LMFDB - Embedded newform 675.2.r.a.631.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] 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("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			631.10
Character	$\chi$	$=$	675.631
Dual form			675.2.r.a.46.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.721003 + 0.800755i) q^{2} +(0.0876938 + 0.834351i) q^{4} +(-2.23594 - 0.0235208i) q^{5} +(0.316483 + 0.548165i) q^{7} +(-2.47480 - 1.79805i) q^{8} +(1.63096 - 1.77348i) q^{10} +(3.49321 - 3.87960i) q^{11} +(-2.54696 - 2.82868i) q^{13} +(-0.667131 - 0.141803i) q^{14} +(1.58291 - 0.336458i) q^{16} +(0.365368 + 0.265455i) q^{17} +(-3.97313 - 2.88665i) q^{19} +(-0.176454 - 1.86763i) q^{20} +(0.587996 + 5.59441i) q^{22} +(-0.100362 - 0.0213327i) q^{23} +(4.99889 + 0.105182i) q^{25} +4.10144 q^{26} +(-0.429608 + 0.312129i) q^{28} +(9.17597 + 4.08540i) q^{29} +(3.69032 - 1.64304i) q^{31} +(2.18716 - 3.78828i) q^{32} +(-0.475995 + 0.101176i) q^{34} +(-0.694745 - 1.23311i) q^{35} +(0.0800637 - 0.246411i) q^{37} +(5.17614 - 1.10022i) q^{38} +(5.49123 + 4.07855i) q^{40} +(-5.23896 - 5.81846i) q^{41} +(3.68846 + 6.38860i) q^{43} +(3.54328 + 2.57435i) q^{44} +(0.0894437 - 0.0649846i) q^{46} +(-9.67748 - 4.30869i) q^{47} +(3.29968 - 5.71521i) q^{49} +(-3.68844 + 3.92705i) q^{50} +(2.13676 - 2.37311i) q^{52} +(4.56626 - 3.31758i) q^{53} +(-7.90187 + 8.59241i) q^{55} +(0.202394 - 1.92565i) q^{56} +(-9.88730 + 4.40211i) q^{58} +(-4.79365 - 5.32388i) q^{59} +(3.08519 - 3.42646i) q^{61} +(-1.34506 + 4.13967i) q^{62} +(2.45668 + 7.56088i) q^{64} +(5.62832 + 6.38468i) q^{65} +(3.18608 - 1.41853i) q^{67} +(-0.189442 + 0.328124i) q^{68} +(1.48833 + 0.332755i) q^{70} +(3.47832 - 2.52715i) q^{71} +(-4.75735 - 14.6416i) q^{73} +(0.139588 + 0.241774i) q^{74} +(2.06006 - 3.56813i) q^{76} +(3.23220 + 0.687026i) q^{77} +(1.24677 + 0.555098i) q^{79} +(-3.54721 + 0.715070i) q^{80} +8.43646 q^{82} +(0.223611 - 2.12752i) q^{83} +(-0.810698 - 0.602136i) q^{85} +(-7.77509 - 1.65265i) q^{86} +(-15.6207 + 3.32029i) q^{88} +(5.42929 + 16.7096i) q^{89} +(0.744515 - 2.29138i) q^{91} +(0.00899778 - 0.0856081i) q^{92} +(10.4277 - 4.64271i) q^{94} +(8.81581 + 6.54784i) q^{95} +(-5.56983 - 2.47985i) q^{97} +(2.19740 + 6.76291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.721003	+	0.800755i	−0.509826	+	0.566219i	−0.942018	−	0.335563i	$-0.891074\pi$
$2$	−0.721003	+	0.800755i	−0.509826	+	0.566219i	0.432192	+	0.901782i	$0.357740\pi$
$3$		0			0
$3$		0			0
$4$	0.0876938	+	0.834351i	0.0438469	+	0.417176i
$5$	−2.23594	−	0.0235208i	−0.999945	−	0.0105188i
$5$	−2.23594	−	0.0235208i	−0.999945	−	0.0105188i
$6$		0			0
$7$	0.316483	+	0.548165i	0.119619	+	0.207187i	0.919617	−	0.392817i	$-0.128499\pi$
$7$	0.316483	+	0.548165i	0.119619	+	0.207187i	−0.799998	+	0.600003i	$0.795166\pi$
$8$	−2.47480	−	1.79805i	−0.874976	−	0.635707i
$9$		0			0
$10$	1.63096	−	1.77348i	0.515754	−	0.560825i
$11$	3.49321	−	3.87960i	1.05324	−	1.16974i	0.0681573	−	0.997675i	$-0.478288\pi$
$11$	3.49321	−	3.87960i	1.05324	−	1.16974i	0.985085	−	0.172069i	$-0.0550453\pi$
$12$		0			0
$13$	−2.54696	−	2.82868i	−0.706399	−	0.784535i	0.277982	−	0.960586i	$-0.410334\pi$
$13$	−2.54696	−	2.82868i	−0.706399	−	0.784535i	−0.984381	+	0.176051i	$0.943668\pi$
$14$	−0.667131	−	0.141803i	−0.178298	−	0.0378984i
$15$		0			0
$16$	1.58291	−	0.336458i	0.395728	−	0.0841145i
$17$	0.365368	+	0.265455i	0.0886146	+	0.0643823i	0.631210	−	0.775612i	$-0.282558\pi$
$17$	0.365368	+	0.265455i	0.0886146	+	0.0643823i	−0.542596	+	0.839994i	$0.682558\pi$
$18$		0			0
$19$	−3.97313	−	2.88665i	−0.911499	−	0.662243i	0.0298945	−	0.999553i	$-0.490483\pi$
$19$	−3.97313	−	2.88665i	−0.911499	−	0.662243i	−0.941394	+	0.337310i	$0.890483\pi$
$20$	−0.176454	−	1.86763i	−0.0394563	−	0.417614i
$21$		0			0
$22$	0.587996	+	5.59441i	0.125361	+	1.19273i
$23$	−0.100362	−	0.0213327i	−0.0209270	−	0.00444817i	0.197436	−	0.980316i	$-0.436738\pi$
$23$	−0.100362	−	0.0213327i	−0.0209270	−	0.00444817i	−0.218363	+	0.975868i	$0.570072\pi$
$24$		0			0
$25$	4.99889	+	0.105182i	0.999779	+	0.0210365i
$26$	4.10144			0.804359
$27$		0			0
$28$	−0.429608	+	0.312129i	−0.0811883	+	0.0589868i
$29$	9.17597	+	4.08540i	1.70393	+	0.758640i	0.998769	+	0.0495967i	$0.0157936\pi$
$29$	9.17597	+	4.08540i	1.70393	+	0.758640i	0.705165	+	0.709044i	$0.250873\pi$
$30$		0			0
$31$	3.69032	−	1.64304i	0.662801	−	0.295098i	−0.0476300	−	0.998865i	$-0.515167\pi$
$31$	3.69032	−	1.64304i	0.662801	−	0.295098i	0.710431	+	0.703767i	$0.248500\pi$
$32$	2.18716	−	3.78828i	0.386640	−	0.669680i
$33$		0			0
$34$	−0.475995	+	0.101176i	−0.0816325	+	0.0173515i
$35$	−0.694745	−	1.23311i	−0.117433	−	0.208434i
$36$		0			0
$37$	0.0800637	−	0.246411i	0.0131624	−	0.0405097i	−0.944260	−	0.329202i	$-0.893220\pi$
$37$	0.0800637	−	0.246411i	0.0131624	−	0.0405097i	0.957422	+	0.288692i	$0.0932204\pi$
$38$	5.17614	−	1.10022i	0.839680	−	0.178480i
$39$		0			0
$40$	5.49123	+	4.07855i	0.868240	+	0.644876i
$41$	−5.23896	−	5.81846i	−0.818188	−	0.908690i	0.178983	−	0.983852i	$-0.442719\pi$
$41$	−5.23896	−	5.81846i	−0.818188	−	0.908690i	−0.997171	+	0.0751620i	$0.976053\pi$
$42$		0			0
$43$	3.68846	+	6.38860i	0.562485	+	0.974253i	0.997279	+	0.0737227i	$0.0234880\pi$
$43$	3.68846	+	6.38860i	0.562485	+	0.974253i	−0.434794	+	0.900530i	$0.643179\pi$
$44$	3.54328	+	2.57435i	0.534170	+	0.388097i
$45$		0			0
$46$	0.0894437	−	0.0649846i	0.0131878	−	0.00958146i
$47$	−9.67748	−	4.30869i	−1.41161	−	0.628487i	−0.447567	−	0.894250i	$-0.647709\pi$
$47$	−9.67748	−	4.30869i	−1.41161	−	0.628487i	−0.964038	+	0.265763i	$0.914376\pi$
$48$		0			0
$49$	3.29968	−	5.71521i	0.471382	−	0.816458i
$50$	−3.68844	+	3.92705i	−0.521624	+	0.555369i
$51$		0			0
$52$	2.13676	−	2.37311i	0.296316	−	0.329092i
$53$	4.56626	−	3.31758i	0.627224	−	0.455705i	−0.228213	−	0.973611i	$-0.573288\pi$
$53$	4.56626	−	3.31758i	0.627224	−	0.455705i	0.855437	+	0.517906i	$0.173288\pi$
$54$		0			0
$55$	−7.90187	+	8.59241i	−1.06549	+	1.15860i
$56$	0.202394	−	1.92565i	0.0270461	−	0.257326i
$57$		0			0
$58$	−9.88730	+	4.40211i	−1.29827	+	0.578025i
$59$	−4.79365	−	5.32388i	−0.624079	−	0.693110i	0.345352	−	0.938473i	$-0.387760\pi$
$59$	−4.79365	−	5.32388i	−0.624079	−	0.693110i	−0.969431	+	0.245363i	$0.921093\pi$
$60$		0			0
$61$	3.08519	−	3.42646i	0.395019	−	0.438713i	−0.512524	−	0.858673i	$-0.671289\pi$
$61$	3.08519	−	3.42646i	0.395019	−	0.438713i	0.907542	+	0.419960i	$0.137956\pi$
$62$	−1.34506	+	4.13967i	−0.170823	+	0.525739i
$63$		0			0
$64$	2.45668	+	7.56088i	0.307085	+	0.945110i
$65$	5.62832	+	6.38468i	0.698107	+	0.791922i
$66$		0			0
$67$	3.18608	−	1.41853i	0.389241	−	0.173301i	−0.202779	−	0.979225i	$-0.564997\pi$
$67$	3.18608	−	1.41853i	0.389241	−	0.173301i	0.592020	+	0.805923i	$0.298331\pi$
$68$	−0.189442	+	0.328124i	−0.0229732	+	0.0397908i
$69$		0			0
$70$	1.48833	+	0.332755i	0.177890	+	0.0397718i
$71$	3.47832	−	2.52715i	0.412801	−	0.299917i	−0.361934	−	0.932204i	$-0.617883\pi$
$71$	3.47832	−	2.52715i	0.412801	−	0.299917i	0.774735	+	0.632286i	$0.217883\pi$
$72$		0			0
$73$	−4.75735	−	14.6416i	−0.556806	−	1.71367i	−0.691126	−	0.722734i	$-0.742885\pi$
$73$	−4.75735	−	14.6416i	−0.556806	−	1.71367i	0.134320	−	0.990938i	$-0.457115\pi$
$74$	0.139588	+	0.241774i	0.0162268	+	0.0281057i
$75$		0			0
$76$	2.06006	−	3.56813i	0.236305	−	0.409292i
$77$	3.23220	+	0.687026i	0.368344	+	0.0782938i
$78$		0			0
$79$	1.24677	+	0.555098i	0.140273	+	0.0624534i	0.475673	−	0.879622i	$-0.342205\pi$
$79$	1.24677	+	0.555098i	0.140273	+	0.0624534i	−0.335400	+	0.942076i	$0.608871\pi$
$80$	−3.54721	+	0.715070i	−0.396591	+	0.0799473i
$81$		0			0
$82$	8.43646			0.931651
$83$	0.223611	−	2.12752i	0.0245445	−	0.233525i	−0.975372	−	0.220568i	$-0.929209\pi$
$83$	0.223611	−	2.12752i	0.0245445	−	0.233525i	0.999916	−	0.0129571i	$-0.00412447\pi$
$84$		0			0
$85$	−0.810698	−	0.602136i	−0.0879325	−	0.0653109i
$86$	−7.77509	−	1.65265i	−0.838410	−	0.178210i
$87$		0			0
$88$	−15.6207	+	3.32029i	−1.66518	+	0.353944i
$89$	5.42929	+	16.7096i	0.575504	+	1.77122i	0.634457	+	0.772958i	$0.281224\pi$
$89$	5.42929	+	16.7096i	0.575504	+	1.77122i	−0.0589537	+	0.998261i	$0.518776\pi$
$90$		0			0
$91$	0.744515	−	2.29138i	0.0780464	−	0.240202i
$92$	0.00899778	−	0.0856081i	0.000938083	−	0.00892526i
$93$		0			0
$94$	10.4277	−	4.64271i	1.07553	−	0.478859i
$95$	8.81581	+	6.54784i	0.904483	+	0.671794i
$96$		0			0
$97$	−5.56983	−	2.47985i	−0.565531	−	0.251791i	0.103997	−	0.994578i	$-0.466837\pi$
$97$	−5.56983	−	2.47985i	−0.565531	−	0.251791i	−0.669528	+	0.742787i	$0.733503\pi$
$98$	2.19740	+	6.76291i	0.221971	+	0.683157i
$99$		0			0
$100$	0.350613	+	4.18006i	0.0350613	+	0.418006i
$101$	−1.98334	−	3.43524i	−0.197350	−	0.341820i	0.750319	−	0.661076i	$-0.229900\pi$
$101$	−1.98334	−	3.43524i	−0.197350	−	0.341820i	−0.947668	+	0.319257i	$0.896567\pi$
$102$		0			0
$103$	−0.119994	−	1.14167i	−0.0118234	−	0.112492i	0.987018	−	0.160607i	$-0.0513452\pi$
$103$	−0.119994	−	1.14167i	−0.0118234	−	0.112492i	−0.998842	+	0.0481151i	$0.984679\pi$
$104$	1.21711	+	11.5800i	0.119347	+	1.13551i
$105$		0			0
$106$	−0.635717	+	6.04844i	−0.0617462	+	0.587476i
$107$	−4.10301			−0.396653			−0.198326	−	0.980136i	$-0.563551\pi$
$107$	−4.10301			−0.396653			−0.198326	+	0.980136i	$0.563551\pi$
$108$		0			0
$109$	0.0306236	−	0.0942499i	0.00293321	−	0.00902750i	−0.949579	−	0.313527i	$-0.898489\pi$
$109$	0.0306236	−	0.0942499i	0.00293321	−	0.00902750i	0.952512	+	0.304500i	$0.0984893\pi$
$110$	−1.18314	−	12.5226i	−0.112808	−	1.19398i
$111$		0			0
$112$	0.685399	+	0.761212i	0.0647641	+	0.0719278i
$113$	−8.89638	−	9.88043i	−0.836901	−	0.929473i	0.161450	−	0.986881i	$-0.448383\pi$
$113$	−8.89638	−	9.88043i	−0.836901	−	0.929473i	−0.998351	+	0.0574080i	$0.981716\pi$
$114$		0			0
$115$	0.223903	+	0.0500592i	0.0208790	+	0.00466805i
$116$	−2.60399	+	8.01424i	−0.241774	+	0.744104i
$117$		0			0
$118$	7.71936			0.710624
$119$	−0.0298805	+	0.284294i	−0.00273914	+	0.0260612i
$120$		0			0
$121$	−1.69899	−	16.1648i	−0.154453	−	1.46953i
$122$	0.519317	+	4.94097i	0.0470167	+	0.447334i
$123$		0			0
$124$	1.69449	+	2.93494i	0.152169	+	0.263565i
$125$	−11.1748	−	0.352760i	−0.999502	−	0.0315518i
$126$		0			0
$127$	1.73383	+	5.33620i	0.153853	+	0.473511i	0.998043	−	0.0625335i	$-0.0199180\pi$
$127$	1.73383	+	5.33620i	0.153853	+	0.473511i	−0.844190	+	0.536044i	$0.819918\pi$
$128$	0.166613	+	0.0741808i	0.0147266	+	0.00655672i
$129$		0			0
$130$	−9.17060	−	0.0964691i	−0.804315	−	0.00846090i
$131$	5.01793	−	2.23413i	0.438418	−	0.195196i	−0.175644	−	0.984454i	$-0.556201\pi$
$131$	5.01793	−	2.23413i	0.438418	−	0.195196i	0.614063	+	0.789257i	$0.289534\pi$
$132$		0			0
$133$	0.324930	−	3.09151i	0.0281750	−	0.268068i
$134$	−1.16127	+	3.57403i	−0.100319	+	0.308749i
$135$		0			0
$136$	−0.426912	−	1.31390i	−0.0366074	−	0.112666i
$137$	−9.73009	+	2.06819i	−0.831298	+	0.176698i	−0.603856	−	0.797094i	$-0.706370\pi$
$137$	−9.73009	+	2.06819i	−0.831298	+	0.176698i	−0.227442	+	0.973792i	$0.573036\pi$
$138$		0			0
$139$	−4.21294	−	0.895488i	−0.357337	−	0.0759543i	0.0257454	−	0.999669i	$-0.491804\pi$
$139$	−4.21294	−	0.895488i	−0.357337	−	0.0759543i	−0.383082	+	0.923714i	$0.625137\pi$
$140$	0.967922	−	0.687798i	0.0818043	−	0.0581295i
$141$		0			0
$142$	−0.484253	+	4.60736i	−0.0406376	+	0.386641i
$143$	−19.8712			−1.66171
$144$		0			0
$145$	−20.4209	−	9.35056i	−1.69586	−	0.776522i
$146$	15.1544	+	6.74718i	1.25419	+	0.558400i
$147$		0			0
$148$	0.212614	+	0.0451925i	0.0174768	+	0.00371480i
$149$	0.0389321	−	0.0674323i	0.00318944	−	0.00552427i	−0.864426	−	0.502760i	$-0.832318\pi$
$149$	0.0389321	−	0.0674323i	0.00318944	−	0.00552427i	0.867616	+	0.497235i	$0.165651\pi$
$150$		0			0
$151$	−8.59717	−	14.8907i	−0.699628	−	1.21179i	−0.968595	−	0.248642i	$-0.920016\pi$
$151$	−8.59717	−	14.8907i	−0.699628	−	1.21179i	0.268968	−	0.963149i	$-0.413318\pi$
$152$	4.64238	+	14.2878i	0.376547	+	1.15889i
$153$		0			0
$154$	−2.88057	+	2.09285i	−0.232123	+	0.168647i
$155$	−8.28999	+	3.58694i	−0.665868	+	0.288110i
$156$		0			0
$157$	−5.71800	+	9.90387i	−0.456346	+	0.790415i	−0.998765	−	0.0496936i	$-0.984176\pi$
$157$	−5.71800	+	9.90387i	−0.456346	+	0.790415i	0.542418	+	0.840109i	$0.317509\pi$
$158$	−1.34342	+	0.598130i	−0.106877	+	0.0475847i
$159$		0			0
$160$	−4.97948	+	8.41894i	−0.393663	+	0.665576i
$161$	−0.0200691	−	0.0617665i	−0.00158167	−	0.00486788i
$162$		0			0
$163$	1.40825	−	4.33413i	0.110302	−	0.339476i	−0.880636	−	0.473793i	$-0.842884\pi$
$163$	1.40825	−	4.33413i	0.110302	−	0.339476i	0.990938	+	0.134318i	$0.0428843\pi$
$164$	4.39521	−	4.88138i	0.343208	−	0.381171i
$165$		0			0
$166$	1.54239	+	1.71300i	0.119713	+	0.132955i
$167$	−13.6779	+	6.08979i	−1.05843	+	0.471242i	−0.860751	−	0.509025i	$-0.830006\pi$
$167$	−13.6779	+	6.08979i	−1.05843	+	0.471242i	−0.197675	+	0.980268i	$0.563339\pi$
$168$		0			0
$169$	−0.155583	+	1.48028i	−0.0119679	+	0.113867i
$170$	1.06668	−	0.215028i	0.0818105	−	0.0164919i
$171$		0			0
$172$	−5.00688	+	3.63771i	−0.381771	+	0.277373i
$173$	−2.39115	+	2.65564i	−0.181796	+	0.201905i	−0.827154	−	0.561975i	$-0.810042\pi$
$173$	−2.39115	+	2.65564i	−0.181796	+	0.201905i	0.645358	+	0.763880i	$0.276708\pi$
$174$		0			0
$175$	1.52441	+	2.77351i	0.115234	+	0.209657i
$176$	4.22411	−	7.31638i	0.318405	−	0.551493i
$177$		0			0
$178$	−17.2949	−	7.70017i	−1.29630	−	0.577152i
$179$	17.6257	−	12.8058i	1.31741	−	0.957151i	0.317445	−	0.948277i	$-0.397175\pi$
$179$	17.6257	−	12.8058i	1.31741	−	0.957151i	0.999961	−	0.00887412i	$-0.00282476\pi$
$180$		0			0
$181$	14.5760	+	10.5901i	1.08343	+	0.787155i	0.978277	−	0.207302i	$-0.0664682\pi$
$181$	14.5760	+	10.5901i	1.08343	+	0.787155i	0.105148	+	0.994457i	$0.466468\pi$
$182$	1.29804	+	2.24827i	0.0962169	+	0.166653i
$183$		0			0
$184$	0.210020	+	0.233251i	0.0154829	+	0.0171955i
$185$	−0.184814	+	0.549078i	−0.0135878	+	0.0403690i
$186$		0			0
$187$	2.30617	−	0.490191i	0.168643	−	0.0358463i
$188$	2.74631	−	8.45226i	0.200295	−	0.616445i
$189$		0			0
$190$	−11.5994	+	2.33829i	−0.841511	+	0.169637i
$191$	9.98949	−	2.12333i	0.722814	−	0.153639i	0.168207	−	0.985752i	$-0.446202\pi$
$191$	9.98949	−	2.12333i	0.722814	−	0.153639i	0.554606	+	0.832113i	$0.312869\pi$
$192$		0			0
$193$	−6.35646	+	11.0097i	−0.457548	+	0.792496i	−0.998831	−	0.0483444i	$-0.984605\pi$
$193$	−6.35646	+	11.0097i	−0.457548	+	0.792496i	0.541283	+	0.840841i	$0.317939\pi$
$194$	6.00162	−	2.67209i	0.430891	−	0.191845i
$195$		0			0
$196$	5.05785	+	2.25190i	0.361275	+	0.160850i
$197$	−5.47291	+	3.97630i	−0.389929	+	0.283300i	−0.765426	−	0.643524i	$-0.777472\pi$
$197$	−5.47291	+	3.97630i	−0.389929	+	0.283300i	0.375498	+	0.926823i	$0.377472\pi$
$198$		0			0
$199$	7.09600			0.503022			0.251511	−	0.967854i	$-0.419073\pi$
$199$	7.09600			0.503022			0.251511	+	0.967854i	$0.419073\pi$
$200$	−12.1822	−	9.24857i	−0.861409	−	0.653973i
$201$		0			0
$202$	4.18078	+	0.888652i	0.294159	+	0.0625254i
$203$	0.664564	+	6.32290i	0.0466432	+	0.443781i
$204$		0			0
$205$	11.5772	+	13.1330i	0.808585	+	0.917246i
$206$	1.00071	+	0.727061i	0.0697230	+	0.0506567i
$207$		0			0
$208$	−4.98334	−	3.62061i	−0.345532	−	0.251044i
$209$	−25.0780	+	5.33050i	−1.73468	+	0.368718i
$210$		0			0
$211$	−25.9163	−	5.50868i	−1.78415	−	0.379233i	−0.806795	−	0.590831i	$-0.798800\pi$
$211$	−25.9163	−	5.50868i	−1.78415	−	0.379233i	−0.977357	+	0.211598i	$0.932133\pi$
$212$	3.16846	+	3.51893i	0.217611	+	0.241681i
$213$		0			0
$214$	2.95828	−	3.28550i	0.202224	−	0.224592i
$215$	−8.09693	−	14.3713i	−0.552206	−	0.980116i
$216$		0			0
$217$	2.06858	+	1.50291i	0.140424	+	0.102024i
$218$	0.0533913	+	0.0924764i	0.00361611	+	0.00626329i
$219$		0			0
$220$	−7.86203	−	5.83943i	−0.530058	−	0.393695i
$221$	−0.179687	−	1.70961i	−0.0120871	−	0.115001i
$222$		0			0
$223$	2.63479	−	2.92623i	0.176438	−	0.195955i	−0.648439	−	0.761267i	$-0.724578\pi$
$223$	2.63479	−	2.92623i	0.176438	−	0.195955i	0.824877	+	0.565312i	$0.191244\pi$
$224$	2.76880			0.184998
$225$		0			0
$226$	14.3261			0.952959
$227$	16.1638	−	17.9518i	1.07283	−	1.19150i	0.0921803	−	0.995742i	$-0.470616\pi$
$227$	16.1638	−	17.9518i	1.07283	−	1.19150i	0.980652	−	0.195759i	$-0.0627169\pi$
$228$		0			0
$229$	1.58289	+	15.0602i	0.104601	+	0.995208i	0.913383	+	0.407100i	$0.133460\pi$
$229$	1.58289	+	15.0602i	0.104601	+	0.995208i	−0.808783	+	0.588107i	$0.799873\pi$
$230$	−0.201520	+	0.143198i	−0.0132878	+	0.00944221i
$231$		0			0
$232$	−15.3630	−	26.6094i	−1.00863	−	1.74699i
$233$	−10.3302	−	7.50529i	−0.676751	−	0.491688i	0.195527	−	0.980698i	$-0.437358\pi$
$233$	−10.3302	−	7.50529i	−0.676751	−	0.491688i	−0.872278	+	0.489010i	$0.837358\pi$
$234$		0			0
$235$	21.5370	+	9.86162i	1.40492	+	0.643301i
$236$	4.02161	−	4.46646i	0.261785	−	0.290742i
$237$		0			0
$238$	−0.206106	−	0.228903i	−0.0133598	−	0.0148376i
$239$	−12.5453	−	2.66658i	−0.811485	−	0.172487i	−0.216562	−	0.976269i	$-0.569484\pi$
$239$	−12.5453	−	2.66658i	−0.811485	−	0.172487i	−0.594923	+	0.803782i	$0.702818\pi$
$240$		0			0
$241$	−27.0379	+	5.74709i	−1.74167	+	0.370203i	−0.965516	−	0.260345i	$-0.916164\pi$
$241$	−27.0379	+	5.74709i	−1.74167	+	0.370203i	−0.776151	+	0.630548i	$0.782830\pi$
$242$	14.1690	+	10.2944i	0.910817	+	0.661748i
$243$		0			0
$244$	3.12942	+	2.27366i	0.200341	+	0.145556i
$245$	−7.51232	+	12.7013i	−0.479945	+	0.811455i
$246$		0			0
$247$	1.95398	+	18.5909i	0.124329	+	1.18291i
$248$	−12.0871	−	2.56919i	−0.767530	−	0.163144i
$249$		0			0
$250$	8.33952	−	8.69391i	0.527437	−	0.549851i
$251$	2.88989			0.182408			0.0912042	−	0.995832i	$-0.470928\pi$
$251$	2.88989			0.182408			0.0912042	+	0.995832i	$0.470928\pi$
$252$		0			0
$253$	−0.433349	+	0.314846i	−0.0272444	+	0.0197942i
$254$	−5.52308	−	2.45903i	−0.346549	−	0.154294i
$255$		0			0
$256$	−14.7049	+	6.54703i	−0.919054	+	0.409189i
$257$	−3.00243	+	5.20037i	−0.187287	+	0.324390i	−0.944345	−	0.328958i	$-0.893303\pi$
$257$	−3.00243	+	5.20037i	−0.187287	+	0.324390i	0.757058	+	0.653348i	$0.226636\pi$
$258$		0			0
$259$	0.160412	−	0.0340967i	0.00996755	−	0.00211867i
$260$	−4.83350	+	5.25589i	−0.299761	+	0.325957i
$261$		0			0
$262$	−1.82895	+	5.62894i	−0.112993	+	0.347757i
$263$	13.4022	−	2.84872i	0.826413	−	0.175660i	0.224757	−	0.974415i	$-0.427841\pi$
$263$	13.4022	−	2.84872i	0.826413	−	0.175660i	0.601656	+	0.798755i	$0.294508\pi$
$264$		0			0
$265$	−10.2879	+	7.31053i	−0.631983	+	0.449082i
$266$	2.24126	+	2.48917i	0.137421	+	0.152621i
$267$		0			0
$268$	1.46295	+	2.53391i	0.0893641	+	0.154783i
$269$	13.3513	+	9.70027i	0.814041	+	0.591436i	0.915000	−	0.403455i	$-0.132191\pi$
$269$	13.3513	+	9.70027i	0.814041	+	0.591436i	−0.100958	+	0.994891i	$0.532191\pi$
$270$		0			0
$271$	−4.70284	+	3.41681i	−0.285677	+	0.207557i	−0.721390	−	0.692529i	$-0.756496\pi$
$271$	−4.70284	+	3.41681i	−0.285677	+	0.207557i	0.435713	+	0.900086i	$0.356496\pi$
$272$	0.667659	+	0.297261i	0.0404828	+	0.0180241i
$273$		0			0
$274$	5.35931	−	9.28259i	0.323768	−	0.560782i
$275$	17.8702	−	19.0263i	1.07762	−	1.14733i
$276$		0			0
$277$	15.0212	−	16.6827i	0.902537	−	1.00237i	−0.0974376	−	0.995242i	$-0.531065\pi$
$277$	15.0212	−	16.6827i	0.902537	−	1.00237i	0.999975	−	0.00712721i	$-0.00226868\pi$
$278$	3.75461	−	2.72788i	0.225186	−	0.163607i
$279$		0			0
$280$	−0.497835	+	4.30089i	−0.0297513	+	0.257027i
$281$	−2.41825	+	23.0081i	−0.144261	+	1.37255i	0.647662	+	0.761928i	$0.275747\pi$
$281$	−2.41825	+	23.0081i	−0.144261	+	1.37255i	−0.791923	+	0.610621i	$0.790920\pi$
$282$		0			0
$283$	17.1116	−	7.61859i	1.01718	−	0.452878i	0.170714	−	0.985321i	$-0.445392\pi$
$283$	17.1116	−	7.61859i	1.01718	−	0.452878i	0.846466	+	0.532443i	$0.178726\pi$
$284$	2.41356	+	2.68053i	0.143218	+	0.159060i
$285$		0			0
$286$	14.3272	−	15.9120i	0.847185	−	0.940894i
$287$	1.53143	−	4.71326i	0.0903974	−	0.278215i
$288$		0			0
$289$	−5.19026	−	15.9740i	−0.305310	−	0.939646i
$290$	22.2110	−	9.61032i	1.30427	−	0.564337i
$291$		0			0
$292$	11.7991	−	5.25328i	0.690488	−	0.307425i
$293$	7.31930	−	12.6774i	0.427598	−	0.740622i	−0.569061	−	0.822295i	$-0.692693\pi$
$293$	7.31930	−	12.6774i	0.427598	−	0.740622i	0.996659	+	0.0816737i	$0.0260265\pi$
$294$		0			0
$295$	10.5931	+	12.0167i	0.616754	+	0.699637i
$296$	−0.641201	+	0.465860i	−0.0372691	+	0.0270776i
$297$		0			0
$298$	0.0259266	+	0.0797939i	0.00150189	+	0.00462234i
$299$	0.195275	+	0.338226i	0.0112930	+	0.0195601i
$300$		0			0
$301$	−2.33467	+	4.04377i	−0.134568	+	0.233079i
$302$	18.1224	+	3.85204i	1.04283	+	0.221660i
$303$		0			0
$304$	−7.26035	−	3.23252i	−0.416410	−	0.185397i
$305$	−6.97892	+	7.58880i	−0.399612	+	0.434533i
$306$		0			0
$307$	33.9350			1.93677			0.968386	−	0.249455i	$-0.0802515\pi$
$307$	33.9350			1.93677			0.968386	+	0.249455i	$0.0802515\pi$
$308$	−0.289777	+	2.75704i	−0.0165115	+	0.157097i
$309$		0			0
$310$	3.10485	−	9.22444i	0.176344	−	0.523913i
$311$	8.92071	+	1.89616i	0.505847	+	0.107521i	0.453764	−	0.891122i	$-0.350081\pi$
$311$	8.92071	+	1.89616i	0.505847	+	0.107521i	0.0520826	+	0.998643i	$0.483414\pi$
$312$		0			0
$313$	23.1828	−	4.92767i	1.31037	−	0.278528i	0.500807	−	0.865559i	$-0.333037\pi$
$313$	23.1828	−	4.92767i	1.31037	−	0.278528i	0.809565	+	0.587031i	$0.199703\pi$
$314$	−3.80788	−	11.7194i	−0.214891	−	0.661366i
$315$		0			0
$316$	−0.353813	+	1.08892i	−0.0199035	+	0.0612567i
$317$	−3.01881	+	28.7221i	−0.169554	+	1.61319i	0.497009	+	0.867745i	$0.334432\pi$
$317$	−3.01881	+	28.7221i	−0.169554	+	1.61319i	−0.666563	+	0.745449i	$0.732235\pi$
$318$		0			0
$319$	47.9033	−	21.3279i	2.68207	−	1.19413i
$320$	−5.31516	−	16.9635i	−0.297127	−	0.948288i
$321$		0			0
$322$	0.0639297	+	0.0284633i	0.00356266	+	0.00158620i
$323$	−0.685378	−	2.10938i	−0.0381354	−	0.117369i
$324$		0			0
$325$	−12.4344	−	14.4082i	−0.689739	−	0.799222i
$326$	2.45523	+	4.25258i	0.135983	+	0.235529i
$327$		0			0
$328$	2.50353	+	23.8195i	0.138234	+	1.31521i
$329$	−0.700886	−	6.66848i	−0.0386411	−	0.367645i
$330$		0			0
$331$	2.55027	−	24.2642i	0.140176	−	1.33368i	−0.667745	−	0.744390i	$-0.732740\pi$
$331$	2.55027	−	24.2642i	0.140176	−	1.33368i	0.807921	−	0.589291i	$-0.200593\pi$
$332$	1.79470			0.0984972
$333$		0			0
$334$	4.98537	−	15.3434i	0.272787	−	0.839553i
$335$	−7.15725	+	3.09682i	−0.391043	+	0.169197i
$336$		0			0
$337$	−0.868681	−	0.964768i	−0.0473201	−	0.0525543i	0.719020	−	0.694989i	$-0.244591\pi$
$337$	−0.868681	−	0.964768i	−0.0473201	−	0.0525543i	−0.766340	+	0.642435i	$0.777924\pi$
$338$	−1.07316	−	1.19187i	−0.0583723	−	0.0648290i
$339$		0			0
$340$	0.431300	−	0.729210i	0.0233905	−	0.0395470i
$341$	6.51673	−	20.0564i	0.352901	−	1.08612i
$342$		0			0
$343$	8.60793			0.464784
$344$	2.35881	−	22.4426i	0.127179	−	1.21002i
$345$		0			0
$346$	−0.402491	−	3.82945i	−0.0216381	−	0.205873i
$347$	1.80712	+	17.1936i	0.0970113	+	0.923000i	0.929466	+	0.368908i	$0.120268\pi$
$347$	1.80712	+	17.1936i	0.0970113	+	0.923000i	−0.832455	+	0.554093i	$0.813065\pi$
$348$		0			0
$349$	14.5339	+	25.1734i	0.777980	+	1.34750i	0.933104	+	0.359606i	$0.117089\pi$
$349$	14.5339	+	25.1734i	0.777980	+	1.34750i	−0.155124	+	0.987895i	$0.549578\pi$
$350$	−3.32000	−	0.779028i	−0.177461	−	0.0416408i
$351$		0			0
$352$	−7.05679	−	21.7186i	−0.376128	−	1.15760i
$353$	17.0643	+	7.59750i	0.908239	+	0.404374i	0.807043	−	0.590493i	$-0.201066\pi$
$353$	17.0643	+	7.59750i	0.908239	+	0.404374i	0.101196	+	0.994867i	$0.467733\pi$
$354$		0			0
$355$	−7.83677	+	5.56875i	−0.415933	+	0.295559i
$356$	−13.4656	+	5.99527i	−0.713675	+	0.317749i
$357$		0			0
$358$	−2.45385	+	23.3469i	−0.129690	+	1.23392i
$359$	−1.18928	+	3.66023i	−0.0627679	+	0.193180i	−0.977523	−	0.210829i	$-0.932384\pi$
$359$	−1.18928	+	3.66023i	−0.0627679	+	0.193180i	0.914755	+	0.404009i	$0.132384\pi$
$360$		0			0
$361$	1.58171	+	4.86800i	0.0832479	+	0.256211i
$362$	−18.9894	+	4.03632i	−0.998060	+	0.212144i
$363$		0			0
$364$	1.97711	+	0.420247i	0.103629	+	0.0220269i
$365$	10.2928	+	32.8497i	0.538749	+	1.71943i
$366$		0			0
$367$	−2.42108	+	23.0350i	−0.126379	+	1.20242i	0.729037	+	0.684475i	$0.239968\pi$
$367$	−2.42108	+	23.0350i	−0.126379	+	1.20242i	−0.855416	+	0.517942i	$0.826698\pi$
$368$	−0.166042			−0.00865554
$369$		0			0
$370$	−0.306425	−	0.543877i	−0.0159303	−	0.0282748i
$371$	3.26372	+	1.45310i	0.169444	+	0.0754414i
$372$		0			0
$373$	16.1831	+	3.43982i	0.837929	+	0.178107i	0.606839	−	0.794825i	$-0.292437\pi$
$373$	16.1831	+	3.43982i	0.837929	+	0.178107i	0.231090	+	0.972932i	$0.425771\pi$
$374$	−1.27023	+	2.20010i	−0.0656820	+	0.113765i
$375$		0			0
$376$	16.2026	+	28.0638i	0.835587	+	1.44728i
$377$	−11.8145	−	36.3612i	−0.608477	−	1.87270i
$378$		0			0
$379$	−18.9711	+	13.7833i	−0.974478	+	0.708000i	−0.956468	−	0.291838i	$-0.905733\pi$
$379$	−18.9711	+	13.7833i	−0.974478	+	0.708000i	−0.0180106	+	0.999838i	$0.505733\pi$
$380$	−4.69010	+	7.92968i	−0.240597	+	0.406784i
$381$		0			0
$382$	−5.50218	+	9.53006i	−0.281516	+	0.487600i
$383$	19.8926	−	8.85675i	1.01646	−	0.452559i	0.170249	−	0.985401i	$-0.445543\pi$
$383$	19.8926	−	8.85675i	1.01646	−	0.452559i	0.846215	+	0.532842i	$0.178876\pi$
$384$		0			0
$385$	−7.21086	−	1.61218i	−0.367500	−	0.0821641i
$386$	−4.23305	−	13.0280i	−0.215457	−	0.663107i
$387$		0			0
$388$	1.58063	−	4.86466i	0.0802441	−	0.246966i
$389$	0.729663	−	0.810373i	0.0369954	−	0.0410875i	−0.724363	−	0.689419i	$-0.757866\pi$
$389$	0.729663	−	0.810373i	0.0369954	−	0.0410875i	0.761359	+	0.648331i	$0.224533\pi$
$390$		0			0
$391$	−0.0310062	−	0.0344359i	−0.00156805	−	0.00174150i
$392$	−18.4423	+	8.21104i	−0.931476	+	0.414720i
$393$		0			0
$394$	0.761941	−	7.24938i	0.0383860	−	0.365219i
$395$	−2.77465	−	1.27049i	−0.139608	−	0.0639255i
$396$		0			0
$397$	−15.4671	+	11.2375i	−0.776274	+	0.563996i	−0.903858	−	0.427832i	$-0.859278\pi$
$397$	−15.4671	+	11.2375i	−0.776274	+	0.563996i	0.127585	+	0.991828i	$0.459278\pi$
$398$	−5.11623	+	5.68215i	−0.256454	+	0.284821i
$399$		0			0
$400$	7.94819	−	1.51542i	0.397410	−	0.0757712i
$401$	−0.466700	+	0.808348i	−0.0233059	+	0.0403670i	−0.877443	−	0.479681i	$-0.840752\pi$
$401$	−0.466700	+	0.808348i	−0.0233059	+	0.0403670i	0.854137	+	0.520048i	$0.174086\pi$
$402$		0			0
$403$	−14.0467	−	6.25400i	−0.699716	−	0.311534i
$404$	2.69227	−	1.95605i	0.133946	−	0.0973172i
$405$		0			0
$406$	−5.54224	−	4.02668i	−0.275057	−	0.199841i
$407$	−0.676296	−	1.17138i	−0.0335228	−	0.0580631i
$408$		0			0
$409$	−15.2857	−	16.9765i	−0.755829	−	0.839433i	0.235357	−	0.971909i	$-0.424374\pi$
$409$	−15.2857	−	16.9765i	−0.755829	−	0.839433i	−0.991186	+	0.132476i	$0.957707\pi$
$410$	−18.8635	−	0.198432i	−0.931600	−	0.00979987i
$411$		0			0
$412$	0.942031	−	0.200235i	0.0464105	−	0.00986486i
$413$	1.40126	−	4.31263i	0.0689514	−	0.212210i
$414$		0			0
$415$	−0.550022	+	4.75175i	−0.0269995	+	0.233254i
$416$	−16.2865	+	3.46179i	−0.798509	+	0.169728i
$417$		0			0
$418$	13.8129	−	23.9247i	0.675611	−	1.17019i
$419$	9.69838	−	4.31800i	0.473797	−	0.210948i	−0.155924	−	0.987769i	$-0.549836\pi$
$419$	9.69838	−	4.31800i	0.473797	−	0.210948i	0.629722	+	0.776821i	$0.283169\pi$
$420$		0			0
$421$	16.7951	+	7.47766i	0.818544	+	0.364439i	0.772907	−	0.634519i	$-0.218802\pi$
$421$	16.7951	+	7.47766i	0.818544	+	0.364439i	0.0456363	+	0.998958i	$0.485468\pi$
$422$	23.0968	−	16.7808i	1.12434	−	0.816878i
$423$		0			0
$424$	−17.2658			−0.838500
$425$	1.79851	+	1.36541i	0.0872407	+	0.0662322i
$426$		0			0
$427$	2.85467	+	0.606780i	0.138147	+	0.0293641i
$428$	−0.359809	−	3.42335i	−0.0173920	−	0.165474i
$429$		0			0
$430$	17.3458	+	3.87810i	0.836489	+	0.187019i
$431$	5.96554	+	4.33422i	0.287350	+	0.208772i	0.722117	−	0.691771i	$-0.243169\pi$
$431$	5.96554	+	4.33422i	0.287350	+	0.208772i	−0.434767	+	0.900543i	$0.643169\pi$
$432$		0			0
$433$	4.26267	+	3.09701i	0.204851	+	0.148833i	0.685481	−	0.728091i	$-0.259592\pi$
$433$	4.26267	+	3.09701i	0.204851	+	0.148833i	−0.480630	+	0.876923i	$0.659592\pi$
$434$	−2.69491	+	0.572821i	−0.129360	+	0.0274963i
$435$		0			0
$436$	0.0813230	+	0.0172857i	0.00389467	+	0.000827837i
$437$	0.337173	+	0.374468i	0.0161292	+	0.0179132i
$438$		0			0
$439$	−22.6157	+	25.1173i	−1.07939	+	1.19878i	−0.100382	+	0.994949i	$0.532007\pi$
$439$	−22.6157	+	25.1173i	−1.07939	+	1.19878i	−0.979006	+	0.203833i	$0.934660\pi$
$440$	35.0052	−	7.05657i	1.66881	−	0.336409i
$441$		0			0
$442$	1.49853	+	1.08875i	0.0712780	+	0.0517865i
$443$	−11.5704	−	20.0405i	−0.549726	−	0.952153i	−0.998293	−	0.0584042i	$-0.981399\pi$
$443$	−11.5704	−	20.0405i	−0.549726	−	0.952153i	0.448567	−	0.893749i	$-0.351935\pi$
$444$		0			0
$445$	−11.7466	−	37.4895i	−0.556841	−	1.77717i
$446$	0.443502	+	4.21964i	0.0210004	+	0.199806i
$447$		0			0
$448$	−3.36711	+	3.73956i	−0.159081	+	0.176677i
$449$	−19.7430			−0.931731			−0.465866	−	0.884856i	$-0.654257\pi$
$449$	−19.7430			−0.931731			−0.465866	+	0.884856i	$0.654257\pi$
$450$		0			0
$451$	−40.8741			−1.92469
$452$	7.46359	−	8.28916i	0.351058	−	0.389889i
$453$		0			0
$454$	2.72079	+	25.8866i	0.127693	+	1.21492i
$455$	−1.71859	+	5.10589i	−0.0805687	+	0.239368i
$456$		0			0
$457$	−0.754881	−	1.30749i	−0.0353119	−	0.0611619i	0.847829	−	0.530269i	$-0.177909\pi$
$457$	−0.754881	−	1.30749i	−0.0353119	−	0.0611619i	−0.883141	+	0.469107i	$0.844576\pi$
$458$	−13.2008	−	9.59095i	−0.616834	−	0.448156i
$459$		0			0
$460$	−0.0221321	+	0.191203i	−0.00103191	+	0.00891490i
$461$	−0.664833	+	0.738372i	−0.0309643	+	0.0343894i	−0.758428	−	0.651757i	$-0.774032\pi$
$461$	−0.664833	+	0.738372i	−0.0309643	+	0.0343894i	0.727464	+	0.686146i	$0.240699\pi$
$462$		0			0
$463$	12.7970	+	14.2125i	0.594726	+	0.660510i	0.963092	−	0.269171i	$-0.0867496\pi$
$463$	12.7970	+	14.2125i	0.594726	+	0.660510i	−0.368367	+	0.929681i	$0.620083\pi$
$464$	15.8993	+	3.37950i	0.738106	+	0.156889i
$465$		0			0
$466$	13.4580	−	2.86058i	0.623428	−	0.132514i
$467$	7.86342	+	5.71311i	0.363875	+	0.264371i	0.754667	−	0.656108i	$-0.227799\pi$
$467$	7.86342	+	5.71311i	0.363875	+	0.264371i	−0.390791	+	0.920479i	$0.627799\pi$
$468$		0			0
$469$	1.78593	+	1.29755i	0.0824665	+	0.0599154i
$470$	−23.4249	+	10.1356i	−1.08051	+	0.467519i
$471$		0			0
$472$	2.29072	+	21.7948i	0.105439	+	1.00319i
$473$	37.6698	+	8.00696i	1.73206	+	0.368161i
$474$		0			0
$475$	−19.5576	−	14.8480i	−0.897366	−	0.681271i
$476$	−0.239821			−0.0109922
$477$		0			0
$478$	11.1804	−	8.12306i	0.511381	−	0.371540i
$479$	14.1221	+	6.28758i	0.645256	+	0.287287i	0.703156	−	0.711036i	$-0.251774\pi$
$479$	14.1221	+	6.28758i	0.645256	+	0.287287i	−0.0578994	+	0.998322i	$0.518440\pi$
$480$		0			0
$481$	−0.900936	+	0.401123i	−0.0410792	+	0.0182896i
$482$	14.8924	−	25.7944i	0.678331	−	1.17490i
$483$		0			0
$484$	13.3381	−	2.83510i	0.606278	−	0.128868i
$485$	12.3955	+	5.67581i	0.562851	+	0.257725i
$486$		0			0
$487$	4.43743	−	13.6570i	0.201079	−	0.618858i	−0.798773	−	0.601633i	$-0.794517\pi$
$487$	4.43743	−	13.6570i	0.201079	−	0.618858i	0.999852	−	0.0172246i	$-0.00548302\pi$
$488$	−13.7962	+	2.93247i	−0.624525	+	0.132747i
$489$		0			0
$490$	−4.75420	−	15.1732i	−0.214773	−	0.685454i
$491$	2.51084	+	2.78857i	0.113313	+	0.125846i	0.797132	−	0.603805i	$-0.206349\pi$
$491$	2.51084	+	2.78857i	0.113313	+	0.125846i	−0.683820	+	0.729651i	$0.739683\pi$
$492$		0			0
$493$	2.26811	+	3.92848i	0.102150	+	0.176930i
$494$	−16.2956	−	11.8394i	−0.733173	−	0.532681i
$495$		0			0
$496$	5.28863	−	3.84242i	0.237467	−	0.172530i
$497$	2.48612	+	1.10689i	0.111518	+	0.0496510i
$498$		0			0
$499$	−1.24260	+	2.15224i	−0.0556263	+	0.0963476i	−0.892498	−	0.451052i	$-0.851049\pi$
$499$	−1.24260	+	2.15224i	−0.0556263	+	0.0963476i	0.836871	+	0.547400i	$0.184382\pi$
$500$	−0.685633	−	9.35462i	−0.0306625	−	0.418351i
$501$		0			0
$502$	−2.08362	+	2.31409i	−0.0929965	+	0.103283i
$503$	2.61295	−	1.89842i	0.116506	−	0.0846463i	−0.528007	−	0.849240i	$-0.677060\pi$
$503$	2.61295	−	1.89842i	0.116506	−	0.0846463i	0.644512	+	0.764594i	$0.277060\pi$
$504$		0			0
$505$	4.35384	+	7.72766i	0.193743	+	0.343877i
$506$	0.0603310	−	0.574011i	0.00268204	−	0.0255179i
$507$		0			0
$508$	−4.30021	+	1.91458i	−0.190791	+	0.0849457i
$509$	−8.30576	−	9.22448i	−0.368146	−	0.408868i	0.530399	−	0.847748i	$-0.322042\pi$
$509$	−8.30576	−	9.22448i	−0.368146	−	0.408868i	−0.898546	+	0.438880i	$0.855375\pi$
$510$		0			0
$511$	6.52040	−	7.24164i	0.288445	−	0.320351i
$512$	5.24697	−	16.1485i	0.231885	−	0.713670i
$513$		0			0
$514$	−1.99946	−	6.15369i	−0.0881922	−	0.271428i
$515$	0.241448	+	2.55553i	0.0106395	+	0.112610i
$516$		0			0
$517$	−50.5215	+	22.4936i	−2.22193	+	0.989268i
$518$	−0.0883547	+	0.153035i	−0.00388208	+	0.00672397i
$519$		0			0
$520$	−2.44901	−	25.9208i	−0.107396	−	1.13670i
$521$	−18.5974	+	13.5118i	−0.814765	+	0.591962i	−0.915208	−	0.402981i	$-0.867974\pi$
$521$	−18.5974	+	13.5118i	−0.814765	+	0.591962i	0.100443	+	0.994943i	$0.467974\pi$
$522$		0			0
$523$	−6.02620	−	18.5468i	−0.263508	−	0.810993i	−0.992033	−	0.125975i	$-0.959794\pi$
$523$	−6.02620	−	18.5468i	−0.263508	−	0.810993i	0.728526	−	0.685018i	$-0.240206\pi$
$524$	2.30409	+	3.99080i	0.100654	+	0.174339i
$525$		0			0
$526$	−7.38188	+	12.7858i	−0.321865	+	0.557487i
$527$	1.78447	+	0.379302i	0.0777329	+	0.0165226i
$528$		0			0
$529$	−21.0019	−	9.35066i	−0.913127	−	0.406550i
$530$	1.56369	−	13.5090i	0.0679224	−	0.586794i
$531$		0			0
$532$	2.60790			0.113067
$533$	−3.11515	+	29.6387i	−0.134932	+	1.28380i
$534$		0			0
$535$	9.17410	+	0.0965060i	0.396631	+	0.00417232i
$536$	−10.4355	−	2.21814i	−0.450745	−	0.0958089i
$537$		0			0
$538$	−17.3938	+	3.69717i	−0.749902	+	0.159397i
$539$	−10.6463	−	32.7658i	−0.458567	−	1.41132i
$540$		0			0
$541$	−4.92323	+	15.1521i	−0.211666	+	0.651442i	0.787707	+	0.616050i	$0.211268\pi$
$541$	−4.92323	+	15.1521i	−0.211666	+	0.651442i	−0.999374	+	0.0353920i	$0.988732\pi$
$542$	0.654731	−	6.22935i	0.0281231	−	0.267574i
$543$		0			0
$544$	1.80474	−	0.803521i	0.0773775	−	0.0344507i
$545$	−0.0706896	+	0.210017i	−0.00302801	+	0.00899615i
$546$		0			0
$547$	−13.2926	−	5.91824i	−0.568350	−	0.253046i	0.102382	−	0.994745i	$-0.467354\pi$
$547$	−13.2926	−	5.91824i	−0.568350	−	0.253046i	−0.670733	+	0.741699i	$0.734020\pi$
$548$	−2.57887	−	7.93695i	−0.110164	−	0.339050i
$549$		0			0
$550$	2.35090	+	28.0277i	0.100243	+	1.19510i
$551$	−24.6642	−	42.7196i	−1.05073	−	1.81992i
$552$		0			0
$553$	0.0902966	+	0.859115i	0.00383980	+	0.0365333i
$554$	2.52845	+	24.0566i	0.107424	+	1.02207i
$555$		0			0
$556$	0.377702	−	3.59360i	0.0160182	−	0.152403i
$557$	−31.2370			−1.32355			−0.661776	−	0.749701i	$-0.730197\pi$
$557$	−31.2370			−1.32355			−0.661776	+	0.749701i	$0.730197\pi$
$558$		0			0
$559$	8.67697	−	26.7050i	0.366997	−	1.12950i
$560$	−1.51461	−	1.71815i	−0.0640039	−	0.0726051i
$561$		0			0
$562$	−16.6803	−	18.5253i	−0.703616	−	0.781444i
$563$	26.8720	+	29.8443i	1.13252	+	1.25779i	0.962183	+	0.272402i	$0.0878182\pi$
$563$	26.8720	+	29.8443i	1.13252	+	1.25779i	0.170335	+	0.985386i	$0.445515\pi$
$564$		0			0
$565$	19.6594	+	22.3013i	0.827078	+	0.938225i
$566$	−6.23691	+	19.1952i	−0.262157	+	0.806836i
$567$		0			0
$568$	−13.1521			−0.551850
$569$	3.32079	−	31.5952i	0.139215	−	1.32454i	−0.672331	−	0.740250i	$-0.734707\pi$
$569$	3.32079	−	31.5952i	0.139215	−	1.32454i	0.811546	−	0.584288i	$-0.198626\pi$
$570$		0			0
$571$	2.01441	+	19.1658i	0.0843005	+	0.802066i	0.952231	+	0.305379i	$0.0987833\pi$
$571$	2.01441	+	19.1658i	0.0843005	+	0.802066i	−0.867930	+	0.496686i	$0.834550\pi$
$572$	−1.74258	−	16.5796i	−0.0728611	−	0.693227i
$573$		0			0
$574$	2.67000	+	4.62457i	0.111444	+	0.193026i
$575$	−0.499456	−	0.117196i	−0.0208288	−	0.00488741i
$576$		0			0
$577$	9.95121	+	30.6267i	0.414274	+	1.27500i	0.912898	+	0.408187i	$0.133839\pi$
$577$	9.95121	+	30.6267i	0.414274	+	1.27500i	−0.498624	+	0.866818i	$0.666161\pi$
$578$	16.5334	+	7.36116i	0.687700	+	0.306184i
$579$		0			0
$580$	6.01087	−	17.8582i	0.249588	−	0.741519i
$581$	1.23700	−	0.550747i	0.0513193	−	0.0228488i
$582$		0			0
$583$	3.08000	−	29.3043i	0.127561	−	1.21366i
$584$	−14.5529	+	44.7891i	−0.602202	+	1.85339i
$585$		0			0
$586$	4.87425	+	15.0014i	0.201353	+	0.619702i
$587$	−11.3286	+	2.40796i	−0.467580	+	0.0993871i	−0.435675	−	0.900104i	$-0.643490\pi$
$587$	−11.3286	+	2.40796i	−0.467580	+	0.0993871i	−0.0319041	+	0.999491i	$0.510157\pi$
$588$		0			0
$589$	−19.4050	−	4.12466i	−0.799569	−	0.169954i
$590$	−17.2600	−	0.181565i	−0.710585	−	0.00747492i
$591$		0			0
$592$	0.0438268	−	0.416984i	0.00180127	−	0.0171379i
$593$	22.3537			0.917955			0.458977	−	0.888448i	$-0.348216\pi$
$593$	22.3537			0.917955			0.458977	+	0.888448i	$0.348216\pi$
$594$		0			0
$595$	0.0734979	−	0.634962i	0.00301312	−	0.0260309i
$596$	0.0596763	+	0.0265696i	0.00244444	+	0.00108833i
$597$		0			0
$598$	−0.411630	−	0.0874947i	−0.0168328	−	0.00357792i
$599$	2.18765	−	3.78911i	0.0893848	−	0.154819i	−0.817866	−	0.575408i	$-0.804843\pi$
$599$	2.18765	−	3.78911i	0.0893848	−	0.154819i	0.907251	+	0.420589i	$0.138177\pi$
$600$		0			0
$601$	−7.07808	−	12.2596i	−0.288721	−	0.500079i	0.684784	−	0.728746i	$-0.259897\pi$
$601$	−7.07808	−	12.2596i	−0.288721	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$602$	−1.55476	−	4.78507i	−0.0633674	−	0.195025i
$603$		0			0
$604$	11.6702	−	8.47889i	0.474853	−	0.345001i
$605$	3.41863	+	36.1835i	0.138987	+	1.47107i
$606$		0			0
$607$	17.2199	−	29.8257i	0.698933	−	1.21059i	−0.269904	−	0.962887i	$-0.586992\pi$
$607$	17.2199	−	29.8257i	0.698933	−	1.21059i	0.968837	−	0.247700i	$-0.0796748\pi$
$608$	−19.6253	+	8.73776i	−0.795912	+	0.354363i
$609$		0			0
$610$	−1.04495	−	11.0599i	−0.0423087	−	0.447804i
$611$	12.4602	+	38.3486i	0.504086	+	1.55142i
$612$		0			0
$613$	−2.88297	+	8.87288i	−0.116442	+	0.358372i	−0.992245	−	0.124297i	$-0.960333\pi$
$613$	−2.88297	+	8.87288i	−0.116442	+	0.358372i	0.875803	+	0.482669i	$0.160333\pi$
$614$	−24.4672	+	27.1736i	−0.987417	+	1.09664i
$615$		0			0
$616$	−6.76376	−	7.51192i	−0.272520	−	0.302664i
$617$	19.7638	−	8.79942i	0.795661	−	0.354251i	0.0316870	−	0.999498i	$-0.489912\pi$
$617$	19.7638	−	8.79942i	0.795661	−	0.354251i	0.763974	+	0.645247i	$0.223245\pi$
$618$		0			0
$619$	−1.68039	+	15.9879i	−0.0675406	+	0.642606i	0.907419	+	0.420226i	$0.138049\pi$
$619$	−1.68039	+	15.9879i	−0.0675406	+	0.642606i	−0.974960	+	0.222380i	$0.928617\pi$
$620$	−3.71975	−	6.60221i	−0.149389	−	0.265151i
$621$		0			0
$622$	−7.95021	+	5.77617i	−0.318774	+	0.231603i
$623$	−7.44136	+	8.26446i	−0.298132	+	0.331109i
$624$		0			0
$625$	24.9779	+	1.05159i	0.999115	+	0.0420636i
$626$	−12.7690	+	22.1166i	−0.510354	+	0.883958i
$627$		0			0
$628$	−8.76474	−	3.90231i	−0.349751	−	0.155719i
$629$	0.0946637	−	0.0687772i	0.00377449	−	0.00274233i
$630$		0			0
$631$	36.4652	+	26.4935i	1.45165	+	1.05469i	0.985441	+	0.170017i	$0.0543823\pi$
$631$	36.4652	+	26.4935i	1.45165	+	1.05469i	0.466214	+	0.884672i	$0.345618\pi$
$632$	−2.08742	−	3.61552i	−0.0830331	−	0.143818i
$633$		0			0
$634$	−20.8228	−	23.1260i	−0.826978	−	0.918453i
$635$	−3.75125	−	11.9722i	−0.148864	−	0.475103i
$636$		0			0
$637$	−24.5706	+	5.22265i	−0.973524	+	0.206929i
$638$	−17.4600	+	53.7363i	−0.691247	+	2.12744i
$639$		0			0
$640$	−0.370792	−	0.169783i	−0.0146568	−	0.00671126i
$641$	−32.0511	+	6.81267i	−1.26594	+	0.269084i	−0.791482	−	0.611192i	$-0.790690\pi$
$641$	−32.0511	+	6.81267i	−1.26594	+	0.269084i	−0.474461	+	0.880277i	$0.657357\pi$
$642$		0			0
$643$	−1.00181	+	1.73519i	−0.0395077	+	0.0684294i	−0.885103	−	0.465395i	$-0.845912\pi$
$643$	−1.00181	+	1.73519i	−0.0395077	+	0.0684294i	0.845595	+	0.533824i	$0.179246\pi$
$644$	0.0497750	−	0.0221613i	0.00196141	−	0.000873276i
$645$		0			0
$646$	2.18325	+	0.972046i	0.0858989	+	0.0382447i
$647$	−8.36159	+	6.07505i	−0.328728	+	0.238835i	−0.739891	−	0.672727i	$-0.765123\pi$
$647$	−8.36159	+	6.07505i	−0.328728	+	0.238835i	0.411163	+	0.911562i	$0.365123\pi$
$648$		0			0
$649$	−37.3997			−1.46807
$650$	20.5027	+	0.431399i	0.804181	+	0.0169209i
$651$		0			0
$652$	3.73968	+	0.794894i	0.146457	+	0.0311305i
$653$	1.34281	+	12.7760i	0.0525481	+	0.499962i	0.988866	+	0.148808i	$0.0475437\pi$
$653$	1.34281	+	12.7760i	0.0525481	+	0.499962i	−0.936318	+	0.351153i	$0.885790\pi$
$654$		0			0
$655$	−11.2724	+	4.87735i	−0.440447	+	0.190574i
$656$	−10.2505	−	7.44740i	−0.400214	−	0.290772i
$657$		0			0
$658$	5.84516	+	4.24676i	0.227868	+	0.165556i
$659$	4.63980	−	0.986219i	0.180741	−	0.0384176i	−0.116652	−	0.993173i	$-0.537216\pi$
$659$	4.63980	−	0.986219i	0.180741	−	0.0384176i	0.297393	+	0.954755i	$0.403883\pi$
$660$		0			0
$661$	−3.96345	−	0.842458i	−0.154160	−	0.0327678i	0.130185	−	0.991490i	$-0.458443\pi$
$661$	−3.96345	−	0.842458i	−0.154160	−	0.0327678i	−0.284345	+	0.958722i	$0.591776\pi$
$662$	17.5909	+	19.5367i	0.683691	+	0.759315i
$663$		0			0
$664$	−4.37878	+	4.86312i	−0.169929	+	0.188726i
$665$	−0.799241	+	6.90479i	−0.0309932	+	0.267756i
$666$		0			0
$667$	−0.833768	−	0.605768i	−0.0322836	−	0.0234554i
$668$	−6.28049	−	10.8781i	−0.242999	−	0.420887i
$669$		0			0
$670$	2.68061	−	7.96402i	0.103561	−	0.307677i
$671$	−2.51605	−	23.9387i	−0.0971312	−	0.924141i
$672$		0			0
$673$	−33.7504	+	37.4836i	−1.30098	+	1.44489i	−0.476309	+	0.879278i	$0.658026\pi$
$673$	−33.7504	+	37.4836i	−1.30098	+	1.44489i	−0.824673	+	0.565610i	$0.808641\pi$
$674$	1.39886			0.0538822
$675$		0			0
$676$	−1.24871			−0.0480274
$677$	23.2519	−	25.8238i	0.893642	−	0.992490i	−0.106357	−	0.994328i	$-0.533919\pi$
$677$	23.2519	−	25.8238i	0.893642	−	0.992490i	0.999998	+	0.00183848i	$0.000585206\pi$
$678$		0			0
$679$	−0.403392	−	3.83802i	−0.0154808	−	0.147290i
$680$	0.923647	+	2.94785i	0.0354202	+	0.113045i
$681$		0			0
$682$	11.3617	+	19.6790i	0.435062	+	0.753549i
$683$	33.1970	+	24.1191i	1.27025	+	0.922890i	0.999213	−	0.0396784i	$-0.0126333\pi$
$683$	33.1970	+	24.1191i	1.27025	+	0.922890i	0.271037	+	0.962569i	$0.412633\pi$
$684$		0			0
$685$	21.8046	−	4.39551i	0.833111	−	0.167944i
$686$	−6.20634	+	6.89284i	−0.236959	+	0.263170i
$687$		0			0
$688$	7.98800	+	8.87158i	0.304540	+	0.338226i
$689$	−21.0144	−	4.46676i	−0.800587	−	0.170170i
$690$		0			0
$691$	21.5694	−	4.58473i	0.820540	−	0.174411i	0.221531	−	0.975153i	$-0.428895\pi$
$691$	21.5694	−	4.58473i	0.820540	−	0.174411i	0.599009	+	0.800742i	$0.295561\pi$
$692$	−2.42543	−	1.76218i	−0.0922009	−	0.0669879i
$693$		0			0
$694$	−15.0708	−	10.9496i	−0.572079	−	0.415640i
$695$	9.39883	+	2.10135i	0.356518	+	0.0797088i
$696$		0			0
$697$	−0.369608	−	3.51658i	−0.0139999	−	0.133200i
$698$	−30.6367	−	6.51203i	−1.15962	−	0.246484i
$699$		0			0
$700$	−2.18040	+	1.51511i	−0.0824112	+	0.0572658i
$701$	−0.897737			−0.0339071			−0.0169535	−	0.999856i	$-0.505397\pi$
$701$	−0.897737			−0.0339071			−0.0169535	+	0.999856i	$0.505397\pi$
$702$		0			0
$703$	−1.02941	+	0.747907i	−0.0388247	+	0.0282078i
$704$	37.9149	+	16.8808i	1.42897	+	0.636219i
$705$		0			0
$706$	−18.3871	+	8.18647i	−0.692008	+	0.308102i
$707$	1.25539	−	2.17439i	0.0472137	−	0.0817765i
$708$		0			0
$709$	−40.6065	+	8.63118i	−1.52501	+	0.324151i	−0.892731	−	0.450590i	$-0.851214\pi$
$709$	−40.6065	+	8.63118i	−1.52501	+	0.324151i	−0.632279	+	0.774741i	$0.717880\pi$
$710$	1.19113	−	10.2904i	0.0447024	−	0.386193i
$711$		0			0
$712$	16.6083	−	51.1152i	0.622424	−	1.91562i
$713$	−0.405419	+	0.0861745i	−0.0151831	+	0.00322726i
$714$		0			0
$715$	44.4309	+	0.467386i	1.66162	+	0.0174793i
$716$	12.2302	+	13.5830i	0.457064	+	0.507621i
$717$		0			0
$718$	−2.07347	−	3.59136i	−0.0773813	−	0.134028i
$719$	−34.2388	−	24.8759i	−1.27689	−	0.927716i	−0.277437	−	0.960744i	$-0.589485\pi$
$719$	−34.2388	−	24.8759i	−1.27689	−	0.927716i	−0.999454	+	0.0330279i	$0.989485\pi$
$720$		0			0
$721$	0.587847	−	0.427096i	0.0218926	−	0.0159059i
$722$	−5.03849	−	2.24328i	−0.187513	−	0.0834863i
$723$		0			0
$724$	−7.55762	+	13.0902i	−0.280877	+	0.486493i
$725$	45.4400	+	21.3876i	1.68760	+	0.794317i
$726$		0			0
$727$	7.32228	−	8.13221i	0.271568	−	0.301607i	−0.591899	−	0.806012i	$-0.701622\pi$
$727$	7.32228	−	8.13221i	0.271568	−	0.301607i	0.863467	+	0.504405i	$0.168288\pi$
$728$	−5.96255	+	4.33205i	−0.220987	+	0.160556i
$729$		0			0
$730$	−33.7257	−	15.4428i	−1.24824	−	0.571562i
$731$	−0.348243	+	3.31331i	−0.0128802	+	0.122547i
$732$		0			0
$733$	1.16076	−	0.516802i	0.0428735	−	0.0190885i	−0.385188	−	0.922838i	$-0.625863\pi$
$733$	1.16076	−	0.516802i	0.0428735	−	0.0190885i	0.428061	+	0.903750i	$0.359197\pi$
$734$	−16.6998	−	18.5470i	−0.616400	−	0.684582i
$735$		0			0
$736$	−0.300323	+	0.333542i	−0.0110700	+	0.0122945i
$737$	5.62629	−	17.3159i	0.207247	−	0.637841i
$738$		0			0
$739$	5.82472	+	17.9267i	0.214266	+	0.659443i	0.999205	+	0.0398696i	$0.0126943\pi$
$739$	5.82472	+	17.9267i	0.214266	+	0.659443i	−0.784939	+	0.619573i	$0.787306\pi$
$740$	−0.474331	−	0.106049i	−0.0174367	−	0.00389843i
$741$		0			0
$742$	−3.51673	+	1.56575i	−0.129103	+	0.0574805i
$743$	−0.560250	+	0.970382i	−0.0205536	+	0.0355999i	−0.876119	−	0.482094i	$-0.839876\pi$
$743$	−0.560250	+	0.970382i	−0.0205536	+	0.0355999i	0.855566	+	0.517694i	$0.173210\pi$
$744$		0			0
$745$	−0.0886360	+	0.149859i	−0.00324737	+	0.00549042i
$746$	−14.4225	+	10.4786i	−0.528046	+	0.383648i
$747$		0			0
$748$	0.611228	+	1.88116i	0.0223487	+	0.0687822i
$749$	−1.29853	−	2.24913i	−0.0474474	−	0.0821813i
$750$		0			0
$751$	6.69286	−	11.5924i	0.244226	−	0.423012i	−0.717688	−	0.696365i	$-0.754799\pi$
$751$	6.69286	−	11.5924i	0.244226	−	0.423012i	0.961914	+	0.273353i	$0.0881328\pi$
$752$	−16.7683	−	3.56421i	−0.611476	−	0.129973i
$753$		0			0
$754$	37.6347	+	16.7560i	1.37057	+	0.610219i
$755$	18.8726	+	33.4971i	0.686843	+	1.21908i
$756$		0			0
$757$	14.0336			0.510062			0.255031	−	0.966933i	$-0.417914\pi$
$757$	14.0336			0.510062			0.255031	+	0.966933i	$0.417914\pi$
$758$	2.64116	−	25.1290i	0.0959313	−	0.912725i
$759$		0			0
$760$	−10.0441	−	32.0559i	−0.364336	−	1.16279i
$761$	12.9526	+	2.75317i	0.469533	+	0.0998023i	0.436601	−	0.899655i	$-0.356182\pi$
$761$	12.9526	+	2.75317i	0.469533	+	0.0998023i	0.0329319	+	0.999458i	$0.489516\pi$
$762$		0			0
$763$	0.0613563	−	0.0130417i	0.00222125	−	0.000472141i
$764$	2.64762	+	8.14854i	0.0957875	+	0.294804i
$765$		0			0
$766$	−7.25052	+	22.3148i	−0.261972	+	0.806267i
$767$	−2.85036	+	27.1194i	−0.102921	+	0.979225i
$768$		0			0
$769$	10.4551	−	4.65492i	0.377021	−	0.167861i	−0.209472	−	0.977815i	$-0.567175\pi$
$769$	10.4551	−	4.65492i	0.377021	−	0.167861i	0.586493	+	0.809954i	$0.300508\pi$
$770$	6.49001	−	4.61175i	0.233884	−	0.166196i
$771$		0			0
$772$	−9.74339	−	4.33803i	−0.350672	−	0.156129i
$773$	9.74410	+	29.9892i	0.350471	+	1.07864i	0.958589	+	0.284792i	$0.0919245\pi$
$773$	9.74410	+	29.9892i	0.350471	+	1.07864i	−0.608119	+	0.793846i	$0.708075\pi$
$774$		0			0
$775$	18.6203	−	7.82520i	0.668862	−	0.281090i
$776$	9.32535	+	16.1520i	0.334761	+	0.579823i
$777$		0			0
$778$	0.122821	+	1.16856i	0.00440334	+	0.0418950i
$779$	4.01924	+	38.2405i	0.144004	+	1.37011i
$780$		0			0
$781$	2.34617	−	22.3224i	0.0839527	−	0.798757i
$782$	0.0499303			0.00178550
$783$		0			0
$784$	3.30017	−	10.1569i	0.117863	−	0.362745i
$785$	13.0181	−	22.0100i	0.464635	−	0.785571i
$786$		0			0
$787$	−22.8901	−	25.4220i	−0.815944	−	0.906197i	0.181066	−	0.983471i	$-0.442045\pi$
$787$	−22.8901	−	25.4220i	−0.815944	−	0.906197i	−0.997010	+	0.0772737i	$0.975378\pi$
$788$	−3.79757	−	4.21763i	−0.135283	−	0.150247i
$789$		0			0
$790$	3.01789	−	1.30579i	0.107372	−	0.0464578i
$791$	2.60055	−	8.00367i	0.0924649	−	0.284578i
$792$		0			0
$793$	−17.5502			−0.623226
$794$	2.15334	−	20.4877i	0.0764192	−	0.727081i
$795$		0			0
$796$	0.622275	+	5.92055i	0.0220560	+	0.209848i
$797$	−3.91915	−	37.2882i	−0.138823	−	1.32082i	−0.813008	−	0.582253i	$-0.802171\pi$
$797$	−3.91915	−	37.2882i	−0.138823	−	1.32082i	0.674185	−	0.738563i	$-0.264495\pi$
$798$		0			0
$799$	−2.39207	−	4.14319i	−0.0846255	−	0.146576i
$800$	11.3319	−	18.7072i	0.400642	−	0.661398i
$801$		0			0
$802$	−0.310796	−	0.956533i	−0.0109746	−	0.0337764i
$803$	−73.4221	−	32.6896i	−2.59101	−	1.15359i
$804$		0			0
$805$	0.0434207	+	0.138578i	0.00153038	+	0.00488425i
$806$	15.1356	−	6.73882i	0.533130	−	0.237365i
$807$		0			0
$808$	−1.26837	+	12.0677i	−0.0446210	+	0.424540i
$809$	2.07744	−	6.39370i	0.0730388	−	0.224790i	−0.907872	−	0.419247i	$-0.862294\pi$
$809$	2.07744	−	6.39370i	0.0730388	−	0.224790i	0.980911	+	0.194456i	$0.0622942\pi$
$810$		0			0
$811$	−0.0417238	−	0.128413i	−0.00146512	−	0.00450918i	0.950321	−	0.311271i	$-0.100755\pi$
$811$	−0.0417238	−	0.128413i	−0.00146512	−	0.00450918i	−0.951786	+	0.306762i	$0.900755\pi$
$812$	−5.21724	+	1.10896i	−0.183089	+	0.0389168i
$813$		0			0
$814$	1.42560	+	0.303020i	0.0499672	+	0.0106209i
$815$	−3.25070	+	9.65776i	−0.113867	+	0.338297i
$816$		0			0
$817$	3.78691	−	36.0301i	0.132487	−	1.26053i
$818$	24.6150			0.860644
$819$		0			0
$820$	−9.94226	+	10.8111i	−0.347199	+	0.377540i
$821$	−2.05660	−	0.915657i	−0.0717758	−	0.0319566i	0.370535	−	0.928819i	$-0.379174\pi$
$821$	−2.05660	−	0.915657i	−0.0717758	−	0.0319566i	−0.442311	+	0.896862i	$0.645841\pi$
$822$		0			0
$823$	54.7025	+	11.6274i	1.90681	+	0.405305i	0.999873	−	0.0159639i	$-0.00508169\pi$
$823$	54.7025	+	11.6274i	1.90681	+	0.405305i	0.906936	+	0.421269i	$0.138415\pi$
$824$	−1.75582	+	3.04117i	−0.0611668	+	0.105944i
$825$		0			0
$826$	2.44304	+	4.23148i	0.0850044	+	0.147232i
$827$	9.90533	+	30.4855i	0.344442	+	1.06008i	0.961882	+	0.273466i	$0.0881700\pi$
$827$	9.90533	+	30.4855i	0.344442	+	1.06008i	−0.617440	+	0.786618i	$0.711830\pi$
$828$		0			0
$829$	−27.9759	+	20.3257i	−0.971642	+	0.705939i	−0.955825	−	0.293936i	$-0.905035\pi$
$829$	−27.9759	+	20.3257i	−0.971642	+	0.705939i	−0.0158167	+	0.999875i	$0.505035\pi$
$830$	−3.40842	−	3.86646i	−0.118308	−	0.134207i
$831$		0			0
$832$	15.1303	−	26.2064i	0.524548	−	0.908544i
$833$	2.72273	−	1.21224i	0.0943369	−	0.0420015i
$834$		0			0
$835$	30.7262	−	13.2947i	1.06333	−	0.460083i
$836$	−6.64670	−	20.4564i	−0.229881	−	0.707500i
$837$		0			0
$838$	−3.53490	+	10.8793i	−0.122111	+	0.375820i
$839$	−20.4800	+	22.7454i	−0.707049	+	0.785258i	−0.984482	−	0.175487i	$-0.943850\pi$
$839$	−20.4800	+	22.7454i	−0.707049	+	0.785258i	0.277432	+	0.960745i	$0.410517\pi$
$840$		0			0
$841$	48.1030	+	53.4238i	1.65873	+	1.84220i
$842$	−18.0971	+	8.05735i	−0.623667	+	0.277674i
$843$		0			0
$844$	2.32347	−	22.1064i	0.0799773	−	0.760933i
$845$	0.382693	−	3.30615i	0.0131650	−	0.113735i
$846$		0			0
$847$	8.32326	−	6.04720i	0.285991	−	0.207784i
$848$	6.11175	−	6.78779i	0.209878	−	0.233094i
$849$		0			0
$850$	−2.39009	+	0.455701i	−0.0819795	+	0.0156304i
$851$	−0.0132920	+	0.0230224i	−0.000455643	+	0.000789197i
$852$		0			0
$853$	24.4106	+	10.8683i	0.835804	+	0.372124i	0.779587	−	0.626294i	$-0.215429\pi$
$853$	24.4106	+	10.8683i	0.835804	+	0.372124i	0.0562178	+	0.998419i	$0.482096\pi$
$854$	−2.54411	+	1.84840i	−0.0870576	+	0.0632511i
$855$		0			0
$856$	10.1541	+	7.37742i	0.347062	+	0.252155i
$857$	14.7634	+	25.5710i	0.504309	+	0.873488i	0.999988	+	0.00498242i	$0.00158596\pi$
$857$	14.7634	+	25.5710i	0.504309	+	0.873488i	−0.495679	+	0.868506i	$0.665081\pi$
$858$		0			0
$859$	3.57379	+	3.96909i	0.121936	+	0.135424i	0.801022	−	0.598635i	$-0.204290\pi$
$859$	3.57379	+	3.96909i	0.121936	+	0.135424i	−0.679086	+	0.734059i	$0.737623\pi$
$860$	11.2807	−	8.01596i	0.384668	−	0.273342i
$861$		0			0
$862$	−7.77182	+	1.65195i	−0.264709	+	0.0562657i
$863$	9.94721	−	30.6144i	0.338607	−	1.04212i	−0.626311	−	0.779573i	$-0.715436\pi$
$863$	9.94721	−	30.6144i	0.338607	−	1.04212i	0.964918	−	0.262552i	$-0.0845640\pi$
$864$		0			0
$865$	5.40894	−	5.88163i	0.183910	−	0.199981i
$866$	−5.55334	+	1.18040i	−0.188710	+	0.0401116i
$867$		0			0
$868$	−1.07255	+	1.85772i	−0.0364048	+	0.0630550i
$869$	6.50879	−	2.89790i	0.220796	−	0.0983046i
$870$		0			0
$871$	−12.1274	−	5.39946i	−0.410920	−	0.182954i
$872$	−0.245254	+	0.178187i	−0.00830533	+	0.00603418i
$873$		0			0
$874$	−0.542959			−0.0183659
$875$	−3.34326	−	6.23726i	−0.113023	−	0.210858i
$876$		0			0
$877$	−31.6963	−	6.73725i	−1.07031	−	0.227501i	−0.361119	−	0.932520i	$-0.617605\pi$
$877$	−31.6963	−	6.73725i	−1.07031	−	0.227501i	−0.709188	+	0.705019i	$0.750938\pi$
$878$	−3.80680	−	36.2192i	−0.128473	−	1.22234i
$879$		0			0
$880$	−9.61697	+	16.2597i	−0.324188	+	0.548113i
$881$	−26.9732	−	19.5972i	−0.908750	−	0.660246i	0.0319481	−	0.999490i	$-0.489829\pi$
$881$	−26.9732	−	19.5972i	−0.908750	−	0.660246i	−0.940699	+	0.339244i	$0.889829\pi$
$882$		0			0
$883$	8.26440	+	6.00444i	0.278119	+	0.202066i	0.718097	−	0.695943i	$-0.245014\pi$
$883$	8.26440	+	6.00444i	0.278119	+	0.202066i	−0.439977	+	0.898009i	$0.645014\pi$
$884$	1.41066	−	0.299845i	0.0474456	−	0.0100849i
$885$		0			0
$886$	24.3898	+	5.18422i	0.819392	+	0.174167i
$887$	−24.5274	−	27.2404i	−0.823548	−	0.914643i	0.173992	−	0.984747i	$-0.444333\pi$
$887$	−24.5274	−	27.2404i	−0.823548	−	0.914643i	−0.997540	+	0.0701043i	$0.977667\pi$
$888$		0			0
$889$	−2.37638	+	2.63924i	−0.0797014	+	0.0885173i
$890$	38.4892	+	17.6239i	1.29016	+	0.590756i
$891$		0			0
$892$	2.67256	+	1.94173i	0.0894838	+	0.0650138i
$893$	26.0122	+	45.0545i	0.870466	+	1.50769i
$894$		0			0
$895$	−39.7112	+	28.2185i	−1.32740	+	0.943240i
$896$	0.0120668	+	0.114808i	0.000403124	+	0.00383547i
$897$		0			0
$898$	14.2348	−	15.8093i	0.475021	−	0.527564i
$899$	40.5747			1.35324
$900$		0			0
$901$	2.54903			0.0849206
$902$	29.4703	−	32.7301i	0.981254	−	1.08979i
$903$		0			0
$904$	4.25129	+	40.4483i	0.141396	+	1.34529i
$905$	−32.3420	−	24.0217i	−1.07509	−	0.798507i
$906$		0			0
$907$	−10.3737	−	17.9678i	−0.344454	−	0.596612i	0.640800	−	0.767708i	$-0.278603\pi$
$907$	−10.3737	−	17.9678i	−0.344454	−	0.596612i	−0.985254	+	0.171095i	$0.945269\pi$
$908$	16.3956	+	11.9121i	0.544106	+	0.395316i
$909$		0			0
$910$	−2.84946	−	5.05753i	−0.0944586	−	0.167655i
$911$	37.9975	−	42.2005i	1.25891	−	1.39816i	0.377367	−	0.926064i	$-0.376829\pi$
$911$	37.9975	−	42.2005i	1.25891	−	1.39816i	0.881545	−	0.472100i	$-0.156504\pi$
$912$		0			0
$913$	−7.47279	−	8.29938i	−0.247313	−	0.274669i
$914$	1.59125	+	0.338231i	0.0526340	+	0.0111877i
$915$		0			0
$916$	−12.4267	+	2.64138i	−0.410590	+	0.0872736i
$917$	2.81276	+	2.04359i	0.0928854	+	0.0674852i
$918$		0			0
$919$	6.57695	+	4.77844i	0.216954	+	0.157626i	0.690954	−	0.722898i	$-0.257191\pi$
$919$	6.57695	+	4.77844i	0.216954	+	0.157626i	−0.474001	+	0.880524i	$0.657191\pi$
$920$	−0.464106	−	0.526475i	−0.0153011	−	0.0173574i
$921$		0			0
$922$	−0.111908	−	1.06474i	−0.00368550	−	0.0350652i
$923$	−16.0076	−	3.40253i	−0.526898	−	0.111996i
$924$		0			0
$925$	0.426148	−	1.22336i	0.0140117	−	0.0402238i
$926$	−20.6074			−0.677200
$927$		0			0
$928$	35.5460	−	25.8257i	1.16685	−	0.847769i
$929$	35.3256	+	15.7280i	1.15899	+	0.516018i	0.893927	−	0.448212i	$-0.147939\pi$
$929$	35.3256	+	15.7280i	1.15899	+	0.516018i	0.265068	+	0.964230i	$0.414606\pi$
$930$		0			0
$931$	−29.6079	+	13.1823i	−0.970358	+	0.432031i
$932$	5.35616	−	9.27714i	0.175447	−	0.303883i
$933$		0			0
$934$	−10.2443	+	2.17750i	−0.335205	+	0.0712500i
$935$	−5.16799	+	1.04180i	−0.169011	+	0.0340704i
$936$		0			0
$937$	7.87414	−	24.2341i	0.257237	−	0.791694i	−0.736144	−	0.676825i	$-0.763355\pi$
$937$	7.87414	−	24.2341i	0.257237	−	0.791694i	0.993381	−	0.114869i	$-0.0366447\pi$
$938$	−2.32668	+	0.494551i	−0.0759688	+	0.0161477i
$939$		0			0
$940$	−6.33939	+	18.8342i	−0.206768	+	0.614304i
$941$	−7.32250	−	8.13246i	−0.238707	−	0.265111i	0.611874	−	0.790955i	$-0.290416\pi$
$941$	−7.32250	−	8.13246i	−0.238707	−	0.265111i	−0.850581	+	0.525845i	$0.823749\pi$
$942$		0			0
$943$	0.401671	+	0.695714i	0.0130802	+	0.0226556i
$944$	−9.37918	−	6.81437i	−0.305266	−	0.221789i
$945$		0			0
$946$	−33.5716	+	24.3912i	−1.09151	+	0.793027i
$947$	44.9071	+	19.9939i	1.45928	+	0.649715i	0.974391	−	0.224859i	$-0.0721921\pi$
$947$	44.9071	+	19.9939i	1.45928	+	0.649715i	0.484892	+	0.874574i	$0.338859\pi$
$948$		0			0
$949$	−29.2997	+	50.7486i	−0.951109	+	1.64737i
$950$	25.9907	−	4.95545i	0.843249	−	0.160776i
$951$		0			0
$952$	0.585123	−	0.649845i	0.0189639	−	0.0210616i
$953$	−13.3275	+	9.68303i	−0.431721	+	0.313664i	−0.782337	−	0.622856i	$-0.785972\pi$
$953$	−13.3275	+	9.68303i	−0.431721	+	0.313664i	0.350615	+	0.936520i	$0.385972\pi$
$954$		0			0
$955$	−22.3859	+	4.51269i	−0.724390	+	0.146027i
$956$	1.12472	−	10.7010i	0.0363760	−	0.346095i
$957$		0			0
$958$	−15.2169	+	6.77500i	−0.491636	+	0.218890i
$959$	−4.21312	−	4.67914i	−0.136049	−	0.151097i
$960$		0			0
$961$	−9.82417	+	10.9108i	−0.316909	+	0.351963i
$962$	0.328377	−	1.01064i	0.0105873	−	0.0325843i
$963$		0			0
$964$	−7.16615	−	22.0551i	−0.230806	−	0.710348i
$965$	14.4716	−	24.4676i	0.465859	−	0.787639i
$966$		0			0
$967$	−36.6655	+	16.3245i	−1.17908	+	0.524962i	−0.900248	−	0.435377i	$-0.856615\pi$
$967$	−36.6655	+	16.3245i	−1.17908	+	0.524962i	−0.278835	+	0.960339i	$0.589948\pi$
$968$	−24.8604	+	43.0595i	−0.799045	+	1.38399i
$969$		0			0
$970$	−13.4821	+	5.83348i	−0.432885	+	0.187302i
$971$	1.48662	−	1.08010i	0.0477080	−	0.0346619i	−0.563676	−	0.825996i	$-0.690613\pi$
$971$	1.48662	−	1.08010i	0.0477080	−	0.0346619i	0.611384	+	0.791334i	$0.290613\pi$
$972$		0			0
$973$	−0.842449	−	2.59279i	−0.0270077	−	0.0831211i
$974$	7.73651	+	13.4000i	0.247894	+	0.429364i
$975$		0			0
$976$	3.73073	−	6.46181i	0.119418	−	0.206838i
$977$	−56.7085	−	12.0538i	−1.81427	−	0.385634i	−0.829358	−	0.558717i	$-0.811294\pi$
$977$	−56.7085	−	12.0538i	−1.81427	−	0.385634i	−0.984907	+	0.173083i	$0.944627\pi$
$978$		0			0
$979$	83.7924	+	37.3068i	2.67802	+	1.19233i
$980$	−11.2561	−	5.15409i	−0.359563	−	0.164641i
$981$		0			0
$982$	−4.04328			−0.129026
$983$	2.01675	−	19.1881i	0.0643242	−	0.612004i	−0.914113	−	0.405460i	$-0.867111\pi$
$983$	2.01675	−	19.1881i	0.0643242	−	0.612004i	0.978437	−	0.206545i	$-0.0662219\pi$
$984$		0			0
$985$	12.3306	−	8.76206i	0.392887	−	0.279182i
$986$	−4.78106	−	1.01625i	−0.152260	−	0.0323639i
$987$		0			0
$988$	−15.3400	+	3.26061i	−0.488030	+	0.103734i
$989$	−0.233896	−	0.719859i	−0.00743748	−	0.0228902i
$990$		0			0
$991$	12.9369	−	39.8158i	0.410956	−	1.26479i	−0.504863	−	0.863199i	$-0.668457\pi$
$991$	12.9369	−	39.8158i	0.410956	−	1.26479i	0.915819	−	0.401592i	$-0.131543\pi$
$992$	1.84705	−	17.5735i	0.0586440	−	0.557961i
$993$		0			0
$994$	−2.67885	+	1.19270i	−0.0849680	+	0.0378302i
$995$	−15.8663	−	0.166903i	−0.502994	−	0.00529119i
$996$		0			0
$997$	31.6504	+	14.0917i	1.00238	+	0.446287i	0.841250	−	0.540646i	$-0.181820\pi$
$997$	31.6504	+	14.0917i	1.00238	+	0.446287i	0.161128	+	0.986934i	$0.448487\pi$
$998$	−0.827501	−	2.54679i	−0.0261941	−	0.0806172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.631.10		224
3.2	odd	2		225.2.q.a.31.19	✓	224
9.2	odd	6		225.2.q.a.106.10	yes	224
9.7	even	3	inner	675.2.r.a.181.19		224
25.21	even	5	inner	675.2.r.a.496.19		224
75.71	odd	10		225.2.q.a.121.10	yes	224
225.146	odd	30		225.2.q.a.196.19	yes	224
225.196	even	15	inner	675.2.r.a.46.10		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.19	✓	224	3.2	odd	2
225.2.q.a.106.10	yes	224	9.2	odd	6
225.2.q.a.121.10	yes	224	75.71	odd	10
225.2.q.a.196.19	yes	224	225.146	odd	30
675.2.r.a.46.10		224	225.196	even	15	inner
675.2.r.a.181.19		224	9.7	even	3	inner
675.2.r.a.496.19		224	25.21	even	5	inner
675.2.r.a.631.10		224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.721003 + 0.800755i) q^{2} +(0.0876938 + 0.834351i) q^{4} +(-2.23594 - 0.0235208i) q^{5} +(0.316483 + 0.548165i) q^{7} +(-2.47480 - 1.79805i) q^{8} +(1.63096 - 1.77348i) q^{10} +(3.49321 - 3.87960i) q^{11} +(-2.54696 - 2.82868i) q^{13} +(-0.667131 - 0.141803i) q^{14} +(1.58291 - 0.336458i) q^{16} +(0.365368 + 0.265455i) q^{17} +(-3.97313 - 2.88665i) q^{19} +(-0.176454 - 1.86763i) q^{20} +(0.587996 + 5.59441i) q^{22} +(-0.100362 - 0.0213327i) q^{23} +(4.99889 + 0.105182i) q^{25} +4.10144 q^{26} +(-0.429608 + 0.312129i) q^{28} +(9.17597 + 4.08540i) q^{29} +(3.69032 - 1.64304i) q^{31} +(2.18716 - 3.78828i) q^{32} +(-0.475995 + 0.101176i) q^{34} +(-0.694745 - 1.23311i) q^{35} +(0.0800637 - 0.246411i) q^{37} +(5.17614 - 1.10022i) q^{38} +(5.49123 + 4.07855i) q^{40} +(-5.23896 - 5.81846i) q^{41} +(3.68846 + 6.38860i) q^{43} +(3.54328 + 2.57435i) q^{44} +(0.0894437 - 0.0649846i) q^{46} +(-9.67748 - 4.30869i) q^{47} +(3.29968 - 5.71521i) q^{49} +(-3.68844 + 3.92705i) q^{50} +(2.13676 - 2.37311i) q^{52} +(4.56626 - 3.31758i) q^{53} +(-7.90187 + 8.59241i) q^{55} +(0.202394 - 1.92565i) q^{56} +(-9.88730 + 4.40211i) q^{58} +(-4.79365 - 5.32388i) q^{59} +(3.08519 - 3.42646i) q^{61} +(-1.34506 + 4.13967i) q^{62} +(2.45668 + 7.56088i) q^{64} +(5.62832 + 6.38468i) q^{65} +(3.18608 - 1.41853i) q^{67} +(-0.189442 + 0.328124i) q^{68} +(1.48833 + 0.332755i) q^{70} +(3.47832 - 2.52715i) q^{71} +(-4.75735 - 14.6416i) q^{73} +(0.139588 + 0.241774i) q^{74} +(2.06006 - 3.56813i) q^{76} +(3.23220 + 0.687026i) q^{77} +(1.24677 + 0.555098i) q^{79} +(-3.54721 + 0.715070i) q^{80} +8.43646 q^{82} +(0.223611 - 2.12752i) q^{83} +(-0.810698 - 0.602136i) q^{85} +(-7.77509 - 1.65265i) q^{86} +(-15.6207 + 3.32029i) q^{88} +(5.42929 + 16.7096i) q^{89} +(0.744515 - 2.29138i) q^{91} +(0.00899778 - 0.0856081i) q^{92} +(10.4277 - 4.64271i) q^{94} +(8.81581 + 6.54784i) q^{95} +(-5.56983 - 2.47985i) q^{97} +(2.19740 + 6.76291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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