
$258$		0			0
$259$	−34.7322	−	20.0526i	−2.15815	−	1.24601i
$260$	7.73871	−	2.81666i	0.479934	−	0.174682i
$261$		0			0
$262$	9.45574	+	1.66730i	0.584178	+	0.103006i
$263$	−8.00018	+	21.9803i	−0.493312	+	1.35536i	0.404320	+	0.914618i	$0.367508\pi$
$263$	−8.00018	+	21.9803i	−0.493312	+	1.35536i	−0.897632	+	0.440746i	$0.854714\pi$
$264$		0			0
$265$		−	56.6853i		−	3.48215i
$266$	−11.4463	+	18.5881i	−0.701816	+	1.13971i
$267$		0			0
$268$	2.98171	+	3.55346i	0.182137	+	0.217062i
$269$	−13.4144	−	4.88245i	−0.817892	−	0.297688i	−0.101012	−	0.994885i	$-0.532208\pi$
$269$	−13.4144	−	4.88245i	−0.817892	−	0.297688i	−0.716880	+	0.697197i	$0.754430\pi$
$270$		0			0
$271$	−2.96954	−	16.8411i	−0.180387	−	1.02303i	−0.931740	−	0.363125i	$-0.881710\pi$
$271$	−2.96954	−	16.8411i	−0.180387	−	1.02303i	0.751353	−	0.659900i	$-0.229401\pi$
$272$	1.10797	+	3.04411i	0.0671804	+	0.184577i
$273$		0			0
$274$	−9.14459	+	5.27963i	−0.552445	+	0.318954i
$275$	−16.3787	+	19.5193i	−0.987671	+	1.17706i
$276$		0			0
$277$	−4.10860	−	7.11630i	−0.246862	−	0.427577i	0.715792	−	0.698314i	$-0.246066\pi$
$277$	−4.10860	−	7.11630i	−0.246862	−	0.427577i	−0.962653	+	0.270737i	$0.912733\pi$
$278$	4.39011	−	7.60389i	0.263301	−	0.456051i
$279$		0			0
$280$	−19.6672	+	3.46786i	−1.17534	+	0.207245i
$281$	2.34750	−	13.3134i	0.140040	−	0.794208i	−0.831176	−	0.556009i	$-0.812332\pi$
$281$	2.34750	−	13.3134i	0.140040	−	0.794208i	0.971216	−	0.238199i	$-0.0765570\pi$
$282$		0			0
$283$	−16.4701	+	13.8200i	−0.979043	+	0.821515i	−0.983945	−	0.178473i	$-0.942884\pi$
$283$	−16.4701	+	13.8200i	−0.979043	+	0.821515i	0.00490139	+	0.999988i	$0.498440\pi$
$284$	14.0108			0.831385
$285$		0			0
$286$	4.82706			0.285430
$287$	22.0087	−	18.4675i	1.29913	−	1.09010i
$288$		0			0
$289$	1.12972	−	6.40694i	0.0664539	−	0.376879i
$290$	−4.02444	+	0.709618i	−0.236323	+	0.0416702i
$291$		0			0
$292$	−2.84028	+	4.91951i	−0.166215	+	0.287893i
$293$	−12.6034	−	21.8297i	−0.736299	−	1.27531i	−0.954151	−	0.299325i	$-0.903238\pi$
$293$	−12.6034	−	21.8297i	−0.736299	−	1.27531i	0.217852	−	0.975982i	$-0.430095\pi$
$294$		0			0
$295$	4.12464	−	4.91555i	0.240146	−	0.286195i
$296$	6.93523	−	4.00406i	0.403102	−	0.232731i
$297$		0			0
$298$	1.70895	+	4.69529i	0.0989967	+	0.271991i
$299$	−0.0114920	−	0.0651742i	−0.000664597	−	0.00376912i
$300$		0			0
$301$	−23.1130	−	8.41243i	−1.33221	−	0.484884i
$302$	−0.498767	−	0.594408i	−0.0287008	−	0.0342043i
$303$		0			0
$304$	−2.07159	−	3.83517i	−0.118814	−	0.219962i
$305$			6.99992i			0.400814i
$306$		0			0
$307$	−4.89466	+	13.4480i	−0.279353	+	0.767517i	0.718083	+	0.695957i	$0.245020\pi$
$307$	−4.89466	+	13.4480i	−0.279353	+	0.767517i	−0.997436	+	0.0715593i	$0.977202\pi$
$308$	−11.5277	−	2.03265i	−0.656853	−	0.115821i
$309$		0			0
$310$	24.2107	−	8.81197i	1.37508	−	0.500487i
$311$	−11.8288	−	6.82937i	−0.670751	−	0.387258i	0.125610	−	0.992080i	$-0.459911\pi$
$311$	−11.8288	−	6.82937i	−0.670751	−	0.387258i	−0.796361	+	0.604822i	$0.793244\pi$
$312$		0			0
$313$	18.2056	+	15.2763i	1.02904	+	0.863468i	0.990736	−	0.135799i	$-0.0433600\pi$
$313$	18.2056	+	15.2763i	1.02904	+	0.863468i	0.0383042	+	0.999266i	$0.487804\pi$
$314$	−0.314009	−	0.263485i	−0.0177205	−	0.0148693i
$315$		0			0
$316$	−9.56767	−	5.52390i	−0.538224	−	0.310744i
$317$	18.8917	−	6.87603i	1.06107	−	0.386196i	0.248237	−	0.968699i	$-0.420149\pi$
$317$	18.8917	−	6.87603i	1.06107	−	0.386196i	0.812828	+	0.582503i	$0.197927\pi$
$318$		0			0
$319$	−2.35888	−	0.415934i	−0.132072	−	0.0232878i
$320$	1.36387	−	3.74720i	0.0762425	−	0.209475i
$321$		0			0
$322$			0.160485i			0.00894345i
$323$	0.400203	−	14.1149i	0.0222679	−	0.785374i
$324$		0			0
$325$	−14.4717	−	17.2467i	−0.802746	−	0.956676i
$326$	10.4880	+	3.81732i	0.580877	+	0.211422i
$327$		0			0
$328$	0.996183	+	5.64964i	0.0550050	+	0.311949i
$329$	2.65555	+	7.29606i	0.146405	+	0.402245i
$330$		0			0
$331$	23.2064	−	13.3982i	1.27554	−	0.736433i	0.299515	−	0.954092i	$-0.403175\pi$
$331$	23.2064	−	13.3982i	1.27554	−	0.736433i	0.976025	+	0.217658i	$0.0698419\pi$
$332$	5.17772	−	6.17056i	0.284164	−	0.338654i
$333$		0			0
$334$	9.54371	+	16.5302i	0.522208	+	0.904492i
$335$	9.24887	−	16.0195i	0.505320	−	0.875239i
$336$		0			0
$337$	27.7603	−	4.89489i	1.51220	−	0.266642i	0.644838	−	0.764320i	$-0.276925\pi$
$337$	27.7603	−	4.89489i	1.51220	−	0.266642i	0.867362	+	0.497678i	$0.165814\pi$
$338$	1.51681	−	8.60225i	0.0825035	−	0.467901i
$339$		0			0
$340$	9.89577	−	8.30354i	0.536674	−	0.450323i
$341$	15.1016			0.817795
$342$		0			0
$343$	55.4939			2.99639
$344$	3.76229	−	3.15694i	0.202849	−	0.170211i
$345$		0			0
$346$	−3.12987	+	17.7504i	−0.168263	+	0.954266i
$347$	17.8544	−	3.14820i	0.958472	−	0.169004i	0.327535	−	0.944839i	$-0.393782\pi$
$347$	17.8544	−	3.14820i	0.958472	−	0.169004i	0.630937	+	0.775834i	$0.282671\pi$
$348$		0			0
$349$	10.4387	−	18.0804i	0.558772	−	0.967821i	−0.438828	−	0.898571i	$-0.644606\pi$
$349$	10.4387	−	18.0804i	0.558772	−	0.967821i	0.997599	−	0.0692496i	$-0.0220605\pi$
$350$	27.2981	+	47.2816i	1.45914	+	2.52731i
$351$		0			0
$352$	1.50241	−	1.79050i	0.0800787	−	0.0954340i
$353$	11.5979	−	6.69605i	0.617294	−	0.356395i	−0.158521	−	0.987356i	$-0.550672\pi$
$353$	11.5979	−	6.69605i	0.617294	−	0.356395i	0.775815	+	0.630961i	$0.217339\pi$
$354$		0			0
$355$	−19.1088	−	52.5010i	−1.01419	−	2.78646i
$356$	−1.37802	−	7.81517i	−0.0730352	−	0.414203i
$357$		0			0
$358$	−8.33535	−	3.03382i	−0.440537	−	0.160342i
$359$	−0.803349	−	0.957395i	−0.0423992	−	0.0505294i	0.744428	−	0.667703i	$-0.232722\pi$
$359$	−0.803349	−	0.957395i	−0.0423992	−	0.0505294i	−0.786827	+	0.617173i	$0.788278\pi$
$360$		0			0
$361$	2.23381	+	18.8682i	0.117569	+	0.993065i
$362$		−	0.134896i		−	0.00708995i
$363$		0			0
$364$	3.53741	−	9.71895i	0.185411	−	0.509411i
$365$	22.3081	+	3.93353i	1.16766	+	0.205890i
$366$		0			0
$367$	7.73078	−	2.81377i	0.403543	−	0.146878i	−0.132271	−	0.991214i	$-0.542227\pi$
$367$	7.73078	−	2.81377i	0.403543	−	0.146878i	0.535814	+	0.844336i	$0.320005\pi$
$368$	−0.0277519	−	0.0160226i	−0.00144667	−	0.000835234i
$369$		0			0
$370$	−24.4627	−	20.5267i	−1.27176	−	1.06713i
$371$	−54.5350	−	45.7603i	−2.83131	−	2.37575i
$372$		0			0
$373$	14.8029	+	8.54649i	0.766468	+	0.442520i	0.831613	−	0.555356i	$-0.187418\pi$
$373$	14.8029	+	8.54649i	0.766468	+	0.442520i	−0.0651455	+	0.997876i	$0.520751\pi$
$374$	7.11511	−	2.58969i	0.367914	−	0.133910i
$375$		0			0
$376$	−1.52680	−	0.269216i	−0.0787388	−	0.0138838i
$377$	0.723848	−	1.98876i	0.0372801	−	0.102426i
$378$		0			0
$379$		−	11.5231i		−	0.591900i	−0.955203	−	0.295950i	$-0.904364\pi$
$379$		−	11.5231i		−	0.591900i	0.955203	−	0.295950i	$-0.0956362\pi$
$380$	−11.5458	+	12.9933i	−0.592285	+	0.666542i
$381$		0			0
$382$	−6.32016	−	7.53207i	−0.323367	−	0.385374i
$383$	9.12662	+	3.32182i	0.466348	+	0.169737i	0.564497	−	0.825435i	$-0.309070\pi$
$383$	9.12662	+	3.32182i	0.466348	+	0.169737i	−0.0981491	+	0.995172i	$0.531292\pi$
$384$		0			0
$385$	8.10555	+	45.9689i	0.413097	+	2.34279i
$386$	5.13511	+	14.1086i	0.261370	+	0.718108i
$387$		0			0
$388$	−10.7524	+	6.20788i	−0.545869	+	0.315157i
$389$	9.78986	−	11.6671i	0.496365	−	0.591545i	−0.458459	−	0.888716i	$-0.651598\pi$
$389$	9.78986	−	11.6671i	0.496365	−	0.591545i	0.954825	+	0.297170i	$0.0960429\pi$
$390$		0			0
$391$	−0.0519048	−	0.0899017i	−0.00262494	−	0.00454652i
$392$	−9.04044	+	15.6585i	−0.456611	+	0.790873i
$393$		0			0
$394$	−1.13048	+	0.199334i	−0.0569526	+	0.0100423i
$395$	−7.65009	+	43.3858i	−0.384918	+	2.18298i
$396$		0			0
$397$	8.22479	−	6.90142i	0.412791	−	0.346372i	−0.412622	−	0.910902i	$-0.635387\pi$
$397$	8.22479	−	6.90142i	0.412791	−	0.346372i	0.825413	+	0.564530i	$0.190943\pi$
$398$	6.07027			0.304275
$399$		0			0
$400$	−10.9016			−0.545080
$401$	−1.84256	+	1.54609i	−0.0920130	+	0.0772081i	−0.687634	−	0.726058i	$-0.741351\pi$
$401$	−1.84256	+	1.54609i	−0.0920130	+	0.0772081i	0.595621	+	0.803266i	$0.296906\pi$
$402$		0			0
$403$	−2.31704	+	13.1406i	−0.115420	+	0.654579i
$404$	1.15238	−	0.203195i	0.0573330	−	0.0101093i
$405$		0			0
$406$	−2.56611	+	4.44463i	−0.127354	+	0.220583i
$407$	−9.35882	−	16.2100i	−0.463899	−	0.803497i
$408$		0			0
$409$	−18.2207	+	21.7146i	−0.900958	+	1.07372i	0.0959694	+	0.995384i	$0.469405\pi$
$409$	−18.2207	+	21.7146i	−0.900958	+	1.07372i	−0.996927	+	0.0783353i	$0.975040\pi$
$410$	19.8116	−	11.4382i	0.978426	−	0.564895i
$411$		0			0
$412$	−0.597071	−	1.64044i	−0.0294156	−	0.0808186i
$413$	−1.39939	−	7.93635i	−0.0688596	−	0.390522i
$414$		0			0
$415$	−30.1840	−	10.9861i	−1.48168	−	0.539286i
$416$	1.32748	+	1.58203i	0.0650853	+	0.0775656i
$417$		0			0
$418$	−8.96407	+	4.84199i	−0.438447	+	0.236829i
$419$			25.3980i			1.24077i	0.784296	+	0.620387i	$0.213024\pi$
$419$			25.3980i			1.24077i	−0.784296	+	0.620387i	$0.786976\pi$
$420$		0			0
$421$	−7.85146	+	21.5717i	−0.382657	+	1.05134i	0.587577	+	0.809168i	$0.300082\pi$
$421$	−7.85146	+	21.5717i	−0.382657	+	1.05134i	−0.970233	+	0.242172i	$0.922140\pi$
$422$	−9.70496	−	1.71125i	−0.472430	−	0.0833022i
$423$		0			0
$424$	13.3578	−	4.86185i	0.648713	−	0.236112i
$425$	−30.5841	−	17.6578i	−1.48355	−	0.856527i
$426$		0			0
$427$	6.73438	+	5.65082i	0.325899	+	0.273462i
$428$	−6.07998	−	5.10171i	−0.293887	−	0.246600i
$429$		0			0
$430$	−16.9609	−	9.79239i	−0.817928	−	0.472231i
$431$	−10.4746	+	3.81243i	−0.504542	+	0.183638i	−0.581736	−	0.813378i	$-0.697626\pi$
$431$	−10.4746	+	3.81243i	−0.504542	+	0.183638i	0.0771936	+	0.997016i	$0.475404\pi$
$432$		0			0
$433$	−5.25842	−	0.927201i	−0.252703	−	0.0445584i	0.0458614	−	0.998948i	$-0.485397\pi$
$433$	−5.25842	−	0.927201i	−0.252703	−	0.0445584i	−0.298565	+	0.954389i	$0.596508\pi$
$434$	11.0669	−	30.4059i	0.531226	−	1.45953i
$435$		0			0
$436$			16.2743i			0.779397i
$437$	0.0867168	+	0.109504i	0.00414823	+	0.00523828i
$438$		0			0
$439$	−1.58122	−	1.88443i	−0.0754677	−	0.0899389i	0.726990	−	0.686649i	$-0.240919\pi$
$439$	−1.58122	−	1.88443i	−0.0754677	−	0.0899389i	−0.802457	+	0.596710i	$0.796474\pi$
$440$	−8.75845	−	3.18781i	−0.417543	−	0.151973i
$441$		0			0
$442$	1.16174	+	6.58853i	0.0552582	+	0.313385i
$443$	6.56007	+	18.0236i	0.311678	+	0.856329i	0.992318	+	0.123711i	$0.0394797\pi$
$443$	6.56007	+	18.0236i	0.311678	+	0.856329i	−0.680640	+	0.732618i	$0.738298\pi$
$444$		0			0
$445$	−27.4055	+	15.8226i	−1.29915	+	0.750062i
$446$	−6.77906	+	8.07897i	−0.320998	+	0.382550i
$447$		0			0
$448$	−2.50404	−	4.33713i	−0.118305	−	0.204910i
$449$	2.22612	−	3.85575i	0.105057	−	0.181964i	−0.808705	−	0.588215i	$-0.799831\pi$
$449$	2.22612	−	3.85575i	0.105057	−	0.181964i	0.913761	+	0.406251i	$0.133164\pi$
$450$		0			0
$451$	13.2051	−	2.32841i	0.621803	−	0.109641i
$452$	1.74930	−	9.92080i	0.0822803	−	0.466635i
$453$		0			0
$454$	0.533802	−	0.447913i	0.0250526	−	0.0210216i
$455$	−41.2433			−1.93352
$456$		0			0
$457$	−10.7894			−0.504708			−0.252354	−	0.967635i	$-0.581205\pi$
$457$	−10.7894			−0.504708			−0.252354	+	0.967635i	$0.581205\pi$
$458$	−10.4651	+	8.78128i	−0.489003	+	0.410322i
$459$		0			0
$460$	−0.0221898	+	0.125844i	−0.00103460	+	0.00586753i
$461$	25.7247	−	4.53596i	1.19812	−	0.211261i	0.461233	−	0.887279i	$-0.347407\pi$
$461$	25.7247	−	4.53596i	1.19812	−	0.211261i	0.736885	+	0.676018i	$0.236296\pi$
$462$		0			0
$463$	−15.7422	+	27.2662i	−0.731600	+	1.26717i	0.224599	+	0.974451i	$0.427893\pi$
$463$	−15.7422	+	27.2662i	−0.731600	+	1.26717i	−0.956199	+	0.292717i	$0.905441\pi$
$464$	−0.512394	−	0.887492i	−0.0237873	−	0.0412008i
$465$		0			0
$466$	−10.6964	+	12.7475i	−0.495501	+	0.590515i
$467$	−23.8427	+	13.7656i	−1.10331	+	0.636994i	−0.937087	−	0.349095i	$-0.886489\pi$
$467$	−23.8427	+	13.7656i	−1.10331	+	0.636994i	−0.166219	+	0.986089i	$0.553156\pi$
$468$		0			0
$469$	−7.94550	−	21.8301i	−0.366889	−	1.00802i
$470$	1.07355	+	6.08840i	0.0495191	+	0.280837i
$471$		0			0
$472$	1.51211	+	0.550364i	0.0696006	+	0.0253325i
$473$	−7.37881	−	8.79373i	−0.339278	−	0.404336i
$474$		0			0
$475$	44.1747	+	17.5115i	2.02687	+	0.803482i
$476$		−	16.2236i		−	0.743606i
$477$		0			0
$478$	9.38973	−	25.7981i	0.429476	−	1.17998i
$479$	7.33459	+	1.29329i	0.335126	+	0.0590917i	0.338679	−	0.940902i	$-0.390020\pi$
$479$	7.33459	+	1.29329i	0.335126	+	0.0590917i	−0.00355322	+	0.999994i	$0.501131\pi$
$480$		0			0
$481$	15.5410	−	5.65645i	0.708607	−	0.257912i
$482$	23.2435	+	13.4196i	1.05871	+	0.611248i
$483$		0			0
$484$	4.24149	+	3.55903i	0.192795	+	0.161774i
$485$	37.9270	+	31.8245i	1.72217	+	1.44508i
$486$		0			0
$487$	−8.67827	−	5.01040i	−0.393250	−	0.227043i	0.290317	−	0.956930i	$-0.406239\pi$
$487$	−8.67827	−	5.01040i	−0.393250	−	0.227043i	−0.683567	+	0.729887i	$0.739572\pi$
$488$	−1.64952	+	0.600377i	−0.0746703	+	0.0271778i
$489$		0			0
$490$	71.0054	+	12.5202i	3.20770	+	0.565603i
$491$	−3.93130	+	10.8012i	−0.177417	+	0.487450i	−0.996244	−	0.0865909i	$-0.972403\pi$
$491$	−3.93130	+	10.8012i	−0.177417	+	0.487450i	0.818827	+	0.574041i	$0.194625\pi$
$492$		0			0
$493$		−	3.31978i		−	0.149515i
$494$	−2.83788	−	8.54297i	−0.127682	−	0.384367i
$495$		0			0
$496$	4.15306	+	4.94943i	0.186478	+	0.222236i
$497$	−65.9354	−	23.9985i	−2.95761	−	1.07648i
$498$		0			0
$499$	−3.72642	−	21.1336i	−0.166818	−	0.946069i	−0.947171	−	0.320730i	$-0.896072\pi$
$499$	−3.72642	−	21.1336i	−0.166818	−	0.946069i	0.780353	−	0.625339i	$-0.215039\pi$
$500$	8.04901	+	22.1145i	0.359963	+	0.988989i
$501$		0			0
$502$	−14.5536	+	8.40254i	−0.649560	+	0.375024i
$503$	−0.695111	+	0.828402i	−0.0309935	+	0.0369366i	−0.781319	−	0.624132i	$-0.785453\pi$
$503$	−0.695111	+	0.828402i	−0.0309935	+	0.0369366i	0.750325	+	0.661069i	$0.229897\pi$
$504$		0			0
$505$	−2.33310	−	4.04105i	−0.103822	−	0.179825i
$506$	−0.0374501	+	0.0648654i	−0.00166486	+	0.00288362i
$507$		0			0
$508$	0.536200	−	0.0945465i	0.0237900	−	0.00419482i
$509$	−0.949340	+	5.38398i	−0.0420788	+	0.238641i	−0.998592	−	0.0530486i	$-0.983106\pi$
$509$	−0.949340	+	5.38398i	−0.0420788	+	0.238641i	0.956513	+	0.291689i	$0.0942173\pi$
$510$		0			0
$511$	21.7930	−	18.2865i	0.964065	−	0.808946i
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.179282			0.00790780
$515$	−5.33272	+	4.47468i	−0.234988	+	0.197178i
$516$		0			0
$517$	−0.629248	+	3.56864i	−0.0276743	+	0.156949i
$518$	−39.4960	+	6.96421i	−1.73535	+	0.305990i
$519$		0			0
$520$	4.11768	−	7.13203i	0.180572	−	0.312760i
$521$	−4.97836	−	8.62277i	−0.218106	−	0.377770i	0.736123	−	0.676848i	$-0.236654\pi$
$521$	−4.97836	−	8.62277i	−0.218106	−	0.377770i	−0.954229	+	0.299077i	$0.903321\pi$
$522$		0			0
$523$	−5.77718	+	6.88497i	−0.252618	+	0.301059i	−0.877418	−	0.479726i	$-0.840736\pi$
$523$	−5.77718	+	6.88497i	−0.252618	+	0.301059i	0.624800	+	0.780785i	$0.285181\pi$
$524$	8.31524	−	4.80080i	0.363253	−	0.209724i
$525$		0			0
$526$	8.00018	+	21.9803i	0.348824	+	0.958387i
$527$	3.63452	+	20.6124i	0.158322	+	0.897889i
$528$		0			0
$529$	−21.6120	−	7.86611i	−0.939651	−	0.342005i
$530$	−36.4366	−	43.4234i	−1.58270	−	1.88619i
$531$		0			0
$532$	3.17987	+	21.5969i	0.137865	+	0.936343i
$533$			11.8476i			0.513177i
$534$		0			0
$535$	−10.8248	+	29.7409i	−0.467997	+	1.28581i
$536$	4.56825	+	0.805505i	0.197318	+	0.0347925i
$537$		0			0
$538$	−13.4144	+	4.88245i	−0.578337	+	0.210497i
$539$	36.5991	+	21.1305i	1.57644	+	0.910156i
$540$		0			0
$541$	21.5477	+	18.0807i	0.926409	+	0.777349i	0.975169	−	0.221461i	$-0.0710826\pi$
$541$	21.5477	+	18.0807i	0.926409	+	0.777349i	−0.0487604	+	0.998811i	$0.515527\pi$
$542$	−13.1001	−	10.9923i	−0.562696	−	0.472158i
$543$		0			0
$544$	2.80547	+	1.61974i	0.120284	+	0.0694458i
$545$	60.9830	−	22.1960i	2.61222	−	0.950771i
$546$		0			0
$547$	−7.18442	−	1.26681i	−0.307184	−	0.0541648i	0.0179315	−	0.999839i	$-0.494292\pi$
$547$	−7.18442	−	1.26681i	−0.307184	−	0.0541648i	−0.325115	+	0.945674i	$0.605403\pi$
$548$	−3.61148	+	9.92246i	−0.154275	+	0.423867i
$549$		0			0
$550$			25.4807i			1.08650i
$551$	0.650687	+	4.41930i	0.0277202	+	0.188268i
$552$		0			0
$553$	35.5643	+	42.3839i	1.51235	+	1.80235i
$554$	−7.72164	−	2.81045i	−0.328061	−	0.119404i
$555$		0			0
$556$	−1.52467	−	8.64682i	−0.0646603	−	0.366707i
$557$	−5.40113	−	14.8395i	−0.228853	−	0.628770i	0.771115	−	0.636696i	$-0.219699\pi$
$557$	−5.40113	−	14.8395i	−0.228853	−	0.628770i	−0.999969	+	0.00792610i	$0.997477\pi$
$558$		0			0
$559$	8.78398	−	5.07143i	0.371523	−	0.214499i
$560$	−12.8369	+	15.2984i	−0.542457	+	0.646475i
$561$		0			0
$562$	−6.75937	−	11.7076i	−0.285127	−	0.493854i
$563$	20.0715	−	34.7649i	0.845913	−	1.46516i	−0.0389135	−	0.999243i	$-0.512390\pi$
$563$	20.0715	−	34.7649i	0.845913	−	1.46516i	0.884826	−	0.465921i	$-0.154277\pi$
$564$		0			0
$565$	−39.5610	+	6.97567i	−1.66434	+	0.293469i
$566$	−3.73346	+	21.1735i	−0.156929	+	0.889989i
$567$		0			0
$568$	10.7329	−	9.00594i	0.450341	−	0.377881i
$569$	−43.5168			−1.82432			−0.912159	−	0.409836i	$-0.865586\pi$
$569$	−43.5168			−1.82432			−0.912159	+	0.409836i	$0.865586\pi$
$570$		0			0
$571$	−21.4386			−0.897177			−0.448588	−	0.893739i	$-0.648073\pi$
$571$	−21.4386			−0.897177			−0.448588	+	0.893739i	$0.648073\pi$
$572$	3.69774	−	3.10277i	0.154610	−	0.129734i
$573$		0			0
$574$	4.98897	−	28.2938i	0.208235	−	1.18096i
$575$	0.344036	−	0.0606628i	0.0143473	−	0.00252981i
$576$		0			0
$577$	−4.01317	+	6.95101i	−0.167070	+	0.289374i	−0.937389	−	0.348285i	$-0.886764\pi$
$577$	−4.01317	+	6.95101i	−0.167070	+	0.289374i	0.770318	+	0.637660i	$0.220097\pi$
$578$	−3.25289	−	5.63417i	−0.135302	−	0.234350i
$579$		0			0
$580$	−2.62677	+	3.13046i	−0.109071	+	0.129985i
$581$	−34.9360	+	20.1703i	−1.44939	+	0.836805i
$582$		0			0
$583$	−11.3638	−	31.2217i	−0.470639	−	1.29307i
$584$	0.986419	+	5.59426i	0.0408183	+	0.231492i
$585$		0			0
$586$	−23.6867	−	8.62124i	−0.978487	−	0.356140i
$587$	−3.75527	−	4.47535i	−0.154996	−	0.184718i	0.682958	−	0.730457i	$-0.260693\pi$
$587$	−3.75527	−	4.47535i	−0.154996	−	0.184718i	−0.837955	+	0.545740i	$0.816249\pi$
$588$		0			0
$589$	−8.87837	−	26.7269i	−0.365827	−	1.10126i
$590$		−	6.41680i		−	0.264175i
$591$		0			0
$592$	2.73894	−	7.52517i	0.112570	−	0.309283i
$593$	−1.50770	−	0.265849i	−0.0619140	−	0.0109171i	0.142605	−	0.989780i	$-0.454452\pi$
$593$	−1.50770	−	0.265849i	−0.0619140	−	0.0109171i	−0.204519	+	0.978863i	$0.565563\pi$
$594$		0			0
$595$	−60.7929	+	22.1268i	−2.49227	+	0.907111i
$596$	4.32721	+	2.49831i	0.177249	+	0.102335i
$597$		0			0
$598$	−0.0506965	−	0.0425394i	−0.00207313	−	0.00173957i
$599$	26.4268	+	22.1747i	1.07977	+	0.906034i	0.995902	−	0.0904424i	$-0.0288281\pi$
$599$	26.4268	+	22.1747i	1.07977	+	0.906034i	0.0838681	+	0.996477i	$0.473273\pi$
$600$		0			0
$601$	19.3078	+	11.1473i	0.787580	+	0.454710i	0.839110	−	0.543962i	$-0.183076\pi$
$601$	19.3078	+	11.1473i	0.787580	+	0.454710i	−0.0515296	+	0.998671i	$0.516410\pi$
$602$	−23.1130	+	8.41243i	−0.942014	+	0.342865i
$603$		0			0
$604$	−0.764156	−	0.134741i	−0.0310931	−	0.00548254i
$605$	7.55156	−	20.7477i	0.307015	−	0.843516i
$606$		0			0
$607$			12.5727i			0.510309i	0.966900	+	0.255154i	$0.0821263\pi$
$607$			12.5727i			0.510309i	−0.966900	+	0.255154i	$0.917874\pi$
$608$	−4.05213	−	1.60632i	−0.164335	−	0.0651449i
$609$		0			0
$610$	4.49946	+	5.36225i	0.182178	+	0.217111i
$611$	−3.00870	−	1.09508i	−0.121719	−	0.0443021i
$612$		0			0
$613$	3.41305	+	19.3564i	0.137852	+	0.781797i	0.972831	+	0.231516i	$0.0743684\pi$
$613$	3.41305	+	19.3564i	0.137852	+	0.781797i	−0.834979	+	0.550281i	$0.814520\pi$
$614$	4.89466	+	13.4480i	0.197533	+	0.542716i
$615$		0			0
$616$	−10.1373	+	5.85278i	−0.408444	+	0.235815i
$617$	−16.8198	+	20.0451i	−0.677140	+	0.806984i	−0.989737	−	0.142902i	$-0.954357\pi$
$617$	−16.8198	+	20.0451i	−0.677140	+	0.806984i	0.312597	+	0.949886i	$0.398801\pi$
$618$		0			0
$619$	7.48059	+	12.9568i	0.300670	+	0.520777i	0.976288	−	0.216476i	$-0.0694562\pi$
$619$	7.48059	+	12.9568i	0.300670	+	0.520777i	−0.675618	+	0.737252i	$0.736123\pi$
$620$	12.8822	−	22.3127i	0.517363	−	0.896100i
$621$		0			0
$622$	−13.4512	+	2.37182i	−0.539345	+	0.0951011i
$623$	−6.90126	+	39.1390i	−0.276493	+	1.56807i
$624$		0			0
$625$	30.1339	−	25.2853i	1.20536	−	1.01141i
$626$	23.7657			0.949869
$627$		0			0
$628$	−0.409909			−0.0163572
$629$	19.8728	−	16.6753i	0.792381	−	0.664887i
$630$		0			0
$631$	4.57598	−	25.9517i	0.182167	−	1.03312i	−0.747374	−	0.664403i	$-0.768686\pi$
$631$	4.57598	−	25.9517i	0.182167	−	1.03312i	0.929541	−	0.368718i	$-0.120203\pi$
$632$	−10.8800	+	1.91843i	−0.432781	+	0.0763110i
$633$		0			0
$634$	10.0521	−	17.4107i	0.399219	−	0.691468i
$635$	−1.08559	−	1.88030i	−0.0430803	−	0.0746173i
$636$		0			0
$637$	−24.0021	+	28.6046i	−0.950997	+	1.13335i
$638$	−2.07436	+	1.19763i	−0.0821249	+	0.0474148i
$639$		0			0
$640$	−1.36387	−	3.74720i	−0.0539116	−	0.148121i
$641$	−6.26553	−	35.5336i	−0.247473	−	1.40349i	−0.814677	−	0.579914i	$-0.803086\pi$
$641$	−6.26553	−	35.5336i	−0.247473	−	1.40349i	0.567204	−	0.823577i	$-0.308025\pi$
$642$		0			0
$643$	45.8970	+	16.7051i	1.81000	+	0.658786i	0.997076	+	0.0764152i	$0.0243475\pi$
$643$	45.8970	+	16.7051i	1.81000	+	0.658786i	0.812923	+	0.582371i	$0.197875\pi$
$644$	0.103157	+	0.122938i	0.00406497	+	0.00484445i
$645$		0			0
$646$	−8.76630	−	11.0699i	−0.344906	−	0.435539i
$647$			23.7677i			0.934403i	0.884151	+	0.467201i	$0.154738\pi$
$647$			23.7677i			0.934403i	−0.884151	+	0.467201i	$0.845262\pi$
$648$		0			0
$649$	1.28638	−	3.53431i	0.0504950	−	0.138734i
$650$	−22.1720	−	3.90951i	−0.869656	−	0.153344i
$651$		0			0
$652$	10.4880	−	3.81732i	0.410742	−	0.149498i
$653$	30.7236	+	17.7383i	1.20231	+	0.694152i	0.961067	−	0.276314i	$-0.0891130\pi$
$653$	30.7236	+	17.7383i	1.20231	+	0.694152i	0.241239	+	0.970466i	$0.422446\pi$
$654$		0			0
$655$	−29.3304	−	24.6112i	−1.14603	−	0.961638i
$656$	4.39464	+	3.68754i	0.171582	+	0.143974i
$657$		0			0
$658$	6.72408	+	3.88215i	0.262132	+	0.151342i
$659$	−13.9388	+	5.07332i	−0.542979	+	0.197628i	−0.598924	−	0.800806i	$-0.704405\pi$
$659$	−13.9388	+	5.07332i	−0.542979	+	0.197628i	0.0559451	+	0.998434i	$0.482183\pi$
$660$		0			0
$661$	−26.6480	−	4.69877i	−1.03649	−	0.182761i	−0.370585	−	0.928799i	$-0.620843\pi$
$661$	−26.6480	−	4.69877i	−1.03649	−	0.182761i	−0.665904	+	0.746038i	$0.731954\pi$
$662$	9.16493	−	25.1804i	0.356205	−	0.978665i
$663$		0			0
$664$		−	8.05510i		−	0.312598i
$665$	76.5908	−	41.3709i	2.97006	−	1.60429i
$666$		0			0
$667$	0.0211088	+	0.0251565i	0.000817335	+	0.000974062i
$668$	17.9363	+	6.52828i	0.693976	+	0.252587i
$669$		0			0
$670$	−3.21210	−	18.2167i	−0.124094	−	0.703773i
$671$	1.40328	+	3.85548i	0.0541731	+	0.148839i
$672$		0			0
$673$	−1.93224	+	1.11558i	−0.0744823	+	0.0430024i	−0.536779	−	0.843723i	$-0.680359\pi$
$673$	−1.93224	+	1.11558i	−0.0744823	+	0.0430024i	0.462296	+	0.886725i	$0.347026\pi$
$674$	18.1192	−	21.5937i	0.697927	−	0.831757i
$675$		0			0
$676$	−4.36747	−	7.56469i	−0.167980	−	0.290950i
$677$	−14.8989	+	25.8057i	−0.572611	+	0.991792i	0.423685	+	0.905809i	$0.360736\pi$
$677$	−14.8989	+	25.8057i	−0.572611	+	0.991792i	−0.996297	+	0.0859823i	$0.972597\pi$
$678$		0			0
$679$	61.2345	−	10.7973i	2.34996	−	0.414362i
$680$	2.24319	−	12.7218i	0.0860224	−	0.487857i
$681$		0			0
$682$	11.5685	−	9.70709i	0.442979	−	0.371704i
$683$	8.00277			0.306217			0.153109	−	0.988209i	$-0.451072\pi$
$683$	8.00277			0.306217			0.153109	+	0.988209i	$0.451072\pi$
$684$		0			0
$685$	42.1070			1.60883
$686$	42.5108	−	35.6708i	1.62307	−	1.36192i
$687$		0			0
$688$	0.852842	−	4.83671i	0.0325143	−	0.184398i
$689$	28.9110	−	5.09779i	1.10142	−	0.194210i
$690$		0			0
$691$	−17.8358	+	30.8925i	−0.678506	+	1.17521i	0.296925	+	0.954901i	$0.404039\pi$
$691$	−17.8358	+	30.8925i	−0.678506	+	1.17521i	−0.975431	+	0.220306i	$0.929294\pi$
$692$	9.01210	+	15.6094i	0.342589	+	0.593381i
$693$		0			0
$694$	11.6536	−	13.8882i	0.442365	−	0.527190i
$695$	−30.3219	+	17.5064i	−1.15017	+	0.664054i
$696$		0			0
$697$	6.35618	+	17.4634i	0.240757	+	0.661475i
$698$	−3.62533	−	20.5603i	−0.137221	−	0.778217i
$699$		0			0
$700$	51.3036	+	18.6730i	1.93909	+	0.705772i
$701$	7.62024	+	9.08145i	0.287813	+	0.343002i	0.890506	−	0.454971i	$-0.150350\pi$
$701$	7.62024	+	9.08145i	0.287813	+	0.343002i	−0.602694	+	0.797973i	$0.705906\pi$
$702$		0			0
$703$	−23.1864	+	26.0933i	−0.874490	+	0.984128i
$704$		−	2.33733i		−	0.0880916i
$705$		0			0
$706$	4.58037	−	12.5845i	0.172384	−	0.473622i
$707$	−5.77120	−	1.01762i	−0.217048	−	0.0382715i
$708$		0			0
$709$	27.4247	−	9.98176i	1.02996	−	0.374873i	0.228891	−	0.973452i	$-0.426490\pi$
$709$	27.4247	−	9.98176i	1.02996	−	0.374873i	0.801064	+	0.598579i	$0.204268\pi$
$710$	−48.3852	−	27.9352i	−1.81586	−	1.04839i
$711$		0			0
$712$	−6.07912	−	5.10099i	−0.227825	−	0.191168i
$713$	−0.158605	−	0.133085i	−0.00593980	−	0.00498409i
$714$		0			0
$715$	−16.6699	−	9.62439i	−0.623420	−	0.359932i
$716$	−8.33535	+	3.03382i	−0.311507	+	0.113379i
$717$		0			0
$718$	−1.23080	−	0.217024i	−0.0459332	−	0.00809925i
$719$	14.5194	−	39.8918i	0.541484	−	1.48771i	−0.303452	−	0.952847i	$-0.598139\pi$
$719$	14.5194	−	39.8918i	0.541484	−	1.48771i	0.844936	−	0.534868i	$-0.179638\pi$
$720$		0			0
$721$			8.74270i			0.325595i
$722$	13.8395	+	13.0180i	0.515051	+	0.484481i
$723$		0			0
$724$	−0.0867092	−	0.103336i	−0.00322252	−	0.00384045i
$725$	10.4981	+	3.82099i	0.389889	+	0.141908i
$726$		0			0
$727$	−4.80233	−	27.2354i	−0.178109	−	1.01010i	−0.934494	−	0.355978i	$-0.884148\pi$
$727$	−4.80233	−	27.2354i	−0.178109	−	1.01010i	0.756386	−	0.654126i	$-0.226963\pi$
$728$	−3.53741	−	9.71895i	−0.131105	−	0.360208i
$729$		0			0
$730$	19.6174	−	11.3261i	0.726074	−	0.419199i
$731$	10.2268	−	12.1879i	0.378253	−	0.450784i
$732$		0			0
$733$	−18.0302	−	31.2292i	−0.665959	−	1.15348i	−0.979024	−	0.203744i	$-0.934689\pi$
$733$	−18.0302	−	31.2292i	−0.665959	−	1.15348i	0.313065	−	0.949732i	$-0.398644\pi$
$734$	4.11346	−	7.12473i	0.151831	−	0.262978i
$735$		0			0
$736$	−0.0315583	+	0.00556458i	−0.00116325	+	0.000205113i
$737$	1.88273	−	10.6775i	0.0693514	−	0.393311i
$738$		0			0
$739$	4.98360	−	4.18173i	0.183325	−	0.153828i	−0.546507	−	0.837454i	$-0.684043\pi$
$739$	4.98360	−	4.18173i	0.183325	−	0.153828i	0.729832	+	0.683627i	$0.239598\pi$
$740$	−31.9338			−1.17391
$741$		0			0
$742$	−71.1903			−2.61348
$743$	−2.96205	+	2.48546i	−0.108667	+	0.0911825i	−0.695502	−	0.718524i	$-0.744818\pi$
$743$	−2.96205	+	2.48546i	−0.108667	+	0.0911825i	0.586835	+	0.809706i	$0.300374\pi$
$744$		0			0
$745$	3.45993	−	19.6223i	0.126762	−	0.718904i
$746$	16.8333	−	2.96816i	0.616311	−	0.108672i
$747$		0			0
$748$	3.78587	−	6.55732i	0.138425	−	0.239759i
$749$	19.8742	+	34.4231i	0.726187	+	1.25779i
$750$		0			0
$751$	11.2206	−	13.3722i	0.409444	−	0.487957i	−0.521431	−	0.853293i	$-0.674602\pi$
$751$	11.2206	−	13.3722i	0.409444	−	0.487957i	0.930876	+	0.365337i	$0.119046\pi$
$752$	−1.34265	+	0.775177i	−0.0489613	+	0.0282678i
$753$		0			0
$754$	−0.723848	−	1.98876i	−0.0263610	−	0.0724262i
$755$	0.537305	+	3.04721i	0.0195545	+	0.110899i
$756$		0			0
$757$	23.0263	+	8.38090i	0.836907	+	0.304609i	0.724690	−	0.689075i	$-0.241983\pi$
$757$	23.0263	+	8.38090i	0.836907	+	0.304609i	0.112216	+	0.993684i	$0.464205\pi$
$758$	−7.40689	−	8.82718i	−0.269030	−	0.320618i
$759$		0			0
$760$	−0.492636	+	17.3749i	−0.0178698	+	0.630255i
$761$			7.92777i			0.287381i	0.989623	+	0.143691i	$0.0458971\pi$
$761$			7.92777i			0.287381i	−0.989623	+	0.143691i	$0.954103\pi$
$762$		0			0
$763$	27.8757	−	76.5878i	1.00917	−	2.77266i
$764$	−9.68304	−	1.70738i	−0.350320	−	0.0617709i
$765$		0			0
$766$	9.12662	−	3.32182i	0.329758	−	0.120022i
$767$	2.87800	+	1.66161i	0.103919	+	0.0599974i
$768$		0			0
$769$	4.24906	+	3.56539i	0.153225	+	0.128571i	0.716178	−	0.697918i	$-0.245890\pi$
$769$	4.24906	+	3.56539i	0.153225	+	0.128571i	−0.562952	+	0.826489i	$0.690335\pi$
$770$	35.7574	+	30.0041i	1.28861	+	1.08127i
$771$		0			0
$772$	13.0025	+	7.50702i	0.467972	+	0.270184i
$773$	8.18532	−	2.97921i	0.294406	−	0.107155i	−0.190595	−	0.981669i	$-0.561042\pi$
$773$	8.18532	−	2.97921i	0.294406	−	0.107155i	0.485000	+	0.874514i	$0.338819\pi$
$774$		0			0
$775$	−69.3654	−	12.2310i	−2.49168	−	0.439350i
$776$	−4.24644	+	11.6670i	−0.152438	+	0.418821i
$777$		0			0
$778$		−	15.2303i		−	0.546033i
$779$	−11.8843	−	22.0016i	−0.425798	−	0.788288i
$780$		0			0
$781$	−21.0499	−	25.0863i	−0.753224	−	0.897657i
$782$	−0.0975490	−	0.0355049i	−0.00348835	−	0.00126965i
$783$		0			0
$784$	3.13971	+	17.8062i	0.112133	+	0.635935i
$785$	0.559062	+	1.53601i	0.0199538	+	0.0548225i
$786$		0			0
$787$	−31.9287	+	18.4340i	−1.13813	+	0.657102i	−0.945968	−	0.324260i	$-0.894885\pi$
$787$	−31.9287	+	18.4340i	−1.13813	+	0.657102i	−0.192166	+	0.981362i	$0.561551\pi$
$788$	−0.737867	+	0.879355i	−0.0262854	+	0.0313257i
$789$		0			0
$790$	22.0276	+	38.1528i	0.783705	+	1.35742i
$791$	−25.2253	+	43.6915i	−0.896908	+	1.55349i
$792$		0			0
$793$	−3.57014	+	0.629513i	−0.126780	+	0.0223547i
$794$	1.86441	−	10.5736i	0.0661654	−	0.375243i
$795$		0			0
$796$	4.65010	−	3.90189i	0.164818	−	0.138299i
$797$	38.3461			1.35829			0.679144	−	0.734005i	$-0.262351\pi$
$797$	38.3461			1.35829			0.679144	+	0.734005i	$0.262351\pi$
$798$		0			0
$799$	−5.02234			−0.177678
$800$	−8.35112	+	7.00742i	−0.295257	+	0.247750i
$801$		0			0
$802$	−0.417674	+	2.36875i	−0.0147486	+	0.0836434i
$803$	13.0757	−	2.30559i	0.461430	−	0.0813625i
$804$		0			0
$805$	0.319981	−	0.554223i	0.0112778	−	0.0195338i
$806$	6.67165	+	11.5556i	0.234999	+	0.407030i
$807$		0			0
$808$	0.752162	−	0.896391i	0.0264609	−	0.0315349i
$809$	−18.2400	+	10.5308i	−0.641283	+	0.370245i	−0.785109	−	0.619358i	$-0.787393\pi$
$809$	−18.2400	+	10.5308i	−0.641283	+	0.370245i	0.143826	+	0.989603i	$0.454060\pi$
$810$		0			0
$811$	18.9191	+	51.9799i	0.664341	+	1.82526i	0.556063	+	0.831140i	$0.312311\pi$
$811$	18.9191	+	51.9799i	0.664341	+	1.82526i	0.108278	+	0.994121i	$0.465466\pi$
$812$	0.891200	+	5.05425i	0.0312750	+	0.177369i
$813$		0			0
$814$	−17.5888	−	6.40181i	−0.616488	−	0.224383i
$815$	−28.6085	−	34.0943i	−1.00211	−	1.19427i
$816$		0			0
$817$	−11.2251	+	18.2290i	−0.392718	+	0.637753i
$818$			28.3464i			0.991110i
$819$		0			0
$820$	7.82422	−	21.4969i	0.273234	−	0.750703i
$821$	1.27132	+	0.224167i	0.0443692	+	0.00782349i	0.195789	−	0.980646i	$-0.437273\pi$
$821$	1.27132	+	0.224167i	0.0443692	+	0.00782349i	−0.151420	+	0.988470i	$0.548384\pi$
$822$		0			0
$823$	−39.8565	+	14.5066i	−1.38931	+	0.505667i	−0.924987	−	0.379999i	$-0.875924\pi$
$823$	−39.8565	+	14.5066i	−1.38931	+	0.505667i	−0.464322	+	0.885666i	$0.653702\pi$
$824$	−1.51184	−	0.872859i	−0.0526673	−	0.0304075i
$825$		0			0
$826$	−6.17338	−	5.18008i	−0.214799	−	0.180238i
$827$	15.4101	+	12.9306i	0.535860	+	0.449640i	0.870119	−	0.492841i	$-0.164042\pi$
$827$	15.4101	+	12.9306i	0.535860	+	0.449640i	−0.334259	+	0.942481i	$0.608486\pi$
$828$		0			0
$829$	1.00665	+	0.581191i	0.0349625	+	0.0201856i	0.517379	−	0.855756i	$-0.326908\pi$
$829$	1.00665	+	0.581191i	0.0349625	+	0.0201856i	−0.482417	+	0.875942i	$0.660241\pi$
$830$	−30.1840	+	10.9861i	−1.04770	+	0.381333i
$831$		0			0
$832$	2.03382	+	0.358618i	0.0705102	+	0.0124328i
$833$	−20.0330	+	55.0402i	−0.694103	+	1.90703i
$834$		0			0
$835$		−	76.1145i		−	2.63405i
$836$	−3.75451	+	9.47117i	−0.129852	+	0.327567i
$837$		0			0
$838$	16.3255	+	19.4560i	0.563956	+	0.672096i
$839$	−13.1575	−	4.78892i	−0.454246	−	0.165332i	0.104757	−	0.994498i	$-0.466594\pi$
$839$	−13.1575	−	4.78892i	−0.454246	−	0.165332i	−0.559003	+	0.829166i	$0.688816\pi$
$840$		0			0
$841$	−4.85343	−	27.5252i	−0.167360	−	0.949145i
$842$	7.85146	+	21.5717i	0.270579	+	0.743410i
$843$		0			0
$844$	−8.53440	+	4.92734i	−0.293766	+	0.169606i
$845$	−22.3897	+	26.6830i	−0.770229	+	0.917924i
$846$		0			0
$847$	−13.8645	−	24.0141i	−0.476392	−	0.825134i
$848$	7.10755	−	12.3106i	0.244074	−	0.422749i
$849$		0			0
$850$	−34.7790	+	6.13248i	−1.19291	+	0.210342i
$851$	−0.0445618	+	0.252722i	−0.00152756	+	0.00866321i
$852$		0			0
$853$	−42.3953	+	35.5739i	−1.45159	+	1.21803i	−0.520178	+	0.854058i	$0.674134\pi$
$853$	−42.3953	+	35.5739i	−1.45159	+	1.21803i	−0.931411	+	0.363969i	$0.881421\pi$
$854$	8.79111			0.300826
$855$		0			0
$856$	−7.93685			−0.271276
$857$	38.9749	−	32.7038i	1.33136	−	1.11714i	0.347598	−	0.937644i	$-0.386998\pi$
$857$	38.9749	−	32.7038i	1.33136	−	1.11714i	0.983759	−	0.179497i	$-0.0574469\pi$
$858$		0			0
$859$	−2.28118	+	12.9372i	−0.0778329	+	0.441412i	0.920841	+	0.389937i	$0.127503\pi$
$859$	−2.28118	+	12.9372i	−0.0778329	+	0.441412i	−0.998674	+	0.0514749i	$0.983608\pi$
$860$	−19.2873	+	3.40086i	−0.657690	+	0.115968i
$861$		0			0
$862$	−5.57340	+	9.65342i	−0.189831	+	0.328797i
$863$	2.53093	+	4.38370i	0.0861539	+	0.149223i	0.905882	−	0.423529i	$-0.139209\pi$
$863$	2.53093	+	4.38370i	0.0861539	+	0.149223i	−0.819728	+	0.572752i	$0.805876\pi$
$864$		0			0
$865$	46.2002	−	55.0593i	1.57086	−	1.87207i
$866$	−4.62417	+	2.66977i	−0.157136	+	0.0907224i
$867$		0			0
$868$	−11.0669	−	30.4059i	−0.375633	−	1.03204i
$869$	4.48401	+	25.4301i	0.152110	+	0.862657i
$870$		0			0
$871$	9.00214	+	3.27651i	0.305026	+	0.111020i
$872$	10.4609	+	12.4668i	0.354251	+	0.422180i
$873$		0			0
$874$	0.136817	+	0.0281444i	0.00462789	+	0.000951998i
$875$		−	117.859i		−	3.98436i
$876$		0			0
$877$	7.22476	−	19.8499i	0.243963	−	0.670283i	−0.755915	−	0.654670i	$-0.772808\pi$
$877$	7.22476	−	19.8499i	0.243963	−	0.670283i	0.999878	−	0.0156131i	$-0.00497001\pi$
$878$	−2.42258	−	0.427166i	−0.0817580	−	0.0144161i
$879$		0			0
$880$	−8.75845	+	3.18781i	−0.295247	+	0.107461i
$881$	40.5718	+	23.4242i	1.36690	+	0.789180i	0.990531	−	0.137290i	$-0.0438393\pi$
$881$	40.5718	+	23.4242i	1.36690	+	0.789180i	0.376369	+	0.926470i	$0.377173\pi$
$882$		0			0
$883$	27.7892	+	23.3179i	0.935181	+	0.784710i	0.976740	−	0.214426i	$-0.0687881\pi$
$883$	27.7892	+	23.3179i	0.935181	+	0.784710i	−0.0415592	+	0.999136i	$0.513233\pi$
$884$	5.12497	+	4.30036i	0.172371	+	0.144637i
$885$		0			0
$886$	16.6107	+	9.59018i	0.558047	+	0.322189i
$887$	−4.88361	+	1.77749i	−0.163976	+	0.0596822i	−0.422704	−	0.906268i	$-0.638919\pi$
$887$	−4.88361	+	1.77749i	−0.163976	+	0.0596822i	0.258728	+	0.965950i	$0.416697\pi$
$888$		0			0
$889$	−2.68533	−	0.473497i	−0.0900632	−	0.0158806i
$890$	−10.8233	+	29.7367i	−0.362797	+	0.996777i
$891$		0			0
$892$			10.5463i			0.353118i
$893$	6.68576	−	0.984395i	0.223730	−	0.0329415i
$894$		0			0
$895$	22.7366	+	27.0965i	0.760002	+	0.905735i
$896$	−4.70606	−	1.71286i	−0.157218	−	0.0572228i
$897$		0			0
$898$	−0.773122	−	4.38459i	−0.0257994	−	0.146316i
$899$	−2.26457	−	6.22186i	−0.0755277	−	0.207511i
$900$		0			0
$901$	39.8800	−	23.0248i	1.32860	−	0.767066i
$902$	8.61901	−	10.2717i	0.286982	−	0.342011i
$903$		0			0
$904$	−5.03692	−	8.72420i	−0.167525	−	0.290163i
$905$	−0.268960	+	0.465853i	−0.00894054	+	0.0154855i
$906$		0			0
$907$	24.3325	−	4.29048i	0.807948	−	0.142463i	0.245608	−	0.969369i	$-0.421012\pi$
$907$	24.3325	−	4.29048i	0.807948	−	0.142463i	0.562340	+	0.826906i	$0.309901\pi$
$908$	0.121003	−	0.686243i	0.00401563	−	0.0227738i
$909$		0			0
$910$	−31.5942	+	26.5107i	−1.04734	+	0.878822i
$911$	−49.2986			−1.63334			−0.816668	−	0.577108i	$-0.804181\pi$
$911$	−49.2986			−1.63334			−0.816668	+	0.577108i	$0.804181\pi$
$912$		0			0
$913$	−18.8274			−0.623098
$914$	−8.26518	+	6.93531i	−0.273388	+	0.229400i
$915$		0			0
$916$	−2.37225	+	13.4537i	−0.0783814	+	0.444523i
$917$	−47.3551	+	8.34998i	−1.56380	+	0.275741i
$918$		0			0
$919$	−17.7183	+	30.6891i	−0.584474	+	1.01234i	0.410467	+	0.911875i	$0.365366\pi$
$919$	−17.7183	+	30.6891i	−0.584474	+	1.01234i	−0.994941	+	0.100463i	$0.967968\pi$
$920$	0.0638929	+	0.110666i	0.00210649	+	0.00364854i
$921$		0			0
$922$	16.7906	−	20.0103i	0.552969	−	0.659003i
$923$	25.0584	−	14.4675i	0.824809	−	0.476204i
$924$		0			0
$925$	29.8588	+	82.0364i	0.981752	+	2.69734i
$926$	5.46719	+	31.0060i	0.179663	+	1.01892i
$927$		0			0
$928$	−0.962985	−	0.350498i	−0.0316115	−	0.0115057i
$929$	−22.4403	−	26.7433i	−0.736241	−	0.877418i	0.259859	−	0.965647i	$-0.416324\pi$
$929$	−22.4403	−	26.7433i	−0.736241	−	0.877418i	−0.996100	+	0.0882286i	$0.971879\pi$
$930$		0			0
$931$	15.8799	−	77.1963i	0.520444	−	2.53001i
$932$			16.6406i			0.545082i
$933$		0			0
$934$	−9.41620	+	25.8708i	−0.308107	+	0.846518i
$935$	−29.7350	−	5.24308i	−0.972438	−	0.171467i
$936$		0			0
$937$	−13.4652	+	4.90094i	−0.439889	+	0.160107i	−0.552464	−	0.833537i	$-0.686312\pi$
$937$	−13.4652	+	4.90094i	−0.439889	+	0.160107i	0.112575	+	0.993643i	$0.464090\pi$
$938$	−20.1187	−	11.6155i	−0.656899	−	0.379261i
$939$		0			0
$940$	4.73593	+	3.97392i	0.154469	+	0.129615i
$941$	−39.9788	−	33.5462i	−1.30327	−	1.09358i	−0.989570	−	0.144055i	$-0.953986\pi$
$941$	−39.9788	−	33.5462i	−1.30327	−	1.09358i	−0.313703	−	0.949521i	$-0.601570\pi$
$942$		0			0
$943$	−0.159207	−	0.0919181i	−0.00518449	−	0.00299326i
$944$	1.51211	−	0.550364i	0.0492150	−	0.0179128i
$945$		0			0
$946$	−11.3050	−	1.99338i	−0.367557	−	0.0648103i
$947$	−19.5014	+	53.5797i	−0.633711	+	1.74111i	0.0369214	+	0.999318i	$0.488245\pi$
$947$	−19.5014	+	53.5797i	−0.633711	+	1.74111i	−0.670633	+	0.741789i	$0.733977\pi$
$948$		0			0
$949$			11.7315i			0.380820i
$950$	45.0959	−	14.9804i	1.46311	−	0.486027i
$951$		0			0
$952$	−10.4283	−	12.4280i	−0.337984	−	0.402793i
$953$	32.2015	+	11.7204i	1.04311	+	0.379660i	0.806058	−	0.591837i	$-0.201597\pi$
$953$	32.2015	+	11.7204i	1.04311	+	0.379660i	0.237051	+	0.971497i	$0.423819\pi$
$954$		0			0
$955$	6.80850	+	38.6129i	0.220318	+	1.24948i
$956$	−9.38973	−	25.7981i	−0.303685	−	0.834369i
$957$		0			0
$958$	6.44993	−	3.72387i	0.208388	−	0.120313i
$959$	33.9917	−	40.5097i	1.09765	−	1.30813i
$960$		0			0
$961$	5.37239	+	9.30525i	0.173303	+	0.300169i
$962$	8.26918	−	14.3226i	0.266609	−	0.461780i
$963$		0			0
$964$	26.4315	−	4.66059i	0.851302	−	0.150108i
$965$	10.3965	−	58.9617i	0.334676	−	1.89804i
$966$		0			0
$967$	4.37468	−	3.67079i	0.140680	−	0.118045i	−0.569732	−	0.821831i	$-0.692953\pi$
$967$	4.37468	−	3.67079i	0.140680	−	0.118045i	0.710412	+	0.703786i	$0.248509\pi$
$968$	5.53687			0.177962
$969$		0			0
$970$	49.5101			1.58967
$971$	−14.7974	+	12.4165i	−0.474870	+	0.398463i	−0.848567	−	0.529088i	$-0.822534\pi$
$971$	−14.7974	+	12.4165i	−0.474870	+	0.398463i	0.373697	+	0.927551i	$0.378090\pi$
$972$		0			0
$973$	−7.63566	+	43.3040i	−0.244788	+	1.38826i
$974$	−9.86856	+	1.74009i	−0.316209	+	0.0557562i
$975$		0			0
$976$	−0.877692	+	1.52021i	−0.0280942	+	0.0486607i
$977$	10.4474	+	18.0954i	0.334241	+	0.578923i	0.983339	−	0.181782i	$-0.0581866\pi$
$977$	10.4474	+	18.0954i	0.334241	+	0.578923i	−0.649097	+	0.760705i	$0.724853\pi$
$978$		0			0
$979$	−11.9227	+	14.2089i	−0.381051	+	0.454119i
$980$	62.4411	−	36.0504i	1.99461	−	1.15159i
$981$		0			0
$982$	3.93130	+	10.8012i	0.125453	+	0.344679i
$983$	−3.49764	−	19.8361i	−0.111557	−	0.632673i	−0.988397	−	0.151891i	$-0.951464\pi$
$983$	−3.49764	−	19.8361i	−0.111557	−	0.632673i	0.876840	−	0.480782i	$-0.159647\pi$
$984$		0			0
$985$	4.30147	+	1.56561i	0.137056	+	0.0498844i
$986$	−2.13391	−	2.54310i	−0.0679576	−	0.0809887i
$987$		0			0
$988$	−7.66526	−	4.72014i	−0.243864	−	0.150168i
$989$			0.157384i			0.00500452i
$990$		0			0
$991$	−15.8415	+	43.5242i	−0.503222	+	1.38259i	0.384888	+	0.922963i	$0.374240\pi$
$991$	−15.8415	+	43.5242i	−0.503222	+	1.38259i	−0.888111	+	0.459629i	$0.847982\pi$
$992$	6.36286	+	1.12194i	0.202021	+	0.0356218i
$993$		0			0
$994$	−65.9354	+	23.9985i	−2.09134	+	0.761187i
$995$	−20.9633	−	12.1032i	−0.664581	−	0.383696i
$996$		0			0
$997$	−8.14208	−	6.83202i	−0.257862	−	0.216372i	0.504687	−	0.863303i	$-0.331608\pi$
$997$	−8.14208	−	6.83202i	−0.257862	−	0.216372i	−0.762549	+	0.646930i	$0.776052\pi$
$998$	−16.4390	−	13.7940i	−0.520368	−	0.436640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bb.a.89.1	✓	24
3.2	odd	2		342.2.bb.b.89.4	yes	24
19.3	odd	18		342.2.bb.b.269.4	yes	24
57.41	even	18	inner	342.2.bb.a.269.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.bb.a.89.1	✓	24	1.1	even	1	trivial
342.2.bb.a.269.1	yes	24	57.41	even	18	inner
342.2.bb.b.89.4	yes	24	3.2	odd	2
342.2.bb.b.269.4	yes	24	19.3	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.92710 + 0.692454i) q^{5} +(-2.50404 + 4.33713i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.92710 + 0.692454i) q^{5} +(-2.50404 + 4.33713i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.56323 + 3.05474i) q^{10} +(-2.02419 + 1.16867i) q^{11} +(-0.706340 - 1.94065i) q^{13} +(0.869644 + 4.93200i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-2.08230 - 2.48159i) q^{17} +(3.25836 + 2.89536i) q^{19} +3.98768i q^{20} +(-0.799415 + 2.19638i) q^{22} +(0.0315583 + 0.00556458i) q^{23} +(10.2442 - 3.72857i) q^{25} +(-1.78852 - 1.03260i) q^{26} +(3.83641 + 3.21913i) q^{28} +(0.785032 + 0.658720i) q^{29} +(-5.59541 - 3.23051i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.19026 - 0.562530i) q^{34} +(6.83036 - 18.7663i) q^{35} +8.00812i q^{37} +(4.35715 + 0.123539i) q^{38} +(2.56323 + 3.05474i) q^{40} +(-5.39082 - 1.96210i) q^{41} +(0.852842 + 4.83671i) q^{43} +(0.799415 + 2.19638i) q^{44} +(0.0277519 - 0.0160226i) q^{46} +(0.996549 - 1.18764i) q^{47} +(-9.04044 - 15.6585i) q^{49} +(5.45080 - 9.44107i) q^{50} +(-2.03382 + 0.358618i) q^{52} +(-2.46843 + 13.9991i) q^{53} +(7.13995 - 5.99113i) q^{55} +5.00808 q^{56} +1.02479 q^{58} +(-1.23268 + 1.03435i) q^{59} +(0.304819 - 1.72872i) q^{61} +(-6.36286 + 1.12194i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(4.11768 + 7.13203i) q^{65} +(-2.98171 + 3.55346i) q^{67} +(-2.80547 + 1.61974i) q^{68} +(-6.83036 - 18.7663i) q^{70} +(2.43294 + 13.7979i) q^{71} +(-5.33798 - 1.94287i) q^{73} +(5.14752 + 6.13457i) q^{74} +(3.41718 - 2.70608i) q^{76} -11.7056i q^{77} +(3.77857 - 10.3815i) q^{79} +(3.92710 + 0.692454i) q^{80} +(-5.39082 + 1.96210i) q^{82} +(6.97592 + 4.02755i) q^{83} +(9.89577 + 8.30354i) q^{85} +(3.76229 + 3.15694i) q^{86} +(2.02419 + 1.16867i) q^{88} +(7.45714 - 2.71418i) q^{89} +(10.1856 + 1.79599i) q^{91} +(0.0109601 - 0.0301126i) q^{92} -1.55035i q^{94} +(-14.8008 - 9.11409i) q^{95} +(-7.98070 - 9.51103i) q^{97} +(-16.9905 - 6.18402i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{8}+O(q^{10}) \) 24 * q - 12 * q^8	\( 24 q - 12 q^{8} - 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} - 36 q^{26} + 12 q^{29} + 12 q^{34} + 48 q^{35} + 12 q^{38} + 12 q^{41} - 12 q^{44} - 36 q^{46} - 60 q^{47} - 36 q^{49} + 24 q^{50} + 48 q^{53} - 60 q^{55} - 24 q^{58} - 24 q^{59} - 60 q^{61} - 24 q^{62} - 12 q^{64} + 24 q^{65} - 48 q^{70} + 36 q^{71} + 24 q^{79} + 12 q^{82} - 72 q^{83} + 36 q^{86} + 120 q^{89} - 24 q^{91} - 12 q^{95}+O(q^{100}) \) 24 * q - 12 * q^8 - 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 - 36 * q^26 + 12 * q^29 + 12 * q^34 + 48 * q^35 + 12 * q^38 + 12 * q^41 - 12 * q^44 - 36 * q^46 - 60 * q^47 - 36 * q^49 + 24 * q^50 + 48 * q^53 - 60 * q^55 - 24 * q^58 - 24 * q^59 - 60 * q^61 - 24 * q^62 - 12 * q^64 + 24 * q^65 - 48 * q^70 + 36 * q^71 + 24 * q^79 + 12 * q^82 - 72 * q^83 + 36 * q^86 + 120 * q^89 - 24 * q^91 - 12 * q^95

Introduction

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