LMFDB - Embedded newform 297.2.t.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	297.17
Dual form			297.2.t.a.35.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.780898 + 0.867275i) q^{2} +(0.0666926 + 0.634537i) q^{4} +(1.15400 - 1.03907i) q^{5} +(1.76474 - 3.96367i) q^{7} +(-2.49070 - 1.80960i) q^{8} +1.81224i q^{10} +(3.19970 + 0.872887i) q^{11} +(1.05340 - 4.95585i) q^{13} +(2.05951 + 4.62574i) q^{14} +(2.26622 - 0.481700i) q^{16} +(-0.248154 + 0.763741i) q^{17} +(-2.19592 + 3.02243i) q^{19} +(0.736289 + 0.662958i) q^{20} +(-3.25567 + 2.09338i) q^{22} +(-2.42777 - 1.40167i) q^{23} +(-0.270585 + 2.57445i) q^{25} +(3.47549 + 4.78360i) q^{26} +(2.63279 + 0.855447i) q^{28} +(6.68223 + 2.97512i) q^{29} +(6.42298 + 1.36525i) q^{31} +(1.72675 - 2.99082i) q^{32} +(-0.468590 - 0.811622i) q^{34} +(-2.08201 - 6.40776i) q^{35} +(-3.70044 + 2.68853i) q^{37} +(-0.906484 - 4.26467i) q^{38} +(-4.75456 + 0.499724i) q^{40} +(0.302935 - 0.134876i) q^{41} +(-0.967761 + 0.558737i) q^{43} +(-0.340483 + 2.08854i) q^{44} +(3.11148 - 1.01098i) q^{46} +(-5.62759 - 0.591483i) q^{47} +(-7.91248 - 8.78770i) q^{49} +(-2.02145 - 2.24505i) q^{50} +(3.21493 + 0.337902i) q^{52} +(5.13255 - 1.66767i) q^{53} +(4.59944 - 2.31739i) q^{55} +(-11.5681 + 6.67884i) q^{56} +(-7.79839 + 3.47207i) q^{58} +(-6.97083 + 0.732664i) q^{59} +(-0.842120 - 3.96186i) q^{61} +(-6.19973 + 4.50437i) q^{62} +(2.67734 + 8.24001i) q^{64} +(-3.93383 - 6.81360i) q^{65} +(-5.22518 + 9.05028i) q^{67} +(-0.501172 - 0.106527i) q^{68} +(7.18312 + 3.19813i) q^{70} +(-4.20477 - 1.36621i) q^{71} +(-1.44520 - 1.98915i) q^{73} +(0.557974 - 5.30877i) q^{74} +(-2.06429 - 1.19182i) q^{76} +(9.10648 - 11.1421i) q^{77} +(0.476003 + 0.428595i) q^{79} +(2.11470 - 2.91063i) q^{80} +(-0.119587 + 0.368052i) q^{82} +(-1.82050 + 0.386959i) q^{83} +(0.507207 + 1.13920i) q^{85} +(0.271144 - 1.27563i) q^{86} +(-6.38991 - 7.96427i) q^{88} +5.49170i q^{89} +(-17.7844 - 12.9211i) q^{91} +(0.727500 - 1.63399i) q^{92} +(4.90755 - 4.41878i) q^{94} +(0.606408 + 5.76958i) q^{95} +(1.29476 - 1.43798i) q^{97} +13.8002 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−0.780898	+	0.867275i	−0.552178	+	0.613256i	−0.953026	−	0.302889i	$-0.902049\pi$
$2$	−0.780898	+	0.867275i	−0.552178	+	0.613256i	0.400848	+	0.916145i	$0.368716\pi$
$3$		0			0
$3$		0			0
$4$	0.0666926	+	0.634537i	0.0333463	+	0.317269i
$5$	1.15400	−	1.03907i	0.516084	−	0.464684i	−0.369455	−	0.929249i	$-0.620456\pi$
$5$	1.15400	−	1.03907i	0.516084	−	0.464684i	0.885539	+	0.464564i	$0.153789\pi$
$6$		0			0
$7$	1.76474	−	3.96367i	0.667009	−	1.49813i	−0.189438	−	0.981893i	$-0.560666\pi$
$7$	1.76474	−	3.96367i	0.667009	−	1.49813i	0.856447	−	0.516235i	$-0.172667\pi$
$8$	−2.49070	−	1.80960i	−0.880595	−	0.639790i
$9$		0			0
$10$			1.81224i			0.573080i
$11$	3.19970	+	0.872887i	0.964745	+	0.263185i
$11$	3.19970	+	0.872887i	0.964745	+	0.263185i
$12$		0			0
$13$	1.05340	−	4.95585i	0.292160	−	1.37451i	−0.549949	−	0.835198i	$-0.685353\pi$
$13$	1.05340	−	4.95585i	0.292160	−	1.37451i	0.842109	−	0.539307i	$-0.181314\pi$
$14$	2.05951	+	4.62574i	0.550428	+	1.23628i
$15$		0			0
$16$	2.26622	−	0.481700i	0.566555	−	0.120425i
$17$	−0.248154	+	0.763741i	−0.0601863	+	0.185234i	−0.976629	−	0.214931i	$-0.931047\pi$
$17$	−0.248154	+	0.763741i	−0.0601863	+	0.185234i	0.916443	+	0.400165i	$0.131047\pi$
$18$		0			0
$19$	−2.19592	+	3.02243i	−0.503779	+	0.693392i	−0.982855	−	0.184381i	$-0.940972\pi$
$19$	−2.19592	+	3.02243i	−0.503779	+	0.693392i	0.479076	+	0.877773i	$0.340972\pi$
$20$	0.736289	+	0.662958i	0.164639	+	0.148242i
$21$		0			0
$22$	−3.25567	+	2.09338i	−0.694111	+	0.446311i
$23$	−2.42777	−	1.40167i	−0.506225	−	0.292269i	0.225055	−	0.974346i	$-0.427744\pi$
$23$	−2.42777	−	1.40167i	−0.506225	−	0.292269i	−0.731281	+	0.682077i	$0.761077\pi$
$24$		0			0
$25$	−0.270585	+	2.57445i	−0.0541171	+	0.514889i
$26$	3.47549	+	4.78360i	0.681599	+	0.938141i
$27$		0			0
$28$	2.63279	+	0.855447i	0.497551	+	0.161664i
$29$	6.68223	+	2.97512i	1.24086	+	0.552466i	0.918976	−	0.394313i	$-0.129017\pi$
$29$	6.68223	+	2.97512i	1.24086	+	0.552466i	0.321883	+	0.946779i	$0.395684\pi$
$30$		0			0
$31$	6.42298	+	1.36525i	1.15360	+	0.245205i	0.744717	−	0.667381i	$-0.232585\pi$
$31$	6.42298	+	1.36525i	1.15360	+	0.245205i	0.408884	+	0.912586i	$0.365918\pi$
$32$	1.72675	−	2.99082i	0.305250	−	0.528708i
$33$		0			0
$34$	−0.468590	−	0.811622i	−0.0803625	−	0.139192i
$35$	−2.08201	−	6.40776i	−0.351923	−	1.08311i
$36$		0			0
$37$	−3.70044	+	2.68853i	−0.608349	+	0.441991i	−0.848833	−	0.528662i	$-0.822694\pi$
$37$	−3.70044	+	2.68853i	−0.608349	+	0.441991i	0.240483	+	0.970653i	$0.422694\pi$
$38$	−0.906484	−	4.26467i	−0.147051	−	0.691821i
$39$		0			0
$40$	−4.75456	+	0.499724i	−0.751761	+	0.0790133i
$41$	0.302935	−	0.134876i	0.0473106	−	0.0210640i	−0.382945	−	0.923771i	$-0.625090\pi$
$41$	0.302935	−	0.134876i	0.0473106	−	0.0210640i	0.430256	+	0.902707i	$0.358423\pi$
$42$		0			0
$43$	−0.967761	+	0.558737i	−0.147582	+	0.0852066i	−0.571973	−	0.820273i	$-0.693822\pi$
$43$	−0.967761	+	0.558737i	−0.147582	+	0.0852066i	0.424391	+	0.905479i	$0.360488\pi$
$44$	−0.340483	+	2.08854i	−0.0513298	+	0.314860i
$45$		0			0
$46$	3.11148	−	1.01098i	0.458762	−	0.149061i
$47$	−5.62759	−	0.591483i	−0.820868	−	0.0862767i	−0.315222	−	0.949018i	$-0.602079\pi$
$47$	−5.62759	−	0.591483i	−0.820868	−	0.0862767i	−0.505646	+	0.862741i	$0.668746\pi$
$48$		0			0
$49$	−7.91248	−	8.78770i	−1.13035	−	1.25539i
$50$	−2.02145	−	2.24505i	−0.285877	−	0.317498i
$51$		0			0
$52$	3.21493	+	0.337902i	0.445830	+	0.0468586i
$53$	5.13255	−	1.66767i	0.705010	−	0.229072i	0.0654981	−	0.997853i	$-0.479136\pi$
$53$	5.13255	−	1.66767i	0.705010	−	0.229072i	0.639512	+	0.768781i	$0.279136\pi$
$54$		0			0
$55$	4.59944	−	2.31739i	0.620188	−	0.312476i
$56$	−11.5681	+	6.67884i	−1.54585	+	0.892498i
$57$		0			0
$58$	−7.79839	+	3.47207i	−1.02398	+	0.455905i
$59$	−6.97083	+	0.732664i	−0.907525	+	0.0953847i	−0.546777	−	0.837279i	$-0.684145\pi$
$59$	−6.97083	+	0.732664i	−0.907525	+	0.0953847i	−0.360748	+	0.932663i	$0.617479\pi$
$60$		0			0
$61$	−0.842120	−	3.96186i	−0.107822	−	0.507265i	−0.998603	−	0.0528318i	$-0.983175\pi$
$61$	−0.842120	−	3.96186i	−0.107822	−	0.507265i	0.890781	−	0.454433i	$-0.150158\pi$
$62$	−6.19973	+	4.50437i	−0.787367	+	0.572056i
$63$		0			0
$64$	2.67734	+	8.24001i	0.334667	+	1.03000i
$65$	−3.93383	−	6.81360i	−0.487932	−	0.845123i
$66$		0			0
$67$	−5.22518	+	9.05028i	−0.638357	+	1.10567i	0.347436	+	0.937704i	$0.387052\pi$
$67$	−5.22518	+	9.05028i	−0.638357	+	1.10567i	−0.985793	+	0.167964i	$0.946281\pi$
$68$	−0.501172	−	0.106527i	−0.0607760	−	0.0129183i
$69$		0			0
$70$	7.18312	+	3.19813i	0.858548	+	0.382250i
$71$	−4.20477	−	1.36621i	−0.499014	−	0.162139i	0.0486863	−	0.998814i	$-0.484497\pi$
$71$	−4.20477	−	1.36621i	−0.499014	−	0.162139i	−0.547700	+	0.836675i	$0.684497\pi$
$72$		0			0
$73$	−1.44520	−	1.98915i	−0.169148	−	0.232812i	0.716025	−	0.698075i	$-0.245960\pi$
$73$	−1.44520	−	1.98915i	−0.169148	−	0.232812i	−0.885173	+	0.465263i	$0.845960\pi$
$74$	0.557974	−	5.30877i	0.0648632	−	0.617132i
$75$		0			0
$76$	−2.06429	−	1.19182i	−0.236791	−	0.136711i
$77$	9.10648	−	11.1421i	1.03778	−	1.26976i
$78$		0			0
$79$	0.476003	+	0.428595i	0.0535545	+	0.0482207i	0.695473	−	0.718552i	$-0.255195\pi$
$79$	0.476003	+	0.428595i	0.0535545	+	0.0482207i	−0.641919	+	0.766773i	$0.721861\pi$
$80$	2.11470	−	2.91063i	0.236431	−	0.325419i
$81$		0			0
$82$	−0.119587	+	0.368052i	−0.0132062	+	0.0406446i
$83$	−1.82050	+	0.386959i	−0.199826	+	0.0424742i	−0.306737	−	0.951794i	$-0.599237\pi$
$83$	−1.82050	+	0.386959i	−0.199826	+	0.0424742i	0.106911	+	0.994269i	$0.465904\pi$
$84$		0			0
$85$	0.507207	+	1.13920i	0.0550143	+	0.123564i
$86$	0.271144	−	1.27563i	0.0292382	−	0.137555i
$87$		0			0
$88$	−6.38991	−	7.96427i	−0.681167	−	0.848994i
$89$			5.49170i			0.582119i	0.956705	+	0.291060i	$0.0940078\pi$
$89$			5.49170i			0.582119i	−0.956705	+	0.291060i	$0.905992\pi$
$90$		0			0
$91$	−17.7844	−	12.9211i	−1.86431	−	1.35450i
$92$	0.727500	−	1.63399i	0.0758472	−	0.170356i
$93$		0			0
$94$	4.90755	−	4.41878i	0.506175	−	0.455762i
$95$	0.606408	+	5.76958i	0.0622161	+	0.591947i
$96$		0			0
$97$	1.29476	−	1.43798i	0.131463	−	0.146005i	−0.673819	−	0.738897i	$-0.735347\pi$
$97$	1.29476	−	1.43798i	0.131463	−	0.146005i	0.805282	+	0.592892i	$0.202014\pi$
$98$	13.8002			1.39403
$99$		0			0
$100$	−1.65163			−0.165163
$101$	8.89682	−	9.88092i	0.885267	−	0.983188i	−0.114681	−	0.993402i	$-0.536585\pi$
$101$	8.89682	−	9.88092i	0.885267	−	0.983188i	0.999948	+	0.0102141i	$0.00325131\pi$
$102$		0			0
$103$	0.227332	+	2.16292i	0.0223997	+	0.213119i	0.999997	+	0.00263271i	$0.000838018\pi$
$103$	0.227332	+	2.16292i	0.0223997	+	0.213119i	−0.977597	+	0.210486i	$0.932495\pi$
$104$	−11.5918	+	10.4373i	−1.13667	+	1.02346i
$105$		0			0
$106$	−2.56167	+	5.75361i	−0.248812	+	0.558840i
$107$	−4.92945	−	3.58146i	−0.476548	−	0.346232i	0.323440	−	0.946249i	$-0.395161\pi$
$107$	−4.92945	−	3.58146i	−0.476548	−	0.346232i	−0.799988	+	0.600016i	$0.795161\pi$
$108$		0			0
$109$			8.21860i			0.787199i	0.919282	+	0.393600i	$0.128770\pi$
$109$			8.21860i			0.787199i	−0.919282	+	0.393600i	$0.871230\pi$
$110$	−1.58188	+	5.79862i	−0.150826	+	0.552877i
$111$		0			0
$112$	2.08999	−	9.83263i	0.197486	−	0.929097i
$113$	2.23354	+	5.01661i	0.210114	+	0.471923i	0.987603	−	0.156973i	$-0.0501736\pi$
$113$	2.23354	+	5.01661i	0.210114	+	0.471923i	−0.777489	+	0.628896i	$0.783507\pi$
$114$		0			0
$115$	−4.25808	+	0.905082i	−0.397068	+	0.0843994i
$116$	−1.44217	+	4.43855i	−0.133902	+	0.412109i
$117$		0			0
$118$	4.80809	−	6.61776i	0.442620	−	0.609214i
$119$	2.58929	+	2.33141i	0.237360	+	0.213720i
$120$		0			0
$121$	9.47614	+	5.58595i	0.861467	+	0.507813i
$122$	4.09364	+	2.36346i	0.370620	+	0.213978i
$123$		0			0
$124$	−0.437935	+	4.16667i	−0.0393277	+	0.374178i
$125$	6.92650	+	9.53351i	0.619525	+	0.852703i
$126$		0			0
$127$	4.26924	+	1.38716i	0.378834	+	0.123091i	0.492243	−	0.870458i	$-0.336177\pi$
$127$	4.26924	+	1.38716i	0.378834	+	0.123091i	−0.113409	+	0.993548i	$0.536177\pi$
$128$	−2.92721	−	1.30328i	−0.258731	−	0.115195i
$129$		0			0
$130$	8.98119	+	1.90901i	0.787702	+	0.167431i
$131$	−3.28173	+	5.68413i	−0.286726	+	0.496625i	−0.973026	−	0.230694i	$-0.925900\pi$
$131$	−3.28173	+	5.68413i	−0.286726	+	0.496625i	0.686300	+	0.727319i	$0.259234\pi$
$132$		0			0
$133$	8.10468	+	14.0377i	0.702765	+	1.21722i
$134$	−3.76875	−	11.5990i	−0.325570	−	1.00200i
$135$		0			0
$136$	2.00014	−	1.45319i	0.171511	−	0.124610i
$137$	1.74887	+	8.22778i	0.149416	+	0.702947i	0.987527	+	0.157448i	$0.0503265\pi$
$137$	1.74887	+	8.22778i	0.149416	+	0.702947i	−0.838111	+	0.545499i	$0.816340\pi$
$138$		0			0
$139$	2.03763	−	0.214164i	0.172830	−	0.0181651i	−0.0177183	−	0.999843i	$-0.505640\pi$
$139$	2.03763	−	0.214164i	0.172830	−	0.0181651i	0.190548	+	0.981678i	$0.438974\pi$
$140$	3.92711	−	1.74846i	0.331901	−	0.147772i
$141$		0			0
$142$	4.46837	−	2.57982i	0.374978	−	0.216493i
$143$	7.69645	−	14.9377i	0.643610	−	1.24916i
$144$		0			0
$145$	10.8026	−	3.50999i	0.897111	−	0.291489i
$146$	2.85369	+	0.299935i	0.236173	+	0.0248228i
$147$		0			0
$148$	−1.95276	−	2.16876i	−0.160516	−	0.178271i
$149$	1.05580	+	1.17258i	0.0864944	+	0.0960618i	0.784838	−	0.619701i	$-0.212746\pi$
$149$	1.05580	+	1.17258i	0.0864944	+	0.0960618i	−0.698344	+	0.715762i	$0.746079\pi$
$150$		0			0
$151$	−10.0273	−	1.05391i	−0.816011	−	0.0857663i	−0.312679	−	0.949859i	$-0.601226\pi$
$151$	−10.0273	−	1.05391i	−0.816011	−	0.0857663i	−0.503333	+	0.864093i	$0.667893\pi$
$152$	10.9388	−	3.55422i	0.887250	−	0.288285i
$153$		0			0
$154$	2.55207	+	16.5987i	0.205652	+	1.33756i
$155$	8.83069	−	5.09840i	0.709298	−	0.409514i
$156$		0			0
$157$	20.3184	−	9.04635i	1.62159	−	0.721977i	0.623386	−	0.781915i	$-0.285757\pi$
$157$	20.3184	−	9.04635i	1.62159	−	0.721977i	0.998202	+	0.0599372i	$0.0190901\pi$
$158$	−0.743420	+	0.0781366i	−0.0591433	+	0.00621621i
$159$		0			0
$160$	−1.11499	−	5.24562i	−0.0881477	−	0.414702i
$161$	−9.84017	+	7.14930i	−0.775514	+	0.563444i
$162$		0			0
$163$	0.588498	+	1.81121i	0.0460947	+	0.141865i	0.971455	−	0.237224i	$-0.0762375\pi$
$163$	0.588498	+	1.81121i	0.0460947	+	0.141865i	−0.925360	+	0.379089i	$0.876237\pi$
$164$	0.105787	+	0.183229i	0.00826059	+	0.0143078i
$165$		0			0
$166$	1.08602	−	1.88105i	0.0842917	−	0.145998i
$167$	−14.7609	−	3.13752i	−1.14223	−	0.242789i	−0.402323	−	0.915498i	$-0.631797\pi$
$167$	−14.7609	−	3.13752i	−1.14223	−	0.242789i	−0.739907	+	0.672709i	$0.765131\pi$
$168$		0			0
$169$	−11.5747	−	5.15340i	−0.890363	−	0.396415i
$170$	−1.38408	−	0.449715i	−0.106154	−	0.0344916i
$171$		0			0
$172$	−0.419082	−	0.576817i	−0.0319547	−	0.0439819i
$173$	−2.29437	+	21.8295i	−0.174438	+	1.65967i	0.460915	+	0.887444i	$0.347521\pi$
$173$	−2.29437	+	21.8295i	−0.174438	+	1.65967i	−0.635353	+	0.772222i	$0.719145\pi$
$174$		0			0
$175$	9.72675	+	5.61574i	0.735273	+	0.424510i
$176$	7.67169	+	0.436859i	0.578275	+	0.0329295i
$177$		0			0
$178$	−4.76282	−	4.28846i	−0.356988	−	0.321434i
$179$	−15.1400	+	20.8384i	−1.13162	+	1.55754i	−0.346654	+	0.937993i	$0.612682\pi$
$179$	−15.1400	+	20.8384i	−1.13162	+	1.55754i	−0.784962	+	0.619544i	$0.787318\pi$
$180$		0			0
$181$	3.96028	−	12.1885i	0.294365	−	0.905964i	−0.689068	−	0.724696i	$-0.741980\pi$
$181$	3.96028	−	12.1885i	0.294365	−	0.905964i	0.983434	−	0.181267i	$-0.0580199\pi$
$182$	25.0940	−	5.33389i	1.86009	−	0.395374i
$183$		0			0
$184$	3.51038	+	7.88444i	0.258789	+	0.581249i
$185$	−1.47675	+	6.94757i	−0.108573	+	0.510795i
$186$		0			0
$187$	−1.46068	+	2.22713i	−0.106815	+	0.162864i
$188$		−	3.61036i		−	0.263313i
$189$		0			0
$190$	−5.47736	−	3.97953i	−0.397369	−	0.288706i
$191$	0.394348	−	0.885721i	0.0285340	−	0.0640885i	−0.898716	−	0.438531i	$-0.855499\pi$
$191$	0.394348	−	0.885721i	0.0285340	−	0.0640885i	0.927250	+	0.374442i	$0.122166\pi$
$192$		0			0
$193$	−16.2667	+	14.6466i	−1.17090	+	1.05428i	−0.173313	+	0.984867i	$0.555447\pi$
$193$	−16.2667	+	14.6466i	−1.17090	+	1.05428i	−0.997588	+	0.0694165i	$0.977886\pi$
$194$	0.236046	+	2.24583i	0.0169472	+	0.161241i
$195$		0			0
$196$	5.04842	−	5.60684i	0.360602	−	0.400489i
$197$	0.389682			0.0277637			0.0138818	−	0.999904i	$-0.495581\pi$
$197$	0.389682			0.0277637			0.0138818	+	0.999904i	$0.495581\pi$
$198$		0			0
$199$	−18.7233			−1.32726			−0.663630	−	0.748061i	$-0.730985\pi$
$199$	−18.7233			−1.32726			−0.663630	+	0.748061i	$0.730985\pi$
$200$	5.33266	−	5.92252i	0.377076	−	0.418785i
$201$		0			0
$202$	1.62197	+	15.4320i	0.114121	+	1.08579i
$203$	23.5848	−	21.2359i	1.65533	−	1.49047i
$204$		0			0
$205$	0.209443	−	0.470416i	0.0146281	−	0.0328553i
$206$	−2.05337	−	1.49186i	−0.143065	−	0.103943i
$207$		0			0
$208$		−	11.7385i		−	0.813917i
$209$	−9.66452	+	7.75406i	−0.668509	+	0.536360i
$210$		0			0
$211$	5.03305	−	23.6787i	0.346490	−	1.63011i	−0.367552	−	0.930003i	$-0.619804\pi$
$211$	5.03305	−	23.6787i	0.346490	−	1.63011i	0.714042	−	0.700103i	$-0.246863\pi$
$212$	1.40050	+	3.14558i	0.0961868	+	0.216039i
$213$		0			0
$214$	6.95550	−	1.47844i	0.475468	−	0.101064i
$215$	−0.536231	+	1.65035i	−0.0365706	+	0.112553i
$216$		0			0
$217$	16.7463	−	23.0493i	1.13681	−	1.56469i
$218$	−7.12779	−	6.41789i	−0.482755	−	0.434674i
$219$		0			0
$220$	1.77722	+	2.76396i	0.119820	+	0.186346i
$221$	3.52358	+	2.03434i	0.237022	+	0.136844i
$222$		0			0
$223$	−2.64226	+	25.1394i	−0.176939	+	1.68346i	0.441215	+	0.897402i	$0.354548\pi$
$223$	−2.64226	+	25.1394i	−0.176939	+	1.68346i	−0.618153	+	0.786058i	$0.712119\pi$
$224$	−8.80737	−	12.1223i	−0.588467	−	0.809956i
$225$		0			0
$226$	−6.09495	−	1.98037i	−0.405430	−	0.131732i
$227$	−13.9031	−	6.19004i	−0.922778	−	0.410847i	−0.110339	−	0.993894i	$-0.535194\pi$
$227$	−13.9031	−	6.19004i	−0.922778	−	0.410847i	−0.812439	+	0.583047i	$0.801860\pi$
$228$		0			0
$229$	−7.66099	−	1.62839i	−0.506252	−	0.107607i	−0.0522967	−	0.998632i	$-0.516654\pi$
$229$	−7.66099	−	1.62839i	−0.506252	−	0.107607i	−0.453956	+	0.891024i	$0.649988\pi$
$230$	2.54017	−	4.39970i	0.167494	−	0.290108i
$231$		0			0
$232$	−11.2597	−	19.5023i	−0.739232	−	1.28039i
$233$	2.52277	+	7.76427i	0.165272	+	0.508655i	0.999056	−	0.0434357i	$-0.0138304\pi$
$233$	2.52277	+	7.76427i	0.165272	+	0.508655i	−0.833784	+	0.552090i	$0.813830\pi$
$234$		0			0
$235$	−7.10882	+	5.16486i	−0.463728	+	0.336918i
$236$	−0.929805	−	4.37439i	−0.0605252	−	0.284749i
$237$		0			0
$238$	−4.04394	+	0.425035i	−0.262130	+	0.0275510i
$239$	−17.0647	+	7.59768i	−1.10382	+	0.491453i	−0.876030	−	0.482257i	$-0.839817\pi$
$239$	−17.0647	+	7.59768i	−1.10382	+	0.491453i	−0.227792	+	0.973710i	$0.573151\pi$
$240$		0			0
$241$	1.06399	−	0.614295i	0.0685377	−	0.0395702i	−0.465340	−	0.885132i	$-0.654068\pi$
$241$	1.06399	−	0.614295i	0.0685377	−	0.0395702i	0.533877	+	0.845562i	$0.320734\pi$
$242$	−12.2444	+	3.85636i	−0.787103	+	0.247896i
$243$		0			0
$244$	2.45779	−	0.798584i	0.157344	−	0.0511241i
$245$	−18.2620	−	1.91941i	−1.16672	−	0.122627i
$246$		0			0
$247$	12.6655	+	14.0665i	0.805887	+	0.895029i
$248$	−13.5272	−	15.0234i	−0.858975	−	0.953989i
$249$		0			0
$250$	−13.6771	−	1.43752i	−0.865014	−	0.0909166i
$251$	24.9635	−	8.11113i	1.57568	−	0.511970i	0.614742	−	0.788728i	$-0.289260\pi$
$251$	24.9635	−	8.11113i	1.57568	−	0.511970i	0.960940	+	0.276759i	$0.0892602\pi$
$252$		0			0
$253$	−6.54463	−	6.60410i	−0.411457	−	0.415196i
$254$	−4.53689	+	2.61937i	−0.284670	+	0.164354i
$255$		0			0
$256$	−12.4139	+	5.52701i	−0.775866	+	0.345438i
$257$	29.8019	−	3.13231i	1.85899	−	0.195388i	0.892320	−	0.451403i	$-0.149076\pi$
$257$	29.8019	−	3.13231i	1.85899	−	0.195388i	0.966673	+	0.256015i	$0.0824097\pi$
$258$		0			0
$259$	4.12613	+	19.4119i	0.256385	+	1.20620i
$260$	4.06113	−	2.95058i	0.251860	−	0.182987i
$261$		0			0
$262$	−2.36700	−	7.28489i	−0.146234	−	0.450062i
$263$	1.05394	+	1.82548i	0.0649888	+	0.112564i	0.896689	−	0.442661i	$-0.145966\pi$
$263$	1.05394	+	1.82548i	0.0649888	+	0.112564i	−0.831700	+	0.555225i	$0.812632\pi$
$264$		0			0
$265$	4.19015	−	7.25755i	0.257399	−	0.445828i
$266$	−18.5035	−	3.93304i	−1.13452	−	0.241150i
$267$		0			0
$268$	−6.09122	−	2.71199i	−0.372081	−	0.165661i
$269$	−26.8186	−	8.71391i	−1.63516	−	0.531296i	−0.659712	−	0.751519i	$-0.729322\pi$
$269$	−26.8186	−	8.71391i	−1.63516	−	0.531296i	−0.975450	+	0.220222i	$0.929322\pi$
$270$		0			0
$271$	−6.37949	−	8.78061i	−0.387526	−	0.533384i	0.570032	−	0.821622i	$-0.306931\pi$
$271$	−6.37949	−	8.78061i	−0.387526	−	0.533384i	−0.957559	+	0.288238i	$0.906931\pi$
$272$	−0.194479	+	1.85034i	−0.0117920	+	0.112193i
$273$		0			0
$274$	−8.50144	−	4.90831i	−0.513590	−	0.296522i
$275$	−3.11299	+	8.00126i	−0.187720	+	0.482494i
$276$		0			0
$277$	9.54318	+	8.59272i	0.573394	+	0.516287i	0.904028	−	0.427472i	$-0.140596\pi$
$277$	9.54318	+	8.59272i	0.573394	+	0.516287i	−0.330634	+	0.943759i	$0.607263\pi$
$278$	−1.40544	+	1.93443i	−0.0842929	+	0.116019i
$279$		0			0
$280$	−6.40982	+	19.7274i	−0.383060	+	1.17894i
$281$	10.3811	−	2.20656i	0.619283	−	0.131633i	0.112422	−	0.993661i	$-0.464139\pi$
$281$	10.3811	−	2.20656i	0.619283	−	0.131633i	0.506861	+	0.862028i	$0.330806\pi$
$282$		0			0
$283$	−9.05356	−	20.3346i	−0.538179	−	1.20877i	−0.954133	−	0.299383i	$-0.903219\pi$
$283$	−9.05356	−	20.3346i	−0.538179	−	1.20877i	0.415954	−	0.909385i	$-0.363448\pi$
$284$	0.586486	−	2.75920i	0.0348015	−	0.163728i
$285$		0			0
$286$	6.94497	+	18.3398i	0.410665	+	1.08445i
$287$		−	1.43876i		−	0.0849272i
$288$		0			0
$289$	13.2316	+	9.61330i	0.778328	+	0.565488i
$290$	−5.39163	+	12.1098i	−0.316608	+	0.711112i
$291$		0			0
$292$	1.16580	−	1.04969i	0.0682235	−	0.0614287i
$293$	−2.30766	−	21.9559i	−0.134815	−	1.28268i	−0.827512	−	0.561448i	$-0.810244\pi$
$293$	−2.30766	−	21.9559i	−0.134815	−	1.28268i	0.692697	−	0.721229i	$-0.256422\pi$
$294$		0			0
$295$	−7.28305	+	8.08865i	−0.424036	+	0.470939i
$296$	14.0818			0.818491
$297$		0			0
$298$	−1.84142			−0.106671
$299$	−9.50390	+	10.5551i	−0.549625	+	0.610420i
$300$		0			0
$301$	0.506803	+	4.82191i	0.0292117	+	0.277930i
$302$	8.74434	−	7.87344i	0.503180	−	0.453066i
$303$		0			0
$304$	−3.52054	+	7.90726i	−0.201917	+	0.453512i
$305$	−5.08844	−	3.69697i	−0.291363	−	0.211688i
$306$		0			0
$307$			12.8256i			0.731997i	0.930616	+	0.365998i	$0.119272\pi$
$307$			12.8256i			0.731997i	−0.930616	+	0.365998i	$0.880728\pi$
$308$	7.67744	+	5.03530i	0.437463	+	0.286913i
$309$		0			0
$310$	−2.47415	+	11.6400i	−0.140522	+	0.661106i
$311$	−2.73879	−	6.15143i	−0.155303	−	0.348816i	0.819091	−	0.573663i	$-0.194478\pi$
$311$	−2.73879	−	6.15143i	−0.155303	−	0.348816i	−0.974394	+	0.224848i	$0.927812\pi$
$312$		0			0
$313$	8.66114	−	1.84098i	0.489557	−	0.104059i	0.0434821	−	0.999054i	$-0.486155\pi$
$313$	8.66114	−	1.84098i	0.489557	−	0.104059i	0.446075	+	0.894996i	$0.352822\pi$
$314$	−8.02095	+	24.6859i	−0.452648	+	1.39311i
$315$		0			0
$316$	−0.240214	+	0.330626i	−0.0135131	+	0.0185992i
$317$	−12.7373	−	11.4687i	−0.715399	−	0.644148i	0.228819	−	0.973469i	$-0.426514\pi$
$317$	−12.7373	−	11.4687i	−0.715399	−	0.644148i	−0.944218	+	0.329321i	$0.893180\pi$
$318$		0			0
$319$	18.7842	+	15.3523i	1.05171	+	0.859565i
$320$	11.6516	+	6.72703i	0.651342	+	0.376052i
$321$		0			0
$322$	1.48376	−	14.1170i	0.0826865	−	0.786710i
$323$	−1.76342	−	2.42714i	−0.0981194	−	0.135050i
$324$		0			0
$325$	12.4735	+	4.05290i	0.691908	+	0.224814i
$326$	−2.03037	−	0.903981i	−0.112452	−	0.0500669i
$327$		0			0
$328$	−0.998592	−	0.212257i	−0.0551380	−	0.0117199i
$329$	−12.2757	+	21.2621i	−0.676780	+	1.17222i
$330$		0			0
$331$	8.18032	+	14.1687i	0.449631	+	0.778783i	0.998362	−	0.0572156i	$-0.0182222\pi$
$331$	8.18032	+	14.1687i	0.449631	+	0.778783i	−0.548731	+	0.835999i	$0.684889\pi$
$332$	−0.366953	−	1.12937i	−0.0201392	−	0.0619820i
$333$		0			0
$334$	14.2478	−	10.3516i	0.779606	−	0.566417i
$335$	3.37398	+	15.8733i	0.184340	+	0.867252i
$336$		0			0
$337$	−13.4563	+	1.41431i	−0.733012	+	0.0770426i	−0.463677	−	0.886004i	$-0.653470\pi$
$337$	−13.4563	+	1.41431i	−0.733012	+	0.0770426i	−0.269334	+	0.963047i	$0.586804\pi$
$338$	13.5081	−	6.01419i	0.734743	−	0.327129i
$339$		0			0
$340$	−0.689041	+	0.397818i	−0.0373685	+	0.0215747i
$341$	19.3599	+	9.97491i	1.04840	+	0.540172i
$342$		0			0
$343$	−19.9101	+	6.46918i	−1.07504	+	0.349303i
$344$	3.42149	+	0.359613i	0.184474	+	0.0193890i
$345$		0			0
$346$	−17.1405	−	19.0365i	−0.921480	−	1.02341i
$347$	−12.8446	−	14.2653i	−0.689533	−	0.765804i	0.292140	−	0.956375i	$-0.405633\pi$
$347$	−12.8446	−	14.2653i	−0.689533	−	0.765804i	−0.981673	+	0.190571i	$0.938966\pi$
$348$		0			0
$349$	−9.72281	−	1.02191i	−0.520450	−	0.0547015i	−0.159338	−	0.987224i	$-0.550936\pi$
$349$	−9.72281	−	1.02191i	−0.520450	−	0.0547015i	−0.361112	+	0.932522i	$0.617603\pi$
$350$	−12.4660	+	4.05045i	−0.666335	+	0.216506i
$351$		0			0
$352$	8.13574	−	8.06247i	0.433636	−	0.429731i
$353$	14.0240	−	8.09678i	0.746424	−	0.430948i	−0.0779763	−	0.996955i	$-0.524846\pi$
$353$	14.0240	−	8.09678i	0.746424	−	0.430948i	0.824400	+	0.566007i	$0.191513\pi$
$354$		0			0
$355$	−6.27188	+	2.79242i	−0.332877	+	0.148206i
$356$	−3.48469	+	0.366256i	−0.184688	+	0.0194115i
$357$		0			0
$358$	−6.24985	−	29.4032i	−0.330315	−	1.55401i
$359$	9.80679	−	7.12505i	0.517583	−	0.376046i	−0.298110	−	0.954532i	$-0.596356\pi$
$359$	9.80679	−	7.12505i	0.517583	−	0.376046i	0.815692	+	0.578486i	$0.196356\pi$
$360$		0			0
$361$	1.55833	+	4.79605i	0.0820175	+	0.252424i
$362$	7.47820	+	12.9526i	0.393045	+	0.680775i
$363$		0			0
$364$	7.01285	−	12.1466i	0.367573	−	0.636655i
$365$	−3.73461	−	0.793817i	−0.195479	−	0.0415503i
$366$		0			0
$367$	−0.799295	−	0.355869i	−0.0417228	−	0.0185762i	0.385769	−	0.922595i	$-0.373936\pi$
$367$	−0.799295	−	0.355869i	−0.0417228	−	0.0185762i	−0.427492	+	0.904019i	$0.640603\pi$
$368$	−6.17705	−	2.00705i	−0.322001	−	0.104624i
$369$		0			0
$370$	−4.87226	−	6.70609i	−0.253297	−	0.348633i
$371$	2.44754	−	23.2868i	0.127070	−	1.20899i
$372$		0			0
$373$	−8.39907	−	4.84920i	−0.434887	−	0.251082i	0.266539	−	0.963824i	$-0.414120\pi$
$373$	−8.39907	−	4.84920i	−0.434887	−	0.251082i	−0.701427	+	0.712742i	$0.747453\pi$
$374$	−0.790893	−	3.00597i	−0.0408961	−	0.155435i
$375$		0			0
$376$	12.9463	+	11.6569i	0.667653	+	0.601158i
$377$	21.7833	−	29.9822i	1.12190	−	1.54416i
$378$		0			0
$379$	−6.50606	+	20.0236i	−0.334194	+	1.02854i	0.632924	+	0.774214i	$0.281855\pi$
$379$	−6.50606	+	20.0236i	−0.334194	+	1.02854i	−0.967118	+	0.254329i	$0.918145\pi$
$380$	−3.62057	+	0.769577i	−0.185732	+	0.0394785i
$381$		0			0
$382$	0.460218	+	1.03367i	0.0235468	+	0.0528869i
$383$	−5.23594	+	24.6332i	−0.267544	+	1.25870i	0.615023	+	0.788509i	$0.289147\pi$
$383$	−5.23594	+	24.6332i	−0.267544	+	1.25870i	−0.882567	+	0.470187i	$0.844187\pi$
$384$		0			0
$385$	−1.06855	−	22.3203i	−0.0544582	−	1.13755i
$386$		−	25.5452i		−	1.30021i
$387$		0			0
$388$	0.998804	+	0.725673i	0.0507066	+	0.0368405i
$389$	13.7990	−	30.9930i	0.699636	−	1.57141i	−0.116267	−	0.993218i	$-0.537093\pi$
$389$	13.7990	−	30.9930i	0.699636	−	1.57141i	0.815903	−	0.578189i	$-0.196241\pi$
$390$		0			0
$391$	1.67298	−	1.50636i	0.0846061	−	0.0761797i
$392$	3.80540	+	36.2059i	0.192202	+	1.82868i
$393$		0			0
$394$	−0.304302	+	0.337961i	−0.0153305	+	0.0170262i
$395$	0.994646			0.0500461
$396$		0			0
$397$	9.40670			0.472109			0.236054	−	0.971740i	$-0.424146\pi$
$397$	9.40670			0.472109			0.236054	+	0.971740i	$0.424146\pi$
$398$	14.6210	−	16.2383i	0.732885	−	0.813951i
$399$		0			0
$400$	0.626905	+	5.96460i	0.0313453	+	0.298230i
$401$	−15.3093	+	13.7845i	−0.764508	+	0.688366i	−0.956078	−	0.293113i	$-0.905309\pi$
$401$	−15.3093	+	13.7845i	−0.764508	+	0.688366i	0.191570	+	0.981479i	$0.438642\pi$
$402$		0			0
$403$	13.5319	−	30.3932i	0.674073	−	1.51399i
$404$	6.86317	+	4.98638i	0.341455	+	0.248082i
$405$		0			0
$406$			37.0376i			1.83814i
$407$	−14.1871	+	5.37241i	−0.703228	+	0.266301i
$408$		0			0
$409$	−3.90107	+	18.3531i	−0.192896	+	0.907503i	0.770087	+	0.637939i	$0.220213\pi$
$409$	−3.90107	+	18.3531i	−0.192896	+	0.907503i	−0.962983	+	0.269564i	$0.913120\pi$
$410$	0.244427	+	0.548992i	0.0120714	+	0.0271128i
$411$		0			0
$412$	−1.35729	+	0.288501i	−0.0668690	+	0.0142134i
$413$	−9.39767	+	28.9231i	−0.462429	+	1.42321i
$414$		0			0
$415$	−1.69878	+	2.33817i	−0.0833897	+	0.114776i
$416$	−13.0031	−	11.7081i	−0.637530	−	0.574035i
$417$		0			0
$418$	0.822101	−	14.4369i	0.0402103	−	0.706133i
$419$	32.3807	+	18.6950i	1.58190	+	0.913310i	0.994582	+	0.103954i	$0.0331495\pi$
$419$	32.3807	+	18.6950i	1.58190	+	0.913310i	0.587318	+	0.809356i	$0.300184\pi$
$420$		0			0
$421$	2.82398	−	26.8684i	0.137633	−	1.30949i	−0.679773	−	0.733423i	$-0.737922\pi$
$421$	2.82398	−	26.8684i	0.137633	−	1.30949i	0.817405	−	0.576063i	$-0.195412\pi$
$422$	16.6056	+	22.8557i	0.808348	+	1.11260i
$423$		0			0
$424$	−15.8014	−	5.13420i	−0.767386	−	0.249339i
$425$	−1.89906	−	0.845517i	−0.0921181	−	0.0410136i
$426$		0			0
$427$	−17.1897	−	3.65377i	−0.831866	−	0.176819i
$428$	1.94381	−	3.36678i	0.0939576	−	0.162739i
$429$		0			0
$430$	−1.01256	−	1.75381i	−0.0488302	−	0.0845764i
$431$	8.97519	+	27.6228i	0.432320	+	1.33054i	0.895808	+	0.444441i	$0.146597\pi$
$431$	8.97519	+	27.6228i	0.432320	+	1.33054i	−0.463489	+	0.886103i	$0.653403\pi$
$432$		0			0
$433$	16.3991	−	11.9146i	0.788089	−	0.572580i	−0.119307	−	0.992857i	$-0.538067\pi$
$433$	16.3991	−	11.9146i	0.788089	−	0.572580i	0.907396	+	0.420277i	$0.138067\pi$
$434$	6.91293	+	32.5228i	0.331831	+	1.56114i
$435$		0			0
$436$	−5.21501	+	0.548120i	−0.249754	+	0.0262502i
$437$	9.56765	−	4.25979i	0.457683	−	0.203774i
$438$		0			0
$439$	24.6512	−	14.2324i	1.17654	−	0.679273i	0.221325	−	0.975200i	$-0.428962\pi$
$439$	24.6512	−	14.2324i	1.17654	−	0.679273i	0.955211	+	0.295927i	$0.0956285\pi$
$440$	−15.6493	−	2.55122i	−0.746053	−	0.121625i
$441$		0			0
$442$	−4.51589	+	1.46730i	−0.214799	+	0.0697924i
$443$	0.349328	+	0.0367158i	0.0165971	+	0.00174442i	0.112823	−	0.993615i	$-0.464011\pi$
$443$	0.349328	+	0.0367158i	0.0165971	+	0.00174442i	−0.0962263	+	0.995359i	$0.530677\pi$
$444$		0			0
$445$	5.70624	+	6.33742i	0.270502	+	0.300423i
$446$	−19.7394	−	21.9229i	−0.934690	−	1.03808i
$447$		0			0
$448$	37.3855	+	3.92937i	1.76630	+	0.185645i
$449$	10.7675	−	3.49858i	0.508151	−	0.165108i	−0.0437100	−	0.999044i	$-0.513918\pi$
$449$	10.7675	−	3.49858i	0.508151	−	0.165108i	0.551861	+	0.833936i	$0.313918\pi$
$450$		0			0
$451$	1.08703	−	0.167133i	0.0511864	−	0.00786997i
$452$	−3.03427	+	1.75184i	−0.142720	+	0.0823994i
$453$		0			0
$454$	16.2253	−	7.22398i	0.761493	−	0.339038i
$455$	−33.9491	+	3.56819i	−1.59156	+	0.167279i
$456$		0			0
$457$	1.73926	+	8.18257i	0.0813591	+	0.382764i	0.999922	−	0.0125110i	$-0.00398248\pi$
$457$	1.73926	+	8.18257i	0.0813591	+	0.382764i	−0.918563	+	0.395275i	$0.870649\pi$
$458$	7.39471	−	5.37257i	0.345532	−	0.251044i
$459$		0			0
$460$	−0.858291	−	2.64155i	−0.0400180	−	0.123163i
$461$	−6.38016	−	11.0508i	−0.297153	−	0.514685i	0.678330	−	0.734757i	$-0.262704\pi$
$461$	−6.38016	−	11.0508i	−0.297153	−	0.514685i	−0.975484	+	0.220072i	$0.929371\pi$
$462$		0			0
$463$	11.0509	−	19.1407i	0.513579	−	0.889544i	−0.486297	−	0.873793i	$-0.661653\pi$
$463$	11.0509	−	19.1407i	0.513579	−	0.889544i	0.999876	−	0.0157509i	$-0.00501388\pi$
$464$	16.5765	+	3.52345i	0.769546	+	0.163572i
$465$		0			0
$466$	−8.70378	−	3.87517i	−0.403195	−	0.179514i
$467$	−7.72240	−	2.50916i	−0.357350	−	0.116110i	0.124840	−	0.992177i	$-0.460158\pi$
$467$	−7.72240	−	2.50916i	−0.357350	−	0.116110i	−0.482190	+	0.876067i	$0.660158\pi$
$468$		0			0
$469$	26.6513	+	36.6823i	1.23064	+	1.69383i
$470$	1.07191	−	10.1985i	0.0494435	−	0.470423i
$471$		0			0
$472$	18.6881	+	10.7896i	0.860188	+	0.496630i
$473$	−3.58426	+	0.943044i	−0.164804	+	0.0433612i
$474$		0			0
$475$	−7.18689	−	6.47111i	−0.329757	−	0.296915i
$476$	−1.30668	+	1.79849i	−0.0598915	+	0.0824336i
$477$		0			0
$478$	6.73649	−	20.7328i	0.308120	−	0.948295i
$479$	33.6876	−	7.16053i	1.53923	−	0.327173i	0.641290	−	0.767298i	$-0.278399\pi$
$479$	33.6876	−	7.16053i	1.53923	−	0.327173i	0.897936	+	0.440125i	$0.145066\pi$
$480$		0			0
$481$	9.42591	+	21.1709i	0.429784	+	0.965312i
$482$	−0.298105	+	1.40247i	−0.0135783	+	0.0638809i
$483$		0			0
$484$	−2.91251	+	6.38551i	−0.132387	+	0.290250i
$485$		−	3.00477i		−	0.136440i
$486$		0			0
$487$	−13.5062	−	9.81282i	−0.612024	−	0.444661i	0.238103	−	0.971240i	$-0.423475\pi$
$487$	−13.5062	−	9.81282i	−0.612024	−	0.444661i	−0.850126	+	0.526579i	$0.823475\pi$
$488$	−5.07191	+	11.3917i	−0.229595	+	0.515678i
$489$		0			0
$490$	15.9254	−	14.3393i	0.719437	−	0.647784i
$491$	−1.79489	−	17.0772i	−0.0810023	−	0.770685i	−0.957335	−	0.288979i	$-0.906684\pi$
$491$	−1.79489	−	17.0772i	−0.0810023	−	0.770685i	0.876333	−	0.481706i	$-0.159983\pi$
$492$		0			0
$493$	−3.93045	+	4.36520i	−0.177018	+	0.196599i
$494$	−22.0900			−0.993875
$495$		0			0
$496$	15.2135			0.683107
$497$	−12.8355	+	14.2553i	−0.575753	+	0.639438i
$498$		0			0
$499$	−3.56755	−	33.9430i	−0.159706	−	1.51950i	−0.721612	−	0.692297i	$-0.756599\pi$
$499$	−3.56755	−	33.9430i	−0.159706	−	1.51950i	0.561907	−	0.827201i	$-0.310068\pi$
$500$	−5.58743	+	5.03094i	−0.249877	+	0.224990i
$501$		0			0
$502$	−12.4594	+	27.9842i	−0.556088	+	1.24899i
$503$	−1.17651	−	0.854786i	−0.0524581	−	0.0381130i	0.561247	−	0.827648i	$-0.310322\pi$
$503$	−1.17651	−	0.854786i	−0.0524581	−	0.0381130i	−0.613705	+	0.789535i	$0.710322\pi$
$504$		0			0
$505$		−	20.6470i		−	0.918778i
$506$	10.8383	−	0.518865i	0.481820	−	0.0230663i
$507$		0			0
$508$	−0.595478	+	2.80150i	−0.0264201	+	0.124297i
$509$	4.77795	+	10.7314i	0.211779	+	0.475663i	0.987933	−	0.154880i	$-0.0494990\pi$
$509$	4.77795	+	10.7314i	0.211779	+	0.475663i	−0.776154	+	0.630543i	$0.782832\pi$
$510$		0			0
$511$	−10.4347	+	2.21797i	−0.461605	+	0.0981172i
$512$	6.88085	−	21.1771i	0.304093	−	0.935903i
$513$		0			0
$514$	−20.5557	+	28.2925i	−0.906672	+	1.24793i
$515$	2.50976	+	2.25980i	0.110593	+	0.0995785i
$516$		0			0
$517$	−17.4903	−	6.80481i	−0.769222	−	0.299275i
$518$	−20.0575	−	11.5802i	−0.881278	−	0.508806i
$519$		0			0
$520$	−2.53189	+	24.0893i	−0.111031	+	1.05638i
$521$	−6.70232	−	9.22495i	−0.293634	−	0.404152i	0.636556	−	0.771230i	$-0.280358\pi$
$521$	−6.70232	−	9.22495i	−0.293634	−	0.404152i	−0.930190	+	0.367078i	$0.880358\pi$
$522$		0			0
$523$	−1.48831	−	0.483583i	−0.0650794	−	0.0211456i	0.276296	−	0.961072i	$-0.410893\pi$
$523$	−1.48831	−	0.483583i	−0.0650794	−	0.0211456i	−0.341376	+	0.939927i	$0.610893\pi$
$524$	−3.82566	−	1.70329i	−0.167125	−	0.0744087i
$525$		0			0
$526$	−2.40621	−	0.511456i	−0.104916	−	0.0223006i
$527$	−2.63658	+	4.56670i	−0.114851	+	0.198928i
$528$		0			0
$529$	−7.57062	−	13.1127i	−0.329157	−	0.570117i
$530$	3.02221	+	9.30141i	0.131276	+	0.404027i
$531$		0			0
$532$	−8.36693	+	6.07893i	−0.362753	+	0.263555i
$533$	−0.349311	−	1.64338i	−0.0151304	−	0.0711827i
$534$		0			0
$535$	−9.40995	+	0.989026i	−0.406828	+	0.0427593i
$536$	29.3917	−	13.0860i	1.26953	−	0.565231i
$537$		0			0
$538$	28.5000	−	16.4545i	1.22872	−	0.709402i
$539$	−17.6469	−	35.0247i	−0.760105	−	1.50862i
$540$		0			0
$541$	−4.01286	+	1.30386i	−0.172527	+	0.0560573i	−0.394007	−	0.919108i	$-0.628911\pi$
$541$	−4.01286	+	1.30386i	−0.172527	+	0.0560573i	0.221480	+	0.975165i	$0.428911\pi$
$542$	12.5969	+	1.32399i	0.541085	+	0.0568703i
$543$		0			0
$544$	1.85571	+	2.06098i	0.0795630	+	0.0883636i
$545$	8.53967	+	9.48426i	0.365799	+	0.406261i
$546$		0			0
$547$	−13.6940	−	1.43930i	−0.585515	−	0.0615401i	−0.192860	−	0.981226i	$-0.561776\pi$
$547$	−13.6940	−	1.43930i	−0.585515	−	0.0615401i	−0.392654	+	0.919686i	$0.628443\pi$
$548$	−5.10420	+	1.65845i	−0.218041	+	0.0708457i
$549$		0			0
$550$	−4.50837	−	8.94799i	−0.192237	−	0.381544i
$551$	−23.6657	+	13.6634i	−1.00819	+	0.582081i
$552$		0			0
$553$	2.53883	−	1.13036i	0.107962	−	0.0480679i
$554$	−14.9045	+	1.56653i	−0.633232	+	0.0665553i
$555$		0			0
$556$	0.271790	+	1.27867i	0.0115265	+	0.0542277i
$557$	5.50700	−	4.00107i	0.233339	−	0.169531i	−0.464971	−	0.885326i	$-0.653935\pi$
$557$	5.50700	−	4.00107i	0.233339	−	0.169531i	0.698311	+	0.715795i	$0.253935\pi$
$558$		0			0
$559$	1.74958	+	5.38465i	0.0739993	+	0.227746i
$560$	−7.80490	−	13.5185i	−0.329817	−	0.571261i
$561$		0			0
$562$	−6.19286	+	10.7263i	−0.261230	+	0.452463i
$563$	29.9874	+	6.37403i	1.26382	+	0.268633i	0.790612	−	0.612317i	$-0.209763\pi$
$563$	29.9874	+	6.37403i	1.26382	+	0.268633i	0.473208	+	0.880951i	$0.343096\pi$
$564$		0			0
$565$	7.79009	+	3.46837i	0.327732	+	0.145916i
$566$	24.7056	+	8.02735i	1.03846	+	0.337415i
$567$		0			0
$568$	8.00051	+	11.0118i	0.335694	+	0.462043i
$569$	−3.94586	+	37.5423i	−0.165419	+	1.57386i	0.525417	+	0.850845i	$0.323909\pi$
$569$	−3.94586	+	37.5423i	−0.165419	+	1.57386i	−0.690836	+	0.723012i	$0.742757\pi$
$570$		0			0
$571$	−26.9194	−	15.5419i	−1.12654	−	0.650409i	−0.183479	−	0.983024i	$-0.558736\pi$
$571$	−26.9194	−	15.5419i	−1.12654	−	0.650409i	−0.943063	+	0.332615i	$0.892069\pi$
$572$	9.99185	+	3.88745i	0.417780	+	0.162543i
$573$		0			0
$574$	1.24780	+	1.12352i	0.0520821	+	0.0468949i
$575$	4.26545	−	5.87089i	0.177882	−	0.244833i
$576$		0			0
$577$	3.06623	−	9.43689i	0.127649	−	0.392863i	−0.866726	−	0.498785i	$-0.833780\pi$
$577$	3.06623	−	9.43689i	0.127649	−	0.392863i	0.994374	+	0.105923i	$0.0337796\pi$
$578$	−18.6699	+	3.96840i	−0.776565	+	0.165064i
$579$		0			0
$580$	2.94768	+	6.62059i	0.122396	+	0.274905i
$581$	−1.67893	+	7.89874i	−0.0696537	+	0.327695i
$582$		0			0
$583$	17.8783	−	0.855895i	0.740444	−	0.0354476i
$584$			7.56960i			0.313232i
$585$		0			0
$586$	20.8438	+	15.1439i	0.861051	+	0.625590i
$587$	0.676425	−	1.51928i	0.0279191	−	0.0627072i	−0.899048	−	0.437851i	$-0.855740\pi$
$587$	0.676425	−	1.51928i	0.0279191	−	0.0627072i	0.926967	+	0.375143i	$0.122407\pi$
$588$		0			0
$589$	−18.2307	+	16.4150i	−0.751183	+	0.676368i
$590$	−1.32776	−	12.6328i	−0.0546631	−	0.520085i
$591$		0			0
$592$	−7.09095	+	7.87530i	−0.291436	+	0.323673i
$593$	16.8012			0.689945			0.344972	−	0.938613i	$-0.387888\pi$
$593$	16.8012			0.689945			0.344972	+	0.938613i	$0.387888\pi$
$594$		0			0
$595$	5.41053			0.221810
$596$	−0.673634	+	0.748146i	−0.0275931	+	0.0306453i
$597$		0			0
$598$	−1.73264	−	16.4850i	−0.0708530	−	0.674121i
$599$	31.7328	−	28.5723i	1.29657	−	1.16743i	0.321159	−	0.947025i	$-0.395928\pi$
$599$	31.7328	−	28.5723i	1.29657	−	1.16743i	0.975408	−	0.220408i	$-0.0707389\pi$
$600$		0			0
$601$	8.37933	−	18.8203i	0.341800	−	0.767696i	−0.658091	−	0.752938i	$-0.728636\pi$
$601$	8.37933	−	18.8203i	0.341800	−	0.767696i	0.999891	−	0.0147573i	$-0.00469755\pi$
$602$	−4.57769	−	3.32588i	−0.186573	−	0.135553i
$603$		0			0
$604$		−	6.43300i		−	0.261755i
$605$	16.7396	−	3.40015i	0.680563	−	0.138236i
$606$		0			0
$607$	−7.64988	+	35.9899i	−0.310499	+	1.46078i	0.495366	+	0.868684i	$0.335034\pi$
$607$	−7.64988	+	35.9899i	−0.310499	+	1.46078i	−0.805865	+	0.592099i	$0.798299\pi$
$608$	5.24773	+	11.7866i	0.212824	+	0.478009i
$609$		0			0
$610$	7.17984	−	1.52612i	0.290703	−	0.0617909i
$611$	−8.85939	+	27.2664i	−0.358413	+	1.10308i
$612$		0			0
$613$	−23.1926	+	31.9219i	−0.936741	+	1.28931i	0.0204297	+	0.999791i	$0.493497\pi$
$613$	−23.1926	+	31.9219i	−0.936741	+	1.28931i	−0.957171	+	0.289523i	$0.906503\pi$
$614$	−11.1233	−	10.0155i	−0.448901	−	0.404193i
$615$		0			0
$616$	−42.8443	+	11.2726i	−1.72625	+	0.454188i
$617$	−14.2499	−	8.22721i	−0.573681	−	0.331215i	0.184937	−	0.982750i	$-0.440792\pi$
$617$	−14.2499	−	8.22721i	−0.573681	−	0.331215i	−0.758618	+	0.651535i	$0.774125\pi$
$618$		0			0
$619$	1.57033	−	14.9407i	0.0631171	−	0.600519i	−0.916554	−	0.399910i	$-0.869041\pi$
$619$	1.57033	−	14.9407i	0.0631171	−	0.600519i	0.979671	−	0.200609i	$-0.0642920\pi$
$620$	3.82407	+	5.26338i	0.153578	+	0.211382i
$621$		0			0
$622$	7.47370	+	2.42835i	0.299668	+	0.0973681i
$623$	21.7673	+	9.69143i	0.872089	+	0.388279i
$624$		0			0
$625$	5.23883	+	1.11355i	0.209553	+	0.0445419i
$626$	−5.16683	+	8.94921i	−0.206508	+	0.357683i
$627$		0			0
$628$	7.09534	+	12.2895i	0.283135	+	0.490404i
$629$	−1.13506	−	3.49335i	−0.0452577	−	0.139289i
$630$		0			0
$631$	−4.93444	+	3.58508i	−0.196437	+	0.142720i	−0.681656	−	0.731673i	$-0.738740\pi$
$631$	−4.93444	+	3.58508i	−0.196437	+	0.142720i	0.485219	+	0.874393i	$0.338740\pi$
$632$	−0.409995	−	1.92888i	−0.0163087	−	0.0767266i
$633$		0			0
$634$	19.8931	−	2.09085i	0.790056	−	0.0830382i
$635$	6.36805	−	2.83524i	0.252708	−	0.112513i
$636$		0			0
$637$	−51.8855	+	29.9561i	−2.05578	+	1.18690i
$638$	−27.9832	+	4.30246i	−1.10787	+	0.170336i
$639$		0			0
$640$	−4.73219	+	1.53758i	−0.187056	+	0.0607783i
$641$	27.9131	+	2.93378i	1.10250	+	0.115877i	0.638252	−	0.769828i	$-0.279658\pi$
$641$	27.9131	+	2.93378i	1.10250	+	0.115877i	0.464248	+	0.885705i	$0.346325\pi$
$642$		0			0
$643$	3.29636	+	3.66098i	0.129996	+	0.144375i	0.804628	−	0.593779i	$-0.202365\pi$
$643$	3.29636	+	3.66098i	0.129996	+	0.144375i	−0.674633	+	0.738154i	$0.735698\pi$
$644$	−5.19276	−	5.76715i	−0.204624	−	0.227257i
$645$		0			0
$646$	3.48205	+	0.365978i	0.137000	+	0.0143992i
$647$	−27.9178	+	9.07106i	−1.09756	+	0.356620i	−0.801165	−	0.598444i	$-0.795786\pi$
$647$	−27.9178	+	9.07106i	−1.09756	+	0.356620i	−0.296399	+	0.955064i	$0.595786\pi$
$648$		0			0
$649$	−22.9441	−	3.74044i	−0.900634	−	0.146825i
$650$	−13.2555	+	7.65309i	−0.519925	+	0.300179i
$651$		0			0
$652$	−1.11003	+	0.494218i	−0.0434722	+	0.0193551i
$653$	−21.2908	+	2.23775i	−0.833172	+	0.0875700i	−0.511502	−	0.859282i	$-0.670911\pi$
$653$	−21.2908	+	2.23775i	−0.833172	+	0.0875700i	−0.321670	+	0.946852i	$0.604244\pi$
$654$		0			0
$655$	2.11907	+	9.96942i	0.0827987	+	0.389537i
$656$	0.621549	−	0.451582i	0.0242674	−	0.0176313i
$657$		0			0
$658$	−8.85404	−	27.2499i	−0.345166	−	1.06231i
$659$	−17.1996	−	29.7905i	−0.670000	−	1.16047i	−0.977904	−	0.209056i	$-0.932961\pi$
$659$	−17.1996	−	29.7905i	−0.670000	−	1.16047i	0.307904	−	0.951418i	$-0.400373\pi$
$660$		0			0
$661$	−3.94192	+	6.82760i	−0.153323	+	0.265563i	−0.932447	−	0.361307i	$-0.882331\pi$
$661$	−3.94192	+	6.82760i	−0.153323	+	0.265563i	0.779124	+	0.626870i	$0.215664\pi$
$662$	−18.6762	−	3.96974i	−0.725870	−	0.154288i
$663$		0			0
$664$	5.23455	+	2.33057i	0.203140	+	0.0904437i
$665$	23.9389	+	7.77822i	0.928311	+	0.301626i
$666$		0			0
$667$	−12.0528	−	16.5892i	−0.466686	−	0.642338i
$668$	1.00643	−	9.57557i	0.0389401	−	0.370490i
$669$		0			0
$670$	−16.4013	−	9.46928i	−0.633636	−	0.365830i
$671$	0.763728	−	13.4118i	0.0294834	−	0.517759i
$672$		0			0
$673$	−37.7770	−	34.0146i	−1.45620	−	1.31117i	−0.862065	−	0.506799i	$-0.830829\pi$
$673$	−37.7770	−	34.0146i	−1.45620	−	1.31117i	−0.594132	−	0.804367i	$-0.702505\pi$
$674$	9.28140	−	12.7748i	0.357506	−	0.492065i
$675$		0			0
$676$	2.49808	−	7.68829i	0.0960798	−	0.295703i
$677$	−23.0560	+	4.90071i	−0.886116	+	0.188350i	−0.628418	−	0.777876i	$-0.716297\pi$
$677$	−23.0560	+	4.90071i	−0.886116	+	0.188350i	−0.257698	+	0.966226i	$0.582964\pi$
$678$		0			0
$679$	−3.41476	−	7.66968i	−0.131047	−	0.294335i
$680$	0.798204	−	3.75526i	0.0306097	−	0.144008i
$681$		0			0
$682$	−23.7691	+	9.00096i	−0.910165	+	0.344665i
$683$		−	14.3587i		−	0.549419i	−0.961527	−	0.274709i	$-0.911418\pi$
$683$		−	14.3587i		−	0.549419i	0.961527	−	0.274709i	$-0.0885816\pi$
$684$		0			0
$685$	10.5674	+	7.67766i	0.403760	+	0.293348i
$686$	9.93718	−	22.3193i	0.379403	−	0.852154i
$687$		0			0
$688$	−1.92402	+	1.73239i	−0.0733524	+	0.0660468i
$689$	−2.85809	−	27.1929i	−0.108884	−	1.03597i
$690$		0			0
$691$	7.90539	−	8.77983i	0.300735	−	0.334000i	−0.573770	−	0.819017i	$-0.694520\pi$
$691$	7.90539	−	8.77983i	0.300735	−	0.334000i	0.874505	+	0.485016i	$0.161186\pi$
$692$	−14.0047			−0.532377
$693$		0			0
$694$	22.4023			0.850379
$695$	2.12890	−	2.36438i	0.0807536	−	0.0896860i
$696$		0			0
$697$	0.0278352	+	0.264834i	0.00105433	+	0.0100313i
$698$	8.47880	−	7.63435i	0.320927	−	0.288964i
$699$		0			0
$700$	−2.91470	+	6.54652i	−0.110165	+	0.247435i
$701$	−35.2967	−	25.6445i	−1.33314	−	0.968581i	−0.999667	−	0.0258206i	$-0.991780\pi$
$701$	−35.2967	−	25.6445i	−1.33314	−	0.968581i	−0.333471	−	0.942760i	$-0.608220\pi$
$702$		0			0
$703$		−	17.0881i		−	0.644490i
$704$	1.37409	+	28.7025i	0.0517879	+	1.08177i
$705$		0			0
$706$	−3.92920	+	18.4855i	−0.147878	+	0.695709i
$707$	−23.4642	−	52.7014i	−0.882460	−	1.98204i
$708$		0			0
$709$	36.0769	−	7.66839i	1.35490	−	0.287992i	0.527475	−	0.849571i	$-0.323139\pi$
$709$	36.0769	−	7.66839i	1.35490	−	0.287992i	0.827424	+	0.561578i	$0.189806\pi$
$710$	2.47590	−	7.62004i	0.0929189	−	0.285975i
$711$		0			0
$712$	9.93777	−	13.6782i	0.372434	−	0.512611i
$713$	−13.6799	−	12.3174i	−0.512316	−	0.461291i
$714$		0			0
$715$	−6.63958	−	25.2353i	−0.248306	−	0.943745i
$716$	−14.2325	−	8.21713i	−0.531893	−	0.307088i
$717$		0			0
$718$	−1.47872	+	14.0691i	−0.0551855	+	0.525055i
$719$	−0.103196	−	0.142037i	−0.00384856	−	0.00529709i	0.807088	−	0.590431i	$-0.201042\pi$
$719$	−0.103196	−	0.142037i	−0.00384856	−	0.00529709i	−0.810937	+	0.585134i	$0.801042\pi$
$720$		0			0
$721$	8.97429	+	2.91592i	0.334220	+	0.108595i
$722$	−5.37640	−	2.39373i	−0.200089	−	0.0890853i
$723$		0			0
$724$	7.99818	+	1.70006i	0.297250	+	0.0631824i
$725$	−9.46741	+	16.3980i	−0.351611	+	0.609008i
$726$		0			0
$727$	10.8837	+	18.8510i	0.403652	+	0.699147i	0.994164	−	0.107883i	$-0.0344072\pi$
$727$	10.8837	+	18.8510i	0.403652	+	0.699147i	−0.590511	+	0.807029i	$0.701074\pi$
$728$	20.9135	+	64.3652i	0.775107	+	2.38553i
$729$		0			0
$730$	3.60481	−	2.61905i	0.133420	−	0.0969353i
$731$	−0.186576	−	0.877771i	−0.00690076	−	0.0324655i
$732$		0			0
$733$	21.9705	−	2.30919i	0.811498	−	0.0852919i	0.310316	−	0.950634i	$-0.399565\pi$
$733$	21.9705	−	2.30919i	0.811498	−	0.0852919i	0.501183	+	0.865342i	$0.332899\pi$
$734$	0.932804	−	0.415311i	0.0344304	−	0.0153294i
$735$		0			0
$736$	−8.38432	+	4.84069i	−0.309050	+	0.178430i
$737$	−24.6189	+	24.3972i	−0.906848	+	0.898681i
$738$		0			0
$739$	20.5897	−	6.69000i	0.757404	−	0.246096i	0.0952401	−	0.995454i	$-0.469638\pi$
$739$	20.5897	−	6.69000i	0.757404	−	0.246096i	0.662164	+	0.749359i	$0.269638\pi$
$740$	−4.50698	−	0.473703i	−0.165680	−	0.0174137i
$741$		0			0
$742$	18.2847	+	20.3073i	0.671254	+	0.745503i
$743$	18.3621	+	20.3932i	0.673640	+	0.748153i	0.978950	−	0.204100i	$-0.0654268\pi$
$743$	18.3621	+	20.3932i	0.673640	+	0.748153i	−0.305310	+	0.952253i	$0.598760\pi$
$744$		0			0
$745$	2.43678	+	0.256116i	0.0892768	+	0.00938337i
$746$	10.7644	−	3.49757i	0.394113	−	0.128055i
$747$		0			0
$748$	−1.51061	−	0.778322i	−0.0552335	−	0.0284583i
$749$	−22.8949	+	13.2184i	−0.836562	+	0.482989i
$750$		0			0
$751$	21.2166	−	9.44624i	0.774205	−	0.344698i	0.0186861	−	0.999825i	$-0.494052\pi$
$751$	21.2166	−	9.44624i	0.774205	−	0.344698i	0.755519	+	0.655127i	$0.227385\pi$
$752$	−13.0383	+	1.37038i	−0.475457	+	0.0499725i
$753$		0			0
$754$	8.99223	+	42.3051i	0.327478	+	1.54066i
$755$	−12.6666	+	9.20283i	−0.460985	+	0.334925i
$756$		0			0
$757$	−10.8996	−	33.5455i	−0.396152	−	1.21923i	−0.928060	−	0.372430i	$-0.878525\pi$
$757$	−10.8996	−	33.5455i	−0.396152	−	1.21923i	0.531908	−	0.846802i	$-0.321475\pi$
$758$	−12.2854	−	21.2789i	−0.446226	−	0.772886i
$759$		0			0
$760$	8.93025	−	15.4677i	0.323934	−	0.561071i
$761$	0.834612	+	0.177402i	0.0302547	+	0.00643083i	0.223014	−	0.974815i	$-0.428410\pi$
$761$	0.834612	+	0.177402i	0.0302547	+	0.00643083i	−0.192759	+	0.981246i	$0.561744\pi$
$762$		0			0
$763$	32.5758	+	14.5037i	1.17932	+	0.525069i
$764$	0.588323	+	0.191158i	0.0212848	+	0.00691585i
$765$		0			0
$766$	−17.2750	−	23.7770i	−0.624171	−	0.859097i
$767$	−3.71209	+	35.3182i	−0.134036	+	1.27527i
$768$		0			0
$769$	−8.78388	−	5.07138i	−0.316755	−	0.182879i	0.333190	−	0.942860i	$-0.391875\pi$
$769$	−8.78388	−	5.07138i	−0.316755	−	0.182879i	−0.649945	+	0.759981i	$0.725208\pi$
$770$	20.1922	+	16.5031i	0.727677	+	0.594731i
$771$		0			0
$772$	−10.3787	−	9.34499i	−0.373536	−	0.336334i
$773$	11.4055	−	15.6983i	0.410228	−	0.564630i	−0.553046	−	0.833151i	$-0.686535\pi$
$773$	11.4055	−	15.6983i	0.410228	−	0.564630i	0.963274	+	0.268520i	$0.0865346\pi$
$774$		0			0
$775$	−5.25272	+	16.1662i	−0.188683	+	0.580707i
$776$	−5.82703	+	1.23857i	−0.209178	+	0.0444622i
$777$		0			0
$778$	16.1039	+	36.1699i	0.577351	+	1.29675i
$779$	−0.257571	+	1.21178i	−0.00922844	+	0.0434164i
$780$		0			0
$781$	−12.2614	−	8.04175i	−0.438749	−	0.287756i
$782$			2.62724i			0.0939500i
$783$		0			0
$784$	−22.1645	−	16.1034i	−0.791588	−	0.575122i
$785$	14.0477	−	31.5517i	0.501384	−	1.12613i
$786$		0			0
$787$	32.8856	−	29.6104i	1.17225	−	1.05550i	0.174762	−	0.984611i	$-0.444084\pi$
$787$	32.8856	−	29.6104i	1.17225	−	1.05550i	0.997485	−	0.0708847i	$-0.0225822\pi$
$788$	0.0259889	+	0.247268i	0.000925816	+	0.00880855i
$789$		0			0
$790$	−0.776717	+	0.862632i	−0.0276343	+	0.0306911i
$791$	23.8258			0.847149
$792$		0			0
$793$	−20.5215			−0.728740
$794$	−7.34567	+	8.15819i	−0.260688	+	0.289523i
$795$		0			0
$796$	−1.24871	−	11.8806i	−0.0442592	−	0.421098i
$797$	10.0748	−	9.07140i	0.356868	−	0.321325i	−0.471122	−	0.882068i	$-0.656151\pi$
$797$	10.0748	−	9.07140i	0.356868	−	0.321325i	0.827990	+	0.560743i	$0.189484\pi$
$798$		0			0
$799$	1.84825	−	4.15124i	0.0653864	−	0.146860i
$800$	7.23248	+	5.25470i	0.255707	+	0.185782i
$801$		0			0
$802$		−	24.0416i		−	0.848940i
$803$	−2.88790	−	7.62617i	−0.101912	−	0.269122i
$804$		0			0
$805$	−3.92695	+	18.4749i	−0.138407	+	0.651154i
$806$	15.7922	+	35.4699i	0.556256	+	1.24937i
$807$		0			0
$808$	−40.0398	+	8.51072i	−1.40859	+	0.299406i
$809$	7.82320	−	24.0773i	0.275049	−	0.846514i	−0.714157	−	0.699985i	$-0.753190\pi$
$809$	7.82320	−	24.0773i	0.275049	−	0.846514i	0.989206	−	0.146529i	$-0.0468100\pi$
$810$		0			0
$811$	−0.204607	+	0.281618i	−0.00718473	+	0.00988893i	−0.812594	−	0.582830i	$-0.801945\pi$
$811$	−0.204607	+	0.281618i	−0.00718473	+	0.00988893i	0.805410	+	0.592719i	$0.201945\pi$
$812$	15.0479	+	13.5492i	0.528077	+	0.475483i
$813$		0			0
$814$	6.41930	−	16.4994i	0.224996	−	0.578304i
$815$	2.56109	+	1.47865i	0.0897111	+	0.0517948i
$816$		0			0
$817$	0.436385	−	4.15193i	0.0152672	−	0.145258i
$818$	−12.8709	−	17.7152i	−0.450019	−	0.619398i
$819$		0			0
$820$	0.312465	+	0.101526i	0.0109118	+	0.00354544i
$821$	49.5773	+	22.0732i	1.73026	+	0.770361i	0.995784	+	0.0917268i	$0.0292386\pi$
$821$	49.5773	+	22.0732i	1.73026	+	0.770361i	0.734476	+	0.678635i	$0.237428\pi$
$822$		0			0
$823$	2.21233	+	0.470246i	0.0771170	+	0.0163917i	0.246309	−	0.969191i	$-0.420782\pi$
$823$	2.21233	+	0.470246i	0.0771170	+	0.0163917i	−0.169192	+	0.985583i	$0.554116\pi$
$824$	3.34780	−	5.79856i	0.116626	−	0.202002i
$825$		0			0
$826$	−17.7456	−	30.7363i	−0.617449	−	1.06945i
$827$	−10.7309	−	33.0262i	−0.373148	−	1.14843i	−0.944719	−	0.327880i	$-0.893666\pi$
$827$	−10.7309	−	33.0262i	−0.373148	−	1.14843i	0.571571	−	0.820553i	$-0.306334\pi$
$828$		0			0
$829$	−21.5813	+	15.6797i	−0.749549	+	0.544579i	−0.895687	−	0.444685i	$-0.853316\pi$
$829$	−21.5813	+	15.6797i	−0.749549	+	0.544579i	0.146138	+	0.989264i	$0.453316\pi$
$830$	−0.701262	−	3.29918i	−0.0243412	−	0.114516i
$831$		0			0
$832$	43.6565	−	4.58849i	1.51352	−	0.159077i
$833$	8.67504	−	3.86238i	0.300572	−	0.133823i
$834$		0			0
$835$	−20.2941	+	11.7168i	−0.702307	+	0.405477i
$836$	−5.56479	−	5.61536i	−0.192462	−	0.194211i
$837$		0			0
$838$	−41.4997	+	13.4841i	−1.43358	+	0.465800i
$839$	−14.7365	−	1.54887i	−0.508760	−	0.0534729i	−0.153329	−	0.988175i	$-0.548999\pi$
$839$	−14.7365	−	1.54887i	−0.508760	−	0.0534729i	−0.355431	+	0.934702i	$0.615666\pi$
$840$		0			0
$841$	16.3961	+	18.2097i	0.565383	+	0.627921i
$842$	21.0971	+	23.4307i	0.727052	+	0.807474i
$843$		0			0
$844$	15.3607	+	1.61447i	0.528736	+	0.0555724i
$845$	−18.7119	+	6.07988i	−0.643710	+	0.209154i
$846$		0			0
$847$	38.8638	−	27.7026i	1.33538	−	0.951871i
$848$	10.8282	−	6.25165i	0.371841	−	0.214683i
$849$		0			0
$850$	2.21627	−	0.986747i	0.0760174	−	0.0338451i
$851$	12.7523	−	1.34032i	0.437142	−	0.0459455i
$852$		0			0
$853$	−6.53175	−	30.7294i	−0.223643	−	1.05216i	−0.936451	−	0.350798i	$-0.885911\pi$
$853$	−6.53175	−	30.7294i	−0.223643	−	1.05216i	0.712809	−	0.701359i	$-0.247423\pi$
$854$	16.5922	−	12.0549i	0.567773	−	0.412511i
$855$		0			0
$856$	5.79678	+	17.8407i	0.198130	+	0.609781i
$857$	13.1784	+	22.8257i	0.450166	+	0.779710i	0.998396	−	0.0566174i	$-0.0180315\pi$
$857$	13.1784	+	22.8257i	0.450166	+	0.779710i	−0.548230	+	0.836328i	$0.684698\pi$
$858$		0			0
$859$	−12.2081	+	21.1450i	−0.416535	+	0.721459i	−0.995588	−	0.0938303i	$-0.970089\pi$
$859$	−12.2081	+	21.1450i	−0.416535	+	0.721459i	0.579054	+	0.815290i	$0.303422\pi$
$860$	−1.08297	−	0.230193i	−0.0369290	−	0.00784950i
$861$		0			0
$862$	−30.9653	−	13.7866i	−1.05468	−	0.469574i
$863$	−8.44399	−	2.74362i	−0.287437	−	0.0933939i	0.161750	−	0.986832i	$-0.448286\pi$
$863$	−8.44399	−	2.74362i	−0.287437	−	0.0933939i	−0.449187	+	0.893438i	$0.648286\pi$
$864$		0			0
$865$	20.0346	+	27.5752i	0.681196	+	0.937586i
$866$	−2.47275	+	23.5266i	−0.0840273	+	0.799467i
$867$		0			0
$868$	15.7425	+	9.08893i	0.534335	+	0.308498i
$869$	1.14895	+	1.78687i	0.0389755	+	0.0606155i
$870$		0			0
$871$	39.3476	+	35.4288i	1.33324	+	1.20046i
$872$	14.8724	−	20.4701i	0.503642	−	0.693204i
$873$		0			0
$874$	−3.77695	+	11.6242i	−0.127757	+	0.393196i
$875$	50.0112	−	10.6302i	1.69069	−	0.359367i
$876$		0			0
$877$	−14.0858	−	31.6371i	−0.475642	−	1.06831i	−0.978931	−	0.204192i	$-0.934543\pi$
$877$	−14.0858	−	31.6371i	−0.475642	−	1.06831i	0.503289	−	0.864118i	$-0.332123\pi$
$878$	−6.90667	+	32.4933i	−0.233089	+	1.09660i
$879$		0			0
$880$	9.30705	−	7.46726i	0.313741	−	0.251721i
$881$			3.07797i			0.103699i	0.998655	+	0.0518497i	$0.0165117\pi$
$881$			3.07797i			0.103699i	−0.998655	+	0.0518497i	$0.983488\pi$
$882$		0			0
$883$	44.0733	+	32.0212i	1.48319	+	1.07760i	0.976513	+	0.215460i	$0.0691250\pi$
$883$	44.0733	+	32.0212i	1.48319	+	1.07760i	0.506673	+	0.862138i	$0.330875\pi$
$884$	−1.05587	+	2.37152i	−0.0355127	+	0.0797628i
$885$		0			0
$886$	−0.304632	+	0.274292i	−0.0102343	+	0.00921502i
$887$	5.47219	+	52.0644i	0.183738	+	1.74815i	0.566281	+	0.824213i	$0.308382\pi$
$887$	5.47219	+	52.0644i	0.183738	+	1.74815i	−0.382543	+	0.923938i	$0.624951\pi$
$888$		0			0
$889$	13.0323	−	14.4739i	0.437091	−	0.485439i
$890$	−9.95228			−0.333601
$891$		0			0
$892$	−16.1281			−0.540009
$893$	14.1455	−	15.7101i	0.473359	−	0.525719i
$894$		0			0
$895$	4.18094	+	39.7790i	0.139753	+	1.32966i
$896$	−10.3315	+	9.30256i	−0.345153	+	0.310777i
$897$		0			0
$898$	−5.37411	+	12.0704i	−0.179336	+	0.402796i
$899$	38.8581	+	28.2320i	1.29599	+	0.941591i
$900$		0			0
$901$			4.33378i			0.144379i
$902$	−0.703912	+	1.07327i	−0.0234377	+	0.0357360i
$903$		0			0
$904$	3.51498	−	16.5367i	0.116906	−	0.550002i
$905$	−8.09448	−	18.1805i	−0.269070	−	0.604341i
$906$		0			0
$907$	−55.0901	+	11.7098i	−1.82924	+	0.388817i	−0.988326	−	0.152355i	$-0.951314\pi$
$907$	−55.0901	+	11.7098i	−1.82924	+	0.388817i	−0.840912	+	0.541172i	$0.817981\pi$
$908$	3.00058	−	9.23484i	0.0995778	−	0.306469i
$909$		0			0
$910$	23.4162	−	32.2296i	0.776238	−	1.06840i
$911$	18.4676	+	16.6283i	0.611860	+	0.550921i	0.915731	−	0.401792i	$-0.131612\pi$
$911$	18.4676	+	16.6283i	0.611860	+	0.550921i	−0.303871	+	0.952713i	$0.598279\pi$
$912$		0			0
$913$	−6.16281	−	0.350937i	−0.203959	−	0.0116143i
$914$	−8.45472	−	4.88134i	−0.279657	−	0.161460i
$915$		0			0
$916$	0.522345	−	4.96978i	0.0172588	−	0.164206i
$917$	16.7386	+	23.0387i	0.552758	+	0.760806i
$918$		0			0
$919$	−17.1331	−	5.56688i	−0.565168	−	0.183634i	0.0124770	−	0.999922i	$-0.496028\pi$
$919$	−17.1331	−	5.56688i	−0.565168	−	0.183634i	−0.577645	+	0.816288i	$0.696028\pi$
$920$	12.2434	+	5.45112i	0.403654	+	0.179718i
$921$		0			0
$922$	14.5663	+	3.09616i	0.479715	+	0.101967i
$923$	−11.2000	+	19.3990i	−0.368654	+	0.638527i
$924$		0			0
$925$	−5.92019	−	10.2541i	−0.194655	−	0.337152i
$926$	7.97064	+	24.5311i	0.261931	+	0.806142i
$927$		0			0
$928$	20.4366	−	14.8481i	0.670865	−	0.487412i
$929$	−6.98358	−	32.8552i	−0.229124	−	1.07794i	−0.930823	−	0.365470i	$-0.880908\pi$
$929$	−6.98358	−	32.8552i	−0.229124	−	1.07794i	0.701699	−	0.712473i	$-0.252425\pi$
$930$		0			0
$931$	43.9354	−	4.61779i	1.43992	−	0.151342i
$932$	−4.75847	+	2.11861i	−0.155869	+	0.0693973i
$933$		0			0
$934$	8.20654	−	4.73805i	0.268526	−	0.155034i
$935$	0.628512	+	4.08785i	0.0205545	+	0.133687i
$936$		0			0
$937$	13.8611	−	4.50374i	0.452822	−	0.147131i	−0.0737215	−	0.997279i	$-0.523488\pi$
$937$	13.8611	−	4.50374i	0.452822	−	0.147131i	0.526544	+	0.850148i	$0.323488\pi$
$938$	−52.6256	−	5.53117i	−1.71829	−	0.180599i
$939$		0			0
$940$	−3.75140	−	4.16636i	−0.122357	−	0.135892i
$941$	−19.4672	−	21.6205i	−0.634613	−	0.704809i	0.336968	−	0.941516i	$-0.390599\pi$
$941$	−19.4672	−	21.6205i	−0.634613	−	0.704809i	−0.971581	+	0.236707i	$0.923932\pi$
$942$		0			0
$943$	−0.924510	−	0.0971699i	−0.0301062	−	0.00316429i
$944$	−15.4445	+	5.01823i	−0.502676	+	0.163329i
$945$		0			0
$946$	1.98106	−	3.84496i	0.0644098	−	0.125010i
$947$	39.8858	−	23.0281i	1.29611	−	0.748311i	0.316383	−	0.948632i	$-0.397532\pi$
$947$	39.8858	−	23.0281i	1.29611	−	0.748311i	0.979730	+	0.200320i	$0.0641983\pi$
$948$		0			0
$949$	−11.3803	+	5.06683i	−0.369420	+	0.164476i
$950$	11.2245	−	1.17974i	0.364169	−	0.0382758i
$951$		0			0
$952$	−2.23023	−	10.4924i	−0.0722822	−	0.340061i
$953$	22.8291	−	16.5863i	0.739509	−	0.537284i	−0.153049	−	0.988219i	$-0.548909\pi$
$953$	22.8291	−	16.5863i	0.739509	−	0.537284i	0.892557	+	0.450934i	$0.148909\pi$
$954$		0			0
$955$	−0.465244	−	1.43188i	−0.0150550	−	0.0463344i
$956$	−5.95910	−	10.3215i	−0.192731	−	0.333820i
$957$		0			0
$958$	−20.0964	+	34.8081i	−0.649287	+	1.12460i
$959$	35.6985	+	7.58796i	1.15277	+	0.245028i
$960$		0			0
$961$	11.0708	+	4.92905i	0.357124	+	0.159002i
$962$	−25.7217	−	8.35749i	−0.829301	−	0.269456i
$963$		0			0
$964$	0.460754	+	0.634173i	0.0148399	+	0.0204253i
$965$	−3.55297	+	33.8043i	−0.114374	+	1.08820i
$966$		0			0
$967$	36.6176	+	21.1412i	1.17754	+	0.679854i	0.955445	−	0.295170i	$-0.0953764\pi$
$967$	36.6176	+	21.1412i	1.17754	+	0.679854i	0.222097	+	0.975025i	$0.428710\pi$
$968$	−13.4939	−	31.0609i	−0.433710	−	0.998336i
$969$		0			0
$970$	2.60596	+	2.34642i	0.0836725	+	0.0753391i
$971$	−0.665728	+	0.916296i	−0.0213642	+	0.0294053i	−0.819566	−	0.572986i	$-0.805785\pi$
$971$	−0.665728	+	0.916296i	−0.0213642	+	0.0294053i	0.798201	+	0.602391i	$0.205785\pi$
$972$		0			0
$973$	2.74702	−	8.45445i	0.0880654	−	0.271037i
$974$	19.0574	−	4.05077i	0.610637	−	0.129795i
$975$		0			0
$976$	−3.81686	−	8.57281i	−0.122175	−	0.274409i
$977$	−8.13400	+	38.2675i	−0.260230	+	1.22428i	0.632810	+	0.774307i	$0.281901\pi$
$977$	−8.13400	+	38.2675i	−0.260230	+	1.22428i	−0.893040	+	0.449978i	$0.851432\pi$
$978$		0			0
$979$	−4.79363	+	17.5718i	−0.153205	+	0.561597i
$980$		−	11.7159i		−	0.374252i
$981$		0			0
$982$	16.2123	+	11.7789i	0.517355	+	0.375880i
$983$	−16.5126	+	37.0879i	−0.526670	+	1.18292i	0.432898	+	0.901443i	$0.357491\pi$
$983$	−16.5126	+	37.0879i	−0.526670	+	1.18292i	−0.959568	+	0.281477i	$0.909176\pi$
$984$		0			0
$985$	0.449693	−	0.404905i	0.0143284	−	0.0129013i
$986$	−0.716554	−	6.81756i	−0.0228197	−	0.217115i
$987$		0			0
$988$	−8.08101	+	8.97487i	−0.257091	+	0.285529i
$989$	3.13267			0.0996131
$990$		0			0
$991$	16.7057			0.530675			0.265338	−	0.964156i	$-0.414517\pi$
$991$	16.7057			0.530675			0.265338	+	0.964156i	$0.414517\pi$
$992$	15.1741	−	16.8525i	0.481778	−	0.535069i
$993$		0			0
$994$	−2.34003	−	22.2639i	−0.0742212	−	0.706167i
$995$	−21.6067	+	19.4548i	−0.684978	+	0.616757i
$996$		0			0
$997$	−0.873727	+	1.96242i	−0.0276712	+	0.0621505i	−0.926852	−	0.375426i	$-0.877496\pi$
$997$	−0.873727	+	1.96242i	−0.0276712	+	0.0621505i	0.899181	+	0.437577i	$0.144163\pi$
$998$	32.2238	+	23.4120i	1.02003	+	0.741093i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.17.3		80
3.2	odd	2		99.2.p.a.50.8	yes	80
9.2	odd	6	inner	297.2.t.a.116.3		80
9.4	even	3		891.2.k.a.809.7		80
9.5	odd	6		891.2.k.a.809.14		80
9.7	even	3		99.2.p.a.83.8	yes	80
11.2	odd	10	inner	297.2.t.a.233.3		80
33.2	even	10		99.2.p.a.68.8	yes	80
99.2	even	30	inner	297.2.t.a.35.3		80
99.13	odd	30		891.2.k.a.728.14		80
99.68	even	30		891.2.k.a.728.7		80
99.79	odd	30		99.2.p.a.2.8	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.8	✓	80	99.79	odd	30
99.2.p.a.50.8	yes	80	3.2	odd	2
99.2.p.a.68.8	yes	80	33.2	even	10
99.2.p.a.83.8	yes	80	9.7	even	3
297.2.t.a.17.3		80	1.1	even	1	trivial
297.2.t.a.35.3		80	99.2	even	30	inner
297.2.t.a.116.3		80	9.2	odd	6	inner
297.2.t.a.233.3		80	11.2	odd	10	inner
891.2.k.a.728.7		80	99.68	even	30
891.2.k.a.728.14		80	99.13	odd	30
891.2.k.a.809.7		80	9.4	even	3
891.2.k.a.809.14		80	9.5	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780898 + 0.867275i) q^{2} +(0.0666926 + 0.634537i) q^{4} +(1.15400 - 1.03907i) q^{5} +(1.76474 - 3.96367i) q^{7} +(-2.49070 - 1.80960i) q^{8} +1.81224i q^{10} +(3.19970 + 0.872887i) q^{11} +(1.05340 - 4.95585i) q^{13} +(2.05951 + 4.62574i) q^{14} +(2.26622 - 0.481700i) q^{16} +(-0.248154 + 0.763741i) q^{17} +(-2.19592 + 3.02243i) q^{19} +(0.736289 + 0.662958i) q^{20} +(-3.25567 + 2.09338i) q^{22} +(-2.42777 - 1.40167i) q^{23} +(-0.270585 + 2.57445i) q^{25} +(3.47549 + 4.78360i) q^{26} +(2.63279 + 0.855447i) q^{28} +(6.68223 + 2.97512i) q^{29} +(6.42298 + 1.36525i) q^{31} +(1.72675 - 2.99082i) q^{32} +(-0.468590 - 0.811622i) q^{34} +(-2.08201 - 6.40776i) q^{35} +(-3.70044 + 2.68853i) q^{37} +(-0.906484 - 4.26467i) q^{38} +(-4.75456 + 0.499724i) q^{40} +(0.302935 - 0.134876i) q^{41} +(-0.967761 + 0.558737i) q^{43} +(-0.340483 + 2.08854i) q^{44} +(3.11148 - 1.01098i) q^{46} +(-5.62759 - 0.591483i) q^{47} +(-7.91248 - 8.78770i) q^{49} +(-2.02145 - 2.24505i) q^{50} +(3.21493 + 0.337902i) q^{52} +(5.13255 - 1.66767i) q^{53} +(4.59944 - 2.31739i) q^{55} +(-11.5681 + 6.67884i) q^{56} +(-7.79839 + 3.47207i) q^{58} +(-6.97083 + 0.732664i) q^{59} +(-0.842120 - 3.96186i) q^{61} +(-6.19973 + 4.50437i) q^{62} +(2.67734 + 8.24001i) q^{64} +(-3.93383 - 6.81360i) q^{65} +(-5.22518 + 9.05028i) q^{67} +(-0.501172 - 0.106527i) q^{68} +(7.18312 + 3.19813i) q^{70} +(-4.20477 - 1.36621i) q^{71} +(-1.44520 - 1.98915i) q^{73} +(0.557974 - 5.30877i) q^{74} +(-2.06429 - 1.19182i) q^{76} +(9.10648 - 11.1421i) q^{77} +(0.476003 + 0.428595i) q^{79} +(2.11470 - 2.91063i) q^{80} +(-0.119587 + 0.368052i) q^{82} +(-1.82050 + 0.386959i) q^{83} +(0.507207 + 1.13920i) q^{85} +(0.271144 - 1.27563i) q^{86} +(-6.38991 - 7.96427i) q^{88} +5.49170i q^{89} +(-17.7844 - 12.9211i) q^{91} +(0.727500 - 1.63399i) q^{92} +(4.90755 - 4.41878i) q^{94} +(0.606408 + 5.76958i) q^{95} +(1.29476 - 1.43798i) q^{97} +13.8002 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

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