LMFDB - Embedded newform 440.2.l.c.309.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(309,440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("440.309"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			309.32
Character	$\chi$	$=$	440.309
Dual form			440.2.l.c.309.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.109317 + 1.40998i) q^{2} +2.58970 q^{3} +(-1.97610 + 0.308271i) q^{4} +(0.464619 + 2.18727i) q^{5} +(0.283099 + 3.65143i) q^{6} +1.54883i q^{7} +(-0.650678 - 2.75257i) q^{8} +3.70654 q^{9} +(-3.03321 + 0.894210i) q^{10} +1.00000i q^{11} +(-5.11750 + 0.798329i) q^{12} -0.752399 q^{13} +(-2.18382 + 0.169314i) q^{14} +(1.20322 + 5.66436i) q^{15} +(3.80994 - 1.21835i) q^{16} -1.76374i q^{17} +(0.405189 + 5.22616i) q^{18} -6.61274i q^{19} +(-1.59240 - 4.17903i) q^{20} +4.01100i q^{21} +(-1.40998 + 0.109317i) q^{22} +4.37442i q^{23} +(-1.68506 - 7.12832i) q^{24} +(-4.56826 + 2.03249i) q^{25} +(-0.0822503 - 1.06087i) q^{26} +1.82973 q^{27} +(-0.477458 - 3.06064i) q^{28} -1.83376i q^{29} +(-7.85511 + 2.31574i) q^{30} +6.97780 q^{31} +(2.13434 + 5.23876i) q^{32} +2.58970i q^{33} +(2.48685 - 0.192808i) q^{34} +(-3.38770 + 0.719615i) q^{35} +(-7.32449 + 1.14262i) q^{36} -4.70395 q^{37} +(9.32385 - 0.722887i) q^{38} -1.94849 q^{39} +(5.71827 - 2.70210i) q^{40} +6.83919 q^{41} +(-5.65543 + 0.438471i) q^{42} +5.43888 q^{43} +(-0.308271 - 1.97610i) q^{44} +(1.72213 + 8.10719i) q^{45} +(-6.16786 + 0.478200i) q^{46} -1.78733i q^{47} +(9.86659 - 3.15515i) q^{48} +4.60113 q^{49} +(-3.36516 - 6.21898i) q^{50} -4.56756i q^{51} +(1.48682 - 0.231943i) q^{52} -3.54061 q^{53} +(0.200021 + 2.57988i) q^{54} +(-2.18727 + 0.464619i) q^{55} +(4.26325 - 1.00779i) q^{56} -17.1250i q^{57} +(2.58556 - 0.200461i) q^{58} +0.926285i q^{59} +(-4.12385 - 10.8224i) q^{60} -11.3104i q^{61} +(0.762794 + 9.83857i) q^{62} +5.74079i q^{63} +(-7.15324 + 3.58207i) q^{64} +(-0.349579 - 1.64570i) q^{65} +(-3.65143 + 0.283099i) q^{66} -10.4970 q^{67} +(0.543710 + 3.48533i) q^{68} +11.3284i q^{69} +(-1.38498 - 4.69793i) q^{70} +10.7739 q^{71} +(-2.41177 - 10.2025i) q^{72} -3.66071i q^{73} +(-0.514223 - 6.63248i) q^{74} +(-11.8304 + 5.26354i) q^{75} +(2.03852 + 13.0674i) q^{76} -1.54883 q^{77} +(-0.213003 - 2.74733i) q^{78} -15.4808 q^{79} +(4.43502 + 7.76728i) q^{80} -6.38118 q^{81} +(0.747642 + 9.64314i) q^{82} -11.5798 q^{83} +(-1.23647 - 7.92613i) q^{84} +(3.85777 - 0.819468i) q^{85} +(0.594564 + 7.66872i) q^{86} -4.74887i q^{87} +(2.75257 - 0.650678i) q^{88} +13.3280 q^{89} +(-11.2427 + 3.31443i) q^{90} -1.16534i q^{91} +(-1.34851 - 8.64430i) q^{92} +18.0704 q^{93} +(2.52010 - 0.195386i) q^{94} +(14.4638 - 3.07241i) q^{95} +(5.52730 + 13.5668i) q^{96} -15.4078i q^{97} +(0.502983 + 6.48752i) q^{98} +3.70654i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{4} - 12 q^{6} + 56 q^{9} - 10 q^{10} - 32 q^{14} - 8 q^{15} + 16 q^{16} + 8 q^{20} - 16 q^{24} + 16 q^{25} - 12 q^{26} + 38 q^{30} + 72 q^{34} - 24 q^{36} - 16 q^{39} + 12 q^{40} - 32 q^{41}+ \cdots - 16 q^{96}+O(q^{100}) $ 56 * q + 4 * q^4 - 12 * q^6 + 56 * q^9 - 10 * q^10 - 32 * q^14 - 8 * q^15 + 16 * q^16 + 8 * q^20 - 16 * q^24 + 16 * q^25 - 12 * q^26 + 38 * q^30 + 72 * q^34 - 24 * q^36 - 16 * q^39 + 12 * q^40 - 32 * q^41 - 12 * q^44 + 20 * q^46 - 24 * q^49 - 54 * q^50 - 52 * q^54 - 8 * q^55 + 4 * q^64 - 32 * q^65 - 8 * q^66 + 48 * q^71 + 12 * q^74 - 32 * q^76 - 32 * q^79 + 24 * q^80 + 88 * q^81 + 16 * q^84 - 68 * q^86 - 16 * q^89 - 8 * q^90 - 24 * q^94 + 24 * q^95 - 16 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	0.109317	+	1.40998i	0.0772990	+	0.997008i
$2$	0.109317	+	1.40998i	0.0772990	+	0.997008i
$3$	2.58970			1.49516			0.747582	−	0.664170i	$-0.231215\pi$
$3$	2.58970			1.49516			0.747582	+	0.664170i	$0.231215\pi$
$4$	−1.97610	+	0.308271i	−0.988050	+	0.154135i
$5$	0.464619	+	2.18727i	0.207784	+	0.978175i
$5$	0.464619	+	2.18727i	0.207784	+	0.978175i
$6$	0.283099	+	3.65143i	0.115575	+	1.49069i
$7$			1.54883i			0.585402i	0.956204	+	0.292701i	$0.0945540\pi$
$7$			1.54883i			0.585402i	−0.956204	+	0.292701i	$0.905446\pi$
$8$	−0.650678	−	2.75257i	−0.230050	−	0.973179i
$9$	3.70654			1.23551
$10$	−3.03321	+	0.894210i	−0.959187	+	0.282774i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−5.11750	+	0.798329i	−1.47730	+	0.230458i
$13$	−0.752399			−0.208678			−0.104339	−	0.994542i	$-0.533273\pi$
$13$	−0.752399			−0.208678			−0.104339	+	0.994542i	$0.533273\pi$
$14$	−2.18382	+	0.169314i	−0.583650	+	0.0452510i
$15$	1.20322	+	5.66436i	0.310671	+	1.46253i
$16$	3.80994	−	1.21835i	0.952485	−	0.304587i
$17$		−	1.76374i		−	0.427770i	−0.976859	−	0.213885i	$-0.931388\pi$
$17$		−	1.76374i		−	0.427770i	0.976859	−	0.213885i	$-0.0686119\pi$
$18$	0.405189	+	5.22616i	0.0955039	+	1.23182i
$19$		−	6.61274i		−	1.51707i	−0.651634	−	0.758534i	$-0.725916\pi$
$19$		−	6.61274i		−	1.51707i	0.651634	−	0.758534i	$-0.274084\pi$
$20$	−1.59240	−	4.17903i	−0.356072	−	0.934458i
$21$			4.01100i			0.875271i
$22$	−1.40998	+	0.109317i	−0.300609	+	0.0233065i
$23$			4.37442i			0.912130i	0.889946	+	0.456065i	$0.150742\pi$
$23$			4.37442i			0.912130i	−0.889946	+	0.456065i	$0.849258\pi$
$24$	−1.68506	−	7.12832i	−0.343962	−	1.45506i
$25$	−4.56826	+	2.03249i	−0.913652	+	0.406498i
$26$	−0.0822503	−	1.06087i	−0.0161306	−	0.208054i
$27$	1.82973			0.352131
$28$	−0.477458	−	3.06064i	−0.0902312	−	0.578406i
$29$		−	1.83376i		−	0.340520i	−0.985399	−	0.170260i	$-0.945539\pi$
$29$		−	1.83376i		−	0.340520i	0.985399	−	0.170260i	$-0.0544607\pi$
$30$	−7.85511	+	2.31574i	−1.43414	+	0.422794i
$31$	6.97780			1.25325			0.626625	−	0.779321i	$-0.284436\pi$
$31$	6.97780			1.25325			0.626625	+	0.779321i	$0.284436\pi$
$32$	2.13434	+	5.23876i	0.377302	+	0.926090i
$33$			2.58970i			0.450809i
$34$	2.48685	−	0.192808i	0.426491	−	0.0330662i
$35$	−3.38770	+	0.719615i	−0.572625	+	0.121637i
$36$	−7.32449	+	1.14262i	−1.22075	+	0.190436i
$37$	−4.70395			−0.773324			−0.386662	−	0.922222i	$-0.626372\pi$
$37$	−4.70395			−0.773324			−0.386662	+	0.922222i	$0.626372\pi$
$38$	9.32385	−	0.722887i	1.51253	−	0.117268i
$39$	−1.94849			−0.312008
$40$	5.71827	−	2.70210i	0.904138	−	0.427240i
$41$	6.83919			1.06810			0.534051	−	0.845452i	$-0.320669\pi$
$41$	6.83919			1.06810			0.534051	+	0.845452i	$0.320669\pi$
$42$	−5.65543	+	0.438471i	−0.872653	+	0.0676576i
$43$	5.43888			0.829421			0.414711	−	0.909953i	$-0.363883\pi$
$43$	5.43888			0.829421			0.414711	+	0.909953i	$0.363883\pi$
$44$	−0.308271	−	1.97610i	−0.0464736	−	0.297908i
$45$	1.72213	+	8.10719i	0.256720	+	1.20855i
$46$	−6.16786	+	0.478200i	−0.909401	+	0.0705068i
$47$		−	1.78733i		−	0.260709i	−0.991467	−	0.130354i	$-0.958389\pi$
$47$		−	1.78733i		−	0.260709i	0.991467	−	0.130354i	$-0.0416115\pi$
$48$	9.86659	−	3.15515i	1.42412	−	0.455407i
$49$	4.60113			0.657305
$50$	−3.36516	−	6.21898i	−0.475906	−	0.879496i
$51$		−	4.56756i		−	0.639587i
$52$	1.48682	−	0.231943i	0.206184	−	0.0321647i
$53$	−3.54061			−0.486340			−0.243170	−	0.969984i	$-0.578187\pi$
$53$	−3.54061			−0.486340			−0.243170	+	0.969984i	$0.578187\pi$
$54$	0.200021	+	2.57988i	0.0272194	+	0.351077i
$55$	−2.18727	+	0.464619i	−0.294931	+	0.0626492i
$56$	4.26325	−	1.00779i	0.569701	−	0.134671i
$57$		−	17.1250i		−	2.26826i
$58$	2.58556	−	0.200461i	0.339501	−	0.0263218i
$59$			0.926285i			0.120592i	0.998181	+	0.0602960i	$0.0192045\pi$
$59$			0.926285i			0.120592i	−0.998181	+	0.0602960i	$0.980796\pi$
$60$	−4.12385	−	10.8224i	−0.532386	−	1.39717i
$61$		−	11.3104i		−	1.44815i	−0.689721	−	0.724075i	$-0.742267\pi$
$61$		−	11.3104i		−	1.44815i	0.689721	−	0.724075i	$-0.257733\pi$
$62$	0.762794	+	9.83857i	0.0968749	+	1.24950i
$63$			5.74079i			0.723272i
$64$	−7.15324	+	3.58207i	−0.894154	+	0.447759i
$65$	−0.349579	−	1.64570i	−0.0433600	−	0.204124i
$66$	−3.65143	+	0.283099i	−0.449460	+	0.0348471i
$67$	−10.4970			−1.28241			−0.641206	−	0.767369i	$-0.721566\pi$
$67$	−10.4970			−1.28241			−0.641206	+	0.767369i	$0.721566\pi$
$68$	0.543710	+	3.48533i	0.0659346	+	0.422658i
$69$			11.3284i			1.36378i
$70$	−1.38498	−	4.69793i	−0.165537	−	0.561510i
$71$	10.7739			1.27863			0.639316	−	0.768944i	$-0.279218\pi$
$71$	10.7739			1.27863			0.639316	+	0.768944i	$0.279218\pi$
$72$	−2.41177	−	10.2025i	−0.284229	−	1.20238i
$73$		−	3.66071i		−	0.428453i	−0.976784	−	0.214227i	$-0.931277\pi$
$73$		−	3.66071i		−	0.428453i	0.976784	−	0.214227i	$-0.0687231\pi$
$74$	−0.514223	−	6.63248i	−0.0597772	−	0.771010i
$75$	−11.8304	+	5.26354i	−1.36606	+	0.607781i
$76$	2.03852	+	13.0674i	0.233834	+	1.49894i
$77$	−1.54883			−0.176505
$78$	−0.213003	−	2.74733i	−0.0241179	−	0.311074i
$79$	−15.4808			−1.74173			−0.870864	−	0.491525i	$-0.836440\pi$
$79$	−15.4808			−1.74173			−0.870864	+	0.491525i	$0.836440\pi$
$80$	4.43502	+	7.76728i	0.495850	+	0.868408i
$81$	−6.38118			−0.709020
$82$	0.747642	+	9.64314i	0.0825632	+	1.06491i
$83$	−11.5798			−1.27105			−0.635524	−	0.772081i	$-0.719216\pi$
$83$	−11.5798			−1.27105			−0.635524	+	0.772081i	$0.719216\pi$
$84$	−1.23647	−	7.92613i	−0.134910	−	0.864812i
$85$	3.85777	−	0.819468i	0.418434	−	0.0888838i
$86$	0.594564	+	7.66872i	0.0641134	+	0.826940i
$87$		−	4.74887i		−	0.509133i
$88$	2.75257	−	0.650678i	0.293424	−	0.0693625i
$89$	13.3280			1.41277			0.706385	−	0.707828i	$-0.250325\pi$
$89$	13.3280			1.41277			0.706385	+	0.707828i	$0.250325\pi$
$90$	−11.2427	+	3.31443i	−1.18509	+	0.349371i
$91$		−	1.16534i		−	0.122161i
$92$	−1.34851	−	8.64430i	−0.140592	−	0.901230i
$93$	18.0704			1.87381
$94$	2.52010	−	0.195386i	0.259928	−	0.0201525i
$95$	14.4638	−	3.07241i	1.48396	−	0.315222i
$96$	5.52730	+	13.5668i	0.564128	+	1.38466i
$97$		−	15.4078i		−	1.56442i	−0.623015	−	0.782210i	$-0.714092\pi$
$97$		−	15.4078i		−	1.56442i	0.623015	−	0.782210i	$-0.285908\pi$
$98$	0.502983	+	6.48752i	0.0508090	+	0.655338i
$99$			3.70654i			0.372521i
$100$	8.40078	−	5.42466i	0.840078	−	0.542466i
$101$		−	10.6198i		−	1.05671i	−0.849024	−	0.528355i	$-0.822809\pi$
$101$		−	10.6198i		−	1.05671i	0.849024	−	0.528355i	$-0.177191\pi$
$102$	6.44018	−	0.499314i	0.637673	−	0.0494394i
$103$			17.7848i			1.75239i	0.481957	+	0.876195i	$0.339926\pi$
$103$			17.7848i			1.75239i	−0.481957	+	0.876195i	$0.660074\pi$
$104$	0.489570	+	2.07103i	0.0480063	+	0.203081i
$105$	−8.77312	+	1.86359i	−0.856168	+	0.181867i
$106$	−0.387050	−	4.99220i	−0.0375936	−	0.484885i
$107$	20.2954			1.96203			0.981013	−	0.193940i	$-0.0621268\pi$
$107$	20.2954			1.96203			0.981013	+	0.193940i	$0.0621268\pi$
$108$	−3.61572	+	0.564051i	−0.347923	+	0.0542759i
$109$		−	7.63435i		−	0.731238i	−0.930765	−	0.365619i	$-0.880857\pi$
$109$		−	7.63435i		−	0.731238i	0.930765	−	0.365619i	$-0.119143\pi$
$110$	−0.894210	−	3.03321i	−0.0852596	−	0.289206i
$111$	−12.1818			−1.15625
$112$	1.88701	+	5.90094i	0.178306	+	0.557586i
$113$		−	10.8737i		−	1.02291i	−0.859311	−	0.511454i	$-0.829107\pi$
$113$		−	10.8737i		−	1.02291i	0.859311	−	0.511454i	$-0.170893\pi$
$114$	24.1460	−	1.87206i	2.26148	−	0.175335i
$115$	−9.56802	+	2.03244i	−0.892223	+	0.189526i
$116$	0.565293	+	3.62368i	0.0524862	+	0.336450i
$117$	−2.78880			−0.257825
$118$	−1.30605	+	0.101259i	−0.120231	+	0.00932164i
$119$	2.73173			0.250418
$120$	14.8086	−	6.99763i	1.35183	−	0.638793i
$121$	−1.00000			−0.0909091
$122$	15.9475	−	1.23642i	1.44382	−	0.111941i
$123$	17.7114			1.59699
$124$	−13.7888	+	2.15105i	−1.23827	+	0.193170i
$125$	−6.56809	−	9.04766i	−0.587468	−	0.809247i
$126$	−8.09441	+	0.627568i	−0.721108	+	0.0559082i
$127$			11.7676i			1.04420i	0.852883	+	0.522101i	$0.174852\pi$
$127$			11.7676i			1.04420i	−0.852883	+	0.522101i	$0.825148\pi$
$128$	−5.83263	−	9.69435i	−0.515536	−	0.856868i
$129$	14.0851			1.24012
$130$	2.28219	−	0.672803i	0.200161	−	0.0590088i
$131$			5.25004i			0.458698i	0.973344	+	0.229349i	$0.0736597\pi$
$131$			5.25004i			0.458698i	−0.973344	+	0.229349i	$0.926340\pi$
$132$	−0.798329	−	5.11750i	−0.0694856	−	0.445421i
$133$	10.2420			0.888094
$134$	−1.14750	−	14.8006i	−0.0991291	−	1.27857i
$135$	0.850126	+	4.00210i	0.0731672	+	0.344446i
$136$	−4.85482	+	1.14763i	−0.416297	+	0.0984084i
$137$			14.0671i			1.20183i	0.799312	+	0.600916i	$0.205197\pi$
$137$			14.0671i			1.20183i	−0.799312	+	0.600916i	$0.794803\pi$
$138$	−15.9729	+	1.23839i	−1.35970	+	0.105419i
$139$			12.2586i			1.03976i	0.854239	+	0.519881i	$0.174024\pi$
$139$			12.2586i			1.03976i	−0.854239	+	0.519881i	$0.825976\pi$
$140$	6.47259	−	2.46636i	0.547034	−	0.208445i
$141$		−	4.62864i		−	0.389802i
$142$	1.17778	+	15.1911i	0.0988370	+	1.27481i
$143$		−	0.752399i		−	0.0629188i
$144$	14.1217	−	4.51585i	1.17681	−	0.376321i
$145$	4.01091	−	0.851998i	0.333088	−	0.0707545i
$146$	5.16153	−	0.400179i	0.427171	−	0.0331190i
$147$	11.9155			0.982778
$148$	9.29546	−	1.45009i	0.764082	−	0.119197i
$149$			1.16054i			0.0950754i	0.998869	+	0.0475377i	$0.0151374\pi$
$149$			1.16054i			0.0950754i	−0.998869	+	0.0475377i	$0.984863\pi$
$150$	−8.71476	−	16.1053i	−0.711557	−	1.31499i
$151$	−14.6795			−1.19460			−0.597301	−	0.802017i	$-0.703760\pi$
$151$	−14.6795			−1.19460			−0.597301	+	0.802017i	$0.703760\pi$
$152$	−18.2020	+	4.30277i	−1.47638	+	0.349001i
$153$		−	6.53738i		−	0.528516i
$154$	−0.169314	−	2.18382i	−0.0136437	−	0.175977i
$155$	3.24202	+	15.2623i	0.260405	+	1.22590i
$156$	3.85041	−	0.600662i	0.308279	−	0.0480915i
$157$	4.01441			0.320385			0.160193	−	0.987086i	$-0.448788\pi$
$157$	4.01441			0.320385			0.160193	+	0.987086i	$0.448788\pi$
$158$	−1.69232	−	21.8277i	−0.134634	−	1.73652i
$159$	−9.16912			−0.727158
$160$	−10.4669	+	7.10240i	−0.827481	+	0.561494i
$161$	−6.77523			−0.533963
$162$	−0.697573	−	8.99735i	−0.0548065	−	0.706899i
$163$	−7.46616			−0.584795			−0.292397	−	0.956297i	$-0.594453\pi$
$163$	−7.46616			−0.584795			−0.292397	+	0.956297i	$0.594453\pi$
$164$	−13.5149	+	2.10832i	−1.05534	+	0.164632i
$165$	−5.66436	+	1.20322i	−0.440970	+	0.0936708i
$166$	−1.26587	−	16.3273i	−0.0982507	−	1.26724i
$167$		−	15.1107i		−	1.16930i	−0.811285	−	0.584651i	$-0.801231\pi$
$167$		−	15.1107i		−	1.16930i	0.811285	−	0.584651i	$-0.198769\pi$
$168$	11.0405	−	2.60987i	0.851796	−	0.201356i
$169$	−12.4339			−0.956453
$170$	1.57716	+	5.34981i	0.120962	+	0.410312i
$171$		−	24.5104i		−	1.87436i
$172$	−10.7478	+	1.67665i	−0.819510	+	0.127843i
$173$	−2.86596			−0.217895			−0.108948	−	0.994047i	$-0.534748\pi$
$173$	−2.86596			−0.217895			−0.108948	+	0.994047i	$0.534748\pi$
$174$	6.69583	−	0.519134i	0.507609	−	0.0393554i
$175$	−3.14798	−	7.07545i	−0.237965	−	0.534853i
$176$	1.21835	+	3.80994i	0.0918364	+	0.287185i
$177$			2.39880i			0.180305i
$178$	1.45699	+	18.7923i	0.109206	+	1.40854i
$179$			19.8650i			1.48478i	0.669969	+	0.742389i	$0.266307\pi$
$179$			19.8650i			1.48478i	−0.669969	+	0.742389i	$0.733693\pi$
$180$	−5.90231	−	15.4897i	−0.439932	−	1.15454i
$181$		−	14.9306i		−	1.10979i	−0.831922	−	0.554893i	$-0.812759\pi$
$181$		−	14.9306i		−	1.10979i	0.831922	−	0.554893i	$-0.187241\pi$
$182$	1.64310	−	0.127391i	0.121795	−	0.00944289i
$183$		−	29.2906i		−	2.16522i
$184$	12.0409	−	2.84634i	0.887666	−	0.209835i
$185$	−2.18554	−	10.2888i	−0.160684	−	0.756446i
$186$	1.97541	+	25.4789i	0.144844	+	1.86821i
$187$	1.76374			0.128978
$188$	0.550981	+	3.53194i	0.0401844	+	0.257593i
$189$			2.83393i			0.206138i
$190$	5.91319	+	20.0579i	0.428988	+	1.45515i
$191$	6.07662			0.439689			0.219844	−	0.975535i	$-0.429445\pi$
$191$	6.07662			0.439689			0.219844	+	0.975535i	$0.429445\pi$
$192$	−18.5247	+	9.27648i	−1.33691	+	0.669472i
$193$			18.0035i			1.29592i	0.761674	+	0.647961i	$0.224378\pi$
$193$			18.0035i			1.29592i	−0.761674	+	0.647961i	$0.775622\pi$
$194$	21.7247	−	1.68433i	1.55974	−	0.120928i
$195$	−0.905305	−	4.26186i	−0.0648302	−	0.305198i
$196$	−9.09230	+	1.41840i	−0.649450	+	0.101314i
$197$	−15.9200			−1.13425			−0.567127	−	0.823630i	$-0.691945\pi$
$197$	−15.9200			−1.13425			−0.567127	+	0.823630i	$0.691945\pi$
$198$	−5.22616	+	0.405189i	−0.371407	+	0.0287955i
$199$	−20.3525			−1.44275			−0.721375	−	0.692545i	$-0.756489\pi$
$199$	−20.3525			−1.44275			−0.721375	+	0.692545i	$0.756489\pi$
$200$	8.56703	+	11.2519i	0.605780	+	0.795632i
$201$	−27.1840			−1.91741
$202$	14.9737	−	1.16093i	1.05355	−	0.0816826i
$203$	2.84017			0.199341
$204$	1.40805	+	9.02596i	0.0985830	+	0.631943i
$205$	3.17762	+	14.9591i	0.221935	+	1.04479i
$206$	−25.0763	+	1.94419i	−1.74715	+	0.135458i
$207$			16.2140i			1.12695i
$208$	−2.86660	+	0.916684i	−0.198763	+	0.0635606i
$209$	6.61274			0.457413
$210$	−3.58668	−	12.1662i	−0.247504	−	0.839549i
$211$			0.768643i			0.0529156i	0.999650	+	0.0264578i	$0.00842276\pi$
$211$			0.768643i			0.0529156i	−0.999650	+	0.0264578i	$0.991577\pi$
$212$	6.99660	−	1.09147i	0.480529	−	0.0749623i
$213$	27.9013			1.91176
$214$	2.21863	+	28.6161i	0.151663	+	1.95616i
$215$	2.52701	+	11.8963i	0.172340	+	0.811319i
$216$	−1.19056	−	5.03644i	−0.0810076	−	0.342686i
$217$			10.8074i			0.733655i
$218$	10.7643	−	0.834566i	0.729050	−	0.0565239i
$219$		−	9.48013i		−	0.640608i
$220$	4.17903	−	1.59240i	0.281750	−	0.107360i
$221$			1.32704i			0.0892663i
$222$	−1.33168	−	17.1761i	−0.0893766	−	1.15279i
$223$			10.2018i			0.683166i	0.939852	+	0.341583i	$0.110963\pi$
$223$			10.2018i			0.683166i	−0.939852	+	0.341583i	$0.889037\pi$
$224$	−8.11393	+	3.30573i	−0.542135	+	0.220873i
$225$	−16.9324	+	7.53351i	−1.12883	+	0.502234i
$226$	15.3317	−	1.18868i	1.01985	−	0.0790697i
$227$	−6.99282			−0.464130			−0.232065	−	0.972700i	$-0.574548\pi$
$227$	−6.99282			−0.464130			−0.232065	+	0.972700i	$0.574548\pi$
$228$	5.27914	+	33.8407i	0.349620	+	2.24116i
$229$			10.2738i			0.678911i	0.940622	+	0.339456i	$0.110243\pi$
$229$			10.2738i			0.678911i	−0.940622	+	0.339456i	$0.889757\pi$
$230$	−3.91166	−	13.2686i	−0.257927	−	0.874903i
$231$	−4.01100			−0.263904
$232$	−5.04753	+	1.19318i	−0.331387	+	0.0783364i
$233$			5.62763i			0.368678i	0.982863	+	0.184339i	$0.0590145\pi$
$233$			5.62763i			0.368678i	−0.982863	+	0.184339i	$0.940986\pi$
$234$	−0.304864	−	3.93216i	−0.0199296	−	0.257053i
$235$	3.90936	−	0.830426i	0.255018	−	0.0541710i
$236$	−0.285547	−	1.83043i	−0.0185875	−	0.119151i
$237$	−40.0906			−2.60417
$238$	0.298626	+	3.85170i	0.0193570	+	0.249668i
$239$	−21.0356			−1.36068			−0.680340	−	0.732897i	$-0.738168\pi$
$239$	−21.0356			−1.36068			−0.680340	+	0.732897i	$0.738168\pi$
$240$	11.4854	+	20.1149i	0.741377	+	1.29841i
$241$	0.611895			0.0394156			0.0197078	−	0.999806i	$-0.493726\pi$
$241$	0.611895			0.0394156			0.0197078	+	0.999806i	$0.493726\pi$
$242$	−0.109317	−	1.40998i	−0.00702718	−	0.0906371i
$243$	−22.0145			−1.41223
$244$	3.48667	+	22.3505i	0.223211	+	1.43084i
$245$	2.13777	+	10.0639i	0.136577	+	0.642959i
$246$	1.93617	+	24.9728i	0.123446	+	1.59221i
$247$			4.97543i			0.316579i
$248$	−4.54030	−	19.2068i	−0.288309	−	1.21964i
$249$	−29.9882			−1.90042
$250$	12.0390	−	10.2500i	0.761415	−	0.648265i
$251$		−	6.66790i		−	0.420874i	−0.977607	−	0.210437i	$-0.932511\pi$
$251$		−	6.66790i		−	0.420874i	0.977607	−	0.210437i	$-0.0674887\pi$
$252$	−1.76972	−	11.3444i	−0.111482	−	0.714629i
$253$	−4.37442			−0.275018
$254$	−16.5921	+	1.28640i	−1.04108	+	0.0807158i
$255$	9.99047	−	2.12218i	0.625628	−	0.132896i
$256$	13.0313	−	9.28366i	0.814454	−	0.580229i
$257$			15.4947i			0.966534i	0.875473	+	0.483267i	$0.160550\pi$
$257$			15.4947i			0.966534i	−0.875473	+	0.483267i	$0.839450\pi$
$258$	1.53974	+	19.8597i	0.0958601	+	1.23641i
$259$		−	7.28560i		−	0.452705i
$260$	1.19812	+	3.14430i	0.0743045	+	0.195001i
$261$		−	6.79689i		−	0.420717i
$262$	−7.40246	+	0.573920i	−0.457325	+	0.0354569i
$263$		−	4.96822i		−	0.306354i	−0.988199	−	0.153177i	$-0.951050\pi$
$263$		−	4.96822i		−	0.306354i	0.988199	−	0.153177i	$-0.0489504\pi$
$264$	7.12832	−	1.68506i	0.438718	−	0.103708i
$265$	−1.64504	−	7.74426i	−0.101054	−	0.475726i
$266$	1.11963	+	14.4410i	0.0686488	+	0.885437i
$267$	34.5156			2.11232
$268$	20.7431	−	3.23592i	1.26709	−	0.197665i
$269$		−	21.2890i		−	1.29801i	−0.760783	−	0.649006i	$-0.775185\pi$
$269$		−	21.2890i		−	1.29801i	0.760783	−	0.649006i	$-0.224815\pi$
$270$	−5.54995	+	1.63616i	−0.337759	+	0.0995735i
$271$	13.5211			0.821346			0.410673	−	0.911783i	$-0.365294\pi$
$271$	13.5211			0.821346			0.410673	+	0.911783i	$0.365294\pi$
$272$	−2.14885	−	6.71975i	−0.130293	−	0.407445i
$273$		−	3.01787i		−	0.182650i
$274$	−19.8343	+	1.53777i	−1.19824	+	0.0929004i
$275$	−2.03249	−	4.56826i	−0.122564	−	0.275476i
$276$	−3.49223	−	22.3861i	−0.210207	−	1.34749i
$277$	−31.6174			−1.89971			−0.949853	−	0.312696i	$-0.898768\pi$
$277$	−31.6174			−1.89971			−0.949853	+	0.312696i	$0.898768\pi$
$278$	−17.2844	+	1.34008i	−1.03665	+	0.0803726i
$279$	25.8635			1.54841
$280$	4.18509	+	8.85662i	0.250107	+	0.529284i
$281$	−4.69073			−0.279825			−0.139913	−	0.990164i	$-0.544682\pi$
$281$	−4.69073			−0.279825			−0.139913	+	0.990164i	$0.544682\pi$
$282$	6.52630	−	0.505990i	0.388636	−	0.0301313i
$283$	−15.8360			−0.941354			−0.470677	−	0.882306i	$-0.655990\pi$
$283$	−15.8360			−0.941354			−0.470677	+	0.882306i	$0.655990\pi$
$284$	−21.2904	+	3.32129i	−1.26335	+	0.197083i
$285$	37.4570	−	7.95661i	2.21876	−	0.471309i
$286$	1.06087	−	0.0822503i	0.0627305	−	0.00486356i
$287$			10.5927i			0.625269i
$288$	7.91102	+	19.4177i	0.466161	+	1.14420i
$289$	13.8892			0.817012
$290$	1.63976	+	5.56217i	0.0962902	+	0.326622i
$291$		−	39.9014i		−	2.33906i
$292$	1.12849	+	7.23392i	0.0660398	+	0.423333i
$293$	−18.9901			−1.10942			−0.554708	−	0.832045i	$-0.687170\pi$
$293$	−18.9901			−1.10942			−0.554708	+	0.832045i	$0.687170\pi$
$294$	1.30258	+	16.8007i	0.0759677	+	0.979837i
$295$	−2.02603	+	0.430370i	−0.117960	+	0.0250571i
$296$	3.06076	+	12.9479i	0.177903	+	0.752583i
$297$			1.82973i			0.106171i
$298$	−1.63635	+	0.126867i	−0.0947910	+	0.00734924i
$299$		−	3.29131i		−	0.190342i
$300$	21.7555	−	14.0482i	1.25605	−	0.811076i
$301$			8.42389i			0.485545i
$302$	−1.60473	−	20.6979i	−0.0923416	−	1.19103i
$303$		−	27.5021i		−	1.57995i
$304$	−8.05662	−	25.1941i	−0.462079	−	1.44498i
$305$	24.7389	−	5.25503i	1.41654	−	0.300902i
$306$	9.21759	−	0.714649i	0.526935	−	0.0408538i
$307$	−17.6155			−1.00537			−0.502684	−	0.864470i	$-0.667654\pi$
$307$	−17.6155			−1.00537			−0.502684	+	0.864470i	$0.667654\pi$
$308$	3.06064	−	0.477458i	0.174396	−	0.0272057i
$309$			46.0573i			2.62011i
$310$	−21.1652	+	6.23962i	−1.20210	+	0.354387i
$311$	18.1360			1.02840			0.514198	−	0.857672i	$-0.328090\pi$
$311$	18.1360			1.02840			0.514198	+	0.857672i	$0.328090\pi$
$312$	1.26784	+	5.36334i	0.0717772	+	0.303639i
$313$		−	4.48441i		−	0.253474i	−0.991936	−	0.126737i	$-0.959550\pi$
$313$		−	4.48441i		−	0.253474i	0.991936	−	0.126737i	$-0.0404504\pi$
$314$	0.438845	+	5.66025i	0.0247654	+	0.319426i
$315$	−12.5566	+	2.66728i	−0.707486	+	0.150284i
$316$	30.5916	−	4.77228i	1.72091	−	0.268462i
$317$	20.5612			1.15483			0.577416	−	0.816450i	$-0.304061\pi$
$317$	20.5612			1.15483			0.577416	+	0.816450i	$0.304061\pi$
$318$	−1.00234	−	12.9283i	−0.0562086	−	0.724983i
$319$	1.83376			0.102671
$320$	−11.1585	−	13.9817i	−0.623777	−	0.781602i
$321$	52.5589			2.93355
$322$	−0.740650	−	9.55295i	−0.0412748	−	0.532365i
$323$	−11.6632			−0.648957
$324$	12.6098	−	1.96713i	0.700547	−	0.109285i
$325$	3.43715	−	1.52924i	0.190659	−	0.0848272i
$326$	−0.816180	−	10.5272i	−0.0452040	−	0.583045i
$327$		−	19.7707i		−	1.09332i
$328$	−4.45011	−	18.8253i	−0.245716	−	1.03945i
$329$	2.76826			0.152619
$330$	−2.31574	−	7.85511i	−0.127477	−	0.432410i
$331$		−	5.32820i		−	0.292864i	−0.989221	−	0.146432i	$-0.953221\pi$
$331$		−	5.32820i		−	0.292864i	0.989221	−	0.146432i	$-0.0467790\pi$
$332$	22.8828	−	3.56971i	1.25586	−	0.195913i
$333$	−17.4354			−0.955452
$334$	21.3058	−	1.65186i	1.16580	−	0.0903859i
$335$	−4.87710	−	22.9597i	−0.266465	−	1.25442i
$336$	4.88679	+	15.2817i	0.266596	+	0.833682i
$337$			9.99173i			0.544284i	0.962257	+	0.272142i	$0.0877321\pi$
$337$			9.99173i			0.544284i	−0.962257	+	0.272142i	$0.912268\pi$
$338$	−1.35924	−	17.5316i	−0.0739329	−	0.953592i
$339$		−	28.1595i		−	1.52941i
$340$	−7.37072	+	2.80859i	−0.399734	+	0.152317i
$341$			6.97780i			0.377869i
$342$	34.5592	−	2.67941i	1.86875	−	0.144886i
$343$			17.9682i			0.970189i
$344$	−3.53896	−	14.9709i	−0.190808	−	0.807175i
$345$	−24.7783	+	5.26341i	−1.33402	+	0.283372i
$346$	−0.313299	−	4.04096i	−0.0168431	−	0.217243i
$347$	14.2821			0.766705			0.383352	−	0.923602i	$-0.374769\pi$
$347$	14.2821			0.766705			0.383352	+	0.923602i	$0.374769\pi$
$348$	1.46394	+	9.38425i	0.0784754	+	0.503048i
$349$		−	1.05785i		−	0.0566253i	−0.999599	−	0.0283126i	$-0.990987\pi$
$349$		−	1.05785i		−	0.0566253i	0.999599	−	0.0283126i	$-0.00901340\pi$
$350$	9.63212	−	5.21206i	0.514859	−	0.278596i
$351$	−1.37668			−0.0734820
$352$	−5.23876	+	2.13434i	−0.279227	+	0.113761i
$353$			27.3191i			1.45405i	0.686612	+	0.727024i	$0.259097\pi$
$353$			27.3191i			1.45405i	−0.686612	+	0.727024i	$0.740903\pi$
$354$	−3.38226	+	0.262230i	−0.179765	+	0.0139374i
$355$	5.00578	+	23.5655i	0.265679	+	1.25073i
$356$	−26.3375	+	4.10865i	−1.39589	+	0.217758i
$357$	7.07437			0.374415
$358$	−28.0093	+	2.17159i	−1.48034	+	0.114772i
$359$	−2.40783			−0.127081			−0.0635403	−	0.997979i	$-0.520239\pi$
$359$	−2.40783			−0.127081			−0.0635403	+	0.997979i	$0.520239\pi$
$360$	21.1950	−	10.0154i	1.11708	−	0.527860i
$361$	−24.7284			−1.30149
$362$	21.0519	−	1.63218i	1.10647	−	0.0857853i
$363$	−2.58970			−0.135924
$364$	0.359239	+	2.30282i	0.0188293	+	0.120701i
$365$	8.00694	−	1.70083i	0.419102	−	0.0890257i
$366$	41.2992	−	3.20196i	2.15874	−	0.167369i
$367$			9.49487i			0.495628i	0.968808	+	0.247814i	$0.0797122\pi$
$367$			9.49487i			0.495628i	−0.968808	+	0.247814i	$0.920288\pi$
$368$	5.32957	+	16.6663i	0.277823	+	0.868790i
$369$	25.3497			1.31965
$370$	14.2681	−	4.20632i	0.741762	−	0.218676i
$371$		−	5.48380i		−	0.284705i
$372$	−35.7089	+	5.57058i	−1.85142	+	0.288821i
$373$	29.3152			1.51788			0.758942	−	0.651158i	$-0.225716\pi$
$373$	29.3152			1.51788			0.758942	+	0.651158i	$0.225716\pi$
$374$	0.192808	+	2.48685i	0.00996984	+	0.128592i
$375$	−17.0094	−	23.4307i	−0.878361	−	1.20996i
$376$	−4.91974	+	1.16298i	−0.253716	+	0.0599759i
$377$			1.37972i			0.0710590i
$378$	−3.99579	+	0.309798i	−0.205521	+	0.0159343i
$379$			28.3027i			1.45381i	0.686738	+	0.726905i	$0.259042\pi$
$379$			28.3027i			1.45381i	−0.686738	+	0.726905i	$0.740958\pi$
$380$	−27.6348	+	10.5302i	−1.41764	+	0.540186i
$381$			30.4745i			1.56125i
$382$	0.664280	+	8.56792i	0.0339875	+	0.438373i
$383$		−	33.1005i		−	1.69136i	−0.533694	−	0.845678i	$-0.679197\pi$
$383$		−	33.1005i		−	1.69136i	0.533694	−	0.845678i	$-0.320803\pi$
$384$	−15.1047	−	25.1055i	−0.770811	−	1.28116i
$385$	−0.719615	−	3.38770i	−0.0366750	−	0.172653i
$386$	−25.3846	+	1.96810i	−1.29204	+	0.100173i
$387$	20.1594			1.02476
$388$	4.74976	+	30.4472i	0.241133	+	1.54572i
$389$			13.3751i			0.678142i	0.940761	+	0.339071i	$0.110113\pi$
$389$			13.3751i			0.678142i	−0.940761	+	0.339071i	$0.889887\pi$
$390$	5.91018	−	1.74236i	0.299274	−	0.0882277i
$391$	7.71536			0.390182
$392$	−2.99386	−	12.6649i	−0.151213	−	0.639675i
$393$			13.5960i			0.685828i
$394$	−1.74033	−	22.4469i	−0.0876767	−	1.13086i
$395$	−7.19268	−	33.8606i	−0.361903	−	1.70371i
$396$	−1.14262	−	7.32449i	−0.0574187	−	0.368070i
$397$	−14.9090			−0.748260			−0.374130	−	0.927376i	$-0.622059\pi$
$397$	−14.9090			−0.748260			−0.374130	+	0.927376i	$0.622059\pi$
$398$	−2.22488	−	28.6966i	−0.111523	−	1.43843i
$399$	26.5237			1.32785
$400$	−14.9285	+	13.3094i	−0.746425	+	0.665469i
$401$	23.1315			1.15513			0.577567	−	0.816343i	$-0.304002\pi$
$401$	23.1315			1.15513			0.577567	+	0.816343i	$0.304002\pi$
$402$	−2.97169	−	38.3290i	−0.148214	−	1.91168i
$403$	−5.25009			−0.261526
$404$	3.27378	+	20.9858i	0.162876	+	1.04408i
$405$	−2.96482	−	13.9573i	−0.147323	−	0.693546i
$406$	0.310480	+	4.00459i	0.0154089	+	0.198744i
$407$		−	4.70395i		−	0.233166i
$408$	−12.5725	+	2.97201i	−0.622432	+	0.147137i
$409$	−20.2052			−0.999084			−0.499542	−	0.866290i	$-0.666498\pi$
$409$	−20.2052			−0.999084			−0.499542	+	0.866290i	$0.666498\pi$
$410$	−20.7447	+	6.11568i	−1.02451	+	0.302032i
$411$			36.4295i			1.79693i
$412$	−5.48254	−	35.1446i	−0.270105	−	1.73145i
$413$	−1.43466			−0.0705948
$414$	−22.8614	+	1.77247i	−1.12358	+	0.0871120i
$415$	−5.38019	−	25.3281i	−0.264103	−	1.24331i
$416$	−1.60588	−	3.94164i	−0.0787346	−	0.193255i
$417$			31.7461i			1.55461i
$418$	0.722887	+	9.32385i	0.0353576	+	0.456044i
$419$			19.8225i			0.968392i	0.874959	+	0.484196i	$0.160888\pi$
$419$			19.8225i			0.968392i	−0.874959	+	0.484196i	$0.839112\pi$
$420$	16.7621	−	6.38713i	0.817905	−	0.311660i
$421$		−	24.7519i		−	1.20633i	−0.797615	−	0.603167i	$-0.793905\pi$
$421$		−	24.7519i		−	1.20633i	0.797615	−	0.603167i	$-0.206095\pi$
$422$	−1.08377	+	0.0840260i	−0.0527573	+	0.00409032i
$423$		−	6.62480i		−	0.322109i
$424$	2.30380	+	9.74577i	0.111882	+	0.473296i
$425$	3.58479	+	8.05723i	0.173888	+	0.390833i
$426$	3.05009	+	39.3403i	0.147777	+	1.90604i
$427$	17.5179			0.847750
$428$	−40.1057	+	6.25647i	−1.93858	+	0.302418i
$429$		−	1.94849i		−	0.0940739i
$430$	−16.4973	+	4.86350i	−0.795570	+	0.234539i
$431$	6.75553			0.325403			0.162701	−	0.986675i	$-0.447979\pi$
$431$	6.75553			0.325403			0.162701	+	0.986675i	$0.447979\pi$
$432$	6.97114	−	2.22924i	0.335399	−	0.107254i
$433$		−	33.0102i		−	1.58637i	−0.608981	−	0.793185i	$-0.708421\pi$
$433$		−	33.0102i		−	1.58637i	0.608981	−	0.793185i	$-0.291579\pi$
$434$	−15.2382	+	1.18144i	−0.731459	+	0.0567108i
$435$	10.3870	−	2.20642i	0.498021	−	0.105790i
$436$	2.35345	+	15.0862i	0.112710	+	0.722499i
$437$	28.9269			1.38376
$438$	13.3668	−	1.03634i	0.638691	−	0.0495183i
$439$	10.0670			0.480474			0.240237	−	0.970714i	$-0.422775\pi$
$439$	10.0670			0.480474			0.240237	+	0.970714i	$0.422775\pi$
$440$	2.70210	+	5.71827i	0.128818	+	0.272608i
$441$	17.0543			0.812109
$442$	−1.87110	+	0.145068i	−0.0889992	+	0.00690020i
$443$	19.9625			0.948447			0.474223	−	0.880405i	$-0.342729\pi$
$443$	19.9625			0.948447			0.474223	+	0.880405i	$0.342729\pi$
$444$	24.0725	−	3.75529i	1.14243	−	0.178218i
$445$	6.19246	+	29.1520i	0.293551	+	1.38194i
$446$	−14.3844	+	1.11524i	−0.681122	+	0.0528080i
$447$			3.00546i			0.142153i
$448$	−5.54801	−	11.0791i	−0.262119	−	0.523440i
$449$	−29.3840			−1.38672			−0.693358	−	0.720593i	$-0.743870\pi$
$449$	−29.3840			−1.38672			−0.693358	+	0.720593i	$0.743870\pi$
$450$	−12.4731	−	23.0509i	−0.587988	−	1.08663i
$451$			6.83919i			0.322045i
$452$	3.35203	+	21.4874i	0.157666	+	1.01068i
$453$	−38.0156			−1.78613
$454$	−0.764436	−	9.85975i	−0.0358768	−	0.462741i
$455$	2.54890	−	0.541438i	0.119494	−	0.0253830i
$456$	−47.1377	+	11.1429i	−2.20743	+	0.521813i
$457$		−	32.0849i		−	1.50087i	−0.660946	−	0.750434i	$-0.729845\pi$
$457$		−	32.0849i		−	1.50087i	0.660946	−	0.750434i	$-0.270155\pi$
$458$	−14.4859	+	1.12310i	−0.676880	+	0.0524792i
$459$		−	3.22717i		−	0.150631i
$460$	18.2808	−	6.96585i	0.852348	−	0.324784i
$461$			12.3766i			0.576438i	0.957565	+	0.288219i	$0.0930631\pi$
$461$			12.3766i			0.576438i	−0.957565	+	0.288219i	$0.906937\pi$
$462$	−0.438471	−	5.65543i	−0.0203995	−	0.263115i
$463$		−	3.33673i		−	0.155071i	−0.996990	−	0.0775355i	$-0.975295\pi$
$463$		−	3.33673i		−	0.155071i	0.996990	−	0.0775355i	$-0.0247051\pi$
$464$	−2.23415	−	6.98649i	−0.103718	−	0.324340i
$465$	8.39585	+	39.5247i	0.389348	+	1.83292i
$466$	−7.93485	+	0.615197i	−0.367575	+	0.0284985i
$467$	26.7818			1.23931			0.619657	−	0.784872i	$-0.287272\pi$
$467$	26.7818			1.23931			0.619657	+	0.784872i	$0.287272\pi$
$468$	5.51094	−	0.859705i	0.254743	−	0.0397399i
$469$		−	16.2580i		−	0.750726i
$470$	1.59825	+	5.42135i	0.0737216	+	0.250068i
$471$	10.3961			0.479028
$472$	2.54966	−	0.602714i	0.117358	−	0.0277421i
$473$			5.43888i			0.250080i
$474$	−4.38260	−	56.5271i	−0.201299	−	2.59637i
$475$	13.4403	+	30.2087i	0.616685	+	1.38607i
$476$	−5.39818	+	0.842114i	−0.247425	+	0.0385982i
$477$	−13.1234			−0.600880
$478$	−2.29955	−	29.6598i	−0.105179	−	1.35661i
$479$	38.3804			1.75365			0.876823	−	0.480814i	$-0.159659\pi$
$479$	38.3804			1.75365			0.876823	+	0.480814i	$0.159659\pi$
$480$	−27.1061	+	18.3931i	−1.23722	+	0.839525i
$481$	3.53925			0.161376
$482$	0.0668907	+	0.862762i	0.00304679	+	0.0392977i
$483$	−17.5458			−0.798362
$484$	1.97610	−	0.308271i	0.0898227	−	0.0140123i
$485$	33.7008	−	7.15873i	1.53028	−	0.325061i
$486$	−2.40657	−	31.0401i	−0.109164	−	1.40801i
$487$		−	2.85907i		−	0.129557i	−0.997900	−	0.0647784i	$-0.979366\pi$
$487$		−	2.85907i		−	0.129557i	0.997900	−	0.0647784i	$-0.0206341\pi$
$488$	−31.1326	+	7.35944i	−1.40931	+	0.333146i
$489$	−19.3351			−0.874364
$490$	−13.9562	+	4.11438i	−0.630478	+	0.185869i
$491$			29.6825i			1.33955i	0.742564	+	0.669775i	$0.233610\pi$
$491$			29.6825i			1.33955i	−0.742564	+	0.669775i	$0.766390\pi$
$492$	−34.9996	+	5.45992i	−1.57790	+	0.246152i
$493$	−3.23427			−0.145664
$494$	−7.01526	+	0.543900i	−0.315631	+	0.0244712i
$495$	−8.10719	+	1.72213i	−0.364391	+	0.0774039i
$496$	26.5850	−	8.50138i	1.19370	−	0.381723i
$497$			16.6870i			0.748514i
$498$	−3.27823	−	42.2828i	−0.146901	−	1.89474i
$499$		−	21.6697i		−	0.970067i	−0.874495	−	0.485034i	$-0.838807\pi$
$499$		−	21.6697i		−	0.970067i	0.874495	−	0.485034i	$-0.161193\pi$
$500$	15.7683	+	15.8543i	0.705182	+	0.709027i
$501$		−	39.1322i		−	1.74830i
$502$	9.40162	−	0.728917i	0.419615	−	0.0325331i
$503$			33.9437i			1.51347i	0.653719	+	0.756737i	$0.273208\pi$
$503$			33.9437i			1.51347i	−0.653719	+	0.756737i	$0.726792\pi$
$504$	15.8019	−	3.73541i	0.703873	−	0.166388i
$505$	23.2283	−	4.93416i	1.03365	−	0.219567i
$506$	−0.478200	−	6.16786i	−0.0212586	−	0.274195i
$507$	−32.2000			−1.43005
$508$	−3.62760	−	23.2539i	−0.160949	−	1.03172i
$509$		−	16.5567i		−	0.733862i	−0.930248	−	0.366931i	$-0.880408\pi$
$509$		−	16.5567i		−	0.733862i	0.930248	−	0.366931i	$-0.119592\pi$
$510$	4.08436	+	13.8544i	0.180859	+	0.613483i
$511$	5.66981			0.250817
$512$	14.5143	+	17.3590i	0.641449	+	0.767166i
$513$		−	12.0995i		−	0.534206i
$514$	−21.8473	+	1.69384i	−0.963642	+	0.0747121i
$515$	−38.9001	+	8.26316i	−1.71414	+	0.364118i
$516$	−27.8335	+	4.34201i	−1.22530	+	0.191146i
$517$	1.78733			0.0786066
$518$	10.2726	−	0.796442i	0.451351	−	0.0349937i
$519$	−7.42198			−0.325789
$520$	−4.30243	+	2.03306i	−0.188674	+	0.0891555i
$521$	−0.518083			−0.0226976			−0.0113488	−	0.999936i	$-0.503613\pi$
$521$	−0.518083			−0.0226976			−0.0113488	+	0.999936i	$0.503613\pi$
$522$	9.58349	−	0.743017i	0.419458	−	0.0325210i
$523$	21.8661			0.956136			0.478068	−	0.878323i	$-0.341337\pi$
$523$	21.8661			0.956136			0.478068	+	0.878323i	$0.341337\pi$
$524$	−1.61843	−	10.3746i	−0.0707016	−	0.453216i
$525$	−8.15231	−	18.3233i	−0.355796	−	0.799693i
$526$	7.00510	−	0.543113i	0.305437	−	0.0236808i
$527$		−	12.3070i		−	0.536103i
$528$	3.15515	+	9.86659i	0.137310	+	0.429388i
$529$	3.86442			0.168018
$530$	10.7394	−	3.16605i	0.466491	−	0.137525i
$531$			3.43331i			0.148993i
$532$	−20.2392	+	3.15731i	−0.877481	+	0.136887i
$533$	−5.14580			−0.222890
$534$	3.77315	+	48.6664i	0.163280	+	2.10600i
$535$	9.42961	+	44.3913i	0.407678	+	1.91920i
$536$	6.83016	+	28.8937i	0.295018	+	1.24802i
$537$			51.4443i			2.21999i
$538$	30.0171	−	2.32725i	1.29413	−	0.100335i
$539$			4.60113i			0.198185i
$540$	−2.91366	−	7.64647i	−0.125384	−	0.329052i
$541$			18.8723i			0.811385i	0.914010	+	0.405693i	$0.132970\pi$
$541$			18.8723i			0.811385i	−0.914010	+	0.405693i	$0.867030\pi$
$542$	1.47809	+	19.0645i	0.0634892	+	0.818888i
$543$		−	38.6659i		−	1.65931i
$544$	9.23982	−	3.76443i	0.396154	−	0.161399i
$545$	16.6983	−	3.54706i	0.715278	−	0.151939i
$546$	4.25515	−	0.329906i	0.182103	−	0.0141187i
$547$	38.1754			1.63226			0.816131	−	0.577867i	$-0.196115\pi$
$547$	38.1754			1.63226			0.816131	+	0.577867i	$0.196115\pi$
$548$	−4.33647	−	27.7979i	−0.185245	−	1.18747i
$549$		−	41.9225i		−	1.78921i
$550$	6.21898	−	3.36516i	0.265178	−	0.143491i
$551$	−12.1262			−0.516592
$552$	31.1823	−	7.37117i	1.32721	−	0.313738i
$553$		−	23.9771i		−	1.01961i
$554$	−3.45633	−	44.5800i	−0.146845	−	1.89402i
$555$	−5.65990	−	26.6448i	−0.240249	−	1.13101i
$556$	−3.77898	−	24.2243i	−0.160264	−	1.02734i
$557$	3.49753			0.148195			0.0740976	−	0.997251i	$-0.476392\pi$
$557$	3.49753			0.148195			0.0740976	+	0.997251i	$0.476392\pi$
$558$	2.82733	+	36.4671i	0.119690	+	1.54377i
$559$	−4.09221			−0.173082
$560$	−12.0302	+	6.86908i	−0.508368	+	0.290272i
$561$	4.56756			0.192843
$562$	−0.512778	−	6.61384i	−0.0216302	−	0.278988i
$563$	20.3136			0.856118			0.428059	−	0.903751i	$-0.359198\pi$
$563$	20.3136			0.856118			0.428059	+	0.903751i	$0.359198\pi$
$564$	1.42687	+	9.14665i	0.0600823	+	0.385144i
$565$	23.7836	−	5.05211i	1.00058	−	0.212544i
$566$	−1.73115	−	22.3285i	−0.0727657	−	0.938537i
$567$		−	9.88335i		−	0.415062i
$568$	−7.01037	−	29.6560i	−0.294149	−	1.24434i
$569$	−5.37387			−0.225284			−0.112642	−	0.993636i	$-0.535931\pi$
$569$	−5.37387			−0.225284			−0.112642	+	0.993636i	$0.535931\pi$
$570$	15.3134	+	51.9438i	0.641406	+	2.17569i
$571$		−	24.1644i		−	1.01125i	−0.862754	−	0.505624i	$-0.831262\pi$
$571$		−	24.1644i		−	1.01125i	0.862754	−	0.505624i	$-0.168738\pi$
$572$	0.231943	+	1.48682i	0.00969802	+	0.0621669i
$573$	15.7366			0.657406
$574$	−14.9356	+	1.15797i	−0.623398	+	0.0483327i
$575$	−8.89097	−	19.9835i	−0.370779	−	0.833369i
$576$	−26.5138	+	13.2771i	−1.10474	+	0.553212i
$577$		−	31.7096i		−	1.32009i	−0.751227	−	0.660044i	$-0.770538\pi$
$577$		−	31.7096i		−	1.32009i	0.751227	−	0.660044i	$-0.229462\pi$
$578$	1.51833	+	19.5835i	0.0631542	+	0.814568i
$579$			46.6237i			1.93761i
$580$	−7.66331	+	2.92008i	−0.318202	+	0.121250i
$581$		−	17.9351i		−	0.744074i
$582$	56.2603	−	4.36192i	2.33206	−	0.180807i
$583$		−	3.54061i		−	0.146637i
$584$	−10.0763	+	2.38194i	−0.416962	+	0.0985655i
$585$	−1.29573	−	6.09984i	−0.0535718	−	0.252197i
$586$	−2.07595	−	26.7757i	−0.0857567	−	1.10610i
$587$	−16.2715			−0.671597			−0.335799	−	0.941934i	$-0.609006\pi$
$587$	−16.2715			−0.671597			−0.335799	+	0.941934i	$0.609006\pi$
$588$	−23.5463	+	3.67322i	−0.971033	+	0.151481i
$589$		−	46.1424i		−	1.90126i
$590$	−0.828294	−	2.80962i	−0.0341003	−	0.115670i
$591$	−41.2280			−1.69589
$592$	−17.9217	+	5.73104i	−0.736579	+	0.235544i
$593$			18.7864i			0.771464i	0.922611	+	0.385732i	$0.126051\pi$
$593$			18.7864i			0.771464i	−0.922611	+	0.385732i	$0.873949\pi$
$594$	−2.57988	+	0.200021i	−0.105854	+	0.00820695i
$595$	1.26922	+	5.97503i	0.0520328	+	0.244952i
$596$	−0.357762	−	2.29335i	−0.0146545	−	0.0939393i
$597$	−52.7068			−2.15715
$598$	4.64069	−	0.359798i	0.189772	−	0.0147132i
$599$	6.60744			0.269973			0.134986	−	0.990847i	$-0.456901\pi$
$599$	6.60744			0.269973			0.134986	+	0.990847i	$0.456901\pi$
$600$	22.1860	+	29.1391i	0.905741	+	1.18960i
$601$	−3.09256			−0.126148			−0.0630742	−	0.998009i	$-0.520090\pi$
$601$	−3.09256			−0.126148			−0.0630742	+	0.998009i	$0.520090\pi$
$602$	−11.8775	+	0.920877i	−0.484092	+	0.0375321i
$603$	−38.9075			−1.58444
$604$	29.0082	−	4.52527i	1.18033	−	0.184131i
$605$	−0.464619	−	2.18727i	−0.0188895	−	0.0889250i
$606$	38.7775	−	3.00645i	1.57523	−	0.122129i
$607$			20.8656i			0.846907i	0.905918	+	0.423453i	$0.139182\pi$
$607$			20.8656i			0.846907i	−0.905918	+	0.423453i	$0.860818\pi$
$608$	34.6426	−	14.1138i	1.40494	−	0.572392i
$609$	7.35519			0.298047
$610$	10.1139	+	34.3069i	0.409499	+	1.38905i
$611$			1.34478i			0.0544041i
$612$	2.01528	+	12.9185i	0.0814631	+	0.522200i
$613$	−16.7190			−0.675273			−0.337636	−	0.941277i	$-0.609627\pi$
$613$	−16.7190			−0.675273			−0.337636	+	0.941277i	$0.609627\pi$
$614$	−1.92568	−	24.8375i	−0.0777139	−	1.00236i
$615$	8.22908	+	38.7396i	0.331828	+	1.56213i
$616$	1.00779	+	4.26325i	0.0406050	+	0.171771i
$617$		−	26.7533i		−	1.07705i	−0.842610	−	0.538524i	$-0.818982\pi$
$617$		−	26.7533i		−	1.07705i	0.842610	−	0.538524i	$-0.181018\pi$
$618$	−64.9400	+	5.03486i	−2.61227	+	0.202532i
$619$		−	32.4786i		−	1.30542i	−0.757606	−	0.652712i	$-0.773631\pi$
$619$		−	32.4786i		−	1.30542i	0.757606	−	0.652712i	$-0.226369\pi$
$620$	−11.1115	−	29.1604i	−0.446247	−	1.17111i
$621$			8.00400i			0.321189i
$622$	1.98257	+	25.5714i	0.0794940	+	1.02532i
$623$			20.6428i			0.827038i
$624$	−7.42362	+	2.37394i	−0.297183	+	0.0950335i
$625$	16.7380	−	18.5699i	0.669519	−	0.742795i
$626$	6.32293	−	0.490223i	0.252715	−	0.0195933i
$627$	17.1250			0.683907
$628$	−7.93288	+	1.23753i	−0.316556	+	0.0493827i
$629$			8.29655i			0.330805i
$630$	−5.13348	−	17.4131i	−0.204523	−	0.693753i
$631$	−8.43395			−0.335750			−0.167875	−	0.985808i	$-0.553691\pi$
$631$	−8.43395			−0.335750			−0.167875	+	0.985808i	$0.553691\pi$
$632$	10.0730	+	42.6119i	0.400684	+	1.69501i
$633$			1.99055i			0.0791175i
$634$	2.24770	+	28.9909i	0.0892674	+	1.15138i
$635$	−25.7388	+	5.46744i	−1.02141	+	0.216969i
$636$	18.1191	−	2.82657i	0.718469	−	0.112081i
$637$	−3.46189			−0.137165
$638$	0.200461	+	2.58556i	0.00793633	+	0.102363i
$639$	39.9341			1.57977
$640$	18.4942	−	17.2617i	0.731046	−	0.682328i
$641$	−4.06790			−0.160672			−0.0803362	−	0.996768i	$-0.525599\pi$
$641$	−4.06790			−0.160672			−0.0803362	+	0.996768i	$0.525599\pi$
$642$	5.74559	+	74.1071i	0.226761	+	2.92477i
$643$	−34.3340			−1.35400			−0.677001	−	0.735982i	$-0.736721\pi$
$643$	−34.3340			−1.35400			−0.677001	+	0.735982i	$0.736721\pi$
$644$	13.3885	−	2.08861i	0.527582	−	0.0823026i
$645$	6.54419	+	30.8078i	0.257677	+	1.21305i
$646$	−1.27499	−	16.4449i	−0.0501637	−	0.647015i
$647$		−	4.00464i		−	0.157439i	−0.996897	−	0.0787194i	$-0.974917\pi$
$647$		−	4.00464i		−	0.157439i	0.996897	−	0.0787194i	$-0.0250831\pi$
$648$	4.15210	+	17.5646i	0.163110	+	0.690003i
$649$	−0.926285			−0.0363599
$650$	2.53195	+	4.67915i	0.0993112	+	0.183532i
$651$			27.9879i			1.09693i
$652$	14.7539	−	2.30160i	0.577806	−	0.0901376i
$653$	−25.8236			−1.01056			−0.505278	−	0.862957i	$-0.668610\pi$
$653$	−25.8236			−1.01056			−0.505278	+	0.862957i	$0.668610\pi$
$654$	27.8763	−	2.16127i	1.09005	−	0.0845125i
$655$	−11.4832	+	2.43927i	−0.448687	+	0.0953100i
$656$	26.0569	−	8.33251i	1.01735	−	0.325330i
$657$		−	13.5686i		−	0.529360i
$658$	0.302619	+	3.90320i	0.0117973	+	0.152163i
$659$			4.97128i			0.193653i	0.995301	+	0.0968267i	$0.0308693\pi$
$659$			4.97128i			0.193653i	−0.995301	+	0.0968267i	$0.969131\pi$
$660$	10.8224	−	4.12385i	0.421262	−	0.160520i
$661$			5.71995i			0.222480i	0.993794	+	0.111240i	$0.0354822\pi$
$661$			5.71995i			0.222480i	−0.993794	+	0.111240i	$0.964518\pi$
$662$	7.51267	−	0.582464i	0.291988	−	0.0226381i
$663$			3.43663i			0.133468i
$664$	7.53472	+	31.8741i	0.292404	+	1.23696i
$665$	4.75863	+	22.4020i	0.184532	+	0.868711i
$666$	−1.90599	−	24.5836i	−0.0738555	−	0.952593i
$667$	8.02162			0.310598
$668$	4.65819	+	29.8603i	0.180231	+	1.15533i
$669$			26.4197i			1.02144i
$670$	31.8396	−	9.38652i	1.23007	−	0.362633i
$671$	11.3104			0.436634
$672$	−21.0126	+	8.56084i	−0.810580	+	0.330241i
$673$			38.8958i			1.49932i	0.661821	+	0.749662i	$0.269784\pi$
$673$			38.8958i			1.49932i	−0.661821	+	0.749662i	$0.730216\pi$
$674$	−14.0882	+	1.09227i	−0.542656	+	0.0420726i
$675$	−8.35866	+	3.71890i	−0.321725	+	0.143141i
$676$	24.5706	−	3.83301i	0.945024	−	0.147423i
$677$	10.2416			0.393617			0.196809	−	0.980442i	$-0.436942\pi$
$677$	10.2416			0.393617			0.196809	+	0.980442i	$0.436942\pi$
$678$	39.7044	−	3.07832i	1.52484	−	0.118222i
$679$	23.8640			0.915814
$680$	−4.76581	−	10.0856i	−0.182760	−	0.386764i
$681$	−18.1093			−0.693950
$682$	−9.83857	+	0.762794i	−0.376738	+	0.0292089i
$683$	−12.9929			−0.497161			−0.248581	−	0.968611i	$-0.579964\pi$
$683$	−12.9929			−0.497161			−0.248581	+	0.968611i	$0.579964\pi$
$684$	7.55584	+	48.4350i	0.288905	+	1.85196i
$685$	−30.7684	+	6.53583i	−1.17560	+	0.249721i
$686$	−25.3348	+	1.96423i	−0.967286	+	0.0749947i
$687$			26.6060i			1.01508i
$688$	20.7218	−	6.62645i	0.790011	−	0.252631i
$689$	2.66395			0.101489
$690$	−10.1300	−	34.3616i	−0.385643	−	1.30812i
$691$			37.5343i			1.42787i	0.700211	+	0.713936i	$0.253089\pi$
$691$			37.5343i			1.42787i	−0.700211	+	0.713936i	$0.746911\pi$
$692$	5.66343	−	0.883493i	0.215291	−	0.0335854i
$693$	−5.74079			−0.218075
$694$	1.56128	+	20.1375i	0.0592655	+	0.764411i
$695$	−26.8129	+	5.69559i	−1.01707	+	0.216046i
$696$	−13.0716	+	3.08999i	−0.495477	+	0.117126i
$697$		−	12.0626i		−	0.456903i
$698$	1.49155	−	0.115641i	0.0564559	−	0.00437708i
$699$			14.5739i			0.551234i
$700$	8.40187	+	13.0114i	0.317561	+	0.491783i
$701$			4.51250i			0.170435i	0.996362	+	0.0852175i	$0.0271585\pi$
$701$			4.51250i			0.170435i	−0.996362	+	0.0852175i	$0.972841\pi$
$702$	−0.150495	−	1.94110i	−0.00568009	−	0.0732621i
$703$			31.1060i			1.17318i
$704$	−3.58207	−	7.15324i	−0.135004	−	0.269598i
$705$	10.1241	−	2.15055i	0.381294	−	0.0809946i
$706$	−38.5194	+	2.98645i	−1.44970	+	0.112396i
$707$	16.4482			0.618600
$708$	−0.739480	−	4.74027i	−0.0277914	−	0.178150i
$709$		−	5.59809i		−	0.210241i	−0.994459	−	0.105120i	$-0.966477\pi$
$709$		−	5.59809i		−	0.210241i	0.994459	−	0.105120i	$-0.0335228\pi$
$710$	−32.6797	+	9.63418i	−1.22645	+	0.361564i
$711$	−57.3802			−2.15193
$712$	−8.67227	−	36.6863i	−0.325007	−	1.37488i
$713$			30.5238i			1.14313i
$714$	0.773351	+	9.97473i	0.0289419	+	0.373295i
$715$	1.64570	−	0.349579i	0.0615456	−	0.0130735i
$716$	−6.12379	−	39.2552i	−0.228857	−	1.46703i
$717$	−54.4759			−2.03444
$718$	−0.263218	−	3.39500i	−0.00982320	−	0.126700i
$719$	34.8322			1.29902			0.649511	−	0.760352i	$-0.274974\pi$
$719$	34.8322			1.29902			0.649511	+	0.760352i	$0.274974\pi$
$720$	16.4386	+	28.7897i	0.612630	+	1.07293i
$721$	−27.5456			−1.02585
$722$	−2.70324	−	34.8666i	−0.100604	−	1.29760i
$723$	1.58462			0.0589328
$724$	4.60268	+	29.5044i	0.171057	+	1.09652i
$725$	3.72709	+	8.37707i	0.138421	+	0.311116i
$726$	−0.283099	−	3.65143i	−0.0105068	−	0.135517i
$727$		−	35.2337i		−	1.30674i	−0.757037	−	0.653372i	$-0.773354\pi$
$727$		−	35.2337i		−	1.30674i	0.757037	−	0.653372i	$-0.226646\pi$
$728$	−3.20767	+	0.758260i	−0.118884	+	0.0281030i
$729$	−37.8674			−1.40250
$730$	3.27344	+	11.1037i	0.121156	+	0.410967i
$731$		−	9.59278i		−	0.354802i
$732$	9.02943	+	57.8811i	0.333737	+	2.13935i
$733$	51.6490			1.90770			0.953849	−	0.300286i	$-0.0970823\pi$
$733$	51.6490			1.90770			0.953849	+	0.300286i	$0.0970823\pi$
$734$	−13.3876	+	1.03795i	−0.494145	+	0.0383115i
$735$	5.53619	+	26.0625i	0.204205	+	0.961328i
$736$	−22.9165	+	9.33651i	−0.844715	+	0.344148i
$737$		−	10.4970i		−	0.386662i
$738$	2.77116	+	35.7427i	0.102008	+	1.31571i
$739$		−	47.9400i		−	1.76350i	−0.471717	−	0.881750i	$-0.656366\pi$
$739$		−	47.9400i		−	1.76350i	0.471717	−	0.881750i	$-0.343634\pi$
$740$	7.49058	+	19.6579i	0.275359	+	0.722639i
$741$			12.8849i			0.473337i
$742$	7.73206	−	0.599474i	0.283853	−	0.0220074i
$743$		−	3.53913i		−	0.129838i	−0.997891	−	0.0649191i	$-0.979321\pi$
$743$		−	3.53913i		−	0.129838i	0.997891	−	0.0649191i	$-0.0206789\pi$
$744$	−11.7580	−	49.7399i	−0.431070	−	1.82355i
$745$	−2.53842	+	0.539211i	−0.0930004	+	0.0197551i
$746$	3.20466	+	41.3339i	0.117331	+	1.51334i
$747$	−42.9210			−1.57040
$748$	−3.48533	+	0.543710i	−0.127436	+	0.0198800i
$749$			31.4340i			1.14857i
$750$	31.1775	−	26.5443i	1.13844	−	0.969261i
$751$	−17.9370			−0.654530			−0.327265	−	0.944933i	$-0.606127\pi$
$751$	−17.9370			−0.654530			−0.327265	+	0.944933i	$0.606127\pi$
$752$	−2.17759	−	6.80961i	−0.0794084	−	0.248321i
$753$		−	17.2679i		−	0.629275i
$754$	−1.94538	+	0.150827i	−0.0708464	+	0.00549279i
$755$	−6.82039	−	32.1080i	−0.248219	−	1.16853i
$756$	−0.873618	−	5.60013i	−0.0317732	−	0.203675i
$757$	47.2219			1.71631			0.858154	−	0.513392i	$-0.171611\pi$
$757$	47.2219			1.71631			0.858154	+	0.513392i	$0.171611\pi$
$758$	−39.9062	+	3.09397i	−1.44946	+	0.112378i
$759$	−11.3284			−0.411196
$760$	−17.8683	−	37.8135i	−0.648151	−	1.37164i
$761$	−31.3600			−1.13680			−0.568400	−	0.822752i	$-0.692437\pi$
$761$	−31.3600			−1.13680			−0.568400	+	0.822752i	$0.692437\pi$
$762$	−42.9684	+	3.33139i	−1.55658	+	0.120683i
$763$	11.8243			0.428068
$764$	−12.0080	+	1.87324i	−0.434434	+	0.0677716i
$765$	14.2990	−	3.03739i	0.516981	−	0.109817i
$766$	46.6711	−	3.61845i	1.68629	−	0.130740i
$767$		−	0.696936i		−	0.0251649i
$768$	33.7470	−	24.0419i	1.21774	−	0.867537i
$769$	4.96828			0.179161			0.0895804	−	0.995980i	$-0.471447\pi$
$769$	4.96828			0.179161			0.0895804	+	0.995980i	$0.471447\pi$
$770$	4.69793	−	1.38498i	0.169302	−	0.0499111i
$771$			40.1266i			1.44513i
$772$	−5.54996	−	35.5767i	−0.199747	−	1.28043i
$773$	−1.93429			−0.0695716			−0.0347858	−	0.999395i	$-0.511075\pi$
$773$	−1.93429			−0.0695716			−0.0347858	+	0.999395i	$0.511075\pi$
$774$	2.20377	+	28.4244i	0.0792130	+	1.02170i
$775$	−31.8764	+	14.1823i	−1.14503	+	0.509443i
$776$	−42.4108	+	10.0255i	−1.52246	+	0.359894i
$777$		−	18.8675i		−	0.676868i
$778$	−18.8586	+	1.46212i	−0.676113	+	0.0524197i
$779$		−	45.2258i		−	1.62038i
$780$	3.10278	+	8.14278i	0.111097	+	0.291558i
$781$			10.7739i			0.385522i
$782$	0.843422	+	10.8785i	0.0301607	+	0.389015i
$783$		−	3.35527i		−	0.119908i
$784$	17.5300	−	5.60578i	0.626073	−	0.200206i
$785$	1.86517	+	8.78059i	0.0665709	+	0.313393i
$786$	−19.1701	+	1.48628i	−0.683776	+	0.0530138i
$787$	−2.37036			−0.0844940			−0.0422470	−	0.999107i	$-0.513452\pi$
$787$	−2.37036			−0.0844940			−0.0422470	+	0.999107i	$0.513452\pi$
$788$	31.4595	−	4.90768i	1.12070	−	0.174829i
$789$		−	12.8662i		−	0.458049i
$790$	46.9566	−	13.8431i	1.67064	−	0.492516i
$791$	16.8414			0.598812
$792$	10.2025	−	2.41177i	0.362530	−	0.0856983i
$793$			8.50995i			0.302197i
$794$	−1.62981	−	21.0214i	−0.0578398	−	0.746021i
$795$	−4.26015	−	20.0553i	−0.151092	−	0.711288i
$796$	40.2185	−	6.27408i	1.42551	−	0.222379i
$797$	42.0252			1.48861			0.744304	−	0.667841i	$-0.232781\pi$
$797$	42.0252			1.48861			0.744304	+	0.667841i	$0.232781\pi$
$798$	2.89950	+	37.3979i	0.102641	+	1.32387i
$799$	−3.15239			−0.111523
$800$	−20.3979	−	19.5940i	−0.721176	−	0.692752i
$801$	49.4009			1.74550
$802$	2.52868	+	32.6151i	0.0892907	+	1.15168i
$803$	3.66071			0.129184
$804$	53.7184	−	8.38005i	1.89450	−	0.295542i
$805$	−3.14790	−	14.8192i	−0.110949	−	0.522309i
$806$	−0.573926	−	7.40253i	−0.0202157	−	0.260743i
$807$		−	55.1321i		−	1.94074i
$808$	−29.2317	+	6.91007i	−1.02837	+	0.243096i
$809$	−6.12119			−0.215210			−0.107605	−	0.994194i	$-0.534318\pi$
$809$	−6.12119			−0.215210			−0.107605	+	0.994194i	$0.534318\pi$
$810$	19.3555	−	5.70612i	0.680082	−	0.200493i
$811$		−	5.62535i		−	0.197533i	−0.995111	−	0.0987663i	$-0.968510\pi$
$811$		−	5.62535i		−	0.197533i	0.995111	−	0.0987663i	$-0.0314896\pi$
$812$	−5.61246	+	0.875542i	−0.196959	+	0.0307255i
$813$	35.0155			1.22805
$814$	6.63248	−	0.514223i	0.232468	−	0.0180235i
$815$	−3.46892	−	16.3305i	−0.121511	−	0.572031i
$816$	−5.56488	−	17.4021i	−0.194810	−	0.609196i
$817$		−	35.9659i		−	1.25829i
$818$	−2.20878	−	28.4890i	−0.0772282	−	0.996094i
$819$		−	4.31937i		−	0.150931i
$820$	−10.8908	−	28.5812i	−0.380322	−	0.998097i
$821$			21.9742i			0.766906i	0.923560	+	0.383453i	$0.125265\pi$
$821$			21.9742i			0.766906i	−0.923560	+	0.383453i	$0.874735\pi$
$822$	−51.3649	+	3.98237i	−1.79156	+	0.138901i
$823$			14.3155i			0.499007i	0.968374	+	0.249504i	$0.0802675\pi$
$823$			14.3155i			0.499007i	−0.968374	+	0.249504i	$0.919733\pi$
$824$	48.9539	−	11.5722i	1.70539	−	0.403136i
$825$	−5.26354	−	11.8304i	−0.183253	−	0.411882i
$826$	−0.156833	−	2.02284i	−0.00545691	−	0.0703836i
$827$	11.4716			0.398906			0.199453	−	0.979907i	$-0.436083\pi$
$827$	11.4716			0.398906			0.199453	+	0.979907i	$0.436083\pi$
$828$	−4.99830	−	32.0404i	−0.173703	−	1.11348i
$829$			40.0081i			1.38954i	0.719233	+	0.694769i	$0.244493\pi$
$829$			40.0081i			1.38954i	−0.719233	+	0.694769i	$0.755507\pi$
$830$	35.1240	−	10.3548i	1.21917	−	0.359419i
$831$	−81.8796			−2.84037
$832$	5.38209	−	2.69515i	0.186590	−	0.0934374i
$833$		−	8.11521i		−	0.281175i
$834$	−44.7615	+	3.47040i	−1.54996	+	0.120170i
$835$	33.0511	−	7.02072i	1.14378	−	0.242962i
$836$	−13.0674	+	2.03852i	−0.451947	+	0.0705036i
$837$	12.7675			0.441308
$838$	−27.9494	+	2.16694i	−0.965495	+	0.0748558i
$839$	−38.0131			−1.31236			−0.656179	−	0.754606i	$-0.727828\pi$
$839$	−38.0131			−1.31236			−0.656179	+	0.754606i	$0.727828\pi$
$840$	10.8381	+	22.9360i	0.373951	+	0.791367i
$841$	25.6373			0.884046
$842$	34.8997	−	2.70581i	1.20272	−	0.0932484i
$843$	−12.1476			−0.418385
$844$	−0.236950	−	1.51892i	−0.00815617	−	0.0522832i
$845$	−5.77702	−	27.1962i	−0.198736	−	0.935579i
$846$	9.34085	−	0.724205i	0.321145	−	0.0248987i
$847$		−	1.54883i		−	0.0532184i
$848$	−13.4895	+	4.31370i	−0.463232	+	0.148133i
$849$	−41.0105			−1.40748
$850$	−10.9687	+	5.93528i	−0.376222	+	0.203579i
$851$		−	20.5771i		−	0.705372i
$852$	−55.1357	+	8.60115i	−1.88892	+	0.294671i
$853$	2.21069			0.0756926			0.0378463	−	0.999284i	$-0.487950\pi$
$853$	2.21069			0.0756926			0.0378463	+	0.999284i	$0.487950\pi$
$854$	1.91501	+	24.6999i	0.0655302	+	0.845213i
$855$	53.6107	−	11.3880i	1.83345	−	0.389461i
$856$	−13.2058	−	55.8643i	−0.451363	−	1.90940i
$857$		−	19.9678i		−	0.682088i	−0.940047	−	0.341044i	$-0.889219\pi$
$857$		−	19.9678i		−	0.682088i	0.940047	−	0.341044i	$-0.110781\pi$
$858$	2.74733	−	0.213003i	0.0937924	−	0.00727182i
$859$		−	31.0521i		−	1.05948i	−0.848159	−	0.529741i	$-0.822289\pi$
$859$		−	31.0521i		−	1.05948i	0.848159	−	0.529741i	$-0.177711\pi$
$860$	−8.66089	−	22.7292i	−0.295334	−	0.775060i
$861$			27.4320i			0.934879i
$862$	0.738497	+	9.52518i	0.0251533	+	0.324429i
$863$			24.6441i			0.838895i	0.907779	+	0.419448i	$0.137776\pi$
$863$			24.6441i			0.838895i	−0.907779	+	0.419448i	$0.862224\pi$
$864$	3.90526	+	9.58549i	0.132860	+	0.326105i
$865$	−1.33158	−	6.26862i	−0.0452751	−	0.213140i
$866$	46.5438	−	3.60859i	1.58162	−	0.122625i
$867$	35.9689			1.22157
$868$	−3.33161	−	21.3565i	−0.113082	−	0.724887i
$869$		−	15.4808i		−	0.525151i
$870$	4.24649	+	14.4044i	0.143970	+	0.488353i
$871$	7.89793			0.267611
$872$	−21.0140	+	4.96750i	−0.711625	+	0.168221i
$873$		−	57.1094i		−	1.93286i
$874$	3.16222	+	40.7865i	0.106964	+	1.37962i
$875$	14.0133	−	10.1728i	0.473735	−	0.343905i
$876$	2.92245	+	18.7337i	0.0987404	+	0.632952i
$877$	−13.9482			−0.470998			−0.235499	−	0.971875i	$-0.575673\pi$
$877$	−13.9482			−0.470998			−0.235499	+	0.971875i	$0.575673\pi$
$878$	1.10050	+	14.1944i	0.0371402	+	0.479036i
$879$	−49.1787			−1.65876
$880$	−7.76728	+	4.43502i	−0.261835	+	0.149504i
$881$	−19.9312			−0.671498			−0.335749	−	0.941952i	$-0.608989\pi$
$881$	−19.9312			−0.671498			−0.335749	+	0.941952i	$0.608989\pi$
$882$	1.86433	+	24.0462i	0.0627752	+	0.809679i
$883$	7.71883			0.259759			0.129880	−	0.991530i	$-0.458541\pi$
$883$	7.71883			0.259759			0.129880	+	0.991530i	$0.458541\pi$
$884$	−0.409087	−	2.62236i	−0.0137591	−	0.0881995i
$885$	−5.24681	+	1.11453i	−0.176370	+	0.0374644i
$886$	2.18225	+	28.1468i	0.0733140	+	0.945609i
$887$			7.61395i			0.255652i	0.991797	+	0.127826i	$0.0407998\pi$
$887$			7.61395i			0.255652i	−0.991797	+	0.127826i	$0.959200\pi$
$888$	7.92643	+	33.5312i	0.265994	+	1.12523i
$889$	−18.2259			−0.611278
$890$	−40.4268	+	11.9181i	−1.35511	+	0.399495i
$891$		−	6.38118i		−	0.213778i
$892$	−3.14493	−	20.1598i	−0.105300	−	0.675002i
$893$	−11.8191			−0.395512
$894$	−4.23764	+	0.328549i	−0.141728	+	0.0109883i
$895$	−43.4500	+	9.22965i	−1.45237	+	0.308513i
$896$	15.0149	−	9.03373i	0.501612	−	0.301796i
$897$		−	8.52351i		−	0.284592i
$898$	−3.21218	−	41.4309i	−0.107192	−	1.38257i
$899$		−	12.7956i		−	0.426756i
$900$	31.1378	−	20.1067i	1.03793	−	0.670224i
$901$			6.24473i			0.208042i
$902$	−9.64314	+	0.747642i	−0.321081	+	0.0248938i
$903$			21.8153i			0.725969i
$904$	−29.9304	+	7.07525i	−0.995472	+	0.235319i
$905$	32.6573	−	6.93706i	1.08556	−	0.230596i
$906$	−4.15576	−	53.6013i	−0.138066	−	1.78078i
$907$	−22.8369			−0.758288			−0.379144	−	0.925338i	$-0.623782\pi$
$907$	−22.8369			−0.758288			−0.379144	+	0.925338i	$0.623782\pi$
$908$	13.8185	−	2.15568i	0.458583	−	0.0715388i
$909$		−	39.3627i		−	1.30558i
$910$	1.04206	+	3.53472i	0.0345438	+	0.117175i
$911$	19.0991			0.632782			0.316391	−	0.948629i	$-0.397529\pi$
$911$	19.0991			0.632782			0.316391	+	0.948629i	$0.397529\pi$
$912$	−20.8642	−	65.2453i	−0.690884	−	2.16049i
$913$		−	11.5798i		−	0.383235i
$914$	45.2391	−	3.50743i	1.49638	−	0.116016i
$915$	64.0662	−	13.6090i	2.11796	−	0.449898i
$916$	−3.16711	−	20.3020i	−0.104644	−	0.670798i
$917$	−8.13140			−0.268523
$918$	4.55025	−	0.352785i	0.150181	−	0.0116436i
$919$	21.0557			0.694562			0.347281	−	0.937761i	$-0.387105\pi$
$919$	21.0557			0.694562			0.347281	+	0.937761i	$0.387105\pi$
$920$	11.8201	+	25.0142i	0.389698	+	0.824692i
$921$	−45.6188			−1.50319
$922$	−17.4508	+	1.35298i	−0.574713	+	0.0445581i
$923$	−8.10631			−0.266823
$924$	7.92613	−	1.23647i	0.260751	−	0.0406770i
$925$	21.4888	−	9.56072i	0.706549	−	0.314355i
$926$	4.70473	−	0.364762i	0.154607	−	0.0119868i
$927$			65.9201i			2.16510i
$928$	9.60660	−	3.91386i	0.315352	−	0.128479i
$929$	7.40557			0.242969			0.121484	−	0.992593i	$-0.461235\pi$
$929$	7.40557			0.242969			0.121484	+	0.992593i	$0.461235\pi$
$930$	−54.8114	+	16.1587i	−1.79734	+	0.529866i
$931$		−	30.4261i		−	0.997176i
$932$	−1.73483	−	11.1208i	−0.0568264	−	0.364272i
$933$	46.9667			1.53762
$934$	2.92772	+	37.7619i	0.0957978	+	1.23561i
$935$	0.819468	+	3.85777i	0.0267995	+	0.126163i
$936$	1.81461	+	7.67635i	0.0593124	+	0.250909i
$937$		−	16.6571i		−	0.544164i	−0.962274	−	0.272082i	$-0.912288\pi$
$937$		−	16.6571i		−	0.544164i	0.962274	−	0.272082i	$-0.0877123\pi$
$938$	22.9235	−	1.77728i	0.748480	−	0.0580304i
$939$		−	11.6133i		−	0.378985i
$940$	−7.46929	+	2.84615i	−0.243621	+	0.0928311i
$941$			35.0071i			1.14120i	0.821229	+	0.570599i	$0.193289\pi$
$941$			35.0071i			1.14120i	−0.821229	+	0.570599i	$0.806711\pi$
$942$	1.13648	+	14.6583i	0.0370284	+	0.477595i
$943$			29.9175i			0.974249i
$944$	1.12854	+	3.52909i	0.0367308	+	0.114862i
$945$	−6.19856	+	1.31670i	−0.201639	+	0.0428322i
$946$	−7.66872	+	0.594564i	−0.249332	+	0.0193309i
$947$	−24.5232			−0.796897			−0.398449	−	0.917191i	$-0.630451\pi$
$947$	−24.5232			−0.796897			−0.398449	+	0.917191i	$0.630451\pi$
$948$	79.2231	−	12.3588i	2.57305	−	0.401394i
$949$			2.75431i			0.0894088i
$950$	−41.1245	+	22.2530i	−1.33425	+	0.721982i
$951$	53.2473			1.72666
$952$	−1.77748	−	7.51928i	−0.0576084	−	0.243701i
$953$			7.01392i			0.227203i	0.993526	+	0.113601i	$0.0362387\pi$
$953$			7.01392i			0.227203i	−0.993526	+	0.113601i	$0.963761\pi$
$954$	−1.43462	−	18.5038i	−0.0464474	−	0.599082i
$955$	2.82331	+	13.2912i	0.0913603	+	0.430092i
$956$	41.5684	−	6.48466i	1.34442	−	0.209729i
$957$	4.74887			0.153509
$958$	4.19564	+	54.1157i	0.135555	+	1.74840i
$959$	−21.7875			−0.703554
$960$	−28.8971	−	36.2085i	−0.932649	−	1.16862i
$961$	17.6897			0.570634
$962$	0.386901	+	4.99027i	0.0124742	+	0.160893i
$963$	75.2256			2.42411
$964$	−1.20917	+	0.188630i	−0.0389446	+	0.00607535i
$965$	−39.3785	+	8.36478i	−1.26764	+	0.269272i
$966$	−1.91806	−	24.7393i	−0.0617126	−	0.795973i
$967$		−	37.5937i		−	1.20893i	−0.796631	−	0.604466i	$-0.793386\pi$
$967$		−	37.5937i		−	1.20893i	0.796631	−	0.604466i	$-0.206614\pi$
$968$	0.650678	+	2.75257i	0.0209136	+	0.0884708i
$969$	−30.2041			−0.970296
$970$	13.7778	+	46.7350i	0.442378	+	1.50057i
$971$			13.8756i			0.445290i	0.974900	+	0.222645i	$0.0714691\pi$
$971$			13.8756i			0.445290i	−0.974900	+	0.222645i	$0.928531\pi$
$972$	43.5029	−	6.78643i	1.39536	−	0.217675i
$973$	−18.9865			−0.608679
$974$	4.03124	−	0.312546i	0.129169	−	0.0100146i
$975$	8.90120	−	3.96028i	0.285066	−	0.126831i
$976$	−13.7800	−	43.0920i	−0.441088	−	1.37934i
$977$		−	11.8798i		−	0.380067i	−0.981778	−	0.190034i	$-0.939140\pi$
$977$		−	11.8798i		−	0.380067i	0.981778	−	0.190034i	$-0.0608597\pi$
$978$	−2.11366	−	27.2622i	−0.0675874	−	0.871748i
$979$			13.3280i			0.425966i
$980$	−7.32686	−	19.2282i	−0.234048	−	0.614224i
$981$		−	28.2970i		−	0.903454i
$982$	−41.8517	+	3.24481i	−1.33554	+	0.103546i
$983$		−	25.7447i		−	0.821128i	−0.911832	−	0.410564i	$-0.865332\pi$
$983$		−	25.7447i		−	0.821128i	0.911832	−	0.410564i	$-0.134668\pi$
$984$	−11.5245	−	48.7519i	−0.367386	−	1.55415i
$985$	−7.39674	−	34.8213i	−0.235680	−	1.10950i
$986$	−0.353562	−	4.56027i	−0.0112597	−	0.145228i
$987$	7.16897			0.228191
$988$	−1.53378	−	9.83193i	−0.0487960	−	0.312796i
$989$			23.7920i			0.756540i
$990$	−3.31443	−	11.2427i	−0.105339	−	0.357317i
$991$	37.3420			1.18621			0.593104	−	0.805126i	$-0.297902\pi$
$991$	37.3420			1.18621			0.593104	+	0.805126i	$0.297902\pi$
$992$	14.8930	+	36.5550i	0.472853	+	1.16062i
$993$		−	13.7984i		−	0.437880i
$994$	−23.5284	+	1.82418i	−0.746274	+	0.0578594i
$995$	−9.45615	−	44.5163i	−0.299780	−	1.41126i
$996$	59.2596	−	9.24448i	1.87771	−	0.292923i
$997$	−52.9198			−1.67599			−0.837994	−	0.545679i	$-0.816272\pi$
$997$	−52.9198			−1.67599			−0.837994	+	0.545679i	$0.816272\pi$
$998$	30.5538	−	2.36887i	0.967165	−	0.0749852i
$999$	−8.60693			−0.272311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.l.c.309.32	yes	56
4.3	odd	2		1760.2.l.c.529.8		56
5.4	even	2	inner	440.2.l.c.309.25	✓	56
8.3	odd	2		1760.2.l.c.529.50		56
8.5	even	2	inner	440.2.l.c.309.26	yes	56
20.19	odd	2		1760.2.l.c.529.49		56
40.19	odd	2		1760.2.l.c.529.7		56
40.29	even	2	inner	440.2.l.c.309.31	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.l.c.309.25	✓	56	5.4	even	2	inner
440.2.l.c.309.26	yes	56	8.5	even	2	inner
440.2.l.c.309.31	yes	56	40.29	even	2	inner
440.2.l.c.309.32	yes	56	1.1	even	1	trivial
1760.2.l.c.529.7		56	40.19	odd	2
1760.2.l.c.529.8		56	4.3	odd	2
1760.2.l.c.529.49		56	20.19	odd	2
1760.2.l.c.529.50		56	8.3	odd	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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.109317 + 1.40998i) q^{2} +2.58970 q^{3} +(-1.97610 + 0.308271i) q^{4} +(0.464619 + 2.18727i) q^{5} +(0.283099 + 3.65143i) q^{6} +1.54883i q^{7} +(-0.650678 - 2.75257i) q^{8} +3.70654 q^{9} +(-3.03321 + 0.894210i) q^{10} +1.00000i q^{11} +(-5.11750 + 0.798329i) q^{12} -0.752399 q^{13} +(-2.18382 + 0.169314i) q^{14} +(1.20322 + 5.66436i) q^{15} +(3.80994 - 1.21835i) q^{16} -1.76374i q^{17} +(0.405189 + 5.22616i) q^{18} -6.61274i q^{19} +(-1.59240 - 4.17903i) q^{20} +4.01100i q^{21} +(-1.40998 + 0.109317i) q^{22} +4.37442i q^{23} +(-1.68506 - 7.12832i) q^{24} +(-4.56826 + 2.03249i) q^{25} +(-0.0822503 - 1.06087i) q^{26} +1.82973 q^{27} +(-0.477458 - 3.06064i) q^{28} -1.83376i q^{29} +(-7.85511 + 2.31574i) q^{30} +6.97780 q^{31} +(2.13434 + 5.23876i) q^{32} +2.58970i q^{33} +(2.48685 - 0.192808i) q^{34} +(-3.38770 + 0.719615i) q^{35} +(-7.32449 + 1.14262i) q^{36} -4.70395 q^{37} +(9.32385 - 0.722887i) q^{38} -1.94849 q^{39} +(5.71827 - 2.70210i) q^{40} +6.83919 q^{41} +(-5.65543 + 0.438471i) q^{42} +5.43888 q^{43} +(-0.308271 - 1.97610i) q^{44} +(1.72213 + 8.10719i) q^{45} +(-6.16786 + 0.478200i) q^{46} -1.78733i q^{47} +(9.86659 - 3.15515i) q^{48} +4.60113 q^{49} +(-3.36516 - 6.21898i) q^{50} -4.56756i q^{51} +(1.48682 - 0.231943i) q^{52} -3.54061 q^{53} +(0.200021 + 2.57988i) q^{54} +(-2.18727 + 0.464619i) q^{55} +(4.26325 - 1.00779i) q^{56} -17.1250i q^{57} +(2.58556 - 0.200461i) q^{58} +0.926285i q^{59} +(-4.12385 - 10.8224i) q^{60} -11.3104i q^{61} +(0.762794 + 9.83857i) q^{62} +5.74079i q^{63} +(-7.15324 + 3.58207i) q^{64} +(-0.349579 - 1.64570i) q^{65} +(-3.65143 + 0.283099i) q^{66} -10.4970 q^{67} +(0.543710 + 3.48533i) q^{68} +11.3284i q^{69} +(-1.38498 - 4.69793i) q^{70} +10.7739 q^{71} +(-2.41177 - 10.2025i) q^{72} -3.66071i q^{73} +(-0.514223 - 6.63248i) q^{74} +(-11.8304 + 5.26354i) q^{75} +(2.03852 + 13.0674i) q^{76} -1.54883 q^{77} +(-0.213003 - 2.74733i) q^{78} -15.4808 q^{79} +(4.43502 + 7.76728i) q^{80} -6.38118 q^{81} +(0.747642 + 9.64314i) q^{82} -11.5798 q^{83} +(-1.23647 - 7.92613i) q^{84} +(3.85777 - 0.819468i) q^{85} +(0.594564 + 7.66872i) q^{86} -4.74887i q^{87} +(2.75257 - 0.650678i) q^{88} +13.3280 q^{89} +(-11.2427 + 3.31443i) q^{90} -1.16534i q^{91} +(-1.34851 - 8.64430i) q^{92} +18.0704 q^{93} +(2.52010 - 0.195386i) q^{94} +(14.4638 - 3.07241i) q^{95} +(5.52730 + 13.5668i) q^{96} -15.4078i q^{97} +(0.502983 + 6.48752i) q^{98} +3.70654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{4} - 12 q^{6} + 56 q^{9} - 10 q^{10} - 32 q^{14} - 8 q^{15} + 16 q^{16} + 8 q^{20} - 16 q^{24} + 16 q^{25} - 12 q^{26} + 38 q^{30} + 72 q^{34} - 24 q^{36} - 16 q^{39} + 12 q^{40} - 32 q^{41}+ \cdots - 16 q^{96}+O(q^{100}) \) 56 * q + 4 * q^4 - 12 * q^6 + 56 * q^9 - 10 * q^10 - 32 * q^14 - 8 * q^15 + 16 * q^16 + 8 * q^20 - 16 * q^24 + 16 * q^25 - 12 * q^26 + 38 * q^30 + 72 * q^34 - 24 * q^36 - 16 * q^39 + 12 * q^40 - 32 * q^41 - 12 * q^44 + 20 * q^46 - 24 * q^49 - 54 * q^50 - 52 * q^54 - 8 * q^55 + 4 * q^64 - 32 * q^65 - 8 * q^66 + 48 * q^71 + 12 * q^74 - 32 * q^76 - 32 * q^79 + 24 * q^80 + 88 * q^81 + 16 * q^84 - 68 * q^86 - 16 * q^89 - 8 * q^90 - 24 * q^94 + 24 * q^95 - 16 * q^96

Introduction

L-functions

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