LMFDB - Embedded newform 297.2.n.b.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	297.91
Dual form			297.2.n.b.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.606887 + 0.270203i) q^{2} +(-1.04296 - 1.15832i) q^{4} +(-1.02009 + 0.454172i) q^{5} +(3.81922 - 0.811800i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(2.09587 - 2.57048i) q^{11} +(-0.279928 - 2.66333i) q^{13} +(2.53719 + 0.539295i) q^{14} +(-0.161688 + 1.53836i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(1.58999 + 0.707907i) q^{20} +(1.96651 - 0.993678i) q^{22} +(1.05719 - 1.83110i) q^{23} +(-2.51135 + 2.78914i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(1.05937 - 0.225177i) q^{29} +(0.0449642 + 0.427806i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(0.356392 - 3.39084i) q^{38} +(1.76638 + 1.96176i) q^{40} +(-2.85529 - 0.606910i) q^{41} +(1.11628 + 1.93346i) q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-8.58861 + 9.53861i) q^{47} +(7.53259 - 3.35373i) q^{49} +(-2.27774 + 1.01411i) q^{50} +(-2.79305 + 3.10200i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +(-4.61537 - 7.99405i) q^{56} +(0.703764 + 0.149590i) q^{58} +(1.58943 + 1.76524i) q^{59} +(0.426942 - 4.06208i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(-0.903682 - 8.59796i) q^{68} +(-2.83308 + 0.602190i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-3.86988 + 4.29793i) q^{74} +(-3.99983 + 6.92792i) q^{76} +(5.91786 - 11.5186i) q^{77} +(4.12439 + 1.83630i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.0503831 - 0.479363i) q^{83} +(-6.05809 - 1.28769i) q^{85} +(0.155030 + 1.47502i) q^{86} +(-7.31058 - 2.83448i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(-3.22362 + 0.685201i) q^{92} +(-7.78968 + 3.46819i) q^{94} +(3.83471 + 4.25888i) q^{95} +(7.32266 + 3.26026i) q^{97} +5.47762 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.606887	+	0.270203i	0.429134	+	0.191063i	0.609926	−	0.792459i	$-0.291199\pi$
$2$	0.606887	+	0.270203i	0.429134	+	0.191063i	−0.180792	+	0.983521i	$0.557866\pi$
$3$		0			0
$3$		0			0
$4$	−1.04296	−	1.15832i	−0.521480	−	0.579162i
$5$	−1.02009	+	0.454172i	−0.456196	+	0.203112i	−0.621952	−	0.783055i	$-0.713660\pi$
$5$	−1.02009	+	0.454172i	−0.456196	+	0.203112i	0.165756	+	0.986167i	$0.446994\pi$
$6$		0			0
$7$	3.81922	−	0.811800i	1.44353	−	0.306832i	0.581440	−	0.813589i	$-0.302489\pi$
$7$	3.81922	−	0.811800i	1.44353	−	0.306832i	0.862089	+	0.506758i	$0.169156\pi$
$8$	−0.730548	−	2.24840i	−0.258288	−	0.794928i
$9$		0			0
$10$	−0.741796			−0.234576
$11$	2.09587	−	2.57048i	0.631928	−	0.775027i
$11$	2.09587	−	2.57048i	0.631928	−	0.775027i
$12$		0			0
$13$	−0.279928	−	2.66333i	−0.0776380	−	0.738676i	−0.962217	−	0.272285i	$-0.912221\pi$
$13$	−0.279928	−	2.66333i	−0.0776380	−	0.738676i	0.884579	−	0.466391i	$-0.154446\pi$
$14$	2.53719	+	0.539295i	0.678091	+	0.144133i
$15$		0			0
$16$	−0.161688	+	1.53836i	−0.0404221	+	0.384590i
$17$	4.48727	+	3.26019i	1.08832	+	0.790713i	0.979115	−	0.203306i	$-0.0651688\pi$
$17$	4.48727	+	3.26019i	1.08832	+	0.790713i	0.109207	+	0.994019i	$0.465169\pi$
$18$		0			0
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	−0.950699	−	0.310116i	$-0.899632\pi$
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	0.586850	−	0.809696i	$-0.300368\pi$
$20$	1.58999	+	0.707907i	0.355532	+	0.158293i
$21$		0			0
$22$	1.96651	−	0.993678i	0.419260	−	0.211853i
$23$	1.05719	−	1.83110i	0.220439	−	0.381812i	−0.734502	−	0.678606i	$-0.762584\pi$
$23$	1.05719	−	1.83110i	0.220439	−	0.381812i	0.954941	+	0.296795i	$0.0959176\pi$
$24$		0			0
$25$	−2.51135	+	2.78914i	−0.502270	+	0.557827i
$26$	0.549758	−	1.69198i	0.107816	−	0.331825i
$27$		0			0
$28$	−4.92362	−	3.57722i	−0.930476	−	0.676030i
$29$	1.05937	−	0.225177i	0.196721	−	0.0418143i	−0.108497	−	0.994097i	$-0.534604\pi$
$29$	1.05937	−	0.225177i	0.196721	−	0.0418143i	0.305218	+	0.952282i	$0.401271\pi$
$30$		0			0
$31$	0.0449642	+	0.427806i	0.00807581	+	0.0768362i	0.997817	−	0.0660323i	$-0.0210340\pi$
$31$	0.0449642	+	0.427806i	0.00807581	+	0.0768362i	−0.989742	+	0.142869i	$0.954367\pi$
$32$	−2.87790	+	4.98467i	−0.508746	+	0.881173i
$33$		0			0
$34$	1.84235	+	3.19104i	0.315960	+	0.547259i
$35$	−3.52724	+	2.56269i	−0.596212	+	0.433173i
$36$		0			0
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	0.443175	+	0.896435i	$0.353852\pi$
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	−0.885447	+	0.464740i	$0.846148\pi$
$38$	0.356392	−	3.39084i	0.0578144	−	0.550067i
$39$		0			0
$40$	1.76638	+	1.96176i	0.279289	+	0.310182i
$41$	−2.85529	−	0.606910i	−0.445921	−	0.0947834i	−0.0205221	−	0.999789i	$-0.506533\pi$
$41$	−2.85529	−	0.606910i	−0.445921	−	0.0947834i	−0.425399	+	0.905006i	$0.639866\pi$
$42$		0			0
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	0.938501	−	0.345277i	$-0.112215\pi$
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	−0.768269	+	0.640127i	$0.778882\pi$
$44$	−5.16335	+	0.253209i	−0.778404	+	0.0381728i
$45$		0			0
$46$	1.13637	−	0.825618i	0.167548	−	0.121731i
$47$	−8.58861	+	9.53861i	−1.25278	+	1.39135i	−0.365044	+	0.930990i	$0.618946\pi$
$47$	−8.58861	+	9.53861i	−1.25278	+	1.39135i	−0.887733	+	0.460359i	$0.847721\pi$
$48$		0			0
$49$	7.53259	−	3.35373i	1.07608	−	0.479104i
$50$	−2.27774	+	1.01411i	−0.322121	+	0.143418i
$51$		0			0
$52$	−2.79305	+	3.10200i	−0.387326	+	0.430169i
$53$	4.56381	−	3.31581i	0.626888	−	0.455461i	−0.228433	−	0.973560i	$-0.573360\pi$
$53$	4.56381	−	3.31581i	0.626888	−	0.455461i	0.855321	+	0.518099i	$0.173360\pi$
$54$		0			0
$55$	−0.970527	+	3.57399i	−0.130866	+	0.481917i
$56$	−4.61537	−	7.99405i	−0.616755	−	1.06825i
$57$		0			0
$58$	0.703764	+	0.149590i	0.0924087	+	0.0196421i
$59$	1.58943	+	1.76524i	0.206927	+	0.229815i	0.837671	−	0.546176i	$-0.183917\pi$
$59$	1.58943	+	1.76524i	0.206927	+	0.229815i	−0.630744	+	0.775991i	$0.717250\pi$
$60$		0			0
$61$	0.426942	−	4.06208i	0.0546643	−	0.520096i	−0.932589	−	0.360940i	$-0.882456\pi$
$61$	0.426942	−	4.06208i	0.0546643	−	0.520096i	0.987253	−	0.159156i	$-0.0508773\pi$
$62$	−0.0883065	+	0.271779i	−0.0112149	+	0.0345160i
$63$		0			0
$64$	−0.590604	+	0.429099i	−0.0738255	+	0.0536374i
$65$	1.49516	+	2.58969i	0.185452	+	0.321212i
$66$		0			0
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	−0.397772	−	0.917484i	$-0.630216\pi$
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	0.993451	−	0.114262i	$-0.0364503\pi$
$68$	−0.903682	−	8.59796i	−0.109587	−	1.04266i
$69$		0			0
$70$	−2.83308	+	0.602190i	−0.338618	+	0.0719754i
$71$	5.11062	+	3.71308i	0.606519	+	0.440662i	0.848187	−	0.529697i	$-0.177694\pi$
$71$	5.11062	+	3.71308i	0.606519	+	0.440662i	−0.241668	+	0.970359i	$0.577694\pi$
$72$		0			0
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	0.483501	+	0.875344i	$0.339365\pi$
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	−0.905675	+	0.423973i	$0.860635\pi$
$74$	−3.86988	+	4.29793i	−0.449864	+	0.499625i
$75$		0			0
$76$	−3.99983	+	6.92792i	−0.458812	+	0.794686i
$77$	5.91786	−	11.5186i	0.674403	−	1.31267i
$78$		0			0
$79$	4.12439	+	1.83630i	0.464030	+	0.206600i	0.625416	−	0.780292i	$-0.284929\pi$
$79$	4.12439	+	1.83630i	0.464030	+	0.206600i	−0.161385	+	0.986891i	$0.551596\pi$
$80$	−0.533744	−	1.64269i	−0.0596744	−	0.183659i
$81$		0			0
$82$	−1.56885	−	1.13983i	−0.173250	−	0.125874i
$83$	0.0503831	−	0.479363i	0.00553026	−	0.0526169i	−0.991409	−	0.130800i	$-0.958245\pi$
$83$	0.0503831	−	0.479363i	0.00553026	−	0.0526169i	0.996939	+	0.0781834i	$0.0249120\pi$
$84$		0			0
$85$	−6.05809	−	1.28769i	−0.657092	−	0.139669i
$86$	0.155030	+	1.47502i	0.0167174	+	0.159055i
$87$		0			0
$88$	−7.31058	−	2.83448i	−0.779310	−	0.302157i
$89$	−16.0830			−1.70480			−0.852399	−	0.522891i	$-0.824853\pi$
$89$	−16.0830			−1.70480			−0.852399	+	0.522891i	$0.824853\pi$
$90$		0			0
$91$	−3.23120	−	9.94461i	−0.338722	−	1.04248i
$92$	−3.22362	+	0.685201i	−0.336085	+	0.0714371i
$93$		0			0
$94$	−7.78968	+	3.46819i	−0.803444	+	0.357716i
$95$	3.83471	+	4.25888i	0.393433	+	0.436952i
$96$		0			0
$97$	7.32266	+	3.26026i	0.743504	+	0.331029i	0.743289	−	0.668971i	$-0.233265\pi$
$97$	7.32266	+	3.26026i	0.743504	+	0.331029i	0.000215058		1.00000i	$0.499932\pi$
$98$	5.47762			0.553323
$99$		0			0
$100$	5.84996			0.584996
$101$	−1.60904	−	0.716391i	−0.160106	−	0.0712836i	0.325119	−	0.945673i	$-0.394596\pi$
$101$	−1.60904	−	0.716391i	−0.160106	−	0.0712836i	−0.485225	+	0.874389i	$0.661262\pi$
$102$		0			0
$103$	1.79840	+	1.99732i	0.177202	+	0.196802i	0.825202	−	0.564838i	$-0.191061\pi$
$103$	1.79840	+	1.99732i	0.177202	+	0.196802i	−0.648001	+	0.761640i	$0.724395\pi$
$104$	−5.78373	+	2.57508i	−0.567141	+	0.252507i
$105$		0			0
$106$	3.66566	−	0.779160i	0.356041	−	0.0756787i
$107$	3.17558	+	9.77342i	0.306995	+	0.944833i	0.978925	+	0.204219i	$0.0654653\pi$
$107$	3.17558	+	9.77342i	0.306995	+	0.944833i	−0.671931	+	0.740614i	$0.734535\pi$
$108$		0			0
$109$	2.36284			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$109$	2.36284			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$110$	−1.55470	+	1.90677i	−0.148235	+	0.181803i
$111$		0			0
$112$	0.631319	+	6.00659i	0.0596540	+	0.567570i
$113$	1.49895	+	0.318611i	0.141009	+	0.0299724i	0.277875	−	0.960617i	$-0.410370\pi$
$113$	1.49895	+	0.318611i	0.141009	+	0.0299724i	−0.136866	+	0.990590i	$0.543703\pi$
$114$		0			0
$115$	−0.246788	+	2.34803i	−0.0230131	+	0.218955i
$116$	−1.36571	−	0.992247i	−0.126803	−	0.0921279i
$117$		0			0
$118$	0.487631	+	1.50077i	0.0448901	+	0.138157i
$119$	19.7845	+	8.80862i	1.81364	+	0.807485i
$120$		0			0
$121$	−2.21469	−	10.7747i	−0.201335	−	0.979522i
$122$	1.35669	−	2.34986i	0.122829	−	0.212746i
$123$		0			0
$124$	0.448642	−	0.498267i	0.0402892	−	0.0447457i
$125$	3.02032	−	9.29560i	0.270146	−	0.831424i
$126$		0			0
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	0.827519	−	0.561437i	$-0.189751\pi$
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	−0.278241	+	0.960511i	$0.589751\pi$
$128$	10.7857	−	2.29256i	0.953328	−	0.202636i
$129$		0			0
$130$	0.207649	+	1.97565i	0.0182120	+	0.173276i
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	−0.959015	−	0.283356i	$-0.908552\pi$
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	0.724901	+	0.688853i	$0.241886\pi$
$132$		0			0
$133$	−10.0197	−	17.3547i	−0.868820	−	1.50484i
$134$	5.24101	−	3.80782i	0.452754	−	0.328945i
$135$		0			0
$136$	4.05203	−	12.4709i	0.347459	−	1.06937i
$137$	1.74889	−	16.6395i	0.149417	−	1.42161i	−0.620869	−	0.783914i	$-0.713220\pi$
$137$	1.74889	−	16.6395i	0.149417	−	1.42161i	0.770287	−	0.637698i	$-0.220113\pi$
$138$		0			0
$139$	9.19393	+	10.2109i	0.779819	+	0.866077i	0.993848	−	0.110751i	$-0.0353255\pi$
$139$	9.19393	+	10.2109i	0.779819	+	0.866077i	−0.214029	+	0.976827i	$0.568659\pi$
$140$	6.64718	+	1.41290i	0.561790	+	0.119412i
$141$		0			0
$142$	2.09828	+	3.63433i	0.176084	+	0.304986i
$143$	−7.43273	−	4.86244i	−0.621556	−	0.406618i
$144$		0			0
$145$	−0.978384	+	0.710837i	−0.0812503	+	0.0590318i
$146$	−5.18870	+	5.76264i	−0.429420	+	0.476919i
$147$		0			0
$148$	12.3964	−	5.51923i	1.01898	−	0.453678i
$149$	−5.07900	+	2.26132i	−0.416088	+	0.185254i	−0.604093	−	0.796914i	$-0.706464\pi$
$149$	−5.07900	+	2.26132i	−0.416088	+	0.185254i	0.188005	+	0.982168i	$0.439798\pi$
$150$		0			0
$151$	−0.109676	+	0.121807i	−0.00892527	+	0.00991252i	−0.747591	−	0.664159i	$-0.768790\pi$
$151$	−0.109676	+	0.121807i	−0.00892527	+	0.00991252i	0.738666	+	0.674072i	$0.235456\pi$
$152$	−9.81611	+	7.13182i	−0.796192	+	0.578467i
$153$		0			0
$154$	6.70385	−	5.39148i	0.540211	−	0.434458i
$155$	−0.240165	−	0.415978i	−0.0192905	−	0.0334121i
$156$		0			0
$157$	−23.3318	−	4.95932i	−1.86208	−	0.395797i	−0.867294	−	0.497797i	$-0.834142\pi$
$157$	−23.3318	−	4.95932i	−1.86208	−	0.395797i	−0.994784	+	0.102000i	$0.967476\pi$
$158$	2.00687	+	2.22885i	0.159658	+	0.177318i
$159$		0			0
$160$	0.671811	−	6.39185i	0.0531113	−	0.505320i
$161$	2.55114	−	7.85161i	0.201058	−	0.618794i
$162$		0			0
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	−0.446850	−	0.894609i	$-0.647454\pi$
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	0.712740	+	0.701429i	$0.247454\pi$
$164$	2.27495	+	3.94033i	0.177644	+	0.307688i
$165$		0			0
$166$	0.160102	−	0.277306i	0.0124264	−	0.0215231i
$167$	1.65577	+	15.7536i	0.128128	+	1.21905i	0.849909	+	0.526930i	$0.176657\pi$
$167$	1.65577	+	15.7536i	0.128128	+	1.21905i	−0.721781	+	0.692121i	$0.756676\pi$
$168$		0			0
$169$	5.70093	−	1.21177i	0.438533	−	0.0932131i
$170$	−3.32864	−	2.41840i	−0.255295	−	0.185482i
$171$		0			0
$172$	1.07533	−	3.30954i	0.0819935	−	0.252350i
$173$	1.74167	−	1.93432i	0.132417	−	0.147064i	−0.673290	−	0.739379i	$-0.735119\pi$
$173$	1.74167	−	1.93432i	0.132417	−	0.147064i	0.805706	+	0.592315i	$0.201786\pi$
$174$		0			0
$175$	−7.32717	+	12.6910i	−0.553882	+	0.959352i
$176$	3.61544	+	3.63981i	0.272524	+	0.274361i
$177$		0			0
$178$	−9.76059	−	4.34569i	−0.731587	−	0.325724i
$179$	−2.34483	−	7.21663i	−0.175261	−	0.539396i	0.824385	−	0.566030i	$-0.191521\pi$
$179$	−2.34483	−	7.21663i	−0.175261	−	0.539396i	−0.999645	+	0.0266334i	$0.991521\pi$
$180$		0			0
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	0.657608	−	0.753360i	$-0.271568\pi$
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	−0.513276	+	0.858224i	$0.671568\pi$
$182$	0.726095	−	6.90833i	0.0538218	−	0.512080i
$183$		0			0
$184$	−4.88937	−	1.03927i	−0.360449	−	0.0766159i
$185$	−1.01613	−	9.66784i	−0.0747074	−	0.710794i
$186$		0			0
$187$	17.7850	−	4.70149i	1.30056	−	0.343807i
$188$	20.0064			1.45911
$189$		0			0
$190$	1.17647	+	3.62081i	0.0853504	+	0.262681i
$191$	−16.1573	+	3.43433i	−1.16910	+	0.248500i	−0.751251	−	0.660017i	$-0.770549\pi$
$191$	−16.1573	+	3.43433i	−1.16910	+	0.248500i	−0.417849	+	0.908517i	$0.637216\pi$
$192$		0			0
$193$	−7.43166	+	3.30879i	−0.534942	+	0.238172i	−0.656384	−	0.754427i	$-0.727915\pi$
$193$	−7.43166	+	3.30879i	−0.534942	+	0.238172i	0.121442	+	0.992599i	$0.461248\pi$
$194$	3.56310	+	3.95722i	0.255815	+	0.284112i
$195$		0			0
$196$	−11.7409	−	5.22738i	−0.838635	−	0.373384i
$197$	22.9072			1.63207			0.816035	−	0.578003i	$-0.196168\pi$
$197$	22.9072			1.63207			0.816035	+	0.578003i	$0.196168\pi$
$198$		0			0
$199$	9.27177			0.657259			0.328629	−	0.944459i	$-0.393413\pi$
$199$	9.27177			0.657259			0.328629	+	0.944459i	$0.393413\pi$
$200$	8.10574	+	3.60891i	0.573162	+	0.255188i
$201$		0			0
$202$	−0.782935	−	0.869537i	−0.0550871	−	0.0611804i
$203$	3.86318	−	1.72000i	0.271142	−	0.120720i
$204$		0			0
$205$	3.18828	−	0.677690i	0.222679	−	0.0473319i
$206$	0.551741	+	1.69808i	0.0384416	+	0.118311i
$207$		0			0
$208$	4.14243			0.287226
$209$	−15.8709	−	6.15351i	−1.09781	−	0.425647i
$210$		0			0
$211$	−0.440125	−	4.18751i	−0.0302995	−	0.288280i	−0.999171	−	0.0407153i	$-0.987036\pi$
$211$	−0.440125	−	4.18751i	−0.0302995	−	0.288280i	0.968871	−	0.247565i	$-0.0796303\pi$
$212$	−8.60065	−	1.82812i	−0.590695	−	0.125556i
$213$		0			0
$214$	−0.713596	+	6.78942i	−0.0487804	+	0.464115i
$215$	−2.01683	−	1.46531i	−0.137547	−	0.0999334i
$216$		0			0
$217$	0.519021	+	1.59738i	0.0352335	+	0.108437i
$218$	1.43398	+	0.638448i	0.0971212	+	0.0432412i
$219$		0			0
$220$	5.15206	−	2.60334i	0.347352	−	0.175517i
$221$	7.42687	−	12.8637i	0.499585	−	0.865307i
$222$		0			0
$223$	−4.58961	+	5.09728i	−0.307343	+	0.341339i	−0.876953	−	0.480576i	$-0.840428\pi$
$223$	−4.58961	+	5.09728i	−0.307343	+	0.341339i	0.569610	+	0.821915i	$0.307094\pi$
$224$	−6.94477	+	21.3738i	−0.464017	+	1.42810i
$225$		0			0
$226$	0.823601	+	0.598381i	0.0547851	+	0.0398037i
$227$	27.5152	−	5.84854i	1.82625	−	0.388181i	0.838585	−	0.544771i	$-0.183383\pi$
$227$	27.5152	−	5.84854i	1.82625	−	0.388181i	0.987664	+	0.156590i	$0.0500502\pi$
$228$		0			0
$229$	1.46703	+	13.9578i	0.0969438	+	0.922358i	0.929600	+	0.368569i	$0.120152\pi$
$229$	1.46703	+	13.9578i	0.0969438	+	0.922358i	−0.832657	+	0.553789i	$0.813181\pi$
$230$	−0.784218	+	1.35831i	−0.0517098	+	0.0895640i
$231$		0			0
$232$	−1.28021	−	2.21739i	−0.0840499	−	0.145579i
$233$	−11.7385	+	8.52854i	−0.769017	+	0.558723i	−0.901663	−	0.432440i	$-0.857653\pi$
$233$	−11.7385	+	8.52854i	−0.769017	+	0.558723i	0.132646	+	0.991163i	$0.457653\pi$
$234$		0			0
$235$	4.42895	−	13.6309i	0.288913	−	0.889182i
$236$	0.387010	−	3.68216i	0.0251922	−	0.239688i
$237$		0			0
$238$	9.62682	+	10.6917i	0.624014	+	0.693038i
$239$	−24.5986	−	5.22859i	−1.59115	−	0.338209i	−0.674617	−	0.738168i	$-0.735691\pi$
$239$	−24.5986	−	5.22859i	−1.59115	−	0.338209i	−0.916533	+	0.399959i	$0.869024\pi$
$240$		0			0
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	−0.996419	−	0.0845570i	$-0.973053\pi$
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	0.424981	−	0.905202i	$-0.360281\pi$
$242$	1.56731	−	7.13747i	0.100750	−	0.458814i
$243$		0			0
$244$	−5.15048	+	3.74205i	−0.329726	+	0.239560i
$245$	−6.16073	+	6.84218i	−0.393594	+	0.437131i
$246$		0			0
$247$	−12.5562	+	5.59036i	−0.798929	+	0.355706i
$248$	0.929029	−	0.413630i	0.0589934	−	0.0262655i
$249$		0			0
$250$	4.34470	−	4.82528i	0.274783	−	0.305177i
$251$	−17.6993	+	12.8593i	−1.11717	+	0.811670i	−0.983777	−	0.179394i	$-0.942586\pi$
$251$	−17.6993	+	12.8593i	−1.11717	+	0.811670i	−0.133390	+	0.991064i	$0.542586\pi$
$252$		0			0
$253$	−2.49108	−	6.55523i	−0.156613	−	0.412124i
$254$	2.54147	+	4.40195i	0.159466	+	0.276203i
$255$		0			0
$256$	8.59329	+	1.82656i	0.537081	+	0.114160i
$257$	−3.45520	−	3.83739i	−0.215530	−	0.239370i	0.625679	−	0.780081i	$-0.284822\pi$
$257$	−3.45520	−	3.83739i	−0.215530	−	0.239370i	−0.841209	+	0.540711i	$0.818155\pi$
$258$		0			0
$259$	−3.55315	+	33.8059i	−0.220782	+	2.10060i
$260$	1.44031	−	4.43283i	0.0893244	−	0.274912i
$261$		0			0
$262$	−2.88024	+	2.09262i	−0.177942	+	0.129282i
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	−0.871798	−	0.489866i	$-0.837046\pi$
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	0.0116625	−	0.999932i	$-0.496288\pi$
$264$		0			0
$265$	−3.14954	+	5.45516i	−0.193475	+	0.335108i
$266$	−1.39155	−	13.2397i	−0.0853212	−	0.811777i
$267$		0			0
$268$	−14.8676	+	3.16020i	−0.908183	+	0.193040i
$269$	2.44290	+	1.77487i	0.148946	+	0.108216i	0.659763	−	0.751474i	$-0.270657\pi$
$269$	2.44290	+	1.77487i	0.148946	+	0.108216i	−0.510816	+	0.859690i	$0.670657\pi$
$270$		0			0
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	0.367845	+	0.929887i	$0.380096\pi$
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	−0.844167	+	0.536081i	$0.819904\pi$
$272$	−5.74089	+	6.37590i	−0.348093	+	0.386596i
$273$		0			0
$274$	5.55744	−	9.62577i	0.335737	−	0.581514i
$275$	1.90595	+	12.3010i	0.114933	+	0.741779i
$276$		0			0
$277$	−9.65105	−	4.29692i	−0.579875	−	0.258177i	0.0957707	−	0.995403i	$-0.469468\pi$
$277$	−9.65105	−	4.29692i	−0.579875	−	0.258177i	−0.675646	+	0.737226i	$0.736135\pi$
$278$	2.82066	+	8.68109i	0.169172	+	0.520657i
$279$		0			0
$280$	8.33875	+	6.05845i	0.498335	+	0.362062i
$281$	−2.35926	+	22.4469i	−0.140742	+	1.33907i	0.665019	+	0.746827i	$0.268424\pi$
$281$	−2.35926	+	22.4469i	−0.140742	+	1.33907i	−0.805761	+	0.592241i	$0.798243\pi$
$282$		0			0
$283$	5.74880	+	1.22195i	0.341731	+	0.0726371i	0.375580	−	0.926790i	$-0.377443\pi$
$283$	5.74880	+	1.22195i	0.341731	+	0.0726371i	−0.0338497	+	0.999427i	$0.510777\pi$
$284$	−1.02922	−	9.79234i	−0.0610728	−	0.581069i
$285$		0			0
$286$	−3.19697	−	4.95930i	−0.189041	−	0.293250i
$287$	−11.3977			−0.672782
$288$		0			0
$289$	4.25344	+	13.0907i	0.250202	+	0.770044i
$290$	−0.785839	+	0.167035i	−0.0461461	+	0.00980865i
$291$		0			0
$292$	16.6210	−	7.40014i	0.972670	−	0.433061i
$293$	−4.74689	−	5.27195i	−0.277316	−	0.307991i	0.588356	−	0.808602i	$-0.299775\pi$
$293$	−4.74689	−	5.27195i	−0.277316	−	0.307991i	−0.865672	+	0.500611i	$0.833109\pi$
$294$		0			0
$295$	−2.42308	−	1.07883i	−0.141077	−	0.0628117i
$296$	20.5814			1.19627
$297$		0			0
$298$	−3.69339			−0.213953
$299$	−5.17278	−	2.30307i	−0.299150	−	0.133190i
$300$		0			0
$301$	5.83291	+	6.47811i	0.336204	+	0.373392i
$302$	−0.0994733	+	0.0442884i	−0.00572405	+	0.00254851i
$303$		0			0
$304$	7.76540	−	1.65059i	0.445376	−	0.0946676i
$305$	1.40936	+	4.33757i	0.0806999	+	0.248369i
$306$		0			0
$307$	−18.5370			−1.05796			−0.528981	−	0.848633i	$-0.677426\pi$
$307$	−18.5370			−1.05796			−0.528981	+	0.848633i	$0.677426\pi$
$308$	−19.5144	+	5.15867i	−1.11194	+	0.293942i
$309$		0			0
$310$	−0.0333543	−	0.317345i	−0.00189440	−	0.0180240i
$311$	6.72598	+	1.42965i	0.381395	+	0.0810680i	0.394620	−	0.918845i	$-0.370876\pi$
$311$	6.72598	+	1.42965i	0.381395	+	0.0810680i	−0.0132247	+	0.999913i	$0.504210\pi$
$312$		0			0
$313$	2.64727	−	25.1871i	0.149632	−	1.42366i	−0.619715	−	0.784827i	$-0.712752\pi$
$313$	2.64727	−	25.1871i	0.149632	−	1.42366i	0.769348	−	0.638830i	$-0.220581\pi$
$314$	−12.8197	−	9.31407i	−0.723459	−	0.525624i
$315$		0			0
$316$	−2.17455	−	6.69256i	−0.122328	−	0.376486i
$317$	−10.0301	−	4.46567i	−0.563344	−	0.250817i	0.105248	−	0.994446i	$-0.466436\pi$
$317$	−10.0301	−	4.46567i	−0.563344	−	0.250817i	−0.668593	+	0.743629i	$0.733103\pi$
$318$		0			0
$319$	1.64149	−	3.19503i	0.0919060	−	0.178888i
$320$	0.407582	−	0.705953i	0.0227845	−	0.0394640i
$321$		0			0
$322$	3.66979	−	4.07571i	0.204509	−	0.227131i
$323$	8.79675	−	27.0736i	0.489464	−	1.50642i
$324$		0			0
$325$	8.13140	+	5.90780i	0.451049	+	0.327706i
$326$	2.72659	−	0.579555i	0.151012	−	0.0320986i
$327$		0			0
$328$	0.721351	+	6.86319i	0.0398299	+	0.378956i
$329$	−25.0583	+	43.4023i	−1.38151	+	2.39284i
$330$		0			0
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	0.912495	−	0.409088i	$-0.134153\pi$
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	−0.810528	+	0.585700i	$0.800820\pi$
$332$	−0.607805	+	0.441596i	−0.0333576	+	0.0242357i
$333$		0			0
$334$	−3.25182	+	10.0081i	−0.177931	+	0.547617i
$335$	−1.13821	+	10.8293i	−0.0621869	+	0.591668i
$336$		0			0
$337$	−21.5428	−	23.9257i	−1.17351	−	1.30331i	−0.943976	−	0.330013i	$-0.892947\pi$
$337$	−21.5428	−	23.9257i	−1.17351	−	1.30331i	−0.229533	−	0.973301i	$-0.573720\pi$
$338$	3.78725	+	0.805004i	0.205999	+	0.0437864i
$339$		0			0
$340$	4.82678	+	8.36023i	0.261769	+	0.453397i
$341$	1.19390	+	0.781045i	0.0646535	+	0.0422960i
$342$		0			0
$343$	3.93417	−	2.85834i	0.212425	−	0.154336i
$344$	3.53168	−	3.92233i	0.190416	−	0.211478i
$345$		0			0
$346$	1.57966	−	0.703310i	0.0849230	−	0.0378102i
$347$	19.6618	−	8.75398i	1.05550	−	0.469939i	0.195749	−	0.980654i	$-0.437286\pi$
$347$	19.6618	−	8.75398i	1.05550	−	0.469939i	0.859750	+	0.510715i	$0.170619\pi$
$348$		0			0
$349$	−11.2547	+	12.4997i	−0.602453	+	0.669092i	−0.964810	−	0.262948i	$-0.915305\pi$
$349$	−11.2547	+	12.4997i	−0.602453	+	0.669092i	0.362357	+	0.932039i	$0.381972\pi$
$350$	−7.87593	+	5.72219i	−0.420986	+	0.305864i
$351$		0			0
$352$	6.78127	+	17.8448i	0.361443	+	0.951129i
$353$	1.56543	+	2.71140i	0.0833193	+	0.144313i	0.904674	−	0.426105i	$-0.140115\pi$
$353$	1.56543	+	2.71140i	0.0833193	+	0.144313i	−0.821355	+	0.570418i	$0.806781\pi$
$354$		0			0
$355$	−6.89965	−	1.46657i	−0.366195	−	0.0778372i
$356$	16.7740	+	18.6294i	0.889018	+	0.987355i
$357$		0			0
$358$	0.526915	−	5.01326i	0.0278483	−	0.264959i
$359$	−2.62315	+	8.07323i	−0.138445	+	0.426089i	−0.996110	−	0.0881197i	$-0.971914\pi$
$359$	−2.62315	+	8.07323i	−0.138445	+	0.426089i	0.857665	+	0.514208i	$0.171914\pi$
$360$		0			0
$361$	−5.93893	+	4.31489i	−0.312575	+	0.227099i
$362$	0.797247	+	1.38087i	0.0419024	+	0.0725770i
$363$		0			0
$364$	−8.14907	+	14.1146i	−0.427127	+	0.739806i
$365$	−1.36242	−	12.9626i	−0.0713124	−	0.678492i
$366$		0			0
$367$	10.7703	−	2.28931i	0.562208	−	0.119501i	0.0819628	−	0.996635i	$-0.473881\pi$
$367$	10.7703	−	2.28931i	0.562208	−	0.119501i	0.480245	+	0.877134i	$0.340548\pi$
$368$	2.64596	+	1.92241i	0.137930	+	0.100212i
$369$		0			0
$370$	1.99561	−	6.14185i	0.103747	−	0.319300i
$371$	14.7384	−	16.3687i	0.765181	−	0.849820i
$372$		0			0
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	−0.972599	−	0.232491i	$-0.925312\pi$
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	0.687642	+	0.726050i	$0.258646\pi$
$374$	12.0638	+	1.95229i	0.623805	+	0.100950i
$375$		0			0
$376$	27.7210	+	12.3422i	1.42960	+	0.636499i
$377$	−0.896269	−	2.75843i	−0.0461602	−	0.142067i
$378$		0			0
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.0818315	−	0.996646i	$-0.526077\pi$
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.973154	+	0.230154i	$0.926077\pi$
$380$	0.933713	−	8.88368i	0.0478984	−	0.455723i
$381$		0			0
$382$	−10.7336	−	2.28150i	−0.549179	−	0.116732i
$383$	−1.26633	−	12.0484i	−0.0647067	−	0.615643i	−0.978038	−	0.208426i	$-0.933166\pi$
$383$	−1.26633	−	12.0484i	−0.0647067	−	0.615643i	0.913331	−	0.407217i	$-0.133501\pi$
$384$		0			0
$385$	−0.805292	+	14.4377i	−0.0410415	+	0.735814i
$386$	−5.40422			−0.275068
$387$		0			0
$388$	−3.86080	−	11.8823i	−0.196003	−	0.603234i
$389$	14.0375	−	2.98376i	0.711728	−	0.151283i	0.162200	−	0.986758i	$-0.448141\pi$
$389$	14.0375	−	2.98376i	0.711728	−	0.151283i	0.549528	+	0.835475i	$0.314808\pi$
$390$		0			0
$391$	10.7136	−	4.77002i	0.541812	−	0.241230i
$392$	−13.0434	−	14.4862i	−0.658792	−	0.731663i
$393$		0			0
$394$	13.9021	+	6.18960i	0.700376	+	0.311828i
$395$	−5.04123			−0.253652
$396$		0			0
$397$	−5.03882			−0.252891			−0.126446	−	0.991974i	$-0.540357\pi$
$397$	−5.03882			−0.252891			−0.126446	+	0.991974i	$0.540357\pi$
$398$	5.62692	+	2.50527i	0.282052	+	0.125578i
$399$		0			0
$400$	−3.88464	−	4.31433i	−0.194232	−	0.215717i
$401$	16.6267	−	7.40268i	0.830297	−	0.369672i	0.0528362	−	0.998603i	$-0.483174\pi$
$401$	16.6267	−	7.40268i	0.830297	−	0.369672i	0.777461	+	0.628931i	$0.216507\pi$
$402$		0			0
$403$	1.12680	−	0.239509i	0.0561301	−	0.0119308i
$404$	0.848352	+	2.61096i	0.0422071	+	0.129900i
$405$		0			0
$406$	2.80926			0.139421
$407$	15.6444	+	24.2683i	0.775464	+	1.20294i
$408$		0			0
$409$	−1.71745	−	16.3404i	−0.0849224	−	0.807983i	−0.951232	−	0.308476i	$-0.900181\pi$
$409$	−1.71745	−	16.3404i	−0.0849224	−	0.807983i	0.866310	−	0.499507i	$-0.166486\pi$
$410$	2.11804	+	0.450203i	0.104603	+	0.0222340i
$411$		0			0
$412$	0.437891	−	4.16626i	0.0215733	−	0.205257i
$413$	7.50342	+	5.45155i	0.369219	+	0.268253i
$414$		0			0
$415$	0.166318	+	0.511874i	0.00816423	+	0.0251269i
$416$	14.0814	+	6.26946i	0.690399	+	0.307386i
$417$		0			0
$418$	−7.96912	−	8.02285i	−0.389783	−	0.392410i
$419$	−8.70324	+	15.0745i	−0.425181	+	0.736435i	−0.996437	−	0.0843365i	$-0.973123\pi$
$419$	−8.70324	+	15.0745i	−0.425181	+	0.736435i	0.571256	+	0.820772i	$0.306456\pi$
$420$		0			0
$421$	3.04364	−	3.38030i	0.148338	−	0.164746i	−0.664397	−	0.747380i	$-0.731311\pi$
$421$	3.04364	−	3.38030i	0.148338	−	0.164746i	0.812734	+	0.582634i	$0.197978\pi$
$422$	0.864374	−	2.66027i	0.0420771	−	0.129500i
$423$		0			0
$424$	−10.7893	−	7.83890i	−0.523976	−	0.380691i
$425$	−20.3622	+	4.32812i	−0.987712	+	0.209945i
$426$		0			0
$427$	−1.66701	−	15.8606i	−0.0806723	−	0.767546i
$428$	8.00879	−	13.8716i	0.387120	−	0.670511i
$429$		0			0
$430$	−0.828055	−	1.43423i	−0.0399323	−	0.0691648i
$431$	10.1004	−	7.33838i	0.486520	−	0.353477i	−0.317325	−	0.948317i	$-0.602784\pi$
$431$	10.1004	−	7.33838i	0.486520	−	0.353477i	0.803844	+	0.594840i	$0.202784\pi$
$432$		0			0
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	−0.476031	−	0.879428i	$-0.657925\pi$
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	0.902032	−	0.431668i	$-0.142075\pi$
$434$	−0.116631	+	1.10967i	−0.00559848	+	0.0532660i
$435$		0			0
$436$	−2.46435	−	2.73694i	−0.118021	−	0.131075i
$437$	−10.6146	−	2.25620i	−0.507764	−	0.107929i
$438$		0			0
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	0.910871	−	0.412692i	$-0.135411\pi$
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	−0.812837	+	0.582491i	$0.802078\pi$
$440$	8.74476	−	0.428841i	0.416890	−	0.0204442i
$441$		0			0
$442$	7.98309	−	5.80005i	0.379717	−	0.275880i
$443$	14.2054	−	15.7767i	0.674921	−	0.749576i	−0.304255	−	0.952591i	$-0.598407\pi$
$443$	14.2054	−	15.7767i	0.674921	−	0.749576i	0.979176	+	0.203015i	$0.0650740\pi$
$444$		0			0
$445$	16.4061	−	7.30446i	0.777723	−	0.346265i
$446$	−4.16267	+	1.85334i	−0.197108	+	0.0877583i
$447$		0			0
$448$	−1.90730	+	2.11827i	−0.0901116	+	0.100079i
$449$	20.9494	−	15.2206i	0.988663	−	0.718306i	0.0290350	−	0.999578i	$-0.490757\pi$
$449$	20.9494	−	15.2206i	0.988663	−	0.718306i	0.959628	+	0.281273i	$0.0907566\pi$
$450$		0			0
$451$	−7.54435	+	6.06744i	−0.355249	+	0.285705i
$452$	−1.19428	−	2.06856i	−0.0561744	−	0.0972970i
$453$		0			0
$454$	18.2789	+	3.88530i	0.857872	+	0.182346i
$455$	7.81266	+	8.67684i	0.366263	+	0.406776i
$456$		0			0
$457$	1.07705	−	10.2474i	0.0503821	−	0.479354i	−0.940018	−	0.341124i	$-0.889192\pi$
$457$	1.07705	−	10.2474i	0.0503821	−	0.479354i	0.990400	−	0.138229i	$-0.0441411\pi$
$458$	−2.88113	+	8.86721i	−0.134626	+	0.414338i
$459$		0			0
$460$	2.97717	−	2.16304i	0.138811	−	0.100852i
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	−0.993862	−	0.110628i	$-0.964714\pi$
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	0.401124	−	0.916024i	$-0.368620\pi$
$462$		0			0
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.136368	−	0.990658i	$-0.456457\pi$
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.789751	−	0.613427i	$-0.210210\pi$
$464$	0.175115	+	1.66611i	0.00812951	+	0.0773471i
$465$		0			0
$466$	−9.42840	+	2.00407i	−0.436762	+	0.0928367i
$467$	−14.0582	−	10.2139i	−0.650537	−	0.472643i	0.212917	−	0.977070i	$-0.431704\pi$
$467$	−14.0582	−	10.2139i	−0.650537	−	0.472643i	−0.863454	+	0.504427i	$0.831704\pi$
$468$		0			0
$469$	11.7661	−	36.2123i	0.543308	−	1.67213i
$470$	6.37099	−	7.07570i	0.293872	−	0.326378i
$471$		0			0
$472$	2.80781	−	4.86327i	0.129240	−	0.223850i
$473$	7.30949	+	1.18289i	0.336091	+	0.0543896i
$474$		0			0
$475$	17.5971	+	7.83475i	0.807412	+	0.359483i
$476$	−10.4312	−	32.1039i	−0.478112	−	1.47148i
$477$		0			0
$478$	−13.5158	−	9.81979i	−0.618197	−	0.449147i
$479$	−2.28875	+	21.7760i	−0.104576	+	0.994972i	0.808863	+	0.587997i	$0.200083\pi$
$479$	−2.28875	+	21.7760i	−0.104576	+	0.994972i	−0.913439	+	0.406975i	$0.866584\pi$
$480$		0			0
$481$	22.8047	+	4.84729i	1.03980	+	0.221017i
$482$	−1.23203	−	11.7219i	−0.0561172	−	0.533920i
$483$		0			0
$484$	−10.1708	+	13.8029i	−0.462310	+	0.627407i
$485$	−8.95046			−0.406420
$486$		0			0
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	0.971344	−	0.237679i	$-0.0763867\pi$
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	−0.925538	+	0.378655i	$0.876387\pi$
$488$	−9.44506	+	2.00761i	−0.427558	+	0.0908802i
$489$		0			0
$490$	−5.58764	+	2.48778i	−0.252424	+	0.112386i
$491$	4.83373	+	5.36841i	0.218143	+	0.242273i	0.842277	−	0.539045i	$-0.181215\pi$
$491$	4.83373	+	5.36841i	0.218143	+	0.242273i	−0.624134	+	0.781318i	$0.714548\pi$
$492$		0			0
$493$	5.48781	+	2.44333i	0.247159	+	0.110042i
$494$	−9.13071			−0.410810
$495$		0			0
$496$	−0.665390			−0.0298769
$497$	22.5328	+	10.0323i	1.01074	+	0.450009i
$498$		0			0
$499$	9.92622	+	11.0242i	0.444359	+	0.493511i	0.923162	−	0.384412i	$-0.125596\pi$
$499$	9.92622	+	11.0242i	0.444359	+	0.493511i	−0.478803	+	0.877922i	$0.658929\pi$
$500$	−13.9174	+	6.19642i	−0.622405	+	0.277112i
$501$		0			0
$502$	−14.2161	+	3.02172i	−0.634494	+	0.134866i
$503$	10.1918	+	31.3671i	0.454430	+	1.39859i	0.871803	+	0.489856i	$0.162951\pi$
$503$	10.1918	+	31.3671i	0.454430	+	1.39859i	−0.417374	+	0.908735i	$0.637049\pi$
$504$		0			0
$505$	1.96673			0.0875181
$506$	0.259440	−	4.65138i	0.0115335	−	0.206779i
$507$		0			0
$508$	−1.24660	−	11.8606i	−0.0553090	−	0.526230i
$509$	37.8244	+	8.03982i	1.67654	+	0.356359i	0.945410	−	0.325884i	$-0.105662\pi$
$509$	37.8244	+	8.03982i	1.67654	+	0.356359i	0.731126	+	0.682243i	$0.238995\pi$
$510$		0			0
$511$	−4.76404	+	45.3268i	−0.210749	+	2.00514i
$512$	−13.1198	−	9.53213i	−0.579821	−	0.421264i
$513$		0			0
$514$	−1.06004	−	3.26247i	−0.0467564	−	0.143901i
$515$	−2.74165	−	1.22066i	−0.120812	−	0.0537888i
$516$		0			0
$517$	6.51820	+	42.0685i	0.286670	+	1.85017i
$518$	−11.2908	+	19.5563i	−0.496091	+	0.859255i
$519$		0			0
$520$	4.73037	−	5.25361i	0.207440	−	0.230386i
$521$	5.40297	−	16.6286i	0.236708	−	0.728514i	−0.760182	−	0.649710i	$-0.774890\pi$
$521$	5.40297	−	16.6286i	0.236708	−	0.728514i	0.996890	−	0.0788032i	$-0.0251099\pi$
$522$		0			0
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	0.301253	−	0.953544i	$-0.402595\pi$
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	−0.813782	+	0.581170i	$0.802595\pi$
$524$	8.17061	−	1.73672i	0.356935	−	0.0758688i
$525$		0			0
$526$	−1.93726	−	18.4318i	−0.0844683	−	0.803663i
$527$	−1.19296	+	2.06627i	−0.0519663	+	0.0900082i
$528$		0			0
$529$	9.26470	+	16.0469i	0.402813	+	0.697693i
$530$	−3.38542	+	2.45965i	−0.147053	+	0.106840i
$531$		0			0
$532$	−9.65216	+	29.7063i	−0.418474	+	1.28793i
$533$	−0.817130	+	7.77447i	−0.0353938	+	0.336750i
$534$		0			0
$535$	−7.67818	−	8.52748i	−0.331956	−	0.368675i
$536$	−22.5502	−	4.79319i	−0.974021	−	0.207034i
$537$		0			0
$538$	1.00299	+	1.73722i	0.0432418	+	0.0748971i
$539$	7.16664	−	26.3913i	0.308689	−	1.13675i
$540$		0			0
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.988645	−	0.150272i	$-0.951985\pi$
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.162591	+	0.986694i	$0.551985\pi$
$542$	−11.2795	+	12.5272i	−0.484498	+	0.538089i
$543$		0			0
$544$	−29.1649	+	12.9850i	−1.25043	+	0.556729i
$545$	−2.41030	+	1.07314i	−0.103246	+	0.0459681i
$546$		0			0
$547$	6.16546	−	6.84744i	0.263616	−	0.292775i	−0.596776	−	0.802408i	$-0.703552\pi$
$547$	6.16546	−	6.84744i	0.263616	−	0.292775i	0.860392	+	0.509633i	$0.170219\pi$
$548$	−21.0980	+	15.3286i	−0.901262	+	0.654805i
$549$		0			0
$550$	−2.16708	+	7.98032i	−0.0924046	+	0.340282i
$551$	−2.77927	−	4.81383i	−0.118401	−	0.205076i
$552$		0			0
$553$	17.2427	+	3.66504i	0.733232	+	0.155853i
$554$	−4.69605	−	5.21549i	−0.199516	−	0.221585i
$555$		0			0
$556$	2.23863	−	21.2991i	0.0949388	−	0.903283i
$557$	−11.4496	+	35.2384i	−0.485137	+	1.49310i	0.346645	+	0.937996i	$0.387321\pi$
$557$	−11.4496	+	35.2384i	−0.485137	+	1.49310i	−0.831782	+	0.555102i	$0.812679\pi$
$558$		0			0
$559$	4.83697	−	3.51427i	0.204582	−	0.148638i
$560$	−3.37202	−	5.84052i	−0.142494	−	0.246807i
$561$		0			0
$562$	−7.49703	+	12.9852i	−0.316243	+	0.547749i
$563$	−2.82165	−	26.8462i	−0.118918	−	1.13143i	−0.877407	−	0.479746i	$-0.840729\pi$
$563$	−2.82165	−	26.8462i	−0.118918	−	1.13143i	0.758489	−	0.651686i	$-0.225938\pi$
$564$		0			0
$565$	−1.67376	+	0.355768i	−0.0704155	+	0.0149673i
$566$	3.15870	+	2.29493i	0.132770	+	0.0964630i
$567$		0			0
$568$	4.61492	−	14.2033i	0.193638	−	0.595956i
$569$	18.3848	−	20.4184i	0.770733	−	0.855985i	−0.222159	−	0.975011i	$-0.571310\pi$
$569$	18.3848	−	20.4184i	0.770733	−	0.855985i	0.992891	+	0.119025i	$0.0379769\pi$
$570$		0			0
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	−0.0921492	−	0.995745i	$-0.529374\pi$
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	0.908415	−	0.418069i	$-0.137293\pi$
$572$	2.11974	+	13.6808i	0.0886310	+	0.572024i
$573$		0			0
$574$	−6.91709	−	3.07969i	−0.288714	−	0.128544i
$575$	2.45223	+	7.54719i	0.102265	+	0.314739i
$576$		0			0
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.958222	−	0.286026i	$-0.0923344\pi$
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.0240800	+	0.999710i	$0.492334\pi$
$578$	−0.955807	+	9.09390i	−0.0397563	+	0.378256i
$579$		0			0
$580$	1.84379	+	0.391910i	0.0765594	+	0.0162732i
$581$	−0.196723	−	1.87169i	−0.00816144	−	0.0776509i
$582$		0			0
$583$	1.04195	−	18.6807i	0.0431532	−	0.773674i
$584$	27.5954			1.14191
$585$		0			0
$586$	−1.45632	−	4.48210i	−0.0601602	−	0.185154i
$587$	−4.97675	+	1.05784i	−0.205412	+	0.0436618i	−0.309469	−	0.950910i	$-0.600151\pi$
$587$	−4.97675	+	1.05784i	−0.205412	+	0.0436618i	0.104056	+	0.994571i	$0.466818\pi$
$588$		0			0
$589$	2.01687	−	0.897969i	0.0831037	−	0.0370002i
$590$	−1.17903	−	1.30945i	−0.0485401	−	0.0539092i
$591$		0			0
$592$	−12.3022	−	5.47729i	−0.505617	−	0.225115i
$593$	−3.46422			−0.142258			−0.0711292	−	0.997467i	$-0.522660\pi$
$593$	−3.46422			−0.142258			−0.0711292	+	0.997467i	$0.522660\pi$
$594$		0			0
$595$	−24.1825			−0.991386
$596$	7.91653	+	3.52466i	0.324274	+	0.144376i
$597$		0			0
$598$	−2.51700	−	2.79541i	−0.102928	−	0.114313i
$599$	−22.7243	+	10.1175i	−0.928489	+	0.413390i	−0.814547	−	0.580097i	$-0.803015\pi$
$599$	−22.7243	+	10.1175i	−0.928489	+	0.413390i	−0.113942	+	0.993487i	$0.536348\pi$
$600$		0			0
$601$	−10.8263	+	2.30119i	−0.441612	+	0.0938676i	−0.423351	−	0.905966i	$-0.639146\pi$
$601$	−10.8263	+	2.30119i	−0.441612	+	0.0938676i	−0.0182611	+	0.999833i	$0.505813\pi$
$602$	1.78951	+	5.50755i	0.0729351	+	0.224471i
$603$		0			0
$604$	0.255479			0.0103953
$605$	7.15276	+	9.98532i	0.290801	+	0.405961i
$606$		0			0
$607$	2.92272	+	27.8078i	0.118630	+	1.12869i	0.878211	+	0.478273i	$0.158737\pi$
$607$	2.92272	+	27.8078i	0.118630	+	1.12869i	−0.759582	+	0.650412i	$0.774596\pi$
$608$	28.8952	+	6.14186i	1.17185	+	0.249085i
$609$		0			0
$610$	−0.316703	+	3.01323i	−0.0128229	+	0.122002i
$611$	27.8087	+	20.2042i	1.12502	+	0.817375i
$612$		0			0
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	0.995925	−	0.0901845i	$-0.0287457\pi$
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	−0.858729	+	0.512429i	$0.828746\pi$
$614$	−11.2499	−	5.00876i	−0.454008	−	0.202137i
$615$		0			0
$616$	−30.2217	−	4.89078i	−1.21767	−	0.197055i
$617$	9.31311	−	16.1308i	0.374932	−	0.649401i	−0.615385	−	0.788227i	$-0.710999\pi$
$617$	9.31311	−	16.1308i	0.374932	−	0.649401i	0.990317	+	0.138826i	$0.0443328\pi$
$618$		0			0
$619$	1.79895	−	1.99793i	0.0723057	−	0.0803036i	−0.705906	−	0.708305i	$-0.749460\pi$
$619$	1.79895	−	1.99793i	0.0723057	−	0.0803036i	0.778212	+	0.628001i	$0.216127\pi$
$620$	−0.231355	+	0.712036i	−0.00929142	+	0.0285961i
$621$		0			0
$622$	3.69561	+	2.68502i	0.148180	+	0.107659i
$623$	−61.4246	+	13.0562i	−2.46093	+	0.523086i
$624$		0			0
$625$	−0.820749	−	7.80890i	−0.0328299	−	0.312356i
$626$	8.41222	−	14.5704i	0.336220	−	0.582350i
$627$		0			0
$628$	18.5896	+	32.1981i	0.741805	+	1.28484i
$629$	−39.0652	+	28.3826i	−1.55763	+	1.13169i
$630$		0			0
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	0.352863	+	0.935675i	$0.385208\pi$
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	−0.835448	+	0.549569i	$0.814792\pi$
$632$	1.11566	−	10.6148i	0.0443784	−	0.422233i
$633$		0			0
$634$	−4.88047	−	5.42031i	−0.193828	−	0.215268i
$635$	−8.35695	−	1.77633i	−0.331636	−	0.0704913i
$636$		0			0
$637$	−11.0407	−	19.1230i	−0.437447	−	0.757681i
$638$	1.85951	−	1.49549i	0.0736187	−	0.0592069i
$639$		0			0
$640$	−9.96109	+	7.23716i	−0.393747	+	0.286074i
$641$	−17.2294	+	19.1352i	−0.680521	+	0.755795i	−0.980149	−	0.198261i	$-0.936471\pi$
$641$	−17.2294	+	19.1352i	−0.680521	+	0.755795i	0.299628	+	0.954056i	$0.403137\pi$
$642$		0			0
$643$	−12.1794	+	5.42264i	−0.480310	+	0.213848i	−0.632586	−	0.774490i	$-0.718007\pi$
$643$	−12.1794	+	5.42264i	−0.480310	+	0.213848i	0.152276	+	0.988338i	$0.451340\pi$
$644$	−11.7555	+	5.23386i	−0.463230	+	0.206243i
$645$		0			0
$646$	12.6540	−	14.0537i	0.497866	−	0.552936i
$647$	19.2955	−	14.0190i	0.758585	−	0.551145i	−0.139891	−	0.990167i	$-0.544675\pi$
$647$	19.2955	−	14.0190i	0.758585	−	0.551145i	0.898476	+	0.439022i	$0.144675\pi$
$648$		0			0
$649$	7.86876	−	0.385882i	0.308876	−	0.0151472i
$650$	3.33853	+	5.78250i	0.130948	+	0.226808i
$651$		0			0
$652$	−6.39733	−	1.35979i	−0.250539	−	0.0532537i
$653$	−8.51464	−	9.45647i	−0.333204	−	0.370060i	0.553140	−	0.833088i	$-0.313430\pi$
$653$	−8.51464	−	9.45647i	−0.333204	−	0.370060i	−0.886344	+	0.463028i	$0.846763\pi$
$654$		0			0
$655$	0.625511	−	5.95134i	0.0244407	−	0.232538i
$656$	1.39531	−	4.29433i	0.0544778	−	0.167666i
$657$		0			0
$658$	−26.9350	+	19.5694i	−1.05004	+	0.762896i
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	−0.999354	−	0.0359452i	$-0.988556\pi$
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	0.468547	−	0.883438i	$-0.344777\pi$
$660$		0			0
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	0.0335234	+	0.999438i	$0.489327\pi$
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	−0.882300	+	0.470687i	$0.844006\pi$
$662$	0.257641	+	2.45129i	0.0100135	+	0.0952723i
$663$		0			0
$664$	−1.11461	+	0.236917i	−0.0432551	+	0.00919415i
$665$	18.1030	+	13.1526i	0.702003	+	0.510035i
$666$		0			0
$667$	0.707636	−	2.17788i	0.0273998	−	0.0843278i
$668$	16.5209	−	18.3483i	0.639212	−	0.709917i
$669$		0			0
$670$	−3.61688	+	6.26462i	−0.139732	+	0.242023i
$671$	−9.54666	−	9.61102i	−0.368545	−	0.371029i
$672$		0			0
$673$	−24.3795	−	10.8545i	−0.939761	−	0.418408i	−0.121070	−	0.992644i	$-0.538633\pi$
$673$	−24.3795	−	10.8545i	−0.939761	−	0.418408i	−0.818690	+	0.574236i	$0.805299\pi$
$674$	−6.60922	−	20.3411i	−0.254578	−	0.783510i
$675$		0			0
$676$	−7.34946	−	5.33970i	−0.282672	−	0.205373i
$677$	2.83095	−	26.9347i	0.108802	−	1.03518i	−0.794817	−	0.606849i	$-0.792433\pi$
$677$	2.83095	−	26.9347i	0.108802	−	1.03518i	0.903620	−	0.428336i	$-0.140900\pi$
$678$		0			0
$679$	30.6135	+	6.50711i	1.17484	+	0.249720i
$680$	1.53050	+	14.5617i	0.0586918	+	0.558415i
$681$		0			0
$682$	0.513524	+	0.796603i	0.0196638	+	0.0305035i
$683$	16.7343			0.640322			0.320161	−	0.947363i	$-0.396263\pi$
$683$	16.7343			0.640322			0.320161	+	0.947363i	$0.396263\pi$
$684$		0			0
$685$	5.77319	+	17.7681i	0.220582	+	0.678883i
$686$	3.15993	−	0.671665i	0.120647	−	0.0256443i
$687$		0			0
$688$	−3.15485	+	1.40463i	−0.120278	+	0.0535510i
$689$	−10.1086	−	11.2268i	−0.385108	−	0.427706i
$690$		0			0
$691$	−34.2758	−	15.2606i	−1.30391	−	0.580540i	−0.367039	−	0.930205i	$-0.619629\pi$
$691$	−34.2758	−	15.2606i	−1.30391	−	0.580540i	−0.936875	+	0.349665i	$0.886295\pi$
$692$	−4.05707			−0.154226
$693$		0			0
$694$	14.2978			0.542738
$695$	−14.0161	−	6.24037i	−0.531661	−	0.236711i
$696$		0			0
$697$	−10.8338	−	12.0322i	−0.410359	−	0.455750i
$698$	−10.2078	+	4.54481i	−0.386371	+	0.172024i
$699$		0			0
$700$	22.3423	−	4.74899i	0.844458	−	0.179495i
$701$	−3.15219	−	9.70143i	−0.119056	−	0.366418i	0.873715	−	0.486438i	$-0.161704\pi$
$701$	−3.15219	−	9.70143i	−0.119056	−	0.366418i	−0.992771	+	0.120020i	$0.961704\pi$
$702$		0			0
$703$	44.6811			1.68518
$704$	−0.134839	+	2.41747i	−0.00508193	+	0.0911117i
$705$		0			0
$706$	0.217408	+	2.06850i	0.00818225	+	0.0778489i
$707$	−6.72685	−	1.42984i	−0.252989	−	0.0537745i
$708$		0			0
$709$	1.51542	−	14.4183i	0.0569128	−	0.541489i	−0.928503	−	0.371325i	$-0.878904\pi$
$709$	1.51542	−	14.4183i	0.0569128	−	0.541489i	0.985416	−	0.170164i	$-0.0544297\pi$
$710$	−3.79104	−	2.75435i	−0.142275	−	0.103369i
$711$		0			0
$712$	11.7494	+	36.1610i	0.440329	+	1.35519i
$713$	0.830893	+	0.369938i	0.0311172	+	0.0138543i
$714$		0			0
$715$	9.79040	+	1.58438i	0.366140	+	0.0592525i
$716$	−5.91364	+	10.2427i	−0.221003	+	0.382789i
$717$		0			0
$718$	−3.77337	+	4.19075i	−0.140821	+	0.156397i
$719$	−5.94135	+	18.2856i	−0.221575	+	0.681938i	0.777046	+	0.629444i	$0.216717\pi$
$719$	−5.94135	+	18.2856i	−0.221575	+	0.681938i	−0.998621	+	0.0524943i	$0.983283\pi$
$720$		0			0
$721$	8.48991	+	6.16828i	0.316181	+	0.229719i
$722$	−4.77016	+	1.01393i	−0.177527	+	0.0377345i
$723$		0			0
$724$	−0.391054	−	3.72063i	−0.0145334	−	0.138276i
$725$	−2.03241	+	3.52023i	−0.0754818	+	0.130738i
$726$		0			0
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	0.859208	−	0.511627i	$-0.170957\pi$
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	−0.872686	+	0.488282i	$0.837624\pi$
$728$	−19.9989	+	14.5300i	−0.741207	+	0.538519i
$729$		0			0
$730$	2.67570	−	8.23495i	0.0990320	−	0.304789i
$731$	−1.29439	+	12.3153i	−0.0478746	+	0.455496i
$732$		0			0
$733$	−1.25521	−	1.39406i	−0.0463624	−	0.0514907i	0.719518	−	0.694474i	$-0.244363\pi$
$733$	−1.25521	−	1.39406i	−0.0463624	−	0.0514907i	−0.765880	+	0.642984i	$0.777696\pi$
$734$	7.15496	+	1.52083i	0.264095	+	0.0561350i
$735$		0			0
$736$	6.08497	+	10.5395i	0.224295	+	0.388490i
$737$	−11.4891	−	30.2333i	−0.423206	−	1.11366i
$738$		0			0
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.632993	−	0.774157i	$-0.281826\pi$
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.931873	−	0.362784i	$-0.118174\pi$
$740$	−10.1387	+	11.2602i	−0.372706	+	0.413932i
$741$		0			0
$742$	13.3674	−	5.95157i	0.490734	−	0.218489i
$743$	30.4510	−	13.5577i	1.11714	−	0.497383i	0.236720	−	0.971578i	$-0.423928\pi$
$743$	30.4510	−	13.5577i	1.11714	−	0.497383i	0.880420	+	0.474195i	$0.157261\pi$
$744$		0			0
$745$	4.15399	−	4.61348i	0.152190	−	0.169025i
$746$	−5.91558	+	4.29792i	−0.216585	+	0.157358i
$747$		0			0
$748$	−23.9948	−	15.6973i	−0.877338	−	0.573949i
$749$	20.0623	+	34.7489i	0.733060	+	1.26970i
$750$		0			0
$751$	22.8535	+	4.85766i	0.833937	+	0.177259i	0.605043	−	0.796193i	$-0.293156\pi$
$751$	22.8535	+	4.85766i	0.833937	+	0.177259i	0.228894	+	0.973451i	$0.426489\pi$
$752$	−13.2852	−	14.7547i	−0.484460	−	0.538047i
$753$		0			0
$754$	0.201404	−	1.91623i	0.00733470	−	0.0697851i
$755$	0.0565572	−	0.174065i	0.00205833	−	0.00633488i
$756$		0			0
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.0331687	−	0.999450i	$-0.489440\pi$
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.960783	+	0.277302i	$0.0894401\pi$
$758$	−8.43250	−	14.6055i	−0.306282	−	0.530496i
$759$		0			0
$760$	6.77421	−	11.7333i	0.245726	−	0.425611i
$761$	2.10227	+	20.0017i	0.0762071	+	0.725062i	0.964195	+	0.265195i	$0.0854363\pi$
$761$	2.10227	+	20.0017i	0.0762071	+	0.725062i	−0.887988	+	0.459867i	$0.847897\pi$
$762$		0			0
$763$	9.02421	−	1.91815i	0.326698	−	0.0694419i
$764$	20.8294	+	15.1335i	0.753583	+	0.547510i
$765$		0			0
$766$	2.48699	−	7.65417i	0.0898586	−	0.276556i
$767$	4.25651	−	4.72733i	0.153694	−	0.170694i
$768$		0			0
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	−0.871623	−	0.490178i	$-0.836932\pi$
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	0.860318	+	0.509759i	$0.170265\pi$
$770$	−4.38984	+	8.54447i	−0.158199	+	0.307921i
$771$		0			0
$772$	11.5836	+	5.15733i	0.416902	+	0.185617i
$773$	−8.88046	−	27.3313i	−0.319408	−	0.983037i	−0.973902	−	0.226970i	$-0.927118\pi$
$773$	−8.88046	−	27.3313i	−0.319408	−	0.983037i	0.654494	−	0.756067i	$-0.272882\pi$
$774$		0			0
$775$	−1.30613	−	0.948959i	−0.0469176	−	0.0340876i
$776$	1.98080	−	18.8460i	0.0711064	−	0.676533i
$777$		0			0
$778$	9.32539	+	1.98217i	0.334331	+	0.0710643i
$779$	1.56601	+	14.8996i	0.0561083	+	0.533834i
$780$		0			0
$781$	20.2556	−	5.35460i	0.724801	−	0.191603i
$782$	7.79085			0.278600
$783$		0			0
$784$	3.94131	+	12.1301i	0.140761	+	0.433218i
$785$	26.0528	−	5.53769i	0.929864	−	0.197649i
$786$		0			0
$787$	−12.8837	+	5.73618i	−0.459254	+	0.204473i	−0.623305	−	0.781979i	$-0.714210\pi$
$787$	−12.8837	+	5.73618i	−0.459254	+	0.204473i	0.164051	+	0.986452i	$0.447544\pi$
$788$	−23.8913	−	26.5339i	−0.851091	−	0.945233i
$789$		0			0
$790$	−3.05946	−	1.36216i	−0.108851	−	0.0484634i
$791$	5.98345			0.212747
$792$		0			0
$793$	−10.9382			−0.388426
$794$	−3.05800	−	1.36151i	−0.108524	−	0.0483181i
$795$		0			0
$796$	−9.67008	−	10.7397i	−0.342747	−	0.380659i
$797$	−23.8935	+	10.6381i	−0.846351	+	0.376820i	−0.783642	−	0.621212i	$-0.786641\pi$
$797$	−23.8935	+	10.6381i	−0.846351	+	0.376820i	−0.0627086	+	0.998032i	$0.519974\pi$
$798$		0			0
$799$	−69.6371	+	14.8018i	−2.46358	+	0.523651i
$800$	−6.67551	−	20.5451i	−0.236015	−	0.726379i
$801$		0			0
$802$	12.0908			0.426939
$803$	20.9759	+	32.5388i	0.740223	+	1.14827i
$804$		0			0
$805$	0.963594	+	9.16798i	0.0339622	+	0.323129i
$806$	0.748559	+	0.159111i	0.0263669	+	0.00560445i
$807$		0			0
$808$	−0.435249	+	4.14112i	−0.0153120	+	0.145684i
$809$	12.8256	+	9.31836i	0.450925	+	0.327616i	0.789961	−	0.613157i	$-0.210101\pi$
$809$	12.8256	+	9.31836i	0.450925	+	0.327616i	−0.339036	+	0.940773i	$0.610101\pi$
$810$		0			0
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	−0.929599	−	0.368573i	$-0.879846\pi$
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	0.535420	−	0.844586i	$-0.320154\pi$
$812$	−6.02146	−	2.68093i	−0.211312	−	0.0940820i
$813$		0			0
$814$	2.93699	+	18.9553i	0.102941	+	0.664383i
$815$	−2.34269	+	4.05766i	−0.0820608	+	0.142134i
$816$		0			0
$817$	7.66710	−	8.51517i	0.268238	−	0.297908i
$818$	3.37295	−	10.3809i	0.117932	−	0.362958i
$819$		0			0
$820$	−4.11023	−	2.98626i	−0.143535	−	0.104285i
$821$	−15.9993	+	3.40076i	−0.558379	+	0.118687i	−0.478452	−	0.878113i	$-0.658802\pi$
$821$	−15.9993	+	3.40076i	−0.558379	+	0.118687i	−0.0799271	+	0.996801i	$0.525469\pi$
$822$		0			0
$823$	2.73598	+	26.0311i	0.0953703	+	0.907388i	0.932691	+	0.360676i	$0.117454\pi$
$823$	2.73598	+	26.0311i	0.0953703	+	0.907388i	−0.837321	+	0.546712i	$0.815879\pi$
$824$	3.17696	−	5.50265i	0.110675	−	0.191694i
$825$		0			0
$826$	3.08070	+	5.33592i	0.107191	+	0.185661i
$827$	4.48139	−	3.25592i	0.155833	−	0.113219i	−0.507136	−	0.861866i	$-0.669296\pi$
$827$	4.48139	−	3.25592i	0.155833	−	0.113219i	0.662969	+	0.748647i	$0.269296\pi$
$828$		0			0
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	−0.801327	−	0.598227i	$-0.795872\pi$
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	0.999916	−	0.0129672i	$-0.00412771\pi$
$830$	−0.0373740	+	0.355590i	−0.00129727	+	0.0123427i
$831$		0			0
$832$	1.30816	+	1.45286i	0.0453523	+	0.0503688i
$833$	44.7346	+	9.50862i	1.54996	+	0.329454i
$834$		0			0
$835$	−8.84388	−	15.3180i	−0.306055	−	0.530103i
$836$	9.42492	+	24.8015i	0.325968	+	0.857776i
$837$		0			0
$838$	−9.35505	+	6.79684i	−0.323165	+	0.234793i
$839$	12.0211	−	13.3508i	0.415015	−	0.460921i	−0.498999	−	0.866602i	$-0.666299\pi$
$839$	12.0211	−	13.3508i	0.415015	−	0.460921i	0.914015	+	0.405681i	$0.132966\pi$
$840$		0			0
$841$	−25.4213	+	11.3183i	−0.876595	+	0.390285i
$842$	2.76051	−	1.22906i	0.0951336	−	0.0423562i
$843$		0			0
$844$	−4.39146	+	4.87721i	−0.151160	+	0.167881i
$845$	−5.26509	+	3.82531i	−0.181125	+	0.131595i
$846$		0			0
$847$	−17.2053	−	39.3532i	−0.591182	−	1.35219i
$848$	4.36299	+	7.55692i	0.149826	+	0.259506i
$849$		0			0
$850$	−13.5270	−	2.87526i	−0.463973	−	0.0986206i
$851$	12.3169	+	13.6793i	0.422218	+	0.468921i
$852$		0			0
$853$	−2.91771	+	27.7602i	−0.0999006	+	0.950490i	0.823672	+	0.567067i	$0.191922\pi$
$853$	−2.91771	+	27.7602i	−0.0999006	+	0.950490i	−0.923573	+	0.383424i	$0.874745\pi$
$854$	3.27389	−	10.0760i	0.112030	−	0.344794i
$855$		0			0
$856$	19.6546	−	14.2799i	0.671781	−	0.488077i
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	0.784265	−	0.620426i	$-0.213040\pi$
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	−0.929437	+	0.368981i	$0.879707\pi$
$858$		0			0
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	−0.999595	−	0.0284667i	$-0.990938\pi$
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	0.524450	+	0.851441i	$0.324271\pi$
$860$	0.406165	+	3.86440i	0.0138501	+	0.131775i
$861$		0			0
$862$	8.11267	−	1.72440i	0.276318	−	0.0587333i
$863$	10.9978	+	7.99035i	0.374368	+	0.271995i	0.759020	−	0.651067i	$-0.225678\pi$
$863$	10.9978	+	7.99035i	0.374368	+	0.271995i	−0.384652	+	0.923062i	$0.625678\pi$
$864$		0			0
$865$	−0.898141	+	2.76419i	−0.0305377	+	0.0939854i
$866$	12.7515	−	14.1620i	0.433313	−	0.481243i
$867$		0			0
$868$	1.30897	−	2.26720i	0.0444293	−	0.0769538i
$869$	13.3643	−	6.75301i	0.453354	−	0.229080i
$870$		0			0
$871$	−23.8573	−	10.6220i	−0.808374	−	0.359911i
$872$	−1.72617	−	5.31260i	−0.0584555	−	0.179907i
$873$		0			0
$874$	−5.83221	−	4.23735i	−0.197278	−	0.143331i
$875$	3.98911	−	37.9538i	0.134856	−	1.28307i
$876$		0			0
$877$	−35.3874	−	7.52182i	−1.19495	−	0.253994i	−0.432856	−	0.901463i	$-0.642494\pi$
$877$	−35.3874	−	7.52182i	−1.19495	−	0.253994i	−0.762092	+	0.647469i	$0.775827\pi$
$878$	0.285266	+	2.71413i	0.00962727	+	0.0915973i
$879$		0			0
$880$	−5.34116	−	2.07089i	−0.180051	−	0.0698098i
$881$	−26.6423			−0.897601			−0.448800	−	0.893632i	$-0.648149\pi$
$881$	−26.6423			−0.897601			−0.448800	+	0.893632i	$0.648149\pi$
$882$		0			0
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	−0.999293	−	0.0375844i	$-0.988034\pi$
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	0.786354	−	0.617776i	$-0.211966\pi$
$884$	−22.6463	+	4.81361i	−0.761676	+	0.161899i
$885$		0			0
$886$	12.8840	−	5.73634i	0.432847	−	0.192716i
$887$	21.4130	+	23.7815i	0.718977	+	0.798505i	0.986275	−	0.165109i	$-0.0527977\pi$
$887$	21.4130	+	23.7815i	0.718977	+	0.798505i	−0.267299	+	0.963614i	$0.586131\pi$
$888$		0			0
$889$	27.2921	+	12.1512i	0.915348	+	0.407539i
$890$	11.9303			0.399906
$891$		0			0
$892$	10.6911			0.357963
$893$	60.1807	+	26.7942i	2.01387	+	0.896633i
$894$		0			0
$895$	5.66951	+	6.29663i	0.189511	+	0.210473i
$896$	39.3317	−	17.5116i	1.31398	−	0.585022i
$897$		0			0
$898$	16.8266	−	3.57660i	0.561510	−	0.119353i
$899$	0.143966	+	0.443082i	0.00480153	+	0.0147776i
$900$		0			0
$901$	31.2892			1.04239
$902$	−6.21801	+	1.64374i	−0.207037	+	0.0547307i
$903$		0			0
$904$	−0.378689	−	3.60298i	−0.0125950	−	0.119833i
$905$	−2.62154	−	0.557225i	−0.0871429	−	0.0185228i
$906$		0			0
$907$	5.12715	−	48.7816i	0.170244	−	1.61977i	−0.492082	−	0.870549i	$-0.663764\pi$
$907$	5.12715	−	48.7816i	0.170244	−	1.61977i	0.662326	−	0.749216i	$-0.269569\pi$
$908$	−35.4717	−	25.7717i	−1.17717	−	0.855265i
$909$		0			0
$910$	2.39689	+	7.37687i	0.0794561	+	0.244541i
$911$	21.3599	+	9.51002i	0.707684	+	0.315081i	0.728829	−	0.684695i	$-0.240065\pi$
$911$	21.3599	+	9.51002i	0.707684	+	0.315081i	−0.0211457	+	0.999776i	$0.506731\pi$
$912$		0			0
$913$	−1.12659	−	1.13419i	−0.0372849	−	0.0375362i
$914$	3.42253	−	5.92800i	0.113207	−	0.196081i
$915$		0			0
$916$	14.6376	−	16.2567i	0.483641	−	0.537137i
$917$	−6.46615	+	19.9008i	−0.213531	+	0.657181i
$918$		0			0
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	0.684551	−	0.728965i	$-0.259998\pi$
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	−0.481749	+	0.876309i	$0.659998\pi$
$920$	5.45959	−	1.16047i	0.179997	−	0.0382596i
$921$		0			0
$922$	−1.76748	−	16.8165i	−0.0582090	−	0.553821i
$923$	8.45857	−	14.6507i	0.278417	−	0.482233i
$924$		0			0
$925$	−16.3371	−	28.2967i	−0.537160	−	0.930389i
$926$	21.4202	−	15.5627i	0.703910	−	0.511421i
$927$		0			0
$928$	−1.92634	+	5.92866i	−0.0632352	+	0.194618i
$929$	−1.55504	+	14.7953i	−0.0510193	+	0.485417i	0.938942	+	0.344076i	$0.111808\pi$
$929$	−1.55504	+	14.7953i	−0.0510193	+	0.485417i	−0.989961	+	0.141340i	$0.954859\pi$
$930$		0			0
$931$	−28.3166	−	31.4487i	−0.928038	−	1.03069i
$932$	22.1216	+	4.70209i	0.724618	+	0.154022i
$933$		0			0
$934$	−5.77192	−	9.99727i	−0.188863	−	0.327121i
$935$	−16.0069	+	12.8733i	−0.523482	+	0.421003i
$936$		0			0
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	−0.797853	−	0.602853i	$-0.794031\pi$
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	0.326797	+	0.945095i	$0.394031\pi$
$938$	16.9254	−	18.7975i	0.552633	−	0.613761i
$939$		0			0
$940$	−20.4082	+	9.08632i	−0.665643	+	0.296363i
$941$	−38.9710	+	17.3510i	−1.27042	+	0.565627i	−0.927530	−	0.373748i	$-0.878072\pi$
$941$	−38.9710	+	17.3510i	−1.27042	+	0.565627i	−0.342890	+	0.939376i	$0.611406\pi$
$942$		0			0
$943$	−4.12989	+	4.58671i	−0.134488	+	0.149364i
$944$	−2.97257	+	2.15970i	−0.0967491	+	0.0702923i
$945$		0			0
$946$	4.11641	+	2.69293i	0.133836	+	0.0875548i
$947$	3.44670	+	5.96986i	0.112003	+	0.193994i	0.916578	−	0.399857i	$-0.130940\pi$
$947$	3.44670	+	5.96986i	0.112003	+	0.193994i	−0.804575	+	0.593851i	$0.797607\pi$
$948$		0			0
$949$	30.5764	+	6.49921i	0.992551	+	0.210973i
$950$	8.56249	+	9.50961i	0.277804	+	0.308533i
$951$		0			0
$952$	5.35175	−	50.9185i	0.173451	−	1.65028i
$953$	7.31766	−	22.5214i	0.237042	−	0.729541i	−0.759802	−	0.650155i	$-0.774704\pi$
$953$	7.31766	−	22.5214i	0.237042	−	0.729541i	0.996844	−	0.0793863i	$-0.0252960\pi$
$954$		0			0
$955$	14.9220	−	10.8415i	0.482866	−	0.350822i
$956$	19.5989	+	33.9463i	0.633874	+	1.09790i
$957$		0			0
$958$	−7.27297	+	12.5972i	−0.234979	+	0.406996i
$959$	−6.82860	−	64.9698i	−0.220507	−	2.09798i
$960$		0			0
$961$	30.1416	−	6.40679i	0.972309	−	0.206671i
$962$	12.5301	+	9.10366i	0.403987	+	0.293514i
$963$		0			0
$964$	−8.54567	+	26.3009i	−0.275238	+	0.847094i
$965$	6.07817	−	6.75050i	0.195663	−	0.217306i
$966$		0			0
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	−0.499303	−	0.866427i	$-0.666411\pi$
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	1.00000		0.000804082i	$-0.000255947\pi$
$968$	−22.6080	+	12.8510i	−0.726647	+	0.413046i
$969$		0			0
$970$	−5.43192	−	2.41845i	−0.174408	−	0.0776516i
$971$	−4.12687	−	12.7012i	−0.132438	−	0.407601i	0.862745	−	0.505639i	$-0.168743\pi$
$971$	−4.12687	−	12.7012i	−0.132438	−	0.407601i	−0.995183	+	0.0980383i	$0.968743\pi$
$972$		0			0
$973$	43.4028	+	31.5340i	1.39143	+	1.01093i
$974$	−0.227151	+	2.16119i	−0.00727838	+	0.0692491i
$975$		0			0
$976$	6.17991	+	1.31358i	0.197814	+	0.0420467i
$977$	−0.931968	−	8.86709i	−0.0298163	−	0.283683i	−0.999263	−	0.0383817i	$-0.987780\pi$
$977$	−0.931968	−	8.86709i	−0.0298163	−	0.283683i	0.969447	−	0.245302i	$-0.0788870\pi$
$978$		0			0
$979$	−33.7079	+	41.3411i	−1.07731	+	1.32127i
$980$	14.3508			0.458421
$981$		0			0
$982$	1.48297	+	4.56411i	0.0473234	+	0.145647i
$983$	−16.4901	+	3.50509i	−0.525954	+	0.111795i	−0.463234	−	0.886236i	$-0.653311\pi$
$983$	−16.4901	+	3.50509i	−0.525954	+	0.111795i	−0.0627203	+	0.998031i	$0.519978\pi$
$984$		0			0
$985$	−23.3673	+	10.4038i	−0.744544	+	0.331492i
$986$	2.67029	+	2.96565i	0.0850392	+	0.0944456i
$987$		0			0
$988$	19.5710	+	8.71358i	0.622637	+	0.277216i
$989$	4.72049			0.150103
$990$		0			0
$991$	−33.5356			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$991$	−33.5356			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$992$	−2.26187	−	1.00705i	−0.0718146	−	0.0319739i
$993$		0			0
$994$	10.9641	+	12.1769i	0.347761	+	0.386228i
$995$	−9.45801	+	4.21098i	−0.299839	+	0.133497i
$996$		0			0
$997$	3.17279	−	0.674397i	0.100483	−	0.0213584i	−0.157396	−	0.987536i	$-0.550310\pi$
$997$	3.17279	−	0.674397i	0.100483	−	0.0213584i	0.257879	+	0.966177i	$0.416976\pi$
$998$	3.04532	+	9.37254i	0.0963980	+	0.296682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.91.6		72
3.2	odd	2		99.2.m.b.58.4	yes	72
9.2	odd	6		99.2.m.b.25.6	yes	72
9.4	even	3		891.2.f.e.487.4		36
9.5	odd	6		891.2.f.f.487.6		36
9.7	even	3	inner	297.2.n.b.289.4		72
11.4	even	5	inner	297.2.n.b.37.4		72
33.2	even	10		1089.2.e.o.364.8		36
33.20	odd	10		1089.2.e.p.364.11		36
33.26	odd	10		99.2.m.b.4.6	✓	72
99.2	even	30		1089.2.e.o.727.8		36
99.4	even	15		891.2.f.e.730.4		36
99.13	odd	30		9801.2.a.cn.1.8		18
99.20	odd	30		1089.2.e.p.727.11		36
99.31	even	15		9801.2.a.cp.1.11		18
99.59	odd	30		891.2.f.f.730.6		36
99.68	even	30		9801.2.a.co.1.11		18
99.70	even	15	inner	297.2.n.b.235.6		72
99.86	odd	30		9801.2.a.cm.1.8		18
99.92	odd	30		99.2.m.b.70.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	33.26	odd	10
99.2.m.b.25.6	yes	72	9.2	odd	6
99.2.m.b.58.4	yes	72	3.2	odd	2
99.2.m.b.70.4	yes	72	99.92	odd	30
297.2.n.b.37.4		72	11.4	even	5	inner
297.2.n.b.91.6		72	1.1	even	1	trivial
297.2.n.b.235.6		72	99.70	even	15	inner
297.2.n.b.289.4		72	9.7	even	3	inner
891.2.f.e.487.4		36	9.4	even	3
891.2.f.e.730.4		36	99.4	even	15
891.2.f.f.487.6		36	9.5	odd	6
891.2.f.f.730.6		36	99.59	odd	30
1089.2.e.o.364.8		36	33.2	even	10
1089.2.e.o.727.8		36	99.2	even	30
1089.2.e.p.364.11		36	33.20	odd	10
1089.2.e.p.727.11		36	99.20	odd	30
9801.2.a.cm.1.8		18	99.86	odd	30
9801.2.a.cn.1.8		18	99.13	odd	30
9801.2.a.co.1.11		18	99.68	even	30
9801.2.a.cp.1.11		18	99.31	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.606887 + 0.270203i) q^{2} +(-1.04296 - 1.15832i) q^{4} +(-1.02009 + 0.454172i) q^{5} +(3.81922 - 0.811800i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(2.09587 - 2.57048i) q^{11} +(-0.279928 - 2.66333i) q^{13} +(2.53719 + 0.539295i) q^{14} +(-0.161688 + 1.53836i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(1.58999 + 0.707907i) q^{20} +(1.96651 - 0.993678i) q^{22} +(1.05719 - 1.83110i) q^{23} +(-2.51135 + 2.78914i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(1.05937 - 0.225177i) q^{29} +(0.0449642 + 0.427806i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(0.356392 - 3.39084i) q^{38} +(1.76638 + 1.96176i) q^{40} +(-2.85529 - 0.606910i) q^{41} +(1.11628 + 1.93346i) q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-8.58861 + 9.53861i) q^{47} +(7.53259 - 3.35373i) q^{49} +(-2.27774 + 1.01411i) q^{50} +(-2.79305 + 3.10200i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +(-4.61537 - 7.99405i) q^{56} +(0.703764 + 0.149590i) q^{58} +(1.58943 + 1.76524i) q^{59} +(0.426942 - 4.06208i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(-0.903682 - 8.59796i) q^{68} +(-2.83308 + 0.602190i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-3.86988 + 4.29793i) q^{74} +(-3.99983 + 6.92792i) q^{76} +(5.91786 - 11.5186i) q^{77} +(4.12439 + 1.83630i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.0503831 - 0.479363i) q^{83} +(-6.05809 - 1.28769i) q^{85} +(0.155030 + 1.47502i) q^{86} +(-7.31058 - 2.83448i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(-3.22362 + 0.685201i) q^{92} +(-7.78968 + 3.46819i) q^{94} +(3.83471 + 4.25888i) q^{95} +(7.32266 + 3.26026i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more