LMFDB - Embedded newform 152.2.c.b.77.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(77,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.1
Root			$-0.182898 - 1.40234i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40234 - 0.182898i) q^{2} -0.840428i q^{3} +(1.93310 + 0.512969i) q^{4} +4.04855i q^{5} +(-0.153712 + 1.17856i) q^{6} -3.59283 q^{7} +(-2.61703 - 1.07291i) q^{8} +2.29368 q^{9} +(0.740472 - 5.67744i) q^{10} +4.29368i q^{11} +(0.431113 - 1.62463i) q^{12} +1.77186i q^{13} +(5.03836 + 0.657121i) q^{14} +3.40252 q^{15} +(3.47373 + 1.98324i) q^{16} +2.86953 q^{17} +(-3.21651 - 0.419509i) q^{18} -1.00000i q^{19} +(-2.07678 + 7.82625i) q^{20} +3.01952i q^{21} +(0.785305 - 6.02119i) q^{22} +2.74118 q^{23} +(-0.901707 + 2.19943i) q^{24} -11.3908 q^{25} +(0.324069 - 2.48474i) q^{26} -4.44896i q^{27} +(-6.94529 - 1.84301i) q^{28} +2.29074i q^{29} +(-4.77148 - 0.622313i) q^{30} +2.33021 q^{31} +(-4.50860 - 3.41650i) q^{32} +3.60853 q^{33} +(-4.02404 - 0.524830i) q^{34} -14.5458i q^{35} +(4.43391 + 1.17659i) q^{36} -8.06260i q^{37} +(-0.182898 + 1.40234i) q^{38} +1.48912 q^{39} +(4.34375 - 10.5952i) q^{40} -2.85960 q^{41} +(0.552263 - 4.23438i) q^{42} +0.241806i q^{43} +(-2.20252 + 8.30010i) q^{44} +9.28609i q^{45} +(-3.84405 - 0.501355i) q^{46} -0.191993 q^{47} +(1.66677 - 2.91942i) q^{48} +5.90844 q^{49} +(15.9737 + 2.08335i) q^{50} -2.41163i q^{51} +(-0.908908 + 3.42517i) q^{52} +8.10207i q^{53} +(-0.813705 + 6.23894i) q^{54} -17.3832 q^{55} +(9.40255 + 3.85480i) q^{56} -0.840428 q^{57} +(0.418972 - 3.21239i) q^{58} -4.36599i q^{59} +(6.57740 + 1.74539i) q^{60} -15.3277i q^{61} +(-3.26774 - 0.426191i) q^{62} -8.24081 q^{63} +(5.69771 + 5.61570i) q^{64} -7.17346 q^{65} +(-5.06037 - 0.659992i) q^{66} +13.2749i q^{67} +(5.54707 + 1.47198i) q^{68} -2.30376i q^{69} +(-2.66039 + 20.3981i) q^{70} +7.44693 q^{71} +(-6.00264 - 2.46092i) q^{72} +9.20686 q^{73} +(-1.47463 + 11.3065i) q^{74} +9.57314i q^{75} +(0.512969 - 1.93310i) q^{76} -15.4265i q^{77} +(-2.08825 - 0.272357i) q^{78} +8.96281 q^{79} +(-8.02924 + 14.0636i) q^{80} +3.14202 q^{81} +(4.01012 + 0.523014i) q^{82} -1.94813i q^{83} +(-1.54892 + 5.83702i) q^{84} +11.6174i q^{85} +(0.0442258 - 0.339094i) q^{86} +1.92520 q^{87} +(4.60675 - 11.2367i) q^{88} -3.24415 q^{89} +(1.69841 - 13.0222i) q^{90} -6.36599i q^{91} +(5.29896 + 1.40614i) q^{92} -1.95838i q^{93} +(0.269239 + 0.0351151i) q^{94} +4.04855 q^{95} +(-2.87132 + 3.78916i) q^{96} +17.6954 q^{97} +(-8.28562 - 1.08064i) q^{98} +9.84833i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.40234	−	0.182898i	−0.991602	−	0.129328i
$2$	−1.40234	−	0.182898i	−0.991602	−	0.129328i
$3$		−	0.840428i		−	0.485221i	−0.970124	−	0.242611i	$-0.921996\pi$
$3$		−	0.840428i		−	0.485221i	0.970124	−	0.242611i	$-0.0780037\pi$
$4$	1.93310	+	0.512969i	0.966548	+	0.256484i
$5$			4.04855i			1.81057i	0.424806	+	0.905284i	$0.360342\pi$
$5$			4.04855i			1.81057i	−0.424806	+	0.905284i	$0.639658\pi$
$6$	−0.153712	+	1.17856i	−0.0627528	+	0.481146i
$7$	−3.59283			−1.35796			−0.678981	−	0.734156i	$-0.737578\pi$
$7$	−3.59283			−1.35796			−0.678981	+	0.734156i	$0.737578\pi$
$8$	−2.61703	−	1.07291i	−0.925260	−	0.379332i
$9$	2.29368			0.764560
$10$	0.740472	−	5.67744i	0.234158	−	1.79536i
$11$			4.29368i			1.29459i	0.762238	+	0.647297i	$0.224101\pi$
$11$			4.29368i			1.29459i	−0.762238	+	0.647297i	$0.775899\pi$
$12$	0.431113	−	1.62463i	0.124452	−	0.468990i
$13$			1.77186i			0.491425i	0.969343	+	0.245712i	$0.0790219\pi$
$13$			1.77186i			0.491425i	−0.969343	+	0.245712i	$0.920978\pi$
$14$	5.03836	+	0.657121i	1.34656	+	0.175623i
$15$	3.40252			0.878526
$16$	3.47373	+	1.98324i	0.868432	+	0.495809i
$17$	2.86953			0.695963			0.347981	−	0.937501i	$-0.386867\pi$
$17$	2.86953			0.695963			0.347981	+	0.937501i	$0.386867\pi$
$18$	−3.21651	−	0.419509i	−0.758139	−	0.0988793i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−2.07678	+	7.82625i	−0.464382	+	1.75000i
$21$			3.01952i			0.658912i
$22$	0.785305	−	6.02119i	0.167428	−	1.28372i
$23$	2.74118			0.571575			0.285787	−	0.958293i	$-0.407745\pi$
$23$	2.74118			0.571575			0.285787	+	0.958293i	$0.407745\pi$
$24$	−0.901707	+	2.19943i	−0.184060	+	0.448956i
$25$	−11.3908			−2.27816
$26$	0.324069	−	2.48474i	0.0635551	−	0.487298i
$27$		−	4.44896i		−	0.856202i
$28$	−6.94529	−	1.84301i	−1.31254	−	0.348296i
$29$			2.29074i			0.425380i	0.977120	+	0.212690i	$0.0682225\pi$
$29$			2.29074i			0.425380i	−0.977120	+	0.212690i	$0.931778\pi$
$30$	−4.77148	−	0.622313i	−0.871148	−	0.113618i
$31$	2.33021			0.418519			0.209259	−	0.977860i	$-0.432895\pi$
$31$	2.33021			0.418519			0.209259	+	0.977860i	$0.432895\pi$
$32$	−4.50860	−	3.41650i	−0.797016	−	0.603958i
$33$	3.60853			0.628164
$34$	−4.02404	−	0.524830i	−0.690118	−	0.0900077i
$35$		−	14.5458i		−	2.45868i
$36$	4.43391	+	1.17659i	0.738985	+	0.196098i
$37$		−	8.06260i		−	1.32548i	−0.748848	−	0.662742i	$-0.769393\pi$
$37$		−	8.06260i		−	1.32548i	0.748848	−	0.662742i	$-0.230607\pi$
$38$	−0.182898	+	1.40234i	−0.0296699	+	0.227489i
$39$	1.48912			0.238450
$40$	4.34375	−	10.5952i	0.686807	−	1.67525i
$41$	−2.85960			−0.446594			−0.223297	−	0.974750i	$-0.571682\pi$
$41$	−2.85960			−0.446594			−0.223297	+	0.974750i	$0.571682\pi$
$42$	0.552263	−	4.23438i	0.0852160	−	0.653379i
$43$			0.241806i			0.0368751i	0.999830	+	0.0184375i	$0.00586918\pi$
$43$			0.241806i			0.0368751i	−0.999830	+	0.0184375i	$0.994131\pi$
$44$	−2.20252	+	8.30010i	−0.332043	+	1.25129i
$45$			9.28609i			1.38429i
$46$	−3.84405	−	0.501355i	−0.566775	−	0.0739208i
$47$	−0.191993			−0.0280050			−0.0140025	−	0.999902i	$-0.504457\pi$
$47$	−0.191993			−0.0280050			−0.0140025	+	0.999902i	$0.504457\pi$
$48$	1.66677	−	2.91942i	0.240577	−	0.421381i
$49$	5.90844			0.844062
$50$	15.9737	+	2.08335i	2.25903	+	0.294630i
$51$		−	2.41163i		−	0.337696i
$52$	−0.908908	+	3.42517i	−0.126043	+	0.474986i
$53$			8.10207i			1.11291i	0.830879	+	0.556453i	$0.187838\pi$
$53$			8.10207i			1.11291i	−0.830879	+	0.556453i	$0.812162\pi$
$54$	−0.813705	+	6.23894i	−0.110731	+	0.849012i
$55$	−17.3832			−2.34395
$56$	9.40255	+	3.85480i	1.25647	+	0.515119i
$57$	−0.840428			−0.111317
$58$	0.418972	−	3.21239i	0.0550137	−	0.421808i
$59$		−	4.36599i		−	0.568403i	−0.958765	−	0.284201i	$-0.908272\pi$
$59$		−	4.36599i		−	0.568403i	0.958765	−	0.284201i	$-0.0917284\pi$
$60$	6.57740	+	1.74539i	0.849138	+	0.225328i
$61$		−	15.3277i		−	1.96251i	−0.192707	−	0.981256i	$-0.561727\pi$
$61$		−	15.3277i		−	1.96251i	0.192707	−	0.981256i	$-0.438273\pi$
$62$	−3.26774	−	0.426191i	−0.415004	−	0.0541263i
$63$	−8.24081			−1.03824
$64$	5.69771	+	5.61570i	0.712214	+	0.701963i
$65$	−7.17346			−0.889758
$66$	−5.06037	−	0.659992i	−0.622889	−	0.0812394i
$67$			13.2749i			1.62178i	0.585197	+	0.810891i	$0.301017\pi$
$67$			13.2749i			1.62178i	−0.585197	+	0.810891i	$0.698983\pi$
$68$	5.54707	+	1.47198i	0.672682	+	0.178504i
$69$		−	2.30376i		−	0.277340i
$70$	−2.66039	+	20.3981i	−0.317977	+	2.43804i
$71$	7.44693			0.883788			0.441894	−	0.897067i	$-0.354307\pi$
$71$	7.44693			0.883788			0.441894	+	0.897067i	$0.354307\pi$
$72$	−6.00264	−	2.46092i	−0.707417	−	0.290023i
$73$	9.20686			1.07758			0.538791	−	0.842440i	$-0.318881\pi$
$73$	9.20686			1.07758			0.538791	+	0.842440i	$0.318881\pi$
$74$	−1.47463	+	11.3065i	−0.171423	+	1.31435i
$75$			9.57314i			1.10541i
$76$	0.512969	−	1.93310i	0.0588415	−	0.221741i
$77$		−	15.4265i		−	1.75801i
$78$	−2.08825	−	0.272357i	−0.236447	−	0.0308383i
$79$	8.96281			1.00839			0.504197	−	0.863588i	$-0.331788\pi$
$79$	8.96281			1.00839			0.504197	+	0.863588i	$0.331788\pi$
$80$	−8.02924	+	14.0636i	−0.897696	+	1.57235i
$81$	3.14202			0.349113
$82$	4.01012	+	0.523014i	0.442844	+	0.0577573i
$83$		−	1.94813i		−	0.213835i	−0.994268	−	0.106917i	$-0.965902\pi$
$83$		−	1.94813i		−	0.213835i	0.994268	−	0.106917i	$-0.0340980\pi$
$84$	−1.54892	+	5.83702i	−0.169001	+	0.636871i
$85$			11.6174i			1.26009i
$86$	0.0442258	−	0.339094i	0.00476899	−	0.0365654i
$87$	1.92520			0.206404
$88$	4.60675	−	11.2367i	0.491081	−	1.19784i
$89$	−3.24415			−0.343879			−0.171940	−	0.985107i	$-0.555003\pi$
$89$	−3.24415			−0.343879			−0.171940	+	0.985107i	$0.555003\pi$
$90$	1.69841	−	13.0222i	0.179028	−	1.37266i
$91$		−	6.36599i		−	0.667337i
$92$	5.29896	+	1.40614i	0.552455	+	0.146600i
$93$		−	1.95838i		−	0.203074i
$94$	0.269239	+	0.0351151i	0.0277698	+	0.00362184i
$95$	4.04855			0.415373
$96$	−2.87132	+	3.78916i	−0.293053	+	0.386729i
$97$	17.6954			1.79670			0.898349	−	0.439283i	$-0.144768\pi$
$97$	17.6954			1.79670			0.898349	+	0.439283i	$0.144768\pi$
$98$	−8.28562	−	1.08064i	−0.836974	−	0.109161i
$99$			9.84833i			0.989795i
$100$	−22.0195	−	5.84312i	−2.20195	−	0.584312i
$101$			0.559270i			0.0556494i	0.999613	+	0.0278247i	$0.00885802\pi$
$101$			0.559270i			0.0556494i	−0.999613	+	0.0278247i	$0.991142\pi$
$102$	−0.441082	+	3.38192i	−0.0436736	+	0.334860i
$103$	15.0529			1.48321			0.741603	−	0.670839i	$-0.234066\pi$
$103$	15.0529			1.48321			0.741603	+	0.670839i	$0.234066\pi$
$104$	1.90105	−	4.63701i	0.186413	−	0.454696i
$105$	−12.2247			−1.19301
$106$	1.48185	−	11.3618i	0.143930	−	1.10356i
$107$		−	7.69697i		−	0.744094i	−0.928214	−	0.372047i	$-0.878656\pi$
$107$		−	7.69697i		−	0.744094i	0.928214	−	0.372047i	$-0.121344\pi$
$108$	2.28218	−	8.60026i	0.219602	−	0.827561i
$109$		−	3.20547i		−	0.307029i	−0.988146	−	0.153514i	$-0.950941\pi$
$109$		−	3.20547i		−	0.307029i	0.988146	−	0.153514i	$-0.0490591\pi$
$110$	24.3771	+	3.17935i	2.32427	+	0.303139i
$111$	−6.77603			−0.643153
$112$	−12.4805	−	7.12543i	−1.17930	−	0.673290i
$113$	−13.2002			−1.24177			−0.620885	−	0.783902i	$-0.713227\pi$
$113$	−13.2002			−1.24177			−0.620885	+	0.783902i	$0.713227\pi$
$114$	1.17856	+	0.153712i	0.110383	+	0.0143965i
$115$			11.0978i			1.03488i
$116$	−1.17508	+	4.42823i	−0.109103	+	0.411151i
$117$			4.06408i			0.375724i
$118$	−0.798529	+	6.12258i	−0.0735106	+	0.563629i
$119$	−10.3097			−0.945091
$120$	−8.90450	−	3.65061i	−0.812866	−	0.333253i
$121$	−7.43570			−0.675972
$122$	−2.80341	+	21.4946i	−0.253808	+	1.94603i
$123$			2.40329i			0.216697i
$124$	4.50453	+	1.19533i	0.404519	+	0.107343i
$125$		−	25.8735i		−	2.31419i
$126$	11.5564	+	1.50723i	1.02952	+	0.134274i
$127$	−12.0428			−1.06862			−0.534311	−	0.845288i	$-0.679429\pi$
$127$	−12.0428			−1.06862			−0.534311	+	0.845288i	$0.679429\pi$
$128$	−6.96301	−	8.91720i	−0.615449	−	0.788177i
$129$	0.203221			0.0178926
$130$	10.0596	+	1.31201i	0.882286	+	0.115071i
$131$		−	2.21935i		−	0.193906i	−0.995289	−	0.0969529i	$-0.969090\pi$
$131$		−	2.21935i		−	0.193906i	0.995289	−	0.0969529i	$-0.0309096\pi$
$132$	6.97564	+	1.85106i	0.607151	+	0.161114i
$133$			3.59283i			0.311538i
$134$	2.42794	−	18.6158i	0.209742	−	1.60816i
$135$	18.0118			1.55021
$136$	−7.50964	−	3.07876i	−0.643947	−	0.264001i
$137$	7.14461			0.610405			0.305203	−	0.952287i	$-0.401276\pi$
$137$	7.14461			0.610405			0.305203	+	0.952287i	$0.401276\pi$
$138$	−0.421353	+	3.23065i	−0.0358680	+	0.275011i
$139$			6.74884i			0.572429i	0.958166	+	0.286215i	$0.0923970\pi$
$139$			6.74884i			0.572429i	−0.958166	+	0.286215i	$0.907603\pi$
$140$	7.46153	−	28.1184i	0.630614	−	2.37644i
$141$			0.161356i			0.0135886i
$142$	−10.4431	−	1.36203i	−0.876366	−	0.114299i
$143$	−7.60779			−0.636195
$144$	7.96762	+	4.54891i	0.663968	+	0.379076i
$145$	−9.27419			−0.770180
$146$	−12.9111	−	1.68391i	−1.06853	−	0.139362i
$147$		−	4.96561i		−	0.409557i
$148$	4.13586	−	15.5858i	0.339966	−	1.28114i
$149$			11.1371i			0.912387i	0.889880	+	0.456194i	$0.150788\pi$
$149$			11.1371i			0.912387i	−0.889880	+	0.456194i	$0.849212\pi$
$150$	1.75091	−	13.4248i	0.142961	−	1.09613i
$151$	−9.26456			−0.753939			−0.376970	−	0.926226i	$-0.623034\pi$
$151$	−9.26456			−0.753939			−0.376970	+	0.926226i	$0.623034\pi$
$152$	−1.07291	+	2.61703i	−0.0870248	+	0.212269i
$153$	6.58178			0.532105
$154$	−2.82147	+	21.6331i	−0.227360	+	1.74325i
$155$			9.43399i			0.757757i
$156$	2.87861	+	0.763871i	0.230473	+	0.0611586i
$157$		−	11.1900i		−	0.893062i	−0.894768	−	0.446531i	$-0.852659\pi$
$157$		−	11.1900i		−	0.893062i	0.894768	−	0.446531i	$-0.147341\pi$
$158$	−12.5689	−	1.63928i	−0.999926	−	0.130414i
$159$	6.80921			0.540005
$160$	13.8319	−	18.2533i	1.09351	−	1.44305i
$161$	−9.84859			−0.776177
$162$	−4.40616	−	0.574668i	−0.346181	−	0.0451502i
$163$			16.2002i			1.26890i	0.772964	+	0.634449i	$0.218773\pi$
$163$			16.2002i			1.26890i	−0.772964	+	0.634449i	$0.781227\pi$
$164$	−5.52788	−	1.46688i	−0.431655	−	0.114544i
$165$			14.6093i			1.13733i
$166$	−0.356308	+	2.73193i	−0.0276549	+	0.212039i
$167$	−11.8527			−0.917192			−0.458596	−	0.888645i	$-0.651648\pi$
$167$	−11.8527			−0.917192			−0.458596	+	0.888645i	$0.651648\pi$
$168$	3.23968	−	7.90217i	0.249947	−	0.609665i
$169$	9.86052			0.758502
$170$	2.12480	−	16.2916i	0.162965	−	1.24951i
$171$		−	2.29368i		−	0.175402i
$172$	−0.124039	+	0.467435i	−0.00945788	+	0.0356416i
$173$		−	0.725489i		−	0.0551579i	−0.999620	−	0.0275790i	$-0.991220\pi$
$173$		−	0.725489i		−	0.0551579i	0.999620	−	0.0275790i	$-0.00877977\pi$
$174$	−2.69978	−	0.352116i	−0.204670	−	0.0266938i
$175$	40.9252			3.09365
$176$	−8.51538	+	14.9151i	−0.641871	+	1.12427i
$177$	−3.66930			−0.275801
$178$	4.54939	+	0.593348i	0.340991	+	0.0444733i
$179$			19.7681i			1.47753i	0.673961	+	0.738767i	$0.264592\pi$
$179$			19.7681i			1.47753i	−0.673961	+	0.738767i	$0.735408\pi$
$180$	−4.76347	+	17.9509i	−0.355048	+	1.33798i
$181$		−	8.74694i		−	0.650155i	−0.945687	−	0.325077i	$-0.894610\pi$
$181$		−	8.74694i		−	0.650155i	0.945687	−	0.325077i	$-0.105390\pi$
$182$	−1.16432	+	8.92726i	−0.0863055	+	0.661732i
$183$	−12.8818			−0.952253
$184$	−7.17375	−	2.94105i	−0.528856	−	0.216817i
$185$	32.6419			2.39988
$186$	−0.358183	+	2.74630i	−0.0262632	+	0.201369i
$187$			12.3208i			0.900989i
$188$	−0.371141	−	0.0984863i	−0.0270682	−	0.00718285i
$189$			15.9844i			1.16269i
$190$	−5.67744	−	0.740472i	−0.411884	−	0.0537195i
$191$	−10.9487			−0.792218			−0.396109	−	0.918204i	$-0.629640\pi$
$191$	−10.9487			−0.792218			−0.396109	+	0.918204i	$0.629640\pi$
$192$	4.71959	−	4.78851i	0.340607	−	0.345581i
$193$	−9.94917			−0.716157			−0.358078	−	0.933692i	$-0.616568\pi$
$193$	−9.94917			−0.716157			−0.358078	+	0.933692i	$0.616568\pi$
$194$	−24.8149	−	3.23645i	−1.78161	−	0.232364i
$195$			6.02878i			0.431730i
$196$	11.4216	+	3.03084i	0.815827	+	0.216489i
$197$		−	9.99431i		−	0.712065i	−0.934474	−	0.356032i	$-0.884129\pi$
$197$		−	9.99431i		−	0.712065i	0.934474	−	0.356032i	$-0.115871\pi$
$198$	1.80124	−	13.8107i	0.128008	−	0.981482i
$199$	8.57990			0.608213			0.304106	−	0.952638i	$-0.401642\pi$
$199$	8.57990			0.608213			0.304106	+	0.952638i	$0.401642\pi$
$200$	29.8101	+	12.2213i	2.10789	+	0.864179i
$201$	11.1566			0.786924
$202$	0.102289	−	0.784284i	0.00719704	−	0.0551820i
$203$		−	8.23025i		−	0.577650i
$204$	1.23709	−	4.66192i	0.0866137	−	0.326399i
$205$		−	11.5772i		−	0.808589i
$206$	−21.1092	−	2.75314i	−1.47075	−	0.191821i
$207$	6.28739			0.437004
$208$	−3.51401	+	6.15495i	−0.243653	+	0.426769i
$209$	4.29368			0.297000
$210$	17.1431	+	2.23587i	1.18299	+	0.154289i
$211$		−	22.7140i		−	1.56370i	−0.623468	−	0.781849i	$-0.714277\pi$
$211$		−	22.7140i		−	1.56370i	0.623468	−	0.781849i	$-0.285723\pi$
$212$	−4.15611	+	15.6621i	−0.285443	+	1.07568i
$213$		−	6.25861i		−	0.428833i
$214$	−1.40776	+	10.7937i	−0.0962324	+	0.737845i
$215$	−0.978965			−0.0667649
$216$	−4.77335	+	11.6431i	−0.324785	+	0.792210i
$217$	−8.37206			−0.568333
$218$	−0.586274	+	4.49515i	−0.0397075	+	0.304450i
$219$		−	7.73770i		−	0.522865i
$220$	−33.6034	−	8.91704i	−2.26554	−	0.601187i
$221$			5.08439i			0.342013i
$222$	9.50228	+	1.23932i	0.637751	+	0.0831778i
$223$	−16.0203			−1.07280			−0.536400	−	0.843964i	$-0.680216\pi$
$223$	−16.0203			−1.07280			−0.536400	+	0.843964i	$0.680216\pi$
$224$	16.1987	+	12.2749i	1.08232	+	0.820152i
$225$	−26.1268			−1.74179
$226$	18.5111	+	2.41429i	1.23134	+	0.160596i
$227$		−	1.36137i		−	0.0903570i	−0.998979	−	0.0451785i	$-0.985614\pi$
$227$		−	1.36137i		−	0.0903570i	0.998979	−	0.0451785i	$-0.0143857\pi$
$228$	−1.62463	−	0.431113i	−0.107594	−	0.0285512i
$229$			10.7387i			0.709634i	0.934936	+	0.354817i	$0.115457\pi$
$229$			10.7387i			0.709634i	−0.934936	+	0.354817i	$0.884543\pi$
$230$	2.02976	−	15.5629i	0.133839	−	1.02618i
$231$	−12.9648			−0.853024
$232$	2.45777	−	5.99495i	0.161361	−	0.393587i
$233$	14.4853			0.948964			0.474482	−	0.880265i	$-0.342635\pi$
$233$	14.4853			0.948964			0.474482	+	0.880265i	$0.342635\pi$
$234$	0.743311	−	5.69920i	0.0485917	−	0.372569i
$235$		−	0.777293i		−	0.0507050i
$236$	2.23961	−	8.43987i	0.145786	−	0.549389i
$237$		−	7.53259i		−	0.489295i
$238$	14.4577	+	1.88563i	0.937154	+	0.122227i
$239$	−0.861343			−0.0557156			−0.0278578	−	0.999612i	$-0.508869\pi$
$239$	−0.861343			−0.0557156			−0.0278578	+	0.999612i	$0.508869\pi$
$240$	11.8194	+	6.74800i	0.762940	+	0.435581i
$241$	10.3858			0.669007			0.334503	−	0.942395i	$-0.391431\pi$
$241$	10.3858			0.669007			0.334503	+	0.942395i	$0.391431\pi$
$242$	10.4274	+	1.35997i	0.670295	+	0.0874224i
$243$		−	15.9875i		−	1.02560i
$244$	7.86264	−	29.6300i	0.503354	−	1.89686i
$245$			23.9206i			1.52823i
$246$	0.439556	−	3.37022i	0.0280251	−	0.214877i
$247$	1.77186			0.112741
$248$	−6.09824	−	2.50012i	−0.387239	−	0.158758i
$249$	−1.63726			−0.103757
$250$	−4.73220	+	36.2833i	−0.299291	+	2.29476i
$251$		−	16.7981i		−	1.06029i	−0.847908	−	0.530144i	$-0.822138\pi$
$251$		−	16.7981i		−	1.06029i	0.847908	−	0.530144i	$-0.177862\pi$
$252$	−15.9303	−	4.22728i	−1.00351	−	0.266293i
$253$			11.7697i			0.739957i
$254$	16.8880	+	2.20260i	1.05965	+	0.138203i
$255$	9.76362			0.611421
$256$	8.13355	+	13.7784i	0.508347	+	0.861153i
$257$	−20.8724			−1.30198			−0.650991	−	0.759085i	$-0.725646\pi$
$257$	−20.8724			−1.30198			−0.650991	+	0.759085i	$0.725646\pi$
$258$	−0.284984	−	0.0371686i	−0.0177423	−	0.00231402i
$259$			28.9676i			1.79996i
$260$	−13.8670	−	3.67976i	−0.859994	−	0.228209i
$261$			5.25423i			0.325229i
$262$	−0.405915	+	3.11228i	−0.0250775	+	0.192277i
$263$	23.0366			1.42050			0.710248	−	0.703952i	$-0.248583\pi$
$263$	23.0366			1.42050			0.710248	+	0.703952i	$0.248583\pi$
$264$	−9.44364	−	3.87164i	−0.581216	−	0.238283i
$265$	−32.8017			−2.01499
$266$	0.657121	−	5.03836i	0.0402907	−	0.308922i
$267$			2.72648i			0.166858i
$268$	−6.80959	+	25.6616i	−0.415962	+	1.56753i
$269$		−	10.5023i		−	0.640337i	−0.947361	−	0.320169i	$-0.896260\pi$
$269$		−	10.5023i		−	0.640337i	0.947361	−	0.320169i	$-0.103740\pi$
$270$	−25.2587	−	3.29433i	−1.53719	−	0.200486i
$271$	−11.4478			−0.695403			−0.347702	−	0.937605i	$-0.613038\pi$
$271$	−11.4478			−0.695403			−0.347702	+	0.937605i	$0.613038\pi$
$272$	9.96795	+	5.69095i	0.604396	+	0.345065i
$273$	−5.35015			−0.323806
$274$	−10.0191	−	1.30673i	−0.605279	−	0.0789427i
$275$		−	48.9084i		−	2.94929i
$276$	1.18176	−	4.45339i	0.0711335	−	0.268063i
$277$			24.1899i			1.45343i	0.686940	+	0.726715i	$0.258954\pi$
$277$			24.1899i			1.45343i	−0.686940	+	0.726715i	$0.741046\pi$
$278$	1.23435	−	9.46415i	0.0740313	−	0.567622i
$279$	5.34477			0.319983
$280$	−15.6064	+	38.0667i	−0.932659	+	2.27492i
$281$	−1.48823			−0.0887804			−0.0443902	−	0.999014i	$-0.514134\pi$
$281$	−1.48823			−0.0887804			−0.0443902	+	0.999014i	$0.514134\pi$
$282$	0.0295117	−	0.226276i	0.00175740	−	0.0134745i
$283$			11.7331i			0.697459i	0.937223	+	0.348730i	$0.113387\pi$
$283$			11.7331i			0.697459i	−0.937223	+	0.348730i	$0.886613\pi$
$284$	14.3956	+	3.82004i	0.854224	+	0.226678i
$285$		−	3.40252i		−	0.201548i
$286$	10.6687	+	1.39145i	0.630853	+	0.0822781i
$287$	10.2741			0.606458
$288$	−10.3413	−	7.83637i	−0.609367	−	0.461762i
$289$	−8.76581			−0.515636
$290$	13.0055	+	1.69623i	0.763712	+	0.0996061i
$291$		−	14.8717i		−	0.871796i
$292$	17.7977	+	4.72283i	1.04153	+	0.276383i
$293$			0.520490i			0.0304073i	0.999884	+	0.0152037i	$0.00483966\pi$
$293$			0.520490i			0.0304073i	−0.999884	+	0.0152037i	$0.995160\pi$
$294$	−0.908200	+	6.96346i	−0.0529673	+	0.406117i
$295$	17.6759			1.02913
$296$	−8.65048	+	21.1001i	−0.502799	+	1.22642i
$297$	19.1024			1.10843
$298$	2.03695	−	15.6180i	0.117998	−	0.904725i
$299$			4.85698i			0.280886i
$300$	−4.91072	+	18.5058i	−0.283521	+	1.06843i
$301$		−	0.868768i		−	0.0500750i
$302$	12.9920	+	1.69447i	0.747607	+	0.0975057i
$303$	0.470026			0.0270023
$304$	1.98324	−	3.47373i	0.113746	−	0.199232i
$305$	62.0551			3.55326
$306$	−9.22987	−	1.20379i	−0.527637	−	0.0688163i
$307$		−	11.5355i		−	0.658364i	−0.944267	−	0.329182i	$-0.893227\pi$
$307$		−	11.5355i		−	0.658364i	0.944267	−	0.329182i	$-0.106773\pi$
$308$	7.91330	−	29.8209i	0.450902	−	1.69920i
$309$		−	12.6509i		−	0.719683i
$310$	1.72546	−	13.2296i	0.0979994	−	0.751393i
$311$	−23.2072			−1.31596			−0.657981	−	0.753034i	$-0.728589\pi$
$311$	−23.2072			−1.31596			−0.657981	+	0.753034i	$0.728589\pi$
$312$	−3.89707	−	1.59770i	−0.220628	−	0.0904517i
$313$	0.924930			0.0522801			0.0261401	−	0.999658i	$-0.491678\pi$
$313$	0.924930			0.0522801			0.0261401	+	0.999658i	$0.491678\pi$
$314$	−2.04663	+	15.6922i	−0.115498	+	0.885562i
$315$		−	33.3634i		−	1.87981i
$316$	17.3260	+	4.59764i	0.974662	+	0.258637i
$317$		−	14.4924i		−	0.813975i	−0.913434	−	0.406987i	$-0.866579\pi$
$317$		−	14.4924i		−	0.813975i	0.913434	−	0.406987i	$-0.133421\pi$
$318$	−9.54880	−	1.24539i	−0.535470	−	0.0698380i
$319$	−9.83572			−0.550694
$320$	−22.7355	+	23.0675i	−1.27095	+	1.28951i
$321$	−6.46875			−0.361050
$322$	13.8110	+	1.80129i	0.769659	+	0.100382i
$323$		−	2.86953i		−	0.159665i
$324$	6.07382	+	1.61176i	0.337434	+	0.0895420i
$325$		−	20.1829i		−	1.11954i
$326$	2.96298	−	22.7182i	0.164105	−	1.25824i
$327$	−2.69397			−0.148977
$328$	7.48366	+	3.06810i	0.413216	+	0.169408i
$329$	0.689798			0.0380298
$330$	2.67201	−	20.4872i	0.147090	−	1.12778i
$331$		−	18.7836i		−	1.03244i	−0.856456	−	0.516220i	$-0.827339\pi$
$331$		−	18.7836i		−	1.03244i	0.856456	−	0.516220i	$-0.172661\pi$
$332$	0.999327	−	3.76591i	0.0548452	−	0.206681i
$333$		−	18.4930i		−	1.01341i
$334$	16.6215	+	2.16784i	0.909490	+	0.118619i
$335$	−53.7440			−2.93635
$336$	−5.98841	+	10.4890i	−0.326695	+	0.572220i
$337$	−18.2695			−0.995202			−0.497601	−	0.867406i	$-0.665786\pi$
$337$	−18.2695			−0.995202			−0.497601	+	0.867406i	$0.665786\pi$
$338$	−13.8278	−	1.80347i	−0.752132	−	0.0980957i
$339$			11.0938i			0.602533i
$340$	−5.95938	+	22.4576i	−0.323193	+	1.21794i
$341$			10.0052i			0.541812i
$342$	−0.419509	+	3.21651i	−0.0226845	+	0.173929i
$343$	3.92180			0.211758
$344$	0.259437	−	0.632814i	0.0139879	−	0.0341191i
$345$	9.32690			0.502144
$346$	−0.132690	+	1.01738i	−0.00713348	+	0.0546947i
$347$		−	0.376993i		−	0.0202380i	−0.999949	−	0.0101190i	$-0.996779\pi$
$347$		−	0.376993i		−	0.0202380i	0.999949	−	0.0101190i	$-0.00322104\pi$
$348$	3.72161	+	0.987569i	0.199499	+	0.0529393i
$349$		−	2.06216i		−	0.110385i	−0.998476	−	0.0551925i	$-0.982423\pi$
$349$		−	2.06216i		−	0.110385i	0.998476	−	0.0551925i	$-0.0175773\pi$
$350$	−57.3909	−	7.48513i	−3.06767	−	0.400097i
$351$	7.88292			0.420759
$352$	14.6694	−	19.3585i	0.781880	−	1.03181i
$353$	−13.2220			−0.703735			−0.351867	−	0.936050i	$-0.614453\pi$
$353$	−13.2220			−0.703735			−0.351867	+	0.936050i	$0.614453\pi$
$354$	5.14559	+	0.671106i	0.273485	+	0.0356689i
$355$			30.1493i			1.60016i
$356$	−6.27126	−	1.66415i	−0.332376	−	0.0881997i
$357$			8.66458i			0.458578i
$358$	3.61554	−	27.7215i	0.191087	−	1.46513i
$359$	−6.30805			−0.332926			−0.166463	−	0.986048i	$-0.553235\pi$
$359$	−6.30805			−0.332926			−0.166463	+	0.986048i	$0.553235\pi$
$360$	9.96318	−	24.3020i	0.525106	−	1.28083i
$361$	−1.00000			−0.0526316
$362$	−1.59980	+	12.2662i	−0.0840834	+	0.644695i
$363$			6.24917i			0.327996i
$364$	3.26555	−	12.3061i	0.171161	−	0.645013i
$365$			37.2745i			1.95103i
$366$	18.0647	+	2.35606i	0.944256	+	0.123153i
$367$	−17.6676			−0.922241			−0.461121	−	0.887337i	$-0.652552\pi$
$367$	−17.6676			−0.922241			−0.461121	+	0.887337i	$0.652552\pi$
$368$	9.52210	+	5.43640i	0.496374	+	0.283392i
$369$	−6.55901			−0.341448
$370$	−45.7749	−	5.97013i	−2.37972	−	0.310372i
$371$		−	29.1094i		−	1.51128i
$372$	1.00459	−	3.78573i	0.0520853	−	0.196281i
$373$			9.50368i			0.492082i	0.969259	+	0.246041i	$0.0791297\pi$
$373$			9.50368i			0.492082i	−0.969259	+	0.246041i	$0.920870\pi$
$374$	2.25345	−	17.2780i	0.116523	−	0.893422i
$375$	−21.7448			−1.12290
$376$	0.502451	+	0.205992i	0.0259119	+	0.0106232i
$377$	−4.05887			−0.209042
$378$	2.92350	−	22.4154i	0.150369	−	1.15293i
$379$		−	19.8431i		−	1.01927i	−0.860390	−	0.509636i	$-0.829780\pi$
$379$		−	19.8431i		−	1.01927i	0.860390	−	0.509636i	$-0.170220\pi$
$380$	7.82625	+	2.07678i	0.401478	+	0.106537i
$381$			10.1211i			0.518518i
$382$	15.3537	+	2.00249i	0.785564	+	0.102456i
$383$	1.43333			0.0732395			0.0366198	−	0.999329i	$-0.488341\pi$
$383$	1.43333			0.0732395			0.0366198	+	0.999329i	$0.488341\pi$
$384$	−7.49427	+	5.85191i	−0.382440	+	0.298629i
$385$	62.4549			3.18300
$386$	13.9521	+	1.81968i	0.710142	+	0.0926193i
$387$			0.554626i			0.0281932i
$388$	34.2069	+	9.07719i	1.73659	+	0.460825i
$389$		−	0.716818i		−	0.0363441i	−0.999835	−	0.0181721i	$-0.994215\pi$
$389$		−	0.716818i		−	0.0363441i	0.999835	−	0.0181721i	$-0.00578466\pi$
$390$	1.10265	−	8.45438i	0.0558349	−	0.428104i
$391$	7.86588			0.397795
$392$	−15.4626	−	6.33924i	−0.780977	−	0.320180i
$393$	−1.86521			−0.0940872
$394$	−1.82794	+	14.0154i	−0.0920901	+	0.706085i
$395$			36.2864i			1.82577i
$396$	−5.05189	+	19.0378i	−0.253867	+	0.956685i
$397$		−	28.3452i		−	1.42260i	−0.702887	−	0.711302i	$-0.748106\pi$
$397$		−	28.3452i		−	1.42260i	0.702887	−	0.711302i	$-0.251894\pi$
$398$	−12.0319	−	1.56924i	−0.603105	−	0.0786591i
$399$	3.01952			0.151165
$400$	−39.5685	−	22.5906i	−1.97842	−	1.12953i
$401$	−12.4794			−0.623192			−0.311596	−	0.950215i	$-0.600864\pi$
$401$	−12.4794			−0.623192			−0.311596	+	0.950215i	$0.600864\pi$
$402$	−15.6453	−	2.04051i	−0.780315	−	0.101771i
$403$			4.12881i			0.205670i
$404$	−0.286888	+	1.08112i	−0.0142732	+	0.0537878i
$405$			12.7206i			0.632093i
$406$	−1.50530	+	11.5416i	−0.0747065	+	0.572799i
$407$	34.6182			1.71596
$408$	−2.58747	+	6.31131i	−0.128099	+	0.312457i
$409$	−34.2772			−1.69490			−0.847449	−	0.530877i	$-0.821862\pi$
$409$	−34.2772			−1.69490			−0.847449	+	0.530877i	$0.821862\pi$
$410$	−2.11745	+	16.2352i	−0.104573	+	0.801799i
$411$		−	6.00453i		−	0.296182i
$412$	29.0987	+	7.72166i	1.43359	+	0.380419i
$413$			15.6862i			0.771870i
$414$	−8.81703	−	1.14995i	−0.433334	−	0.0565169i
$415$	7.88709			0.387162
$416$	6.05356	−	7.98860i	0.296800	−	0.391674i
$417$	5.67191			0.277755
$418$	−6.02119	−	0.785305i	−0.294506	−	0.0384105i
$419$		−	36.7958i		−	1.79759i	−0.438366	−	0.898797i	$-0.644442\pi$
$419$		−	36.7958i		−	1.79759i	0.438366	−	0.898797i	$-0.355558\pi$
$420$	−23.6315	−	6.27087i	−1.15310	−	0.305987i
$421$			16.4467i			0.801564i	0.916173	+	0.400782i	$0.131261\pi$
$421$			16.4467i			0.801564i	−0.916173	+	0.400782i	$0.868739\pi$
$422$	−4.15434	+	31.8527i	−0.202230	+	1.55056i
$423$	−0.440370			−0.0214115
$424$	8.69283	−	21.2034i	0.422161	−	1.02973i
$425$	−32.6862			−1.58551
$426$	−1.14469	+	8.77668i	−0.0554602	+	0.425231i
$427$			55.0699i			2.66502i
$428$	3.94830	−	14.8790i	0.190848	−	0.719203i
$429$			6.39380i			0.308696i
$430$	1.37284	+	0.179051i	0.0662042	+	0.00863459i
$431$	40.3614			1.94414			0.972070	−	0.234690i	$-0.0754074\pi$
$431$	40.3614			1.94414			0.972070	+	0.234690i	$0.0754074\pi$
$432$	8.82333	−	15.4545i	0.424513	−	0.743553i
$433$	37.1588			1.78574			0.892868	−	0.450318i	$-0.148689\pi$
$433$	37.1588			1.78574			0.892868	+	0.450318i	$0.148689\pi$
$434$	11.7405	+	1.53123i	0.563560	+	0.0735015i
$435$			7.79429i			0.373708i
$436$	1.64431	−	6.19649i	0.0787480	−	0.296758i
$437$		−	2.74118i		−	0.131128i
$438$	−1.41521	+	10.8509i	−0.0676213	+	0.518474i
$439$	10.8753			0.519050			0.259525	−	0.965736i	$-0.416434\pi$
$439$	10.8753			0.519050			0.259525	+	0.965736i	$0.416434\pi$
$440$	45.4924	+	18.6507i	2.16876	+	0.889136i
$441$	13.5521			0.645337
$442$	0.929925	−	7.13003i	0.0442320	−	0.339141i
$443$			31.3210i			1.48811i	0.668120	+	0.744053i	$0.267099\pi$
$443$			31.3210i			1.48811i	−0.668120	+	0.744053i	$0.732901\pi$
$444$	−13.0987	−	3.47589i	−0.621638	−	0.164959i
$445$		−	13.1341i		−	0.622617i
$446$	22.4659	+	2.93008i	1.06379	+	0.138743i
$447$	9.35994			0.442710
$448$	−20.4709	−	20.1763i	−0.967160	−	0.953239i
$449$	−17.7109			−0.835829			−0.417914	−	0.908486i	$-0.637239\pi$
$449$	−17.7109			−0.835829			−0.417914	+	0.908486i	$0.637239\pi$
$450$	36.6386	+	4.77854i	1.72716	+	0.225263i
$451$		−	12.2782i		−	0.578158i
$452$	−25.5172	−	6.77129i	−1.20023	−	0.318495i
$453$			7.78619i			0.365827i
$454$	−0.248991	+	1.90909i	−0.0116857	+	0.0895982i
$455$	25.7730			1.20826
$456$	2.19943	+	0.901707i	0.102998	+	0.0422263i
$457$	−12.8520			−0.601190			−0.300595	−	0.953752i	$-0.597185\pi$
$457$	−12.8520			−0.601190			−0.300595	+	0.953752i	$0.597185\pi$
$458$	1.96409	−	15.0593i	0.0917758	−	0.703675i
$459$		−	12.7664i		−	0.595885i
$460$	−5.69283	+	21.4531i	−0.265429	+	1.00026i
$461$			20.3622i			0.948362i	0.880427	+	0.474181i	$0.157256\pi$
$461$			20.3622i			0.948362i	−0.880427	+	0.474181i	$0.842744\pi$
$462$	18.1811	+	2.37124i	0.845860	+	0.110320i
$463$	20.8316			0.968125			0.484062	−	0.875034i	$-0.339161\pi$
$463$	20.8316			0.968125			0.484062	+	0.875034i	$0.339161\pi$
$464$	−4.54308	+	7.95741i	−0.210907	+	0.369414i
$465$	7.92859			0.367680
$466$	−20.3133	−	2.64933i	−0.940994	−	0.122728i
$467$			14.1083i			0.652854i	0.945222	+	0.326427i	$0.105845\pi$
$467$			14.1083i			0.652854i	−0.945222	+	0.326427i	$0.894155\pi$
$468$	−2.08474	+	7.85625i	−0.0963673	+	0.363155i
$469$		−	47.6943i		−	2.20232i
$470$	−0.142165	+	1.09003i	−0.00655759	+	0.0502792i
$471$	−9.40442			−0.433333
$472$	−4.68433	+	11.4259i	−0.215614	+	0.525921i
$473$	−1.03824			−0.0477382
$474$	−1.37770	+	10.5632i	−0.0632796	+	0.485185i
$475$			11.3908i			0.522645i
$476$	−19.9297	−	5.28857i	−0.913476	−	0.242401i
$477$			18.5836i			0.850883i
$478$	1.20789	+	0.157538i	0.0552477	+	0.00720561i
$479$	3.58494			0.163800			0.0819001	−	0.996641i	$-0.473901\pi$
$479$	3.58494			0.163800			0.0819001	+	0.996641i	$0.473901\pi$
$480$	−15.3406	−	11.6247i	−0.700200	−	0.530593i
$481$	14.2858			0.651375
$482$	−14.5644	−	1.89954i	−0.663388	−	0.0865215i
$483$			8.27703i			0.376618i
$484$	−14.3739	−	3.81428i	−0.653360	−	0.173376i
$485$			71.6408i			3.25304i
$486$	−2.92408	+	22.4199i	−0.132639	+	1.01699i
$487$	−22.5062			−1.01985			−0.509926	−	0.860219i	$-0.670327\pi$
$487$	−22.5062			−1.01985			−0.509926	+	0.860219i	$0.670327\pi$
$488$	−16.4453	+	40.1131i	−0.744445	+	1.81584i
$489$	13.6151			0.615697
$490$	4.37503	−	33.5448i	0.197644	−	1.51540i
$491$			5.13695i			0.231827i	0.993259	+	0.115914i	$0.0369796\pi$
$491$			5.13695i			0.231827i	−0.993259	+	0.115914i	$0.963020\pi$
$492$	−1.23281	+	4.64578i	−0.0555794	+	0.209448i
$493$			6.57335i			0.296049i
$494$	−2.48474	−	0.324069i	−0.111794	−	0.0145806i
$495$	−39.8715			−1.79209
$496$	8.09452	+	4.62136i	0.363455	+	0.207505i
$497$	−26.7556			−1.20015
$498$	2.29599	+	0.299451i	0.102886	+	0.0134187i
$499$		−	16.1056i		−	0.720986i	−0.932762	−	0.360493i	$-0.882608\pi$
$499$		−	16.1056i		−	0.720986i	0.932762	−	0.360493i	$-0.117392\pi$
$500$	13.2723	−	50.0159i	0.593554	−	2.23678i
$501$			9.96137i			0.445041i
$502$	−3.07234	+	23.5566i	−0.137125	+	1.05138i
$503$	31.8839			1.42163			0.710816	−	0.703378i	$-0.248326\pi$
$503$	31.8839			1.42163			0.710816	+	0.703378i	$0.248326\pi$
$504$	21.5665	+	8.84168i	0.960646	+	0.393840i
$505$	−2.26423			−0.100757
$506$	2.15266	−	16.5051i	0.0956974	−	0.733743i
$507$		−	8.28706i		−	0.368041i
$508$	−23.2798	−	6.17756i	−1.03288	−	0.274085i
$509$		−	32.3019i		−	1.43176i	−0.698225	−	0.715878i	$-0.746027\pi$
$509$		−	32.3019i		−	1.43176i	0.698225	−	0.715878i	$-0.253973\pi$
$510$	−13.6919	−	1.78574i	−0.606287	−	0.0790741i
$511$	−33.0787			−1.46331
$512$	−8.88592	−	20.8096i	−0.392706	−	0.919664i
$513$	−4.44896			−0.196426
$514$	29.2701	+	3.81751i	1.29105	+	0.168383i
$515$			60.9425i			2.68545i
$516$	0.392845	+	0.104246i	0.0172940	+	0.00458917i
$517$		−	0.824356i		−	0.0362551i
$518$	5.29810	−	40.6223i	0.232785	−	1.78484i
$519$	−0.609721			−0.0267638
$520$	18.7732	+	7.69651i	0.823258	+	0.337514i
$521$	−23.7138			−1.03892			−0.519460	−	0.854495i	$-0.673867\pi$
$521$	−23.7138			−1.03892			−0.519460	+	0.854495i	$0.673867\pi$
$522$	0.960988	−	7.36820i	0.0420613	−	0.322498i
$523$			7.74931i			0.338854i	0.985543	+	0.169427i	$0.0541916\pi$
$523$			7.74931i			0.338854i	−0.985543	+	0.169427i	$0.945808\pi$
$524$	1.13846	−	4.29023i	0.0497338	−	0.187419i
$525$		−	34.3947i		−	1.50111i
$526$	−32.3050	−	4.21334i	−1.40857	−	0.183710i
$527$	6.68661			0.291273
$528$	12.5350	+	7.15657i	0.545518	+	0.311450i
$529$	−15.4859			−0.673302
$530$	45.9990	+	5.99935i	1.99807	+	0.260595i
$531$		−	10.0142i		−	0.434578i
$532$	−1.84301	+	6.94529i	−0.0799046	+	0.301117i
$533$		−	5.06680i		−	0.219467i
$534$	0.498667	−	3.82344i	0.0215794	−	0.165456i
$535$	31.1616			1.34723
$536$	14.2428	−	34.7407i	0.615195	−	1.50057i
$537$	16.6136			0.716931
$538$	−1.92085	+	14.7278i	−0.0828137	+	0.634959i
$539$			25.3689i			1.09272i
$540$	34.8186	+	9.23951i	1.49836	+	0.397605i
$541$		−	7.57937i		−	0.325862i	−0.986637	−	0.162931i	$-0.947905\pi$
$541$		−	7.57937i		−	0.325862i	0.986637	−	0.162931i	$-0.0520949\pi$
$542$	16.0536	+	2.09378i	0.689563	+	0.0899353i
$543$	−7.35117			−0.315469
$544$	−12.9376	−	9.80375i	−0.554693	−	0.420332i
$545$	12.9775			0.555896
$546$	7.50271	+	0.978531i	0.321087	+	0.0418773i
$547$			34.8739i			1.49110i	0.666450	+	0.745549i	$0.267813\pi$
$547$			34.8739i			1.49110i	−0.666450	+	0.745549i	$0.732187\pi$
$548$	13.8112	+	3.66496i	0.589986	+	0.156559i
$549$		−	35.1569i		−	1.50046i
$550$	−8.94524	+	68.5861i	−0.381426	+	2.92452i
$551$	2.29074			0.0975889
$552$	−2.47174	+	6.02902i	−0.105204	+	0.256612i
$553$	−32.2019			−1.36936
$554$	4.42428	−	33.9224i	0.187970	−	1.44122i
$555$		−	27.4331i		−	1.16447i
$556$	−3.46194	+	13.0462i	−0.146819	+	0.553281i
$557$		−	31.2771i		−	1.32525i	−0.748950	−	0.662627i	$-0.769442\pi$
$557$		−	31.2771i		−	1.32525i	0.748950	−	0.662627i	$-0.230558\pi$
$558$	−7.49516	−	0.977546i	−0.317295	−	0.0413828i
$559$	−0.428446			−0.0181213
$560$	28.8477	−	50.5280i	1.21904	−	2.13520i
$561$	10.3548			0.437179
$562$	2.08700	+	0.272194i	0.0880348	+	0.0114818i
$563$			26.6292i			1.12229i	0.827718	+	0.561144i	$0.189639\pi$
$563$			26.6292i			1.12229i	−0.827718	+	0.561144i	$0.810361\pi$
$564$	−0.0827706	+	0.311917i	−0.00348527	+	0.0131341i
$565$		−	53.4417i		−	2.24831i
$566$	2.14596	−	16.4537i	0.0902012	−	0.691602i
$567$	−11.2887			−0.474082
$568$	−19.4889	−	7.98992i	−0.817734	−	0.335250i
$569$	6.61114			0.277154			0.138577	−	0.990352i	$-0.455747\pi$
$569$	6.61114			0.277154			0.138577	+	0.990352i	$0.455747\pi$
$570$	−0.622313	+	4.77148i	−0.0260658	+	0.199855i
$571$		−	14.0590i		−	0.588353i	−0.955751	−	0.294176i	$-0.904955\pi$
$571$		−	14.0590i		−	0.588353i	0.955751	−	0.294176i	$-0.0950453\pi$
$572$	−14.7066	−	3.90256i	−0.614914	−	0.163174i
$573$			9.20156i			0.384401i
$574$	−14.4077	−	1.87910i	−0.601365	−	0.0784322i
$575$	−31.2242			−1.30214
$576$	13.0687	+	12.8806i	0.544530	+	0.536693i
$577$	12.0687			0.502427			0.251214	−	0.967932i	$-0.419170\pi$
$577$	12.0687			0.502427			0.251214	+	0.967932i	$0.419170\pi$
$578$	12.2926	+	1.60325i	0.511306	+	0.0666863i
$579$			8.36156i			0.347495i
$580$	−17.9279	−	4.75737i	−0.744416	−	0.197539i
$581$			6.99928i			0.290379i
$582$	−2.72001	+	20.8552i	−0.112748	+	0.864474i
$583$	−34.7877			−1.44076
$584$	−24.0946	−	9.87817i	−0.997043	−	0.408761i
$585$	−16.4536			−0.680274
$586$	0.0951964	−	0.729902i	0.00393253	−	0.0301520i
$587$		−	28.7621i		−	1.18714i	−0.804783	−	0.593569i	$-0.797718\pi$
$587$		−	28.7621i		−	1.18714i	0.804783	−	0.593569i	$-0.202282\pi$
$588$	2.54720	−	9.59901i	0.105045	−	0.395857i
$589$		−	2.33021i		−	0.0960148i
$590$	−24.7876	−	3.23289i	−1.02049	−	0.133096i
$591$	−8.39949			−0.345509
$592$	15.9900	−	28.0073i	0.657187	−	1.15109i
$593$	−18.3434			−0.753275			−0.376637	−	0.926361i	$-0.622920\pi$
$593$	−18.3434			−0.753275			−0.376637	+	0.926361i	$0.622920\pi$
$594$	−26.7880	−	3.49379i	−1.09912	−	0.143352i
$595$		−	41.7395i		−	1.71115i
$596$	−5.71299	+	21.5291i	−0.234013	+	0.881867i
$597$		−	7.21078i		−	0.295118i
$598$	0.888330	−	6.81112i	0.0363265	−	0.278527i
$599$	−13.1215			−0.536130			−0.268065	−	0.963401i	$-0.586384\pi$
$599$	−13.1215			−0.536130			−0.268065	+	0.963401i	$0.586384\pi$
$600$	10.2712	−	25.0532i	0.419318	−	1.02279i
$601$	16.6052			0.677341			0.338670	−	0.940905i	$-0.390023\pi$
$601$	16.6052			0.677341			0.338670	+	0.940905i	$0.390023\pi$
$602$	−0.158896	+	1.21831i	−0.00647611	+	0.0496544i
$603$			30.4483i			1.23995i
$604$	−17.9093	−	4.75243i	−0.728719	−	0.193374i
$605$		−	30.1038i		−	1.22389i
$606$	−0.659134	−	0.0859667i	−0.0267755	−	0.00349216i
$607$	15.5782			0.632299			0.316149	−	0.948709i	$-0.397610\pi$
$607$	15.5782			0.632299			0.316149	+	0.948709i	$0.397610\pi$
$608$	−3.41650	+	4.50860i	−0.138557	+	0.182848i
$609$	−6.91693			−0.280288
$610$	−87.0221	−	11.3497i	−3.52342	−	0.459538i
$611$		−	0.340184i		−	0.0137624i
$612$	12.7232	+	3.37625i	0.514306	+	0.136477i
$613$		−	26.0508i		−	1.05218i	−0.850428	−	0.526091i	$-0.823657\pi$
$613$		−	26.0508i		−	1.05218i	0.850428	−	0.526091i	$-0.176343\pi$
$614$	−2.10981	+	16.1766i	−0.0851451	+	0.652835i
$615$	−9.72983			−0.392345
$616$	−16.5513	+	40.3716i	−0.666870	+	1.62662i
$617$	30.7470			1.23783			0.618913	−	0.785460i	$-0.287573\pi$
$617$	30.7470			1.23783			0.618913	+	0.785460i	$0.287573\pi$
$618$	−2.31382	+	17.7408i	−0.0930754	+	0.713639i
$619$		−	39.6939i		−	1.59543i	−0.603032	−	0.797717i	$-0.706041\pi$
$619$		−	39.6939i		−	1.59543i	0.603032	−	0.797717i	$-0.293959\pi$
$620$	−4.83934	+	18.2368i	−0.194353	+	0.732408i
$621$		−	12.1954i		−	0.489384i
$622$	32.5444	+	4.24456i	1.30491	+	0.170191i
$623$	11.6557			0.466975
$624$	5.17279	+	2.95327i	0.207077	+	0.118226i
$625$	47.7961			1.91185
$626$	−1.29706	−	0.169168i	−0.0518411	−	0.00676130i
$627$		−	3.60853i		−	0.144111i
$628$	5.74014	−	21.6314i	0.229056	−	0.863188i
$629$		−	23.1359i		−	0.922487i
$630$	−6.10209	+	46.7867i	−0.243113	+	1.86403i
$631$	20.1050			0.800368			0.400184	−	0.916435i	$-0.368946\pi$
$631$	20.1050			0.800368			0.400184	+	0.916435i	$0.368946\pi$
$632$	−23.4560	−	9.61632i	−0.933028	−	0.382517i
$633$	−19.0895			−0.758739
$634$	−2.65063	+	20.3232i	−0.105270	+	0.807139i
$635$		−	48.7558i		−	1.93481i
$636$	13.1629	+	3.49291i	0.521941	+	0.138503i
$637$			10.4689i			0.414793i
$638$	13.7930	+	1.79893i	0.546070	+	0.0712204i
$639$	17.0809			0.675709
$640$	36.1018	−	28.1901i	1.42705	−	1.11431i
$641$	36.4567			1.43995			0.719976	−	0.693998i	$-0.244153\pi$
$641$	36.4567			1.43995			0.719976	+	0.693998i	$0.244153\pi$
$642$	9.07136	+	1.18312i	0.358018	+	0.0466940i
$643$		−	22.3779i		−	0.882498i	−0.897385	−	0.441249i	$-0.854536\pi$
$643$		−	22.3779i		−	0.882498i	0.897385	−	0.441249i	$-0.145464\pi$
$644$	−19.0383	−	5.05202i	−0.750213	−	0.199077i
$645$			0.822749i			0.0323957i
$646$	−0.524830	+	4.02404i	−0.0206492	+	0.158324i
$647$	−47.9816			−1.88635			−0.943175	−	0.332297i	$-0.892176\pi$
$647$	−47.9816			−1.88635			−0.943175	+	0.332297i	$0.892176\pi$
$648$	−8.22275	−	3.37111i	−0.323020	−	0.132430i
$649$	18.7461			0.735851
$650$	−3.69140	+	28.3032i	−0.144789	+	1.11014i
$651$			7.03611i			0.275767i
$652$	−8.31020	+	31.3166i	−0.325453	+	1.22645i
$653$			14.9823i			0.586304i	0.956066	+	0.293152i	$0.0947041\pi$
$653$			14.9823i			0.586304i	−0.956066	+	0.293152i	$0.905296\pi$
$654$	3.77785	+	0.492721i	0.147726	+	0.0192669i
$655$	8.98517			0.351080
$656$	−9.93346	−	5.67126i	−0.387836	−	0.221425i
$657$	21.1176			0.823876
$658$	−0.967329	−	0.126163i	−0.0377104	−	0.00491833i
$659$			39.2286i			1.52813i	0.645140	+	0.764064i	$0.276799\pi$
$659$			39.2286i			1.52813i	−0.645140	+	0.764064i	$0.723201\pi$
$660$	−7.49413	+	28.2412i	−0.291708	+	1.09929i
$661$			34.8438i			1.35527i	0.735400	+	0.677634i	$0.236995\pi$
$661$			34.8438i			1.35527i	−0.735400	+	0.677634i	$0.763005\pi$
$662$	−3.43548	+	26.3409i	−0.133524	+	1.02377i
$663$	4.27307			0.165952
$664$	−2.09017	+	5.09831i	−0.0811144	+	0.197853i
$665$	−14.5458			−0.564061
$666$	−3.38234	+	25.9335i	−0.131063	+	1.00490i
$667$			6.27933i			0.243137i
$668$	−22.9125	−	6.08008i	−0.886511	−	0.235246i
$669$			13.4639i			0.520545i
$670$	75.3672	+	9.82966i	2.91169	+	0.379753i
$671$	65.8123			2.54066
$672$	10.3162	−	13.6138i	0.397955	−	0.525164i
$673$	0.379432			0.0146260			0.00731301	−	0.999973i	$-0.497672\pi$
$673$	0.379432			0.0146260			0.00731301	+	0.999973i	$0.497672\pi$
$674$	25.6200	+	3.34145i	0.986844	+	0.128708i
$675$			50.6771i			1.95056i
$676$	19.0613	+	5.05814i	0.733128	+	0.194544i
$677$		−	0.0782626i		−	0.00300788i	−0.999999	−	0.00150394i	$-0.999521\pi$
$677$		−	0.0782626i		−	0.00300788i	0.999999	−	0.00150394i	$-0.000478719\pi$
$678$	2.02903	−	15.5573i	0.0779246	−	0.597473i
$679$	−63.5766			−2.43985
$680$	12.4645	−	30.4032i	0.477992	−	1.16591i
$681$	−1.14413			−0.0438432
$682$	1.82993	−	14.0306i	0.0700716	−	0.537261i
$683$			31.3208i			1.19846i	0.800578	+	0.599229i	$0.204526\pi$
$683$			31.3208i			1.19846i	−0.800578	+	0.599229i	$0.795474\pi$
$684$	1.17659	−	4.43391i	0.0449879	−	0.169535i
$685$			28.9253i			1.10518i
$686$	−5.49969	−	0.717290i	−0.209979	−	0.0273862i
$687$	9.02512			0.344330
$688$	−0.479559	+	0.839968i	−0.0182830	+	0.0320235i
$689$	−14.3557			−0.546909
$690$	−13.0795	−	1.70587i	−0.497927	−	0.0649414i
$691$		−	25.8372i		−	0.982892i	−0.870908	−	0.491446i	$-0.836469\pi$
$691$		−	25.8372i		−	0.982892i	0.870908	−	0.491446i	$-0.163531\pi$
$692$	0.372153	−	1.40244i	0.0141471	−	0.0533128i
$693$		−	35.3834i		−	1.34410i
$694$	−0.0689512	+	0.528671i	−0.00261735	+	0.0200681i
$695$	−27.3230			−1.03642
$696$	−5.03832	−	2.06558i	−0.190977	−	0.0782955i
$697$	−8.20569			−0.310813
$698$	−0.377165	+	2.89185i	−0.0142759	+	0.109458i
$699$		−	12.1739i		−	0.460457i
$700$	79.1123	+	20.9933i	2.99017	+	0.793474i
$701$			3.90849i			0.147622i	0.997272	+	0.0738108i	$0.0235161\pi$
$701$			3.90849i			0.147622i	−0.997272	+	0.0738108i	$0.976484\pi$
$702$	−11.0545	−	1.44177i	−0.417225	−	0.0544161i
$703$	−8.06260			−0.304087
$704$	−24.1120	+	24.4642i	−0.908756	+	0.922027i
$705$	−0.653259			−0.0246032
$706$	18.5417	+	2.41827i	0.697825	+	0.0910128i
$707$		−	2.00936i		−	0.0755698i
$708$	−7.09310	−	1.88223i	−0.266575	−	0.0707387i
$709$			1.94801i			0.0731592i	0.999331	+	0.0365796i	$0.0116462\pi$
$709$			1.94801i			0.0731592i	−0.999331	+	0.0365796i	$0.988354\pi$
$710$	5.51424	−	42.2795i	0.206946	−	1.58672i
$711$	20.5578			0.770979
$712$	8.49005	+	3.48070i	0.318178	+	0.130445i
$713$	6.38753			0.239215
$714$	1.58473	−	12.1507i	0.0593072	−	0.454727i
$715$		−	30.8006i		−	1.15188i
$716$	−10.1404	+	38.2136i	−0.378965	+	1.42811i
$717$			0.723897i			0.0270344i
$718$	8.84602	+	1.15373i	0.330130	+	0.0430568i
$719$	10.0969			0.376553			0.188276	−	0.982116i	$-0.439710\pi$
$719$	10.0969			0.376553			0.188276	+	0.982116i	$0.439710\pi$
$720$	−18.4165	+	32.2573i	−0.686343	+	1.20216i
$721$	−54.0825			−2.01414
$722$	1.40234	+	0.182898i	0.0521896	+	0.00680675i
$723$		−	8.72850i		−	0.324616i
$724$	4.48691	−	16.9087i	0.166755	−	0.628406i
$725$		−	26.0934i		−	0.969083i
$726$	1.14296	−	8.76344i	0.0424192	−	0.325242i
$727$	22.5683			0.837011			0.418505	−	0.908214i	$-0.362554\pi$
$727$	22.5683			0.837011			0.418505	+	0.908214i	$0.362554\pi$
$728$	−6.83016	+	16.6600i	−0.253142	+	0.617460i
$729$	−4.01030			−0.148530
$730$	6.81742	−	52.2713i	0.252324	−	1.93465i
$731$			0.693869i			0.0256637i
$732$	−24.9018	−	6.60798i	−0.920399	−	0.244238i
$733$			26.6129i			0.982968i	0.870887	+	0.491484i	$0.163545\pi$
$733$			26.6129i			0.982968i	−0.870887	+	0.491484i	$0.836455\pi$
$734$	24.7759	+	3.23137i	0.914496	+	0.119272i
$735$	20.1036			0.741531
$736$	−12.3589	−	9.36524i	−0.455554	−	0.345207i
$737$	−56.9980			−2.09955
$738$	9.19793	+	1.19963i	0.338581	+	0.0441589i
$739$			31.7755i			1.16888i	0.811436	+	0.584441i	$0.198686\pi$
$739$			31.7755i			1.16888i	−0.811436	+	0.584441i	$0.801314\pi$
$740$	63.0999	+	16.7443i	2.31960	+	0.615531i
$741$		−	1.48912i		−	0.0547041i
$742$	−5.32404	+	40.8211i	−0.195452	+	1.49859i
$743$	5.02428			0.184323			0.0921615	−	0.995744i	$-0.470622\pi$
$743$	5.02428			0.184323			0.0921615	+	0.995744i	$0.470622\pi$
$744$	−2.10117	+	5.12513i	−0.0770326	+	0.187896i
$745$	−45.0892			−1.65194
$746$	1.73820	−	13.3274i	0.0636401	−	0.487949i
$747$		−	4.46838i		−	0.163489i
$748$	−6.32020	+	23.8174i	−0.231090	+	0.870849i
$749$			27.6539i			1.01045i
$750$	30.4935	+	3.97707i	1.11346	+	0.145222i
$751$	0.0361898			0.00132058			0.000660292	−	1.00000i	$-0.499790\pi$
$751$	0.0361898			0.00132058			0.000660292		1.00000i	$0.499790\pi$
$752$	−0.666930	−	0.380767i	−0.0243204	−	0.0138851i
$753$	−14.1176			−0.514474
$754$	5.69190	+	0.742359i	0.207287	+	0.0270351i
$755$		−	37.5081i		−	1.36506i
$756$	−8.19947	+	30.8993i	−0.298212	+	1.12380i
$757$		−	35.1099i		−	1.27609i	−0.769999	−	0.638045i	$-0.779743\pi$
$757$		−	35.1099i		−	1.27609i	0.769999	−	0.638045i	$-0.220257\pi$
$758$	−3.62926	+	27.8267i	−0.131821	+	1.01071i
$759$	9.89162			0.359043
$760$	−10.5952	−	4.34375i	−0.384328	−	0.157564i
$761$	−21.2359			−0.769800			−0.384900	−	0.922958i	$-0.625764\pi$
$761$	−21.2359			−0.769800			−0.384900	+	0.922958i	$0.625764\pi$
$762$	1.85112	−	14.1932i	0.0670591	−	0.514164i
$763$			11.5167i			0.416933i
$764$	−21.1648	−	5.61632i	−0.765717	−	0.203191i
$765$			26.6467i			0.963413i
$766$	−2.01000	−	0.262152i	−0.0726244	−	0.00947194i
$767$	7.73590			0.279327
$768$	11.5798	−	6.83566i	0.417850	−	0.246661i
$769$	−45.2697			−1.63247			−0.816233	−	0.577722i	$-0.803942\pi$
$769$	−45.2697			−1.63247			−0.816233	+	0.577722i	$0.803942\pi$
$770$	−87.5828	−	11.4229i	−3.15627	−	0.411652i
$771$			17.5417i			0.631749i
$772$	−19.2327	−	5.10361i	−0.692200	−	0.183683i
$773$			16.7218i			0.601441i	0.953712	+	0.300721i	$0.0972271\pi$
$773$			16.7218i			0.601441i	−0.953712	+	0.300721i	$0.902773\pi$
$774$	0.101440	−	0.777772i	0.00364618	−	0.0279565i
$775$	−26.5430			−0.953451
$776$	−46.3095	−	18.9857i	−1.66241	−	0.681545i
$777$	24.3451			0.873377
$778$	−0.131104	+	1.00522i	−0.00470032	+	0.0360389i
$779$			2.85960i			0.102456i
$780$	−3.09257	+	11.6542i	−0.110732	+	0.417288i
$781$			31.9748i			1.14415i
$782$	−11.0306	−	1.43865i	−0.394454	−	0.0514461i
$783$	10.1914			0.364211
$784$	20.5243	+	11.7178i	0.733010	+	0.418494i
$785$	45.3035			1.61695
$786$	2.61565	+	0.341142i	0.0932971	+	0.0121681i
$787$			21.8519i			0.778937i	0.921040	+	0.389468i	$0.127341\pi$
$787$			21.8519i			0.778937i	−0.921040	+	0.389468i	$0.872659\pi$
$788$	5.12677	−	19.3200i	0.182634	−	0.688245i
$789$		−	19.3606i		−	0.689255i
$790$	6.63671	−	50.8858i	0.236123	−	1.81043i
$791$	47.4261			1.68628
$792$	10.5664	−	25.7734i	0.375461	−	0.915818i
$793$	27.1585			0.964428
$794$	−5.18427	+	39.7495i	−0.183983	+	1.41066i
$795$			27.5674i			0.977716i
$796$	16.5858	+	4.40122i	0.587867	+	0.155997i
$797$		−	32.9426i		−	1.16689i	−0.812154	−	0.583443i	$-0.801705\pi$
$797$		−	32.9426i		−	1.16689i	0.812154	−	0.583443i	$-0.198295\pi$
$798$	−4.23438	−	0.552263i	−0.149895	−	0.0195499i
$799$	−0.550929			−0.0194905
$800$	51.3566	+	38.9167i	1.81573	+	1.37591i
$801$	−7.44105			−0.262917
$802$	17.5003	+	2.28246i	0.617959	+	0.0805964i
$803$			39.5313i			1.39503i
$804$	21.5667	+	5.72297i	0.760600	+	0.201834i
$805$		−	39.8725i		−	1.40532i
$806$	0.755150	−	5.78998i	0.0265990	−	0.203943i
$807$	−8.82643			−0.310705
$808$	0.600048	−	1.46363i	0.0211096	−	0.0514902i
$809$	48.5465			1.70680			0.853402	−	0.521253i	$-0.174535\pi$
$809$	48.5465			1.70680			0.853402	+	0.521253i	$0.174535\pi$
$810$	2.32657	−	17.8386i	0.0817475	−	0.626784i
$811$		−	51.3558i		−	1.80335i	−0.432419	−	0.901673i	$-0.642340\pi$
$811$		−	51.3558i		−	1.80335i	0.432419	−	0.901673i	$-0.357660\pi$
$812$	4.22186	−	15.9099i	0.148158	−	0.558327i
$813$			9.62104i			0.337425i
$814$	−48.5464	−	6.33160i	−1.70155	−	0.221922i
$815$	−65.5874			−2.29743
$816$	4.78283	−	8.37735i	0.167433	−	0.293266i
$817$	0.241806			0.00845972
$818$	48.0681	+	6.26922i	1.68066	+	0.219198i
$819$		−	14.6015i		−	0.510219i
$820$	5.93876	−	22.3799i	0.207391	−	0.781541i
$821$			21.7904i			0.760488i	0.924886	+	0.380244i	$0.124160\pi$
$821$			21.7904i			0.760488i	−0.924886	+	0.380244i	$0.875840\pi$
$822$	−1.09822	+	8.42037i	−0.0383047	+	0.293694i
$823$	10.1987			0.355505			0.177752	−	0.984075i	$-0.443117\pi$
$823$	10.1987			0.355505			0.177752	+	0.984075i	$0.443117\pi$
$824$	−39.3939	−	16.1505i	−1.37235	−	0.562628i
$825$	−41.1040			−1.43106
$826$	2.86898	−	21.9974i	0.0998246	−	0.765388i
$827$		−	44.9735i		−	1.56388i	−0.623352	−	0.781942i	$-0.714229\pi$
$827$		−	44.9735i		−	1.56388i	0.623352	−	0.781942i	$-0.285771\pi$
$828$	12.1541	+	3.22523i	0.422385	+	0.112085i
$829$			34.9629i			1.21431i	0.794583	+	0.607156i	$0.207690\pi$
$829$			34.9629i			1.21431i	−0.794583	+	0.607156i	$0.792310\pi$
$830$	−11.0604	−	1.44253i	−0.383911	−	0.0500710i
$831$	20.3299			0.705235
$832$	−9.95022	+	10.0955i	−0.344962	+	0.350000i
$833$	16.9544			0.587436
$834$	−7.95393	−	1.03738i	−0.275422	−	0.0359216i
$835$		−	47.9865i		−	1.66064i
$836$	8.30010	+	2.20252i	0.287065	+	0.0761759i
$837$		−	10.3670i		−	0.358337i
$838$	−6.72988	+	51.6001i	−0.232480	+	1.78250i
$839$	49.9301			1.72378			0.861889	−	0.507098i	$-0.169282\pi$
$839$	49.9301			1.72378			0.861889	+	0.507098i	$0.169282\pi$
$840$	31.9924	+	13.1160i	1.10384	+	0.452546i
$841$	23.7525			0.819052
$842$	3.00807	−	23.0638i	0.103665	−	0.794832i
$843$			1.25075i			0.0430782i
$844$	11.6516	−	43.9084i	0.401064	−	1.51139i
$845$			39.9208i			1.37332i
$846$	0.617547	+	0.0805428i	0.0212317	+	0.00276912i
$847$	26.7152			0.917945
$848$	−16.0683	+	28.1444i	−0.551788	+	0.966482i
$849$	9.86081			0.338422
$850$	45.8370	+	5.97823i	1.57220	+	0.205052i
$851$		−	22.1010i		−	0.757613i
$852$	3.21047	−	12.0985i	0.109989	−	0.414488i
$853$			27.5836i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$853$			27.5836i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$854$	10.0722	−	77.2265i	0.344662	−	2.64264i
$855$	9.28609			0.317578
$856$	−8.25818	+	20.1432i	−0.282259	+	0.688481i
$857$	11.7397			0.401021			0.200510	−	0.979692i	$-0.435740\pi$
$857$	11.7397			0.401021			0.200510	+	0.979692i	$0.435740\pi$
$858$	1.16941	−	8.96626i	0.0399231	−	0.306103i
$859$		−	14.0409i		−	0.479070i	−0.970888	−	0.239535i	$-0.923005\pi$
$859$		−	14.0409i		−	0.479070i	0.970888	−	0.239535i	$-0.0769950\pi$
$860$	−1.89243	−	0.502178i	−0.0645315	−	0.0171241i
$861$		−	8.63460i		−	0.294266i
$862$	−56.6003	−	7.38201i	−1.92781	−	0.251432i
$863$	−9.95337			−0.338817			−0.169408	−	0.985546i	$-0.554186\pi$
$863$	−9.95337			−0.338817			−0.169408	+	0.985546i	$0.554186\pi$
$864$	−15.1999	+	20.0586i	−0.517110	+	0.682407i
$865$	2.93718			0.0998672
$866$	−52.1091	−	6.79626i	−1.77074	−	0.230946i
$867$			7.36703i			0.250198i
$868$	−16.1840	−	4.29461i	−0.549321	−	0.145768i
$869$			38.4834i			1.30546i
$870$	1.42556	−	10.9302i	0.0483310	−	0.370569i
$871$	−23.5212			−0.796984
$872$	−3.43920	+	8.38882i	−0.116466	+	0.284081i
$873$	40.5876			1.37368
$874$	−0.501355	+	3.84405i	−0.0169586	+	0.130027i
$875$			92.9590i			3.14259i
$876$	3.96920	−	14.9577i	0.134107	−	0.505375i
$877$			11.6328i			0.392811i	0.980523	+	0.196405i	$0.0629268\pi$
$877$			11.6328i			0.392811i	−0.980523	+	0.196405i	$0.937073\pi$
$878$	−15.2508	−	1.98907i	−0.514691	−	0.0671279i
$879$	0.437434			0.0147543
$880$	−60.3845	−	34.4750i	−2.03556	−	1.16215i
$881$	6.68746			0.225306			0.112653	−	0.993634i	$-0.464065\pi$
$881$	6.68746			0.225306			0.112653	+	0.993634i	$0.464065\pi$
$882$	−19.0046	−	2.47864i	−0.639917	−	0.0834603i
$883$		−	33.4677i		−	1.12628i	−0.826362	−	0.563139i	$-0.809593\pi$
$883$		−	33.4677i		−	1.12628i	0.826362	−	0.563139i	$-0.190407\pi$
$884$	−2.60814	+	9.82863i	−0.0877211	+	0.330572i
$885$		−	14.8553i		−	0.499357i
$886$	5.72855	−	43.9226i	0.192454	−	1.47561i
$887$	−40.8377			−1.37120			−0.685598	−	0.727981i	$-0.740459\pi$
$887$	−40.8377			−1.37120			−0.685598	+	0.727981i	$0.740459\pi$
$888$	17.7331	+	7.27010i	0.595084	+	0.243969i
$889$	43.2676			1.45115
$890$	−2.40220	+	18.4185i	−0.0805220	+	0.617388i
$891$			13.4908i			0.451959i
$892$	−30.9688	−	8.21792i	−1.03691	−	0.275156i
$893$			0.191993i			0.00642479i
$894$	−13.1258	−	1.71191i	−0.438992	−	0.0572549i
$895$	−80.0321			−2.67518
$896$	25.0169	+	32.0380i	0.835757	+	1.07031i
$897$	4.08194			0.136292
$898$	24.8366	+	3.23929i	0.828810	+	0.108096i
$899$			5.33792i			0.178030i
$900$	−50.5057	−	13.4023i	−1.68352	−	0.446742i
$901$			23.2491i			0.774540i
$902$	−2.24566	+	17.2182i	−0.0747722	+	0.573302i
$903$	−0.730137			−0.0242974
$904$	34.5453	+	14.1627i	1.14896	+	0.471044i
$905$	35.4125			1.17715
$906$	1.42408	−	10.9189i	0.0473118	−	0.362755i
$907$			46.4030i			1.54079i	0.637569	+	0.770393i	$0.279940\pi$
$907$			46.4030i			1.54079i	−0.637569	+	0.770393i	$0.720060\pi$
$908$	0.698338	−	2.63165i	0.0231752	−	0.0873345i
$909$			1.28279i			0.0425473i
$910$	−36.1425	−	4.71383i	−1.19811	−	0.156262i
$911$	−18.5958			−0.616105			−0.308053	−	0.951369i	$-0.599677\pi$
$911$	−18.5958			−0.616105			−0.308053	+	0.951369i	$0.599677\pi$
$912$	−2.91942	−	1.66677i	−0.0966715	−	0.0551922i
$913$	8.36463			0.276829
$914$	18.0228	+	2.35060i	0.596141	+	0.0777508i
$915$		−	52.1528i		−	1.72412i
$916$	−5.50863	+	20.7590i	−0.182010	+	0.685896i
$917$			7.97376i			0.263317i
$918$	−2.33495	+	17.9028i	−0.0770648	+	0.590880i
$919$	28.2952			0.933373			0.466686	−	0.884423i	$-0.345448\pi$
$919$	28.2952			0.933373			0.466686	+	0.884423i	$0.345448\pi$
$920$	11.9070	−	29.0433i	0.392562	−	0.957529i
$921$	−9.69473			−0.319452
$922$	3.72420	−	28.5547i	0.122650	−	0.940398i
$923$			13.1949i			0.434316i
$924$	−25.0623	−	6.65056i	−0.824489	−	0.218787i
$925$			91.8394i			3.01966i
$926$	−29.2129	−	3.81005i	−0.959994	−	0.125206i
$927$	34.5265			1.13400
$928$	7.82633	−	10.3281i	0.256912	−	0.339035i
$929$	23.7582			0.779481			0.389740	−	0.920925i	$-0.372565\pi$
$929$	23.7582			0.779481			0.389740	+	0.920925i	$0.372565\pi$
$930$	−11.1186	−	1.45012i	−0.364592	−	0.0475514i
$931$		−	5.90844i		−	0.193641i
$932$	28.0015	+	7.43051i	0.917219	+	0.243394i
$933$			19.5040i			0.638533i
$934$	2.58037	−	19.7846i	0.0844324	−	0.647371i
$935$	−49.8816			−1.63130
$936$	4.36040	−	10.6358i	0.142524	−	0.347643i
$937$	−27.4926			−0.898145			−0.449073	−	0.893495i	$-0.648246\pi$
$937$	−27.4926			−0.898145			−0.449073	+	0.893495i	$0.648246\pi$
$938$	−8.72319	+	66.8835i	−0.284822	+	2.18382i
$939$		−	0.777337i		−	0.0253674i
$940$	0.398727	−	1.50258i	0.0130050	−	0.0490089i
$941$		−	24.8654i		−	0.810590i	−0.914186	−	0.405295i	$-0.867169\pi$
$941$		−	24.8654i		−	0.810590i	0.914186	−	0.405295i	$-0.132831\pi$
$942$	13.1882	+	1.72005i	0.429694	+	0.0560422i
$943$	−7.83866			−0.255262
$944$	8.65878	−	15.1662i	0.281819	−	0.493619i
$945$	−64.7135			−2.10513
$946$	1.45596	+	0.189892i	0.0473373	+	0.00617391i
$947$		−	32.8465i		−	1.06737i	−0.845684	−	0.533684i	$-0.820807\pi$
$947$		−	32.8465i		−	1.06737i	0.845684	−	0.533684i	$-0.179193\pi$
$948$	3.86399	−	14.5612i	0.125496	−	0.472927i
$949$			16.3132i			0.529550i
$950$	2.08335	−	15.9737i	0.0675928	−	0.518256i
$951$	−12.1798			−0.394958
$952$	26.9809	+	11.0615i	0.874456	+	0.358504i
$953$	18.9330			0.613301			0.306650	−	0.951822i	$-0.400792\pi$
$953$	18.9330			0.613301			0.306650	+	0.951822i	$0.400792\pi$
$954$	3.39889	−	26.0604i	0.110043	−	0.843737i
$955$		−	44.3263i		−	1.43436i
$956$	−1.66506	−	0.441842i	−0.0538519	−	0.0142902i
$957$			8.26621i			0.267209i
$958$	−5.02729	−	0.655678i	−0.162424	−	0.0211840i
$959$	−25.6694			−0.828907
$960$	19.3866	+	19.1075i	0.625699	+	0.616693i
$961$	−25.5701			−0.824842
$962$	−20.0335	−	2.61284i	−0.645905	−	0.0842413i
$963$		−	17.6544i		−	0.568905i
$964$	20.0767	+	5.32758i	0.646627	+	0.171590i
$965$		−	40.2797i		−	1.29665i
$966$	1.51385	−	11.6072i	0.0487073	−	0.373455i
$967$	49.1555			1.58073			0.790367	−	0.612634i	$-0.209890\pi$
$967$	49.1555			1.58073			0.790367	+	0.612634i	$0.209890\pi$
$968$	19.4595	+	7.97786i	0.625451	+	0.256418i
$969$	−2.41163			−0.0774727
$970$	13.1030	−	100.465i	0.420711	−	3.22572i
$971$		−	32.1742i		−	1.03252i	−0.856432	−	0.516260i	$-0.827324\pi$
$971$		−	32.1742i		−	1.03252i	0.856432	−	0.516260i	$-0.172676\pi$
$972$	8.20109	−	30.9054i	0.263050	−	0.991291i
$973$		−	24.2474i		−	0.777338i
$974$	31.5612	+	4.11633i	1.01129	+	0.131896i
$975$	−16.9622			−0.543226
$976$	30.3985	−	53.2443i	0.973032	−	1.70431i
$977$	−53.1734			−1.70117			−0.850583	−	0.525840i	$-0.823751\pi$
$977$	−53.1734			−1.70117			−0.850583	+	0.525840i	$0.823751\pi$
$978$	−19.0930	−	2.49017i	−0.610526	−	0.0796270i
$979$		−	13.9294i		−	0.445184i
$980$	−12.2705	+	46.2409i	−0.391968	+	1.47711i
$981$		−	7.35233i		−	0.234742i
$982$	0.939536	−	7.20373i	0.0299818	−	0.229880i
$983$	24.9473			0.795696			0.397848	−	0.917451i	$-0.369757\pi$
$983$	24.9473			0.795696			0.397848	+	0.917451i	$0.369757\pi$
$984$	2.57852	−	6.28948i	0.0822002	−	0.200501i
$985$	40.4625			1.28924
$986$	1.20225	−	9.21805i	0.0382875	−	0.293562i
$987$		−	0.579725i		−	0.0184529i
$988$	3.42517	+	0.908908i	0.108969	+	0.0289162i
$989$			0.662833i			0.0210769i
$990$	55.9133	+	7.29241i	1.77704	+	0.231768i
$991$	0.298799			0.00949166			0.00474583	−	0.999989i	$-0.498489\pi$
$991$	0.298799			0.00949166			0.00474583	+	0.999989i	$0.498489\pi$
$992$	−10.5060	−	7.96118i	−0.333566	−	0.252768i
$993$	−15.7863			−0.500962
$994$	37.5203	+	4.89354i	1.19007	+	0.155214i
$995$			34.7362i			1.10121i
$996$	−3.16498	−	0.839862i	−0.100286	−	0.0266121i
$997$		−	16.5705i		−	0.524793i	−0.964960	−	0.262396i	$-0.915487\pi$
$997$		−	16.5705i		−	0.524793i	0.964960	−	0.262396i	$-0.0845128\pi$
$998$	−2.94568	+	22.5855i	−0.0932439	+	0.714931i
$999$	−35.8702			−1.13488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.1	✓	16
3.2	odd	2		1368.2.g.b.685.16		16
4.3	odd	2		608.2.c.b.305.10		16
8.3	odd	2		608.2.c.b.305.7		16
8.5	even	2	inner	152.2.c.b.77.2	yes	16
12.11	even	2		5472.2.g.b.2737.1		16
16.3	odd	4		4864.2.a.bp.1.4		8
16.5	even	4		4864.2.a.bo.1.4		8
16.11	odd	4		4864.2.a.bn.1.5		8
16.13	even	4		4864.2.a.bq.1.5		8
24.5	odd	2		1368.2.g.b.685.15		16
24.11	even	2		5472.2.g.b.2737.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.1	✓	16	1.1	even	1	trivial
152.2.c.b.77.2	yes	16	8.5	even	2	inner
608.2.c.b.305.7		16	8.3	odd	2
608.2.c.b.305.10		16	4.3	odd	2
1368.2.g.b.685.15		16	24.5	odd	2
1368.2.g.b.685.16		16	3.2	odd	2
4864.2.a.bn.1.5		8	16.11	odd	4
4864.2.a.bo.1.4		8	16.5	even	4
4864.2.a.bp.1.4		8	16.3	odd	4
4864.2.a.bq.1.5		8	16.13	even	4
5472.2.g.b.2737.1		16	12.11	even	2
5472.2.g.b.2737.16		16	24.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40234 - 0.182898i) q^{2} -0.840428i q^{3} +(1.93310 + 0.512969i) q^{4} +4.04855i q^{5} +(-0.153712 + 1.17856i) q^{6} -3.59283 q^{7} +(-2.61703 - 1.07291i) q^{8} +2.29368 q^{9} +(0.740472 - 5.67744i) q^{10} +4.29368i q^{11} +(0.431113 - 1.62463i) q^{12} +1.77186i q^{13} +(5.03836 + 0.657121i) q^{14} +3.40252 q^{15} +(3.47373 + 1.98324i) q^{16} +2.86953 q^{17} +(-3.21651 - 0.419509i) q^{18} -1.00000i q^{19} +(-2.07678 + 7.82625i) q^{20} +3.01952i q^{21} +(0.785305 - 6.02119i) q^{22} +2.74118 q^{23} +(-0.901707 + 2.19943i) q^{24} -11.3908 q^{25} +(0.324069 - 2.48474i) q^{26} -4.44896i q^{27} +(-6.94529 - 1.84301i) q^{28} +2.29074i q^{29} +(-4.77148 - 0.622313i) q^{30} +2.33021 q^{31} +(-4.50860 - 3.41650i) q^{32} +3.60853 q^{33} +(-4.02404 - 0.524830i) q^{34} -14.5458i q^{35} +(4.43391 + 1.17659i) q^{36} -8.06260i q^{37} +(-0.182898 + 1.40234i) q^{38} +1.48912 q^{39} +(4.34375 - 10.5952i) q^{40} -2.85960 q^{41} +(0.552263 - 4.23438i) q^{42} +0.241806i q^{43} +(-2.20252 + 8.30010i) q^{44} +9.28609i q^{45} +(-3.84405 - 0.501355i) q^{46} -0.191993 q^{47} +(1.66677 - 2.91942i) q^{48} +5.90844 q^{49} +(15.9737 + 2.08335i) q^{50} -2.41163i q^{51} +(-0.908908 + 3.42517i) q^{52} +8.10207i q^{53} +(-0.813705 + 6.23894i) q^{54} -17.3832 q^{55} +(9.40255 + 3.85480i) q^{56} -0.840428 q^{57} +(0.418972 - 3.21239i) q^{58} -4.36599i q^{59} +(6.57740 + 1.74539i) q^{60} -15.3277i q^{61} +(-3.26774 - 0.426191i) q^{62} -8.24081 q^{63} +(5.69771 + 5.61570i) q^{64} -7.17346 q^{65} +(-5.06037 - 0.659992i) q^{66} +13.2749i q^{67} +(5.54707 + 1.47198i) q^{68} -2.30376i q^{69} +(-2.66039 + 20.3981i) q^{70} +7.44693 q^{71} +(-6.00264 - 2.46092i) q^{72} +9.20686 q^{73} +(-1.47463 + 11.3065i) q^{74} +9.57314i q^{75} +(0.512969 - 1.93310i) q^{76} -15.4265i q^{77} +(-2.08825 - 0.272357i) q^{78} +8.96281 q^{79} +(-8.02924 + 14.0636i) q^{80} +3.14202 q^{81} +(4.01012 + 0.523014i) q^{82} -1.94813i q^{83} +(-1.54892 + 5.83702i) q^{84} +11.6174i q^{85} +(0.0442258 - 0.339094i) q^{86} +1.92520 q^{87} +(4.60675 - 11.2367i) q^{88} -3.24415 q^{89} +(1.69841 - 13.0222i) q^{90} -6.36599i q^{91} +(5.29896 + 1.40614i) q^{92} -1.95838i q^{93} +(0.269239 + 0.0351151i) q^{94} +4.04855 q^{95} +(-2.87132 + 3.78916i) q^{96} +17.6954 q^{97} +(-8.28562 - 1.08064i) q^{98} +9.84833i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more