LMFDB - Embedded newform 288.2.bc.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	288.13
Dual form			288.2.bc.a.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41394 - 0.0276581i) q^{2} +(-0.219683 - 1.71806i) q^{3} +(1.99847 + 0.0782141i) q^{4} +(-0.0865625 + 0.657507i) q^{5} +(0.263101 + 2.43532i) q^{6} +(-3.40174 - 0.911495i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(-2.90348 + 0.754859i) q^{9} +O(q^{10})$	\(q+(-1.41394 - 0.0276581i) q^{2} +(-0.219683 - 1.71806i) q^{3} +(1.99847 + 0.0782141i) q^{4} +(-0.0865625 + 0.657507i) q^{5} +(0.263101 + 2.43532i) q^{6} +(-3.40174 - 0.911495i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(-2.90348 + 0.754859i) q^{9} +(0.140580 - 0.927284i) q^{10} +(-3.13318 + 4.08325i) q^{11} +(-0.304653 - 3.45068i) q^{12} +(2.36536 - 1.81501i) q^{13} +(4.78466 + 1.38289i) q^{14} +(1.14866 + 0.00427652i) q^{15} +(3.98777 + 0.312617i) q^{16} -0.364422i q^{17} +(4.12623 - 0.987022i) q^{18} +(-4.46287 - 1.84858i) q^{19} +(-0.224419 + 1.30724i) q^{20} +(-0.818699 + 6.04465i) q^{21} +(4.54308 - 5.68682i) q^{22} +(-4.98224 + 1.33499i) q^{23} +(0.335323 + 4.88749i) q^{24} +(4.40481 + 1.18026i) q^{25} +(-3.39469 + 2.50090i) q^{26} +(1.93474 + 4.82253i) q^{27} +(-6.72699 - 2.08766i) q^{28} +(-5.78895 + 0.762130i) q^{29} +(-1.62401 - 0.0378164i) q^{30} +(-3.01601 + 5.22388i) q^{31} +(-5.62983 - 0.552317i) q^{32} +(7.70358 + 4.48599i) q^{33} +(-0.0100792 + 0.515272i) q^{34} +(0.893778 - 2.15777i) q^{35} +(-5.86156 + 1.28147i) q^{36} +(-7.56014 + 3.13151i) q^{37} +(6.25912 + 2.73722i) q^{38} +(-3.63793 - 3.66512i) q^{39} +(0.353471 - 1.84215i) q^{40} +(3.29929 - 0.884042i) q^{41} +(1.32478 - 8.52415i) q^{42} +(5.92133 - 7.71683i) q^{43} +(-6.58094 + 7.91518i) q^{44} +(-0.244993 - 1.97440i) q^{45} +(7.08153 - 1.74980i) q^{46} +(4.45774 - 2.57368i) q^{47} +(-0.338949 - 6.91991i) q^{48} +(4.67887 + 2.70134i) q^{49} +(-6.19550 - 1.79066i) q^{50} +(-0.626099 + 0.0800573i) q^{51} +(4.86907 - 3.44223i) q^{52} +(-3.65397 - 8.82145i) q^{53} +(-2.60223 - 6.87229i) q^{54} +(-2.41355 - 2.41355i) q^{55} +(9.45384 + 3.13789i) q^{56} +(-2.19556 + 8.07359i) q^{57} +(8.20633 - 0.917497i) q^{58} +(0.382404 - 2.90465i) q^{59} +(2.29522 + 0.0983875i) q^{60} +(-10.5019 + 1.38260i) q^{61} +(4.40895 - 7.30285i) q^{62} +(10.5649 + 0.0786691i) q^{63} +(7.94498 + 0.936655i) q^{64} +(0.988629 + 1.71236i) q^{65} +(-10.7683 - 6.55600i) q^{66} +(-4.48467 - 5.84453i) q^{67} +(0.0285029 - 0.728286i) q^{68} +(3.38811 + 8.26653i) q^{69} +(-1.32343 + 3.02624i) q^{70} +(5.87298 - 5.87298i) q^{71} +(8.32335 - 1.64981i) q^{72} +(5.72879 + 5.72879i) q^{73} +(10.7762 - 4.21868i) q^{74} +(1.06011 - 7.82702i) q^{75} +(-8.77433 - 4.04339i) q^{76} +(14.3801 - 11.0343i) q^{77} +(5.04245 + 5.28288i) q^{78} +(-4.12486 + 2.38149i) q^{79} +(-0.550739 + 2.59492i) q^{80} +(7.86038 - 4.38343i) q^{81} +(-4.68946 + 1.15873i) q^{82} +(1.08585 + 8.24788i) q^{83} +(-2.10892 + 12.0160i) q^{84} +(0.239610 + 0.0315453i) q^{85} +(-8.58586 + 10.7474i) q^{86} +(2.58112 + 9.77836i) q^{87} +(9.52400 - 11.0096i) q^{88} +(1.17717 - 1.17717i) q^{89} +(0.291798 + 2.79847i) q^{90} +(-9.70073 + 4.01817i) q^{91} +(-10.0613 + 2.27825i) q^{92} +(9.63752 + 4.03409i) q^{93} +(-6.37417 + 3.51574i) q^{94} +(1.60177 - 2.77435i) q^{95} +(0.287863 + 9.79373i) q^{96} +(0.00601054 + 0.0104106i) q^{97} +(-6.54094 - 3.94896i) q^{98} +(6.01486 - 14.2207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.41394	−	0.0276581i	−0.999809	−	0.0195573i
$2$	−1.41394	−	0.0276581i	−0.999809	−	0.0195573i
$3$	−0.219683	−	1.71806i	−0.126834	−	0.991924i
$3$	−0.219683	−	1.71806i	−0.126834	−	0.991924i
$4$	1.99847	+	0.0782141i	0.999235	+	0.0391070i
$5$	−0.0865625	+	0.657507i	−0.0387119	+	0.294046i	0.961127	+	0.276106i	$0.0890441\pi$
$5$	−0.0865625	+	0.657507i	−0.0387119	+	0.294046i	−0.999839	+	0.0179401i	$0.994289\pi$
$6$	0.263101	+	2.43532i	0.107411	+	0.994215i
$7$	−3.40174	−	0.911495i	−1.28574	−	0.344513i	−0.449698	−	0.893181i	$-0.648468\pi$
$7$	−3.40174	−	0.911495i	−1.28574	−	0.344513i	−0.836040	+	0.548668i	$0.815135\pi$
$8$	−2.82356	−	0.165864i	−0.998279	−	0.0586419i
$9$	−2.90348	+	0.754859i	−0.967826	+	0.251620i
$10$	0.140580	−	0.927284i	0.0444553	−	0.293233i
$11$	−3.13318	+	4.08325i	−0.944691	+	1.23114i	0.0281346	+	0.999604i	$0.491043\pi$
$11$	−3.13318	+	4.08325i	−0.944691	+	1.23114i	−0.972825	+	0.231541i	$0.925623\pi$
$12$	−0.304653	−	3.45068i	−0.0879459	−	0.996125i
$13$	2.36536	−	1.81501i	0.656034	−	0.503392i	−0.226275	−	0.974063i	$-0.572655\pi$
$13$	2.36536	−	1.81501i	0.656034	−	0.503392i	0.882309	+	0.470671i	$0.155988\pi$
$14$	4.78466	+	1.38289i	1.27876	+	0.369592i
$15$	1.14866	+	0.00427652i	0.296581	+	0.00110419i
$16$	3.98777	+	0.312617i	0.996941	+	0.0781542i
$17$		−	0.364422i		−	0.0883853i	−0.999023	−	0.0441926i	$-0.985928\pi$
$17$		−	0.364422i		−	0.0883853i	0.999023	−	0.0441926i	$-0.0140715\pi$
$18$	4.12623	−	0.987022i	0.972562	−	0.232643i
$19$	−4.46287	−	1.84858i	−1.02385	−	0.424094i	−0.193363	−	0.981127i	$-0.561939\pi$
$19$	−4.46287	−	1.84858i	−1.02385	−	0.424094i	−0.830490	+	0.557034i	$0.811939\pi$
$20$	−0.224419	+	1.30724i	−0.0501816	+	0.292307i
$21$	−0.818699	+	6.04465i	−0.178655	+	1.31905i
$22$	4.54308	−	5.68682i	0.968588	−	1.21243i
$23$	−4.98224	+	1.33499i	−1.03887	+	0.278364i	−0.737645	−	0.675189i	$-0.764062\pi$
$23$	−4.98224	+	1.33499i	−1.03887	+	0.278364i	−0.301224	+	0.953553i	$0.597395\pi$
$24$	0.335323	+	4.88749i	0.0684476	+	0.997655i
$25$	4.40481	+	1.18026i	0.880961	+	0.236053i
$26$	−3.39469	+	2.50090i	−0.665753	+	0.490466i
$27$	1.93474	+	4.82253i	0.372341	+	0.928096i
$28$	−6.72699	−	2.08766i	−1.27128	−	0.394531i
$29$	−5.78895	+	0.762130i	−1.07498	+	0.141524i	−0.647171	−	0.762345i	$-0.724048\pi$
$29$	−5.78895	+	0.762130i	−1.07498	+	0.141524i	−0.427810	+	0.903869i	$0.640715\pi$
$30$	−1.62401	−	0.0378164i	−0.296503	−	0.00690430i
$31$	−3.01601	+	5.22388i	−0.541691	+	0.938236i	0.457116	+	0.889407i	$0.348882\pi$
$31$	−3.01601	+	5.22388i	−0.541691	+	0.938236i	−0.998807	+	0.0488293i	$0.984451\pi$
$32$	−5.62983	−	0.552317i	−0.995222	−	0.0976367i
$33$	7.70358	+	4.48599i	1.34102	+	0.780910i
$34$	−0.0100792	+	0.515272i	−0.00172857	+	0.0883684i
$35$	0.893778	−	2.15777i	0.151076	−	0.364730i
$36$	−5.86156	+	1.28147i	−0.976926	+	0.213578i
$37$	−7.56014	+	3.13151i	−1.24288	+	0.514817i	−0.904613	−	0.426234i	$-0.859840\pi$
$37$	−7.56014	+	3.13151i	−1.24288	+	0.514817i	−0.338265	+	0.941051i	$0.609840\pi$
$38$	6.25912	+	2.73722i	1.01536	+	0.444036i
$39$	−3.63793	−	3.66512i	−0.582534	−	0.586888i
$40$	0.353471	−	1.84215i	0.0558887	−	0.291270i
$41$	3.29929	−	0.884042i	0.515263	−	0.138064i	0.00818826	−	0.999966i	$-0.497394\pi$
$41$	3.29929	−	0.884042i	0.515263	−	0.138064i	0.507074	+	0.861902i	$0.330727\pi$
$42$	1.32478	−	8.52415i	0.204418	−	1.31530i
$43$	5.92133	−	7.71683i	0.902995	−	1.17681i	−0.0806598	−	0.996742i	$-0.525703\pi$
$43$	5.92133	−	7.71683i	0.902995	−	1.17681i	0.983655	−	0.180064i	$-0.0576306\pi$
$44$	−6.58094	+	7.91518i	−0.992114	+	1.19326i
$45$	−0.244993	−	1.97440i	−0.0365214	−	0.294326i
$46$	7.08153	−	1.74980i	1.04411	−	0.257993i
$47$	4.45774	−	2.57368i	0.650228	−	0.375409i	−0.138316	−	0.990388i	$-0.544169\pi$
$47$	4.45774	−	2.57368i	0.650228	−	0.375409i	0.788543	+	0.614979i	$0.210836\pi$
$48$	−0.338949	−	6.91991i	−0.0489231	−	0.998803i
$49$	4.67887	+	2.70134i	0.668409	+	0.385906i
$50$	−6.19550	−	1.79066i	−0.876176	−	0.253237i
$51$	−0.626099	+	0.0800573i	−0.0876715	+	0.0112103i
$52$	4.86907	−	3.44223i	0.675218	−	0.477352i
$53$	−3.65397	−	8.82145i	−0.501911	−	1.21172i	−0.948442	−	0.316952i	$-0.897341\pi$
$53$	−3.65397	−	8.82145i	−0.501911	−	1.21172i	0.446531	−	0.894768i	$-0.352659\pi$
$54$	−2.60223	−	6.87229i	−0.354119	−	0.935201i
$55$	−2.41355	−	2.41355i	−0.325443	−	0.325443i
$56$	9.45384	+	3.13789i	1.26332	+	0.419318i
$57$	−2.19556	+	8.07359i	−0.290809	+	1.06937i
$58$	8.20633	−	0.917497i	1.07754	−	0.120473i
$59$	0.382404	−	2.90465i	0.0497848	−	0.378153i	−0.948356	−	0.317207i	$-0.897255\pi$
$59$	0.382404	−	2.90465i	0.0497848	−	0.378153i	0.998141	−	0.0609460i	$-0.0194118\pi$
$60$	2.29522	+	0.0983875i	0.296311	+	0.0127018i
$61$	−10.5019	+	1.38260i	−1.34463	+	0.177024i	−0.768247	−	0.640154i	$-0.778871\pi$
$61$	−10.5019	+	1.38260i	−1.34463	+	0.177024i	−0.576386	+	0.817178i	$0.695537\pi$
$62$	4.40895	−	7.30285i	0.559937	−	0.927463i
$63$	10.5649	+	0.0786691i	1.33106	+	0.00991137i
$64$	7.94498	+	0.936655i	0.993122	+	0.117082i
$65$	0.988629	+	1.71236i	0.122624	+	0.212392i
$66$	−10.7683	−	6.55600i	−1.32549	−	0.806987i
$67$	−4.48467	−	5.84453i	−0.547889	−	0.714023i	0.434541	−	0.900652i	$-0.356911\pi$
$67$	−4.48467	−	5.84453i	−0.547889	−	0.714023i	−0.982431	+	0.186629i	$0.940244\pi$
$68$	0.0285029	−	0.728286i	0.00345649	−	0.0883176i
$69$	3.38811	+	8.26653i	0.407880	+	0.995173i
$70$	−1.32343	+	3.02624i	−0.158180	+	0.361705i
$71$	5.87298	−	5.87298i	0.696995	−	0.696995i	−0.266766	−	0.963761i	$-0.585955\pi$
$71$	5.87298	−	5.87298i	0.696995	−	0.696995i	0.963761	+	0.266766i	$0.0859552\pi$
$72$	8.32335	−	1.64981i	0.980916	−	0.194431i
$73$	5.72879	+	5.72879i	0.670504	+	0.670504i	0.957832	−	0.287328i	$-0.0927669\pi$
$73$	5.72879	+	5.72879i	0.670504	+	0.670504i	−0.287328	+	0.957832i	$0.592767\pi$
$74$	10.7762	−	4.21868i	1.25271	−	0.490411i
$75$	1.06011	−	7.82702i	0.122411	−	0.903786i
$76$	−8.77433	−	4.04339i	−1.00648	−	0.463809i
$77$	14.3801	−	11.0343i	1.63877	−	1.25747i
$78$	5.04245	+	5.28288i	0.570945	+	0.598169i
$79$	−4.12486	+	2.38149i	−0.464083	+	0.267939i	−0.713760	−	0.700391i	$-0.753009\pi$
$79$	−4.12486	+	2.38149i	−0.464083	+	0.267939i	0.249676	+	0.968329i	$0.419676\pi$
$80$	−0.550739	+	2.59492i	−0.0615745	+	0.290121i
$81$	7.86038	−	4.38343i	0.873375	−	0.487048i
$82$	−4.68946	+	1.15873i	−0.517864	+	0.127961i
$83$	1.08585	+	8.24788i	0.119188	+	0.905322i	0.941672	+	0.336533i	$0.109254\pi$
$83$	1.08585	+	8.24788i	0.119188	+	0.905322i	−0.822484	+	0.568789i	$0.807412\pi$
$84$	−2.10892	+	12.0160i	−0.230102	+	1.31106i
$85$	0.239610	+	0.0315453i	0.0259894	+	0.00342156i
$86$	−8.58586	+	10.7474i	−0.925837	+	1.15892i
$87$	2.58112	+	9.77836i	0.276725	+	1.04835i
$88$	9.52400	−	11.0096i	1.01526	−	1.17363i
$89$	1.17717	−	1.17717i	0.124780	−	0.124780i	−0.641959	−	0.766739i	$-0.721878\pi$
$89$	1.17717	−	1.17717i	0.124780	−	0.124780i	0.766739	+	0.641959i	$0.221878\pi$
$90$	0.291798	+	2.79847i	0.0307582	+	0.294984i
$91$	−9.70073	+	4.01817i	−1.01691	+	0.421219i
$92$	−10.0613	+	2.27825i	−1.04896	+	0.237524i
$93$	9.63752	+	4.03409i	0.999364	+	0.418316i
$94$	−6.37417	+	3.51574i	−0.657445	+	0.362621i
$95$	1.60177	−	2.77435i	0.164338	−	0.284643i
$96$	0.287863	+	9.79373i	0.0293799	+	0.999568i
$97$	0.00601054	+	0.0104106i	0.000610278	+	0.00105703i	0.866330	−	0.499471i	$-0.166472\pi$
$97$	0.00601054	+	0.0104106i	0.000610278	+	0.00105703i	−0.865720	+	0.500528i	$0.833139\pi$
$98$	−6.54094	−	3.94896i	−0.660734	−	0.398905i
$99$	6.01486	−	14.2207i	0.604516	−	1.42924i
$100$	8.71056	+	2.70324i	0.871056	+	0.270324i
$101$	−11.9413	−	9.16289i	−1.18820	−	0.911742i	−0.190652	−	0.981658i	$-0.561060\pi$
$101$	−11.9413	−	9.16289i	−1.18820	−	0.911742i	−0.997553	+	0.0699162i	$0.977727\pi$
$102$	0.887483	−	0.0958797i	0.0878739	−	0.00949351i
$103$	−1.58550	−	5.91718i	−0.156224	−	0.583037i	−0.998997	−	0.0447682i	$-0.985745\pi$
$103$	−1.58550	−	5.91718i	−0.156224	−	0.583037i	0.842773	−	0.538269i	$-0.180922\pi$
$104$	−6.97979	+	4.73245i	−0.684425	+	0.464055i
$105$	−3.90353	−	1.06154i	−0.380946	−	0.103596i
$106$	4.92252	+	12.5741i	0.478117	+	1.22130i
$107$	−6.78660	−	16.3843i	−0.656086	−	1.58393i	−0.803799	−	0.594901i	$-0.797191\pi$
$107$	−6.78660	−	16.3843i	−0.656086	−	1.58393i	0.147714	−	0.989030i	$-0.452809\pi$
$108$	3.48933	+	9.78900i	0.335761	+	0.941947i
$109$	−1.32634	−	0.549387i	−0.127040	−	0.0526217i	0.318258	−	0.948004i	$-0.396902\pi$
$109$	−1.32634	−	0.549387i	−0.127040	−	0.0526217i	−0.445298	+	0.895382i	$0.646902\pi$
$110$	3.34586	+	3.47937i	0.319016	+	0.331745i
$111$	7.04097	+	12.3008i	0.668299	+	1.16754i
$112$	−13.2804	−	4.69827i	−1.25488	−	0.443945i
$113$	2.03598	+	1.17547i	0.191529	+	0.110579i	0.592698	−	0.805425i	$-0.298063\pi$
$113$	2.03598	+	1.17547i	0.191529	+	0.110579i	−0.401169	+	0.916004i	$0.631396\pi$
$114$	3.32770	−	11.3549i	0.311668	−	1.06348i
$115$	−0.446489	−	3.39142i	−0.0416353	−	0.316251i
$116$	−11.6287	+	1.07032i	−1.07969	+	0.0993764i
$117$	−5.49771	+	7.05535i	−0.508263	+	0.652267i
$118$	−0.621035	+	4.09643i	−0.0571709	+	0.377107i
$119$	−0.332169	+	1.23967i	−0.0304498	+	0.113640i
$120$	−3.24259	−	0.202596i	−0.296006	−	0.0184944i
$121$	−4.00904	−	14.9619i	−0.364458	−	1.36018i
$122$	14.8873	−	1.66446i	1.34784	−	0.150693i
$123$	−2.24364	−	5.47418i	−0.202302	−	0.493590i
$124$	−6.43598	+	10.2039i	−0.577968	+	0.916335i
$125$	−2.42627	+	5.85752i	−0.217012	+	0.523913i
$126$	−14.9361	−	0.403440i	−1.33061	−	0.0359413i
$127$	−6.25944			−0.555435			−0.277718	−	0.960663i	$-0.589578\pi$
$127$	−6.25944			−0.555435			−0.277718	+	0.960663i	$0.589578\pi$
$128$	−11.2078	−	1.54412i	−0.990643	−	0.136482i
$129$	−14.5588	−	8.47797i	−1.28183	−	0.746443i
$130$	−1.35050	−	2.44852i	−0.118447	−	0.214749i
$131$	2.50305	+	3.26204i	0.218693	+	0.285006i	0.889797	−	0.456358i	$-0.150846\pi$
$131$	2.50305	+	3.26204i	0.218693	+	0.285006i	−0.671104	+	0.741363i	$0.734180\pi$
$132$	15.0445	+	9.56764i	1.30946	+	0.832756i
$133$	13.4966	+	10.3563i	1.17030	+	0.898004i
$134$	6.17942	+	8.38788i	0.533820	+	0.724602i
$135$	−3.33832	+	0.854655i	−0.287317	+	0.0735570i
$136$	−0.0604445	+	1.02897i	−0.00518308	+	0.0882332i
$137$	−2.41484	+	9.01232i	−0.206314	+	0.769974i	0.782731	+	0.622360i	$0.213826\pi$
$137$	−2.41484	+	9.01232i	−0.206314	+	0.769974i	−0.989045	+	0.147614i	$0.952841\pi$
$138$	−4.56195	−	11.7821i	−0.388339	−	1.00296i
$139$	21.1323	+	2.78211i	1.79241	+	0.235976i	0.952028	−	0.306012i	$-0.0989946\pi$
$139$	21.1323	+	2.78211i	1.79241	+	0.235976i	0.840387	+	0.541987i	$0.182328\pi$
$140$	1.95496	−	4.24233i	0.165224	−	0.358543i
$141$	−5.40103	−	7.09328i	−0.454848	−	0.597362i
$142$	−8.46650	+	8.14163i	−0.710493	+	0.683230i
$143$			15.3451i			1.28322i
$144$	−11.8144	+	2.10252i	−0.984531	+	0.175210i
$145$		−	3.87225i		−	0.321573i
$146$	−7.94174	−	8.25863i	−0.657263	−	0.683489i
$147$	3.61321	−	8.63203i	0.298013	−	0.711957i
$148$	−15.3536	+	5.66692i	−1.26206	+	0.465818i
$149$	1.06487	+	0.140193i	0.0872375	+	0.0114850i	0.174019	−	0.984742i	$-0.444325\pi$
$149$	1.06487	+	0.140193i	0.0872375	+	0.0114850i	−0.0867811	+	0.996227i	$0.527658\pi$
$150$	−1.71541	+	11.0376i	−0.140063	+	0.901219i
$151$	1.78350	−	6.65612i	0.145139	−	0.541667i	−0.854610	−	0.519271i	$-0.826204\pi$
$151$	1.78350	−	6.65612i	0.145139	−	0.541667i	0.999749	−	0.0223966i	$-0.00712966\pi$
$152$	12.2946	+	5.95981i	0.997221	+	0.483405i
$153$	0.275087	+	1.05809i	0.0222395	+	0.0855416i
$154$	−20.6379	+	15.2041i	−1.66305	+	1.22518i
$155$	−3.17367	−	2.43524i	−0.254915	−	0.195603i
$156$	−6.98362	−	7.60916i	−0.559137	−	0.609221i
$157$	4.21661	+	5.49519i	0.336522	+	0.438564i	0.930708	−	0.365764i	$-0.119192\pi$
$157$	4.21661	+	5.49519i	0.336522	+	0.438564i	−0.594186	+	0.804328i	$0.702526\pi$
$158$	5.89819	−	3.25321i	0.469235	−	0.258811i
$159$	−14.3531	+	8.21567i	−1.13827	+	0.651545i
$160$	0.850484	−	3.65384i	0.0672367	−	0.288862i
$161$	18.1651			1.43161
$162$	−11.2354	+	5.98052i	−0.882733	+	0.469874i
$163$	−8.00966	+	19.3370i	−0.627365	+	1.51459i	0.215520	+	0.976499i	$0.430855\pi$
$163$	−8.00966	+	19.3370i	−0.627365	+	1.51459i	−0.842885	+	0.538094i	$0.819145\pi$
$164$	6.66268	−	1.50868i	0.520268	−	0.117808i
$165$	−3.61641	+	4.67684i	−0.281537	+	0.364092i
$166$	−1.30721	−	11.6921i	−0.101460	−	0.907480i
$167$	−0.742811	−	2.77221i	−0.0574804	−	0.214520i	0.931212	−	0.364478i	$-0.118753\pi$
$167$	−0.742811	−	2.77221i	−0.0574804	−	0.214520i	−0.988692	+	0.149958i	$0.952086\pi$
$168$	3.31424	−	16.9316i	0.255699	−	1.30630i
$169$	−1.06395	+	3.97073i	−0.0818427	+	0.305441i
$170$	−0.337922	−	0.0512304i	−0.0259175	−	0.00392919i
$171$	14.3533	+	1.99848i	1.09762	+	0.152828i
$172$	12.4372	−	14.9587i	0.948326	−	1.14059i
$173$	−2.50732	−	19.0450i	−0.190628	−	1.44797i	−0.772671	−	0.634807i	$-0.781080\pi$
$173$	−2.50732	−	19.0450i	−0.190628	−	1.44797i	0.582042	−	0.813159i	$-0.302254\pi$
$174$	−3.37911	−	13.8974i	−0.256170	−	1.05356i
$175$	−13.9082	−	8.02992i	−1.05136	−	0.607005i
$176$	−13.7709	+	15.3035i	−1.03802	+	1.15355i
$177$	−5.07438	−	0.0188923i	−0.381414	−	0.00142003i
$178$	−1.69701	+	1.63190i	−0.127196	+	0.122316i
$179$	9.45002	+	3.91433i	0.706328	+	0.292571i	0.706784	−	0.707429i	$-0.250145\pi$
$179$	9.45002	+	3.91433i	0.706328	+	0.292571i	−0.000456333		1.00000i	$0.500145\pi$
$180$	−0.335185	−	3.96494i	−0.0249832	−	0.295529i
$181$	3.88557	+	9.38059i	0.288812	+	0.697254i	0.999983	−	0.00576488i	$-0.00183503\pi$
$181$	3.88557	+	9.38059i	0.288812	+	0.697254i	−0.711171	+	0.703019i	$0.751835\pi$
$182$	13.8274	−	5.41317i	1.02496	−	0.401251i
$183$	4.68249	+	17.7392i	0.346140	+	1.31132i
$184$	14.2891	−	2.94304i	1.05340	−	0.216964i
$185$	−1.40457	−	5.24192i	−0.103266	−	0.385393i
$186$	−13.5153	−	5.97053i	−0.990992	−	0.437781i
$187$	1.48802	+	1.14180i	0.108815	+	0.0834967i
$188$	9.10995	−	4.79476i	0.664412	−	0.349694i
$189$	−2.18578	−	18.1685i	−0.158992	−	1.32157i
$190$	−2.34155	+	3.87847i	−0.169874	+	0.281374i
$191$	8.97326	+	15.5421i	0.649283	+	1.12459i	0.983295	+	0.182022i	$0.0582641\pi$
$191$	8.97326	+	15.5421i	0.649283	+	1.12459i	−0.334012	+	0.942569i	$0.608403\pi$
$192$	−0.136145	−	13.8557i	−0.00982545	−	0.999952i
$193$	2.28960	−	3.96571i	0.164809	−	0.285458i	−0.771778	−	0.635892i	$-0.780632\pi$
$193$	2.28960	−	3.96571i	0.164809	−	0.285458i	0.936588	+	0.350434i	$0.113966\pi$
$194$	−0.00821062	−	0.0148862i	−0.000589488	−	0.00106876i
$195$	2.72475	−	2.07470i	0.195123	−	0.148572i
$196$	9.13929	+	5.76451i	0.652807	+	0.411751i
$197$	−6.24771	+	2.58789i	−0.445131	+	0.184379i	−0.593978	−	0.804481i	$-0.702444\pi$
$197$	−6.24771	+	2.58789i	−0.445131	+	0.184379i	0.148848	+	0.988860i	$0.452444\pi$
$198$	−8.89799	+	19.9409i	−0.632353	+	1.41714i
$199$	−10.8310	+	10.8310i	−0.767787	+	0.767787i	−0.977716	−	0.209930i	$-0.932676\pi$
$199$	−10.8310	+	10.8310i	−0.767787	+	0.767787i	0.209930	+	0.977716i	$0.432676\pi$
$200$	−12.2415	−	4.06315i	−0.865603	−	0.287308i
$201$	−9.05607	+	8.98889i	−0.638766	+	0.634027i
$202$	16.6309	+	13.2861i	1.17015	+	0.934805i
$203$	20.3872	+	2.68403i	1.43090	+	0.188382i
$204$	−1.25750	+	0.111022i	−0.0880428	+	0.00777312i
$205$	0.295670	+	2.24583i	0.0206505	+	0.156856i
$206$	2.07815	+	8.41041i	0.144792	+	0.585981i
$207$	13.4581	−	7.63699i	0.935403	−	0.530808i
$208$	9.99992	−	6.49837i	0.693369	−	0.450581i
$209$	21.5312	−	12.4311i	1.48934	−	0.859874i
$210$	5.49001	+	1.60892i	0.378847	+	0.111026i
$211$	−20.6356	+	15.8343i	−1.42062	+	1.09008i	−0.439157	+	0.898411i	$0.644723\pi$
$211$	−20.6356	+	15.8343i	−1.42062	+	1.09008i	−0.981460	+	0.191667i	$0.938611\pi$
$212$	−6.61238	−	17.9152i	−0.454140	−	1.23042i
$213$	−11.3803	−	8.79996i	−0.779769	−	0.602963i
$214$	9.14271	+	23.3542i	0.624983	+	1.59646i
$215$	4.56131	+	4.56131i	0.311079	+	0.311079i
$216$	−4.66297	−	13.9376i	−0.317275	−	0.948334i
$217$	15.0212	−	15.0212i	1.01971	−	1.01971i
$218$	1.86017	+	0.813486i	0.125987	+	0.0550962i
$219$	8.58391	−	11.1009i	0.580047	−	0.750132i
$220$	−4.63463	−	5.01218i	−0.312467	−	0.337921i
$221$	−0.661428	−	0.861990i	−0.0444925	−	0.0579837i
$222$	−9.61531	−	17.5874i	−0.645337	−	1.18039i
$223$	7.49609	+	12.9836i	0.501976	+	0.869447i	0.999997	+	0.00228276i	$0.000726627\pi$
$223$	7.49609	+	12.9836i	0.501976	+	0.869447i	−0.498022	+	0.867165i	$0.665940\pi$
$224$	18.6478	+	7.01040i	1.24596	+	0.468402i
$225$	−13.6802	−	0.101866i	−0.912013	−	0.00679107i
$226$	−2.84624	−	1.71836i	−0.189329	−	0.114304i
$227$	−26.0249	+	3.42624i	−1.72733	+	0.227408i	−0.927764	−	0.373168i	$-0.878271\pi$
$227$	−26.0249	+	3.42624i	−1.72733	+	0.227408i	−0.799568	+	0.600576i	$0.794938\pi$
$228$	−5.01923	+	15.9631i	−0.332407	+	1.05718i
$229$	−1.82254	+	13.8436i	−0.120437	+	0.914810i	0.819408	+	0.573210i	$0.194302\pi$
$229$	−1.82254	+	13.8436i	−0.120437	+	0.914810i	−0.939845	+	0.341600i	$0.889031\pi$
$230$	0.537509	+	4.80762i	0.0354423	+	0.317005i
$231$	−22.1167	−	22.2820i	−1.45517	−	1.46604i
$232$	16.4719	−	1.19174i	1.08143	−	0.0782415i
$233$	−10.0276	−	10.0276i	−0.656932	−	0.656932i	0.297721	−	0.954653i	$-0.403773\pi$
$233$	−10.0276	−	10.0276i	−0.656932	−	0.656932i	−0.954653	+	0.297721i	$0.903773\pi$
$234$	7.96858	−	9.82381i	0.520923	−	0.642202i
$235$	1.30634	+	3.15378i	0.0852161	+	0.205730i
$236$	0.991408	−	5.77495i	0.0645352	−	0.375917i
$237$	4.99771	+	6.56360i	0.324636	+	0.426352i
$238$	0.503954	−	1.74364i	0.0326665	−	0.113023i
$239$	14.6640	+	8.46629i	0.948538	+	0.547639i	0.892627	−	0.450797i	$-0.148860\pi$
$239$	14.6640	+	8.46629i	0.948538	+	0.547639i	0.0559118	+	0.998436i	$0.482193\pi$
$240$	4.57923	+	0.376143i	0.295588	+	0.0242799i
$241$	−9.10955	+	5.25940i	−0.586798	+	0.338788i	−0.763830	−	0.645417i	$-0.776684\pi$
$241$	−9.10955	+	5.25940i	−0.586798	+	0.338788i	0.177032	+	0.984205i	$0.443350\pi$
$242$	5.25473	+	21.2662i	0.337787	+	1.36704i
$243$	−9.25780	−	12.5417i	−0.593888	−	0.804547i
$244$	−21.0959	+	1.94169i	−1.35053	+	0.124304i
$245$	−2.18117	+	2.84255i	−0.139350	+	0.181604i
$246$	3.02097	+	7.80223i	0.192610	+	0.497452i
$247$	−13.9115	+	3.72758i	−0.885168	+	0.237180i
$248$	9.38233	−	14.2497i	0.595779	−	0.904856i
$249$	13.9318	−	3.67748i	0.882894	−	0.233051i
$250$	3.59261	−	8.21510i	0.227217	−	0.519568i
$251$	1.80970	−	0.749602i	0.114227	−	0.0473144i	−0.324838	−	0.945770i	$-0.605310\pi$
$251$	1.80970	−	0.749602i	0.114227	−	0.0473144i	0.439065	+	0.898455i	$0.355310\pi$
$252$	21.1076	+	0.983545i	1.32965	+	0.0619575i
$253$	10.1592	−	24.5265i	0.638703	−	1.54197i
$254$	8.85049	+	0.173124i	0.555329	+	0.0108628i
$255$	0.00155846	−	0.418595i	9.75944e−5	−	0.0262134i
$256$	15.8045	+	2.49329i	0.987784	+	0.155830i
$257$	−7.85438	+	13.6042i	−0.489943	+	0.848606i	−0.999933	−	0.0115743i	$-0.996316\pi$
$257$	−7.85438	+	13.6042i	−0.489943	+	0.848606i	0.509990	+	0.860180i	$0.329649\pi$
$258$	20.3509	+	12.3900i	1.26699	+	0.771370i
$259$	28.5720	−	3.76158i	1.77538	−	0.233733i
$260$	1.84181	+	3.49942i	0.114224	+	0.217025i
$261$	16.2328	−	6.58267i	1.00479	−	0.407457i
$262$	−3.44895	−	4.68157i	−0.213077	−	0.289228i
$263$	12.2128	+	3.27241i	0.753075	+	0.201786i	0.614881	−	0.788620i	$-0.289204\pi$
$263$	12.2128	+	3.27241i	0.753075	+	0.201786i	0.138193	+	0.990405i	$0.455871\pi$
$264$	−21.0074	−	13.9442i	−1.29292	−	0.858206i
$265$	6.11647	−	1.63890i	0.375732	−	0.100677i
$266$	−18.7970	−	15.0165i	−1.15252	−	0.920720i
$267$	−2.28106	−	1.76385i	−0.139599	−	0.107946i
$268$	−8.50535	−	12.0309i	−0.519547	−	0.734904i
$269$	1.03549	+	0.428914i	0.0631350	+	0.0261514i	0.414027	−	0.910264i	$-0.364122\pi$
$269$	1.03549	+	0.428914i	0.0631350	+	0.0261514i	−0.350892	+	0.936416i	$0.614122\pi$
$270$	4.74384	−	1.11610i	0.288701	−	0.0679238i
$271$		−	11.2278i		−	0.682043i	−0.940055	−	0.341022i	$-0.889227\pi$
$271$		−	11.2278i		−	0.682043i	0.940055	−	0.341022i	$-0.110773\pi$
$272$	0.113924	−	1.45323i	0.00690768	−	0.0881149i
$273$	9.03456	+	15.7837i	0.546797	+	0.955275i
$274$	3.66372	−	12.6761i	0.221333	−	0.765792i
$275$	−18.6204	+	14.2879i	−1.12285	+	0.861594i
$276$	6.12447	+	16.7854i	0.368650	+	1.01036i
$277$	5.42877	−	7.07491i	0.326183	−	0.425090i	−0.601260	−	0.799053i	$-0.705335\pi$
$277$	5.42877	−	7.07491i	0.326183	−	0.425090i	0.927444	+	0.373963i	$0.122001\pi$
$278$	−29.8029	−	4.51823i	−1.78746	−	0.270985i
$279$	4.81362	−	17.4441i	0.288184	−	1.04435i
$280$	−2.88153	+	5.94435i	−0.172204	+	0.355243i
$281$	−17.8390	−	4.77995i	−1.06419	−	0.285148i	−0.316085	−	0.948731i	$-0.602368\pi$
$281$	−17.8390	−	4.77995i	−1.06419	−	0.285148i	−0.748103	+	0.663583i	$0.769035\pi$
$282$	7.44056	+	10.1789i	0.443079	+	0.606143i
$283$	3.34338	−	25.3955i	0.198743	−	1.50960i	−0.543463	−	0.839433i	$-0.682887\pi$
$283$	3.34338	−	25.3955i	0.198743	−	1.50960i	0.742206	−	0.670171i	$-0.233779\pi$
$284$	12.1963	−	11.2776i	0.723719	−	0.669204i
$285$	−5.11839	−	2.14247i	−0.303187	−	0.126909i
$286$	0.424417	−	21.6971i	0.0250963	−	1.28298i
$287$	−12.0291			−0.710058
$288$	16.7630	−	2.64608i	0.987769	−	0.155922i
$289$	16.8672			0.992188
$290$	−0.107099	+	5.47514i	−0.00628908	+	0.321511i
$291$	0.0165656	−	0.0126135i	0.000971091	−	0.000739417i
$292$	11.0007	+	11.8969i	0.643770	+	0.696213i
$293$	0.149428	−	1.13502i	0.00872967	−	0.0663084i	−0.986526	−	0.163607i	$-0.947687\pi$
$293$	0.149428	−	1.13502i	0.00872967	−	0.0663084i	0.995255	+	0.0972990i	$0.0310203\pi$
$294$	−5.34762	+	12.1053i	−0.311880	+	0.705993i
$295$	1.87673	+	0.502867i	0.109267	+	0.0292781i
$296$	21.8659	−	7.58805i	1.27093	−	0.441046i
$297$	−25.7535	−	7.20985i	−1.49437	−	0.418358i
$298$	−1.50179	−	0.227677i	−0.0869962	−	0.0131890i
$299$	−9.36180	+	12.2005i	−0.541407	+	0.705575i
$300$	2.73077	−	15.5591i	0.157661	−	0.898308i
$301$	−27.1767	+	20.8534i	−1.56644	+	1.20197i
$302$	−2.70587	+	9.36204i	−0.155705	+	0.538725i
$303$	−13.1191	+	22.5288i	−0.753673	+	1.29425i
$304$	−17.2190	−	8.76688i	−0.987576	−	0.502815i
$305$		−	7.02477i		−	0.402237i
$306$	−0.359692	−	1.50369i	−0.0205622	−	0.0859602i
$307$	0.619785	+	0.256723i	0.0353730	+	0.0146520i	0.400300	−	0.916384i	$-0.368906\pi$
$307$	0.619785	+	0.256723i	0.0353730	+	0.0146520i	−0.364927	+	0.931036i	$0.618906\pi$
$308$	29.6013	−	20.9269i	1.68669	−	1.19242i
$309$	−9.81778	+	4.02390i	−0.558514	+	0.228912i
$310$	4.42003	+	3.53107i	0.251041	+	0.200551i
$311$	12.6882	−	3.39980i	0.719484	−	0.192785i	0.119543	−	0.992829i	$-0.461857\pi$
$311$	12.6882	−	3.39980i	0.719484	−	0.192785i	0.599941	+	0.800044i	$0.295191\pi$
$312$	9.66399	+	10.9521i	0.547116	+	0.620039i
$313$	−25.5103	−	6.83546i	−1.44193	−	0.386363i	−0.548718	−	0.836007i	$-0.684884\pi$
$313$	−25.5103	−	6.83546i	−1.44193	−	0.386363i	−0.893208	+	0.449644i	$0.851551\pi$
$314$	−5.81006	−	7.88651i	−0.327880	−	0.445061i
$315$	−0.966253	+	6.93972i	−0.0544422	+	0.391009i
$316$	−8.42968	+	4.43672i	−0.474207	+	0.249585i
$317$	−17.2306	+	2.26846i	−0.967768	+	0.127409i	−0.597809	−	0.801639i	$-0.703962\pi$
$317$	−17.2306	+	2.26846i	−0.967768	+	0.127409i	−0.369960	+	0.929048i	$0.620628\pi$
$318$	20.5217	−	11.2195i	1.15080	−	0.629159i
$319$	15.0259	−	26.0256i	0.841288	−	1.45715i
$320$	−1.30359	+	5.14280i	−0.0728731	+	0.287491i
$321$	−26.6584	+	15.2592i	−1.48792	+	0.851684i
$322$	−25.6845	−	0.502414i	−1.43134	−	0.0279984i
$323$	−0.673663	+	1.62637i	−0.0374836	+	0.0904935i
$324$	16.0516	−	8.14537i	0.891754	−	0.452520i
$325$	12.5612	−	5.20300i	0.696768	−	0.288611i
$326$	11.8600	−	27.1199i	0.656866	−	1.50203i
$327$	−0.652507	+	2.39942i	−0.0360837	+	0.132688i
$328$	−9.46238	+	1.94891i	−0.522472	+	0.107611i
$329$	−17.5100	+	4.69178i	−0.965356	+	0.258666i
$330$	5.24275	−	6.51276i	0.288604	−	0.358516i
$331$	−8.90453	+	11.6046i	−0.489437	+	0.637847i	−0.971146	−	0.238484i	$-0.923350\pi$
$331$	−8.90453	+	11.6046i	−0.489437	+	0.637847i	0.481709	+	0.876331i	$0.340016\pi$
$332$	1.52495	+	16.5681i	0.0836923	+	0.909291i
$333$	19.5868	−	14.7991i	1.07335	−	0.810986i
$334$	0.973618	+	3.94029i	0.0532740	+	0.215603i
$335$	4.23103	−	2.44279i	0.231166	−	0.133464i
$336$	−5.15444	+	23.8487i	−0.281198	+	1.30105i
$337$	28.8231	+	16.6410i	1.57010	+	0.906495i	0.996156	+	0.0875974i	$0.0279189\pi$
$337$	28.8231	+	16.6410i	1.57010	+	0.906495i	0.573940	+	0.818898i	$0.305414\pi$
$338$	1.61419	−	5.58496i	0.0878006	−	0.303782i
$339$	1.57226	−	3.75617i	0.0853937	−	0.204007i
$340$	0.476386	+	0.0817831i	0.0258357	+	0.00443531i
$341$	−11.8807	−	28.6825i	−0.643374	−	1.55324i
$342$	−20.2394	−	3.22272i	−1.09442	−	0.174265i
$343$	3.97770	+	3.97770i	0.214776	+	0.214776i
$344$	−17.9992	+	20.8068i	−0.970451	+	1.12183i
$345$	−5.72858	+	1.51213i	−0.308417	+	0.0814105i
$346$	3.01846	+	26.9979i	0.162274	+	1.45142i
$347$	−3.08034	+	23.3975i	−0.165362	+	1.25605i	0.684489	+	0.729023i	$0.260025\pi$
$347$	−3.08034	+	23.3975i	−0.165362	+	1.25605i	−0.849851	+	0.527023i	$0.823308\pi$
$348$	4.39349	+	19.7436i	0.235516	+	1.05837i
$349$	−14.0711	+	1.85250i	−0.753211	+	0.0991622i	−0.497348	−	0.867551i	$-0.665693\pi$
$349$	−14.0711	+	1.85250i	−0.753211	+	0.0991622i	−0.255863	+	0.966713i	$0.582360\pi$
$350$	19.4433	+	11.7385i	1.03929	+	0.627450i
$351$	13.3293	+	7.89547i	0.711465	+	0.421429i
$352$	19.8945	−	21.2575i	1.06038	−	1.13303i
$353$	5.11951	+	8.86725i	0.272484	+	0.471956i	0.969497	−	0.245102i	$-0.0788215\pi$
$353$	5.11951	+	8.86725i	0.272484	+	0.471956i	−0.697013	+	0.717058i	$0.745488\pi$
$354$	7.17436	+	0.167060i	0.381313	+	0.00887916i
$355$	3.35315	+	4.36991i	0.177967	+	0.231931i
$356$	2.44461	−	2.26047i	0.129564	−	0.119805i
$357$	2.20280	+	0.298352i	0.116585	+	0.0157905i
$358$	−13.2535	−	5.79601i	−0.700471	−	0.306328i
$359$	7.16055	−	7.16055i	0.377919	−	0.377919i	−0.492432	−	0.870351i	$-0.663892\pi$
$359$	7.16055	−	7.16055i	0.377919	−	0.377919i	0.870351	+	0.492432i	$0.163892\pi$
$360$	0.364269	+	5.61547i	0.0191987	+	0.295961i
$361$	3.06494	+	3.06494i	0.161312	+	0.161312i
$362$	−5.23452	−	13.3711i	−0.275120	−	0.702769i
$363$	−24.8248	+	10.1747i	−1.30297	+	0.534031i
$364$	−19.7009	+	7.27147i	−1.03261	+	0.381128i
$365$	−4.26262	+	3.27082i	−0.223116	+	0.171203i
$366$	−6.13014	−	25.2117i	−0.320428	−	1.31784i
$367$	11.9247	−	6.88475i	0.622466	−	0.359381i	−0.155362	−	0.987858i	$-0.549655\pi$
$367$	11.9247	−	6.88475i	0.622466	−	0.359381i	0.777829	+	0.628476i	$0.216321\pi$
$368$	−20.2853	+	3.76608i	−1.05745	+	0.196321i
$369$	−8.91209	+	5.05730i	−0.463945	+	0.263272i
$370$	1.84100	+	7.45062i	0.0957088	+	0.387339i
$371$	4.38915	+	33.3389i	0.227873	+	1.73087i
$372$	18.9448	+	8.81580i	0.982240	+	0.457078i
$373$	4.27522	+	0.562844i	0.221363	+	0.0291430i	0.240392	−	0.970676i	$-0.422724\pi$
$373$	4.27522	+	0.562844i	0.221363	+	0.0291430i	−0.0190289	+	0.999819i	$0.506057\pi$
$374$	−2.07240	−	1.65560i	−0.107161	−	0.0856089i
$375$	10.5966	+	2.88168i	0.547206	+	0.148809i
$376$	−13.0136	+	6.52755i	−0.671124	+	0.336633i
$377$	−12.3097	+	12.3097i	−0.633982	+	0.633982i
$378$	2.58806	+	25.7497i	0.133116	+	1.32442i
$379$	19.5152	−	8.08347i	1.00243	−	0.415220i	0.179742	−	0.983714i	$-0.442474\pi$
$379$	19.5152	−	8.08347i	1.00243	−	0.415220i	0.822688	+	0.568494i	$0.192474\pi$
$380$	3.41809	−	5.41918i	0.175344	−	0.277998i
$381$	1.37509	+	10.7541i	0.0704481	+	0.550950i
$382$	−12.2578	−	22.2239i	−0.627164	−	1.13707i
$383$	−18.6303	+	32.2686i	−0.951962	+	1.64885i	−0.210791	+	0.977531i	$0.567604\pi$
$383$	−18.6303	+	32.2686i	−0.951962	+	1.64885i	−0.741171	+	0.671316i	$0.765729\pi$
$384$	−0.190722	+	19.5950i	−0.00973274	+	0.999953i
$385$	6.01034	+	10.4102i	0.306315	+	0.530553i
$386$	−3.34705	+	5.54396i	−0.170361	+	0.282180i
$387$	−11.3673	+	26.8754i	−0.577835	+	1.36615i
$388$	0.0111976	+	0.0212753i	0.000568473	+	0.00108009i
$389$	13.9038	+	10.6688i	0.704953	+	0.540929i	0.897856	−	0.440288i	$-0.145124\pi$
$389$	13.9038	+	10.6688i	0.704953	+	0.540929i	−0.192904	+	0.981218i	$0.561790\pi$
$390$	−3.91002	+	2.85815i	−0.197992	+	0.144728i
$391$	0.486498	+	1.81564i	0.0246033	+	0.0918207i
$392$	−12.7630	−	8.40346i	−0.644629	−	0.424439i
$393$	5.05451	−	5.01702i	0.254966	−	0.253075i
$394$	8.90548	−	3.48632i	0.448652	−	0.175638i
$395$	−1.20879	−	2.91828i	−0.0608208	−	0.146834i
$396$	13.1328	−	27.9493i	0.659947	−	1.40450i
$397$	−15.8643	−	6.57122i	−0.796208	−	0.329800i	−0.0527716	−	0.998607i	$-0.516806\pi$
$397$	−15.8643	−	6.57122i	−0.796208	−	0.329800i	−0.743437	+	0.668806i	$0.766806\pi$
$398$	15.6139	−	15.0148i	0.782655	−	0.752624i
$399$	14.8278	−	25.4631i	0.742317	−	1.27475i
$400$	17.1964	+	6.08363i	0.859818	+	0.304182i
$401$	10.2206	+	5.90086i	0.510392	+	0.294675i	0.732995	−	0.680234i	$-0.238122\pi$
$401$	10.2206	+	5.90086i	0.510392	+	0.294675i	−0.222603	+	0.974909i	$0.571455\pi$
$402$	13.0534	−	12.4593i	0.651044	−	0.621413i
$403$	2.34742	+	17.8304i	0.116933	+	0.888198i
$404$	−23.1477	−	19.2457i	−1.15164	−	0.957511i
$405$	2.20172	+	5.54770i	0.109405	+	0.275667i
$406$	−28.7521	−	4.35894i	−1.42694	−	0.216330i
$407$	10.9006	−	40.6815i	0.540321	−	2.01651i
$408$	1.78111	−	0.122199i	0.0881780	−	0.00604976i
$409$	−7.72795	−	28.8411i	−0.382123	−	1.42610i	−0.842653	−	0.538457i	$-0.819007\pi$
$409$	−7.72795	−	28.8411i	−0.382123	−	1.42610i	0.460531	−	0.887644i	$-0.347659\pi$
$410$	−0.355944	−	3.18366i	−0.0175788	−	0.157230i
$411$	16.0142	+	2.16900i	0.789924	+	0.106989i
$412$	−2.70578	−	11.9493i	−0.133304	−	0.588701i
$413$	−3.94842	+	9.53232i	−0.194289	+	0.469055i
$414$	−19.2402	+	10.4260i	−0.945605	+	0.512412i
$415$	−5.51703			−0.270821
$416$	−14.3190	+	8.91175i	−0.702049	+	0.436934i
$417$	0.137447	−	36.9177i	0.00673082	−	1.80787i
$418$	−30.7877	+	16.9813i	−1.50588	+	0.830582i
$419$	−13.0277	−	16.9781i	−0.636447	−	0.829433i	0.358105	−	0.933681i	$-0.383423\pi$
$419$	−13.0277	−	16.9781i	−0.636447	−	0.829433i	−0.994551	+	0.104248i	$0.966756\pi$
$420$	−7.71807	−	2.42677i	−0.376603	−	0.118414i
$421$	−11.1158	−	8.52948i	−0.541753	−	0.415702i	0.301302	−	0.953529i	$-0.402579\pi$
$421$	−11.1158	−	8.52948i	−0.541753	−	0.415702i	−0.843055	+	0.537827i	$0.819245\pi$
$422$	29.6156	−	21.8180i	1.44166	−	1.06209i
$423$	−11.0002	+	10.8376i	−0.534847	+	0.526941i
$424$	8.85403	+	25.5140i	0.429990	+	1.23907i
$425$	0.430114	−	1.60521i	0.0208636	−	0.0778640i
$426$	15.8478	+	12.7574i	0.767827	+	0.618098i
$427$	36.9851	+	4.86918i	1.78983	+	0.235636i
$428$	−12.2813	−	33.2744i	−0.593641	−	1.60838i
$429$	26.3639	−	3.37106i	1.27286	−	0.162756i
$430$	−6.32327	−	6.57559i	−0.304935	−	0.317103i
$431$		−	18.2965i		−	0.881310i	−0.897677	−	0.440655i	$-0.854746\pi$
$431$		−	18.2965i		−	0.881310i	0.897677	−	0.440655i	$-0.145254\pi$
$432$	6.20768	+	19.8359i	0.298667	+	0.954357i
$433$		−	25.3301i		−	1.21729i	−0.793443	−	0.608644i	$-0.791714\pi$
$433$		−	25.3301i		−	1.21729i	0.793443	−	0.608644i	$-0.208286\pi$
$434$	−21.6546	+	20.8237i	−1.03945	+	0.999570i
$435$	−6.65277	+	0.850668i	−0.318976	+	0.0407864i
$436$	−2.60768	−	1.20167i	−0.124885	−	0.0575496i
$437$	24.7029	+	3.25220i	1.18170	+	0.155574i
$438$	−12.4442	+	15.4587i	−0.594606	+	0.738645i
$439$	−1.42852	+	5.33132i	−0.0681796	+	0.254450i	−0.991600	−	0.129339i	$-0.958714\pi$
$439$	−1.42852	+	5.33132i	−0.0681796	+	0.254450i	0.923421	+	0.383789i	$0.125381\pi$
$440$	6.41447	+	7.21512i	0.305798	+	0.343967i
$441$	−15.6241	−	4.31141i	−0.744006	−	0.205305i
$442$	0.911381	+	1.23710i	0.0433500	+	0.0588428i
$443$	−21.6355	−	16.6015i	−1.02793	−	0.788760i	−0.0502263	−	0.998738i	$-0.515994\pi$
$443$	−21.6355	−	16.6015i	−1.02793	−	0.788760i	−0.977706	+	0.209977i	$0.932661\pi$
$444$	13.1091	+	25.1336i	0.622128	+	1.19279i
$445$	0.672100	+	0.875898i	0.0318606	+	0.0415216i
$446$	−10.2399	−	18.5654i	−0.484876	−	0.879098i
$447$	0.00692606	−	1.86031i	0.000327591	−	0.0879896i
$448$	−26.1730	−	10.4281i	−1.23656	−	0.492680i
$449$	19.5429			0.922287			0.461144	−	0.887325i	$-0.347439\pi$
$449$	19.5429			0.922287			0.461144	+	0.887325i	$0.347439\pi$
$450$	19.3402	+	0.522401i	0.911706	+	0.0246262i
$451$	−6.72753	+	16.2417i	−0.316787	+	0.764791i
$452$	3.97690	+	2.50839i	0.187058	+	0.117985i
$453$	−11.8274	−	1.60193i	−0.555701	−	0.0752653i
$454$	36.8925	−	4.12471i	1.73145	−	0.193582i
$455$	−1.80226	−	6.72612i	−0.0844912	−	0.315326i
$456$	7.53842	−	22.4321i	0.353019	−	1.05048i
$457$	5.17182	−	19.3015i	0.241928	−	0.902886i	−0.732975	−	0.680255i	$-0.761869\pi$
$457$	5.17182	−	19.3015i	0.241928	−	0.902886i	0.974903	−	0.222631i	$-0.0714645\pi$
$458$	2.95986	−	19.5236i	0.138305	−	0.912280i
$459$	1.75743	−	0.705061i	0.0820300	−	0.0329094i
$460$	−0.627038	−	6.81257i	−0.0292358	−	0.317638i
$461$	3.72080	+	28.2623i	0.173295	+	1.31630i	0.828131	+	0.560534i	$0.189404\pi$
$461$	3.72080	+	28.2623i	0.173295	+	1.31630i	−0.654837	+	0.755770i	$0.727263\pi$
$462$	30.6554	+	32.1171i	1.42622	+	1.49422i
$463$	−27.8633	−	16.0869i	−1.29492	−	0.747620i	−0.315394	−	0.948961i	$-0.602137\pi$
$463$	−27.8633	−	16.0869i	−1.29492	−	0.747620i	−0.979521	+	0.201341i	$0.935470\pi$
$464$	−23.3232	+	1.22947i	−1.08275	+	0.0570768i
$465$	−3.48669	+	5.98754i	−0.161691	+	0.277665i
$466$	13.9012	+	14.4558i	0.643958	+	0.669654i
$467$	24.3959	+	10.1051i	1.12891	+	0.467609i	0.867409	−	0.497595i	$-0.165783\pi$
$467$	24.3959	+	10.1051i	1.12891	+	0.467609i	0.261498	+	0.965204i	$0.415783\pi$
$468$	−11.5388	+	13.6699i	−0.533383	+	0.631892i
$469$	9.92844	+	23.9694i	0.458453	+	1.10680i
$470$	−1.75986	−	4.49539i	−0.0811763	−	0.207357i
$471$	8.51476	−	8.45160i	0.392340	−	0.389429i
$472$	−1.56152	+	8.13803i	−0.0718748	+	0.374583i
$473$	12.9571	+	48.3565i	0.595768	+	2.22344i
$474$	−6.88495	−	9.41879i	−0.316236	−	0.432619i
$475$	−17.4763	−	13.4100i	−0.801866	−	0.615294i
$476$	−0.760788	+	2.45146i	−0.0348707	+	0.112363i
$477$	17.2682	+	22.8547i	0.790655	+	1.04644i
$478$	−20.5000	−	12.3764i	−0.937647	−	0.566085i
$479$	−15.7051	−	27.2021i	−0.717586	−	1.24289i	−0.961954	−	0.273212i	$-0.911914\pi$
$479$	−15.7051	−	27.2021i	−0.717586	−	1.24289i	0.244368	−	0.969683i	$-0.421419\pi$
$480$	−6.46437	−	0.658498i	−0.295057	−	0.0300562i
$481$	−12.1988	+	21.1289i	−0.556215	+	0.963393i
$482$	13.0259	−	7.18454i	0.593311	−	0.327247i
$483$	−3.99057	−	31.2089i	−0.181577	−	1.42005i
$484$	−6.84171	−	30.2145i	−0.310987	−	1.37339i
$485$	−0.00736530	+	0.00305081i	−0.000334441	+	0.000138530i
$486$	12.7431	+	17.9892i	0.578040	+	0.816008i
$487$	5.85560	−	5.85560i	0.265343	−	0.265343i	−0.561878	−	0.827220i	$-0.689921\pi$
$487$	5.85560	−	5.85560i	0.265343	−	0.265343i	0.827220	+	0.561878i	$0.189921\pi$
$488$	29.8821	−	2.16197i	1.35270	−	0.0978678i
$489$	34.9818	+	9.51308i	1.58193	+	0.430196i
$490$	3.16267	−	3.95888i	0.142875	−	0.178844i
$491$	−22.6417	−	2.98084i	−1.02181	−	0.134523i	−0.399042	−	0.916933i	$-0.630657\pi$
$491$	−22.6417	−	2.98084i	−1.02181	−	0.134523i	−0.622765	+	0.782409i	$0.713991\pi$
$492$	−4.05569	−	11.1155i	−0.182844	−	0.501124i
$493$	0.277737	+	2.10962i	0.0125086	+	0.0950125i
$494$	19.7732	−	4.88581i	0.889637	−	0.219823i
$495$	8.82957	+	5.18580i	0.396860	+	0.233084i
$496$	−13.6602	+	19.8887i	−0.613361	+	0.893031i
$497$	−25.3316	+	14.6252i	−1.13628	+	0.656030i
$498$	−19.8005	+	4.81442i	−0.887283	+	0.215740i
$499$	7.70368	−	5.91124i	0.344864	−	0.264624i	−0.421777	−	0.906700i	$-0.638593\pi$
$499$	7.70368	−	5.91124i	0.344864	−	0.264624i	0.766641	+	0.642076i	$0.221927\pi$
$500$	−5.30696	+	11.5163i	−0.237334	+	0.515025i
$501$	−4.59964	+	1.88520i	−0.205497	+	0.0842247i
$502$	−2.57954	+	1.00984i	−0.115131	+	0.0450714i
$503$	−19.8682	−	19.8682i	−0.885879	−	0.885879i	0.108245	−	0.994124i	$-0.465477\pi$
$503$	−19.8682	−	19.8682i	−0.885879	−	0.885879i	−0.994124	+	0.108245i	$0.965477\pi$
$504$	−29.8177	−	1.97447i	−1.32819	−	0.0879500i
$505$	7.05834	−	7.05834i	0.314092	−	0.314092i
$506$	−15.0429	+	34.3980i	−0.668738	+	1.52918i
$507$	7.05570	+	0.955638i	0.313355	+	0.0424414i
$508$	−12.5093	−	0.489576i	−0.555010	−	0.0217214i
$509$	−2.69701	−	3.51481i	−0.119543	−	0.155791i	0.729749	−	0.683716i	$-0.239637\pi$
$509$	−2.69701	−	3.51481i	−0.119543	−	0.155791i	−0.849291	+	0.527924i	$0.822970\pi$
$510$	−0.0137811	+	0.591826i	−0.000610239	+	0.0262065i
$511$	−14.2661	−	24.7097i	−0.631096	−	1.09309i
$512$	−22.2778	−	3.96249i	−0.984547	−	0.175119i
$513$	0.280345	−	25.0988i	0.0123775	−	1.10814i
$514$	11.4819	−	19.0183i	0.506446	−	0.838862i
$515$	4.02784	−	0.530275i	0.177488	−	0.0233667i
$516$	−28.4323	−	18.0817i	−1.25166	−	0.796001i
$517$	−3.45796	+	26.2658i	−0.152081	+	1.15517i
$518$	−40.5032	+	4.52841i	−1.77961	+	0.198967i
$519$	−32.1697	+	8.49161i	−1.41209	+	0.372740i
$520$	−2.50743	−	4.99892i	−0.109958	−	0.219217i
$521$	2.21180	+	2.21180i	0.0969006	+	0.0969006i	0.753895	−	0.656995i	$-0.228173\pi$
$521$	2.21180	+	2.21180i	0.0969006	+	0.0969006i	−0.656995	+	0.753895i	$0.728173\pi$
$522$	−23.1343	+	8.85855i	−1.01256	+	0.387728i
$523$	5.64862	+	13.6370i	0.246997	+	0.596303i	0.997946	−	0.0640565i	$-0.0204038\pi$
$523$	5.64862	+	13.6370i	0.246997	+	0.596303i	−0.750949	+	0.660360i	$0.770404\pi$
$524$	4.74714	+	6.71487i	0.207380	+	0.293340i
$525$	−10.7405	+	25.6592i	−0.468754	+	1.11986i
$526$	−17.1777	−	4.96479i	−0.748984	−	0.216475i
$527$	1.90369	+	1.09910i	0.0829263	+	0.0478775i
$528$	29.3177	+	20.2973i	1.27589	+	0.883328i
$529$	3.12194	−	1.80245i	0.135736	−	0.0783674i
$530$	−8.69367	+	2.14814i	−0.377629	+	0.0933094i
$531$	1.08230	+	8.72225i	0.0469677	+	0.378514i
$532$	26.1625	+	21.7524i	1.13429	+	0.943084i
$533$	6.19948	−	8.07932i	0.268529	−	0.349954i
$534$	3.17650	+	2.55707i	0.137461	+	0.110655i
$535$	11.3603	−	3.04397i	0.491147	−	0.131602i
$536$	11.6933	+	17.2462i	0.505075	+	0.744924i
$537$	4.64905	−	17.0956i	0.200621	−	0.737731i
$538$	−1.45226	−	0.635100i	−0.0626115	−	0.0273811i
$539$	−25.6900	+	10.6411i	−1.10655	+	0.458347i
$540$	−6.73839	+	1.44690i	−0.289974	+	0.0622646i
$541$	6.82229	−	16.4705i	0.293313	−	0.708120i	−0.706687	−	0.707526i	$-0.749811\pi$
$541$	6.82229	−	16.4705i	0.293313	−	0.708120i	1.00000		0.000593663i	$-0.000188969\pi$
$542$	−0.310541	+	15.8755i	−0.0133389	+	0.681913i
$543$	15.2628	−	8.73641i	0.654992	−	0.374915i
$544$	−0.201276	+	2.05163i	−0.00862965	+	0.0879630i
$545$	0.476037	−	0.824520i	0.0203912	−	0.0353186i
$546$	−12.3378	−	22.5672i	−0.528009	−	0.965787i
$547$	6.15258	−	0.810003i	0.263065	−	0.0346332i	0.00216029	−	0.999998i	$-0.499312\pi$
$547$	6.15258	−	0.810003i	0.263065	−	0.0346332i	0.260905	+	0.965364i	$0.415979\pi$
$548$	−5.53088	+	17.8220i	−0.236268	+	0.761317i
$549$	29.4484	−	11.9418i	1.25683	−	0.509664i
$550$	26.7233	−	19.6873i	1.13949	−	0.839469i
$551$	27.2442	+	7.30006i	1.16064	+	0.310993i
$552$	−8.19540	−	23.9030i	−0.348819	−	1.01738i
$553$	16.2025	−	4.34143i	0.688998	−	0.184617i
$554$	−7.87165	+	9.85338i	−0.334435	+	0.418630i
$555$	−8.69738	+	3.56469i	−0.369183	+	0.151313i
$556$	42.0146	+	7.21281i	1.78181	+	0.305891i
$557$	−4.90627	−	2.03224i	−0.207885	−	0.0861089i	0.276311	−	0.961068i	$-0.410888\pi$
$557$	−4.90627	−	2.03224i	−0.207885	−	0.0861089i	−0.484196	+	0.874959i	$0.660888\pi$
$558$	−7.28866	+	24.5318i	−0.308554	+	1.03851i
$559$		−	29.0004i		−	1.22659i
$560$	4.23873	−	8.32527i	0.179119	−	0.351807i
$561$	1.63479	−	2.80735i	0.0690209	−	0.118526i
$562$	25.0912	+	7.25198i	1.05841	+	0.305906i
$563$	25.3176	−	19.4269i	1.06701	−	0.818745i	0.0829446	−	0.996554i	$-0.473568\pi$
$563$	25.3176	−	19.4269i	1.06701	−	0.818745i	0.984065	+	0.177809i	$0.0569009\pi$
$564$	−10.2390	−	14.5981i	−0.431139	−	0.614693i
$565$	−0.949120	+	1.23692i	−0.0399298	+	0.0520375i
$566$	−5.42974	+	35.8153i	−0.228229	+	1.50543i
$567$	−30.7345	+	7.74662i	−1.29073	+	0.325328i
$568$	−17.5568	+	15.6086i	−0.736669	+	0.654922i
$569$	8.65606	+	2.31938i	0.362881	+	0.0972336i	0.435652	−	0.900115i	$-0.356518\pi$
$569$	8.65606	+	2.31938i	0.362881	+	0.0972336i	−0.0727715	+	0.997349i	$0.523184\pi$
$570$	7.17786	+	3.17089i	0.300648	+	0.132814i
$571$	−3.04973	+	23.1650i	−0.127627	+	0.969424i	0.801066	+	0.598576i	$0.204266\pi$
$571$	−3.04973	+	23.1650i	−0.127627	+	0.969424i	−0.928693	+	0.370848i	$0.879067\pi$
$572$	−1.20020	+	30.6667i	−0.0501830	+	1.28224i
$573$	24.7311	−	18.8310i	1.03316	−	0.786675i
$574$	17.0085	+	0.332704i	0.709922	+	0.0138868i
$575$	−23.5214			−0.980912
$576$	−23.7751	+	3.27778i	−0.990630	+	0.136574i
$577$	−37.3273			−1.55396			−0.776978	−	0.629528i	$-0.783248\pi$
$577$	−37.3273			−1.55396			−0.776978	+	0.629528i	$0.783248\pi$
$578$	−23.8493	−	0.466515i	−0.991998	−	0.0194045i
$579$	−7.31633	−	3.06248i	−0.304056	−	0.127272i
$580$	0.302865	−	7.73858i	0.0125758	−	0.321327i
$581$	3.82410	−	29.0469i	0.158650	−	1.20507i
$582$	−0.0237716	+	0.0173766i	−0.000985366	+	0.000720283i
$583$	47.4687	+	12.7192i	1.96595	+	0.526776i
$584$	−15.2254	−	17.1258i	−0.630031	−	0.708670i
$585$	−4.16305	−	4.22551i	−0.172121	−	0.174703i
$586$	−0.242675	+	1.60072i	−0.0100248	+	0.0661250i
$587$	2.42810	−	3.16436i	0.100219	−	0.130607i	−0.740552	−	0.671999i	$-0.765436\pi$
$587$	2.42810	−	3.16436i	0.100219	−	0.130607i	0.840770	+	0.541392i	$0.182102\pi$
$588$	7.89604	−	16.9682i	0.325627	−	0.699758i
$589$	23.1168	−	17.7382i	0.952512	−	0.730888i
$590$	−2.63968	−	0.762933i	−0.108674	−	0.0314094i
$591$	5.81867	+	10.1654i	0.239348	+	0.418150i
$592$	−31.1270	+	10.1243i	−1.27931	+	0.416106i
$593$			15.9184i			0.653691i	0.945078	+	0.326845i	$0.105986\pi$
$593$			15.9184i			0.653691i	−0.945078	+	0.326845i	$0.894014\pi$
$594$	36.2145	+	10.9066i	1.48590	+	0.447504i
$595$	−0.786339	−	0.325712i	−0.0322367	−	0.0133529i
$596$	2.11714	+	0.363459i	0.0867216	+	0.0148878i
$597$	20.9877	+	16.2289i	0.858967	+	0.664204i
$598$	13.5745	−	16.9919i	0.555102	−	0.694851i
$599$	−1.05313	+	0.282184i	−0.0430296	+	0.0115297i	−0.280270	−	0.959921i	$-0.590424\pi$
$599$	−1.05313	+	0.282184i	−0.0430296	+	0.0115297i	0.237240	+	0.971451i	$0.423757\pi$
$600$	−4.29150	+	21.9242i	−0.175200	+	0.895052i
$601$	−12.6468	−	3.38870i	−0.515874	−	0.138228i	−0.00851666	−	0.999964i	$-0.502711\pi$
$601$	−12.6468	−	3.38870i	−0.515874	−	0.138228i	−0.507358	+	0.861736i	$0.669378\pi$
$602$	39.0031	−	28.7339i	1.58965	−	1.17111i
$603$	17.4329	+	13.5842i	0.709924	+	0.553191i
$604$	4.08488	−	13.1626i	0.166211	−	0.535577i
$605$	10.1846	−	1.34083i	0.414063	−	0.0545125i
$606$	19.1728	−	31.4917i	0.778841	−	1.27926i
$607$	−12.8234	+	22.2108i	−0.520486	+	0.901508i	0.479231	+	0.877689i	$0.340916\pi$
$607$	−12.8234	+	22.2108i	−0.520486	+	0.901508i	−0.999716	+	0.0238187i	$0.992418\pi$
$608$	24.1042	+	12.8721i	0.977554	+	0.522033i
$609$	0.132601	−	35.6162i	0.00537328	−	1.44324i
$610$	−0.194292	+	9.93262i	−0.00786665	+	0.402160i
$611$	5.87293	−	14.1785i	0.237593	−	0.573601i
$612$	0.466995	+	2.13608i	0.0188772	+	0.0863459i
$613$	3.23462	−	1.33982i	0.130645	−	0.0541149i	−0.316403	−	0.948625i	$-0.602475\pi$
$613$	3.23462	−	1.33982i	0.130645	−	0.0541149i	0.447048	+	0.894510i	$0.352475\pi$
$614$	−0.869240	−	0.380134i	−0.0350797	−	0.0153410i
$615$	3.79353	−	1.00135i	0.152970	−	0.0403783i
$616$	−42.4334	+	28.7708i	−1.70969	+	1.15921i
$617$	−20.3536	+	5.45373i	−0.819405	+	0.219559i	−0.644086	−	0.764953i	$-0.722762\pi$
$617$	−20.3536	+	5.45373i	−0.819405	+	0.219559i	−0.175319	+	0.984512i	$0.556096\pi$
$618$	13.9931	−	5.41802i	0.562884	−	0.217945i
$619$	5.75884	−	7.50507i	0.231467	−	0.301654i	−0.663151	−	0.748486i	$-0.730781\pi$
$619$	5.75884	−	7.50507i	0.231467	−	0.301654i	0.894618	+	0.446832i	$0.147448\pi$
$620$	−6.15200	−	5.11498i	−0.247070	−	0.205422i
$621$	−16.0774	−	21.4441i	−0.645162	−	0.860524i
$622$	−18.0345	+	4.45619i	−0.723117	+	0.178677i
$623$	−5.07743	+	2.93145i	−0.203423	+	0.117446i
$624$	−13.3614	−	15.7529i	−0.534885	−	0.630621i
$625$	16.1049	+	9.29815i	0.644195	+	0.371926i
$626$	35.8810	+	10.3705i	1.43409	+	0.414489i
$627$	−26.0874	−	34.2611i	−1.04183	−	1.36826i
$628$	7.99696	+	11.3118i	0.319114	+	0.451389i
$629$	1.14119	+	2.75508i	0.0455022	+	0.109852i
$630$	1.55817	−	9.78564i	0.0620788	−	0.389869i
$631$	2.19037	+	2.19037i	0.0871974	+	0.0871974i	0.749360	−	0.662163i	$-0.230361\pi$
$631$	2.19037	+	2.19037i	0.0871974	+	0.0871974i	−0.662163	+	0.749360i	$0.730361\pi$
$632$	12.0418	−	6.04012i	0.478997	−	0.240263i
$633$	31.7376	+	31.9748i	1.26146	+	1.27088i
$634$	24.4259	−	2.73090i	0.970075	−	0.108458i
$635$	0.541833	−	4.11563i	0.0215020	−	0.163324i
$636$	−29.3268	+	15.2962i	−1.16288	+	0.606532i
$637$	15.9702	−	2.10251i	0.632762	−	0.0833046i
$638$	−21.9656	+	36.3831i	−0.869626	+	1.44042i
$639$	−12.6188	+	21.4854i	−0.499192	+	0.849948i
$640$	1.98545	−	7.23557i	0.0784818	−	0.286011i
$641$	0.687774	+	1.19126i	0.0271654	+	0.0470519i	0.879289	−	0.476290i	$-0.158019\pi$
$641$	0.687774	+	1.19126i	0.0271654	+	0.0470519i	−0.852123	+	0.523341i	$0.824685\pi$
$642$	38.1155	−	20.8383i	1.50430	−	0.822421i
$643$	−22.2096	−	28.9441i	−0.875861	−	1.14144i	−0.989007	−	0.147866i	$-0.952760\pi$
$643$	−22.2096	−	28.9441i	−0.875861	−	1.14144i	0.113147	−	0.993578i	$-0.463907\pi$
$644$	36.3025	+	1.42077i	1.43052	+	0.0559862i
$645$	6.83457	−	8.83866i	0.269111	−	0.348022i
$646$	0.997504	−	2.28096i	0.0392463	−	0.0897431i
$647$	−1.20432	+	1.20432i	−0.0473466	+	0.0473466i	−0.730384	−	0.683037i	$-0.760659\pi$
$647$	−1.20432	+	1.20432i	−0.0473466	+	0.0473466i	0.683037	+	0.730384i	$0.260659\pi$
$648$	−22.9213	+	11.0731i	−0.900434	+	0.434993i
$649$	10.6623	+	10.6623i	0.418530	+	0.418530i
$650$	−17.9047	+	7.00933i	−0.702279	+	0.274929i
$651$	−29.1073	−	22.5075i	−1.14081	−	0.882138i
$652$	−17.5195	+	38.0180i	−0.686116	+	1.48890i
$653$	27.6310	−	21.2020i	1.08128	−	0.829697i	0.0951181	−	0.995466i	$-0.469677\pi$
$653$	27.6310	−	21.2020i	1.08128	−	0.829697i	0.986165	+	0.165769i	$0.0530105\pi$
$654$	0.988972	−	3.37460i	0.0386719	−	0.131957i
$655$	−2.36149	+	1.36340i	−0.0922709	+	0.0532726i
$656$	13.4332	−	2.49394i	0.524477	−	0.0973720i
$657$	−20.9579	−	12.3090i	−0.817644	−	0.480220i
$658$	24.8879	−	6.14962i	0.970230	−	0.239737i
$659$	−3.05050	−	23.1708i	−0.118830	−	0.902607i	−0.942188	−	0.335084i	$-0.891235\pi$
$659$	−3.05050	−	23.1708i	−0.118830	−	0.902607i	0.823358	−	0.567523i	$-0.192098\pi$
$660$	−7.59308	+	9.06367i	−0.295560	+	0.352803i
$661$	11.4278	+	1.50450i	0.444491	+	0.0585184i	0.349450	−	0.936955i	$-0.386368\pi$
$661$	11.4278	+	1.50450i	0.444491	+	0.0585184i	0.0950412	+	0.995473i	$0.469702\pi$
$662$	12.9115	−	16.1620i	0.501818	−	0.628153i
$663$	−1.33565	+	1.32574i	−0.0518723	+	0.0514875i
$664$	−1.69794	−	23.4685i	−0.0658930	−	0.910754i
$665$	−7.97763	+	7.97763i	−0.309359	+	0.309359i
$666$	−28.1040	+	20.3834i	−1.08901	+	0.789839i
$667$	27.8245	−	11.5253i	1.07737	−	0.446261i
$668$	−1.26766	−	5.59827i	−0.0490472	−	0.216604i
$669$	20.6599	−	15.7310i	0.798758	−	0.608197i
$670$	−6.05000	+	3.33694i	−0.233732	+	0.128917i
$671$	27.2589	−	47.2138i	1.05232	−	1.82267i
$672$	7.94770	−	33.5782i	0.306589	−	1.29531i
$673$	−21.3364	−	36.9557i	−0.822458	−	1.42454i	−0.903847	−	0.427857i	$-0.859269\pi$
$673$	−21.3364	−	36.9557i	−0.822458	−	1.42454i	0.0813884	−	0.996682i	$-0.474065\pi$
$674$	−40.2940	−	24.3267i	−1.55207	−	0.937028i
$675$	2.83030	+	23.5258i	0.108938	+	0.905509i
$676$	−2.43685	+	7.85218i	−0.0937250	+	0.302007i
$677$	29.6468	+	22.7488i	1.13942	+	0.874306i	0.993369	−	0.114972i	$-0.0366778\pi$
$677$	29.6468	+	22.7488i	1.13942	+	0.874306i	0.146048	+	0.989277i	$0.453344\pi$
$678$	−2.32698	+	5.26752i	−0.0893672	+	0.202298i
$679$	−0.0109571	−	0.0408926i	−0.000420497	−	0.00156931i
$680$	−0.671321	−	0.128813i	−0.0257440	−	0.00493974i
$681$	11.6037	+	43.9597i	0.444655	+	1.68454i
$682$	16.0053	+	40.8840i	0.612874	+	1.56553i
$683$	1.78395	+	4.30684i	0.0682611	+	0.164797i	0.954328	−	0.298760i	$-0.0965730\pi$
$683$	1.78395	+	4.30684i	0.0682611	+	0.164797i	−0.886067	+	0.463557i	$0.846573\pi$
$684$	28.5283	+	5.11653i	1.09081	+	0.195635i
$685$	−5.71663	−	2.36791i	−0.218421	−	0.0904730i
$686$	−5.51423	−	5.73426i	−0.210534	−	0.218935i
$687$	24.1845	+	0.0900407i	0.922698	+	0.00343527i
$688$	26.0253	−	28.9218i	0.992205	−	1.10263i
$689$	−24.6540	−	14.2340i	−0.939241	−	0.542271i
$690$	8.14171	−	1.97963i	0.309950	−	0.0753632i
$691$	−1.27807	−	9.70788i	−0.0486199	−	0.369305i	−0.998408	−	0.0564102i	$-0.982035\pi$
$691$	−1.27807	−	9.70788i	−0.0486199	−	0.369305i	0.949788	−	0.312895i	$-0.101299\pi$
$692$	−3.52122	−	38.2570i	−0.133857	−	1.45431i
$693$	−33.4231	+	42.8928i	−1.26964	+	1.62936i
$694$	5.00256	−	32.9976i	0.189895	−	1.25257i
$695$	−3.65852	+	13.6538i	−0.138776	+	0.517918i
$696$	−5.66607	−	28.0379i	−0.214772	−	1.06277i
$697$	−0.322164	−	1.20233i	−0.0122028	−	0.0455416i
$698$	19.9470	−	2.23015i	0.755007	−	0.0844124i
$699$	−15.0252	+	19.4310i	−0.568305	+	0.734948i
$700$	−27.1671	−	17.1354i	−1.02682	−	0.647656i
$701$	1.53880	−	3.71500i	0.0581197	−	0.140313i	−0.892152	−	0.451735i	$-0.850805\pi$
$701$	1.53880	−	3.71500i	0.0581197	−	0.140313i	0.950272	+	0.311422i	$0.100805\pi$
$702$	−18.6285	−	11.5324i	−0.703087	−	0.435262i
$703$	39.5288			1.49086
$704$	−28.7177	+	29.5066i	−1.08234	+	1.11207i
$705$	5.13141	−	2.93720i	0.193260	−	0.110621i
$706$	−6.99344	−	12.6794i	−0.263202	−	0.477195i
$707$	32.2694	+	42.0543i	1.21361	+	1.58161i
$708$	−10.1395	−	0.434643i	−0.381066	−	0.0163349i
$709$	−27.6101	−	21.1860i	−1.03692	−	0.795657i	−0.0576748	−	0.998335i	$-0.518369\pi$
$709$	−27.6101	−	21.1860i	−1.03692	−	0.795657i	−0.979245	+	0.202679i	$0.935035\pi$
$710$	−4.62030	−	6.27155i	−0.173397	−	0.235367i
$711$	10.1788	−	10.0283i	0.381734	−	0.376091i
$712$	−3.51907	+	3.12856i	−0.131883	+	0.117248i
$713$	8.05266	−	30.0529i	0.301575	−	1.12549i
$714$	−3.10639	−	0.482778i	−0.116254	−	0.0180675i
$715$	−10.0895	−	1.32831i	−0.377327	−	0.0496760i
$716$	18.5794	+	8.56179i	0.694346	+	0.319969i
$717$	11.3242	−	27.0537i	0.422909	−	1.01034i
$718$	−10.3227	+	9.92656i	−0.385238	+	0.370456i
$719$			48.6842i			1.81562i	0.419386	+	0.907808i	$0.362245\pi$
$719$			48.6842i			1.81562i	−0.419386	+	0.907808i	$0.637755\pi$
$720$	−0.359742	−	7.95004i	−0.0134068	−	0.296280i
$721$			21.5739i			0.803455i
$722$	−4.24887	−	4.41841i	−0.158127	−	0.164436i
$723$	11.0372	+	14.4954i	0.410478	+	0.539089i
$724$	7.03150	+	19.0507i	0.261324	+	0.708015i
$725$	−26.3987	−	3.47546i	−0.980424	−	0.129075i
$726$	35.3823	−	13.6998i	1.31316	−	0.508447i
$727$	−5.32966	+	19.8906i	−0.197666	+	0.737701i	0.793894	+	0.608056i	$0.208050\pi$
$727$	−5.32966	+	19.8906i	−0.197666	+	0.737701i	−0.991560	+	0.129645i	$0.958616\pi$
$728$	28.0571	−	9.73655i	1.03986	−	0.360861i
$729$	−19.5136	+	18.6607i	−0.722725	+	0.691136i
$730$	6.11757	−	4.50686i	0.226421	−	0.166806i
$731$	−2.81218	−	2.15786i	−0.104012	−	0.0798115i
$732$	7.97036	+	35.8175i	0.294593	+	1.32385i
$733$	9.60491	+	12.5174i	0.354765	+	0.462339i	0.936310	−	0.351175i	$-0.114218\pi$
$733$	9.60491	+	12.5174i	0.354765	+	0.462339i	−0.581544	+	0.813515i	$0.697551\pi$
$734$	−17.0513	+	9.40483i	−0.629376	+	0.347139i
$735$	5.36285	+	3.12292i	0.197812	+	0.115191i
$736$	28.7865	−	4.76397i	1.06108	−	0.175602i
$737$	37.9160			1.39665
$738$	12.7411	−	6.90424i	0.469005	−	0.254149i
$739$	0.521486	−	1.25898i	0.0191832	−	0.0463123i	−0.913998	−	0.405719i	$-0.867021\pi$
$739$	0.521486	−	1.25898i	0.0191832	−	0.0463123i	0.933181	+	0.359407i	$0.117021\pi$
$740$	−2.39699	−	10.5857i	−0.0881152	−	0.389137i
$741$	9.46033	+	23.0819i	0.347534	+	0.847936i
$742$	−5.28392	−	47.2607i	−0.193979	−	1.73500i
$743$	−12.3870	−	46.2290i	−0.454436	−	1.69598i	−0.689740	−	0.724057i	$-0.742275\pi$
$743$	−12.3870	−	46.2290i	−0.454436	−	1.69598i	0.235304	−	0.971922i	$-0.424391\pi$
$744$	−26.5430	−	12.9890i	−0.973113	−	0.476201i
$745$	−0.184355	+	0.688024i	−0.00675426	+	0.0252072i
$746$	−6.02936	−	0.914074i	−0.220750	−	0.0334666i
$747$	−9.37874	−	23.1279i	−0.343150	−	0.846205i
$748$	2.88447	+	2.39824i	0.105467	+	0.0876883i
$749$	8.15208	+	61.9212i	0.297870	+	2.26255i
$750$	−14.9033	−	4.36761i	−0.544191	−	0.159483i
$751$	−23.6971	−	13.6815i	−0.864721	−	0.499247i	0.000869577	−	1.00000i	$-0.499723\pi$
$751$	−23.6971	−	13.6815i	−0.864721	−	0.499247i	−0.865590	+	0.500753i	$0.833057\pi$
$752$	18.5810	−	8.86965i	0.677579	−	0.323443i
$753$	−1.68542	−	2.94450i	−0.0614202	−	0.107304i
$754$	17.7457	−	17.0648i	0.646260	−	0.621462i
$755$	4.22206	+	1.74884i	0.153657	+	0.0636466i
$756$	−2.94718	−	36.4802i	−0.107188	−	1.32677i
$757$	−10.1539	−	24.5137i	−0.369050	−	0.890966i	−0.993907	−	0.110226i	$-0.964843\pi$
$757$	−10.1539	−	24.5137i	−0.369050	−	0.890966i	0.624856	−	0.780740i	$-0.285157\pi$
$758$	−27.8170	+	10.8898i	−1.01036	+	0.395536i
$759$	−44.3698	−	12.0661i	−1.61052	−	0.437971i
$760$	−4.98287	+	7.56787i	−0.180748	+	0.274516i
$761$	−1.49839	−	5.59207i	−0.0543166	−	0.202712i	0.933435	−	0.358746i	$-0.116796\pi$
$761$	−1.49839	−	5.59207i	−0.0543166	−	0.202712i	−0.987752	+	0.156034i	$0.950129\pi$
$762$	−1.64686	−	15.2437i	−0.0596596	−	0.552222i
$763$	4.01110	+	3.07782i	0.145212	+	0.111425i
$764$	16.7172	+	31.7624i	0.604806	+	1.14912i
$765$	−0.719515	+	0.0892807i	−0.0260141	+	0.00322795i
$766$	27.2346	−	45.1106i	0.984027	−	1.62991i
$767$	−4.36744	−	7.56462i	−0.157699	−	0.273143i
$768$	0.811631	−	27.7009i	0.0292872	−	0.999571i
$769$	−23.5101	+	40.7207i	−0.847795	+	1.46842i	0.0353762	+	0.999374i	$0.488737\pi$
$769$	−23.5101	+	40.7207i	−0.847795	+	1.46842i	−0.883171	+	0.469050i	$0.844596\pi$
$770$	−8.21035	−	14.8857i	−0.295880	−	0.536443i
$771$	25.0983	+	10.5057i	0.903894	+	0.378354i
$772$	4.88588	−	7.74628i	0.175847	−	0.278795i
$773$	−42.6292	+	17.6576i	−1.53326	+	0.635099i	−0.980195	−	0.198036i	$-0.936544\pi$
$773$	−42.6292	+	17.6576i	−1.53326	+	0.635099i	−0.553070	+	0.833135i	$0.686544\pi$
$774$	16.8161	−	37.6859i	0.604443	−	1.35459i
$775$	−19.4505	+	19.4505i	−0.698682	+	0.698682i
$776$	−0.0152444	−	0.0303918i	−0.000547241	−	0.00109100i
$777$	−12.7394	−	48.2621i	−0.457024	−	1.73139i
$778$	−19.3642	−	15.4696i	−0.694239	−	0.554613i
$779$	−16.3585	−	2.15364i	−0.586105	−	0.0771622i
$780$	5.60760	−	3.93312i	0.200784	−	0.140828i
$781$	5.57969	+	42.3820i	0.199657	+	1.51655i
$782$	−0.637664	−	2.58066i	−0.0228028	−	0.0922843i
$783$	−14.8755	−	26.4429i	−0.531607	−	0.944991i
$784$	17.8137	+	12.2350i	0.636205	+	0.436965i
$785$	−3.97813	+	2.29677i	−0.141985	+	0.0819753i
$786$	−7.28556	+	6.95398i	−0.259867	+	0.248040i
$787$	−31.6818	+	24.3103i	−1.12933	+	0.866569i	−0.992283	−	0.123995i	$-0.960429\pi$
$787$	−31.6818	+	24.3103i	−1.12933	+	0.866569i	−0.137052	+	0.990564i	$0.543763\pi$
$788$	−12.6883	+	4.68315i	−0.452001	+	0.166830i
$789$	2.93926	−	21.7013i	0.104641	−	0.772586i
$790$	1.62845	+	4.15971i	0.0579375	+	0.147996i
$791$	−5.85444	−	5.85444i	−0.208160	−	0.208160i
$792$	−19.3420	+	39.1554i	−0.687289	+	1.39133i
$793$	−22.3314	+	22.3314i	−0.793012	+	0.793012i
$794$	22.2495	+	9.73011i	0.789606	+	0.345309i
$795$	−4.15942	−	10.1484i	−0.147519	−	0.359928i
$796$	−22.4925	+	20.7982i	−0.797225	+	0.737173i
$797$	15.1820	+	19.7855i	0.537772	+	0.700839i	0.980656	−	0.195741i	$-0.0627111\pi$
$797$	15.1820	+	19.7855i	0.537772	+	0.700839i	−0.442883	+	0.896579i	$0.646044\pi$
$798$	−21.6699	+	35.5932i	−0.767106	+	1.25999i
$799$	−0.937903	−	1.62450i	−0.0331806	−	0.0574706i
$800$	−24.1464	−	9.07753i	−0.853705	−	0.320939i
$801$	−2.52930	+	4.30649i	−0.0893683	+	0.152162i
$802$	−14.2881	−	8.62616i	−0.504531	−	0.304600i
$803$	−41.3414	+	5.44270i	−1.45891	+	0.192069i
$804$	−18.8013	+	17.2557i	−0.663072	+	0.608562i
$805$	−1.57242	+	11.9437i	−0.0554205	+	0.420961i
$806$	−2.82597	−	25.2762i	−0.0995404	−	0.890315i
$807$	0.509422	−	1.87326i	0.0179325	−	0.0659420i
$808$	32.1972	+	27.8526i	1.13269	+	0.979851i
$809$	38.0030	+	38.0030i	1.33611	+	1.33611i	0.899789	+	0.436325i	$0.143720\pi$
$809$	38.0030	+	38.0030i	1.33611	+	1.33611i	0.436325	+	0.899789i	$0.356280\pi$
$810$	−2.95967	−	7.90502i	−0.103992	−	0.277754i
$811$	2.57804	+	6.22395i	0.0905273	+	0.218552i	0.962658	−	0.270721i	$-0.0872621\pi$
$811$	2.57804	+	6.22395i	0.0905273	+	0.218552i	−0.872131	+	0.489273i	$0.837262\pi$
$812$	40.5333	+	6.95852i	1.42244	+	0.244196i
$813$	−19.2901	+	2.46657i	−0.676535	+	0.0865063i
$814$	−16.5380	+	57.2198i	−0.579655	+	2.00555i
$815$	−12.0209	−	6.94027i	−0.421074	−	0.243107i
$816$	−2.52176	+	0.123520i	−0.0882794	+	0.00432408i
$817$	−40.6913	+	23.4932i	−1.42361	+	0.821922i
$818$	10.1292	+	40.9934i	0.354159	+	1.43330i
$819$	25.1327	−	18.9894i	0.878208	−	0.663542i
$820$	0.415231	+	4.51136i	0.0145005	+	0.157543i
$821$	23.6429	−	30.8120i	0.825142	−	1.07535i	−0.170796	−	0.985306i	$-0.554634\pi$
$821$	23.6429	−	30.8120i	0.825142	−	1.07535i	0.995938	−	0.0900400i	$-0.0286995\pi$
$822$	−22.5832	−	3.50976i	−0.787680	−	0.122417i
$823$	16.9051	−	4.52971i	0.589275	−	0.157896i	0.0481532	−	0.998840i	$-0.484666\pi$
$823$	16.9051	−	4.52971i	0.589275	−	0.157896i	0.541122	+	0.840944i	$0.318000\pi$
$824$	3.49532	+	16.9705i	0.121765	+	0.591195i
$825$	28.6381	+	28.8522i	0.997051	+	1.00450i
$826$	5.84648	−	13.3690i	0.203425	−	0.465165i
$827$	6.40373	−	2.65251i	0.222679	−	0.0922368i	−0.268555	−	0.963264i	$-0.586546\pi$
$827$	6.40373	−	2.65251i	0.222679	−	0.0922368i	0.491234	+	0.871028i	$0.336546\pi$
$828$	27.4929	−	14.2097i	0.955445	−	0.493821i
$829$	−7.76228	+	18.7398i	−0.269595	+	0.650860i	−0.999464	−	0.0327264i	$-0.989581\pi$
$829$	−7.76228	+	18.7398i	−0.269595	+	0.650860i	0.729869	+	0.683587i	$0.239581\pi$
$830$	7.80077	+	0.152591i	0.270769	+	0.00529651i
$831$	−13.3478	−	7.77273i	−0.463028	−	0.269633i
$832$	20.4928	−	12.2047i	0.710460	−	0.423121i
$833$	0.984429	−	1.70508i	0.0341084	−	0.0590775i
$834$	−1.21542	+	52.1958i	−0.0420865	+	1.80739i
$835$	1.88705	−	0.248434i	0.0653039	−	0.00859743i
$836$	44.0018	−	23.1590i	1.52183	−	0.800972i
$837$	−31.0275	−	4.43794i	−1.07247	−	0.153398i
$838$	17.9509	+	24.3664i	0.620103	+	0.841722i
$839$	43.6649	+	11.7000i	1.50748	+	0.403928i	0.915598	−	0.402096i	$-0.131718\pi$
$839$	43.6649	+	11.7000i	1.50748	+	0.403928i	0.591883	+	0.806024i	$0.298385\pi$
$840$	10.8458	+	3.64478i	0.374215	+	0.125757i
$841$	4.91929	−	1.31812i	0.169631	−	0.0454524i
$842$	15.4813	+	12.3676i	0.533519	+	0.426217i
$843$	−4.29333	+	31.6986i	−0.147870	+	1.09176i
$844$	−42.4782	+	30.0304i	−1.46216	+	1.03369i
$845$	−2.51869	−	1.04327i	−0.0866455	−	0.0358897i
$846$	15.8534	−	15.0195i	0.545050	−	0.516380i
$847$			54.5509i			1.87439i
$848$	−11.8134	−	36.3202i	−0.405675	−	1.24724i
$849$	−44.3655	−	0.165176i	−1.52262	−	0.00566882i
$850$	−0.652554	+	2.25778i	−0.0223824	+	0.0774411i
$851$	33.4859	−	25.6946i	1.14788	−	0.880800i
$852$	−22.0550	−	18.4766i	−0.755592	−	0.632996i
$853$	9.50736	−	12.3902i	0.325526	−	0.424233i	−0.601708	−	0.798716i	$-0.705513\pi$
$853$	9.50736	−	12.3902i	0.325526	−	0.424233i	0.927234	+	0.374483i	$0.122180\pi$
$854$	−52.1601	−	7.90768i	−1.78488	−	0.270595i
$855$	−2.55647	+	9.26439i	−0.0874294	+	0.316835i
$856$	16.4448	+	47.3877i	0.562072	+	1.61968i
$857$	−23.7553	−	6.36520i	−0.811464	−	0.217431i	−0.170853	−	0.985297i	$-0.554652\pi$
$857$	−23.7553	−	6.36520i	−0.811464	−	0.217431i	−0.640611	+	0.767865i	$0.721319\pi$
$858$	−37.3702	+	4.03731i	−1.27580	+	0.137832i
$859$	−1.21075	+	9.19654i	−0.0413102	+	0.313782i	0.958297	+	0.285773i	$0.0922502\pi$
$859$	−1.21075	+	9.19654i	−0.0413102	+	0.313782i	−0.999608	+	0.0280095i	$0.991083\pi$
$860$	8.75888	+	9.47240i	0.298675	+	0.323006i
$861$	2.64260	+	20.6668i	0.0900596	+	0.704324i
$862$	−0.506046	+	25.8702i	−0.0172360	+	0.881141i
$863$	20.8415			0.709454			0.354727	−	0.934970i	$-0.384574\pi$
$863$	20.8415			0.709454			0.354727	+	0.934970i	$0.384574\pi$
$864$	−8.22869	−	28.2186i	−0.279946	−	0.960016i
$865$	12.7393			0.433148
$866$	−0.700584	+	35.8153i	−0.0238068	+	1.21706i
$867$	−3.70544	−	28.9789i	−0.125843	−	0.984175i
$868$	31.1943	−	28.8446i	1.05880	−	0.979049i
$869$	3.19975	−	24.3045i	0.108544	−	0.824473i
$870$	9.43017	−	1.01879i	0.319713	−	0.0345403i
$871$	−21.2157	−	5.68474i	−0.718868	−	0.192620i
$872$	3.65387	+	1.77122i	0.123736	+	0.0599810i
$873$	−0.0253100	−	0.0256897i	−0.000856612	−	0.000869465i
$874$	−34.8386	−	5.28167i	−1.17843	−	0.178655i
$875$	13.5926	−	17.7143i	0.459515	−	0.598852i
$876$	18.0229	−	21.5135i	0.608938	−	0.726874i
$877$	−24.0241	+	18.4344i	−0.811237	+	0.622484i	−0.928800	−	0.370581i	$-0.879159\pi$
$877$	−24.0241	+	18.4344i	−0.811237	+	0.622484i	0.117563	+	0.993065i	$0.462492\pi$
$878$	2.16730	−	7.49867i	0.0731430	−	0.253068i
$879$	−1.98286	−	0.00738231i	−0.0668801	−	0.000248999i
$880$	−8.87014	−	10.3792i	−0.299012	−	0.349882i
$881$		−	33.1137i		−	1.11563i	−0.829966	−	0.557814i	$-0.811640\pi$
$881$		−	33.1137i		−	1.11563i	0.829966	−	0.557814i	$-0.188360\pi$
$882$	21.9724	+	6.52823i	0.739848	+	0.219817i
$883$	7.72620	+	3.20030i	0.260007	+	0.107699i	0.508879	−	0.860838i	$-0.330060\pi$
$883$	7.72620	+	3.20030i	0.260007	+	0.107699i	−0.248872	+	0.968536i	$0.580060\pi$
$884$	−1.25442	−	1.77439i	−0.0421909	−	0.0596793i
$885$	0.451673	−	3.33481i	0.0151828	−	0.112098i
$886$	30.1322	+	24.0720i	1.01231	+	0.808713i
$887$	−26.9041	+	7.20893i	−0.903351	+	0.242052i	−0.680455	−	0.732790i	$-0.738218\pi$
$887$	−26.9041	+	7.20893i	−0.903351	+	0.242052i	−0.222896	+	0.974842i	$0.571551\pi$
$888$	−17.8403	−	35.9000i	−0.598682	−	1.20473i
$889$	21.2930	+	5.70545i	0.714145	+	0.191354i
$890$	−0.926086	−	1.25706i	−0.0310425	−	0.0421367i
$891$	−6.72938	+	45.8299i	−0.225443	+	1.53536i
$892$	13.9652	+	26.5337i	0.467590	+	0.888413i
$893$	−24.6520	+	3.24549i	−0.824946	+	0.108606i
$894$	−0.0612458	+	2.63018i	−0.00204836	+	0.0879664i
$895$	−3.39172	+	5.87462i	−0.113373	+	0.196367i
$896$	36.7188	+	15.4686i	1.22669	+	0.516769i
$897$	23.0179	+	13.4039i	0.768545	+	0.447543i
$898$	−27.6326	−	0.540521i	−0.922111	−	0.0180374i
$899$	13.4783	−	32.5394i	0.449525	−	1.08525i
$900$	−27.3315	−	1.27356i	−0.911050	−	0.0424520i
$901$	−3.21473	+	1.33158i	−0.107098	+	0.0443615i
$902$	9.96155	−	22.7787i	0.331683	−	0.758449i
$903$	41.7978	+	42.1102i	1.39094	+	1.40134i
$904$	−5.55373	−	3.65671i	−0.184714	−	0.121620i
$905$	−6.50415	+	1.74278i	−0.216205	+	0.0579320i
$906$	16.6790	+	2.59216i	0.554123	+	0.0861189i
$907$	−18.1836	+	23.6973i	−0.603775	+	0.786855i	−0.990817	−	0.135207i	$-0.956830\pi$
$907$	−18.1836	+	23.6973i	−0.603775	+	0.786855i	0.387042	+	0.922062i	$0.373497\pi$
$908$	−52.2779	+	4.81173i	−1.73490	+	0.159683i
$909$	41.5880	+	17.5903i	1.37939	+	0.583432i
$910$	2.36226	+	9.56020i	0.0783082	+	0.316918i
$911$	−3.23823	+	1.86959i	−0.107287	+	0.0619423i	−0.552683	−	0.833391i	$-0.686396\pi$
$911$	−3.23823	+	1.86959i	−0.107287	+	0.0619423i	0.445396	+	0.895334i	$0.353063\pi$
$912$	−11.2793	+	31.5092i	−0.373496	+	1.04337i
$913$	−37.0803	−	21.4083i	−1.22718	−	0.708512i
$914$	−7.84651	+	27.1482i	−0.259539	+	0.897982i
$915$	−12.0690	+	1.54322i	−0.398989	+	0.0510174i
$916$	−4.72506	+	27.5234i	−0.156120	+	0.909400i
$917$	−5.54141	−	13.3782i	−0.182994	−	0.441785i
$918$	−2.50441	+	0.948309i	−0.0826579	+	0.0312989i
$919$	−19.7686	−	19.7686i	−0.652106	−	0.652106i	0.301394	−	0.953500i	$-0.402548\pi$
$919$	−19.7686	−	19.7686i	−0.652106	−	0.652106i	−0.953500	+	0.301394i	$0.902548\pi$
$920$	0.698173	+	9.64993i	0.0230181	+	0.318149i
$921$	0.304910	−	1.12123i	0.0100471	−	0.0369457i
$922$	−4.47931	−	40.0641i	−0.147518	−	1.31944i
$923$	3.23223	−	24.5512i	0.106390	−	0.808114i
$924$	−42.4567	−	46.2597i	−1.39672	−	1.52183i
$925$	−36.9969	+	4.87074i	−1.21645	+	0.160149i
$926$	38.9521	+	23.5165i	1.28005	+	0.772802i
$927$	9.07011	+	15.9836i	0.297902	+	0.524970i
$928$	33.0117	−	1.09332i	1.08366	−	0.0358901i
$929$	0.818762	+	1.41814i	0.0268627	+	0.0465276i	0.879144	−	0.476556i	$-0.158115\pi$
$929$	0.818762	+	1.41814i	0.0268627	+	0.0465276i	−0.852282	+	0.523083i	$0.824782\pi$
$930$	5.09559	−	8.36960i	0.167091	−	0.274450i
$931$	−15.8875	−	20.7050i	−0.520692	−	0.678580i
$932$	−19.2556	−	20.8242i	−0.630739	−	0.682120i
$933$	−8.62847	−	21.0523i	−0.282483	−	0.689222i
$934$	−34.2149	−	14.9628i	−1.11955	−	0.489598i
$935$	−0.879549	+	0.879549i	−0.0287643	+	0.0287643i
$936$	16.6933	−	19.0093i	0.545639	−	0.621339i
$937$	−34.2841	−	34.2841i	−1.12001	−	1.12001i	−0.991739	−	0.128273i	$-0.959057\pi$
$937$	−34.2841	−	34.2841i	−1.12001	−	1.12001i	−0.128273	−	0.991739i	$-0.540943\pi$
$938$	−13.3753	−	34.1659i	−0.436719	−	1.11556i
$939$	−6.13957	+	45.3299i	−0.200357	+	1.47928i
$940$	2.36401	+	6.40491i	0.0771054	+	0.208905i
$941$	−7.13631	+	5.47588i	−0.232637	+	0.178509i	−0.718501	−	0.695526i	$-0.755172\pi$
$941$	−7.13631	+	5.47588i	−0.232637	+	0.178509i	0.485864	+	0.874034i	$0.338505\pi$
$942$	−12.2731	+	11.7146i	−0.399881	+	0.381681i
$943$	−15.2577	+	8.80902i	−0.496858	+	0.286861i
$944$	2.43298	−	11.4635i	0.0791868	−	0.373106i
$945$	12.1351	+	0.135545i	0.394756	+	0.00440927i
$946$	−16.9831	−	68.7317i	−0.552169	−	2.23466i
$947$	−1.69617	−	12.8837i	−0.0551182	−	0.418664i	−0.996653	−	0.0817485i	$-0.973950\pi$
$947$	−1.69617	−	12.8837i	−0.0551182	−	0.418664i	0.941535	−	0.336916i	$-0.109384\pi$
$948$	9.47442	+	13.5081i	0.307715	+	0.438721i
$949$	23.9485	+	3.15288i	0.777400	+	0.102347i
$950$	24.3396	+	19.4444i	0.789679	+	0.630858i
$951$	7.68263	+	29.1050i	0.249126	+	0.943793i
$952$	1.14351	−	3.44519i	0.0370615	−	0.111659i
$953$	28.2602	−	28.2602i	0.915437	−	0.915437i	−0.0812562	−	0.996693i	$-0.525893\pi$
$953$	28.2602	−	28.2602i	0.915437	−	0.915437i	0.996693	+	0.0812562i	$0.0258932\pi$
$954$	−23.7841	−	32.7928i	−0.770038	−	1.06171i
$955$	−10.9958	+	4.55462i	−0.355817	+	0.147384i
$956$	28.6435	+	18.0666i	0.926396	+	0.584315i
$957$	−48.0146	−	20.0980i	−1.55209	−	0.649677i
$958$	21.4538	+	38.8966i	0.693141	+	1.25669i
$959$	16.4294	−	28.4565i	0.530532	−	0.918908i
$960$	9.12203	+	1.10987i	0.294412	+	0.0358209i
$961$	−2.69260	−	4.66373i	−0.0868582	−	0.150443i
$962$	17.8327	−	29.5376i	0.574950	−	0.952331i
$963$	32.0726	+	42.4486i	1.03352	+	1.36789i
$964$	−18.6165	+	9.79826i	−0.599598	+	0.315581i
$965$	2.40929	+	1.84871i	0.0775578	+	0.0595122i
$966$	4.77927	+	44.2379i	0.153770	+	1.42333i
$967$	8.61509	+	32.1519i	0.277043	+	1.03394i	0.954460	+	0.298338i	$0.0964324\pi$
$967$	8.61509	+	32.1519i	0.277043	+	1.03394i	−0.677418	+	0.735599i	$0.736901\pi$
$968$	8.83811	+	42.9109i	0.284068	+	1.37921i
$969$	2.94219	+	0.800111i	0.0945169	+	0.0257033i
$970$	0.0104985	−	0.00410996i	0.000337086	−	0.000131963i
$971$	−15.4074	−	37.1968i	−0.494448	−	1.19370i	−0.952435	−	0.304743i	$-0.901429\pi$
$971$	−15.4074	−	37.1968i	−0.494448	−	1.19370i	0.457987	−	0.888959i	$-0.348571\pi$
$972$	−17.5205	−	25.7882i	−0.561971	−	0.827157i
$973$	−69.3506	−	28.7260i	−2.22328	−	0.920913i
$974$	−8.44144	+	8.11753i	−0.270481	+	0.260102i
$975$	−11.6986	−	20.4378i	−0.374654	−	0.654535i
$976$	−42.3114	+	2.23042i	−1.35435	+	0.0713940i
$977$	−31.2571	−	18.0463i	−1.00000	−	0.577352i	−0.0917535	−	0.995782i	$-0.529247\pi$
$977$	−31.2571	−	18.0463i	−1.00000	−	0.577352i	−0.908249	+	0.418430i	$0.862581\pi$
$978$	−49.1992	−	14.4185i	−1.57322	−	0.461052i
$979$	1.11839	+	8.49498i	0.0357437	+	0.271501i
$980$	−4.58133	+	5.51016i	−0.146345	+	0.176016i
$981$	4.26570	+	0.593936i	0.136193	+	0.0189629i
$982$	31.9317	+	4.84097i	1.01898	+	0.154481i
$983$	−0.247437	+	0.923447i	−0.00789201	+	0.0294534i	−0.969760	−	0.244062i	$-0.921520\pi$
$983$	−0.247437	+	0.923447i	−0.00789201	+	0.0294534i	0.961868	+	0.273516i	$0.0881865\pi$
$984$	5.42708	+	15.8288i	0.173009	+	0.504604i
$985$	−1.16074	−	4.33193i	−0.0369841	−	0.138027i
$986$	−0.334356	−	2.99057i	−0.0106481	−	0.0952390i
$987$	11.9074	+	29.0525i	0.379018	+	0.924752i
$988$	−28.0933	+	6.36137i	−0.893766	+	0.202382i
$989$	−19.1996	+	46.3520i	−0.610513	+	1.47391i
$990$	−12.3411	−	7.57663i	−0.392225	−	0.240801i
$991$	42.0988			1.33731			0.668657	−	0.743571i	$-0.266869\pi$
$991$	42.0988			1.33731			0.668657	+	0.743571i	$0.266869\pi$
$992$	19.8648	−	27.7437i	0.630709	−	0.880865i
$993$	21.8936	+	12.7492i	0.694773	+	0.404584i
$994$	36.2219	−	19.9786i	1.14889	−	0.633682i
$995$	−6.18388	−	8.05899i	−0.196042	−	0.255487i
$996$	28.1300	−	6.25968i	0.891332	−	0.198345i
$997$	−5.68687	−	4.36369i	−0.180105	−	0.138199i	0.514775	−	0.857326i	$-0.327876\pi$
$997$	−5.68687	−	4.36369i	−0.180105	−	0.138199i	−0.694879	+	0.719126i	$0.744542\pi$
$998$	−11.0561	+	8.14509i	−0.349974	+	0.257828i
$999$	−29.7287	−	30.4003i	−0.940574	−	0.961823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.13.1	✓	368
3.2	odd	2		864.2.bk.a.685.46		368
9.2	odd	6		864.2.bk.a.397.17		368
9.7	even	3	inner	288.2.bc.a.205.30	yes	368
32.5	even	8	inner	288.2.bc.a.229.30	yes	368
96.5	odd	8		864.2.bk.a.37.17		368
288.101	odd	24		864.2.bk.a.613.46		368
288.133	even	24	inner	288.2.bc.a.133.1	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.1	✓	368	1.1	even	1	trivial
288.2.bc.a.133.1	yes	368	288.133	even	24	inner
288.2.bc.a.205.30	yes	368	9.7	even	3	inner
288.2.bc.a.229.30	yes	368	32.5	even	8	inner
864.2.bk.a.37.17		368	96.5	odd	8
864.2.bk.a.397.17		368	9.2	odd	6
864.2.bk.a.613.46		368	288.101	odd	24
864.2.bk.a.685.46		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41394 - 0.0276581i) q^{2} +(-0.219683 - 1.71806i) q^{3} +(1.99847 + 0.0782141i) q^{4} +(-0.0865625 + 0.657507i) q^{5} +(0.263101 + 2.43532i) q^{6} +(-3.40174 - 0.911495i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(-2.90348 + 0.754859i) q^{9} +O(q^{10})\)	\(q+(-1.41394 - 0.0276581i) q^{2} +(-0.219683 - 1.71806i) q^{3} +(1.99847 + 0.0782141i) q^{4} +(-0.0865625 + 0.657507i) q^{5} +(0.263101 + 2.43532i) q^{6} +(-3.40174 - 0.911495i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(-2.90348 + 0.754859i) q^{9} +(0.140580 - 0.927284i) q^{10} +(-3.13318 + 4.08325i) q^{11} +(-0.304653 - 3.45068i) q^{12} +(2.36536 - 1.81501i) q^{13} +(4.78466 + 1.38289i) q^{14} +(1.14866 + 0.00427652i) q^{15} +(3.98777 + 0.312617i) q^{16} -0.364422i q^{17} +(4.12623 - 0.987022i) q^{18} +(-4.46287 - 1.84858i) q^{19} +(-0.224419 + 1.30724i) q^{20} +(-0.818699 + 6.04465i) q^{21} +(4.54308 - 5.68682i) q^{22} +(-4.98224 + 1.33499i) q^{23} +(0.335323 + 4.88749i) q^{24} +(4.40481 + 1.18026i) q^{25} +(-3.39469 + 2.50090i) q^{26} +(1.93474 + 4.82253i) q^{27} +(-6.72699 - 2.08766i) q^{28} +(-5.78895 + 0.762130i) q^{29} +(-1.62401 - 0.0378164i) q^{30} +(-3.01601 + 5.22388i) q^{31} +(-5.62983 - 0.552317i) q^{32} +(7.70358 + 4.48599i) q^{33} +(-0.0100792 + 0.515272i) q^{34} +(0.893778 - 2.15777i) q^{35} +(-5.86156 + 1.28147i) q^{36} +(-7.56014 + 3.13151i) q^{37} +(6.25912 + 2.73722i) q^{38} +(-3.63793 - 3.66512i) q^{39} +(0.353471 - 1.84215i) q^{40} +(3.29929 - 0.884042i) q^{41} +(1.32478 - 8.52415i) q^{42} +(5.92133 - 7.71683i) q^{43} +(-6.58094 + 7.91518i) q^{44} +(-0.244993 - 1.97440i) q^{45} +(7.08153 - 1.74980i) q^{46} +(4.45774 - 2.57368i) q^{47} +(-0.338949 - 6.91991i) q^{48} +(4.67887 + 2.70134i) q^{49} +(-6.19550 - 1.79066i) q^{50} +(-0.626099 + 0.0800573i) q^{51} +(4.86907 - 3.44223i) q^{52} +(-3.65397 - 8.82145i) q^{53} +(-2.60223 - 6.87229i) q^{54} +(-2.41355 - 2.41355i) q^{55} +(9.45384 + 3.13789i) q^{56} +(-2.19556 + 8.07359i) q^{57} +(8.20633 - 0.917497i) q^{58} +(0.382404 - 2.90465i) q^{59} +(2.29522 + 0.0983875i) q^{60} +(-10.5019 + 1.38260i) q^{61} +(4.40895 - 7.30285i) q^{62} +(10.5649 + 0.0786691i) q^{63} +(7.94498 + 0.936655i) q^{64} +(0.988629 + 1.71236i) q^{65} +(-10.7683 - 6.55600i) q^{66} +(-4.48467 - 5.84453i) q^{67} +(0.0285029 - 0.728286i) q^{68} +(3.38811 + 8.26653i) q^{69} +(-1.32343 + 3.02624i) q^{70} +(5.87298 - 5.87298i) q^{71} +(8.32335 - 1.64981i) q^{72} +(5.72879 + 5.72879i) q^{73} +(10.7762 - 4.21868i) q^{74} +(1.06011 - 7.82702i) q^{75} +(-8.77433 - 4.04339i) q^{76} +(14.3801 - 11.0343i) q^{77} +(5.04245 + 5.28288i) q^{78} +(-4.12486 + 2.38149i) q^{79} +(-0.550739 + 2.59492i) q^{80} +(7.86038 - 4.38343i) q^{81} +(-4.68946 + 1.15873i) q^{82} +(1.08585 + 8.24788i) q^{83} +(-2.10892 + 12.0160i) q^{84} +(0.239610 + 0.0315453i) q^{85} +(-8.58586 + 10.7474i) q^{86} +(2.58112 + 9.77836i) q^{87} +(9.52400 - 11.0096i) q^{88} +(1.17717 - 1.17717i) q^{89} +(0.291798 + 2.79847i) q^{90} +(-9.70073 + 4.01817i) q^{91} +(-10.0613 + 2.27825i) q^{92} +(9.63752 + 4.03409i) q^{93} +(-6.37417 + 3.51574i) q^{94} +(1.60177 - 2.77435i) q^{95} +(0.287863 + 9.79373i) q^{96} +(0.00601054 + 0.0104106i) q^{97} +(-6.54094 - 3.94896i) q^{98} +(6.01486 - 14.2207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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