LMFDB - Embedded newform 243.2.i.a.103.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.24894 - 0.626034i) q^{2} +(-1.63585 + 0.569198i) q^{3} +(2.95346 + 1.78242i) q^{4} +(-0.812747 + 0.0315383i) q^{5} +(4.03526 - 0.255991i) q^{6} +(1.20842 + 0.188994i) q^{7} +(-2.32230 - 2.46149i) q^{8} +(2.35203 - 1.86225i) q^{9} +(1.84756 + 0.437879i) q^{10} +(-0.262100 - 1.91892i) q^{11} +(-5.84597 - 1.23468i) q^{12} +(-1.56973 + 2.28872i) q^{13} +(-2.59935 - 1.18155i) q^{14} +(1.31158 - 0.514206i) q^{15} +(0.466363 + 0.885368i) q^{16} +(-3.40839 + 1.71176i) q^{17} +(-6.45539 + 2.71563i) q^{18} +(-0.0225985 - 0.388002i) q^{19} +(-2.45663 - 1.35551i) q^{20} +(-2.08438 + 0.378666i) q^{21} +(-0.611859 + 4.47960i) q^{22} +(-1.72522 + 4.46842i) q^{23} +(5.20001 + 2.70479i) q^{24} +(-4.32540 + 0.336197i) q^{25} +(4.96303 - 4.16448i) q^{26} +(-2.78758 + 4.38513i) q^{27} +(3.23216 + 2.71210i) q^{28} +(-5.20543 - 3.72061i) q^{29} +(-3.27157 + 0.335321i) q^{30} +(-3.58945 + 4.11306i) q^{31} +(0.938296 + 4.33166i) q^{32} +(1.52100 + 2.98987i) q^{33} +(8.73687 - 1.71587i) q^{34} +(-0.988102 - 0.115493i) q^{35} +(10.2659 - 1.30777i) q^{36} +(-5.86331 - 7.87579i) q^{37} +(-0.192080 + 0.886739i) q^{38} +(1.26511 - 4.63749i) q^{39} +(1.96507 + 1.92733i) q^{40} +(-0.617630 + 2.39779i) q^{41} +(4.92469 + 0.453295i) q^{42} +(0.752751 + 0.683085i) q^{43} +(2.64621 - 6.13461i) q^{44} +(-1.85287 + 1.58772i) q^{45} +(6.67729 - 8.96915i) q^{46} +(1.84929 + 2.11906i) q^{47} +(-1.26685 - 1.18288i) q^{48} +(-5.24117 - 1.68051i) q^{49} +(9.93802 + 1.95176i) q^{50} +(4.60129 - 4.74023i) q^{51} +(-8.71559 + 3.96172i) q^{52} +(1.44784 - 8.21109i) q^{53} +(9.01433 - 8.11676i) q^{54} +(0.273541 + 1.55133i) q^{55} +(-2.34111 - 3.41342i) q^{56} +(0.257818 + 0.621851i) q^{57} +(9.37743 + 11.6262i) q^{58} +(-0.578998 + 0.236547i) q^{59} +(4.79023 + 0.819106i) q^{60} +(10.0154 - 6.04435i) q^{61} +(10.6474 - 7.00288i) q^{62} +(3.19420 - 1.80587i) q^{63} +(0.717966 - 12.3270i) q^{64} +(1.20361 - 1.90965i) q^{65} +(-1.54887 - 7.67623i) q^{66} +(-7.98108 + 5.70453i) q^{67} +(-13.1176 - 1.01958i) q^{68} +(0.278781 - 8.29167i) q^{69} +(2.14988 + 0.878321i) q^{70} +(2.59953 + 8.68305i) q^{71} +(-10.0460 - 1.46480i) q^{72} +(-13.5233 + 3.20508i) q^{73} +(8.25569 + 21.3828i) q^{74} +(6.88436 - 3.01198i) q^{75} +(0.624839 - 1.18623i) q^{76} +(0.0459350 - 2.36840i) q^{77} +(-5.74837 + 9.63742i) q^{78} +(-5.21181 + 5.11171i) q^{79} +(-0.406958 - 0.704872i) q^{80} +(2.06406 - 8.76012i) q^{81} +(2.89011 - 5.00581i) q^{82} +(-0.514050 - 1.99566i) q^{83} +(-6.83106 - 2.59686i) q^{84} +(2.71617 - 1.49872i) q^{85} +(-1.26525 - 2.00746i) q^{86} +(10.6331 + 3.12346i) q^{87} +(-4.11472 + 5.10145i) q^{88} +(-1.84629 + 6.16704i) q^{89} +(5.16095 - 2.41071i) q^{90} +(-2.32945 + 2.46907i) q^{91} +(-13.0600 + 10.1222i) q^{92} +(3.53067 - 8.77146i) q^{93} +(-2.83234 - 5.92334i) q^{94} +(0.0306038 + 0.314635i) q^{95} +(-4.00048 - 6.55187i) q^{96} +(5.74213 + 0.222821i) q^{97} +(10.7350 + 7.06051i) q^{98} +(-4.18996 - 4.02524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

Coefficient data

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

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

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

$2$	−2.24894	−	0.626034i	−1.59024	−	0.442673i	−0.643703	−	0.765275i	$-0.722603\pi$
$2$	−2.24894	−	0.626034i	−1.59024	−	0.442673i	−0.946535	+	0.322602i	$0.895442\pi$
$3$	−1.63585	+	0.569198i	−0.944460	+	0.328627i
$3$	−1.63585	+	0.569198i	−0.944460	+	0.328627i
$4$	2.95346	+	1.78242i	1.47673	+	0.891211i
$5$	−0.812747	+	0.0315383i	−0.363471	+	0.0141043i	−0.219864	−	0.975530i	$-0.570561\pi$
$5$	−0.812747	+	0.0315383i	−0.363471	+	0.0141043i	−0.143607	+	0.989635i	$0.545870\pi$
$6$	4.03526	−	0.255991i	1.64739	−	0.104508i
$7$	1.20842	+	0.188994i	0.456741	+	0.0714330i	0.378705	−	0.925518i	$-0.376370\pi$
$7$	1.20842	+	0.188994i	0.456741	+	0.0714330i	0.0780362	+	0.996951i	$0.475135\pi$
$8$	−2.32230	−	2.46149i	−0.821056	−	0.870268i
$9$	2.35203	−	1.86225i	0.784009	−	0.620750i
$10$	1.84756	+	0.437879i	0.584249	+	0.138470i
$11$	−0.262100	−	1.91892i	−0.0790263	−	0.578575i	−0.987141	−	0.159853i	$-0.948898\pi$
$11$	−0.262100	−	1.91892i	−0.0790263	−	0.578575i	0.908115	−	0.418722i	$-0.137522\pi$
$12$	−5.84597	−	1.23468i	−1.68759	−	0.356420i
$13$	−1.56973	+	2.28872i	−0.435364	+	0.634776i	−0.978835	−	0.204652i	$-0.934394\pi$
$13$	−1.56973	+	2.28872i	−0.435364	+	0.634776i	0.543471	+	0.839428i	$0.317110\pi$
$14$	−2.59935	−	1.18155i	−0.694705	−	0.315782i
$15$	1.31158	−	0.514206i	0.338649	−	0.132767i
$16$	0.466363	+	0.885368i	0.116591	+	0.221342i
$17$	−3.40839	+	1.71176i	−0.826656	+	0.415162i	−0.811236	−	0.584719i	$-0.801205\pi$
$17$	−3.40839	+	1.71176i	−0.826656	+	0.415162i	−0.0154201	+	0.999881i	$0.504909\pi$
$18$	−6.45539	+	2.71563i	−1.52155	+	0.640080i
$19$	−0.0225985	−	0.388002i	−0.00518446	−	0.0890137i	0.994723	−	0.102594i	$-0.0327142\pi$
$19$	−0.0225985	−	0.388002i	−0.00518446	−	0.0890137i	−0.999908	+	0.0135801i	$0.995677\pi$
$20$	−2.45663	−	1.35551i	−0.549319	−	0.303101i
$21$	−2.08438	+	0.378666i	−0.454848	+	0.0826317i
$22$	−0.611859	+	4.47960i	−0.130449	+	0.955054i
$23$	−1.72522	+	4.46842i	−0.359733	+	0.931731i	0.628367	+	0.777917i	$0.283724\pi$
$23$	−1.72522	+	4.46842i	−0.359733	+	0.931731i	−0.988100	+	0.153814i	$0.950844\pi$
$24$	5.20001	+	2.70479i	1.06145	+	0.552113i
$25$	−4.32540	+	0.336197i	−0.865080	+	0.0672394i
$26$	4.96303	−	4.16448i	0.973330	−	0.816721i
$27$	−2.78758	+	4.38513i	−0.536470	+	0.843919i
$28$	3.23216	+	2.71210i	0.610821	+	0.512540i
$29$	−5.20543	−	3.72061i	−0.966623	−	0.690901i	−0.0155541	−	0.999879i	$-0.504951\pi$
$29$	−5.20543	−	3.72061i	−0.966623	−	0.690901i	−0.951069	+	0.308978i	$0.900013\pi$
$30$	−3.27157	+	0.335321i	−0.597305	+	0.0612210i
$31$	−3.58945	+	4.11306i	−0.644685	+	0.738727i	−0.979028	−	0.203725i	$-0.934695\pi$
$31$	−3.58945	+	4.11306i	−0.644685	+	0.738727i	0.334344	+	0.942451i	$0.391485\pi$
$32$	0.938296	+	4.33166i	0.165869	+	0.765736i
$33$	1.52100	+	2.98987i	0.264772	+	0.520470i
$34$	8.73687	−	1.71587i	1.49836	−	0.294268i
$35$	−0.988102	−	0.115493i	−0.167020	−	0.0195218i
$36$	10.2659	−	1.30777i	1.71099	−	0.217962i
$37$	−5.86331	−	7.87579i	−0.963922	−	1.29477i	−0.955557	−	0.294807i	$-0.904745\pi$
$37$	−5.86331	−	7.87579i	−0.963922	−	1.29477i	−0.00836474	−	0.999965i	$-0.502663\pi$
$38$	−0.192080	+	0.886739i	−0.0311594	+	0.143848i
$39$	1.26511	−	4.63749i	0.202579	−	0.742593i
$40$	1.96507	+	1.92733i	0.310705	+	0.304737i
$41$	−0.617630	+	2.39779i	−0.0964576	+	0.374471i	−0.998346	−	0.0574986i	$-0.981688\pi$
$41$	−0.617630	+	2.39779i	−0.0964576	+	0.374471i	0.901888	+	0.431970i	$0.142181\pi$
$42$	4.92469	+	0.453295i	0.759896	+	0.0699450i
$43$	0.752751	+	0.683085i	0.114793	+	0.104169i	0.727383	−	0.686232i	$-0.240736\pi$
$43$	0.752751	+	0.683085i	0.114793	+	0.104169i	−0.612590	+	0.790401i	$0.709872\pi$
$44$	2.64621	−	6.13461i	0.398932	−	0.924827i
$45$	−1.85287	+	1.58772i	−0.276209	+	0.236683i
$46$	6.67729	−	8.96915i	0.984512	−	1.32243i
$47$	1.84929	+	2.11906i	0.269747	+	0.309096i	0.872288	−	0.488992i	$-0.162635\pi$
$47$	1.84929	+	2.11906i	0.269747	+	0.309096i	−0.602541	+	0.798088i	$0.705845\pi$
$48$	−1.26685	−	1.18288i	−0.182854	−	0.170734i
$49$	−5.24117	−	1.68051i	−0.748738	−	0.240073i
$50$	9.93802	+	1.95176i	1.40545	+	0.276021i
$51$	4.60129	−	4.74023i	0.644310	−	0.663765i
$52$	−8.71559	+	3.96172i	−1.20863	+	0.549392i
$53$	1.44784	−	8.21109i	0.198876	−	1.12788i	−0.707915	−	0.706298i	$-0.750364\pi$
$53$	1.44784	−	8.21109i	0.198876	−	1.12788i	0.906790	−	0.421582i	$-0.138525\pi$
$54$	9.01433	−	8.11676i	1.22670	−	1.10455i
$55$	0.273541	+	1.55133i	0.0368842	+	0.209181i
$56$	−2.34111	−	3.41342i	−0.312844	−	0.456138i
$57$	0.257818	+	0.621851i	0.0341488	+	0.0823662i
$58$	9.37743	+	11.6262i	1.23132	+	1.52659i
$59$	−0.578998	+	0.236547i	−0.0753792	+	0.0307958i	−0.415576	−	0.909559i	$-0.636420\pi$
$59$	−0.578998	+	0.236547i	−0.0753792	+	0.0307958i	0.340197	+	0.940354i	$0.389506\pi$
$60$	4.79023	+	0.819106i	0.618417	+	0.105746i
$61$	10.0154	−	6.04435i	1.28234	−	0.773899i	0.298757	−	0.954329i	$-0.403428\pi$
$61$	10.0154	−	6.04435i	1.28234	−	0.773899i	0.983588	+	0.180430i	$0.0577489\pi$
$62$	10.6474	−	7.00288i	1.35222	−	0.889367i
$63$	3.19420	−	1.80587i	0.402431	−	0.227518i
$64$	0.717966	−	12.3270i	0.0897458	−	1.54088i
$65$	1.20361	−	1.90965i	0.149289	−	0.236863i
$66$	−1.54887	−	7.67623i	−0.190653	−	0.944879i
$67$	−7.98108	+	5.70453i	−0.975044	+	0.696920i	−0.953042	−	0.302838i	$-0.902066\pi$
$67$	−7.98108	+	5.70453i	−0.975044	+	0.696920i	−0.0220023	+	0.999758i	$0.507004\pi$
$68$	−13.1176	−	1.01958i	−1.59074	−	0.123642i
$69$	0.278781	−	8.29167i	0.0335613	−	0.998200i
$70$	2.14988	+	0.878321i	0.256959	+	0.104979i
$71$	2.59953	+	8.68305i	0.308508	+	1.03049i	0.961885	+	0.273455i	$0.0881666\pi$
$71$	2.59953	+	8.68305i	0.308508	+	1.03049i	−0.653377	+	0.757033i	$0.726648\pi$
$72$	−10.0460	−	1.46480i	−1.18393	−	0.172628i
$73$	−13.5233	+	3.20508i	−1.58278	+	0.375127i	−0.925570	−	0.378577i	$-0.876414\pi$
$73$	−13.5233	+	3.20508i	−1.58278	+	0.375127i	−0.657214	+	0.753704i	$0.728265\pi$
$74$	8.25569	+	21.3828i	0.959704	+	2.48570i
$75$	6.88436	−	3.01198i	0.794937	−	0.347793i
$76$	0.624839	−	1.18623i	0.0716740	−	0.136070i
$77$	0.0459350	−	2.36840i	0.00523478	−	0.269904i
$78$	−5.74837	+	9.63742i	−0.650875	+	1.09122i
$79$	−5.21181	+	5.11171i	−0.586374	+	0.575112i	−0.931635	−	0.363395i	$-0.881618\pi$
$79$	−5.21181	+	5.11171i	−0.586374	+	0.575112i	0.345261	+	0.938507i	$0.387790\pi$
$80$	−0.406958	−	0.704872i	−0.0454993	−	0.0788070i
$81$	2.06406	−	8.76012i	0.229340	−	0.973346i
$82$	2.89011	−	5.00581i	0.319159	−	0.552799i
$83$	−0.514050	−	1.99566i	−0.0564243	−	0.219053i	0.933964	−	0.357367i	$-0.116325\pi$
$83$	−0.514050	−	1.99566i	−0.0564243	−	0.219053i	−0.990388	+	0.138314i	$0.955832\pi$
$84$	−6.83106	−	2.59686i	−0.745330	−	0.283341i
$85$	2.71617	−	1.49872i	0.294610	−	0.162559i
$86$	−1.26525	−	2.00746i	−0.136436	−	0.216470i
$87$	10.6331	+	3.12346i	1.13999	+	0.334870i
$88$	−4.11472	+	5.10145i	−0.438630	+	0.543816i
$89$	−1.84629	+	6.16704i	−0.195706	+	0.653705i	0.802653	+	0.596446i	$0.203421\pi$
$89$	−1.84629	+	6.16704i	−0.195706	+	0.653705i	−0.998359	+	0.0572586i	$0.981764\pi$
$90$	5.16095	−	2.41071i	0.544012	−	0.254111i
$91$	−2.32945	+	2.46907i	−0.244193	+	0.258829i
$92$	−13.0600	+	10.1222i	−1.36160	+	1.05532i
$93$	3.53067	−	8.77146i	0.366113	−	0.909558i
$94$	−2.83234	−	5.92334i	−0.292134	−	0.610946i
$95$	0.0306038	+	0.314635i	0.00313988	+	0.0322808i
$96$	−4.00048	−	6.55187i	−0.408298	−	0.668698i
$97$	5.74213	+	0.222821i	0.583025	+	0.0226240i	0.328601	−	0.944469i	$-0.393423\pi$
$97$	5.74213	+	0.222821i	0.583025	+	0.0226240i	0.254424	+	0.967093i	$0.418114\pi$
$98$	10.7350	+	7.06051i	1.08440	+	0.713220i
$99$	−4.18996	−	4.02524i	−0.421107	−	0.404552i
$100$	−13.3741	−	6.71675i	−1.33741	−	0.671675i
$101$	0.203754	+	10.5055i	0.0202743	+	1.04534i	0.862453	+	0.506137i	$0.168927\pi$
$101$	0.203754	+	10.5055i	0.0202743	+	1.04534i	−0.842179	+	0.539199i	$0.818727\pi$
$102$	−13.3156	+	7.77991i	−1.31844	+	0.770326i
$103$	9.24977	+	7.16912i	0.911407	+	0.706394i	0.956235	−	0.292601i	$-0.0945207\pi$
$103$	9.24977	+	7.16912i	0.911407	+	0.706394i	−0.0448273	+	0.998995i	$0.514274\pi$
$104$	9.27903	−	1.45121i	0.909884	−	0.142303i
$105$	1.68213	−	0.373497i	0.164159	−	0.0364496i
$106$	−8.39651	+	17.5598i	−0.815541	+	1.70556i
$107$	5.22484	+	1.90168i	0.505104	+	0.183843i	0.581988	−	0.813197i	$-0.302275\pi$
$107$	5.22484	+	1.90168i	0.505104	+	0.183843i	−0.0768843	+	0.997040i	$0.524497\pi$
$108$	−16.0492	+	7.98267i	−1.54433	+	0.768133i
$109$	−9.12963	+	3.32291i	−0.874460	+	0.318277i	−0.739972	−	0.672638i	$-0.765161\pi$
$109$	−9.12963	+	3.32291i	−0.874460	+	0.318277i	−0.134488	+	0.990915i	$0.542939\pi$
$110$	0.356007	−	3.66008i	0.0339440	−	0.348975i
$111$	14.0744	+	9.54624i	1.33588	+	0.906089i
$112$	0.396234	+	1.15804i	0.0374406	+	0.109424i
$113$	−14.1772	+	12.8651i	−1.33368	+	1.21025i	−0.374569	+	0.927199i	$0.622209\pi$
$113$	−14.1772	+	12.8651i	−1.33368	+	1.21025i	−0.959106	+	0.283047i	$0.908655\pi$
$114$	−0.190516	−	1.55991i	−0.0178435	−	0.146099i
$115$	1.26124	−	3.68611i	0.117611	−	0.343731i
$116$	−8.74231	−	20.2669i	−0.811703	−	1.88174i
$117$	0.570122	+	8.30635i	0.0527078	+	0.767922i
$118$	1.45022	−	0.169506i	0.133503	−	0.0156043i
$119$	−4.44229	+	1.42436i	−0.407224	+	0.130571i
$120$	−4.31159	−	2.03431i	−0.393593	−	0.185706i
$121$	6.98354	−	1.94400i	0.634867	−	0.176727i
$122$	−26.3080	+	7.32334i	−2.38182	+	0.663024i
$123$	−0.354465	−	4.27398i	−0.0319610	−	0.385372i
$124$	−17.9325	+	5.74982i	−1.61039	+	0.516349i
$125$	7.54415	−	0.881784i	0.674769	−	0.0788692i
$126$	−8.31408	+	2.06160i	−0.740677	+	0.183662i
$127$	−6.58900	−	15.2750i	−0.584679	−	1.35544i	−0.911869	−	0.410480i	$-0.865361\pi$
$127$	−6.58900	−	15.2750i	−0.584679	−	1.35544i	0.327190	−	0.944958i	$-0.393898\pi$
$128$	−6.46213	+	18.8863i	−0.571177	+	1.66933i
$129$	−1.62020	−	0.688962i	−0.142651	−	0.0606597i
$130$	−3.90235	+	3.54119i	−0.342258	+	0.310583i
$131$	−2.87785	−	8.41085i	−0.251439	−	0.734859i	−0.997609	−	0.0691038i	$-0.977986\pi$
$131$	−2.87785	−	8.41085i	−0.251439	−	0.734859i	0.746170	−	0.665755i	$-0.231891\pi$
$132$	−0.837004	+	11.5415i	−0.0728518	+	1.00456i
$133$	0.0460214	−	0.473141i	0.00399056	−	0.0410266i
$134$	21.5202	−	7.83270i	1.85906	−	0.676642i
$135$	2.12730	−	3.65192i	0.183089	−	0.314307i
$136$	12.1288	+	4.41451i	1.04003	+	0.378541i
$137$	6.37384	−	13.3298i	0.544554	−	1.13884i	−0.427486	−	0.904022i	$-0.640601\pi$
$137$	6.37384	−	13.3298i	0.544554	−	1.13884i	0.972040	−	0.234816i	$-0.0754487\pi$
$138$	−5.81783	+	18.4729i	−0.495247	+	1.57252i
$139$	22.5519	−	3.52705i	1.91282	−	0.299160i	0.917658	−	0.397371i	$-0.130077\pi$
$139$	22.5519	−	3.52705i	1.91282	−	0.299160i	0.995166	+	0.0982109i	$0.0313120\pi$
$140$	−2.71246	−	2.10232i	−0.229245	−	0.177678i
$141$	−4.23134	−	2.41385i	−0.356343	−	0.203283i
$142$	−0.410301	−	21.1550i	−0.0344317	−	1.77529i
$143$	4.80328	+	2.41230i	0.401671	+	0.201727i
$144$	2.74567	+	1.21393i	0.228806	+	0.101160i
$145$	4.34803	+	2.85975i	0.361085	+	0.237489i
$146$	32.4196	+	1.25803i	2.68306	+	0.104115i
$147$	9.53032	−	0.234192i	0.786048	−	0.0193159i
$148$	−3.27906	−	33.7117i	−0.269537	−	2.77108i
$149$	−3.78360	−	7.91273i	−0.309965	−	0.648236i	0.686952	−	0.726703i	$-0.258948\pi$
$149$	−3.78360	−	7.91273i	−0.309965	−	0.648236i	−0.996917	+	0.0784666i	$0.974998\pi$
$150$	−17.3681	+	2.46391i	−1.41810	+	0.201177i
$151$	−6.63152	+	5.13981i	−0.539665	+	0.418272i	−0.845629	−	0.533771i	$-0.820774\pi$
$151$	−6.63152	+	5.13981i	−0.539665	+	0.418272i	0.305964	+	0.952043i	$0.401021\pi$
$152$	−0.902582	+	0.956681i	−0.0732091	+	0.0775971i
$153$	−4.82891	+	10.3734i	−0.390394	+	0.838637i
$154$	−1.58600	+	5.29761i	−0.127804	+	0.426894i
$155$	2.78760	−	3.45608i	0.223905	−	0.277599i
$156$	12.0024	−	11.4417i	0.960962	−	0.916068i
$157$	−3.29632	−	5.22996i	−0.263075	−	0.417397i	0.688303	−	0.725423i	$-0.258356\pi$
$157$	−3.29632	−	5.22996i	−0.263075	−	0.417397i	−0.951378	+	0.308027i	$0.900331\pi$
$158$	14.9211	−	8.23313i	1.18706	−	0.654992i
$159$	2.30529	+	14.2562i	0.182821	+	1.13059i
$160$	−0.899210	−	3.49095i	−0.0710888	−	0.275984i
$161$	−2.92930	+	5.07369i	−0.230861	+	0.399863i
$162$	−10.1261	+	18.4088i	−0.795579	+	1.44633i
$163$	−1.12503	−	1.94861i	−0.0881191	−	0.152627i	0.818597	−	0.574368i	$-0.194752\pi$
$163$	−1.12503	−	1.94861i	−0.0881191	−	0.152627i	−0.906716	+	0.421742i	$0.861419\pi$
$164$	−6.09801	+	5.98089i	−0.476175	+	0.467029i
$165$	−1.33048	−	2.38204i	−0.103578	−	0.185442i
$166$	−0.0932885	+	4.80993i	−0.00724059	+	0.373323i
$167$	11.2371	−	21.3330i	0.869550	−	1.65080i	0.116154	−	0.993231i	$-0.462943\pi$
$167$	11.2371	−	21.3330i	0.869550	−	1.65080i	0.753395	−	0.657568i	$-0.228415\pi$
$168$	5.77262	+	4.25130i	0.445368	+	0.327995i
$169$	1.90812	+	4.94216i	0.146779	+	0.380166i
$170$	−7.04675	+	1.67011i	−0.540461	+	0.128092i
$171$	−0.775708	−	0.870507i	−0.0593199	−	0.0665693i
$172$	1.00567	+	3.35918i	0.0766819	+	0.256135i
$173$	−18.9667	−	7.74875i	−1.44201	−	0.589126i	−0.483797	−	0.875180i	$-0.660743\pi$
$173$	−18.9667	−	7.74875i	−1.44201	−	0.589126i	−0.958214	+	0.286054i	$0.907656\pi$
$174$	−21.9577	−	13.6811i	−1.66461	−	1.03716i
$175$	−5.29046	−	0.411207i	−0.399921	−	0.0310843i
$176$	1.57671	−	1.12697i	0.118849	−	0.0849483i
$177$	0.812514	−	0.716520i	0.0610723	−	0.0538570i
$178$	8.01297	−	12.7134i	0.600597	−	0.952912i
$179$	−0.974992	+	16.7400i	−0.0728743	+	1.25120i	0.741536	+	0.670914i	$0.234098\pi$
$179$	−0.974992	+	16.7400i	−0.0728743	+	1.25120i	−0.814410	+	0.580290i	$0.802939\pi$
$180$	−8.30235	+	1.38666i	−0.618821	+	0.103355i
$181$	8.99829	−	5.91827i	0.668837	−	0.439901i	−0.169150	−	0.985590i	$-0.554102\pi$
$181$	8.99829	−	5.91827i	0.668837	−	0.439901i	0.837988	+	0.545689i	$0.183732\pi$
$182$	6.78450	−	4.09447i	0.502901	−	0.303502i
$183$	−12.9433	+	15.5884i	−0.956799	+	1.15233i
$184$	15.0054	−	6.13040i	1.10622	−	0.451939i
$185$	5.01377	+	6.21610i	0.368620	+	0.457017i
$186$	−13.4315	+	17.5161i	−0.984844	+	1.28435i
$187$	4.17806	+	6.09176i	0.305530	+	0.445474i
$188$	1.68476	+	9.55477i	0.122874	+	0.696853i
$189$	−4.19734	+	4.77226i	−0.305312	+	0.347131i
$190$	0.128146	−	0.726752i	0.00929668	−	0.0527241i
$191$	21.6491	−	9.84070i	1.56647	−	0.712048i	0.572318	−	0.820032i	$-0.306044\pi$
$191$	21.6491	−	9.84070i	1.56647	−	0.712048i	0.994153	+	0.107984i	$0.0344394\pi$
$192$	5.84202	+	20.5738i	0.421612	+	1.48479i
$193$	−3.79909	−	0.746116i	−0.273464	−	0.0537066i	0.0541000	−	0.998536i	$-0.482771\pi$
$193$	−3.79909	−	0.746116i	−0.273464	−	0.0537066i	−0.327564	+	0.944829i	$0.606228\pi$
$194$	−12.7742	−	4.09588i	−0.917133	−	0.294067i
$195$	−0.881954	+	3.80900i	−0.0631580	+	0.272768i
$196$	−12.4842	−	14.3053i	−0.891728	−	1.02181i
$197$	−0.668486	+	0.897932i	−0.0476276	+	0.0639750i	−0.825299	−	0.564696i	$-0.808993\pi$
$197$	−0.668486	+	0.897932i	−0.0476276	+	0.0639750i	0.777671	+	0.628671i	$0.216401\pi$
$198$	6.90302	+	11.6756i	0.490576	+	0.829747i
$199$	−8.85993	+	20.5396i	−0.628064	+	1.45602i	0.245544	+	0.969385i	$0.421033\pi$
$199$	−8.85993	+	20.5396i	−0.628064	+	1.45602i	−0.873608	+	0.486630i	$0.838226\pi$
$200$	10.8724	+	9.86619i	0.768796	+	0.697645i
$201$	9.80886	−	13.8746i	0.691864	−	0.978638i
$202$	6.11857	−	23.7537i	0.430501	−	1.67131i
$203$	−5.58718	−	5.47987i	−0.392143	−	0.384611i
$204$	22.0388	−	5.79864i	1.54303	−	0.405986i
$205$	0.426355	−	1.96827i	0.0297779	−	0.137470i
$206$	−16.3140	−	21.9136i	−1.13665	−	1.52679i
$207$	4.26356	+	13.7226i	0.296338	+	0.953789i
$208$	−2.75842	−	0.322413i	−0.191262	−	0.0223553i
$209$	−0.738620	+	0.145060i	−0.0510914	+	0.0100340i
$210$	−4.01682	−	0.213098i	−0.277187	−	0.0147052i
$211$	2.07197	+	9.56528i	0.142640	+	0.658501i	0.991524	+	0.129922i	$0.0414726\pi$
$211$	2.07197	+	9.56528i	0.142640	+	0.658501i	−0.848884	+	0.528579i	$0.822725\pi$
$212$	18.9117	−	21.6705i	1.29886	−	1.48833i
$213$	−9.19483	−	12.7245i	−0.630019	−	0.871871i
$214$	−10.5598	−	7.54769i	−0.721853	−	0.515950i
$215$	−0.633339	−	0.531434i	−0.0431934	−	0.0362435i
$216$	17.2676	−	3.32198i	1.17491	−	0.226032i
$217$	−5.11492	+	4.29193i	−0.347223	+	0.291355i
$218$	22.6122	−	1.75756i	1.53149	−	0.119037i
$219$	20.2978	−	12.9405i	1.37160	−	0.874437i
$220$	−1.95723	+	5.06934i	−0.131956	+	0.341775i
$221$	1.43251	−	10.4878i	0.0963611	−	0.705488i
$222$	−25.6761	−	30.2799i	−1.72327	−	2.03226i
$223$	13.5939	+	7.50082i	0.910318	+	0.502292i	0.867862	−	0.496806i	$-0.165494\pi$
$223$	13.5939	+	7.50082i	0.910318	+	0.502292i	0.0424564	+	0.999098i	$0.486482\pi$
$224$	0.315202	+	5.41181i	0.0210603	+	0.361591i
$225$	−9.54738	+	8.84572i	−0.636492	+	0.589715i
$226$	39.9375	−	20.0574i	2.65660	−	1.33420i
$227$	−5.64784	−	10.7222i	−0.374861	−	0.711655i	0.622625	−	0.782520i	$-0.286066\pi$
$227$	−5.64784	−	10.7222i	−0.374861	−	0.711655i	−0.997486	+	0.0708648i	$0.977424\pi$
$228$	−0.346946	+	2.29615i	−0.0229770	+	0.152066i
$229$	−6.33592	−	2.88003i	−0.418689	−	0.190318i	0.193376	−	0.981125i	$-0.438056\pi$
$229$	−6.33592	−	2.88003i	−0.418689	−	0.190318i	−0.612065	+	0.790807i	$0.709661\pi$
$230$	−5.14407	+	7.50024i	−0.339190	+	0.494551i
$231$	1.27294	+	3.90049i	0.0837536	+	0.256634i
$232$	2.93028	+	21.4535i	0.192383	+	1.40849i
$233$	8.53758	+	2.02344i	0.559315	+	0.132560i	0.500544	−	0.865711i	$-0.333133\pi$
$233$	8.53758	+	2.02344i	0.559315	+	0.132560i	0.0587716	+	0.998271i	$0.481282\pi$
$234$	3.91789	−	19.0374i	0.256120	−	1.24451i
$235$	−1.56984	−	1.66393i	−0.102405	−	0.108543i
$236$	−2.13167	−	0.333388i	−0.138760	−	0.0217017i
$237$	5.61618	−	11.3285i	0.364810	−	0.735868i
$238$	10.8821	−	0.422276i	0.705383	−	0.0273721i
$239$	−7.81731	−	4.71777i	−0.505660	−	0.305167i	0.240826	−	0.970568i	$-0.422582\pi$
$239$	−7.81731	−	4.71777i	−0.505660	−	0.305167i	−0.746486	+	0.665401i	$0.768261\pi$
$240$	1.06693	+	0.921426i	0.0688703	+	0.0594778i
$241$	13.9241	+	3.87605i	0.896933	+	0.249678i	0.685810	−	0.727781i	$-0.259448\pi$
$241$	13.9241	+	3.87605i	0.896933	+	0.249678i	0.211124	+	0.977459i	$0.432288\pi$
$242$	−16.9225			−1.08782
$243$	1.60975	+	15.5051i	0.103265	+	0.994654i
$244$	40.3537			2.58338
$245$	4.31274	+	1.20053i	0.275531	+	0.0766993i
$246$	−1.87849	+	9.83381i	−0.119768	+	0.626981i
$247$	0.923501	+	0.557335i	0.0587609	+	0.0354624i
$248$	18.4600	−	0.716333i	1.17221	−	0.0454872i
$249$	1.97684	+	2.97201i	0.125277	+	0.188344i
$250$	−17.5183	−	2.73982i	−1.10796	−	0.173281i
$251$	−14.0757	−	14.9194i	−0.888451	−	0.941703i	0.110186	−	0.993911i	$-0.464855\pi$
$251$	−14.0757	−	14.9194i	−0.888451	−	0.941703i	−0.998636	+	0.0522083i	$0.983374\pi$
$252$	12.6527	+	0.359856i	0.797048	+	0.0226688i
$253$	9.02671	+	2.13937i	0.567504	+	0.134501i
$254$	5.25556	+	38.4775i	0.329763	+	2.41429i
$255$	−3.59019	+	3.99773i	−0.224826	+	0.250347i
$256$	12.3883	−	18.0625i	0.774267	−	1.12891i
$257$	20.8559	+	9.48017i	1.30096	+	0.591357i	0.939983	−	0.341220i	$-0.110840\pi$
$257$	20.8559	+	9.48017i	1.30096	+	0.591357i	0.360972	+	0.932577i	$0.382445\pi$
$258$	3.21241	+	2.56373i	0.199996	+	0.159611i
$259$	−5.59688	−	10.6254i	−0.347773	−	0.660231i
$260$	6.95862	−	3.49475i	0.431555	−	0.216735i
$261$	−19.1720	+	0.942812i	−1.18672	+	0.0583586i
$262$	1.20663	+	20.7171i	0.0745460	+	1.27991i
$263$	−21.7733	−	12.0140i	−1.34260	−	0.740816i	−0.361146	−	0.932509i	$-0.617614\pi$
$263$	−21.7733	−	12.0140i	−1.34260	−	0.740816i	−0.981455	+	0.191693i	$0.938602\pi$
$264$	3.82733	−	10.6873i	0.235556	−	0.657758i
$265$	−0.917761	+	6.71920i	−0.0563776	+	0.412757i
$266$	−0.399702	+	1.03525i	−0.0245073	+	0.0634755i
$267$	−0.490009	−	11.1393i	−0.0299881	−	0.681712i
$268$	−33.7397	+	2.62246i	−2.06098	+	0.160192i
$269$	−17.5142	+	14.6961i	−1.06786	+	0.896039i	−0.994857	−	0.101293i	$-0.967702\pi$
$269$	−17.5142	+	14.6961i	−1.06786	+	0.896039i	−0.0730012	+	0.997332i	$0.523258\pi$
$270$	−7.07038	+	6.88117i	−0.430289	+	0.418775i
$271$	2.94493	+	2.47109i	0.178892	+	0.150108i	0.727837	−	0.685750i	$-0.240526\pi$
$271$	2.94493	+	2.47109i	0.178892	+	0.150108i	−0.548945	+	0.835859i	$0.684970\pi$
$272$	−3.10508	−	2.21938i	−0.188273	−	0.134570i
$273$	2.40524	−	5.36495i	0.145572	−	0.324702i
$274$	−22.6792	+	25.9875i	−1.37010	+	1.56996i
$275$	1.77882	+	8.21196i	0.107267	+	0.495200i
$276$	15.6026	−	23.9922i	0.939168	−	1.44416i
$277$	13.3314	−	2.61819i	0.801004	−	0.157312i	0.224572	−	0.974457i	$-0.427901\pi$
$277$	13.3314	−	2.61819i	0.801004	−	0.157312i	0.576432	+	0.817145i	$0.304445\pi$
$278$	−52.9257	−	6.18613i	−3.17427	−	0.371019i
$279$	−0.782954	+	16.3585i	−0.0468743	+	0.979356i
$280$	2.01038	+	2.70041i	0.120143	+	0.161380i
$281$	1.97291	−	9.10797i	0.117694	−	0.543336i	−0.879970	−	0.475029i	$-0.842438\pi$
$281$	1.97291	−	9.10797i	0.117694	−	0.543336i	0.997664	−	0.0683073i	$-0.0217598\pi$
$282$	8.00485	+	8.07755i	0.476682	+	0.481011i
$283$	20.0443	+	19.6593i	1.19151	+	1.16862i	0.981610	+	0.190898i	$0.0611401\pi$
$283$	20.0443	+	19.6593i	1.19151	+	1.16862i	0.209897	+	0.977723i	$0.432687\pi$
$284$	−7.79924	+	30.2785i	−0.462799	+	1.79670i
$285$	−0.229153	−	0.497276i	−0.0135738	−	0.0294561i
$286$	−9.29209	−	8.43212i	−0.549453	−	0.498602i
$287$	−1.19953	+	2.78081i	−0.0708058	+	0.164146i
$288$	10.2735	+	8.44083i	0.605373	+	0.497381i
$289$	−1.46469	+	1.96741i	−0.0861580	+	0.115730i
$290$	−7.98815	−	9.15340i	−0.469080	−	0.537506i
$291$	−9.52011	+	2.90391i	−0.558079	+	0.170230i
$292$	−45.6534	−	14.6382i	−2.67166	−	0.856634i
$293$	−17.0419	−	3.34693i	−0.995601	−	0.195530i	−0.331728	−	0.943375i	$-0.607632\pi$
$293$	−17.0419	−	3.34693i	−0.995601	−	0.195530i	−0.663873	+	0.747845i	$0.731088\pi$
$294$	−21.5797	−	5.43962i	−1.25855	−	0.317245i
$295$	0.463119	−	0.210513i	0.0269638	−	0.0122566i
$296$	−5.76984	+	32.7224i	−0.335365	+	1.90195i
$297$	9.14533	+	4.19978i	0.530666	+	0.243696i
$298$	3.55544	+	20.1639i	0.205961	+	1.16806i
$299$	−7.51884	−	10.9627i	−0.434826	−	0.633992i
$300$	25.7013	+	3.37507i	1.48386	+	0.194860i
$301$	0.780542	+	0.967721i	0.0449897	+	0.0557785i
$302$	18.1316	−	7.40756i	1.04335	−	0.426257i
$303$	−6.31302	−	17.0695i	−0.362674	−	0.980615i
$304$	0.332985	−	0.200958i	0.0190980	−	0.0115257i
$305$	−7.94938	+	5.22839i	−0.455180	+	0.299377i
$306$	17.3540	−	20.3060i	0.992061	−	1.16082i
$307$	0.0490107	−	0.841481i	0.00279719	−	0.0480258i	−0.996621	−	0.0821409i	$-0.973824\pi$
$307$	0.0490107	−	0.841481i	0.00279719	−	0.0480258i	0.999418	+	0.0341151i	$0.0108613\pi$
$308$	4.35715	−	6.91309i	0.248272	−	0.393910i
$309$	−19.2119	−	6.46266i	−1.09293	−	0.367648i
$310$	−8.43275	+	6.02737i	−0.478948	+	0.342331i
$311$	−1.14875	−	0.0892880i	−0.0651397	−	0.00506306i	0.0448812	−	0.998992i	$-0.485709\pi$
$311$	−1.14875	−	0.0892880i	−0.0651397	−	0.00506306i	−0.110021	+	0.993929i	$0.535092\pi$
$312$	−14.3531	+	7.65558i	−0.812584	+	0.433412i
$313$	−9.93266	−	4.05794i	−0.561427	−	0.229368i	0.0796789	−	0.996821i	$-0.474610\pi$
$313$	−9.93266	−	4.05794i	−0.561427	−	0.229368i	−0.641106	+	0.767452i	$0.721524\pi$
$314$	4.13907	+	13.8255i	0.233581	+	0.780216i
$315$	−2.53912	+	1.56845i	−0.143063	+	0.0883722i
$316$	−24.5041	+	5.80757i	−1.37846	+	0.326701i
$317$	9.98259	+	25.8556i	0.560678	+	1.45219i	0.866049	+	0.499960i	$0.166652\pi$
$317$	9.98259	+	25.8556i	0.560678	+	1.45219i	−0.305371	+	0.952234i	$0.598780\pi$
$318$	3.74044	−	33.5046i	0.209753	−	1.87884i
$319$	−5.77520	+	10.9639i	−0.323349	+	0.613863i
$320$	−0.194752	+	10.0414i	−0.0108870	+	0.561330i
$321$	−9.62950	−	0.136908i	−0.537466	−	0.00764148i
$322$	9.76410	−	9.57657i	0.544132	−	0.533681i
$323$	0.741190	+	1.28378i	0.0412409	+	0.0714314i
$324$	21.7103	−	22.1936i	1.20613	−	1.23298i
$325$	6.02024	−	10.4274i	0.333943	−	0.578406i
$326$	1.31022	+	5.08660i	0.0725666	+	0.281721i
$327$	13.0433	−	10.6324i	0.721298	−	0.587971i
$328$	7.33645	−	4.04808i	0.405088	−	0.223518i
$329$	1.83424	+	2.91022i	0.101125	+	0.160446i
$330$	1.50093	+	6.18998i	0.0826237	+	0.340747i
$331$	−16.6070	+	20.5895i	−0.912805	+	1.13170i	0.0780738	+	0.996948i	$0.475123\pi$
$331$	−16.6070	+	20.5895i	−0.912805	+	1.13170i	−0.990879	+	0.134754i	$0.956976\pi$
$332$	2.03889	−	6.81036i	0.111899	−	0.373767i
$333$	−28.4573	−	7.60513i	−1.55945	−	0.416758i
$334$	−38.6266	+	40.9418i	−2.11355	+	2.24024i
$335$	6.30669	−	4.88805i	0.344571	−	0.267063i
$336$	−1.30733	−	1.66884i	−0.0713210	−	0.0910430i
$337$	−5.74555	−	12.0158i	−0.312980	−	0.654542i	0.684224	−	0.729272i	$-0.260141\pi$
$337$	−5.74555	−	12.0158i	−0.312980	−	0.654542i	−0.997204	+	0.0747299i	$0.976191\pi$
$338$	−1.19728	−	12.3092i	−0.0651236	−	0.669530i
$339$	15.8690	−	29.1150i	0.861884	−	1.58131i
$340$	10.6935	+	0.414955i	0.579934	+	0.0225041i
$341$	8.83340	+	5.80982i	0.478356	+	0.314619i
$342$	1.19955	+	2.44333i	0.0648643	+	0.132120i
$343$	−13.6670	−	6.86384i	−0.737951	−	0.370613i
$344$	−0.0667035	−	3.43921i	−0.00359641	−	0.185430i
$345$	0.0349264	+	6.74782i	0.00188038	+	0.363291i
$346$	37.8039	+	29.3002i	2.03235	+	1.57519i
$347$	7.27949	−	1.13849i	0.390784	−	0.0611175i	0.0439250	−	0.999035i	$-0.486014\pi$
$347$	7.27949	−	1.13849i	0.390784	−	0.0611175i	0.346859	+	0.937917i	$0.387248\pi$
$348$	25.8370	+	28.1776i	1.38501	+	1.51048i
$349$	−6.86066	+	14.3479i	−0.367243	+	0.768023i	−0.999980	−	0.00634366i	$-0.997981\pi$
$349$	−6.86066	+	14.3479i	−0.367243	+	0.768023i	0.632737	+	0.774367i	$0.281931\pi$
$350$	11.6405	+	4.23678i	0.622209	+	0.226466i
$351$	−5.66060	−	13.2634i	−0.302140	−	0.707951i
$352$	8.06615	−	2.93584i	0.429927	−	0.156481i
$353$	1.95223	−	20.0707i	0.103907	−	1.06825i	−0.787890	−	0.615816i	$-0.788826\pi$
$353$	1.95223	−	20.0707i	0.103907	−	1.06825i	0.891796	−	0.452437i	$-0.149445\pi$
$354$	−2.27586	+	1.10275i	−0.120960	+	0.0586104i
$355$	−2.38661	−	6.97513i	−0.126668	−	0.370202i
$356$	−16.4452	+	14.9232i	−0.871594	+	0.790930i
$357$	6.45619	−	4.85859i	0.341698	−	0.257144i
$358$	12.6725	−	37.0367i	0.669761	−	1.95745i
$359$	−4.03608	−	9.35668i	−0.213016	−	0.493827i	0.777887	−	0.628404i	$-0.216292\pi$
$359$	−4.03608	−	9.35668i	−0.213016	−	0.493827i	−0.990903	+	0.134577i	$0.957032\pi$
$360$	8.21106	+	0.873675i	0.432761	+	0.0460467i
$361$	18.7215	−	2.18823i	0.985342	−	0.115170i
$362$	−23.9416	+	7.67657i	−1.25834	+	0.403471i
$363$	−10.3175	+	7.15512i	−0.541529	+	0.375546i
$364$	−11.2809	+	3.14024i	−0.591277	+	0.164593i
$365$	10.8899	−	3.03142i	0.570006	−	0.158672i
$366$	38.8676	−	26.9544i	2.03164	−	1.40893i
$367$	0.836497	−	0.268212i	0.0436648	−	0.0140006i	−0.283413	−	0.958998i	$-0.591467\pi$
$367$	0.836497	−	0.268212i	0.0436648	−	0.0140006i	0.327078	+	0.944997i	$0.393936\pi$
$368$	−4.76078	+	0.556455i	−0.248173	+	0.0290072i
$369$	3.01259	+	6.78984i	0.156829	+	0.353465i
$370$	−7.38416	−	17.1184i	−0.383884	−	0.889943i
$371$	3.30145	−	9.64884i	0.171403	−	0.500943i
$372$	26.0621	−	19.6130i	1.35126	−	1.01689i
$373$	7.26335	−	6.59114i	0.376082	−	0.341276i	−0.461941	−	0.886910i	$-0.652847\pi$
$373$	7.26335	−	6.59114i	0.376082	−	0.341276i	0.838024	+	0.545634i	$0.183711\pi$
$374$	−5.58254	−	16.3156i	−0.288666	−	0.843659i
$375$	−11.8392	+	5.73658i	−0.611374	+	0.296236i
$376$	0.921427	−	9.47310i	0.0475190	−	0.488538i
$377$	16.6865	−	6.07340i	0.859400	−	0.312796i
$378$	12.4271	−	8.10483i	0.639183	−	0.416867i
$379$	−26.4212	−	9.61652i	−1.35716	−	0.493967i	−0.441988	−	0.897021i	$-0.645727\pi$
$379$	−26.4212	−	9.61652i	−1.35716	−	0.493967i	−0.915176	+	0.403054i	$0.867949\pi$
$380$	−0.470424	+	0.983809i	−0.0241323	+	0.0504683i
$381$	19.4731	+	21.2372i	0.997639	+	1.08802i
$382$	−54.8479	+	8.57806i	−2.80626	+	0.438892i
$383$	10.5854	+	8.20428i	0.540887	+	0.419219i	0.846068	−	0.533076i	$-0.178964\pi$
$383$	10.5854	+	8.20428i	0.540887	+	0.419219i	−0.305181	+	0.952294i	$0.598717\pi$
$384$	−0.178950	−	34.5734i	−0.00913203	−	1.76432i
$385$	0.0373616	+	1.92636i	0.00190412	+	0.0981761i
$386$	8.07681	+	4.05632i	0.411099	+	0.206461i
$387$	3.04256	+	0.204825i	0.154662	+	0.0104118i
$388$	16.5620	+	10.8930i	0.840808	+	0.553008i
$389$	24.9296	+	0.967381i	1.26398	+	0.0490481i	0.662024	−	0.749482i	$-0.269697\pi$
$389$	24.9296	+	0.967381i	1.26398	+	0.0490481i	0.601955	+	0.798530i	$0.294389\pi$
$390$	4.36802	−	8.01407i	0.221183	−	0.405808i
$391$	−1.76865	−	18.1833i	−0.0894444	−	0.919569i
$392$	8.03498	+	16.8037i	0.405828	+	0.848717i
$393$	9.49518	+	12.1208i	0.478969	+	0.611415i
$394$	2.06552	−	1.60090i	0.104059	−	0.0806520i
$395$	4.07467	−	4.31889i	0.205019	−	0.217307i
$396$	−5.20021	−	19.3567i	−0.261320	−	0.972709i
$397$	−5.45169	+	18.2099i	−0.273613	+	0.913930i	0.705172	+	0.709037i	$0.250870\pi$
$397$	−5.45169	+	18.2099i	−0.273613	+	0.913930i	−0.978784	+	0.204893i	$0.934315\pi$
$398$	32.7839	−	40.6457i	1.64331	−	2.03738i
$399$	0.194027	+	0.800185i	0.00971350	+	0.0400594i
$400$	−2.31487	−	3.67278i	−0.115743	−	0.183639i
$401$	−29.9203	+	16.5093i	−1.49415	+	0.824436i	−0.999015	−	0.0443805i	$-0.985869\pi$
$401$	−29.9203	+	16.5093i	−1.49415	+	0.824436i	−0.495134	+	0.868817i	$0.664881\pi$
$402$	−30.7455	+	25.0624i	−1.53344	+	1.25000i
$403$	−3.77917	−	14.6716i	−0.188254	−	0.730846i
$404$	−18.1234	+	31.3907i	−0.901675	+	1.56175i
$405$	−1.40128	+	7.18485i	−0.0696301	+	0.357018i
$406$	9.13463	+	15.8216i	0.453344	+	0.785215i
$407$	−13.5762	+	13.3154i	−0.672947	+	0.660022i
$408$	−22.3536	−	0.317815i	−1.10667	−	0.0157342i
$409$	0.446182	−	23.0051i	0.0220623	−	1.13753i	−0.811241	−	0.584711i	$-0.801208\pi$
$409$	0.446182	−	23.0051i	0.0220623	−	1.13753i	0.833304	−	0.552815i	$-0.186447\pi$
$410$	−2.19105	+	4.15960i	−0.108208	+	0.205428i
$411$	−2.83939	+	25.4335i	−0.140057	+	1.25454i
$412$	14.5404	+	37.6607i	0.716356	+	1.85541i
$413$	−0.744381	+	0.176421i	−0.0366286	+	0.00868113i
$414$	−0.997637	−	33.5305i	−0.0490312	−	1.64793i
$415$	0.480732	+	1.60576i	0.0235982	+	0.0788235i
$416$	−11.3868	−	4.65202i	−0.558284	−	0.228084i
$417$	−34.8839	+	18.6062i	−1.70827	+	0.911150i
$418$	1.75192	+	0.136170i	0.0856892	+	0.00666029i
$419$	13.2396	−	9.46309i	0.646796	−	0.462302i	−0.210177	−	0.977663i	$-0.567404\pi$
$419$	13.2396	−	9.46309i	0.646796	−	0.462302i	0.856973	+	0.515361i	$0.172342\pi$
$420$	5.63382	+	1.89515i	0.274902	+	0.0924739i
$421$	7.47157	−	11.8545i	0.364142	−	0.577751i	−0.613067	−	0.790031i	$-0.710064\pi$
$421$	7.47157	−	11.8545i	0.364142	−	0.577751i	0.977209	+	0.212280i	$0.0680890\pi$
$422$	1.32846	−	22.8088i	0.0646686	−	1.11032i
$423$	8.29580	+	1.54023i	0.403356	+	0.0748886i
$424$	−23.5738	+	15.5047i	−1.14485	+	0.752977i
$425$	14.1672	−	8.54993i	0.687209	−	0.414733i
$426$	12.7126	+	34.3729i	0.615927	+	1.66537i
$427$	13.2452	−	5.41127i	0.640981	−	0.261870i
$428$	12.0417	+	14.9294i	0.582059	+	0.721640i
$429$	−9.23054	−	1.21215i	−0.445655	−	0.0585229i
$430$	1.09164	+	1.59165i	0.0526437	+	0.0767563i
$431$	−0.922395	−	5.23116i	−0.0444302	−	0.251976i	0.954500	−	0.298209i	$-0.0963894\pi$
$431$	−0.922395	−	5.23116i	−0.0444302	−	0.251976i	−0.998931	+	0.0462332i	$0.985278\pi$
$432$	−5.18248	−	0.422971i	−0.249342	−	0.0203502i
$433$	2.81395	−	15.9587i	0.135230	−	0.766926i	−0.839470	−	0.543406i	$-0.817134\pi$
$433$	2.81395	−	15.9587i	0.135230	−	0.766926i	0.974700	−	0.223519i	$-0.0717546\pi$
$434$	14.1900	−	6.45015i	0.681143	−	0.309617i
$435$	−8.74050	−	2.20323i	−0.419075	−	0.105637i
$436$	−32.8868	−	6.45876i	−1.57499	−	0.309318i
$437$	1.77274	+	0.568408i	0.0848019	+	0.0271906i
$438$	−53.7497	+	16.3952i	−2.56826	+	0.783393i
$439$	11.4686	+	13.1415i	0.547364	+	0.627210i	0.958750	−	0.284252i	$-0.0917451\pi$
$439$	11.4686	+	13.1415i	0.547364	+	0.627210i	−0.411385	+	0.911462i	$0.634955\pi$
$440$	3.18333	−	4.27595i	0.151759	−	0.203848i
$441$	−15.4569	+	5.80775i	−0.736043	+	0.276559i
$442$	−9.78737	+	22.6897i	−0.465538	+	1.07924i
$443$	−3.32472	−	3.01702i	−0.157962	−	0.143343i	0.589194	−	0.807992i	$-0.299445\pi$
$443$	−3.32472	−	3.01702i	−0.157962	−	0.143343i	−0.747156	+	0.664649i	$0.768581\pi$
$444$	24.5527	+	53.2809i	1.16522	+	2.52860i
$445$	1.30607	−	5.07047i	0.0619136	−	0.240363i
$446$	−25.8761	−	25.3791i	−1.22527	−	1.20174i
$447$	10.6933	+	10.7904i	0.505777	+	0.510370i
$448$	3.19734	−	14.7605i	0.151060	−	0.697370i
$449$	8.69914	+	11.6850i	0.410538	+	0.551448i	0.958514	−	0.285046i	$-0.0920089\pi$
$449$	8.69914	+	11.6850i	0.410538	+	0.551448i	−0.547976	+	0.836494i	$0.684601\pi$
$450$	27.0092	−	13.9165i	1.27322	−	0.656029i
$451$	4.76303	+	0.556718i	0.224282	+	0.0262148i
$452$	−64.8027	+	12.7268i	−3.04806	+	0.598620i
$453$	7.92261	−	12.1826i	0.372237	−	0.572390i
$454$	5.98920	+	27.6492i	0.281087	+	1.29764i
$455$	1.81538	−	2.08020i	0.0851064	−	0.0975211i
$456$	0.931950	−	2.07874i	0.0436426	−	0.0973458i
$457$	28.1791	+	20.1412i	1.31816	+	0.942167i	0.999983	−	0.00586262i	$-0.00186614\pi$
$457$	28.1791	+	20.1412i	1.31816	+	0.942167i	0.318181	+	0.948030i	$0.396928\pi$
$458$	12.4461	+	10.4435i	0.581567	+	0.487992i
$459$	1.99487	−	19.7179i	0.0931127	−	0.920353i
$460$	10.2952	−	8.63871i	0.480017	−	0.402782i
$461$	−14.3824	+	1.11789i	−0.669857	+	0.0520654i	−0.407917	−	0.913019i	$-0.633745\pi$
$461$	−14.3824	+	1.11789i	−0.669857	+	0.0520654i	−0.261940	+	0.965084i	$0.584362\pi$
$462$	−0.420928	−	9.56887i	−0.0195833	−	0.445184i
$463$	1.22936	−	3.18413i	0.0571333	−	0.147979i	−0.901378	−	0.433033i	$-0.857444\pi$
$463$	1.22936	−	3.18413i	0.0571333	−	0.147979i	0.958512	+	0.285054i	$0.0920114\pi$
$464$	0.866496	−	6.34387i	0.0402261	−	0.294507i
$465$	−2.59290	+	7.24033i	−0.120243	+	0.335762i
$466$	−17.9337	−	9.89541i	−0.830763	−	0.458396i
$467$	1.36945	+	23.5126i	0.0633707	+	1.08803i	0.868743	+	0.495263i	$0.164928\pi$
$467$	1.36945	+	23.5126i	0.0633707	+	1.08803i	−0.805372	+	0.592770i	$0.798035\pi$
$468$	−13.1216	+	25.5487i	−0.606545	+	1.18099i
$469$	−10.7226	+	5.38512i	−0.495126	+	0.248662i
$470$	2.48879	+	4.72485i	0.114799	+	0.217941i
$471$	8.36918	+	6.67919i	0.385631	+	0.307761i
$472$	1.92686	+	0.875867i	0.0886911	+	0.0403150i
$473$	1.11349	−	1.62350i	0.0511981	−	0.0746487i
$474$	−19.7225	+	21.9613i	−0.905883	+	1.00871i
$475$	0.228193	+	1.67067i	0.0104702	+	0.0766555i
$476$	−15.6589	−	3.71124i	−0.717726	−	0.170104i
$477$	−11.8857	−	22.0089i	−0.544211	−	1.00772i
$478$	14.6271	+	15.5039i	0.669030	+	0.709130i
$479$	−36.6453	−	5.73122i	−1.67437	−	0.261866i	−0.755131	−	0.655574i	$-0.772427\pi$
$479$	−36.6453	−	5.73122i	−1.67437	−	0.261866i	−0.919236	+	0.393708i	$0.871192\pi$
$480$	3.45802	+	5.19884i	0.157836	+	0.237294i
$481$	27.2293	−	1.05662i	1.24155	−	0.0481777i
$482$	−28.8880	−	17.4340i	−1.31581	−	0.794096i
$483$	1.90396	−	9.96716i	0.0866333	−	0.453522i
$484$	24.0906	+	6.70609i	1.09503	+	0.304822i
$485$	−4.67393			−0.212232
$486$	6.08651	−	35.8778i	0.276090	−	1.62745i
$487$	2.68562			0.121697			0.0608486	−	0.998147i	$-0.480619\pi$
$487$	2.68562			0.121697			0.0608486	+	0.998147i	$0.480619\pi$
$488$	−38.1369	−	10.6161i	−1.72638	−	0.480570i
$489$	2.94953	+	2.54727i	0.133382	+	0.115192i
$490$	−8.94750	−	5.39985i	−0.404207	−	0.243940i
$491$	17.8796	−	0.693811i	0.806896	−	0.0313112i	0.367974	−	0.929836i	$-0.380052\pi$
$491$	17.8796	−	0.693811i	0.806896	−	0.0313112i	0.438922	+	0.898525i	$0.355360\pi$
$492$	6.57114	−	13.2548i	0.296250	−	0.597574i
$493$	24.1109	+	3.77088i	1.08590	+	0.169832i
$494$	−1.72798	−	1.83155i	−0.0777456	−	0.0824055i
$495$	3.53233	+	3.13936i	0.158766	+	0.141104i
$496$	−5.31556	−	1.25981i	−0.238676	−	0.0565671i
$497$	1.50029	+	10.9841i	0.0672974	+	0.492704i
$498$	−2.58520	−	7.92144i	−0.115845	−	0.354968i
$499$	−14.7926	+	21.5682i	−0.662209	+	0.965524i	0.337498	+	0.941326i	$0.390419\pi$
$499$	−14.7926	+	21.5682i	−0.662209	+	0.965524i	−0.999707	+	0.0241979i	$0.992297\pi$
$500$	23.8530	+	10.8425i	1.06674	+	0.484893i
$501$	−6.23945	+	41.2938i	−0.278758	+	1.84487i
$502$	22.3153	+	42.3646i	0.995981	+	1.89082i
$503$	27.0288	−	13.5744i	1.20515	−	0.605250i	0.271157	−	0.962535i	$-0.412594\pi$
$503$	27.0288	−	13.5744i	1.20515	−	0.605250i	0.933996	+	0.357285i	$0.116297\pi$
$504$	−11.8630	−	3.66873i	−0.528420	−	0.163418i
$505$	−0.496925	−	8.53188i	−0.0221129	−	0.379664i
$506$	−18.9612	−	10.4623i	−0.842927	−	0.465107i
$507$	−5.93448	−	6.99855i	−0.263559	−	0.310816i
$508$	7.76618	−	56.8585i	0.344569	−	2.52269i
$509$	−0.703671	+	1.82255i	−0.0311897	+	0.0807833i	−0.947604	−	0.319448i	$-0.896502\pi$
$509$	−0.703671	+	1.82255i	−0.0311897	+	0.0807833i	0.916414	+	0.400232i	$0.131070\pi$
$510$	10.5768	−	6.74305i	0.468349	−	0.298587i
$511$	−16.9476	+	1.31727i	−0.749719	+	0.0582728i
$512$	−8.58579	+	7.20433i	−0.379442	+	0.318389i
$513$	1.76444	+	0.982489i	0.0779017	+	0.0433779i
$514$	−40.9687	−	34.3768i	−1.80705	−	1.51630i
$515$	−7.74382	−	5.53495i	−0.341234	−	0.243899i
$516$	−3.55717	−	4.92270i	−0.156596	−	0.216710i
$517$	3.58159	−	4.10405i	0.157518	−	0.180496i
$518$	5.93515	+	27.3997i	0.260776	+	1.20387i
$519$	35.4373	+	1.88000i	1.55552	+	0.0825228i
$520$	−7.49573	+	1.47211i	−0.328710	+	0.0645564i
$521$	−19.2337	−	2.24809i	−0.842642	−	0.0984907i	−0.316190	−	0.948696i	$-0.602404\pi$
$521$	−19.2337	−	2.24809i	−0.842642	−	0.0984907i	−0.526452	+	0.850205i	$0.676478\pi$
$522$	43.7068	+	9.88201i	1.91300	+	0.432524i
$523$	9.62812	+	12.9328i	0.421008	+	0.565512i	0.961138	−	0.276070i	$-0.0890321\pi$
$523$	9.62812	+	12.9328i	0.421008	+	0.565512i	−0.540129	+	0.841582i	$0.681625\pi$
$524$	6.49205	−	29.9706i	0.283606	−	1.30927i
$525$	8.88846	−	2.33864i	0.387924	−	0.102067i
$526$	41.4456	+	40.6496i	1.80712	+	1.77241i
$527$	5.19370	−	20.1632i	0.226241	−	0.878322i
$528$	−1.93780	+	2.74101i	−0.0843320	+	0.119287i
$529$	0.0420672	+	0.0381740i	0.00182901	+	0.00165974i
$530$	6.27043	−	14.5365i	0.272370	−	0.631425i
$531$	−0.921310	+	1.63460i	−0.0399815	+	0.0709357i
$532$	0.979260	−	1.31537i	0.0424563	−	0.0570287i
$533$	−4.51835	−	5.17745i	−0.195711	−	0.224260i
$534$	−5.87156	+	25.3583i	−0.254087	+	1.09736i
$535$	−4.30644	−	1.38081i	−0.186184	−	0.0596974i
$536$	32.5761	+	6.39774i	1.40707	+	0.276340i
$537$	−7.93341	−	27.9391i	−0.342352	−	1.20566i
$538$	48.5885	−	22.0862i	2.09480	−	0.952203i
$539$	−1.85105	+	10.4978i	−0.0797303	+	0.452173i
$540$	12.7921	−	6.99405i	0.550486	−	0.300976i
$541$	−3.83719	−	21.7618i	−0.164974	−	0.935612i	−0.949092	−	0.315000i	$-0.897995\pi$
$541$	−3.83719	−	21.7618i	−0.164974	−	0.935612i	0.784118	−	0.620612i	$-0.213116\pi$
$542$	−5.07597	−	7.40095i	−0.218032	−	0.317898i
$543$	−11.3512	+	14.8032i	−0.487127	+	0.635267i
$544$	−10.6128	−	13.1578i	−0.455021	−	0.564138i
$545$	7.31527	−	2.98862i	0.313352	−	0.128018i
$546$	−8.76788	+	10.5597i	−0.375231	+	0.451912i
$547$	18.0787	−	10.9106i	0.772990	−	0.466502i	−0.0745603	−	0.997217i	$-0.523755\pi$
$547$	18.0787	−	10.9106i	0.772990	−	0.466502i	0.847551	+	0.530714i	$0.178076\pi$
$548$	42.5841	−	28.0080i	1.81910	−	1.19644i
$549$	12.3005	−	32.8677i	0.524972	−	1.40276i
$550$	1.14051	−	19.5818i	0.0486315	−	0.834970i
$551$	−1.32597	+	2.10380i	−0.0564882	+	0.0896247i
$552$	−21.0573	+	18.5695i	−0.896258	+	0.790371i
$553$	−7.26415	+	5.19210i	−0.308903	+	0.220791i
$554$	−31.6205	−	2.45774i	−1.34342	−	0.104419i
$555$	−11.7400	−	7.31479i	−0.498335	−	0.310496i
$556$	72.8927	+	29.7799i	3.09134	+	1.26295i
$557$	−3.03735	−	10.1455i	−0.128697	−	0.429877i	0.869218	−	0.494430i	$-0.164623\pi$
$557$	−3.03735	−	10.1455i	−0.128697	−	0.429877i	−0.997914	+	0.0645527i	$0.979438\pi$
$558$	12.0018	−	36.2990i	0.508076	−	1.53666i
$559$	−2.74500	+	0.650577i	−0.116101	+	0.0275165i
$560$	−0.358561	−	0.928696i	−0.0151520	−	0.0392446i
$561$	−10.3021	−	7.58708i	−0.434955	−	0.320327i
$562$	−10.1388	+	19.2481i	−0.427682	+	0.811933i
$563$	−0.0673809	+	3.47414i	−0.00283977	+	0.146418i	0.995708	+	0.0925481i	$0.0295012\pi$
$563$	−0.0673809	+	3.47414i	−0.00283977	+	0.146418i	−0.998548	+	0.0538695i	$0.982844\pi$
$564$	−8.19458	−	14.6712i	−0.345054	−	0.617770i
$565$	11.1167	−	10.9032i	0.467683	−	0.458700i
$566$	−32.7709	−	56.7608i	−1.37746	−	2.38583i
$567$	4.14987	−	10.1958i	0.174278	−	0.428185i
$568$	15.3363	−	26.5633i	0.643499	−	1.11457i
$569$	9.72314	+	37.7476i	0.407615	+	1.58246i	0.762139	+	0.647413i	$0.224149\pi$
$569$	9.72314	+	37.7476i	0.407615	+	1.58246i	−0.354524	+	0.935047i	$0.615357\pi$
$570$	0.204038	+	1.26180i	0.00854621	+	0.0528510i
$571$	9.78465	−	5.39894i	0.409475	−	0.225939i	−0.264981	−	0.964254i	$-0.585366\pi$
$571$	9.78465	−	5.39894i	0.409475	−	0.225939i	0.674456	+	0.738315i	$0.264378\pi$
$572$	9.88656	+	15.6861i	0.413378	+	0.655869i
$573$	−29.8133	+	28.4205i	−1.24547	+	1.18729i
$574$	4.43854	−	5.50292i	0.185261	−	0.229688i
$575$	5.95999	−	19.9077i	0.248549	−	0.830210i
$576$	−21.2673	−	30.3305i	−0.886136	−	1.26377i
$577$	−17.8279	+	18.8965i	−0.742185	+	0.786670i	−0.982942	−	0.183915i	$-0.941123\pi$
$577$	−17.8279	+	18.8965i	−0.742185	+	0.786670i	0.240757	+	0.970585i	$0.422604\pi$
$578$	4.52565	−	3.50765i	0.188242	−	0.145899i
$579$	6.63943	−	0.941897i	0.275925	−	0.0391439i
$580$	7.74446	+	16.1962i	0.321571	+	0.672509i
$581$	−0.244021	−	2.50876i	−0.0101237	−	0.104081i
$582$	23.2281	−	0.570792i	0.962834	−	0.0236601i
$583$	−16.1359	−	0.626145i	−0.668279	−	0.0259323i
$584$	39.2944	+	25.8444i	1.62602	+	1.06945i
$585$	−0.725333	−	6.73298i	−0.0299888	−	0.278374i
$586$	36.2310	+	18.1959i	1.49669	+	0.751664i
$587$	0.627955	+	32.3772i	0.0259185	+	1.33635i	0.756710	+	0.653750i	$0.226805\pi$
$587$	0.627955	+	32.3772i	0.0259185	+	1.33635i	−0.730792	+	0.682600i	$0.760849\pi$
$588$	28.5648	+	16.2954i	1.17799	+	0.672010i
$589$	1.67699	+	1.29977i	0.0690992	+	0.0535559i
$590$	−1.17331	+	0.183503i	−0.0483045	+	0.00755469i
$591$	0.582443	−	1.84939i	0.0239585	−	0.0760736i
$592$	4.23854	−	8.86416i	0.174203	−	0.364315i
$593$	−6.96329	−	2.53443i	−0.285948	−	0.104077i	0.195064	−	0.980790i	$-0.437508\pi$
$593$	−6.96329	−	2.53443i	−0.285948	−	0.104077i	−0.481012	+	0.876714i	$0.659731\pi$
$594$	−17.9380	−	15.1703i	−0.736007	−	0.622446i
$595$	3.56553	−	1.29775i	0.146173	−	0.0532025i
$596$	2.92911	−	30.1139i	0.119981	−	1.23351i
$597$	2.80242	−	38.6429i	0.114695	−	1.58155i
$598$	10.0463	+	29.3616i	0.410826	+	1.20068i
$599$	2.31541	−	2.10112i	0.0946051	−	0.0858496i	−0.623333	−	0.781957i	$-0.714222\pi$
$599$	2.31541	−	2.10112i	0.0946051	−	0.0858496i	0.717938	+	0.696107i	$0.245086\pi$
$600$	−23.4015	−	9.95107i	−0.955361	−	0.406251i
$601$	−2.05783	+	6.01424i	−0.0839407	+	0.245326i	−0.980134	−	0.198339i	$-0.936445\pi$
$601$	−2.05783	+	6.01424i	−0.0839407	+	0.245326i	0.896193	+	0.443665i	$0.146322\pi$
$602$	−1.14956	−	2.66499i	−0.0468527	−	0.108617i
$603$	−8.14846	+	28.2800i	−0.331831	+	1.15165i
$604$	−28.7472	+	3.36007i	−1.16971	+	0.136719i
$605$	−5.61454	+	1.80023i	−0.228263	+	0.0731897i
$606$	3.51151	+	42.3403i	0.142645	+	1.71996i
$607$	−39.9301	+	11.1153i	−1.62071	+	0.451156i	−0.955378	−	0.295388i	$-0.904551\pi$
$607$	−39.9301	+	11.1153i	−1.62071	+	0.451156i	−0.665336	+	0.746544i	$0.731712\pi$
$608$	1.65949	−	0.461950i	0.0673011	−	0.0187345i
$609$	12.2589	+	5.78404i	0.496757	+	0.234381i
$610$	21.1508	−	6.78173i	0.856371	−	0.274584i
$611$	−7.75281	+	0.906174i	−0.313645	+	0.0366599i
$612$	−32.7517	+	22.0302i	−1.32391	+	0.890517i
$613$	−14.1462	−	32.7946i	−0.571361	−	1.32456i	−0.921687	−	0.387935i	$-0.873188\pi$
$613$	−14.1462	−	32.7946i	−0.571361	−	1.32456i	0.350326	−	0.936628i	$-0.386071\pi$
$614$	−0.637017	+	1.86175i	−0.0257079	+	0.0751343i
$615$	0.422884	+	3.46248i	0.0170523	+	0.139621i
$616$	−5.93646	+	5.38705i	−0.239187	+	0.217050i
$617$	3.78004	+	11.0476i	0.152178	+	0.444758i	0.995733	−	0.0922858i	$-0.0294174\pi$
$617$	3.78004	+	11.0476i	0.152178	+	0.444758i	−0.843554	+	0.537044i	$0.819541\pi$
$618$	39.1605	+	26.5614i	1.57527	+	1.06846i
$619$	0.0269366	−	0.276933i	0.00108268	−	0.0111309i	−0.994746	−	0.102375i	$-0.967356\pi$
$619$	0.0269366	−	0.276933i	0.00108268	−	0.0111309i	0.995829	+	0.0912439i	$0.0290843\pi$
$620$	14.3932	−	5.23871i	0.578046	−	0.210392i
$621$	−14.7855	−	20.0214i	−0.593320	−	0.803431i
$622$	2.52757	+	0.919960i	0.101346	+	0.0368870i
$623$	−3.39663	+	7.10346i	−0.136083	+	0.284594i
$624$	4.69589	−	1.04267i	0.187986	−	0.0417401i
$625$	15.3280	−	2.39726i	0.613122	−	0.0958905i
$626$	19.7975	+	15.3442i	0.791267	+	0.613278i
$627$	1.12570	−	0.657718i	0.0449563	−	0.0262667i
$628$	−0.413538	−	21.3219i	−0.0165020	−	0.850837i
$629$	33.4659	+	16.8072i	1.33437	+	0.670147i
$630$	6.69222	−	1.93777i	0.266624	−	0.0772026i
$631$	−16.1228	−	10.6042i	−0.641840	−	0.422145i	0.186434	−	0.982467i	$-0.440307\pi$
$631$	−16.1228	−	10.6042i	−0.641840	−	0.422145i	−0.828274	+	0.560323i	$0.810677\pi$
$632$	24.6858	+	0.957921i	0.981947	+	0.0381040i
$633$	−8.83398	−	14.4680i	−0.351119	−	0.575052i
$634$	−6.26375	−	64.3969i	−0.248765	−	2.55753i
$635$	5.83694	+	12.2069i	0.231632	+	0.484417i
$636$	−18.6020	+	46.2142i	−0.737619	+	1.83251i
$637$	12.0734	−	9.35761i	0.478366	−	0.370762i
$638$	19.8519	−	21.0417i	0.785942	−	0.833050i
$639$	22.2842	+	15.5818i	0.881548	+	0.616406i
$640$	4.65643	−	15.5536i	0.184062	−	0.614809i
$641$	3.84742	−	4.77005i	0.151964	−	0.188406i	−0.696661	−	0.717400i	$-0.745332\pi$
$641$	3.84742	−	4.77005i	0.151964	−	0.188406i	0.848625	+	0.528994i	$0.177431\pi$
$642$	21.5704	+	6.33629i	0.851316	+	0.250073i
$643$	−15.1504	−	24.0377i	−0.597473	−	0.947955i	−0.999478	−	0.0323175i	$-0.989711\pi$
$643$	−15.1504	−	24.0377i	−0.597473	−	0.947955i	0.402005	−	0.915637i	$-0.368313\pi$
$644$	−17.6950	+	9.76370i	−0.697281	+	0.384744i
$645$	1.33854	+	0.508853i	0.0527050	+	0.0200361i
$646$	−0.863199	−	3.35115i	−0.0339621	−	0.131849i
$647$	−4.69966	+	8.14006i	−0.184763	+	0.320019i	−0.943497	−	0.331382i	$-0.892485\pi$
$647$	−4.69966	+	8.14006i	−0.184763	+	0.320019i	0.758734	+	0.651401i	$0.225818\pi$
$648$	−26.3563	+	15.2629i	−1.03537	+	0.599584i
$649$	0.605669	+	1.04905i	0.0237746	+	0.0411788i
$650$	−20.0670	+	19.6816i	−0.787093	+	0.771976i
$651$	5.92430	−	9.93236i	0.232192	−	0.389280i
$652$	0.150513	−	7.76041i	0.00589454	−	0.303921i
$653$	−11.8873	+	22.5674i	−0.465185	+	0.883131i	0.534104	+	0.845419i	$0.320649\pi$
$653$	−11.8873	+	22.5674i	−0.465185	+	0.883131i	−0.999289	+	0.0377124i	$0.987993\pi$
$654$	−35.9898	+	15.7459i	−1.40731	+	0.615715i
$655$	2.60423	+	6.74512i	0.101756	+	0.263554i
$656$	−2.41096	+	0.571409i	−0.0941323	+	0.0223098i
$657$	−25.8385	+	32.7222i	−1.00806	+	1.27662i
$658$	−2.30319	−	7.69320i	−0.0897878	−	0.299912i
$659$	−16.2922	−	6.65609i	−0.634654	−	0.259285i	0.0379589	−	0.999279i	$-0.487914\pi$
$659$	−16.2922	−	6.65609i	−0.634654	−	0.259285i	−0.672613	+	0.739995i	$0.734828\pi$
$660$	0.316272	−	9.40674i	0.0123109	−	0.366157i
$661$	−25.6983	−	1.99743i	−0.999547	−	0.0776909i	−0.432720	−	0.901528i	$-0.642446\pi$
$661$	−25.6983	−	1.99743i	−0.999547	−	0.0776909i	−0.566826	+	0.823837i	$0.691829\pi$
$662$	50.2379	−	35.9079i	1.95255	−	1.39560i
$663$	3.62628	+	17.9719i	0.140833	+	0.697972i
$664$	−3.71853	+	5.89985i	−0.144307	+	0.228959i
$665$	−0.0224817	+	0.385996i	−0.000871802	+	0.0149683i
$666$	59.2376	+	34.9187i	2.29541	+	1.35307i
$667$	25.6058	−	16.8412i	0.991460	−	0.652093i
$668$	71.2126	−	42.9770i	2.75530	−	1.66283i
$669$	−26.5071	−	4.53259i	−1.02483	−	0.175240i
$670$	−17.2434	+	7.04471i	−0.666171	+	0.272161i
$671$	−14.2236	−	17.6345i	−0.549097	−	0.680774i
$672$	−3.59601	−	8.67350i	−0.138719	−	0.334588i
$673$	−19.0594	−	27.7893i	−0.734686	−	1.07120i	−0.994417	−	0.105518i	$-0.966350\pi$
$673$	−19.0594	−	27.7893i	−0.734686	−	1.07120i	0.259731	−	0.965681i	$-0.416366\pi$
$674$	5.39907	+	30.6197i	0.207965	+	1.17943i
$675$	10.5831	−	19.9046i	0.407345	−	0.766130i
$676$	−3.17345	+	17.9975i	−0.122056	+	0.692213i
$677$	9.41787	−	4.28095i	0.361958	−	0.164530i	−0.224572	−	0.974457i	$-0.572098\pi$
$677$	9.41787	−	4.28095i	0.361958	−	0.164530i	0.586530	+	0.809927i	$0.300493\pi$
$678$	−53.9153	+	55.5433i	−2.07060	+	2.13313i
$679$	6.89681	+	1.35449i	0.264675	+	0.0519805i
$680$	−9.99684	−	3.20536i	−0.383361	−	0.122920i
$681$	15.3421	+	14.3251i	0.587910	+	0.548941i
$682$	−16.2286	−	18.5959i	−0.621426	−	0.712075i
$683$	−16.9417	+	22.7566i	−0.648255	+	0.870757i	−0.997809	−	0.0661589i	$-0.978926\pi$
$683$	−16.9417	+	22.7566i	−0.648255	+	0.870757i	0.349554	+	0.936916i	$0.386333\pi$
$684$	−0.739413	−	3.95365i	−0.0282722	−	0.151171i
$685$	−4.75992	+	11.0347i	−0.181867	+	0.421615i
$686$	26.4393	+	23.9924i	1.00946	+	0.916033i
$687$	12.0039	+	1.10491i	0.457979	+	0.0421548i
$688$	−0.253727	+	0.985027i	−0.00967323	+	0.0375538i
$689$	16.5202	+	16.2029i	0.629368	+	0.617280i
$690$	4.14582	−	15.1973i	0.157829	−	0.578551i
$691$	−3.06411	+	14.1455i	−0.116564	+	0.538120i	0.881286	+	0.472583i	$0.156678\pi$
$691$	−3.06411	+	14.1455i	−0.116564	+	0.538120i	−0.997850	+	0.0655367i	$0.979124\pi$
$692$	−42.2058	−	56.6922i	−1.60442	−	2.15512i
$693$	−4.30250	−	5.65607i	−0.163439	−	0.214857i
$694$	−17.0838	−	1.99682i	−0.648494	−	0.0757981i
$695$	−18.2177	+	3.57784i	−0.691037	+	0.135715i
$696$	−17.0048	−	33.4268i	−0.644565	−	1.26704i
$697$	−1.99931	−	9.22983i	−0.0757291	−	0.349605i
$698$	24.4114	−	27.9724i	0.923986	−	1.05877i
$699$	−15.1180	+	1.54952i	−0.571814	+	0.0586082i
$700$	−14.8922	−	10.6443i	−0.562872	−	0.402317i
$701$	−26.7077	−	22.4104i	−1.00874	−	0.846431i	−0.0205663	−	0.999788i	$-0.506547\pi$
$701$	−26.7077	−	22.4104i	−1.00874	−	0.846431i	−0.988171	+	0.153358i	$0.950991\pi$
$702$	4.42694	+	33.3724i	0.167084	+	1.25956i
$703$	−2.92332	+	2.45296i	−0.110255	+	0.0925150i
$704$	−23.8427	+	1.85320i	−0.898604	+	0.0698450i
$705$	3.51513	+	1.82840i	0.132388	+	0.0688615i
$706$	−16.9553	+	43.9155i	−0.638123	+	1.65278i
$707$	−1.73925	+	12.7336i	−0.0654114	+	0.478896i
$708$	3.67687	−	0.667972i	0.138185	−	0.0251039i
$709$	−38.1099	−	21.0282i	−1.43125	−	0.789729i	−0.437272	−	0.899329i	$-0.644055\pi$
$709$	−38.1099	−	21.0282i	−1.43125	−	0.789729i	−0.993976	+	0.109601i	$0.965043\pi$
$710$	1.00066	+	17.1807i	0.0375542	+	0.644781i
$711$	−2.73905	+	21.7286i	−0.102722	+	0.814884i
$712$	19.4677	−	9.77707i	0.729585	−	0.366411i
$713$	−12.1863	−	23.1351i	−0.456380	−	0.866417i
$714$	−17.5612	+	6.88487i	−0.657211	+	0.257660i
$715$	−3.97993	−	1.80910i	−0.148841	−	0.0676565i
$716$	−32.7173	+	47.7029i	−1.22270	+	1.78274i
$717$	15.4733	+	3.26798i	0.577861	+	0.122045i
$718$	3.21928	+	23.5693i	0.120142	+	0.879598i
$719$	0.820677	+	0.194504i	0.0306061	+	0.00725377i	0.245890	−	0.969298i	$-0.420920\pi$
$719$	0.820677	+	0.194504i	0.0306061	+	0.00725377i	−0.215284	+	0.976551i	$0.569068\pi$
$720$	−2.26982	−	0.900020i	−0.0845913	−	0.0335418i
$721$	9.82272	+	10.4115i	0.365817	+	0.387744i
$722$	−43.4733	−	6.79911i	−1.61791	−	0.253037i
$723$	−24.9841	+	1.58495i	−0.929168	+	0.0589450i
$724$	37.1249	−	1.44062i	1.37974	−	0.0535401i
$725$	23.7664	+	14.3431i	0.882663	+	0.532690i
$726$	27.6828	−	9.63228i	1.02740	−	0.357488i
$727$	−33.6113	−	9.35634i	−1.24657	−	0.347008i	−0.418805	−	0.908076i	$-0.637551\pi$
$727$	−33.6113	−	9.35634i	−1.24657	−	0.347008i	−0.827769	+	0.561069i	$0.810390\pi$
$728$	11.4873			0.425746
$729$	−11.4588	−	24.4478i	−0.424400	−	0.905475i
$730$	−26.3886			−0.976684
$731$	−3.73494	−	1.03969i	−0.138142	−	0.0384544i
$732$	−66.0128	+	22.9693i	−2.43990	+	0.848969i
$733$	−22.0139	−	13.2855i	−0.813104	−	0.490711i	0.0481778	−	0.998839i	$-0.484659\pi$
$733$	−22.0139	−	13.2855i	−0.813104	−	0.490711i	−0.861281	+	0.508128i	$0.830338\pi$
$734$	−2.04914	+	0.0795159i	−0.0756351	+	0.00293498i
$735$	−7.73835	+	0.490909i	−0.285433	+	0.0181074i
$736$	−20.9744	−	3.28034i	−0.773128	−	0.120915i
$737$	13.0384	+	13.8199i	0.480274	+	0.509061i
$738$	−2.52446	−	17.1559i	−0.0929266	−	0.631517i
$739$	−14.1298	−	3.34881i	−0.519771	−	0.123188i	−0.0376474	−	0.999291i	$-0.511986\pi$
$739$	−14.1298	−	3.34881i	−0.519771	−	0.123188i	−0.482124	+	0.876103i	$0.660135\pi$
$740$	3.72825	+	27.2957i	0.137053	+	1.00341i
$741$	−1.82795	−	0.386064i	−0.0671512	−	0.0141824i
$742$	−13.4652	+	19.6328i	−0.494324	+	0.720743i
$743$	2.97450	+	1.35208i	0.109124	+	0.0496029i	0.467629	−	0.883925i	$-0.345108\pi$
$743$	2.97450	+	1.35208i	0.109124	+	0.0496029i	−0.358505	+	0.933528i	$0.616713\pi$
$744$	−29.7901	+	11.6792i	−1.09216	+	0.428181i
$745$	3.32466	+	6.31172i	0.121806	+	0.231243i
$746$	−20.4611	+	10.2759i	−0.749134	+	0.376229i
$747$	−4.92548	−	3.73657i	−0.180214	−	0.136714i
$748$	1.48164	+	25.4388i	0.0541742	+	0.930135i
$749$	5.95440	+	3.28550i	0.217569	+	0.120050i
$750$	30.2169	−	5.48947i	1.10336	−	0.200447i
$751$	2.46802	−	18.0691i	0.0900592	−	0.659350i	−0.889315	−	0.457295i	$-0.848818\pi$
$751$	2.46802	−	18.0691i	0.0900592	−	0.659350i	0.979374	−	0.202055i	$-0.0647620\pi$
$752$	−1.01370	+	2.62556i	−0.0369659	+	0.0957442i
$753$	31.5179	+	16.3940i	1.14857	+	0.597432i
$754$	−41.3291	+	3.21235i	−1.50512	+	0.116987i
$755$	5.22764	−	4.38651i	0.190253	−	0.159642i
$756$	−20.9028	+	6.61325i	−0.760229	+	0.240521i
$757$	−20.5966	−	17.2826i	−0.748597	−	0.628147i	0.186535	−	0.982448i	$-0.440274\pi$
$757$	−20.5966	−	17.2826i	−0.748597	−	0.628147i	−0.935131	+	0.354301i	$0.884719\pi$
$758$	53.3992	+	38.1675i	1.93955	+	1.38631i
$759$	−15.9841	+	1.63829i	−0.580186	+	0.0594663i
$760$	0.703399	−	0.806005i	0.0255150	−	0.0292369i
$761$	5.95279	+	27.4811i	0.215788	+	0.996190i	0.948776	+	0.315948i	$0.102323\pi$
$761$	5.95279	+	27.4811i	0.215788	+	0.996190i	−0.732988	+	0.680242i	$0.761875\pi$
$762$	−30.4986	−	59.9520i	−1.10485	−	2.17183i
$763$	−11.6605	+	2.29004i	−0.422137	+	0.0829050i
$764$	81.4799	+	9.52363i	2.94784	+	0.344553i
$765$	3.59752	−	8.58322i	0.130069	−	0.310327i
$766$	−18.6696	−	25.0777i	−0.674562	−	0.906094i
$767$	0.367480	−	1.69648i	0.0132689	−	0.0612563i
$768$	−9.98422	+	36.5990i	−0.360274	+	1.32065i
$769$	22.7067	+	22.2706i	0.818824	+	0.803097i	0.983052	−	0.183325i	$-0.0586862\pi$
$769$	22.7067	+	22.2706i	0.818824	+	0.803097i	−0.164228	+	0.986422i	$0.552513\pi$
$770$	1.12194	−	4.35564i	0.0404319	−	0.156966i
$771$	−39.5133	−	3.63702i	−1.42304	−	0.130984i
$772$	−9.89055	−	8.97520i	−0.355969	−	0.323024i
$773$	−11.0897	+	25.7088i	−0.398868	+	0.924681i	0.593889	+	0.804547i	$0.297592\pi$
$773$	−11.0897	+	25.7088i	−0.398868	+	0.924681i	−0.992758	+	0.120134i	$0.961668\pi$
$774$	−6.71430	−	2.36539i	−0.241341	−	0.0850220i
$775$	14.1430	−	18.9974i	0.508033	−	0.682406i
$776$	−12.7865	−	14.6517i	−0.459007	−	0.525964i
$777$	15.2036	+	14.1959i	0.545427	+	0.509274i
$778$	−55.4594	−	17.7823i	−1.98831	−	0.637527i
$779$	0.944303	+	0.185455i	0.0338332	+	0.00664462i
$780$	−9.39407	+	9.67773i	−0.336361	+	0.346518i
$781$	15.9807	−	7.26412i	0.571834	−	0.259931i
$782$	−7.40578	+	42.0003i	−0.264830	+	1.50193i
$783$	30.8259	−	12.4550i	1.10163	−	0.445104i
$784$	−0.956414	−	5.42409i	−0.0341576	−	0.193718i
$785$	2.84401	+	4.14668i	0.101507	+	0.148001i
$786$	−13.7660	−	33.2033i	−0.491017	−	1.18432i
$787$	−10.2271	−	12.6797i	−0.364558	−	0.451982i	0.562556	−	0.826759i	$-0.309818\pi$
$787$	−10.2271	−	12.6797i	−0.364558	−	0.451982i	−0.927115	+	0.374777i	$0.877719\pi$
$788$	−3.57484	+	1.46048i	−0.127348	+	0.0520275i
$789$	42.4563	+	7.25982i	1.51148	+	0.258456i
$790$	−11.8674	+	7.16203i	−0.422224	+	0.254814i
$791$	−19.5634	+	12.8671i	−0.695596	+	0.457500i
$792$	−0.177758	+	19.6614i	−0.00631635	+	0.698636i
$793$	−1.88770	+	32.4105i	−0.0670340	+	1.15093i
$794$	23.6605	−	37.5400i	0.839681	−	1.33224i
$795$	−2.32323	−	11.5140i	−0.0823966	−	0.408360i
$796$	−62.7777	+	44.8708i	−2.22510	+	1.59040i
$797$	7.82040	+	0.607849i	0.277013	+	0.0215311i	0.215247	−	0.976560i	$-0.430944\pi$
$797$	7.82040	+	0.607849i	0.277013	+	0.0215311i	0.0617653	+	0.998091i	$0.480327\pi$
$798$	0.0645886	−	1.92103i	0.00228641	−	0.0680038i
$799$	−9.93043	−	4.05703i	−0.351313	−	0.143527i
$800$	−5.51480	−	18.4207i	−0.194977	−	0.651270i
$801$	7.14204	+	17.9433i	0.252352	+	0.633995i
$802$	77.6242	−	18.3973i	2.74101	−	0.649630i
$803$	9.69475	+	25.1100i	0.342120	+	0.886114i
$804$	53.7004	−	23.4945i	1.89387	−	0.828588i
$805$	2.22076	−	4.21601i	0.0782715	−	0.148595i
$806$	−0.685834	+	35.3614i	−0.0241575	+	1.24555i
$807$	20.2856	−	34.0097i	0.714086	−	1.19720i
$808$	25.3860	−	24.8984i	0.893076	−	0.875923i
$809$	−10.7323	−	18.5889i	−0.377329	−	0.653552i	0.613344	−	0.789816i	$-0.289824\pi$
$809$	−10.7323	−	18.5889i	−0.377329	−	0.653552i	−0.990673	+	0.136264i	$0.956491\pi$
$810$	7.64935	−	15.2810i	0.268771	−	0.536920i
$811$	−16.6033	+	28.7578i	−0.583022	+	1.00982i	0.412097	+	0.911140i	$0.364796\pi$
$811$	−16.6033	+	28.7578i	−0.583022	+	1.00982i	−0.995119	+	0.0986833i	$0.968537\pi$
$812$	−6.73407	−	26.1433i	−0.236320	−	0.917449i
$813$	−6.22401	−	2.36609i	−0.218286	−	0.0829824i
$814$	38.8679	−	21.4464i	1.36232	−	0.751696i
$815$	0.975819	+	1.54824i	0.0341815	+	0.0542326i
$816$	6.34272	+	1.86317i	0.222040	+	0.0652240i
$817$	0.248027	−	0.307505i	0.00867737	−	0.0107583i
$818$	−15.4054	+	51.4576i	−0.538636	+	1.79917i
$819$	−0.880900	+	10.1453i	−0.0307812	+	0.354507i
$820$	4.76751	−	5.05327i	0.166489	−	0.176468i
$821$	41.6942	−	32.3154i	1.45514	−	1.12782i	0.488220	−	0.872721i	$-0.337646\pi$
$821$	41.6942	−	32.3154i	1.45514	−	1.12782i	0.966916	−	0.255095i	$-0.0821067\pi$
$822$	22.3078	−	55.4207i	0.778075	−	1.93302i
$823$	11.8706	+	24.8253i	0.413784	+	0.865356i	0.998533	+	0.0541419i	$0.0172423\pi$
$823$	11.8706	+	24.8253i	0.413784	+	0.865356i	−0.584749	+	0.811214i	$0.698807\pi$
$824$	−3.83401	−	39.4170i	−0.133564	−	1.37316i
$825$	−7.58413	−	12.4211i	−0.264045	−	0.432446i
$826$	1.78451	+	0.0692471i	0.0620911	+	0.00240942i
$827$	23.6932	+	15.5832i	0.823893	+	0.541883i	0.890016	−	0.455929i	$-0.150693\pi$
$827$	23.6932	+	15.5832i	0.823893	+	0.541883i	−0.0661237	+	0.997811i	$0.521063\pi$
$828$	−11.8673	+	48.1287i	−0.412416	+	1.67259i
$829$	33.8194	+	16.9847i	1.17460	+	0.589904i	0.925564	−	0.378591i	$-0.123591\pi$
$829$	33.8194	+	16.9847i	1.17460	+	0.589904i	0.249032	+	0.968495i	$0.419888\pi$
$830$	−0.0758770	−	3.91220i	−0.00263373	−	0.135794i
$831$	−20.3179	+	11.8712i	−0.704819	+	0.411806i
$832$	27.0860	+	20.9933i	0.939039	+	0.727810i
$833$	20.7406	−	3.24377i	0.718618	−	0.112390i
$834$	90.0998	−	20.0056i	3.11990	−	0.692738i
$835$	−8.46007	+	17.6927i	−0.292773	+	0.612283i
$836$	−2.44004	−	0.888102i	−0.0843906	−	0.0307157i
$837$	−8.03042	−	27.2057i	−0.277572	−	0.940367i
$838$	−35.6992	+	12.9934i	−1.23321	+	0.448851i
$839$	1.32987	−	13.6722i	0.0459121	−	0.472017i	−0.943960	−	0.330058i	$-0.892932\pi$
$839$	1.32987	−	13.6722i	0.0459121	−	0.472017i	0.989873	−	0.141959i	$-0.0453401\pi$
$840$	−4.82576	−	3.27317i	−0.166504	−	0.112935i
$841$	3.86520	+	11.2965i	0.133283	+	0.389533i
$842$	−24.2244	+	21.9825i	−0.834827	+	0.757565i
$843$	1.95685	+	16.0223i	0.0673975	+	0.551836i
$844$	−10.9299	+	31.9438i	−0.376222	+	1.09955i
$845$	−1.70669	−	3.95655i	−0.0587118	−	0.136109i
$846$	−17.6925	−	8.65733i	−0.608280	−	0.297645i
$847$	8.80648	−	1.02933i	0.302594	−	0.0353682i
$848$	7.94505	−	2.54748i	0.272834	−	0.0874808i
$849$	−43.9795	−	20.7505i	−1.50937	−	0.712155i
$850$	−37.2136	+	10.3591i	−1.27642	+	0.355315i
$851$	45.3078	−	12.6123i	1.55313	−	0.432344i
$852$	−4.47606	−	53.9705i	−0.153347	−	1.84900i
$853$	−27.3306	+	8.76319i	−0.935780	+	0.300046i	−0.733817	−	0.679347i	$-0.762263\pi$
$853$	−27.3306	+	8.76319i	−0.935780	+	0.300046i	−0.201963	+	0.979393i	$0.564732\pi$
$854$	−33.1753	+	3.87764i	−1.13524	+	0.132690i
$855$	0.657909	+	0.683037i	0.0225000	+	0.0233594i
$856$	−7.45264	−	17.2772i	−0.254726	−	0.590521i
$857$	−18.2451	+	53.3233i	−0.623240	+	1.82149i	−0.0552208	+	0.998474i	$0.517586\pi$
$857$	−18.2451	+	53.3233i	−0.623240	+	1.82149i	−0.568020	+	0.823015i	$0.692290\pi$
$858$	20.0000	+	8.50467i	0.682790	+	0.290345i
$859$	31.3780	−	28.4740i	1.07060	−	0.971519i	0.0709389	−	0.997481i	$-0.477400\pi$
$859$	31.3780	−	28.4740i	1.07060	−	0.971519i	0.999663	+	0.0259613i	$0.00826466\pi$
$860$	−0.923300	−	2.69845i	−0.0314843	−	0.0920163i
$861$	0.379413	−	5.23177i	0.0129304	−	0.178298i
$862$	−1.20048	+	12.3420i	−0.0408884	+	0.420370i
$863$	−18.9181	+	6.88562i	−0.643979	+	0.234389i	−0.643304	−	0.765610i	$-0.722437\pi$
$863$	−18.9181	+	6.88562i	−0.643979	+	0.234389i	−0.000674900		1.00000i	$0.500215\pi$
$864$	−21.6105	−	7.96028i	−0.735203	−	0.270814i
$865$	15.6595	+	5.69959i	0.532439	+	0.193792i
$866$	−16.3191	+	34.1284i	−0.554544	+	1.15973i
$867$	1.27616	−	4.05210i	0.0433407	−	0.137616i
$868$	−22.7567	+	3.55909i	−0.772414	+	0.120803i
$869$	11.1749	+	8.66124i	0.379084	+	0.293812i
$870$	18.2775	+	10.4268i	0.619666	+	0.353501i
$871$	−0.527951	−	27.2210i	−0.0178889	−	0.922349i
$872$	29.3810	+	14.7557i	0.994967	+	0.499691i
$873$	13.9206	−	10.1692i	0.471141	−	0.344175i
$874$	−3.63095	−	2.38811i	−0.122819	−	0.0807791i
$875$	9.28317	+	0.360229i	0.313829	+	0.0121780i
$876$	83.0142	−	2.03994i	2.80479	−	0.0689232i
$877$	−4.81065	−	49.4578i	−0.162444	−	1.67007i	−0.622834	−	0.782354i	$-0.714019\pi$
$877$	−4.81065	−	49.4578i	−0.162444	−	1.67007i	0.460390	−	0.887717i	$-0.347710\pi$
$878$	−17.5650	−	36.7341i	−0.592791	−	1.23972i
$879$	29.7832	−	4.22516i	1.00456	−	0.142511i
$880$	−1.24592	+	0.965665i	−0.0420001	+	0.0325526i
$881$	−4.24135	+	4.49556i	−0.142895	+	0.151459i	−0.794868	−	0.606782i	$-0.792460\pi$
$881$	−4.24135	+	4.49556i	−0.142895	+	0.151459i	0.651973	+	0.758242i	$0.273941\pi$
$882$	38.3974	−	3.38470i	1.29291	−	0.113969i
$883$	5.31605	−	17.7569i	0.178899	−	0.597566i	−0.820755	−	0.571280i	$-0.806447\pi$
$883$	5.31605	−	17.7569i	0.178899	−	0.597566i	0.999654	−	0.0262855i	$-0.00836789\pi$
$884$	22.9246	−	28.4221i	0.771038	−	0.955937i
$885$	−0.637770	+	0.607975i	−0.0214384	+	0.0204369i
$886$	5.58832	+	8.86647i	0.187743	+	0.297875i
$887$	0.529876	−	0.292373i	0.0177915	−	0.00981694i	−0.474192	−	0.880422i	$-0.657260\pi$
$887$	0.529876	−	0.292373i	0.0177915	−	0.00981694i	0.491983	+	0.870605i	$0.336272\pi$
$888$	−9.18692	−	56.8132i	−0.308293	−	1.90653i
$889$	−5.07541	−	19.7040i	−0.170224	−	0.660850i
$890$	−6.11155	+	10.5855i	−0.204860	+	0.354827i
$891$	−17.3509	−	1.66472i	−0.581277	−	0.0557703i
$892$	26.7795	+	46.3835i	0.896645	+	1.55303i
$893$	0.780407	−	0.765417i	0.0261153	−	0.0256137i
$894$	−17.2934	−	30.9614i	−0.578378	−	1.03550i
$895$	0.264472	−	13.6361i	0.00884032	−	0.455804i
$896$	−11.3784	+	21.6013i	−0.380125	+	0.721650i
$897$	18.5397	+	13.6537i	0.619022	+	0.455884i
$898$	−12.2486	−	31.7247i	−0.408742	−	1.05867i
$899$	33.9877	−	8.05524i	1.13355	−	0.268657i
$900$	−43.9646	+	9.10801i	−1.46549	+	0.303600i
$901$	9.12061	+	30.4649i	0.303851	+	1.01493i
$902$	−10.3632	−	4.23384i	−0.345058	−	0.140972i
$903$	−1.82768	−	1.13877i	−0.0608213	−	0.0378957i
$904$	64.5909	+	5.02040i	2.14826	+	0.166976i
$905$	−7.12667	+	5.09384i	−0.236899	+	0.169325i
$906$	−25.4442	+	22.4381i	−0.845326	+	0.745457i
$907$	−18.9160	+	30.0122i	−0.628095	+	0.996540i	0.369634	+	0.929178i	$0.379483\pi$
$907$	−18.9160	+	30.0122i	−0.628095	+	0.996540i	−0.997729	+	0.0673627i	$0.978542\pi$
$908$	2.43075	−	41.7343i	0.0806672	−	1.38500i
$909$	20.0431	+	24.3298i	0.664787	+	0.806967i
$910$	−5.38495	+	3.54174i	−0.178509	+	0.117407i
$911$	11.3004	−	6.81982i	0.374399	−	0.225951i	−0.316998	−	0.948426i	$-0.602675\pi$
$911$	11.3004	−	6.81982i	0.374399	−	0.225951i	0.691396	+	0.722476i	$0.256996\pi$
$912$	−0.430330	+	0.518272i	−0.0142497	+	0.0171617i
$913$	−3.69478	+	1.50948i	−0.122279	+	0.0499566i
$914$	−50.7640	−	62.9374i	−1.67912	−	2.08179i
$915$	10.0280	−	13.0777i	0.331516	−	0.432334i
$916$	−13.5794	−	19.7993i	−0.448677	−	0.654188i
$917$	−1.88807	−	10.7078i	−0.0623494	−	0.353601i
$918$	−16.8304	+	43.0955i	−0.555487	+	1.42236i
$919$	4.79556	−	27.1970i	0.158191	−	0.897146i	−0.797619	−	0.603161i	$-0.793908\pi$
$919$	4.79556	−	27.1970i	0.158191	−	0.897146i	0.955810	−	0.293984i	$-0.0949813\pi$
$920$	−12.0023	+	5.45571i	−0.395704	+	0.179869i
$921$	0.398795	+	1.40444i	0.0131407	+	0.0462777i
$922$	33.0450	+	6.48983i	1.08828	+	0.213731i
$923$	−23.9536	−	7.68042i	−0.788443	−	0.252804i
$924$	−3.19274	+	13.7889i	−0.105033	+	0.453621i
$925$	28.0090	+	32.0947i	0.920929	+	1.05527i
$926$	−4.75813	+	6.39127i	−0.156362	+	0.210030i
$927$	35.1064	−	0.363428i	1.15305	−	0.0119365i
$928$	11.2322	−	26.0391i	0.368715	−	0.854777i
$929$	38.8634	+	35.2666i	1.27507	+	1.15706i	0.979436	+	0.201757i	$0.0646653\pi$
$929$	38.8634	+	35.2666i	1.27507	+	1.15706i	0.295630	+	0.955303i	$0.404471\pi$
$930$	10.3640	−	14.6598i	0.339848	−	0.480713i
$931$	−0.533599	+	2.07156i	−0.0174880	+	0.0678926i
$932$	21.6088	+	21.1937i	0.707818	+	0.694223i
$933$	1.93001	−	0.507805i	0.0631857	−	0.0166248i
$934$	11.6399	−	53.7356i	0.380868	−	1.75828i
$935$	−3.58783	−	4.81929i	−0.117334	−	0.157608i
$936$	19.1220	−	20.6932i	0.625022	−	0.676377i
$937$	24.0684	+	2.81319i	0.786280	+	0.0919030i	0.499752	−	0.866169i	$-0.333425\pi$
$937$	24.0684	+	2.81319i	0.786280	+	0.0919030i	0.286529	+	0.958072i	$0.407499\pi$
$938$	27.4858	−	5.39804i	0.897443	−	0.176252i
$939$	18.5581	+	0.984535i	0.605622	+	0.0321291i
$940$	−1.67063	−	7.71247i	−0.0544898	−	0.251553i
$941$	−21.8130	+	24.9949i	−0.711083	+	0.814811i	−0.989329	−	0.145699i	$-0.953457\pi$
$941$	−21.8130	+	24.9949i	−0.711083	+	0.814811i	0.278246	+	0.960510i	$0.410247\pi$
$942$	−14.6403	−	20.2605i	−0.477008	−	0.660121i
$943$	−9.64878	−	6.89654i	−0.314208	−	0.224582i
$944$	−0.479454	−	0.402310i	−0.0156049	−	0.0130941i
$945$	3.26086	−	4.01102i	0.106076	−	0.130478i
$946$	−3.52052	+	2.95407i	−0.114462	+	0.0960451i
$947$	−21.8446	+	1.69790i	−0.709855	+	0.0551743i	−0.427343	−	0.904089i	$-0.640550\pi$
$947$	−21.8446	+	1.69790i	−0.709855	+	0.0551743i	−0.282512	+	0.959264i	$0.591168\pi$
$948$	36.7794	−	23.4480i	1.19454	−	0.761556i
$949$	13.8924	−	35.9822i	0.450966	−	1.16803i
$950$	0.532703	−	3.90008i	0.0172832	−	0.126535i
$951$	−31.0470	−	36.6138i	−1.00677	−	1.18728i
$952$	13.8224	+	7.62686i	0.447986	+	0.247188i
$953$	−0.0739212	−	1.26918i	−0.00239454	−	0.0411127i	0.996899	−	0.0786889i	$-0.0250734\pi$
$953$	−0.0739212	−	1.26918i	−0.00239454	−	0.0411127i	−0.999294	+	0.0375761i	$0.988036\pi$
$954$	12.9519	+	56.9376i	0.419334	+	1.84342i
$955$	−17.2848	+	8.68077i	−0.559324	+	0.280903i
$956$	−14.6790	−	27.8675i	−0.474754	−	0.901299i
$957$	3.20672	−	21.2226i	0.103658	−	0.686030i
$958$	78.8250	+	35.8303i	2.54672	+	1.15763i
$959$	10.2215	−	14.9034i	0.330071	−	0.481255i
$960$	−5.39695	−	16.5371i	−0.174186	−	0.533731i
$961$	0.162208	+	1.18757i	0.00523252	+	0.0383088i
$962$	−61.8983	−	14.6702i	−1.99568	−	0.472985i
$963$	15.8304	−	5.25713i	0.510126	−	0.169409i
$964$	34.2156	+	36.2665i	1.10201	+	1.16806i
$965$	3.11123	+	0.486587i	0.100154	+	0.0156638i
$966$	−10.5217	+	21.2236i	−0.338529	+	0.682857i
$967$	−8.08126	+	0.313590i	−0.259876	+	0.0100844i	−0.168384	−	0.985721i	$-0.553855\pi$
$967$	−8.08126	+	0.313590i	−0.259876	+	0.0100844i	−0.0914918	+	0.995806i	$0.529164\pi$
$968$	−21.0030	−	12.6754i	−0.675062	−	0.407402i
$969$	−1.94320	−	1.67819i	−0.0624246	−	0.0539112i
$970$	10.5114	+	2.92604i	0.337499	+	0.0939494i
$971$	−35.7658			−1.14778			−0.573890	−	0.818933i	$-0.694566\pi$
$971$	−35.7658			−1.14778			−0.573890	+	0.818933i	$0.694566\pi$
$972$	−22.8823	+	48.6630i	−0.733951	+	1.56087i
$973$	27.9188			0.895035
$974$	−6.03980	−	1.68129i	−0.193528	−	0.0538721i
$975$	−3.91299	+	20.4843i	−0.125316	+	0.656024i
$976$	10.0223	+	6.04849i	0.320806	+	0.193607i
$977$	−19.3789	+	0.751988i	−0.619985	+	0.0240582i	−0.346855	−	0.937919i	$-0.612750\pi$
$977$	−19.3789	+	0.751988i	−0.619985	+	0.0240582i	−0.273130	+	0.961977i	$0.588059\pi$
$978$	−5.03861	−	7.57515i	−0.161117	−	0.242227i
$979$	12.3179	+	1.92649i	0.393683	+	0.0615709i
$980$	10.5976	+	11.2328i	0.338529	+	0.358820i
$981$	−15.2850	+	24.8172i	−0.488014	+	0.792353i
$982$	−40.6445	−	9.63291i	−1.29702	−	0.307399i
$983$	−7.43815	−	54.4569i	−0.237240	−	1.73690i	−0.595565	−	0.803307i	$-0.703072\pi$
$983$	−7.43815	−	54.4569i	−0.237240	−	1.73690i	0.358325	−	0.933597i	$-0.383348\pi$
$984$	−9.69719	+	10.7980i	−0.309135	+	0.344226i
$985$	0.514990	−	0.750874i	0.0164090	−	0.0239248i
$986$	−51.8632	−	23.5747i	−1.65166	−	0.750772i
$987$	−4.65704	−	3.71665i	−0.148235	−	0.118302i
$988$	1.73411	+	3.29213i	0.0551695	+	0.104737i
$989$	−4.35097	+	2.18514i	−0.138353	+	0.0694834i
$990$	−5.97863	−	9.27157i	−0.190013	−	0.294670i
$991$	1.50556	+	25.8494i	0.0478256	+	0.821134i	0.933888	+	0.357567i	$0.116394\pi$
$991$	1.50556	+	25.8494i	0.0478256	+	0.821134i	−0.886062	+	0.463567i	$0.846569\pi$
$992$	−21.1843	−	11.6890i	−0.672603	−	0.371126i
$993$	15.4472	−	43.1341i	0.490201	−	1.36882i
$994$	3.50235	−	25.6417i	0.111088	−	0.813307i
$995$	6.55309	−	16.9729i	0.207747	−	0.538078i
$996$	0.541125	+	12.3013i	0.0171462	+	0.389781i
$997$	41.9352	−	3.25946i	1.32810	−	0.103228i	0.606249	−	0.795275i	$-0.292674\pi$
$997$	41.9352	−	3.25946i	1.32810	−	0.103228i	0.721853	+	0.692047i	$0.243291\pi$
$998$	46.7701	−	39.2447i	1.48048	−	1.24227i
$999$	50.8808	−	3.75700i	1.60980	−	0.118866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.3	✓	1404
3.2	odd	2		729.2.i.a.685.24		1404
243.92	odd	162		729.2.i.a.613.24		1404
243.151	even	81	inner	243.2.i.a.151.3	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.3	✓	1404	1.1	even	1	trivial
243.2.i.a.151.3	yes	1404	243.151	even	81	inner
729.2.i.a.613.24		1404	243.92	odd	162
729.2.i.a.685.24		1404	3.2	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24894 - 0.626034i) q^{2} +(-1.63585 + 0.569198i) q^{3} +(2.95346 + 1.78242i) q^{4} +(-0.812747 + 0.0315383i) q^{5} +(4.03526 - 0.255991i) q^{6} +(1.20842 + 0.188994i) q^{7} +(-2.32230 - 2.46149i) q^{8} +(2.35203 - 1.86225i) q^{9} +(1.84756 + 0.437879i) q^{10} +(-0.262100 - 1.91892i) q^{11} +(-5.84597 - 1.23468i) q^{12} +(-1.56973 + 2.28872i) q^{13} +(-2.59935 - 1.18155i) q^{14} +(1.31158 - 0.514206i) q^{15} +(0.466363 + 0.885368i) q^{16} +(-3.40839 + 1.71176i) q^{17} +(-6.45539 + 2.71563i) q^{18} +(-0.0225985 - 0.388002i) q^{19} +(-2.45663 - 1.35551i) q^{20} +(-2.08438 + 0.378666i) q^{21} +(-0.611859 + 4.47960i) q^{22} +(-1.72522 + 4.46842i) q^{23} +(5.20001 + 2.70479i) q^{24} +(-4.32540 + 0.336197i) q^{25} +(4.96303 - 4.16448i) q^{26} +(-2.78758 + 4.38513i) q^{27} +(3.23216 + 2.71210i) q^{28} +(-5.20543 - 3.72061i) q^{29} +(-3.27157 + 0.335321i) q^{30} +(-3.58945 + 4.11306i) q^{31} +(0.938296 + 4.33166i) q^{32} +(1.52100 + 2.98987i) q^{33} +(8.73687 - 1.71587i) q^{34} +(-0.988102 - 0.115493i) q^{35} +(10.2659 - 1.30777i) q^{36} +(-5.86331 - 7.87579i) q^{37} +(-0.192080 + 0.886739i) q^{38} +(1.26511 - 4.63749i) q^{39} +(1.96507 + 1.92733i) q^{40} +(-0.617630 + 2.39779i) q^{41} +(4.92469 + 0.453295i) q^{42} +(0.752751 + 0.683085i) q^{43} +(2.64621 - 6.13461i) q^{44} +(-1.85287 + 1.58772i) q^{45} +(6.67729 - 8.96915i) q^{46} +(1.84929 + 2.11906i) q^{47} +(-1.26685 - 1.18288i) q^{48} +(-5.24117 - 1.68051i) q^{49} +(9.93802 + 1.95176i) q^{50} +(4.60129 - 4.74023i) q^{51} +(-8.71559 + 3.96172i) q^{52} +(1.44784 - 8.21109i) q^{53} +(9.01433 - 8.11676i) q^{54} +(0.273541 + 1.55133i) q^{55} +(-2.34111 - 3.41342i) q^{56} +(0.257818 + 0.621851i) q^{57} +(9.37743 + 11.6262i) q^{58} +(-0.578998 + 0.236547i) q^{59} +(4.79023 + 0.819106i) q^{60} +(10.0154 - 6.04435i) q^{61} +(10.6474 - 7.00288i) q^{62} +(3.19420 - 1.80587i) q^{63} +(0.717966 - 12.3270i) q^{64} +(1.20361 - 1.90965i) q^{65} +(-1.54887 - 7.67623i) q^{66} +(-7.98108 + 5.70453i) q^{67} +(-13.1176 - 1.01958i) q^{68} +(0.278781 - 8.29167i) q^{69} +(2.14988 + 0.878321i) q^{70} +(2.59953 + 8.68305i) q^{71} +(-10.0460 - 1.46480i) q^{72} +(-13.5233 + 3.20508i) q^{73} +(8.25569 + 21.3828i) q^{74} +(6.88436 - 3.01198i) q^{75} +(0.624839 - 1.18623i) q^{76} +(0.0459350 - 2.36840i) q^{77} +(-5.74837 + 9.63742i) q^{78} +(-5.21181 + 5.11171i) q^{79} +(-0.406958 - 0.704872i) q^{80} +(2.06406 - 8.76012i) q^{81} +(2.89011 - 5.00581i) q^{82} +(-0.514050 - 1.99566i) q^{83} +(-6.83106 - 2.59686i) q^{84} +(2.71617 - 1.49872i) q^{85} +(-1.26525 - 2.00746i) q^{86} +(10.6331 + 3.12346i) q^{87} +(-4.11472 + 5.10145i) q^{88} +(-1.84629 + 6.16704i) q^{89} +(5.16095 - 2.41071i) q^{90} +(-2.32945 + 2.46907i) q^{91} +(-13.0600 + 10.1222i) q^{92} +(3.53067 - 8.77146i) q^{93} +(-2.83234 - 5.92334i) q^{94} +(0.0306038 + 0.314635i) q^{95} +(-4.00048 - 6.55187i) q^{96} +(5.74213 + 0.222821i) q^{97} +(10.7350 + 7.06051i) q^{98} +(-4.18996 - 4.02524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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