LMFDB - Embedded newform 288.2.w.a.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			251.6
Character	$\chi$	$=$	288.251
Dual form			288.2.w.a.179.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.450008 + 1.34071i) q^{2} +(-1.59499 + 1.20666i) q^{4} +(-0.739921 + 1.78633i) q^{5} +(0.385417 - 0.385417i) q^{7} +(-2.33553 - 1.59540i) q^{8} +O(q^{10})$	\(q+(0.450008 + 1.34071i) q^{2} +(-1.59499 + 1.20666i) q^{4} +(-0.739921 + 1.78633i) q^{5} +(0.385417 - 0.385417i) q^{7} +(-2.33553 - 1.59540i) q^{8} +(-2.72791 - 0.188155i) q^{10} +(-2.36398 + 5.70716i) q^{11} +(-2.30916 + 0.956485i) q^{13} +(0.690171 + 0.343290i) q^{14} +(1.08796 - 3.84920i) q^{16} +5.05518 q^{17} +(-1.27305 - 3.07341i) q^{19} +(-0.975320 - 3.74200i) q^{20} +(-8.71543 - 0.601139i) q^{22} +(-2.28291 + 2.28291i) q^{23} +(0.892052 + 0.892052i) q^{25} +(-2.32151 - 2.66548i) q^{26} +(-0.149669 + 1.07980i) q^{28} +(0.735171 - 0.304518i) q^{29} -3.40740i q^{31} +(5.65024 - 0.273536i) q^{32} +(2.27487 + 6.77751i) q^{34} +(0.403302 + 0.973658i) q^{35} +(9.56094 + 3.96027i) q^{37} +(3.54766 - 3.08984i) q^{38} +(4.57802 - 2.99155i) q^{40} +(5.27801 + 5.27801i) q^{41} +(2.53597 + 1.05043i) q^{43} +(-3.11606 - 11.9553i) q^{44} +(-4.08804 - 2.03338i) q^{46} -6.85609i q^{47} +6.70291i q^{49} +(-0.794549 + 1.59741i) q^{50} +(2.52893 - 4.31194i) q^{52} +(-7.45793 - 3.08917i) q^{53} +(-8.44569 - 8.44569i) q^{55} +(-1.51505 + 0.285257i) q^{56} +(0.739101 + 0.848613i) q^{58} +(6.14066 + 2.54355i) q^{59} +(2.67989 + 6.46983i) q^{61} +(4.56833 - 1.53336i) q^{62} +(2.90938 + 7.45221i) q^{64} -4.83264i q^{65} +(10.2890 - 4.26184i) q^{67} +(-8.06294 + 6.09987i) q^{68} +(-1.12390 + 0.978864i) q^{70} +(-6.37064 - 6.37064i) q^{71} +(9.03739 - 9.03739i) q^{73} +(-1.00706 + 14.6006i) q^{74} +(5.73905 + 3.36592i) q^{76} +(1.28852 + 3.11075i) q^{77} +1.22095 q^{79} +(6.07093 + 4.79156i) q^{80} +(-4.70112 + 9.45141i) q^{82} +(-14.8416 + 6.14761i) q^{83} +(-3.74043 + 9.03021i) q^{85} +(-0.267116 + 3.87270i) q^{86} +(14.6264 - 9.55772i) q^{88} +(4.97492 - 4.97492i) q^{89} +(-0.521343 + 1.25863i) q^{91} +(0.886520 - 6.39590i) q^{92} +(9.19200 - 3.08529i) q^{94} +6.43208 q^{95} +1.23680 q^{97} +(-8.98663 + 3.01636i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$

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 $

$2$	0.450008	+	1.34071i	0.318204	+	0.948022i
$2$	0.450008	+	1.34071i	0.318204	+	0.948022i
$3$		0			0
$3$		0			0
$4$	−1.59499	+	1.20666i	−0.797493	+	0.603328i
$5$	−0.739921	+	1.78633i	−0.330903	+	0.798870i	0.667618	+	0.744504i	$0.267314\pi$
$5$	−0.739921	+	1.78633i	−0.330903	+	0.798870i	−0.998521	+	0.0543661i	$0.982686\pi$
$6$		0			0
$7$	0.385417	−	0.385417i	0.145674	−	0.145674i	−0.630509	−	0.776182i	$-0.717154\pi$
$7$	0.385417	−	0.385417i	0.145674	−	0.145674i	0.776182	+	0.630509i	$0.217154\pi$
$8$	−2.33553	−	1.59540i	−0.825734	−	0.564060i
$9$		0			0
$10$	−2.72791	−	0.188155i	−0.862641	−	0.0594999i
$11$	−2.36398	+	5.70716i	−0.712767	+	1.72077i	−0.0197998	+	0.999804i	$0.506303\pi$
$11$	−2.36398	+	5.70716i	−0.712767	+	1.72077i	−0.692968	+	0.720969i	$0.743697\pi$
$12$		0			0
$13$	−2.30916	+	0.956485i	−0.640446	+	0.265281i	−0.679184	−	0.733968i	$-0.737666\pi$
$13$	−2.30916	+	0.956485i	−0.640446	+	0.265281i	0.0387383	+	0.999249i	$0.487666\pi$
$14$	0.690171	+	0.343290i	0.184456	+	0.0917481i
$15$		0			0
$16$	1.08796	−	3.84920i	0.271990	−	0.962300i
$17$	5.05518			1.22606			0.613031	−	0.790059i	$-0.289950\pi$
$17$	5.05518			1.22606			0.613031	+	0.790059i	$0.289950\pi$
$18$		0			0
$19$	−1.27305	−	3.07341i	−0.292057	−	0.705089i	0.707942	−	0.706271i	$-0.249624\pi$
$19$	−1.27305	−	3.07341i	−0.292057	−	0.705089i	−0.999999	+	0.00118164i	$0.999624\pi$
$20$	−0.975320	−	3.74200i	−0.218088	−	0.836736i
$21$		0			0
$22$	−8.71543	−	0.601139i	−1.85814	−	0.128163i
$23$	−2.28291	+	2.28291i	−0.476020	+	0.476020i	−0.903856	−	0.427837i	$-0.859276\pi$
$23$	−2.28291	+	2.28291i	−0.476020	+	0.476020i	0.427837	+	0.903856i	$0.359276\pi$
$24$		0			0
$25$	0.892052	+	0.892052i	0.178410	+	0.178410i
$26$	−2.32151	−	2.66548i	−0.455285	−	0.522743i
$27$		0			0
$28$	−0.149669	+	1.07980i	−0.0282847	+	0.204063i
$29$	0.735171	−	0.304518i	0.136518	−	0.0565475i	−0.313379	−	0.949628i	$-0.601461\pi$
$29$	0.735171	−	0.304518i	0.136518	−	0.0565475i	0.449896	+	0.893081i	$0.351461\pi$
$30$		0			0
$31$		−	3.40740i		−	0.611988i	−0.952033	−	0.305994i	$-0.901011\pi$
$31$		−	3.40740i		−	0.611988i	0.952033	−	0.305994i	$-0.0989887\pi$
$32$	5.65024	−	0.273536i	0.998830	−	0.0483549i
$33$		0			0
$34$	2.27487	+	6.77751i	0.390137	+	1.16233i
$35$	0.403302	+	0.973658i	0.0681705	+	0.164578i
$36$		0			0
$37$	9.56094	+	3.96027i	1.57181	+	0.651065i	0.987089	−	0.160170i	$-0.0512043\pi$
$37$	9.56094	+	3.96027i	1.57181	+	0.651065i	0.584720	+	0.811235i	$0.301204\pi$
$38$	3.54766	−	3.08984i	0.575507	−	0.501239i
$39$		0			0
$40$	4.57802	−	2.99155i	0.723848	−	0.473005i
$41$	5.27801	+	5.27801i	0.824287	+	0.824287i	0.986720	−	0.162432i	$-0.0519340\pi$
$41$	5.27801	+	5.27801i	0.824287	+	0.824287i	−0.162432	+	0.986720i	$0.551934\pi$
$42$		0			0
$43$	2.53597	+	1.05043i	0.386732	+	0.160190i	0.567574	−	0.823323i	$-0.307882\pi$
$43$	2.53597	+	1.05043i	0.386732	+	0.160190i	−0.180842	+	0.983512i	$0.557882\pi$
$44$	−3.11606	−	11.9553i	−0.469764	−	1.80234i
$45$		0			0
$46$	−4.08804	−	2.03338i	−0.602748	−	0.299806i
$47$		−	6.85609i		−	1.00006i	−0.866007	−	0.500031i	$-0.833322\pi$
$47$		−	6.85609i		−	1.00006i	0.866007	−	0.500031i	$-0.166678\pi$
$48$		0			0
$49$			6.70291i			0.957558i
$50$	−0.794549	+	1.59741i	−0.112366	+	0.225908i
$51$		0			0
$52$	2.52893	−	4.31194i	0.350699	−	0.597959i
$53$	−7.45793	−	3.08917i	−1.02442	−	0.424331i	−0.193728	−	0.981055i	$-0.562058\pi$
$53$	−7.45793	−	3.08917i	−1.02442	−	0.424331i	−0.830697	+	0.556725i	$0.812058\pi$
$54$		0			0
$55$	−8.44569	−	8.44569i	−1.13882	−	1.13882i
$56$	−1.51505	+	0.285257i	−0.202456	+	0.0381190i
$57$		0			0
$58$	0.739101	+	0.848613i	0.0970488	+	0.111428i
$59$	6.14066	+	2.54355i	0.799446	+	0.331142i	0.744735	−	0.667361i	$-0.232576\pi$
$59$	6.14066	+	2.54355i	0.799446	+	0.331142i	0.0547117	+	0.998502i	$0.482576\pi$
$60$		0			0
$61$	2.67989	+	6.46983i	0.343125	+	0.828376i	0.997396	+	0.0721165i	$0.0229753\pi$
$61$	2.67989	+	6.46983i	0.343125	+	0.828376i	−0.654272	+	0.756260i	$0.727025\pi$
$62$	4.56833	−	1.53336i	0.580178	−	0.194737i
$63$		0			0
$64$	2.90938	+	7.45221i	0.363673	+	0.931527i
$65$		−	4.83264i		−	0.599415i
$66$		0			0
$67$	10.2890	−	4.26184i	1.25700	−	0.520666i	0.348012	−	0.937490i	$-0.386857\pi$
$67$	10.2890	−	4.26184i	1.25700	−	0.520666i	0.908987	+	0.416824i	$0.136857\pi$
$68$	−8.06294	+	6.09987i	−0.977775	+	0.739718i
$69$		0			0
$70$	−1.12390	+	0.978864i	−0.134332	+	0.116997i
$71$	−6.37064	−	6.37064i	−0.756056	−	0.756056i	0.219546	−	0.975602i	$-0.429542\pi$
$71$	−6.37064	−	6.37064i	−0.756056	−	0.756056i	−0.975602	+	0.219546i	$0.929542\pi$
$72$		0			0
$73$	9.03739	−	9.03739i	1.05775	−	1.05775i	0.0595198	−	0.998227i	$-0.481043\pi$
$73$	9.03739	−	9.03739i	1.05775	−	1.05775i	0.998227	−	0.0595198i	$-0.0189570\pi$
$74$	−1.00706	+	14.6006i	−0.117069	+	1.69728i
$75$		0			0
$76$	5.73905	+	3.36592i	0.658314	+	0.386097i
$77$	1.28852	+	3.11075i	0.146840	+	0.354503i
$78$		0			0
$79$	1.22095			0.137367			0.0686837	−	0.997638i	$-0.478120\pi$
$79$	1.22095			0.137367			0.0686837	+	0.997638i	$0.478120\pi$
$80$	6.07093	+	4.79156i	0.678750	+	0.535712i
$81$		0			0
$82$	−4.70112	+	9.45141i	−0.519152	+	1.04373i
$83$	−14.8416	+	6.14761i	−1.62908	+	0.674788i	−0.995129	−	0.0985841i	$-0.968569\pi$
$83$	−14.8416	+	6.14761i	−1.62908	+	0.674788i	−0.633953	+	0.773372i	$0.718569\pi$
$84$		0			0
$85$	−3.74043	+	9.03021i	−0.405707	+	0.979464i
$86$	−0.267116	+	3.87270i	−0.0288038	+	0.417603i
$87$		0			0
$88$	14.6264	−	9.55772i	1.55918	−	1.01886i
$89$	4.97492	−	4.97492i	0.527340	−	0.527340i	−0.392438	−	0.919778i	$-0.628368\pi$
$89$	4.97492	−	4.97492i	0.527340	−	0.527340i	0.919778	+	0.392438i	$0.128368\pi$
$90$		0			0
$91$	−0.521343	+	1.25863i	−0.0546516	+	0.131941i
$92$	0.886520	−	6.39590i	0.0924261	−	0.666818i
$93$		0			0
$94$	9.19200	−	3.08529i	0.948082	−	0.318224i
$95$	6.43208			0.659917
$96$		0			0
$97$	1.23680			0.125579			0.0627893	−	0.998027i	$-0.480000\pi$
$97$	1.23680			0.125579			0.0627893	+	0.998027i	$0.480000\pi$
$98$	−8.98663	+	3.01636i	−0.907787	+	0.304699i
$99$		0			0
$100$	−2.49921	−	0.346410i	−0.249921	−	0.0346410i
$101$	5.61006	−	13.5439i	0.558222	−	1.34767i	−0.352950	−	0.935642i	$-0.614821\pi$
$101$	5.61006	−	13.5439i	0.558222	−	1.34767i	0.911172	−	0.412025i	$-0.135179\pi$
$102$		0			0
$103$	−13.0799	+	13.0799i	−1.28880	+	1.28880i	−0.353279	+	0.935518i	$0.614933\pi$
$103$	−13.0799	+	13.0799i	−1.28880	+	1.28880i	−0.935518	+	0.353279i	$0.885067\pi$
$104$	6.91909	+	1.45014i	0.678472	+	0.142198i
$105$		0			0
$106$	0.785549	−	11.3890i	0.0762993	−	1.10620i
$107$	−1.16330	+	2.80844i	−0.112460	+	0.271502i	−0.970082	−	0.242779i	$-0.921941\pi$
$107$	−1.16330	+	2.80844i	−0.112460	+	0.271502i	0.857622	+	0.514281i	$0.171941\pi$
$108$		0			0
$109$	−13.5958	+	5.63158i	−1.30225	+	0.539408i	−0.922612	−	0.385729i	$-0.873950\pi$
$109$	−13.5958	+	5.63158i	−1.30225	+	0.539408i	−0.379634	+	0.925137i	$0.623950\pi$
$110$	7.52256	−	15.1238i	0.717248	−	1.44200i
$111$		0			0
$112$	−1.06423	−	1.90286i	−0.100560	−	0.179804i
$113$	13.6829			1.28718			0.643591	−	0.765369i	$-0.277444\pi$
$113$	13.6829			1.28718			0.643591	+	0.765369i	$0.277444\pi$
$114$		0			0
$115$	−2.38885	−	5.76720i	−0.222761	−	0.537794i
$116$	−0.805139	+	1.37280i	−0.0747552	+	0.127461i
$117$		0			0
$118$	−0.646801	+	9.37744i	−0.0595429	+	0.863264i
$119$	1.94835	−	1.94835i	0.178605	−	0.178605i
$120$		0			0
$121$	−19.2051	−	19.2051i	−1.74591	−	1.74591i
$122$	−7.46816	+	6.50442i	−0.676136	+	0.588882i
$123$		0			0
$124$	4.11157	+	5.43476i	0.369230	+	0.488056i
$125$	−11.1852	+	4.63305i	−1.00043	+	0.414393i
$126$		0			0
$127$			8.19707i			0.727372i	0.931522	+	0.363686i	$0.118482\pi$
$127$			8.19707i			0.727372i	−0.931522	+	0.363686i	$0.881518\pi$
$128$	−8.68198	+	7.25418i	−0.767386	+	0.641185i
$129$		0			0
$130$	6.47915	−	2.17473i	0.568259	−	0.190736i
$131$	−1.61003	−	3.88695i	−0.140669	−	0.339604i	0.837807	−	0.545967i	$-0.183837\pi$
$131$	−1.61003	−	3.88695i	−0.140669	−	0.339604i	−0.978476	+	0.206362i	$0.933837\pi$
$132$		0			0
$133$	−1.67520	−	0.693890i	−0.145258	−	0.0601679i
$134$	10.3440	+	11.8766i	0.893585	+	1.02599i
$135$		0			0
$136$	−11.8065	−	8.06505i	−1.01240	−	0.691572i
$137$	−6.79006	−	6.79006i	−0.580114	−	0.580114i	0.354821	−	0.934934i	$-0.384542\pi$
$137$	−6.79006	−	6.79006i	−0.580114	−	0.580114i	−0.934934	+	0.354821i	$0.884542\pi$
$138$		0			0
$139$	−3.08589	−	1.27822i	−0.261742	−	0.108417i	0.247954	−	0.968772i	$-0.420242\pi$
$139$	−3.08589	−	1.27822i	−0.261742	−	0.108417i	−0.509695	+	0.860355i	$0.670242\pi$
$140$	−1.81813	−	1.06632i	−0.153660	−	0.0901208i
$141$		0			0
$142$	5.67432	−	11.4080i	0.476178	−	0.957338i
$143$		−	15.4399i		−	1.29115i
$144$		0			0
$145$			1.53857i			0.127772i
$146$	16.1834	+	8.04959i	1.33935	+	0.666189i
$147$		0			0
$148$	−20.0283	+	5.22020i	−1.64631	+	0.429098i
$149$	−8.40712	−	3.48234i	−0.688738	−	0.285285i	0.0107364	−	0.999942i	$-0.496582\pi$
$149$	−8.40712	−	3.48234i	−0.688738	−	0.285285i	−0.699474	+	0.714658i	$0.746582\pi$
$150$		0			0
$151$	−13.7649	−	13.7649i	−1.12017	−	1.12017i	−0.991715	−	0.128459i	$-0.958997\pi$
$151$	−13.7649	−	13.7649i	−1.12017	−	1.12017i	−0.128459	−	0.991715i	$-0.541003\pi$
$152$	−1.93009	+	9.20907i	−0.156551	+	0.746954i
$153$		0			0
$154$	−3.59076	+	3.12738i	−0.289352	+	0.252012i
$155$	6.08674	+	2.52121i	0.488899	+	0.202508i
$156$		0			0
$157$	1.16741	+	2.81838i	0.0931694	+	0.224931i	0.963593	−	0.267372i	$-0.0861553\pi$
$157$	1.16741	+	2.81838i	0.0931694	+	0.224931i	−0.870424	+	0.492303i	$0.836155\pi$
$158$	0.549436	+	1.63693i	0.0437108	+	0.130227i
$159$		0			0
$160$	−3.69210	+	10.2956i	−0.291886	+	0.813936i
$161$			1.75974i			0.138687i
$162$		0			0
$163$	11.1679	−	4.62591i	0.874740	−	0.362329i	0.100285	−	0.994959i	$-0.468024\pi$
$163$	11.1679	−	4.62591i	0.874740	−	0.362329i	0.774455	+	0.632630i	$0.218024\pi$
$164$	−14.7871	−	2.04961i	−1.15468	−	0.160047i
$165$		0			0
$166$	−14.9210	−	17.1318i	−1.15809	−	1.32969i
$167$	2.51551	+	2.51551i	0.194656	+	0.194656i	0.797704	−	0.603049i	$-0.206048\pi$
$167$	2.51551	+	2.51551i	0.194656	+	0.194656i	−0.603049	+	0.797704i	$0.706048\pi$
$168$		0			0
$169$	−4.77503	+	4.77503i	−0.367310	+	0.367310i
$170$	−13.7901	−	0.951159i	−1.05765	−	0.0729506i
$171$		0			0
$172$	−5.31235	+	1.38462i	−0.405063	+	0.105576i
$173$	0.737563	+	1.78063i	0.0560759	+	0.135379i	0.949434	−	0.313965i	$-0.101658\pi$
$173$	0.737563	+	1.78063i	0.0560759	+	0.135379i	−0.893359	+	0.449344i	$0.851658\pi$
$174$		0			0
$175$	0.687623			0.0519794
$176$	19.3961	+	15.3086i	1.46203	+	1.15393i
$177$		0			0
$178$	8.90866	+	4.43115i	0.667732	+	0.332129i
$179$	9.47042	−	3.92278i	0.707852	−	0.293202i	0.000436715	−	1.00000i	$-0.499861\pi$
$179$	9.47042	−	3.92278i	0.707852	−	0.293202i	0.707416	+	0.706798i	$0.249861\pi$
$180$		0			0
$181$	9.91984	−	23.9486i	0.737336	−	1.78009i	0.120927	−	0.992661i	$-0.461413\pi$
$181$	9.91984	−	23.9486i	0.737336	−	1.78009i	0.616410	−	0.787426i	$-0.288587\pi$
$182$	−1.92207	−	0.132573i	−0.142473	−	0.00982696i
$183$		0			0
$184$	8.97396	−	1.68964i	0.661569	−	0.124562i
$185$	−14.1487	+	14.1487i	−1.04023	+	1.04023i
$186$		0			0
$187$	−11.9504	+	28.8507i	−0.873897	+	2.10977i
$188$	8.27294	+	10.9354i	0.603366	+	0.797543i
$189$		0			0
$190$	2.89448	+	8.62352i	0.209988	+	0.625616i
$191$	−3.03200			−0.219388			−0.109694	−	0.993965i	$-0.534987\pi$
$191$	−3.03200			−0.219388			−0.109694	+	0.993965i	$0.534987\pi$
$192$		0			0
$193$	4.75813			0.342498			0.171249	−	0.985228i	$-0.445220\pi$
$193$	4.75813			0.342498			0.171249	+	0.985228i	$0.445220\pi$
$194$	0.556572	+	1.65819i	0.0399595	+	0.119051i
$195$		0			0
$196$	−8.08811	−	10.6910i	−0.577722	−	0.763646i
$197$	−3.20309	+	7.73295i	−0.228211	+	0.550950i	−0.995960	−	0.0898012i	$-0.971377\pi$
$197$	−3.20309	+	7.73295i	−0.228211	+	0.550950i	0.767749	+	0.640751i	$0.221377\pi$
$198$		0			0
$199$	15.9060	−	15.9060i	1.12755	−	1.12755i	0.136973	−	0.990575i	$-0.456263\pi$
$199$	15.9060	−	15.9060i	1.12755	−	1.12755i	0.990575	−	0.136973i	$-0.0437372\pi$
$200$	−0.660231	−	3.50659i	−0.0466854	−	0.247954i
$201$		0			0
$202$	20.6830	+	1.42659i	1.45525	+	0.100374i
$203$	0.165981	−	0.400713i	0.0116496	−	0.0281245i
$204$		0			0
$205$	−13.3336	+	5.52295i	−0.931257	+	0.385739i
$206$	−23.4223	−	11.6502i	−1.63191	−	0.811708i
$207$		0			0
$208$	1.16943	+	9.92904i	0.0810855	+	0.688455i
$209$	20.5499			1.42147
$210$		0			0
$211$	2.38241	+	5.75165i	0.164012	+	0.395960i	0.984423	−	0.175814i	$-0.0562557\pi$
$211$	2.38241	+	5.75165i	0.164012	+	0.395960i	−0.820412	+	0.571773i	$0.806256\pi$
$212$	15.6229	−	4.07197i	1.07298	−	0.279664i
$213$		0			0
$214$	−4.28879	−	0.295816i	−0.293176	−	0.0202215i
$215$	−3.75284	+	3.75284i	−0.255941	+	0.255941i
$216$		0			0
$217$	−1.31327	−	1.31327i	−0.0891506	−	0.0891506i
$218$	−13.6685	−	15.6938i	−0.925750	−	1.06292i
$219$		0			0
$220$	23.6618	+	3.27971i	1.59528	+	0.221118i
$221$	−11.6732	+	4.83521i	−0.785226	+	0.325251i
$222$		0			0
$223$			24.2829i			1.62611i	0.582190	+	0.813053i	$0.302196\pi$
$223$			24.2829i			1.62611i	−0.582190	+	0.813053i	$0.697804\pi$
$224$	2.07227	−	2.28312i	0.138459	−	0.152547i
$225$		0			0
$226$	6.15743	+	18.3448i	0.409586	+	1.22028i
$227$	3.57334	+	8.62682i	0.237171	+	0.572582i	0.996988	−	0.0775552i	$-0.0247114\pi$
$227$	3.57334	+	8.62682i	0.237171	+	0.572582i	−0.759817	+	0.650137i	$0.774711\pi$
$228$		0			0
$229$	14.4317	+	5.97779i	0.953672	+	0.395024i	0.804610	−	0.593804i	$-0.202375\pi$
$229$	14.4317	+	5.97779i	0.953672	+	0.395024i	0.149062	+	0.988828i	$0.452375\pi$
$230$	6.65711	−	5.79803i	0.438957	−	0.382311i
$231$		0			0
$232$	−2.20284	−	0.461683i	−0.144624	−	0.0303110i
$233$	−6.50138	−	6.50138i	−0.425920	−	0.425920i	0.461316	−	0.887236i	$-0.347377\pi$
$233$	−6.50138	−	6.50138i	−0.425920	−	0.425920i	−0.887236	+	0.461316i	$0.847377\pi$
$234$		0			0
$235$	12.2472	+	5.07296i	0.798920	+	0.330923i
$236$	−12.8635	+	3.35275i	−0.837340	+	0.218246i
$237$		0			0
$238$	3.48894	+	1.73539i	0.226154	+	0.112489i
$239$		−	19.9787i		−	1.29232i	−0.763203	−	0.646159i	$-0.776374\pi$
$239$		−	19.9787i		−	1.29232i	0.763203	−	0.646159i	$-0.223626\pi$
$240$		0			0
$241$		−	0.606349i		−	0.0390584i	−0.999809	−	0.0195292i	$-0.993783\pi$
$241$		−	0.606349i		−	0.0390584i	0.999809	−	0.0195292i	$-0.00621673\pi$
$242$	17.1059	−	34.3908i	1.09961	−	2.21072i
$243$		0			0
$244$	−12.0812	−	7.08557i	−0.773422	−	0.453607i
$245$	−11.9736	−	4.95962i	−0.764964	−	0.316859i
$246$		0			0
$247$	5.87935	+	5.87935i	0.374094	+	0.374094i
$248$	−5.43618	+	7.95809i	−0.345198	+	0.505339i
$249$		0			0
$250$	−11.2450	−	12.9111i	−0.711195	−	0.816572i
$251$	14.5988	+	6.04703i	0.921470	+	0.381685i	0.792436	−	0.609955i	$-0.208813\pi$
$251$	14.5988	+	6.04703i	0.921470	+	0.381685i	0.129034	+	0.991640i	$0.458813\pi$
$252$		0			0
$253$	−7.63217	−	18.4257i	−0.479830	−	1.15841i
$254$	−10.9899	+	3.68874i	−0.689565	+	0.231452i
$255$		0			0
$256$	−13.6327	−	8.37555i	−0.852043	−	0.523472i
$257$			10.5962i			0.660974i	0.943811	+	0.330487i	$0.107213\pi$
$257$			10.5962i			0.660974i	−0.943811	+	0.330487i	$0.892787\pi$
$258$		0			0
$259$	5.21130	−	2.15859i	0.323815	−	0.134128i
$260$	5.83134	+	7.70799i	0.361644	+	0.478029i
$261$		0			0
$262$	4.48673	−	3.90773i	0.277191	−	0.241420i
$263$	19.2991	+	19.2991i	1.19004	+	1.19004i	0.977057	+	0.212979i	$0.0683166\pi$
$263$	19.2991	+	19.2991i	1.19004	+	1.19004i	0.212979	+	0.977057i	$0.431683\pi$
$264$		0			0
$265$	11.0366	−	11.0366i	0.677970	−	0.677970i
$266$	0.176450	−	2.55820i	0.0108188	−	0.156854i
$267$		0			0
$268$	−11.2682	+	19.2128i	−0.688315	+	1.17361i
$269$	4.57782	+	11.0518i	0.279114	+	0.673842i	0.999812	−	0.0194081i	$-0.00617818\pi$
$269$	4.57782	+	11.0518i	0.279114	+	0.673842i	−0.720697	+	0.693250i	$0.756178\pi$
$270$		0			0
$271$	29.0069			1.76204			0.881022	−	0.473075i	$-0.156856\pi$
$271$	29.0069			1.76204			0.881022	+	0.473075i	$0.156856\pi$
$272$	5.49983	−	19.4584i	0.333476	−	1.17984i
$273$		0			0
$274$	6.04789	−	12.1591i	0.365367	−	0.734555i
$275$	−7.19988	+	2.98229i	−0.434169	+	0.179839i
$276$		0			0
$277$	3.29625	−	7.95785i	0.198053	−	0.478141i	−0.793385	−	0.608720i	$-0.791683\pi$
$277$	3.29625	−	7.95785i	0.198053	−	0.478141i	0.991438	+	0.130578i	$0.0416834\pi$
$278$	0.325039	−	4.71248i	0.0194946	−	0.282636i
$279$		0			0
$280$	0.611452	−	2.91743i	0.0365413	−	0.174350i
$281$	−6.61069	+	6.61069i	−0.394361	+	0.394361i	−0.876238	−	0.481878i	$-0.839955\pi$
$281$	−6.61069	+	6.61069i	−0.394361	+	0.394361i	0.481878	+	0.876238i	$0.339955\pi$
$282$		0			0
$283$	−0.300555	+	0.725605i	−0.0178662	+	0.0431327i	−0.932561	−	0.361013i	$-0.882431\pi$
$283$	−0.300555	+	0.725605i	−0.0178662	+	0.0431327i	0.914695	+	0.404146i	$0.132431\pi$
$284$	17.8483	+	2.47391i	1.05910	+	0.146799i
$285$		0			0
$286$	20.7003	−	6.94805i	1.22403	−	0.410847i
$287$	4.06847			0.240154
$288$		0			0
$289$	8.55486			0.503227
$290$	−2.06278	+	0.692371i	−0.121130	+	0.0406574i
$291$		0			0
$292$	−3.50948	+	25.3195i	−0.205377	+	1.48171i
$293$	0.400806	−	0.967632i	0.0234154	−	0.0565297i	−0.911739	−	0.410769i	$-0.865260\pi$
$293$	0.400806	−	0.967632i	0.0234154	−	0.0565297i	0.935155	+	0.354239i	$0.115260\pi$
$294$		0			0
$295$	−9.08721	+	9.08721i	−0.529078	+	0.529078i
$296$	−16.0116	−	24.5029i	−0.930657	−	1.42420i
$297$		0			0
$298$	0.885528	−	12.8386i	0.0512973	−	0.743717i
$299$	3.08803	−	7.45517i	0.178586	−	0.431144i
$300$		0			0
$301$	1.38226	−	0.572551i	0.0796721	−	0.0330013i
$302$	12.2604	−	24.6491i	0.705507	−	1.41839i
$303$		0			0
$304$	−13.2152	+	1.55647i	−0.757944	+	0.0892698i
$305$	−13.5401			−0.775306
$306$		0			0
$307$	−3.22266	−	7.78018i	−0.183927	−	0.444038i	0.804843	−	0.593488i	$-0.202250\pi$
$307$	−3.22266	−	7.78018i	−0.183927	−	0.444038i	−0.988769	+	0.149450i	$0.952250\pi$
$308$	−5.80877	−	3.40681i	−0.330985	−	0.194121i
$309$		0			0
$310$	−0.641121	+	9.29509i	−0.0364132	+	0.527926i
$311$	7.17660	−	7.17660i	0.406948	−	0.406948i	−0.473725	−	0.880673i	$-0.657091\pi$
$311$	7.17660	−	7.17660i	0.406948	−	0.406948i	0.880673	+	0.473725i	$0.157091\pi$
$312$		0			0
$313$	0.108611	+	0.108611i	0.00613907	+	0.00613907i	0.710170	−	0.704031i	$-0.248618\pi$
$313$	0.108611	+	0.108611i	0.00613907	+	0.00613907i	−0.704031	+	0.710170i	$0.748618\pi$
$314$	−3.25327	+	2.83344i	−0.183593	+	0.159901i
$315$		0			0
$316$	−1.94740	+	1.47327i	−0.109550	+	0.0828776i
$317$	9.89983	−	4.10065i	0.556030	−	0.230315i	−0.0869307	−	0.996214i	$-0.527706\pi$
$317$	9.89983	−	4.10065i	0.556030	−	0.230315i	0.642961	+	0.765899i	$0.277706\pi$
$318$		0			0
$319$			4.91561i			0.275221i
$320$	−15.4648	−	0.316939i	−0.864509	−	0.0177174i
$321$		0			0
$322$	−2.35930	+	0.791898i	−0.131479	+	0.0441307i
$323$	−6.43549	−	15.5367i	−0.358080	−	0.864483i
$324$		0			0
$325$	−2.91312	−	1.20666i	−0.161591	−	0.0669332i
$326$	11.2276	+	12.8912i	0.621842	+	0.713979i
$327$		0			0
$328$	−3.90639	−	20.7475i	−0.215695	−	1.14559i
$329$	−2.64245	−	2.64245i	−0.145683	−	0.145683i
$330$		0			0
$331$	−14.7254	−	6.09946i	−0.809381	−	0.335257i	−0.0606740	−	0.998158i	$-0.519325\pi$
$331$	−14.7254	−	6.09946i	−0.809381	−	0.335257i	−0.748707	+	0.662901i	$0.769325\pi$
$332$	16.2542	−	27.7141i	0.892062	−	1.52101i
$333$		0			0
$334$	−2.24056	+	4.50455i	−0.122598	+	0.246478i
$335$			21.5329i			1.17647i
$336$		0			0
$337$			15.5033i			0.844517i	0.906475	+	0.422259i	$0.138763\pi$
$337$			15.5033i			0.844517i	−0.906475	+	0.422259i	$0.861237\pi$
$338$	−8.55072	−	4.25311i	−0.465098	−	0.231339i
$339$		0			0
$340$	−4.93042	−	18.9165i	−0.267390	−	1.02589i
$341$	19.4466	+	8.05504i	1.05309	+	0.436205i
$342$		0			0
$343$	5.28133	+	5.28133i	0.285165	+	0.285165i
$344$	−4.24697	−	6.49921i	−0.228981	−	0.350414i
$345$		0			0
$346$	−2.05540	+	1.79015i	−0.110499	+	0.0962393i
$347$	0.714667	+	0.296025i	0.0383654	+	0.0158914i	0.401784	−	0.915735i	$-0.368390\pi$
$347$	0.714667	+	0.296025i	0.0383654	+	0.0158914i	−0.363418	+	0.931626i	$0.618390\pi$
$348$		0			0
$349$	−3.21246	−	7.75558i	−0.171959	−	0.415146i	0.814280	−	0.580473i	$-0.197132\pi$
$349$	−3.21246	−	7.75558i	−0.171959	−	0.415146i	−0.986239	+	0.165326i	$0.947132\pi$
$350$	0.309436	+	0.921901i	0.0165400	+	0.0492777i
$351$		0			0
$352$	−11.7959	+	32.8934i	−0.628726	+	1.75323i
$353$		−	11.9668i		−	0.636927i	−0.947935	−	0.318463i	$-0.896833\pi$
$353$		−	11.9668i		−	0.636927i	0.947935	−	0.318463i	$-0.103167\pi$
$354$		0			0
$355$	16.0938	−	6.66628i	0.854171	−	0.353809i
$356$	−1.93191	+	13.9379i	−0.102391	+	0.738710i
$357$		0			0
$358$	9.52105	+	10.9318i	0.503203	+	0.577762i
$359$	−10.0179	−	10.0179i	−0.528723	−	0.528723i	0.391469	−	0.920191i	$-0.371967\pi$
$359$	−10.0179	−	10.0179i	−0.528723	−	0.528723i	−0.920191	+	0.391469i	$0.871967\pi$
$360$		0			0
$361$	5.60982	−	5.60982i	0.295254	−	0.295254i
$362$	36.5721	+	2.52253i	1.92219	+	0.132581i
$363$		0			0
$364$	−0.687204	−	2.63659i	−0.0360193	−	0.138195i
$365$	9.45679	+	22.8307i	0.494991	+	1.19501i
$366$		0			0
$367$	26.0524			1.35992			0.679961	−	0.733248i	$-0.261996\pi$
$367$	26.0524			1.35992			0.679961	+	0.733248i	$0.261996\pi$
$368$	6.30366	+	11.2711i	0.328601	+	0.587546i
$369$		0			0
$370$	−25.3363	−	12.6022i	−1.31717	−	0.655158i
$371$	−4.06503	+	1.68379i	−0.211046	+	0.0874180i
$372$		0			0
$373$	1.11398	−	2.68939i	0.0576797	−	0.139251i	−0.892412	−	0.451221i	$-0.850989\pi$
$373$	1.11398	−	2.68939i	0.0576797	−	0.139251i	0.950092	+	0.311970i	$0.100989\pi$
$374$	−44.0581	−	3.03887i	−2.27819	−	0.157136i
$375$		0			0
$376$	−10.9382	+	16.0126i	−0.564095	+	0.825786i
$377$	−1.40636	+	1.40636i	−0.0724312	+	0.0724312i
$378$		0			0
$379$	−2.87476	+	6.94029i	−0.147667	+	0.356499i	−0.980354	−	0.197244i	$-0.936801\pi$
$379$	−2.87476	+	6.94029i	−0.147667	+	0.356499i	0.832688	+	0.553743i	$0.186801\pi$
$380$	−10.2591	+	7.76131i	−0.526279	+	0.398147i
$381$		0			0
$382$	−1.36442	−	4.06502i	−0.0698099	−	0.207984i
$383$	18.2355			0.931792			0.465896	−	0.884839i	$-0.345732\pi$
$383$	18.2355			0.931792			0.465896	+	0.884839i	$0.345732\pi$
$384$		0			0
$385$	−6.51022			−0.331791
$386$	2.14120	+	6.37926i	0.108984	+	0.324696i
$387$		0			0
$388$	−1.97269	+	1.49240i	−0.100148	+	0.0757651i
$389$	9.18501	−	22.1746i	0.465699	−	1.12430i	−0.500324	−	0.865838i	$-0.666786\pi$
$389$	9.18501	−	22.1746i	0.465699	−	1.12430i	0.966023	−	0.258458i	$-0.0832143\pi$
$390$		0			0
$391$	−11.5405	+	11.5405i	−0.583629	+	0.583629i
$392$	10.6938	−	15.6548i	0.540120	−	0.790688i
$393$		0			0
$394$	−11.8090	−	0.814517i	−0.594930	−	0.0410348i
$395$	−0.903405	+	2.18101i	−0.0454552	+	0.109739i
$396$		0			0
$397$	3.77144	−	1.56218i	0.189283	−	0.0784037i	−0.286029	−	0.958221i	$-0.592335\pi$
$397$	3.77144	−	1.56218i	0.189283	−	0.0784037i	0.475312	+	0.879817i	$0.342335\pi$
$398$	28.4831	+	14.1675i	1.42773	+	0.710150i
$399$		0			0
$400$	4.40420	−	2.46317i	0.220210	−	0.123159i
$401$	−32.5110			−1.62352			−0.811761	−	0.583990i	$-0.801491\pi$
$401$	−32.5110			−1.62352			−0.811761	+	0.583990i	$0.801491\pi$
$402$		0			0
$403$	3.25913	+	7.86824i	0.162349	+	0.391945i
$404$	7.39485	+	28.3717i	0.367908	+	1.41155i
$405$		0			0
$406$	0.611931	+	0.0422074i	0.0303696	+	0.00209472i
$407$	−45.2038	+	45.2038i	−2.24067	+	2.24067i
$408$		0			0
$409$	−15.0850	−	15.0850i	−0.745903	−	0.745903i	0.227804	−	0.973707i	$-0.426845\pi$
$409$	−15.0850	−	15.0850i	−0.745903	−	0.745903i	−0.973707	+	0.227804i	$0.926845\pi$
$410$	−13.4049	−	15.3910i	−0.662019	−	0.760109i
$411$		0			0
$412$	5.07929	−	36.6451i	0.250239	−	1.80537i
$413$	3.34704	−	1.38639i	0.164697	−	0.0682197i
$414$		0			0
$415$		−	31.0608i		−	1.52471i
$416$	−12.7857	+	6.03601i	−0.626869	+	0.295940i
$417$		0			0
$418$	9.24762	+	27.5514i	0.452316	+	1.34758i
$419$	−6.41529	−	15.4879i	−0.313407	−	0.756632i	−0.999574	−	0.0291878i	$-0.990708\pi$
$419$	−6.41529	−	15.4879i	−0.313407	−	0.756632i	0.686167	−	0.727444i	$-0.259292\pi$
$420$		0			0
$421$	−13.8675	−	5.74412i	−0.675863	−	0.279951i	0.0182335	−	0.999834i	$-0.494196\pi$
$421$	−13.8675	−	5.74412i	−0.675863	−	0.279951i	−0.694096	+	0.719882i	$0.744196\pi$
$422$	−6.63916	+	5.78240i	−0.323189	+	0.281483i
$423$		0			0
$424$	12.4897	+	19.1132i	0.606554	+	0.928221i
$425$	4.50948	+	4.50948i	0.218742	+	0.218742i
$426$		0			0
$427$	3.52645	+	1.46070i	0.170657	+	0.0706884i
$428$	−1.53339	−	5.88312i	−0.0741191	−	0.284372i
$429$		0			0
$430$	−6.72026	−	3.34264i	−0.324080	−	0.161197i
$431$			39.1679i			1.88665i	0.331870	+	0.943325i	$0.392320\pi$
$431$			39.1679i			1.88665i	−0.331870	+	0.943325i	$0.607680\pi$
$432$		0			0
$433$			20.6897i			0.994283i	0.867669	+	0.497142i	$0.165617\pi$
$433$			20.6897i			0.994283i	−0.867669	+	0.497142i	$0.834383\pi$
$434$	1.16973	−	2.35169i	0.0561487	−	0.112885i
$435$		0			0
$436$	14.8898	−	25.3878i	0.713092	−	1.21586i
$437$	9.92258	+	4.11007i	0.474661	+	0.196611i
$438$		0			0
$439$	−7.49686	−	7.49686i	−0.357805	−	0.357805i	0.505198	−	0.863003i	$-0.331419\pi$
$439$	−7.49686	−	7.49686i	−0.357805	−	0.357805i	−0.863003	+	0.505198i	$0.831419\pi$
$440$	6.25087	+	33.1994i	0.297999	+	1.58272i
$441$		0			0
$442$	−11.7356	−	13.4745i	−0.558207	−	0.640916i
$443$	5.58792	+	2.31459i	0.265490	+	0.109970i	0.511458	−	0.859308i	$-0.329106\pi$
$443$	5.58792	+	2.31459i	0.265490	+	0.109970i	−0.245968	+	0.969278i	$0.579106\pi$
$444$		0			0
$445$	5.20579	+	12.5679i	0.246778	+	0.595775i
$446$	−32.5563	+	10.9275i	−1.54158	+	0.517433i
$447$		0			0
$448$	3.99353	+	1.75088i	0.188677	+	0.0827214i
$449$			9.22927i			0.435556i	0.975998	+	0.217778i	$0.0698809\pi$
$449$			9.22927i			0.435556i	−0.975998	+	0.217778i	$0.930119\pi$
$450$		0			0
$451$	−42.5996	+	17.6453i	−2.00594	+	0.830886i
$452$	−21.8241	+	16.5106i	−1.02652	+	0.776594i
$453$		0			0
$454$	−9.95799	+	8.67294i	−0.467352	+	0.407041i
$455$	−1.86258	−	1.86258i	−0.0873190	−	0.0873190i
$456$		0			0
$457$	−15.0540	+	15.0540i	−0.704197	+	0.704197i	−0.965309	−	0.261112i	$-0.915911\pi$
$457$	−15.0540	+	15.0540i	−0.704197	+	0.704197i	0.261112	+	0.965309i	$0.415911\pi$
$458$	−1.52010	+	22.0387i	−0.0710296	+	1.02980i
$459$		0			0
$460$	10.7692	+	6.31607i	0.502117	+	0.294488i
$461$	−2.11682	−	5.11046i	−0.0985902	−	0.238018i	0.866887	−	0.498504i	$-0.166117\pi$
$461$	−2.11682	−	5.11046i	−0.0985902	−	0.238018i	−0.965478	+	0.260486i	$0.916117\pi$
$462$		0			0
$463$	−30.2844			−1.40743			−0.703717	−	0.710481i	$-0.748478\pi$
$463$	−30.2844			−1.40743			−0.703717	+	0.710481i	$0.748478\pi$
$464$	−0.372314	−	3.16112i	−0.0172842	−	0.146751i
$465$		0			0
$466$	5.79077	−	11.6421i	0.268252	−	0.539311i
$467$	12.9725	−	5.37338i	0.600295	−	0.248650i	−0.0617775	−	0.998090i	$-0.519677\pi$
$467$	12.9725	−	5.37338i	0.600295	−	0.248650i	0.662073	+	0.749439i	$0.269677\pi$
$468$		0			0
$469$	2.32296	−	5.60813i	0.107264	−	0.258959i
$470$	−1.29001	+	18.7028i	−0.0595037	+	0.862695i
$471$		0			0
$472$	−10.2837	−	15.7374i	−0.473346	−	0.724370i
$473$	−11.9900	+	11.9900i	−0.551300	+	0.551300i
$474$		0			0
$475$	1.60602	−	3.87727i	0.0736891	−	0.177901i
$476$	−0.756601	+	5.45858i	−0.0346788	+	0.250194i
$477$		0			0
$478$	26.7856	−	8.99059i	1.22515	−	0.411220i
$479$	−2.51607			−0.114962			−0.0574810	−	0.998347i	$-0.518307\pi$
$479$	−2.51607			−0.114962			−0.0574810	+	0.998347i	$0.518307\pi$
$480$		0			0
$481$	−25.8657			−1.17937
$482$	0.812936	−	0.272862i	0.0370282	−	0.0124285i
$483$		0			0
$484$	53.8057	+	7.45789i	2.44571	+	0.338995i
$485$	−0.915138	+	2.20934i	−0.0415543	+	0.100321i
$486$		0			0
$487$	1.66386	−	1.66386i	0.0753965	−	0.0753965i	−0.668403	−	0.743799i	$-0.733022\pi$
$487$	1.66386	−	1.66386i	0.0753965	−	0.0753965i	0.743799	+	0.668403i	$0.233022\pi$
$488$	4.06302	−	19.3860i	0.183924	−	0.877561i
$489$		0			0
$490$	1.26119	−	18.2849i	0.0569746	−	0.826029i
$491$	12.2708	−	29.6244i	0.553775	−	1.33693i	−0.360849	−	0.932624i	$-0.617513\pi$
$491$	12.2708	−	29.6244i	0.553775	−	1.33693i	0.914624	−	0.404306i	$-0.132487\pi$
$492$		0			0
$493$	3.71642	−	1.53939i	0.167379	−	0.0693307i
$494$	−5.23672	+	10.5282i	−0.235611	+	0.473687i
$495$		0			0
$496$	−13.1158	−	3.70712i	−0.588916	−	0.166454i
$497$	−4.91070			−0.220275
$498$		0			0
$499$	−13.7034	−	33.0830i	−0.613450	−	1.48100i	−0.859186	−	0.511663i	$-0.829029\pi$
$499$	−13.7034	−	33.0830i	−0.613450	−	1.48100i	0.245736	−	0.969337i	$-0.420971\pi$
$500$	12.2497	−	20.8863i	0.547823	−	0.934065i
$501$		0			0
$502$	−1.53771	+	22.2939i	−0.0686312	+	0.995027i
$503$	23.6161	−	23.6161i	1.05299	−	1.05299i	0.0544742	−	0.998515i	$-0.482652\pi$
$503$	23.6161	−	23.6161i	1.05299	−	1.05299i	0.998515	−	0.0544742i	$-0.0173483\pi$
$504$		0			0
$505$	20.0428	+	20.0428i	0.891894	+	0.891894i
$506$	21.2689	−	18.5242i	0.945517	−	0.823501i
$507$		0			0
$508$	−9.89104	−	13.0742i	−0.438844	−	0.580074i
$509$	33.8424	−	14.0180i	1.50004	−	0.621336i	0.526565	−	0.850135i	$-0.323480\pi$
$509$	33.8424	−	14.0180i	1.50004	−	0.621336i	0.973474	+	0.228798i	$0.0734797\pi$
$510$		0			0
$511$		−	6.96632i		−	0.308172i
$512$	5.09433	−	22.0465i	0.225140	−	0.974326i
$513$		0			0
$514$	−14.2064	+	4.76838i	−0.626618	+	0.210324i
$515$	−13.6868	−	33.0430i	−0.603115	−	1.45605i
$516$		0			0
$517$	39.1288	+	16.2077i	1.72088	+	0.712812i
$518$	5.23916	+	6.01544i	0.230196	+	0.264303i
$519$		0			0
$520$	−7.71000	+	11.2868i	−0.338106	+	0.494957i
$521$	1.30745	+	1.30745i	0.0572804	+	0.0572804i	0.735167	−	0.677886i	$-0.237104\pi$
$521$	1.30745	+	1.30745i	0.0572804	+	0.0572804i	−0.677886	+	0.735167i	$0.737104\pi$
$522$		0			0
$523$	−21.7896	−	9.02554i	−0.952792	−	0.394660i	−0.148513	−	0.988911i	$-0.547449\pi$
$523$	−21.7896	−	9.02554i	−0.952792	−	0.394660i	−0.804280	+	0.594251i	$0.797449\pi$
$524$	7.25818	+	4.25688i	0.317075	+	0.185963i
$525$		0			0
$526$	−17.1897	+	34.5592i	−0.749507	+	1.50685i
$527$		−	17.2250i		−	0.750335i
$528$		0			0
$529$			12.5766i			0.546811i
$530$	19.7633	+	9.83024i	0.858463	+	0.426998i
$531$		0			0
$532$	3.50920	−	0.914645i	0.152143	−	0.0396549i
$533$	−17.2361	−	7.13943i	−0.746579	−	0.309243i
$534$		0			0
$535$	−4.15605	−	4.15605i	−0.179682	−	0.179682i
$536$	−30.8296	−	6.46143i	−1.33163	−	0.279091i
$537$		0			0
$538$	−12.7572	+	11.1109i	−0.550002	+	0.479026i
$539$	−38.2546	−	15.8456i	−1.64774	−	0.682516i
$540$		0			0
$541$	−3.04512	−	7.35157i	−0.130920	−	0.316069i	0.844803	−	0.535078i	$-0.179718\pi$
$541$	−3.04512	−	7.35157i	−0.130920	−	0.316069i	−0.975723	+	0.219009i	$0.929718\pi$
$542$	13.0533	+	38.8897i	0.560689	+	1.67046i
$543$		0			0
$544$	28.5630	−	1.38278i	1.22463	−	0.0592860i
$545$		−	28.4536i		−	1.21882i
$546$		0			0
$547$	5.38090	−	2.22884i	0.230071	−	0.0952984i	−0.264670	−	0.964339i	$-0.585263\pi$
$547$	5.38090	−	2.22884i	0.230071	−	0.0952984i	0.494741	+	0.869041i	$0.335263\pi$
$548$	19.0233	+	2.63678i	0.812636	+	0.112638i
$549$		0			0
$550$	−7.23837	−	8.31086i	−0.308645	−	0.354376i
$551$	−1.87182	−	1.87182i	−0.0797421	−	0.0797421i
$552$		0			0
$553$	0.470574	−	0.470574i	0.0200108	−	0.0200108i
$554$	12.1525	+	0.838207i	0.516310	+	0.0356120i
$555$		0			0
$556$	6.46432	−	1.68487i	0.274148	−	0.0714544i
$557$	−8.63425	−	20.8449i	−0.365845	−	0.883228i	−0.994421	−	0.105480i	$-0.966362\pi$
$557$	−8.63425	−	20.8449i	−0.365845	−	0.883228i	0.628576	−	0.777748i	$-0.283638\pi$
$558$		0			0
$559$	−6.86069			−0.290176
$560$	4.18658	−	0.493091i	0.176915	−	0.0208369i
$561$		0			0
$562$	−11.8379	−	5.88813i	−0.499350	−	0.248376i
$563$	17.1318	−	7.09624i	0.722021	−	0.299071i	0.00875227	−	0.999962i	$-0.497214\pi$
$563$	17.1318	−	7.09624i	0.722021	−	0.299071i	0.713268	+	0.700891i	$0.247214\pi$
$564$		0			0
$565$	−10.1243	+	24.4422i	−0.425932	+	1.02829i
$566$	−1.10807	−	0.0764285i	−0.0465759	−	0.00321253i
$567$		0			0
$568$	4.71508	+	25.0425i	0.197840	+	1.05076i
$569$	15.5020	−	15.5020i	0.649877	−	0.649877i	−0.303086	−	0.952963i	$-0.598017\pi$
$569$	15.5020	−	15.5020i	0.649877	−	0.649877i	0.952963	+	0.303086i	$0.0980169\pi$
$570$		0			0
$571$	11.3574	−	27.4193i	0.475294	−	1.14746i	−0.486499	−	0.873681i	$-0.661726\pi$
$571$	11.3574	−	27.4193i	0.475294	−	1.14746i	0.961793	−	0.273779i	$-0.0882737\pi$
$572$	18.6306	+	24.6263i	0.778985	+	1.02968i
$573$		0			0
$574$	1.83084	+	5.45462i	0.0764179	+	0.227671i
$575$	−4.07295			−0.169854
$576$		0			0
$577$	19.6105			0.816396			0.408198	−	0.912893i	$-0.366157\pi$
$577$	19.6105			0.816396			0.408198	+	0.912893i	$0.366157\pi$
$578$	3.84975	+	11.4695i	0.160129	+	0.477070i
$579$		0			0
$580$	−1.85653	−	2.45400i	−0.0770883	−	0.101897i
$581$	−3.35082	+	8.08960i	−0.139016	+	0.335613i
$582$		0			0
$583$	35.2608	−	35.2608i	1.46035	−	1.46035i
$584$	−35.5254	+	6.68881i	−1.47005	+	0.276785i
$585$		0			0
$586$	1.47768	+	0.101921i	0.0610422	+	0.00421034i
$587$	−6.56890	+	15.8587i	−0.271128	+	0.654560i	−0.999532	−	0.0305874i	$-0.990262\pi$
$587$	−6.56890	+	15.8587i	−0.271128	+	0.654560i	0.728404	+	0.685147i	$0.240262\pi$
$588$		0			0
$589$	−10.4724	+	4.33779i	−0.431506	+	0.178736i
$590$	−16.2726	−	8.09396i	−0.669932	−	0.333223i
$591$		0			0
$592$	25.6458	−	32.4934i	1.05404	−	1.33547i
$593$	0.287201			0.0117939			0.00589697	−	0.999983i	$-0.498123\pi$
$593$	0.287201			0.0117939			0.00589697	+	0.999983i	$0.498123\pi$
$594$		0			0
$595$	2.03877	+	4.92202i	0.0835813	+	0.201783i
$596$	17.6112	−	4.59022i	0.721384	−	0.188023i
$597$		0			0
$598$	11.3848	+	0.785259i	0.465560	+	0.0321116i
$599$	−12.5596	+	12.5596i	−0.513170	+	0.513170i	−0.915496	−	0.402326i	$-0.868202\pi$
$599$	−12.5596	+	12.5596i	−0.513170	+	0.513170i	0.402326	+	0.915496i	$0.368202\pi$
$600$		0			0
$601$	23.9708	+	23.9708i	0.977791	+	0.977791i	0.999759	−	0.0219673i	$-0.00699298\pi$
$601$	23.9708	+	23.9708i	0.977791	+	0.977791i	−0.0219673	+	0.999759i	$0.506993\pi$
$602$	1.38965	+	1.59555i	0.0566379	+	0.0650298i
$603$		0			0
$604$	38.5644	+	5.34532i	1.56916	+	0.217498i
$605$	48.5168	−	20.0963i	1.97249	−	0.817031i
$606$		0			0
$607$			27.9757i			1.13550i	0.823202	+	0.567749i	$0.192185\pi$
$607$			27.9757i			1.13550i	−0.823202	+	0.567749i	$0.807815\pi$
$608$	−8.03372	−	17.0173i	−0.325810	−	0.690142i
$609$		0			0
$610$	−6.09317	−	18.1533i	−0.246705	−	0.735007i
$611$	6.55774	+	15.8318i	0.265298	+	0.640486i
$612$		0			0
$613$	−30.2175	−	12.5165i	−1.22047	−	0.505537i	−0.322913	−	0.946429i	$-0.604662\pi$
$613$	−30.2175	−	12.5165i	−1.22047	−	0.505537i	−0.897560	+	0.440892i	$0.854662\pi$
$614$	8.98071	−	7.82177i	0.362432	−	0.315661i
$615$		0			0
$616$	1.95354	−	9.32095i	0.0787102	−	0.375552i
$617$	−23.4695	−	23.4695i	−0.944848	−	0.944848i	0.0537086	−	0.998557i	$-0.482896\pi$
$617$	−23.4695	−	23.4695i	−0.944848	−	0.944848i	−0.998557	+	0.0537086i	$0.982896\pi$
$618$		0			0
$619$	−16.2802	−	6.74349i	−0.654357	−	0.271044i	0.0307046	−	0.999529i	$-0.490225\pi$
$619$	−16.2802	−	6.74349i	−0.654357	−	0.271044i	−0.685062	+	0.728485i	$0.740225\pi$
$620$	−12.7505	+	3.32331i	−0.512072	+	0.133467i
$621$		0			0
$622$	12.8512	+	6.39218i	0.515288	+	0.256303i
$623$		−	3.83483i		−	0.153639i
$624$		0			0
$625$		−	17.1007i		−	0.684029i
$626$	−0.0967398	+	0.194492i	−0.00386650	+	0.00777345i
$627$		0			0
$628$	−5.26281	−	3.08661i	−0.210009	−	0.123169i
$629$	48.3323	+	20.0199i	1.92714	+	0.798246i
$630$		0			0
$631$	18.7206	+	18.7206i	0.745256	+	0.745256i	0.973584	−	0.228328i	$-0.0733259\pi$
$631$	18.7206	+	18.7206i	0.745256	+	0.745256i	−0.228328	+	0.973584i	$0.573326\pi$
$632$	−2.85156	−	1.94790i	−0.113429	−	0.0774834i
$633$		0			0
$634$	9.95276	+	11.4274i	0.395275	+	0.453842i
$635$	−14.6426	−	6.06518i	−0.581076	−	0.240689i
$636$		0			0
$637$	−6.41123	−	15.4781i	−0.254022	−	0.613264i
$638$	−6.59039	+	2.21206i	−0.260916	+	0.0875764i
$639$		0			0
$640$	−6.53436	−	20.8764i	−0.258293	−	0.825212i
$641$		−	39.5671i		−	1.56281i	−0.624026	−	0.781404i	$-0.714504\pi$
$641$		−	39.5671i		−	1.56281i	0.624026	−	0.781404i	$-0.285496\pi$
$642$		0			0
$643$	−32.9323	+	13.6410i	−1.29872	+	0.537949i	−0.921573	−	0.388204i	$-0.873096\pi$
$643$	−32.9323	+	13.6410i	−1.29872	+	0.537949i	−0.377149	+	0.926153i	$0.623096\pi$
$644$	−2.12340	−	2.80676i	−0.0836739	−	0.110602i
$645$		0			0
$646$	17.9341	−	15.6197i	0.705606	−	0.614550i
$647$	15.1226	+	15.1226i	0.594532	+	0.594532i	0.938852	−	0.344320i	$-0.111891\pi$
$647$	15.1226	+	15.1226i	0.594532	+	0.594532i	−0.344320	+	0.938852i	$0.611891\pi$
$648$		0			0
$649$	−29.0328	+	29.0328i	−1.13964	+	1.13964i
$650$	0.306842	−	4.44865i	0.0120353	−	0.174490i
$651$		0			0
$652$	−12.2308	+	20.8541i	−0.478995	+	0.816710i
$653$	−5.76633	−	13.9212i	−0.225654	−	0.544777i	0.769985	−	0.638061i	$-0.220263\pi$
$653$	−5.76633	−	13.9212i	−0.225654	−	0.544777i	−0.995640	+	0.0932843i	$0.970263\pi$
$654$		0			0
$655$	8.13465			0.317847
$656$	26.0584	−	14.5739i	1.01741	−	0.569014i
$657$		0			0
$658$	2.35362	−	4.73187i	0.0917538	−	0.184467i
$659$	−21.9719	+	9.10108i	−0.855905	+	0.354528i	−0.767105	−	0.641522i	$-0.778303\pi$
$659$	−21.9719	+	9.10108i	−0.855905	+	0.354528i	−0.0888005	+	0.996049i	$0.528303\pi$
$660$		0			0
$661$	6.04221	−	14.5872i	0.235015	−	0.567376i	−0.761739	−	0.647884i	$-0.775654\pi$
$661$	6.04221	−	14.5872i	0.235015	−	0.567376i	0.996754	+	0.0805079i	$0.0256542\pi$
$662$	1.55104	−	22.4872i	0.0602828	−	0.873991i
$663$		0			0
$664$	44.4710	+	9.32047i	1.72581	+	0.361704i
$665$	2.47903	−	2.47903i	0.0961326	−	0.0961326i
$666$		0			0
$667$	−0.983142	+	2.37351i	−0.0380674	+	0.0919029i
$668$	−7.04755	−	0.976844i	−0.272678	−	0.0377952i
$669$		0			0
$670$	−28.8693	+	9.68998i	−1.11532	+	0.374357i
$671$	−43.2595			−1.67002
$672$		0			0
$673$	23.2501			0.896225			0.448113	−	0.893977i	$-0.352096\pi$
$673$	23.2501			0.896225			0.448113	+	0.893977i	$0.352096\pi$
$674$	−20.7853	+	6.97659i	−0.800621	+	0.268728i
$675$		0			0
$676$	1.85429	−	13.3779i	0.0713187	−	0.514536i
$677$	−8.28073	+	19.9914i	−0.318254	+	0.768333i	0.681093	+	0.732197i	$0.261505\pi$
$677$	−8.28073	+	19.9914i	−0.318254	+	0.768333i	−0.999347	+	0.0361363i	$0.988495\pi$
$678$		0			0
$679$	0.476685	−	0.476685i	0.0182935	−	0.0182935i
$680$	23.1427	−	15.1228i	0.887482	−	0.579933i
$681$		0			0
$682$	−2.04832	+	29.6970i	−0.0784344	+	1.13716i
$683$	−6.09927	+	14.7249i	−0.233382	+	0.563434i	−0.996571	−	0.0827411i	$-0.973633\pi$
$683$	−6.09927	+	14.7249i	−0.233382	+	0.563434i	0.763189	+	0.646175i	$0.223633\pi$
$684$		0			0
$685$	17.1534	−	7.10516i	0.655397	−	0.271474i
$686$	−4.70407	+	9.45735i	−0.179602	+	0.361083i
$687$		0			0
$688$	6.80236	−	8.61863i	0.259338	−	0.328582i
$689$	20.1763			0.768655
$690$		0			0
$691$	−6.28104	−	15.1638i	−0.238942	−	0.576857i	0.758232	−	0.651985i	$-0.226063\pi$
$691$	−6.28104	−	15.1638i	−0.238942	−	0.576857i	−0.997174	+	0.0751281i	$0.976063\pi$
$692$	−3.32502	−	1.95010i	−0.126398	−	0.0741317i
$693$		0			0
$694$	−0.0752765	+	1.09137i	−0.00285746	+	0.0414279i
$695$	4.56663	−	4.56663i	0.173222	−	0.173222i
$696$		0			0
$697$	26.6813	+	26.6813i	1.01063	+	1.01063i
$698$	8.95231	−	7.79704i	0.338850	−	0.295122i
$699$		0			0
$700$	−1.09675	+	0.829725i	−0.0414532	+	0.0313607i
$701$	−24.6746	+	10.2205i	−0.931946	+	0.386025i	−0.796416	−	0.604749i	$-0.793274\pi$
$701$	−24.6746	+	10.2205i	−0.931946	+	0.386025i	−0.135529	+	0.990773i	$0.543274\pi$
$702$		0			0
$703$		−	34.4263i		−	1.29841i
$704$	−49.4087	−	1.01259i	−1.86216	−	0.0381635i
$705$		0			0
$706$	16.0439	−	5.38514i	0.603821	−	0.202672i
$707$	−3.05783	−	7.38225i	−0.115001	−	0.277638i
$708$		0			0
$709$	−11.4821	−	4.75606i	−0.431221	−	0.178617i	0.156506	−	0.987677i	$-0.449977\pi$
$709$	−11.4821	−	4.75606i	−0.431221	−	0.178617i	−0.587727	+	0.809060i	$0.699977\pi$
$710$	16.1799	+	18.5772i	0.607220	+	0.697190i
$711$		0			0
$712$	−19.5561	+	3.68207i	−0.732895	+	0.137991i
$713$	7.77879	+	7.77879i	0.291318	+	0.291318i
$714$		0			0
$715$	27.5806	+	11.4243i	1.03146	+	0.427243i
$716$	−10.3717	+	17.6843i	−0.387610	+	0.660894i
$717$		0			0
$718$	8.92289	−	17.9391i	0.332999	−	0.669482i
$719$			24.1182i			0.899455i	0.893166	+	0.449728i	$0.148479\pi$
$719$			24.1182i			0.899455i	−0.893166	+	0.449728i	$0.851521\pi$
$720$		0			0
$721$			10.0824i			0.375488i
$722$	10.0456	+	4.99666i	0.373858	+	0.185956i
$723$		0			0
$724$	13.0758	+	50.1676i	0.485957	+	1.86446i
$725$	0.927456	+	0.384165i	0.0344449	+	0.0142675i
$726$		0			0
$727$	23.8328	+	23.8328i	0.883909	+	0.883909i	0.993929	−	0.110020i	$-0.0350915\pi$
$727$	23.8328	+	23.8328i	0.883909	+	0.883909i	−0.110020	+	0.993929i	$0.535092\pi$
$728$	3.22564	−	2.10782i	0.119550	−	0.0781211i
$729$		0			0
$730$	−26.3536	+	22.9528i	−0.975392	+	0.849520i
$731$	12.8198	+	5.31013i	0.474157	+	0.196402i
$732$		0			0
$733$	7.22918	+	17.4528i	0.267016	+	0.644633i	0.999340	−	0.0363227i	$-0.0115644\pi$
$733$	7.22918	+	17.4528i	0.267016	+	0.644633i	−0.732324	+	0.680956i	$0.761564\pi$
$734$	11.7238	+	34.9286i	0.432732	+	1.28924i
$735$		0			0
$736$	−12.2745	+	13.5234i	−0.452445	+	0.498481i
$737$			68.7958i			2.53412i
$738$		0			0
$739$	2.37240	−	0.982682i	0.0872703	−	0.0361485i	−0.338621	−	0.940923i	$-0.609961\pi$
$739$	2.37240	−	0.982682i	0.0872703	−	0.0361485i	0.425892	+	0.904774i	$0.359961\pi$
$740$	5.49435	−	39.6396i	0.201976	−	1.45718i
$741$		0			0
$742$	−4.08676	−	4.69229i	−0.150030	−	0.172259i
$743$	−9.84906	−	9.84906i	−0.361327	−	0.361327i	0.502974	−	0.864301i	$-0.332239\pi$
$743$	−9.84906	−	9.84906i	−0.361327	−	0.361327i	−0.864301	+	0.502974i	$0.832239\pi$
$744$		0			0
$745$	12.4412	−	12.4412i	0.455810	−	0.455810i
$746$	4.10698	+	0.283275i	0.150367	+	0.0103714i
$747$		0			0
$748$	−15.7523	−	60.4365i	−0.575960	−	2.20978i
$749$	0.634067	+	1.53077i	0.0231683	+	0.0559333i
$750$		0			0
$751$	−14.4324			−0.526644			−0.263322	−	0.964708i	$-0.584818\pi$
$751$	−14.4324			−0.526644			−0.263322	+	0.964708i	$0.584818\pi$
$752$	−26.3904	−	7.45914i	−0.962361	−	0.272007i
$753$		0			0
$754$	−2.51839	−	1.25264i	−0.0917143	−	0.0456185i
$755$	34.7736	−	14.4037i	1.26554	−	0.524205i
$756$		0			0
$757$	−12.5839	+	30.3803i	−0.457371	+	1.10419i	0.512088	+	0.858933i	$0.328872\pi$
$757$	−12.5839	+	30.3803i	−0.457371	+	1.10419i	−0.969458	+	0.245257i	$0.921128\pi$
$758$	−10.5986	−	0.731026i	−0.384957	−	0.0265521i
$759$		0			0
$760$	−15.0223	−	10.2617i	−0.544916	−	0.372233i
$761$	10.8012	−	10.8012i	0.391543	−	0.391543i	−0.483694	−	0.875237i	$-0.660705\pi$
$761$	10.8012	−	10.8012i	0.391543	−	0.391543i	0.875237	+	0.483694i	$0.160705\pi$
$762$		0			0
$763$	−3.06956	+	7.41057i	−0.111125	+	0.268281i
$764$	4.83599	−	3.65858i	0.174960	−	0.132363i
$765$		0			0
$766$	8.20613	+	24.4485i	0.296500	+	0.883360i
$767$	−16.6126			−0.599848
$768$		0			0
$769$	−31.6614			−1.14174			−0.570869	−	0.821041i	$-0.693394\pi$
$769$	−31.6614			−1.14174			−0.570869	+	0.821041i	$0.693394\pi$
$770$	−2.92965	−	8.72829i	−0.105577	−	0.314546i
$771$		0			0
$772$	−7.58916	+	5.74143i	−0.273140	+	0.206639i
$773$	7.73399	−	18.6715i	0.278172	−	0.671567i	−0.721613	−	0.692297i	$-0.756599\pi$
$773$	7.73399	−	18.6715i	0.278172	−	0.671567i	0.999785	+	0.0207297i	$0.00659894\pi$
$774$		0			0
$775$	3.03958	−	3.03958i	0.109185	−	0.109185i
$776$	−2.88859	−	1.97320i	−0.103694	−	0.0708338i
$777$		0			0
$778$	33.8629	+	2.33567i	1.21404	+	0.0837377i
$779$	9.50234	−	22.9407i	0.340457	−	0.821935i
$780$		0			0
$781$	51.4183	−	21.2982i	1.83989	−	0.762108i
$782$	−20.6658	−	10.2791i	−0.739007	−	0.367581i
$783$		0			0
$784$	25.8008	+	7.29249i	0.921458	+	0.260446i
$785$	−5.89833			−0.210520
$786$		0			0
$787$	7.03017	+	16.9723i	0.250598	+	0.604998i	0.998253	−	0.0590900i	$-0.0188199\pi$
$787$	7.03017	+	16.9723i	0.250598	+	0.604998i	−0.747654	+	0.664088i	$0.768820\pi$
$788$	−4.22213	−	16.1990i	−0.150407	−	0.577065i
$789$		0			0
$790$	−3.33064	−	0.229728i	−0.118499	−	0.00817335i
$791$	5.27363	−	5.27363i	0.187509	−	0.187509i
$792$		0			0
$793$	−12.3766	−	12.3766i	−0.439505	−	0.439505i
$794$	3.79161	+	4.35340i	0.134559	+	0.154496i
$795$		0			0
$796$	−6.17677	+	44.5630i	−0.218930	+	1.57949i
$797$	−43.7568	+	18.1246i	−1.54994	+	0.642008i	−0.983306	−	0.181959i	$-0.941756\pi$
$797$	−43.7568	+	18.1246i	−1.54994	+	0.642008i	−0.566638	+	0.823967i	$0.691756\pi$
$798$		0			0
$799$		−	34.6588i		−	1.22614i
$800$	5.28431	+	4.79630i	0.186829	+	0.169575i
$801$		0			0
$802$	−14.6302	−	43.5877i	−0.516611	−	1.53914i
$803$	30.2136	+	72.9421i	1.06621	+	2.57407i
$804$		0			0
$805$	−3.14348	−	1.30207i	−0.110793	−	0.0458919i
$806$	−9.08236	+	7.91031i	−0.319913	+	0.278629i
$807$		0			0
$808$	−34.7104	+	22.6818i	−1.22111	+	0.797944i
$809$	6.34143	+	6.34143i	0.222953	+	0.222953i	0.809741	−	0.586788i	$-0.199608\pi$
$809$	6.34143	+	6.34143i	0.222953	+	0.222953i	−0.586788	+	0.809741i	$0.699608\pi$
$810$		0			0
$811$	−12.8711	−	5.33139i	−0.451966	−	0.187210i	0.145076	−	0.989421i	$-0.453657\pi$
$811$	−12.8711	−	5.33139i	−0.451966	−	0.187210i	−0.597042	+	0.802210i	$0.703657\pi$
$812$	0.218786	+	0.839414i	0.00767789	+	0.0294576i
$813$		0			0
$814$	−80.9471	−	40.2629i	−2.83719	−	1.41122i
$815$			23.3724i			0.818699i
$816$		0			0
$817$		−	9.13134i		−	0.319465i
$818$	13.4361	−	27.0128i	0.469784	−	0.944482i
$819$		0			0
$820$	14.6026	−	24.8981i	0.509943	−	0.869478i
$821$	12.6767	+	5.25088i	0.442421	+	0.183257i	0.592763	−	0.805377i	$-0.298037\pi$
$821$	12.6767	+	5.25088i	0.442421	+	0.183257i	−0.150341	+	0.988634i	$0.548037\pi$
$822$		0			0
$823$	−21.6528	−	21.6528i	−0.754770	−	0.754770i	0.220596	−	0.975365i	$-0.429200\pi$
$823$	−21.6528	−	21.6528i	−0.754770	−	0.754770i	−0.975365	+	0.220596i	$0.929200\pi$
$824$	51.4160	−	9.68074i	1.79116	−	0.337245i
$825$		0			0
$826$	3.36493	+	3.86351i	0.117081	+	0.134429i
$827$	−26.0418	−	10.7869i	−0.905563	−	0.375096i	−0.119206	−	0.992869i	$-0.538035\pi$
$827$	−26.0418	−	10.7869i	−0.905563	−	0.375096i	−0.786356	+	0.617773i	$0.788035\pi$
$828$		0			0
$829$	5.29036	+	12.7721i	0.183742	+	0.443592i	0.988732	−	0.149696i	$-0.0478295\pi$
$829$	5.29036	+	12.7721i	0.183742	+	0.443592i	−0.804990	+	0.593288i	$0.797830\pi$
$830$	41.6434	−	13.9776i	1.44546	−	0.485169i
$831$		0			0
$832$	−13.8462	−	14.4256i	−0.480029	−	0.500117i
$833$			33.8844i			1.17403i
$834$		0			0
$835$	−6.35479	+	2.63224i	−0.219917	+	0.0910924i
$836$	−32.7768	+	24.7967i	−1.13361	+	0.857611i
$837$		0			0
$838$	17.8778	−	15.5707i	0.617577	−	0.537880i
$839$	14.9362	+	14.9362i	0.515654	+	0.515654i	0.916253	−	0.400600i	$-0.131198\pi$
$839$	14.9362	+	14.9362i	0.515654	+	0.515654i	−0.400600	+	0.916253i	$0.631198\pi$
$840$		0			0
$841$	−20.0584	+	20.0584i	−0.691667	+	0.691667i
$842$	1.46068	−	21.1772i	0.0503383	−	0.729815i
$843$		0			0
$844$	−10.7402	−	6.29904i	−0.369692	−	0.216822i
$845$	−4.99663	−	12.0629i	−0.171889	−	0.414977i
$846$		0			0
$847$	−14.8039			−0.508668
$848$	−20.0048	+	25.3462i	−0.686967	+	0.870391i
$849$		0			0
$850$	−4.01659	+	8.07520i	−0.137768	+	0.276977i
$851$	−30.8677	+	12.7858i	−1.05813	+	0.438292i
$852$		0			0
$853$	10.9239	−	26.3725i	0.374026	−	0.902978i	−0.619034	−	0.785364i	$-0.712476\pi$
$853$	10.9239	−	26.3725i	0.374026	−	0.902978i	0.993059	−	0.117613i	$-0.0375243\pi$
$854$	−0.371444	+	5.38526i	−0.0127105	+	0.184280i
$855$		0			0
$856$	7.19751	−	4.70327i	0.246006	−	0.160755i
$857$	−2.77666	+	2.77666i	−0.0948488	+	0.0948488i	−0.752939	−	0.658090i	$-0.771365\pi$
$857$	−2.77666	+	2.77666i	−0.0948488	+	0.0948488i	0.658090	+	0.752939i	$0.271365\pi$
$858$		0			0
$859$	21.8775	−	52.8170i	0.746452	−	1.80209i	0.169100	−	0.985599i	$-0.445914\pi$
$859$	21.8775	−	52.8170i	0.746452	−	1.80209i	0.577352	−	0.816495i	$-0.304086\pi$
$860$	1.45734	−	10.5141i	0.0496947	−	0.358528i
$861$		0			0
$862$	−52.5126	+	17.6259i	−1.78859	+	0.600339i
$863$	35.8729			1.22113			0.610564	−	0.791967i	$-0.290943\pi$
$863$	35.8729			1.22113			0.610564	+	0.791967i	$0.290943\pi$
$864$		0			0
$865$	−3.72653			−0.126706
$866$	−27.7388	+	9.31053i	−0.942603	+	0.316385i
$867$		0			0
$868$	3.67931	+	0.509981i	0.124884	+	0.0173099i
$869$	−2.88630	+	6.96814i	−0.0979110	+	0.236378i
$870$		0			0
$871$	−19.6825	+	19.6825i	−0.666917	+	0.666917i
$872$	40.7381	+	8.53812i	1.37957	+	0.289137i
$873$		0			0
$874$	−1.04515	+	15.1528i	−0.0353528	+	0.512552i
$875$	−2.52530	+	6.09661i	−0.0853707	+	0.206103i
$876$		0			0
$877$	14.2190	−	5.88971i	0.480142	−	0.198882i	−0.129466	−	0.991584i	$-0.541326\pi$
$877$	14.2190	−	5.88971i	0.480142	−	0.198882i	0.609609	+	0.792702i	$0.291326\pi$
$878$	6.67744	−	13.4247i	0.225353	−	0.453063i
$879$		0			0
$880$	−41.6977	+	23.3206i	−1.40563	+	0.786137i
$881$	−51.9652			−1.75075			−0.875377	−	0.483442i	$-0.839386\pi$
$881$	−51.9652			−1.75075			−0.875377	+	0.483442i	$0.839386\pi$
$882$		0			0
$883$	20.6623	+	49.8832i	0.695342	+	1.67870i	0.733731	+	0.679440i	$0.237777\pi$
$883$	20.6623	+	49.8832i	0.695342	+	1.67870i	−0.0383892	+	0.999263i	$0.512223\pi$
$884$	12.7842	−	21.7977i	0.429979	−	0.733134i
$885$		0			0
$886$	−0.588580	+	8.53334i	−0.0197737	+	0.286683i
$887$	24.4215	−	24.4215i	0.819994	−	0.819994i	−0.166112	−	0.986107i	$-0.553121\pi$
$887$	24.4215	−	24.4215i	0.819994	−	0.819994i	0.986107	+	0.166112i	$0.0531215\pi$
$888$		0			0
$889$	3.15928	+	3.15928i	0.105959	+	0.105959i
$890$	−14.5072	+	12.6351i	−0.486282	+	0.423529i
$891$		0			0
$892$	−29.3012	−	38.7309i	−0.981075	−	1.29681i
$893$	−21.0716	+	8.72813i	−0.705133	+	0.292076i
$894$		0			0
$895$			19.8198i			0.662503i
$896$	−0.550298	+	6.14206i	−0.0183842	+	0.205192i
$897$		0			0
$898$	−12.3737	+	4.15324i	−0.412917	+	0.138595i
$899$	−1.03761	−	2.50502i	−0.0346064	−	0.0835472i
$900$		0			0
$901$	−37.7012	−	15.6163i	−1.25601	−	0.520256i
$902$	−42.8273	−	49.1730i	−1.42599	−	1.63728i
$903$		0			0
$904$	−31.9569	−	21.8298i	−1.06287	−	0.726048i
$905$	35.4402	+	35.4402i	1.17807	+	1.17807i
$906$		0			0
$907$	−1.89537	−	0.785090i	−0.0629349	−	0.0260685i	0.350994	−	0.936378i	$-0.385844\pi$
$907$	−1.89537	−	0.785090i	−0.0629349	−	0.0260685i	−0.413929	+	0.910309i	$0.635844\pi$
$908$	−16.1090	−	9.44785i	−0.534597	−	0.313538i
$909$		0			0
$910$	1.65900	−	3.33535i	0.0549952	−	0.110566i
$911$			1.10306i			0.0365460i	0.999833	+	0.0182730i	$0.00581679\pi$
$911$			1.10306i			0.0365460i	−0.999833	+	0.0182730i	$0.994183\pi$
$912$		0			0
$913$		−	99.2364i		−	3.28425i
$914$	−26.9574	−	13.4086i	−0.891673	−	0.443516i
$915$		0			0
$916$	−30.2315	+	7.87957i	−0.998875	+	0.260348i
$917$	−2.11862	−	0.877563i	−0.0699632	−	0.0289797i
$918$		0			0
$919$	21.1448	+	21.1448i	0.697501	+	0.697501i	0.963871	−	0.266370i	$-0.0858242\pi$
$919$	21.1448	+	21.1448i	0.697501	+	0.697501i	−0.266370	+	0.963871i	$0.585824\pi$
$920$	−3.62177	+	17.2806i	−0.119406	+	0.569725i
$921$		0			0
$922$	5.89904	−	5.13778i	0.194275	−	0.169204i
$923$	20.8042	+	8.61740i	0.684780	+	0.283645i
$924$		0			0
$925$	4.99609	+	12.0616i	0.164270	+	0.396584i
$926$	−13.6282	−	40.6024i	−0.447851	−	1.33428i
$927$		0			0
$928$	4.07059	−	1.92169i	0.133624	−	0.0630827i
$929$		−	8.59550i		−	0.282009i	−0.990009	−	0.141005i	$-0.954967\pi$
$929$		−	8.59550i		−	0.282009i	0.990009	−	0.141005i	$-0.0450332\pi$
$930$		0			0
$931$	20.6008	−	8.53313i	0.675164	−	0.279662i
$932$	18.2145	+	2.52468i	0.596637	+	0.0826985i
$933$		0			0
$934$	13.0418	+	14.9742i	0.426742	+	0.489972i
$935$	−42.6945	−	42.6945i	−1.39626	−	1.39626i
$936$		0			0
$937$	5.50940	−	5.50940i	0.179984	−	0.179984i	−0.611365	−	0.791349i	$-0.709379\pi$
$937$	5.50940	−	5.50940i	0.179984	−	0.179984i	0.791349	+	0.611365i	$0.209379\pi$
$938$	8.56420	+	0.590708i	0.279631	+	0.0192873i
$939$		0			0
$940$	−25.6555	+	6.68688i	−0.836789	+	0.218102i
$941$	7.60686	+	18.3646i	0.247977	+	0.598669i	0.998032	−	0.0627064i	$-0.0199732\pi$
$941$	7.60686	+	18.3646i	0.247977	+	0.598669i	−0.750055	+	0.661375i	$0.769973\pi$
$942$		0			0
$943$	−24.0985			−0.784754
$944$	16.4714	−	20.8694i	0.536099	−	0.679240i
$945$		0			0
$946$	−21.4706	−	10.6795i	−0.698070	−	0.347219i
$947$	−0.912836	+	0.378109i	−0.0296632	+	0.0122869i	−0.397466	−	0.917617i	$-0.630110\pi$
$947$	−0.912836	+	0.378109i	−0.0296632	+	0.0122869i	0.367803	+	0.929904i	$0.380110\pi$
$948$		0			0
$949$	−12.2247	+	29.5129i	−0.396829	+	0.958030i
$950$	5.92100	+	0.408396i	0.192103	+	0.0132501i
$951$		0			0
$952$	−7.65883	+	1.44202i	−0.248224	+	0.0467363i
$953$	32.2689	−	32.2689i	1.04529	−	1.04529i	0.0463673	−	0.998924i	$-0.485236\pi$
$953$	32.2689	−	32.2689i	1.04529	−	1.04529i	0.998924	−	0.0463673i	$-0.0147645\pi$
$954$		0			0
$955$	2.24344	−	5.41614i	0.0725960	−	0.175262i
$956$	24.1075	+	31.8658i	0.779692	+	1.03061i
$957$		0			0
$958$	−1.13225	−	3.37331i	−0.0365813	−	0.108987i
$959$	−5.23400			−0.169015
$960$		0			0
$961$	19.3896			0.625471
$962$	−11.6398	−	34.6783i	−0.375281	−	1.11807i
$963$		0			0
$964$	0.731656	+	0.967119i	0.0235650	+	0.0311488i
$965$	−3.52064	+	8.49958i	−0.113334	+	0.273611i
$966$		0			0
$967$	13.4056	−	13.4056i	0.431097	−	0.431097i	−0.457905	−	0.889001i	$-0.651400\pi$
$967$	13.4056	−	13.4056i	0.431097	−	0.431097i	0.889001	+	0.457905i	$0.151400\pi$
$968$	14.2142	+	75.4938i	0.456860	+	2.42646i
$969$		0			0
$970$	−3.37389	−	0.232711i	−0.108329	−	0.00747191i
$971$	7.93498	−	19.1567i	0.254645	−	0.614769i	−0.743923	−	0.668266i	$-0.767037\pi$
$971$	7.93498	−	19.1567i	0.254645	−	0.614769i	0.998568	+	0.0534973i	$0.0170369\pi$
$972$		0			0
$973$	−1.68200	+	0.696707i	−0.0539224	+	0.0223354i
$974$	2.97949	+	1.48199i	0.0954690	+	0.0474861i
$975$		0			0
$976$	27.8193	−	3.27652i	0.890473	−	0.104879i
$977$	−5.52723			−0.176832			−0.0884159	−	0.996084i	$-0.528180\pi$
$977$	−5.52723			−0.176832			−0.0884159	+	0.996084i	$0.528180\pi$
$978$		0			0
$979$	16.6320	+	40.1533i	0.531562	+	1.28330i
$980$	25.0823	−	6.53748i	0.801224	−	0.208832i
$981$		0			0
$982$	45.2396	+	3.12036i	1.44365	+	0.0995747i
$983$	28.1493	−	28.1493i	0.897822	−	0.897822i	−0.0974212	−	0.995243i	$-0.531059\pi$
$983$	28.1493	−	28.1493i	0.897822	−	0.897822i	0.995243	+	0.0974212i	$0.0310594\pi$
$984$		0			0
$985$	−11.4435	−	11.4435i	−0.364622	−	0.364622i
$986$	3.73629	+	4.28989i	0.118988	+	0.136618i
$987$		0			0
$988$	−16.4718	−	2.28312i	−0.524039	−	0.0726358i
$989$	−8.18744	+	3.39135i	−0.260345	+	0.107839i
$990$		0			0
$991$			24.7160i			0.785131i	0.919724	+	0.392565i	$0.128412\pi$
$991$			24.7160i			0.785131i	−0.919724	+	0.392565i	$0.871588\pi$
$992$	−0.932049	−	19.2526i	−0.0295926	−	0.611272i
$993$		0			0
$994$	−2.20985	−	6.58381i	−0.0700923	−	0.208826i
$995$	16.6442	+	40.1825i	0.527655	+	1.27387i
$996$		0			0
$997$	−26.8087	−	11.1045i	−0.849039	−	0.351684i	−0.0846280	−	0.996413i	$-0.526970\pi$
$997$	−26.8087	−	11.1045i	−0.849039	−	0.351684i	−0.764411	+	0.644729i	$0.776970\pi$
$998$	38.1880	−	33.2599i	1.20882	−	1.05282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.251.6	yes	32
3.2	odd	2		288.2.w.b.251.3	yes	32
4.3	odd	2		1152.2.w.b.143.3		32
12.11	even	2		1152.2.w.a.143.6		32
32.13	even	8		1152.2.w.a.1007.6		32
32.19	odd	8		288.2.w.b.179.3	yes	32
96.77	odd	8		1152.2.w.b.1007.3		32
96.83	even	8	inner	288.2.w.a.179.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.6	✓	32	96.83	even	8	inner
288.2.w.a.251.6	yes	32	1.1	even	1	trivial
288.2.w.b.179.3	yes	32	32.19	odd	8
288.2.w.b.251.3	yes	32	3.2	odd	2
1152.2.w.a.143.6		32	12.11	even	2
1152.2.w.a.1007.6		32	32.13	even	8
1152.2.w.b.143.3		32	4.3	odd	2
1152.2.w.b.1007.3		32	96.77	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.450008 + 1.34071i) q^{2} +(-1.59499 + 1.20666i) q^{4} +(-0.739921 + 1.78633i) q^{5} +(0.385417 - 0.385417i) q^{7} +(-2.33553 - 1.59540i) q^{8} +O(q^{10})\)	\(q+(0.450008 + 1.34071i) q^{2} +(-1.59499 + 1.20666i) q^{4} +(-0.739921 + 1.78633i) q^{5} +(0.385417 - 0.385417i) q^{7} +(-2.33553 - 1.59540i) q^{8} +(-2.72791 - 0.188155i) q^{10} +(-2.36398 + 5.70716i) q^{11} +(-2.30916 + 0.956485i) q^{13} +(0.690171 + 0.343290i) q^{14} +(1.08796 - 3.84920i) q^{16} +5.05518 q^{17} +(-1.27305 - 3.07341i) q^{19} +(-0.975320 - 3.74200i) q^{20} +(-8.71543 - 0.601139i) q^{22} +(-2.28291 + 2.28291i) q^{23} +(0.892052 + 0.892052i) q^{25} +(-2.32151 - 2.66548i) q^{26} +(-0.149669 + 1.07980i) q^{28} +(0.735171 - 0.304518i) q^{29} -3.40740i q^{31} +(5.65024 - 0.273536i) q^{32} +(2.27487 + 6.77751i) q^{34} +(0.403302 + 0.973658i) q^{35} +(9.56094 + 3.96027i) q^{37} +(3.54766 - 3.08984i) q^{38} +(4.57802 - 2.99155i) q^{40} +(5.27801 + 5.27801i) q^{41} +(2.53597 + 1.05043i) q^{43} +(-3.11606 - 11.9553i) q^{44} +(-4.08804 - 2.03338i) q^{46} -6.85609i q^{47} +6.70291i q^{49} +(-0.794549 + 1.59741i) q^{50} +(2.52893 - 4.31194i) q^{52} +(-7.45793 - 3.08917i) q^{53} +(-8.44569 - 8.44569i) q^{55} +(-1.51505 + 0.285257i) q^{56} +(0.739101 + 0.848613i) q^{58} +(6.14066 + 2.54355i) q^{59} +(2.67989 + 6.46983i) q^{61} +(4.56833 - 1.53336i) q^{62} +(2.90938 + 7.45221i) q^{64} -4.83264i q^{65} +(10.2890 - 4.26184i) q^{67} +(-8.06294 + 6.09987i) q^{68} +(-1.12390 + 0.978864i) q^{70} +(-6.37064 - 6.37064i) q^{71} +(9.03739 - 9.03739i) q^{73} +(-1.00706 + 14.6006i) q^{74} +(5.73905 + 3.36592i) q^{76} +(1.28852 + 3.11075i) q^{77} +1.22095 q^{79} +(6.07093 + 4.79156i) q^{80} +(-4.70112 + 9.45141i) q^{82} +(-14.8416 + 6.14761i) q^{83} +(-3.74043 + 9.03021i) q^{85} +(-0.267116 + 3.87270i) q^{86} +(14.6264 - 9.55772i) q^{88} +(4.97492 - 4.97492i) q^{89} +(-0.521343 + 1.25863i) q^{91} +(0.886520 - 6.39590i) q^{92} +(9.19200 - 3.08529i) q^{94} +6.43208 q^{95} +1.23680 q^{97} +(-8.98663 + 3.01636i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more