LMFDB - Embedded newform 972.2.l.b.539.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(107,972)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("972.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			539.2
Character	$\chi$	$=$	972.539
Dual form			972.2.l.b.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33749 - 0.459470i) q^{2} +(1.57777 + 1.22908i) q^{4} +(1.74209 + 0.307177i) q^{5} +(-0.488252 - 0.581876i) q^{7} +(-1.54554 - 2.36882i) q^{8} +O(q^{10})$	\(q+(-1.33749 - 0.459470i) q^{2} +(1.57777 + 1.22908i) q^{4} +(1.74209 + 0.307177i) q^{5} +(-0.488252 - 0.581876i) q^{7} +(-1.54554 - 2.36882i) q^{8} +(-2.18889 - 1.21129i) q^{10} +(-0.557667 - 3.16269i) q^{11} +(1.31459 - 0.478472i) q^{13} +(0.385679 + 1.00259i) q^{14} +(0.978743 + 3.87841i) q^{16} +(-5.55887 - 3.20941i) q^{17} +(2.51793 - 1.45373i) q^{19} +(2.37108 + 2.62582i) q^{20} +(-0.707285 + 4.48630i) q^{22} +(-4.71486 - 3.95624i) q^{23} +(-1.75794 - 0.639840i) q^{25} +(-1.97810 + 0.0359374i) q^{26} +(-0.0551813 - 1.51817i) q^{28} +(2.59357 - 7.12578i) q^{29} +(-6.07378 + 7.23845i) q^{31} +(0.472953 - 5.63705i) q^{32} +(5.96031 + 6.84670i) q^{34} +(-0.671839 - 1.16366i) q^{35} +(1.62042 - 2.80666i) q^{37} +(-4.03566 + 0.787437i) q^{38} +(-1.96482 - 4.60145i) q^{40} +(2.20716 + 6.06412i) q^{41} +(7.20692 - 1.27077i) q^{43} +(3.00731 - 5.67542i) q^{44} +(4.48832 + 7.45778i) q^{46} +(3.25340 - 2.72993i) q^{47} +(1.11535 - 6.32545i) q^{49} +(2.05725 + 1.66350i) q^{50} +(2.66221 + 0.860813i) q^{52} +9.63986i q^{53} -5.68099i q^{55} +(-0.623748 + 2.05589i) q^{56} +(-6.74296 + 8.33901i) q^{58} +(-0.0734356 + 0.416474i) q^{59} +(6.10682 - 5.12423i) q^{61} +(11.4495 - 6.89065i) q^{62} +(-3.22263 + 7.32220i) q^{64} +(2.43711 - 0.429729i) q^{65} +(-1.94500 - 5.34384i) q^{67} +(-4.82602 - 11.8960i) q^{68} +(0.363913 + 1.86508i) q^{70} +(1.88825 - 3.27054i) q^{71} +(-5.59853 - 9.69694i) q^{73} +(-3.45688 + 3.00935i) q^{74} +(5.75947 + 0.801075i) q^{76} +(-1.56801 + 1.86868i) q^{77} +(-3.47514 + 9.54787i) q^{79} +(0.513698 + 7.05719i) q^{80} +(-0.165777 - 9.12484i) q^{82} +(-4.66624 - 1.69837i) q^{83} +(-8.69818 - 7.29864i) q^{85} +(-10.2231 - 1.61171i) q^{86} +(-6.62994 + 6.20907i) q^{88} +(0.509288 - 0.294037i) q^{89} +(-0.920264 - 0.531314i) q^{91} +(-2.57647 - 12.0370i) q^{92} +(-5.60572 + 2.15642i) q^{94} +(4.83301 - 1.75907i) q^{95} +(-2.93471 - 16.6435i) q^{97} +(-4.39813 + 7.94778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38} - 12 q^{40} - 66 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 66 q^{50} - 24 q^{52} + 81 q^{56} - 24 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} + 42 q^{65} - 51 q^{68} - 30 q^{70} - 6 q^{73} + 96 q^{74} - 9 q^{76} - 30 q^{77} - 12 q^{82} + 66 q^{85} - 141 q^{86} - 45 q^{88} + 24 q^{92} - 51 q^{94} + 42 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.33749	−	0.459470i	−0.945750	−	0.324895i
$2$	−1.33749	−	0.459470i	−0.945750	−	0.324895i
$3$		0			0
$3$		0			0
$4$	1.57777	+	1.22908i	0.788887	+	0.614538i
$5$	1.74209	+	0.307177i	0.779086	+	0.137374i	0.549029	−	0.835803i	$-0.314998\pi$
$5$	1.74209	+	0.307177i	0.779086	+	0.137374i	0.230057	+	0.973177i	$0.426109\pi$
$6$		0			0
$7$	−0.488252	−	0.581876i	−0.184542	−	0.219928i	0.665840	−	0.746095i	$-0.268073\pi$
$7$	−0.488252	−	0.581876i	−0.184542	−	0.219928i	−0.850382	+	0.526166i	$0.823629\pi$
$8$	−1.54554	−	2.36882i	−0.546430	−	0.837505i
$9$		0			0
$10$	−2.18889	−	1.21129i	−0.692189	−	0.383042i
$11$	−0.557667	−	3.16269i	−0.168143	−	0.953586i	−0.945764	−	0.324853i	$-0.894685\pi$
$11$	−0.557667	−	3.16269i	−0.168143	−	0.953586i	0.777621	−	0.628733i	$-0.216426\pi$
$12$		0			0
$13$	1.31459	−	0.478472i	0.364602	−	0.132704i	−0.153221	−	0.988192i	$-0.548965\pi$
$13$	1.31459	−	0.478472i	0.364602	−	0.132704i	0.517823	+	0.855488i	$0.326742\pi$
$14$	0.385679	+	1.00259i	0.103077	+	0.267954i
$15$		0			0
$16$	0.978743	+	3.87841i	0.244686	+	0.969602i
$17$	−5.55887	−	3.20941i	−1.34822	−	0.778397i	−0.360225	−	0.932865i	$-0.617300\pi$
$17$	−5.55887	−	3.20941i	−1.34822	−	0.778397i	−0.987998	+	0.154469i	$0.950633\pi$
$18$		0			0
$19$	2.51793	−	1.45373i	0.577653	−	0.333508i	−0.182547	−	0.983197i	$-0.558434\pi$
$19$	2.51793	−	1.45373i	0.577653	−	0.333508i	0.760200	+	0.649689i	$0.225101\pi$
$20$	2.37108	+	2.62582i	0.530190	+	0.587151i
$21$		0			0
$22$	−0.707285	+	4.48630i	−0.150794	+	0.956483i
$23$	−4.71486	−	3.95624i	−0.983117	−	0.824933i	0.00143998	−	0.999999i	$-0.499542\pi$
$23$	−4.71486	−	3.95624i	−0.983117	−	0.824933i	−0.984557	+	0.175066i	$0.943986\pi$
$24$		0			0
$25$	−1.75794	−	0.639840i	−0.351589	−	0.127968i
$26$	−1.97810	+	0.0359374i	−0.387938	+	0.00704791i
$27$		0			0
$28$	−0.0551813	−	1.51817i	−0.0104283	−	0.286907i
$29$	2.59357	−	7.12578i	0.481614	−	1.32322i	−0.426495	−	0.904490i	$-0.640252\pi$
$29$	2.59357	−	7.12578i	0.481614	−	1.32322i	0.908109	−	0.418734i	$-0.137526\pi$
$30$		0			0
$31$	−6.07378	+	7.23845i	−1.09088	+	1.30006i	−0.140124	+	0.990134i	$0.544750\pi$
$31$	−6.07378	+	7.23845i	−1.09088	+	1.30006i	−0.950759	+	0.309930i	$0.899694\pi$
$32$	0.472953	−	5.63705i	0.0836070	−	0.996499i
$33$		0			0
$34$	5.96031	+	6.84670i	1.02219	+	1.17420i
$35$	−0.671839	−	1.16366i	−0.113562	−	0.196694i
$36$		0			0
$37$	1.62042	−	2.80666i	0.266396	−	0.461411i	−0.701532	−	0.712638i	$-0.747500\pi$
$37$	1.62042	−	2.80666i	0.266396	−	0.461411i	0.967928	+	0.251226i	$0.0808338\pi$
$38$	−4.03566	+	0.787437i	−0.654670	+	0.127739i
$39$		0			0
$40$	−1.96482	−	4.60145i	−0.310665	−	0.727554i
$41$	2.20716	+	6.06412i	0.344700	+	0.947056i	0.984011	+	0.178107i	$0.0569975\pi$
$41$	2.20716	+	6.06412i	0.344700	+	0.947056i	−0.639311	+	0.768948i	$0.720780\pi$
$42$		0			0
$43$	7.20692	−	1.27077i	1.09904	−	0.193791i	0.405422	−	0.914130i	$-0.367125\pi$
$43$	7.20692	−	1.27077i	1.09904	−	0.193791i	0.693623	+	0.720338i	$0.256013\pi$
$44$	3.00731	−	5.67542i	0.453369	−	0.855602i
$45$		0			0
$46$	4.48832	+	7.45778i	0.661767	+	1.09959i
$47$	3.25340	−	2.72993i	0.474557	−	0.398200i	−0.373897	−	0.927470i	$-0.621979\pi$
$47$	3.25340	−	2.72993i	0.474557	−	0.398200i	0.848454	+	0.529270i	$0.177534\pi$
$48$		0			0
$49$	1.11535	−	6.32545i	0.159335	−	0.903636i
$50$	2.05725	+	1.66350i	0.290939	+	0.235255i
$51$		0			0
$52$	2.66221	+	0.860813i	0.369182	+	0.119373i
$53$			9.63986i			1.32414i	0.749444	+	0.662068i	$0.230321\pi$
$53$			9.63986i			1.32414i	−0.749444	+	0.662068i	$0.769679\pi$
$54$		0			0
$55$		−	5.68099i		−	0.766024i
$56$	−0.623748	+	2.05589i	−0.0833519	+	0.274730i
$57$		0			0
$58$	−6.74296	+	8.33901i	−0.885395	+	1.09497i
$59$	−0.0734356	+	0.416474i	−0.00956051	+	0.0542203i	−0.989215	−	0.146472i	$-0.953208\pi$
$59$	−0.0734356	+	0.416474i	−0.00956051	+	0.0542203i	0.979654	+	0.200693i	$0.0643192\pi$
$60$		0			0
$61$	6.10682	−	5.12423i	0.781898	−	0.656090i	−0.161828	−	0.986819i	$-0.551739\pi$
$61$	6.10682	−	5.12423i	0.781898	−	0.656090i	0.943726	+	0.330729i	$0.107295\pi$
$62$	11.4495	−	6.89065i	1.45409	−	0.875114i
$63$		0			0
$64$	−3.22263	+	7.32220i	−0.402828	+	0.915276i
$65$	2.43711	−	0.429729i	0.302287	−	0.0533013i
$66$		0			0
$67$	−1.94500	−	5.34384i	−0.237620	−	0.652855i	−0.999984	−	0.00570618i	$-0.998184\pi$
$67$	−1.94500	−	5.34384i	−0.237620	−	0.652855i	0.762364	−	0.647148i	$-0.224039\pi$
$68$	−4.82602	−	11.8960i	−0.585241	−	1.44260i
$69$		0			0
$70$	0.363913	+	1.86508i	0.0434959	+	0.222919i
$71$	1.88825	−	3.27054i	0.224094	−	0.388142i	−0.731953	−	0.681355i	$-0.761391\pi$
$71$	1.88825	−	3.27054i	0.224094	−	0.388142i	0.956047	+	0.293213i	$0.0947245\pi$
$72$		0			0
$73$	−5.59853	−	9.69694i	−0.655258	−	1.13494i	−0.981829	−	0.189768i	$-0.939226\pi$
$73$	−5.59853	−	9.69694i	−0.655258	−	1.13494i	0.326571	−	0.945173i	$-0.394107\pi$
$74$	−3.45688	+	3.00935i	−0.401854	+	0.349829i
$75$		0			0
$76$	5.75947	+	0.801075i	0.660657	+	0.0918896i
$77$	−1.56801	+	1.86868i	−0.178691	+	0.212956i
$78$		0			0
$79$	−3.47514	+	9.54787i	−0.390984	+	1.07422i	0.575569	+	0.817753i	$0.304781\pi$
$79$	−3.47514	+	9.54787i	−0.390984	+	1.07422i	−0.966553	+	0.256467i	$0.917442\pi$
$80$	0.513698	+	7.05719i	0.0574331	+	0.789017i
$81$		0			0
$82$	−0.165777	−	9.12484i	−0.0183070	−	1.00767i
$83$	−4.66624	−	1.69837i	−0.512187	−	0.186421i	0.0729805	−	0.997333i	$-0.476749\pi$
$83$	−4.66624	−	1.69837i	−0.512187	−	0.186421i	−0.585167	+	0.810913i	$0.698971\pi$
$84$		0			0
$85$	−8.69818	−	7.29864i	−0.943450	−	0.791649i
$86$	−10.2231	−	1.61171i	−1.10238	−	0.173796i
$87$		0			0
$88$	−6.62994	+	6.20907i	−0.706754	+	0.661889i
$89$	0.509288	−	0.294037i	0.0539844	−	0.0311679i	−0.472765	−	0.881189i	$-0.656744\pi$
$89$	0.509288	−	0.294037i	0.0539844	−	0.0311679i	0.526749	+	0.850021i	$0.323411\pi$
$90$		0			0
$91$	−0.920264	−	0.531314i	−0.0964698	−	0.0556969i
$92$	−2.57647	−	12.0370i	−0.268615	−	1.25494i
$93$		0			0
$94$	−5.60572	+	2.15642i	−0.578185	+	0.222417i
$95$	4.83301	−	1.75907i	0.495857	−	0.180477i
$96$		0			0
$97$	−2.93471	−	16.6435i	−0.297974	−	1.68990i	−0.654862	−	0.755749i	$-0.727273\pi$
$97$	−2.93471	−	16.6435i	−0.297974	−	1.68990i	0.356887	−	0.934147i	$-0.383838\pi$
$98$	−4.39813	+	7.94778i	−0.444278	+	0.802847i
$99$		0			0
$100$	−1.98723	−	3.17017i	−0.198723	−	0.317017i
$101$	−3.52367	−	4.19935i	−0.350618	−	0.417851i	0.561694	−	0.827345i	$-0.310150\pi$
$101$	−3.52367	−	4.19935i	−0.350618	−	0.417851i	−0.912313	+	0.409494i	$0.865705\pi$
$102$		0			0
$103$	5.94863	+	1.04890i	0.586135	+	0.103351i	0.458849	−	0.888514i	$-0.348262\pi$
$103$	5.94863	+	1.04890i	0.586135	+	0.103351i	0.127287	+	0.991866i	$0.459373\pi$
$104$	−3.16517	−	2.37454i	−0.310370	−	0.232842i
$105$		0			0
$106$	4.42923	−	12.8932i	0.430205	−	1.25230i
$107$	−4.28762			−0.414500			−0.207250	−	0.978288i	$-0.566451\pi$
$107$	−4.28762			−0.414500			−0.207250	+	0.978288i	$0.566451\pi$
$108$		0			0
$109$	−4.75148			−0.455109			−0.227554	−	0.973765i	$-0.573073\pi$
$109$	−4.75148			−0.455109			−0.227554	+	0.973765i	$0.573073\pi$
$110$	−2.61024	+	7.59828i	−0.248877	+	0.724468i
$111$		0			0
$112$	1.77888	−	2.46315i	0.168088	−	0.232746i
$113$	8.96226	+	1.58029i	0.843099	+	0.148661i	0.578485	−	0.815693i	$-0.303644\pi$
$113$	8.96226	+	1.58029i	0.843099	+	0.148661i	0.264614	+	0.964354i	$0.414755\pi$
$114$		0			0
$115$	−6.99845	−	8.34042i	−0.652608	−	0.777748i
$116$	12.8502	−	8.05517i	1.19311	−	0.747904i
$117$		0			0
$118$	0.289577	−	0.523290i	0.0266577	−	0.0481727i
$119$	0.846646	+	4.80157i	0.0776120	+	0.440159i
$120$		0			0
$121$	0.645022	−	0.234769i	0.0586384	−	0.0213426i
$122$	−10.5223	+	4.04772i	−0.952640	+	0.366463i
$123$		0			0
$124$	−18.4797	+	3.95550i	−1.65952	+	0.355214i
$125$	−10.5258	−	6.07707i	−0.941456	−	0.543550i
$126$		0			0
$127$	−7.58333	+	4.37824i	−0.672911	+	0.388506i	−0.797179	−	0.603743i	$-0.793675\pi$
$127$	−7.58333	+	4.37824i	−0.672911	+	0.388506i	0.124267	+	0.992249i	$0.460342\pi$
$128$	7.67458	−	8.31269i	0.678343	−	0.734745i
$129$		0			0
$130$	−3.45707	−	0.545022i	−0.303205	−	0.0478016i
$131$	5.65968	+	4.74904i	0.494489	+	0.414925i	0.855632	−	0.517585i	$-0.173169\pi$
$131$	5.65968	+	4.74904i	0.494489	+	0.414925i	−0.361143	+	0.932510i	$0.617613\pi$
$132$		0			0
$133$	−2.07527	−	0.755338i	−0.179949	−	0.0654961i
$134$	0.146086	+	8.04102i	0.0126199	+	0.694639i
$135$		0			0
$136$	0.988912	+	18.1282i	0.0847985	+	1.55448i
$137$	−1.85078	+	5.08499i	−0.158123	+	0.434440i	−0.993303	−	0.115537i	$-0.963141\pi$
$137$	−1.85078	+	5.08499i	−0.158123	+	0.434440i	0.835180	+	0.549977i	$0.185363\pi$
$138$		0			0
$139$	9.38523	−	11.1849i	0.796045	−	0.948689i	−0.203493	−	0.979076i	$-0.565230\pi$
$139$	9.38523	−	11.1849i	0.796045	−	0.948689i	0.999538	+	0.0303870i	$0.00967396\pi$
$140$	0.370216	−	2.66173i	0.0312890	−	0.224958i
$141$		0			0
$142$	−4.02824	+	3.50673i	−0.338042	+	0.294278i
$143$	−2.24636	−	3.89082i	−0.187850	−	0.325366i
$144$		0			0
$145$	6.70711	−	11.6171i	0.556995	−	0.964744i
$146$	3.03254	+	15.5419i	0.250975	+	1.28626i
$147$		0			0
$148$	6.00626	−	2.43665i	0.493711	−	0.200291i
$149$	0.355393	+	0.976434i	0.0291149	+	0.0799926i	0.953399	−	0.301714i	$-0.0975587\pi$
$149$	0.355393	+	0.976434i	0.0291149	+	0.0799926i	−0.924284	+	0.381707i	$0.875337\pi$
$150$		0			0
$151$	14.9356	−	2.63354i	1.21544	−	0.214315i	0.471077	−	0.882092i	$-0.343865\pi$
$151$	14.9356	−	2.63354i	1.21544	−	0.214315i	0.744361	+	0.667777i	$0.232754\pi$
$152$	−7.33518	−	3.71774i	−0.594962	−	0.301548i
$153$		0			0
$154$	2.95580	−	1.77889i	0.238185	−	0.143347i
$155$	−12.8046	+	10.7443i	−1.02849	+	0.863003i
$156$		0			0
$157$	1.35995	−	7.71265i	0.108536	−	0.615537i	−0.881213	−	0.472719i	$-0.843273\pi$
$157$	1.35995	−	7.71265i	0.108536	−	0.615537i	0.989749	−	0.142818i	$-0.0456163\pi$
$158$	9.03494	−	11.1735i	0.718781	−	0.888915i
$159$		0			0
$160$	2.55550	−	9.67496i	0.202030	−	0.764873i
$161$			4.67510i			0.368450i
$162$		0			0
$163$			14.8714i			1.16482i	0.812897	+	0.582408i	$0.197889\pi$
$163$			14.8714i			1.16482i	−0.812897	+	0.582408i	$0.802111\pi$
$164$	−3.97087	+	12.2806i	−0.310072	+	0.958952i
$165$		0			0
$166$	5.46071	+	4.41556i	0.423834	+	0.342714i
$167$	−0.176711	+	1.00218i	−0.0136743	+	0.0775508i	−0.990881	−	0.134738i	$-0.956981\pi$
$167$	−0.176711	+	1.00218i	−0.0136743	+	0.0775508i	0.977207	+	0.212289i	$0.0680918\pi$
$168$		0			0
$169$	−8.45936	+	7.09825i	−0.650720	+	0.546019i
$170$	8.28025	+	13.7584i	0.635066	+	1.05522i
$171$		0			0
$172$	12.9328	+	6.85286i	0.986114	+	0.522526i
$173$	7.69469	−	1.35678i	0.585016	−	0.103154i	0.126696	−	0.991942i	$-0.459563\pi$
$173$	7.69469	−	1.35678i	0.585016	−	0.103154i	0.458320	+	0.888787i	$0.348451\pi$
$174$		0			0
$175$	0.486012	+	1.33531i	0.0367391	+	0.100940i
$176$	11.7204	−	5.25832i	0.883457	−	0.396361i
$177$		0			0
$178$	−0.816270	+	0.159270i	−0.0611820	+	0.0119378i
$179$	−3.90388	+	6.76172i	−0.291790	+	0.505395i	−0.974233	−	0.225544i	$-0.927584\pi$
$179$	−3.90388	+	6.76172i	−0.291790	+	0.505395i	0.682443	+	0.730939i	$0.260917\pi$
$180$		0			0
$181$	1.45395	+	2.51831i	0.108071	+	0.187184i	0.914989	−	0.403479i	$-0.132199\pi$
$181$	1.45395	+	2.51831i	0.108071	+	0.187184i	−0.806918	+	0.590664i	$0.798866\pi$
$182$	0.986723	+	1.13346i	0.0731408	+	0.0840179i
$183$		0			0
$184$	−2.08463	+	17.2832i	−0.153681	+	1.27413i
$185$	3.68506	−	4.39169i	0.270931	−	0.322883i
$186$		0			0
$187$	−7.05037	+	19.3707i	−0.515574	+	1.41653i
$188$	8.48841	−	0.308531i	0.619081	−	0.0225019i
$189$		0			0
$190$	−7.27236	+	0.132122i	−0.527593	+	0.00958512i
$191$	14.8824	+	5.41676i	1.07685	+	0.391943i	0.818736	−	0.574171i	$-0.194675\pi$
$191$	14.8824	+	5.41676i	1.07685	+	0.391943i	0.258118	+	0.966113i	$0.416898\pi$
$192$		0			0
$193$	9.76988	+	8.19791i	0.703252	+	0.590098i	0.922697	−	0.385527i	$-0.125980\pi$
$193$	9.76988	+	8.19791i	0.703252	+	0.590098i	−0.219445	+	0.975625i	$0.570425\pi$
$194$	−3.72207	+	23.6090i	−0.267229	+	1.69503i
$195$		0			0
$196$	9.53423	−	8.60929i	0.681016	−	0.614949i
$197$	6.84336	−	3.95102i	0.487570	−	0.281498i	−0.235996	−	0.971754i	$-0.575835\pi$
$197$	6.84336	−	3.95102i	0.487570	−	0.281498i	0.723566	+	0.690256i	$0.242502\pi$
$198$		0			0
$199$	−3.36883	−	1.94499i	−0.238810	−	0.137877i	0.375820	−	0.926693i	$-0.377361\pi$
$199$	−3.36883	−	1.94499i	−0.238810	−	0.137877i	−0.614630	+	0.788816i	$0.710694\pi$
$200$	1.20130	+	5.15315i	0.0849450	+	0.364383i
$201$		0			0
$202$	2.78341	+	7.23562i	0.195840	+	0.509096i
$203$	−5.41263	+	1.97004i	−0.379892	+	0.138269i
$204$		0			0
$205$	1.98231	+	11.2422i	0.138450	+	0.785191i
$206$	−7.47430	−	4.13612i	−0.520759	−	0.288177i
$207$		0			0
$208$	3.14236	+	4.63023i	0.217883	+	0.321048i
$209$	−6.00185	−	7.15273i	−0.415157	−	0.494765i
$210$		0			0
$211$	3.80697	+	0.671271i	0.262082	+	0.0462122i	0.303145	−	0.952944i	$-0.401963\pi$
$211$	3.80697	+	0.671271i	0.262082	+	0.0462122i	−0.0410628	+	0.999157i	$0.513074\pi$
$212$	−11.8481	+	15.2095i	−0.813732	+	1.04459i
$213$		0			0
$214$	5.73466	+	1.97003i	0.392013	+	0.134669i
$215$	12.9455			0.882872
$216$		0			0
$217$	7.17741			0.487235
$218$	6.35507	+	2.18316i	0.430419	+	0.147862i
$219$		0			0
$220$	6.98237	−	8.96331i	0.470751	−	0.604307i
$221$	−8.84326	−	1.55930i	−0.594862	−	0.104890i
$222$		0			0
$223$	−15.0229	−	17.9036i	−1.00601	−	1.19891i	−0.979948	−	0.199251i	$-0.936149\pi$
$223$	−15.0229	−	17.9036i	−1.00601	−	1.19891i	−0.0260578	−	0.999660i	$-0.508295\pi$
$224$	−3.51098	+	2.47710i	−0.234587	+	0.165508i
$225$		0			0
$226$	−11.2609	−	6.23152i	−0.749062	−	0.414514i
$227$	1.84331	+	10.4539i	0.122345	+	0.693853i	0.982849	+	0.184410i	$0.0590374\pi$
$227$	1.84331	+	10.4539i	0.122345	+	0.693853i	−0.860504	+	0.509443i	$0.829852\pi$
$228$		0			0
$229$	6.53737	−	2.37941i	0.432002	−	0.157236i	−0.116861	−	0.993148i	$-0.537283\pi$
$229$	6.53737	−	2.37941i	0.432002	−	0.157236i	0.548863	+	0.835913i	$0.315061\pi$
$230$	5.52819	+	14.3708i	0.364518	+	0.947585i
$231$		0			0
$232$	−20.8881	+	4.86945i	−1.37137	+	0.319695i
$233$	−13.9988	−	8.08221i	−0.917091	−	0.529483i	−0.0343854	−	0.999409i	$-0.510947\pi$
$233$	−13.9988	−	8.08221i	−0.917091	−	0.529483i	−0.882706	+	0.469926i	$0.844281\pi$
$234$		0			0
$235$	6.50628	−	3.75640i	0.424423	−	0.245041i
$236$	−0.627743	+	0.566844i	−0.0408626	+	0.0368984i
$237$		0			0
$238$	1.07380	−	6.81108i	0.0696038	−	0.441496i
$239$	17.3353	+	14.5461i	1.12133	+	0.940906i	0.998671	−	0.0515430i	$-0.0164139\pi$
$239$	17.3353	+	14.5461i	1.12133	+	0.940906i	0.122657	+	0.992449i	$0.460858\pi$
$240$		0			0
$241$	0.202431	+	0.0736790i	0.0130398	+	0.00474608i	0.348532	−	0.937297i	$-0.386680\pi$
$241$	0.202431	+	0.0736790i	0.0130398	+	0.00474608i	−0.335492	+	0.942043i	$0.608903\pi$
$242$	−0.970582	+	0.0176332i	−0.0623914	+	0.00113350i
$243$		0			0
$244$	15.9332	−	0.579130i	1.02002	−	0.0370750i
$245$	3.88607	−	10.6769i	0.248272	−	0.682122i
$246$		0			0
$247$	2.61448	−	3.11582i	0.166356	−	0.198255i
$248$	26.5339	+	3.20040i	1.68490	+	0.203226i
$249$		0			0
$250$	11.2859	+	12.9643i	0.713786	+	0.819936i
$251$	11.9282	+	20.6602i	0.752899	+	1.30406i	0.946412	+	0.322961i	$0.104678\pi$
$251$	11.9282	+	20.6602i	0.752899	+	1.30406i	−0.193513	+	0.981098i	$0.561988\pi$
$252$		0			0
$253$	−9.88302	+	17.1179i	−0.621340	+	1.07619i
$254$	12.1543	−	2.37155i	0.762630	−	0.148804i
$255$		0			0
$256$	−14.0841	+	7.59193i	−0.880258	+	0.474496i
$257$	0.466416	+	1.28147i	0.0290942	+	0.0799358i	0.953389	−	0.301743i	$-0.0975684\pi$
$257$	0.466416	+	1.28147i	0.0290942	+	0.0799358i	−0.924295	+	0.381679i	$0.875346\pi$
$258$		0			0
$259$	−2.42430	+	0.427469i	−0.150639	+	0.0265617i
$260$	4.37338	+	2.31738i	0.271226	+	0.143718i
$261$		0			0
$262$	−5.38774	−	8.95226i	−0.332856	−	0.553073i
$263$	13.1527	−	11.0364i	0.811028	−	0.680533i	−0.139825	−	0.990176i	$-0.544654\pi$
$263$	13.1527	−	11.0364i	0.811028	−	0.680533i	0.950853	+	0.309643i	$0.100210\pi$
$264$		0			0
$265$	−2.96115	+	16.7935i	−0.181902	+	1.03162i
$266$	2.42861	+	1.96379i	0.148908	+	0.120407i
$267$		0			0
$268$	3.49922	−	10.8219i	0.213749	−	0.661055i
$269$			8.79633i			0.536322i	0.963374	+	0.268161i	$0.0864159\pi$
$269$			8.79633i			0.536322i	−0.963374	+	0.268161i	$0.913584\pi$
$270$		0			0
$271$		−	3.18958i		−	0.193753i	−0.995296	−	0.0968765i	$-0.969115\pi$
$271$		−	3.18958i		−	0.193753i	0.995296	−	0.0968765i	$-0.0308852\pi$
$272$	7.00672	−	24.7007i	0.424845	−	1.49770i
$273$		0			0
$274$	4.81181	−	5.95075i	0.290692	−	0.359498i
$275$	−1.04326	+	5.91665i	−0.0629112	+	0.356787i
$276$		0			0
$277$	10.7101	−	8.98682i	0.643506	−	0.539966i	−0.261587	−	0.965180i	$-0.584246\pi$
$277$	10.7101	−	8.98682i	0.643506	−	0.539966i	0.905093	+	0.425214i	$0.139801\pi$
$278$	−17.6918	+	10.6475i	−1.06108	+	0.638593i
$279$		0			0
$280$	−1.71815	+	3.38995i	−0.102679	+	0.202588i
$281$	−4.62175	+	0.814938i	−0.275710	+	0.0486152i	−0.309794	−	0.950804i	$-0.600260\pi$
$281$	−4.62175	+	0.814938i	−0.275710	+	0.0486152i	0.0340833	+	0.999419i	$0.489149\pi$
$282$		0			0
$283$	1.47750	+	4.05941i	0.0878284	+	0.241307i	0.975829	−	0.218536i	$-0.0701281\pi$
$283$	1.47750	+	4.05941i	0.0878284	+	0.241307i	−0.888000	+	0.459843i	$0.847906\pi$
$284$	6.99898	−	2.83938i	0.415313	−	0.168486i
$285$		0			0
$286$	1.21678	+	6.23608i	0.0719498	+	0.368747i
$287$	2.45091	−	4.24511i	0.144673	−	0.250581i
$288$		0			0
$289$	12.1007	+	20.9590i	0.711803	+	1.23288i
$290$	−14.3084	+	12.4560i	−0.840218	+	0.731442i
$291$		0			0
$292$	3.08506	−	22.1806i	0.180540	−	1.29802i
$293$	−7.32061	+	8.72436i	−0.427674	+	0.509683i	−0.936250	−	0.351335i	$-0.885728\pi$
$293$	−7.32061	+	8.72436i	−0.427674	+	0.509683i	0.508575	+	0.861017i	$0.330172\pi$
$294$		0			0
$295$	−0.255863	+	0.702978i	−0.0148969	+	0.0409289i
$296$	−9.15289	+	0.499299i	−0.532001	+	0.0290212i
$297$		0			0
$298$	−0.0266931	−	1.46927i	−0.00154629	−	0.0851123i
$299$	−8.09107	−	2.94491i	−0.467919	−	0.170309i
$300$		0			0
$301$	−4.25822	−	3.57307i	−0.245440	−	0.205949i
$302$	−21.1862	−	3.34010i	−1.21913	−	0.192201i
$303$		0			0
$304$	8.10256	+	8.34274i	0.464714	+	0.478489i
$305$	12.2127	−	7.05099i	0.699295	−	0.403738i
$306$		0			0
$307$	18.5894	+	10.7326i	1.06095	+	0.612541i	0.925696	−	0.378269i	$-0.123481\pi$
$307$	18.5894	+	10.7326i	1.06095	+	0.612541i	0.135257	+	0.990811i	$0.456814\pi$
$308$	−4.77072	+	1.02115i	−0.271837	+	0.0581856i
$309$		0			0
$310$	22.0627	−	8.48711i	1.25308	−	0.482036i
$311$	−10.6711	+	3.88397i	−0.605103	+	0.220240i	−0.626359	−	0.779534i	$-0.715456\pi$
$311$	−10.6711	+	3.88397i	−0.605103	+	0.220240i	0.0212559	+	0.999774i	$0.493234\pi$
$312$		0			0
$313$	4.45753	+	25.2799i	0.251955	+	1.42891i	0.803770	+	0.594940i	$0.202824\pi$
$313$	4.45753	+	25.2799i	0.251955	+	1.42891i	−0.551816	+	0.833966i	$0.686065\pi$
$314$	−5.36266	+	9.69076i	−0.302632	+	0.546881i
$315$		0			0
$316$	−17.2181	+	10.7932i	−0.968591	+	0.607163i
$317$	16.0102	+	19.0802i	0.899221	+	1.07165i	0.997074	+	0.0764488i	$0.0243582\pi$
$317$	16.0102	+	19.0802i	0.899221	+	1.07165i	−0.0978526	+	0.995201i	$0.531197\pi$
$318$		0			0
$319$	−23.9829	−	4.22884i	−1.34279	−	0.236770i
$320$	−7.86332	+	11.7660i	−0.439573	+	0.657740i
$321$		0			0
$322$	2.14807	−	6.25292i	0.119707	−	0.348462i
$323$	−18.6625			−1.03841
$324$		0			0
$325$	−2.61713			−0.145172
$326$	6.83295	−	19.8903i	0.378442	−	1.10162i
$327$		0			0
$328$	10.9536	−	14.6007i	0.604809	−	0.806188i
$329$	−3.17695	−	0.560183i	−0.175151	−	0.0308839i
$330$		0			0
$331$	−20.2811	−	24.1701i	−1.11475	−	1.32851i	−0.938939	−	0.344083i	$-0.888190\pi$
$331$	−20.2811	−	24.1701i	−1.11475	−	1.32851i	−0.175811	−	0.984424i	$-0.556255\pi$
$332$	−5.27485	−	8.41482i	−0.289495	−	0.461823i
$333$		0			0
$334$	0.696820	−	1.25921i	0.0381283	−	0.0689010i
$335$	−1.74686	−	9.90692i	−0.0954410	−	0.541273i
$336$		0			0
$337$	−19.4322	+	7.07274i	−1.05854	+	0.385277i	−0.811879	−	0.583825i	$-0.801555\pi$
$337$	−19.4322	+	7.07274i	−1.05854	+	0.385277i	−0.246660	+	0.969102i	$0.579333\pi$
$338$	14.5758	−	5.60703i	0.792817	−	0.304982i
$339$		0			0
$340$	−4.75318	−	22.2063i	−0.257777	−	1.20431i
$341$	26.2801	+	15.1728i	1.42315	+	0.821655i
$342$		0			0
$343$	−8.82994	+	5.09797i	−0.476772	+	0.275264i
$344$	−14.1488	−	15.1079i	−0.762852	−	0.814562i
$345$		0			0
$346$	−10.9150	−	1.72079i	−0.586793	−	0.0925105i
$347$	−21.8999	−	18.3762i	−1.17565	−	0.986488i	−0.999998	−	0.00203559i	$-0.999352\pi$
$347$	−21.8999	−	18.3762i	−1.17565	−	0.986488i	−0.175652	−	0.984452i	$-0.556204\pi$
$348$		0			0
$349$	13.5536	+	4.93311i	0.725507	+	0.264063i	0.678262	−	0.734820i	$-0.262733\pi$
$349$	13.5536	+	4.93311i	0.725507	+	0.264063i	0.0472455	+	0.998883i	$0.484956\pi$
$350$	−0.0365038	−	2.00927i	−0.00195121	−	0.107400i
$351$		0			0
$352$	−18.0920	+	1.64780i	−0.964305	+	0.0878278i
$353$	−8.68239	+	23.8547i	−0.462117	+	1.26966i	0.461773	+	0.886998i	$0.347213\pi$
$353$	−8.68239	+	23.8547i	−0.462117	+	1.26966i	−0.923890	+	0.382658i	$0.875009\pi$
$354$		0			0
$355$	4.29413	−	5.11755i	0.227909	−	0.271611i
$356$	1.16494	+	0.162029i	0.0617414	+	0.00858751i
$357$		0			0
$358$	8.32822	−	7.25004i	0.440160	−	0.383176i
$359$	−2.61678	−	4.53239i	−0.138108	−	0.239211i	0.788672	−	0.614814i	$-0.210769\pi$
$359$	−2.61678	−	4.53239i	−0.138108	−	0.239211i	−0.926781	+	0.375603i	$0.877436\pi$
$360$		0			0
$361$	−5.27335	+	9.13371i	−0.277545	+	0.480721i
$362$	−0.787555	−	4.03627i	−0.0413930	−	0.212141i
$363$		0			0
$364$	−0.798942	−	1.96937i	−0.0418759	−	0.103223i
$365$	−6.77446	−	18.6127i	−0.354591	−	0.974232i
$366$		0			0
$367$	31.9519	−	5.63398i	1.66788	−	0.294092i	0.741574	−	0.670872i	$-0.234080\pi$
$367$	31.9519	−	5.63398i	1.66788	−	0.294092i	0.926303	+	0.376780i	$0.122969\pi$
$368$	10.7293	−	22.1583i	0.559302	−	1.15508i
$369$		0			0
$370$	−6.94660	+	4.18067i	−0.361136	+	0.217343i
$371$	5.60920	−	4.70668i	0.291215	−	0.244359i
$372$		0			0
$373$	−2.56004	+	14.5187i	−0.132554	+	0.751751i	0.843978	+	0.536378i	$0.180208\pi$
$373$	−2.56004	+	14.5187i	−0.132554	+	0.751751i	−0.976532	+	0.215373i	$0.930903\pi$
$374$	18.3301	−	22.6688i	0.947827	−	1.17217i
$375$		0			0
$376$	−11.4950	−	3.48752i	−0.592807	−	0.179855i
$377$		−	10.6084i		−	0.546363i
$378$		0			0
$379$		−	2.17390i		−	0.111666i	−0.998440	−	0.0558329i	$-0.982219\pi$
$379$		−	2.17390i		−	0.111666i	0.998440	−	0.0558329i	$-0.0177814\pi$
$380$	9.78744	+	3.16472i	0.502085	+	0.162347i
$381$		0			0
$382$	−17.4163	−	14.0829i	−0.891095	−	0.720544i
$383$	4.70816	−	26.7013i	0.240576	−	1.36437i	−0.589971	−	0.807424i	$-0.700861\pi$
$383$	4.70816	−	26.7013i	0.240576	−	1.36437i	0.830547	−	0.556949i	$-0.188028\pi$
$384$		0			0
$385$	−3.30563	+	2.77375i	−0.168470	+	0.141363i
$386$	−9.30046	−	15.4536i	−0.473381	−	0.786568i
$387$		0			0
$388$	15.8259	−	29.8667i	0.803438	−	1.51625i
$389$	−26.7645	+	4.71931i	−1.35702	+	0.239278i	−0.804365	−	0.594135i	$-0.797494\pi$
$389$	−26.7645	+	4.71931i	−1.35702	+	0.239278i	−0.552650	+	0.833414i	$0.686383\pi$
$390$		0			0
$391$	13.5121	+	37.1241i	0.683335	+	1.87745i
$392$	−16.7077	+	7.13416i	−0.843865	+	0.360330i
$393$		0			0
$394$	−10.9683	+	2.14014i	−0.552576	+	0.107819i
$395$	−8.98690	+	15.5658i	−0.452180	+	0.783199i
$396$		0			0
$397$	−4.91342	−	8.51029i	−0.246597	−	0.427119i	0.715982	−	0.698119i	$-0.245979\pi$
$397$	−4.91342	−	8.51029i	−0.246597	−	0.427119i	−0.962579	+	0.271000i	$0.912646\pi$
$398$	3.61211	+	4.14929i	0.181059	+	0.207985i
$399$		0			0
$400$	0.760984	−	7.44427i	0.0380492	−	0.372213i
$401$	5.82735	−	6.94476i	0.291004	−	0.346805i	−0.600659	−	0.799506i	$-0.705095\pi$
$401$	5.82735	−	6.94476i	0.291004	−	0.346805i	0.891663	+	0.452701i	$0.149539\pi$
$402$		0			0
$403$	−4.52115	+	12.4218i	−0.225214	+	0.618771i
$404$	−0.398238	−	10.9565i	−0.0198131	−	0.545105i
$405$		0			0
$406$	8.14453	−	0.147967i	0.404206	−	0.00734348i
$407$	−9.78023	−	3.55971i	−0.484788	−	0.176448i
$408$		0			0
$409$	21.9557	+	18.4231i	1.08564	+	0.910961i	0.996377	−	0.0850468i	$-0.0271040\pi$
$409$	21.9557	+	18.4231i	1.08564	+	0.910961i	0.0892643	+	0.996008i	$0.471548\pi$
$410$	2.51415	−	15.9472i	0.124165	−	0.787576i
$411$		0			0
$412$	8.09641	+	8.96625i	0.398881	+	0.441735i
$413$	0.278191	−	0.160614i	0.0136889	−	0.00790329i
$414$		0			0
$415$	−7.60731	−	4.39208i	−0.373428	−	0.215599i
$416$	−2.07543	−	7.63672i	−0.101756	−	0.374421i
$417$		0			0
$418$	4.74097	+	12.3244i	0.231888	+	0.602806i
$419$	−15.7950	+	5.74893i	−0.771639	+	0.280853i	−0.697682	−	0.716408i	$-0.745785\pi$
$419$	−15.7950	+	5.74893i	−0.771639	+	0.280853i	−0.0739570	+	0.997261i	$0.523563\pi$
$420$		0			0
$421$	−1.75445	−	9.94997i	−0.0855065	−	0.484932i	−0.997246	−	0.0741630i	$-0.976371\pi$
$421$	−1.75445	−	9.94997i	−0.0855065	−	0.484932i	0.911740	−	0.410769i	$-0.134740\pi$
$422$	−4.78336	−	2.64701i	−0.232850	−	0.128854i
$423$		0			0
$424$	22.8351	−	14.8988i	1.10897	−	0.723548i
$425$	7.71867	+	9.19875i	0.374410	+	0.446205i
$426$		0			0
$427$	−5.96333	−	1.05150i	−0.288586	−	0.0508854i
$428$	−6.76489	−	5.26981i	−0.326993	−	0.254726i
$429$		0			0
$430$	−17.3144	−	5.94805i	−0.834977	−	0.286840i
$431$	27.3550			1.31764			0.658822	−	0.752299i	$-0.271055\pi$
$431$	27.3550			1.31764			0.658822	+	0.752299i	$0.271055\pi$
$432$		0			0
$433$	−8.86214			−0.425887			−0.212944	−	0.977065i	$-0.568305\pi$
$433$	−8.86214			−0.425887			−0.212944	+	0.977065i	$0.568305\pi$
$434$	−9.59974	−	3.29781i	−0.460802	−	0.158300i
$435$		0			0
$436$	−7.49676	−	5.83993i	−0.359030	−	0.279682i
$437$	−17.6230	−	3.10741i	−0.843022	−	0.148648i
$438$		0			0
$439$	15.8526	+	18.8924i	0.756603	+	0.901685i	0.997628	−	0.0688344i	$-0.0219280\pi$
$439$	15.8526	+	18.8924i	0.756603	+	0.901685i	−0.241025	+	0.970519i	$0.577484\pi$
$440$	−13.4572	+	8.78018i	−0.641549	+	0.418579i
$441$		0			0
$442$	11.1113	+	6.14877i	0.528513	+	0.292467i
$443$	−2.16421	−	12.2738i	−0.102825	−	0.583147i	−0.992067	−	0.125711i	$-0.959879\pi$
$443$	−2.16421	−	12.2738i	−0.102825	−	0.583147i	0.889242	−	0.457436i	$-0.151232\pi$
$444$		0			0
$445$	0.977546	−	0.355798i	0.0463401	−	0.0168664i
$446$	11.8668	+	30.8485i	0.561911	+	1.46072i
$447$		0			0
$448$	5.83407	−	1.69991i	0.275634	−	0.0803132i
$449$	30.7560	+	17.7570i	1.45146	+	0.838003i	0.998565	−	0.0535589i	$-0.0170565\pi$
$449$	30.7560	+	17.7570i	1.45146	+	0.838003i	0.452899	+	0.891562i	$0.350390\pi$
$450$		0			0
$451$	17.9480	−	10.3623i	0.845140	−	0.487942i
$452$	12.1981	+	13.5086i	0.573752	+	0.635393i
$453$		0			0
$454$	2.33786	−	14.8290i	0.109721	−	0.695961i
$455$	−1.43997	−	1.20828i	−0.0675070	−	0.0566451i
$456$		0			0
$457$	−15.7030	−	5.71544i	−0.734557	−	0.267357i	−0.0524645	−	0.998623i	$-0.516708\pi$
$457$	−15.7030	−	5.71544i	−0.734557	−	0.267357i	−0.682092	+	0.731266i	$0.738930\pi$
$458$	−9.83695	+	0.178714i	−0.459651	+	0.00835077i
$459$		0			0
$460$	−0.790951	−	21.7609i	−0.0368783	−	1.01461i
$461$	−2.50466	+	6.88148i	−0.116653	+	0.320503i	−0.984254	−	0.176759i	$-0.943439\pi$
$461$	−2.50466	+	6.88148i	−0.116653	+	0.320503i	0.867601	+	0.497261i	$0.165661\pi$
$462$		0			0
$463$	−9.59586	+	11.4359i	−0.445957	+	0.531471i	−0.941455	−	0.337138i	$-0.890541\pi$
$463$	−9.59586	+	11.4359i	−0.445957	+	0.531471i	0.495498	+	0.868609i	$0.334986\pi$
$464$	30.1751	+	3.08463i	1.40084	+	0.143200i
$465$		0			0
$466$	15.0098	+	17.2419i	0.695313	+	0.798717i
$467$	−15.8668	−	27.4821i	−0.734227	−	1.27172i	−0.955062	−	0.296408i	$-0.904211\pi$
$467$	−15.8668	−	27.4821i	−0.734227	−	1.27172i	0.220834	−	0.975311i	$-0.429122\pi$
$468$		0			0
$469$	−2.15980	+	3.74089i	−0.0997305	+	0.172738i
$470$	−10.4281	+	2.03472i	−0.481011	+	0.0938546i
$471$		0			0
$472$	1.10005	−	0.469721i	0.0506339	−	0.0216206i
$473$	−8.03812	−	22.0846i	−0.369593	−	1.01545i
$474$		0			0
$475$	−5.35654	+	0.944502i	−0.245775	+	0.0433367i
$476$	−4.56568	+	8.61639i	−0.209268	+	0.394931i
$477$		0			0
$478$	−16.5024	−	27.4203i	−0.754801	−	1.25418i
$479$	−10.3470	+	8.68214i	−0.472765	+	0.396697i	−0.847802	−	0.530313i	$-0.822074\pi$
$479$	−10.3470	+	8.68214i	−0.472765	+	0.396697i	0.375037	+	0.927010i	$0.377630\pi$
$480$		0			0
$481$	0.787289	−	4.46494i	0.0358973	−	0.203584i
$482$	−0.236897	−	0.191556i	−0.0107904	−	0.00872515i
$483$		0			0
$484$	1.30625	+	0.422369i	0.0593749	+	0.0191986i
$485$		−	29.8960i		−	1.35751i
$486$		0			0
$487$		−	21.1864i		−	0.960045i	−0.877256	−	0.480023i	$-0.840628\pi$
$487$		−	21.1864i		−	0.960045i	0.877256	−	0.480023i	$-0.159372\pi$
$488$	−21.5767	−	6.54627i	−0.976731	−	0.296336i
$489$		0			0
$490$	−10.1033	+	12.4947i	−0.456421	+	0.564454i
$491$	−3.43573	+	19.4850i	−0.155052	+	0.879346i	0.803685	+	0.595055i	$0.202870\pi$
$491$	−3.43573	+	19.4850i	−0.155052	+	0.879346i	−0.958738	+	0.284292i	$0.908242\pi$
$492$		0			0
$493$	−37.2869	+	31.2874i	−1.67932	+	1.40911i
$494$	−4.92848	+	2.96611i	−0.221743	+	0.133452i
$495$		0			0
$496$	−34.0184	−	16.4720i	−1.52747	−	0.739616i
$497$	−2.82499	+	0.498122i	−0.126718	+	0.0223438i
$498$		0			0
$499$	−10.0691	−	27.6648i	−0.450757	−	1.23844i	−0.932192	−	0.361963i	$-0.882107\pi$
$499$	−10.0691	−	27.6648i	−0.450757	−	1.23844i	0.481435	−	0.876482i	$-0.340116\pi$
$500$	−9.13814	−	22.5252i	−0.408670	−	1.00736i
$501$		0			0
$502$	−6.46109	−	33.1135i	−0.288373	−	1.47793i
$503$	15.3565	−	26.5983i	0.684714	−	1.18596i	−0.288812	−	0.957386i	$-0.593260\pi$
$503$	15.3565	−	26.5983i	0.684714	−	1.18596i	0.973527	−	0.228574i	$-0.0734063\pi$
$504$		0			0
$505$	−4.84861	−	8.39803i	−0.215760	−	0.373707i
$506$	21.0836	−	18.3541i	0.937282	−	0.815940i
$507$		0			0
$508$	−17.3460	−	2.41262i	−0.769603	−	0.107043i
$509$	8.64363	−	10.3011i	0.383122	−	0.456587i	−0.539675	−	0.841873i	$-0.681453\pi$
$509$	8.64363	−	10.3011i	0.383122	−	0.456587i	0.922797	+	0.385286i	$0.125897\pi$
$510$		0			0
$511$	−2.90892	+	7.99219i	−0.128683	+	0.353554i
$512$	22.3257	−	3.68292i	0.986665	−	0.162763i
$513$		0			0
$514$	−0.0350319	−	1.92826i	−0.00154519	−	0.0850518i
$515$	10.0408	+	3.65457i	0.442452	+	0.161039i
$516$		0			0
$517$	−10.4482	−	8.76709i	−0.459512	−	0.385576i
$518$	3.43889	+	0.542156i	0.151096	+	0.0238210i
$519$		0			0
$520$	−4.78460	−	5.10892i	−0.209819	−	0.224041i
$521$	−9.44955	+	5.45570i	−0.413992	+	0.239018i	−0.692504	−	0.721414i	$-0.743492\pi$
$521$	−9.44955	+	5.45570i	−0.413992	+	0.239018i	0.278511	+	0.960433i	$0.410159\pi$
$522$		0			0
$523$	−16.1086	−	9.30028i	−0.704378	−	0.406673i	0.104598	−	0.994515i	$-0.466644\pi$
$523$	−16.1086	−	9.30028i	−0.704378	−	0.406673i	−0.808976	+	0.587842i	$0.799978\pi$
$524$	3.09277	+	14.4491i	0.135108	+	0.631212i
$525$		0			0
$526$	−22.6625	+	8.71784i	−0.988131	+	0.380116i
$527$	56.9945	−	20.7443i	2.48272	−	0.903636i
$528$		0			0
$529$	2.58419	+	14.6557i	0.112356	+	0.637203i
$530$	11.6766	−	21.1006i	0.507200	−	0.916553i
$531$		0			0
$532$	−2.34595	−	3.74242i	−0.101710	−	0.162255i
$533$	5.80303	+	6.91578i	0.251357	+	0.299556i
$534$		0			0
$535$	−7.46941	−	1.31706i	−0.322931	−	0.0569414i
$536$	−9.65254	+	12.8665i	−0.416926	+	0.555747i
$537$		0			0
$538$	4.04165	−	11.7650i	0.174248	−	0.507226i
$539$	−20.6274			−0.888486
$540$		0			0
$541$	16.5311			0.710730			0.355365	−	0.934728i	$-0.384357\pi$
$541$	16.5311			0.710730			0.355365	+	0.934728i	$0.384357\pi$
$542$	−1.46552	+	4.26604i	−0.0629493	+	0.183242i
$543$		0			0
$544$	−20.7207	+	29.8177i	−0.888392	+	1.27842i
$545$	−8.27750	−	1.45955i	−0.354569	−	0.0625201i
$546$		0			0
$547$	6.26046	+	7.46092i	0.267678	+	0.319006i	0.883094	−	0.469196i	$-0.155456\pi$
$547$	6.26046	+	7.46092i	0.267678	+	0.319006i	−0.615416	+	0.788203i	$0.711012\pi$
$548$	−9.16995	+	5.74821i	−0.391721	+	0.245551i
$549$		0			0
$550$	4.11388	−	7.43412i	0.175417	−	0.316992i
$551$	−3.82851	−	21.7126i	−0.163100	−	0.924986i
$552$		0			0
$553$	7.25242	−	2.63967i	0.308404	−	0.112250i
$554$	−18.4538	+	7.09885i	−0.784028	+	0.301601i
$555$		0			0
$556$	28.5549	−	6.11205i	1.21100	−	0.259209i
$557$	16.9093	+	9.76261i	0.716471	+	0.413655i	0.813453	−	0.581631i	$-0.197585\pi$
$557$	16.9093	+	9.76261i	0.716471	+	0.413655i	−0.0969812	+	0.995286i	$0.530919\pi$
$558$		0			0
$559$	8.86613	−	5.11886i	0.374997	−	0.216505i
$560$	3.85559	−	3.74459i	0.162928	−	0.158238i
$561$		0			0
$562$	6.55599	+	1.03358i	0.276548	+	0.0435990i
$563$	−0.0372524	−	0.0312585i	−0.00157000	−	0.00131739i	0.642002	−	0.766703i	$-0.278104\pi$
$563$	−0.0372524	−	0.0312585i	−0.00157000	−	0.00131739i	−0.643572	+	0.765385i	$0.722548\pi$
$564$		0			0
$565$	15.1276	+	5.50601i	0.636424	+	0.231640i
$566$	−0.110973	−	6.10829i	−0.00466456	−	0.256751i
$567$		0			0
$568$	−10.6657	+	0.581823i	−0.447522	+	0.0244128i
$569$	−7.64048	+	20.9921i	−0.320306	+	0.880033i	0.670153	+	0.742223i	$0.266228\pi$
$569$	−7.64048	+	20.9921i	−0.320306	+	0.880033i	−0.990459	+	0.137810i	$0.955994\pi$
$570$		0			0
$571$	−4.92260	+	5.86652i	−0.206004	+	0.245506i	−0.859147	−	0.511728i	$-0.829006\pi$
$571$	−4.92260	+	5.86652i	−0.206004	+	0.245506i	0.653143	+	0.757234i	$0.273450\pi$
$572$	1.23786	−	8.89978i	0.0517573	−	0.372119i
$573$		0			0
$574$	−5.22858	+	4.55168i	−0.218237	+	0.189983i
$575$	5.75711	+	9.97161i	0.240088	+	0.415845i
$576$		0			0
$577$	−0.594755	+	1.03015i	−0.0247600	+	0.0428855i	−0.878140	−	0.478404i	$-0.841215\pi$
$577$	−0.594755	+	1.03015i	−0.0247600	+	0.0428855i	0.853380	+	0.521289i	$0.174549\pi$
$578$	−6.55453	−	33.5923i	−0.272632	−	1.39726i
$579$		0			0
$580$	24.8606	−	10.0855i	1.03228	−	0.418779i
$581$	1.29006	+	3.54441i	0.0535207	+	0.147047i
$582$		0			0
$583$	30.4879	−	5.37583i	1.26268	−	0.222644i
$584$	−14.3176	+	28.2489i	−0.592465	+	1.16895i
$585$		0			0
$586$	13.7998	−	8.30517i	0.570066	−	0.343083i
$587$	−9.17272	+	7.69683i	−0.378599	+	0.317682i	−0.812152	−	0.583446i	$-0.801704\pi$
$587$	−9.17272	+	7.69683i	−0.378599	+	0.317682i	0.433553	+	0.901128i	$0.357260\pi$
$588$		0			0
$589$	−4.77062	+	27.0556i	−0.196570	+	1.11480i
$590$	0.665212	−	0.822666i	0.0273864	−	0.0338686i
$591$		0			0
$592$	12.4713	+	3.53767i	0.512569	+	0.145397i
$593$		−	33.8346i		−	1.38942i	−0.719290	−	0.694710i	$-0.755533\pi$
$593$		−	33.8346i		−	1.38942i	0.719290	−	0.694710i	$-0.244467\pi$
$594$		0			0
$595$			8.62484i			0.353584i
$596$	−0.639382	+	1.97740i	−0.0261901	+	0.0809974i
$597$		0			0
$598$	9.46865	+	7.65640i	0.387202	+	0.313094i
$599$	0.818715	−	4.64316i	0.0334518	−	0.189714i	−0.963503	−	0.267698i	$-0.913737\pi$
$599$	0.818715	−	4.64316i	0.0334518	−	0.189714i	0.996955	+	0.0779836i	$0.0248482\pi$
$600$		0			0
$601$	12.8107	−	10.7495i	0.522560	−	0.438480i	−0.342963	−	0.939349i	$-0.611431\pi$
$601$	12.8107	−	10.7495i	0.522560	−	0.438480i	0.865523	+	0.500869i	$0.166986\pi$
$602$	4.05362	+	6.73549i	0.165213	+	0.274518i
$603$		0			0
$604$	26.8018	+	14.2018i	1.09055	+	0.577863i
$605$	1.19580	−	0.210852i	0.0486163	−	0.00857236i
$606$		0			0
$607$	−8.69910	−	23.9006i	−0.353086	−	0.970095i	−0.981373	−	0.192113i	$-0.938466\pi$
$607$	−8.69910	−	23.9006i	−0.353086	−	0.970095i	0.628287	−	0.777982i	$-0.283756\pi$
$608$	−7.00387	−	14.8812i	−0.284045	−	0.603514i
$609$		0			0
$610$	−19.5741	+	3.81929i	−0.792531	+	0.154638i
$611$	2.97070	−	5.14540i	0.120182	−	0.208161i
$612$		0			0
$613$	23.0173	+	39.8671i	0.929658	+	1.61022i	0.783893	+	0.620896i	$0.213231\pi$
$613$	23.0173	+	39.8671i	0.929658	+	1.61022i	0.145765	+	0.989319i	$0.453436\pi$
$614$	−19.9319	−	22.8960i	−0.804385	−	0.924009i
$615$		0			0
$616$	6.84999	+	0.826217i	0.275994	+	0.0332892i
$617$	−0.105965	+	0.126285i	−0.00426601	+	0.00508403i	−0.768173	−	0.640242i	$-0.778834\pi$
$617$	−0.105965	+	0.126285i	−0.00426601	+	0.00508403i	0.763907	+	0.645326i	$0.223278\pi$
$618$		0			0
$619$	−4.71817	+	12.9631i	−0.189639	+	0.521029i	−0.997679	−	0.0680991i	$-0.978307\pi$
$619$	−4.71817	+	12.9631i	−0.189639	+	0.521029i	0.808039	+	0.589129i	$0.200529\pi$
$620$	−33.4083	+	1.21430i	−1.34171	+	0.0487675i
$621$		0			0
$622$	16.0571	−	0.291720i	0.643831	−	0.0116969i
$623$	−0.419754	−	0.152778i	−0.0168171	−	0.00612092i
$624$		0			0
$625$	−9.30469	−	7.80756i	−0.372187	−	0.312302i
$626$	5.65345	−	35.8598i	0.225957	−	1.43325i
$627$		0			0
$628$	11.6251	−	10.4973i	0.463893	−	0.418890i
$629$	−18.0154	+	10.4012i	−0.718322	+	0.414724i
$630$		0			0
$631$	−28.8999	−	16.6854i	−1.15049	−	0.664234i	−0.201481	−	0.979492i	$-0.564575\pi$
$631$	−28.8999	−	16.6854i	−1.15049	−	0.664234i	−0.949006	+	0.315259i	$0.897909\pi$
$632$	27.9882	−	6.52461i	1.11331	−	0.259535i
$633$		0			0
$634$	−12.6467	−	32.8758i	−0.502265	−	1.30567i
$635$	−14.5557	+	5.29785i	−0.577627	+	0.210239i
$636$		0			0
$637$	−1.56033	−	8.84905i	−0.0618224	−	0.350612i
$638$	30.1340	+	16.6755i	1.19302	+	0.660189i
$639$		0			0
$640$	15.9233	−	12.1240i	0.629423	−	0.479243i
$641$	−28.8323	−	34.3610i	−1.13881	−	1.35718i	−0.924849	−	0.380334i	$-0.875809\pi$
$641$	−28.8323	−	34.3610i	−1.13881	−	1.35718i	−0.213957	−	0.976843i	$-0.568635\pi$
$642$		0			0
$643$	27.3680	+	4.82571i	1.07929	+	0.190307i	0.684900	−	0.728637i	$-0.259846\pi$
$643$	27.3680	+	4.82571i	1.07929	+	0.190307i	0.394387	+	0.918945i	$0.370957\pi$
$644$	−5.74606	+	7.37626i	−0.226427	+	0.290665i
$645$		0			0
$646$	24.9609	+	8.57484i	0.982073	+	0.337373i
$647$	−29.6395			−1.16525			−0.582624	−	0.812742i	$-0.697974\pi$
$647$	−29.6395			−1.16525			−0.582624	+	0.812742i	$0.697974\pi$
$648$		0			0
$649$	1.35813			0.0533113
$650$	3.50039	+	1.20249i	0.137297	+	0.0471656i
$651$		0			0
$652$	−18.2780	+	23.4637i	−0.715824	+	0.918908i
$653$	9.33752	+	1.64646i	0.365405	+	0.0644308i	0.353336	−	0.935496i	$-0.385047\pi$
$653$	9.33752	+	1.64646i	0.365405	+	0.0644308i	0.0120690	+	0.999927i	$0.496158\pi$
$654$		0			0
$655$	8.40088	+	10.0118i	0.328250	+	0.391193i
$656$	−21.3589	+	14.4955i	−0.833924	+	0.565953i
$657$		0			0
$658$	3.99177	+	2.20896i	0.155615	+	0.0861141i
$659$	7.20764	+	40.8765i	0.280770	+	1.59232i	0.720016	+	0.693957i	$0.244134\pi$
$659$	7.20764	+	40.8765i	0.280770	+	1.59232i	−0.439246	+	0.898367i	$0.644754\pi$
$660$		0			0
$661$	1.38969	−	0.505806i	0.0540527	−	0.0196736i	−0.314852	−	0.949141i	$-0.601955\pi$
$661$	1.38969	−	0.505806i	0.0540527	−	0.0196736i	0.368905	+	0.929467i	$0.379733\pi$
$662$	16.0204	+	41.6459i	0.622650	+	1.61861i
$663$		0			0
$664$	3.18871	+	13.6784i	0.123746	+	0.530825i
$665$	−3.38329	−	1.95334i	−0.131198	−	0.0757474i
$666$		0			0
$667$	−40.4196	+	23.3363i	−1.56505	+	0.903584i
$668$	−1.51056	+	1.36402i	−0.0584454	+	0.0527755i
$669$		0			0
$670$	−2.21553	+	14.0531i	−0.0855932	+	0.542917i
$671$	−19.6119	−	16.4563i	−0.757109	−	0.635290i
$672$		0			0
$673$	8.11397	+	2.95324i	0.312770	+	0.113839i	0.493636	−	0.869669i	$-0.335668\pi$
$673$	8.11397	+	2.95324i	0.312770	+	0.113839i	−0.180865	+	0.983508i	$0.557890\pi$
$674$	29.2401	−	0.531224i	1.12629	−	0.0204620i
$675$		0			0
$676$	−22.0712	+	0.802230i	−0.848894	+	0.0308550i
$677$	8.60234	−	23.6347i	0.330615	−	0.908357i	−0.657337	−	0.753597i	$-0.728317\pi$
$677$	8.60234	−	23.6347i	0.330615	−	0.908357i	0.987952	−	0.154760i	$-0.0494605\pi$
$678$		0			0
$679$	−8.25160	+	9.83388i	−0.316667	+	0.377390i
$680$	−3.84581	+	31.8848i	−0.147480	+	1.22272i
$681$		0			0
$682$	−28.1780	−	32.3685i	−1.07899	−	1.23945i
$683$	−10.1910	−	17.6513i	−0.389948	−	0.675409i	0.602494	−	0.798123i	$-0.294174\pi$
$683$	−10.1910	−	17.6513i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$684$		0			0
$685$	−4.78622	+	8.28998i	−0.182872	+	0.316744i
$686$	14.1523	−	2.76140i	0.540339	−	0.105431i
$687$		0			0
$688$	11.9823	+	26.7076i	0.456821	+	1.01822i
$689$	4.61241	+	12.6725i	0.175719	+	0.482783i
$690$		0			0
$691$	−30.6309	+	5.40105i	−1.16525	+	0.205465i	−0.722625	−	0.691240i	$-0.757065\pi$
$691$	−30.6309	+	5.40105i	−1.16525	+	0.205465i	−0.442627	+	0.896706i	$0.645954\pi$
$692$	13.8081	+	7.31666i	0.524904	+	0.278138i
$693$		0			0
$694$	20.8477	+	34.6405i	0.791367	+	1.31493i
$695$	19.7857	−	16.6021i	0.750513	−	0.629755i
$696$		0			0
$697$	7.19296	−	40.7933i	0.272453	−	1.54516i
$698$	−15.8612	−	12.8255i	−0.600356	−	0.485451i
$699$		0			0
$700$	−0.874378	+	2.70416i	−0.0330484	+	0.102208i
$701$			6.46847i			0.244311i	0.992511	+	0.122155i	$0.0389806\pi$
$701$			6.46847i			0.244311i	−0.992511	+	0.122155i	$0.961019\pi$
$702$		0			0
$703$		−	9.42262i		−	0.355381i
$704$	24.9550	+	6.10881i	0.940527	+	0.230234i
$705$		0			0
$706$	22.5731	−	27.9161i	0.849551	−	1.05064i
$707$	−0.723060	+	4.10068i	−0.0271935	+	0.154222i
$708$		0			0
$709$	16.5291	−	13.8695i	0.620762	−	0.520881i	−0.277281	−	0.960789i	$-0.589433\pi$
$709$	16.5291	−	13.8695i	0.620762	−	0.520881i	0.898043	+	0.439908i	$0.144989\pi$
$710$	−8.09474	+	4.87166i	−0.303790	+	0.182830i
$711$		0			0
$712$	−1.48365	−	0.751965i	−0.0556019	−	0.0281811i
$713$	57.2741	−	10.0990i	2.14493	−	0.378209i
$714$		0			0
$715$	−2.71820	−	7.46818i	−0.101655	−	0.279294i
$716$	−14.4701	+	5.87030i	−0.540774	+	0.219383i
$717$		0			0
$718$	1.41742	+	7.26438i	0.0528977	+	0.271104i
$719$	−4.48435	+	7.76713i	−0.167238	+	0.289665i	−0.937448	−	0.348126i	$-0.886818\pi$
$719$	−4.48435	+	7.76713i	−0.167238	+	0.289665i	0.770210	+	0.637791i	$0.220152\pi$
$720$		0			0
$721$	−2.29410	−	3.97349i	−0.0854366	−	0.147980i
$722$	11.2497	−	9.79332i	0.418672	−	0.364470i
$723$		0			0
$724$	−0.801195	+	5.76033i	−0.0297762	+	0.214081i
$725$	−9.11871	+	10.8673i	−0.338660	+	0.403600i
$726$		0			0
$727$	13.6111	−	37.3961i	0.504807	−	1.38694i	−0.381725	−	0.924276i	$-0.624670\pi$
$727$	13.6111	−	37.3961i	0.504807	−	1.38694i	0.886531	−	0.462669i	$-0.153108\pi$
$728$	0.163713	+	3.00111i	0.00606762	+	0.111228i
$729$		0			0
$730$	0.508821	+	28.0070i	0.0188323	+	1.03658i
$731$	−44.1407	−	16.0659i	−1.63260	−	0.594219i
$732$		0			0
$733$	24.7179	+	20.7408i	0.912978	+	0.766079i	0.972683	−	0.232137i	$-0.0745717\pi$
$733$	24.7179	+	20.7408i	0.912978	+	0.766079i	−0.0597054	+	0.998216i	$0.519016\pi$
$734$	−45.3241	−	7.14554i	−1.67294	−	0.263747i
$735$		0			0
$736$	−24.5314	+	24.7068i	−0.904240	+	0.910704i
$737$	−15.8162	+	9.13151i	−0.582599	+	0.336364i
$738$		0			0
$739$	45.5964	+	26.3251i	1.67729	+	0.968384i	0.963378	+	0.268148i	$0.0864118\pi$
$739$	45.5964	+	26.3251i	1.67729	+	0.968384i	0.713912	+	0.700235i	$0.246922\pi$
$740$	11.2119	−	2.39987i	0.412158	−	0.0882209i
$741$		0			0
$742$	−9.66485	+	3.71789i	−0.354808	+	0.136488i
$743$	6.92256	−	2.51961i	0.253964	−	0.0924354i	−0.211901	−	0.977291i	$-0.567965\pi$
$743$	6.92256	−	2.51961i	0.253964	−	0.0924354i	0.465865	+	0.884856i	$0.345743\pi$
$744$		0			0
$745$	0.319188	+	1.81020i	0.0116941	+	0.0663208i
$746$	10.0950	−	18.2424i	0.369603	−	0.667902i
$747$		0			0
$748$	−34.9320	+	21.8972i	−1.27724	+	0.800641i
$749$	2.09344	+	2.49486i	0.0764925	+	0.0911602i
$750$		0			0
$751$	41.5769	+	7.33112i	1.51716	+	0.267516i	0.869316	−	0.494256i	$-0.164559\pi$
$751$	41.5769	+	7.33112i	1.51716	+	0.267516i	0.647845	+	0.761772i	$0.275671\pi$
$752$	13.7720	+	9.94612i	0.502213	+	0.362698i
$753$		0			0
$754$	−4.87426	+	14.1887i	−0.177510	+	0.516723i
$755$	26.8280			0.976373
$756$		0			0
$757$	−18.7376			−0.681028			−0.340514	−	0.940239i	$-0.610601\pi$
$757$	−18.7376			−0.681028			−0.340514	+	0.940239i	$0.610601\pi$
$758$	−0.998843	+	2.90758i	−0.0362796	+	0.105608i
$759$		0			0
$760$	−11.6365	−	8.72983i	−0.422102	−	0.316664i
$761$	8.62082	+	1.52008i	0.312504	+	0.0551030i	0.327701	−	0.944782i	$-0.393726\pi$
$761$	8.62082	+	1.52008i	0.312504	+	0.0551030i	−0.0151963	+	0.999885i	$0.504837\pi$
$762$		0			0
$763$	2.31992	+	2.76477i	0.0839866	+	0.100091i
$764$	16.8235	+	26.8380i	0.608652	+	0.970966i
$765$		0			0
$766$	−18.5656	+	33.5496i	−0.670802	+	1.21219i
$767$	0.102734	+	0.582631i	0.00370949	+	0.0210376i
$768$		0			0
$769$	−22.0844	+	8.03807i	−0.796385	+	0.289860i	−0.707987	−	0.706225i	$-0.750397\pi$
$769$	−22.0844	+	8.03807i	−0.796385	+	0.289860i	−0.0883971	+	0.996085i	$0.528174\pi$
$770$	5.69571	−	2.19104i	0.205259	−	0.0789594i
$771$		0			0
$772$	5.33882	+	24.9424i	0.192148	+	0.897696i
$773$	−13.5604	−	7.82910i	−0.487733	−	0.281593i	0.235900	−	0.971777i	$-0.424196\pi$
$773$	−13.5604	−	7.82910i	−0.487733	−	0.281593i	−0.723634	+	0.690184i	$0.757529\pi$
$774$		0			0
$775$	15.3088	−	8.83855i	0.549909	−	0.317490i
$776$	−34.8899	+	32.6750i	−1.25247	+	1.17296i
$777$		0			0
$778$	37.9657	+	5.98546i	1.36114	+	0.214589i
$779$	14.3730	+	12.0604i	0.514968	+	0.432109i
$780$		0			0
$781$	−11.3967	−	4.14806i	−0.407807	−	0.148429i
$782$	−1.01487	−	55.8617i	−0.0362919	−	1.99761i
$783$		0			0
$784$	25.6243	−	1.86521i	0.915155	−	0.0666148i
$785$	4.73831	−	13.0184i	0.169117	−	0.464646i
$786$		0			0
$787$	10.4059	−	12.4012i	0.370929	−	0.442056i	−0.548000	−	0.836478i	$-0.684611\pi$
$787$	10.4059	−	12.4012i	0.370929	−	0.442056i	0.918929	+	0.394422i	$0.129055\pi$
$788$	15.6534	+	2.17720i	0.557629	+	0.0775596i
$789$		0			0
$790$	19.1719	−	16.6899i	0.682106	−	0.593800i
$791$	−3.45631	−	5.98650i	−0.122892	−	0.212856i
$792$		0			0
$793$	5.57617	−	9.65821i	0.198016	−	0.342973i
$794$	2.66144	+	13.6400i	0.0944508	+	0.484066i
$795$		0			0
$796$	−2.92470	−	7.20930i	−0.103663	−	0.255527i
$797$	10.1430	+	27.8675i	0.359282	+	0.987119i	0.979279	+	0.202515i	$0.0649115\pi$
$797$	10.1430	+	27.8675i	0.359282	+	0.987119i	−0.619997	+	0.784604i	$0.712866\pi$
$798$		0			0
$799$	−26.8467	+	4.73379i	−0.949766	+	0.167469i
$800$	−4.43823	+	9.60701i	−0.156915	+	0.339659i
$801$		0			0
$802$	−10.9850	+	6.61108i	−0.387892	+	0.233445i
$803$	−27.5463	+	23.1141i	−0.972086	+	0.815677i
$804$		0			0
$805$	−1.43609	+	8.14445i	−0.0506154	+	0.287054i
$806$	11.7544	−	14.5367i	0.414032	−	0.512032i
$807$		0			0
$808$	−4.50154	+	14.8372i	−0.158363	+	0.521971i
$809$			28.2066i			0.991690i	0.868411	+	0.495845i	$0.165142\pi$
$809$			28.2066i			0.991690i	−0.868411	+	0.495845i	$0.834858\pi$
$810$		0			0
$811$			28.0396i			0.984605i	0.870424	+	0.492302i	$0.163845\pi$
$811$			28.0396i			0.984605i	−0.870424	+	0.492302i	$0.836155\pi$
$812$	−10.9612	−	3.54426i	−0.384664	−	0.124379i
$813$		0			0
$814$	11.4454	+	9.25482i	0.401161	+	0.324381i
$815$	−4.56815	+	25.9073i	−0.160015	+	0.907492i
$816$		0			0
$817$	16.2992	−	13.6766i	0.570236	−	0.478484i
$818$	−20.9008	−	34.7287i	−0.730779	−	1.21426i
$819$		0			0
$820$	−10.6899	+	20.1741i	−0.373308	+	0.704510i
$821$	−29.2028	+	5.14925i	−1.01919	+	0.179710i	−0.658186	−	0.752856i	$-0.728676\pi$
$821$	−29.2028	+	5.14925i	−1.01919	+	0.179710i	−0.361001	+	0.932566i	$0.617565\pi$
$822$		0			0
$823$	4.18887	+	11.5088i	0.146015	+	0.401172i	0.991042	−	0.133551i	$-0.0426380\pi$
$823$	4.18887	+	11.5088i	0.146015	+	0.401172i	−0.845027	+	0.534723i	$0.820416\pi$
$824$	−6.70916	−	15.7123i	−0.233725	−	0.547366i
$825$		0			0
$826$	−0.445876	+	0.0869992i	−0.0155140	+	0.00302709i
$827$	−5.15219	+	8.92386i	−0.179159	+	0.310313i	−0.941593	−	0.336754i	$-0.890671\pi$
$827$	−5.15219	+	8.92386i	−0.179159	+	0.310313i	0.762434	+	0.647067i	$0.224004\pi$
$828$		0			0
$829$	−20.0735	−	34.7684i	−0.697183	−	1.20756i	−0.969439	−	0.245332i	$-0.921103\pi$
$829$	−20.0735	−	34.7684i	−0.697183	−	1.20756i	0.272256	−	0.962225i	$-0.412230\pi$
$830$	8.15669	+	9.36971i	0.283123	+	0.325227i
$831$		0			0
$832$	−0.732967	+	11.1677i	−0.0254111	+	0.387169i
$833$	−26.5010	+	31.5827i	−0.918207	+	1.09428i
$834$		0			0
$835$	−0.615693	+	1.69160i	−0.0213069	+	0.0585403i
$836$	−0.678318	−	18.6621i	−0.0234601	−	0.645443i
$837$		0			0
$838$	23.7672	−	0.431795i	0.821025	−	0.0149161i
$839$	45.6141	+	16.6022i	1.57477	+	0.573171i	0.974059	−	0.226293i	$-0.0726605\pi$
$839$	45.6141	+	16.6022i	1.57477	+	0.573171i	0.600715	+	0.799463i	$0.294883\pi$
$840$		0			0
$841$	−21.8348	−	18.3216i	−0.752924	−	0.631778i
$842$	−2.22515	+	14.1141i	−0.0766838	+	0.486405i
$843$		0			0
$844$	5.18149	+	5.73817i	0.178354	+	0.197516i
$845$	−16.9174	+	9.76726i	−0.581976	+	0.336004i
$846$		0			0
$847$	−0.451540	−	0.260697i	−0.0155151	−	0.00895764i
$848$	−37.3873	+	9.43494i	−1.28389	+	0.323997i
$849$		0			0
$850$	−6.09711	−	15.8498i	−0.209129	−	0.543642i
$851$	−18.7439	+	6.82221i	−0.642532	+	0.233862i
$852$		0			0
$853$	1.86794	+	10.5936i	0.0639571	+	0.362719i	0.999943	+	0.0106811i	$0.00339997\pi$
$853$	1.86794	+	10.5936i	0.0639571	+	0.362719i	−0.935986	+	0.352038i	$0.885489\pi$
$854$	7.49278	+	4.14634i	0.256398	+	0.141885i
$855$		0			0
$856$	6.62667	+	10.1566i	0.226495	+	0.347145i
$857$	−2.17923	−	2.59711i	−0.0744411	−	0.0887154i	0.727539	−	0.686067i	$-0.240664\pi$
$857$	−2.17923	−	2.59711i	−0.0744411	−	0.0887154i	−0.801980	+	0.597351i	$0.796220\pi$
$858$		0			0
$859$	−19.3027	−	3.40359i	−0.658601	−	0.116129i	−0.165648	−	0.986185i	$-0.552971\pi$
$859$	−19.3027	−	3.40359i	−0.658601	−	0.116129i	−0.492953	+	0.870056i	$0.664083\pi$
$860$	20.4250	+	15.9109i	0.696487	+	0.542559i
$861$		0			0
$862$	−36.5871	−	12.5688i	−1.24616	−	0.428095i
$863$	48.0692			1.63629			0.818147	−	0.575009i	$-0.195001\pi$
$863$	48.0692			1.63629			0.818147	+	0.575009i	$0.195001\pi$
$864$		0			0
$865$	13.8216			0.469949
$866$	11.8530	+	4.07189i	0.402783	+	0.138368i
$867$		0			0
$868$	11.3243	+	8.82159i	0.384373	+	0.299424i
$869$	32.1349	+	5.66625i	1.09010	+	0.192214i
$870$		0			0
$871$	−5.11377	−	6.09435i	−0.173273	−	0.206499i
$872$	7.34359	+	11.2554i	0.248685	+	0.381156i
$873$		0			0
$874$	22.1429	+	12.2534i	0.748994	+	0.414477i
$875$	1.60314	+	9.09184i	0.0541959	+	0.307360i
$876$		0			0
$877$	44.6403	−	16.2477i	1.50740	−	0.548647i	0.549432	−	0.835538i	$-0.314844\pi$
$877$	44.6403	−	16.2477i	1.50740	−	0.548647i	0.957963	+	0.286891i	$0.0926218\pi$
$878$	−12.5222	−	32.5522i	−0.422605	−	1.09858i
$879$		0			0
$880$	22.0332	−	5.56022i	0.742739	−	0.187435i
$881$	9.71356	+	5.60813i	0.327258	+	0.188943i	0.654623	−	0.755955i	$-0.272827\pi$
$881$	9.71356	+	5.60813i	0.327258	+	0.188943i	−0.327365	+	0.944898i	$0.606161\pi$
$882$		0			0
$883$	−7.49573	+	4.32766i	−0.252251	+	0.145637i	−0.620795	−	0.783973i	$-0.713190\pi$
$883$	−7.49573	+	4.32766i	−0.252251	+	0.145637i	0.368543	+	0.929611i	$0.379857\pi$
$884$	−12.0362	−	13.3293i	−0.404820	−	0.448312i
$885$		0			0
$886$	−2.74485	+	17.4105i	−0.0922150	+	0.584919i
$887$	24.9250	+	20.9145i	0.836899	+	0.702242i	0.956864	−	0.290537i	$-0.0938338\pi$
$887$	24.9250	+	20.9145i	0.836899	+	0.702242i	−0.119965	+	0.992778i	$0.538278\pi$
$888$		0			0
$889$	6.25016	+	2.27487i	0.209624	+	0.0762968i
$890$	−1.47094	+	0.0267235i	−0.0493060	+	0.000895774i
$891$		0			0
$892$	−1.69786	−	46.7120i	−0.0568484	−	1.56404i
$893$	4.22326	−	11.6033i	0.141326	−	0.388290i
$894$		0			0
$895$	−8.87796	+	10.5803i	−0.296757	+	0.353662i
$896$	−8.58408	−	0.406962i	−0.286774	−	0.0135956i
$897$		0			0
$898$	−32.9771	−	37.8813i	−1.10046	−	1.26411i
$899$	35.8268	+	62.0538i	1.19489	+	2.06961i
$900$		0			0
$901$	30.9383	−	53.5867i	1.03070	−	1.78523i
$902$	−28.7665	+	5.61292i	−0.957821	+	0.186890i
$903$		0			0
$904$	−10.1081	−	23.6724i	−0.336190	−	0.787332i
$905$	1.75934	+	4.83374i	0.0584823	+	0.160679i
$906$		0			0
$907$	−39.7192	+	7.00356i	−1.31885	+	0.232549i	−0.788399	−	0.615164i	$-0.789090\pi$
$907$	−39.7192	+	7.00356i	−1.31885	+	0.232549i	−0.530454	+	0.847714i	$0.677979\pi$
$908$	−9.94037	+	18.7595i	−0.329883	+	0.622557i
$909$		0			0
$910$	1.37079	+	2.27769i	0.0454411	+	0.0755048i
$911$	35.3881	−	29.6941i	1.17246	−	0.983810i	0.172460	−	0.985016i	$-0.444828\pi$
$911$	35.3881	−	29.6941i	1.17246	−	0.983810i	0.999999	+	0.00120596i	$0.000383868\pi$
$912$		0			0
$913$	−2.76921	+	15.7050i	−0.0916476	+	0.519759i
$914$	18.3766	+	14.8594i	0.607845	+	0.491506i
$915$		0			0
$916$	13.2390	+	4.28076i	0.437428	+	0.141440i
$917$		−	5.61196i		−	0.185323i
$918$		0			0
$919$		−	1.23662i		−	0.0407922i	−0.999792	−	0.0203961i	$-0.993507\pi$
$919$		−	1.23662i		−	0.0407922i	0.999792	−	0.0203961i	$-0.00649274\pi$
$920$	−8.94061	+	29.4685i	−0.294763	+	0.971548i
$921$		0			0
$922$	6.51180	−	8.05312i	0.214455	−	0.265215i
$923$	0.917412	−	5.20290i	0.0301970	−	0.171256i
$924$		0			0
$925$	−4.64442	+	3.89714i	−0.152708	+	0.128137i
$926$	18.0888	−	10.8864i	0.594436	−	0.357750i
$927$		0			0
$928$	−38.9417	−	17.9902i	−1.27832	−	0.590558i
$929$	25.3343	−	4.46711i	0.831190	−	0.146561i	0.258167	−	0.966100i	$-0.416882\pi$
$929$	25.3343	−	4.46711i	0.831190	−	0.146561i	0.573023	+	0.819539i	$0.305770\pi$
$930$		0			0
$931$	−6.38712	−	17.5485i	−0.209329	−	0.575128i
$932$	−12.1533	−	29.9575i	−0.398094	−	0.981290i
$933$		0			0
$934$	8.59451	+	44.0474i	0.281221	+	1.44127i
$935$	−18.2326	+	31.5798i	−0.596271	+	1.03277i
$936$		0			0
$937$	−13.9758	−	24.2068i	−0.456569	−	0.790801i	0.542208	−	0.840244i	$-0.317588\pi$
$937$	−13.9758	−	24.2068i	−0.456569	−	0.790801i	−0.998777	+	0.0494437i	$0.984255\pi$
$938$	4.60755	−	4.01105i	0.150442	−	0.130965i
$939$		0			0
$940$	14.8824	+	2.06996i	0.485409	+	0.0675147i
$941$	31.6771	−	37.7513i	1.03264	−	1.23066i	0.0600392	−	0.998196i	$-0.480877\pi$
$941$	31.6771	−	37.7513i	1.03264	−	1.23066i	0.972605	−	0.232462i	$-0.0746781\pi$
$942$		0			0
$943$	13.5846	−	37.3235i	0.442377	−	1.21542i
$944$	−1.68713	+	0.122808i	−0.0549115	+	0.00399705i
$945$		0			0
$946$	0.603733	+	33.2312i	0.0196291	+	1.08044i
$947$	26.5813	+	9.67481i	0.863777	+	0.314389i	0.735644	−	0.677368i	$-0.236879\pi$
$947$	26.5813	+	9.67481i	0.863777	+	0.314389i	0.128133	+	0.991757i	$0.459102\pi$
$948$		0			0
$949$	−11.9995	−	10.0688i	−0.389520	−	0.326846i
$950$	7.59830	+	1.19790i	0.246521	+	0.0388652i
$951$		0			0
$952$	10.0655	−	9.42656i	0.326226	−	0.305517i
$953$	−18.2626	+	10.5439i	−0.591583	+	0.341551i	−0.765723	−	0.643170i	$-0.777619\pi$
$953$	−18.2626	+	10.5439i	−0.591583	+	0.341551i	0.174140	+	0.984721i	$0.444285\pi$
$954$		0			0
$955$	24.2626	+	14.0080i	0.785119	+	0.453289i
$956$	9.47300	+	44.2568i	0.306379	+	1.43137i
$957$		0			0
$958$	17.8282	−	6.85817i	0.576002	−	0.221578i
$959$	3.86248	−	1.40583i	0.124726	−	0.0453965i
$960$		0			0
$961$	−10.1213	−	57.4005i	−0.326492	−	1.85163i
$962$	−3.10450	+	5.61009i	−0.100093	+	0.180876i
$963$		0			0
$964$	0.228834	+	0.365052i	0.00737024	+	0.0117575i
$965$	14.5018	+	17.2826i	0.466829	+	0.556346i
$966$		0			0
$967$	9.89451	+	1.74467i	0.318186	+	0.0561048i	0.330460	−	0.943820i	$-0.392796\pi$
$967$	9.89451	+	1.74467i	0.318186	+	0.0561048i	−0.0122743	+	0.999925i	$0.503907\pi$
$968$	−1.55303	−	1.16510i	−0.0499163	−	0.0374477i
$969$		0			0
$970$	−13.7363	+	39.9857i	−0.441047	+	1.28386i
$971$	−38.1342			−1.22378			−0.611892	−	0.790942i	$-0.709591\pi$
$971$	−38.1342			−1.22378			−0.611892	+	0.790942i	$0.709591\pi$
$972$		0			0
$973$	−11.0906			−0.355547
$974$	−9.73450	+	28.3366i	−0.311914	+	0.907963i
$975$		0			0
$976$	25.8509	+	18.6694i	0.827466	+	0.597594i
$977$	−5.93135	−	1.04586i	−0.189761	−	0.0334599i	0.0779601	−	0.996956i	$-0.475159\pi$
$977$	−5.93135	−	1.04586i	−0.189761	−	0.0334599i	−0.267721	+	0.963497i	$0.586270\pi$
$978$		0			0
$979$	−1.21396	−	1.44674i	−0.0387984	−	0.0462381i
$980$	19.2541	−	12.0694i	0.615048	−	0.385544i
$981$		0			0
$982$	13.5481	−	24.4824i	0.432336	−	0.781266i
$983$	−0.386949	−	2.19450i	−0.0123417	−	0.0699935i	0.978015	−	0.208535i	$-0.0668696\pi$
$983$	−0.386949	−	2.19450i	−0.0123417	−	0.0699935i	−0.990357	+	0.138542i	$0.955758\pi$
$984$		0			0
$985$	13.1354	−	4.78090i	0.418529	−	0.152332i
$986$	64.2465	−	24.7145i	2.04603	−	0.787069i
$987$		0			0
$988$	7.95465	−	1.70266i	0.253071	−	0.0541689i
$989$	−39.0071	−	22.5208i	−1.24035	−	0.716119i
$990$		0			0
$991$	29.4685	−	17.0137i	0.936098	−	0.540457i	0.0473631	−	0.998878i	$-0.484918\pi$
$991$	29.4685	−	17.0137i	0.936098	−	0.540457i	0.888735	+	0.458421i	$0.151585\pi$
$992$	37.9309	+	37.6616i	1.20431	+	1.19576i
$993$		0			0
$994$	4.00728	+	0.631764i	0.127103	+	0.0200383i
$995$	−5.27134	−	4.42318i	−0.167113	−	0.140224i
$996$		0			0
$997$	−44.3114	−	16.1280i	−1.40336	−	0.510780i	−0.474185	−	0.880425i	$-0.657257\pi$
$997$	−44.3114	−	16.1280i	−1.40336	−	0.510780i	−0.929173	+	0.369645i	$0.879479\pi$
$998$	0.756281	+	41.6279i	0.0239396	+	1.31771i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.539.2		96
3.2	odd	2		972.2.l.c.539.15		96
4.3	odd	2	inner	972.2.l.b.539.14		96
9.2	odd	6		972.2.l.d.215.7		96
9.4	even	3		324.2.l.a.287.13		96
9.5	odd	6		108.2.l.a.59.4	yes	96
9.7	even	3		972.2.l.a.215.10		96
12.11	even	2		972.2.l.c.539.3		96
27.2	odd	18		324.2.l.a.35.4		96
27.7	even	9		972.2.l.c.431.3		96
27.11	odd	18		972.2.l.a.755.9		96
27.16	even	9		972.2.l.d.755.8		96
27.20	odd	18	inner	972.2.l.b.431.14		96
27.25	even	9		108.2.l.a.11.13	yes	96
36.7	odd	6		972.2.l.a.215.9		96
36.11	even	6		972.2.l.d.215.8		96
36.23	even	6		108.2.l.a.59.13	yes	96
36.31	odd	6		324.2.l.a.287.4		96
108.7	odd	18		972.2.l.c.431.15		96
108.11	even	18		972.2.l.a.755.10		96
108.43	odd	18		972.2.l.d.755.7		96
108.47	even	18	inner	972.2.l.b.431.2		96
108.79	odd	18		108.2.l.a.11.4	✓	96
108.83	even	18		324.2.l.a.35.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.4	✓	96	108.79	odd	18
108.2.l.a.11.13	yes	96	27.25	even	9
108.2.l.a.59.4	yes	96	9.5	odd	6
108.2.l.a.59.13	yes	96	36.23	even	6
324.2.l.a.35.4		96	27.2	odd	18
324.2.l.a.35.13		96	108.83	even	18
324.2.l.a.287.4		96	36.31	odd	6
324.2.l.a.287.13		96	9.4	even	3
972.2.l.a.215.9		96	36.7	odd	6
972.2.l.a.215.10		96	9.7	even	3
972.2.l.a.755.9		96	27.11	odd	18
972.2.l.a.755.10		96	108.11	even	18
972.2.l.b.431.2		96	108.47	even	18	inner
972.2.l.b.431.14		96	27.20	odd	18	inner
972.2.l.b.539.2		96	1.1	even	1	trivial
972.2.l.b.539.14		96	4.3	odd	2	inner
972.2.l.c.431.3		96	27.7	even	9
972.2.l.c.431.15		96	108.7	odd	18
972.2.l.c.539.3		96	12.11	even	2
972.2.l.c.539.15		96	3.2	odd	2
972.2.l.d.215.7		96	9.2	odd	6
972.2.l.d.215.8		96	36.11	even	6
972.2.l.d.755.7		96	108.43	odd	18
972.2.l.d.755.8		96	27.16	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33749 - 0.459470i) q^{2} +(1.57777 + 1.22908i) q^{4} +(1.74209 + 0.307177i) q^{5} +(-0.488252 - 0.581876i) q^{7} +(-1.54554 - 2.36882i) q^{8} +O(q^{10})\)	\(q+(-1.33749 - 0.459470i) q^{2} +(1.57777 + 1.22908i) q^{4} +(1.74209 + 0.307177i) q^{5} +(-0.488252 - 0.581876i) q^{7} +(-1.54554 - 2.36882i) q^{8} +(-2.18889 - 1.21129i) q^{10} +(-0.557667 - 3.16269i) q^{11} +(1.31459 - 0.478472i) q^{13} +(0.385679 + 1.00259i) q^{14} +(0.978743 + 3.87841i) q^{16} +(-5.55887 - 3.20941i) q^{17} +(2.51793 - 1.45373i) q^{19} +(2.37108 + 2.62582i) q^{20} +(-0.707285 + 4.48630i) q^{22} +(-4.71486 - 3.95624i) q^{23} +(-1.75794 - 0.639840i) q^{25} +(-1.97810 + 0.0359374i) q^{26} +(-0.0551813 - 1.51817i) q^{28} +(2.59357 - 7.12578i) q^{29} +(-6.07378 + 7.23845i) q^{31} +(0.472953 - 5.63705i) q^{32} +(5.96031 + 6.84670i) q^{34} +(-0.671839 - 1.16366i) q^{35} +(1.62042 - 2.80666i) q^{37} +(-4.03566 + 0.787437i) q^{38} +(-1.96482 - 4.60145i) q^{40} +(2.20716 + 6.06412i) q^{41} +(7.20692 - 1.27077i) q^{43} +(3.00731 - 5.67542i) q^{44} +(4.48832 + 7.45778i) q^{46} +(3.25340 - 2.72993i) q^{47} +(1.11535 - 6.32545i) q^{49} +(2.05725 + 1.66350i) q^{50} +(2.66221 + 0.860813i) q^{52} +9.63986i q^{53} -5.68099i q^{55} +(-0.623748 + 2.05589i) q^{56} +(-6.74296 + 8.33901i) q^{58} +(-0.0734356 + 0.416474i) q^{59} +(6.10682 - 5.12423i) q^{61} +(11.4495 - 6.89065i) q^{62} +(-3.22263 + 7.32220i) q^{64} +(2.43711 - 0.429729i) q^{65} +(-1.94500 - 5.34384i) q^{67} +(-4.82602 - 11.8960i) q^{68} +(0.363913 + 1.86508i) q^{70} +(1.88825 - 3.27054i) q^{71} +(-5.59853 - 9.69694i) q^{73} +(-3.45688 + 3.00935i) q^{74} +(5.75947 + 0.801075i) q^{76} +(-1.56801 + 1.86868i) q^{77} +(-3.47514 + 9.54787i) q^{79} +(0.513698 + 7.05719i) q^{80} +(-0.165777 - 9.12484i) q^{82} +(-4.66624 - 1.69837i) q^{83} +(-8.69818 - 7.29864i) q^{85} +(-10.2231 - 1.61171i) q^{86} +(-6.62994 + 6.20907i) q^{88} +(0.509288 - 0.294037i) q^{89} +(-0.920264 - 0.531314i) q^{91} +(-2.57647 - 12.0370i) q^{92} +(-5.60572 + 2.15642i) q^{94} +(4.83301 - 1.75907i) q^{95} +(-2.93471 - 16.6435i) q^{97} +(-4.39813 + 7.94778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38} - 12 q^{40} - 66 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 66 q^{50} - 24 q^{52} + 81 q^{56} - 24 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} + 42 q^{65} - 51 q^{68} - 30 q^{70} - 6 q^{73} + 96 q^{74} - 9 q^{76} - 30 q^{77} - 12 q^{82} + 66 q^{85} - 141 q^{86} - 45 q^{88} + 24 q^{92} - 51 q^{94} + 42 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Introduction

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