LMFDB - Embedded newform 441.2.bb.f.46.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			46.5
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.f.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576178 - 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(0.810468 + 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(2.14952 - 1.03515i) q^{8} +O(q^{10})$	\(q+(0.576178 - 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(0.810468 + 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(2.14952 - 1.03515i) q^{8} +(1.27819 - 0.871452i) q^{10} +(1.80258 - 0.271695i) q^{11} +(-1.72771 - 2.16648i) q^{13} +(-4.04390 + 1.02835i) q^{14} +(-0.354001 - 4.72382i) q^{16} +(4.65252 + 1.43511i) q^{17} +(0.644188 + 1.11577i) q^{19} +(-0.106349 - 0.465946i) q^{20} +(0.639736 - 2.80287i) q^{22} +(3.68254 - 1.13591i) q^{23} +(-1.47518 - 3.75869i) q^{25} +(-4.17602 + 1.28813i) q^{26} +(-0.160692 + 1.27903i) q^{28} +(-0.492320 - 2.15699i) q^{29} +(0.292528 - 0.506674i) q^{31} +(-2.57932 - 0.795613i) q^{32} +(4.78753 - 6.00338i) q^{34} +(-0.0638864 - 2.59446i) q^{35} +(-6.77479 + 6.28609i) q^{37} +(2.00920 - 0.302837i) q^{38} +(2.31411 + 0.348796i) q^{40} +(-10.0896 + 4.85890i) q^{41} +(4.98694 + 2.40158i) q^{43} +(-0.733855 - 0.500334i) q^{44} +(0.454190 - 6.06074i) q^{46} +(-4.07192 + 10.3751i) q^{47} +(-2.23357 + 6.63409i) q^{49} -6.36801 q^{50} +(-0.100895 + 1.34635i) q^{52} +(4.99617 + 4.63577i) q^{53} +(1.61106 + 0.775846i) q^{55} +(-5.54255 - 3.02057i) q^{56} +(-3.45030 - 0.520049i) q^{58} +(2.97181 - 2.02615i) q^{59} +(-6.40633 + 5.94420i) q^{61} +(-0.575288 - 0.721388i) q^{62} +(3.25286 - 4.07896i) q^{64} +(-0.203127 - 2.71054i) q^{65} +(0.712256 - 1.23366i) q^{67} +(-1.18612 - 2.05442i) q^{68} +(-3.84568 - 1.40108i) q^{70} +(2.19834 - 9.63156i) q^{71} +(3.06719 + 7.81508i) q^{73} +(5.32498 + 13.5678i) q^{74} +(0.139684 - 0.611995i) q^{76} +(-3.36654 - 3.45371i) q^{77} +(-1.80317 - 3.12318i) q^{79} +(2.32332 - 4.02411i) q^{80} +(1.31983 + 17.6119i) q^{82} +(-4.89464 + 6.13768i) q^{83} +(2.97772 + 3.73395i) q^{85} +(6.39907 - 5.93747i) q^{86} +(3.59343 - 2.44996i) q^{88} +(9.38904 + 1.41517i) q^{89} +(-1.98787 + 7.05681i) q^{91} +(-1.69171 - 0.814686i) q^{92} +(12.8853 + 11.9558i) q^{94} +(-0.0944427 + 1.26025i) q^{95} -2.17773 q^{97} +(8.45241 + 7.10147i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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 $

$2$	0.576178	−	1.46808i	0.407419	−	1.03809i	−0.569026	−	0.822320i	$-0.692680\pi$
$2$	0.576178	−	1.46808i	0.407419	−	1.03809i	0.976445	−	0.215767i	$-0.0692252\pi$
$3$		0			0
$3$		0			0
$4$	−0.357164	−	0.331400i	−0.178582	−	0.165700i
$5$	0.810468	+	0.552568i	0.362452	+	0.247116i	0.730829	−	0.682561i	$-0.239134\pi$
$5$	0.810468	+	0.552568i	0.362452	+	0.247116i	−0.368376	+	0.929677i	$0.620086\pi$
$6$		0			0
$7$	−1.54377	−	2.14867i	−0.583489	−	0.812121i
$7$	−1.54377	−	2.14867i	−0.583489	−	0.812121i
$8$	2.14952	−	1.03515i	0.759969	−	0.365982i
$9$		0			0
$10$	1.27819	−	0.871452i	0.404198	−	0.275577i
$11$	1.80258	−	0.271695i	0.543498	−	0.0819191i	0.128445	−	0.991717i	$-0.459001\pi$
$11$	1.80258	−	0.271695i	0.543498	−	0.0819191i	0.415052	+	0.909798i	$0.363763\pi$
$12$		0			0
$13$	−1.72771	−	2.16648i	−0.479180	−	0.600873i	0.482212	−	0.876054i	$-0.339833\pi$
$13$	−1.72771	−	2.16648i	−0.479180	−	0.600873i	−0.961392	+	0.275182i	$0.911262\pi$
$14$	−4.04390	+	1.02835i	−1.08078	+	0.274838i
$15$		0			0
$16$	−0.354001	−	4.72382i	−0.0885003	−	1.18095i
$17$	4.65252	+	1.43511i	1.12840	+	0.348066i	0.802094	−	0.597197i	$-0.203719\pi$
$17$	4.65252	+	1.43511i	1.12840	+	0.348066i	0.326308	+	0.945263i	$0.394195\pi$
$18$		0			0
$19$	0.644188	+	1.11577i	0.147787	+	0.255974i	0.930409	−	0.366523i	$-0.119452\pi$
$19$	0.644188	+	1.11577i	0.147787	+	0.255974i	−0.782622	+	0.622497i	$0.786118\pi$
$20$	−0.106349	−	0.465946i	−0.0237804	−	0.104189i
$21$		0			0
$22$	0.639736	−	2.80287i	0.136392	−	0.597573i
$23$	3.68254	−	1.13591i	0.767863	−	0.236854i	0.114014	−	0.993479i	$-0.463629\pi$
$23$	3.68254	−	1.13591i	0.767863	−	0.236854i	0.653849	+	0.756625i	$0.273153\pi$
$24$		0			0
$25$	−1.47518	−	3.75869i	−0.295036	−	0.751738i
$26$	−4.17602	+	1.28813i	−0.818985	+	0.252623i
$27$		0			0
$28$	−0.160692	+	1.27903i	−0.0303678	+	0.241714i
$29$	−0.492320	−	2.15699i	−0.0914215	−	0.400544i	0.908425	−	0.418047i	$-0.137285\pi$
$29$	−0.492320	−	2.15699i	−0.0914215	−	0.400544i	−0.999847	+	0.0175034i	$0.994428\pi$
$30$		0			0
$31$	0.292528	−	0.506674i	0.0525397	−	0.0910014i	−0.838559	−	0.544810i	$-0.816602\pi$
$31$	0.292528	−	0.506674i	0.0525397	−	0.0910014i	0.891099	+	0.453809i	$0.149935\pi$
$32$	−2.57932	−	0.795613i	−0.455963	−	0.140646i
$33$		0			0
$34$	4.78753	−	6.00338i	0.821055	−	1.02957i
$35$	−0.0638864	−	2.59446i	−0.0107988	−	0.438545i
$36$		0			0
$37$	−6.77479	+	6.28609i	−1.11377	+	1.03343i	−0.114570	+	0.993415i	$0.536549\pi$
$37$	−6.77479	+	6.28609i	−1.11377	+	1.03343i	−0.999199	+	0.0400117i	$0.987260\pi$
$38$	2.00920	−	0.302837i	0.325935	−	0.0491267i
$39$		0			0
$40$	2.31411	+	0.348796i	0.365892	+	0.0551494i
$41$	−10.0896	+	4.85890i	−1.57573	+	0.758833i	−0.998338	−	0.0576326i	$-0.981645\pi$
$41$	−10.0896	+	4.85890i	−1.57573	+	0.758833i	−0.577395	+	0.816465i	$0.695931\pi$
$42$		0			0
$43$	4.98694	+	2.40158i	0.760501	+	0.366238i	0.773598	−	0.633676i	$-0.218455\pi$
$43$	4.98694	+	2.40158i	0.760501	+	0.366238i	−0.0130975	+	0.999914i	$0.504169\pi$
$44$	−0.733855	−	0.500334i	−0.110633	−	0.0754282i
$45$		0			0
$46$	0.454190	−	6.06074i	0.0669666	−	0.893607i
$47$	−4.07192	+	10.3751i	−0.593950	+	1.51336i	0.245207	+	0.969471i	$0.421144\pi$
$47$	−4.07192	+	10.3751i	−0.593950	+	1.51336i	−0.839157	+	0.543889i	$0.816951\pi$
$48$		0			0
$49$	−2.23357	+	6.63409i	−0.319082	+	0.947727i
$50$	−6.36801			−0.900573
$51$		0			0
$52$	−0.100895	+	1.34635i	−0.0139916	+	0.186705i
$53$	4.99617	+	4.63577i	0.686277	+	0.636772i	0.944192	−	0.329395i	$-0.106845\pi$
$53$	4.99617	+	4.63577i	0.686277	+	0.636772i	−0.257915	+	0.966168i	$0.583035\pi$
$54$		0			0
$55$	1.61106	+	0.775846i	0.217235	+	0.104615i
$56$	−5.54255	−	3.02057i	−0.740655	−	0.403641i
$57$		0			0
$58$	−3.45030	−	0.520049i	−0.453046	−	0.0682857i
$59$	2.97181	−	2.02615i	0.386897	−	0.263782i	−0.354214	−	0.935164i	$-0.615252\pi$
$59$	2.97181	−	2.02615i	0.386897	−	0.263782i	0.741111	+	0.671382i	$0.234299\pi$
$60$		0			0
$61$	−6.40633	+	5.94420i	−0.820246	+	0.761077i	−0.973883	−	0.227050i	$-0.927092\pi$
$61$	−6.40633	+	5.94420i	−0.820246	+	0.761077i	0.153637	+	0.988127i	$0.450901\pi$
$62$	−0.575288	−	0.721388i	−0.0730617	−	0.0916164i
$63$		0			0
$64$	3.25286	−	4.07896i	0.406607	−	0.509870i
$65$	−0.203127	−	2.71054i	−0.0251948	−	0.336201i
$66$		0			0
$67$	0.712256	−	1.23366i	0.0870160	−	0.150716i	−0.819233	−	0.573461i	$-0.805600\pi$
$67$	0.712256	−	1.23366i	0.0870160	−	0.150716i	0.906248	+	0.422745i	$0.138934\pi$
$68$	−1.18612	−	2.05442i	−0.143838	−	0.249134i
$69$		0			0
$70$	−3.84568	−	1.40108i	−0.459647	−	0.167461i
$71$	2.19834	−	9.63156i	0.260895	−	1.14306i	−0.659388	−	0.751803i	$-0.729184\pi$
$71$	2.19834	−	9.63156i	0.260895	−	1.14306i	0.920283	−	0.391253i	$-0.127958\pi$
$72$		0			0
$73$	3.06719	+	7.81508i	0.358988	+	0.914686i	0.990273	+	0.139135i	$0.0444323\pi$
$73$	3.06719	+	7.81508i	0.358988	+	0.914686i	−0.631286	+	0.775550i	$0.717472\pi$
$74$	5.32498	+	13.5678i	0.619016	+	1.57723i
$75$		0			0
$76$	0.139684	−	0.611995i	0.0160228	−	0.0702006i
$77$	−3.36654	−	3.45371i	−0.383653	−	0.393587i
$78$		0			0
$79$	−1.80317	−	3.12318i	−0.202872	−	0.351385i	0.746580	−	0.665295i	$-0.231694\pi$
$79$	−1.80317	−	3.12318i	−0.202872	−	0.351385i	−0.949453	+	0.313910i	$0.898361\pi$
$80$	2.32332	−	4.02411i	0.259756	−	0.449910i
$81$		0			0
$82$	1.31983	+	17.6119i	0.145751	+	1.94491i
$83$	−4.89464	+	6.13768i	−0.537256	+	0.673698i	−0.974173	−	0.225804i	$-0.927499\pi$
$83$	−4.89464	+	6.13768i	−0.537256	+	0.673698i	0.436917	+	0.899502i	$0.356071\pi$
$84$		0			0
$85$	2.97772	+	3.73395i	0.322979	+	0.405003i
$86$	6.39907	−	5.93747i	0.690029	−	0.640253i
$87$		0			0
$88$	3.59343	−	2.44996i	0.383060	−	0.261166i
$89$	9.38904	+	1.41517i	0.995236	+	0.150008i	0.626413	−	0.779492i	$-0.284523\pi$
$89$	9.38904	+	1.41517i	0.995236	+	0.150008i	0.368824	+	0.929499i	$0.379761\pi$
$90$		0			0
$91$	−1.98787	+	7.05681i	−0.208386	+	0.739755i
$92$	−1.69171	−	0.814686i	−0.176373	−	0.0849369i
$93$		0			0
$94$	12.8853	+	11.9558i	1.32901	+	1.23314i
$95$	−0.0944427	+	1.26025i	−0.00968961	+	0.129299i
$96$		0			0
$97$	−2.17773			−0.221115			−0.110557	−	0.993870i	$-0.535264\pi$
$97$	−2.17773			−0.221115			−0.110557	+	0.993870i	$0.535264\pi$
$98$	8.45241	+	7.10147i	0.853823	+	0.717357i
$99$		0			0
$100$	−0.718749	+	1.83134i	−0.0718749	+	0.183134i
$101$	0.137283	−	1.83191i	0.0136602	−	0.182282i	−0.986200	−	0.165558i	$-0.947057\pi$
$101$	0.137283	−	1.83191i	0.0136602	−	0.182282i	0.999860	−	0.0167238i	$-0.00532361\pi$
$102$		0			0
$103$	0.652706	+	0.445007i	0.0643130	+	0.0438479i	0.595050	−	0.803689i	$-0.297132\pi$
$103$	0.652706	+	0.445007i	0.0643130	+	0.0438479i	−0.530737	+	0.847537i	$0.678085\pi$
$104$	−5.95637	−	2.86844i	−0.584071	−	0.281274i
$105$		0			0
$106$	9.68435	−	4.66374i	0.940627	−	0.452982i
$107$	12.6269	+	1.90320i	1.22069	+	0.183990i	0.727608	−	0.685993i	$-0.240632\pi$
$107$	12.6269	+	1.90320i	1.22069	+	0.183990i	0.493083	+	0.869982i	$0.335870\pi$
$108$		0			0
$109$	−16.0702	+	2.42220i	−1.53925	+	0.232004i	−0.863203	−	0.504857i	$-0.831545\pi$
$109$	−16.0702	+	2.42220i	−1.53925	+	0.232004i	−0.676044	+	0.736861i	$0.736307\pi$
$110$	2.06726	−	1.91814i	0.197105	−	0.182887i
$111$		0			0
$112$	−9.60344	+	8.05310i	−0.907440	+	0.760947i
$113$	2.79568	−	3.50567i	0.262995	−	0.329786i	−0.632748	−	0.774358i	$-0.718073\pi$
$113$	2.79568	−	3.50567i	0.262995	−	0.329786i	0.895743	+	0.444572i	$0.146644\pi$
$114$		0			0
$115$	3.61225	+	1.11423i	0.336844	+	0.103903i
$116$	−0.538988	+	0.933555i	−0.0500438	+	0.0866784i
$117$		0			0
$118$	−1.26225	−	5.53027i	−0.116199	−	0.509103i
$119$	−4.09882	−	12.2122i	−0.375738	−	1.11949i
$120$		0			0
$121$	−7.33583	+	2.26280i	−0.666894	+	0.205710i
$122$	5.03536	+	12.8299i	0.455880	+	1.16156i
$123$		0			0
$124$	−0.272392	+	0.0840219i	−0.0244616	+	0.00754539i
$125$	1.97272	−	8.64303i	0.176445	−	0.773056i
$126$		0			0
$127$	1.72089	+	7.53971i	0.152704	+	0.669041i	0.992093	+	0.125509i	$0.0400563\pi$
$127$	1.72089	+	7.53971i	0.152704	+	0.669041i	−0.839388	+	0.543532i	$0.817087\pi$
$128$	−6.81323	−	11.8009i	−0.602210	−	1.04306i
$129$		0			0
$130$	−4.09631	−	1.26355i	−0.359270	−	0.110820i
$131$	0.0177821	+	0.237286i	0.00155363	+	0.0207318i	0.997927	−	0.0643602i	$-0.0205006\pi$
$131$	0.0177821	+	0.237286i	0.00155363	+	0.0207318i	−0.996373	+	0.0850919i	$0.972882\pi$
$132$		0			0
$133$	1.40294	−	3.10663i	0.121650	−	0.269379i
$134$	−1.40073	−	1.75646i	−0.121004	−	0.151735i
$135$		0			0
$136$	11.4862	−	1.73127i	0.984937	−	0.148455i
$137$	7.11680	−	4.85215i	0.608029	−	0.414547i	−0.219786	−	0.975548i	$-0.570536\pi$
$137$	7.11680	−	4.85215i	0.608029	−	0.414547i	0.827815	+	0.561001i	$0.189584\pi$
$138$		0			0
$139$	16.4947	−	7.94342i	1.39906	−	0.673752i	0.426090	−	0.904681i	$-0.359891\pi$
$139$	16.4947	−	7.94342i	1.39906	−	0.673752i	0.972971	+	0.230928i	$0.0741763\pi$
$140$	−0.836987	+	0.947821i	−0.0707383	+	0.0801055i
$141$		0			0
$142$	−12.8732	−	8.77682i	−1.08030	−	0.736535i
$143$	−3.70295	−	3.43584i	−0.309656	−	0.287319i
$144$		0			0
$145$	0.792876	−	2.02022i	0.0658448	−	0.167770i
$146$	13.2404			1.09578
$147$		0			0
$148$	4.50292			0.370138
$149$	−7.84938	+	19.9999i	−0.643046	+	1.63845i	0.120509	+	0.992712i	$0.461547\pi$
$149$	−7.84938	+	19.9999i	−0.643046	+	1.63845i	−0.763555	+	0.645743i	$0.776548\pi$
$150$		0			0
$151$	−1.35911	−	1.26107i	−0.110603	−	0.102624i	0.622933	−	0.782275i	$-0.285941\pi$
$151$	−1.35911	−	1.26107i	−0.110603	−	0.102624i	−0.733536	+	0.679651i	$0.762131\pi$
$152$	2.53968	+	1.73152i	0.205995	+	0.140445i
$153$		0			0
$154$	−7.01004	+	2.95239i	−0.564885	+	0.237910i
$155$	0.517057	−	0.249001i	0.0415310	−	0.0200003i
$156$		0			0
$157$	−13.0284	+	8.88264i	−1.03978	+	0.708912i	−0.957716	−	0.287715i	$-0.907105\pi$
$157$	−13.0284	+	8.88264i	−1.03978	+	0.708912i	−0.0820670	+	0.996627i	$0.526152\pi$
$158$	−5.62401	+	0.847683i	−0.447422	+	0.0674380i
$159$		0			0
$160$	−1.65082	−	2.07007i	−0.130509	−	0.163653i
$161$	−8.12569	−	6.15899i	−0.640394	−	0.485396i
$162$		0			0
$163$	0.201848	+	2.69348i	0.0158100	+	0.210970i	0.999514	+	0.0311740i	$0.00992461\pi$
$163$	0.201848	+	2.69348i	0.0158100	+	0.210970i	−0.983704	+	0.179796i	$0.942456\pi$
$164$	5.21388	+	1.60827i	0.407136	+	0.125585i
$165$		0			0
$166$	6.19040	+	10.7221i	0.480469	+	0.832196i
$167$	3.16201	+	13.8537i	0.244684	+	1.07203i	0.936696	+	0.350144i	$0.113867\pi$
$167$	3.16201	+	13.8537i	0.244684	+	1.07203i	−0.692012	+	0.721886i	$0.743276\pi$
$168$		0			0
$169$	1.18412	−	5.18798i	0.0910863	−	0.399075i
$170$	7.19742	−	2.22011i	0.552017	−	0.170275i
$171$		0			0
$172$	−0.985270	−	2.51043i	−0.0751262	−	0.191418i
$173$	−13.1286	+	4.04964i	−0.998149	+	0.307888i	−0.750434	−	0.660945i	$-0.770156\pi$
$173$	−13.1286	+	4.04964i	−0.998149	+	0.307888i	−0.247714	+	0.968833i	$0.579679\pi$
$174$		0			0
$175$	−5.79886	+	8.97221i	−0.438353	+	0.678235i
$176$	−1.92155	−	8.41887i	−0.144842	−	0.634596i
$177$		0			0
$178$	7.48733	−	12.9684i	0.561199	−	0.972025i
$179$	−4.27716	−	1.31933i	−0.319690	−	0.0986113i	0.130757	−	0.991414i	$-0.458259\pi$
$179$	−4.27716	−	1.31933i	−0.319690	−	0.0986113i	−0.450447	+	0.892803i	$0.648735\pi$
$180$		0			0
$181$	4.39373	−	5.50956i	0.326583	−	0.409522i	−0.591250	−	0.806488i	$-0.701365\pi$
$181$	4.39373	−	5.50956i	0.326583	−	0.409522i	0.917833	+	0.396966i	$0.129937\pi$
$182$	9.21457	+	6.98432i	0.683029	+	0.517712i
$183$		0			0
$184$	6.73984	−	6.25366i	0.496868	−	0.461026i
$185$	−8.96425	+	1.35114i	−0.659064	+	0.0993380i
$186$		0			0
$187$	8.77644	+	1.32284i	0.641797	+	0.0967354i
$188$	4.89264	−	2.35617i	0.356832	−	0.171841i
$189$		0			0
$190$	1.79573	+	0.864777i	0.130276	+	0.0627375i
$191$	−15.8564	−	10.8107i	−1.14733	−	0.782238i	−0.168258	−	0.985743i	$-0.553814\pi$
$191$	−15.8564	−	10.8107i	−1.14733	−	0.782238i	−0.979074	+	0.203505i	$0.934767\pi$
$192$		0			0
$193$	1.69283	−	22.5892i	0.121852	−	1.62601i	−0.516517	−	0.856277i	$-0.672772\pi$
$193$	1.69283	−	22.5892i	0.121852	−	1.62601i	0.638369	−	0.769730i	$-0.279609\pi$
$194$	−1.25476	+	3.19707i	−0.0900863	+	0.229536i
$195$		0			0
$196$	2.99629	−	1.62925i	0.214021	−	0.116375i
$197$	−3.49854			−0.249260			−0.124630	−	0.992203i	$-0.539774\pi$
$197$	−3.49854			−0.249260			−0.124630	+	0.992203i	$0.539774\pi$
$198$		0			0
$199$	−0.673086	+	8.98170i	−0.0477138	+	0.636696i	0.921167	+	0.389168i	$0.127237\pi$
$199$	−0.673086	+	8.98170i	−0.0477138	+	0.636696i	−0.968881	+	0.247528i	$0.920382\pi$
$200$	−7.06174	−	6.55234i	−0.499340	−	0.463320i
$201$		0			0
$202$	−2.61029	−	1.25705i	−0.183659	−	0.0884457i
$203$	−3.87465	+	4.38773i	−0.271947	+	0.307958i
$204$		0			0
$205$	−10.8622	−	1.63721i	−0.758647	−	0.114348i
$206$	1.02938	−	0.701819i	0.0717203	−	0.0488980i
$207$		0			0
$208$	−9.62244	+	8.92832i	−0.667196	+	0.619068i
$209$	1.46435	+	1.83623i	0.101291	+	0.127015i
$210$		0			0
$211$	5.64473	−	7.07827i	0.388599	−	0.487288i	−0.548599	−	0.836086i	$-0.684839\pi$
$211$	5.64473	−	7.07827i	0.388599	−	0.487288i	0.937198	+	0.348798i	$0.113410\pi$
$212$	−0.248160	−	3.31146i	−0.0170437	−	0.227432i
$213$		0			0
$214$	10.0694	−	17.4407i	0.688330	−	1.19222i
$215$	2.71472	+	4.70203i	0.185142	+	0.320676i
$216$		0			0
$217$	−1.54027	+	0.153639i	−0.104560	+	0.0104297i
$218$	−5.70333	+	24.9879i	−0.386278	+	1.69240i
$219$		0			0
$220$	−0.318298	−	0.811010i	−0.0214596	−	0.0546783i
$221$	−4.92906	−	12.5590i	−0.331565	−	0.844813i
$222$		0			0
$223$	6.05723	−	26.5384i	0.405622	−	1.77715i	−0.198341	−	0.980133i	$-0.563555\pi$
$223$	6.05723	−	26.5384i	0.405622	−	1.77715i	0.603963	−	0.797013i	$-0.293588\pi$
$224$	2.27235	+	6.77034i	0.151828	+	0.452362i
$225$		0			0
$226$	−3.53578	−	6.12416i	−0.235197	−	0.407373i
$227$	−8.69808	+	15.0655i	−0.577312	+	0.999934i	0.418474	+	0.908229i	$0.362565\pi$
$227$	−8.69808	+	15.0655i	−0.577312	+	0.999934i	−0.995786	+	0.0917050i	$0.970768\pi$
$228$		0			0
$229$	−0.918872	−	12.2615i	−0.0607207	−	0.810262i	−0.941560	−	0.336846i	$-0.890640\pi$
$229$	−0.918872	−	12.2615i	−0.0607207	−	0.810262i	0.880839	−	0.473416i	$-0.156979\pi$
$230$	3.71708	−	4.66107i	0.245097	−	0.307342i
$231$		0			0
$232$	−3.29107	−	4.12687i	−0.216069	−	0.270942i
$233$	−19.5478	+	18.1377i	−1.28062	+	1.18824i	−0.309168	+	0.951007i	$0.600051\pi$
$233$	−19.5478	+	18.1377i	−1.28062	+	1.18824i	−0.971452	+	0.237235i	$0.923759\pi$
$234$		0			0
$235$	−9.03309	+	6.15866i	−0.589254	+	0.401746i
$236$	−1.73289	−	0.261191i	−0.112801	−	0.0170021i
$237$		0			0
$238$	−20.2901	−	1.01903i	−1.31521	−	0.0660537i
$239$	16.0330	+	7.72108i	1.03709	+	0.499435i	0.873362	−	0.487071i	$-0.161935\pi$
$239$	16.0330	+	7.72108i	1.03709	+	0.499435i	0.163725	+	0.986506i	$0.447649\pi$
$240$		0			0
$241$	−3.94767	−	3.66290i	−0.254292	−	0.235948i	0.542717	−	0.839915i	$-0.317395\pi$
$241$	−3.94767	−	3.66290i	−0.254292	−	0.235948i	−0.797009	+	0.603967i	$0.793586\pi$
$242$	−0.904772	+	12.0733i	−0.0581609	+	0.776104i
$243$		0			0
$244$	4.25802			0.272592
$245$	−5.47603	+	4.14252i	−0.349850	+	0.264656i
$246$		0			0
$247$	1.30431	−	3.32334i	0.0829915	−	0.211459i
$248$	0.104310	−	1.39192i	0.00662367	−	0.0883868i
$249$		0			0
$250$	−11.5520	−	7.87602i	−0.730612	−	0.498123i
$251$	−25.6008	−	12.3287i	−1.61591	−	0.778180i	−0.615954	−	0.787782i	$-0.711229\pi$
$251$	−25.6008	−	12.3287i	−1.61591	−	0.778180i	−0.999954	+	0.00960250i	$0.996943\pi$
$252$		0			0
$253$	6.32944	−	3.04810i	0.397929	−	0.191632i
$254$	12.0604	+	1.81781i	0.756737	+	0.114060i
$255$		0			0
$256$	−10.9324	+	1.64779i	−0.683273	+	0.102987i
$257$	14.1645	−	13.1427i	0.883557	−	0.819821i	−0.101000	−	0.994886i	$-0.532204\pi$
$257$	14.1645	−	13.1427i	0.883557	−	0.819821i	0.984557	+	0.175066i	$0.0560138\pi$
$258$		0			0
$259$	23.9654	+	4.85255i	1.48914	+	0.301523i
$260$	−0.825722	+	1.03542i	−0.0512091	+	0.0642142i
$261$		0			0
$262$	0.358600	+	0.110613i	0.0221544	+	0.00683371i
$263$	12.1783	−	21.0934i	0.750945	−	1.30067i	−0.196421	−	0.980520i	$-0.562932\pi$
$263$	12.1783	−	21.0934i	0.750945	−	1.30067i	0.947365	−	0.320155i	$-0.103735\pi$
$264$		0			0
$265$	1.48766	+	6.51787i	0.0913863	+	0.400390i
$266$	−3.75243	−	3.84959i	−0.230076	−	0.236034i
$267$		0			0
$268$	−0.663228	+	0.204579i	−0.0405131	+	0.0124966i
$269$	−9.23847	−	23.5392i	−0.563279	−	1.43521i	−0.874571	−	0.484898i	$-0.838857\pi$
$269$	−9.23847	−	23.5392i	−0.563279	−	1.43521i	0.311291	−	0.950315i	$-0.399239\pi$
$270$		0			0
$271$	−13.7508	+	4.24155i	−0.835299	+	0.257656i	−0.682761	−	0.730642i	$-0.739221\pi$
$271$	−13.7508	+	4.24155i	−0.835299	+	0.257656i	−0.152538	+	0.988298i	$0.548745\pi$
$272$	5.13222	−	22.4857i	0.311186	−	1.36340i
$273$		0			0
$274$	−3.02279	−	13.2437i	−0.182613	−	0.800082i
$275$	−3.68034	−	6.37454i	−0.221933	−	0.384399i
$276$		0			0
$277$	−6.48717	−	2.00103i	−0.389776	−	0.120230i	0.0936717	−	0.995603i	$-0.470140\pi$
$277$	−6.48717	−	2.00103i	−0.389776	−	0.120230i	−0.483448	+	0.875373i	$0.660616\pi$
$278$	−2.15768	−	28.7923i	−0.129409	−	1.72685i
$279$		0			0
$280$	−2.82299	−	5.51071i	−0.168706	−	0.329328i
$281$	13.3608	+	16.7539i	0.797038	+	0.999454i	0.999795	+	0.0202251i	$0.00643829\pi$
$281$	13.3608	+	16.7539i	0.797038	+	0.999454i	−0.202757	+	0.979229i	$0.564990\pi$
$282$		0			0
$283$	22.7564	−	3.42997i	1.35273	−	0.203891i	0.567639	−	0.823277i	$-0.307857\pi$
$283$	22.7564	−	3.42997i	1.35273	−	0.203891i	0.785086	+	0.619387i	$0.212619\pi$
$284$	−3.97707	+	2.71152i	−0.235995	+	0.160899i
$285$		0			0
$286$	−7.17762	+	3.45656i	−0.424422	+	0.204391i
$287$	26.0162	+	14.1783i	1.53569	+	0.836916i
$288$		0			0
$289$	5.54035	+	3.77735i	0.325903	+	0.222197i
$290$	−2.50899	−	2.32801i	−0.147333	−	0.136705i
$291$		0			0
$292$	1.49442	−	3.80773i	0.0874546	−	0.222831i
$293$	30.3611			1.77371			0.886857	−	0.462044i	$-0.152884\pi$
$293$	30.3611			1.77371			0.886857	+	0.462044i	$0.152884\pi$
$294$		0			0
$295$	3.52814			0.205416
$296$	−8.05547	+	20.5250i	−0.468215	+	1.19299i
$297$		0			0
$298$	24.8387	+	23.0470i	1.43887	+	1.33508i
$299$	−8.82329	−	6.01562i	−0.510264	−	0.347892i
$300$		0			0
$301$	−2.53845	−	14.4228i	−0.146314	−	0.831314i
$302$	−2.63443	+	1.26868i	−0.151595	+	0.0730041i
$303$		0			0
$304$	5.04263	−	3.43801i	0.289215	−	0.197183i
$305$	−8.47670	+	1.27766i	−0.485374	+	0.0731584i
$306$		0			0
$307$	−3.81992	−	4.79003i	−0.218014	−	0.273381i	0.660783	−	0.750577i	$-0.270225\pi$
$307$	−3.81992	−	4.79003i	−0.218014	−	0.273381i	−0.878797	+	0.477196i	$0.841653\pi$
$308$	0.0578473	+	2.34921i	0.00329615	+	0.133859i
$309$		0			0
$310$	−0.0676366	−	0.902548i	−0.00384150	−	0.0512613i
$311$	−14.8937	−	4.59411i	−0.844547	−	0.260508i	−0.157860	−	0.987462i	$-0.550459\pi$
$311$	−14.8937	−	4.59411i	−0.844547	−	0.260508i	−0.686687	+	0.726953i	$0.740936\pi$
$312$		0			0
$313$	7.45529	+	12.9129i	0.421398	+	0.729883i	0.996077	−	0.0884963i	$-0.0282062\pi$
$313$	7.45529	+	12.9129i	0.421398	+	0.729883i	−0.574678	+	0.818379i	$0.694873\pi$
$314$	5.53370	+	24.2447i	0.312285	+	1.36821i
$315$		0			0
$316$	−0.390994	+	1.71306i	−0.0219951	+	0.0963670i
$317$	20.0427	−	6.18235i	1.12571	−	0.347235i	0.324658	−	0.945832i	$-0.394751\pi$
$317$	20.0427	−	6.18235i	1.12571	−	0.347235i	0.801051	+	0.598596i	$0.204275\pi$
$318$		0			0
$319$	−1.47349	−	3.75439i	−0.0824996	−	0.210205i
$320$	4.89024	−	1.50844i	0.273373	−	0.0843243i
$321$		0			0
$322$	−13.7237	+	8.38046i	−0.764792	+	0.467025i
$323$	1.39585	+	6.11561i	0.0776670	+	0.340281i
$324$		0			0
$325$	−5.59445	+	9.68986i	−0.310324	+	0.537497i
$326$	4.07054	+	1.25559i	0.225446	+	0.0695409i
$327$		0			0
$328$	−16.6581	+	20.8886i	−0.919789	+	1.15338i
$329$	28.5787	−	7.26747i	1.57559	−	0.400669i
$330$		0			0
$331$	−2.80260	+	2.60043i	−0.154045	+	0.142933i	−0.753430	−	0.657528i	$-0.771602\pi$
$331$	−2.80260	+	2.60043i	−0.154045	+	0.142933i	0.599385	+	0.800461i	$0.295412\pi$
$332$	3.78221	−	0.570077i	0.207576	−	0.0312870i
$333$		0			0
$334$	22.1601	+	3.34010i	1.21255	+	0.182762i
$335$	1.25894	−	0.606276i	0.0687835	−	0.0331244i
$336$		0			0
$337$	−6.99780	−	3.36996i	−0.381195	−	0.183574i	0.233467	−	0.972365i	$-0.424993\pi$
$337$	−6.99780	−	3.36996i	−0.381195	−	0.183574i	−0.614661	+	0.788791i	$0.710707\pi$
$338$	−6.93408	−	4.72758i	−0.377164	−	0.257146i
$339$		0			0
$340$	0.173894	−	2.32045i	0.00943070	−	0.125844i
$341$	0.389645	−	0.992798i	0.0211004	−	0.0537630i
$342$		0			0
$343$	17.7026	−	5.44226i	0.955850	−	0.293855i
$344$	13.2055			0.711993
$345$		0			0
$346$	−1.61923	+	21.6071i	−0.0870502	+	1.16160i
$347$	−5.68525	−	5.27514i	−0.305200	−	0.283185i	0.512672	−	0.858585i	$-0.328656\pi$
$347$	−5.68525	−	5.27514i	−0.305200	−	0.283185i	−0.817872	+	0.575400i	$0.804846\pi$
$348$		0			0
$349$	−2.92294	−	1.40762i	−0.156462	−	0.0753479i	0.354014	−	0.935240i	$-0.384816\pi$
$349$	−2.92294	−	1.40762i	−0.156462	−	0.0753479i	−0.510476	+	0.859892i	$0.670531\pi$
$350$	9.83072	+	13.6828i	0.525474	+	0.731374i
$351$		0			0
$352$	−4.86558	−	0.733368i	−0.259336	−	0.0390887i
$353$	−10.9183	+	7.44395i	−0.581121	+	0.396201i	−0.817899	−	0.575362i	$-0.804861\pi$
$353$	−10.9183	+	7.44395i	−0.581121	+	0.396201i	0.236778	+	0.971564i	$0.423909\pi$
$354$		0			0
$355$	7.10378	−	6.59134i	0.377029	−	0.349832i
$356$	−2.88444	−	3.61697i	−0.152875	−	0.191699i
$357$		0			0
$358$	−4.40128	+	5.51903i	−0.232615	+	0.291690i
$359$	1.85359	+	24.7345i	0.0978289	+	1.30544i	0.802821	+	0.596221i	$0.203332\pi$
$359$	1.85359	+	24.7345i	0.0978289	+	1.30544i	−0.704992	+	0.709216i	$0.749049\pi$
$360$		0			0
$361$	8.67004	−	15.0170i	0.456318	−	0.790366i
$362$	−5.55689	−	9.62481i	−0.292064	−	0.505869i
$363$		0			0
$364$	3.04862	−	1.86166i	0.159791	−	0.0975774i
$365$	−1.83250	+	8.02870i	−0.0959174	+	0.420241i
$366$		0			0
$367$	−6.94109	−	17.6856i	−0.362322	−	0.923182i	−0.989530	−	0.144329i	$-0.953897\pi$
$367$	−6.94109	−	17.6856i	−0.362322	−	0.923182i	0.627208	−	0.778852i	$-0.284198\pi$
$368$	−6.66948	−	16.9935i	−0.347670	−	0.885850i
$369$		0			0
$370$	−3.18142	+	13.9387i	−0.165394	+	0.724638i
$371$	2.24783	−	17.8917i	0.116701	−	0.928890i
$372$		0			0
$373$	7.37297	+	12.7704i	0.381758	+	0.661224i	0.991314	−	0.131519i	$-0.0419854\pi$
$373$	7.37297	+	12.7704i	0.381758	+	0.661224i	−0.609556	+	0.792743i	$0.708652\pi$
$374$	6.99881	−	12.1223i	0.361900	−	0.626829i
$375$		0			0
$376$	1.98713	+	26.5165i	0.102479	+	1.36748i
$377$	−3.82250	+	4.79326i	−0.196869	+	0.246865i
$378$		0			0
$379$	20.4541	+	25.6487i	1.05066	+	1.31748i	0.946423	+	0.322930i	$0.104668\pi$
$379$	20.4541	+	25.6487i	1.05066	+	1.31748i	0.104235	+	0.994553i	$0.466761\pi$
$380$	0.451378	−	0.418817i	0.0231552	−	0.0214849i
$381$		0			0
$382$	−25.0071	+	17.0496i	−1.27948	+	0.872331i
$383$	37.7257	+	5.68624i	1.92769	+	0.290553i	0.997138	−	0.0755973i	$-0.0240864\pi$
$383$	37.7257	+	5.68624i	1.92769	+	0.290553i	0.930556	+	0.366150i	$0.119324\pi$
$384$		0			0
$385$	−0.820063	−	4.65937i	−0.0417943	−	0.237463i
$386$	−32.1873	−	15.5006i	−1.63829	−	0.788960i
$387$		0			0
$388$	0.777805	+	0.721698i	0.0394871	+	0.0366387i
$389$	1.85242	−	24.7188i	0.0939212	−	1.25329i	−0.728752	−	0.684777i	$-0.759899\pi$
$389$	1.85242	−	24.7188i	0.0939212	−	1.25329i	0.822673	−	0.568514i	$-0.192482\pi$
$390$		0			0
$391$	18.7633			0.948899
$392$	2.06619	+	16.5722i	0.104358	+	0.837022i
$393$		0			0
$394$	−2.01578	+	5.13612i	−0.101553	+	0.258754i
$395$	0.264358	−	3.52761i	0.0133013	−	0.177493i
$396$		0			0
$397$	−28.8606	−	19.6768i	−1.44847	−	0.987551i	−0.995373	−	0.0960904i	$-0.969366\pi$
$397$	−28.8606	−	19.6768i	−1.44847	−	0.987551i	−0.453099	−	0.891460i	$-0.649681\pi$
$398$	12.7980	+	6.16320i	0.641506	+	0.308933i
$399$		0			0
$400$	−17.2332	+	8.29906i	−0.861658	+	0.414953i
$401$	9.06529	+	1.36637i	0.452699	+	0.0682334i	0.371434	−	0.928459i	$-0.378866\pi$
$401$	9.06529	+	1.36637i	0.452699	+	0.0682334i	0.0812645	+	0.996693i	$0.474104\pi$
$402$		0			0
$403$	−1.60310	+	0.241629i	−0.0798562	+	0.0120364i
$404$	−0.656129	+	0.608798i	−0.0326436	+	0.0302888i
$405$		0			0
$406$	4.20904	+	8.21639i	0.208891	+	0.407772i
$407$	−10.5042	+	13.1718i	−0.520674	+	0.652904i
$408$		0			0
$409$	−36.0305	−	11.1139i	−1.78159	−	0.549548i	−0.784119	−	0.620610i	$-0.786885\pi$
$409$	−36.0305	−	11.1139i	−1.78159	−	0.549548i	−0.997472	+	0.0710621i	$0.977361\pi$
$410$	−8.66209	+	15.0032i	−0.427790	+	0.740954i
$411$		0			0
$412$	−0.0856477	−	0.375247i	−0.00421956	−	0.0184871i
$413$	−8.94131	−	3.25755i	−0.439973	−	0.160294i
$414$		0			0
$415$	−7.35843	+	2.26978i	−0.361211	+	0.111419i
$416$	2.73263	+	6.96262i	0.133978	+	0.341370i
$417$		0			0
$418$	3.53945	−	1.09178i	0.173120	−	0.0534005i
$419$	3.06592	−	13.4327i	0.149780	−	0.656230i	−0.843165	−	0.537655i	$-0.819310\pi$
$419$	3.06592	−	13.4327i	0.149780	−	0.656230i	0.992945	−	0.118575i	$-0.0378325\pi$
$420$		0			0
$421$	4.90355	+	21.4839i	0.238984	+	1.04706i	0.941928	+	0.335814i	$0.109011\pi$
$421$	4.90355	+	21.4839i	0.238984	+	1.04706i	−0.702944	+	0.711245i	$0.748132\pi$
$422$	−7.13907	−	12.3652i	−0.347525	−	0.601930i
$423$		0			0
$424$	15.5381	+	4.79287i	0.754597	+	0.232762i
$425$	−1.46915	−	19.6044i	−0.0712642	−	0.950955i
$426$		0			0
$427$	22.6620	+	4.58863i	1.09669	+	0.222060i
$428$	−3.87916	−	4.86432i	−0.187506	−	0.235126i
$429$		0			0
$430$	8.46709	−	1.27621i	0.408319	−	0.0615442i
$431$	−11.2152	+	7.64637i	−0.540216	+	0.368313i	−0.802476	−	0.596684i	$-0.796484\pi$
$431$	−11.2152	+	7.64637i	−0.540216	+	0.368313i	0.262260	+	0.964997i	$0.415532\pi$
$432$		0			0
$433$	−12.6117	+	6.07346i	−0.606078	+	0.291872i	−0.711644	−	0.702540i	$-0.752049\pi$
$433$	−12.6117	+	6.07346i	−0.606078	+	0.291872i	0.105566	+	0.994412i	$0.466335\pi$
$434$	−0.661916	+	2.34976i	−0.0317730	+	0.112792i
$435$		0			0
$436$	6.54242	+	4.46054i	0.313325	+	0.213621i
$437$	3.63966	+	3.37711i	0.174109	+	0.161549i
$438$		0			0
$439$	14.9350	−	38.0538i	0.712809	−	1.81621i	0.151778	−	0.988415i	$-0.451500\pi$
$439$	14.9350	−	38.0538i	0.712809	−	1.81621i	0.561032	−	0.827794i	$-0.310405\pi$
$440$	4.26612			0.203379
$441$		0			0
$442$	−21.2776			−1.01207
$443$	−12.0541	+	30.7134i	−0.572709	+	1.45924i	0.291729	+	0.956501i	$0.405769\pi$
$443$	−12.0541	+	30.7134i	−0.572709	+	1.45924i	−0.864439	+	0.502738i	$0.832326\pi$
$444$		0			0
$445$	6.82754	+	6.33503i	0.323656	+	0.300309i
$446$	−35.4704	−	24.1833i	−1.67957	−	1.14511i
$447$		0			0
$448$	−13.7860	−	0.692372i	−0.651327	−	0.0327115i
$449$	7.94141	−	3.82438i	0.374778	−	0.180484i	−0.237006	−	0.971508i	$-0.576166\pi$
$449$	7.94141	−	3.82438i	0.374778	−	0.180484i	0.611785	+	0.791024i	$0.290452\pi$
$450$		0			0
$451$	−16.8672	+	11.4998i	−0.794244	+	0.541506i
$452$	−2.16029	+	0.325612i	−0.101612	+	0.0153155i
$453$		0			0
$454$	17.1057	+	21.4499i	0.802810	+	1.00669i
$455$	−5.51047	+	4.62089i	−0.258335	+	0.216631i
$456$		0			0
$457$	1.71516	+	22.8873i	0.0802320	+	1.07062i	0.881459	+	0.472261i	$0.156562\pi$
$457$	1.71516	+	22.8873i	0.0802320	+	1.07062i	−0.801227	+	0.598361i	$0.795819\pi$
$458$	−18.5302	−	5.71582i	−0.865861	−	0.267083i
$459$		0			0
$460$	−0.920910	−	1.59506i	−0.0429376	−	0.0743702i
$461$	4.73476	+	20.7443i	0.220520	+	0.966160i	0.957088	+	0.289797i	$0.0935878\pi$
$461$	4.73476	+	20.7443i	0.220520	+	0.966160i	−0.736568	+	0.676363i	$0.763555\pi$
$462$		0			0
$463$	−0.343768	+	1.50615i	−0.0159762	+	0.0699965i	−0.982288	−	0.187379i	$-0.940001\pi$
$463$	−0.343768	+	1.50615i	−0.0159762	+	0.0699965i	0.966311	+	0.257376i	$0.0828578\pi$
$464$	−10.0150	+	3.08921i	−0.464933	+	0.143413i
$465$		0			0
$466$	15.3646	+	39.1482i	0.711749	+	1.81351i
$467$	−1.27752	+	0.394062i	−0.0591164	+	0.0182350i	−0.324172	−	0.945998i	$-0.605086\pi$
$467$	−1.27752	+	0.394062i	−0.0591164	+	0.0182350i	0.265056	+	0.964233i	$0.414610\pi$
$468$		0			0
$469$	−3.75030	+	0.374084i	−0.173173	+	0.0172736i
$470$	3.83671	+	16.8097i	0.176974	+	0.775376i
$471$		0			0
$472$	4.29059	−	7.43152i	0.197490	−	0.342063i
$473$	9.64184	+	2.97411i	0.443332	+	0.136750i
$474$		0			0
$475$	3.24353	−	4.06725i	0.148823	−	0.186618i
$476$	−2.58318	+	5.72011i	−0.118400	+	0.262181i
$477$		0			0
$478$	20.5730	−	19.0889i	0.940986	−	0.873107i
$479$	−11.7812	+	1.77573i	−0.538297	+	0.0811352i	−0.412563	−	0.910929i	$-0.635366\pi$
$479$	−11.7812	+	1.77573i	−0.538297	+	0.0811352i	−0.125733	+	0.992064i	$0.540128\pi$
$480$		0			0
$481$	25.3235	+	3.81691i	1.15465	+	0.174036i
$482$	−7.65198	+	3.68500i	−0.348538	+	0.167847i
$483$		0			0
$484$	3.36999	+	1.62290i	0.153181	+	0.0737682i
$485$	−1.76498	−	1.20334i	−0.0801435	−	0.0546409i
$486$		0			0
$487$	0.265737	−	3.54601i	0.0120417	−	0.160685i	−0.987941	−	0.154830i	$-0.950517\pi$
$487$	0.265737	−	3.54601i	0.0120417	−	0.160685i	0.999983	−	0.00585546i	$-0.00186386\pi$
$488$	−7.61735	+	19.4087i	−0.344821	+	0.878591i
$489$		0			0
$490$	2.92637	+	10.4260i	0.132200	+	0.471001i
$491$	3.71083			0.167467			0.0837336	−	0.996488i	$-0.473316\pi$
$491$	3.71083			0.167467			0.0837336	+	0.996488i	$0.473316\pi$
$492$		0			0
$493$	0.805002	−	10.7420i	0.0362554	−	0.483795i
$494$	−4.12739	−	3.82966i	−0.185700	−	0.172305i
$495$		0			0
$496$	−2.49699	−	1.20249i	−0.112118	−	0.0539933i
$497$	−24.0888	+	10.1454i	−1.08053	+	0.455082i
$498$		0			0
$499$	30.6734	+	4.62327i	1.37313	+	0.206966i	0.793825	−	0.608146i	$-0.208086\pi$
$499$	30.6734	+	4.62327i	1.37313	+	0.206966i	0.579304	+	0.815112i	$0.303325\pi$
$500$	−3.56888	+	2.43322i	−0.159605	+	0.108817i
$501$		0			0
$502$	−32.8501	+	30.4804i	−1.46617	+	1.36041i
$503$	−13.0212	−	16.3281i	−0.580587	−	0.728033i	0.401626	−	0.915804i	$-0.368445\pi$
$503$	−13.0212	−	16.3281i	−0.580587	−	0.728033i	−0.982213	+	0.187771i	$0.939874\pi$
$504$		0			0
$505$	1.12352	−	1.40885i	0.0499960	−	0.0626930i
$506$	−0.827960	−	11.0484i	−0.0368073	−	0.491159i
$507$		0			0
$508$	1.88402	−	3.26321i	0.0835898	−	0.144782i
$509$	16.4615	+	28.5122i	0.729643	+	1.26378i	0.957034	+	0.289976i	$0.0936473\pi$
$509$	16.4615	+	28.5122i	0.729643	+	1.26378i	−0.227390	+	0.973804i	$0.573019\pi$
$510$		0			0
$511$	12.0570	−	18.6550i	0.533370	−	0.825250i
$512$	2.18444	−	9.57065i	0.0965395	−	0.422967i
$513$		0			0
$514$	−11.1333	−	28.3671i	−0.491067	−	1.25122i
$515$	0.283101	+	0.721329i	0.0124749	+	0.0317855i
$516$		0			0
$517$	−4.52109	+	19.8082i	−0.198837	+	0.871163i
$518$	20.9323	−	32.3872i	0.919711	−	1.42301i
$519$		0			0
$520$	−3.24244	−	5.61608i	−0.142191	−	0.246281i
$521$	−3.86730	+	6.69836i	−0.169430	+	0.293461i	−0.938219	−	0.346041i	$-0.887526\pi$
$521$	−3.86730	+	6.69836i	−0.169430	+	0.293461i	0.768790	+	0.639501i	$0.220859\pi$
$522$		0			0
$523$	0.145534	+	1.94202i	0.00636376	+	0.0849184i	0.999481	−	0.0322031i	$-0.0102523\pi$
$523$	0.145534	+	1.94202i	0.00636376	+	0.0849184i	−0.993118	+	0.117122i	$0.962633\pi$
$524$	0.0722854	−	0.0906430i	0.00315780	−	0.00395976i
$525$		0			0
$526$	−23.9499	−	30.0322i	−1.04426	−	1.30947i
$527$	2.08813	−	1.93750i	0.0909604	−	0.0843989i
$528$		0			0
$529$	−6.73268	+	4.59026i	−0.292725	+	0.199577i
$530$	10.4259	+	1.57145i	0.452872	+	0.0682594i
$531$		0			0
$532$	−1.53061	+	0.644642i	−0.0663606	+	0.0279488i
$533$	27.9586	+	13.4642i	1.21102	+	0.583197i
$534$		0			0
$535$	9.18207	+	8.51972i	0.396976	+	0.368340i
$536$	0.253976	−	3.38908i	0.0109701	−	0.146386i
$537$		0			0
$538$	−39.8804			−1.71937
$539$	−2.22374	+	12.5653i	−0.0957835	+	0.541226i
$540$		0			0
$541$	−1.46372	+	3.72949i	−0.0629301	+	0.160343i	−0.958880	−	0.283812i	$-0.908401\pi$
$541$	−1.46372	+	3.72949i	−0.0629301	+	0.160343i	0.895950	+	0.444155i	$0.146496\pi$
$542$	−1.69596	+	22.6310i	−0.0728478	+	0.972087i
$543$		0			0
$544$	−10.8585	−	7.40322i	−0.465555	−	0.317410i
$545$	−14.3628	−	6.91677i	−0.615236	−	0.296282i
$546$		0			0
$547$	−20.6693	+	9.95381i	−0.883756	+	0.425594i	−0.819995	−	0.572371i	$-0.806024\pi$
$547$	−20.6693	+	9.95381i	−0.883756	+	0.425594i	−0.0637608	+	0.997965i	$0.520309\pi$
$548$	−4.14987	−	0.625492i	−0.177274	−	0.0267197i
$549$		0			0
$550$	−11.4788	+	1.73016i	−0.489459	+	0.0737741i
$551$	2.08955	−	1.93882i	0.0890180	−	0.0825966i
$552$		0			0
$553$	−3.92701	+	8.69587i	−0.166994	+	0.369786i
$554$	−6.67542	+	8.37072i	−0.283612	+	0.355638i
$555$		0			0
$556$	−8.52376	−	2.62923i	−0.361488	−	0.111504i
$557$	−15.7311	+	27.2471i	−0.666548	+	1.15449i	0.312315	+	0.949978i	$0.398895\pi$
$557$	−15.7311	+	27.2471i	−0.666548	+	1.15449i	−0.978863	+	0.204516i	$0.934438\pi$
$558$		0			0
$559$	−3.41300	−	14.9533i	−0.144354	−	0.632458i
$560$	−12.2332	+	1.22023i	−0.516946	+	0.0515642i
$561$		0			0
$562$	32.2942	−	9.96144i	1.36225	−	0.420198i
$563$	0.895432	+	2.28152i	0.0377379	+	0.0961547i	0.948500	−	0.316776i	$-0.102600\pi$
$563$	0.895432	+	2.28152i	0.0377379	+	0.0961547i	−0.910762	+	0.412931i	$0.864505\pi$
$564$		0			0
$565$	4.20293	−	1.29643i	0.176818	−	0.0545413i
$566$	8.07625	−	35.3844i	0.339470	−	1.48732i
$567$		0			0
$568$	−5.24477	−	22.9788i	−0.220066	−	0.964170i
$569$	−20.8347	−	36.0867i	−0.873436	−	1.51283i	−0.858420	−	0.512948i	$-0.828553\pi$
$569$	−20.8347	−	36.0867i	−0.873436	−	1.51283i	−0.0150158	−	0.999887i	$-0.504780\pi$
$570$		0			0
$571$	6.80024	+	2.09760i	0.284581	+	0.0877817i	0.433760	−	0.901029i	$-0.357187\pi$
$571$	6.80024	+	2.09760i	0.284581	+	0.0877817i	−0.149178	+	0.988810i	$0.547663\pi$
$572$	0.183925	+	2.45431i	0.00769030	+	0.102620i
$573$		0			0
$574$	35.8047	−	30.0245i	1.49446	−	1.25320i
$575$	−9.70195	−	12.1659i	−0.404599	−	0.507352i
$576$		0			0
$577$	−13.7617	+	2.07425i	−0.572908	+	0.0863520i	−0.429106	−	0.903254i	$-0.641171\pi$
$577$	−13.7617	+	2.07425i	−0.572908	+	0.0863520i	−0.143803	+	0.989606i	$0.545933\pi$
$578$	8.73766	−	5.95723i	0.363439	−	0.247788i
$579$		0			0
$580$	−0.952686	+	0.458789i	−0.0395581	+	0.0190502i
$581$	20.7440	+	1.04182i	0.860607	+	0.0432222i
$582$		0			0
$583$	10.2655	+	6.99891i	0.425154	+	0.289865i
$584$	14.6828	+	13.6236i	0.607578	+	0.563750i
$585$		0			0
$586$	17.4934	−	44.5724i	0.722645	−	1.84127i
$587$	45.9865			1.89807			0.949034	−	0.315174i	$-0.102063\pi$
$587$	45.9865			1.89807			0.949034	+	0.315174i	$0.102063\pi$
$588$		0			0
$589$	0.753773			0.0310587
$590$	2.03284	−	5.17958i	0.0836906	−	0.213240i
$591$		0			0
$592$	32.0926	+	29.7776i	1.31900	+	1.22385i
$593$	4.05079	+	2.76178i	0.166346	+	0.113413i	0.643632	−	0.765335i	$-0.277427\pi$
$593$	4.05079	+	2.76178i	0.166346	+	0.113413i	−0.477286	+	0.878748i	$0.658379\pi$
$594$		0			0
$595$	3.42612	−	12.1625i	0.140457	−	0.498613i
$596$	9.43147	−	4.54196i	0.386328	−	0.186046i
$597$		0			0
$598$	−13.9152	+	9.48720i	−0.569033	+	0.387960i
$599$	33.1327	−	4.99396i	1.35377	−	0.204047i	0.568234	−	0.822867i	$-0.307627\pi$
$599$	33.1327	−	4.99396i	1.35377	−	0.204047i	0.785533	+	0.618820i	$0.212389\pi$
$600$		0			0
$601$	−10.2815	−	12.8926i	−0.419390	−	0.525898i	0.526592	−	0.850118i	$-0.323470\pi$
$601$	−10.2815	−	12.8926i	−0.419390	−	0.525898i	−0.945982	+	0.324220i	$0.894898\pi$
$602$	−22.6363	−	4.58343i	−0.922588	−	0.186807i
$603$		0			0
$604$	0.0675068	+	0.900816i	0.00274681	+	0.0366537i
$605$	−7.19581	−	2.21961i	−0.292551	−	0.0902401i
$606$		0			0
$607$	−20.1768	−	34.9473i	−0.818952	−	1.41847i	−0.906455	−	0.422301i	$-0.861222\pi$
$607$	−20.1768	−	34.9473i	−0.818952	−	1.41847i	0.0875039	−	0.996164i	$-0.472111\pi$
$608$	−0.773845	−	3.39044i	−0.0313835	−	0.137500i
$609$		0			0
$610$	−3.00839	+	13.1806i	−0.121806	+	0.533667i
$611$	29.5124	−	9.10338i	1.19395	−	0.368284i
$612$		0			0
$613$	4.29486	+	10.9431i	0.173468	+	0.441989i	0.990995	−	0.133902i	$-0.0427506\pi$
$613$	4.29486	+	10.9431i	0.173468	+	0.441989i	−0.817527	+	0.575891i	$0.804655\pi$
$614$	−9.23308	+	2.84803i	−0.372617	+	0.114937i
$615$		0			0
$616$	−10.8116	−	3.93893i	−0.435610	−	0.158704i
$617$	−6.39881	−	28.0350i	−0.257606	−	1.12865i	−0.923802	−	0.382870i	$-0.874936\pi$
$617$	−6.39881	−	28.0350i	−0.257606	−	1.12865i	0.666196	−	0.745777i	$-0.267922\pi$
$618$		0			0
$619$	9.15775	−	15.8617i	0.368081	−	0.637535i	−0.621185	−	0.783664i	$-0.713348\pi$
$619$	9.15775	−	15.8617i	0.368081	−	0.637535i	0.989265	+	0.146129i	$0.0466816\pi$
$620$	−0.267193	−	0.0824181i	−0.0107307	−	0.00330999i
$621$		0			0
$622$	−15.3259	+	19.2181i	−0.614515	+	0.770577i
$623$	−11.4537	−	22.3586i	−0.458884	−	0.895780i
$624$		0			0
$625$	−8.42494	+	7.81720i	−0.336998	+	0.312688i
$626$	23.2528	−	3.50479i	0.929368	−	0.140080i
$627$		0			0
$628$	7.59700	+	1.14506i	0.303153	+	0.0456930i
$629$	−40.5411	+	19.5236i	−1.61648	+	0.778456i
$630$		0			0
$631$	−14.2211	−	6.84854i	−0.566134	−	0.272636i	0.128846	−	0.991665i	$-0.458873\pi$
$631$	−14.2211	−	6.84854i	−0.566134	−	0.272636i	−0.694980	+	0.719029i	$0.744587\pi$
$632$	−7.10891	−	4.84677i	−0.282777	−	0.192794i
$633$		0			0
$634$	2.47198	−	32.9863i	0.0981749	−	1.31005i
$635$	−2.77147	+	7.06160i	−0.109983	+	0.280231i
$636$		0			0
$637$	18.2316	−	6.62278i	0.722361	−	0.262404i
$638$	−6.36072			−0.251823
$639$		0			0
$640$	0.998870	−	13.3290i	0.0394838	−	0.526875i
$641$	19.2939	+	17.9021i	0.762062	+	0.707090i	0.962100	−	0.272698i	$-0.0879160\pi$
$641$	19.2939	+	17.9021i	0.762062	+	0.707090i	−0.200038	+	0.979788i	$0.564106\pi$
$642$		0			0
$643$	36.3534	+	17.5069i	1.43364	+	0.690404i	0.979671	−	0.200613i	$-0.0642935\pi$
$643$	36.3534	+	17.5069i	1.43364	+	0.690404i	0.453969	+	0.891018i	$0.350008\pi$
$644$	0.861116	+	4.89262i	0.0339327	+	0.192796i
$645$		0			0
$646$	9.78243	+	1.47446i	0.384885	+	0.0580120i
$647$	30.9391	−	21.0939i	1.21634	−	0.829287i	0.226856	−	0.973928i	$-0.427155\pi$
$647$	30.9391	−	21.0939i	1.21634	−	0.829287i	0.989484	+	0.144641i	$0.0462028\pi$
$648$		0			0
$649$	4.80643	−	4.45971i	0.188669	−	0.175059i
$650$	11.0021	+	13.7962i	0.431537	+	0.541130i
$651$		0			0
$652$	0.820526	−	1.02891i	0.0321343	−	0.0402951i
$653$	0.228595	+	3.05039i	0.00894563	+	0.119371i	0.999889	−	0.0149106i	$-0.00474636\pi$
$653$	0.228595	+	3.05039i	0.00894563	+	0.119371i	−0.990943	+	0.134282i	$0.957127\pi$
$654$		0			0
$655$	−0.116705	+	0.202139i	−0.00456003	+	0.00789820i
$656$	26.5243	+	45.9414i	1.03560	+	1.79371i
$657$		0			0
$658$	5.79720	−	46.1431i	0.225998	−	1.79884i
$659$	5.70915	−	25.0134i	0.222397	−	0.974384i	−0.733271	−	0.679937i	$-0.762007\pi$
$659$	5.70915	−	25.0134i	0.222397	−	0.974384i	0.955668	−	0.294448i	$-0.0951356\pi$
$660$		0			0
$661$	−6.83253	−	17.4090i	−0.265755	−	0.677132i	0.734244	−	0.678886i	$-0.237537\pi$
$661$	−6.83253	−	17.4090i	−0.265755	−	0.677132i	−0.999998	+	0.00175402i	$0.999442\pi$
$662$	2.20284	+	5.61274i	0.0856158	+	0.218145i
$663$		0			0
$664$	−4.16767	+	18.2597i	−0.161737	+	0.708616i
$665$	2.85366	−	1.74260i	0.110660	−	0.0675753i
$666$		0			0
$667$	−4.26315	−	7.38399i	−0.165070	−	0.285909i
$668$	3.46175	−	5.99592i	0.133939	−	0.231989i
$669$		0			0
$670$	−0.164684	−	2.19755i	−0.00636228	−	0.0848987i
$671$	−9.93290	+	12.4555i	−0.383455	+	0.480838i
$672$		0			0
$673$	−1.18995	−	1.49214i	−0.0458690	−	0.0575179i	0.758368	−	0.651827i	$-0.225997\pi$
$673$	−1.18995	−	1.49214i	−0.0458690	−	0.0575179i	−0.804237	+	0.594309i	$0.797426\pi$
$674$	−8.97934	+	8.33161i	−0.345871	+	0.320922i
$675$		0			0
$676$	−2.14222	+	1.46054i	−0.0823931	+	0.0561747i
$677$	−31.7283	−	4.78227i	−1.21942	−	0.183797i	−0.492370	−	0.870386i	$-0.663869\pi$
$677$	−31.7283	−	4.78227i	−1.21942	−	0.183797i	−0.727046	+	0.686588i	$0.759107\pi$
$678$		0			0
$679$	3.36190	+	4.67922i	0.129018	+	0.179572i
$680$	10.2659	+	4.94378i	0.393678	+	0.189585i
$681$		0			0
$682$	−1.23300	−	1.14406i	−0.0472140	−	0.0438082i
$683$	−0.394922	+	5.26986i	−0.0151113	+	0.201646i	0.984538	+	0.175170i	$0.0560475\pi$
$683$	−0.394922	+	5.26986i	−0.0151113	+	0.201646i	−0.999649	+	0.0264757i	$0.991572\pi$
$684$		0			0
$685$	8.44908			0.322823
$686$	2.21018	−	29.1245i	0.0843851	−	1.11198i
$687$		0			0
$688$	9.57926	−	24.4076i	0.365206	−	0.930529i
$689$	1.41137	−	18.8334i	0.0537688	−	0.717494i
$690$		0			0
$691$	−37.9438	−	25.8697i	−1.44345	−	0.984128i	−0.995956	−	0.0898421i	$-0.971364\pi$
$691$	−37.9438	−	25.8697i	−1.44345	−	0.984128i	−0.447495	−	0.894286i	$-0.647684\pi$
$692$	6.03111	+	2.90443i	0.229268	+	0.110410i
$693$		0			0
$694$	−11.0200	+	5.30697i	−0.418315	+	0.201450i
$695$	17.7577	+	2.67654i	0.673588	+	0.101527i
$696$		0			0
$697$	−53.9152	+	8.12641i	−2.04218	+	0.307810i
$698$	−3.75062	+	3.48007i	−0.141963	+	0.131723i
$699$		0			0
$700$	5.04453	−	1.28281i	0.190665	−	0.0484856i
$701$	13.2240	−	16.5824i	0.499465	−	0.626310i	−0.466643	−	0.884446i	$-0.654537\pi$
$701$	13.2240	−	16.5824i	0.499465	−	0.626310i	0.966109	+	0.258136i	$0.0831083\pi$
$702$		0			0
$703$	−11.3780	−	3.50966i	−0.429131	−	0.132369i
$704$	4.75530	−	8.23642i	0.179222	−	0.310422i
$705$		0			0
$706$	4.63743	+	20.3179i	0.174532	+	0.764674i
$707$	−4.14811	+	2.53307i	−0.156006	+	0.0952659i
$708$		0			0
$709$	−13.0499	+	4.02535i	−0.490098	+	0.151175i	−0.529947	−	0.848031i	$-0.677788\pi$
$709$	−13.0499	+	4.02535i	−0.490098	+	0.151175i	0.0398497	+	0.999206i	$0.487312\pi$
$710$	−5.58356	−	14.2267i	−0.209547	−	0.533917i
$711$		0			0
$712$	21.6468	−	6.67716i	0.811249	−	0.250237i
$713$	0.501710	−	2.19814i	0.0187892	−	0.0823208i
$714$		0			0
$715$	−1.10259	−	4.83077i	−0.0412346	−	0.180660i
$716$	1.09042	+	1.88867i	0.0407510	+	0.0705828i
$717$		0			0
$718$	37.3801	+	11.5302i	1.39501	+	0.430305i
$719$	0.184875	+	2.46699i	0.00689468	+	0.0920032i	0.999590	−	0.0286490i	$-0.00912050\pi$
$719$	0.184875	+	2.46699i	0.00689468	+	0.0920032i	−0.992695	+	0.120652i	$0.961501\pi$
$720$		0			0
$721$	−0.0514506	−	2.08944i	−0.00191612	−	0.0778147i
$722$	−17.0506	−	21.3807i	−0.634556	−	0.795708i
$723$		0			0
$724$	−3.39515	+	0.511736i	−0.126180	+	0.0190185i
$725$	−7.38122	+	5.03243i	−0.274132	+	0.186900i
$726$		0			0
$727$	−22.8931	+	11.0247i	−0.849059	+	0.408885i	−0.807228	−	0.590239i	$-0.799033\pi$
$727$	−22.8931	+	11.0247i	−0.849059	+	0.408885i	−0.0418307	+	0.999125i	$0.513319\pi$
$728$	3.03192	+	17.2265i	0.112370	+	0.638456i
$729$		0			0
$730$	10.7309	+	7.31621i	0.397169	+	0.270785i
$731$	19.7553	+	18.3302i	0.730676	+	0.677968i
$732$		0			0
$733$	17.5793	−	44.7914i	0.649308	−	1.65441i	−0.102264	−	0.994757i	$-0.532609\pi$
$733$	17.5793	−	44.7914i	0.649308	−	1.65441i	0.751572	−	0.659652i	$-0.229296\pi$
$734$	−29.9631			−1.10596
$735$		0			0
$736$	−10.4022			−0.383430
$737$	0.948717	−	2.41729i	0.0349464	−	0.0890421i
$738$		0			0
$739$	15.1924	+	14.0965i	0.558862	+	0.518548i	0.908249	−	0.418431i	$-0.137420\pi$
$739$	15.1924	+	14.0965i	0.558862	+	0.518548i	−0.349387	+	0.936978i	$0.613610\pi$
$740$	3.64947	+	2.48817i	0.134157	+	0.0914669i
$741$		0			0
$742$	−24.9712	−	13.6088i	−0.916722	−	0.499594i
$743$	−24.6672	+	11.8791i	−0.904952	+	0.435802i	−0.827675	−	0.561208i	$-0.810337\pi$
$743$	−24.6672	+	11.8791i	−0.904952	+	0.435802i	−0.0772768	+	0.997010i	$0.524623\pi$
$744$		0			0
$745$	−17.4130	+	11.8720i	−0.637962	+	0.434955i
$746$	22.9960	−	3.46609i	0.841944	−	0.126903i
$747$		0			0
$748$	−2.69624	−	3.38098i	−0.0985844	−	0.123621i
$749$	−15.4037	−	30.0692i	−0.562837	−	1.09871i
$750$		0			0
$751$	−2.82950	−	37.7570i	−0.103250	−	1.37777i	−0.772631	−	0.634855i	$-0.781060\pi$
$751$	−2.82950	−	37.7570i	−0.103250	−	1.37777i	0.669382	−	0.742919i	$-0.266559\pi$
$752$	50.4514	+	15.5622i	1.83977	+	0.567495i
$753$		0			0
$754$	4.83443	+	8.37348i	0.176060	+	0.304944i
$755$	−0.404688	−	1.77305i	−0.0147281	−	0.0645281i
$756$		0			0
$757$	−1.71911	+	7.53191i	−0.0624821	+	0.273752i	−0.996513	−	0.0834410i	$-0.973409\pi$
$757$	−1.71911	+	7.53191i	−0.0624821	+	0.273752i	0.934031	+	0.357193i	$0.116266\pi$
$758$	49.4394	−	15.2500i	1.79572	−	0.553906i
$759$		0			0
$760$	1.10154	+	2.80669i	0.0399572	+	0.101809i
$761$	−25.4811	+	7.85989i	−0.923691	+	0.284921i	−0.719887	−	0.694091i	$-0.755807\pi$
$761$	−25.4811	+	7.85989i	−0.923691	+	0.284921i	−0.203804	+	0.979012i	$0.565330\pi$
$762$		0			0
$763$	30.0131	+	30.7903i	1.08655	+	1.11468i
$764$	2.08067	+	9.11603i	0.0752761	+	0.329806i
$765$		0			0
$766$	30.0845	−	52.1080i	1.08700	−	1.88274i
$767$	−9.52403	−	2.93777i	−0.343893	−	0.106077i
$768$		0			0
$769$	13.1660	−	16.5096i	0.474777	−	0.595352i	−0.485557	−	0.874205i	$-0.661383\pi$
$769$	13.1660	−	16.5096i	0.474777	−	0.595352i	0.960334	+	0.278854i	$0.0899545\pi$
$770$	−7.31281	−	1.48071i	−0.263535	−	0.0533610i
$771$		0			0
$772$	−8.09068	+	7.50705i	−0.291190	+	0.270185i
$773$	19.4909	−	2.93778i	0.701038	−	0.105665i	0.211155	−	0.977453i	$-0.432278\pi$
$773$	19.4909	−	2.93778i	0.701038	−	0.105665i	0.489883	+	0.871788i	$0.337039\pi$
$774$		0			0
$775$	−2.33596	−	0.352090i	−0.0839103	−	0.0126474i
$776$	−4.68106	+	2.25428i	−0.168040	+	0.0809239i
$777$		0			0
$778$	−35.2217	−	16.9619i	−1.26276	−	0.608113i
$779$	−11.9210	−	8.12760i	−0.427114	−	0.291201i
$780$		0			0
$781$	1.34584	−	17.9589i	0.0481578	−	0.642621i
$782$	10.8110	−	27.5459i	0.386600	−	0.985040i
$783$		0			0
$784$	32.1289	+	8.20253i	1.14746	+	0.292947i
$785$	−15.4674			−0.552055
$786$		0			0
$787$	−2.80339	+	37.4086i	−0.0999301	+	1.33347i	0.691572	+	0.722308i	$0.256918\pi$
$787$	−2.80339	+	37.4086i	−0.0999301	+	1.33347i	−0.791502	+	0.611166i	$0.790701\pi$
$788$	1.24955	+	1.15941i	0.0445134	+	0.0413024i
$789$		0			0
$790$	−5.02648	−	2.42063i	−0.178834	−	0.0861220i
$791$	−11.8484	−	0.595060i	−0.421281	−	0.0211579i
$792$		0			0
$793$	23.9463	+	3.60932i	0.850356	+	0.128171i
$794$	−45.5159	+	31.0322i	−1.61530	+	1.10129i
$795$		0			0
$796$	3.21694	−	2.98488i	0.114021	−	0.105796i
$797$	1.63719	+	2.05297i	0.0579921	+	0.0727198i	0.809982	−	0.586455i	$-0.199477\pi$
$797$	1.63719	+	2.05297i	0.0579921	+	0.0727198i	−0.751989	+	0.659175i	$0.770906\pi$
$798$		0			0
$799$	−33.8341	+	42.4266i	−1.19696	+	1.50094i
$800$	0.814483	+	10.8685i	0.0287963	+	0.384260i
$801$		0			0
$802$	7.22915	−	12.5213i	0.255270	−	0.442141i
$803$	7.65217	+	13.2539i	0.270039	+	0.467722i
$804$		0			0
$805$	−3.18235	−	9.48165i	−0.112163	−	0.334184i
$806$	−0.568942	+	2.49270i	−0.0200401	+	0.0878015i
$807$		0			0
$808$	−1.60122	−	4.07984i	−0.0563307	−	0.143528i
$809$	8.21399	+	20.9289i	0.288789	+	0.735821i	0.999478	+	0.0323151i	$0.0102880\pi$
$809$	8.21399	+	20.9289i	0.288789	+	0.735821i	−0.710689	+	0.703506i	$0.751617\pi$
$810$		0			0
$811$	−0.265942	+	1.16517i	−0.00933848	+	0.0409146i	−0.979382	−	0.202015i	$-0.935251\pi$
$811$	−0.265942	+	1.16517i	−0.00933848	+	0.0409146i	0.970044	+	0.242929i	$0.0781083\pi$
$812$	2.83798	−	0.283082i	0.0995934	−	0.00993423i
$813$		0			0
$814$	13.2850	+	23.0103i	0.465639	+	0.806510i
$815$	−1.32474	+	2.29452i	−0.0464036	+	0.0803734i
$816$		0			0
$817$	0.532920	+	7.11132i	0.0186445	+	0.248794i
$818$	−37.0760	+	46.4919i	−1.29633	+	1.62555i
$819$		0			0
$820$	3.33701	+	4.18448i	0.116533	+	0.146128i
$821$	9.54245	−	8.85410i	0.333034	−	0.309010i	−0.495875	−	0.868394i	$-0.665153\pi$
$821$	9.54245	−	8.85410i	0.333034	−	0.309010i	0.828909	+	0.559384i	$0.188962\pi$
$822$		0			0
$823$	−31.6425	+	21.5735i	−1.10299	+	0.752005i	−0.970960	−	0.239241i	$-0.923101\pi$
$823$	−31.6425	+	21.5735i	−1.10299	+	0.752005i	−0.132028	+	0.991246i	$0.542149\pi$
$824$	1.86365	+	0.280901i	0.0649234	+	0.00978563i
$825$		0			0
$826$	−9.93411	+	11.2496i	−0.345652	+	0.391423i
$827$	−31.6793	−	15.2559i	−1.10160	−	0.530501i	−0.207437	−	0.978248i	$-0.566512\pi$
$827$	−31.6793	−	15.2559i	−1.10160	−	0.530501i	−0.894160	+	0.447747i	$0.852226\pi$
$828$		0			0
$829$	−6.30110	−	5.84657i	−0.218846	−	0.203060i	0.563129	−	0.826369i	$-0.309597\pi$
$829$	−6.30110	−	5.84657i	−0.218846	−	0.203060i	−0.781976	+	0.623309i	$0.785788\pi$
$830$	−0.907559	+	12.1105i	−0.0315018	+	0.420363i
$831$		0			0
$832$	−14.4570			−0.501205
$833$	−19.9124	+	27.6598i	−0.689925	+	0.958356i
$834$		0			0
$835$	−5.09238	+	12.9752i	−0.176229	+	0.449025i
$836$	0.0855151	−	1.14112i	0.00295760	−	0.0394664i
$837$		0			0
$838$	−17.9537	−	12.2406i	−0.620200	−	0.422845i
$839$	−39.0723	−	18.8162i	−1.34893	−	0.649608i	−0.386787	−	0.922169i	$-0.626415\pi$
$839$	−39.0723	−	18.8162i	−1.34893	−	0.649608i	−0.962139	+	0.272561i	$0.912129\pi$
$840$		0			0
$841$	21.7179	−	10.4588i	0.748891	−	0.360647i
$842$	34.3653	+	5.17973i	1.18431	+	0.178505i
$843$		0			0
$844$	−4.36183	+	0.657440i	−0.150140	+	0.0226300i
$845$	3.82640	−	3.55038i	0.131632	−	0.122137i
$846$		0			0
$847$	16.1868	+	12.2691i	0.556186	+	0.421570i
$848$	20.1299	−	25.2421i	0.691264	−	0.866817i
$849$		0			0
$850$	−29.6273	−	9.13881i	−1.01621	−	0.313459i
$851$	−17.8080	+	30.8444i	−0.610450	+	1.05733i
$852$		0			0
$853$	9.41102	+	41.2324i	0.322227	+	1.41177i	0.833580	+	0.552399i	$0.186287\pi$
$853$	9.41102	+	41.2324i	0.322227	+	1.41177i	−0.511353	+	0.859371i	$0.670855\pi$
$854$	19.7938	−	30.6257i	0.677330	−	1.04799i
$855$		0			0
$856$	29.1119	−	8.97983i	0.995024	−	0.306924i
$857$	3.36529	+	8.57462i	0.114956	+	0.292903i	0.976759	−	0.214340i	$-0.0687599\pi$
$857$	3.36529	+	8.57462i	0.114956	+	0.292903i	−0.861803	+	0.507243i	$0.830665\pi$
$858$		0			0
$859$	−6.03607	+	1.86188i	−0.205948	+	0.0635266i	−0.396013	−	0.918245i	$-0.629606\pi$
$859$	−6.03607	+	1.86188i	−0.205948	+	0.0635266i	0.190065	+	0.981772i	$0.439130\pi$
$860$	0.588651	−	2.57905i	0.0200728	−	0.0879449i
$861$		0			0
$862$	4.76353	+	20.8704i	0.162246	+	0.710848i
$863$	−6.05094	−	10.4805i	−0.205976	−	0.356761i	0.744467	−	0.667659i	$-0.232704\pi$
$863$	−6.05094	−	10.4805i	−0.205976	−	0.356761i	−0.950443	+	0.310898i	$0.899370\pi$
$864$		0			0
$865$	−12.8780	−	3.97234i	−0.437865	−	0.135064i
$866$	1.64974	+	22.0143i	0.0560605	+	0.748076i
$867$		0			0
$868$	0.601045	+	0.455571i	0.0204008	+	0.0154631i
$869$	−4.09890	−	5.13986i	−0.139046	−	0.174358i
$870$		0			0
$871$	−3.90328	+	0.588324i	−0.132258	+	0.0199346i
$872$	−32.0359	+	21.8417i	−1.08487	+	0.739653i
$873$		0			0
$874$	7.05495	−	3.39748i	0.238637	−	0.114922i
$875$	−21.6164	+	9.10410i	−0.730769	+	0.307775i
$876$		0			0
$877$	33.4776	+	22.8246i	1.13046	+	0.770733i	0.976109	−	0.217284i	$-0.0697196\pi$
$877$	33.4776	+	22.8246i	1.13046	+	0.770733i	0.154349	+	0.988016i	$0.450672\pi$
$878$	−47.2607	−	43.8515i	−1.59497	−	1.47992i
$879$		0			0
$880$	3.09464	−	7.88502i	0.104320	−	0.265804i
$881$	7.37500			0.248470			0.124235	−	0.992253i	$-0.460352\pi$
$881$	7.37500			0.248470			0.124235	+	0.992253i	$0.460352\pi$
$882$		0			0
$883$	−6.83587			−0.230045			−0.115023	−	0.993363i	$-0.536694\pi$
$883$	−6.83587			−0.230045			−0.115023	+	0.993363i	$0.536694\pi$
$884$	−2.40158	+	6.11913i	−0.0807739	+	0.205809i
$885$		0			0
$886$	38.1443	+	35.3928i	1.28148	+	1.18904i
$887$	−36.0312	−	24.5657i	−1.20981	−	0.824835i	−0.221185	−	0.975232i	$-0.570992\pi$
$887$	−36.0312	−	24.5657i	−1.20981	−	0.824835i	−0.988626	+	0.150397i	$0.951945\pi$
$888$		0			0
$889$	13.5437	−	15.3372i	0.454241	−	0.514392i
$890$	13.2342	−	6.37325i	0.443611	−	0.213632i
$891$		0			0
$892$	−10.9583	+	7.47121i	−0.366910	+	0.250155i
$893$	−14.1992	+	2.14019i	−0.475159	+	0.0716187i
$894$		0			0
$895$	−2.73748	−	3.43270i	−0.0915040	−	0.114742i
$896$	−14.8381	+	32.8572i	−0.495707	+	1.09768i
$897$		0			0
$898$	−1.03882	−	13.8621i	−0.0346659	−	0.462585i
$899$	−1.23691	−	0.381537i	−0.0412533	−	0.0127250i
$900$		0			0
$901$	16.5920	+	28.7381i	0.552758	+	0.957405i
$902$	7.16416	+	31.3882i	0.238540	+	1.04511i
$903$		0			0
$904$	2.38045	−	10.4295i	0.0791727	−	0.346878i
$905$	6.60538	−	2.03749i	0.219570	−	0.0677285i
$906$		0			0
$907$	19.9294	+	50.7793i	0.661745	+	1.68610i	0.725579	+	0.688139i	$0.241572\pi$
$907$	19.9294	+	50.7793i	0.661745	+	1.68610i	−0.0638339	+	0.997961i	$0.520333\pi$
$908$	8.09935	−	2.49832i	0.268786	−	0.0829096i
$909$		0			0
$910$	3.60880	+	10.7522i	0.119631	+	0.356433i
$911$	3.81557	+	16.7171i	0.126415	+	0.553862i	0.997977	+	0.0635761i	$0.0202506\pi$
$911$	3.81557	+	16.7171i	0.126415	+	0.553862i	−0.871562	+	0.490286i	$0.836892\pi$
$912$		0			0
$913$	−7.15539	+	12.3935i	−0.236809	+	0.410165i
$914$	34.5885	+	10.6691i	1.14409	+	0.352904i
$915$		0			0
$916$	−3.73527	+	4.68388i	−0.123417	+	0.154760i
$917$	0.482398	−	0.404522i	0.0159302	−	0.0133585i
$918$		0			0
$919$	−36.6523	+	34.0083i	−1.20905	+	1.12183i	−0.219804	+	0.975544i	$0.570542\pi$
$919$	−36.6523	+	34.0083i	−1.20905	+	1.12183i	−0.989242	+	0.146287i	$0.953268\pi$
$920$	8.91800	−	1.34417i	0.294018	−	0.0443160i
$921$		0			0
$922$	33.1823	+	5.00143i	1.09280	+	0.164713i
$923$	−24.6647	+	11.8779i	−0.811847	+	0.390965i
$924$		0			0
$925$	33.6215	+	16.1913i	1.10547	+	0.532365i
$926$	2.01307	+	1.37248i	0.0661534	+	0.0451026i
$927$		0			0
$928$	−0.446285	+	5.95527i	−0.0146500	+	0.195491i
$929$	−8.86963	+	22.5994i	−0.291003	+	0.741464i	0.708363	+	0.705849i	$0.249434\pi$
$929$	−8.86963	+	22.5994i	−0.291003	+	0.741464i	−0.999366	+	0.0356149i	$0.988661\pi$
$930$		0			0
$931$	−8.84093	+	1.78145i	−0.289750	+	0.0583847i
$932$	12.9926			0.425587
$933$		0			0
$934$	−0.157564	+	2.10254i	−0.00515564	+	0.0687972i
$935$	6.38207	+	5.92170i	0.208716	+	0.193660i
$936$		0			0
$937$	−22.6593	−	10.9121i	−0.740246	−	0.356484i	0.0254587	−	0.999676i	$-0.491895\pi$
$937$	−22.6593	−	10.9121i	−0.740246	−	0.356484i	−0.765705	+	0.643192i	$0.777610\pi$
$938$	−1.61165	+	5.72126i	−0.0526223	+	0.186806i
$939$		0			0
$940$	5.26727	+	0.793913i	0.171799	+	0.0258946i
$941$	23.2468	−	15.8494i	0.757823	−	0.516675i	−0.121680	−	0.992569i	$-0.538828\pi$
$941$	23.2468	−	15.8494i	0.757823	−	0.516675i	0.879502	+	0.475895i	$0.157876\pi$
$942$		0			0
$943$	−31.6361	+	29.3540i	−1.03021	+	0.955899i
$944$	−10.6232	−	13.3210i	−0.345755	−	0.433563i
$945$		0			0
$946$	9.92164	−	12.4413i	0.322580	−	0.404503i
$947$	−3.95065	−	52.7177i	−0.128379	−	1.71310i	−0.574817	−	0.818282i	$-0.694927\pi$
$947$	−3.95065	−	52.7177i	−0.128379	−	1.71310i	0.446438	−	0.894815i	$-0.352692\pi$
$948$		0			0
$949$	11.6320	−	20.1472i	0.377590	−	0.654005i
$950$	−4.10219	−	7.10521i	−0.133093	−	0.230523i
$951$		0			0
$952$	−21.4520	−	22.0075i	−0.695263	−	0.713266i
$953$	7.34553	−	32.1829i	0.237945	−	1.04251i	−0.704909	−	0.709298i	$-0.749012\pi$
$953$	7.34553	−	32.1829i	0.237945	−	1.04251i	0.942854	−	0.333207i	$-0.108131\pi$
$954$		0			0
$955$	−6.87747	−	17.5235i	−0.222550	−	0.567048i
$956$	−3.16764	−	8.07102i	−0.102449	−	0.261035i
$957$		0			0
$958$	−4.18116	+	18.3188i	−0.135087	+	0.591855i
$959$	−21.4124	−	7.80108i	−0.691441	−	0.251910i
$960$		0			0
$961$	15.3289	+	26.5504i	0.494479	+	0.856463i
$962$	20.1944	−	34.9777i	0.651093	−	1.12773i
$963$		0			0
$964$	0.196081	+	2.61651i	0.00631533	+	0.0842723i
$965$	13.8541	−	17.3724i	0.445978	−	0.559239i
$966$		0			0
$967$	−29.1688	−	36.5766i	−0.938007	−	1.17622i	−0.984159	−	0.177289i	$-0.943267\pi$
$967$	−29.1688	−	36.5766i	−0.938007	−	1.17622i	0.0461521	−	0.998934i	$-0.485304\pi$
$968$	−13.4261	+	12.4576i	−0.431533	+	0.400404i
$969$		0			0
$970$	−2.78354	+	1.89778i	−0.0893740	+	0.0609342i
$971$	7.62194	+	1.14882i	0.244600	+	0.0368675i	0.270198	−	0.962805i	$-0.412911\pi$
$971$	7.62194	+	1.14882i	0.244600	+	0.0368675i	−0.0255981	+	0.999672i	$0.508149\pi$
$972$		0			0
$973$	−42.5317	−	23.1789i	−1.36350	−	0.743081i
$974$	−5.05271	−	2.43326i	−0.161899	−	0.0779665i
$975$		0			0
$976$	30.3472	+	28.1581i	0.971390	+	0.901318i
$977$	−0.569471	+	7.59906i	−0.0182190	+	0.243116i	0.980658	+	0.195731i	$0.0627078\pi$
$977$	−0.569471	+	7.59906i	−0.0182190	+	0.243116i	−0.998877	+	0.0473850i	$0.984911\pi$
$978$		0			0
$979$	17.3090			0.553197
$980$	3.32867	+	0.335196i	0.106330	+	0.0107074i
$981$		0			0
$982$	2.13809	−	5.44778i	0.0682293	−	0.173846i
$983$	−1.78661	+	23.8407i	−0.0569841	+	0.760399i	0.893388	+	0.449285i	$0.148321\pi$
$983$	−1.78661	+	23.8407i	−0.0569841	+	0.760399i	−0.950372	+	0.311114i	$0.899298\pi$
$984$		0			0
$985$	−2.83545	−	1.93318i	−0.0903450	−	0.0615962i
$986$	−15.3063	−	7.37110i	−0.487450	−	0.234744i
$987$		0			0
$988$	−1.56721	+	0.754727i	−0.0498595	+	0.0240111i
$989$	21.0926	+	3.17920i	0.670705	+	0.101093i
$990$		0			0
$991$	−29.2692	+	4.41162i	−0.929766	+	0.140140i	−0.596427	−	0.802667i	$-0.703414\pi$
$991$	−29.2692	+	4.41162i	−0.929766	+	0.140140i	−0.333339	+	0.942807i	$0.608175\pi$
$992$	−1.15764	+	1.07413i	−0.0367551	+	0.0341038i
$993$		0			0
$994$	1.01475	+	41.2097i	0.0321860	+	1.30709i
$995$	−5.50851	+	6.90746i	−0.174632	+	0.218981i
$996$		0			0
$997$	−33.1407	−	10.2225i	−1.04958	−	0.323751i	−0.278461	−	0.960447i	$-0.589824\pi$
$997$	−33.1407	−	10.2225i	−1.04958	−	0.323751i	−0.771115	+	0.636696i	$0.780301\pi$
$998$	24.4606	−	42.3670i	0.774287	−	1.34111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.46.5	yes	72
3.2	odd	2	inner	441.2.bb.f.46.2	✓	72
49.16	even	21	inner	441.2.bb.f.163.5	yes	72
147.65	odd	42	inner	441.2.bb.f.163.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.46.2	✓	72	3.2	odd	2	inner
441.2.bb.f.46.5	yes	72	1.1	even	1	trivial
441.2.bb.f.163.2	yes	72	147.65	odd	42	inner
441.2.bb.f.163.5	yes	72	49.16	even	21	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.576178 - 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(0.810468 + 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(2.14952 - 1.03515i) q^{8} +O(q^{10})\)	\(q+(0.576178 - 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(0.810468 + 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(2.14952 - 1.03515i) q^{8} +(1.27819 - 0.871452i) q^{10} +(1.80258 - 0.271695i) q^{11} +(-1.72771 - 2.16648i) q^{13} +(-4.04390 + 1.02835i) q^{14} +(-0.354001 - 4.72382i) q^{16} +(4.65252 + 1.43511i) q^{17} +(0.644188 + 1.11577i) q^{19} +(-0.106349 - 0.465946i) q^{20} +(0.639736 - 2.80287i) q^{22} +(3.68254 - 1.13591i) q^{23} +(-1.47518 - 3.75869i) q^{25} +(-4.17602 + 1.28813i) q^{26} +(-0.160692 + 1.27903i) q^{28} +(-0.492320 - 2.15699i) q^{29} +(0.292528 - 0.506674i) q^{31} +(-2.57932 - 0.795613i) q^{32} +(4.78753 - 6.00338i) q^{34} +(-0.0638864 - 2.59446i) q^{35} +(-6.77479 + 6.28609i) q^{37} +(2.00920 - 0.302837i) q^{38} +(2.31411 + 0.348796i) q^{40} +(-10.0896 + 4.85890i) q^{41} +(4.98694 + 2.40158i) q^{43} +(-0.733855 - 0.500334i) q^{44} +(0.454190 - 6.06074i) q^{46} +(-4.07192 + 10.3751i) q^{47} +(-2.23357 + 6.63409i) q^{49} -6.36801 q^{50} +(-0.100895 + 1.34635i) q^{52} +(4.99617 + 4.63577i) q^{53} +(1.61106 + 0.775846i) q^{55} +(-5.54255 - 3.02057i) q^{56} +(-3.45030 - 0.520049i) q^{58} +(2.97181 - 2.02615i) q^{59} +(-6.40633 + 5.94420i) q^{61} +(-0.575288 - 0.721388i) q^{62} +(3.25286 - 4.07896i) q^{64} +(-0.203127 - 2.71054i) q^{65} +(0.712256 - 1.23366i) q^{67} +(-1.18612 - 2.05442i) q^{68} +(-3.84568 - 1.40108i) q^{70} +(2.19834 - 9.63156i) q^{71} +(3.06719 + 7.81508i) q^{73} +(5.32498 + 13.5678i) q^{74} +(0.139684 - 0.611995i) q^{76} +(-3.36654 - 3.45371i) q^{77} +(-1.80317 - 3.12318i) q^{79} +(2.32332 - 4.02411i) q^{80} +(1.31983 + 17.6119i) q^{82} +(-4.89464 + 6.13768i) q^{83} +(2.97772 + 3.73395i) q^{85} +(6.39907 - 5.93747i) q^{86} +(3.59343 - 2.44996i) q^{88} +(9.38904 + 1.41517i) q^{89} +(-1.98787 + 7.05681i) q^{91} +(-1.69171 - 0.814686i) q^{92} +(12.8853 + 11.9558i) q^{94} +(-0.0944427 + 1.26025i) q^{95} -2.17773 q^{97} +(8.45241 + 7.10147i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

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