LMFDB - Embedded newform 819.2.fm.f.496.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.6
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.f.748.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(0.512287 + 0.512287i) q^{5} +(-1.54136 + 2.15040i) q^{7} +(-1.97762 - 1.97762i) q^{8} +O(q^{10})$	\(q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(0.512287 + 0.512287i) q^{5} +(-1.54136 + 2.15040i) q^{7} +(-1.97762 - 1.97762i) q^{8} +(0.517838 + 0.896921i) q^{10} +(-1.38992 + 5.18727i) q^{11} +(0.0545462 + 3.60514i) q^{13} +(-2.92397 + 2.39904i) q^{14} +(-2.04263 - 3.53793i) q^{16} +(-1.31681 + 2.28077i) q^{17} +(5.26328 - 1.41029i) q^{19} +(0.00817077 + 0.0304937i) q^{20} +(-3.83849 + 6.64846i) q^{22} +(-5.51236 + 3.18256i) q^{23} -4.47512i q^{25} +(-1.25855 + 4.99825i) q^{26} +(-0.105018 + 0.0475676i) q^{28} +(-0.300703 - 0.520832i) q^{29} +(6.22737 + 6.22737i) q^{31} +(-0.0637871 - 0.238057i) q^{32} +(-2.66215 + 2.66215i) q^{34} +(-1.89124 + 0.312006i) q^{35} +(0.172749 - 0.644708i) q^{37} +7.78948 q^{38} -2.02622i q^{40} +(-2.11401 + 7.88960i) q^{41} +(4.10340 + 2.36910i) q^{43} +(-0.165470 + 0.165470i) q^{44} +(-8.78913 + 2.35504i) q^{46} +(4.25821 - 4.25821i) q^{47} +(-2.24845 - 6.62906i) q^{49} +(1.65576 - 6.17937i) q^{50} +(-0.0764887 + 0.137236i) q^{52} -0.282101 q^{53} +(-3.36941 + 1.94533i) q^{55} +(7.30090 - 1.20446i) q^{56} +(-0.222515 - 0.830436i) q^{58} +(-1.21690 - 4.54153i) q^{59} +(-13.0884 - 7.55656i) q^{61} +(6.29485 + 10.9030i) q^{62} +7.81819i q^{64} +(-1.81892 + 1.87481i) q^{65} +(4.48192 + 1.20093i) q^{67} +(-0.0993850 + 0.0573799i) q^{68} +(-2.72691 - 0.268916i) q^{70} +(-4.11194 - 15.3460i) q^{71} +(-3.04327 + 3.04327i) q^{73} +(0.477073 - 0.826314i) q^{74} +(0.229348 + 0.0614536i) q^{76} +(-9.01234 - 10.9843i) q^{77} +4.77147 q^{79} +(0.766026 - 2.85885i) q^{80} +(-5.83817 + 10.1120i) q^{82} +(2.42351 + 2.42351i) q^{83} +(-1.84299 + 0.493829i) q^{85} +(4.78954 + 4.78954i) q^{86} +(13.0072 - 7.50971i) q^{88} +(-5.75969 - 1.54330i) q^{89} +(-7.83657 - 5.43950i) q^{91} -0.277361 q^{92} +(7.45535 - 4.30435i) q^{94} +(3.41879 + 1.97384i) q^{95} +(15.7347 - 4.21610i) q^{97} +(-0.652020 - 9.98549i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.38083	+	0.369991i	0.976392	+	0.261623i	0.711524	−	0.702661i	$-0.248005\pi$
$2$	1.38083	+	0.369991i	0.976392	+	0.261623i	0.264867	+	0.964285i	$0.414672\pi$
$3$		0			0
$3$		0			0
$4$	0.0377371	+	0.0217876i	0.0188686	+	0.0108938i
$5$	0.512287	+	0.512287i	0.229102	+	0.229102i	0.812317	−	0.583216i	$-0.198206\pi$
$5$	0.512287	+	0.512287i	0.229102	+	0.229102i	−0.583216	+	0.812317i	$0.698206\pi$
$6$		0			0
$7$	−1.54136	+	2.15040i	−0.582578	+	0.812775i
$7$	−1.54136	+	2.15040i	−0.582578	+	0.812775i
$8$	−1.97762	−	1.97762i	−0.699195	−	0.699195i
$9$		0			0
$10$	0.517838	+	0.896921i	0.163755	+	0.283631i
$11$	−1.38992	+	5.18727i	−0.419078	+	1.56402i	0.357447	+	0.933933i	$0.383647\pi$
$11$	−1.38992	+	5.18727i	−0.419078	+	1.56402i	−0.776525	+	0.630086i	$0.783019\pi$
$12$		0			0
$13$	0.0545462	+	3.60514i	0.0151284	+	0.999886i
$13$	0.0545462	+	3.60514i	0.0151284	+	0.999886i
$14$	−2.92397	+	2.39904i	−0.781465	+	0.641171i
$15$		0			0
$16$	−2.04263	−	3.53793i	−0.510656	−	0.884483i
$17$	−1.31681	+	2.28077i	−0.319372	+	0.553169i	−0.980357	−	0.197230i	$-0.936805\pi$
$17$	−1.31681	+	2.28077i	−0.319372	+	0.553169i	0.660985	+	0.750399i	$0.270139\pi$
$18$		0			0
$19$	5.26328	−	1.41029i	1.20748	−	0.323543i	0.401707	−	0.915768i	$-0.368417\pi$
$19$	5.26328	−	1.41029i	1.20748	−	0.323543i	0.805773	+	0.592225i	$0.201750\pi$
$20$	0.00817077	+	0.0304937i	0.00182704	+	0.00681861i
$21$		0			0
$22$	−3.83849	+	6.64846i	−0.818368	+	1.41746i
$23$	−5.51236	+	3.18256i	−1.14941	+	0.663610i	−0.948742	−	0.316051i	$-0.897643\pi$
$23$	−5.51236	+	3.18256i	−1.14941	+	0.663610i	−0.200663	+	0.979660i	$0.564310\pi$
$24$		0			0
$25$		−	4.47512i		−	0.895025i
$26$	−1.25855	+	4.99825i	−0.246822	+	0.980238i
$27$		0			0
$28$	−0.105018	+	0.0475676i	−0.0198466	+	0.00898944i
$29$	−0.300703	−	0.520832i	−0.0558391	−	0.0967161i	0.836755	−	0.547578i	$-0.184450\pi$
$29$	−0.300703	−	0.520832i	−0.0558391	−	0.0967161i	−0.892594	+	0.450862i	$0.851117\pi$
$30$		0			0
$31$	6.22737	+	6.22737i	1.11847	+	1.11847i	0.991966	+	0.126503i	$0.0403752\pi$
$31$	6.22737	+	6.22737i	1.11847	+	1.11847i	0.126503	+	0.991966i	$0.459625\pi$
$32$	−0.0637871	−	0.238057i	−0.0112761	−	0.0420829i
$33$		0			0
$34$	−2.66215	+	2.66215i	−0.456554	+	0.456554i
$35$	−1.89124	+	0.312006i	−0.319678	+	0.0527387i
$36$		0			0
$37$	0.172749	−	0.644708i	0.0283998	−	0.105989i	−0.950271	−	0.311424i	$-0.899194\pi$
$37$	0.172749	−	0.644708i	0.0283998	−	0.105989i	0.978671	+	0.205435i	$0.0658608\pi$
$38$	7.78948			1.26362
$39$		0			0
$40$		−	2.02622i		−	0.320374i
$41$	−2.11401	+	7.88960i	−0.330153	+	1.23215i	0.578876	+	0.815416i	$0.303492\pi$
$41$	−2.11401	+	7.88960i	−0.330153	+	1.23215i	−0.909029	+	0.416733i	$0.863175\pi$
$42$		0			0
$43$	4.10340	+	2.36910i	0.625762	+	0.361284i	0.779109	−	0.626888i	$-0.215672\pi$
$43$	4.10340	+	2.36910i	0.625762	+	0.361284i	−0.153347	+	0.988172i	$0.549005\pi$
$44$	−0.165470	+	0.165470i	−0.0249455	+	0.0249455i
$45$		0			0
$46$	−8.78913	+	2.35504i	−1.29589	+	0.347232i
$47$	4.25821	−	4.25821i	0.621123	−	0.621123i	−0.324695	−	0.945819i	$-0.605262\pi$
$47$	4.25821	−	4.25821i	0.621123	−	0.621123i	0.945819	+	0.324695i	$0.105262\pi$
$48$		0			0
$49$	−2.24845	−	6.62906i	−0.321207	−	0.947009i
$50$	1.65576	−	6.17937i	0.234159	−	0.873895i
$51$		0			0
$52$	−0.0764887	+	0.137236i	−0.0106071	+	0.0190312i
$53$	−0.282101			−0.0387495			−0.0193748	−	0.999812i	$-0.506168\pi$
$53$	−0.282101			−0.0387495			−0.0193748	+	0.999812i	$0.506168\pi$
$54$		0			0
$55$	−3.36941	+	1.94533i	−0.454331	+	0.262308i
$56$	7.30090	−	1.20446i	0.975624	−	0.160953i
$57$		0			0
$58$	−0.222515	−	0.830436i	−0.0292176	−	0.109042i
$59$	−1.21690	−	4.54153i	−0.158427	−	0.591257i	−0.998787	−	0.0492295i	$-0.984323\pi$
$59$	−1.21690	−	4.54153i	−0.158427	−	0.591257i	0.840361	−	0.542028i	$-0.182343\pi$
$60$		0			0
$61$	−13.0884	−	7.55656i	−1.67579	−	0.967519i	−0.964295	−	0.264829i	$-0.914684\pi$
$61$	−13.0884	−	7.55656i	−1.67579	−	0.967519i	−0.711497	−	0.702690i	$-0.751982\pi$
$62$	6.29485	+	10.9030i	0.799446	+	1.38468i
$63$		0			0
$64$			7.81819i			0.977273i
$65$	−1.81892	+	1.87481i	−0.225610	+	0.232541i
$66$		0			0
$67$	4.48192	+	1.20093i	0.547553	+	0.146716i	0.521982	−	0.852957i	$-0.325193\pi$
$67$	4.48192	+	1.20093i	0.547553	+	0.146716i	0.0255714	+	0.999673i	$0.491859\pi$
$68$	−0.0993850	+	0.0573799i	−0.0120522	+	0.00695834i
$69$		0			0
$70$	−2.72691	−	0.268916i	−0.325928	−	0.0321416i
$71$	−4.11194	−	15.3460i	−0.487998	−	1.82123i	−0.566165	−	0.824292i	$-0.691573\pi$
$71$	−4.11194	−	15.3460i	−0.487998	−	1.82123i	0.0781668	−	0.996940i	$-0.475093\pi$
$72$		0			0
$73$	−3.04327	+	3.04327i	−0.356188	+	0.356188i	−0.862406	−	0.506218i	$-0.831043\pi$
$73$	−3.04327	+	3.04327i	−0.356188	+	0.356188i	0.506218	+	0.862406i	$0.331043\pi$
$74$	0.477073	−	0.826314i	0.0554586	−	0.0960571i
$75$		0			0
$76$	0.229348	+	0.0614536i	0.0263080	+	0.00704922i
$77$	−9.01234	−	10.9843i	−1.02705	−	1.25178i
$78$		0			0
$79$	4.77147			0.536832			0.268416	−	0.963303i	$-0.413500\pi$
$79$	4.77147			0.536832			0.268416	+	0.963303i	$0.413500\pi$
$80$	0.766026	−	2.85885i	0.0856443	−	0.319629i
$81$		0			0
$82$	−5.83817	+	10.1120i	−0.644718	+	1.11668i
$83$	2.42351	+	2.42351i	0.266015	+	0.266015i	0.827492	−	0.561477i	$-0.189767\pi$
$83$	2.42351	+	2.42351i	0.266015	+	0.266015i	−0.561477	+	0.827492i	$0.689767\pi$
$84$		0			0
$85$	−1.84299	+	0.493829i	−0.199901	+	0.0535632i
$86$	4.78954	+	4.78954i	0.516469	+	0.516469i
$87$		0			0
$88$	13.0072	−	7.50971i	1.38657	−	0.800538i
$89$	−5.75969	−	1.54330i	−0.610526	−	0.163590i	−0.0597085	−	0.998216i	$-0.519017\pi$
$89$	−5.75969	−	1.54330i	−0.610526	−	0.163590i	−0.550817	+	0.834626i	$0.685684\pi$
$90$		0			0
$91$	−7.83657	−	5.43950i	−0.821496	−	0.570215i
$92$	−0.277361			−0.0289169
$93$		0			0
$94$	7.45535	−	4.30435i	0.768960	−	0.443959i
$95$	3.41879	+	1.97384i	0.350760	+	0.202511i
$96$		0			0
$97$	15.7347	−	4.21610i	1.59762	−	0.428080i	0.653296	−	0.757103i	$-0.273386\pi$
$97$	15.7347	−	4.21610i	1.59762	−	0.428080i	0.944322	+	0.329022i	$0.106719\pi$
$98$	−0.652020	−	9.98549i	−0.0658640	−	1.00869i
$99$		0			0
$100$	0.0975020	−	0.168878i	0.00975020	−	0.0168878i
$101$	8.39661	+	14.5434i	0.835494	+	1.44712i	0.893627	+	0.448810i	$0.148152\pi$
$101$	8.39661	+	14.5434i	0.835494	+	1.44712i	−0.0581328	+	0.998309i	$0.518515\pi$
$102$		0			0
$103$	−0.962454			−0.0948334			−0.0474167	−	0.998875i	$-0.515099\pi$
$103$	−0.962454			−0.0948334			−0.0474167	+	0.998875i	$0.515099\pi$
$104$	7.02173	−	7.23748i	0.688538	−	0.709693i
$105$		0			0
$106$	−0.389532	−	0.104375i	−0.0378347	−	0.0101378i
$107$	5.96703	+	10.3352i	0.576854	+	0.999141i	0.995837	+	0.0911468i	$0.0290533\pi$
$107$	5.96703	+	10.3352i	0.576854	+	0.999141i	−0.418983	+	0.907994i	$0.637613\pi$
$108$		0			0
$109$	3.42240	−	3.42240i	0.327807	−	0.327807i	−0.523945	−	0.851752i	$-0.675540\pi$
$109$	3.42240	−	3.42240i	0.327807	−	0.327807i	0.851752	+	0.523945i	$0.175540\pi$
$110$	−5.37233	+	1.43951i	−0.512231	+	0.137252i
$111$		0			0
$112$	10.7564	+	1.06075i	1.01638	+	0.100231i
$113$	−6.78443	+	11.7510i	−0.638226	+	1.10544i	0.347596	+	0.937644i	$0.386998\pi$
$113$	−6.78443	+	11.7510i	−0.638226	+	1.10544i	−0.985822	+	0.167795i	$0.946335\pi$
$114$		0			0
$115$	−4.45429	−	1.19352i	−0.415365	−	0.111297i
$116$		−	0.0262063i		−	0.00243319i
$117$		0			0
$118$		−	6.72131i		−	0.618747i
$119$	−2.87491	−	6.34714i	−0.263543	−	0.581842i
$120$		0			0
$121$	−15.4496	−	8.91981i	−1.40451	−	0.810892i
$122$	−15.2769	−	15.2769i	−1.38310	−	1.38310i
$123$		0			0
$124$	0.0993241	+	0.370682i	0.00891956	+	0.0332883i
$125$	4.85398	−	4.85398i	0.434153	−	0.434153i
$126$		0			0
$127$	11.3554	−	6.55606i	1.00763	−	0.581757i	0.0971344	−	0.995271i	$-0.469032\pi$
$127$	11.3554	−	6.55606i	1.00763	−	0.581757i	0.910497	+	0.413515i	$0.135699\pi$
$128$	−3.02024	+	11.2717i	−0.266954	+	0.996285i
$129$		0			0
$130$	−3.20528	+	1.91580i	−0.281122	+	0.168027i
$131$			6.96325i			0.608382i	0.952611	+	0.304191i	$0.0983861\pi$
$131$			6.96325i			0.608382i	−0.952611	+	0.304191i	$0.901614\pi$
$132$		0			0
$133$	−5.07990	+	13.4919i	−0.440483	+	1.16990i
$134$	5.74442	+	3.31654i	0.496242	+	0.286506i
$135$		0			0
$136$	7.11466	−	1.90637i	0.610077	−	0.163470i
$137$	0.989826	−	0.265223i	0.0845665	−	0.0226595i	−0.216288	−	0.976330i	$-0.569395\pi$
$137$	0.989826	−	0.265223i	0.0845665	−	0.0226595i	0.300854	+	0.953670i	$0.402728\pi$
$138$		0			0
$139$	13.5680	+	7.83346i	1.15082	+	0.664426i	0.949087	−	0.315015i	$-0.102010\pi$
$139$	13.5680	+	7.83346i	1.15082	+	0.664426i	0.201732	+	0.979441i	$0.435343\pi$
$140$	−0.0781678	−	0.0294312i	−0.00660639	−	0.00248739i
$141$		0			0
$142$		−	22.7115i		−	1.90591i
$143$	−18.7766	−	4.72792i	−1.57018	−	0.395369i
$144$		0			0
$145$	0.112770	−	0.420862i	0.00936500	−	0.0349507i
$146$	−5.32821	+	3.07624i	−0.440966	+	0.254592i
$147$		0			0
$148$	0.0205657	−	0.0205657i	0.00169049	−	0.00169049i
$149$	−3.05630	−	11.4063i	−0.250382	−	0.934438i	−0.970602	−	0.240692i	$-0.922626\pi$
$149$	−3.05630	−	11.4063i	−0.250382	−	0.934438i	0.720220	−	0.693746i	$-0.244041\pi$
$150$		0			0
$151$	−8.50103	−	8.50103i	−0.691804	−	0.691804i	0.270825	−	0.962629i	$-0.412704\pi$
$151$	−8.50103	−	8.50103i	−0.691804	−	0.691804i	−0.962629	+	0.270825i	$0.912704\pi$
$152$	−13.1978	−	7.61976i	−1.07048	−	0.618044i
$153$		0			0
$154$	−8.38037	−	18.5019i	−0.675310	−	1.49093i
$155$			6.38040i			0.512486i
$156$		0			0
$157$			0.627679i			0.0500942i	0.999686	+	0.0250471i	$0.00797357\pi$
$157$			0.627679i			0.0500942i	−0.999686	+	0.0250471i	$0.992026\pi$
$158$	6.58857	+	1.76540i	0.524158	+	0.140448i
$159$		0			0
$160$	0.0892761	−	0.154631i	0.00705789	−	0.0122246i
$161$	1.65272	−	16.7592i	0.130252	−	1.32081i
$162$		0			0
$163$	12.2260	−	3.27594i	0.957613	−	0.256592i	0.254023	−	0.967198i	$-0.418246\pi$
$163$	12.2260	−	3.27594i	0.957613	−	0.256592i	0.703590	+	0.710607i	$0.251579\pi$
$164$	−0.251672	+	0.251672i	−0.0196523	+	0.0196523i
$165$		0			0
$166$	2.44977	+	4.24312i	0.190139	+	0.329330i
$167$	14.4241	+	3.86492i	1.11617	+	0.299076i	0.769332	−	0.638849i	$-0.220589\pi$
$167$	14.4241	+	3.86492i	1.11617	+	0.299076i	0.346837	+	0.937926i	$0.387256\pi$
$168$		0			0
$169$	−12.9940	+	0.393293i	−0.999542	+	0.0302533i
$170$	−2.72757			−0.209195
$171$		0			0
$172$	0.103234	+	0.178806i	0.00787150	+	0.0136338i
$173$	6.31043	−	10.9300i	0.479773	−	0.830991i	−0.519958	−	0.854192i	$-0.674052\pi$
$173$	6.31043	−	10.9300i	0.479773	−	0.830991i	0.999731	+	0.0232010i	$0.00738576\pi$
$174$		0			0
$175$	9.62331	+	6.89776i	0.727454	+	0.521421i
$176$	21.1913	−	5.67819i	1.59735	−	0.428010i
$177$		0			0
$178$	−7.38212	−	4.26207i	−0.553313	−	0.319456i
$179$	9.45522	−	5.45897i	0.706716	−	0.408023i	−0.103128	−	0.994668i	$-0.532885\pi$
$179$	9.45522	−	5.45897i	0.706716	−	0.408023i	0.809844	+	0.586645i	$0.199552\pi$
$180$		0			0
$181$	5.94105			0.441595			0.220797	−	0.975320i	$-0.429134\pi$
$181$	5.94105			0.441595			0.220797	+	0.975320i	$0.429134\pi$
$182$	−8.80837	−	10.4105i	−0.652920	−	0.771676i
$183$		0			0
$184$	17.1953	+	4.60746i	1.26765	+	0.339666i
$185$	0.418773	−	0.241779i	0.0307888	−	0.0177759i
$186$		0			0
$187$	−10.0007	−	10.0007i	−0.731326	−	0.731326i
$188$	0.253469	−	0.0679167i	0.0184861	−	0.00495333i
$189$		0			0
$190$	3.99045	+	3.99045i	0.289498	+	0.289498i
$191$	0.805155	−	1.39457i	0.0582590	−	0.100907i	−0.835425	−	0.549604i	$-0.814778\pi$
$191$	0.805155	−	1.39457i	0.0582590	−	0.100907i	0.893684	+	0.448697i	$0.148112\pi$
$192$		0			0
$193$	−6.36607	+	23.7585i	−0.458240	+	1.71017i	0.220144	+	0.975467i	$0.429347\pi$
$193$	−6.36607	+	23.7585i	−0.458240	+	1.71017i	−0.678384	+	0.734707i	$0.737319\pi$
$194$	23.2868			1.67190
$195$		0			0
$196$	0.0595811	−	0.299150i	0.00425579	−	0.0213679i
$197$	4.77159	+	1.27854i	0.339962	+	0.0910925i	0.424761	−	0.905306i	$-0.360358\pi$
$197$	4.77159	+	1.27854i	0.339962	+	0.0910925i	−0.0847991	+	0.996398i	$0.527025\pi$
$198$		0			0
$199$	2.30866	−	3.99871i	0.163656	−	0.283461i	−0.772521	−	0.634989i	$-0.781005\pi$
$199$	2.30866	−	3.99871i	0.163656	−	0.283461i	0.936177	+	0.351528i	$0.114338\pi$
$200$	−8.85011	+	8.85011i	−0.625797	+	0.625797i
$201$		0			0
$202$	6.21335	+	23.1885i	0.437170	+	1.63154i
$203$	1.58349	+	0.156156i	0.111139	+	0.0109600i
$204$		0			0
$205$	−5.12472	+	2.95876i	−0.357926	+	0.206649i
$206$	−1.32898	−	0.356100i	−0.0925946	−	0.0248106i
$207$		0			0
$208$	12.6433	−	7.55693i	0.876656	−	0.523979i
$209$			29.2623i			2.02411i
$210$		0			0
$211$	−3.39083	−	5.87308i	−0.233434	−	0.404320i	0.725382	−	0.688346i	$-0.241663\pi$
$211$	−3.39083	−	5.87308i	−0.233434	−	0.404320i	−0.958816	+	0.284026i	$0.908330\pi$
$212$	−0.0106457	−	0.00614629i	−0.000731149	−	0.000422129i
$213$		0			0
$214$	4.41550	+	16.4789i	0.301837	+	1.12647i
$215$	0.888460	+	3.31578i	0.0605924	+	0.226134i
$216$		0			0
$217$	−22.9899	+	3.79275i	−1.56066	+	0.257469i
$218$	5.99200	−	3.45948i	0.405830	−	0.234306i
$219$		0			0
$220$	−0.169536			−0.0114301
$221$	−8.29434	−	4.62286i	−0.557937	−	0.310967i
$222$		0			0
$223$	−5.00651	+	18.6845i	−0.335260	+	1.25121i	0.568326	+	0.822803i	$0.307591\pi$
$223$	−5.00651	+	18.6845i	−0.335260	+	1.25121i	−0.903587	+	0.428406i	$0.859075\pi$
$224$	0.610236	+	0.229762i	0.0407731	+	0.0153516i
$225$		0			0
$226$	−13.7159	+	13.7159i	−0.912367	+	0.912367i
$227$	11.5655	−	3.09897i	0.767631	−	0.205686i	0.146306	−	0.989239i	$-0.453262\pi$
$227$	11.5655	−	3.09897i	0.767631	−	0.205686i	0.621324	+	0.783553i	$0.286595\pi$
$228$		0			0
$229$	0.755536	−	0.755536i	0.0499272	−	0.0499272i	−0.681702	−	0.731630i	$-0.738760\pi$
$229$	0.755536	−	0.755536i	0.0499272	−	0.0499272i	0.731630	+	0.681702i	$0.238760\pi$
$230$	−5.70901	−	3.29610i	−0.376441	−	0.217338i
$231$		0			0
$232$	−0.435333	+	1.62469i	−0.0285810	+	0.106666i
$233$		−	16.2619i		−	1.06535i	−0.846318	−	0.532677i	$-0.821186\pi$
$233$		−	16.2619i		−	1.06535i	0.846318	−	0.532677i	$-0.178814\pi$
$234$		0			0
$235$	4.36285			0.284601
$236$	0.0530266	−	0.197898i	0.00345173	−	0.0128820i
$237$		0			0
$238$	−1.62137	−	9.82800i	−0.105098	−	0.637054i
$239$	−15.1795	+	15.1795i	−0.981878	+	0.981878i	−0.999839	−	0.0179604i	$-0.994283\pi$
$239$	−15.1795	+	15.1795i	−0.981878	+	0.981878i	0.0179604	+	0.999839i	$0.494283\pi$
$240$		0			0
$241$	3.31373	+	12.3670i	0.213456	+	0.796630i	0.986704	+	0.162526i	$0.0519642\pi$
$241$	3.31373	+	12.3670i	0.213456	+	0.796630i	−0.773248	+	0.634104i	$0.781369\pi$
$242$	−18.0329	−	18.0329i	−1.15920	−	1.15920i
$243$		0			0
$244$	−0.329278	−	0.570326i	−0.0210799	−	0.0365114i
$245$	2.24413	−	4.54783i	0.143372	−	0.290550i
$246$		0			0
$247$	5.37139	+	18.8979i	0.341773	+	1.20245i
$248$		−	24.6308i		−	1.56406i
$249$		0			0
$250$	8.49844	−	4.90658i	0.537489	−	0.310319i
$251$	−3.61972	+	6.26954i	−0.228475	+	0.395730i	−0.957356	−	0.288910i	$-0.906707\pi$
$251$	−3.61972	+	6.26954i	−0.228475	+	0.395730i	0.728881	+	0.684640i	$0.240041\pi$
$252$		0			0
$253$	−8.84703	−	33.0176i	−0.556208	−	2.07580i
$254$	18.1056	−	4.85137i	1.13604	−	0.304402i
$255$		0			0
$256$	−0.522655	+	0.905265i	−0.0326659	+	0.0565790i
$257$	−1.90293	−	3.29597i	−0.118701	−	0.205597i	0.800552	−	0.599263i	$-0.204540\pi$
$257$	−1.90293	−	3.29597i	−0.118701	−	0.205597i	−0.919253	+	0.393667i	$0.871206\pi$
$258$		0			0
$259$	1.12011	+	1.36520i	0.0696005	+	0.0848296i
$260$	−0.109488	+	0.0311201i	−0.00679019	+	0.00192999i
$261$		0			0
$262$	−2.57634	+	9.61504i	−0.159167	+	0.594019i
$263$	−2.01647	−	3.49263i	−0.124341	−	0.215365i	0.797134	−	0.603802i	$-0.206348\pi$
$263$	−2.01647	−	3.49263i	−0.124341	−	0.215365i	−0.921475	+	0.388437i	$0.873015\pi$
$264$		0			0
$265$	−0.144517	−	0.144517i	−0.00887759	−	0.00887759i
$266$	−12.0064	+	16.7505i	−0.736157	+	1.02704i
$267$		0			0
$268$	0.142970	+	0.142970i	0.00873325	+	0.00873325i
$269$	6.03395	+	3.48370i	0.367897	+	0.212405i	0.672539	−	0.740062i	$-0.265204\pi$
$269$	6.03395	+	3.48370i	0.367897	+	0.212405i	−0.304643	+	0.952467i	$0.598537\pi$
$270$		0			0
$271$	−8.12317	−	2.17660i	−0.493447	−	0.132219i	0.00350987	−	0.999994i	$-0.498883\pi$
$271$	−8.12317	−	2.17660i	−0.493447	−	0.132219i	−0.496957	+	0.867775i	$0.665549\pi$
$272$	10.7590			0.652358
$273$		0			0
$274$	1.46491			0.0884983
$275$	23.2137	+	6.22008i	1.39984	+	0.375085i
$276$		0			0
$277$	−8.34222	−	4.81638i	−0.501236	−	0.289388i	0.227988	−	0.973664i	$-0.426785\pi$
$277$	−8.34222	−	4.81638i	−0.501236	−	0.289388i	−0.729224	+	0.684275i	$0.760119\pi$
$278$	15.8367	+	15.8367i	0.949821	+	0.949821i
$279$		0			0
$280$	4.35719	+	3.12313i	0.260392	+	0.186643i
$281$	9.81783	+	9.81783i	0.585683	+	0.585683i	0.936459	−	0.350777i	$-0.114082\pi$
$281$	9.81783	+	9.81783i	0.585683	+	0.585683i	−0.350777	+	0.936459i	$0.614082\pi$
$282$		0			0
$283$	−0.916453	−	1.58734i	−0.0544775	−	0.0943578i	0.837501	−	0.546436i	$-0.184016\pi$
$283$	−0.916453	−	1.58734i	−0.0544775	−	0.0943578i	−0.891978	+	0.452079i	$0.850683\pi$
$284$	0.179178	−	0.668703i	0.0106323	−	0.0396802i
$285$		0			0
$286$	−24.1780	−	13.4756i	−1.42967	−	0.796831i
$287$	−13.7074	−	16.7067i	−0.809120	−	0.986163i
$288$		0			0
$289$	5.03204	+	8.71576i	0.296003	+	0.512692i
$290$	0.311430	−	0.539413i	0.0182878	−	0.0316754i
$291$		0			0
$292$	−0.181150	+	0.0485389i	−0.0106010	+	0.00284052i
$293$	7.17194	+	26.7660i	0.418989	+	1.56369i	0.776709	+	0.629860i	$0.216888\pi$
$293$	7.17194	+	26.7660i	0.418989	+	1.56369i	−0.357719	+	0.933829i	$0.616446\pi$
$294$		0			0
$295$	1.70317	−	2.94997i	0.0991622	−	0.171754i
$296$	−1.61662	+	0.933357i	−0.0939642	+	0.0542503i
$297$		0			0
$298$		−	16.8809i		−	0.977883i
$299$	−11.7742	−	19.6992i	−0.680922	−	1.13923i
$300$		0			0
$301$	−11.4193	+	5.17233i	−0.658198	+	0.298128i
$302$	−8.59314	−	14.8838i	−0.494480	−	0.856464i
$303$		0			0
$304$	−15.7404	−	15.7404i	−0.902776	−	0.902776i
$305$	−2.83386	−	10.5761i	−0.162267	−	0.605587i
$306$		0			0
$307$	−16.7091	+	16.7091i	−0.953641	+	0.953641i	−0.998972	−	0.0453311i	$-0.985566\pi$
$307$	−16.7091	+	16.7091i	−0.953641	+	0.953641i	0.0453311	+	0.998972i	$0.485566\pi$
$308$	−0.100779	−	0.610873i	−0.00574239	−	0.0348077i
$309$		0			0
$310$	−2.36069	+	8.81023i	−0.134078	+	0.500387i
$311$	−1.88740			−0.107025			−0.0535124	−	0.998567i	$-0.517042\pi$
$311$	−1.88740			−0.107025			−0.0535124	+	0.998567i	$0.517042\pi$
$312$		0			0
$313$			4.73972i			0.267905i	0.990988	+	0.133953i	$0.0427670\pi$
$313$			4.73972i			0.267905i	−0.990988	+	0.133953i	$0.957233\pi$
$314$	−0.232236	+	0.866715i	−0.0131058	+	0.0489116i
$315$		0			0
$316$	0.180062	+	0.103959i	0.0101293	+	0.00584813i
$317$	−12.0340	+	12.0340i	−0.675897	+	0.675897i	−0.959069	−	0.283172i	$-0.908613\pi$
$317$	−12.0340	+	12.0340i	−0.675897	+	0.675897i	0.283172	+	0.959069i	$0.408613\pi$
$318$		0			0
$319$	3.11965	−	0.835908i	0.174667	−	0.0468019i
$320$	−4.00516	+	4.00516i	−0.223895	+	0.223895i
$321$		0			0
$322$	8.48289	−	22.5301i	0.472733	−	1.25555i
$323$	−3.71416	+	13.8614i	−0.206662	+	0.771271i
$324$		0			0
$325$	16.1334	−	0.244101i	0.894922	−	0.0135403i
$326$	18.0940			1.00214
$327$		0			0
$328$	19.7834	−	11.4219i	1.09235	−	0.630671i
$329$	2.59344	+	15.7203i	0.142981	+	0.866686i
$330$		0			0
$331$	−4.49452	−	16.7738i	−0.247041	−	0.921969i	−0.972347	−	0.233542i	$-0.924968\pi$
$331$	−4.49452	−	16.7738i	−0.247041	−	0.921969i	0.725306	−	0.688427i	$-0.241698\pi$
$332$	0.0386540	+	0.144259i	0.00212141	+	0.00791722i
$333$		0			0
$334$	18.4872	+	10.6736i	1.01157	+	0.584032i
$335$	1.68081	+	2.91125i	0.0918324	+	0.159058i
$336$		0			0
$337$			10.9597i			0.597011i	0.954408	+	0.298506i	$0.0964882\pi$
$337$			10.9597i			0.597011i	−0.954408	+	0.298506i	$0.903512\pi$
$338$	−18.0880	−	4.26462i	−0.983860	−	0.231965i
$339$		0			0
$340$	−0.0803086	−	0.0215186i	−0.00435535	−	0.00116701i
$341$	−40.9586	+	23.6475i	−2.21803	+	1.28058i
$342$		0			0
$343$	17.7208	+	5.38268i	0.956833	+	0.290637i
$344$	−3.42979	−	12.8002i	−0.184922	−	0.690138i
$345$		0			0
$346$	12.7576	−	12.7576i	0.685853	−	0.685853i
$347$	1.04935	−	1.81754i	0.0563323	−	0.0975704i	−0.836484	−	0.547991i	$-0.815393\pi$
$347$	1.04935	−	1.81754i	0.0563323	−	0.0975704i	0.892816	+	0.450421i	$0.148726\pi$
$348$		0			0
$349$	4.33364	+	1.16119i	0.231974	+	0.0621573i	0.372933	−	0.927858i	$-0.378352\pi$
$349$	4.33364	+	1.16119i	0.231974	+	0.0621573i	−0.140959	+	0.990015i	$0.545019\pi$
$350$	10.7360	+	13.0851i	0.573864	+	0.699430i
$351$		0			0
$352$	1.32352			0.0705440
$353$	3.60851	−	13.4671i	0.192061	−	0.716783i	−0.800946	−	0.598736i	$-0.795670\pi$
$353$	3.60851	−	13.4671i	0.192061	−	0.716783i	0.993008	−	0.118047i	$-0.0376634\pi$
$354$		0			0
$355$	5.75505	−	9.96804i	0.305446	−	0.529049i
$356$	−0.183729	−	0.183729i	−0.00973764	−	0.00973764i
$357$		0			0
$358$	15.0758	−	4.03954i	0.796780	−	0.213497i
$359$	−14.5777	−	14.5777i	−0.769383	−	0.769383i	0.208615	−	0.977998i	$-0.433104\pi$
$359$	−14.5777	−	14.5777i	−0.769383	−	0.769383i	−0.977998	+	0.208615i	$0.933104\pi$
$360$		0			0
$361$	9.25874	−	5.34554i	0.487302	−	0.281344i
$362$	8.20356	+	2.19814i	0.431169	+	0.115531i
$363$		0			0
$364$	−0.177216	−	0.376011i	−0.00928866	−	0.0197083i
$365$	−3.11805			−0.163206
$366$		0			0
$367$	−6.13097	+	3.53972i	−0.320034	+	0.184772i	−0.651408	−	0.758728i	$-0.725821\pi$
$367$	−6.13097	+	3.53972i	−0.320034	+	0.184772i	0.331374	+	0.943500i	$0.392488\pi$
$368$	22.5194	+	13.0016i	1.17390	+	0.677753i
$369$		0			0
$370$	0.667708	−	0.178912i	0.0347125	−	0.00930119i
$371$	0.434818	−	0.606630i	0.0225746	−	0.0314947i
$372$		0			0
$373$	−8.61866	+	14.9280i	−0.446257	+	0.772941i	−0.998139	−	0.0609820i	$-0.980577\pi$
$373$	−8.61866	+	14.9280i	−0.446257	+	0.772941i	0.551881	+	0.833923i	$0.313910\pi$
$374$	−10.1091	−	17.5094i	−0.522728	−	0.905392i
$375$		0			0
$376$	−16.8423			−0.868573
$377$	1.86127	−	1.11248i	0.0958603	−	0.0572959i
$378$		0			0
$379$	4.36936	+	1.17077i	0.224439	+	0.0601382i	0.369286	−	0.929316i	$-0.379602\pi$
$379$	4.36936	+	1.17077i	0.224439	+	0.0601382i	−0.144847	+	0.989454i	$0.546269\pi$
$380$	0.0860102	+	0.148974i	0.00441223	+	0.00764220i
$381$		0			0
$382$	1.62776	−	1.62776i	0.0832833	−	0.0832833i
$383$	27.6971	−	7.42141i	1.41525	−	0.379216i	0.531456	−	0.847086i	$-0.321645\pi$
$383$	27.6971	−	7.42141i	1.41525	−	0.379216i	0.883798	+	0.467870i	$0.154978\pi$
$384$		0			0
$385$	1.01022	−	10.2440i	0.0514855	−	0.522084i
$386$	−17.5809	+	30.4510i	−0.894843	+	1.54991i
$387$		0			0
$388$	0.685642	+	0.183717i	0.0348082	+	0.00932682i
$389$			6.44786i			0.326919i	0.986550	+	0.163460i	$0.0522654\pi$
$389$			6.44786i			0.326919i	−0.986550	+	0.163460i	$0.947735\pi$
$390$		0			0
$391$		−	16.7633i		−	0.847754i
$392$	−8.66321	+	17.5564i	−0.437558	+	0.886731i
$393$		0			0
$394$	6.11569	+	3.53089i	0.308104	+	0.177884i
$395$	2.44436	+	2.44436i	0.122989	+	0.122989i
$396$		0			0
$397$	−7.70578	−	28.7583i	−0.386742	−	1.44334i	−0.835403	−	0.549638i	$-0.814766\pi$
$397$	−7.70578	−	28.7583i	−0.386742	−	1.44334i	0.448661	−	0.893702i	$-0.351901\pi$
$398$	4.66734	−	4.66734i	0.233953	−	0.233953i
$399$		0			0
$400$	−15.8327	+	9.14100i	−0.791634	+	0.457050i
$401$	5.89581	−	22.0035i	0.294423	−	1.09880i	−0.647252	−	0.762276i	$-0.724082\pi$
$401$	5.89581	−	22.0035i	0.294423	−	1.09880i	0.941675	−	0.336524i	$-0.109251\pi$
$402$		0			0
$403$	−22.1109	+	22.7902i	−1.10142	+	1.13526i
$404$			0.731767i			0.0364068i
$405$		0			0
$406$	2.12875	+	0.801502i	0.105648	+	0.0397779i
$407$	3.10417	+	1.79219i	0.153868	+	0.0888356i
$408$		0			0
$409$	2.36322	−	0.633222i	0.116854	−	0.0313108i	−0.199918	−	0.979813i	$-0.564068\pi$
$409$	2.36322	−	0.633222i	0.116854	−	0.0313108i	0.316772	+	0.948502i	$0.397401\pi$
$410$	−8.17107	+	2.18943i	−0.403540	+	0.108128i
$411$		0			0
$412$	−0.0363203	−	0.0209695i	−0.00178937	−	0.00103309i
$413$	11.6418	+	4.38329i	0.572855	+	0.215688i
$414$		0			0
$415$			2.48306i			0.121889i
$416$	0.854748	−	0.242946i	0.0419075	−	0.0119114i
$417$		0			0
$418$	−10.8268	+	40.4061i	−0.529555	+	1.97633i
$419$	16.9152	−	9.76598i	0.826361	−	0.477100i	−0.0262443	−	0.999656i	$-0.508355\pi$
$419$	16.9152	−	9.76598i	0.826361	−	0.477100i	0.852605	+	0.522556i	$0.175021\pi$
$420$		0			0
$421$	14.8560	−	14.8560i	0.724035	−	0.724035i	−0.245389	−	0.969425i	$-0.578916\pi$
$421$	14.8560	−	14.8560i	0.724035	−	0.724035i	0.969425	+	0.245389i	$0.0789158\pi$
$422$	−2.50915	−	9.36428i	−0.122144	−	0.455846i
$423$		0			0
$424$	0.557889	+	0.557889i	0.0270935	+	0.0270935i
$425$	10.2067	+	5.89287i	0.495100	+	0.285846i
$426$		0			0
$427$	36.4234	−	16.4979i	1.76265	−	0.798387i
$428$			0.520028i			0.0251365i
$429$		0			0
$430$			4.90723i			0.236648i
$431$	−13.8720	−	3.71698i	−0.668188	−	0.179041i	−0.0912498	−	0.995828i	$-0.529086\pi$
$431$	−13.8720	−	3.71698i	−0.668188	−	0.179041i	−0.576939	+	0.816788i	$0.695753\pi$
$432$		0			0
$433$	−18.2103	+	31.5412i	−0.875131	+	1.51577i	−0.0185084	+	0.999829i	$0.505892\pi$
$433$	−18.2103	+	31.5412i	−0.875131	+	1.51577i	−0.856623	+	0.515943i	$0.827442\pi$
$434$	−33.1484	−	3.26894i	−1.59117	−	0.156914i
$435$		0			0
$436$	0.203717	−	0.0545859i	0.00975630	−	0.00261419i
$437$	−24.5248	+	24.5248i	−1.17318	+	1.17318i
$438$		0			0
$439$	16.0130	+	27.7354i	0.764259	+	1.32374i	0.940637	+	0.339414i	$0.110229\pi$
$439$	16.0130	+	27.7354i	0.764259	+	1.32374i	−0.176378	+	0.984323i	$0.556438\pi$
$440$	10.5106	+	2.81629i	0.501071	+	0.134262i
$441$		0			0
$442$	−9.74262	−	9.45220i	−0.463409	−	0.449595i
$443$	−13.4249			−0.637834			−0.318917	−	0.947783i	$-0.603319\pi$
$443$	−13.4249			−0.637834			−0.318917	+	0.947783i	$0.603319\pi$
$444$		0			0
$445$	−2.16000	−	3.74123i	−0.102394	−	0.177351i
$446$	−13.8262	+	23.9477i	−0.654691	+	1.13396i
$447$		0			0
$448$	−16.8122	−	12.0506i	−0.794304	−	0.569338i
$449$	−18.5886	+	4.98079i	−0.877248	+	0.235058i	−0.669220	−	0.743065i	$-0.733371\pi$
$449$	−18.5886	+	4.98079i	−0.877248	+	0.235058i	−0.208029	+	0.978123i	$0.566705\pi$
$450$		0			0
$451$	−37.9872	−	21.9319i	−1.78875	−	1.03273i
$452$	−0.512050	+	0.295632i	−0.0240848	+	0.0139054i
$453$		0			0
$454$	17.1166			0.803320
$455$	−1.22799	−	6.80116i	−0.0575688	−	0.318843i
$456$		0			0
$457$	24.5036	+	6.56571i	1.14623	+	0.307131i	0.781453	−	0.623964i	$-0.214479\pi$
$457$	24.5036	+	6.56571i	1.14623	+	0.307131i	0.364776	+	0.931095i	$0.381146\pi$
$458$	1.32281	−	0.763722i	0.0618107	−	0.0356864i
$459$		0			0
$460$	−0.142088	−	0.142088i	−0.00662490	−	0.00662490i
$461$	−23.2002	+	6.21648i	−1.08054	+	0.289530i	−0.754818	−	0.655935i	$-0.772275\pi$
$461$	−23.2002	+	6.21648i	−1.08054	+	0.289530i	−0.325724	+	0.945465i	$0.605608\pi$
$462$		0			0
$463$	1.96489	+	1.96489i	0.0913160	+	0.0913160i	0.751289	−	0.659973i	$-0.229432\pi$
$463$	1.96489	+	1.96489i	0.0913160	+	0.0913160i	−0.659973	+	0.751289i	$0.729432\pi$
$464$	−1.22845	+	2.12773i	−0.0570292	+	0.0987774i
$465$		0			0
$466$	6.01678	−	22.4549i	0.278722	−	1.04020i
$467$	1.05748			0.0489341			0.0244671	−	0.999701i	$-0.492211\pi$
$467$	1.05748			0.0489341			0.0244671	+	0.999701i	$0.492211\pi$
$468$		0			0
$469$	−9.49070	+	7.78687i	−0.438240	+	0.359564i
$470$	6.02434	+	1.61422i	0.277882	+	0.0744582i
$471$		0			0
$472$	−6.57487	+	11.3880i	−0.302633	+	0.524176i
$473$	−17.9926	+	17.9926i	−0.827299	+	0.827299i
$474$		0			0
$475$	−6.31123	−	23.5538i	−0.289579	−	1.08072i
$476$	0.0297977	−	0.302160i	0.00136577	−	0.0138495i
$477$		0			0
$478$	−26.5765	+	15.3439i	−1.21558	+	0.701816i
$479$	−4.87277	−	1.30565i	−0.222643	−	0.0596569i	0.145773	−	0.989318i	$-0.453433\pi$
$479$	−4.87277	−	1.30565i	−0.222643	−	0.0596569i	−0.368416	+	0.929661i	$0.620100\pi$
$480$		0			0
$481$	2.33369	+	0.587618i	0.106407	+	0.0267931i
$482$			18.3028i			0.833668i
$483$		0			0
$484$	−0.388682	−	0.673217i	−0.0176674	−	0.0306008i
$485$	10.2205	+	5.90083i	0.464091	+	0.267943i
$486$		0			0
$487$	0.725342	+	2.70701i	0.0328684	+	0.122666i	0.980411	−	0.196964i	$-0.0631081\pi$
$487$	0.725342	+	2.70701i	0.0328684	+	0.122666i	−0.947542	+	0.319630i	$0.896441\pi$
$488$	10.9398	+	40.8279i	0.495221	+	1.84819i
$489$		0			0
$490$	4.78142	−	5.44946i	0.216002	−	0.246182i
$491$	10.7778	−	6.22255i	0.486394	−	0.280820i	−0.236683	−	0.971587i	$-0.576060\pi$
$491$	10.7778	−	6.22255i	0.486394	−	0.280820i	0.723077	+	0.690767i	$0.242727\pi$
$492$		0			0
$493$	1.58387			0.0713338
$494$	0.424886	+	28.0821i	0.0191165	+	1.26348i
$495$		0			0
$496$	9.31182	−	34.7522i	0.418113	−	1.56042i
$497$	39.3380	+	14.8113i	1.76455	+	0.664377i
$498$		0			0
$499$	−6.23994	+	6.23994i	−0.279338	+	0.279338i	−0.832845	−	0.553507i	$-0.813289\pi$
$499$	−6.23994	+	6.23994i	−0.279338	+	0.279338i	0.553507	+	0.832845i	$0.313289\pi$
$500$	0.288932	−	0.0774191i	0.0129214	−	0.00346229i
$501$		0			0
$502$	−7.31788	+	7.31788i	−0.326613	+	0.326613i
$503$	−13.6723	−	7.89370i	−0.609617	−	0.351963i	0.163198	−	0.986593i	$-0.447819\pi$
$503$	−13.6723	−	7.89370i	−0.609617	−	0.351963i	−0.772816	+	0.634631i	$0.781152\pi$
$504$		0			0
$505$	−3.14890	+	11.7519i	−0.140124	+	0.522951i
$506$		−	48.8649i		−	2.17231i
$507$		0			0
$508$	0.571362			0.0253501
$509$	6.32401	−	23.6015i	0.280307	−	1.04612i	−0.671894	−	0.740647i	$-0.734519\pi$
$509$	6.32401	−	23.6015i	0.280307	−	1.04612i	0.952201	−	0.305472i	$-0.0988142\pi$
$510$		0			0
$511$	−1.85349	−	11.2350i	−0.0819936	−	0.497007i
$512$	15.4462	−	15.4462i	0.682634	−	0.682634i
$513$		0			0
$514$	−1.40813	−	5.25523i	−0.0621101	−	0.231798i
$515$	−0.493053	−	0.493053i	−0.0217265	−	0.0217265i
$516$		0			0
$517$	16.1699	+	28.0070i	0.711150	+	1.23175i
$518$	1.04157	+	2.29954i	0.0457639	+	0.101036i
$519$		0			0
$520$	7.30481	−	0.110523i	0.320337	−	0.00484674i
$521$		−	2.98806i		−	0.130909i	−0.997856	−	0.0654547i	$-0.979150\pi$
$521$		−	2.98806i		−	0.130909i	0.997856	−	0.0654547i	$-0.0208498\pi$
$522$		0			0
$523$	23.5900	−	13.6197i	1.03152	−	0.595547i	0.114099	−	0.993469i	$-0.463602\pi$
$523$	23.5900	−	13.6197i	1.03152	−	0.595547i	0.917419	+	0.397922i	$0.130269\pi$
$524$	−0.151712	+	0.262773i	−0.00662757	+	0.0114793i
$525$		0			0
$526$	−1.49215	−	5.56879i	−0.0650610	−	0.242811i
$527$	−22.4035	+	6.00299i	−0.975910	+	0.261494i
$528$		0			0
$529$	8.75738	−	15.1682i	0.380756	−	0.659488i
$530$	−0.146083	−	0.253022i	−0.00634542	−	0.0109906i
$531$		0			0
$532$	−0.485657	+	0.398468i	−0.0210559	+	0.0172758i
$533$	−28.5584	−	7.19096i	−1.23700	−	0.311475i
$534$		0			0
$535$	−2.23776	+	8.35142i	−0.0967466	+	0.361063i
$536$	−6.48856	−	11.2385i	−0.280263	−	0.485430i
$537$		0			0
$538$	7.04290	+	7.04290i	0.303641	+	0.303641i
$539$	37.5119	−	2.44941i	1.61575	−	0.105503i
$540$		0			0
$541$	−5.00068	−	5.00068i	−0.214996	−	0.214996i	0.591390	−	0.806386i	$-0.298579\pi$
$541$	−5.00068	−	5.00068i	−0.214996	−	0.214996i	−0.806386	+	0.591390i	$0.798579\pi$
$542$	−10.4114	−	6.01100i	−0.447206	−	0.258195i
$543$		0			0
$544$	0.626949	+	0.167990i	0.0268802	+	0.00720253i
$545$	3.50650			0.150202
$546$		0			0
$547$	−23.2544			−0.994288			−0.497144	−	0.867668i	$-0.665618\pi$
$547$	−23.2544			−0.994288			−0.497144	+	0.867668i	$0.665618\pi$
$548$	0.0431318	+	0.0115571i	0.00184250	+	0.000493696i
$549$		0			0
$550$	29.7527	+	17.1777i	1.26866	+	0.732460i
$551$	−2.31721	−	2.31721i	−0.0987164	−	0.0987164i
$552$		0			0
$553$	−7.35453	+	10.2606i	−0.312746	+	0.436324i
$554$	−9.73714	−	9.73714i	−0.413691	−	0.413691i
$555$		0			0
$556$	0.341344	+	0.591225i	0.0144762	+	0.0250735i
$557$	4.49356	−	16.7702i	0.190398	−	0.710576i	−0.803012	−	0.595963i	$-0.796770\pi$
$557$	4.49356	−	16.7702i	0.190398	−	0.710576i	0.993410	−	0.114613i	$-0.0365629\pi$
$558$		0			0
$559$	−8.31710	+	14.9225i	−0.351776	+	0.631156i
$560$	4.96695	+	6.05376i	0.209892	+	0.255818i
$561$		0			0
$562$	9.92421	+	17.1892i	0.418627	+	0.725084i
$563$	−9.17267	+	15.8875i	−0.386582	+	0.669579i	−0.991987	−	0.126338i	$-0.959678\pi$
$563$	−9.17267	+	15.8875i	−0.386582	+	0.669579i	0.605405	+	0.795917i	$0.293011\pi$
$564$		0			0
$565$	−9.49545	+	2.54430i	−0.399477	+	0.107039i
$566$	−0.678159	−	2.53093i	−0.0285052	−	0.106383i
$567$		0			0
$568$	−22.2167	+	38.4804i	−0.932191	+	1.61460i
$569$	12.1394	−	7.00867i	0.508909	−	0.293819i	−0.223476	−	0.974709i	$-0.571740\pi$
$569$	12.1394	−	7.00867i	0.508909	−	0.293819i	0.732385	+	0.680891i	$0.238407\pi$
$570$		0			0
$571$			10.4239i			0.436226i	0.975924	+	0.218113i	$0.0699901\pi$
$571$			10.4239i			0.436226i	−0.975924	+	0.218113i	$0.930010\pi$
$572$	−0.605567	−	0.587515i	−0.0253200	−	0.0245652i
$573$		0			0
$574$	−12.7462	−	28.1406i	−0.532015	−	1.17457i
$575$	14.2424	+	24.6685i	0.593947	+	1.02875i
$576$		0			0
$577$	−11.2444	−	11.2444i	−0.468111	−	0.468111i	0.433191	−	0.901302i	$-0.357388\pi$
$577$	−11.2444	−	11.2444i	−0.468111	−	0.468111i	−0.901302	+	0.433191i	$0.857388\pi$
$578$	3.72363	+	13.8968i	0.154882	+	0.578029i
$579$		0			0
$580$	0.0134252	−	0.0134252i	0.000557449	−	0.000557449i
$581$	−8.94700	+	1.47603i	−0.371184	+	0.0612359i
$582$		0			0
$583$	0.392099	−	1.46333i	0.0162391	−	0.0606051i
$584$	12.0369			0.498090
$585$		0			0
$586$			39.6128i			1.63639i
$587$	−10.3083	+	38.4710i	−0.425468	+	1.58787i	0.337432	+	0.941350i	$0.390442\pi$
$587$	−10.3083	+	38.4710i	−0.425468	+	1.58787i	−0.762900	+	0.646517i	$0.776225\pi$
$588$		0			0
$589$	41.5588	+	23.9940i	1.71240	+	0.988656i
$590$	3.44324	−	3.44324i	0.141756	−	0.141756i
$591$		0			0
$592$	−2.63379	+	0.705723i	−0.108248	+	0.0290050i
$593$	23.4934	−	23.4934i	0.964759	−	0.964759i	−0.0346408	−	0.999400i	$-0.511029\pi$
$593$	23.4934	−	23.4934i	0.964759	−	0.964759i	0.999400	+	0.0346408i	$0.0110287\pi$
$594$		0			0
$595$	1.77878	−	4.72434i	0.0729228	−	0.193679i
$596$	0.133179	−	0.497029i	0.00545521	−	0.0203591i
$597$		0			0
$598$	−8.96966	−	31.5576i	−0.366797	−	1.29048i
$599$	45.3452			1.85276			0.926378	−	0.376594i	$-0.122905\pi$
$599$	45.3452			1.85276			0.926378	+	0.376594i	$0.122905\pi$
$600$		0			0
$601$	−24.8361	+	14.3392i	−1.01309	+	0.584906i	−0.912094	−	0.409981i	$-0.865535\pi$
$601$	−24.8361	+	14.3392i	−1.01309	+	0.584906i	−0.100993	+	0.994887i	$0.532202\pi$
$602$	−17.6818	+	2.91705i	−0.720656	+	0.118890i
$603$		0			0
$604$	−0.135588	−	0.506021i	−0.00551700	−	0.0205897i
$605$	−3.34511	−	12.4841i	−0.135998	−	0.507552i
$606$		0			0
$607$	8.50843	+	4.91234i	0.345347	+	0.199386i	0.662634	−	0.748944i	$-0.269439\pi$
$607$	8.50843	+	4.91234i	0.345347	+	0.199386i	−0.317287	+	0.948329i	$0.602772\pi$
$608$	−0.671459	−	1.16300i	−0.0272313	−	0.0471659i
$609$		0			0
$610$		−	15.6523i		−	0.633743i
$611$	15.5837	+	15.1192i	0.630449	+	0.611656i
$612$		0			0
$613$	−24.7029	−	6.61912i	−0.997741	−	0.267344i	−0.277242	−	0.960800i	$-0.589420\pi$
$613$	−24.7029	−	6.61912i	−0.997741	−	0.267344i	−0.720499	+	0.693456i	$0.756087\pi$
$614$	−29.2547	+	16.8902i	−1.18062	+	0.681632i
$615$		0			0
$616$	−3.89983	+	39.5458i	−0.157129	+	1.59335i
$617$	−1.62469	−	6.06341i	−0.0654074	−	0.244104i	0.925480	−	0.378796i	$-0.123662\pi$
$617$	−1.62469	−	6.06341i	−0.0654074	−	0.244104i	−0.990887	+	0.134693i	$0.956995\pi$
$618$		0			0
$619$	28.4665	−	28.4665i	1.14416	−	1.14416i	0.156484	−	0.987680i	$-0.449984\pi$
$619$	28.4665	−	28.4665i	1.14416	−	1.14416i	0.987680	−	0.156484i	$-0.0500161\pi$
$620$	−0.139013	+	0.240778i	−0.00558291	+	0.00966989i
$621$		0			0
$622$	−2.60617	−	0.698322i	−0.104498	−	0.0280002i
$623$	12.1964	−	10.0069i	0.488640	−	0.400916i
$624$		0			0
$625$	−17.4024			−0.696094
$626$	−1.75366	+	6.54474i	−0.0700902	+	0.261580i
$627$		0			0
$628$	−0.0136756	+	0.0236868i	−0.000545715	+	0.000945206i
$629$	1.24296	+	1.24296i	0.0495599	+	0.0495599i
$630$		0			0
$631$	12.2380	−	3.27917i	0.487188	−	0.130542i	−0.00685968	−	0.999976i	$-0.502184\pi$
$631$	12.2380	−	3.27917i	0.487188	−	0.130542i	0.494048	+	0.869435i	$0.335517\pi$
$632$	−9.43616	−	9.43616i	−0.375350	−	0.375350i
$633$		0			0
$634$	−21.0693	+	12.1644i	−0.836771	+	0.483110i
$635$	9.17583	+	2.45866i	0.364132	+	0.0975688i
$636$		0			0
$637$	23.7760	−	8.46756i	0.942041	−	0.335497i
$638$	4.61697			0.182788
$639$		0			0
$640$	−7.32156	+	4.22710i	−0.289410	+	0.167091i
$641$	−24.0436	−	13.8816i	−0.949666	−	0.548290i	−0.0566885	−	0.998392i	$-0.518054\pi$
$641$	−24.0436	−	13.8816i	−0.949666	−	0.548290i	−0.892977	+	0.450102i	$0.851388\pi$
$642$		0			0
$643$	17.1125	−	4.58528i	0.674851	−	0.180826i	0.0949121	−	0.995486i	$-0.469743\pi$
$643$	17.1125	−	4.58528i	0.674851	−	0.180826i	0.579939	+	0.814660i	$0.303076\pi$
$644$	0.427512	−	0.596437i	0.0168463	−	0.0235029i
$645$		0			0
$646$	−10.2572	+	17.7660i	−0.403565	+	0.698995i
$647$	−3.33450	−	5.77553i	−0.131093	−	0.227059i	0.793005	−	0.609215i	$-0.208515\pi$
$647$	−3.33450	−	5.77553i	−0.131093	−	0.227059i	−0.924098	+	0.382155i	$0.875182\pi$
$648$		0			0
$649$	25.2495			0.991131
$650$	22.3678	+	5.63217i	0.877337	+	0.220912i
$651$		0			0
$652$	0.532748	+	0.142749i	0.0208640	+	0.00559050i
$653$	0.491840	+	0.851891i	0.0192472	+	0.0333371i	0.875489	−	0.483239i	$-0.160540\pi$
$653$	0.491840	+	0.851891i	0.0192472	+	0.0333371i	−0.856241	+	0.516576i	$0.827206\pi$
$654$		0			0
$655$	−3.56718	+	3.56718i	−0.139381	+	0.139381i
$656$	32.2310	−	8.63627i	1.25841	−	0.337190i
$657$		0			0
$658$	−2.23527	+	22.6665i	−0.0871398	+	0.883632i
$659$	10.5833	−	18.3308i	0.412267	−	0.714067i	−0.582871	−	0.812565i	$-0.698071\pi$
$659$	10.5833	−	18.3308i	0.412267	−	0.714067i	0.995137	+	0.0984983i	$0.0314039\pi$
$660$		0			0
$661$	−16.8983	−	4.52790i	−0.657270	−	0.176115i	−0.0852561	−	0.996359i	$-0.527171\pi$
$661$	−16.8983	−	4.52790i	−0.657270	−	0.176115i	−0.572013	+	0.820244i	$0.693837\pi$
$662$		−	24.8246i		−	0.964835i
$663$		0			0
$664$		−	9.58557i		−	0.371992i
$665$	−9.51411	+	4.30938i	−0.368941	+	0.167110i
$666$		0			0
$667$	3.31516	+	1.91401i	0.128364	+	0.0741107i
$668$	0.460116	+	0.460116i	0.0178024	+	0.0178024i
$669$		0			0
$670$	1.24377	+	4.64181i	0.0480510	+	0.179329i
$671$	57.3897	−	57.3897i	2.21551	−	2.21551i
$672$		0			0
$673$	21.4934	−	12.4092i	0.828511	−	0.478341i	−0.0248316	−	0.999692i	$-0.507905\pi$
$673$	21.4934	−	12.4092i	0.828511	−	0.478341i	0.853343	+	0.521351i	$0.174572\pi$
$674$	−4.05498	+	15.1334i	−0.156192	+	0.582917i
$675$		0			0
$676$	−0.498927	−	0.268267i	−0.0191895	−	0.0103180i
$677$		−	18.0191i		−	0.692531i	−0.938137	−	0.346266i	$-0.887450\pi$
$677$		−	18.0191i		−	0.692531i	0.938137	−	0.346266i	$-0.112550\pi$
$678$		0			0
$679$	−15.1865	+	40.3345i	−0.582803	+	1.54789i
$680$	4.62135	+	2.66814i	0.177221	+	0.102318i
$681$		0			0
$682$	−65.3061	+	17.4987i	−2.50070	+	0.670060i
$683$	31.7978	−	8.52018i	1.21671	−	0.326016i	0.407317	−	0.913287i	$-0.366464\pi$
$683$	31.7978	−	8.52018i	1.21671	−	0.326016i	0.809390	+	0.587271i	$0.199798\pi$
$684$		0			0
$685$	0.642945	+	0.371205i	0.0245657	+	0.0141830i
$686$	22.4778	+	13.9891i	0.858207	+	0.534106i
$687$		0			0
$688$		−	19.3567i		−	0.737968i
$689$	−0.0153875	−	1.01701i	−0.000586218	−	0.0387451i
$690$		0			0
$691$	−4.58957	+	17.1285i	−0.174595	+	0.651599i	0.822025	+	0.569452i	$0.192844\pi$
$691$	−4.58957	+	17.1285i	−0.174595	+	0.651599i	−0.996620	+	0.0821472i	$0.973822\pi$
$692$	0.476275	−	0.274977i	0.0181053	−	0.0104531i
$693$		0			0
$694$	2.12145	−	2.12145i	0.0805291	−	0.0805291i
$695$	2.93771	+	10.9637i	0.111434	+	0.415876i
$696$		0			0
$697$	−15.2107	−	15.2107i	−0.576145	−	0.576145i
$698$	5.55437	+	3.20682i	0.210236	+	0.121380i
$699$		0			0
$700$	0.212871	+	0.469970i	0.00804577	+	0.0177632i
$701$		−	41.2421i		−	1.55769i	−0.627214	−	0.778847i	$-0.715805\pi$
$701$		−	41.2421i		−	1.55769i	0.627214	−	0.778847i	$-0.284195\pi$
$702$		0			0
$703$		−	3.63691i		−	0.137169i
$704$	−40.5550	−	10.8667i	−1.52848	−	0.409554i
$705$		0			0
$706$	9.96545	−	17.2607i	0.375054	−	0.649613i
$707$	−44.2162	−	4.36040i	−1.66292	−	0.163990i
$708$		0			0
$709$	−23.1654	+	6.20716i	−0.869996	+	0.233115i	−0.666086	−	0.745875i	$-0.732032\pi$
$709$	−23.1654	+	6.20716i	−0.869996	+	0.233115i	−0.203910	+	0.978990i	$0.565365\pi$
$710$	11.6348	−	11.6348i	0.436647	−	0.436647i
$711$		0			0
$712$	8.33842	+	14.4426i	0.312495	+	0.541258i
$713$	−54.1465	−	14.5085i	−2.02780	−	0.543348i
$714$		0			0
$715$	−7.19697	−	12.0411i	−0.269151	−	0.450311i
$716$	0.475751			0.0177796
$717$		0			0
$718$	−14.7357	−	25.5229i	−0.549930	−	0.952507i
$719$	−10.7383	+	18.5992i	−0.400469	+	0.693633i	−0.993783	−	0.111338i	$-0.964486\pi$
$719$	−10.7383	+	18.5992i	−0.400469	+	0.693633i	0.593313	+	0.804972i	$0.297820\pi$
$720$		0			0
$721$	1.48348	−	2.06966i	0.0552478	−	0.0770783i
$722$	14.7625	−	3.95561i	0.549404	−	0.147212i
$723$		0			0
$724$	0.224198	+	0.129441i	0.00833226	+	0.00481063i
$725$	−2.33079	+	1.34568i	−0.0865633	+	0.0499774i
$726$		0			0
$727$	16.2550			0.602863			0.301431	−	0.953488i	$-0.402536\pi$
$727$	16.2550			0.602863			0.301431	+	0.953488i	$0.402536\pi$
$728$	4.74049	+	26.2551i	0.175694	+	0.973077i
$729$		0			0
$730$	−4.30549	−	1.15365i	−0.159353	−	0.0426986i
$731$	−10.8068	+	6.23928i	−0.399702	+	0.230768i
$732$		0			0
$733$	−37.7313	−	37.7313i	−1.39364	−	1.39364i	−0.817001	−	0.576637i	$-0.804365\pi$
$733$	−37.7313	−	37.7313i	−1.39364	−	1.39364i	−0.576637	−	0.817001i	$-0.695635\pi$
$734$	−9.77547	+	2.61933i	−0.360819	+	0.0966812i
$735$		0			0
$736$	1.10925	+	1.10925i	0.0408874	+	0.0408874i
$737$	−12.4591	+	21.5797i	−0.458935	+	0.794899i
$738$		0			0
$739$	−11.5735	+	43.1929i	−0.425738	+	1.58888i	0.336567	+	0.941660i	$0.390734\pi$
$739$	−11.5735	+	43.1929i	−0.425738	+	1.58888i	−0.762305	+	0.647218i	$0.775932\pi$
$740$	0.0210711			0.000774587
$741$		0			0
$742$	0.824856	−	0.676772i	0.0302814	−	0.0248451i
$743$	43.8408	+	11.7471i	1.60836	+	0.430959i	0.947554	−	0.319596i	$-0.103547\pi$
$743$	43.8408	+	11.7471i	1.60836	+	0.430959i	0.660808	+	0.750555i	$0.270214\pi$
$744$		0			0
$745$	4.27758	−	7.40899i	0.156718	−	0.271444i
$746$	−17.4241	+	17.4241i	−0.637941	+	0.637941i
$747$		0			0
$748$	−0.159508	−	0.595290i	−0.00583217	−	0.0217660i
$749$	−31.4221	−	3.09870i	−1.14814	−	0.113224i
$750$		0			0
$751$	27.9904	−	16.1603i	1.02138	−	0.589696i	0.106880	−	0.994272i	$-0.465914\pi$
$751$	27.9904	−	16.1603i	1.02138	−	0.589696i	0.914505	+	0.404575i	$0.132581\pi$
$752$	−23.7632	−	6.36732i	−0.866554	−	0.232192i
$753$		0			0
$754$	2.98170	−	0.847494i	0.108587	−	0.0308639i
$755$		−	8.70994i		−	0.316987i
$756$		0			0
$757$	−14.5363	−	25.1776i	−0.528331	−	0.915097i	−0.999454	−	0.0330294i	$-0.989484\pi$
$757$	−14.5363	−	25.1776i	−0.528331	−	0.915097i	0.471123	−	0.882068i	$-0.343849\pi$
$758$	5.60015	+	3.23325i	0.203407	+	0.117437i
$759$		0			0
$760$	−2.85756	−	10.6646i	−0.103655	−	0.386845i
$761$	−7.58218	−	28.2971i	−0.274854	−	1.02577i	−0.955939	−	0.293564i	$-0.905159\pi$
$761$	−7.58218	−	28.2971i	−0.274854	−	1.02577i	0.681086	−	0.732204i	$-0.261508\pi$
$762$		0			0
$763$	2.08440	+	12.6347i	0.0754603	+	0.457406i
$764$	0.0607685	−	0.0350847i	0.00219853	−	0.00126932i
$765$		0			0
$766$	40.9907			1.48105
$767$	16.3065	−	4.63482i	0.588793	−	0.167354i
$768$		0			0
$769$	13.2029	−	49.2739i	0.476109	−	1.77686i	−0.141027	−	0.990006i	$-0.545040\pi$
$769$	13.2029	−	49.2739i	0.476109	−	1.77686i	0.617136	−	0.786857i	$-0.288293\pi$
$770$	5.18514	−	13.7714i	0.186859	−	0.496289i
$771$		0			0
$772$	−0.757877	+	0.757877i	−0.0272766	+	0.0272766i
$773$	7.92985	−	2.12480i	0.285217	−	0.0764236i	−0.113374	−	0.993552i	$-0.536166\pi$
$773$	7.92985	−	2.12480i	0.285217	−	0.0764236i	0.398591	+	0.917129i	$0.369499\pi$
$774$		0			0
$775$	27.8683	−	27.8683i	1.00106	−	1.00106i
$776$	−39.4552	−	22.7795i	−1.41636	−	0.817735i
$777$		0			0
$778$	−2.38565	+	8.90337i	−0.0855298	+	0.319201i
$779$			44.5066i			1.59461i
$780$		0			0
$781$	85.3190			3.05295
$782$	6.20226	−	23.1471i	0.221792	−	0.827740i
$783$		0			0
$784$	−18.8604	+	21.4956i	−0.673587	+	0.767698i
$785$	−0.321552	+	0.321552i	−0.0114767	+	0.0114767i
$786$		0			0
$787$	−0.450270	−	1.68043i	−0.0160504	−	0.0599009i	0.957436	−	0.288645i	$-0.0932047\pi$
$787$	−0.450270	−	1.68043i	−0.0160504	−	0.0599009i	−0.973487	+	0.228744i	$0.926538\pi$
$788$	0.152210	+	0.152210i	0.00542225	+	0.00542225i
$789$		0			0
$790$	2.47085	+	4.27963i	0.0879088	+	0.152262i
$791$	−14.8121	−	32.7017i	−0.526658	−	1.16274i
$792$		0			0
$793$	26.5285	−	47.5975i	0.942056	−	1.69024i
$794$		−	42.5614i		−	1.51045i
$795$		0			0
$796$	0.174244	−	0.100600i	0.00617592	−	0.00356567i
$797$	−0.464274	+	0.804146i	−0.0164454	+	0.0284843i	−0.874131	−	0.485690i	$-0.838568\pi$
$797$	−0.464274	+	0.804146i	−0.0164454	+	0.0284843i	0.857686	+	0.514175i	$0.171902\pi$
$798$		0			0
$799$	4.10478	+	15.3192i	0.145217	+	0.541956i
$800$	−1.06533	+	0.285455i	−0.0376652	+	0.0100924i
$801$		0			0
$802$	16.2822	−	28.2016i	0.574944	−	0.995832i
$803$	−11.5563	−	20.0162i	−0.407814	−	0.706355i
$804$		0			0
$805$	9.43220	−	7.73887i	0.332442	−	0.272759i
$806$	−38.9634	+	23.2885i	−1.37243	+	0.820303i
$807$		0			0
$808$	12.1560	−	45.3666i	0.427645	−	1.59599i
$809$	27.3761	+	47.4168i	0.962492	+	1.66709i	0.716207	+	0.697888i	$0.245877\pi$
$809$	27.3761	+	47.4168i	0.962492	+	1.66709i	0.246286	+	0.969197i	$0.420790\pi$
$810$		0			0
$811$	−15.2089	−	15.2089i	−0.534055	−	0.534055i	0.387721	−	0.921777i	$-0.373262\pi$
$811$	−15.2089	−	15.2089i	−0.534055	−	0.534055i	−0.921777	+	0.387721i	$0.873262\pi$
$812$	0.0563541	+	0.0403932i	0.00197764	+	0.00141752i
$813$		0			0
$814$	3.62322	+	3.62322i	0.126994	+	0.126994i
$815$	7.94143	+	4.58499i	0.278176	+	0.160605i
$816$		0			0
$817$	24.9385	+	6.68224i	0.872487	+	0.233782i
$818$	3.49748			0.122287
$819$		0			0
$820$	−0.257857			−0.00900474
$821$	25.5931	+	6.85765i	0.893206	+	0.239334i	0.676096	−	0.736814i	$-0.263670\pi$
$821$	25.5931	+	6.85765i	0.893206	+	0.239334i	0.217110	+	0.976147i	$0.430337\pi$
$822$		0			0
$823$	34.5953	+	19.9736i	1.20592	+	0.696237i	0.961865	−	0.273525i	$-0.0881897\pi$
$823$	34.5953	+	19.9736i	1.20592	+	0.696237i	0.244053	+	0.969762i	$0.421523\pi$
$824$	1.90337	+	1.90337i	0.0663071	+	0.0663071i
$825$		0			0
$826$	14.4535	+	10.3599i	0.502902	+	0.360468i
$827$	16.8364	+	16.8364i	0.585458	+	0.585458i	0.936398	−	0.350940i	$-0.114138\pi$
$827$	16.8364	+	16.8364i	0.585458	+	0.585458i	−0.350940	+	0.936398i	$0.614138\pi$
$828$		0			0
$829$	−1.41086	−	2.44368i	−0.0490011	−	0.0848724i	0.840485	−	0.541836i	$-0.182270\pi$
$829$	−1.41086	−	2.44368i	−0.0490011	−	0.0848724i	−0.889486	+	0.456963i	$0.848937\pi$
$830$	−0.918712	+	3.42868i	−0.0318890	+	0.119011i
$831$		0			0
$832$	−28.1856	+	0.426452i	−0.977162	+	0.0147846i
$833$	18.0802	+	3.60099i	0.626441	+	0.124767i
$834$		0			0
$835$	5.40932	+	9.36922i	0.187197	+	0.324235i
$836$	−0.637553	+	1.10427i	−0.0220502	+	0.0381921i
$837$		0			0
$838$	26.9703	−	7.22666i	0.931672	−	0.249641i
$839$	−3.56318	−	13.2980i	−0.123015	−	0.459097i	0.876746	−	0.480953i	$-0.159709\pi$
$839$	−3.56318	−	13.2980i	−0.123015	−	0.459097i	−0.999761	+	0.0218557i	$0.993043\pi$
$840$		0			0
$841$	14.3192	−	24.8015i	0.493764	−	0.855224i
$842$	26.0101	−	15.0169i	0.896367	−	0.517517i
$843$		0			0
$844$		−	0.295511i		−	0.0101719i
$845$	−6.85816	−	6.45520i	−0.235928	−	0.222066i
$846$		0			0
$847$	42.9945	−	19.4742i	1.47731	−	0.669140i
$848$	0.576227	+	0.998054i	0.0197877	+	0.0342733i
$849$		0			0
$850$	11.9134	+	11.9134i	0.408628	+	0.408628i
$851$	1.09957	+	4.10365i	0.0376927	+	0.140671i
$852$		0			0
$853$	−23.8704	+	23.8704i	−0.817307	+	0.817307i	−0.985717	−	0.168410i	$-0.946137\pi$
$853$	−23.8704	+	23.8704i	−0.817307	+	0.817307i	0.168410	+	0.985717i	$0.446137\pi$
$854$	56.3985	−	9.30432i	1.92992	−	0.318387i
$855$		0			0
$856$	8.63859	−	32.2396i	0.295261	−	1.10193i
$857$	−10.9745			−0.374882			−0.187441	−	0.982276i	$-0.560019\pi$
$857$	−10.9745			−0.374882			−0.187441	+	0.982276i	$0.560019\pi$
$858$		0			0
$859$		−	29.4072i		−	1.00336i	−0.865053	−	0.501681i	$-0.832715\pi$
$859$		−	29.4072i		−	1.00336i	0.865053	−	0.501681i	$-0.167285\pi$
$860$	−0.0387147	+	0.144485i	−0.00132016	+	0.00492691i
$861$		0			0
$862$	−17.7795	−	10.2650i	−0.605572	−	0.349627i
$863$	16.1604	−	16.1604i	0.550105	−	0.550105i	−0.376366	−	0.926471i	$-0.622827\pi$
$863$	16.1604	−	16.1604i	0.550105	−	0.550105i	0.926471	+	0.376366i	$0.122827\pi$
$864$		0			0
$865$	8.83204	−	2.36654i	0.300298	−	0.0804647i
$866$	−36.8152	+	36.8152i	−1.25103	+	1.25103i
$867$		0			0
$868$	−0.950209	−	0.357767i	−0.0322522	−	0.0121434i
$869$	−6.63198	+	24.7509i	−0.224974	+	0.839616i
$870$		0			0
$871$	−4.08503	+	16.2234i	−0.138416	+	0.549710i
$872$	−13.5364			−0.458402
$873$		0			0
$874$	−42.9384	+	24.7905i	−1.45241	+	0.838550i
$875$	2.95630	+	17.9197i	0.0999411	+	0.605797i
$876$		0			0
$877$	−10.5333	−	39.3110i	−0.355686	−	1.32744i	−0.879620	−	0.475678i	$-0.842203\pi$
$877$	−10.5333	−	39.3110i	−0.355686	−	1.32744i	0.523934	−	0.851759i	$-0.324464\pi$
$878$	11.8494	+	44.2224i	0.399896	+	1.49243i
$879$		0			0
$880$	13.7649	+	7.94716i	0.464014	+	0.267899i
$881$	−11.2270	−	19.4458i	−0.378248	−	0.655145i	0.612559	−	0.790425i	$-0.290140\pi$
$881$	−11.2270	−	19.4458i	−0.378248	−	0.655145i	−0.990807	+	0.135280i	$0.956807\pi$
$882$		0			0
$883$		−	0.128296i		−	0.00431752i	−0.999998	−	0.00215876i	$-0.999313\pi$
$883$		−	0.128296i		−	0.00431752i	0.999998	−	0.00215876i	$-0.000687155\pi$
$884$	−0.212284	−	0.355167i	−0.00713987	−	0.0119456i
$885$		0			0
$886$	−18.5374	−	4.96708i	−0.622776	−	0.166872i
$887$	7.73247	−	4.46434i	0.259631	−	0.149898i	−0.364535	−	0.931190i	$-0.618772\pi$
$887$	7.73247	−	4.46434i	0.259631	−	0.149898i	0.624166	+	0.781292i	$0.285439\pi$
$888$		0			0
$889$	−3.40459	+	34.5240i	−0.114186	+	1.15790i
$890$	−1.59836	−	5.96517i	−0.0535772	−	0.199953i
$891$		0			0
$892$	−0.596022	+	0.596022i	−0.0199563	+	0.0199563i
$893$	16.4068	−	28.4175i	0.549034	−	0.950954i
$894$		0			0
$895$	7.64035	+	2.04722i	0.255389	+	0.0684312i
$896$	−19.5834	−	23.8684i	−0.654234	−	0.797386i
$897$		0			0
$898$	−27.5104			−0.918035
$899$	1.37083	−	5.11600i	0.0457197	−	0.170628i
$900$		0			0
$901$	0.371472	−	0.643409i	0.0123755	−	0.0214350i
$902$	−44.3391	−	44.3391i	−1.47633	−	1.47633i
$903$		0			0
$904$	36.6561	−	9.82196i	1.21916	−	0.326674i
$905$	3.04352	+	3.04352i	0.101170	+	0.101170i
$906$		0			0
$907$	−29.2036	+	16.8607i	−0.969690	+	0.559851i	−0.899142	−	0.437658i	$-0.855808\pi$
$907$	−29.2036	+	16.8607i	−0.969690	+	0.559851i	−0.0705480	+	0.997508i	$0.522475\pi$
$908$	0.503969	+	0.135038i	0.0167248	+	0.00448139i
$909$		0			0
$910$	0.820735	−	9.84556i	0.0272071	−	0.326377i
$911$	−12.1553			−0.402724			−0.201362	−	0.979517i	$-0.564537\pi$
$911$	−12.1553			−0.402724			−0.201362	+	0.979517i	$0.564537\pi$
$912$		0			0
$913$	−15.9399	+	9.20289i	−0.527533	+	0.304571i
$914$	31.4059	+	18.1322i	1.03882	+	0.599760i
$915$		0			0
$916$	0.0449731	−	0.0120505i	0.00148595	−	0.000398160i
$917$	−14.9738	−	10.7328i	−0.494478	−	0.354430i
$918$		0			0
$919$	27.1965	−	47.1057i	0.897129	−	1.55387i	0.0659808	−	0.997821i	$-0.478982\pi$
$919$	27.1965	−	47.1057i	0.897129	−	1.55387i	0.831148	−	0.556052i	$-0.187684\pi$
$920$	6.44857	+	11.1693i	0.212603	+	0.368239i
$921$		0			0
$922$	−34.3355			−1.13078
$923$	55.1001	−	15.6612i	1.81364	−	0.515494i
$924$		0			0
$925$	−2.88515	−	0.773073i	−0.0948631	−	0.0254185i
$926$	1.98617	+	3.44016i	0.0652698	+	0.113051i
$927$		0			0
$928$	−0.104807	+	0.104807i	−0.00344045	+	0.00344045i
$929$	11.3587	−	3.04356i	0.372667	−	0.0998559i	−0.0676240	−	0.997711i	$-0.521542\pi$
$929$	11.3587	−	3.04356i	0.372667	−	0.0998559i	0.440291	+	0.897855i	$0.354875\pi$
$930$		0			0
$931$	−21.1831	−	31.7197i	−0.694249	−	1.03957i
$932$	0.354308	−	0.613679i	0.0116057	−	0.0201017i
$933$		0			0
$934$	1.46019	+	0.391257i	0.0477789	+	0.0128023i
$935$		−	10.2465i		−	0.335096i
$936$		0			0
$937$		−	23.7187i		−	0.774857i	−0.921900	−	0.387428i	$-0.873363\pi$
$937$		−	23.7187i		−	0.774857i	0.921900	−	0.387428i	$-0.126637\pi$
$938$	−15.9861	+	7.24083i	−0.521964	+	0.236422i
$939$		0			0
$940$	0.164641	+	0.0950558i	0.00537001	+	0.00310038i
$941$	−8.77975	−	8.77975i	−0.286212	−	0.286212i	0.549368	−	0.835580i	$-0.314868\pi$
$941$	−8.77975	−	8.77975i	−0.286212	−	0.286212i	−0.835580	+	0.549368i	$0.814868\pi$
$942$		0			0
$943$	−13.4559	−	50.2183i	−0.438186	−	1.63533i
$944$	−13.5820	+	13.5820i	−0.442055	+	0.442055i
$945$		0			0
$946$	−31.5017	+	18.1875i	−1.02421	+	0.591327i
$947$	3.45357	−	12.8889i	0.112226	−	0.418833i	−0.886838	−	0.462080i	$-0.847103\pi$
$947$	3.45357	−	12.8889i	0.112226	−	0.418833i	0.999064	+	0.0432464i	$0.0137701\pi$
$948$		0			0
$949$	−11.1374	−	10.8054i	−0.361535	−	0.350758i
$950$		−	34.8589i		−	1.13097i
$951$		0			0
$952$	−6.86676	+	18.2378i	−0.222553	+	0.591089i
$953$	−2.94104	−	1.69801i	−0.0952697	−	0.0550040i	0.451608	−	0.892216i	$-0.350850\pi$
$953$	−2.94104	−	1.69801i	−0.0952697	−	0.0550040i	−0.546878	+	0.837212i	$0.684184\pi$
$954$		0			0
$955$	1.12689	−	0.301949i	0.0364653	−	0.00977085i
$956$	−0.903553	+	0.242106i	−0.0292230	+	0.00783028i
$957$		0			0
$958$	−6.24537	−	3.60577i	−0.201779	−	0.116497i
$959$	−0.955338	+	2.53733i	−0.0308495	+	0.0819345i
$960$		0			0
$961$			46.5603i			1.50195i
$962$	3.00500	+	1.67484i	0.0968851	+	0.0539991i
$963$		0			0
$964$	−0.144396	+	0.538894i	−0.00465069	+	0.0173566i
$965$	−15.4324	+	8.90992i	−0.496788	+	0.286820i
$966$		0			0
$967$	−32.6551	+	32.6551i	−1.05012	+	1.05012i	−0.0514398	+	0.998676i	$0.516381\pi$
$967$	−32.6551	+	32.6551i	−1.05012	+	1.05012i	−0.998676	+	0.0514398i	$0.983619\pi$
$968$	12.9134	+	48.1935i	0.415052	+	1.54900i
$969$		0			0
$970$	11.9295	+	11.9295i	0.383034	+	0.383034i
$971$	−8.75213	−	5.05305i	−0.280869	−	0.162160i	0.352948	−	0.935643i	$-0.385179\pi$
$971$	−8.75213	−	5.05305i	−0.280869	−	0.162160i	−0.633817	+	0.773483i	$0.718513\pi$
$972$		0			0
$973$	−37.7581	+	17.1024i	−1.21047	+	0.548278i
$974$			4.00629i			0.128370i
$975$		0			0
$976$			61.7409i			1.97628i
$977$	−57.0790	−	15.2943i	−1.82612	−	0.489307i	−0.828608	−	0.559829i	$-0.810867\pi$
$977$	−57.0790	−	15.2943i	−1.82612	−	0.489307i	−0.997510	+	0.0705222i	$0.977533\pi$
$978$		0			0
$979$	16.0111	−	27.7320i	0.511716	−	0.886317i
$980$	0.183773	−	0.122728i	0.00587042	−	0.00392041i
$981$		0			0
$982$	17.1845	−	4.60458i	0.548380	−	0.146938i
$983$	32.3474	−	32.3474i	1.03172	−	1.03172i	0.0322405	−	0.999480i	$-0.489736\pi$
$983$	32.3474	−	32.3474i	1.03172	−	1.03172i	0.999480	−	0.0322405i	$-0.0102642\pi$
$984$		0			0
$985$	1.78944	+	3.09940i	0.0570164	+	0.0987552i
$986$	2.18705	+	0.586018i	0.0696498	+	0.0186626i
$987$		0			0
$988$	−0.209039	+	0.830184i	−0.00665041	+	0.0264117i
$989$	−30.1592			−0.959007
$990$		0			0
$991$	−1.26677	−	2.19411i	−0.0402402	−	0.0696981i	0.845204	−	0.534444i	$-0.179479\pi$
$991$	−1.26677	−	2.19411i	−0.0402402	−	0.0696981i	−0.885444	+	0.464746i	$0.846146\pi$
$992$	1.08524	−	1.87969i	0.0344565	−	0.0596803i
$993$		0			0
$994$	48.8389	+	35.0065i	1.54907	+	1.11034i
$995$	3.23118	−	0.865793i	0.102435	−	0.0274475i
$996$		0			0
$997$	10.4694	+	6.04452i	0.331570	+	0.191432i	0.656538	−	0.754293i	$-0.272020\pi$
$997$	10.4694	+	6.04452i	0.331570	+	0.191432i	−0.324968	+	0.945725i	$0.605354\pi$
$998$	−10.9250	+	6.30755i	−0.345825	+	0.199662i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.496.6		32
3.2	odd	2		273.2.by.c.223.3	yes	32
7.6	odd	2		819.2.fm.e.496.6		32
13.7	odd	12		819.2.fm.e.748.6		32
21.20	even	2		273.2.by.d.223.3	yes	32
39.20	even	12		273.2.by.d.202.3	yes	32
91.20	even	12	inner	819.2.fm.f.748.6		32
273.20	odd	12		273.2.by.c.202.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.3	✓	32	273.20	odd	12
273.2.by.c.223.3	yes	32	3.2	odd	2
273.2.by.d.202.3	yes	32	39.20	even	12
273.2.by.d.223.3	yes	32	21.20	even	2
819.2.fm.e.496.6		32	7.6	odd	2
819.2.fm.e.748.6		32	13.7	odd	12
819.2.fm.f.496.6		32	1.1	even	1	trivial
819.2.fm.f.748.6		32	91.20	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(0.512287 + 0.512287i) q^{5} +(-1.54136 + 2.15040i) q^{7} +(-1.97762 - 1.97762i) q^{8} +O(q^{10})\)	\(q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(0.512287 + 0.512287i) q^{5} +(-1.54136 + 2.15040i) q^{7} +(-1.97762 - 1.97762i) q^{8} +(0.517838 + 0.896921i) q^{10} +(-1.38992 + 5.18727i) q^{11} +(0.0545462 + 3.60514i) q^{13} +(-2.92397 + 2.39904i) q^{14} +(-2.04263 - 3.53793i) q^{16} +(-1.31681 + 2.28077i) q^{17} +(5.26328 - 1.41029i) q^{19} +(0.00817077 + 0.0304937i) q^{20} +(-3.83849 + 6.64846i) q^{22} +(-5.51236 + 3.18256i) q^{23} -4.47512i q^{25} +(-1.25855 + 4.99825i) q^{26} +(-0.105018 + 0.0475676i) q^{28} +(-0.300703 - 0.520832i) q^{29} +(6.22737 + 6.22737i) q^{31} +(-0.0637871 - 0.238057i) q^{32} +(-2.66215 + 2.66215i) q^{34} +(-1.89124 + 0.312006i) q^{35} +(0.172749 - 0.644708i) q^{37} +7.78948 q^{38} -2.02622i q^{40} +(-2.11401 + 7.88960i) q^{41} +(4.10340 + 2.36910i) q^{43} +(-0.165470 + 0.165470i) q^{44} +(-8.78913 + 2.35504i) q^{46} +(4.25821 - 4.25821i) q^{47} +(-2.24845 - 6.62906i) q^{49} +(1.65576 - 6.17937i) q^{50} +(-0.0764887 + 0.137236i) q^{52} -0.282101 q^{53} +(-3.36941 + 1.94533i) q^{55} +(7.30090 - 1.20446i) q^{56} +(-0.222515 - 0.830436i) q^{58} +(-1.21690 - 4.54153i) q^{59} +(-13.0884 - 7.55656i) q^{61} +(6.29485 + 10.9030i) q^{62} +7.81819i q^{64} +(-1.81892 + 1.87481i) q^{65} +(4.48192 + 1.20093i) q^{67} +(-0.0993850 + 0.0573799i) q^{68} +(-2.72691 - 0.268916i) q^{70} +(-4.11194 - 15.3460i) q^{71} +(-3.04327 + 3.04327i) q^{73} +(0.477073 - 0.826314i) q^{74} +(0.229348 + 0.0614536i) q^{76} +(-9.01234 - 10.9843i) q^{77} +4.77147 q^{79} +(0.766026 - 2.85885i) q^{80} +(-5.83817 + 10.1120i) q^{82} +(2.42351 + 2.42351i) q^{83} +(-1.84299 + 0.493829i) q^{85} +(4.78954 + 4.78954i) q^{86} +(13.0072 - 7.50971i) q^{88} +(-5.75969 - 1.54330i) q^{89} +(-7.83657 - 5.43950i) q^{91} -0.277361 q^{92} +(7.45535 - 4.30435i) q^{94} +(3.41879 + 1.97384i) q^{95} +(15.7347 - 4.21610i) q^{97} +(-0.652020 - 9.98549i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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