LMFDB - Embedded newform 387.2.y.c.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	387.271
Dual form			387.2.y.c.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.188565 + 0.826155i) q^{2} +(1.15496 + 0.556200i) q^{4} +(3.39819 + 0.512194i) q^{5} +(-0.134521 + 0.232998i) q^{7} +(-1.73398 + 2.17435i) q^{8} +O(q^{10})$	\(q+(-0.188565 + 0.826155i) q^{2} +(1.15496 + 0.556200i) q^{4} +(3.39819 + 0.512194i) q^{5} +(-0.134521 + 0.232998i) q^{7} +(-1.73398 + 2.17435i) q^{8} +(-1.06393 + 2.71085i) q^{10} +(2.96782 - 1.42923i) q^{11} +(-0.736485 - 1.87653i) q^{13} +(-0.167127 - 0.155071i) q^{14} +(0.129136 + 0.161931i) q^{16} +(-6.37398 + 0.960723i) q^{17} +(-0.449267 - 5.99506i) q^{19} +(3.63989 + 2.48164i) q^{20} +(0.621139 + 2.72139i) q^{22} +(1.83546 + 1.25139i) q^{23} +(6.50747 + 2.00729i) q^{25} +(1.68918 - 0.254603i) q^{26} +(-0.284961 + 0.194283i) q^{28} +(-1.75989 - 1.63294i) q^{29} +(-4.93996 + 1.52378i) q^{31} +(-5.16949 + 2.48950i) q^{32} +(0.408200 - 5.44706i) q^{34} +(-0.576470 + 0.722870i) q^{35} +(2.63757 + 4.56841i) q^{37} +(5.03756 + 0.759291i) q^{38} +(-7.00609 + 6.50071i) q^{40} +(0.643386 - 2.81886i) q^{41} +(-4.01778 + 5.18242i) q^{43} +4.22266 q^{44} +(-1.37995 + 1.28040i) q^{46} +(5.31835 + 2.56118i) q^{47} +(3.46381 + 5.99949i) q^{49} +(-2.88541 + 4.99768i) q^{50} +(0.193116 - 2.57696i) q^{52} +(-2.34453 + 5.97377i) q^{53} +(10.8173 - 3.33669i) q^{55} +(-0.273361 - 0.696512i) q^{56} +(1.68091 - 1.14603i) q^{58} +(-8.36244 - 10.4862i) q^{59} +(-9.50158 - 2.93085i) q^{61} +(-0.327374 - 4.36851i) q^{62} +(-0.989752 - 4.33638i) q^{64} +(-1.54156 - 6.75403i) q^{65} +(-0.950106 - 12.6783i) q^{67} +(-7.89606 - 2.43561i) q^{68} +(-0.488501 - 0.612561i) q^{70} +(4.98725 - 3.40025i) q^{71} +(0.609746 + 1.55361i) q^{73} +(-4.27157 + 1.31761i) q^{74} +(2.81557 - 7.17394i) q^{76} +(-0.0662286 + 0.883759i) q^{77} +(6.97172 - 12.0754i) q^{79} +(0.355887 + 0.616414i) q^{80} +(2.20750 + 1.06307i) q^{82} +(5.60384 - 5.19960i) q^{83} -22.1521 q^{85} +(-3.52387 - 4.29653i) q^{86} +(-2.03852 + 8.93135i) q^{88} +(1.32654 - 1.23085i) q^{89} +(0.536302 + 0.0808345i) q^{91} +(1.42386 + 2.46619i) q^{92} +(-3.11879 + 3.91084i) q^{94} +(1.54394 - 20.6024i) q^{95} +(2.36508 - 1.13896i) q^{97} +(-5.60966 + 1.73035i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.188565	+	0.826155i	−0.133335	+	0.584180i	0.863476	+	0.504389i	$0.168282\pi$
$2$	−0.188565	+	0.826155i	−0.133335	+	0.584180i	−0.996812	+	0.0797907i	$0.974575\pi$
$3$		0			0
$3$		0			0
$4$	1.15496	+	0.556200i	0.577481	+	0.278100i
$5$	3.39819	+	0.512194i	1.51972	+	0.229060i	0.855233	−	0.518243i	$-0.173414\pi$
$5$	3.39819	+	0.512194i	1.51972	+	0.229060i	0.664483	+	0.747304i	$0.268652\pi$
$6$		0			0
$7$	−0.134521	+	0.232998i	−0.0508443	+	0.0880650i	−0.890327	−	0.455321i	$-0.849525\pi$
$7$	−0.134521	+	0.232998i	−0.0508443	+	0.0880650i	0.839483	+	0.543386i	$0.182858\pi$
$8$	−1.73398	+	2.17435i	−0.613056	+	0.768748i
$9$		0			0
$10$	−1.06393	+	2.71085i	−0.336444	+	0.857246i
$11$	2.96782	−	1.42923i	0.894833	−	0.430929i	0.0708129	−	0.997490i	$-0.477441\pi$
$11$	2.96782	−	1.42923i	0.894833	−	0.430929i	0.824020	+	0.566561i	$0.191726\pi$
$12$		0			0
$13$	−0.736485	−	1.87653i	−0.204264	−	0.520457i	0.791628	−	0.611003i	$-0.209234\pi$
$13$	−0.736485	−	1.87653i	−0.204264	−	0.520457i	−0.995892	+	0.0905467i	$0.971139\pi$
$14$	−0.167127	−	0.155071i	−0.0446665	−	0.0414444i
$15$		0			0
$16$	0.129136	+	0.161931i	0.0322839	+	0.0404827i
$17$	−6.37398	+	0.960723i	−1.54592	+	0.233010i	−0.865911	−	0.500197i	$-0.833261\pi$
$17$	−6.37398	+	0.960723i	−1.54592	+	0.233010i	−0.680006	+	0.733207i	$0.738023\pi$
$18$		0			0
$19$	−0.449267	−	5.99506i	−0.103069	−	1.37536i	−0.773692	−	0.633562i	$-0.781592\pi$
$19$	−0.449267	−	5.99506i	−0.103069	−	1.37536i	0.670623	−	0.741798i	$-0.266027\pi$
$20$	3.63989	+	2.48164i	0.813905	+	0.554911i
$21$		0			0
$22$	0.621139	+	2.72139i	0.132427	+	0.580201i
$23$	1.83546	+	1.25139i	0.382719	+	0.260934i	0.739363	−	0.673307i	$-0.235127\pi$
$23$	1.83546	+	1.25139i	0.382719	+	0.260934i	−0.356644	+	0.934240i	$0.616079\pi$
$24$		0			0
$25$	6.50747	+	2.00729i	1.30149	+	0.401458i
$26$	1.68918	−	0.254603i	0.331276	−	0.0499318i
$27$		0			0
$28$	−0.284961	+	0.194283i	−0.0538525	+	0.0367160i
$29$	−1.75989	−	1.63294i	−0.326803	−	0.303229i	0.499658	−	0.866223i	$-0.333459\pi$
$29$	−1.75989	−	1.63294i	−0.326803	−	0.303229i	−0.826461	+	0.562994i	$0.809649\pi$
$30$		0			0
$31$	−4.93996	+	1.52378i	−0.887243	+	0.273678i	−0.704688	−	0.709517i	$-0.748913\pi$
$31$	−4.93996	+	1.52378i	−0.887243	+	0.273678i	−0.182555	+	0.983196i	$0.558437\pi$
$32$	−5.16949	+	2.48950i	−0.913846	+	0.440085i
$33$		0			0
$34$	0.408200	−	5.44706i	0.0700058	−	0.934162i
$35$	−0.576470	+	0.722870i	−0.0974411	+	0.122187i
$36$		0			0
$37$	2.63757	+	4.56841i	0.433615	+	0.751042i	0.997181	−	0.0750281i	$-0.0239046\pi$
$37$	2.63757	+	4.56841i	0.433615	+	0.751042i	−0.563567	+	0.826070i	$0.690571\pi$
$38$	5.03756	+	0.759291i	0.817201	+	0.123173i
$39$		0			0
$40$	−7.00609	+	6.50071i	−1.10776	+	1.02785i
$41$	0.643386	−	2.81886i	0.100480	−	0.440232i	−0.899514	−	0.436891i	$-0.856079\pi$
$41$	0.643386	−	2.81886i	0.100480	−	0.440232i	0.999994	−	0.00334069i	$-0.00106338\pi$
$42$		0			0
$43$	−4.01778	+	5.18242i	−0.612705	+	0.790311i
$43$	−4.01778	+	5.18242i	−0.612705	+	0.790311i
$44$	4.22266			0.636590
$45$		0			0
$46$	−1.37995	+	1.28040i	−0.203462	+	0.188785i
$47$	5.31835	+	2.56118i	0.775761	+	0.373587i	0.779497	−	0.626406i	$-0.215475\pi$
$47$	5.31835	+	2.56118i	0.775761	+	0.373587i	−0.00373559	+	0.999993i	$0.501189\pi$
$48$		0			0
$49$	3.46381	+	5.99949i	0.494830	+	0.857070i
$50$	−2.88541	+	4.99768i	−0.408059	+	0.706778i
$51$		0			0
$52$	0.193116	−	2.57696i	0.0267804	−	0.357360i
$53$	−2.34453	+	5.97377i	−0.322046	+	0.820561i	0.674558	+	0.738222i	$0.264334\pi$
$53$	−2.34453	+	5.97377i	−0.322046	+	0.820561i	−0.996604	+	0.0823389i	$0.973761\pi$
$54$		0			0
$55$	10.8173	−	3.33669i	1.45860	−	0.449919i
$56$	−0.273361	−	0.696512i	−0.0365294	−	0.0930753i
$57$		0			0
$58$	1.68091	−	1.14603i	0.220715	−	0.150481i
$59$	−8.36244	−	10.4862i	−1.08870	−	1.36518i	−0.925569	−	0.378578i	$-0.876413\pi$
$59$	−8.36244	−	10.4862i	−1.08870	−	1.36518i	−0.163128	−	0.986605i	$-0.552158\pi$
$60$		0			0
$61$	−9.50158	−	2.93085i	−1.21655	−	0.375257i	−0.380952	−	0.924595i	$-0.624404\pi$
$61$	−9.50158	−	2.93085i	−1.21655	−	0.375257i	−0.835600	+	0.549338i	$0.814880\pi$
$62$	−0.327374	−	4.36851i	−0.0415766	−	0.554801i
$63$		0			0
$64$	−0.989752	−	4.33638i	−0.123719	−	0.542048i
$65$	−1.54156	−	6.75403i	−0.191208	−	0.837735i
$66$		0			0
$67$	−0.950106	−	12.6783i	−0.116074	−	1.54890i	−0.686243	−	0.727372i	$-0.740741\pi$
$67$	−0.950106	−	12.6783i	−0.116074	−	1.54890i	0.570169	−	0.821527i	$-0.306878\pi$
$68$	−7.89606	−	2.43561i	−0.957538	−	0.295361i
$69$		0			0
$70$	−0.488501	−	0.612561i	−0.0583870	−	0.0732150i
$71$	4.98725	−	3.40025i	0.591877	−	0.403535i	−0.230007	−	0.973189i	$-0.573875\pi$
$71$	4.98725	−	3.40025i	0.591877	−	0.403535i	0.821885	+	0.569654i	$0.192923\pi$
$72$		0			0
$73$	0.609746	+	1.55361i	0.0713654	+	0.181836i	0.962106	−	0.272676i	$-0.0879088\pi$
$73$	0.609746	+	1.55361i	0.0713654	+	0.181836i	−0.890740	+	0.454512i	$0.849814\pi$
$74$	−4.27157	+	1.31761i	−0.496560	+	0.153168i
$75$		0			0
$76$	2.81557	−	7.17394i	0.322968	−	0.822908i
$77$	−0.0662286	+	0.883759i	−0.00754745	+	0.100714i
$78$		0			0
$79$	6.97172	−	12.0754i	0.784380	−	1.35859i	−0.144989	−	0.989433i	$-0.546315\pi$
$79$	6.97172	−	12.0754i	0.784380	−	1.35859i	0.929369	−	0.369153i	$-0.120352\pi$
$80$	0.355887	+	0.616414i	0.0397893	+	0.0689172i
$81$		0			0
$82$	2.20750	+	1.06307i	0.243777	+	0.117397i
$83$	5.60384	−	5.19960i	0.615101	−	0.570731i	−0.309864	−	0.950781i	$-0.600284\pi$
$83$	5.60384	−	5.19960i	0.615101	−	0.570731i	0.924966	+	0.380050i	$0.124093\pi$
$84$		0			0
$85$	−22.1521			−2.40273
$86$	−3.52387	−	4.29653i	−0.379989	−	0.463307i
$87$		0			0
$88$	−2.03852	+	8.93135i	−0.217307	+	0.952085i
$89$	1.32654	−	1.23085i	0.140613	−	0.130470i	−0.606730	−	0.794908i	$-0.707519\pi$
$89$	1.32654	−	1.23085i	0.140613	−	0.130470i	0.747344	+	0.664437i	$0.231329\pi$
$90$		0			0
$91$	0.536302	+	0.0808345i	0.0562197	+	0.00847375i
$92$	1.42386	+	2.46619i	0.148447	+	0.257118i
$93$		0			0
$94$	−3.11879	+	3.91084i	−0.321678	+	0.403372i
$95$	1.54394	−	20.6024i	0.158405	−	2.11377i
$96$		0			0
$97$	2.36508	−	1.13896i	0.240138	−	0.115644i	−0.309945	−	0.950755i	$-0.600311\pi$
$97$	2.36508	−	1.13896i	0.240138	−	0.115644i	0.550082	+	0.835110i	$0.314596\pi$
$98$	−5.60966	+	1.73035i	−0.566662	+	0.174792i
$99$		0			0
$100$	6.39943	+	5.93780i	0.639943	+	0.593780i
$101$	−7.32150	+	4.99172i	−0.728517	+	0.496694i	−0.869880	−	0.493264i	$-0.835804\pi$
$101$	−7.32150	+	4.99172i	−0.728517	+	0.496694i	0.141363	+	0.989958i	$0.454851\pi$
$102$		0			0
$103$	−0.748654	+	0.112841i	−0.0737671	+	0.0111186i	−0.185822	−	0.982583i	$-0.559495\pi$
$103$	−0.748654	+	0.112841i	−0.0737671	+	0.0111186i	0.112055	+	0.993702i	$0.464257\pi$
$104$	5.35729	+	1.65251i	0.525326	+	0.162041i
$105$		0			0
$106$	−4.49317	−	3.06339i	−0.436415	−	0.297543i
$107$	−0.737592	−	3.23160i	−0.0713057	−	0.312411i	0.926680	−	0.375852i	$-0.122650\pi$
$107$	−0.737592	−	3.23160i	−0.0713057	−	0.312411i	−0.997986	+	0.0634408i	$0.979793\pi$
$108$		0			0
$109$	8.34007	+	5.68616i	0.798833	+	0.544635i	0.892542	−	0.450964i	$-0.148920\pi$
$109$	8.34007	+	5.68616i	0.798833	+	0.544635i	−0.0937085	+	0.995600i	$0.529872\pi$
$110$	0.716867	+	9.56592i	0.0683506	+	0.912075i
$111$		0			0
$112$	−0.0551011	+	0.00830515i	−0.00520656	+	0.000784763i
$113$	3.49529	+	4.38295i	0.328809	+	0.412313i	0.918566	−	0.395267i	$-0.129348\pi$
$113$	3.49529	+	4.38295i	0.328809	+	0.412313i	−0.589757	+	0.807581i	$0.700777\pi$
$114$		0			0
$115$	5.59627	+	5.19258i	0.521855	+	0.484211i
$116$	−1.12436	−	2.86483i	−0.104394	−	0.265993i
$117$		0			0
$118$	10.2401	−	4.93135i	0.942674	−	0.453968i
$119$	0.633591	−	1.61436i	0.0580812	−	0.147988i
$120$		0			0
$121$	−0.0931005	+	0.116744i	−0.00846368	+	0.0106131i
$122$	4.21300	−	7.29713i	0.381427	−	0.660651i
$123$		0			0
$124$	−6.55299	−	0.987705i	−0.588476	−	0.0886985i
$125$	5.60427	+	2.69887i	0.501261	+	0.241395i
$126$		0			0
$127$	2.06730	−	9.05743i	0.183443	−	0.803717i	−0.796532	−	0.604597i	$-0.793334\pi$
$127$	2.06730	−	9.05743i	0.183443	−	0.803717i	0.979975	−	0.199121i	$-0.0638086\pi$
$128$	−7.70625			−0.681142
$129$		0			0
$130$	5.87057			0.514883
$131$	−1.20701	+	5.28827i	−0.105457	+	0.462039i	0.894433	+	0.447203i	$0.147580\pi$
$131$	−1.20701	+	5.28827i	−0.105457	+	0.462039i	−0.999890	+	0.0148359i	$0.995277\pi$
$132$		0			0
$133$	1.45727	+	0.701786i	0.126362	+	0.0608525i
$134$	10.6534	+	1.60574i	0.920313	+	0.138715i
$135$		0			0
$136$	8.96344	−	15.5251i	0.768609	−	1.33127i
$137$	−6.88665	+	8.63559i	−0.588366	+	0.737788i	−0.983514	−	0.180829i	$-0.942122\pi$
$137$	−6.88665	+	8.63559i	−0.588366	+	0.737788i	0.395148	+	0.918617i	$0.370693\pi$
$138$		0			0
$139$	−2.80876	+	7.15661i	−0.238236	+	0.607016i	−0.999123	−	0.0418687i	$-0.986669\pi$
$139$	−2.80876	+	7.15661i	−0.238236	+	0.607016i	0.760887	+	0.648884i	$0.224764\pi$
$140$	−1.06786	+	0.514255i	−0.0902507	+	0.0434624i
$141$		0			0
$142$	1.86871	+	4.76141i	0.156819	+	0.399568i
$143$	−4.86775	−	4.51662i	−0.407062	−	0.377698i
$144$		0			0
$145$	−5.14405	−	6.45043i	−0.427190	−	0.535679i
$146$	−1.39850	+	0.210790i	−0.115741	+	0.0174451i
$147$		0			0
$148$	0.505345	+	6.74336i	0.0415391	+	0.554301i
$149$	0.776822	+	0.529628i	0.0636397	+	0.0433888i	0.594722	−	0.803931i	$-0.297262\pi$
$149$	0.776822	+	0.529628i	0.0636397	+	0.0433888i	−0.531082	+	0.847320i	$0.678215\pi$
$150$		0			0
$151$	2.44733	+	10.7224i	0.199161	+	0.872579i	0.971438	+	0.237294i	$0.0762604\pi$
$151$	2.44733	+	10.7224i	0.199161	+	0.872579i	−0.772277	+	0.635285i	$0.780882\pi$
$152$	13.8144	+	9.41847i	1.12049	+	0.763939i
$153$		0			0
$154$	−0.717634	−	0.221361i	−0.0578286	−	0.0178378i
$155$	−17.5674	+	2.64786i	−1.41105	+	0.212681i
$156$		0			0
$157$	−15.8917	+	10.8348i	−1.26829	+	0.864708i	−0.995256	−	0.0972949i	$-0.968981\pi$
$157$	−15.8917	+	10.8348i	−1.26829	+	0.864708i	−0.273038	+	0.962003i	$0.588029\pi$
$158$	8.66152	+	8.03671i	0.689073	+	0.639366i
$159$		0			0
$160$	−18.8420	+	5.81199i	−1.48959	+	0.459478i
$161$	−0.538481	+	0.259319i	−0.0424382	+	0.0204372i
$162$		0			0
$163$	1.43404	−	19.1360i	0.112323	−	1.49884i	−0.601700	−	0.798722i	$-0.705510\pi$
$163$	1.43404	−	19.1360i	0.112323	−	1.49884i	0.714023	−	0.700122i	$-0.246871\pi$
$164$	2.31094	−	2.89782i	0.180454	−	0.226282i
$165$		0			0
$166$	3.23899	+	5.61010i	0.251395	+	0.435429i
$167$	−6.00399	−	0.904956i	−0.464603	−	0.0700276i	−0.0874302	−	0.996171i	$-0.527865\pi$
$167$	−6.00399	−	0.904956i	−0.464603	−	0.0700276i	−0.377172	+	0.926143i	$0.623104\pi$
$168$		0			0
$169$	6.55071	−	6.07817i	0.503901	−	0.467551i
$170$	4.17709	−	18.3010i	0.320368	−	1.40363i
$171$		0			0
$172$	−7.52284	+	3.75081i	−0.573611	+	0.285996i
$173$	11.0260			0.838294			0.419147	−	0.907918i	$-0.362329\pi$
$173$	11.0260			0.838294			0.419147	+	0.907918i	$0.362329\pi$
$174$		0			0
$175$	−1.34309	+	1.24620i	−0.101528	+	0.0942042i
$176$	0.614688	+	0.296018i	0.0463338	+	0.0223132i
$177$		0			0
$178$	0.766737	+	1.32803i	0.0574694	+	0.0995398i
$179$	4.06679	−	7.04389i	0.303966	−	0.526485i	−0.673064	−	0.739584i	$-0.735022\pi$
$179$	4.06679	−	7.04389i	0.303966	−	0.526485i	0.977031	+	0.213099i	$0.0683557\pi$
$180$		0			0
$181$	0.451827	−	6.02922i	0.0335841	−	0.448148i	−0.954911	−	0.296893i	$-0.904049\pi$
$181$	0.451827	−	6.02922i	0.0335841	−	0.448148i	0.988495	−	0.151255i	$-0.0483315\pi$
$182$	−0.167909	+	0.427826i	−0.0124463	+	0.0317126i
$183$		0			0
$184$	−5.90362	+	1.82103i	−0.435221	+	0.134248i
$185$	6.62306	+	16.8753i	0.486937	+	1.24069i
$186$		0			0
$187$	−17.5438	+	11.9611i	−1.28293	+	0.874685i
$188$	4.71796	+	5.91614i	0.344093	+	0.431479i
$189$		0			0
$190$	16.7297	+	5.16042i	1.21370	+	0.374376i
$191$	1.15304	+	15.3862i	0.0834307	+	1.11331i	0.869093	+	0.494649i	$0.164703\pi$
$191$	1.15304	+	15.3862i	0.0834307	+	1.11331i	−0.785662	+	0.618656i	$0.787677\pi$
$192$		0			0
$193$	0.542270	+	2.37584i	0.0390335	+	0.171017i	0.990688	−	0.136155i	$-0.0434745\pi$
$193$	0.542270	+	2.37584i	0.0390335	+	0.171017i	−0.951654	+	0.307172i	$0.900617\pi$
$194$	0.494990	+	2.16869i	0.0355382	+	0.155703i
$195$		0			0
$196$	0.663647	+	8.85575i	0.0474034	+	0.632554i
$197$	2.38077	+	0.734371i	0.169623	+	0.0523218i	0.378403	−	0.925641i	$-0.376473\pi$
$197$	2.38077	+	0.734371i	0.169623	+	0.0523218i	−0.208780	+	0.977963i	$0.566949\pi$
$198$		0			0
$199$	5.15076	+	6.45884i	0.365127	+	0.457855i	0.930128	−	0.367235i	$-0.119696\pi$
$199$	5.15076	+	6.45884i	0.365127	+	0.457855i	−0.565001	+	0.825090i	$0.691124\pi$
$200$	−15.6484	+	10.6689i	−1.10651	+	0.754405i
$201$		0			0
$202$	−2.74336	−	6.98996i	−0.193022	−	0.491812i
$203$	0.617214	−	0.190385i	0.0433199	−	0.0133624i
$204$		0			0
$205$	3.63015	−	9.24947i	0.253541	−	0.646011i
$206$	0.0479451	−	0.639782i	0.00334049	−	0.0445757i
$207$		0			0
$208$	0.208762	−	0.361587i	0.0144751	−	0.0250715i
$209$	−9.90166	−	17.1502i	−0.684912	−	1.18630i
$210$		0			0
$211$	12.8995	+	6.21209i	0.888041	+	0.427658i	0.821555	−	0.570129i	$-0.193107\pi$
$211$	12.8995	+	6.21209i	0.888041	+	0.427658i	0.0664862	+	0.997787i	$0.478821\pi$
$212$	−6.03046	+	5.59545i	−0.414174	+	0.384297i
$213$		0			0
$214$	2.80889			0.192012
$215$	−16.3076	+	15.5529i	−1.11217	+	1.06070i
$216$		0			0
$217$	0.309494	−	1.35598i	0.0210098	−	0.0920501i
$218$	−6.27029	+	5.81798i	−0.424678	+	0.394043i
$219$		0			0
$220$	14.3494	+	2.16282i	0.967436	+	0.145818i
$221$	6.49717	+	11.2534i	0.437047	+	0.756987i
$222$		0			0
$223$	−4.25565	+	5.33642i	−0.284980	+	0.357353i	−0.903631	−	0.428313i	$-0.859108\pi$
$223$	−4.25565	+	5.33642i	−0.284980	+	0.357353i	0.618651	+	0.785666i	$0.287680\pi$
$224$	0.115360	−	1.53937i	0.00770781	−	0.102854i
$225$		0			0
$226$	−4.28009	+	2.06118i	−0.284707	+	0.137108i
$227$	22.4926	−	6.93804i	1.49288	−	0.460494i	0.562412	−	0.826857i	$-0.309874\pi$
$227$	22.4926	−	6.93804i	1.49288	−	0.460494i	0.930472	+	0.366364i	$0.119397\pi$
$228$		0			0
$229$	−11.5699	−	10.7353i	−0.764562	−	0.709410i	0.198080	−	0.980186i	$-0.436529\pi$
$229$	−11.5699	−	10.7353i	−0.764562	−	0.709410i	−0.962642	+	0.270776i	$0.912720\pi$
$230$	−5.34514	+	3.64425i	−0.352448	+	0.240295i
$231$		0			0
$232$	6.60219	−	0.995121i	0.433455	−	0.0653329i
$233$	2.67367	+	0.824717i	0.175158	+	0.0540290i	0.381093	−	0.924537i	$-0.375548\pi$
$233$	2.67367	+	0.824717i	0.175158	+	0.0540290i	−0.205936	+	0.978566i	$0.566024\pi$
$234$		0			0
$235$	16.7609	+	11.4274i	1.09336	+	0.745442i
$236$	−3.82589	−	16.7623i	−0.249044	−	1.09113i
$237$		0			0
$238$	1.21424	+	0.827856i	0.0787076	+	0.0536619i
$239$	−0.382464	−	5.10363i	−0.0247396	−	0.330127i	−0.995818	−	0.0913641i	$-0.970877\pi$
$239$	−0.382464	−	5.10363i	−0.0247396	−	0.330127i	0.971078	−	0.238763i	$-0.0767418\pi$
$240$		0			0
$241$	5.77630	−	0.870636i	0.372084	−	0.0560826i	0.0396614	−	0.999213i	$-0.487372\pi$
$241$	5.77630	−	0.870636i	0.372084	−	0.0560826i	0.332423	+	0.943131i	$0.392134\pi$
$242$	−0.0788935	−	0.0989293i	−0.00507147	−	0.00635942i
$243$		0			0
$244$	−9.34382	−	8.66980i	−0.598177	−	0.555027i
$245$	8.69776	+	22.1615i	0.555680	+	1.41585i
$246$		0			0
$247$	−10.9190	+	5.25833i	−0.694762	+	0.334580i
$248$	5.25260	−	13.3834i	0.333540	−	0.849847i
$249$		0			0
$250$	−3.28645	+	4.12108i	−0.207854	+	0.260640i
$251$	−4.39608	+	7.61423i	−0.277478	+	0.480606i	−0.970757	−	0.240063i	$-0.922832\pi$
$251$	−4.39608	+	7.61423i	−0.277478	+	0.480606i	0.693279	+	0.720669i	$0.256165\pi$
$252$		0			0
$253$	7.23584	+	1.09063i	0.454914	+	0.0685672i
$254$	7.09303	+	3.41582i	0.445056	+	0.214328i
$255$		0			0
$256$	3.43263	−	15.0393i	0.214539	−	0.939958i
$257$	6.02274			0.375688			0.187844	−	0.982199i	$-0.439850\pi$
$257$	6.02274			0.375688			0.187844	+	0.982199i	$0.439850\pi$
$258$		0			0
$259$	−1.41924			−0.0881874
$260$	1.97615	−	8.65807i	0.122556	−	0.536951i
$261$		0			0
$262$	−4.14134	−	1.99436i	−0.255853	−	0.123212i
$263$	23.8955	+	3.60167i	1.47346	+	0.222089i	0.836143	−	0.548512i	$-0.184805\pi$
$263$	23.8955	+	3.60167i	1.47346	+	0.222089i	0.637319	+	0.770600i	$0.280044\pi$
$264$		0			0
$265$	−11.0269	+	19.0991i	−0.677377	+	1.17325i
$266$	−0.854574	+	1.07160i	−0.0523973	+	0.0657041i
$267$		0			0
$268$	5.95433	−	15.1714i	0.363719	−	0.926740i
$269$	−3.94932	+	1.90189i	−0.240794	+	0.115960i	−0.550389	−	0.834908i	$-0.685521\pi$
$269$	−3.94932	+	1.90189i	−0.240794	+	0.115960i	0.309595	+	0.950868i	$0.399806\pi$
$270$		0			0
$271$	10.3289	+	26.3177i	0.627437	+	1.59868i	0.790770	+	0.612113i	$0.209680\pi$
$271$	10.3289	+	26.3177i	0.627437	+	1.59868i	−0.163333	+	0.986571i	$0.552225\pi$
$272$	−0.978678	−	0.908081i	−0.0593411	−	0.0550605i
$273$		0			0
$274$	−5.83576	−	7.31781i	−0.352551	−	0.442085i
$275$	22.1819	−	3.34339i	1.33762	−	0.201614i
$276$		0			0
$277$	1.72237	+	22.9834i	0.103487	+	1.38094i	0.771235	+	0.636550i	$0.219639\pi$
$277$	1.72237	+	22.9834i	0.103487	+	1.38094i	−0.667748	+	0.744387i	$0.732742\pi$
$278$	−5.38284	−	3.66996i	−0.322841	−	0.220109i
$279$		0			0
$280$	−0.572182	−	2.50689i	−0.0341944	−	0.149815i
$281$	−14.7612	−	10.0640i	−0.880582	−	0.600371i	0.0363832	−	0.999338i	$-0.488416\pi$
$281$	−14.7612	−	10.0640i	−0.880582	−	0.600371i	−0.916965	+	0.398967i	$0.869369\pi$
$282$		0			0
$283$	−13.4802	−	4.15809i	−0.801315	−	0.247173i	−0.133063	−	0.991108i	$-0.542481\pi$
$283$	−13.4802	−	4.15809i	−0.801315	−	0.247173i	−0.668252	+	0.743935i	$0.732957\pi$
$284$	7.65130	−	1.15325i	0.454021	−	0.0684327i
$285$		0			0
$286$	4.64931	−	3.16985i	0.274920	−	0.187437i
$287$	0.570239	+	0.529105i	0.0336602	+	0.0312321i
$288$		0			0
$289$	23.4599	−	7.23642i	1.37999	−	0.425672i
$290$	6.29904	−	3.03346i	0.369893	−	0.178131i
$291$		0			0
$292$	−0.159884	+	2.13350i	−0.00935648	+	0.124854i
$293$	−3.88985	+	4.87772i	−0.227247	+	0.284959i	−0.882363	−	0.470569i	$-0.844049\pi$
$293$	−3.88985	+	4.87772i	−0.227247	+	0.284959i	0.655115	+	0.755529i	$0.272620\pi$
$294$		0			0
$295$	−23.0462	−	39.9172i	−1.34180	−	2.32407i
$296$	−14.5068	−	2.18655i	−0.843193	−	0.127091i
$297$		0			0
$298$	−0.584036	+	0.541906i	−0.0338323	+	0.0313918i
$299$	0.996495	−	4.36593i	0.0576288	−	0.252488i
$300$		0			0
$301$	−0.667016	−	1.63328i	−0.0384462	−	0.0941407i
$302$	−9.31987			−0.536298
$303$		0			0
$304$	0.912768	−	0.846925i	0.0523509	−	0.0485745i
$305$	−30.7870	−	14.8262i	−1.76286	−	0.848947i
$306$		0			0
$307$	−2.49936	−	4.32902i	−0.142646	−	0.247070i	0.785846	−	0.618422i	$-0.212228\pi$
$307$	−2.49936	−	4.32902i	−0.142646	−	0.247070i	−0.928492	+	0.371352i	$0.878894\pi$
$308$	−0.568039	+	0.983872i	−0.0323670	+	0.0560613i
$309$		0			0
$310$	1.12504	−	15.0127i	0.0638983	−	0.852663i
$311$	−1.80281	+	4.59348i	−0.102228	+	0.260473i	−0.972832	−	0.231511i	$-0.925633\pi$
$311$	−1.80281	+	4.59348i	−0.102228	+	0.260473i	0.870604	+	0.491984i	$0.163728\pi$
$312$		0			0
$313$	8.00980	−	2.47070i	0.452741	−	0.139652i	−0.0599948	−	0.998199i	$-0.519108\pi$
$313$	8.00980	−	2.47070i	0.452741	−	0.139652i	0.512735	+	0.858547i	$0.328632\pi$
$314$	−5.95459	−	15.1720i	−0.336037	−	0.856208i
$315$		0			0
$316$	14.7684	−	10.0689i	0.830787	−	0.566421i
$317$	−11.2630	−	14.1233i	−0.632593	−	0.793246i	0.357462	−	0.933928i	$-0.383642\pi$
$317$	−11.2630	−	14.1233i	−0.632593	−	0.793246i	−0.990055	+	0.140681i	$0.955071\pi$
$318$		0			0
$319$	−7.55688	−	2.33099i	−0.423104	−	0.130510i
$320$	−1.14229	−	15.2428i	−0.0638559	−	0.852098i
$321$		0			0
$322$	−0.112699	−	0.493767i	−0.00628048	−	0.0275166i
$323$	8.62321	+	37.7808i	0.479808	+	2.10218i
$324$		0			0
$325$	−1.02591	−	13.6898i	−0.0569073	−	0.759375i
$326$	15.5389	+	4.79310i	0.860618	+	0.265466i
$327$		0			0
$328$	5.01356	+	6.28681i	0.276828	+	0.347131i
$329$	−1.31218	+	0.894631i	−0.0723430	+	0.0493226i
$330$		0			0
$331$	0.691785	+	1.76264i	0.0380239	+	0.0968834i	0.948624	−	0.316404i	$-0.102476\pi$
$331$	0.691785	+	1.76264i	0.0380239	+	0.0968834i	−0.910600	+	0.413288i	$0.864380\pi$
$332$	9.36424	−	2.88849i	0.513930	−	0.158526i
$333$		0			0
$334$	1.87977	−	4.78958i	0.102857	−	0.262074i
$335$	3.26511	−	43.5698i	0.178392	−	2.38047i
$336$		0			0
$337$	−0.158818	+	0.275080i	−0.00865135	+	0.0149846i	−0.870319	−	0.492489i	$-0.836087\pi$
$337$	−0.158818	+	0.275080i	−0.00865135	+	0.0149846i	0.861667	+	0.507474i	$0.169421\pi$
$338$	3.78628	+	6.55803i	0.205946	+	0.356710i
$339$		0			0
$340$	−25.5848	−	12.3210i	−1.38753	−	0.668199i
$341$	−12.4831	+	11.5826i	−0.675999	+	0.627235i
$342$		0			0
$343$	−3.74713			−0.202326
$344$	−4.30162	−	17.7223i	−0.231928	−	0.955521i
$345$		0			0
$346$	−2.07912	+	9.10921i	−0.111774	+	0.489714i
$347$	−20.3150	+	18.8496i	−1.09057	+	1.01190i	−0.0906939	+	0.995879i	$0.528908\pi$
$347$	−20.3150	+	18.8496i	−1.09057	+	1.01190i	−0.999872	+	0.0160182i	$0.994901\pi$
$348$		0			0
$349$	26.8636	+	4.04904i	1.43798	+	0.216740i	0.821309	−	0.570484i	$-0.193244\pi$
$349$	26.8636	+	4.04904i	1.43798	+	0.216740i	0.616668	+	0.787224i	$0.288482\pi$
$350$	−0.776300	−	1.34459i	−0.0414950	−	0.0718714i
$351$		0			0
$352$	−11.7841	+	14.7768i	−0.628094	+	0.787605i
$353$	−1.46955	+	19.6097i	−0.0782160	+	1.04372i	0.810643	+	0.585540i	$0.199118\pi$
$353$	−1.46955	+	19.6097i	−0.0782160	+	1.04372i	−0.888859	+	0.458180i	$0.848501\pi$
$354$		0			0
$355$	18.6892	−	9.00024i	0.991919	−	0.477683i
$356$	2.21671	−	0.683764i	0.117485	−	0.0362394i
$357$		0			0
$358$	5.05249	+	4.68803i	0.267033	+	0.247770i
$359$	6.52863	−	4.45114i	0.344568	−	0.234922i	−0.378654	−	0.925538i	$-0.623613\pi$
$359$	6.52863	−	4.45114i	0.344568	−	0.234922i	0.723222	+	0.690616i	$0.242660\pi$
$360$		0			0
$361$	−16.9511	+	2.55496i	−0.892162	+	0.134472i
$362$	4.89587	+	1.51018i	0.257321	+	0.0793731i
$363$		0			0
$364$	0.574448	+	0.391652i	0.0301092	+	0.0205281i
$365$	1.27628	+	5.59176i	0.0668037	+	0.292686i
$366$		0			0
$367$	16.6615	+	11.3596i	0.869723	+	0.592967i	0.913847	−	0.406059i	$-0.133097\pi$
$367$	16.6615	+	11.3596i	0.869723	+	0.592967i	−0.0441239	+	0.999026i	$0.514050\pi$
$368$	0.0343836	+	0.458817i	0.00179237	+	0.0239175i
$369$		0			0
$370$	−15.1905	+	2.28959i	−0.789715	+	0.119030i
$371$	−1.07649	−	1.34987i	−0.0558884	−	0.0700819i
$372$		0			0
$373$	5.79496	+	5.37693i	0.300051	+	0.278407i	0.815801	−	0.578332i	$-0.196296\pi$
$373$	5.79496	+	5.37693i	0.300051	+	0.278407i	−0.515750	+	0.856739i	$0.672487\pi$
$374$	−6.57362	−	16.7493i	−0.339914	−	0.866087i
$375$		0			0
$376$	−14.7908	+	7.12290i	−0.762780	+	0.367335i
$377$	−1.76813	+	4.50512i	−0.0910633	+	0.232026i
$378$		0			0
$379$	−15.2679	+	19.1453i	−0.784258	+	0.983428i	0.215718	+	0.976456i	$0.430791\pi$
$379$	−15.2679	+	19.1453i	−0.784258	+	0.983428i	−0.999976	+	0.00697248i	$0.997781\pi$
$380$	13.2423	−	22.9363i	0.679314	−	1.17661i
$381$		0			0
$382$	−12.9288	−	1.94870i	−0.661495	−	0.0997043i
$383$	−24.8833	−	11.9832i	−1.27148	−	0.612311i	−0.328291	−	0.944577i	$-0.606473\pi$
$383$	−24.8833	−	11.9832i	−1.27148	−	0.612311i	−0.943186	+	0.332266i	$0.892187\pi$
$384$		0			0
$385$	−0.677714	+	2.96926i	−0.0345395	+	0.151327i
$386$	−2.06507			−0.105109
$387$		0			0
$388$	3.36507			0.170836
$389$	6.15713	−	26.9761i	0.312179	−	1.36774i	−0.538751	−	0.842465i	$-0.681104\pi$
$389$	6.15713	−	26.9761i	0.312179	−	1.36774i	0.850930	−	0.525279i	$-0.176039\pi$
$390$		0			0
$391$	−12.9014	−	6.21299i	−0.652452	−	0.314205i
$392$	−19.0512	−	2.87150i	−0.962230	−	0.145033i
$393$		0			0
$394$	−1.05563	+	1.82841i	−0.0531821	+	0.0921141i
$395$	29.8762	−	37.4635i	1.50323	−	1.88499i
$396$		0			0
$397$	3.68917	−	9.39985i	0.185154	−	0.471765i	−0.807915	−	0.589300i	$-0.799404\pi$
$397$	3.68917	−	9.39985i	0.185154	−	0.471765i	0.993069	+	0.117534i	$0.0374990\pi$
$398$	−6.30726	+	3.03742i	−0.316154	+	0.152252i
$399$		0			0
$400$	0.515304	+	1.31297i	0.0257652	+	0.0656486i
$401$	24.5225	+	22.7536i	1.22460	+	1.13626i	0.986282	+	0.165070i	$0.0527851\pi$
$401$	24.5225	+	22.7536i	1.22460	+	1.13626i	0.238314	+	0.971188i	$0.423405\pi$
$402$		0			0
$403$	6.49762	+	8.14776i	0.323670	+	0.405869i
$404$	−11.2324	+	1.69302i	−0.558835	+	0.0842309i
$405$		0			0
$406$	0.0409031	+	0.545814i	0.00202999	+	0.0270883i
$407$	14.3572	+	9.78855i	0.711658	+	0.485200i
$408$		0			0
$409$	−5.20581	−	22.8081i	−0.257411	−	1.12779i	−0.924008	−	0.382372i	$-0.875107\pi$
$409$	−5.20581	−	22.8081i	−0.257411	−	1.12779i	0.666598	−	0.745418i	$-0.267750\pi$
$410$	6.95698	+	4.74319i	0.343581	+	0.234250i
$411$		0			0
$412$	−0.927429	−	0.286074i	−0.0456912	−	0.0140939i
$413$	3.56818	−	0.537817i	0.175579	−	0.0264643i
$414$		0			0
$415$	21.7061	−	14.7990i	1.06551	−	0.726453i
$416$	8.47887	+	7.86725i	0.415711	+	0.385723i
$417$		0			0
$418$	16.0358	−	4.94639i	0.784337	−	0.241936i
$419$	−16.3740	+	7.88529i	−0.799921	+	0.385221i	−0.788748	−	0.614716i	$-0.789271\pi$
$419$	−16.3740	+	7.88529i	−0.799921	+	0.385221i	−0.0111722	+	0.999938i	$0.503556\pi$
$420$		0			0
$421$	−2.18943	+	29.2159i	−0.106706	+	1.42390i	0.644892	+	0.764274i	$0.276902\pi$
$421$	−2.18943	+	29.2159i	−0.106706	+	1.42390i	−0.751598	+	0.659621i	$0.770717\pi$
$422$	−7.56455	+	9.48565i	−0.368237	+	0.461754i
$423$		0			0
$424$	−8.92368	−	15.4563i	−0.433372	−	0.750622i
$425$	−43.4069	−	6.54254i	−2.10555	−	0.317360i
$426$		0			0
$427$	1.96105	−	1.81959i	0.0949018	−	0.0880560i
$428$	0.945527	−	4.14263i	0.0457038	−	0.200241i
$429$		0			0
$430$	−9.77412	−	16.4053i	−0.471350	−	0.791135i
$431$	−2.95198			−0.142192			−0.0710959	−	0.997469i	$-0.522650\pi$
$431$	−2.95198			−0.142192			−0.0710959	+	0.997469i	$0.522650\pi$
$432$		0			0
$433$	−24.6385	+	22.8611i	−1.18405	+	1.09864i	−0.190920	+	0.981606i	$0.561147\pi$
$433$	−24.6385	+	22.8611i	−1.18405	+	1.09864i	−0.993128	+	0.117031i	$0.962662\pi$
$434$	1.06189	+	0.511380i	0.0509725	+	0.0245470i
$435$		0			0
$436$	6.46981	+	11.2060i	0.309848	+	0.536672i
$437$	6.67757	−	11.5659i	0.319431	−	0.553271i
$438$		0			0
$439$	1.61347	−	21.5302i	0.0770066	−	1.02758i	−0.816151	−	0.577838i	$-0.803896\pi$
$439$	1.61347	−	21.5302i	0.0770066	−	1.02758i	0.893158	−	0.449743i	$-0.148484\pi$
$440$	−11.5019	+	29.3063i	−0.548330	+	1.39712i
$441$		0			0
$442$	−10.5222	+	3.24567i	−0.500491	+	0.154381i
$443$	−1.29471	−	3.29887i	−0.0615135	−	0.156734i	0.896812	−	0.442411i	$-0.145877\pi$
$443$	−1.29471	−	3.29887i	−0.0615135	−	0.156734i	−0.958326	+	0.285677i	$0.907782\pi$
$444$		0			0
$445$	5.13828	−	3.50322i	0.243578	−	0.166069i
$446$	−3.60625	−	4.52209i	−0.170761	−	0.214127i
$447$		0			0
$448$	1.14351	+	0.352727i	0.0540259	+	0.0166648i
$449$	1.72113	+	22.9668i	0.0812249	+	1.08387i	0.877703	+	0.479204i	$0.159075\pi$
$449$	1.72113	+	22.9668i	0.0812249	+	1.08387i	−0.796478	+	0.604667i	$0.793306\pi$
$450$		0			0
$451$	−2.11934	−	9.28543i	−0.0997957	−	0.437234i
$452$	1.59912	+	7.00622i	0.0752165	+	0.329545i
$453$		0			0
$454$	1.49060	+	19.8906i	0.0699571	+	0.933513i
$455$	1.78105	+	0.549381i	0.0834969	+	0.0257554i
$456$		0			0
$457$	−5.04145	−	6.32177i	−0.235829	−	0.295720i	0.649808	−	0.760098i	$-0.274849\pi$
$457$	−5.04145	−	6.32177i	−0.235829	−	0.295720i	−0.885637	+	0.464378i	$0.846278\pi$
$458$	11.0507	−	7.53425i	0.516366	−	0.352053i
$459$		0			0
$460$	3.57537	+	9.10988i	0.166702	+	0.424750i
$461$	−9.39710	+	2.89862i	−0.437667	+	0.135002i	−0.505755	−	0.862677i	$-0.668786\pi$
$461$	−9.39710	+	2.89862i	−0.437667	+	0.135002i	0.0680886	+	0.997679i	$0.478310\pi$
$462$		0			0
$463$	−11.0144	+	28.0644i	−0.511885	+	1.30426i	0.408325	+	0.912837i	$0.366113\pi$
$463$	−11.0144	+	28.0644i	−0.511885	+	1.30426i	−0.920210	+	0.391425i	$0.871982\pi$
$464$	0.0371589	−	0.495850i	0.00172506	−	0.0230193i
$465$		0			0
$466$	−1.18550	+	2.05335i	−0.0549174	+	0.0951197i
$467$	−12.1322	−	21.0135i	−0.561409	−	0.972389i	−0.997374	−	0.0724256i	$-0.976926\pi$
$467$	−12.1322	−	21.0135i	−0.561409	−	0.972389i	0.435965	−	0.899964i	$-0.356407\pi$
$468$		0			0
$469$	3.08183	+	1.48413i	0.142305	+	0.0685307i
$470$	−12.6013	+	11.6923i	−0.581256	+	0.539327i
$471$		0			0
$472$	37.3009			1.71691
$473$	−4.51720	+	21.1228i	−0.207701	+	0.971229i
$474$		0			0
$475$	9.11022	−	39.9145i	0.418005	−	1.83140i
$476$	1.62968	−	1.51212i	0.0746964	−	0.0693081i
$477$		0			0
$478$	4.28851	+	0.646389i	0.196152	+	0.0295652i
$479$	−0.0305712	−	0.0529509i	−0.00139683	−	0.00241939i	0.865326	−	0.501209i	$-0.167111\pi$
$479$	−0.0305712	−	0.0529509i	−0.00139683	−	0.00241939i	−0.866723	+	0.498790i	$0.833778\pi$
$480$		0			0
$481$	6.63024	−	8.31406i	0.302313	−	0.379089i
$482$	−0.369924	+	4.93629i	−0.0168496	+	0.224842i
$483$		0			0
$484$	−0.172461	+	0.0830527i	−0.00783913	+	0.00377512i
$485$	8.62036	−	2.65903i	0.391430	−	0.120740i
$486$		0			0
$487$	−17.0165	−	15.7890i	−0.771093	−	0.715470i	0.192952	−	0.981208i	$-0.438194\pi$
$487$	−17.0165	−	15.7890i	−0.771093	−	0.715470i	−0.964045	+	0.265738i	$0.914384\pi$
$488$	22.8483	−	15.5777i	1.03429	−	0.705169i
$489$		0			0
$490$	−19.9490	+	3.00682i	−0.901202	+	0.135834i
$491$	9.90993	+	3.05681i	0.447229	+	0.137952i	0.510185	−	0.860064i	$-0.329577\pi$
$491$	9.90993	+	3.05681i	0.447229	+	0.137952i	−0.0629566	+	0.998016i	$0.520053\pi$
$492$		0			0
$493$	12.7863	+	8.71755i	0.575866	+	0.392619i
$494$	−2.28526	−	10.0124i	−0.102819	−	0.450477i
$495$		0			0
$496$	−0.884671	−	0.603159i	−0.0397229	−	0.0270826i
$497$	0.121359	+	1.61943i	0.00544370	+	0.0726412i
$498$		0			0
$499$	−11.9560	+	1.80208i	−0.535224	+	0.0806720i	−0.411092	−	0.911594i	$-0.634853\pi$
$499$	−11.9560	+	1.80208i	−0.535224	+	0.0806720i	−0.124132	+	0.992266i	$0.539615\pi$
$500$	4.97160	+	6.23419i	0.222337	+	0.278802i
$501$		0			0
$502$	−5.46159	−	5.06762i	−0.243763	−	0.226179i
$503$	6.09669	+	15.5341i	0.271838	+	0.692632i	0.999974	+	0.00719925i	$0.00229161\pi$
$503$	6.09669	+	15.5341i	0.271838	+	0.692632i	−0.728136	+	0.685433i	$0.759613\pi$
$504$		0			0
$505$	−27.4366	+	13.2128i	−1.22091	+	0.587960i
$506$	−2.26545	+	5.77228i	−0.100712	+	0.256609i
$507$		0			0
$508$	7.42540	−	9.31116i	0.329449	−	0.413116i
$509$	16.1598	−	27.9896i	0.716271	−	1.24062i	−0.246197	−	0.969220i	$-0.579181\pi$
$509$	16.1598	−	27.9896i	0.716271	−	1.24062i	0.962467	−	0.271397i	$-0.0874858\pi$
$510$		0			0
$511$	−0.444012	−	0.0669240i	−0.0196419	−	0.00296054i
$512$	−2.10863	−	1.01546i	−0.0931892	−	0.0448776i
$513$		0			0
$514$	−1.13568	+	4.97572i	−0.0500925	+	0.219470i
$515$	−2.60186			−0.114652
$516$		0			0
$517$	19.4445			0.855166
$518$	0.267619	−	1.17251i	0.0117585	−	0.0515173i
$519$		0			0
$520$	17.3587	+	8.35950i	0.761228	+	0.366588i
$521$	36.0446	+	5.43284i	1.57914	+	0.238017i	0.879295	−	0.476277i	$-0.158014\pi$
$521$	36.0446	+	5.43284i	1.57914	+	0.238017i	0.699845	+	0.714294i	$0.253252\pi$
$522$		0			0
$523$	−13.2662	+	22.9777i	−0.580088	+	1.00474i	0.415380	+	0.909648i	$0.363649\pi$
$523$	−13.2662	+	22.9777i	−0.580088	+	1.00474i	−0.995468	+	0.0950946i	$0.969685\pi$
$524$	−4.33539	+	5.43641i	−0.189393	+	0.237491i
$525$		0			0
$526$	−7.48139	+	19.0623i	−0.326204	+	0.831154i
$527$	30.0233	−	14.4585i	1.30784	−	0.629820i
$528$		0			0
$529$	−6.59993	−	16.8163i	−0.286953	−	0.731145i
$530$	−13.6996	−	12.7113i	−0.595071	−	0.552146i
$531$		0			0
$532$	1.29276	+	1.62107i	0.0560483	+	0.0702823i
$533$	−5.76353	+	0.868712i	−0.249646	+	0.0376281i
$534$		0			0
$535$	−0.851268	−	11.3594i	−0.0368035	−	0.491109i
$536$	29.2145	+	19.9181i	1.26187	+	0.860331i
$537$		0			0
$538$	−0.826556	−	3.62138i	−0.0356354	−	0.156129i
$539$	18.8546	+	12.8549i	0.812126	+	0.553698i
$540$		0			0
$541$	−15.5995	−	4.81180i	−0.670674	−	0.206875i	−0.0593272	−	0.998239i	$-0.518896\pi$
$541$	−15.5995	−	4.81180i	−0.670674	−	0.206875i	−0.611346	+	0.791363i	$0.709372\pi$
$542$	−23.6901	+	3.57071i	−1.01758	+	0.153375i
$543$		0			0
$544$	30.5585	−	20.8344i	1.31019	−	0.893270i
$545$	25.4287	+	23.5944i	1.08925	+	1.01067i
$546$		0			0
$547$	25.6168	−	7.90174i	1.09530	−	0.337854i	0.306103	−	0.951999i	$-0.400975\pi$
$547$	25.6168	−	7.90174i	1.09530	−	0.337854i	0.789194	+	0.614144i	$0.210499\pi$
$548$	−12.7569	+	6.14342i	−0.544949	+	0.262434i
$549$		0			0
$550$	−1.42057	+	18.9561i	−0.0605732	+	0.808293i
$551$	−8.99889	+	11.2843i	−0.383366	+	0.480725i
$552$		0			0
$553$	1.87569	+	3.24879i	0.0797626	+	0.138153i
$554$	−19.3126	−	2.91091i	−0.820515	−	0.123673i
$555$		0			0
$556$	−7.22452	+	6.70338i	−0.306388	+	0.284286i
$557$	0.445481	−	1.95178i	0.0188756	−	0.0826996i	−0.964613	−	0.263670i	$-0.915067\pi$
$557$	0.445481	−	1.95178i	0.0188756	−	0.0826996i	0.983488	+	0.180971i	$0.0579240\pi$
$558$		0			0
$559$	12.6840	+	3.72272i	0.536477	+	0.157454i
$560$	−0.191498			−0.00809225
$561$		0			0
$562$	11.0979	−	10.2974i	0.468137	−	0.434368i
$563$	−27.9871	−	13.4779i	−1.17952	−	0.568025i	−0.261745	−	0.965137i	$-0.584298\pi$
$563$	−27.9871	−	13.4779i	−1.17952	−	0.568025i	−0.917770	+	0.397112i	$0.870012\pi$
$564$		0			0
$565$	9.63272	+	16.6844i	0.405252	+	0.701916i
$566$	5.97712	−	10.3527i	0.251237	−	0.435155i
$567$		0			0
$568$	−1.25449	+	16.7400i	−0.0526372	+	0.702395i
$569$	−0.695255	+	1.77148i	−0.0291466	+	0.0742643i	−0.944706	−	0.327918i	$-0.893653\pi$
$569$	−0.695255	+	1.77148i	−0.0291466	+	0.0742643i	0.915560	+	0.402182i	$0.131748\pi$
$570$		0			0
$571$	−1.82295	+	0.562306i	−0.0762882	+	0.0235318i	−0.332664	−	0.943045i	$-0.607948\pi$
$571$	−1.82295	+	0.562306i	−0.0762882	+	0.0235318i	0.256376	+	0.966577i	$0.417471\pi$
$572$	−3.10993	−	7.92396i	−0.130033	−	0.331318i
$573$		0			0
$574$	−0.544650	+	0.371336i	−0.0227332	+	0.0154993i
$575$	9.43228	+	11.8277i	0.393353	+	0.493249i
$576$		0			0
$577$	11.4249	+	3.52412i	0.475626	+	0.146711i	0.523294	−	0.852152i	$-0.324703\pi$
$577$	11.4249	+	3.52412i	0.475626	+	0.146711i	−0.0476684	+	0.998863i	$0.515179\pi$
$578$	1.55470	+	20.7460i	0.0646671	+	0.862922i
$579$		0			0
$580$	−2.35345	−	10.3111i	−0.0977216	−	0.428146i
$581$	0.457661	+	2.00514i	0.0189870	+	0.0831873i
$582$		0			0
$583$	1.57973	+	21.0800i	0.0654256	+	0.873044i
$584$	−4.43538	−	1.36813i	−0.183537	−	0.0566137i
$585$		0			0
$586$	−3.29626	−	4.13339i	−0.136167	−	0.170749i
$587$	−10.5277	+	7.17769i	−0.434526	+	0.296255i	−0.760759	−	0.649034i	$-0.775173\pi$
$587$	−10.5277	+	7.17769i	−0.434526	+	0.296255i	0.326233	+	0.945289i	$0.394221\pi$
$588$		0			0
$589$	11.3545	+	28.9308i	0.467854	+	1.19207i
$590$	37.3235	−	11.5128i	1.53658	−	0.473973i
$591$		0			0
$592$	−0.399162	+	1.01705i	−0.0164055	+	0.0418005i
$593$	−1.69336	+	22.5963i	−0.0695380	+	0.927920i	0.847930	+	0.530109i	$0.177849\pi$
$593$	−1.69336	+	22.5963i	−0.0695380	+	0.927920i	−0.917468	+	0.397811i	$0.869770\pi$
$594$		0			0
$595$	2.97993	−	5.16139i	0.122165	−	0.211596i
$596$	0.602620	+	1.04377i	0.0246843	+	0.0427544i
$597$		0			0
$598$	3.41903	+	1.64652i	0.139815	+	0.0673312i
$599$	−19.4871	+	18.0814i	−0.796221	+	0.738785i	−0.969236	−	0.246134i	$-0.920840\pi$
$599$	−19.4871	+	18.0814i	−0.796221	+	0.738785i	0.173015	+	0.984919i	$0.444649\pi$
$600$		0			0
$601$	5.51022			0.224766			0.112383	−	0.993665i	$-0.464152\pi$
$601$	5.51022			0.224766			0.112383	+	0.993665i	$0.464152\pi$
$602$	1.47512	−	0.243080i	0.0601214	−	0.00990720i
$603$		0			0
$604$	−3.13725	+	13.7452i	−0.127653	+	0.559284i
$605$	−0.376169	+	0.349034i	−0.0152934	+	0.0141902i
$606$		0			0
$607$	2.78541	+	0.419833i	0.113056	+	0.0170405i	0.205327	−	0.978693i	$-0.434174\pi$
$607$	2.78541	+	0.419833i	0.113056	+	0.0170405i	−0.0922704	+	0.995734i	$0.529412\pi$
$608$	17.2472	+	29.8730i	0.699465	+	1.21151i
$609$		0			0
$610$	18.0541	−	22.6391i	0.730989	−	0.916631i
$611$	0.889259	−	11.8663i	0.0359756	−	0.480061i
$612$		0			0
$613$	3.46419	−	1.66826i	0.139917	−	0.0673805i	−0.362615	−	0.931939i	$-0.618116\pi$
$613$	3.46419	−	1.66826i	0.139917	−	0.0673805i	0.502532	+	0.864558i	$0.332402\pi$
$614$	4.04774	−	1.24856i	0.163353	−	0.0503878i
$615$		0			0
$616$	−1.80676	−	1.67643i	−0.0727965	−	0.0675453i
$617$	−33.6620	+	22.9504i	−1.35518	+	0.923947i	−0.999941	−	0.0108275i	$-0.996553\pi$
$617$	−33.6620	+	22.9504i	−1.35518	+	0.923947i	−0.355241	+	0.934775i	$0.615601\pi$
$618$		0			0
$619$	32.9850	−	4.97168i	1.32578	−	0.199829i	0.552296	−	0.833648i	$-0.313752\pi$
$619$	32.9850	−	4.97168i	1.32578	−	0.199829i	0.773481	+	0.633819i	$0.218514\pi$
$620$	−21.7624	−	6.71281i	−0.873999	−	0.269593i
$621$		0			0
$622$	−3.45498	−	2.35557i	−0.138532	−	0.0944497i
$623$	0.108338	+	0.474659i	0.00434046	+	0.0190168i
$624$		0			0
$625$	−10.4715	−	7.13936i	−0.418861	−	0.285574i
$626$	0.530814	+	7.08322i	0.0212156	+	0.283102i
$627$		0			0
$628$	−24.3806	+	3.67478i	−0.972891	+	0.146640i
$629$	−21.2008	−	26.5850i	−0.845332	−	1.06001i
$630$		0			0
$631$	19.6700	+	18.2511i	0.783049	+	0.726563i	0.966556	−	0.256455i	$-0.0825545\pi$
$631$	19.6700	+	18.2511i	0.783049	+	0.726563i	−0.183507	+	0.983018i	$0.558745\pi$
$632$	14.1672	+	36.0975i	0.563541	+	1.43588i
$633$		0			0
$634$	13.7919	−	6.64182i	0.547746	−	0.263780i
$635$	11.6642	−	29.7200i	0.462881	−	1.17940i
$636$		0			0
$637$	8.70720	−	10.9185i	0.344992	−	0.432606i
$638$	3.35072	−	5.80361i	0.132656	−	0.229767i
$639$		0			0
$640$	−26.1873	−	3.94710i	−1.03514	−	0.156023i
$641$	35.6933	+	17.1890i	1.40980	+	0.678923i	0.975123	−	0.221663i	$-0.0711486\pi$
$641$	35.6933	+	17.1890i	1.40980	+	0.678923i	0.434676	+	0.900587i	$0.356863\pi$
$642$		0			0
$643$	2.12257	−	9.29957i	0.0837059	−	0.366739i	−0.915675	−	0.401919i	$-0.868343\pi$
$643$	2.12257	−	9.29957i	0.0837059	−	0.366739i	0.999381	+	0.0351799i	$0.0112004\pi$
$644$	−0.766158			−0.0301908
$645$		0			0
$646$	−32.8388			−1.29203
$647$	5.25960	−	23.0438i	0.206776	−	0.905946i	−0.759919	−	0.650017i	$-0.774762\pi$
$647$	5.25960	−	23.0438i	0.206776	−	0.905946i	0.966696	−	0.255929i	$-0.0823813\pi$
$648$		0			0
$649$	−39.8054	−	19.1693i	−1.56250	−	0.752460i
$650$	11.5034	+	1.73385i	0.451199	+	0.0680074i
$651$		0			0
$652$	12.2997	−	21.3037i	0.481693	−	0.834317i
$653$	−0.844715	+	1.05924i	−0.0330562	+	0.0414512i	−0.798085	−	0.602545i	$-0.794153\pi$
$653$	−0.844715	+	1.05924i	−0.0330562	+	0.0414512i	0.765029	+	0.643996i	$0.222725\pi$
$654$		0			0
$655$	−6.81028	+	17.3523i	−0.266100	+	0.678011i
$656$	0.539544	−	0.259831i	0.0210657	−	0.0101447i
$657$		0			0
$658$	−0.491673	−	1.25276i	−0.0191674	−	0.0488378i
$659$	−11.3008	−	10.4856i	−0.440216	−	0.408461i	0.428679	−	0.903457i	$-0.358979\pi$
$659$	−11.3008	−	10.4856i	−0.440216	−	0.408461i	−0.868895	+	0.494996i	$0.835169\pi$
$660$		0			0
$661$	−9.58249	−	12.0161i	−0.372716	−	0.467371i	0.559733	−	0.828673i	$-0.310904\pi$
$661$	−9.58249	−	12.0161i	−0.372716	−	0.467371i	−0.932449	+	0.361302i	$0.882332\pi$
$662$	−1.58666	+	0.239151i	−0.0616673	+	0.00929485i
$663$		0			0
$664$	1.58878	+	21.2007i	0.0616565	+	0.822748i
$665$	4.59264	+	3.13121i	0.178095	+	0.121423i
$666$		0			0
$667$	−1.18675	−	5.19950i	−0.0459512	−	0.201325i
$668$	−6.43104	−	4.38461i	−0.248824	−	0.169646i
$669$		0			0
$670$	35.3798	+	10.9132i	1.36684	+	0.421614i
$671$	−32.3879	+	4.88169i	−1.25032	+	0.188455i
$672$		0			0
$673$	−37.4014	+	25.4998i	−1.44172	+	0.982946i	−0.445570	+	0.895247i	$0.646999\pi$
$673$	−37.4014	+	25.4998i	−1.44172	+	0.982946i	−0.996147	+	0.0876984i	$0.972049\pi$
$674$	−0.197312	−	0.183078i	−0.00760016	−	0.00705192i
$675$		0			0
$676$	10.9465	−	3.37655i	0.421019	−	0.129867i
$677$	5.42739	−	2.61370i	0.208592	−	0.100452i	−0.326671	−	0.945138i	$-0.605927\pi$
$677$	5.42739	−	2.61370i	0.208592	−	0.100452i	0.535263	+	0.844686i	$0.320213\pi$
$678$		0			0
$679$	−0.0527781	+	0.704274i	−0.00202544	+	0.0270276i
$680$	38.4113	−	48.1663i	1.47301	−	1.84709i
$681$		0			0
$682$	−7.21518	−	12.4971i	−0.276284	−	0.478537i
$683$	2.80582	+	0.422910i	0.107362	+	0.0161822i	0.202503	−	0.979282i	$-0.435092\pi$
$683$	2.80582	+	0.422910i	0.107362	+	0.0161822i	−0.0951416	+	0.995464i	$0.530330\pi$
$684$		0			0
$685$	−27.8252	+	25.8180i	−1.06315	+	0.986457i
$686$	0.706575	−	3.09571i	0.0269772	−	0.118195i
$687$		0			0
$688$	−1.35803	+	0.0186323i	−0.0517745	+	0.000710349i
$689$	12.9367			0.492849
$690$		0			0
$691$	18.2969	−	16.9771i	0.696048	−	0.645839i	−0.250606	−	0.968089i	$-0.580630\pi$
$691$	18.2969	−	16.9771i	0.696048	−	0.645839i	0.946654	+	0.322251i	$0.104439\pi$
$692$	12.7346	+	6.13268i	0.484099	+	0.233130i
$693$		0			0
$694$	−11.7420	−	20.3377i	−0.445719	−	0.772008i
$695$	−13.2103	+	22.8809i	−0.501094	+	0.867921i
$696$		0			0
$697$	−1.39279	+	18.5855i	−0.0527556	+	0.703975i
$698$	−8.41066	+	21.4300i	−0.318348	+	0.811138i
$699$		0			0
$700$	−2.24436	+	0.692292i	−0.0848287	+	0.0261662i
$701$	−3.98473	−	10.1529i	−0.150501	−	0.383471i	0.835663	−	0.549243i	$-0.185084\pi$
$701$	−3.98473	−	10.1529i	−0.150501	−	0.383471i	−0.986164	+	0.165772i	$0.946989\pi$
$702$		0			0
$703$	26.2029	−	17.8648i	0.988262	−	0.673785i
$704$	−9.13510	−	11.4550i	−0.344292	−	0.431728i
$705$		0			0
$706$	−15.9236	−	4.91177i	−0.599292	−	0.184857i
$707$	−0.178161	−	2.37739i	−0.00670042	−	0.0894109i
$708$		0			0
$709$	1.03191	+	4.52108i	0.0387541	+	0.169793i	0.990602	−	0.136779i	$-0.0436751\pi$
$709$	1.03191	+	4.52108i	0.0387541	+	0.169793i	−0.951847	+	0.306572i	$0.900818\pi$
$710$	3.91148	+	17.1373i	0.146795	+	0.643151i
$711$		0			0
$712$	0.376096	+	5.01865i	0.0140948	+	0.188082i
$713$	−10.9739	−	3.38501i	−0.410977	−	0.126770i
$714$		0			0
$715$	−14.2282	−	17.8415i	−0.532103	−	0.667236i
$716$	8.61480	−	5.87347i	0.321950	−	0.219502i
$717$		0			0
$718$	2.44627	+	6.23299i	0.0912939	+	0.232613i
$719$	40.4359	−	12.4728i	1.50801	−	0.465158i	0.572929	−	0.819605i	$-0.305807\pi$
$719$	40.4359	−	12.4728i	1.50801	−	0.465158i	0.935076	+	0.354447i	$0.115331\pi$
$720$		0			0
$721$	0.0744182	−	0.189614i	0.00277148	−	0.00706161i
$722$	1.08558	−	14.4860i	0.0404010	−	0.539113i
$723$		0			0
$724$	3.87530	−	6.71221i	0.144024	−	0.249457i
$725$	−8.17464	−	14.1589i	−0.303599	−	0.525848i
$726$		0			0
$727$	2.50295	+	1.20536i	0.0928293	+	0.0447042i	0.479722	−	0.877420i	$-0.340737\pi$
$727$	2.50295	+	1.20536i	0.0928293	+	0.0447042i	−0.386893	+	0.922125i	$0.626452\pi$
$728$	−1.10570	+	1.02594i	−0.0409800	+	0.0380239i
$729$		0			0
$730$	−4.86032			−0.179889
$731$	20.6304	−	36.8926i	0.763042	−	1.36452i
$732$		0			0
$733$	9.70495	−	42.5201i	0.358460	−	1.57052i	−0.398570	−	0.917138i	$-0.630493\pi$
$733$	9.70495	−	42.5201i	0.358460	−	1.57052i	0.757031	−	0.653380i	$-0.226649\pi$
$734$	−12.5266	+	11.6230i	−0.462364	+	0.429011i
$735$		0			0
$736$	−12.6037	−	1.89971i	−0.464579	−	0.0700241i
$737$	−20.9399	−	36.2690i	−0.771332	−	1.33599i
$738$		0			0
$739$	−1.70413	+	2.13692i	−0.0626876	+	0.0786077i	−0.812187	−	0.583398i	$-0.801723\pi$
$739$	−1.70413	+	2.13692i	−0.0626876	+	0.0786077i	0.749499	+	0.662005i	$0.230294\pi$
$740$	−1.73665	+	23.1740i	−0.0638407	+	0.851895i
$741$		0			0
$742$	1.31819	−	0.634807i	0.0483923	−	0.0233045i
$743$	−38.0996	+	11.7522i	−1.39774	+	0.431145i	−0.899889	−	0.436119i	$-0.856353\pi$
$743$	−38.0996	+	11.7522i	−1.39774	+	0.431145i	−0.497849	+	0.867264i	$0.665877\pi$
$744$		0			0
$745$	2.36851	+	2.19766i	0.0867756	+	0.0805160i
$746$	−5.53490	+	3.77363i	−0.202647	+	0.138163i
$747$		0			0
$748$	−26.9152	+	4.05681i	−0.984116	+	0.148332i
$749$	0.852179	+	0.262862i	0.0311379	+	0.00960478i
$750$		0			0
$751$	37.1303	+	25.3150i	1.35491	+	0.923759i	0.999938	−	0.0111198i	$-0.00353962\pi$
$751$	37.1303	+	25.3150i	1.35491	+	0.923759i	0.354967	+	0.934879i	$0.384492\pi$
$752$	0.272054	+	1.19194i	0.00992078	+	0.0434658i
$753$		0			0
$754$	−3.38852	−	2.31026i	−0.123403	−	0.0841346i
$755$	2.82450	+	37.6903i	0.102794	+	1.37169i
$756$		0			0
$757$	−12.7269	+	1.91827i	−0.462566	+	0.0697207i	−0.376191	−	0.926542i	$-0.622766\pi$
$757$	−12.7269	+	1.91827i	−0.462566	+	0.0697207i	−0.0863751	+	0.996263i	$0.527528\pi$
$758$	−12.9380	−	16.2238i	−0.469930	−	0.589273i
$759$		0			0
$760$	42.1197	+	39.0814i	1.52784	+	1.41763i
$761$	3.08333	+	7.85619i	0.111771	+	0.284787i	0.975804	−	0.218648i	$-0.0701646\pi$
$761$	3.08333	+	7.85619i	0.111771	+	0.284787i	−0.864033	+	0.503435i	$0.832069\pi$
$762$		0			0
$763$	−2.44678	+	1.17831i	−0.0885795	+	0.0426576i
$764$	−7.22609	+	18.4118i	−0.261431	+	0.666115i
$765$		0			0
$766$	14.5921	−	18.2979i	0.527233	−	0.661129i
$767$	−13.5188	+	23.4153i	−0.488137	+	0.845478i
$768$		0			0
$769$	−29.1469	−	4.39319i	−1.05106	−	0.158422i	−0.399282	−	0.916828i	$-0.630740\pi$
$769$	−29.1469	−	4.39319i	−1.05106	−	0.158422i	−0.651783	+	0.758406i	$0.725979\pi$
$770$	−2.32528	−	1.11979i	−0.0837971	−	0.0403546i
$771$		0			0
$772$	−0.695142	+	3.04562i	−0.0250187	+	0.109614i
$773$	32.7084			1.17644			0.588220	−	0.808701i	$-0.299829\pi$
$773$	32.7084			1.17644			0.588220	+	0.808701i	$0.299829\pi$
$774$		0			0
$775$	−35.2053			−1.26461
$776$	−1.62451	+	7.11745i	−0.0583166	+	0.255502i
$777$		0			0
$778$	21.1255	+	10.1735i	0.757384	+	0.364737i
$779$	−17.1883	−	2.59072i	−0.615834	−	0.0928220i
$780$		0			0
$781$	9.94154	−	17.2193i	0.355736	−	0.616154i
$782$	7.56565	−	9.48702i	0.270547	−	0.339255i
$783$		0			0
$784$	−0.524202	+	1.33564i	−0.0187215	+	0.0477016i
$785$	−59.5524	+	28.6789i	−2.12552	+	1.02359i
$786$		0			0
$787$	1.27793	+	3.25611i	0.0455532	+	0.116068i	0.951840	−	0.306596i	$-0.0991902\pi$
$787$	1.27793	+	3.25611i	0.0455532	+	0.116068i	−0.906286	+	0.422664i	$0.861095\pi$
$788$	2.34124	+	2.17236i	0.0834034	+	0.0773870i
$789$		0			0
$790$	25.3171	+	31.7466i	0.900742	+	1.12949i
$791$	−1.49141	+	0.224794i	−0.0530285	+	0.00799275i
$792$		0			0
$793$	1.49794	+	19.9886i	0.0531932	+	0.709814i
$794$	7.07009	+	4.82031i	0.250908	+	0.171066i
$795$		0			0
$796$	2.35652	+	10.3246i	0.0835245	+	0.365945i
$797$	−8.19917	−	5.59010i	−0.290429	−	0.198011i	0.409337	−	0.912383i	$-0.365760\pi$
$797$	−8.19917	−	5.59010i	−0.290429	−	0.198011i	−0.699766	+	0.714372i	$0.746713\pi$
$798$		0			0
$799$	−36.3597	−	11.2155i	−1.28631	−	0.396775i
$800$	−38.6375	+	5.82366i	−1.36604	+	0.205897i
$801$		0			0
$802$	−23.4220	+	15.9689i	−0.827061	+	0.563881i
$803$	4.03008	+	3.73937i	0.142218	+	0.131959i
$804$		0			0
$805$	−1.96268	+	0.605407i	−0.0691754	+	0.0213378i
$806$	−7.95654	+	3.83167i	−0.280257	+	0.134965i
$807$		0			0
$808$	1.84165	−	24.5751i	0.0647889	−	0.864547i
$809$	4.95941	−	6.21890i	0.174363	−	0.218645i	−0.686969	−	0.726687i	$-0.741059\pi$
$809$	4.95941	−	6.21890i	0.174363	−	0.218645i	0.861332	+	0.508042i	$0.169631\pi$
$810$		0			0
$811$	23.5508	+	40.7913i	0.826982	+	1.43238i	0.900395	+	0.435073i	$0.143278\pi$
$811$	23.5508	+	40.7913i	0.826982	+	1.43238i	−0.0734128	+	0.997302i	$0.523389\pi$
$812$	0.818751	+	0.123407i	0.0287325	+	0.00433073i
$813$		0			0
$814$	−10.7941	+	10.0155i	−0.378333	+	0.351042i
$815$	14.6745	−	64.2931i	0.514024	−	2.25209i
$816$		0			0
$817$	32.8740	+	21.7585i	1.15011	+	0.761234i
$818$	19.8247			0.693154
$819$		0			0
$820$	9.33725	−	8.66370i	0.326071	−	0.302549i
$821$	39.4286	+	18.9878i	1.37607	+	0.662679i	0.968157	−	0.250344i	$-0.0805437\pi$
$821$	39.4286	+	18.9878i	1.37607	+	0.662679i	0.407909	+	0.913022i	$0.366258\pi$
$822$		0			0
$823$	−27.9019	−	48.3275i	−0.972599	−	1.68459i	−0.687642	−	0.726050i	$-0.741354\pi$
$823$	−27.9019	−	48.3275i	−0.972599	−	1.68459i	−0.284956	−	0.958541i	$-0.591979\pi$
$824$	1.05280	−	1.82350i	0.0366760	−	0.0635246i
$825$		0			0
$826$	−0.228513	+	3.04929i	−0.00795097	+	0.106098i
$827$	1.87676	−	4.78192i	0.0652615	−	0.166284i	−0.894523	−	0.447023i	$-0.852484\pi$
$827$	1.87676	−	4.78192i	0.0652615	−	0.166284i	0.959784	+	0.280739i	$0.0905796\pi$
$828$		0			0
$829$	−3.41761	+	1.05419i	−0.118698	+	0.0366136i	−0.353535	−	0.935421i	$-0.615021\pi$
$829$	−3.41761	+	1.05419i	−0.118698	+	0.0366136i	0.234837	+	0.972035i	$0.424544\pi$
$830$	8.13325	+	20.7232i	0.282309	+	0.719312i
$831$		0			0
$832$	−7.40843	+	5.05098i	−0.256841	+	0.175111i
$833$	−27.8421	−	34.9129i	−0.964671	−	1.20966i
$834$		0			0
$835$	−19.9392	−	6.15042i	−0.690023	−	0.212844i
$836$	−1.89710	−	25.3151i	−0.0656127	−	0.875541i
$837$		0			0
$838$	−3.42692	−	15.0143i	−0.118381	−	0.518661i
$839$	−9.15090	−	40.0927i	−0.315924	−	1.38415i	−0.844631	−	0.535350i	$-0.820180\pi$
$839$	−9.15090	−	40.0927i	−0.315924	−	1.38415i	0.528706	−	0.848805i	$-0.322677\pi$
$840$		0			0
$841$	−1.73645	−	23.1713i	−0.0598776	−	0.799012i
$842$	−23.7240	−	7.31789i	−0.817583	−	0.252191i
$843$		0			0
$844$	11.4433	+	14.3495i	0.393895	+	0.493929i
$845$	25.3737	−	17.2995i	0.872883	−	0.595122i
$846$		0			0
$847$	−0.0146772	−	0.0373969i	−0.000504314	−	0.00128497i
$848$	−1.27010	+	0.391774i	−0.0436154	+	0.0134536i
$849$		0			0
$850$	13.5902	−	34.6272i	0.466139	−	1.18770i
$851$	−0.875727	+	11.6858i	−0.0300195	+	0.400583i
$852$		0			0
$853$	10.5523	−	18.2771i	0.361304	−	0.625797i	−0.626871	−	0.779123i	$-0.715665\pi$
$853$	10.5523	−	18.2771i	0.361304	−	0.625797i	0.988176	+	0.153325i	$0.0489982\pi$
$854$	1.13348	+	1.96324i	0.0387868	+	0.0671807i
$855$		0			0
$856$	8.30560	+	3.99977i	0.283880	+	0.136709i
$857$	23.2674	−	21.5890i	0.794799	−	0.737466i	−0.174152	−	0.984719i	$-0.555718\pi$
$857$	23.2674	−	21.5890i	0.794799	−	0.737466i	0.968951	+	0.247253i	$0.0795279\pi$
$858$		0			0
$859$	−29.8703			−1.01916			−0.509581	−	0.860423i	$-0.670200\pi$
$859$	−29.8703			−1.01916			−0.509581	+	0.860423i	$0.670200\pi$
$860$	−27.4852	+	8.89279i	−0.937237	+	0.303241i
$861$		0			0
$862$	0.556639	−	2.43879i	0.0189592	−	0.0830656i
$863$	21.8250	−	20.2507i	0.742933	−	0.689341i	−0.214910	−	0.976634i	$-0.568946\pi$
$863$	21.8250	−	20.2507i	0.742933	−	0.689341i	0.957843	+	0.287293i	$0.0927553\pi$
$864$		0			0
$865$	37.4685	+	5.64747i	1.27397	+	0.192020i
$866$	−14.2409	−	24.6660i	−0.483926	−	0.838185i
$867$		0			0
$868$	1.11165	−	1.39397i	0.0377319	−	0.0473143i
$869$	3.43237	−	45.8018i	0.116435	−	1.55372i
$870$		0			0
$871$	−23.0915	+	11.1203i	−0.782425	+	0.376796i
$872$	−26.8252	+	8.27449i	−0.908417	+	0.280210i
$873$		0			0
$874$	8.29606	+	7.69762i	0.280619	+	0.260376i
$875$	−1.38273	+	0.942727i	−0.0467447	+	0.0318700i
$876$		0			0
$877$	−10.5286	+	1.58692i	−0.355524	+	0.0535866i	−0.324376	−	0.945928i	$-0.605154\pi$
$877$	−10.5286	+	1.58692i	−0.355524	+	0.0535866i	−0.0311478	+	0.999515i	$0.509916\pi$
$878$	17.4831	+	5.39281i	0.590025	+	0.181999i
$879$		0			0
$880$	1.93721	+	1.32076i	0.0653032	+	0.0445230i
$881$	−1.95405	−	8.56125i	−0.0658336	−	0.288436i	0.931285	−	0.364291i	$-0.118689\pi$
$881$	−1.95405	−	8.56125i	−0.0658336	−	0.288436i	−0.997119	+	0.0758550i	$0.975831\pi$
$882$		0			0
$883$	−37.3482	−	25.4636i	−1.25687	−	0.856918i	−0.262712	−	0.964874i	$-0.584617\pi$
$883$	−37.3482	−	25.4636i	−1.25687	−	0.856918i	−0.994156	+	0.107956i	$0.965569\pi$
$884$	1.24482	+	16.6110i	0.0418679	+	0.558689i
$885$		0			0
$886$	2.96951	−	0.447582i	0.0997627	−	0.0150368i
$887$	18.9884	+	23.8107i	0.637569	+	0.799486i	0.990697	−	0.136089i	$-0.0434532\pi$
$887$	18.9884	+	23.8107i	0.637569	+	0.799486i	−0.353128	+	0.935575i	$0.614882\pi$
$888$		0			0
$889$	1.83227	+	1.70010i	0.0614523	+	0.0570194i
$890$	1.92531	+	4.90560i	0.0645365	+	0.164436i
$891$		0			0
$892$	−7.88324	+	3.79637i	−0.263950	+	0.127112i
$893$	12.9651	−	33.0345i	0.433860	−	1.10546i
$894$		0			0
$895$	17.4276	−	21.8535i	0.582539	−	0.730481i
$896$	1.03666	−	1.79554i	0.0346322	−	0.0599848i
$897$		0			0
$898$	−19.2987	−	2.90881i	−0.644006	−	0.0970683i
$899$	11.1820	+	5.38497i	0.372941	+	0.179599i
$900$		0			0
$901$	9.20487	−	40.3291i	0.306659	−	1.34356i
$902$	8.07084			0.268729
$903$		0			0
$904$	−15.5908			−0.518544
$905$	4.62352	−	20.2570i	0.153691	−	0.673365i
$906$		0			0
$907$	−33.3055	−	16.0391i	−1.10589	−	0.532570i	−0.210386	−	0.977618i	$-0.567472\pi$
$907$	−33.3055	−	16.0391i	−1.10589	−	0.532570i	−0.895506	+	0.445049i	$0.853186\pi$
$908$	29.8370	+	4.49720i	0.990175	+	0.149245i
$909$		0			0
$910$	−0.789717	+	1.36783i	−0.0261789	+	0.0453431i
$911$	−2.30448	+	2.88972i	−0.0763507	+	0.0957407i	−0.818540	−	0.574450i	$-0.805216\pi$
$911$	−2.30448	+	2.88972i	−0.0763507	+	0.0957407i	0.742189	+	0.670190i	$0.233788\pi$
$912$		0			0
$913$	9.19979	−	23.4407i	0.304469	−	0.775773i
$914$	6.17340	−	2.97295i	0.204198	−	0.0983366i
$915$		0			0
$916$	−7.39183	−	18.8341i	−0.244233	−	0.622296i
$917$	−1.06979	−	0.992618i	−0.0353275	−	0.0327791i
$918$		0			0
$919$	−9.80585	−	12.2961i	−0.323465	−	0.405612i	0.593337	−	0.804954i	$-0.297810\pi$
$919$	−9.80585	−	12.2961i	−0.323465	−	0.405612i	−0.916802	+	0.399342i	$0.869239\pi$
$920$	−20.9943	+	3.16439i	−0.692163	+	0.104327i
$921$		0			0
$922$	−0.622752	−	8.31004i	−0.0205092	−	0.273677i
$923$	−10.0537	−	6.85450i	−0.330922	−	0.225619i
$924$		0			0
$925$	7.99381	+	35.0232i	0.262835	+	1.15156i
$926$	−21.1086	−	14.3916i	−0.693671	−	0.472937i
$927$		0			0
$928$	13.1629	+	4.06022i	0.432094	+	0.133283i
$929$	−18.5921	+	2.80230i	−0.609986	+	0.0919406i	−0.446769	−	0.894649i	$-0.647425\pi$
$929$	−18.5921	+	2.80230i	−0.609986	+	0.0919406i	−0.163217	+	0.986590i	$0.552187\pi$
$930$		0			0
$931$	34.4111	−	23.4611i	1.12778	−	0.768907i
$932$	2.62928	+	2.43961i	0.0861248	+	0.0799121i
$933$		0			0
$934$	19.6481	−	6.06064i	0.642906	−	0.198310i
$935$	−65.7434	+	31.6604i	−2.15004	+	1.03540i
$936$		0			0
$937$	0.851277	−	11.3595i	0.0278100	−	0.371099i	−0.965884	−	0.258974i	$-0.916615\pi$
$937$	0.851277	−	11.3595i	0.0278100	−	0.371099i	0.993694	−	0.112124i	$-0.0357655\pi$
$938$	−1.80724	+	2.26621i	−0.0590086	+	0.0739945i
$939$		0			0
$940$	13.0023	+	22.5207i	0.424089	+	0.734543i
$941$	−38.2402	−	5.76378i	−1.24660	−	0.187894i	−0.507593	−	0.861597i	$-0.669465\pi$
$941$	−38.2402	−	5.76378i	−1.24660	−	0.187894i	−0.739002	+	0.673703i	$0.764703\pi$
$942$		0			0
$943$	4.70841	−	4.36877i	0.153327	−	0.142267i
$944$	0.618146	−	2.70827i	0.0201189	−	0.0881468i
$945$		0			0
$946$	−16.5990	−	7.71492i	−0.539679	−	0.250834i
$947$	13.9735			0.454077			0.227039	−	0.973886i	$-0.427096\pi$
$947$	13.9735			0.454077			0.227039	+	0.973886i	$0.427096\pi$
$948$		0			0
$949$	2.46633	−	2.28842i	0.0800604	−	0.0742852i
$950$	31.2577	+	15.0529i	1.01413	+	0.488381i
$951$		0			0
$952$	2.41155	+	4.17693i	0.0781588	+	0.135375i
$953$	−29.1009	+	50.4042i	−0.942670	+	1.63275i	−0.182321	+	0.983239i	$0.558361\pi$
$953$	−29.1009	+	50.4042i	−0.942670	+	1.63275i	−0.760350	+	0.649514i	$0.774972\pi$
$954$		0			0
$955$	−3.96249	+	52.8757i	−0.128223	+	1.71102i
$956$	2.39691	−	6.10723i	0.0775216	−	0.197522i
$957$		0			0
$958$	0.0495103	−	0.0152719i	0.00159961	−	0.000493413i
$959$	−1.08567	−	2.76625i	−0.0350582	−	0.0893268i
$960$		0			0
$961$	−3.53207	+	2.40813i	−0.113938	+	0.0776815i
$962$	5.61848	+	7.04535i	0.181147	+	0.227151i
$963$		0			0
$964$	7.15565	+	2.20723i	0.230468	+	0.0710899i
$965$	0.625843	+	8.35130i	0.0201466	+	0.268838i
$966$		0			0
$967$	4.46525	+	19.5635i	0.143593	+	0.629121i	0.994584	+	0.103940i	$0.0331451\pi$
$967$	4.46525	+	19.5635i	0.143593	+	0.629121i	−0.850991	+	0.525181i	$0.823998\pi$
$968$	−0.0924080	−	0.404866i	−0.00297011	−	0.0130129i
$969$		0			0
$970$	0.571276	+	7.62315i	0.0183426	+	0.244765i
$971$	−56.6062	−	17.4607i	−1.81658	−	0.560340i	−0.816718	−	0.577038i	$-0.804209\pi$
$971$	−56.6062	−	17.4607i	−1.81658	−	0.560340i	−0.999861	+	0.0166975i	$0.994685\pi$
$972$		0			0
$973$	−1.28964	−	1.61715i	−0.0413439	−	0.0518436i
$974$	16.2529	−	11.0811i	0.520777	−	0.355060i
$975$		0			0
$976$	−0.752397	−	1.91708i	−0.0240836	−	0.0613641i
$977$	41.6110	−	12.8353i	1.33125	−	0.410637i	0.454144	−	0.890928i	$-0.349945\pi$
$977$	41.6110	−	12.8353i	1.33125	−	0.410637i	0.877109	+	0.480291i	$0.159469\pi$
$978$		0			0
$979$	2.17778	−	5.54889i	0.0696022	−	0.177343i
$980$	−2.28067	+	30.4334i	−0.0728533	+	0.972160i
$981$		0			0
$982$	−4.39406	+	7.61073i	−0.140220	+	0.242868i
$983$	1.58270	+	2.74132i	0.0504804	+	0.0874346i	0.890161	−	0.455645i	$-0.150591\pi$
$983$	1.58270	+	2.74132i	0.0504804	+	0.0874346i	−0.839681	+	0.543080i	$0.817258\pi$
$984$		0			0
$985$	7.71417	+	3.71495i	0.245794	+	0.118368i
$986$	−9.61309	+	8.91964i	−0.306143	+	0.284059i
$987$		0			0
$988$	−15.5358			−0.494259
$989$	−13.8597	+	4.48429i	−0.440713	+	0.142592i
$990$		0			0
$991$	−0.746829	+	3.27207i	−0.0237238	+	0.103941i	−0.985404	−	0.170234i	$-0.945548\pi$
$991$	−0.746829	+	3.27207i	−0.0237238	+	0.103941i	0.961680	+	0.274175i	$0.0884047\pi$
$992$	21.7437	−	20.1752i	0.690362	−	0.640562i
$993$		0			0
$994$	−1.36078	−	0.205105i	−0.0431614	−	0.00650553i
$995$	14.1951	+	24.5866i	0.450013	+	0.779446i
$996$		0			0
$997$	33.5063	−	42.0156i	1.06116	−	1.33065i	0.119963	−	0.992778i	$-0.461722\pi$
$997$	33.5063	−	42.0156i	1.06116	−	1.33065i	0.941193	−	0.337869i	$-0.109706\pi$
$998$	0.765682	−	10.2173i	0.0242372	−	0.323424i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.271.2		36
3.2	odd	2		43.2.g.a.13.2	yes	36
12.11	even	2		688.2.bg.c.529.1		36
43.10	even	21	inner	387.2.y.c.10.2		36
129.53	odd	42		43.2.g.a.10.2	✓	36
129.71	even	42		1849.2.a.o.1.10		18
129.101	odd	42		1849.2.a.n.1.9		18
516.311	even	42		688.2.bg.c.225.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.2	✓	36	129.53	odd	42
43.2.g.a.13.2	yes	36	3.2	odd	2
387.2.y.c.10.2		36	43.10	even	21	inner
387.2.y.c.271.2		36	1.1	even	1	trivial
688.2.bg.c.225.1		36	516.311	even	42
688.2.bg.c.529.1		36	12.11	even	2
1849.2.a.n.1.9		18	129.101	odd	42
1849.2.a.o.1.10		18	129.71	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.188565 + 0.826155i) q^{2} +(1.15496 + 0.556200i) q^{4} +(3.39819 + 0.512194i) q^{5} +(-0.134521 + 0.232998i) q^{7} +(-1.73398 + 2.17435i) q^{8} +O(q^{10})\)	\(q+(-0.188565 + 0.826155i) q^{2} +(1.15496 + 0.556200i) q^{4} +(3.39819 + 0.512194i) q^{5} +(-0.134521 + 0.232998i) q^{7} +(-1.73398 + 2.17435i) q^{8} +(-1.06393 + 2.71085i) q^{10} +(2.96782 - 1.42923i) q^{11} +(-0.736485 - 1.87653i) q^{13} +(-0.167127 - 0.155071i) q^{14} +(0.129136 + 0.161931i) q^{16} +(-6.37398 + 0.960723i) q^{17} +(-0.449267 - 5.99506i) q^{19} +(3.63989 + 2.48164i) q^{20} +(0.621139 + 2.72139i) q^{22} +(1.83546 + 1.25139i) q^{23} +(6.50747 + 2.00729i) q^{25} +(1.68918 - 0.254603i) q^{26} +(-0.284961 + 0.194283i) q^{28} +(-1.75989 - 1.63294i) q^{29} +(-4.93996 + 1.52378i) q^{31} +(-5.16949 + 2.48950i) q^{32} +(0.408200 - 5.44706i) q^{34} +(-0.576470 + 0.722870i) q^{35} +(2.63757 + 4.56841i) q^{37} +(5.03756 + 0.759291i) q^{38} +(-7.00609 + 6.50071i) q^{40} +(0.643386 - 2.81886i) q^{41} +(-4.01778 + 5.18242i) q^{43} +4.22266 q^{44} +(-1.37995 + 1.28040i) q^{46} +(5.31835 + 2.56118i) q^{47} +(3.46381 + 5.99949i) q^{49} +(-2.88541 + 4.99768i) q^{50} +(0.193116 - 2.57696i) q^{52} +(-2.34453 + 5.97377i) q^{53} +(10.8173 - 3.33669i) q^{55} +(-0.273361 - 0.696512i) q^{56} +(1.68091 - 1.14603i) q^{58} +(-8.36244 - 10.4862i) q^{59} +(-9.50158 - 2.93085i) q^{61} +(-0.327374 - 4.36851i) q^{62} +(-0.989752 - 4.33638i) q^{64} +(-1.54156 - 6.75403i) q^{65} +(-0.950106 - 12.6783i) q^{67} +(-7.89606 - 2.43561i) q^{68} +(-0.488501 - 0.612561i) q^{70} +(4.98725 - 3.40025i) q^{71} +(0.609746 + 1.55361i) q^{73} +(-4.27157 + 1.31761i) q^{74} +(2.81557 - 7.17394i) q^{76} +(-0.0662286 + 0.883759i) q^{77} +(6.97172 - 12.0754i) q^{79} +(0.355887 + 0.616414i) q^{80} +(2.20750 + 1.06307i) q^{82} +(5.60384 - 5.19960i) q^{83} -22.1521 q^{85} +(-3.52387 - 4.29653i) q^{86} +(-2.03852 + 8.93135i) q^{88} +(1.32654 - 1.23085i) q^{89} +(0.536302 + 0.0808345i) q^{91} +(1.42386 + 2.46619i) q^{92} +(-3.11879 + 3.91084i) q^{94} +(1.54394 - 20.6024i) q^{95} +(2.36508 - 1.13896i) q^{97} +(-5.60966 + 1.73035i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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