LMFDB - Embedded newform 680.2.h.c.509.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.11
Character	$\chi$	$=$	680.509
Dual form			680.2.h.c.509.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.909039 - 1.08335i) q^{2} +1.45525i q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.747066 - 2.10758i) q^{5} +(1.57654 - 1.32288i) q^{6} +4.94720 q^{7} +(2.44949 - 1.41421i) q^{8} +0.882256 q^{9} +(-2.96236 + 1.10654i) q^{10} -4.73901 q^{11} +(-2.86628 - 0.505402i) q^{12} +2.44949 q^{13} +(-4.49720 - 5.35955i) q^{14} +(3.06705 + 1.08717i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(3.07637 - 2.74517i) q^{17} +(-0.802005 - 0.955793i) q^{18} -2.57115i q^{19} +(3.89167 + 2.20339i) q^{20} +7.19939i q^{21} +(4.30795 + 5.13401i) q^{22} -5.78168 q^{23} +(2.05803 + 3.56461i) q^{24} +(-3.88378 - 3.14900i) q^{25} +(-2.22668 - 2.65366i) q^{26} +5.64964i q^{27} +(-1.71814 + 9.74408i) q^{28} +5.76104 q^{29} +(-1.61029 - 4.31096i) q^{30} +6.40633i q^{31} +(1.93476 + 5.31570i) q^{32} -6.89643i q^{33} +(-5.77052 - 0.837319i) q^{34} +(3.69588 - 10.4266i) q^{35} +(-0.306404 + 1.73771i) q^{36} -2.99523i q^{37} +(-2.78546 + 2.33728i) q^{38} +3.56461i q^{39} +(-1.15064 - 6.21901i) q^{40} +1.53509i q^{41} +(7.79947 - 6.54453i) q^{42} +1.18389 q^{43} +(1.64584 - 9.33403i) q^{44} +(0.659104 - 1.85943i) q^{45} +(5.25577 + 6.26359i) q^{46} -12.1672i q^{47} +(1.99090 - 5.46994i) q^{48} +17.4748 q^{49} +(0.119037 + 7.07007i) q^{50} +(3.99490 + 4.47688i) q^{51} +(-0.850699 + 4.82455i) q^{52} +3.30819 q^{53} +(6.12054 - 5.13574i) q^{54} +(-3.54036 + 9.98784i) q^{55} +(12.1181 - 6.99639i) q^{56} +3.74166 q^{57} +(-5.23701 - 6.24123i) q^{58} -0.471202i q^{59} +(-3.20647 + 5.66334i) q^{60} -3.52280 q^{61} +(6.94030 - 5.82360i) q^{62} +4.36470 q^{63} +(4.00000 - 6.92820i) q^{64} +(1.82993 - 5.16249i) q^{65} +(-7.47125 + 6.26913i) q^{66} +14.2350 q^{67} +(4.33852 + 7.01265i) q^{68} -8.41377i q^{69} +(-14.6554 + 5.47426i) q^{70} +3.40562i q^{71} +(2.16108 - 1.24770i) q^{72} +2.04886 q^{73} +(-3.24488 + 2.72278i) q^{74} +(4.58258 - 5.65186i) q^{75} +(5.06418 + 0.892951i) q^{76} -23.4448 q^{77} +(3.86172 - 3.24037i) q^{78} +11.5822i q^{79} +(-5.69139 + 6.89986i) q^{80} -5.57485 q^{81} +(1.66304 - 1.39546i) q^{82} -8.53610 q^{83} +(-14.1800 - 2.50032i) q^{84} +(-3.48741 - 8.53452i) q^{85} +(-1.07620 - 1.28257i) q^{86} +8.38374i q^{87} +(-11.6082 + 6.70197i) q^{88} -2.93764 q^{89} +(-2.61356 + 0.976250i) q^{90} +12.1181 q^{91} +(2.00796 - 11.3877i) q^{92} -9.32279 q^{93} +(-13.1814 + 11.0605i) q^{94} +(-5.41890 - 1.92082i) q^{95} +(-7.73566 + 2.81555i) q^{96} -5.58663 q^{97} +(-15.8852 - 18.9313i) q^{98} -4.18102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) $ 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$3$			1.45525i			0.840187i	0.907481	+	0.420094i	$0.138003\pi$
$3$			1.45525i			0.840187i	−0.907481	+	0.420094i	$0.861997\pi$
$4$	−0.347296	+	1.96962i	−0.173648	+	0.984808i
$5$	0.747066	−	2.10758i	0.334098	−	0.942538i
$5$	0.747066	−	2.10758i	0.334098	−	0.942538i
$6$	1.57654	−	1.32288i	0.643621	−	0.540062i
$7$	4.94720			1.86987			0.934933	−	0.354826i	$-0.115460\pi$
$7$	4.94720			1.86987			0.934933	+	0.354826i	$0.115460\pi$
$8$	2.44949	−	1.41421i	0.866025	−	0.500000i
$9$	0.882256			0.294085
$10$	−2.96236	+	1.10654i	−0.936780	+	0.349918i
$11$	−4.73901			−1.42887			−0.714433	−	0.699704i	$-0.753315\pi$
$11$	−4.73901			−1.42887			−0.714433	+	0.699704i	$0.753315\pi$
$12$	−2.86628	−	0.505402i	−0.827423	−	0.145897i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	−4.49720	−	5.35955i	−1.20193	−	1.43240i
$15$	3.06705	+	1.08717i	0.791909	+	0.280705i
$16$	−3.75877	−	1.36808i	−0.939693	−	0.342020i
$17$	3.07637	−	2.74517i	0.746129	−	0.665801i
$17$	3.07637	−	2.74517i	0.746129	−	0.665801i
$18$	−0.802005	−	0.955793i	−0.189034	−	0.225283i
$19$		−	2.57115i		−	0.589862i	−0.955518	−	0.294931i	$-0.904703\pi$
$19$		−	2.57115i		−	0.589862i	0.955518	−	0.294931i	$-0.0952967\pi$
$20$	3.89167	+	2.20339i	0.870203	+	0.492693i
$21$			7.19939i			1.57104i
$22$	4.30795	+	5.13401i	0.918457	+	1.09457i
$23$	−5.78168			−1.20556			−0.602782	−	0.797906i	$-0.705941\pi$
$23$	−5.78168			−1.20556			−0.602782	+	0.797906i	$0.705941\pi$
$24$	2.05803	+	3.56461i	0.420094	+	0.727623i
$25$	−3.88378	−	3.14900i	−0.776757	−	0.629801i
$26$	−2.22668	−	2.65366i	−0.436688	−	0.520425i
$27$			5.64964i			1.08727i
$28$	−1.71814	+	9.74408i	−0.324699	+	1.84146i
$29$	5.76104			1.06980			0.534899	−	0.844916i	$-0.320350\pi$
$29$	5.76104			1.06980			0.534899	+	0.844916i	$0.320350\pi$
$30$	−1.61029	−	4.31096i	−0.293997	−	0.787071i
$31$			6.40633i			1.15061i	0.817939	+	0.575305i	$0.195117\pi$
$31$			6.40633i			1.15061i	−0.817939	+	0.575305i	$0.804883\pi$
$32$	1.93476	+	5.31570i	0.342020	+	0.939693i
$33$		−	6.89643i		−	1.20051i
$34$	−5.77052	−	0.837319i	−0.989636	−	0.143599i
$35$	3.69588	−	10.4266i	0.624719	−	1.76242i
$36$	−0.306404	+	1.73771i	−0.0510674	+	0.289618i
$37$		−	2.99523i		−	0.492412i	−0.969218	−	0.246206i	$-0.920816\pi$
$37$		−	2.99523i		−	0.492412i	0.969218	−	0.246206i	$-0.0791840\pi$
$38$	−2.78546	+	2.33728i	−0.451861	+	0.379156i
$39$			3.56461i			0.570795i
$40$	−1.15064	−	6.21901i	−0.181932	−	0.983311i
$41$			1.53509i			0.239741i	0.992790	+	0.119870i	$0.0382479\pi$
$41$			1.53509i			0.239741i	−0.992790	+	0.119870i	$0.961752\pi$
$42$	7.79947	−	6.54453i	1.20348	−	1.00984i
$43$	1.18389			0.180541			0.0902707	−	0.995917i	$-0.471227\pi$
$43$	1.18389			0.180541			0.0902707	+	0.995917i	$0.471227\pi$
$44$	1.64584	−	9.33403i	0.248120	−	1.40716i
$45$	0.659104	−	1.85943i	0.0982534	−	0.277187i
$46$	5.25577	+	6.26359i	0.774922	+	0.923516i
$47$		−	12.1672i		−	1.77477i	−0.461025	−	0.887387i	$-0.652518\pi$
$47$		−	12.1672i		−	1.77477i	0.461025	−	0.887387i	$-0.347482\pi$
$48$	1.99090	−	5.46994i	0.287361	−	0.789518i
$49$	17.4748			2.49640
$50$	0.119037	+	7.07007i	0.0168343	+	0.999858i
$51$	3.99490	+	4.47688i	0.559398	+	0.626888i
$52$	−0.850699	+	4.82455i	−0.117971	+	0.669045i
$53$	3.30819			0.454414			0.227207	−	0.973846i	$-0.427041\pi$
$53$	3.30819			0.454414			0.227207	+	0.973846i	$0.427041\pi$
$54$	6.12054	−	5.13574i	0.832900	−	0.698886i
$55$	−3.54036	+	9.98784i	−0.477381	+	1.34676i
$56$	12.1181	−	6.99639i	1.61935	−	0.934933i
$57$	3.74166			0.495595
$58$	−5.23701	−	6.24123i	−0.687653	−	0.819513i
$59$		−	0.471202i		−	0.0613452i	−0.999529	−	0.0306726i	$-0.990235\pi$
$59$		−	0.471202i		−	0.0613452i	0.999529	−	0.0306726i	$-0.00976493\pi$
$60$	−3.20647	+	5.66334i	−0.413954	+	0.731134i
$61$	−3.52280			−0.451048			−0.225524	−	0.974238i	$-0.572409\pi$
$61$	−3.52280			−0.451048			−0.225524	+	0.974238i	$0.572409\pi$
$62$	6.94030	−	5.82360i	0.881418	−	0.739598i
$63$	4.36470			0.549900
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$	1.82993	−	5.16249i	0.226975	−	0.640329i
$66$	−7.47125	+	6.26913i	−0.919648	+	0.771676i
$67$	14.2350			1.73908			0.869540	−	0.493863i	$-0.164415\pi$
$67$	14.2350			1.73908			0.869540	+	0.493863i	$0.164415\pi$
$68$	4.33852	+	7.01265i	0.526123	+	0.850409i
$69$		−	8.41377i		−	1.01290i
$70$	−14.6554	+	5.47426i	−1.75165	+	0.654299i
$71$			3.40562i			0.404173i	0.979368	+	0.202086i	$0.0647722\pi$
$71$			3.40562i			0.404173i	−0.979368	+	0.202086i	$0.935228\pi$
$72$	2.16108	−	1.24770i	0.254685	−	0.147043i
$73$	2.04886			0.239800			0.119900	−	0.992786i	$-0.461743\pi$
$73$	2.04886			0.239800			0.119900	+	0.992786i	$0.461743\pi$
$74$	−3.24488	+	2.72278i	−0.377210	+	0.316516i
$75$	4.58258	−	5.65186i	0.529150	−	0.652621i
$76$	5.06418	+	0.892951i	0.580901	+	0.102429i
$77$	−23.4448			−2.67179
$78$	3.86172	−	3.24037i	0.437254	−	0.366900i
$79$			11.5822i			1.30309i	0.758608	+	0.651547i	$0.225880\pi$
$79$			11.5822i			1.30309i	−0.758608	+	0.651547i	$0.774120\pi$
$80$	−5.69139	+	6.89986i	−0.636317	+	0.771428i
$81$	−5.57485			−0.619428
$82$	1.66304	−	1.39546i	0.183652	−	0.154103i
$83$	−8.53610			−0.936959			−0.468479	−	0.883474i	$-0.655198\pi$
$83$	−8.53610			−0.936959			−0.468479	+	0.883474i	$0.655198\pi$
$84$	−14.1800	−	2.50032i	−1.54717	−	0.272808i
$85$	−3.48741	−	8.53452i	−0.378263	−	0.925698i
$86$	−1.07620	−	1.28257i	−0.116050	−	0.138303i
$87$			8.38374i			0.898831i
$88$	−11.6082	+	6.70197i	−1.23743	+	0.714433i
$89$	−2.93764			−0.311389			−0.155694	−	0.987805i	$-0.549762\pi$
$89$	−2.93764			−0.311389			−0.155694	+	0.987805i	$0.549762\pi$
$90$	−2.61356	+	0.976250i	−0.275493	+	0.102906i
$91$	12.1181			1.27032
$92$	2.00796	−	11.3877i	0.209344	−	1.18725i
$93$	−9.32279			−0.966728
$94$	−13.1814	+	11.0605i	−1.35956	+	1.14080i
$95$	−5.41890	−	1.92082i	−0.555968	−	0.197072i
$96$	−7.73566	+	2.81555i	−0.789518	+	0.287361i
$97$	−5.58663			−0.567236			−0.283618	−	0.958937i	$-0.591535\pi$
$97$	−5.58663			−0.567236			−0.283618	+	0.958937i	$0.591535\pi$
$98$	−15.8852	−	18.9313i	−1.60465	−	1.91235i
$99$	−4.18102			−0.420209
$100$	7.55115	−	6.55592i	0.755115	−	0.655592i
$101$			2.77372i			0.275996i	0.990433	+	0.137998i	$0.0440667\pi$
$101$			2.77372i			0.275996i	−0.990433	+	0.137998i	$0.955933\pi$
$102$	1.21851	−	8.39753i	0.120650	−	0.831479i
$103$		−	2.49275i		−	0.245618i	−0.992430	−	0.122809i	$-0.960810\pi$
$103$		−	2.49275i		−	0.245618i	0.992430	−	0.122809i	$-0.0391902\pi$
$104$	6.00000	−	3.46410i	0.588348	−	0.339683i
$105$	15.1733	+	5.37842i	1.48076	+	0.524881i
$106$	−3.00727	−	3.58392i	−0.292092	−	0.348102i
$107$			10.0490i			0.971475i	0.874105	+	0.485737i	$0.161449\pi$
$107$			10.0490i			0.971475i	−0.874105	+	0.485737i	$0.838551\pi$
$108$	−11.1276	−	1.96210i	−1.07076	−	0.188803i
$109$	−3.53991			−0.339062			−0.169531	−	0.985525i	$-0.554225\pi$
$109$	−3.53991			−0.339062			−0.169531	+	0.985525i	$0.554225\pi$
$110$	14.0387	−	5.24389i	1.33853	−	0.499986i
$111$	4.35879			0.413718
$112$	−18.5954	−	6.76817i	−1.75710	−	0.639532i
$113$	−3.49425			−0.328711			−0.164356	−	0.986401i	$-0.552554\pi$
$113$	−3.49425			−0.328711			−0.164356	+	0.986401i	$0.552554\pi$
$114$	−3.40131	−	4.05353i	−0.318562	−	0.379648i
$115$	−4.31930	+	12.1854i	−0.402777	+	1.13629i
$116$	−2.00079	+	11.3470i	−0.185769	+	1.05355i
$117$	2.16108			0.199792
$118$	−0.510476	+	0.428341i	−0.0469932	+	0.0394319i
$119$	15.2194	−	13.5809i	1.39516	−	1.24496i
$120$	9.05019	−	1.67446i	0.826165	−	0.152857i
$121$	11.4582			1.04166
$122$	3.20236	+	3.81642i	0.289928	+	0.345523i
$123$	−2.23394			−0.201427
$124$	−12.6180	−	2.22489i	−1.13313	−	0.199801i
$125$	−9.53822	+	5.83287i	−0.853124	+	0.521708i
$126$	−3.96768	−	4.72850i	−0.353469	−	0.421248i
$127$			17.7182i			1.57224i	0.618075	+	0.786119i	$0.287913\pi$
$127$			17.7182i			1.57224i	−0.618075	+	0.786119i	$0.712087\pi$
$128$	−11.1418	+	1.96460i	−0.984808	+	0.173648i
$129$			1.72285i			0.151689i
$130$	−7.25627	+	2.71045i	−0.636417	+	0.237722i
$131$	10.2738			0.897622			0.448811	−	0.893627i	$-0.351848\pi$
$131$	10.2738			0.897622			0.448811	+	0.893627i	$0.351848\pi$
$132$	13.5833	+	2.39511i	1.18228	+	0.208467i
$133$		−	12.7200i		−	1.10296i
$134$	−12.9402	−	15.4215i	−1.11786	−	1.33221i
$135$	11.9071	+	4.22066i	1.02480	+	0.363256i
$136$	3.65328	−	11.0749i	0.313266	−	0.949665i
$137$			7.60186i			0.649471i	0.945805	+	0.324735i	$0.105275\pi$
$137$			7.60186i			0.649471i	−0.945805	+	0.324735i	$0.894725\pi$
$138$	−9.11507	+	7.64845i	−0.775926	+	0.651079i
$139$	−7.84711			−0.665583			−0.332791	−	0.943000i	$-0.607991\pi$
$139$	−7.84711			−0.665583			−0.332791	+	0.943000i	$0.607991\pi$
$140$	19.2529	+	10.9006i	1.62716	+	0.921269i
$141$	17.7063			1.49114
$142$	3.68948	−	3.09584i	0.309614	−	0.259797i
$143$	−11.6082			−0.970723
$144$	−3.31620	−	1.20700i	−0.276350	−	0.100583i
$145$	4.30388	−	12.1419i	0.357418	−	1.00833i
$146$	−1.86249	−	2.21963i	−0.154141	−	0.183698i
$147$			25.4301i			2.09744i
$148$	5.89944	+	1.04023i	0.484931	+	0.0855065i
$149$			5.15361i			0.422200i	0.977464	+	0.211100i	$0.0677046\pi$
$149$			5.15361i			0.422200i	−0.977464	+	0.211100i	$0.932295\pi$
$150$	−10.2887	+	0.173228i	−0.840068	+	0.0141440i
$151$	5.88912			0.479250			0.239625	−	0.970866i	$-0.422976\pi$
$151$	5.88912			0.479250			0.239625	+	0.970866i	$0.422976\pi$
$152$	−3.63616	−	6.29801i	−0.294931	−	0.510836i
$153$	2.71415	−	2.42194i	0.219426	−	0.195803i
$154$	21.3123	+	25.3990i	1.71739	+	2.04671i
$155$	13.5018	+	4.78595i	1.08449	+	0.384417i
$156$	−7.02092	−	1.23798i	−0.562123	−	0.0991175i
$157$	−10.1419			−0.809414			−0.404707	−	0.914447i	$-0.632626\pi$
$157$	−10.1419			−0.809414			−0.404707	+	0.914447i	$0.632626\pi$
$158$	12.5475	−	10.5286i	0.998228	−	0.837613i
$159$			4.81423i			0.381793i
$160$	12.6487	−	0.106474i	0.999965	−	0.00841747i
$161$	−28.6031			−2.25424
$162$	5.06776	+	6.03952i	0.398161	+	0.474510i
$163$		−	17.9031i		−	1.40228i	−0.713024	−	0.701139i	$-0.752675\pi$
$163$		−	17.9031i		−	1.40228i	0.713024	−	0.701139i	$-0.247325\pi$
$164$	−3.02354	−	0.533132i	−0.236099	−	0.0416306i
$165$	−14.5348	−	5.15209i	−1.13153	−	0.401090i
$166$	7.75965	+	9.24759i	0.602265	+	0.717752i
$167$	−4.98132			−0.385466			−0.192733	−	0.981251i	$-0.561735\pi$
$167$	−4.98132			−0.385466			−0.192733	+	0.981251i	$0.561735\pi$
$168$	10.1815	+	17.6348i	0.785518	+	1.36056i
$169$	−7.00000			−0.538462
$170$	−6.07568	+	11.5363i	−0.465983	+	0.884794i
$171$		−	2.26841i		−	0.173470i
$172$	−0.411160	+	2.33181i	−0.0313507	+	0.177798i
$173$			14.1029i			1.07223i	0.844146	+	0.536114i	$0.180108\pi$
$173$			14.1029i			1.07223i	−0.844146	+	0.536114i	$0.819892\pi$
$174$	9.08253	−	7.62114i	0.688545	−	0.577757i
$175$	−19.2138	−	15.5787i	−1.45243	−	1.17764i
$176$	17.8129	+	6.48335i	1.34269	+	0.488701i
$177$	0.685715			0.0515415
$178$	2.67043	+	3.18249i	0.200157	+	0.238538i
$179$		−	16.9126i		−	1.26411i	−0.774924	−	0.632055i	$-0.782212\pi$
$179$		−	16.9126i		−	1.26411i	0.774924	−	0.632055i	$-0.217788\pi$
$180$	3.43345	+	1.94395i	0.255914	+	0.144894i
$181$	−13.1779			−0.979505			−0.489752	−	0.871862i	$-0.662913\pi$
$181$	−13.1779			−0.979505			−0.489752	+	0.871862i	$0.662913\pi$
$182$	−11.0158	−	13.1282i	−0.816548	−	0.973124i
$183$		−	5.12654i		−	0.378965i
$184$	−14.1622	+	8.17653i	−1.04405	+	0.602782i
$185$	−6.31268	−	2.23763i	−0.464117	−	0.164514i
$186$	8.47478	+	10.0998i	0.621401	+	0.740556i
$187$	−14.5789	+	13.0094i	−1.06612	+	0.951341i
$188$	23.9648	+	4.22564i	1.74781	+	0.308186i
$189$			27.9499i			2.03306i
$190$	2.84507	+	7.61667i	0.206403	+	0.552571i
$191$	−16.3482			−1.18292			−0.591458	−	0.806336i	$-0.701447\pi$
$191$	−16.3482			−1.18292			−0.591458	+	0.806336i	$0.701447\pi$
$192$	10.0822	+	5.82099i	0.727623	+	0.420094i
$193$	−18.1514			−1.30656			−0.653282	−	0.757115i	$-0.726608\pi$
$193$	−18.1514			−1.30656			−0.653282	+	0.757115i	$0.726608\pi$
$194$	5.07846	+	6.05227i	0.364612	+	0.434528i
$195$	7.51270	+	2.66300i	0.537996	+	0.190702i
$196$	−6.06892	+	34.4186i	−0.433494	+	2.45847i
$197$		−	13.8965i		−	0.990083i	−0.868869	−	0.495042i	$-0.835153\pi$
$197$		−	13.8965i		−	0.990083i	0.868869	−	0.495042i	$-0.164847\pi$
$198$	3.80071	+	4.52951i	0.270105	+	0.321898i
$199$			18.3730i			1.30242i	0.758896	+	0.651212i	$0.225739\pi$
$199$			18.3730i			1.30242i	−0.758896	+	0.651212i	$0.774261\pi$
$200$	−13.9667	−	2.22095i	−0.987591	−	0.157045i
$201$			20.7154i			1.46115i
$202$	3.00492	−	2.52142i	0.211425	−	0.177407i
$203$	28.5010			2.00038
$204$	−10.2051	+	6.31361i	−0.714503	+	0.442041i
$205$	3.23533	+	1.14681i	0.225965	+	0.0800970i
$206$	−2.70052	+	2.26600i	−0.188154	+	0.157880i
$207$	−5.10093			−0.354539
$208$	−9.20707	−	3.35110i	−0.638395	−	0.232357i
$209$			12.1847i			0.842834i
$210$	−7.96640	−	21.3272i	−0.549734	−	1.47172i
$211$	−0.0206361			−0.00142065			−0.000710324	−	1.00000i	$-0.500226\pi$
$211$	−0.0206361			−0.00142065			−0.000710324		1.00000i	$0.500226\pi$
$212$	−1.14892	+	6.51585i	−0.0789082	+	0.447511i
$213$	−4.95602			−0.339581
$214$	10.8866	−	9.13494i	0.744193	−	0.624452i
$215$	0.884443	−	2.49514i	0.0603185	−	0.170167i
$216$	7.98980	+	13.8387i	0.543637	+	0.941607i
$217$			31.6934i			2.15149i
$218$	3.21792	+	3.83497i	0.217945	+	0.259737i
$219$			2.98159i			0.201477i
$220$	−18.4427	−	10.4419i	−1.24340	−	0.703992i
$221$	7.53553	−	6.72427i	0.506895	−	0.452323i
$222$	−3.96231	−	4.72210i	−0.265933	−	0.316927i
$223$		−	9.43023i		−	0.631495i	−0.948843	−	0.315748i	$-0.897745\pi$
$223$		−	9.43023i		−	0.631495i	0.948843	−	0.315748i	$-0.102255\pi$
$224$	9.57163	+	26.2978i	0.639532	+	1.75710i
$225$	−3.42649	−	2.77823i	−0.228433	−	0.185215i
$226$	3.17641	+	3.78549i	0.211291	+	0.251807i
$227$		−	24.4475i		−	1.62263i	−0.584606	−	0.811317i	$-0.698751\pi$
$227$		−	24.4475i		−	1.62263i	0.584606	−	0.811317i	$-0.301249\pi$
$228$	−1.29946	+	7.36963i	−0.0860591	+	0.488066i
$229$		−	3.59019i		−	0.237246i	−0.992939	−	0.118623i	$-0.962152\pi$
$229$		−	3.59019i		−	0.237246i	0.992939	−	0.118623i	$-0.0378480\pi$
$230$	17.1274	−	6.39765i	1.12935	−	0.421848i
$231$		−	34.1180i		−	2.24480i
$232$	14.1116	−	8.14734i	0.926473	−	0.534899i
$233$	26.3245			1.72458			0.862289	−	0.506416i	$-0.169030\pi$
$233$	26.3245			1.72458			0.862289	+	0.506416i	$0.169030\pi$
$234$	−1.96450	−	2.34120i	−0.128424	−	0.153049i
$235$	−25.6434	−	9.08973i	−1.67279	−	0.592949i
$236$	0.928086	+	0.163647i	0.0604132	+	0.0106525i
$237$	−16.8549			−1.09484
$238$	−28.5479	−	4.14238i	−1.85049	−	0.268511i
$239$	−17.7793			−1.15005			−0.575024	−	0.818137i	$-0.695007\pi$
$239$	−17.7793			−1.15005			−0.575024	+	0.818137i	$0.695007\pi$
$240$	−10.0410	−	8.28238i	−0.648144	−	0.534625i
$241$		−	11.2427i		−	0.724204i	−0.932138	−	0.362102i	$-0.882059\pi$
$241$		−	11.2427i		−	0.724204i	0.932138	−	0.362102i	$-0.117941\pi$
$242$	−10.4160	−	12.4133i	−0.669565	−	0.797956i
$243$			8.83613i			0.566838i
$244$	1.22345	−	6.93856i	0.0783237	−	0.444195i
$245$	13.0548	−	36.8295i	0.834041	−	2.35295i
$246$	2.03074	+	2.42014i	0.129475	+	0.154302i
$247$		−	6.29801i		−	0.400733i
$248$	9.05991	+	15.6922i	0.575305	+	0.996457i
$249$		−	12.4221i		−	0.787221i
$250$	14.9897	+	5.03093i	0.948029	+	0.318184i
$251$			16.2812i			1.02766i	0.857891	+	0.513831i	$0.171774\pi$
$251$			16.2812i			1.02766i	−0.857891	+	0.513831i	$0.828226\pi$
$252$	−1.51584	+	8.59677i	−0.0954891	+	0.541546i
$253$	27.3995			1.72259
$254$	19.1950	−	16.1066i	1.20440	−	1.01062i
$255$	12.4198	−	5.07505i	0.777760	−	0.317812i
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$		−	26.2126i		−	1.63510i	−0.575858	−	0.817550i	$-0.695332\pi$
$257$		−	26.2126i		−	1.63510i	0.575858	−	0.817550i	$-0.304668\pi$
$258$	1.86645	−	1.56614i	0.116200	−	0.0975035i
$259$		−	14.8180i		−	0.920744i
$260$	9.53260	+	5.39718i	0.591187	+	0.334719i
$261$	5.08272			0.314612
$262$	−9.33924	−	11.1301i	−0.576980	−	0.687619i
$263$			26.1954i			1.61528i	0.589678	+	0.807638i	$0.299255\pi$
$263$			26.1954i			1.61528i	−0.589678	+	0.807638i	$0.700745\pi$
$264$	−9.75303	−	16.8927i	−0.600257	−	1.03968i
$265$	2.47143	−	6.97227i	0.151819	−	0.428303i
$266$	−13.7802	+	11.5630i	−0.844919	+	0.708971i
$267$		−	4.27499i		−	0.261625i
$268$	−4.94376	+	28.0374i	−0.301988	+	1.71266i
$269$	−11.2525			−0.686078			−0.343039	−	0.939321i	$-0.611456\pi$
$269$	−11.2525			−0.686078			−0.343039	+	0.939321i	$0.611456\pi$
$270$	−6.25154	−	16.7363i	−0.380457	−	1.01854i
$271$	7.85440			0.477121			0.238560	−	0.971128i	$-0.423324\pi$
$271$	7.85440			0.477121			0.238560	+	0.971128i	$0.423324\pi$
$272$	−15.3190	+	6.10974i	−0.928849	+	0.370458i
$273$			17.6348i			1.06731i
$274$	8.23548	−	6.91039i	0.497523	−	0.417472i
$275$	18.4053	+	14.9232i	1.10988	+	0.899901i
$276$	16.5719	+	2.92207i	0.997511	+	0.175888i
$277$			18.6472i			1.12040i	0.828356	+	0.560202i	$0.189276\pi$
$277$			18.6472i			1.12040i	−0.828356	+	0.560202i	$0.810724\pi$
$278$	7.13333	+	8.50117i	0.427828	+	0.509866i
$279$			5.65202i			0.338378i
$280$	−5.69243	−	30.7667i	−0.340188	−	1.83866i
$281$	−2.03004			−0.121102			−0.0605509	−	0.998165i	$-0.519286\pi$
$281$	−2.03004			−0.121102			−0.0605509	+	0.998165i	$0.519286\pi$
$282$	−16.0957	−	19.1822i	−0.958488	−	1.14228i
$283$		−	18.2762i		−	1.08641i	−0.839600	−	0.543205i	$-0.817211\pi$
$283$		−	18.2762i		−	1.08641i	0.839600	−	0.543205i	$-0.182789\pi$
$284$	−6.70776	−	1.18276i	−0.398032	−	0.0701839i
$285$	2.79527	−	7.88584i	0.165577	−	0.467117i
$286$	10.5523	+	12.5757i	0.623969	+	0.743617i
$287$			7.59440i			0.448283i
$288$	1.70695	+	4.68981i	0.100583	+	0.276350i
$289$	1.92809	−	16.8903i	0.113417	−	0.993547i
$290$	−17.0663	+	6.37481i	−1.00217	+	0.374342i
$291$		−	8.12992i		−	0.476584i
$292$	−0.711560	+	4.03546i	−0.0416409	+	0.236157i
$293$	28.4115			1.65981			0.829907	−	0.557901i	$-0.188393\pi$
$293$	28.4115			1.65981			0.829907	+	0.557901i	$0.188393\pi$
$294$	27.5497	−	23.1170i	1.60673	−	1.34821i
$295$	−0.993095	−	0.352019i	−0.0578202	−	0.0204953i
$296$	−4.23589	−	7.33678i	−0.246206	−	0.426441i
$297$		−	26.7737i		−	1.55357i
$298$	5.58317	−	4.68483i	0.323424	−	0.271385i
$299$	−14.1622			−0.819019
$300$	9.54049	+	10.9888i	0.550820	+	0.634438i
$301$	5.85693			0.337588
$302$	−5.35344	−	6.37998i	−0.308056	−	0.367127i
$303$	−4.03645			−0.231888
$304$	−3.51754	+	9.66436i	−0.201745	+	0.554289i
$305$	−2.63176	+	7.42458i	−0.150694	+	0.425130i
$306$	−5.09108	−	0.738730i	−0.291038	−	0.0422304i
$307$	−25.2629			−1.44183			−0.720915	−	0.693023i	$-0.756278\pi$
$307$	−25.2629			−1.44183			−0.720915	+	0.693023i	$0.756278\pi$
$308$	8.14230	−	46.1773i	0.463951	−	2.63120i
$309$	3.62756			0.206365
$310$	−7.08884	−	18.9778i	−0.402619	−	1.07787i
$311$		−	1.42370i		−	0.0807308i	−0.999185	−	0.0403654i	$-0.987148\pi$
$311$		−	1.42370i		−	0.0807308i	0.999185	−	0.0403654i	$-0.0128522\pi$
$312$	5.04112	+	8.73148i	0.285397	+	0.494323i
$313$	−23.4725			−1.32674			−0.663372	−	0.748290i	$-0.730875\pi$
$313$	−23.4725			−1.32674			−0.663372	+	0.748290i	$0.730875\pi$
$314$	9.21940	+	10.9873i	0.520281	+	0.620047i
$315$	3.26072	−	9.19895i	0.183721	−	0.518302i
$316$	−22.8124	−	4.02244i	−1.28330	−	0.226280i
$317$			22.1764i			1.24555i	0.782400	+	0.622777i	$0.213995\pi$
$317$			22.1764i			1.24555i	−0.782400	+	0.622777i	$0.786005\pi$
$318$	5.21550	−	4.37632i	0.292470	−	0.245412i
$319$	−27.3016			−1.52860
$320$	−11.6135	−	13.6061i	−0.649213	−	0.760607i
$321$	−14.6238			−0.816221
$322$	26.0014	+	30.9872i	1.44900	+	1.72685i
$323$	−7.05824	−	7.90981i	−0.392731	−	0.440113i
$324$	1.93613	−	10.9803i	0.107563	−	0.610018i
$325$	−9.51329	−	7.71345i	−0.527702	−	0.427865i
$326$	−19.3953	+	16.2746i	−1.07421	+	0.901367i
$327$		−	5.15145i		−	0.284876i
$328$	2.17095	+	3.76019i	0.119870	+	0.207622i
$329$		−	60.1937i		−	3.31859i
$330$	7.63116	+	20.4297i	0.420082	+	1.12462i
$331$			12.3931i			0.681189i	0.940210	+	0.340594i	$0.110628\pi$
$331$			12.3931i			0.681189i	−0.940210	+	0.340594i	$0.889372\pi$
$332$	2.96456	−	16.8128i	0.162701	−	0.922724i
$333$		−	2.64256i		−	0.144811i
$334$	4.52822	+	5.39652i	0.247773	+	0.295284i
$335$	10.6345	−	30.0014i	0.581023	−	1.63915i
$336$	9.84935	−	27.0609i	0.537326	−	1.47629i
$337$	9.05864			0.493455			0.246728	−	0.969085i	$-0.420645\pi$
$337$	9.05864			0.493455			0.246728	+	0.969085i	$0.420645\pi$
$338$	6.36327	+	7.58345i	0.346116	+	0.412485i
$339$		−	5.08499i		−	0.276179i
$340$	18.0209	−	3.90486i	0.977319	−	0.211771i
$341$		−	30.3597i		−	1.64407i
$342$	−2.45749	+	2.06208i	−0.132886	+	0.111504i
$343$	51.8207			2.79806
$344$	2.89992	−	1.67427i	0.156353	−	0.0902707i
$345$	−17.7327	−	6.28565i	−0.954696	−	0.338408i
$346$	15.2784	−	12.8201i	0.821374	−	0.689214i
$347$			21.1707i			1.13650i	0.822855	+	0.568251i	$0.192380\pi$
$347$			21.1707i			1.13650i	−0.822855	+	0.568251i	$0.807620\pi$
$348$	−16.5127	−	2.91164i	−0.885176	−	0.156080i
$349$		−	1.13582i		−	0.0607989i	−0.999538	−	0.0303994i	$-0.990322\pi$
$349$		−	1.13582i		−	0.0607989i	0.999538	−	0.0303994i	$-0.00967793\pi$
$350$	0.588899	+	34.9770i	0.0314780	+	1.86960i
$351$			13.8387i			0.738657i
$352$	−9.16884	−	25.1912i	−0.488701	−	1.34269i
$353$			6.77008i			0.360335i	0.983636	+	0.180167i	$0.0576640\pi$
$353$			6.77008i			0.360335i	−0.983636	+	0.180167i	$0.942336\pi$
$354$	−0.623341	−	0.742869i	−0.0331302	−	0.0394831i
$355$	7.17762	+	2.54422i	0.380948	+	0.135033i
$356$	1.02023	−	5.78601i	0.0540721	−	0.306658i
$357$	19.7636	+	22.1480i	1.04600	+	1.17220i
$358$	−18.3223	+	15.3742i	−0.968364	+	0.812554i
$359$	−30.9290			−1.63237			−0.816185	−	0.577790i	$-0.803915\pi$
$359$	−30.9290			−1.63237			−0.816185	+	0.577790i	$0.803915\pi$
$360$	−1.01516	−	5.48676i	−0.0535034	−	0.289178i
$361$	12.3892			0.652062
$362$	11.9792	+	14.2763i	0.629614	+	0.750344i
$363$			16.6746i			0.875187i
$364$	−4.20858	+	23.8680i	−0.220589	+	1.25102i
$365$	1.53063	−	4.31813i	0.0801169	−	0.226021i
$366$	−5.55384	+	4.66022i	−0.290304	+	0.243594i
$367$	−7.04986			−0.368000			−0.184000	−	0.982926i	$-0.558905\pi$
$367$	−7.04986			−0.368000			−0.184000	+	0.982926i	$0.558905\pi$
$368$	21.7320	+	7.90981i	1.13286	+	0.412327i
$369$			1.35434i			0.0705043i
$370$	3.31433	+	8.87294i	0.172304	+	0.461282i
$371$	16.3663			0.849693
$372$	3.23777	−	18.3623i	0.167871	−	0.952041i
$373$	−32.1456			−1.66444			−0.832219	−	0.554448i	$-0.812930\pi$
$373$	−32.1456			−1.66444			−0.832219	+	0.554448i	$0.812930\pi$
$374$	27.3466	+	3.96806i	1.41406	+	0.205184i
$375$	−8.48827	−	13.8805i	−0.438332	−	0.716784i
$376$	−17.2071	−	29.8035i	−0.887387	−	1.53700i
$377$	14.1116			0.726785
$378$	30.2795	−	25.4075i	1.55741	−	1.30682i
$379$	14.3052			0.734808			0.367404	−	0.930061i	$-0.380247\pi$
$379$	14.3052			0.734808			0.367404	+	0.930061i	$0.380247\pi$
$380$	5.66524	−	10.0061i	0.290621	−	0.513300i
$381$	−25.7844			−1.32097
$382$	14.8612	+	17.7109i	0.760364	+	0.906166i
$383$			10.8031i			0.552015i	0.961156	+	0.276007i	$0.0890114\pi$
$383$			10.8031i			0.552015i	−0.961156	+	0.276007i	$0.910989\pi$
$384$	−2.85899	−	16.2141i	−0.145897	−	0.827423i
$385$	−17.5148	+	49.4118i	−0.892639	+	2.51826i
$386$	16.5003	+	19.6643i	0.839843	+	1.00089i
$387$	1.04449			0.0530946
$388$	1.94021	−	11.0035i	0.0984995	−	0.558618i
$389$			17.3203i			0.878177i	0.898444	+	0.439088i	$0.144698\pi$
$389$			17.3203i			0.878177i	−0.898444	+	0.439088i	$0.855302\pi$
$390$	−3.94438	−	10.5597i	−0.199731	−	0.534709i
$391$	−17.7866	+	15.8717i	−0.899506	+	0.802666i
$392$	42.8043	−	24.7131i	2.16194	−	1.24820i
$393$			14.9509i			0.754171i
$394$	−15.0548	+	12.6324i	−0.758448	+	0.636413i
$395$	24.4103	+	8.65264i	1.22822	+	0.435361i
$396$	1.45205	−	8.23501i	0.0729685	−	0.413825i
$397$		−	17.7930i		−	0.893006i	−0.894782	−	0.446503i	$-0.852669\pi$
$397$		−	17.7930i		−	0.893006i	0.894782	−	0.446503i	$-0.147331\pi$
$398$	19.9044	−	16.7017i	0.997715	−	0.837182i
$399$	18.5107			0.926695
$400$	10.2902	+	17.1497i	0.514508	+	0.857486i
$401$		−	6.10499i		−	0.304869i	−0.988314	−	0.152434i	$-0.951289\pi$
$401$		−	6.10499i		−	0.304869i	0.988314	−	0.152434i	$-0.0487113\pi$
$402$	22.4421	−	18.8311i	1.11931	−	0.939211i
$403$			15.6922i			0.781686i
$404$	−5.46317	−	0.963304i	−0.271803	−	0.0479262i
$405$	−4.16479	+	11.7495i	−0.206950	+	0.583835i
$406$	−25.9085	−	30.8766i	−1.28582	−	1.53238i
$407$			14.1944i			0.703591i
$408$	16.1167	+	5.31642i	0.797897	+	0.263202i
$409$	−2.10231			−0.103952			−0.0519762	−	0.998648i	$-0.516552\pi$
$409$	−2.10231			−0.103952			−0.0519762	+	0.998648i	$0.516552\pi$
$410$	−1.69864	−	4.54749i	−0.0838896	−	0.224585i
$411$	−11.0626			−0.545677
$412$	4.90975	+	0.865722i	0.241886	+	0.0426511i
$413$		−	2.33113i		−	0.114707i
$414$	4.63694	+	5.52609i	0.227893	+	0.271592i
$415$	−6.37703	+	17.9905i	−0.313036	+	0.883119i
$416$	4.73917	+	13.0208i	0.232357	+	0.638395i
$417$		−	11.4195i		−	0.559214i
$418$	13.2003	−	11.0764i	0.645648	−	0.541763i
$419$	−3.07410			−0.150180			−0.0750899	−	0.997177i	$-0.523924\pi$
$419$	−3.07410			−0.150180			−0.0750899	+	0.997177i	$0.523924\pi$
$420$	−15.8631	+	28.0177i	−0.774038	+	1.36712i
$421$			27.2865i			1.32986i	0.746904	+	0.664932i	$0.231540\pi$
$421$			27.2865i			1.32986i	−0.746904	+	0.664932i	$0.768460\pi$
$422$	0.0187590	+	0.0223561i	0.000913174	+	0.00108828i
$423$		−	10.7346i		−	0.521935i
$424$	8.10337	−	4.67848i	0.393534	−	0.227207i
$425$	−20.5925	+	0.974152i	−0.998883	+	0.0472533i
$426$	4.50521	+	5.36910i	0.218278	+	0.260134i
$427$	−17.4280			−0.843399
$428$	−19.7927	−	3.48999i	−0.956716	−	0.168695i
$429$		−	16.8927i		−	0.815589i
$430$	−3.50710	+	1.31002i	−0.169128	+	0.0631746i
$431$		−	3.13668i		−	0.151088i	−0.997142	−	0.0755442i	$-0.975931\pi$
$431$		−	3.13668i		−	0.151088i	0.997142	−	0.0755442i	$-0.0240694\pi$
$432$	7.72917	−	21.2357i	0.371870	−	1.02170i
$433$		−	23.7320i		−	1.14049i	−0.821476	−	0.570243i	$-0.806849\pi$
$433$		−	23.7320i		−	1.14049i	0.821476	−	0.570243i	$-0.193151\pi$
$434$	34.3350	−	28.8105i	1.64813	−	1.38295i
$435$	17.6694	+	6.26321i	0.847183	+	0.300298i
$436$	1.22940	−	6.97227i	0.0588775	−	0.333911i
$437$			14.8656i			0.711117i
$438$	3.23011	−	2.71038i	0.154340	−	0.129507i
$439$		−	1.83356i		−	0.0875111i	−0.999042	−	0.0437555i	$-0.986068\pi$
$439$		−	1.83356i		−	0.0875111i	0.999042	−	0.0437555i	$-0.0139323\pi$
$440$	5.45288	+	29.4719i	0.259956	+	1.40502i
$441$	15.4172			0.734154
$442$	−14.1348	−	2.05100i	−0.672325	−	0.0975563i
$443$	−29.7733			−1.41457			−0.707286	−	0.706927i	$-0.750081\pi$
$443$	−29.7733			−1.41457			−0.707286	+	0.706927i	$0.750081\pi$
$444$	−1.51379	+	8.58515i	−0.0718414	+	0.407433i
$445$	−2.19461	+	6.19130i	−0.104034	+	0.293496i
$446$	−10.2162	+	8.57245i	−0.483753	+	0.405917i
$447$	−7.49978			−0.354727
$448$	19.7888	−	34.2752i	0.934933	−	1.61935i
$449$		−	11.6844i		−	0.551423i	−0.961240	−	0.275711i	$-0.911087\pi$
$449$		−	11.6844i		−	0.551423i	0.961240	−	0.275711i	$-0.0889134\pi$
$450$	0.105021	+	6.23761i	0.00495074	+	0.294044i
$451$		−	7.27482i		−	0.342558i
$452$	1.21354	−	6.88232i	0.0570801	−	0.323717i
$453$			8.57012i			0.402660i
$454$	−26.4852	+	22.2237i	−1.24301	+	1.04301i
$455$	9.05303	−	25.5399i	0.424413	−	1.19733i
$456$	9.16515	−	5.29150i	0.429198	−	0.247797i
$457$		−	15.6232i		−	0.730822i	−0.930846	−	0.365411i	$-0.880928\pi$
$457$		−	15.6232i		−	0.730822i	0.930846	−	0.365411i	$-0.119072\pi$
$458$	−3.88943	+	3.26362i	−0.181741	+	0.152499i
$459$	15.5092	+	17.3804i	0.723909	+	0.811247i
$460$	−22.5004	−	12.7393i	−1.04909	−	0.593972i
$461$			19.2989i			0.898838i	0.893321	+	0.449419i	$0.148369\pi$
$461$			19.2989i			0.898838i	−0.893321	+	0.449419i	$0.851631\pi$
$462$	−36.9618	+	31.0146i	−1.71962	+	1.44293i
$463$		−	37.9048i		−	1.76159i	−0.473500	−	0.880794i	$-0.657010\pi$
$463$		−	37.9048i		−	1.76159i	0.473500	−	0.880794i	$-0.342990\pi$
$464$	−21.6544	−	7.88157i	−1.00528	−	0.365893i
$465$	−6.96474	+	19.6485i	−0.322982	+	0.911178i
$466$	−23.9300	−	28.5187i	−1.10854	−	1.32110i
$467$	−22.1812			−1.02642			−0.513211	−	0.858263i	$-0.671544\pi$
$467$	−22.1812			−1.02642			−0.513211	+	0.858263i	$0.671544\pi$
$468$	−0.750534	+	4.25649i	−0.0346935	+	0.196756i
$469$	70.4233			3.25184
$470$	13.4635	+	36.0437i	0.621025	+	1.66257i
$471$		−	14.7590i		−	0.680059i
$472$	−0.666380	−	1.15420i	−0.0306726	−	0.0531265i
$473$	−5.61046			−0.257969
$474$	15.3218	+	18.2598i	0.703751	+	0.838698i
$475$	−8.09656	+	9.98579i	−0.371496	+	0.458180i
$476$	21.4635	+	34.6930i	0.983778	+	1.59015i
$477$	2.91867			0.133637
$478$	16.1621	+	19.2612i	0.739236	+	0.880987i
$479$			0.0664941i			0.00303819i	0.999999	+	0.00151910i	$0.000483544\pi$
$479$			0.0664941i			0.00303819i	−0.999999	+	0.00151910i	$0.999516\pi$
$480$	0.154945	+	18.4069i	0.00707225	+	0.840157i
$481$		−	7.33678i		−	0.334528i
$482$	−12.1798	+	10.2200i	−0.554773	+	0.465510i
$483$		−	41.6246i		−	1.89399i
$484$	−3.97940	+	22.5683i	−0.180882	+	1.02583i
$485$	−4.17358	+	11.7743i	−0.189512	+	0.534642i
$486$	9.57263	−	8.03239i	0.434223	−	0.364357i
$487$	−15.3571			−0.695896			−0.347948	−	0.937514i	$-0.613121\pi$
$487$	−15.3571			−0.695896			−0.347948	+	0.937514i	$0.613121\pi$
$488$	−8.62905	+	4.98199i	−0.390619	+	0.225524i
$489$	26.0534			1.17818
$490$	−51.7665	+	19.3365i	−2.33857	+	0.873533i
$491$			25.2216i			1.13823i	0.822256	+	0.569117i	$0.192715\pi$
$491$			25.2216i			1.13823i	−0.822256	+	0.569117i	$0.807285\pi$
$492$	0.775838	−	4.40000i	0.0349775	−	0.198367i
$493$	17.7231	−	15.8150i	0.798208	−	0.712273i
$494$	−6.82295	+	5.72513i	−0.306979	+	0.257586i
$495$	−3.12350	+	8.81184i	−0.140391	+	0.396063i
$496$	8.76437	−	24.0799i	0.393532	−	1.08122i
$497$			16.8483i			0.755748i
$498$	−13.4575	+	11.2922i	−0.603046	+	0.506016i
$499$	−8.80324			−0.394087			−0.197044	−	0.980395i	$-0.563134\pi$
$499$	−8.80324			−0.394087			−0.197044	+	0.980395i	$0.563134\pi$
$500$	−8.17592	−	20.8124i	−0.365638	−	0.930757i
$501$		−	7.24905i		−	0.323864i
$502$	17.6383	−	14.8003i	0.787235	−	0.660569i
$503$	14.5657			0.649454			0.324727	−	0.945808i	$-0.394728\pi$
$503$	14.5657			0.649454			0.324727	+	0.945808i	$0.394728\pi$
$504$	10.6913	−	6.17261i	0.476227	−	0.274950i
$505$	5.84584	+	2.07216i	0.260137	+	0.0922097i
$506$	−24.9072	−	29.6832i	−1.10726	−	1.31958i
$507$		−	10.1867i		−	0.452409i
$508$	−34.8981	−	6.15348i	−1.54835	−	0.273016i
$509$			26.8141i			1.18851i	0.804276	+	0.594257i	$0.202554\pi$
$509$			26.8141i			1.18851i	−0.804276	+	0.594257i	$0.797446\pi$
$510$	−16.7882	−	8.84161i	−0.743392	−	0.391513i
$511$	10.1361			0.448394
$512$		−	22.6274i		−	1.00000i
$513$	14.5261			0.641342
$514$	−28.3975	+	23.8283i	−1.25256	+	1.05102i
$515$	−5.25366	−	1.86225i	−0.231504	−	0.0820604i
$516$	−3.39335	−	0.598340i	−0.149384	−	0.0263404i
$517$			57.6607i			2.53591i
$518$	−16.0531	+	13.4701i	−0.705331	+	0.591843i
$519$	−20.5233			−0.900872
$520$	−2.81847	−	15.2334i	−0.123598	−	0.668028i
$521$			34.1951i			1.49812i	0.662504	+	0.749058i	$0.269494\pi$
$521$			34.1951i			1.49812i	−0.662504	+	0.749058i	$0.730506\pi$
$522$	−4.62039	−	5.50636i	−0.202229	−	0.241007i
$523$	10.3834			0.454034			0.227017	−	0.973891i	$-0.427103\pi$
$523$	10.3834			0.454034			0.227017	+	0.973891i	$0.427103\pi$
$524$	−3.56804	+	20.2353i	−0.155870	+	0.883985i
$525$	22.6709	−	27.9609i	0.989440	−	1.22031i
$526$	28.3788	−	23.8126i	1.23737	−	1.03828i
$527$	17.5865	+	19.7082i	0.766078	+	0.858503i
$528$	−9.43488	+	25.9221i	−0.410600	+	1.12811i
$529$	10.4278			0.453384
$530$	−9.80004	+	3.66063i	−0.425686	+	0.159008i
$531$		−	0.415721i		−	0.0180407i
$532$	25.0535	+	4.41761i	1.08621	+	0.191528i
$533$			3.76019i			0.162872i
$534$	−4.63131	+	3.88613i	−0.200416	+	0.168169i
$535$	21.1791	+	7.50728i	0.915652	+	0.324568i
$536$	34.8684	−	20.1313i	1.50609	−	0.869540i
$537$	24.6121			1.06209
$538$	10.2290	+	12.1904i	0.441002	+	0.525566i
$539$	−82.8131			−3.56701
$540$	−12.4484	+	21.9865i	−0.535692	+	0.946150i
$541$	−6.38412			−0.274475			−0.137237	−	0.990538i	$-0.543822\pi$
$541$	−6.38412			−0.274475			−0.137237	+	0.990538i	$0.543822\pi$
$542$	−7.13996	−	8.50907i	−0.306687	−	0.365496i
$543$		−	19.1771i		−	0.822968i
$544$	20.5445	+	11.0418i	0.880840	+	0.473414i
$545$	−2.64455	+	7.46065i	−0.113280	+	0.319579i
$546$	19.1047	−	16.0308i	0.817606	−	0.686053i
$547$		−	30.5569i		−	1.30652i	−0.757134	−	0.653259i	$-0.773401\pi$
$547$		−	30.5569i		−	1.30652i	0.757134	−	0.653259i	$-0.226599\pi$
$548$	−14.9727	−	2.64010i	−0.639604	−	0.112779i
$549$	−3.10801			−0.132647
$550$	−0.564117	−	33.5051i	−0.0240540	−	1.42866i
$551$		−	14.8125i		−	0.631034i
$552$	−11.8989	−	20.6095i	−0.506450	−	0.877197i
$553$			57.2992i			2.43661i
$554$	20.2015	−	16.9511i	0.858279	−	0.720182i
$555$	3.25631	−	9.18650i	0.138223	−	0.389945i
$556$	2.72527	−	15.4558i	0.115577	−	0.655471i
$557$	20.3581			0.862599			0.431300	−	0.902209i	$-0.358055\pi$
$557$	20.3581			0.862599			0.431300	+	0.902209i	$0.358055\pi$
$558$	6.12312	−	5.13791i	0.259212	−	0.217505i
$559$	2.89992			0.122654
$560$	−28.1564	+	34.1350i	−1.18983	+	1.44247i
$561$	−18.9319	−	21.2160i	−0.799305	−	0.895739i
$562$	1.84538	+	2.19924i	0.0778428	+	0.0927694i
$563$	−2.37430			−0.100065			−0.0500323	−	0.998748i	$-0.515932\pi$
$563$	−2.37430			−0.100065			−0.0500323	+	0.998748i	$0.515932\pi$
$564$	−6.14935	+	34.8747i	−0.258934	+	1.46849i
$565$	−2.61043	+	7.36441i	−0.109822	+	0.309823i
$566$	−19.7996	+	16.6138i	−0.832238	+	0.698331i
$567$	−27.5799			−1.15825
$568$	4.81627	+	8.34203i	0.202086	+	0.350024i
$569$	22.3013			0.934919			0.467459	−	0.884015i	$-0.345169\pi$
$569$	22.3013			0.934919			0.467459	+	0.884015i	$0.345169\pi$
$570$	−11.0841	+	4.14029i	−0.464264	+	0.173417i
$571$	−36.2364			−1.51645			−0.758223	−	0.651995i	$-0.773932\pi$
$571$	−36.2364			−1.51645			−0.758223	+	0.651995i	$0.773932\pi$
$572$	4.03147	−	22.8636i	0.168564	−	0.955976i
$573$		−	23.7907i		−	0.993871i
$574$	8.22740	−	6.90361i	0.343405	−	0.288151i
$575$	22.4548	+	18.2065i	0.936430	+	0.759265i
$576$	3.52903	−	6.11245i	0.147043	−	0.254685i
$577$			32.5244i			1.35401i	0.735979	+	0.677004i	$0.236722\pi$
$577$			32.5244i			1.35401i	−0.735979	+	0.677004i	$0.763278\pi$
$578$	−20.0508	+	13.2652i	−0.834004	+	0.551758i
$579$		−	26.4147i		−	1.09776i
$580$	22.4201	+	12.6938i	0.930942	+	0.527082i
$581$	−42.2298			−1.75199
$582$	−8.80755	+	7.39041i	−0.365085	+	0.306343i
$583$	−15.6775			−0.649297
$584$	5.01865	−	2.89752i	0.207673	−	0.119900i
$585$	1.61447	−	4.55464i	0.0667501	−	0.188311i
$586$	−25.8271	−	30.7796i	−1.06691	−	1.27149i
$587$	27.8951			1.15135			0.575677	−	0.817677i	$-0.304739\pi$
$587$	27.8951			1.15135			0.575677	+	0.817677i	$0.304739\pi$
$588$	−50.0875	−	8.83178i	−2.06557	−	0.364217i
$589$	16.4716			0.678702
$590$	0.521402	+	1.39587i	0.0214658	+	0.0574670i
$591$	20.2228			0.831855
$592$	−4.09771	+	11.2584i	−0.168415	+	0.462716i
$593$			8.65462i			0.355402i	0.984084	+	0.177701i	$0.0568661\pi$
$593$			8.65462i			0.355402i	−0.984084	+	0.177701i	$0.943134\pi$
$594$	−29.0053	+	24.3384i	−1.19010	+	0.998615i
$595$	−17.2529	−	42.2219i	−0.707301	−	1.73093i
$596$	−10.1506	−	1.78983i	−0.415786	−	0.0733143i
$597$	−26.7372			−1.09428
$598$	12.8740	+	15.3426i	0.526456	+	0.627405i
$599$	−2.72192			−0.111215			−0.0556073	−	0.998453i	$-0.517709\pi$
$599$	−2.72192			−0.111215			−0.0556073	+	0.998453i	$0.517709\pi$
$600$	3.23203	−	20.3249i	0.131947	−	0.829762i
$601$			29.7746i			1.21453i	0.794499	+	0.607266i	$0.207734\pi$
$601$			29.7746i			1.21453i	−0.794499	+	0.607266i	$0.792266\pi$
$602$	−5.32418	−	6.34511i	−0.216997	−	0.258607i
$603$	12.5589			0.511438
$604$	−2.04527	+	11.5993i	−0.0832209	+	0.471969i
$605$	8.56006	−	24.1491i	0.348016	−	0.981802i
$606$	3.66929	+	4.37289i	0.149055	+	0.177637i
$607$	44.1777			1.79312			0.896559	−	0.442925i	$-0.146059\pi$
$607$	44.1777			1.79312			0.896559	+	0.442925i	$0.146059\pi$
$608$	13.6675	−	4.97455i	0.554289	−	0.201745i
$609$			41.4760i			1.68069i
$610$	10.4358	−	3.89811i	0.422533	−	0.157830i
$611$		−	29.8035i		−	1.20572i
$612$	3.82768	+	6.18696i	0.154725	+	0.250093i
$613$	1.05984			0.0428066			0.0214033	−	0.999771i	$-0.493187\pi$
$613$	1.05984			0.0428066			0.0214033	+	0.999771i	$0.493187\pi$
$614$	22.9650	+	27.3686i	0.926791	+	1.10451i
$615$	−1.66890	+	4.70820i	−0.0672965	+	0.189853i
$616$	−57.4279	+	33.1560i	−2.31383	+	1.33589i
$617$	−33.4848			−1.34805			−0.674023	−	0.738710i	$-0.735435\pi$
$617$	−33.4848			−1.34805			−0.674023	+	0.738710i	$0.735435\pi$
$618$	−3.29760	−	3.92992i	−0.132649	−	0.158085i
$619$	7.84711			0.315402			0.157701	−	0.987487i	$-0.449592\pi$
$619$	7.84711			0.315402			0.157701	+	0.987487i	$0.449592\pi$
$620$	−14.1156	+	24.9313i	−0.566897	+	1.00126i
$621$		−	32.6644i		−	1.31078i
$622$	−1.54237	+	1.29420i	−0.0618434	+	0.0518928i
$623$	−14.5331			−0.582255
$624$	4.87668	−	13.3986i	0.195223	−	0.536372i
$625$	5.16756	+	24.4601i	0.206702	+	0.978404i
$626$	21.3374	+	25.4289i	0.852814	+	1.01634i
$627$	−17.7318			−0.708138
$628$	3.52225	−	19.9757i	0.140553	−	0.797117i
$629$	−8.22240	−	9.21442i	−0.327849	−	0.367403i
$630$	−12.9298	+	4.82970i	−0.515136	+	0.192420i
$631$	49.0188			1.95141			0.975703	−	0.219098i	$-0.0703113\pi$
$631$	49.0188			1.95141			0.975703	+	0.219098i	$0.0703113\pi$
$632$	16.3796	+	28.3704i	0.651547	+	1.12851i
$633$		−	0.0300306i		−	0.00119361i
$634$	24.0249	−	20.1593i	0.954149	−	0.800626i
$635$	37.3426	+	13.2367i	1.48189	+	0.525282i
$636$	−9.48218	−	1.67196i	−0.375993	−	0.0662977i
$637$	42.8043			1.69597
$638$	24.8183	+	29.5772i	0.982564	+	1.17097i
$639$			3.00463i			0.118861i
$640$	−4.18312	+	24.9500i	−0.165352	+	0.986235i
$641$			21.3815i			0.844518i	0.906475	+	0.422259i	$0.138763\pi$
$641$			21.3815i			0.844518i	−0.906475	+	0.422259i	$0.861237\pi$
$642$	13.2936	+	15.8427i	0.524657	+	0.625261i
$643$			21.4973i			0.847772i	0.905716	+	0.423886i	$0.139334\pi$
$643$			21.4973i			0.847772i	−0.905716	+	0.423886i	$0.860666\pi$
$644$	9.93376	−	56.3372i	0.391445	−	2.21999i
$645$	3.63104	+	1.28708i	0.142972	+	0.0506789i
$646$	−2.15287	+	14.8369i	−0.0847036	+	0.583749i
$647$		−	34.9460i		−	1.37387i	−0.726720	−	0.686934i	$-0.758956\pi$
$647$		−	34.9460i		−	1.37387i	0.726720	−	0.686934i	$-0.241044\pi$
$648$	−13.6555	+	7.88404i	−0.536441	+	0.309714i
$649$			2.23303i			0.0876541i
$650$	0.291579	+	17.3181i	0.0114367	+	0.679270i
$651$	−46.1217			−1.80765
$652$	35.2622	+	6.21768i	1.38097	+	0.243503i
$653$			12.0189i			0.470335i	0.971955	+	0.235168i	$0.0755639\pi$
$653$			12.0189i			0.470335i	−0.971955	+	0.235168i	$0.924436\pi$
$654$	−5.58082	+	4.68287i	−0.218227	+	0.183115i
$655$	7.67518	−	21.6528i	0.299894	−	0.846043i
$656$	2.10013	−	5.77006i	0.0819962	−	0.225283i
$657$	1.80762			0.0705218
$658$	−65.2109	+	54.7184i	−2.54219	+	2.13315i
$659$		−	22.2352i		−	0.866160i	−0.901356	−	0.433080i	$-0.857427\pi$
$659$		−	22.2352i		−	0.866160i	0.901356	−	0.433080i	$-0.142573\pi$
$660$	15.1955	−	26.8386i	0.591485	−	1.04469i
$661$			8.70623i			0.338633i	0.985562	+	0.169317i	$0.0541560\pi$
$661$			8.70623i			0.338633i	−0.985562	+	0.169317i	$0.945844\pi$
$662$	13.4261	−	11.2659i	0.521821	−	0.437860i
$663$	9.78547	+	10.9661i	0.380036	+	0.425887i
$664$	−20.9091	+	12.0719i	−0.811430	+	0.468479i
$665$	−26.8084	−	9.50268i	−1.03958	−	0.368498i
$666$	−2.86282	+	2.40219i	−0.110932	+	0.0930829i
$667$	−33.3085			−1.28971
$668$	1.72999	−	9.81129i	0.0669355	−	0.379610i
$669$	13.7233			0.530574
$670$	−42.1691	+	15.7515i	−1.62914	+	0.608535i
$671$	16.6946			0.644487
$672$	−38.2699	+	13.9291i	−1.47629	+	0.537326i
$673$	−31.3331			−1.20780			−0.603901	−	0.797059i	$-0.706388\pi$
$673$	−31.3331			−1.20780			−0.603901	+	0.797059i	$0.706388\pi$
$674$	−8.23465	−	9.81368i	−0.317187	−	0.378009i
$675$	17.7907	−	21.9420i	0.684766	−	0.844548i
$676$	2.43107	−	13.7873i	0.0935029	−	0.530281i
$677$		−	14.4106i		−	0.553844i	−0.960892	−	0.276922i	$-0.910686\pi$
$677$		−	14.4106i		−	0.553844i	0.960892	−	0.276922i	$-0.0893144\pi$
$678$	−5.50883	+	4.62246i	−0.211565	+	0.177524i
$679$	−27.6381			−1.06065
$680$	−20.6120	−	15.9733i	−0.790434	−	0.612547i
$681$	35.5771			1.36332
$682$	−32.8901	+	27.5981i	−1.25943	+	1.05679i
$683$		−	11.9338i		−	0.456634i	−0.973587	−	0.228317i	$-0.926678\pi$
$683$		−	11.9338i		−	0.456634i	0.973587	−	0.228317i	$-0.0733222\pi$
$684$	4.46790	+	0.787812i	0.170835	+	0.0301227i
$685$	16.0215	+	5.67909i	0.612151	+	0.216987i
$686$	−47.1071	−	56.1400i	−1.79856	−	2.14344i
$687$	5.22461			0.199331
$688$	−4.44997	−	1.61966i	−0.169653	−	0.0617488i
$689$	8.10337			0.308714
$690$	9.31016	+	24.9246i	0.354432	+	0.948864i
$691$	13.7386			0.522641			0.261321	−	0.965252i	$-0.415842\pi$
$691$	13.7386			0.522641			0.261321	+	0.965252i	$0.415842\pi$
$692$	−27.7774	−	4.89790i	−1.05594	−	0.186190i
$693$	−20.6843			−0.785733
$694$	22.9353	−	19.2450i	0.870612	−	0.730530i
$695$	−5.86231	+	16.5384i	−0.222370	+	0.627337i
$696$	11.8564	+	20.5359i	0.449416	+	0.778411i
$697$	4.21409	+	4.72251i	0.159620	+	0.178878i
$698$	−1.23049	+	1.03250i	−0.0465746	+	0.0390808i
$699$			38.3087i			1.44897i
$700$	37.3570	−	32.4335i	1.41196	−	1.22587i
$701$		−	37.5554i		−	1.41845i	−0.704983	−	0.709224i	$-0.749045\pi$
$701$		−	37.5554i		−	1.41845i	0.704983	−	0.709224i	$-0.250955\pi$
$702$	14.9922	−	12.5800i	0.565844	−	0.474800i
$703$	−7.70118			−0.290455
$704$	−18.9560	+	32.8328i	−0.714433	+	1.23743i
$705$	13.2278	−	37.3175i	0.498188	−	1.40546i
$706$	7.33437	−	6.15427i	0.276033	−	0.231619i
$707$			13.7222i			0.516075i
$708$	−0.238146	+	1.35059i	−0.00895008	+	0.0507584i
$709$	39.7775			1.49388			0.746938	−	0.664894i	$-0.231523\pi$
$709$	39.7775			1.49388			0.746938	+	0.664894i	$0.231523\pi$
$710$	−3.76845	−	10.0887i	−0.141427	−	0.378621i
$711$			10.2184i			0.383221i
$712$	−7.19571	+	4.15445i	−0.269671	+	0.155694i
$713$		−	37.0393i		−	1.38713i
$714$	6.02819	−	41.5442i	0.225599	−	1.55475i
$715$	−8.67207	+	24.4651i	−0.324317	+	0.914944i
$716$	33.3114	+	5.87370i	1.24490	+	0.219510i
$717$		−	25.8733i		−	0.966255i
$718$	28.1157	+	33.5070i	1.04927	+	1.25047i
$719$		−	1.06554i		−	0.0397381i	−0.999803	−	0.0198690i	$-0.993675\pi$
$719$		−	1.06554i		−	0.0397381i	0.999803	−	0.0198690i	$-0.00632493\pi$
$720$	−5.02126	+	6.08745i	−0.187131	+	0.226866i
$721$		−	12.3321i		−	0.459272i
$722$	−11.2623	−	13.4218i	−0.419138	−	0.499509i
$723$	16.3609			0.608467
$724$	4.57663	−	25.9554i	0.170089	−	0.964624i
$725$	−22.3746	−	18.1415i	−0.830973	−	0.673760i
$726$	18.0644	−	15.1578i	0.670432	−	0.562560i
$727$		−	19.9877i		−	0.741301i	−0.928772	−	0.370651i	$-0.879135\pi$
$727$		−	19.9877i		−	0.741301i	0.928772	−	0.370651i	$-0.120865\pi$
$728$	29.6832	−	17.1376i	1.10013	−	0.635162i
$729$	−29.5833			−1.09568
$730$	−6.06945	+	2.26713i	−0.224640	+	0.0839104i
$731$	3.64208	−	3.24998i	0.134707	−	0.120205i
$732$	10.0973	+	1.78043i	0.373207	+	0.0658065i
$733$	40.8897			1.51029			0.755147	−	0.655555i	$-0.227565\pi$
$733$	40.8897			1.51029			0.755147	+	0.655555i	$0.227565\pi$
$734$	6.40860	+	7.63747i	0.236546	+	0.281904i
$735$	53.5960	+	18.9980i	1.97692	+	0.700751i
$736$	−11.1862	−	30.7337i	−0.412327	−	1.13286i
$737$	−67.4597			−2.48491
$738$	1.46723	−	1.23115i	0.0540094	−	0.0453193i
$739$		−	25.3149i		−	0.931225i	−0.884989	−	0.465613i	$-0.845834\pi$
$739$		−	25.3149i		−	0.931225i	0.884989	−	0.465613i	$-0.154166\pi$
$740$	6.59964	−	11.6564i	0.242608	−	0.428499i
$741$	9.16515			0.336690
$742$	−14.8776	−	17.7304i	−0.546172	−	0.650903i
$743$	−29.7101			−1.08996			−0.544979	−	0.838450i	$-0.683462\pi$
$743$	−29.7101			−1.08996			−0.544979	+	0.838450i	$0.683462\pi$
$744$	−22.8361	+	13.1844i	−0.837211	+	0.483364i
$745$	10.8616	+	3.85009i	0.397940	+	0.141056i
$746$	29.2216	+	34.8250i	1.06988	+	1.27503i
$747$	−7.53103			−0.275546
$748$	−20.5603	−	33.2330i	−0.751758	−	1.21512i
$749$			49.7145i			1.81653i
$750$	−7.32124	+	21.8136i	−0.267334	+	0.796522i
$751$			14.1647i			0.516877i	0.966028	+	0.258438i	$0.0832079\pi$
$751$			14.1647i			0.516877i	−0.966028	+	0.258438i	$0.916792\pi$
$752$	−16.6458	+	45.7339i	−0.607008	+	1.66774i
$753$	−23.6932			−0.863429
$754$	−12.8280	−	15.2878i	−0.467168	−	0.556750i
$755$	4.39956	−	12.4118i	0.160116	−	0.451711i
$756$	−55.0505	−	9.70690i	−2.00217	−	0.353036i
$757$	29.4570			1.07063			0.535316	−	0.844652i	$-0.320193\pi$
$757$	29.4570			1.07063			0.535316	+	0.844652i	$0.320193\pi$
$758$	−13.0040	−	15.4975i	−0.472325	−	0.562895i
$759$			39.8730i			1.44730i
$760$	−15.9900	+	2.95846i	−0.580018	+	0.107315i
$761$	38.5494			1.39741			0.698707	−	0.715408i	$-0.253759\pi$
$761$	38.5494			1.39741			0.698707	+	0.715408i	$0.253759\pi$
$762$	23.4390	+	27.9335i	0.849106	+	1.01193i
$763$	−17.5126			−0.634000
$764$	5.67768	−	32.1997i	0.205411	−	1.16494i
$765$	−3.07679	−	7.52963i	−0.111242	−	0.272234i
$766$	11.7036	−	9.82047i	0.422868	−	0.354828i
$767$		−	1.15420i		−	0.0416759i
$768$	−14.9666	+	17.8365i	−0.540062	+	0.643621i
$769$	21.9595			0.791881			0.395941	−	0.918276i	$-0.370419\pi$
$769$	21.9595			0.791881			0.395941	+	0.918276i	$0.370419\pi$
$770$	69.4520	−	25.9426i	2.50288	−	0.934906i
$771$	38.1459			1.37379
$772$	6.30390	−	35.7512i	0.226882	−	1.28671i
$773$	0.160158			0.00576050			0.00288025	−	0.999996i	$-0.499083\pi$
$773$	0.160158			0.00576050			0.00288025	+	0.999996i	$0.499083\pi$
$774$	−0.949485	−	1.13155i	−0.0341285	−	0.0406728i
$775$	20.1735	−	24.8808i	0.724655	−	0.893744i
$776$	−13.6844	+	7.90068i	−0.491241	+	0.283618i
$777$	21.5638			0.773597
$778$	18.7640	−	15.7449i	0.672722	−	0.564481i
$779$	3.94695			0.141414
$780$	−7.85422	+	13.8723i	−0.281226	+	0.496708i
$781$		−	16.1393i		−	0.577509i
$782$	33.3633	+	4.84111i	1.19307	+	0.173118i
$783$			32.5478i			1.16316i
$784$	−65.6836	−	23.9069i	−2.34584	−	0.853817i
$785$	−7.57669	+	21.3749i	−0.270424	+	0.762903i
$786$	16.1970	−	13.5909i	0.577728	−	0.484772i
$787$		−	10.2694i		−	0.366066i	−0.983107	−	0.183033i	$-0.941408\pi$
$787$		−	10.2694i		−	0.366066i	0.983107	−	0.183033i	$-0.0585916\pi$
$788$	27.3707	+	4.82620i	0.975041	+	0.171926i
$789$	−38.1208			−1.35713
$790$	−12.8161	−	34.3105i	−0.455976	−	1.22071i
$791$	−17.2867			−0.614646
$792$	−10.2414	+	5.91286i	−0.363911	+	0.210104i
$793$	−8.62905			−0.306427
$794$	−19.2761	+	16.1745i	−0.684082	+	0.574013i
$795$	10.1464	+	3.59655i	0.359855	+	0.127556i
$796$	−36.1877	−	6.38086i	−1.28264	−	0.226164i
$797$	−48.3492			−1.71262			−0.856309	−	0.516464i	$-0.827248\pi$
$797$	−48.3492			−1.71262			−0.856309	+	0.516464i	$0.827248\pi$
$798$	−16.8270	−	20.0536i	−0.595668	−	0.709890i
$799$	−33.4011	−	37.4309i	−1.18165	−	1.32421i
$800$	9.22499	−	26.7376i	0.326153	−	0.945317i
$801$	−2.59175			−0.0915749
$802$	−6.61384	+	5.54967i	−0.233543	+	0.195966i
$803$	−9.70955			−0.342643
$804$	−40.8014	−	7.19439i	−1.43895	−	0.253726i
$805$	−21.3684	+	60.2834i	−0.753138	+	2.12471i
$806$	17.0002	−	14.2648i	0.598806	−	0.502458i
$807$		−	16.3752i		−	0.576434i
$808$	3.92264	+	6.79421i	0.137998	+	0.239019i
$809$		−	33.2009i		−	1.16728i	−0.812012	−	0.583641i	$-0.801627\pi$
$809$		−	33.2009i		−	1.16728i	0.812012	−	0.583641i	$-0.198373\pi$
$810$	16.5147	−	6.16879i	0.580268	−	0.216749i
$811$	6.21778			0.218336			0.109168	−	0.994023i	$-0.465181\pi$
$811$	6.21778			0.218336			0.109168	+	0.994023i	$0.465181\pi$
$812$	−9.89830	+	56.1360i	−0.347362	+	1.96999i
$813$			11.4301i			0.400871i
$814$	15.3775	−	12.9033i	0.538982	−	0.452259i
$815$	−37.7322	−	13.3748i	−1.32170	−	0.468499i
$816$	−8.89119	−	22.2929i	−0.311254	−	0.780407i
$817$		−	3.04396i		−	0.106495i
$818$	1.91108	+	2.27753i	0.0668193	+	0.0796321i
$819$	10.6913			0.373584
$820$	−3.38240	+	5.97407i	−0.118119	+	0.208623i
$821$	37.7686			1.31813			0.659067	−	0.752084i	$-0.270951\pi$
$821$	37.7686			1.31813			0.659067	+	0.752084i	$0.270951\pi$
$822$	10.0563	+	11.9847i	0.350754	+	0.418013i
$823$	1.29018			0.0449727			0.0224864	−	0.999747i	$-0.492842\pi$
$823$	1.29018			0.0449727			0.0224864	+	0.999747i	$0.492842\pi$
$824$	−3.52528	−	6.10596i	−0.122809	−	0.212711i
$825$	−21.7169	+	26.7843i	−0.756085	+	0.932508i
$826$	−2.52543	+	2.11909i	−0.0878709	+	0.0737324i
$827$			18.1062i			0.629614i	0.949156	+	0.314807i	$0.101940\pi$
$827$			18.1062i			0.629614i	−0.949156	+	0.314807i	$0.898060\pi$
$828$	1.77153	−	10.0469i	0.0615650	−	0.349153i
$829$		−	26.7609i		−	0.929444i	−0.885457	−	0.464722i	$-0.846154\pi$
$829$		−	26.7609i		−	0.929444i	0.885457	−	0.464722i	$-0.153846\pi$
$830$	25.2870	−	9.44551i	0.877725	−	0.327859i
$831$	−27.1363			−0.941349
$832$	9.79796	−	16.9706i	0.339683	−	0.588348i
$833$	53.7588	−	47.9712i	1.86263	−	1.66210i
$834$	−12.3713	+	10.3807i	−0.428383	+	0.359456i
$835$	−3.72138	+	10.4985i	−0.128784	+	0.363317i
$836$	−23.9992	−	4.23171i	−0.830030	−	0.146357i
$837$	−36.1934			−1.25103
$838$	2.79448	+	3.33033i	0.0965337	+	0.115044i
$839$			45.5709i			1.57328i	0.617410	+	0.786642i	$0.288182\pi$
$839$			45.5709i			1.57328i	−0.617410	+	0.786642i	$0.711818\pi$
$840$	44.7731	−	8.28389i	1.54482	−	0.285821i
$841$	4.18960			0.144469
$842$	29.5609	−	24.8045i	1.01874	−	0.854820i
$843$		−	2.95421i		−	0.101748i
$844$	0.00716684	−	0.0406452i	0.000246693	−	0.00139906i
$845$	−5.22946	+	14.7531i	−0.179899	+	0.507521i
$846$	−11.6294	+	9.75819i	−0.399826	+	0.335493i
$847$	56.6861			1.94776
$848$	−12.4347	−	4.52586i	−0.427010	−	0.155419i
$849$	26.5964			0.912787
$850$	19.7747	+	21.4234i	0.678268	+	0.734815i
$851$			17.3174i			0.593634i
$852$	1.72121	−	9.76145i	0.0589676	−	0.334422i
$853$			16.6460i			0.569947i	0.958535	+	0.284973i	$0.0919848\pi$
$853$			16.6460i			0.569947i	−0.958535	+	0.284973i	$0.908015\pi$
$854$	15.8427	+	18.8806i	0.542126	+	0.646081i
$855$	−4.78086	−	1.69466i	−0.163502	−	0.0579560i
$856$	14.2114	+	24.6150i	0.485737	+	0.841322i
$857$	−5.93229			−0.202643			−0.101322	−	0.994854i	$-0.532307\pi$
$857$	−5.93229			−0.202643			−0.101322	+	0.994854i	$0.532307\pi$
$858$	−18.3008	+	15.3562i	−0.624778	+	0.524251i
$859$			32.1718i			1.09769i	0.835925	+	0.548844i	$0.184932\pi$
$859$			32.1718i			1.09769i	−0.835925	+	0.548844i	$0.815068\pi$
$860$	4.60730	+	2.60857i	0.157108	+	0.0889514i
$861$	−11.0517			−0.376642
$862$	−3.39812	+	2.85136i	−0.115740	+	0.0971177i
$863$			1.43942i			0.0489984i	0.999700	+	0.0244992i	$0.00779911\pi$
$863$			1.43942i			0.0489984i	−0.999700	+	0.0244992i	$0.992201\pi$
$864$	−30.0318	+	10.9307i	−1.02170	+	0.371870i
$865$	29.7231	+	10.5358i	1.01062	+	0.358229i
$866$	−25.7101	+	21.5733i	−0.873663	+	0.733090i
$867$	24.5796	+	2.80584i	0.834766	+	0.0952914i
$868$	−62.4237	−	11.0070i	−2.11880	−	0.373602i
$869$		−	54.8880i		−	1.86195i
$870$	−9.27692	−	24.8356i	−0.314517	−	0.842007i
$871$	34.8684			1.18147
$872$	−8.67098	+	5.00619i	−0.293636	+	0.169531i
$873$	−4.92884			−0.166816
$874$	16.1046	−	13.5134i	0.544747	−	0.457097i
$875$	−47.1875	+	28.8564i	−1.59523	+	0.975523i
$876$	−5.87259	−	1.03550i	−0.198416	−	0.0349861i
$877$		−	11.1491i		−	0.376477i	−0.982123	−	0.188239i	$-0.939722\pi$
$877$		−	11.1491i		−	0.376477i	0.982123	−	0.188239i	$-0.0602778\pi$
$878$	−1.98639	+	1.66678i	−0.0670374	+	0.0562510i
$879$			41.3457i			1.39456i
$880$	26.9716	−	32.6985i	0.909211	−	1.10227i
$881$		−	25.0028i		−	0.842367i	−0.906975	−	0.421183i	$-0.861615\pi$
$881$		−	25.0028i		−	0.842367i	0.906975	−	0.421183i	$-0.138385\pi$
$882$	−14.0149	−	16.7023i	−0.471905	−	0.562394i
$883$	−7.10014			−0.238939			−0.119469	−	0.992838i	$-0.538119\pi$
$883$	−7.10014			−0.238939			−0.119469	+	0.992838i	$0.538119\pi$
$884$	10.6272	+	17.1774i	0.357430	+	0.577739i
$885$	0.512274	−	1.44520i	0.0172199	−	0.0485798i
$886$	27.0651	+	32.2549i	0.909270	+	1.08363i
$887$	46.1557			1.54976			0.774878	−	0.632111i	$-0.217811\pi$
$887$	46.1557			1.54976			0.774878	+	0.632111i	$0.217811\pi$
$888$	10.6768	−	6.16426i	0.358291	−	0.206859i
$889$			87.6556i			2.93987i
$890$	8.70234	−	3.25060i	0.291703	−	0.108961i
$891$	26.4193			0.885080
$892$	18.5739	+	3.27509i	0.621901	+	0.109658i
$893$	−31.2838			−1.04687
$894$	6.81759	+	8.12489i	0.228014	+	0.271737i
$895$	−35.6447	−	12.6349i	−1.19147	−	0.422337i
$896$	−55.1208	+	9.71929i	−1.84146	+	0.324699i
$897$		−	20.6095i		−	0.688130i
$898$	−12.6583	+	10.6216i	−0.422414	+	0.354448i
$899$			36.9071i			1.23092i
$900$	6.66205	−	5.78401i	0.222068	−	0.192800i
$901$	10.1772	−	9.08153i	0.339052	−	0.302550i
$902$	−7.88117	+	6.61309i	−0.262414	+	0.220192i
$903$			8.52328i			0.283637i
$904$	−8.55912	+	4.94161i	−0.284672	+	0.164356i
$905$	−9.84476	+	27.7735i	−0.327251	+	0.923221i
$906$	9.28445	−	7.79058i	0.308455	−	0.258825i
$907$		−	51.7736i		−	1.71912i	−0.511039	−	0.859558i	$-0.670739\pi$
$907$		−	51.7736i		−	1.71912i	0.511039	−	0.859558i	$-0.329261\pi$
$908$	48.1521	+	8.49051i	1.59798	+	0.281768i
$909$			2.44714i			0.0811664i
$910$	−35.8982	+	13.4091i	−1.19001	+	0.444509i
$911$		−	53.5985i		−	1.77580i	−0.460039	−	0.887899i	$-0.652165\pi$
$911$		−	53.5985i		−	1.77580i	0.460039	−	0.887899i	$-0.347835\pi$
$912$	−14.0640	−	5.11889i	−0.465707	−	0.169503i
$913$	40.4527			1.33879
$914$	−16.9254	+	14.2021i	−0.559842	+	0.469763i
$915$	−10.8046	−	3.82986i	−0.357189	−	0.126611i
$916$	7.07128	+	1.24686i	0.233642	+	0.0411974i
$917$	50.8263			1.67843
$918$	4.73055	−	32.6014i	0.156131	−	1.07601i
$919$	9.30095			0.306810			0.153405	−	0.988163i	$-0.450976\pi$
$919$	9.30095			0.306810			0.153405	+	0.988163i	$0.450976\pi$
$920$	6.65261	+	35.9563i	0.219330	+	1.18544i
$921$		−	36.7638i		−	1.21141i
$922$	20.9075	−	17.5434i	0.688550	−	0.577762i
$923$			8.34203i			0.274581i
$924$	67.1994	+	11.8491i	2.21070	+	0.389806i
$925$	−9.43198	+	11.6328i	−0.310121	+	0.382484i
$926$	−41.0642	+	34.4570i	−1.34945	+	1.13233i
$927$		−	2.19924i		−	0.0722326i
$928$	11.1462	+	30.6240i	0.365893	+	1.00528i
$929$		−	20.5786i		−	0.675163i	−0.941296	−	0.337581i	$-0.890391\pi$
$929$		−	20.5786i		−	0.675163i	0.941296	−	0.337581i	$-0.109609\pi$
$930$	27.6174	−	10.3160i	0.905612	−	0.338275i
$931$		−	44.9303i		−	1.47253i
$932$	−9.14242	+	51.8492i	−0.299470	+	1.69838i
$933$	2.07184			0.0678290
$934$	20.1635	+	24.0300i	0.659771	+	0.786285i
$935$	16.5269	+	40.4452i	0.540487	+	1.32270i
$936$	5.29354	−	3.05623i	0.173025	−	0.0998959i
$937$			42.3504i			1.38353i	0.722123	+	0.691764i	$0.243166\pi$
$937$			42.3504i			1.38353i	−0.722123	+	0.691764i	$0.756834\pi$
$938$	−64.0175	−	76.2931i	−2.09025	−	2.49106i
$939$		−	34.1583i		−	1.11471i
$940$	26.8091	−	47.3509i	0.874418	−	1.54441i
$941$	−38.3381			−1.24979			−0.624893	−	0.780711i	$-0.714857\pi$
$941$	−38.3381			−1.24979			−0.624893	+	0.780711i	$0.714857\pi$
$942$	−15.9892	+	13.4165i	−0.520955	+	0.437133i
$943$		−	8.87541i		−	0.289023i
$944$	−0.644642	+	1.77114i	−0.0209813	+	0.0576456i
$945$	58.9066	+	20.8804i	1.91623	+	0.679240i
$946$	5.10013	+	6.07810i	0.165819	+	0.197616i
$947$			16.9252i			0.549994i	0.961445	+	0.274997i	$0.0886769\pi$
$947$			16.9252i			0.549994i	−0.961445	+	0.274997i	$0.911323\pi$
$948$	5.85364	−	33.1977i	0.190117	−	1.07821i
$949$	5.01865			0.162912
$950$	18.1782	−	0.306062i	0.589779	−	0.00992995i
$951$	−32.2722			−1.04650
$952$	18.0735	−	54.7898i	0.585765	−	1.77575i
$953$		−	41.0752i		−	1.33056i	−0.746595	−	0.665278i	$-0.768313\pi$
$953$		−	41.0752i		−	1.33056i	0.746595	−	0.665278i	$-0.231687\pi$
$954$	−2.65318	−	3.16194i	−0.0859000	−	0.102372i
$955$	−12.2132	+	34.4552i	−0.395210	+	1.11494i
$956$	6.17469	−	35.0184i	0.199704	−	1.13258i
$957$		−	39.7306i		−	1.28431i
$958$	0.0720364	−	0.0604457i	0.00232739	−	0.00195291i
$959$			37.6079i			1.21442i
$960$	19.8003	−	16.9005i	0.639052	−	0.545460i
$961$	−10.0410			−0.323903
$962$	−7.94830	+	6.66941i	−0.256263	+	0.215031i
$963$			8.86580i			0.285697i
$964$	22.1437	+	3.90454i	0.713202	+	0.125757i
$965$	−13.5603	+	38.2554i	−0.436521	+	1.23149i
$966$	−45.0940	+	37.8384i	−1.45088	+	1.21743i
$967$		−	24.2611i		−	0.780186i	−0.920776	−	0.390093i	$-0.872443\pi$
$967$		−	24.2611i		−	0.780186i	0.920776	−	0.390093i	$-0.127557\pi$
$968$	28.0668	−	16.2044i	0.902102	−	0.520829i
$969$	11.5107	−	10.2715i	0.369778	−	0.329968i
$970$	16.5496	−	6.18181i	0.531375	−	0.198486i
$971$		−	25.2618i		−	0.810690i	−0.914164	−	0.405345i	$-0.867151\pi$
$971$		−	25.2618i		−	0.810690i	0.914164	−	0.405345i	$-0.132849\pi$
$972$	−17.4038	−	3.06876i	−0.558227	−	0.0984304i
$973$	−38.8212			−1.24455
$974$	13.9602	+	16.6371i	0.447313	+	0.533087i
$975$	11.2250	−	13.8442i	0.359487	−	0.443369i
$976$	13.2414	+	4.81947i	0.423846	+	0.154267i
$977$			45.6616i			1.46084i	0.682997	+	0.730422i	$0.260676\pi$
$977$			45.6616i			1.46084i	−0.682997	+	0.730422i	$0.739324\pi$
$978$	−23.6836	−	28.2250i	−0.757317	−	0.902535i
$979$	13.9215			0.444933
$980$	68.0060	+	38.5037i	2.17237	+	1.22996i
$981$	−3.12311			−0.0997132
$982$	27.3238	−	22.9274i	0.871938	−	0.731643i
$983$	−54.8613			−1.74980			−0.874901	−	0.484302i	$-0.839074\pi$
$983$	−54.8613			−1.74980			−0.874901	+	0.484302i	$0.839074\pi$
$984$	−5.47201	+	3.15926i	−0.174441	+	0.100714i
$985$	−29.2879	−	10.3816i	−0.933191	−	0.330785i
$986$	−33.2442	−	4.82383i	−1.05871	−	0.153622i
$987$	87.5967			2.78824
$988$	12.4047	+	2.18727i	0.394645	+	0.0695865i
$989$	−6.84487			−0.217654
$990$	12.3857	−	4.62646i	0.393643	−	0.147039i
$991$		−	39.4679i		−	1.25374i	−0.779124	−	0.626870i	$-0.784336\pi$
$991$		−	39.4679i		−	1.25374i	0.779124	−	0.626870i	$-0.215664\pi$
$992$	−34.0541	+	12.3947i	−1.08122	+	0.393532i
$993$	−18.0351			−0.572326
$994$	18.2526	−	15.3157i	0.578937	−	0.485786i
$995$	38.7225	+	13.7258i	1.22758	+	0.435138i
$996$	24.4668	+	4.31416i	0.775261	+	0.136699i
$997$		−	0.717186i		−	0.0227135i	−0.999936	−	0.0113567i	$-0.996385\pi$
$997$		−	0.717186i		−	0.0227135i	0.999936	−	0.0113567i	$-0.00361504\pi$
$998$	8.00249	+	9.53700i	0.253314	+	0.301888i
$999$	16.9220			0.535387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.c.509.11	yes	48
5.4	even	2	inner	680.2.h.c.509.38	yes	48
8.5	even	2	inner	680.2.h.c.509.34	yes	48
17.16	even	2	inner	680.2.h.c.509.10	✓	48
40.29	even	2	inner	680.2.h.c.509.15	yes	48
85.84	even	2	inner	680.2.h.c.509.39	yes	48
136.101	even	2	inner	680.2.h.c.509.35	yes	48
680.509	even	2	inner	680.2.h.c.509.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.c.509.10	✓	48	17.16	even	2	inner
680.2.h.c.509.11	yes	48	1.1	even	1	trivial
680.2.h.c.509.14	yes	48	680.509	even	2	inner
680.2.h.c.509.15	yes	48	40.29	even	2	inner
680.2.h.c.509.34	yes	48	8.5	even	2	inner
680.2.h.c.509.35	yes	48	136.101	even	2	inner
680.2.h.c.509.38	yes	48	5.4	even	2	inner
680.2.h.c.509.39	yes	48	85.84	even	2	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 - 1.08335i) q^{2} +1.45525i q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.747066 - 2.10758i) q^{5} +(1.57654 - 1.32288i) q^{6} +4.94720 q^{7} +(2.44949 - 1.41421i) q^{8} +0.882256 q^{9} +(-2.96236 + 1.10654i) q^{10} -4.73901 q^{11} +(-2.86628 - 0.505402i) q^{12} +2.44949 q^{13} +(-4.49720 - 5.35955i) q^{14} +(3.06705 + 1.08717i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(3.07637 - 2.74517i) q^{17} +(-0.802005 - 0.955793i) q^{18} -2.57115i q^{19} +(3.89167 + 2.20339i) q^{20} +7.19939i q^{21} +(4.30795 + 5.13401i) q^{22} -5.78168 q^{23} +(2.05803 + 3.56461i) q^{24} +(-3.88378 - 3.14900i) q^{25} +(-2.22668 - 2.65366i) q^{26} +5.64964i q^{27} +(-1.71814 + 9.74408i) q^{28} +5.76104 q^{29} +(-1.61029 - 4.31096i) q^{30} +6.40633i q^{31} +(1.93476 + 5.31570i) q^{32} -6.89643i q^{33} +(-5.77052 - 0.837319i) q^{34} +(3.69588 - 10.4266i) q^{35} +(-0.306404 + 1.73771i) q^{36} -2.99523i q^{37} +(-2.78546 + 2.33728i) q^{38} +3.56461i q^{39} +(-1.15064 - 6.21901i) q^{40} +1.53509i q^{41} +(7.79947 - 6.54453i) q^{42} +1.18389 q^{43} +(1.64584 - 9.33403i) q^{44} +(0.659104 - 1.85943i) q^{45} +(5.25577 + 6.26359i) q^{46} -12.1672i q^{47} +(1.99090 - 5.46994i) q^{48} +17.4748 q^{49} +(0.119037 + 7.07007i) q^{50} +(3.99490 + 4.47688i) q^{51} +(-0.850699 + 4.82455i) q^{52} +3.30819 q^{53} +(6.12054 - 5.13574i) q^{54} +(-3.54036 + 9.98784i) q^{55} +(12.1181 - 6.99639i) q^{56} +3.74166 q^{57} +(-5.23701 - 6.24123i) q^{58} -0.471202i q^{59} +(-3.20647 + 5.66334i) q^{60} -3.52280 q^{61} +(6.94030 - 5.82360i) q^{62} +4.36470 q^{63} +(4.00000 - 6.92820i) q^{64} +(1.82993 - 5.16249i) q^{65} +(-7.47125 + 6.26913i) q^{66} +14.2350 q^{67} +(4.33852 + 7.01265i) q^{68} -8.41377i q^{69} +(-14.6554 + 5.47426i) q^{70} +3.40562i q^{71} +(2.16108 - 1.24770i) q^{72} +2.04886 q^{73} +(-3.24488 + 2.72278i) q^{74} +(4.58258 - 5.65186i) q^{75} +(5.06418 + 0.892951i) q^{76} -23.4448 q^{77} +(3.86172 - 3.24037i) q^{78} +11.5822i q^{79} +(-5.69139 + 6.89986i) q^{80} -5.57485 q^{81} +(1.66304 - 1.39546i) q^{82} -8.53610 q^{83} +(-14.1800 - 2.50032i) q^{84} +(-3.48741 - 8.53452i) q^{85} +(-1.07620 - 1.28257i) q^{86} +8.38374i q^{87} +(-11.6082 + 6.70197i) q^{88} -2.93764 q^{89} +(-2.61356 + 0.976250i) q^{90} +12.1181 q^{91} +(2.00796 - 11.3877i) q^{92} -9.32279 q^{93} +(-13.1814 + 11.0605i) q^{94} +(-5.41890 - 1.92082i) q^{95} +(-7.73566 + 2.81555i) q^{96} -5.58663 q^{97} +(-15.8852 - 18.9313i) q^{98} -4.18102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) \) 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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