LMFDB - Embedded newform 819.2.fn.e.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (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 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.6
Character	$\chi$	$=$	819.73
Dual form			819.2.fn.e.460.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.211401 - 0.788958i) q^{2} +(1.15429 + 0.666428i) q^{4} +(-3.03793 - 0.814012i) q^{5} +(2.28951 - 1.32595i) q^{7} +(1.92491 - 1.92491i) q^{8} +O(q^{10})$	\(q+(0.211401 - 0.788958i) q^{2} +(1.15429 + 0.666428i) q^{4} +(-3.03793 - 0.814012i) q^{5} +(2.28951 - 1.32595i) q^{7} +(1.92491 - 1.92491i) q^{8} +(-1.28444 + 2.22472i) q^{10} +(0.131620 + 0.491212i) q^{11} +(-1.73717 - 3.15947i) q^{13} +(-0.562115 - 2.08663i) q^{14} +(0.221107 + 0.382969i) q^{16} +(0.606654 - 1.05076i) q^{17} +(-1.72169 - 0.461325i) q^{19} +(-2.96417 - 2.96417i) q^{20} +0.415370 q^{22} +(4.51168 - 2.60482i) q^{23} +(4.23629 + 2.44583i) q^{25} +(-2.85993 + 0.702638i) q^{26} +(3.52640 - 0.00473432i) q^{28} -1.64443 q^{29} +(-0.976210 - 3.64327i) q^{31} +(5.60785 - 1.50262i) q^{32} +(-0.700755 - 0.700755i) q^{34} +(-8.03472 + 2.16446i) q^{35} +(-2.66889 - 0.715128i) q^{37} +(-0.727931 + 1.26081i) q^{38} +(-7.41466 + 4.28086i) q^{40} +(5.55629 - 5.55629i) q^{41} -7.46499i q^{43} +(-0.175430 + 0.654714i) q^{44} +(-1.10132 - 4.11018i) q^{46} +(1.26875 - 4.73504i) q^{47} +(3.48371 - 6.07155i) q^{49} +(2.82521 - 2.82521i) q^{50} +(0.100369 - 4.80463i) q^{52} +(-4.30982 + 7.46483i) q^{53} -1.59941i q^{55} +(1.85477 - 6.95945i) q^{56} +(-0.347632 + 1.29738i) q^{58} +(2.41901 - 0.648171i) q^{59} +(-9.09759 + 5.25249i) q^{61} -3.08076 q^{62} -3.85758i q^{64} +(2.70555 + 11.0123i) q^{65} +(7.15134 - 1.91620i) q^{67} +(1.40051 - 0.808582i) q^{68} +(0.00912470 + 6.79662i) q^{70} +(-0.840390 - 0.840390i) q^{71} +(2.36118 - 0.632677i) q^{73} +(-1.12841 + 1.95447i) q^{74} +(-1.67988 - 1.67988i) q^{76} +(0.952667 + 0.950113i) q^{77} +(6.20571 + 10.7486i) q^{79} +(-0.359968 - 1.34342i) q^{80} +(-3.20908 - 5.55828i) q^{82} +(7.31472 - 7.31472i) q^{83} +(-2.69830 + 2.69830i) q^{85} +(-5.88956 - 1.57810i) q^{86} +(1.19890 + 0.692184i) q^{88} +(-2.52599 + 9.42713i) q^{89} +(-8.16656 - 4.93024i) q^{91} +6.94369 q^{92} +(-3.46753 - 2.00198i) q^{94} +(4.85484 + 2.80295i) q^{95} +(-2.93184 + 2.93184i) q^{97} +(-4.05374 - 4.03203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.211401	−	0.788958i	0.149483	−	0.557877i	−0.850032	−	0.526731i	$-0.823418\pi$
$2$	0.211401	−	0.788958i	0.149483	−	0.557877i	0.999515	−	0.0311464i	$-0.00991581\pi$
$3$		0			0
$3$		0			0
$4$	1.15429	+	0.666428i	0.577143	+	0.333214i
$5$	−3.03793	−	0.814012i	−1.35860	−	0.364037i	−0.495301	−	0.868721i	$-0.664942\pi$
$5$	−3.03793	−	0.814012i	−1.35860	−	0.364037i	−0.863304	+	0.504684i	$0.831609\pi$
$6$		0			0
$7$	2.28951	−	1.32595i	0.865353	−	0.501162i
$7$	2.28951	−	1.32595i	0.865353	−	0.501162i
$8$	1.92491	−	1.92491i	0.680560	−	0.680560i
$9$		0			0
$10$	−1.28444	+	2.22472i	−0.406176	+	0.703518i
$11$	0.131620	+	0.491212i	0.0396849	+	0.148106i	0.982925	−	0.184004i	$-0.0589061\pi$
$11$	0.131620	+	0.491212i	0.0396849	+	0.148106i	−0.943241	+	0.332110i	$0.892239\pi$
$12$		0			0
$13$	−1.73717	−	3.15947i	−0.481804	−	0.876279i
$13$	−1.73717	−	3.15947i	−0.481804	−	0.876279i
$14$	−0.562115	−	2.08663i	−0.150232	−	0.557676i
$15$		0			0
$16$	0.221107	+	0.382969i	0.0552768	+	0.0957423i
$17$	0.606654	−	1.05076i	0.147135	−	0.254846i	−0.783032	−	0.621981i	$-0.786328\pi$
$17$	0.606654	−	1.05076i	0.147135	−	0.254846i	0.930168	+	0.367135i	$0.119661\pi$
$18$		0			0
$19$	−1.72169	−	0.461325i	−0.394982	−	0.105835i	0.0558606	−	0.998439i	$-0.482210\pi$
$19$	−1.72169	−	0.461325i	−0.394982	−	0.105835i	−0.450843	+	0.892603i	$0.648876\pi$
$20$	−2.96417	−	2.96417i	−0.662808	−	0.662808i
$21$		0			0
$22$	0.415370			0.0885572
$23$	4.51168	−	2.60482i	0.940750	−	0.543142i	0.0505543	−	0.998721i	$-0.483901\pi$
$23$	4.51168	−	2.60482i	0.940750	−	0.543142i	0.890195	+	0.455579i	$0.150568\pi$
$24$		0			0
$25$	4.23629	+	2.44583i	0.847259	+	0.489165i
$26$	−2.85993	+	0.702638i	−0.560878	+	0.137799i
$27$		0			0
$28$	3.52640	−	0.00473432i	0.666427	−	0.000894702i
$29$	−1.64443			−0.305362			−0.152681	−	0.988276i	$-0.548791\pi$
$29$	−1.64443			−0.305362			−0.152681	+	0.988276i	$0.548791\pi$
$30$		0			0
$31$	−0.976210	−	3.64327i	−0.175333	−	0.654350i	−0.996495	−	0.0836552i	$-0.973341\pi$
$31$	−0.976210	−	3.64327i	−0.175333	−	0.654350i	0.821162	−	0.570695i	$-0.193326\pi$
$32$	5.60785	−	1.50262i	0.991338	−	0.265628i
$33$		0			0
$34$	−0.700755	−	0.700755i	−0.120178	−	0.120178i
$35$	−8.03472	+	2.16446i	−1.35811	+	0.365861i
$36$		0			0
$37$	−2.66889	−	0.715128i	−0.438764	−	0.117566i	0.0326734	−	0.999466i	$-0.489598\pi$
$37$	−2.66889	−	0.715128i	−0.438764	−	0.117566i	−0.471437	+	0.881900i	$0.656265\pi$
$38$	−0.727931	+	1.26081i	−0.118086	+	0.204531i
$39$		0			0
$40$	−7.41466	+	4.28086i	−1.17236	+	0.676863i
$41$	5.55629	−	5.55629i	0.867747	−	0.867747i	−0.124476	−	0.992223i	$-0.539725\pi$
$41$	5.55629	−	5.55629i	0.867747	−	0.867747i	0.992223	+	0.124476i	$0.0397250\pi$
$42$		0			0
$43$		−	7.46499i		−	1.13840i	−0.822199	−	0.569200i	$-0.807253\pi$
$43$		−	7.46499i		−	1.13840i	0.822199	−	0.569200i	$-0.192747\pi$
$44$	−0.175430	+	0.654714i	−0.0264471	+	0.0987019i
$45$		0			0
$46$	−1.10132	−	4.11018i	−0.162381	−	0.606013i
$47$	1.26875	−	4.73504i	0.185066	−	0.690677i	−0.809550	−	0.587051i	$-0.800289\pi$
$47$	1.26875	−	4.73504i	0.185066	−	0.690677i	0.994616	−	0.103626i	$-0.0330445\pi$
$48$		0			0
$49$	3.48371	−	6.07155i	0.497673	−	0.867365i
$50$	2.82521	−	2.82521i	0.399545	−	0.399545i
$51$		0			0
$52$	0.100369	−	4.80463i	0.0139187	−	0.666282i
$53$	−4.30982	+	7.46483i	−0.591999	+	1.02537i	0.401964	+	0.915656i	$0.368328\pi$
$53$	−4.30982	+	7.46483i	−0.591999	+	1.02537i	−0.993963	+	0.109717i	$0.965006\pi$
$54$		0			0
$55$		−	1.59941i		−	0.215664i
$56$	1.85477	−	6.95945i	0.247854	−	0.929996i
$57$		0			0
$58$	−0.347632	+	1.29738i	−0.0456464	+	0.170355i
$59$	2.41901	−	0.648171i	0.314928	−	0.0843847i	−0.0978928	−	0.995197i	$-0.531210\pi$
$59$	2.41901	−	0.648171i	0.314928	−	0.0843847i	0.412821	+	0.910812i	$0.364544\pi$
$60$		0			0
$61$	−9.09759	+	5.25249i	−1.16483	+	0.672513i	−0.952456	−	0.304676i	$-0.901452\pi$
$61$	−9.09759	+	5.25249i	−1.16483	+	0.672513i	−0.212371	+	0.977189i	$0.568118\pi$
$62$	−3.08076			−0.391256
$63$		0			0
$64$		−	3.85758i		−	0.482198i
$65$	2.70555	+	11.0123i	0.335582	+	1.36591i
$66$		0			0
$67$	7.15134	−	1.91620i	0.873675	−	0.234101i	0.205999	−	0.978552i	$-0.433956\pi$
$67$	7.15134	−	1.91620i	0.873675	−	0.234101i	0.667676	+	0.744452i	$0.267289\pi$
$68$	1.40051	−	0.808582i	0.169836	−	0.0980550i
$69$		0			0
$70$	0.00912470	+	6.79662i	0.00109061	+	0.812351i
$71$	−0.840390	−	0.840390i	−0.0997360	−	0.0997360i	0.655478	−	0.755214i	$-0.272467\pi$
$71$	−0.840390	−	0.840390i	−0.0997360	−	0.0997360i	−0.755214	+	0.655478i	$0.772467\pi$
$72$		0			0
$73$	2.36118	−	0.632677i	0.276355	−	0.0740492i	−0.117979	−	0.993016i	$-0.537642\pi$
$73$	2.36118	−	0.632677i	0.276355	−	0.0740492i	0.394335	+	0.918967i	$0.370975\pi$
$74$	−1.12841	+	1.95447i	−0.131175	+	0.227202i
$75$		0			0
$76$	−1.67988	−	1.67988i	−0.192695	−	0.192695i
$77$	0.952667	+	0.950113i	0.108567	+	0.108275i
$78$		0			0
$79$	6.20571	+	10.7486i	0.698197	+	1.20931i	0.969091	+	0.246704i	$0.0793474\pi$
$79$	6.20571	+	10.7486i	0.698197	+	1.20931i	−0.270894	+	0.962609i	$0.587319\pi$
$80$	−0.359968	−	1.34342i	−0.0402456	−	0.150199i
$81$		0			0
$82$	−3.20908	−	5.55828i	−0.354383	−	0.613809i
$83$	7.31472	−	7.31472i	0.802894	−	0.802894i	−0.180653	−	0.983547i	$-0.557821\pi$
$83$	7.31472	−	7.31472i	0.802894	−	0.802894i	0.983547	+	0.180653i	$0.0578209\pi$
$84$		0			0
$85$	−2.69830	+	2.69830i	−0.292672	+	0.292672i
$86$	−5.88956	−	1.57810i	−0.635088	−	0.170171i
$87$		0			0
$88$	1.19890	+	0.692184i	0.127803	+	0.0737870i
$89$	−2.52599	+	9.42713i	−0.267755	+	0.999273i	0.692788	+	0.721141i	$0.256382\pi$
$89$	−2.52599	+	9.42713i	−0.267755	+	0.999273i	−0.960543	+	0.278132i	$0.910285\pi$
$90$		0			0
$91$	−8.16656	−	4.93024i	−0.856088	−	0.516830i
$92$	6.94369			0.723930
$93$		0			0
$94$	−3.46753	−	2.00198i	−0.357649	−	0.206489i
$95$	4.85484	+	2.80295i	0.498097	+	0.287576i
$96$		0			0
$97$	−2.93184	+	2.93184i	−0.297683	+	0.297683i	−0.840106	−	0.542423i	$-0.817507\pi$
$97$	−2.93184	+	2.93184i	−0.297683	+	0.297683i	0.542423	+	0.840106i	$0.317507\pi$
$98$	−4.05374	−	4.03203i	−0.409490	−	0.407297i
$99$		0			0
$100$	3.25993	+	5.64637i	0.325993	+	0.564637i
$101$	−7.72587	+	13.3816i	−0.768753	+	1.33152i	0.169487	+	0.985532i	$0.445789\pi$
$101$	−7.72587	+	13.3816i	−0.768753	+	1.33152i	−0.938240	+	0.345986i	$0.887544\pi$
$102$		0			0
$103$	8.75030	+	15.1560i	0.862192	+	1.49336i	0.869808	+	0.493390i	$0.164242\pi$
$103$	8.75030	+	15.1560i	0.862192	+	1.49336i	−0.00761617	+	0.999971i	$0.502424\pi$
$104$	−9.42561	−	2.73781i	−0.924257	−	0.268464i
$105$		0			0
$106$	4.97833	+	4.97833i	0.483538	+	0.483538i
$107$	1.06208	+	1.83958i	0.102675	+	0.177839i	0.912786	−	0.408438i	$-0.133926\pi$
$107$	1.06208	+	1.83958i	0.102675	+	0.177839i	−0.810111	+	0.586277i	$0.800593\pi$
$108$		0			0
$109$	−10.3442	+	2.77172i	−0.990796	+	0.265483i	−0.717585	−	0.696471i	$-0.754752\pi$
$109$	−10.3442	+	2.77172i	−0.990796	+	0.265483i	−0.273211	+	0.961954i	$0.588086\pi$
$110$	−1.26187	−	0.338116i	−0.120314	−	0.0322381i
$111$		0			0
$112$	1.01403	+	0.583634i	0.0958164	+	0.0551482i
$113$	−5.21100			−0.490210			−0.245105	−	0.969497i	$-0.578822\pi$
$113$	−5.21100			−0.490210			−0.245105	+	0.969497i	$0.578822\pi$
$114$		0			0
$115$	−15.8265	+	4.24070i	−1.47583	+	0.395448i
$116$	−1.89814	−	1.09589i	−0.176238	−	0.101751i
$117$		0			0
$118$		−	2.04552i		−	0.188305i
$119$	−0.00430968	−	3.21011i	−0.000395068	−	0.294270i
$120$		0			0
$121$	9.30231	−	5.37069i	0.845665	−	0.488245i
$122$	2.22076	+	8.28799i	0.201058	+	0.750359i
$123$		0			0
$124$	1.30115	−	4.85595i	0.116846	−	0.436077i
$125$	0.240960	+	0.240960i	0.0215521	+	0.0215521i
$126$		0			0
$127$			11.4359i			1.01477i	0.861720	+	0.507384i	$0.169387\pi$
$127$			11.4359i			1.01477i	−0.861720	+	0.507384i	$0.830613\pi$
$128$	8.17223	+	2.18974i	0.722330	+	0.193548i
$129$		0			0
$130$	9.26022	+	0.193447i	0.812175	+	0.0169664i
$131$	−6.07972	+	3.51013i	−0.531188	+	0.306681i	−0.741500	−	0.670953i	$-0.765885\pi$
$131$	−6.07972	+	3.51013i	−0.531188	+	0.306681i	0.210312	+	0.977634i	$0.432552\pi$
$132$		0			0
$133$	−4.55351	+	1.22666i	−0.394840	+	0.106365i
$134$		−	6.04719i		−	0.522398i
$135$		0			0
$136$	−0.854858	−	3.19037i	−0.0733034	−	0.273572i
$137$	−1.60979	−	6.00784i	−0.137534	−	0.513284i	−0.999975	−	0.00712570i	$-0.997732\pi$
$137$	−1.60979	−	6.00784i	−0.137534	−	0.513284i	0.862441	−	0.506158i	$-0.168935\pi$
$138$		0			0
$139$		−	1.91666i		−	0.162569i	−0.996691	−	0.0812847i	$-0.974098\pi$
$139$		−	1.91666i		−	0.162569i	0.996691	−	0.0812847i	$-0.0259023\pi$
$140$	−10.7168	−	2.85615i	−0.905737	−	0.241389i
$141$		0			0
$142$	−0.840691	+	0.485373i	−0.0705493	+	0.0407316i
$143$	1.32332	−	1.26917i	0.110662	−	0.106133i
$144$		0			0
$145$	4.99565	+	1.33858i	0.414866	+	0.111163i
$146$		−	1.99662i		−	0.165242i
$147$		0			0
$148$	−2.60409	−	2.60409i	−0.214055	−	0.214055i
$149$	−0.289039	+	1.07871i	−0.0236790	+	0.0883711i	−0.976754	−	0.214363i	$-0.931233\pi$
$149$	−0.289039	+	1.07871i	−0.0236790	+	0.0883711i	0.953075	+	0.302734i	$0.0978993\pi$
$150$		0			0
$151$	−3.41102	−	12.7301i	−0.277585	−	1.03596i	−0.954089	−	0.299522i	$-0.903173\pi$
$151$	−3.41102	−	12.7301i	−0.277585	−	1.03596i	0.676505	−	0.736438i	$-0.263494\pi$
$152$	−4.20211	+	2.42609i	−0.340836	+	0.196782i
$153$		0			0
$154$	0.950993	−	0.550760i	0.0766332	−	0.0443815i
$155$			11.8626i			0.952831i
$156$		0			0
$157$	12.0413	+	6.95203i	0.960998	+	0.554833i	0.896480	−	0.443084i	$-0.146116\pi$
$157$	12.0413	+	6.95203i	0.960998	+	0.554833i	0.0645182	+	0.997917i	$0.479449\pi$
$158$	9.79209	−	2.62378i	0.779017	−	0.208737i
$159$		0			0
$160$	−18.2594			−1.44353
$161$	6.87567	−	11.9460i	0.541879	−	0.941478i
$162$		0			0
$163$	7.90791	+	2.11892i	0.619396	+	0.165967i	0.554853	−	0.831948i	$-0.312774\pi$
$163$	7.90791	+	2.11892i	0.619396	+	0.165967i	0.0645426	+	0.997915i	$0.479441\pi$
$164$	10.1164	−	2.71069i	0.789959	−	0.211669i
$165$		0			0
$166$	−4.22467	−	7.31734i	−0.327898	−	0.567936i
$167$	−1.97146	−	1.97146i	−0.152556	−	0.152556i	0.626702	−	0.779259i	$-0.284404\pi$
$167$	−1.97146	−	1.97146i	−0.152556	−	0.152556i	−0.779259	+	0.626702i	$0.784404\pi$
$168$		0			0
$169$	−6.96450	+	10.9771i	−0.535731	+	0.844389i
$170$	1.55842	+	2.69927i	0.119526	+	0.207024i
$171$		0			0
$172$	4.97487	−	8.61674i	0.379331	−	0.657020i
$173$	−0.901884	−	1.56211i	−0.0685690	−	0.118765i	0.829703	−	0.558206i	$-0.188510\pi$
$173$	−0.901884	−	1.56211i	−0.0685690	−	0.118765i	−0.898272	+	0.439441i	$0.855177\pi$
$174$		0			0
$175$	12.9421	−	0.0173752i	0.978329	−	0.00131344i
$176$	−0.159017	+	0.159017i	−0.0119863	+	0.0119863i
$177$		0			0
$178$	6.90361	+	3.98580i	0.517447	+	0.298748i
$179$	−14.8199	−	8.55629i	−1.10769	−	0.639527i	−0.169462	−	0.985537i	$-0.554203\pi$
$179$	−14.8199	−	8.55629i	−1.10769	−	0.639527i	−0.938231	+	0.346010i	$0.887536\pi$
$180$		0			0
$181$	23.4682			1.74438			0.872190	−	0.489168i	$-0.162699\pi$
$181$	23.4682			1.74438			0.872190	+	0.489168i	$0.162699\pi$
$182$	−5.61617	+	5.40082i	−0.416298	+	0.400335i
$183$		0			0
$184$	3.67054	−	13.6986i	0.270596	−	1.00988i
$185$	7.52580	+	4.34502i	0.553308	+	0.319452i
$186$		0			0
$187$	0.595991	+	0.159695i	0.0435832	+	0.0116781i
$188$	4.62006	−	4.62006i	0.336953	−	0.336953i
$189$		0			0
$190$	3.23772	−	3.23772i	0.234889	−	0.234889i
$191$	12.6234	+	21.8644i	0.913400	+	1.58206i	0.809227	+	0.587496i	$0.199886\pi$
$191$	12.6234	+	21.8644i	0.913400	+	1.58206i	0.104173	+	0.994559i	$0.466780\pi$
$192$		0			0
$193$	1.38209	+	5.15802i	0.0994848	+	0.371282i	0.997661	−	0.0683529i	$-0.0217744\pi$
$193$	1.38209	+	5.15802i	0.0994848	+	0.371282i	−0.898176	+	0.439635i	$0.855108\pi$
$194$	1.69330	+	2.93289i	0.121572	+	0.210569i
$195$		0			0
$196$	8.06745	−	4.68667i	0.576247	−	0.334762i
$197$	10.7141	+	10.7141i	0.763345	+	0.763345i	0.976926	−	0.213580i	$-0.0685125\pi$
$197$	10.7141	+	10.7141i	0.763345	+	0.763345i	−0.213580	+	0.976926i	$0.568513\pi$
$198$		0			0
$199$	−3.59015	+	6.21832i	−0.254499	+	0.440805i	−0.964759	−	0.263134i	$-0.915244\pi$
$199$	−3.59015	+	6.21832i	−0.254499	+	0.440805i	0.710260	+	0.703939i	$0.248577\pi$
$200$	12.8625	−	3.44650i	0.909517	−	0.243704i
$201$		0			0
$202$	8.92426	+	8.92426i	0.627909	+	0.627909i
$203$	−3.76493	+	2.18043i	−0.264246	+	0.153036i
$204$		0			0
$205$	−21.4025	+	12.3568i	−1.49482	+	0.863033i
$206$	13.8072	−	3.69964i	0.961995	−	0.257766i
$207$		0			0
$208$	0.825879	−	1.36386i	0.0572644	−	0.0945669i
$209$		−	0.906432i		−	0.0626992i
$210$		0			0
$211$	−2.72556			−0.187636			−0.0938178	−	0.995589i	$-0.529907\pi$
$211$	−2.72556			−0.187636			−0.0938178	+	0.995589i	$0.529907\pi$
$212$	−9.94953	+	5.74437i	−0.683337	+	0.394525i
$213$		0			0
$214$	1.67587	−	0.449049i	0.114560	−	0.0306964i
$215$	−6.07659	+	22.6781i	−0.414420	+	1.54664i
$216$		0			0
$217$	−7.06584	−	7.04689i	−0.479660	−	0.478374i
$218$			8.74709i			0.592428i
$219$		0			0
$220$	1.06589	−	1.84618i	0.0718623	−	0.124469i
$221$	−4.37369	−	0.0913669i	−0.294206	−	0.00614601i
$222$		0			0
$223$	−15.3311	+	15.3311i	−1.02665	+	1.02665i	−0.0270132	+	0.999635i	$0.508600\pi$
$223$	−15.3311	+	15.3311i	−1.02665	+	1.02665i	−0.999635	+	0.0270132i	$0.991400\pi$
$224$	10.8468	−	10.8760i	0.724735	−	0.726683i
$225$		0			0
$226$	−1.10161	+	4.11126i	−0.0732779	+	0.273477i
$227$	4.68443	+	17.4825i	0.310916	+	1.16036i	0.927732	+	0.373248i	$0.121756\pi$
$227$	4.68443	+	17.4825i	0.310916	+	1.16036i	−0.616815	+	0.787108i	$0.711577\pi$
$228$		0			0
$229$	1.11881	−	4.17546i	0.0739331	−	0.275922i	−0.919056	−	0.394126i	$-0.871047\pi$
$229$	1.11881	−	4.17546i	0.0739331	−	0.275922i	0.992989	+	0.118205i	$0.0377138\pi$
$230$			13.3829i			0.882445i
$231$		0			0
$232$	−3.16538	+	3.16538i	−0.207817	+	0.207817i
$233$	−8.56327	+	4.94400i	−0.560998	+	0.323892i	−0.753546	−	0.657395i	$-0.771658\pi$
$233$	−8.56327	+	4.94400i	−0.560998	+	0.323892i	0.192548	+	0.981288i	$0.438325\pi$
$234$		0			0
$235$	−7.70876	+	13.3520i	−0.502864	+	0.870986i
$236$	3.22419	+	0.863919i	0.209877	+	0.0562363i
$237$		0			0
$238$	−2.53355	−	0.675219i	−0.164226	−	0.0437679i
$239$	8.13735	+	8.13735i	0.526361	+	0.526361i	0.919485	−	0.393124i	$-0.128606\pi$
$239$	8.13735	+	8.13735i	0.526361	+	0.526361i	−0.393124	+	0.919485i	$0.628606\pi$
$240$		0			0
$241$	14.0777	−	3.77210i	0.906822	−	0.242982i	0.224878	−	0.974387i	$-0.427802\pi$
$241$	14.0777	−	3.77210i	0.906822	−	0.242982i	0.681944	+	0.731405i	$0.261135\pi$
$242$	−2.27074	−	8.47450i	−0.145968	−	0.544762i
$243$		0			0
$244$	−14.0016			−0.896362
$245$	−15.5256	+	15.6092i	−0.991894	+	0.997235i
$246$		0			0
$247$	1.53332	+	6.24101i	0.0975626	+	0.397106i
$248$	−8.89210	−	5.13386i	−0.564649	−	0.326000i
$249$		0			0
$250$	0.241046	−	0.139168i	0.0152451	−	0.00880177i
$251$	−2.29786			−0.145040			−0.0725198	−	0.997367i	$-0.523104\pi$
$251$	−2.29786			−0.145040			−0.0725198	+	0.997367i	$0.523104\pi$
$252$		0			0
$253$	1.87334	+	1.87334i	0.117776	+	0.117776i
$254$	9.02241	+	2.41755i	0.566116	+	0.151690i
$255$		0			0
$256$	7.31281	−	12.6662i	0.457051	−	0.791635i
$257$	−9.02516	−	15.6320i	−0.562974	−	0.975100i	−0.997235	−	0.0743128i	$-0.976324\pi$
$257$	−9.02516	−	15.6320i	−0.562974	−	0.975100i	0.434261	−	0.900787i	$-0.357010\pi$
$258$		0			0
$259$	−7.05869	+	1.90153i	−0.438605	+	0.118155i
$260$	−4.21594	+	14.5144i	−0.261462	+	0.900148i
$261$		0			0
$262$	1.48409	+	5.53869i	0.0916872	+	0.342181i
$263$	3.98168	−	6.89647i	0.245521	−	0.425255i	−0.716757	−	0.697323i	$-0.754374\pi$
$263$	3.98168	−	6.89647i	0.245521	−	0.425255i	0.962278	+	0.272068i	$0.0877077\pi$
$264$		0			0
$265$	19.1694	−	19.1694i	1.17757	−	1.17757i
$266$	0.00517124	+	3.85185i	0.000317069	+	0.236172i
$267$		0			0
$268$	9.53170	+	2.55401i	0.582241	+	0.156011i
$269$	−6.97055	−	4.02445i	−0.425002	−	0.245375i	0.272213	−	0.962237i	$-0.412244\pi$
$269$	−6.97055	−	4.02445i	−0.425002	−	0.245375i	−0.697215	+	0.716862i	$0.745578\pi$
$270$		0			0
$271$	5.74808	−	21.4521i	0.349171	−	1.30312i	−0.538492	−	0.842631i	$-0.681006\pi$
$271$	5.74808	−	21.4521i	0.349171	−	1.30312i	0.887663	−	0.460494i	$-0.152328\pi$
$272$	0.536543			0.0325327
$273$		0			0
$274$	−5.08024			−0.306909
$275$	−0.643838	+	2.40284i	−0.0388249	+	0.144897i
$276$		0			0
$277$	−1.27323	−	0.735098i	−0.0765008	−	0.0441678i	0.461262	−	0.887264i	$-0.347397\pi$
$277$	−1.27323	−	0.735098i	−0.0765008	−	0.0441678i	−0.537762	+	0.843096i	$0.680730\pi$
$278$	−1.51217	−	0.405184i	−0.0906938	−	0.0243013i
$279$		0			0
$280$	−11.2997	+	19.6325i	−0.675289	+	1.17327i
$281$	13.2274	−	13.2274i	0.789081	−	0.789081i	−0.192263	−	0.981343i	$-0.561583\pi$
$281$	13.2274	−	13.2274i	0.789081	−	0.789081i	0.981343	+	0.192263i	$0.0615826\pi$
$282$		0			0
$283$	2.39327	−	4.14527i	0.142265	−	0.246411i	−0.786084	−	0.618120i	$-0.787895\pi$
$283$	2.39327	−	4.14527i	0.142265	−	0.246411i	0.928349	+	0.371709i	$0.121228\pi$
$284$	−0.409992	−	1.53011i	−0.0243285	−	0.0907954i
$285$		0			0
$286$	−0.721567	−	1.31235i	−0.0426671	−	0.0776008i
$287$	5.35381	−	20.0885i	0.316026	−	1.18579i
$288$		0			0
$289$	7.76394	+	13.4475i	0.456702	+	0.791032i
$290$	2.11217	−	3.65838i	0.124031	−	0.214828i
$291$		0			0
$292$	3.14711	+	0.843267i	0.184171	+	0.0493484i
$293$	15.3136	+	15.3136i	0.894628	+	0.894628i	0.994955	−	0.100326i	$-0.0319887\pi$
$293$	15.3136	+	15.3136i	0.894628	+	0.894628i	−0.100326	+	0.994955i	$0.531989\pi$
$294$		0			0
$295$	−7.87640			−0.458582
$296$	−6.51395	+	3.76083i	−0.378616	+	0.218594i
$297$		0			0
$298$	0.789951	+	0.456079i	0.0457607	+	0.0264199i
$299$	−16.0674	−	9.72950i	−0.929200	−	0.562672i
$300$		0			0
$301$	−9.89820	−	17.0912i	−0.570523	−	0.985118i
$302$	−10.7646			−0.619433
$303$		0			0
$304$	−0.204004	−	0.761355i	−0.0117005	−	0.0436667i
$305$	31.9134	−	8.55118i	1.82736	−	0.489639i
$306$		0			0
$307$	9.36619	+	9.36619i	0.534556	+	0.534556i	0.921925	−	0.387369i	$-0.126616\pi$
$307$	9.36619	+	9.36619i	0.534556	+	0.534556i	−0.387369	+	0.921925i	$0.626616\pi$
$308$	0.466470	+	1.73159i	0.0265796	+	0.0986663i
$309$		0			0
$310$	9.35913	+	2.50777i	0.531563	+	0.142432i
$311$	2.71082	−	4.69528i	0.153716	−	0.266245i	−0.778874	−	0.627180i	$-0.784209\pi$
$311$	2.71082	−	4.69528i	0.153716	−	0.266245i	0.932591	+	0.360935i	$0.117542\pi$
$312$		0			0
$313$	−18.2670	+	10.5464i	−1.03251	+	0.596120i	−0.917703	−	0.397268i	$-0.869958\pi$
$313$	−18.2670	+	10.5464i	−1.03251	+	0.596120i	−0.114807	+	0.993388i	$0.536625\pi$
$314$	8.03039	−	8.03039i	0.453181	−	0.453181i
$315$		0			0
$316$			16.5426i			0.930596i
$317$	3.98815	−	14.8840i	0.223997	−	0.835968i	−0.758807	−	0.651316i	$-0.774217\pi$
$317$	3.98815	−	14.8840i	0.223997	−	0.835968i	0.982804	−	0.184652i	$-0.0591159\pi$
$318$		0			0
$319$	−0.216439	−	0.807761i	−0.0121183	−	0.0452259i
$320$	−3.14012	+	11.7191i	−0.175538	+	0.655117i
$321$		0			0
$322$	−7.97138	−	7.95001i	−0.444228	−	0.443036i
$323$	−1.52921	+	1.52921i	−0.0850874	+	0.0850874i
$324$		0			0
$325$	0.368361	−	17.6333i	0.0204330	−	0.978117i
$326$	3.34348	−	5.79107i	0.185178	−	0.320738i
$327$		0			0
$328$		−	21.3908i		−	1.18111i
$329$	−3.37361	−	12.5232i	−0.185993	−	0.690428i
$330$		0			0
$331$	−2.44797	+	9.13594i	−0.134552	+	0.502156i	0.865447	+	0.501001i	$0.167035\pi$
$331$	−2.44797	+	9.13594i	−0.134552	+	0.502156i	−0.999999	+	0.00115583i	$0.999632\pi$
$332$	13.3180	−	3.56855i	0.730921	−	0.195850i
$333$		0			0
$334$	−1.97217	+	1.13863i	−0.107912	+	0.0623031i
$335$	−23.2851			−1.27220
$336$		0			0
$337$		−	30.8890i		−	1.68263i	−0.540545	−	0.841315i	$-0.681782\pi$
$337$		−	30.8890i		−	1.68263i	0.540545	−	0.841315i	$-0.318218\pi$
$338$	7.18813	+	7.81525i	0.390983	+	0.425094i
$339$		0			0
$340$	−4.91284	+	1.31639i	−0.266436	+	0.0713913i
$341$	1.66113	−	0.959052i	0.0899551	−	0.0519356i
$342$		0			0
$343$	−0.0745920	−	18.5201i	−0.00402759	−	0.999992i
$344$	−14.3695	−	14.3695i	−0.774750	−	0.774750i
$345$		0			0
$346$	−1.42310	+	0.381318i	−0.0765062	+	0.0204998i
$347$	5.48714	−	9.50400i	0.294565	−	0.510201i	−0.680319	−	0.732916i	$-0.738159\pi$
$347$	5.48714	−	9.50400i	0.294565	−	0.510201i	0.974884	+	0.222715i	$0.0714920\pi$
$348$		0			0
$349$	−14.1593	−	14.1593i	−0.757930	−	0.757930i	0.218015	−	0.975945i	$-0.430042\pi$
$349$	−14.1593	−	14.1593i	−0.757930	−	0.757930i	−0.975945	+	0.218015i	$0.930042\pi$
$350$	2.72226	−	10.2144i	0.145511	−	0.545984i
$351$		0			0
$352$	1.47621	+	2.55687i	0.0786822	+	0.136282i
$353$	−4.93709	−	18.4255i	−0.262775	−	0.980688i	−0.963598	−	0.267354i	$-0.913851\pi$
$353$	−4.93709	−	18.4255i	−0.262775	−	0.980688i	0.700824	−	0.713334i	$-0.252816\pi$
$354$		0			0
$355$	1.86896	+	3.23714i	0.0991942	+	0.171809i
$356$	−9.19822	+	9.19822i	−0.487504	+	0.487504i
$357$		0			0
$358$	−9.88349	+	9.88349i	−0.522359	+	0.522359i
$359$	−27.0728	−	7.25413i	−1.42885	−	0.382858i	−0.540233	−	0.841515i	$-0.681664\pi$
$359$	−27.0728	−	7.25413i	−1.42885	−	0.382858i	−0.888613	+	0.458657i	$0.848331\pi$
$360$		0			0
$361$	−13.7031	−	7.91149i	−0.721216	−	0.416394i
$362$	4.96120	−	18.5154i	0.260755	−	0.973150i
$363$		0			0
$364$	−6.14091	−	11.1333i	−0.321871	−	0.583545i
$365$	−7.68812			−0.402414
$366$		0			0
$367$	14.4837	+	8.36218i	0.756044	+	0.436502i	0.827874	−	0.560915i	$-0.189550\pi$
$367$	14.4837	+	8.36218i	0.756044	+	0.436502i	−0.0718297	+	0.997417i	$0.522884\pi$
$368$	1.99513	+	1.15189i	0.104003	+	0.0600463i
$369$		0			0
$370$	5.01900	−	5.01900i	0.260925	−	0.260925i
$371$	0.0306170	+	22.8054i	0.00158956	+	1.18400i
$372$		0			0
$373$	−8.19490	−	14.1940i	−0.424316	−	0.734937i	0.572040	−	0.820226i	$-0.306152\pi$
$373$	−8.19490	−	14.1940i	−0.424316	−	0.734937i	−0.996356	+	0.0852887i	$0.972819\pi$
$374$	0.251986	−	0.436452i	0.0130299	−	0.0225684i
$375$		0			0
$376$	−6.67231	−	11.5568i	−0.344098	−	0.595996i
$377$	2.85664	+	5.19551i	0.147125	+	0.267582i
$378$		0			0
$379$	2.80924	+	2.80924i	0.144301	+	0.144301i	0.775567	−	0.631266i	$-0.217464\pi$
$379$	2.80924	+	2.80924i	0.144301	+	0.144301i	−0.631266	+	0.775567i	$0.717464\pi$
$380$	3.73592	+	6.47081i	0.191649	+	0.331945i
$381$		0			0
$382$	19.9187	−	5.33721i	1.01913	−	0.273075i
$383$	−37.4573	−	10.0367i	−1.91398	−	0.512849i	−0.992114	−	0.125342i	$-0.959997\pi$
$383$	−37.4573	−	10.0367i	−1.91398	−	0.512849i	−0.921867	−	0.387508i	$-0.873336\pi$
$384$		0			0
$385$	−2.12074	−	3.66186i	−0.108083	−	0.186626i
$386$	4.36163			0.222001
$387$		0			0
$388$	−5.33804	+	1.43032i	−0.270998	+	0.0726137i
$389$	−4.22632	−	2.44006i	−0.214283	−	0.123716i	0.389017	−	0.921230i	$-0.372815\pi$
$389$	−4.22632	−	2.44006i	−0.214283	−	0.123716i	−0.603300	+	0.797514i	$0.706148\pi$
$390$		0			0
$391$		−	6.32089i		−	0.319661i
$392$	−4.98138	−	18.3931i	−0.251598	−	0.928990i
$393$		0			0
$394$	10.7179	−	6.18798i	0.539960	−	0.311746i
$395$	−10.1030	−	37.7051i	−0.508339	−	1.89715i
$396$		0			0
$397$	−8.19329	+	30.5778i	−0.411210	+	1.53466i	0.381099	+	0.924534i	$0.375546\pi$
$397$	−8.19329	+	30.5778i	−0.411210	+	1.53466i	−0.792308	+	0.610121i	$0.791121\pi$
$398$	4.14703	+	4.14703i	0.207872	+	0.207872i
$399$		0			0
$400$			2.16316i			0.108158i
$401$	9.34436	+	2.50381i	0.466635	+	0.125035i	0.484473	−	0.874806i	$-0.339011\pi$
$401$	9.34436	+	2.50381i	0.466635	+	0.125035i	−0.0178375	+	0.999841i	$0.505678\pi$
$402$		0			0
$403$	−9.81495	+	9.41327i	−0.488918	+	0.468908i
$404$	−17.8357	+	10.2975i	−0.887361	+	0.512318i
$405$		0			0
$406$	0.924356	+	3.43131i	0.0458750	+	0.170293i
$407$		−	1.40512i		−	0.0696491i
$408$		0			0
$409$	3.09562	+	11.5530i	0.153068	+	0.571259i	0.999263	+	0.0383851i	$0.0122214\pi$
$409$	3.09562	+	11.5530i	0.153068	+	0.571259i	−0.846195	+	0.532874i	$0.821112\pi$
$410$	5.22445	+	19.4979i	0.258017	+	0.962933i
$411$		0			0
$412$			23.3258i			1.14918i
$413$	4.67890	−	4.69148i	0.230234	−	0.230853i
$414$		0			0
$415$	−28.1759	+	16.2674i	−1.38310	+	0.798533i
$416$	−14.4893	−	15.1075i	−0.710394	−	0.740708i
$417$		0			0
$418$	−0.715137	−	0.191620i	−0.0349785	−	0.00937246i
$419$		−	18.5355i		−	0.905516i	−0.891633	−	0.452758i	$-0.850440\pi$
$419$		−	18.5355i		−	0.905516i	0.891633	−	0.452758i	$-0.149560\pi$
$420$		0			0
$421$	19.2884	+	19.2884i	0.940060	+	0.940060i	0.998302	−	0.0582422i	$-0.0185496\pi$
$421$	19.2884	+	19.2884i	0.940060	+	0.940060i	−0.0582422	+	0.998302i	$0.518550\pi$
$422$	−0.576186	+	2.15036i	−0.0280483	+	0.104678i
$423$		0			0
$424$	6.07312	+	22.6652i	0.294937	+	1.10072i
$425$	5.13993	−	2.96754i	0.249323	−	0.143947i
$426$		0			0
$427$	−13.8645	+	24.0886i	−0.670948	+	1.16573i
$428$			2.83120i			0.136851i
$429$		0			0
$430$	16.6075	+	9.58834i	0.800884	+	0.462391i
$431$	−8.84924	+	2.37115i	−0.426253	+	0.114214i	−0.465567	−	0.885013i	$-0.654149\pi$
$431$	−8.84924	+	2.37115i	−0.426253	+	0.114214i	0.0393138	+	0.999227i	$0.487483\pi$
$432$		0			0
$433$	23.6700			1.13751			0.568755	−	0.822507i	$-0.307425\pi$
$433$	23.6700			1.13751			0.568755	+	0.822507i	$0.307425\pi$
$434$	−7.05342	+	4.08493i	−0.338575	+	0.196083i
$435$		0			0
$436$	−13.7873	−	3.69431i	−0.660294	−	0.176925i
$437$	−8.96936	+	2.40333i	−0.429063	+	0.114967i
$438$		0			0
$439$	−5.64906	−	9.78446i	−0.269615	−	0.466987i	0.699148	−	0.714977i	$-0.253563\pi$
$439$	−5.64906	−	9.78446i	−0.269615	−	0.466987i	−0.968762	+	0.247991i	$0.920230\pi$
$440$	−3.07872	−	3.07872i	−0.146772	−	0.146772i
$441$		0			0
$442$	−0.996685	+	3.43134i	−0.0474075	+	0.163212i
$443$	19.5144	+	33.7999i	0.927157	+	1.60588i	0.788054	+	0.615606i	$0.211089\pi$
$443$	19.5144	+	33.7999i	0.927157	+	1.60588i	0.139103	+	0.990278i	$0.455578\pi$
$444$		0			0
$445$	15.3476	−	26.5828i	0.727545	−	1.26015i
$446$	8.85460	+	15.3366i	0.419278	+	0.726210i
$447$		0			0
$448$	−5.11497	−	8.83198i	−0.241659	−	0.417272i
$449$	8.82288	−	8.82288i	0.416378	−	0.416378i	−0.467576	−	0.883953i	$-0.654872\pi$
$449$	8.82288	−	8.82288i	0.416378	−	0.416378i	0.883953	+	0.467576i	$0.154872\pi$
$450$		0			0
$451$	3.46063	+	1.99800i	0.162955	+	0.0940820i
$452$	−6.01499	−	3.47276i	−0.282921	−	0.163345i
$453$		0			0
$454$	14.7833			0.693813
$455$	20.7962	+	21.6254i	0.974941	+	1.01381i
$456$		0			0
$457$	5.91700	−	22.0825i	0.276786	−	1.03298i	−0.677850	−	0.735200i	$-0.737088\pi$
$457$	5.91700	−	22.0825i	0.276786	−	1.03298i	0.954635	−	0.297777i	$-0.0962453\pi$
$458$	−3.05774	−	1.76539i	−0.142879	−	0.0824912i
$459$		0			0
$460$	−21.0945	−	5.65224i	−0.983534	−	0.263537i
$461$	7.67189	−	7.67189i	0.357316	−	0.357316i	−0.505507	−	0.862823i	$-0.668694\pi$
$461$	7.67189	−	7.67189i	0.357316	−	0.357316i	0.862823	+	0.505507i	$0.168694\pi$
$462$		0			0
$463$	14.0571	−	14.0571i	0.653289	−	0.653289i	−0.300495	−	0.953783i	$-0.597152\pi$
$463$	14.0571	−	14.0571i	0.653289	−	0.653289i	0.953783	+	0.300495i	$0.0971518\pi$
$464$	−0.363594	−	0.629764i	−0.0168794	−	0.0292361i
$465$		0			0
$466$	2.09033	+	7.80122i	0.0968327	+	0.361385i
$467$	−4.96276	−	8.59575i	−0.229649	−	0.397764i	0.728055	−	0.685519i	$-0.240424\pi$
$467$	−4.96276	−	8.59575i	−0.229649	−	0.397764i	−0.957704	+	0.287755i	$0.907091\pi$
$468$		0			0
$469$	13.8323	−	13.8695i	0.638715	−	0.640433i
$470$	8.90450	+	8.90450i	0.410734	+	0.410734i
$471$		0			0
$472$	3.40871	−	5.90406i	0.156899	−	0.271756i
$473$	3.66689	−	0.982540i	0.168604	−	0.0451772i
$474$		0			0
$475$	−6.16525	−	6.16525i	−0.282881	−	0.282881i
$476$	2.13433	−	3.70826i	0.0978269	−	0.169968i
$477$		0			0
$478$	8.14026	−	4.69978i	0.372327	−	0.214963i
$479$	−20.3767	+	5.45991i	−0.931034	+	0.249470i	−0.692295	−	0.721614i	$-0.743400\pi$
$479$	−20.3767	+	5.45991i	−0.931034	+	0.249470i	−0.238738	+	0.971084i	$0.576734\pi$
$480$		0			0
$481$	2.37689	+	9.67459i	0.108377	+	0.441123i
$482$		−	11.9041i		−	0.542217i
$483$		0			0
$484$	14.3167			0.650760
$485$	11.2933	−	6.52018i	0.512801	−	0.296066i
$486$		0			0
$487$	−42.3475	+	11.3470i	−1.91895	+	0.514181i	−0.929610	+	0.368544i	$0.879856\pi$
$487$	−42.3475	+	11.3470i	−1.91895	+	0.514181i	−0.989338	+	0.145637i	$0.953477\pi$
$488$	−7.40147	+	27.6227i	−0.335049	+	1.25042i
$489$		0			0
$490$	9.03287	+	15.5488i	0.408064	+	0.702424i
$491$		−	37.1276i		−	1.67554i	−0.546021	−	0.837772i	$-0.683858\pi$
$491$		−	37.1276i		−	1.67554i	0.546021	−	0.837772i	$-0.316142\pi$
$492$		0			0
$493$	−0.997597	+	1.72789i	−0.0449295	+	0.0778202i
$494$	5.24804	+	0.109632i	0.236121	+	0.00493259i
$495$		0			0
$496$	1.17941	−	1.17941i	0.0529571	−	0.0529571i
$497$	−3.03840	−	0.809766i	−0.136291	−	0.0363230i
$498$		0			0
$499$	−1.38618	+	5.17328i	−0.0620538	+	0.231588i	−0.989987	−	0.141159i	$-0.954917\pi$
$499$	−1.38618	+	5.17328i	−0.0620538	+	0.231588i	0.927933	+	0.372747i	$0.121584\pi$
$500$	0.117555	+	0.438720i	0.00525720	+	0.0196201i
$501$		0			0
$502$	−0.485769	+	1.81292i	−0.0216809	+	0.0809144i
$503$			27.7355i			1.23666i	0.785917	+	0.618332i	$0.212191\pi$
$503$			27.7355i			1.23666i	−0.785917	+	0.618332i	$0.787809\pi$
$504$		0			0
$505$	34.3634	−	34.3634i	1.52915	−	1.52915i
$506$	1.87401	−	1.08196i	0.0833101	−	0.0480991i
$507$		0			0
$508$	−7.62117	+	13.2003i	−0.338135	+	0.585667i
$509$	29.2382	+	7.83435i	1.29596	+	0.347252i	0.839921	−	0.542708i	$-0.182601\pi$
$509$	29.2382	+	7.83435i	1.29596	+	0.347252i	0.456039	+	0.889960i	$0.349268\pi$
$510$		0			0
$511$	4.56705	−	4.57933i	0.202034	−	0.202578i
$512$	3.51784	+	3.51784i	0.155468	+	0.155468i
$513$		0			0
$514$	−14.2409	+	3.81585i	−0.628141	+	0.168310i
$515$	−14.2457	−	53.1656i	−0.627740	−	2.34276i
$516$		0			0
$517$	2.49290			0.109638
$518$	0.00801626	+	5.97099i	0.000352214	+	0.262350i
$519$		0			0
$520$	26.4058	+	15.9898i	1.15797	+	0.701201i
$521$	36.7196	+	21.2001i	1.60872	+	0.928792i	0.989658	+	0.143446i	$0.0458183\pi$
$521$	36.7196	+	21.2001i	1.60872	+	0.928792i	0.619057	+	0.785346i	$0.287515\pi$
$522$		0			0
$523$	−3.60227	+	2.07977i	−0.157516	+	0.0909420i	−0.576686	−	0.816966i	$-0.695654\pi$
$523$	−3.60227	+	2.07977i	−0.157516	+	0.0909420i	0.419170	+	0.907908i	$0.362321\pi$
$524$	−9.35699			−0.408762
$525$		0			0
$526$	−4.59929	−	4.59929i	−0.200539	−	0.200539i
$527$	−4.42040	−	1.18444i	−0.192556	−	0.0515952i
$528$		0			0
$529$	2.07015	−	3.58560i	0.0900064	−	0.155896i
$530$	−11.0714	−	19.1763i	−0.480912	−	0.832964i
$531$		0			0
$532$	−6.07354	−	1.61866i	−0.263321	−	0.0701780i
$533$	−27.2071	−	7.90273i	−1.17847	−	0.342305i
$534$		0			0
$535$	−1.72909	−	6.45306i	−0.0747552	−	0.278990i
$536$	10.0772	−	17.4542i	0.435269	−	0.753908i
$537$		0			0
$538$	−4.64870	+	4.64870i	−0.200420	+	0.200420i
$539$	3.44094	+	0.912103i	0.148212	+	0.0392870i
$540$		0			0
$541$	−40.4410	−	10.8361i	−1.73869	−	0.465882i	−0.756538	−	0.653950i	$-0.773111\pi$
$541$	−40.4410	−	10.8361i	−1.73869	−	0.465882i	−0.982156	+	0.188068i	$0.939777\pi$
$542$	−15.7097	−	9.06999i	−0.674789	−	0.389589i
$543$		0			0
$544$	1.82314	−	6.80405i	0.0781665	−	0.291721i
$545$	33.6812			1.44275
$546$		0			0
$547$	−13.4403			−0.574667			−0.287334	−	0.957831i	$-0.592769\pi$
$547$	−13.4403			−0.574667			−0.287334	+	0.957831i	$0.592769\pi$
$548$	2.14562	−	8.00758i	0.0916565	−	0.342067i
$549$		0			0
$550$	1.75963	+	1.01592i	0.0750308	+	0.0433191i
$551$	2.83118	+	0.758614i	0.120613	+	0.0323180i
$552$		0			0
$553$	28.4602	+	16.3806i	1.21025	+	0.696573i
$554$	−0.849123	+	0.849123i	−0.0360758	+	0.0360758i
$555$		0			0
$556$	1.27732	−	2.21238i	0.0541704	−	0.0938258i
$557$	−5.40317	−	20.1649i	−0.228940	−	0.854415i	−0.980788	−	0.195078i	$-0.937504\pi$
$557$	−5.40317	−	20.1649i	−0.228940	−	0.854415i	0.751848	−	0.659337i	$-0.229163\pi$
$558$		0			0
$559$	−23.5854	+	12.9679i	−0.997556	+	0.548485i
$560$	−2.60546	−	2.59847i	−0.110101	−	0.109805i
$561$		0			0
$562$	−7.63958	−	13.2321i	−0.322256	−	0.558164i
$563$	−13.5788	+	23.5192i	−0.572278	+	0.991215i	0.424053	+	0.905637i	$0.360607\pi$
$563$	−13.5788	+	23.5192i	−0.572278	+	0.991215i	−0.996331	+	0.0855779i	$0.972726\pi$
$564$		0			0
$565$	15.8307	+	4.24181i	0.666001	+	0.178454i
$566$	−2.76450	−	2.76450i	−0.116201	−	0.116201i
$567$		0			0
$568$	−3.23536			−0.135753
$569$	10.6066	−	6.12370i	0.444650	−	0.256719i	−0.260918	−	0.965361i	$-0.584025\pi$
$569$	10.6066	−	6.12370i	0.444650	−	0.256719i	0.705568	+	0.708642i	$0.250692\pi$
$570$		0			0
$571$	−4.06355	−	2.34609i	−0.170054	−	0.0981809i	0.412557	−	0.910932i	$-0.364636\pi$
$571$	−4.06355	−	2.34609i	−0.170054	−	0.0981809i	−0.582611	+	0.812751i	$0.697969\pi$
$572$	2.37330	−	0.583082i	0.0992327	−	0.0243799i
$573$		0			0
$574$	−14.7172	−	8.47066i	−0.614285	−	0.353559i
$575$	25.4837			1.06274
$576$		0			0
$577$	−4.41741	−	16.4860i	−0.183899	−	0.686321i	−0.994864	−	0.101225i	$-0.967724\pi$
$577$	−4.41741	−	16.4860i	−0.183899	−	0.686321i	0.810964	−	0.585095i	$-0.198943\pi$
$578$	12.2508	−	3.28260i	0.509568	−	0.136538i
$579$		0			0
$580$	4.87435	+	4.87435i	0.202396	+	0.202396i
$581$	7.04816	−	26.4461i	0.292407	−	1.09717i
$582$		0			0
$583$	−4.23407	−	1.13452i	−0.175357	−	0.0469868i
$584$	3.32722	−	5.76292i	0.137682	−	0.238471i
$585$		0			0
$586$	15.3191	−	8.84446i	0.632824	−	0.365361i
$587$	6.21734	−	6.21734i	0.256617	−	0.256617i	−0.567060	−	0.823677i	$-0.691919\pi$
$587$	6.21734	−	6.21734i	0.256617	−	0.256617i	0.823677	+	0.567060i	$0.191919\pi$
$588$		0			0
$589$			6.72291i			0.277013i
$590$	−1.66508	+	6.21415i	−0.0685501	+	0.255833i
$591$		0			0
$592$	−0.316240	−	1.18022i	−0.0129974	−	0.0485069i
$593$	−10.0703	+	37.5829i	−0.413538	+	1.54334i	0.374209	+	0.927344i	$0.377914\pi$
$593$	−10.0703	+	37.5829i	−0.413538	+	1.54334i	−0.787747	+	0.615999i	$0.788752\pi$
$594$		0			0
$595$	−2.59997	+	9.75560i	−0.106589	+	0.399941i
$596$	−1.05251	+	1.05251i	−0.0431127	+	0.0431127i
$597$		0			0
$598$	−11.0728	+	10.6197i	−0.452801	+	0.434270i
$599$	−17.4902	+	30.2939i	−0.714629	+	1.23777i	0.248474	+	0.968639i	$0.420071\pi$
$599$	−17.4902	+	30.2939i	−0.714629	+	1.23777i	−0.963103	+	0.269135i	$0.913262\pi$
$600$		0			0
$601$		−	11.7882i		−	0.480852i	−0.970667	−	0.240426i	$-0.922713\pi$
$601$		−	11.7882i		−	0.480852i	0.970667	−	0.240426i	$-0.0772872\pi$
$602$	−15.5767	+	4.19618i	−0.634859	+	0.171024i
$603$		0			0
$604$	4.54639	−	16.9674i	0.184990	−	0.690393i
$605$	−32.6316	+	8.74361i	−1.32666	+	0.355478i
$606$		0			0
$607$	16.5407	−	9.54978i	0.671366	−	0.387614i	−0.125228	−	0.992128i	$-0.539966\pi$
$607$	16.5407	−	9.54978i	0.671366	−	0.387614i	0.796594	+	0.604514i	$0.206633\pi$
$608$	−10.3482			−0.419673
$609$		0			0
$610$		−	26.9861i		−	1.09263i
$611$	−17.1643	+	4.21698i	−0.694391	+	0.170601i
$612$		0			0
$613$	24.5517	−	6.57860i	0.991632	−	0.265707i	0.273696	−	0.961816i	$-0.411754\pi$
$613$	24.5517	−	6.57860i	0.991632	−	0.265707i	0.717936	+	0.696109i	$0.245087\pi$
$614$	9.36954	−	5.40951i	0.378124	−	0.218310i
$615$		0			0
$616$	3.66269	−	0.00491729i	0.147574	−	0.000198123i
$617$	10.4089	+	10.4089i	0.419046	+	0.419046i	0.884875	−	0.465829i	$-0.154244\pi$
$617$	10.4089	+	10.4089i	0.419046	+	0.419046i	−0.465829	+	0.884875i	$0.654244\pi$
$618$		0			0
$619$	−30.7106	+	8.22887i	−1.23436	+	0.330746i	−0.816276	−	0.577661i	$-0.803965\pi$
$619$	−30.7106	+	8.22887i	−1.23436	+	0.330746i	−0.418085	+	0.908408i	$0.637299\pi$
$620$	−7.90560	+	13.6929i	−0.317496	+	0.549920i
$621$		0			0
$622$	−3.13131	−	3.13131i	−0.125554	−	0.125554i
$623$	6.71662	+	24.9328i	0.269096	+	0.998913i
$624$		0			0
$625$	−12.7650	−	22.1096i	−0.510600	−	0.884385i
$626$	4.45905	+	16.6414i	0.178219	+	0.665124i
$627$		0			0
$628$	9.26606	+	16.0493i	0.369756	+	0.640436i
$629$	−2.37052	+	2.37052i	−0.0945188	+	0.0945188i
$630$		0			0
$631$	26.3103	−	26.3103i	1.04739	−	1.04739i	0.0485754	−	0.998820i	$-0.484532\pi$
$631$	26.3103	−	26.3103i	1.04739	−	1.04739i	0.998820	−	0.0485754i	$-0.0154681\pi$
$632$	32.6356	+	8.74469i	1.29817	+	0.347845i
$633$		0			0
$634$	−10.8997	−	6.29297i	−0.432884	−	0.249926i
$635$	9.30892	−	34.7414i	0.369413	−	1.37867i
$636$		0			0
$637$	−25.2347	−	0.459373i	−0.999834	−	0.0182010i
$638$	−0.683045			−0.0270420
$639$		0			0
$640$	−23.0442	−	13.3046i	−0.910903	−	0.525910i
$641$	20.0412	+	11.5708i	0.791579	+	0.457018i	0.840518	−	0.541784i	$-0.182251\pi$
$641$	20.0412	+	11.5708i	0.791579	+	0.457018i	−0.0489393	+	0.998802i	$0.515584\pi$
$642$		0			0
$643$	11.9385	−	11.9385i	0.470808	−	0.470808i	−0.431368	−	0.902176i	$-0.641969\pi$
$643$	11.9385	−	11.9385i	0.470808	−	0.470808i	0.902176	+	0.431368i	$0.141969\pi$
$644$	15.8976	−	9.20699i	0.626455	−	0.362806i
$645$		0			0
$646$	0.883205	+	1.52976i	0.0347492	+	0.0601874i
$647$	−10.2367	+	17.7305i	−0.402446	+	0.697056i	−0.994020	−	0.109194i	$-0.965173\pi$
$647$	−10.2367	+	17.7305i	−0.402446	+	0.697056i	0.591575	+	0.806250i	$0.298506\pi$
$648$		0			0
$649$	0.636779	+	1.10293i	0.0249958	+	0.0432939i
$650$	−13.8340	−	4.01830i	−0.542615	−	0.157611i
$651$		0			0
$652$	7.71589	+	7.71589i	0.302178	+	0.302178i
$653$	−20.9319	−	36.2552i	−0.819130	−	1.41878i	−0.906324	−	0.422584i	$-0.861123\pi$
$653$	−20.9319	−	36.2552i	−0.819130	−	1.41878i	0.0871932	−	0.996191i	$-0.472210\pi$
$654$		0			0
$655$	21.3271	−	5.71457i	0.833318	−	0.223287i
$656$	3.35642	+	0.899351i	0.131046	+	0.0351138i
$657$		0			0
$658$	−10.5935	+	0.0142221i	−0.412977	+	0.000554436i
$659$	36.8332			1.43482			0.717410	−	0.696651i	$-0.245328\pi$
$659$	36.8332			1.43482			0.717410	+	0.696651i	$0.245328\pi$
$660$		0			0
$661$	7.01384	−	1.87935i	0.272807	−	0.0730983i	−0.119822	−	0.992795i	$-0.538232\pi$
$661$	7.01384	−	1.87935i	0.272807	−	0.0730983i	0.392629	+	0.919697i	$0.371566\pi$
$662$	6.69037	+	3.86268i	0.260028	+	0.150128i
$663$		0			0
$664$		−	28.1604i		−	1.09284i
$665$	14.8318	−	0.0199122i	0.575152	−	0.000772161i
$666$		0			0
$667$	−7.41911	+	4.28343i	−0.287269	+	0.165855i
$668$	−0.961794	−	3.58947i	−0.0372129	−	0.138881i
$669$		0			0
$670$	−4.92248	+	18.3710i	−0.190172	+	0.709732i
$671$	−3.77751	−	3.77751i	−0.145829	−	0.145829i
$672$		0			0
$673$			28.4985i			1.09854i	0.835646	+	0.549269i	$0.185094\pi$
$673$			28.4985i			1.09854i	−0.835646	+	0.549269i	$0.814906\pi$
$674$	−24.3701	−	6.52995i	−0.938701	−	0.251524i
$675$		0			0
$676$	−15.3544	+	8.02933i	−0.590556	+	0.308820i
$677$	−13.1864	+	7.61318i	−0.506795	+	0.292598i	−0.731515	−	0.681825i	$-0.761186\pi$
$677$	−13.1864	+	7.61318i	−0.506795	+	0.292598i	0.224720	+	0.974423i	$0.427853\pi$
$678$		0			0
$679$	−2.82500	+	10.5999i	−0.108414	+	0.406788i
$680$			10.3880i			0.398362i
$681$		0			0
$682$	−0.405488	−	1.51330i	−0.0155270	−	0.0579474i
$683$	11.1843	+	41.7404i	0.427956	+	1.59715i	0.757382	+	0.652972i	$0.226478\pi$
$683$	11.1843	+	41.7404i	0.427956	+	1.59715i	−0.329426	+	0.944182i	$0.606855\pi$
$684$		0			0
$685$			19.5618i			0.747418i
$686$	−14.6274	−	3.85631i	−0.558475	−	0.147235i
$687$		0			0
$688$	2.85886	−	1.65056i	0.108993	−	0.0629271i
$689$	31.0718	+	0.649093i	1.18374	+	0.0247285i
$690$		0			0
$691$	9.69593	+	2.59802i	0.368851	+	0.0988332i	0.438483	−	0.898739i	$-0.355516\pi$
$691$	9.69593	+	2.59802i	0.368851	+	0.0988332i	−0.0696323	+	0.997573i	$0.522183\pi$
$692$		−	2.40416i		−	0.0913926i
$693$		0			0
$694$	−6.33827	−	6.33827i	−0.240597	−	0.240597i
$695$	−1.56019	+	5.82270i	−0.0591813	+	0.220868i
$696$		0			0
$697$	−2.46756	−	9.20905i	−0.0934654	−	0.348818i
$698$	−14.1644	+	8.17781i	−0.536130	+	0.309535i
$699$		0			0
$700$	14.9504	+	8.60490i	0.565074	+	0.325235i
$701$		−	24.4239i		−	0.922479i	−0.887276	−	0.461239i	$-0.847405\pi$
$701$		−	24.4239i		−	0.922479i	0.887276	−	0.461239i	$-0.152595\pi$
$702$		0			0
$703$	4.26509	+	2.46245i	0.160861	+	0.0928732i
$704$	1.89489	−	0.507735i	0.0714164	−	0.0191360i
$705$		0			0
$706$	−15.5806			−0.586384
$707$	0.0548847	+	40.8814i	0.00206415	+	1.53750i
$708$		0			0
$709$	−26.8785	−	7.20208i	−1.00944	−	0.270480i	−0.284047	−	0.958810i	$-0.591677\pi$
$709$	−26.8785	−	7.20208i	−1.00944	−	0.270480i	−0.725397	+	0.688330i	$0.758344\pi$
$710$	2.94906	−	0.790199i	0.110676	−	0.0296556i
$711$		0			0
$712$	13.2841	+	23.0087i	0.497843	+	0.862289i
$713$	−13.8944	−	13.8944i	−0.520349	−	0.520349i
$714$		0			0
$715$	−5.05328	+	2.77844i	−0.188982	+	0.103908i
$716$	−11.4043	−	19.7528i	−0.426199	−	0.738197i
$717$		0			0
$718$	−11.4464	+	19.8258i	−0.427176	+	0.739890i
$719$	6.94803	+	12.0343i	0.259118	+	0.448805i	0.966006	−	0.258520i	$-0.0832349\pi$
$719$	6.94803	+	12.0343i	0.259118	+	0.448805i	−0.706888	+	0.707325i	$0.749902\pi$
$720$		0			0
$721$	40.1299	+	23.0972i	1.49452	+	0.860187i
$722$	−9.13867	+	9.13867i	−0.340106	+	0.340106i
$723$		0			0
$724$	27.0891	+	15.6399i	1.00676	+	0.581251i
$725$	−6.96627	−	4.02198i	−0.258721	−	0.149372i
$726$		0			0
$727$	14.0631			0.521572			0.260786	−	0.965397i	$-0.416018\pi$
$727$	14.0631			0.521572			0.260786	+	0.965397i	$0.416018\pi$
$728$	−25.2102	+	6.22965i	−0.934353	+	0.230886i
$729$		0			0
$730$	−1.62527	+	6.06560i	−0.0601540	+	0.224498i
$731$	−7.84388	−	4.52866i	−0.290116	−	0.167499i
$732$		0			0
$733$	−21.8735	−	5.86099i	−0.807917	−	0.216481i	−0.168860	−	0.985640i	$-0.554009\pi$
$733$	−21.8735	−	5.86099i	−0.807917	−	0.216481i	−0.639057	+	0.769159i	$0.720675\pi$
$734$	9.65927	−	9.65927i	0.356530	−	0.356530i
$735$		0			0
$736$	21.3868	−	21.3868i	0.788327	−	0.788327i
$737$	1.88252	+	3.26061i	0.0693434	+	0.120106i
$738$		0			0
$739$	0.258550	+	0.964923i	0.00951093	+	0.0354953i	0.970518	−	0.241028i	$-0.0774845\pi$
$739$	0.258550	+	0.964923i	0.00951093	+	0.0354953i	−0.961007	+	0.276523i	$0.910818\pi$
$740$	5.79129	+	10.0308i	0.212892	+	0.368740i
$741$		0			0
$742$	17.9990	+	4.79692i	0.660763	+	0.176100i
$743$	7.54553	+	7.54553i	0.276819	+	0.276819i	0.831838	−	0.555019i	$-0.187289\pi$
$743$	7.54553	+	7.54553i	0.276819	+	0.276819i	−0.555019	+	0.831838i	$0.687289\pi$
$744$		0			0
$745$	1.75616	−	3.04176i	0.0643407	−	0.111441i
$746$	−12.9309	+	3.46481i	−0.473433	+	0.126856i
$747$		0			0
$748$	0.581519	+	0.581519i	0.0212625	+	0.0212625i
$749$	4.87084	+	2.80347i	0.177976	+	0.102436i
$750$		0			0
$751$	36.8341	−	21.2662i	1.34409	−	0.776013i	0.356689	−	0.934223i	$-0.383906\pi$
$751$	36.8341	−	21.2662i	1.34409	−	0.776013i	0.987405	+	0.158210i	$0.0505723\pi$
$752$	2.09390	−	0.561060i	0.0763568	−	0.0204598i
$753$		0			0
$754$	4.70293	−	1.15544i	0.171271	−	0.0420785i
$755$			41.4498i			1.50851i
$756$		0			0
$757$	44.6260			1.62196			0.810979	−	0.585075i	$-0.198935\pi$
$757$	44.6260			1.62196			0.810979	+	0.585075i	$0.198935\pi$
$758$	2.81025	−	1.62250i	0.102073	−	0.0589317i
$759$		0			0
$760$	14.7406	−	3.94973i	0.534697	−	0.143272i
$761$	12.2522	−	45.7257i	0.444141	−	1.65756i	−0.274054	−	0.961714i	$-0.588365\pi$
$761$	12.2522	−	45.7257i	0.444141	−	1.65756i	0.718195	−	0.695842i	$-0.244968\pi$
$762$		0			0
$763$	−20.0080	+	20.0618i	−0.724338	+	0.726286i
$764$			33.6504i			1.21743i
$765$		0			0
$766$	−15.8370	+	27.4305i	−0.572214	+	0.991104i
$767$	−6.25010	−	6.51680i	−0.225678	−	0.235308i
$768$		0			0
$769$	−17.0724	+	17.0724i	−0.615648	+	0.615648i	−0.944412	−	0.328764i	$-0.893368\pi$
$769$	−17.0724	+	17.0724i	−0.615648	+	0.615648i	0.328764	+	0.944412i	$0.393368\pi$
$770$	−3.33738	+	0.899052i	−0.120271	+	0.0323996i
$771$		0			0
$772$	−1.84212	+	6.87490i	−0.0662994	+	0.247433i
$773$	10.1986	+	38.0617i	0.366818	+	1.36898i	0.864939	+	0.501876i	$0.167357\pi$
$773$	10.1986	+	38.0617i	0.366818	+	1.36898i	−0.498121	+	0.867107i	$0.665977\pi$
$774$		0			0
$775$	4.77528	−	17.8216i	0.171533	−	0.640170i
$776$			11.2871i			0.405182i
$777$		0			0
$778$	−2.81855	+	2.81855i	−0.101050	+	0.101050i
$779$	−12.1294	+	7.00294i	−0.434582	+	0.250906i
$780$		0			0
$781$	0.302198	−	0.523422i	0.0108135	−	0.0187295i
$782$	−4.98692	−	1.33624i	−0.178332	−	0.0477839i
$783$		0			0
$784$	3.09549	−	0.00831162i	0.110553	−	0.000296844i
$785$	−30.9215	−	30.9215i	−1.10364	−	1.10364i
$786$		0			0
$787$	14.0502	−	3.76475i	0.500837	−	0.134199i	0.000448541	−	1.00000i	$-0.499857\pi$
$787$	14.0502	−	3.76475i	0.500837	−	0.134199i	0.500388	+	0.865801i	$0.333191\pi$
$788$	5.22695	+	19.5072i	0.186202	+	0.694917i
$789$		0			0
$790$	−31.8835			−1.13436
$791$	−11.9306	+	6.90953i	−0.424205	+	0.245675i
$792$		0			0
$793$	32.3991	+	19.6191i	1.15053	+	0.696694i
$794$	22.3925	+	12.9283i	0.794681	+	0.458809i
$795$		0			0
$796$	−8.28813	+	4.78515i	−0.293765	+	0.169605i
$797$	2.90737			0.102984			0.0514922	−	0.998673i	$-0.483602\pi$
$797$	2.90737			0.102984			0.0514922	+	0.998673i	$0.483602\pi$
$798$		0			0
$799$	−4.20568	−	4.20568i	−0.148786	−	0.148786i
$800$	27.4317	+	7.35029i	0.969856	+	0.259872i
$801$		0			0
$802$	3.95081	−	6.84300i	0.139508	−	0.241635i
$803$	0.621557	+	1.07657i	0.0219343	+	0.0379912i
$804$		0			0
$805$	−30.6120	+	30.6943i	−1.07893	+	1.08183i
$806$	5.35179	+	9.73355i	0.188509	+	0.342850i
$807$		0			0
$808$	10.8868	+	40.6301i	0.382996	+	1.42936i
$809$	0.931766	−	1.61387i	0.0327591	−	0.0567405i	−0.849181	−	0.528102i	$-0.822904\pi$
$809$	0.931766	−	1.61387i	0.0327591	−	0.0567405i	0.881940	+	0.471361i	$0.156237\pi$
$810$		0			0
$811$	−12.4905	+	12.4905i	−0.438602	+	0.438602i	−0.891541	−	0.452940i	$-0.850375\pi$
$811$	−12.4905	+	12.4905i	−0.438602	+	0.438602i	0.452940	+	0.891541i	$0.350375\pi$
$812$	−5.79890	+	0.00778523i	−0.203502	+	0.000273208i
$813$		0			0
$814$	−1.10858	−	0.297043i	−0.0388557	−	0.0104113i
$815$	−22.2989	−	12.8743i	−0.781096	−	0.450966i
$816$		0			0
$817$	−3.44378	+	12.8524i	−0.120483	+	0.449647i
$818$	9.76924			0.341574
$819$		0			0
$820$	−32.9395			−1.15030
$821$	6.65758	−	24.8464i	0.232351	−	0.867147i	−0.746974	−	0.664853i	$-0.768494\pi$
$821$	6.65758	−	24.8464i	0.232351	−	0.867147i	0.979325	−	0.202293i	$-0.0648394\pi$
$822$		0			0
$823$	14.7104	+	8.49308i	0.512774	+	0.296050i	0.733973	−	0.679178i	$-0.237664\pi$
$823$	14.7104	+	8.49308i	0.512774	+	0.296050i	−0.221199	+	0.975229i	$0.570997\pi$
$824$	46.0175	+	12.3303i	1.60310	+	0.429548i
$825$		0			0
$826$	−2.71226	−	4.68324i	−0.0943715	−	0.162951i
$827$	10.3024	−	10.3024i	0.358251	−	0.358251i	−0.504917	−	0.863168i	$-0.668477\pi$
$827$	10.3024	−	10.3024i	0.358251	−	0.358251i	0.863168	+	0.504917i	$0.168477\pi$
$828$		0			0
$829$	2.24299	−	3.88497i	0.0779023	−	0.134931i	−0.824442	−	0.565946i	$-0.808511\pi$
$829$	2.24299	−	3.88497i	0.0779023	−	0.134931i	0.902345	+	0.431015i	$0.141844\pi$
$830$	6.87786	+	25.6685i	0.238734	+	0.890967i
$831$		0			0
$832$	−12.1879	+	6.70127i	−0.422540	+	0.232325i
$833$	−4.26631	−	7.34386i	−0.147819	−	0.254450i
$834$		0			0
$835$	4.38437	+	7.59395i	0.151727	+	0.262800i
$836$	0.604072	−	1.04628i	0.0208923	−	0.0361864i
$837$		0			0
$838$	−14.6237	−	3.91841i	−0.505167	−	0.135359i
$839$	−3.77561	−	3.77561i	−0.130348	−	0.130348i	0.638923	−	0.769271i	$-0.279380\pi$
$839$	−3.77561	−	3.77561i	−0.130348	−	0.130348i	−0.769271	+	0.638923i	$0.779380\pi$
$840$		0			0
$841$	−26.2959			−0.906754
$842$	19.2953	−	11.1402i	0.664961	−	0.383916i
$843$		0			0
$844$	−3.14608	−	1.81639i	−0.108293	−	0.0625228i
$845$	30.0931	−	27.6784i	1.03524	−	0.952165i
$846$		0			0
$847$	14.1765	−	24.6307i	0.487109	−	0.846320i
$848$	−3.81173			−0.130895
$849$		0			0
$850$	−1.25468	−	4.68253i	−0.0430351	−	0.160609i
$851$	−13.9040	+	3.72556i	−0.476622	+	0.127710i
$852$		0			0
$853$	18.5441	+	18.5441i	0.634938	+	0.634938i	0.949302	−	0.314364i	$-0.101791\pi$
$853$	18.5441	+	18.5441i	0.634938	+	0.634938i	−0.314364	+	0.949302i	$0.601791\pi$
$854$	16.0739	+	16.0308i	0.550038	+	0.548563i
$855$		0			0
$856$	5.58545	+	1.49662i	0.190907	+	0.0511533i
$857$	23.3241	−	40.3984i	0.796734	−	1.37998i	−0.124997	−	0.992157i	$-0.539892\pi$
$857$	23.3241	−	40.3984i	0.796734	−	1.37998i	0.921732	−	0.387828i	$-0.126774\pi$
$858$		0			0
$859$	2.09313	−	1.20847i	0.0714165	−	0.0412323i	−0.463867	−	0.885905i	$-0.653538\pi$
$859$	2.09313	−	1.20847i	0.0714165	−	0.0412323i	0.535283	+	0.844673i	$0.320205\pi$
$860$	−22.1275	+	22.1275i	−0.754540	+	0.754540i
$861$		0			0
$862$			7.48294i			0.254870i
$863$	−14.2951	+	53.3502i	−0.486612	+	1.81606i	0.0860781	+	0.996288i	$0.472567\pi$
$863$	−14.2951	+	53.3502i	−0.486612	+	1.81606i	−0.572690	+	0.819772i	$0.694100\pi$
$864$		0			0
$865$	1.46829	+	5.47973i	0.0499233	+	0.186316i
$866$	5.00386	−	18.6747i	0.170038	−	0.634591i
$867$		0			0
$868$	−3.45976	−	12.8430i	−0.117432	−	0.435920i
$869$	−4.46305	+	4.46305i	−0.151399	+	0.151399i
$870$		0			0
$871$	−18.4772	−	19.2657i	−0.626077	−	0.652793i
$872$	−14.5764	+	25.2470i	−0.493619	+	0.854973i
$873$		0			0
$874$			7.58451i			0.256550i
$875$	0.871182	+	0.232179i	0.0294513	+	0.00784909i
$876$		0			0
$877$	−6.65127	+	24.8229i	−0.224597	+	0.838208i	0.757968	+	0.652292i	$0.226192\pi$
$877$	−6.65127	+	24.8229i	−0.224597	+	0.838208i	−0.982565	+	0.185917i	$0.940474\pi$
$878$	−8.91374	+	2.38843i	−0.300824	+	0.0806056i
$879$		0			0
$880$	0.612524	−	0.353641i	0.0206482	−	0.0119212i
$881$	14.0101			0.472014			0.236007	−	0.971751i	$-0.424161\pi$
$881$	14.0101			0.472014			0.236007	+	0.971751i	$0.424161\pi$
$882$		0			0
$883$			26.0607i			0.877012i	0.898728	+	0.438506i	$0.144492\pi$
$883$			26.0607i			0.877012i	−0.898728	+	0.438506i	$0.855508\pi$
$884$	−4.98760	−	3.02021i	−0.167751	−	0.101581i
$885$		0			0
$886$	30.7921	−	8.25071i	1.03448	−	0.277188i
$887$	19.8272	−	11.4472i	0.665731	−	0.384360i	−0.128726	−	0.991680i	$-0.541089\pi$
$887$	19.8272	−	11.4472i	0.665731	−	0.384360i	0.794457	+	0.607320i	$0.207756\pi$
$888$		0			0
$889$	15.1634	+	26.1825i	0.508563	+	0.878133i
$890$	−17.7282	−	17.7282i	−0.594251	−	0.594251i
$891$		0			0
$892$	−27.9136	+	7.47943i	−0.934617	+	0.250430i
$893$	−4.36878	+	7.56695i	−0.146196	+	0.253218i
$894$		0			0
$895$	38.0570	+	38.0570i	1.27211	+	1.27211i
$896$	21.6139	−	5.82254i	0.722070	−	0.194517i
$897$		0			0
$898$	−5.09572	−	8.82605i	−0.170046	−	0.294529i
$899$	1.60530	+	5.99108i	0.0535399	+	0.199814i
$900$		0			0
$901$	5.22914	+	9.05713i	0.174208	+	0.301737i
$902$	2.30792	−	2.30792i	0.0768452	−	0.0768452i
$903$		0			0
$904$	−10.0307	+	10.0307i	−0.333617	+	0.333617i
$905$	−71.2949	−	19.1034i	−2.36992	−	0.635019i
$906$		0			0
$907$	−19.6282	−	11.3323i	−0.651742	−	0.376284i	0.137381	−	0.990518i	$-0.456132\pi$
$907$	−19.6282	−	11.3323i	−0.651742	−	0.376284i	−0.789123	+	0.614235i	$0.789465\pi$
$908$	−6.24367	+	23.3017i	−0.207203	+	0.773293i
$909$		0			0
$910$	21.4579	−	11.8357i	0.711321	−	0.392349i
$911$	5.46179			0.180957			0.0904786	−	0.995898i	$-0.471160\pi$
$911$	5.46179			0.180957			0.0904786	+	0.995898i	$0.471160\pi$
$912$		0			0
$913$	4.55584	+	2.63031i	0.150776	+	0.0870507i
$914$	−16.1713	−	9.33653i	−0.534900	−	0.308825i
$915$		0			0
$916$	4.07407	−	4.07407i	0.134611	−	0.134611i
$917$	−9.26532	+	16.0979i	−0.305968	+	0.531599i
$918$		0			0
$919$	10.9646	+	18.9912i	0.361688	+	0.626461i	0.988239	−	0.152919i	$-0.0488674\pi$
$919$	10.9646	+	18.9912i	0.361688	+	0.626461i	−0.626551	+	0.779380i	$0.715534\pi$
$920$	−22.3017	+	38.6277i	−0.735266	+	1.27352i
$921$		0			0
$922$	−4.43096	−	7.67464i	−0.145926	−	0.252751i
$923$	−1.19529	+	4.11509i	−0.0393434	+	0.135450i
$924$		0			0
$925$	−9.55714	−	9.55714i	−0.314237	−	0.314237i
$926$	−8.11878	−	14.0621i	−0.266800	−	0.462110i
$927$		0			0
$928$	−9.22169	+	2.47095i	−0.302717	+	0.0811128i
$929$	8.97788	+	2.40562i	0.294555	+	0.0789257i	0.403070	−	0.915169i	$-0.367943\pi$
$929$	8.97788	+	2.40562i	0.294555	+	0.0789257i	−0.108515	+	0.994095i	$0.534610\pi$
$930$		0			0
$931$	−8.79881	+	8.84619i	−0.288369	+	0.289922i
$932$	−13.1793			−0.431702
$933$		0			0
$934$	−7.83081	+	2.09826i	−0.256232	+	0.0686572i
$935$	−1.68059	−	0.970288i	−0.0549611	−	0.0317318i
$936$		0			0
$937$			3.37326i			0.110200i	0.998481	+	0.0550998i	$0.0175477\pi$
$937$			3.37326i			0.110200i	−0.998481	+	0.0550998i	$0.982452\pi$
$938$	−8.01827	−	13.8451i	−0.261806	−	0.452058i
$939$		0			0
$940$	−17.7962	+	10.2747i	−0.580449	+	0.335122i
$941$	0.289236	+	1.07944i	0.00942881	+	0.0351888i	0.970480	−	0.241182i	$-0.0775350\pi$
$941$	0.289236	+	1.07944i	0.00942881	+	0.0351888i	−0.961051	+	0.276371i	$0.910868\pi$
$942$		0			0
$943$	10.5951	−	39.5413i	0.345023	−	1.28764i
$944$	0.783090	+	0.783090i	0.0254874	+	0.0254874i
$945$		0			0
$946$		−	3.10073i		−	0.100813i
$947$	11.4772	+	3.07530i	0.372958	+	0.0999338i	0.440429	−	0.897787i	$-0.354826\pi$
$947$	11.4772	+	3.07530i	0.372958	+	0.0999338i	−0.0674710	+	0.997721i	$0.521493\pi$
$948$		0			0
$949$	−6.10069	−	6.36102i	−0.198037	−	0.206487i
$950$	−6.16746	+	3.56078i	−0.200099	+	0.115527i
$951$		0			0
$952$	−6.18748	−	6.17089i	−0.200537	−	0.200000i
$953$		−	27.4279i		−	0.888478i	−0.895908	−	0.444239i	$-0.853474\pi$
$953$		−	27.4279i		−	0.888478i	0.895908	−	0.444239i	$-0.146526\pi$
$954$		0			0
$955$	−20.5513	−	76.6983i	−0.665023	−	2.48190i
$956$	3.96988	+	14.8158i	0.128395	+	0.479177i
$957$		0			0
$958$			17.2306i			0.556694i
$959$	−11.6517	−	11.6205i	−0.376254	−	0.375245i
$960$		0			0
$961$	14.5264	−	8.38681i	0.468593	−	0.270542i
$962$	8.13532	+	0.169948i	0.262293	+	0.00547934i
$963$		0			0
$964$	18.7635	+	5.02766i	0.604331	+	0.161930i
$965$		−	16.7948i		−	0.540642i
$966$		0			0
$967$	−1.22569	−	1.22569i	−0.0394155	−	0.0394155i	0.687124	−	0.726540i	$-0.258873\pi$
$967$	−1.22569	−	1.22569i	−0.0394155	−	0.0394155i	−0.726540	+	0.687124i	$0.758873\pi$
$968$	7.56803	−	28.2443i	0.243246	−	0.907806i
$969$		0			0
$970$	−2.75674	−	10.2883i	−0.0885135	−	0.330337i
$971$	10.7056	−	6.18087i	0.343559	−	0.198354i	−0.318286	−	0.947995i	$-0.603107\pi$
$971$	10.7056	−	6.18087i	0.343559	−	0.198354i	0.661845	+	0.749641i	$0.269774\pi$
$972$		0			0
$973$	−2.54140	−	4.38822i	−0.0814736	−	0.140680i
$974$			35.8091i			1.14740i
$975$		0			0
$976$	−4.02309	−	2.32273i	−0.128776	−	0.0743488i
$977$	−0.161930	+	0.0433889i	−0.00518058	+	0.00138813i	−0.261408	−	0.965228i	$-0.584187\pi$
$977$	−0.161930	+	0.0433889i	−0.00518058	+	0.00138813i	0.256228	+	0.966616i	$0.417520\pi$
$978$		0			0
$979$	−4.96319			−0.158624
$980$	−28.3234	+	7.67080i	−0.904757	+	0.245035i
$981$		0			0
$982$	−29.2921	−	7.84879i	−0.934748	−	0.250465i
$983$	11.2297	−	3.00899i	0.358172	−	0.0959718i	−0.0752459	−	0.997165i	$-0.523974\pi$
$983$	11.2297	−	3.00899i	0.358172	−	0.0959718i	0.433418	+	0.901193i	$0.357307\pi$
$984$		0			0
$985$	−23.8272	−	41.2700i	−0.759199	−	1.31497i
$986$	1.15234	+	1.15234i	0.0366979	+	0.0366979i
$987$		0			0
$988$	−2.38930	+	8.22576i	−0.0760137	+	0.261696i
$989$	−19.4449	−	33.6796i	−0.618313	−	1.07095i
$990$		0			0
$991$	−4.59806	+	7.96408i	−0.146062	+	0.252987i	−0.929769	−	0.368144i	$-0.879993\pi$
$991$	−4.59806	+	7.96408i	−0.146062	+	0.252987i	0.783707	+	0.621131i	$0.213327\pi$
$992$	−10.9489	−	18.9640i	−0.347628	−	0.602109i
$993$		0			0
$994$	−1.28119	+	2.22598i	−0.0406369	+	0.0706039i
$995$	15.9684	−	15.9684i	0.506233	−	0.506233i
$996$		0			0
$997$	−25.9655	−	14.9912i	−0.822337	−	0.474776i	0.0288849	−	0.999583i	$-0.490804\pi$
$997$	−25.9655	−	14.9912i	−0.822337	−	0.474776i	−0.851222	+	0.524806i	$0.824138\pi$
$998$	3.78846	+	2.18727i	0.119922	+	0.0692368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.73.6		32
3.2	odd	2		91.2.bb.a.73.3	yes	32
7.5	odd	6	inner	819.2.fn.e.775.3		32
13.5	odd	4	inner	819.2.fn.e.577.3		32
21.2	odd	6		637.2.bc.b.411.6		32
21.5	even	6		91.2.bb.a.47.6	yes	32
21.11	odd	6		637.2.i.a.489.6		32
21.17	even	6		637.2.i.a.489.5		32
21.20	even	2		637.2.bc.b.619.3		32
39.5	even	4		91.2.bb.a.31.6	yes	32
91.5	even	12	inner	819.2.fn.e.460.6		32
273.5	odd	12		91.2.bb.a.5.3	✓	32
273.44	even	12		637.2.bc.b.460.3		32
273.83	odd	4		637.2.bc.b.31.6		32
273.122	odd	12		637.2.i.a.538.5		32
273.200	even	12		637.2.i.a.538.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.3	✓	32	273.5	odd	12
91.2.bb.a.31.6	yes	32	39.5	even	4
91.2.bb.a.47.6	yes	32	21.5	even	6
91.2.bb.a.73.3	yes	32	3.2	odd	2
637.2.i.a.489.5		32	21.17	even	6
637.2.i.a.489.6		32	21.11	odd	6
637.2.i.a.538.5		32	273.122	odd	12
637.2.i.a.538.6		32	273.200	even	12
637.2.bc.b.31.6		32	273.83	odd	4
637.2.bc.b.411.6		32	21.2	odd	6
637.2.bc.b.460.3		32	273.44	even	12
637.2.bc.b.619.3		32	21.20	even	2
819.2.fn.e.73.6		32	1.1	even	1	trivial
819.2.fn.e.460.6		32	91.5	even	12	inner
819.2.fn.e.577.3		32	13.5	odd	4	inner
819.2.fn.e.775.3		32	7.5	odd	6	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.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.211401 - 0.788958i) q^{2} +(1.15429 + 0.666428i) q^{4} +(-3.03793 - 0.814012i) q^{5} +(2.28951 - 1.32595i) q^{7} +(1.92491 - 1.92491i) q^{8} +O(q^{10})\)	\(q+(0.211401 - 0.788958i) q^{2} +(1.15429 + 0.666428i) q^{4} +(-3.03793 - 0.814012i) q^{5} +(2.28951 - 1.32595i) q^{7} +(1.92491 - 1.92491i) q^{8} +(-1.28444 + 2.22472i) q^{10} +(0.131620 + 0.491212i) q^{11} +(-1.73717 - 3.15947i) q^{13} +(-0.562115 - 2.08663i) q^{14} +(0.221107 + 0.382969i) q^{16} +(0.606654 - 1.05076i) q^{17} +(-1.72169 - 0.461325i) q^{19} +(-2.96417 - 2.96417i) q^{20} +0.415370 q^{22} +(4.51168 - 2.60482i) q^{23} +(4.23629 + 2.44583i) q^{25} +(-2.85993 + 0.702638i) q^{26} +(3.52640 - 0.00473432i) q^{28} -1.64443 q^{29} +(-0.976210 - 3.64327i) q^{31} +(5.60785 - 1.50262i) q^{32} +(-0.700755 - 0.700755i) q^{34} +(-8.03472 + 2.16446i) q^{35} +(-2.66889 - 0.715128i) q^{37} +(-0.727931 + 1.26081i) q^{38} +(-7.41466 + 4.28086i) q^{40} +(5.55629 - 5.55629i) q^{41} -7.46499i q^{43} +(-0.175430 + 0.654714i) q^{44} +(-1.10132 - 4.11018i) q^{46} +(1.26875 - 4.73504i) q^{47} +(3.48371 - 6.07155i) q^{49} +(2.82521 - 2.82521i) q^{50} +(0.100369 - 4.80463i) q^{52} +(-4.30982 + 7.46483i) q^{53} -1.59941i q^{55} +(1.85477 - 6.95945i) q^{56} +(-0.347632 + 1.29738i) q^{58} +(2.41901 - 0.648171i) q^{59} +(-9.09759 + 5.25249i) q^{61} -3.08076 q^{62} -3.85758i q^{64} +(2.70555 + 11.0123i) q^{65} +(7.15134 - 1.91620i) q^{67} +(1.40051 - 0.808582i) q^{68} +(0.00912470 + 6.79662i) q^{70} +(-0.840390 - 0.840390i) q^{71} +(2.36118 - 0.632677i) q^{73} +(-1.12841 + 1.95447i) q^{74} +(-1.67988 - 1.67988i) q^{76} +(0.952667 + 0.950113i) q^{77} +(6.20571 + 10.7486i) q^{79} +(-0.359968 - 1.34342i) q^{80} +(-3.20908 - 5.55828i) q^{82} +(7.31472 - 7.31472i) q^{83} +(-2.69830 + 2.69830i) q^{85} +(-5.88956 - 1.57810i) q^{86} +(1.19890 + 0.692184i) q^{88} +(-2.52599 + 9.42713i) q^{89} +(-8.16656 - 4.93024i) q^{91} +6.94369 q^{92} +(-3.46753 - 2.00198i) q^{94} +(4.85484 + 2.80295i) q^{95} +(-2.93184 + 2.93184i) q^{97} +(-4.05374 - 4.03203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Introduction

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