LMFDB - Embedded newform 1200.3.bg.q.1057.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,3,Mod(193,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1200.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1200.bg (of order $4$, degree $2$, not 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:	$32.6976317232$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 269x^{4} - 1116x^{3} + 2312x^{2} + 680x + 100 $ x^8 - 4x^7 + 8x^6 + 269x^4 - 1116x^3 + 2312x^2 + 680x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.2
Root			$-2.88489 - 2.88489i$ of defining polynomial
Character	$\chi$	$=$	1200.1057
Dual form			1200.3.bg.q.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(6.02356 + 6.02356i) q^{7} -3.00000i q^{9} +O(q^{10})$	$q+(-1.22474 + 1.22474i) q^{3} +(6.02356 + 6.02356i) q^{7} -3.00000i q^{9} -17.0038 q^{11} +(-0.124585 + 0.124585i) q^{13} +(-10.7744 - 10.7744i) q^{17} -4.04713i q^{19} -14.7547 q^{21} +(1.85568 - 1.85568i) q^{23} +(3.67423 + 3.67423i) q^{27} -54.4448i q^{29} +53.1995 q^{31} +(20.8254 - 20.8254i) q^{33} +(-21.2693 - 21.2693i) q^{37} -0.305169i q^{39} -52.1414 q^{41} +(-50.4554 + 50.4554i) q^{43} +(13.4045 + 13.4045i) q^{47} +23.5667i q^{49} +26.3918 q^{51} +(-12.4315 + 12.4315i) q^{53} +(4.95670 + 4.95670i) q^{57} -8.79413i q^{59} +105.860 q^{61} +(18.0707 - 18.0707i) q^{63} +(-46.8595 - 46.8595i) q^{67} +4.54547i q^{69} +56.8955 q^{71} +(52.7296 - 52.7296i) q^{73} +(-102.424 - 102.424i) q^{77} -15.2920i q^{79} -9.00000 q^{81} +(46.1914 - 46.1914i) q^{83} +(66.6810 + 66.6810i) q^{87} -0.948538i q^{89} -1.50089 q^{91} +(-65.1558 + 65.1558i) q^{93} +(-77.6693 - 77.6693i) q^{97} +51.0115i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 32 q^{11} + 4 q^{13} - 52 q^{17} - 24 q^{21} - 40 q^{23} - 96 q^{31} - 60 q^{33} + 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} + 168 q^{51} - 108 q^{53} + 24 q^{57} + 264 q^{61} + 12 q^{63} - 216 q^{67} + 240 q^{71} + 208 q^{73} - 168 q^{77} - 72 q^{81} + 336 q^{83} + 252 q^{87} - 592 q^{91} - 264 q^{93} + 208 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 32 * q^11 + 4 * q^13 - 52 * q^17 - 24 * q^21 - 40 * q^23 - 96 * q^31 - 60 * q^33 + 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 + 168 * q^51 - 108 * q^53 + 24 * q^57 + 264 * q^61 + 12 * q^63 - 216 * q^67 + 240 * q^71 + 208 * q^73 - 168 * q^77 - 72 * q^81 + 336 * q^83 + 252 * q^87 - 592 * q^91 - 264 * q^93 + 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	6.02356	+	6.02356i	0.860509	+	0.860509i	0.991397	−	0.130888i	$-0.0417828\pi$
$7$	6.02356	+	6.02356i	0.860509	+	0.860509i	−0.130888	+	0.991397i	$0.541783\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−17.0038			−1.54580			−0.772901	−	0.634526i	$-0.781195\pi$
$11$	−17.0038			−1.54580			−0.772901	+	0.634526i	$0.781195\pi$
$12$		0			0
$13$	−0.124585	+	0.124585i	−0.00958344	+	0.00958344i	−0.711882	−	0.702299i	$-0.752157\pi$
$13$	−0.124585	+	0.124585i	−0.00958344	+	0.00958344i	0.702299	+	0.711882i	$0.252157\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−10.7744	−	10.7744i	−0.633788	−	0.633788i	0.315228	−	0.949016i	$-0.397919\pi$
$17$	−10.7744	−	10.7744i	−0.633788	−	0.633788i	−0.949016	+	0.315228i	$0.897919\pi$
$18$		0			0
$19$		−	4.04713i		−	0.213007i	−0.994312	−	0.106503i	$-0.966035\pi$
$19$		−	4.04713i		−	0.213007i	0.994312	−	0.106503i	$-0.0339655\pi$
$20$		0			0
$21$	−14.7547			−0.702603
$22$		0			0
$23$	1.85568	−	1.85568i	0.0806817	−	0.0806817i	−0.665614	−	0.746296i	$-0.731830\pi$
$23$	1.85568	−	1.85568i	0.0806817	−	0.0806817i	0.746296	+	0.665614i	$0.231830\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$		−	54.4448i		−	1.87741i	−0.344724	−	0.938704i	$-0.612028\pi$
$29$		−	54.4448i		−	1.87741i	0.344724	−	0.938704i	$-0.387972\pi$
$30$		0			0
$31$	53.1995			1.71611			0.858056	−	0.513556i	$-0.171672\pi$
$31$	53.1995			1.71611			0.858056	+	0.513556i	$0.171672\pi$
$32$		0			0
$33$	20.8254	−	20.8254i	0.631071	−	0.631071i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−21.2693	−	21.2693i	−0.574846	−	0.574846i	0.358633	−	0.933479i	$-0.383243\pi$
$37$	−21.2693	−	21.2693i	−0.574846	−	0.574846i	−0.933479	+	0.358633i	$0.883243\pi$
$38$		0			0
$39$		−	0.305169i		−	0.00782484i
$40$		0			0
$41$	−52.1414			−1.27174			−0.635871	−	0.771796i	$-0.719359\pi$
$41$	−52.1414			−1.27174			−0.635871	+	0.771796i	$0.719359\pi$
$42$		0			0
$43$	−50.4554	+	50.4554i	−1.17338	+	1.17338i	−0.191984	+	0.981398i	$0.561492\pi$
$43$	−50.4554	+	50.4554i	−1.17338	+	1.17338i	−0.981398	+	0.191984i	$0.938508\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	13.4045	+	13.4045i	0.285201	+	0.285201i	0.835179	−	0.549978i	$-0.185364\pi$
$47$	13.4045	+	13.4045i	0.285201	+	0.285201i	−0.549978	+	0.835179i	$0.685364\pi$
$48$		0			0
$49$			23.5667i			0.480952i
$50$		0			0
$51$	26.3918			0.517486
$52$		0			0
$53$	−12.4315	+	12.4315i	−0.234556	+	0.234556i	−0.814591	−	0.580035i	$-0.803039\pi$
$53$	−12.4315	+	12.4315i	−0.234556	+	0.234556i	0.580035	+	0.814591i	$0.303039\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.95670	+	4.95670i	0.0869596	+	0.0869596i
$58$		0			0
$59$		−	8.79413i		−	0.149053i	−0.997219	−	0.0745265i	$-0.976255\pi$
$59$		−	8.79413i		−	0.149053i	0.997219	−	0.0745265i	$-0.0237445\pi$
$60$		0			0
$61$	105.860			1.73542			0.867708	−	0.497074i	$-0.165592\pi$
$61$	105.860			1.73542			0.867708	+	0.497074i	$0.165592\pi$
$62$		0			0
$63$	18.0707	−	18.0707i	0.286836	−	0.286836i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−46.8595	−	46.8595i	−0.699396	−	0.699396i	0.264885	−	0.964280i	$-0.414666\pi$
$67$	−46.8595	−	46.8595i	−0.699396	−	0.699396i	−0.964280	+	0.264885i	$0.914666\pi$
$68$		0			0
$69$			4.54547i			0.0658763i
$70$		0			0
$71$	56.8955			0.801346			0.400673	−	0.916221i	$-0.368776\pi$
$71$	56.8955			0.801346			0.400673	+	0.916221i	$0.368776\pi$
$72$		0			0
$73$	52.7296	−	52.7296i	0.722324	−	0.722324i	−0.246754	−	0.969078i	$-0.579364\pi$
$73$	52.7296	−	52.7296i	0.722324	−	0.722324i	0.969078	+	0.246754i	$0.0793640\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−102.424	−	102.424i	−1.33018	−	1.33018i
$78$		0			0
$79$		−	15.2920i		−	0.193569i	−0.995305	−	0.0967846i	$-0.969144\pi$
$79$		−	15.2920i		−	0.193569i	0.995305	−	0.0967846i	$-0.0308558\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	46.1914	−	46.1914i	0.556523	−	0.556523i	−0.371792	−	0.928316i	$-0.621257\pi$
$83$	46.1914	−	46.1914i	0.556523	−	0.556523i	0.928316	+	0.371792i	$0.121257\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	66.6810	+	66.6810i	0.766449	+	0.766449i
$88$		0			0
$89$		−	0.948538i		−	0.0106577i	−0.999986	−	0.00532886i	$-0.998304\pi$
$89$		−	0.948538i		−	0.0106577i	0.999986	−	0.00532886i	$-0.00169624\pi$
$90$		0			0
$91$	−1.50089			−0.0164933
$92$		0			0
$93$	−65.1558	+	65.1558i	−0.700600	+	0.700600i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−77.6693	−	77.6693i	−0.800715	−	0.800715i	0.182492	−	0.983207i	$-0.441583\pi$
$97$	−77.6693	−	77.6693i	−0.800715	−	0.800715i	−0.983207	+	0.182492i	$0.941583\pi$
$98$		0			0
$99$			51.0115i			0.515268i
$100$		0			0
$101$	−49.6243			−0.491329			−0.245665	−	0.969355i	$-0.579006\pi$
$101$	−49.6243			−0.491329			−0.245665	+	0.969355i	$0.579006\pi$
$102$		0			0
$103$	18.7930	−	18.7930i	0.182457	−	0.182457i	−0.609969	−	0.792425i	$-0.708818\pi$
$103$	18.7930	−	18.7930i	0.182457	−	0.182457i	0.792425	+	0.609969i	$0.208818\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−69.0004	−	69.0004i	−0.644863	−	0.644863i	0.306884	−	0.951747i	$-0.400714\pi$
$107$	−69.0004	−	69.0004i	−0.644863	−	0.644863i	−0.951747	+	0.306884i	$0.900714\pi$
$108$		0			0
$109$		−	130.003i		−	1.19268i	−0.802730	−	0.596342i	$-0.796620\pi$
$109$		−	130.003i		−	1.19268i	0.802730	−	0.596342i	$-0.203380\pi$
$110$		0			0
$111$	52.0989			0.469360
$112$		0			0
$113$	157.585	−	157.585i	1.39456	−	1.39456i	0.579799	−	0.814760i	$-0.303131\pi$
$113$	157.585	−	157.585i	1.39456	−	1.39456i	0.814760	−	0.579799i	$-0.196869\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.373754	+	0.373754i	0.00319448	+	0.00319448i
$118$		0			0
$119$		−	129.801i		−	1.09076i
$120$		0			0
$121$	168.130			1.38951
$122$		0			0
$123$	63.8599	−	63.8599i	0.519186	−	0.519186i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−106.268	−	106.268i	−0.836753	−	0.836753i	0.151677	−	0.988430i	$-0.451533\pi$
$127$	−106.268	−	106.268i	−0.836753	−	0.836753i	−0.988430	+	0.151677i	$0.951533\pi$
$128$		0			0
$129$		−	123.590i		−	0.958062i
$130$		0			0
$131$	102.890			0.785421			0.392711	−	0.919662i	$-0.371537\pi$
$131$	102.890			0.785421			0.392711	+	0.919662i	$0.371537\pi$
$132$		0			0
$133$	24.3781	−	24.3781i	0.183294	−	0.183294i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	84.7079	+	84.7079i	0.618306	+	0.618306i	0.945097	−	0.326791i	$-0.105967\pi$
$137$	84.7079	+	84.7079i	0.618306	+	0.618306i	−0.326791	+	0.945097i	$0.605967\pi$
$138$		0			0
$139$		−	244.050i		−	1.75575i	−0.478887	−	0.877877i	$-0.658960\pi$
$139$		−	244.050i		−	1.75575i	0.478887	−	0.877877i	$-0.341040\pi$
$140$		0			0
$141$	−32.8341			−0.232866
$142$		0			0
$143$	2.11842	−	2.11842i	0.0148141	−	0.0148141i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−28.8631	−	28.8631i	−0.196348	−	0.196348i
$148$		0			0
$149$		−	220.759i		−	1.48161i	−0.671722	−	0.740803i	$-0.734445\pi$
$149$		−	220.759i		−	1.48161i	0.671722	−	0.740803i	$-0.265555\pi$
$150$		0			0
$151$	−217.984			−1.44360			−0.721802	−	0.692099i	$-0.756686\pi$
$151$	−217.984			−1.44360			−0.721802	+	0.692099i	$0.756686\pi$
$152$		0			0
$153$	−32.3232	+	32.3232i	−0.211263	+	0.211263i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	185.043	+	185.043i	1.17862	+	1.17862i	0.980096	+	0.198522i	$0.0636141\pi$
$157$	185.043	+	185.043i	1.17862	+	1.17862i	0.198522	+	0.980096i	$0.436386\pi$
$158$		0			0
$159$		−	30.4508i		−	0.191514i
$160$		0			0
$161$	22.3556			0.138855
$162$		0			0
$163$	−15.5263	+	15.5263i	−0.0952533	+	0.0952533i	−0.753128	−	0.657874i	$-0.771456\pi$
$163$	−15.5263	+	15.5263i	−0.0952533	+	0.0952533i	0.657874	+	0.753128i	$0.271456\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−21.5448	−	21.5448i	−0.129011	−	0.129011i	0.639653	−	0.768664i	$-0.279078\pi$
$167$	−21.5448	−	21.5448i	−0.129011	−	0.129011i	−0.768664	+	0.639653i	$0.779078\pi$
$168$		0			0
$169$			168.969i			0.999816i
$170$		0			0
$171$	−12.1414			−0.0710023
$172$		0			0
$173$	−86.5808	+	86.5808i	−0.500467	+	0.500467i	−0.911583	−	0.411116i	$-0.865139\pi$
$173$	−86.5808	+	86.5808i	−0.500467	+	0.500467i	0.411116	+	0.911583i	$0.365139\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.7706	+	10.7706i	0.0608507	+	0.0608507i
$178$		0			0
$179$		−	45.4647i		−	0.253993i	−0.991903	−	0.126996i	$-0.959466\pi$
$179$		−	45.4647i		−	0.253993i	0.991903	−	0.126996i	$-0.0405336\pi$
$180$		0			0
$181$	13.4991			0.0745807			0.0372903	−	0.999304i	$-0.488127\pi$
$181$	13.4991			0.0745807			0.0372903	+	0.999304i	$0.488127\pi$
$182$		0			0
$183$	−129.652	+	129.652i	−0.708481	+	0.708481i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	183.206	+	183.206i	0.979711	+	0.979711i
$188$		0			0
$189$			44.2640i			0.234201i
$190$		0			0
$191$	−67.6690			−0.354288			−0.177144	−	0.984185i	$-0.556686\pi$
$191$	−67.6690			−0.354288			−0.177144	+	0.984185i	$0.556686\pi$
$192$		0			0
$193$	−31.9967	+	31.9967i	−0.165786	+	0.165786i	−0.785124	−	0.619338i	$-0.787401\pi$
$193$	−31.9967	+	31.9967i	−0.165786	+	0.165786i	0.619338	+	0.785124i	$0.287401\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−122.056	−	122.056i	−0.619575	−	0.619575i	0.325848	−	0.945422i	$-0.394350\pi$
$197$	−122.056	−	122.056i	−0.619575	−	0.619575i	−0.945422	+	0.325848i	$0.894350\pi$
$198$		0			0
$199$		−	4.36392i		−	0.0219292i	−0.999940	−	0.0109646i	$-0.996510\pi$
$199$		−	4.36392i		−	0.0219292i	0.999940	−	0.0109646i	$-0.00349022\pi$
$200$		0			0
$201$	114.782			0.571054
$202$		0			0
$203$	327.952	−	327.952i	1.61553	−	1.61553i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.56704	−	5.56704i	−0.0268939	−	0.0268939i
$208$		0			0
$209$			68.8167i			0.329266i
$210$		0			0
$211$	−183.096			−0.867756			−0.433878	−	0.900972i	$-0.642855\pi$
$211$	−183.096			−0.867756			−0.433878	+	0.900972i	$0.642855\pi$
$212$		0			0
$213$	−69.6825	+	69.6825i	−0.327148	+	0.327148i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	320.451	+	320.451i	1.47673	+	1.47673i
$218$		0			0
$219$			129.161i			0.589775i
$220$		0			0
$221$	2.68465			0.0121477
$222$		0			0
$223$	−5.03964	+	5.03964i	−0.0225993	+	0.0225993i	−0.718316	−	0.695717i	$-0.755087\pi$
$223$	−5.03964	+	5.03964i	−0.0225993	+	0.0225993i	0.695717	+	0.718316i	$0.255087\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−226.475	−	226.475i	−0.997689	−	0.997689i	0.00230792	−	0.999997i	$-0.499265\pi$
$227$	−226.475	−	226.475i	−0.997689	−	0.997689i	−0.999997	+	0.00230792i	$0.999265\pi$
$228$		0			0
$229$			276.917i			1.20924i	0.796513	+	0.604621i	$0.206676\pi$
$229$			276.917i			1.20924i	−0.796513	+	0.604621i	$0.793324\pi$
$230$		0			0
$231$	250.886			1.08609
$232$		0			0
$233$	−198.106	+	198.106i	−0.850242	+	0.850242i	−0.990163	−	0.139921i	$-0.955315\pi$
$233$	−198.106	+	198.106i	−0.850242	+	0.850242i	0.139921	+	0.990163i	$0.455315\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	18.7288	+	18.7288i	0.0790243	+	0.0790243i
$238$		0			0
$239$			230.183i			0.963111i	0.876416	+	0.481555i	$0.159928\pi$
$239$			230.183i			0.963111i	−0.876416	+	0.481555i	$0.840072\pi$
$240$		0			0
$241$	283.542			1.17652			0.588261	−	0.808671i	$-0.299813\pi$
$241$	283.542			1.17652			0.588261	+	0.808671i	$0.299813\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.504210	+	0.504210i	0.00204134	+	0.00204134i
$248$		0			0
$249$			113.145i			0.454400i
$250$		0			0
$251$	−202.731			−0.807694			−0.403847	−	0.914826i	$-0.632327\pi$
$251$	−202.731			−0.807694			−0.403847	+	0.914826i	$0.632327\pi$
$252$		0			0
$253$	−31.5536	+	31.5536i	−0.124718	+	0.124718i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−202.151	−	202.151i	−0.786580	−	0.786580i	0.194352	−	0.980932i	$-0.437740\pi$
$257$	−202.151	−	202.151i	−0.786580	−	0.786580i	−0.980932	+	0.194352i	$0.937740\pi$
$258$		0			0
$259$		−	256.234i		−	0.989320i
$260$		0			0
$261$	−163.334			−0.625803
$262$		0			0
$263$	−34.3895	+	34.3895i	−0.130759	+	0.130759i	−0.769457	−	0.638699i	$-0.779473\pi$
$263$	−34.3895	+	34.3895i	−0.130759	+	0.130759i	0.638699	+	0.769457i	$0.279473\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.16172	+	1.16172i	0.00435100	+	0.00435100i
$268$		0			0
$269$			32.5471i			0.120993i	0.998168	+	0.0604964i	$0.0192684\pi$
$269$			32.5471i			0.120993i	−0.998168	+	0.0604964i	$0.980732\pi$
$270$		0			0
$271$	91.9490			0.339295			0.169648	−	0.985505i	$-0.445737\pi$
$271$	91.9490			0.339295			0.169648	+	0.985505i	$0.445737\pi$
$272$		0			0
$273$	1.83820	−	1.83820i	0.00673335	−	0.00673335i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−27.6712	−	27.6712i	−0.0998959	−	0.0998959i	0.655393	−	0.755288i	$-0.272503\pi$
$277$	−27.6712	−	27.6712i	−0.0998959	−	0.0998959i	−0.755288	+	0.655393i	$0.772503\pi$
$278$		0			0
$279$		−	159.598i		−	0.572038i
$280$		0			0
$281$	183.408			0.652697			0.326348	−	0.945250i	$-0.394182\pi$
$281$	183.408			0.652697			0.326348	+	0.945250i	$0.394182\pi$
$282$		0			0
$283$	−333.158	+	333.158i	−1.17724	+	1.17724i	−0.196793	+	0.980445i	$0.563053\pi$
$283$	−333.158	+	333.158i	−1.17724	+	1.17724i	−0.980445	+	0.196793i	$0.936947\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−314.077	−	314.077i	−1.09434	−	1.09434i
$288$		0			0
$289$		−	56.8248i		−	0.196626i
$290$		0			0
$291$	190.250			0.653781
$292$		0			0
$293$	185.884	−	185.884i	0.634417	−	0.634417i	−0.314756	−	0.949173i	$-0.601923\pi$
$293$	185.884	−	185.884i	0.634417	−	0.634417i	0.949173	+	0.314756i	$0.101923\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−62.4761	−	62.4761i	−0.210357	−	0.210357i
$298$		0			0
$299$			0.462378i			0.00154642i
$300$		0			0
$301$	−607.843			−2.01941
$302$		0			0
$303$	60.7770	−	60.7770i	0.200584	−	0.200584i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−184.175	−	184.175i	−0.599920	−	0.599920i	0.340371	−	0.940291i	$-0.389447\pi$
$307$	−184.175	−	184.175i	−0.599920	−	0.599920i	−0.940291	+	0.340371i	$0.889447\pi$
$308$		0			0
$309$			46.0333i			0.148975i
$310$		0			0
$311$	−191.522			−0.615826			−0.307913	−	0.951415i	$-0.599631\pi$
$311$	−191.522			−0.615826			−0.307913	+	0.951415i	$0.599631\pi$
$312$		0			0
$313$	257.541	−	257.541i	0.822815	−	0.822815i	−0.163696	−	0.986511i	$-0.552342\pi$
$313$	257.541	−	257.541i	0.822815	−	0.822815i	0.986511	+	0.163696i	$0.0523415\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−162.518	−	162.518i	−0.512674	−	0.512674i	0.402671	−	0.915345i	$-0.368082\pi$
$317$	−162.518	−	162.518i	−0.512674	−	0.512674i	−0.915345	+	0.402671i	$0.868082\pi$
$318$		0			0
$319$			925.771i			2.90210i
$320$		0			0
$321$	169.016			0.526529
$322$		0			0
$323$	−43.6054	+	43.6054i	−0.135001	+	0.135001i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	159.220	+	159.220i	0.486911	+	0.486911i
$328$		0			0
$329$			161.485i			0.490837i
$330$		0			0
$331$	−49.0405			−0.148159			−0.0740793	−	0.997252i	$-0.523602\pi$
$331$	−49.0405			−0.148159			−0.0740793	+	0.997252i	$0.523602\pi$
$332$		0			0
$333$	−63.8079	+	63.8079i	−0.191615	+	0.191615i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	17.6580	+	17.6580i	0.0523977	+	0.0523977i	0.732820	−	0.680422i	$-0.238204\pi$
$337$	17.6580	+	17.6580i	0.0523977	+	0.0523977i	−0.680422	+	0.732820i	$0.738204\pi$
$338$		0			0
$339$			386.003i			1.13865i
$340$		0			0
$341$	−904.595			−2.65277
$342$		0			0
$343$	153.199	−	153.199i	0.446646	−	0.446646i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	296.136	+	296.136i	0.853417	+	0.853417i	0.990552	−	0.137135i	$-0.0437894\pi$
$347$	296.136	+	296.136i	0.853417	+	0.853417i	−0.137135	+	0.990552i	$0.543789\pi$
$348$		0			0
$349$			217.733i			0.623877i	0.950102	+	0.311939i	$0.100978\pi$
$349$			217.733i			0.623877i	−0.950102	+	0.311939i	$0.899022\pi$
$350$		0			0
$351$	−0.915507			−0.00260828
$352$		0			0
$353$	−70.0501	+	70.0501i	−0.198442	+	0.198442i	−0.799332	−	0.600890i	$-0.794813\pi$
$353$	−70.0501	+	70.0501i	−0.198442	+	0.198442i	0.600890	+	0.799332i	$0.294813\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	158.973	+	158.973i	0.445301	+	0.445301i
$358$		0			0
$359$		−	265.093i		−	0.738422i	−0.929346	−	0.369211i	$-0.879628\pi$
$359$		−	265.093i		−	0.738422i	0.929346	−	0.369211i	$-0.120372\pi$
$360$		0			0
$361$	344.621			0.954628
$362$		0			0
$363$	−205.917	+	205.917i	−0.567263	+	0.567263i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	473.377	+	473.377i	1.28986	+	1.28986i	0.934872	+	0.354984i	$0.115514\pi$
$367$	473.377	+	473.377i	1.28986	+	1.28986i	0.354984	+	0.934872i	$0.384486\pi$
$368$		0			0
$369$			156.424i			0.423914i
$370$		0			0
$371$	−149.764			−0.403675
$372$		0			0
$373$	−201.623	+	201.623i	−0.540544	+	0.540544i	−0.923688	−	0.383144i	$-0.874841\pi$
$373$	−201.623	+	201.623i	−0.540544	+	0.540544i	0.383144	+	0.923688i	$0.374841\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.78299	+	6.78299i	0.0179920	+	0.0179920i
$378$		0			0
$379$			230.312i			0.607684i	0.952722	+	0.303842i	$0.0982695\pi$
$379$			230.312i			0.607684i	−0.952722	+	0.303842i	$0.901730\pi$
$380$		0			0
$381$	260.301			0.683206
$382$		0			0
$383$	−312.599	+	312.599i	−0.816185	+	0.816185i	−0.985553	−	0.169368i	$-0.945827\pi$
$383$	−312.599	+	312.599i	−0.816185	+	0.816185i	0.169368	+	0.985553i	$0.445827\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	151.366	+	151.366i	0.391127	+	0.391127i
$388$		0			0
$389$		−	555.109i		−	1.42702i	−0.700647	−	0.713508i	$-0.747105\pi$
$389$		−	555.109i		−	1.42702i	0.700647	−	0.713508i	$-0.252895\pi$
$390$		0			0
$391$	−39.9876			−0.102270
$392$		0			0
$393$	−126.014	+	126.014i	−0.320647	+	0.320647i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−221.888	−	221.888i	−0.558911	−	0.558911i	0.370086	−	0.928997i	$-0.379328\pi$
$397$	−221.888	−	221.888i	−0.558911	−	0.558911i	−0.928997	+	0.370086i	$0.879328\pi$
$398$		0			0
$399$			59.7140i			0.149659i
$400$		0			0
$401$	−319.629			−0.797079			−0.398540	−	0.917151i	$-0.630483\pi$
$401$	−319.629			−0.797079			−0.398540	+	0.917151i	$0.630483\pi$
$402$		0			0
$403$	−6.62784	+	6.62784i	−0.0164463	+	0.0164463i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	361.659	+	361.659i	0.888598	+	0.888598i
$408$		0			0
$409$		−	40.1118i		−	0.0980730i	−0.998797	−	0.0490365i	$-0.984385\pi$
$409$		−	40.1118i		−	0.0980730i	0.998797	−	0.0490365i	$-0.0156151\pi$
$410$		0			0
$411$	−207.491			−0.504844
$412$		0			0
$413$	52.9720	−	52.9720i	0.128262	−	0.128262i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	298.899	+	298.899i	0.716783	+	0.716783i
$418$		0			0
$419$			345.933i			0.825616i	0.910818	+	0.412808i	$0.135452\pi$
$419$			345.933i			0.825616i	−0.910818	+	0.412808i	$0.864548\pi$
$420$		0			0
$421$	−105.186			−0.249849			−0.124925	−	0.992166i	$-0.539869\pi$
$421$	−105.186			−0.249849			−0.124925	+	0.992166i	$0.539869\pi$
$422$		0			0
$423$	40.2134	−	40.2134i	0.0950672	−	0.0950672i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	637.657	+	637.657i	1.49334	+	1.49334i
$428$		0			0
$429$			5.18904i			0.0120957i
$430$		0			0
$431$	−147.504			−0.342236			−0.171118	−	0.985251i	$-0.554738\pi$
$431$	−147.504			−0.342236			−0.171118	+	0.985251i	$0.554738\pi$
$432$		0			0
$433$	−202.619	+	202.619i	−0.467942	+	0.467942i	−0.901247	−	0.433305i	$-0.857347\pi$
$433$	−202.619	+	202.619i	−0.467942	+	0.467942i	0.433305	+	0.901247i	$0.357347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.51017	−	7.51017i	−0.0171857	−	0.0171857i
$438$		0			0
$439$		−	513.562i		−	1.16985i	−0.811089	−	0.584923i	$-0.801125\pi$
$439$		−	513.562i		−	1.16985i	0.811089	−	0.584923i	$-0.198875\pi$
$440$		0			0
$441$	70.7000			0.160317
$442$		0			0
$443$	−200.016	+	200.016i	−0.451503	+	0.451503i	−0.895853	−	0.444350i	$-0.853435\pi$
$443$	−200.016	+	200.016i	−0.451503	+	0.451503i	0.444350	+	0.895853i	$0.353435\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	270.374	+	270.374i	0.604863	+	0.604863i
$448$		0			0
$449$			387.201i			0.862363i	0.902265	+	0.431182i	$0.141903\pi$
$449$			387.201i			0.862363i	−0.902265	+	0.431182i	$0.858097\pi$
$450$		0			0
$451$	886.603			1.96586
$452$		0			0
$453$	266.975	−	266.975i	0.589349	−	0.589349i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	124.992	+	124.992i	0.273505	+	0.273505i	0.830509	−	0.557005i	$-0.188049\pi$
$457$	124.992	+	124.992i	0.273505	+	0.273505i	−0.557005	+	0.830509i	$0.688049\pi$
$458$		0			0
$459$		−	79.1753i		−	0.172495i
$460$		0			0
$461$	−420.024			−0.911114			−0.455557	−	0.890207i	$-0.650560\pi$
$461$	−420.024			−0.911114			−0.455557	+	0.890207i	$0.650560\pi$
$462$		0			0
$463$	228.184	−	228.184i	0.492839	−	0.492839i	−0.416361	−	0.909200i	$-0.636695\pi$
$463$	228.184	−	228.184i	0.492839	−	0.492839i	0.909200	+	0.416361i	$0.136695\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.4129	+	17.4129i	0.0372867	+	0.0372867i	0.725504	−	0.688218i	$-0.241607\pi$
$467$	17.4129	+	17.4129i	0.0372867	+	0.0372867i	−0.688218	+	0.725504i	$0.741607\pi$
$468$		0			0
$469$		−	564.522i		−	1.20367i
$470$		0			0
$471$	−453.261			−0.962338
$472$		0			0
$473$	857.935	−	857.935i	1.81382	−	1.81382i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	37.2944	+	37.2944i	0.0781854	+	0.0781854i
$478$		0			0
$479$		−	319.260i		−	0.666514i	−0.942836	−	0.333257i	$-0.891852\pi$
$479$		−	319.260i		−	0.666514i	0.942836	−	0.333257i	$-0.108148\pi$
$480$		0			0
$481$	5.29966			0.0110180
$482$		0			0
$483$	−27.3799	+	27.3799i	−0.0566872	+	0.0566872i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−276.414	−	276.414i	−0.567586	−	0.567586i	0.363865	−	0.931452i	$-0.381457\pi$
$487$	−276.414	−	276.414i	−0.567586	−	0.567586i	−0.931452	+	0.363865i	$0.881457\pi$
$488$		0			0
$489$		−	38.0315i		−	0.0777740i
$490$		0			0
$491$	−42.5613			−0.0866829			−0.0433414	−	0.999060i	$-0.513800\pi$
$491$	−42.5613			−0.0866829			−0.0433414	+	0.999060i	$0.513800\pi$
$492$		0			0
$493$	−586.610	+	586.610i	−1.18988	+	1.18988i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	342.714	+	342.714i	0.689565	+	0.689565i
$498$		0			0
$499$			669.280i			1.34124i	0.741800	+	0.670621i	$0.233972\pi$
$499$			669.280i			1.34124i	−0.741800	+	0.670621i	$0.766028\pi$
$500$		0			0
$501$	52.7739			0.105337
$502$		0			0
$503$	−3.01493	+	3.01493i	−0.00599389	+	0.00599389i	−0.710097	−	0.704103i	$-0.751349\pi$
$503$	−3.01493	+	3.01493i	−0.00599389	+	0.00599389i	0.704103	+	0.710097i	$0.251349\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−206.944	−	206.944i	−0.408173	−	0.408173i
$508$		0			0
$509$			506.628i			0.995339i	0.867367	+	0.497670i	$0.165811\pi$
$509$			506.628i			0.995339i	−0.867367	+	0.497670i	$0.834189\pi$
$510$		0			0
$511$	635.241			1.24313
$512$		0			0
$513$	14.8701	−	14.8701i	0.0289865	−	0.0289865i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−227.927	−	227.927i	−0.440865	−	0.440865i
$518$		0			0
$519$		−	212.079i		−	0.408630i
$520$		0			0
$521$	399.589			0.766966			0.383483	−	0.923548i	$-0.374725\pi$
$521$	399.589			0.766966			0.383483	+	0.923548i	$0.374725\pi$
$522$		0			0
$523$	−404.156	+	404.156i	−0.772764	+	0.772764i	−0.978589	−	0.205824i	$-0.934012\pi$
$523$	−404.156	+	404.156i	−0.772764	+	0.772764i	0.205824	+	0.978589i	$0.434012\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−573.192	−	573.192i	−1.08765	−	1.08765i
$528$		0			0
$529$			522.113i			0.986981i
$530$		0			0
$531$	−26.3824			−0.0496844
$532$		0			0
$533$	6.49602	−	6.49602i	0.0121877	−	0.0121877i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	55.6826	+	55.6826i	0.103692	+	0.103692i
$538$		0			0
$539$		−	400.723i		−	0.743457i
$540$		0			0
$541$	−766.639			−1.41708			−0.708538	−	0.705672i	$-0.750645\pi$
$541$	−766.639			−1.41708			−0.708538	+	0.705672i	$0.750645\pi$
$542$		0			0
$543$	−16.5330	+	16.5330i	−0.0304474	+	0.0304474i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−192.460	−	192.460i	−0.351846	−	0.351846i	0.508950	−	0.860796i	$-0.330034\pi$
$547$	−192.460	−	192.460i	−0.351846	−	0.351846i	−0.860796	+	0.508950i	$0.830034\pi$
$548$		0			0
$549$		−	317.581i		−	0.578472i
$550$		0			0
$551$	−220.345			−0.399901
$552$		0			0
$553$	92.1121	−	92.1121i	0.166568	−	0.166568i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	162.407	+	162.407i	0.291574	+	0.291574i	0.837702	−	0.546128i	$-0.183899\pi$
$557$	162.407	+	162.407i	0.291574	+	0.291574i	−0.546128	+	0.837702i	$0.683899\pi$
$558$		0			0
$559$		−	12.5719i		−	0.0224901i
$560$		0			0
$561$	−448.761			−0.799931
$562$		0			0
$563$	687.682	−	687.682i	1.22146	−	1.22146i	0.254346	−	0.967113i	$-0.418140\pi$
$563$	687.682	−	687.682i	1.22146	−	1.22146i	0.967113	−	0.254346i	$-0.0818603\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−54.2121	−	54.2121i	−0.0956121	−	0.0956121i
$568$		0			0
$569$		−	452.621i		−	0.795468i	−0.917501	−	0.397734i	$-0.869797\pi$
$569$		−	452.621i		−	0.795468i	0.917501	−	0.397734i	$-0.130203\pi$
$570$		0			0
$571$	−8.52498			−0.0149299			−0.00746496	−	0.999972i	$-0.502376\pi$
$571$	−8.52498			−0.0149299			−0.00746496	+	0.999972i	$0.502376\pi$
$572$		0			0
$573$	82.8772	−	82.8772i	0.144637	−	0.144637i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−271.812	−	271.812i	−0.471078	−	0.471078i	0.431186	−	0.902263i	$-0.358095\pi$
$577$	−271.812	−	271.812i	−0.471078	−	0.471078i	−0.902263	+	0.431186i	$0.858095\pi$
$578$		0			0
$579$		−	78.3755i		−	0.135364i
$580$		0			0
$581$	556.474			0.957787
$582$		0			0
$583$	211.383	−	211.383i	0.362577	−	0.362577i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	160.042	+	160.042i	0.272644	+	0.272644i	0.830164	−	0.557519i	$-0.188247\pi$
$587$	160.042	+	160.042i	0.272644	+	0.272644i	−0.557519	+	0.830164i	$0.688247\pi$
$588$		0			0
$589$		−	215.305i		−	0.365544i
$590$		0			0
$591$	298.975			0.505881
$592$		0			0
$593$	25.3238	−	25.3238i	0.0427045	−	0.0427045i	−0.685432	−	0.728137i	$-0.740387\pi$
$593$	25.3238	−	25.3238i	0.0427045	−	0.0427045i	0.728137	+	0.685432i	$0.240387\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.34469	+	5.34469i	0.00895257	+	0.00895257i
$598$		0			0
$599$			1017.30i			1.69832i	0.528132	+	0.849162i	$0.322893\pi$
$599$			1017.30i			1.69832i	−0.528132	+	0.849162i	$0.677107\pi$
$600$		0			0
$601$	−322.485			−0.536580			−0.268290	−	0.963338i	$-0.586459\pi$
$601$	−322.485			−0.536580			−0.268290	+	0.963338i	$0.586459\pi$
$602$		0			0
$603$	−140.579	+	140.579i	−0.233132	+	0.233132i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−151.189	−	151.189i	−0.249076	−	0.249076i	0.571515	−	0.820591i	$-0.306356\pi$
$607$	−151.189	−	151.189i	−0.249076	−	0.249076i	−0.820591	+	0.571515i	$0.806356\pi$
$608$		0			0
$609$			803.315i			1.31907i
$610$		0			0
$611$	−3.33998			−0.00546642
$612$		0			0
$613$	−397.727	+	397.727i	−0.648821	+	0.648821i	−0.952708	−	0.303887i	$-0.901715\pi$
$613$	−397.727	+	397.727i	−0.648821	+	0.648821i	0.303887	+	0.952708i	$0.401715\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−657.460	−	657.460i	−1.06557	−	1.06557i	−0.997693	−	0.0678812i	$-0.978376\pi$
$617$	−657.460	−	657.460i	−1.06557	−	1.06557i	−0.0678812	−	0.997693i	$-0.521624\pi$
$618$		0			0
$619$			984.228i			1.59003i	0.606590	+	0.795015i	$0.292537\pi$
$619$			984.228i			1.59003i	−0.606590	+	0.795015i	$0.707463\pi$
$620$		0			0
$621$	13.6364			0.0219588
$622$		0			0
$623$	5.71358	−	5.71358i	0.00917107	−	0.00917107i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−84.2829	−	84.2829i	−0.134422	−	0.134422i
$628$		0			0
$629$			458.328i			0.728661i
$630$		0			0
$631$	242.533			0.384362			0.192181	−	0.981359i	$-0.438444\pi$
$631$	242.533			0.384362			0.192181	+	0.981359i	$0.438444\pi$
$632$		0			0
$633$	224.246	−	224.246i	0.354260	−	0.354260i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.93604	−	2.93604i	−0.00460917	−	0.00460917i
$638$		0			0
$639$		−	170.687i		−	0.267115i
$640$		0			0
$641$	761.727			1.18834			0.594171	−	0.804339i	$-0.297480\pi$
$641$	761.727			1.18834			0.594171	+	0.804339i	$0.297480\pi$
$642$		0			0
$643$	11.3113	−	11.3113i	0.0175914	−	0.0175914i	−0.698256	−	0.715848i	$-0.746040\pi$
$643$	11.3113	−	11.3113i	0.0175914	−	0.0175914i	0.715848	+	0.698256i	$0.246040\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−290.292	−	290.292i	−0.448674	−	0.448674i	0.446240	−	0.894914i	$-0.352763\pi$
$647$	−290.292	−	290.292i	−0.448674	−	0.448674i	−0.894914	+	0.446240i	$0.852763\pi$
$648$		0			0
$649$			149.534i			0.230407i
$650$		0			0
$651$	−784.940			−1.20575
$652$		0			0
$653$	−791.306	+	791.306i	−1.21180	+	1.21180i	−0.241368	+	0.970434i	$0.577596\pi$
$653$	−791.306	+	791.306i	−1.21180	+	1.21180i	−0.970434	+	0.241368i	$0.922404\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−158.189	−	158.189i	−0.240775	−	0.240775i
$658$		0			0
$659$		−	1153.66i		−	1.75062i	−0.483559	−	0.875312i	$-0.660656\pi$
$659$		−	1153.66i		−	1.75062i	0.483559	−	0.875312i	$-0.339344\pi$
$660$		0			0
$661$	1250.76			1.89222			0.946111	−	0.323842i	$-0.104975\pi$
$661$	1250.76			1.89222			0.946111	+	0.323842i	$0.104975\pi$
$662$		0			0
$663$	−3.28801	+	3.28801i	−0.00495929	+	0.00495929i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−101.032	−	101.032i	−0.151472	−	0.151472i
$668$		0			0
$669$		−	12.3445i		−	0.0184522i
$670$		0			0
$671$	−1800.03			−2.68261
$672$		0			0
$673$	320.198	−	320.198i	0.475778	−	0.475778i	−0.428001	−	0.903778i	$-0.640782\pi$
$673$	320.198	−	320.198i	0.475778	−	0.475778i	0.903778	+	0.428001i	$0.140782\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−105.922	−	105.922i	−0.156457	−	0.156457i	0.624538	−	0.780995i	$-0.285287\pi$
$677$	−105.922	−	105.922i	−0.156457	−	0.156457i	−0.780995	+	0.624538i	$0.785287\pi$
$678$		0			0
$679$		−	935.692i		−	1.37804i
$680$		0			0
$681$	554.749			0.814610
$682$		0			0
$683$	467.606	−	467.606i	0.684636	−	0.684636i	−0.276405	−	0.961041i	$-0.589143\pi$
$683$	467.606	−	467.606i	0.684636	−	0.684636i	0.961041	+	0.276405i	$0.0891432\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−339.152	−	339.152i	−0.493671	−	0.493671i
$688$		0			0
$689$		−	3.09754i		−	0.00449571i
$690$		0			0
$691$	−47.2980			−0.0684487			−0.0342243	−	0.999414i	$-0.510896\pi$
$691$	−47.2980			−0.0684487			−0.0342243	+	0.999414i	$0.510896\pi$
$692$		0			0
$693$	−307.271	+	307.271i	−0.443392	+	0.443392i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	561.792	+	561.792i	0.806014	+	0.806014i
$698$		0			0
$699$		−	485.260i		−	0.694220i
$700$		0			0
$701$	444.721			0.634409			0.317204	−	0.948357i	$-0.397256\pi$
$701$	444.721			0.634409			0.317204	+	0.948357i	$0.397256\pi$
$702$		0			0
$703$	−86.0796	+	86.0796i	−0.122446	+	0.122446i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−298.915	−	298.915i	−0.422793	−	0.422793i
$708$		0			0
$709$		−	996.549i		−	1.40557i	−0.711403	−	0.702785i	$-0.751940\pi$
$709$		−	996.549i		−	1.40557i	0.711403	−	0.702785i	$-0.248060\pi$
$710$		0			0
$711$	−45.8759			−0.0645231
$712$		0			0
$713$	98.7212	−	98.7212i	0.138459	−	0.138459i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−281.916	−	281.916i	−0.393188	−	0.393188i
$718$		0			0
$719$			319.778i			0.444753i	0.974961	+	0.222377i	$0.0713814\pi$
$719$			319.778i			0.444753i	−0.974961	+	0.222377i	$0.928619\pi$
$720$		0			0
$721$	226.402			0.314011
$722$		0			0
$723$	−347.266	+	347.266i	−0.480313	+	0.480313i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−116.716	−	116.716i	−0.160545	−	0.160545i	0.622263	−	0.782808i	$-0.286213\pi$
$727$	−116.716	−	116.716i	−0.160545	−	0.160545i	−0.782808	+	0.622263i	$0.786213\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	1087.25			1.48735
$732$		0			0
$733$	121.699	−	121.699i	0.166028	−	0.166028i	−0.619203	−	0.785231i	$-0.712544\pi$
$733$	121.699	−	121.699i	0.166028	−	0.166028i	0.785231	+	0.619203i	$0.212544\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	796.791	+	796.791i	1.08113	+	1.08113i
$738$		0			0
$739$		−	498.476i		−	0.674528i	−0.941410	−	0.337264i	$-0.890499\pi$
$739$		−	498.476i		−	0.674528i	0.941410	−	0.337264i	$-0.109501\pi$
$740$		0			0
$741$	−1.23506			−0.00166674
$742$		0			0
$743$	13.9317	−	13.9317i	0.0187507	−	0.0187507i	−0.697669	−	0.716420i	$-0.745779\pi$
$743$	13.9317	−	13.9317i	0.0187507	−	0.0187507i	0.716420	+	0.697669i	$0.245779\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−138.574	−	138.574i	−0.185508	−	0.185508i
$748$		0			0
$749$		−	831.257i		−	1.10982i
$750$		0			0
$751$	148.692			0.197992			0.0989962	−	0.995088i	$-0.468437\pi$
$751$	148.692			0.197992			0.0989962	+	0.995088i	$0.468437\pi$
$752$		0			0
$753$	248.294	−	248.294i	0.329740	−	0.329740i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−243.978	−	243.978i	−0.322296	−	0.322296i	0.527352	−	0.849647i	$-0.323185\pi$
$757$	−243.978	−	243.978i	−0.322296	−	0.322296i	−0.849647	+	0.527352i	$0.823185\pi$
$758$		0			0
$759$		−	77.2903i		−	0.101832i
$760$		0			0
$761$	838.059			1.10126			0.550630	−	0.834749i	$-0.314387\pi$
$761$	838.059			1.10126			0.550630	+	0.834749i	$0.314387\pi$
$762$		0			0
$763$	783.079	−	783.079i	1.02632	−	1.02632i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.09561	+	1.09561i	0.00142844	+	0.00142844i
$768$		0			0
$769$			48.7943i			0.0634516i	0.999497	+	0.0317258i	$0.0101003\pi$
$769$			48.7943i			0.0634516i	−0.999497	+	0.0317258i	$0.989900\pi$
$770$		0			0
$771$	495.167			0.642240
$772$		0			0
$773$	−349.857	+	349.857i	−0.452596	+	0.452596i	−0.896215	−	0.443619i	$-0.853694\pi$
$773$	−349.857	+	349.857i	−0.452596	+	0.452596i	0.443619	+	0.896215i	$0.353694\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	313.821	+	313.821i	0.403888	+	0.403888i
$778$		0			0
$779$			211.023i			0.270889i
$780$		0			0
$781$	−967.442			−1.23872
$782$		0			0
$783$	200.043	−	200.043i	0.255483	−	0.255483i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−504.294	−	504.294i	−0.640780	−	0.640780i	0.309967	−	0.950747i	$-0.399682\pi$
$787$	−504.294	−	504.294i	−0.640780	−	0.640780i	−0.950747	+	0.309967i	$0.899682\pi$
$788$		0			0
$789$		−	84.2367i		−	0.106764i
$790$		0			0
$791$	1898.45			2.40006
$792$		0			0
$793$	−13.1886	+	13.1886i	−0.0166313	+	0.0166313i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	275.451	+	275.451i	0.345610	+	0.345610i	0.858471	−	0.512862i	$-0.171415\pi$
$797$	275.451	+	275.451i	0.345610	+	0.345610i	−0.512862	+	0.858471i	$0.671415\pi$
$798$		0			0
$799$		−	288.850i		−	0.361514i
$800$		0			0
$801$	−2.84561			−0.00355258
$802$		0			0
$803$	−896.606	+	896.606i	−1.11657	+	1.11657i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−39.8619	−	39.8619i	−0.0493951	−	0.0493951i
$808$		0			0
$809$			472.171i			0.583648i	0.956472	+	0.291824i	$0.0942621\pi$
$809$			472.171i			0.583648i	−0.956472	+	0.291824i	$0.905738\pi$
$810$		0			0
$811$	−1383.85			−1.70636			−0.853178	−	0.521620i	$-0.825328\pi$
$811$	−1383.85			−1.70636			−0.853178	+	0.521620i	$0.825328\pi$
$812$		0			0
$813$	−112.614	+	112.614i	−0.138517	+	0.138517i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	204.200	+	204.200i	0.249938	+	0.249938i
$818$		0			0
$819$			4.50266i			0.00549776i
$820$		0			0
$821$	−280.480			−0.341632			−0.170816	−	0.985303i	$-0.554640\pi$
$821$	−280.480			−0.341632			−0.170816	+	0.985303i	$0.554640\pi$
$822$		0			0
$823$	256.396	−	256.396i	0.311539	−	0.311539i	−0.533967	−	0.845505i	$-0.679299\pi$
$823$	256.396	−	256.396i	0.311539	−	0.311539i	0.845505	+	0.533967i	$0.179299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	325.679	+	325.679i	0.393808	+	0.393808i	0.876042	−	0.482234i	$-0.160175\pi$
$827$	325.679	+	325.679i	0.393808	+	0.393808i	−0.482234	+	0.876042i	$0.660175\pi$
$828$		0			0
$829$		−	5.87954i		−	0.00709232i	−0.999994	−	0.00354616i	$-0.998871\pi$
$829$		−	5.87954i		−	0.00709232i	0.999994	−	0.00354616i	$-0.00112878\pi$
$830$		0			0
$831$	67.7803			0.0815647
$832$		0			0
$833$	253.916	−	253.916i	0.304822	−	0.304822i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	195.467	+	195.467i	0.233533	+	0.233533i
$838$		0			0
$839$		−	141.023i		−	0.168085i	−0.996462	−	0.0840424i	$-0.973217\pi$
$839$		−	141.023i		−	0.168085i	0.996462	−	0.0840424i	$-0.0267831\pi$
$840$		0			0
$841$	−2123.24			−2.52466
$842$		0			0
$843$	−224.628	+	224.628i	−0.266462	+	0.266462i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1012.74	+	1012.74i	1.19568	+	1.19568i
$848$		0			0
$849$		−	816.068i		−	0.961211i
$850$		0			0
$851$	−78.9380			−0.0927591
$852$		0			0
$853$	322.940	−	322.940i	0.378593	−	0.378593i	−0.492002	−	0.870594i	$-0.663735\pi$
$853$	322.940	−	322.940i	0.378593	−	0.378593i	0.870594	+	0.492002i	$0.163735\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−277.382	−	277.382i	−0.323667	−	0.323667i	0.526505	−	0.850172i	$-0.323502\pi$
$857$	−277.382	−	277.382i	−0.323667	−	0.323667i	−0.850172	+	0.526505i	$0.823502\pi$
$858$		0			0
$859$		−	530.257i		−	0.617295i	−0.951176	−	0.308648i	$-0.900124\pi$
$859$		−	530.257i		−	0.617295i	0.951176	−	0.308648i	$-0.0998764\pi$
$860$		0			0
$861$	769.328			0.893529
$862$		0			0
$863$	−725.484	+	725.484i	−0.840653	+	0.840653i	−0.988944	−	0.148291i	$-0.952623\pi$
$863$	−725.484	+	725.484i	−0.840653	+	0.840653i	0.148291	+	0.988944i	$0.452623\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	69.5959	+	69.5959i	0.0802721	+	0.0802721i
$868$		0			0
$869$			260.022i			0.299220i
$870$		0			0
$871$	11.6760			0.0134052
$872$		0			0
$873$	−233.008	+	233.008i	−0.266905	+	0.266905i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−114.761	−	114.761i	−0.130856	−	0.130856i	0.638645	−	0.769501i	$-0.279495\pi$
$877$	−114.761	−	114.761i	−0.130856	−	0.130856i	−0.769501	+	0.638645i	$0.779495\pi$
$878$		0			0
$879$			455.321i			0.517999i
$880$		0			0
$881$	−582.431			−0.661102			−0.330551	−	0.943788i	$-0.607235\pi$
$881$	−582.431			−0.661102			−0.330551	+	0.943788i	$0.607235\pi$
$882$		0			0
$883$	1140.67	−	1140.67i	1.29182	−	1.29182i	0.358153	−	0.933663i	$-0.383406\pi$
$883$	1140.67	−	1140.67i	1.29182	−	1.29182i	0.933663	−	0.358153i	$-0.116594\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−910.472	−	910.472i	−1.02646	−	1.02646i	−0.999640	−	0.0268221i	$-0.991461\pi$
$887$	−910.472	−	910.472i	−1.02646	−	1.02646i	−0.0268221	−	0.999640i	$-0.508539\pi$
$888$		0			0
$889$		−	1280.22i		−	1.44007i
$890$		0			0
$891$	153.034			0.171756
$892$		0			0
$893$	54.2496	−	54.2496i	0.0607498	−	0.0607498i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.566296	−	0.566296i	−0.000631322	−	0.000631322i
$898$		0			0
$899$		−	2896.44i		−	3.22184i
$900$		0			0
$901$	267.883			0.297318
$902$		0			0
$903$	744.453	−	744.453i	0.824421	−	0.824421i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−928.527	−	928.527i	−1.02373	−	1.02373i	−0.999711	−	0.0240232i	$-0.992352\pi$
$907$	−928.527	−	928.527i	−1.02373	−	1.02373i	−0.0240232	−	0.999711i	$-0.507648\pi$
$908$		0			0
$909$			148.873i			0.163776i
$910$		0			0
$911$	−751.939			−0.825400			−0.412700	−	0.910867i	$-0.635414\pi$
$911$	−751.939			−0.825400			−0.412700	+	0.910867i	$0.635414\pi$
$912$		0			0
$913$	−785.431	+	785.431i	−0.860275	+	0.860275i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	619.766	+	619.766i	0.675862	+	0.675862i
$918$		0			0
$919$		−	612.491i		−	0.666476i	−0.942843	−	0.333238i	$-0.891859\pi$
$919$		−	612.491i		−	0.666476i	0.942843	−	0.333238i	$-0.108141\pi$
$920$		0			0
$921$	451.136			0.489833
$922$		0			0
$923$	−7.08831	+	7.08831i	−0.00767965	+	0.00767965i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−56.3791	−	56.3791i	−0.0608189	−	0.0608189i
$928$		0			0
$929$		−	487.299i		−	0.524541i	−0.964994	−	0.262271i	$-0.915529\pi$
$929$		−	487.299i		−	0.524541i	0.964994	−	0.262271i	$-0.0844713\pi$
$930$		0			0
$931$	95.3773			0.102446
$932$		0			0
$933$	234.565	−	234.565i	0.251410	−	0.251410i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−943.521	−	943.521i	−1.00696	−	1.00696i	−0.999976	−	0.00698356i	$-0.997777\pi$
$937$	−943.521	−	943.521i	−1.00696	−	1.00696i	−0.00698356	−	0.999976i	$-0.502223\pi$
$938$		0			0
$939$			630.844i			0.671826i
$940$		0			0
$941$	243.515			0.258784			0.129392	−	0.991594i	$-0.458698\pi$
$941$	243.515			0.258784			0.129392	+	0.991594i	$0.458698\pi$
$942$		0			0
$943$	−96.7577	+	96.7577i	−0.102606	+	0.102606i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	792.978	+	792.978i	0.837358	+	0.837358i	0.988510	−	0.151153i	$-0.0482985\pi$
$947$	792.978	+	792.978i	0.837358	+	0.837358i	−0.151153	+	0.988510i	$0.548299\pi$
$948$		0			0
$949$			13.1386i			0.0138447i
$950$		0			0
$951$	398.085			0.418596
$952$		0			0
$953$	77.6634	−	77.6634i	0.0814936	−	0.0814936i	−0.665185	−	0.746679i	$-0.731647\pi$
$953$	77.6634	−	77.6634i	0.0814936	−	0.0814936i	0.746679	+	0.665185i	$0.231647\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1133.83	−	1133.83i	−1.18478	−	1.18478i
$958$		0			0
$959$			1020.49i			1.06412i
$960$		0			0
$961$	1869.19			1.94504
$962$		0			0
$963$	−207.001	+	207.001i	−0.214954	+	0.214954i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	294.078	+	294.078i	0.304113	+	0.304113i	0.842621	−	0.538507i	$-0.181012\pi$
$967$	294.078	+	294.078i	0.304113	+	0.304113i	−0.538507	+	0.842621i	$0.681012\pi$
$968$		0			0
$969$		−	106.811i		−	0.110228i
$970$		0			0
$971$	322.263			0.331888			0.165944	−	0.986135i	$-0.446933\pi$
$971$	322.263			0.331888			0.165944	+	0.986135i	$0.446933\pi$
$972$		0			0
$973$	1470.05	−	1470.05i	1.51084	−	1.51084i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−739.522	−	739.522i	−0.756932	−	0.756932i	0.218831	−	0.975763i	$-0.429776\pi$
$977$	−739.522	−	739.522i	−0.756932	−	0.756932i	−0.975763	+	0.218831i	$0.929776\pi$
$978$		0			0
$979$			16.1288i			0.0164747i
$980$		0			0
$981$	−390.008			−0.397561
$982$		0			0
$983$	−767.218	+	767.218i	−0.780486	+	0.780486i	−0.979913	−	0.199427i	$-0.936092\pi$
$983$	−767.218	+	767.218i	−0.780486	+	0.780486i	0.199427	+	0.979913i	$0.436092\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−197.778	−	197.778i	−0.200383	−	0.200383i
$988$		0			0
$989$			187.258i			0.189341i
$990$		0			0
$991$	−908.418			−0.916668			−0.458334	−	0.888780i	$-0.651554\pi$
$991$	−908.418			−0.916668			−0.458334	+	0.888780i	$0.651554\pi$
$992$		0			0
$993$	60.0621	−	60.0621i	0.0604855	−	0.0604855i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	397.062	+	397.062i	0.398257	+	0.398257i	0.877618	−	0.479361i	$-0.159132\pi$
$997$	397.062	+	397.062i	0.398257	+	0.398257i	−0.479361	+	0.877618i	$0.659132\pi$
$998$		0			0
$999$		−	156.297i		−	0.156453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.q.1057.2		8
4.3	odd	2		600.3.u.h.457.3		8
5.2	odd	4		240.3.bg.e.193.4		8
5.3	odd	4	inner	1200.3.bg.q.193.2		8
5.4	even	2		240.3.bg.e.97.4		8
12.11	even	2		1800.3.v.t.1657.2		8
15.2	even	4		720.3.bh.o.433.1		8
15.14	odd	2		720.3.bh.o.577.1		8
20.3	even	4		600.3.u.h.193.3		8
20.7	even	4		120.3.u.b.73.2	✓	8
20.19	odd	2		120.3.u.b.97.2	yes	8
40.19	odd	2		960.3.bg.l.577.3		8
40.27	even	4		960.3.bg.l.193.3		8
40.29	even	2		960.3.bg.k.577.1		8
40.37	odd	4		960.3.bg.k.193.1		8
60.23	odd	4		1800.3.v.t.793.2		8
60.47	odd	4		360.3.v.f.73.1		8
60.59	even	2		360.3.v.f.217.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.b.73.2	✓	8	20.7	even	4
120.3.u.b.97.2	yes	8	20.19	odd	2
240.3.bg.e.97.4		8	5.4	even	2
240.3.bg.e.193.4		8	5.2	odd	4
360.3.v.f.73.1		8	60.47	odd	4
360.3.v.f.217.1		8	60.59	even	2
600.3.u.h.193.3		8	20.3	even	4
600.3.u.h.457.3		8	4.3	odd	2
720.3.bh.o.433.1		8	15.2	even	4
720.3.bh.o.577.1		8	15.14	odd	2
960.3.bg.k.193.1		8	40.37	odd	4
960.3.bg.k.577.1		8	40.29	even	2
960.3.bg.l.193.3		8	40.27	even	4
960.3.bg.l.577.3		8	40.19	odd	2
1200.3.bg.q.193.2		8	5.3	odd	4	inner
1200.3.bg.q.1057.2		8	1.1	even	1	trivial
1800.3.v.t.793.2		8	60.23	odd	4
1800.3.v.t.1657.2		8	12.11	even	2

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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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(6.02356 + 6.02356i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(6.02356 + 6.02356i) q^{7} -3.00000i q^{9} -17.0038 q^{11} +(-0.124585 + 0.124585i) q^{13} +(-10.7744 - 10.7744i) q^{17} -4.04713i q^{19} -14.7547 q^{21} +(1.85568 - 1.85568i) q^{23} +(3.67423 + 3.67423i) q^{27} -54.4448i q^{29} +53.1995 q^{31} +(20.8254 - 20.8254i) q^{33} +(-21.2693 - 21.2693i) q^{37} -0.305169i q^{39} -52.1414 q^{41} +(-50.4554 + 50.4554i) q^{43} +(13.4045 + 13.4045i) q^{47} +23.5667i q^{49} +26.3918 q^{51} +(-12.4315 + 12.4315i) q^{53} +(4.95670 + 4.95670i) q^{57} -8.79413i q^{59} +105.860 q^{61} +(18.0707 - 18.0707i) q^{63} +(-46.8595 - 46.8595i) q^{67} +4.54547i q^{69} +56.8955 q^{71} +(52.7296 - 52.7296i) q^{73} +(-102.424 - 102.424i) q^{77} -15.2920i q^{79} -9.00000 q^{81} +(46.1914 - 46.1914i) q^{83} +(66.6810 + 66.6810i) q^{87} -0.948538i q^{89} -1.50089 q^{91} +(-65.1558 + 65.1558i) q^{93} +(-77.6693 - 77.6693i) q^{97} +51.0115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 32 q^{11} + 4 q^{13} - 52 q^{17} - 24 q^{21} - 40 q^{23} - 96 q^{31} - 60 q^{33} + 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} + 168 q^{51} - 108 q^{53} + 24 q^{57} + 264 q^{61} + 12 q^{63} - 216 q^{67} + 240 q^{71} + 208 q^{73} - 168 q^{77} - 72 q^{81} + 336 q^{83} + 252 q^{87} - 592 q^{91} - 264 q^{93} + 208 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 32 * q^11 + 4 * q^13 - 52 * q^17 - 24 * q^21 - 40 * q^23 - 96 * q^31 - 60 * q^33 + 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 + 168 * q^51 - 108 * q^53 + 24 * q^57 + 264 * q^61 + 12 * q^63 - 216 * q^67 + 240 * q^71 + 208 * q^73 - 168 * q^77 - 72 * q^81 + 336 * q^83 + 252 * q^87 - 592 * q^91 - 264 * q^93 + 208 * q^97

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