LMFDB - Embedded newform 840.2.z.d.811.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(811,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.811"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.z (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,2,0,-2,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.5
Character	$\chi$	$=$	840.811
Dual form			840.2.z.d.811.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22597 - 0.704981i) q^{2} -1.00000i q^{3} +(1.00600 + 1.72857i) q^{4} +1.00000 q^{5} +(-0.704981 + 1.22597i) q^{6} +(2.37591 - 1.16407i) q^{7} +(-0.0147234 - 2.82839i) q^{8} -1.00000 q^{9} +(-1.22597 - 0.704981i) q^{10} -2.29742 q^{11} +(1.72857 - 1.00600i) q^{12} -6.22162 q^{13} +(-3.73344 - 0.247852i) q^{14} -1.00000i q^{15} +(-1.97591 + 3.47790i) q^{16} -2.99183i q^{17} +(1.22597 + 0.704981i) q^{18} +0.901647i q^{19} +(1.00600 + 1.72857i) q^{20} +(-1.16407 - 2.37591i) q^{21} +(2.81657 + 1.61964i) q^{22} -8.15215i q^{23} +(-2.82839 + 0.0147234i) q^{24} +1.00000 q^{25} +(7.62752 + 4.38612i) q^{26} +1.00000i q^{27} +(4.40235 + 2.93586i) q^{28} -1.15423i q^{29} +(-0.704981 + 1.22597i) q^{30} -1.82156 q^{31} +(4.87426 - 2.87082i) q^{32} +2.29742i q^{33} +(-2.10918 + 3.66790i) q^{34} +(2.37591 - 1.16407i) q^{35} +(-1.00600 - 1.72857i) q^{36} -1.80548i q^{37} +(0.635644 - 1.10539i) q^{38} +6.22162i q^{39} +(-0.0147234 - 2.82839i) q^{40} -11.3040i q^{41} +(-0.247852 + 3.73344i) q^{42} +11.5218 q^{43} +(-2.31121 - 3.97125i) q^{44} -1.00000 q^{45} +(-5.74710 + 9.99429i) q^{46} -9.48888 q^{47} +(3.47790 + 1.97591i) q^{48} +(4.28987 - 5.53145i) q^{49} +(-1.22597 - 0.704981i) q^{50} -2.99183 q^{51} +(-6.25898 - 10.7545i) q^{52} -4.44952i q^{53} +(0.704981 - 1.22597i) q^{54} -2.29742 q^{55} +(-3.32743 - 6.70285i) q^{56} +0.901647 q^{57} +(-0.813710 + 1.41505i) q^{58} +5.71571i q^{59} +(1.72857 - 1.00600i) q^{60} -11.0303 q^{61} +(2.23318 + 1.28417i) q^{62} +(-2.37591 + 1.16407i) q^{63} +(-7.99957 + 0.0832869i) q^{64} -6.22162 q^{65} +(1.61964 - 2.81657i) q^{66} +6.42834 q^{67} +(5.17159 - 3.00980i) q^{68} -8.15215 q^{69} +(-3.73344 - 0.247852i) q^{70} -7.96854i q^{71} +(0.0147234 + 2.82839i) q^{72} +4.10159i q^{73} +(-1.27282 + 2.21346i) q^{74} -1.00000i q^{75} +(-1.55856 + 0.907061i) q^{76} +(-5.45846 + 2.67436i) q^{77} +(4.38612 - 7.62752i) q^{78} +14.9684i q^{79} +(-1.97591 + 3.47790i) q^{80} +1.00000 q^{81} +(-7.96912 + 13.8584i) q^{82} +10.3637i q^{83} +(2.93586 - 4.40235i) q^{84} -2.99183i q^{85} +(-14.1254 - 8.12264i) q^{86} -1.15423 q^{87} +(0.0338258 + 6.49800i) q^{88} -1.36087i q^{89} +(1.22597 + 0.704981i) q^{90} +(-14.7820 + 7.24242i) q^{91} +(14.0916 - 8.20110i) q^{92} +1.82156i q^{93} +(11.6331 + 6.68948i) q^{94} +0.901647i q^{95} +(-2.87082 - 4.87426i) q^{96} -8.12945i q^{97} +(-9.15882 + 3.75712i) q^{98} +2.29742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 2 q^{4} + 28 q^{5} + 4 q^{6} + 4 q^{7} - 10 q^{8} - 28 q^{9} + 2 q^{10} - 8 q^{12} - 8 q^{13} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 - 2 * q^4 + 28 * q^5 + 4 * q^6 + 4 * q^7 - 10 * q^8 - 28 * q^9 + 2 * q^10 - 8 * q^12 - 8 * q^13 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * q^28 + 4 * q^30 + 24 * q^31 + 2 * q^32 + 8 * q^34 + 4 * q^35 + 2 * q^36 + 36 * q^38 - 10 * q^40 + 24 * q^43 - 4 * q^44 - 28 * q^45 - 44 * q^46 - 24 * q^47 + 16 * q^48 + 28 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^54 - 22 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 - 16 * q^61 - 28 * q^62 - 4 * q^63 + 22 * q^64 - 8 * q^65 - 20 * q^66 - 8 * q^67 - 12 * q^68 - 24 * q^69 + 2 * q^70 + 10 * q^72 - 8 * q^74 - 16 * q^76 + 16 * q^77 + 20 * q^78 + 6 * q^80 + 28 * q^81 + 24 * q^82 - 12 * q^84 - 4 * q^86 + 16 * q^87 + 40 * q^88 - 2 * q^90 + 48 * q^91 + 40 * q^92 + 52 * q^94 - 16 * q^96 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.22597	−	0.704981i	−0.866892	−	0.498497i
$2$	−1.22597	−	0.704981i	−0.866892	−	0.498497i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00600	+	1.72857i	0.503002	+	0.864285i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.704981	+	1.22597i	−0.287807	+	0.500500i
$7$	2.37591	−	1.16407i	0.898009	−	0.439978i
$7$	2.37591	−	1.16407i	0.898009	−	0.439978i
$8$	−0.0147234	−	2.82839i	−0.00520550	−	0.999986i
$9$	−1.00000			−0.333333
$10$	−1.22597	−	0.704981i	−0.387686	−	0.222934i
$11$	−2.29742			−0.692698			−0.346349	−	0.938106i	$-0.612579\pi$
$11$	−2.29742			−0.692698			−0.346349	+	0.938106i	$0.612579\pi$
$12$	1.72857	−	1.00600i	0.498995	−	0.290409i
$13$	−6.22162			−1.72557			−0.862784	−	0.505573i	$-0.831281\pi$
$13$	−6.22162			−1.72557			−0.862784	+	0.505573i	$0.831281\pi$
$14$	−3.73344	−	0.247852i	−0.997804	−	0.0662412i
$15$		−	1.00000i		−	0.258199i
$16$	−1.97591	+	3.47790i	−0.493977	+	0.869475i
$17$		−	2.99183i		−	0.725626i	−0.931862	−	0.362813i	$-0.881816\pi$
$17$		−	2.99183i		−	0.725626i	0.931862	−	0.362813i	$-0.118184\pi$
$18$	1.22597	+	0.704981i	0.288964	+	0.166166i
$19$			0.901647i			0.206852i	0.994637	+	0.103426i	$0.0329805\pi$
$19$			0.901647i			0.206852i	−0.994637	+	0.103426i	$0.967019\pi$
$20$	1.00600	+	1.72857i	0.224950	+	0.386520i
$21$	−1.16407	−	2.37591i	−0.254021	−	0.518466i
$22$	2.81657	+	1.61964i	0.600494	+	0.345308i
$23$		−	8.15215i		−	1.69984i	−0.526912	−	0.849920i	$-0.676650\pi$
$23$		−	8.15215i		−	1.69984i	0.526912	−	0.849920i	$-0.323350\pi$
$24$	−2.82839	+	0.0147234i	−0.577342	+	0.00300540i
$25$	1.00000			0.200000
$26$	7.62752	+	4.38612i	1.49588	+	0.860190i
$27$			1.00000i			0.192450i
$28$	4.40235	+	2.93586i	0.831967	+	0.554826i
$29$		−	1.15423i		−	0.214335i	−0.994241	−	0.107168i	$-0.965822\pi$
$29$		−	1.15423i		−	0.214335i	0.994241	−	0.107168i	$-0.0341781\pi$
$30$	−0.704981	+	1.22597i	−0.128711	+	0.223830i
$31$	−1.82156			−0.327163			−0.163581	−	0.986530i	$-0.552305\pi$
$31$	−1.82156			−0.327163			−0.163581	+	0.986530i	$0.552305\pi$
$32$	4.87426	−	2.87082i	0.861655	−	0.507495i
$33$			2.29742i			0.399929i
$34$	−2.10918	+	3.66790i	−0.361722	+	0.629039i
$35$	2.37591	−	1.16407i	0.401602	−	0.196764i
$36$	−1.00600	−	1.72857i	−0.167667	−	0.288095i
$37$		−	1.80548i		−	0.296818i	−0.988926	−	0.148409i	$-0.952585\pi$
$37$		−	1.80548i		−	0.296818i	0.988926	−	0.148409i	$-0.0474153\pi$
$38$	0.635644	−	1.10539i	0.103115	−	0.179318i
$39$			6.22162i			0.996257i
$40$	−0.0147234	−	2.82839i	−0.00232797	−	0.447208i
$41$		−	11.3040i		−	1.76539i	−0.469944	−	0.882696i	$-0.655726\pi$
$41$		−	11.3040i		−	1.76539i	0.469944	−	0.882696i	$-0.344274\pi$
$42$	−0.247852	+	3.73344i	−0.0382444	+	0.576082i
$43$	11.5218			1.75706			0.878528	−	0.477691i	$-0.158526\pi$
$43$	11.5218			1.75706			0.878528	+	0.477691i	$0.158526\pi$
$44$	−2.31121	−	3.97125i	−0.348429	−	0.598688i
$45$	−1.00000			−0.149071
$46$	−5.74710	+	9.99429i	−0.847364	+	1.47358i
$47$	−9.48888			−1.38410			−0.692048	−	0.721852i	$-0.743291\pi$
$47$	−9.48888			−1.38410			−0.692048	+	0.721852i	$0.743291\pi$
$48$	3.47790	+	1.97591i	0.501992	+	0.285198i
$49$	4.28987	−	5.53145i	0.612839	−	0.790208i
$50$	−1.22597	−	0.704981i	−0.173378	−	0.0996993i
$51$	−2.99183			−0.418940
$52$	−6.25898	−	10.7545i	−0.867965	−	1.49138i
$53$		−	4.44952i		−	0.611188i	−0.952162	−	0.305594i	$-0.901145\pi$
$53$		−	4.44952i		−	0.611188i	0.952162	−	0.305594i	$-0.0988551\pi$
$54$	0.704981	−	1.22597i	0.0959357	−	0.166833i
$55$	−2.29742			−0.309784
$56$	−3.32743	−	6.70285i	−0.444646	−	0.895706i
$57$	0.901647			0.119426
$58$	−0.813710	+	1.41505i	−0.106845	+	0.185805i
$59$			5.71571i			0.744122i	0.928208	+	0.372061i	$0.121349\pi$
$59$			5.71571i			0.744122i	−0.928208	+	0.372061i	$0.878651\pi$
$60$	1.72857	−	1.00600i	0.223157	−	0.129875i
$61$	−11.0303			−1.41229			−0.706145	−	0.708067i	$-0.749567\pi$
$61$	−11.0303			−1.41229			−0.706145	+	0.708067i	$0.749567\pi$
$62$	2.23318	+	1.28417i	0.283614	+	0.163089i
$63$	−2.37591	+	1.16407i	−0.299336	+	0.146659i
$64$	−7.99957	+	0.0832869i	−0.999946	+	0.0104109i
$65$	−6.22162			−0.771697
$66$	1.61964	−	2.81657i	0.199363	−	0.346695i
$67$	6.42834			0.785347			0.392673	−	0.919678i	$-0.371550\pi$
$67$	6.42834			0.785347			0.392673	+	0.919678i	$0.371550\pi$
$68$	5.17159	−	3.00980i	0.627148	−	0.364992i
$69$	−8.15215			−0.981403
$70$	−3.73344	−	0.247852i	−0.446231	−	0.0296240i
$71$		−	7.96854i		−	0.945692i	−0.881145	−	0.472846i	$-0.843227\pi$
$71$		−	7.96854i		−	0.945692i	0.881145	−	0.472846i	$-0.156773\pi$
$72$	0.0147234	+	2.82839i	0.00173517	+	0.333329i
$73$			4.10159i			0.480055i	0.970766	+	0.240027i	$0.0771565\pi$
$73$			4.10159i			0.480055i	−0.970766	+	0.240027i	$0.922844\pi$
$74$	−1.27282	+	2.21346i	−0.147963	+	0.257309i
$75$		−	1.00000i		−	0.115470i
$76$	−1.55856	+	0.907061i	−0.178779	+	0.104047i
$77$	−5.45846	+	2.67436i	−0.622049	+	0.304772i
$78$	4.38612	−	7.62752i	0.496631	−	0.863647i
$79$			14.9684i			1.68408i	0.539419	+	0.842038i	$0.318644\pi$
$79$			14.9684i			1.68408i	−0.539419	+	0.842038i	$0.681356\pi$
$80$	−1.97591	+	3.47790i	−0.220913	+	0.388841i
$81$	1.00000			0.111111
$82$	−7.96912	+	13.8584i	−0.880042	+	1.53040i
$83$			10.3637i			1.13756i	0.822489	+	0.568782i	$0.192585\pi$
$83$			10.3637i			1.13756i	−0.822489	+	0.568782i	$0.807415\pi$
$84$	2.93586	−	4.40235i	0.320329	−	0.480336i
$85$		−	2.99183i		−	0.324510i
$86$	−14.1254	−	8.12264i	−1.52318	−	0.875886i
$87$	−1.15423			−0.123746
$88$	0.0338258	+	6.49800i	0.00360584	+	0.692689i
$89$		−	1.36087i		−	0.144252i	−0.997396	−	0.0721260i	$-0.977022\pi$
$89$		−	1.36087i		−	0.144252i	0.997396	−	0.0721260i	$-0.0229784\pi$
$90$	1.22597	+	0.704981i	0.129229	+	0.0743115i
$91$	−14.7820	+	7.24242i	−1.54958	+	0.759211i
$92$	14.0916	−	8.20110i	1.46915	−	0.855024i
$93$			1.82156i			0.188887i
$94$	11.6331	+	6.68948i	1.19986	+	0.689967i
$95$			0.901647i			0.0925071i
$96$	−2.87082	−	4.87426i	−0.293002	−	0.497477i
$97$		−	8.12945i		−	0.825420i	−0.910862	−	0.412710i	$-0.864582\pi$
$97$		−	8.12945i		−	0.825420i	0.910862	−	0.412710i	$-0.135418\pi$
$98$	−9.15882	+	3.75712i	−0.925181	+	0.379526i
$99$	2.29742			0.230899
$100$	1.00600	+	1.72857i	0.100600	+	0.172857i
$101$	−4.56052			−0.453789			−0.226894	−	0.973919i	$-0.572857\pi$
$101$	−4.56052			−0.453789			−0.226894	+	0.973919i	$0.572857\pi$
$102$	3.66790	+	2.10918i	0.363176	+	0.208840i
$103$	1.65646			0.163216			0.0816079	−	0.996665i	$-0.473994\pi$
$103$	1.65646			0.163216			0.0816079	+	0.996665i	$0.473994\pi$
$104$	0.0916033	+	17.5972i	0.00898244	+	1.72554i
$105$	−1.16407	−	2.37591i	−0.113602	−	0.231865i
$106$	−3.13682	+	5.45498i	−0.304675	+	0.529834i
$107$	−5.99730			−0.579781			−0.289891	−	0.957060i	$-0.593619\pi$
$107$	−5.99730			−0.579781			−0.289891	+	0.957060i	$0.593619\pi$
$108$	−1.72857	+	1.00600i	−0.166332	+	0.0968029i
$109$		−	14.4206i		−	1.38124i	−0.723215	−	0.690622i	$-0.757337\pi$
$109$		−	14.4206i		−	1.38124i	0.723215	−	0.690622i	$-0.242663\pi$
$110$	2.81657	+	1.61964i	0.268549	+	0.154426i
$111$	−1.80548			−0.171368
$112$	−0.646053	+	10.5633i	−0.0610463	+	0.998135i
$113$	20.3916			1.91828			0.959139	−	0.282936i	$-0.0913083\pi$
$113$	20.3916			1.91828			0.959139	+	0.282936i	$0.0913083\pi$
$114$	−1.10539	−	0.635644i	−0.103529	−	0.0595335i
$115$		−	8.15215i		−	0.760192i
$116$	1.99517	−	1.16116i	0.185247	−	0.107811i
$117$	6.22162			0.575189
$118$	4.02946	−	7.00729i	0.370942	−	0.645073i
$119$	−3.48271	−	7.10832i	−0.319259	−	0.651619i
$120$	−2.82839	+	0.0147234i	−0.258195	+	0.00134405i
$121$	−5.72186			−0.520170
$122$	13.5229	+	7.77617i	1.22430	+	0.704022i
$123$	−11.3040			−1.01925
$124$	−1.83250	−	3.14870i	−0.164564	−	0.282762i
$125$	1.00000			0.0894427
$126$	3.73344	+	0.247852i	0.332601	+	0.0220804i
$127$		−	7.73916i		−	0.686739i	−0.939200	−	0.343370i	$-0.888432\pi$
$127$		−	7.73916i		−	0.686739i	0.939200	−	0.343370i	$-0.111568\pi$
$128$	9.86594	+	5.53743i	0.872034	+	0.489444i
$129$		−	11.5218i		−	1.01444i
$130$	7.62752	+	4.38612i	0.668978	+	0.384689i
$131$			0.428007i			0.0373951i	0.999825	+	0.0186976i	$0.00595197\pi$
$131$			0.428007i			0.0373951i	−0.999825	+	0.0186976i	$0.994048\pi$
$132$	−3.97125	+	2.31121i	−0.345653	+	0.201165i
$133$	1.04958	+	2.14223i	0.0910103	+	0.185755i
$134$	−7.88095	−	4.53185i	−0.680811	−	0.391493i
$135$			1.00000i			0.0860663i
$136$	−8.46207	+	0.0440499i	−0.725616	+	0.00377725i
$137$	−12.2390			−1.04564			−0.522822	−	0.852442i	$-0.675121\pi$
$137$	−12.2390			−1.04564			−0.522822	+	0.852442i	$0.675121\pi$
$138$	9.99429	+	5.74710i	0.850770	+	0.489226i
$139$			10.3041i			0.873980i	0.899466	+	0.436990i	$0.143955\pi$
$139$			10.3041i			0.873980i	−0.899466	+	0.436990i	$0.856045\pi$
$140$	4.40235	+	2.93586i	0.372067	+	0.248126i
$141$			9.48888i			0.799108i
$142$	−5.61767	+	9.76920i	−0.471424	+	0.819813i
$143$	14.2937			1.19530
$144$	1.97591	−	3.47790i	0.164659	−	0.289825i
$145$		−	1.15423i		−	0.0958536i
$146$	2.89154	−	5.02843i	0.239306	−	0.416156i
$147$	−5.53145	−	4.28987i	−0.456227	−	0.353823i
$148$	3.12089	−	1.81632i	0.256536	−	0.149300i
$149$			3.34559i			0.274081i	0.990565	+	0.137041i	$0.0437591\pi$
$149$			3.34559i			0.274081i	−0.990565	+	0.137041i	$0.956241\pi$
$150$	−0.704981	+	1.22597i	−0.0575614	+	0.100100i
$151$		−	10.4431i		−	0.849850i	−0.905228	−	0.424925i	$-0.860300\pi$
$151$		−	10.4431i		−	0.849850i	0.905228	−	0.424925i	$-0.139700\pi$
$152$	2.55021	−	0.0132753i	0.206849	−	0.00107677i
$153$			2.99183i			0.241875i
$154$	8.57728	+	0.569420i	0.691177	+	0.0458852i
$155$	−1.82156			−0.146312
$156$	−10.7545	+	6.25898i	−0.861050	+	0.501120i
$157$	−3.76672			−0.300617			−0.150309	−	0.988639i	$-0.548027\pi$
$157$	−3.76672			−0.300617			−0.150309	+	0.988639i	$0.548027\pi$
$158$	10.5524	−	18.3508i	0.839506	−	1.45991i
$159$	−4.44952			−0.352870
$160$	4.87426	−	2.87082i	0.385344	−	0.226958i
$161$	−9.48968	−	19.3687i	−0.747892	−	1.52647i
$162$	−1.22597	−	0.704981i	−0.0963213	−	0.0553885i
$163$	−11.7746			−0.922259			−0.461129	−	0.887333i	$-0.652556\pi$
$163$	−11.7746			−0.922259			−0.461129	+	0.887333i	$0.652556\pi$
$164$	19.5398	−	11.3719i	1.52580	−	0.887997i
$165$			2.29742i			0.178854i
$166$	7.30620	−	12.7056i	0.567071	−	0.986144i
$167$	24.1292			1.86717			0.933587	−	0.358352i	$-0.116661\pi$
$167$	24.1292			1.86717			0.933587	+	0.358352i	$0.116661\pi$
$168$	−6.70285	+	3.32743i	−0.517136	+	0.256717i
$169$	25.7086			1.97758
$170$	−2.10918	+	3.66790i	−0.161767	+	0.281315i
$171$		−	0.901647i		−	0.0689507i
$172$	11.5910	+	19.9162i	0.883803	+	1.51860i
$173$	−11.5661			−0.879354			−0.439677	−	0.898156i	$-0.644907\pi$
$173$	−11.5661			−0.879354			−0.439677	+	0.898156i	$0.644907\pi$
$174$	1.41505	+	0.813710i	0.107275	+	0.0616872i
$175$	2.37591	−	1.16407i	0.179602	−	0.0879955i
$176$	4.53949	−	7.99019i	0.342177	−	0.602283i
$177$	5.71571			0.429619
$178$	−0.959387	+	1.66839i	−0.0719091	+	0.125051i
$179$	26.1436			1.95407			0.977033	−	0.213086i	$-0.0683514\pi$
$179$	26.1436			1.95407			0.977033	+	0.213086i	$0.0683514\pi$
$180$	−1.00600	−	1.72857i	−0.0749832	−	0.128840i
$181$	12.9659			0.963749			0.481875	−	0.876240i	$-0.339956\pi$
$181$	12.9659			0.963749			0.481875	+	0.876240i	$0.339956\pi$
$182$	23.2281	+	1.54204i	1.72178	+	0.114304i
$183$			11.0303i			0.815386i
$184$	−23.0574	+	0.120027i	−1.69982	+	0.00884852i
$185$		−	1.80548i		−	0.132741i
$186$	1.28417	−	2.23318i	0.0941597	−	0.163745i
$187$			6.87350i			0.502640i
$188$	−9.54586	−	16.4022i	−0.696203	−	1.19625i
$189$	1.16407	+	2.37591i	0.0846737	+	0.172822i
$190$	0.635644	−	1.10539i	0.0461144	−	0.0801936i
$191$			21.5890i			1.56212i	0.624454	+	0.781062i	$0.285322\pi$
$191$			21.5890i			1.56212i	−0.624454	+	0.781062i	$0.714678\pi$
$192$	0.0832869	+	7.99957i	0.00601071	+	0.577319i
$193$	16.0794			1.15742			0.578711	−	0.815532i	$-0.303556\pi$
$193$	16.0794			1.15742			0.578711	+	0.815532i	$0.303556\pi$
$194$	−5.73110	+	9.96646i	−0.411469	+	0.715550i
$195$			6.22162i			0.445540i
$196$	13.8771	+	1.85068i	0.991224	+	0.132191i
$197$		−	2.13232i		−	0.151922i	−0.997111	−	0.0759609i	$-0.975798\pi$
$197$		−	2.13232i		−	0.151922i	0.997111	−	0.0759609i	$-0.0242024\pi$
$198$	−2.81657	−	1.61964i	−0.200165	−	0.115103i
$199$	4.06306			0.288023			0.144011	−	0.989576i	$-0.454000\pi$
$199$	4.06306			0.288023			0.144011	+	0.989576i	$0.454000\pi$
$200$	−0.0147234	−	2.82839i	−0.00104110	−	0.199997i
$201$		−	6.42834i		−	0.453420i
$202$	5.59106	+	3.21508i	0.393386	+	0.226212i
$203$	−1.34361	−	2.74234i	−0.0943027	−	0.192475i
$204$	−3.00980	−	5.17159i	−0.210728	−	0.362084i
$205$		−	11.3040i		−	0.789507i
$206$	−2.03077	−	1.16777i	−0.141490	−	0.0813625i
$207$			8.15215i			0.566613i
$208$	12.2934	−	21.6382i	0.852391	−	1.50034i
$209$		−	2.07146i		−	0.143286i
$210$	−0.247852	+	3.73344i	−0.0171034	+	0.257632i
$211$	−9.66474			−0.665348			−0.332674	−	0.943042i	$-0.607951\pi$
$211$	−9.66474			−0.665348			−0.332674	+	0.943042i	$0.607951\pi$
$212$	7.69130	−	4.47624i	0.528241	−	0.307429i
$213$	−7.96854			−0.545996
$214$	7.35251	+	4.22798i	0.502607	+	0.289019i
$215$	11.5218			0.785779
$216$	2.82839	−	0.0147234i	0.192447	−	0.00100180i
$217$	−4.32787	+	2.12043i	−0.293795	+	0.143944i
$218$	−10.1663	+	17.6792i	−0.688546	+	1.19739i
$219$	4.10159			0.277160
$220$	−2.31121	−	3.97125i	−0.155822	−	0.267742i
$221$			18.6141i			1.25212i
$222$	2.21346	+	1.27282i	0.148558	+	0.0854264i
$223$	15.6666			1.04912			0.524558	−	0.851375i	$-0.324231\pi$
$223$	15.6666			1.04912			0.524558	+	0.851375i	$0.324231\pi$
$224$	8.23894	−	12.4948i	0.550487	−	0.834844i
$225$	−1.00000			−0.0666667
$226$	−24.9995	−	14.3757i	−1.66294	−	0.956255i
$227$			2.75915i			0.183131i	0.995799	+	0.0915657i	$0.0291871\pi$
$227$			2.75915i			0.183131i	−0.995799	+	0.0915657i	$0.970813\pi$
$228$	0.907061	+	1.55856i	0.0600716	+	0.103218i
$229$	18.5792			1.22775			0.613873	−	0.789405i	$-0.289611\pi$
$229$	18.5792			1.22775			0.613873	+	0.789405i	$0.289611\pi$
$230$	−5.74710	+	9.99429i	−0.378953	+	0.659004i
$231$	2.67436	+	5.45846i	0.175960	+	0.359140i
$232$	−3.26461	+	0.0169942i	−0.214332	+	0.00111572i
$233$	−13.6689			−0.895481			−0.447740	−	0.894164i	$-0.647771\pi$
$233$	−13.6689			−0.895481			−0.447740	+	0.894164i	$0.647771\pi$
$234$	−7.62752	−	4.38612i	−0.498627	−	0.286730i
$235$	−9.48888			−0.618986
$236$	−9.88000	+	5.75003i	−0.643133	+	0.374295i
$237$	14.9684			0.972301
$238$	−0.741532	+	11.1698i	−0.0480664	+	0.724032i
$239$			17.4682i			1.12993i	0.825116	+	0.564964i	$0.191110\pi$
$239$			17.4682i			1.12993i	−0.825116	+	0.564964i	$0.808890\pi$
$240$	3.47790	+	1.97591i	0.224497	+	0.127544i
$241$			29.1215i			1.87588i	0.346799	+	0.937939i	$0.387268\pi$
$241$			29.1215i			1.87588i	−0.346799	+	0.937939i	$0.612732\pi$
$242$	7.01483	+	4.03380i	0.450931	+	0.259303i
$243$		−	1.00000i		−	0.0641500i
$244$	−11.0966	−	19.0667i	−0.710385	−	1.22062i
$245$	4.28987	−	5.53145i	0.274070	−	0.353392i
$246$	13.8584	+	7.96912i	0.883579	+	0.508092i
$247$		−	5.60971i		−	0.356937i
$248$	0.0268196	+	5.15209i	0.00170304	+	0.327158i
$249$	10.3637			0.656773
$250$	−1.22597	−	0.704981i	−0.0775371	−	0.0445869i
$251$		−	11.4415i		−	0.722178i	−0.932531	−	0.361089i	$-0.882405\pi$
$251$		−	11.4415i		−	0.722178i	0.932531	−	0.361089i	$-0.117595\pi$
$252$	−4.40235	−	2.93586i	−0.277322	−	0.184942i
$253$			18.7289i			1.17748i
$254$	−5.45596	+	9.48798i	−0.342337	+	0.595329i
$255$	−2.99183			−0.187356
$256$	−8.19157	−	13.7440i	−0.511973	−	0.859001i
$257$			7.10334i			0.443094i	0.975150	+	0.221547i	$0.0711107\pi$
$257$			7.10334i			0.443094i	−0.975150	+	0.221547i	$0.928889\pi$
$258$	−8.12264	+	14.1254i	−0.505693	+	0.879407i
$259$	−2.10170	−	4.28964i	−0.130593	−	0.266545i
$260$	−6.25898	−	10.7545i	−0.388166	−	0.666967i
$261$			1.15423i			0.0714450i
$262$	0.301736	−	0.524723i	0.0186413	−	0.0324175i
$263$			4.84190i			0.298565i	0.988795	+	0.149282i	$0.0476963\pi$
$263$			4.84190i			0.298565i	−0.988795	+	0.149282i	$0.952304\pi$
$264$	6.49800	−	0.0338258i	0.399924	−	0.00208183i
$265$		−	4.44952i		−	0.273332i
$266$	0.223475	−	3.36625i	0.0137021	−	0.206398i
$267$	−1.36087			−0.0832839
$268$	6.46694	+	11.1118i	0.395031	+	0.678763i
$269$	4.83187			0.294605			0.147302	−	0.989092i	$-0.452941\pi$
$269$	4.83187			0.294605			0.147302	+	0.989092i	$0.452941\pi$
$270$	0.704981	−	1.22597i	0.0429038	−	0.0746102i
$271$	10.5338			0.639885			0.319942	−	0.947437i	$-0.396336\pi$
$271$	10.5338			0.639885			0.319942	+	0.947437i	$0.396336\pi$
$272$	10.4053	+	5.91159i	0.630914	+	0.358443i
$273$	7.24242	+	14.7820i	0.438331	+	0.894648i
$274$	15.0046	+	8.62822i	0.906460	+	0.521250i
$275$	−2.29742			−0.138540
$276$	−8.20110	−	14.0916i	−0.493648	−	0.848212i
$277$		−	24.5049i		−	1.47236i	−0.676787	−	0.736179i	$-0.736628\pi$
$277$		−	24.5049i		−	1.47236i	0.676787	−	0.736179i	$-0.263372\pi$
$278$	7.26417	−	12.6325i	0.435676	−	0.757646i
$279$	1.82156			0.109054
$280$	−3.32743	−	6.70285i	−0.198852	−	0.400572i
$281$	4.78715			0.285577			0.142789	−	0.989753i	$-0.454393\pi$
$281$	4.78715			0.285577			0.142789	+	0.989753i	$0.454393\pi$
$282$	6.68948	−	11.6331i	0.398353	−	0.692740i
$283$			9.64555i			0.573369i	0.958025	+	0.286684i	$0.0925531\pi$
$283$			9.64555i			0.573369i	−0.958025	+	0.286684i	$0.907447\pi$
$284$	13.7742	−	8.01639i	0.817348	−	0.475685i
$285$	0.901647			0.0534090
$286$	−17.5236	−	10.0768i	−1.03619	−	0.595852i
$287$	−13.1587	−	26.8573i	−0.776733	−	1.58534i
$288$	−4.87426	+	2.87082i	−0.287218	+	0.169165i
$289$	8.04893			0.473467
$290$	−0.813710	+	1.41505i	−0.0477827	+	0.0830947i
$291$	−8.12945			−0.476557
$292$	−7.08989	+	4.12622i	−0.414904	+	0.241469i
$293$	−21.5351			−1.25809			−0.629047	−	0.777367i	$-0.716555\pi$
$293$	−21.5351			−1.25809			−0.629047	+	0.777367i	$0.716555\pi$
$294$	3.75712	+	9.15882i	0.219120	+	0.534154i
$295$			5.71571i			0.332781i
$296$	−5.10659	+	0.0265827i	−0.296814	+	0.00154509i
$297$		−	2.29742i		−	0.133310i
$298$	2.35857	−	4.10159i	0.136628	−	0.237599i
$299$			50.7196i			2.93319i
$300$	1.72857	−	1.00600i	0.0997990	−	0.0580817i
$301$	27.3747	−	13.4122i	1.57785	−	0.773065i
$302$	−7.36221	+	12.8030i	−0.423647	+	0.736728i
$303$			4.56052i			0.261995i
$304$	−3.13584	−	1.78157i	−0.179853	−	0.102180i
$305$	−11.0303			−0.631595
$306$	2.10918	−	3.66790i	0.120574	−	0.209680i
$307$		−	9.82813i		−	0.560921i	−0.959866	−	0.280461i	$-0.909513\pi$
$307$		−	9.82813i		−	0.560921i	0.959866	−	0.280461i	$-0.0904872\pi$
$308$	−10.1141	−	6.74490i	−0.576302	−	0.384327i
$309$		−	1.65646i		−	0.0942326i
$310$	2.23318	+	1.28417i	0.126836	+	0.0729358i
$311$	1.48451			0.0841788			0.0420894	−	0.999114i	$-0.486599\pi$
$311$	1.48451			0.0841788			0.0420894	+	0.999114i	$0.486599\pi$
$312$	17.5972	−	0.0916033i	0.996244	−	0.00518602i
$313$		−	32.7794i		−	1.85280i	−0.376539	−	0.926401i	$-0.622886\pi$
$313$		−	32.7794i		−	1.85280i	0.376539	−	0.926401i	$-0.377114\pi$
$314$	4.61789	+	2.65547i	0.260603	+	0.149857i
$315$	−2.37591	+	1.16407i	−0.133867	+	0.0655880i
$316$	−25.8739	+	15.0583i	−1.45552	+	0.847094i
$317$			4.41901i			0.248196i	0.992270	+	0.124098i	$0.0396038\pi$
$317$			4.41901i			0.248196i	−0.992270	+	0.124098i	$0.960396\pi$
$318$	5.45498	+	3.13682i	0.305900	+	0.175904i
$319$			2.65175i			0.148470i
$320$	−7.99957	+	0.0832869i	−0.447189	+	0.00465588i
$321$			5.99730i			0.334737i
$322$	−2.02053	+	30.4355i	−0.112599	+	1.69611i
$323$	2.69758			0.150097
$324$	1.00600	+	1.72857i	0.0558892	+	0.0960317i
$325$	−6.22162			−0.345114
$326$	14.4353	+	8.30087i	0.799498	+	0.459743i
$327$	−14.4206			−0.797462
$328$	−31.9722	+	0.166433i	−1.76537	+	0.00918975i
$329$	−22.5447	+	11.0457i	−1.24293	+	0.608971i
$330$	1.61964	−	2.81657i	0.0891580	−	0.155047i
$331$	1.77031			0.0973051			0.0486526	−	0.998816i	$-0.484507\pi$
$331$	1.77031			0.0973051			0.0486526	+	0.998816i	$0.484507\pi$
$332$	−17.9144	+	10.4259i	−0.983179	+	0.572197i
$333$			1.80548i			0.0989394i
$334$	−29.5817	−	17.0106i	−1.61864	−	0.930779i
$335$	6.42834			0.351218
$336$	10.5633	+	0.646053i	0.576273	+	0.0352451i
$337$	9.97437			0.543339			0.271669	−	0.962391i	$-0.412424\pi$
$337$	9.97437			0.543339			0.271669	+	0.962391i	$0.412424\pi$
$338$	−31.5180	−	18.1241i	−1.71435	−	0.985819i
$339$		−	20.3916i		−	1.10752i
$340$	5.17159	−	3.00980i	0.280469	−	0.163229i
$341$	4.18490			0.226625
$342$	−0.635644	+	1.10539i	−0.0343717	+	0.0597728i
$343$	3.75334	−	18.1359i	0.202661	−	0.979249i
$344$	−0.169640	−	32.5881i	−0.00914636	−	1.75703i
$345$	−8.15215			−0.438897
$346$	14.1797	+	8.15388i	0.762305	+	0.438355i
$347$	−3.02998			−0.162658			−0.0813289	−	0.996687i	$-0.525916\pi$
$347$	−3.02998			−0.162658			−0.0813289	+	0.996687i	$0.525916\pi$
$348$	−1.16116	−	1.99517i	−0.0622448	−	0.106952i
$349$	−7.89793			−0.422766			−0.211383	−	0.977403i	$-0.567797\pi$
$349$	−7.89793			−0.422766			−0.211383	+	0.977403i	$0.567797\pi$
$350$	−3.73344	−	0.247852i	−0.199561	−	0.0132482i
$351$		−	6.22162i		−	0.332086i
$352$	−11.1982	+	6.59548i	−0.596867	+	0.351540i
$353$			0.204746i			0.0108975i	0.999985	+	0.00544876i	$0.00173440\pi$
$353$			0.204746i			0.0108975i	−0.999985	+	0.00544876i	$0.998266\pi$
$354$	−7.00729	−	4.02946i	−0.372433	−	0.214164i
$355$		−	7.96854i		−	0.422926i
$356$	2.35236	−	1.36904i	0.124675	−	0.0725591i
$357$	−7.10832	+	3.48271i	−0.376212	+	0.184324i
$358$	−32.0513	−	18.4308i	−1.69396	−	0.974096i
$359$			22.8226i			1.20453i	0.798295	+	0.602267i	$0.205736\pi$
$359$			22.8226i			1.20453i	−0.798295	+	0.602267i	$0.794264\pi$
$360$	0.0147234	+	2.82839i	0.000775990	+	0.149069i
$361$	18.1870			0.957212
$362$	−15.8958	−	9.14072i	−0.835466	−	0.480426i
$363$			5.72186i			0.300320i
$364$	−27.3898	−	18.2658i	−1.43562	−	0.957389i
$365$			4.10159i			0.214687i
$366$	7.77617	−	13.5229i	0.406467	−	0.706851i
$367$	20.8979			1.09086			0.545430	−	0.838156i	$-0.316366\pi$
$367$	20.8979			1.09086			0.545430	+	0.838156i	$0.316366\pi$
$368$	28.3523	+	16.1079i	1.47797	+	0.839682i
$369$			11.3040i			0.588464i
$370$	−1.27282	+	2.21346i	−0.0661710	+	0.115072i
$371$	−5.17956	−	10.5716i	−0.268909	−	0.548852i
$372$	−3.14870	+	1.83250i	−0.163253	+	0.0950108i
$373$		−	23.6880i		−	1.22652i	−0.789881	−	0.613260i	$-0.789858\pi$
$373$		−	23.6880i		−	1.22652i	0.789881	−	0.613260i	$-0.210142\pi$
$374$	4.84568	−	8.42670i	0.250564	−	0.435734i
$375$		−	1.00000i		−	0.0516398i
$376$	0.139708	+	26.8382i	0.00720491	+	1.38408i
$377$			7.18119i			0.369850i
$378$	0.247852	−	3.73344i	0.0127481	−	0.192027i
$379$	17.8551			0.917157			0.458579	−	0.888654i	$-0.348359\pi$
$379$	17.8551			0.917157			0.458579	+	0.888654i	$0.348359\pi$
$380$	−1.55856	+	0.907061i	−0.0799525	+	0.0465313i
$381$	−7.73916			−0.396489
$382$	15.2198	−	26.4674i	0.778713	−	1.35419i
$383$	−11.0569			−0.564981			−0.282490	−	0.959270i	$-0.591161\pi$
$383$	−11.0569			−0.564981			−0.282490	+	0.959270i	$0.591161\pi$
$384$	5.53743	−	9.86594i	0.282581	−	0.503469i
$385$	−5.45846	+	2.67436i	−0.278189	+	0.136298i
$386$	−19.7129	−	11.3357i	−1.00336	−	0.576971i
$387$	−11.5218			−0.585685
$388$	14.0523	−	8.17826i	0.713398	−	0.415188i
$389$			3.00471i			0.152345i	0.997095	+	0.0761724i	$0.0242699\pi$
$389$			3.00471i			0.152345i	−0.997095	+	0.0761724i	$0.975730\pi$
$390$	4.38612	−	7.62752i	0.222100	−	0.386235i
$391$	−24.3899			−1.23345
$392$	−15.7083	−	12.0520i	−0.793387	−	0.608718i
$393$	0.428007			0.0215901
$394$	−1.50325	+	2.61417i	−0.0757325	+	0.131700i
$395$			14.9684i			0.753141i
$396$	2.31121	+	3.97125i	0.116143	+	0.199563i
$397$	−2.11804			−0.106302			−0.0531508	−	0.998586i	$-0.516926\pi$
$397$	−2.11804			−0.106302			−0.0531508	+	0.998586i	$0.516926\pi$
$398$	−4.98119	−	2.86438i	−0.249684	−	0.143578i
$399$	2.14223	−	1.04958i	0.107246	−	0.0525448i
$400$	−1.97591	+	3.47790i	−0.0987954	+	0.173895i
$401$	−12.4039			−0.619420			−0.309710	−	0.950831i	$-0.600232\pi$
$401$	−12.4039			−0.619420			−0.309710	+	0.950831i	$0.600232\pi$
$402$	−4.53185	+	7.88095i	−0.226028	+	0.393066i
$403$	11.3331			0.564541
$404$	−4.58791	−	7.88318i	−0.228257	−	0.392203i
$405$	1.00000			0.0496904
$406$	−0.286078	+	4.30925i	−0.0141978	+	0.213864i
$407$			4.14793i			0.205605i
$408$	0.0440499	+	8.46207i	0.00218079	+	0.418935i
$409$			11.7088i			0.578961i	0.957184	+	0.289480i	$0.0934825\pi$
$409$			11.7088i			0.578961i	−0.957184	+	0.289480i	$0.906518\pi$
$410$	−7.96912	+	13.8584i	−0.393567	+	0.684417i
$411$			12.2390i			0.603703i
$412$	1.66641	+	2.86330i	0.0820979	+	0.141065i
$413$	6.65349	+	13.5800i	0.327397	+	0.668228i
$414$	5.74710	−	9.99429i	0.282455	−	0.491192i
$415$			10.3637i			0.508734i
$416$	−30.3258	+	17.8612i	−1.48684	+	0.875716i
$417$	10.3041			0.504593
$418$	−1.46034	+	2.53955i	−0.0714276	+	0.124213i
$419$		−	27.1287i		−	1.32532i	−0.748919	−	0.662661i	$-0.769427\pi$
$419$		−	27.1287i		−	1.32532i	0.748919	−	0.662661i	$-0.230573\pi$
$420$	2.93586	−	4.40235i	0.143255	−	0.214813i
$421$			29.4793i			1.43673i	0.695665	+	0.718367i	$0.255110\pi$
$421$			29.4793i			1.43673i	−0.695665	+	0.718367i	$0.744890\pi$
$422$	11.8487	+	6.81346i	0.576785	+	0.331674i
$423$	9.48888			0.461365
$424$	−12.5850	+	0.0655119i	−0.611180	+	0.00318154i
$425$		−	2.99183i		−	0.145125i
$426$	9.76920	+	5.61767i	0.473319	+	0.272177i
$427$	−26.2071	+	12.8401i	−1.26825	+	0.621376i
$428$	−6.03331	−	10.3668i	−0.291631	−	0.501096i
$429$		−	14.2937i		−	0.690105i
$430$	−14.1254	−	8.12264i	−0.681186	−	0.391708i
$431$		−	36.4672i		−	1.75656i	−0.478143	−	0.878282i	$-0.658690\pi$
$431$		−	36.4672i		−	1.75656i	0.478143	−	0.878282i	$-0.341310\pi$
$432$	−3.47790	−	1.97591i	−0.167331	−	0.0950660i
$433$		−	3.04286i		−	0.146231i	−0.997323	−	0.0731153i	$-0.976706\pi$
$433$		−	3.04286i		−	0.146231i	0.997323	−	0.0731153i	$-0.0232941\pi$
$434$	6.80070	+	0.451478i	0.326444	+	0.0216716i
$435$	−1.15423			−0.0553411
$436$	24.9271	−	14.5072i	1.19379	−	0.694770i
$437$	7.35036			0.351615
$438$	−5.02843	−	2.89154i	−0.240268	−	0.138163i
$439$	−10.5106			−0.501645			−0.250823	−	0.968033i	$-0.580701\pi$
$439$	−10.5106			−0.501645			−0.250823	+	0.968033i	$0.580701\pi$
$440$	0.0338258	+	6.49800i	0.00161258	+	0.309780i
$441$	−4.28987	+	5.53145i	−0.204280	+	0.263403i
$442$	13.1226	−	22.8203i	0.624176	−	1.08545i
$443$	15.1671			0.720610			0.360305	−	0.932835i	$-0.382673\pi$
$443$	15.1671			0.720610			0.360305	+	0.932835i	$0.382673\pi$
$444$	−1.81632	−	3.12089i	−0.0861986	−	0.148111i
$445$		−	1.36087i		−	0.0645115i
$446$	−19.2068	−	11.0447i	−0.909470	−	0.522980i
$447$	3.34559			0.158241
$448$	−18.9093	+	9.50995i	−0.893379	+	0.449303i
$449$	8.62232			0.406912			0.203456	−	0.979084i	$-0.434783\pi$
$449$	8.62232			0.406912			0.203456	+	0.979084i	$0.434783\pi$
$450$	1.22597	+	0.704981i	0.0577928	+	0.0332331i
$451$			25.9701i			1.22288i
$452$	20.5140	+	35.2483i	0.964898	+	1.65794i
$453$	−10.4431			−0.490661
$454$	1.94515	−	3.38264i	0.0912903	−	0.158755i
$455$	−14.7820	+	7.24242i	−0.692991	+	0.339530i
$456$	−0.0132753	−	2.55021i	−0.000621673	−	0.119424i
$457$	−13.9018			−0.650299			−0.325149	−	0.945663i	$-0.605415\pi$
$457$	−13.9018			−0.650299			−0.325149	+	0.945663i	$0.605415\pi$
$458$	−22.7775	−	13.0980i	−1.06432	−	0.612027i
$459$	2.99183			0.139647
$460$	14.0916	−	8.20110i	0.657022	−	0.382378i
$461$	−10.0656			−0.468802			−0.234401	−	0.972140i	$-0.575313\pi$
$461$	−10.0656			−0.468802			−0.234401	+	0.972140i	$0.575313\pi$
$462$	0.569420	−	8.57728i	0.0264918	−	0.399051i
$463$		−	14.4980i		−	0.673777i	−0.941545	−	0.336889i	$-0.890625\pi$
$463$		−	14.4980i		−	0.673777i	0.941545	−	0.336889i	$-0.109375\pi$
$464$	4.01430	+	2.28065i	0.186359	+	0.105877i
$465$			1.82156i			0.0844730i
$466$	16.7577	+	9.63632i	0.776285	+	0.446394i
$467$			18.9342i			0.876171i	0.898933	+	0.438085i	$0.144343\pi$
$467$			18.9342i			0.876171i	−0.898933	+	0.438085i	$0.855657\pi$
$468$	6.25898	+	10.7545i	0.289322	+	0.497128i
$469$	15.2731	−	7.48305i	0.705248	−	0.345535i
$470$	11.6331	+	6.68948i	0.536594	+	0.308563i
$471$			3.76672i			0.173561i
$472$	16.1662	−	0.0841545i	0.744112	−	0.00387353i
$473$	−26.4704			−1.21711
$474$	−18.3508	−	10.5524i	−0.842880	−	0.484689i
$475$			0.901647i			0.0413704i
$476$	8.78361	−	13.1711i	0.402596	−	0.603697i
$477$			4.44952i			0.203729i
$478$	12.3148	−	21.4155i	0.563265	−	0.979524i
$479$	−1.61491			−0.0737871			−0.0368935	−	0.999319i	$-0.511746\pi$
$479$	−1.61491			−0.0737871			−0.0368935	+	0.999319i	$0.511746\pi$
$480$	−2.87082	−	4.87426i	−0.131035	−	0.222478i
$481$			11.2330i			0.512180i
$482$	20.5301	−	35.7020i	0.935119	−	1.62618i
$483$	−19.3687	+	9.48968i	−0.881309	+	0.431795i
$484$	−5.75622	−	9.89064i	−0.261647	−	0.449575i
$485$		−	8.12945i		−	0.369139i
$486$	−0.704981	+	1.22597i	−0.0319786	+	0.0556111i
$487$			3.92912i			0.178045i	0.996030	+	0.0890226i	$0.0283743\pi$
$487$			3.92912i			0.178045i	−0.996030	+	0.0890226i	$0.971626\pi$
$488$	0.162404	+	31.1981i	0.00735167	+	1.41227i
$489$			11.7746i			0.532466i
$490$	−9.15882	+	3.75712i	−0.413754	+	0.169729i
$491$	31.7817			1.43429			0.717143	−	0.696926i	$-0.245449\pi$
$491$	31.7817			1.43429			0.717143	+	0.696926i	$0.245449\pi$
$492$	−11.3719	−	19.5398i	−0.512685	−	0.880922i
$493$	−3.45326			−0.155527
$494$	−3.95474	+	6.87734i	−0.177932	+	0.309426i
$495$	2.29742			0.103261
$496$	3.59924	−	6.33522i	0.161611	−	0.284460i
$497$	−9.27595	−	18.9325i	−0.416083	−	0.849240i
$498$	−12.7056	−	7.30620i	−0.569351	−	0.327399i
$499$	35.4380			1.58642			0.793210	−	0.608948i	$-0.208408\pi$
$499$	35.4380			1.58642			0.793210	+	0.608948i	$0.208408\pi$
$500$	1.00600	+	1.72857i	0.0449899	+	0.0773040i
$501$		−	24.1292i		−	1.07801i
$502$	−8.06600	+	14.0269i	−0.360003	+	0.626050i
$503$	3.85502			0.171887			0.0859435	−	0.996300i	$-0.472610\pi$
$503$	3.85502			0.171887			0.0859435	+	0.996300i	$0.472610\pi$
$504$	3.32743	+	6.70285i	0.148215	+	0.298569i
$505$	−4.56052			−0.202941
$506$	13.2035	−	22.9611i	0.586968	−	1.02074i
$507$		−	25.7086i		−	1.14176i
$508$	13.3777	−	7.78563i	0.593538	−	0.345431i
$509$	−6.50757			−0.288443			−0.144222	−	0.989545i	$-0.546068\pi$
$509$	−6.50757			−0.288443			−0.144222	+	0.989545i	$0.546068\pi$
$510$	3.66790	+	2.10918i	0.162417	+	0.0933963i
$511$	4.77455	+	9.74500i	0.211213	+	0.431093i
$512$	0.353348	+	22.6247i	0.0156159	+	0.999878i
$513$	−0.901647			−0.0398087
$514$	5.00772	−	8.70849i	0.220881	−	0.384115i
$515$	1.65646			0.0729923
$516$	19.9162	−	11.5910i	0.876763	−	0.510264i
$517$	21.7999			0.958760
$518$	−0.447491	+	6.74063i	−0.0196616	+	0.296166i
$519$			11.5661i			0.507695i
$520$	0.0916033	+	17.5972i	0.00401707	+	0.771687i
$521$		−	28.8683i		−	1.26474i	−0.774666	−	0.632371i	$-0.782082\pi$
$521$		−	28.8683i		−	1.26474i	0.774666	−	0.632371i	$-0.217918\pi$
$522$	0.813710	−	1.41505i	0.0356151	−	0.0619351i
$523$		−	38.1691i		−	1.66902i	−0.550996	−	0.834508i	$-0.685752\pi$
$523$		−	38.1691i		−	1.66902i	0.550996	−	0.834508i	$-0.314248\pi$
$524$	−0.739840	+	0.430577i	−0.0323200	+	0.0188098i
$525$	−1.16407	−	2.37591i	−0.0508042	−	0.103693i
$526$	3.41345	−	5.93603i	0.148833	−	0.258823i
$527$			5.44982i			0.237398i
$528$	−7.99019	−	4.53949i	−0.347729	−	0.197556i
$529$	−43.4575			−1.88946
$530$	−3.13682	+	5.45498i	−0.136255	+	0.236949i
$531$		−	5.71571i		−	0.248041i
$532$	−2.64711	+	3.96937i	−0.114767	+	0.172094i
$533$			70.3294i			3.04630i
$534$	1.66839	+	0.959387i	0.0721982	+	0.0415168i
$535$	−5.99730			−0.259286
$536$	−0.0946469	−	18.1818i	−0.00408812	−	0.785336i
$537$		−	26.1436i		−	1.12818i
$538$	−5.92373	−	3.40638i	−0.255390	−	0.146859i
$539$	−9.85564	+	12.7081i	−0.424513	+	0.547375i
$540$	−1.72857	+	1.00600i	−0.0743858	+	0.0432916i
$541$		−	35.9517i		−	1.54568i	−0.634598	−	0.772842i	$-0.718834\pi$
$541$		−	35.9517i		−	1.54568i	0.634598	−	0.772842i	$-0.281166\pi$
$542$	−12.9142	−	7.42615i	−0.554711	−	0.318980i
$543$		−	12.9659i		−	0.556421i
$544$	−8.58902	−	14.5830i	−0.368251	−	0.625239i
$545$		−	14.4206i		−	0.617712i
$546$	1.54204	−	23.2281i	0.0659933	−	0.994069i
$547$	−6.04725			−0.258562			−0.129281	−	0.991608i	$-0.541267\pi$
$547$	−6.04725			−0.258562			−0.129281	+	0.991608i	$0.541267\pi$
$548$	−12.3124	−	21.1559i	−0.525962	−	0.903735i
$549$	11.0303			0.470763
$550$	2.81657	+	1.61964i	0.120099	+	0.0690615i
$551$	1.04071			0.0443357
$552$	0.120027	+	23.0574i	0.00510869	+	0.981390i
$553$	17.4243	+	35.5635i	0.740956	+	1.51231i
$554$	−17.2755	+	30.0423i	−0.733965	+	1.27637i
$555$	−1.80548			−0.0766382
$556$	−17.8113	+	10.3659i	−0.755368	+	0.439614i
$557$		−	18.3660i		−	0.778191i	−0.921197	−	0.389095i	$-0.872788\pi$
$557$		−	18.3660i		−	0.778191i	0.921197	−	0.389095i	$-0.127212\pi$
$558$	−2.23318	−	1.28417i	−0.0945382	−	0.0543631i
$559$	−71.6842			−3.03192
$560$	−0.646053	+	10.5633i	−0.0273007	+	0.446380i
$561$	6.87350			0.290199
$562$	−5.86890	−	3.37485i	−0.247565	−	0.142359i
$563$		−	30.6429i		−	1.29144i	−0.763573	−	0.645722i	$-0.776557\pi$
$563$		−	30.6429i		−	1.29144i	0.763573	−	0.645722i	$-0.223443\pi$
$564$	−16.4022	+	9.54586i	−0.690657	+	0.401953i
$565$	20.3916			0.857880
$566$	6.79993	−	11.8252i	0.285822	−	0.497048i
$567$	2.37591	−	1.16407i	0.0997787	−	0.0488864i
$568$	−22.5381	+	0.117324i	−0.945679	+	0.00492280i
$569$	−22.9060			−0.960271			−0.480135	−	0.877194i	$-0.659412\pi$
$569$	−22.9060			−0.960271			−0.480135	+	0.877194i	$0.659412\pi$
$570$	−1.10539	−	0.635644i	−0.0462998	−	0.0266242i
$571$	−22.5813			−0.944997			−0.472499	−	0.881331i	$-0.656648\pi$
$571$	−22.5813			−0.944997			−0.472499	+	0.881331i	$0.656648\pi$
$572$	14.3795	+	24.7076i	0.601237	+	1.03308i
$573$	21.5890			0.901892
$574$	−2.80173	+	42.2029i	−0.116942	+	1.76151i
$575$		−	8.15215i		−	0.339968i
$576$	7.99957	−	0.0832869i	0.333315	−	0.00347029i
$577$			10.6634i			0.443922i	0.975056	+	0.221961i	$0.0712458\pi$
$577$			10.6634i			0.443922i	−0.975056	+	0.221961i	$0.928754\pi$
$578$	−9.86775	−	5.67434i	−0.410444	−	0.236021i
$579$		−	16.0794i		−	0.668238i
$580$	1.99517	−	1.16116i	0.0828448	−	0.0482146i
$581$	12.0641	+	24.6232i	0.500503	+	1.02154i
$582$	9.96646	+	5.73110i	0.413123	+	0.237562i
$583$			10.2224i			0.423369i
$584$	11.6009	−	0.0603893i	0.480048	−	0.00249893i
$585$	6.22162			0.257232
$586$	26.4014	+	15.1818i	1.09063	+	0.627155i
$587$		−	6.52728i		−	0.269410i	−0.990886	−	0.134705i	$-0.956991\pi$
$587$		−	6.52728i		−	0.269410i	0.990886	−	0.134705i	$-0.0430086\pi$
$588$	1.85068	−	13.8771i	0.0763208	−	0.572284i
$589$		−	1.64241i		−	0.0676742i
$590$	4.02946	−	7.00729i	0.165890	−	0.288485i
$591$	−2.13232			−0.0877121
$592$	6.27926	+	3.56745i	0.258076	+	0.146621i
$593$			39.6101i			1.62659i	0.581849	+	0.813297i	$0.302329\pi$
$593$			39.6101i			1.62659i	−0.581849	+	0.813297i	$0.697671\pi$
$594$	−1.61964	+	2.81657i	−0.0664545	+	0.115565i
$595$	−3.48271	−	7.10832i	−0.142777	−	0.291413i
$596$	−5.78308	+	3.36568i	−0.236884	+	0.137863i
$597$		−	4.06306i		−	0.166290i
$598$	35.7563	−	62.1807i	1.46218	−	2.54276i
$599$			27.7828i			1.13518i	0.823313	+	0.567588i	$0.192123\pi$
$599$			27.7828i			1.13518i	−0.823313	+	0.567588i	$0.807877\pi$
$600$	−2.82839	+	0.0147234i	−0.115468	+	0.000601079i
$601$			27.2341i			1.11090i	0.831549	+	0.555451i	$0.187454\pi$
$601$			27.2341i			1.11090i	−0.831549	+	0.555451i	$0.812546\pi$
$602$	−43.0159	−	2.85570i	−1.75320	−	0.116390i
$603$	−6.42834			−0.261782
$604$	18.0517	−	10.5058i	0.734513	−	0.427477i
$605$	−5.72186			−0.232627
$606$	3.21508	−	5.59106i	0.130604	−	0.227121i
$607$	34.4235			1.39720			0.698602	−	0.715510i	$-0.253806\pi$
$607$	34.4235			1.39720			0.698602	+	0.715510i	$0.253806\pi$
$608$	2.58847	+	4.39486i	0.104976	+	0.178235i
$609$	−2.74234	+	1.34361i	−0.111125	+	0.0544457i
$610$	13.5229	+	7.77617i	0.547525	+	0.314848i
$611$	59.0363			2.38835
$612$	−5.17159	+	3.00980i	−0.209049	+	0.121664i
$613$			44.2261i			1.78628i	0.449781	+	0.893139i	$0.351502\pi$
$613$			44.2261i			1.78628i	−0.449781	+	0.893139i	$0.648498\pi$
$614$	−6.92864	+	12.0490i	−0.279617	+	0.486258i
$615$	−11.3040			−0.455822
$616$	7.64450	+	15.3993i	0.308006	+	0.620454i
$617$	−6.97816			−0.280930			−0.140465	−	0.990086i	$-0.544860\pi$
$617$	−6.97816			−0.280930			−0.140465	+	0.990086i	$0.544860\pi$
$618$	−1.16777	+	2.03077i	−0.0469746	+	0.0816895i
$619$			27.7858i			1.11681i	0.829569	+	0.558404i	$0.188586\pi$
$619$			27.7858i			1.11681i	−0.829569	+	0.558404i	$0.811414\pi$
$620$	−1.83250	−	3.14870i	−0.0735951	−	0.126455i
$621$	8.15215			0.327134
$622$	−1.81996	−	1.04655i	−0.0729739	−	0.0419628i
$623$	−1.58415	−	3.23330i	−0.0634677	−	0.129540i
$624$	−21.6382	−	12.2934i	−0.866221	−	0.492128i
$625$	1.00000			0.0400000
$626$	−23.1088	+	40.1866i	−0.923615	+	1.60618i
$627$	−2.07146			−0.0827262
$628$	−3.78934	−	6.51105i	−0.151211	−	0.259819i
$629$	−5.40168			−0.215379
$630$	3.73344	+	0.247852i	0.148744	+	0.00987466i
$631$		−	20.7366i		−	0.825511i	−0.910842	−	0.412755i	$-0.864566\pi$
$631$		−	20.7366i		−	0.825511i	0.910842	−	0.412755i	$-0.135434\pi$
$632$	42.3364	−	0.220385i	1.68405	−	0.00876645i
$633$			9.66474i			0.384139i
$634$	3.11532	−	5.41758i	0.123725	−	0.215159i
$635$		−	7.73916i		−	0.307119i
$636$	−4.47624	−	7.69130i	−0.177494	−	0.304980i
$637$	−26.6900	+	34.4146i	−1.05750	+	1.36356i
$638$	1.86943	−	3.25097i	0.0740115	−	0.128707i
$639$			7.96854i			0.315231i
$640$	9.86594	+	5.53743i	0.389986	+	0.218886i
$641$	45.9031			1.81306			0.906531	−	0.422139i	$-0.138721\pi$
$641$	45.9031			1.81306			0.906531	+	0.422139i	$0.138721\pi$
$642$	4.22798	−	7.35251i	0.166865	−	0.290181i
$643$		−	23.5366i		−	0.928194i	−0.885784	−	0.464097i	$-0.846379\pi$
$643$		−	23.5366i		−	0.928194i	0.885784	−	0.464097i	$-0.153621\pi$
$644$	23.9336	−	35.8886i	0.943115	−	1.41421i
$645$		−	11.5218i		−	0.453670i
$646$	−3.30715	−	1.90174i	−0.130118	−	0.0748230i
$647$	−33.7916			−1.32849			−0.664243	−	0.747517i	$-0.731246\pi$
$647$	−33.7916			−1.32849			−0.664243	+	0.747517i	$0.731246\pi$
$648$	−0.0147234	−	2.82839i	−0.000578389	−	0.111110i
$649$		−	13.1314i		−	0.515452i
$650$	7.62752	+	4.38612i	0.299176	+	0.172038i
$651$	2.12043	+	4.32787i	0.0831062	+	0.169623i
$652$	−11.8453	−	20.3532i	−0.463898	−	0.797094i
$653$		−	5.09217i		−	0.199272i	−0.995024	−	0.0996360i	$-0.968232\pi$
$653$		−	5.09217i		−	0.199272i	0.995024	−	0.0996360i	$-0.0317678\pi$
$654$	17.6792	+	10.1663i	0.691313	+	0.397532i
$655$			0.428007i			0.0167236i
$656$	39.3143	+	22.3357i	1.53496	+	0.872064i
$657$		−	4.10159i		−	0.160018i
$658$	35.4262	+	2.35184i	1.38106	+	0.0916842i
$659$	33.9376			1.32202			0.661011	−	0.750376i	$-0.270128\pi$
$659$	33.9376			1.32202			0.661011	+	0.750376i	$0.270128\pi$
$660$	−3.97125	+	2.31121i	−0.154581	+	0.0899639i
$661$	−38.7912			−1.50880			−0.754401	−	0.656414i	$-0.772073\pi$
$661$	−38.7912			−1.50880			−0.754401	+	0.656414i	$0.772073\pi$
$662$	−2.17035	−	1.24804i	−0.0843530	−	0.0485063i
$663$	18.6141			0.722910
$664$	29.3126	−	0.152589i	1.13755	−	0.00592159i
$665$	1.04958	+	2.14223i	0.0407010	+	0.0830721i
$666$	1.27282	−	2.21346i	0.0493210	−	0.0857698i
$667$	−9.40945			−0.364335
$668$	24.2741	+	41.7090i	0.939193	+	1.61377i
$669$		−	15.6666i		−	0.605707i
$670$	−7.88095	−	4.53185i	−0.304468	−	0.175081i
$671$	25.3413			0.978290
$672$	−12.4948	−	8.23894i	−0.481997	−	0.317824i
$673$	0.899363			0.0346679			0.0173339	−	0.999850i	$-0.494482\pi$
$673$	0.899363			0.0346679			0.0173339	+	0.999850i	$0.494482\pi$
$674$	−12.2283	−	7.03174i	−0.471016	−	0.270852i
$675$			1.00000i			0.0384900i
$676$	25.8630	+	44.4391i	0.994730	+	1.70920i
$677$	3.54935			0.136413			0.0682064	−	0.997671i	$-0.478272\pi$
$677$	3.54935			0.136413			0.0682064	+	0.997671i	$0.478272\pi$
$678$	−14.3757	+	24.9995i	−0.552094	+	0.960098i
$679$	−9.46326	−	19.3148i	−0.363167	−	0.741235i
$680$	−8.46207	+	0.0440499i	−0.324506	+	0.00168924i
$681$	2.75915			0.105731
$682$	−5.13056	−	2.95027i	−0.196459	−	0.112972i
$683$	−9.48240			−0.362834			−0.181417	−	0.983406i	$-0.558068\pi$
$683$	−9.48240			−0.362834			−0.181417	+	0.983406i	$0.558068\pi$
$684$	1.55856	−	0.907061i	0.0595930	−	0.0346824i
$685$	−12.2390			−0.467626
$686$	−17.3870	+	19.5881i	−0.663838	+	0.747877i
$687$		−	18.5792i		−	0.708840i
$688$	−22.7660	+	40.0716i	−0.867946	+	1.52772i
$689$			27.6832i			1.05465i
$690$	9.99429	+	5.74710i	0.380476	+	0.218789i
$691$		−	33.5009i		−	1.27443i	−0.770684	−	0.637217i	$-0.780086\pi$
$691$		−	33.5009i		−	1.27443i	0.770684	−	0.637217i	$-0.219914\pi$
$692$	−11.6356	−	19.9928i	−0.442317	−	0.760013i
$693$	5.45846	−	2.67436i	0.207350	−	0.101591i
$694$	3.71466	+	2.13608i	0.141007	+	0.0810843i
$695$			10.3041i			0.390856i
$696$	0.0169942	+	3.26461i	0.000644162	+	0.123745i
$697$	−33.8198			−1.28101
$698$	9.68262	+	5.56788i	0.366493	+	0.210748i
$699$			13.6689i			0.517006i
$700$	4.40235	+	2.93586i	0.166393	+	0.110965i
$701$			20.6009i			0.778084i	0.921220	+	0.389042i	$0.127194\pi$
$701$			20.6009i			0.778084i	−0.921220	+	0.389042i	$0.872806\pi$
$702$	−4.38612	+	7.62752i	−0.165544	+	0.287882i
$703$	1.62790			0.0613975
$704$	18.3784	−	0.191345i	0.692660	−	0.00721158i
$705$			9.48888i			0.357372i
$706$	0.144342	−	0.251012i	0.00543238	−	0.00944697i
$707$	−10.8354	+	5.30877i	−0.407506	+	0.199657i
$708$	5.75003	+	9.88000i	0.216099	+	0.371313i
$709$			19.7440i			0.741503i	0.928732	+	0.370751i	$0.120900\pi$
$709$			19.7440i			0.741503i	−0.928732	+	0.370751i	$0.879100\pi$
$710$	−5.61767	+	9.76920i	−0.210827	+	0.366631i
$711$		−	14.9684i		−	0.561358i
$712$	−3.84907	+	0.0200366i	−0.144250	+	0.000750904i
$713$			14.8497i			0.556124i
$714$	11.1698	+	0.741532i	0.418020	+	0.0277511i
$715$	14.2937			0.534553
$716$	26.3006	+	45.1911i	0.982900	+	1.68887i
$717$	17.4682			0.652364
$718$	16.0895	−	27.9799i	0.600456	−	1.04420i
$719$	15.5196			0.578783			0.289391	−	0.957211i	$-0.406547\pi$
$719$	15.5196			0.578783			0.289391	+	0.957211i	$0.406547\pi$
$720$	1.97591	−	3.47790i	0.0736378	−	0.129614i
$721$	3.93559	−	1.92824i	0.146569	−	0.0718113i
$722$	−22.2968	−	12.8215i	−0.829799	−	0.477167i
$723$	29.1215			1.08304
$724$	13.0438	+	22.4125i	0.484768	+	0.832954i
$725$		−	1.15423i		−	0.0428670i
$726$	4.03380	−	7.01483i	0.149708	−	0.260345i
$727$	35.0266			1.29907			0.649533	−	0.760334i	$-0.274965\pi$
$727$	35.0266			1.29907			0.649533	+	0.760334i	$0.274965\pi$
$728$	20.7020	+	41.7026i	0.767267	+	1.54560i
$729$	−1.00000			−0.0370370
$730$	2.89154	−	5.02843i	0.107021	−	0.186110i
$731$		−	34.4713i		−	1.27497i
$732$	−19.0667	+	11.0966i	−0.704726	+	0.410141i
$733$	29.2688			1.08107			0.540534	−	0.841322i	$-0.318222\pi$
$733$	29.2688			1.08107			0.540534	+	0.841322i	$0.318222\pi$
$734$	−25.6202	−	14.7326i	−0.945657	−	0.543790i
$735$	−5.53145	−	4.28987i	−0.204031	−	0.158234i
$736$	−23.4034	−	39.7357i	−0.862660	−	1.46468i
$737$	−14.7686			−0.544008
$738$	7.96912	−	13.8584i	0.293347	−	0.510135i
$739$	−0.196034			−0.00721123			−0.00360561	−	0.999993i	$-0.501148\pi$
$739$	−0.196034			−0.00721123			−0.00360561	+	0.999993i	$0.501148\pi$
$740$	3.12089	−	1.81632i	0.114726	−	0.0667691i
$741$	−5.60971			−0.206078
$742$	−1.10282	+	16.6120i	−0.0404859	+	0.609846i
$743$		−	28.7856i		−	1.05604i	−0.849232	−	0.528020i	$-0.822935\pi$
$743$		−	28.7856i		−	1.05604i	0.849232	−	0.528020i	$-0.177065\pi$
$744$	5.15209	−	0.0268196i	0.188885	−	0.000983253i
$745$			3.34559i			0.122573i
$746$	−16.6996	+	29.0408i	−0.611416	+	1.06326i
$747$		−	10.3637i		−	0.379188i
$748$	−11.8813	+	6.91477i	−0.434424	+	0.252829i
$749$	−14.2490	+	6.98129i	−0.520648	+	0.255091i
$750$	−0.704981	+	1.22597i	−0.0257423	+	0.0447661i
$751$		−	0.377068i		−	0.0137594i	−0.999976	−	0.00687971i	$-0.997810\pi$
$751$		−	0.377068i		−	0.0137594i	0.999976	−	0.00687971i	$-0.00218990\pi$
$752$	18.7492	−	33.0014i	0.683712	−	1.20344i
$753$	−11.4415			−0.416950
$754$	5.06260	−	8.80392i	0.184369	−	0.320620i
$755$		−	10.4431i		−	0.380065i
$756$	−2.93586	+	4.40235i	−0.106776	+	0.160112i
$757$		−	1.79202i		−	0.0651322i	−0.999470	−	0.0325661i	$-0.989632\pi$
$757$		−	1.79202i		−	0.0651322i	0.999470	−	0.0325661i	$-0.0103679\pi$
$758$	−21.8899	−	12.5875i	−0.795076	−	0.457200i
$759$	18.7289			0.679816
$760$	2.55021	−	0.0132753i	0.0925058	−	0.000481545i
$761$		−	17.8760i		−	0.648004i	−0.946056	−	0.324002i	$-0.894972\pi$
$761$		−	17.8760i		−	0.648004i	0.946056	−	0.324002i	$-0.105028\pi$
$762$	9.48798	+	5.45596i	0.343713	+	0.197648i
$763$	−16.7866	−	34.2621i	−0.607717	−	1.24037i
$764$	−37.3181	+	21.7186i	−1.35012	+	0.785752i
$765$			2.99183i			0.108170i
$766$	13.5554	+	7.79489i	0.489777	+	0.281641i
$767$		−	35.5610i		−	1.28403i
$768$	−13.7440	+	8.19157i	−0.495945	+	0.295588i
$769$		−	18.0096i		−	0.649444i	−0.945809	−	0.324722i	$-0.894729\pi$
$769$		−	18.0096i		−	0.649444i	0.945809	−	0.324722i	$-0.105271\pi$
$770$	8.57728	+	0.569420i	0.309104	+	0.0205205i
$771$	7.10334			0.255821
$772$	16.1760	+	27.7944i	0.582186	+	1.00034i
$773$	−4.23548			−0.152339			−0.0761697	−	0.997095i	$-0.524269\pi$
$773$	−4.23548			−0.152339			−0.0761697	+	0.997095i	$0.524269\pi$
$774$	14.1254	+	8.12264i	0.507726	+	0.291962i
$775$	−1.82156			−0.0654325
$776$	−22.9932	+	0.119693i	−0.825409	+	0.00429673i
$777$	−4.28964	+	2.10170i	−0.153890	+	0.0753982i
$778$	2.11826	−	3.68368i	0.0759433	−	0.132066i
$779$	10.1922			0.365175
$780$	−10.7545	+	6.25898i	−0.385073	+	0.224108i
$781$			18.3071i			0.655079i
$782$	29.9012	+	17.1944i	1.06927	+	0.614870i
$783$	1.15423			0.0412488
$784$	10.7614	+	25.8494i	0.384337	+	0.923193i
$785$	−3.76672			−0.134440
$786$	−0.524723	−	0.301736i	−0.0187163	−	0.0107626i
$787$		−	45.4344i		−	1.61956i	−0.586732	−	0.809781i	$-0.699586\pi$
$787$		−	45.4344i		−	1.61956i	0.586732	−	0.809781i	$-0.300414\pi$
$788$	3.68587	−	2.14513i	0.131304	−	0.0764170i
$789$	4.84190			0.172376
$790$	10.5524	−	18.3508i	0.375438	−	0.652892i
$791$	48.4485	−	23.7373i	1.72263	−	0.843999i
$792$	−0.0338258	−	6.49800i	−0.00120195	−	0.230896i
$793$	68.6266			2.43700
$794$	2.59666	+	1.49318i	0.0921520	+	0.0529910i
$795$	−4.44952			−0.157808
$796$	4.08746	+	7.02328i	0.144876	+	0.248934i
$797$	−0.590784			−0.0209266			−0.0104633	−	0.999945i	$-0.503331\pi$
$797$	−0.590784			−0.0209266			−0.0104633	+	0.999945i	$0.503331\pi$
$798$	−3.36625	−	0.223475i	−0.119164	−	0.00791093i
$799$			28.3892i			1.00434i
$800$	4.87426	−	2.87082i	0.172331	−	0.101499i
$801$			1.36087i			0.0480840i
$802$	15.2068	+	8.74449i	0.536970	+	0.308779i
$803$		−	9.42307i		−	0.332533i
$804$	11.1118	−	6.46694i	0.391884	−	0.228071i
$805$	−9.48968	−	19.3687i	−0.334467	−	0.682659i
$806$	−13.8940	−	7.98961i	−0.489396	−	0.281422i
$807$		−	4.83187i		−	0.170090i
$808$	0.0671463	+	12.8989i	0.00236220	+	0.453783i
$809$	−36.1351			−1.27044			−0.635222	−	0.772330i	$-0.719091\pi$
$809$	−36.1351			−1.27044			−0.635222	+	0.772330i	$0.719091\pi$
$810$	−1.22597	−	0.704981i	−0.0430762	−	0.0247705i
$811$			34.3052i			1.20462i	0.798262	+	0.602310i	$0.205753\pi$
$811$			34.3052i			1.20462i	−0.798262	+	0.602310i	$0.794247\pi$
$812$	3.38866	−	5.08133i	0.118919	−	0.178320i
$813$		−	10.5338i		−	0.369438i
$814$	2.92421	−	5.08524i	0.102494	−	0.178238i
$815$	−11.7746			−0.412447
$816$	5.91159	−	10.4053i	0.206947	−	0.364258i
$817$			10.3886i			0.363451i
$818$	8.25444	−	14.3546i	0.288610	−	0.501896i
$819$	14.7820	−	7.24242i	0.516525	−	0.253070i
$820$	19.5398	−	11.3719i	0.682359	−	0.397124i
$821$			16.9389i			0.591172i	0.955316	+	0.295586i	$0.0955148\pi$
$821$			16.9389i			0.591172i	−0.955316	+	0.295586i	$0.904485\pi$
$822$	8.62822	−	15.0046i	0.300944	−	0.523345i
$823$		−	5.74264i		−	0.200176i	−0.994979	−	0.100088i	$-0.968088\pi$
$823$		−	5.74264i		−	0.200176i	0.994979	−	0.100088i	$-0.0319124\pi$
$824$	−0.0243887	−	4.68511i	−0.000849619	−	0.163214i
$825$			2.29742i			0.0799859i
$826$	1.41665	−	21.3392i	0.0492915	−	0.742487i
$827$	−32.5276			−1.13110			−0.565548	−	0.824715i	$-0.691335\pi$
$827$	−32.5276			−1.13110			−0.565548	+	0.824715i	$0.691335\pi$
$828$	−14.0916	+	8.20110i	−0.489715	+	0.285008i
$829$	41.7857			1.45128			0.725639	−	0.688075i	$-0.241544\pi$
$829$	41.7857			1.45128			0.725639	+	0.688075i	$0.241544\pi$
$830$	7.30620	−	12.7056i	0.253602	−	0.441017i
$831$	−24.5049			−0.850066
$832$	49.7703	−	0.518180i	1.72547	−	0.0179646i
$833$	−16.5492	−	12.8346i	−0.573395	−	0.444692i
$834$	−12.6325	−	7.26417i	−0.437427	−	0.251538i
$835$	24.1292			0.835025
$836$	3.58067	−	2.08390i	0.123840	−	0.0720732i
$837$		−	1.82156i		−	0.0629625i
$838$	−19.1252	+	33.2589i	−0.660669	+	1.14891i
$839$	−30.2011			−1.04266			−0.521329	−	0.853356i	$-0.674563\pi$
$839$	−30.2011			−1.04266			−0.521329	+	0.853356i	$0.674563\pi$
$840$	−6.70285	+	3.32743i	−0.231270	+	0.114807i
$841$	27.6678			0.954060
$842$	20.7823	−	36.1407i	0.716207	−	1.24549i
$843$		−	4.78715i		−	0.164878i
$844$	−9.72278	−	16.7062i	−0.334672	−	0.575051i
$845$	25.7086			0.884403
$846$	−11.6331	−	6.68948i	−0.399954	−	0.229989i
$847$	−13.5946	+	6.66066i	−0.467117	+	0.228863i
$848$	15.4750	+	8.79184i	0.531413	+	0.301913i
$849$	9.64555			0.331034
$850$	−2.10918	+	3.66790i	−0.0723444	+	0.125808i
$851$	−14.7185			−0.504544
$852$	−8.01639	−	13.7742i	−0.274637	−	0.471896i
$853$	−14.7231			−0.504110			−0.252055	−	0.967713i	$-0.581106\pi$
$853$	−14.7231			−0.504110			−0.252055	+	0.967713i	$0.581106\pi$
$854$	41.1811	+	2.73389i	1.40919	+	0.0935518i
$855$		−	0.901647i		−	0.0308357i
$856$	0.0883005	+	16.9627i	0.00301805	+	0.579773i
$857$		−	26.9516i		−	0.920649i	−0.887751	−	0.460324i	$-0.847733\pi$
$857$		−	26.9516i		−	0.920649i	0.887751	−	0.460324i	$-0.152267\pi$
$858$	−10.0768	+	17.5236i	−0.344015	+	0.598247i
$859$		−	6.46227i		−	0.220490i	−0.993904	−	0.110245i	$-0.964836\pi$
$859$		−	6.46227i		−	0.220490i	0.993904	−	0.110245i	$-0.0351635\pi$
$860$	11.5910	+	19.9162i	0.395249	+	0.679137i
$861$	−26.8573	+	13.1587i	−0.915295	+	0.448447i
$862$	−25.7087	+	44.7077i	−0.875641	+	1.52275i
$863$		−	47.9907i		−	1.63362i	−0.576905	−	0.816811i	$-0.695740\pi$
$863$		−	47.9907i		−	1.63362i	0.576905	−	0.816811i	$-0.304260\pi$
$864$	2.87082	+	4.87426i	0.0976674	+	0.165826i
$865$	−11.5661			−0.393259
$866$	−2.14516	+	3.73046i	−0.0728955	+	0.126766i
$867$		−	8.04893i		−	0.273356i
$868$	−8.01917	−	5.34786i	−0.272188	−	0.181518i
$869$		−	34.3887i		−	1.16656i
$870$	1.41505	+	0.813710i	0.0479747	+	0.0275873i
$871$	−39.9947			−1.35517
$872$	−40.7871	+	0.212320i	−1.38123	+	0.00719007i
$873$			8.12945i			0.275140i
$874$	−9.01132	−	5.18186i	−0.304812	−	0.175279i
$875$	2.37591	−	1.16407i	0.0803203	−	0.0393528i
$876$	4.12622	+	7.08989i	0.139412	+	0.239545i
$877$		−	36.1441i		−	1.22050i	−0.792209	−	0.610250i	$-0.791069\pi$
$877$		−	36.1441i		−	1.22050i	0.792209	−	0.610250i	$-0.208931\pi$
$878$	12.8857	+	7.40979i	0.434872	+	0.250068i
$879$			21.5351i			0.726361i
$880$	4.53949	−	7.99019i	0.153026	−	0.269349i
$881$			38.9201i			1.31125i	0.755087	+	0.655625i	$0.227595\pi$
$881$			38.9201i			1.31125i	−0.755087	+	0.655625i	$0.772405\pi$
$882$	9.15882	−	3.75712i	0.308394	−	0.126509i
$883$	−30.3454			−1.02120			−0.510601	−	0.859818i	$-0.670577\pi$
$883$	−30.3454			−1.02120			−0.510601	+	0.859818i	$0.670577\pi$
$884$	−32.1757	+	18.7258i	−1.08219	+	0.629818i
$885$	5.71571			0.192131
$886$	−18.5944	−	10.6925i	−0.624691	−	0.359221i
$887$	−26.4748			−0.888935			−0.444468	−	0.895795i	$-0.646607\pi$
$887$	−26.4748			−0.888935			−0.444468	+	0.895795i	$0.646607\pi$
$888$	0.0265827	+	5.10659i	0.000892057	+	0.171366i
$889$	−9.00893	−	18.3875i	−0.302150	−	0.616698i
$890$	−0.959387	+	1.66839i	−0.0321587	+	0.0559245i
$891$	−2.29742			−0.0769664
$892$	15.7607	+	27.0809i	0.527708	+	0.906735i
$893$		−	8.55562i		−	0.286303i
$894$	−4.10159	−	2.35857i	−0.137178	−	0.0788825i
$895$	26.1436			0.873885
$896$	29.8865	+	1.67176i	0.998439	+	0.0558496i
$897$	50.7196			1.69348
$898$	−10.5707	−	6.07857i	−0.352749	−	0.202844i
$899$			2.10250i			0.0701224i
$900$	−1.00600	−	1.72857i	−0.0335335	−	0.0576190i
$901$	−13.3122			−0.443494
$902$	18.3084	−	31.8385i	0.609603	−	1.06011i
$903$	−13.4122	−	27.3747i	−0.446330	−	0.910973i
$904$	−0.300233	−	57.6753i	−0.00998560	−	1.91825i
$905$	12.9659			0.431002
$906$	12.8030	+	7.36221i	0.425350	+	0.244593i
$907$	11.6034			0.385285			0.192642	−	0.981269i	$-0.438294\pi$
$907$	11.6034			0.385285			0.192642	+	0.981269i	$0.438294\pi$
$908$	−4.76939	+	2.77572i	−0.158278	+	0.0921155i
$909$	4.56052			0.151263
$910$	23.2281	+	1.54204i	0.770003	+	0.0511182i
$911$		−	8.63401i		−	0.286058i	−0.989719	−	0.143029i	$-0.954316\pi$
$911$		−	8.63401i		−	0.286058i	0.989719	−	0.143029i	$-0.0456841\pi$
$912$	−1.78157	+	3.13584i	−0.0589938	+	0.103838i
$913$		−	23.8098i		−	0.787988i
$914$	17.0432	+	9.80050i	0.563739	+	0.324172i
$915$			11.0303i			0.364652i
$916$	18.6907	+	32.1154i	0.617559	+	1.06112i
$917$	0.498231	+	1.01690i	0.0164530	+	0.0335811i
$918$	−3.66790	−	2.10918i	−0.121059	−	0.0696135i
$919$			31.2405i			1.03053i	0.857031	+	0.515264i	$0.172306\pi$
$919$			31.2405i			1.03053i	−0.857031	+	0.515264i	$0.827694\pi$
$920$	−23.0574	+	0.120027i	−0.760181	+	0.00395718i
$921$	−9.82813			−0.323848
$922$	12.3401	+	7.09605i	0.406400	+	0.233696i
$923$			49.5773i			1.63186i
$924$	−6.74490	+	10.1141i	−0.221891	+	0.332728i
$925$		−	1.80548i		−	0.0593637i
$926$	−10.2208	+	17.7741i	−0.335876	+	0.584092i
$927$	−1.65646			−0.0544052
$928$	−3.31359	−	5.62601i	−0.108774	−	0.184683i
$929$			35.5969i			1.16790i	0.811791	+	0.583949i	$0.198493\pi$
$929$			35.5969i			1.16790i	−0.811791	+	0.583949i	$0.801507\pi$
$930$	1.28417	−	2.23318i	0.0421095	−	0.0732289i
$931$	4.98742	+	3.86795i	0.163456	+	0.126767i
$932$	−13.7510	−	23.6277i	−0.450429	−	0.773950i
$933$		−	1.48451i		−	0.0486007i
$934$	13.3482	−	23.2128i	0.436768	−	0.759545i
$935$			6.87350i			0.224787i
$936$	−0.0916033	−	17.5972i	−0.00299415	−	0.575182i
$937$			24.2014i			0.790625i	0.918547	+	0.395312i	$0.129364\pi$
$937$			24.2014i			0.790625i	−0.918547	+	0.395312i	$0.870636\pi$
$938$	−23.9998	−	1.59328i	−0.783622	−	0.0520223i
$939$	−32.7794			−1.06972
$940$	−9.54586	−	16.4022i	−0.311352	−	0.534981i
$941$	25.0093			0.815280			0.407640	−	0.913143i	$-0.366352\pi$
$941$	25.0093			0.815280			0.407640	+	0.913143i	$0.366352\pi$
$942$	2.65547	−	4.61789i	0.0865198	−	0.150459i
$943$	−92.1521			−3.00088
$944$	−19.8787	−	11.2937i	−0.646995	−	0.367579i
$945$	1.16407	+	2.37591i	0.0378673	+	0.0772883i
$946$	32.4519	+	18.6611i	1.05510	+	0.606725i
$947$	31.5832			1.02632			0.513158	−	0.858294i	$-0.328475\pi$
$947$	31.5832			1.02632			0.513158	+	0.858294i	$0.328475\pi$
$948$	15.0583	+	25.8739i	0.489070	+	0.840345i
$949$		−	25.5186i		−	0.828367i
$950$	0.635644	−	1.10539i	0.0206230	−	0.0358637i
$951$	4.41901			0.143296
$952$	−20.0538	+	9.95511i	−0.649948	+	0.322647i
$953$	24.1766			0.783156			0.391578	−	0.920145i	$-0.371929\pi$
$953$	24.1766			0.783156			0.391578	+	0.920145i	$0.371929\pi$
$954$	3.13682	−	5.45498i	0.101558	−	0.176611i
$955$			21.5890i			0.698603i
$956$	−30.1951	+	17.5731i	−0.976579	+	0.568356i
$957$	2.65175			0.0857189
$958$	1.97983	+	1.13848i	0.0639654	+	0.0367826i
$959$	−29.0786	+	14.2470i	−0.938998	+	0.460060i
$960$	0.0832869	+	7.99957i	0.00268807	+	0.258185i
$961$	−27.6819			−0.892965
$962$	7.91904	−	13.7713i	0.255320	−	0.444005i
$963$	5.99730			0.193260
$964$	−50.3385	+	29.2963i	−1.62129	+	0.943571i
$965$	16.0794			0.517615
$966$	30.4355	+	2.02053i	0.979248	+	0.0650093i
$967$			43.4745i			1.39805i	0.715100	+	0.699023i	$0.246381\pi$
$967$			43.4745i			1.39805i	−0.715100	+	0.699023i	$0.753619\pi$
$968$	0.0842452	+	16.1837i	0.00270774	+	0.520162i
$969$		−	2.69758i		−	0.0866587i
$970$	−5.73110	+	9.96646i	−0.184015	+	0.320004i
$971$			14.1268i			0.453350i	0.973970	+	0.226675i	$0.0727856\pi$
$971$			14.1268i			0.453350i	−0.973970	+	0.226675i	$0.927214\pi$
$972$	1.72857	−	1.00600i	0.0554439	−	0.0322676i
$973$	11.9947	+	24.4815i	0.384532	+	0.784842i
$974$	2.76995	−	4.81698i	0.0887549	−	0.154346i
$975$			6.22162i			0.199251i
$976$	21.7949	−	38.3624i	0.697639	−	1.22795i
$977$	−36.8170			−1.17788			−0.588940	−	0.808177i	$-0.700455\pi$
$977$	−36.8170			−1.17788			−0.588940	+	0.808177i	$0.700455\pi$
$978$	8.30087	−	14.4353i	0.265433	−	0.461591i
$979$			3.12649i			0.0999231i
$980$	13.8771	+	1.85068i	0.443289	+	0.0591178i
$981$			14.4206i			0.460415i
$982$	−38.9634	−	22.4054i	−1.24337	−	0.714987i
$983$	7.29735			0.232749			0.116375	−	0.993205i	$-0.462873\pi$
$983$	7.29735			0.232749			0.116375	+	0.993205i	$0.462873\pi$
$984$	0.166433	+	31.9722i	0.00530570	+	1.01924i
$985$		−	2.13232i		−	0.0679415i
$986$	4.23360	+	2.43448i	0.134825	+	0.0775298i
$987$	11.0457	+	22.5447i	0.351590	+	0.717606i
$988$	9.69678	−	5.64340i	0.308496	−	0.179540i
$989$		−	93.9273i		−	2.98671i
$990$	−2.81657	−	1.61964i	−0.0895164	−	0.0514754i
$991$			33.4174i			1.06154i	0.847517	+	0.530769i	$0.178097\pi$
$991$			33.4174i			1.06154i	−0.847517	+	0.530769i	$0.821903\pi$
$992$	−8.87877	+	5.22939i	−0.281901	+	0.166033i
$993$		−	1.77031i		−	0.0561791i
$994$	−1.97502	+	29.7501i	−0.0626438	+	0.943615i
$995$	4.06306			0.128808
$996$	10.4259	+	17.9144i	0.330358	+	0.567639i
$997$	−47.1312			−1.49266			−0.746330	−	0.665576i	$-0.768186\pi$
$997$	−47.1312			−1.49266			−0.746330	+	0.665576i	$0.768186\pi$
$998$	−43.4459	−	24.9831i	−1.37526	−	0.790825i
$999$	1.80548			0.0571227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.d.811.5	yes	28
4.3	odd	2		3360.2.z.d.1231.12		28
7.6	odd	2		840.2.z.c.811.5	✓	28
8.3	odd	2		840.2.z.c.811.6	yes	28
8.5	even	2		3360.2.z.c.1231.18		28
28.27	even	2		3360.2.z.c.1231.17		28
56.13	odd	2		3360.2.z.d.1231.11		28
56.27	even	2	inner	840.2.z.d.811.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.c.811.5	✓	28	7.6	odd	2
840.2.z.c.811.6	yes	28	8.3	odd	2
840.2.z.d.811.5	yes	28	1.1	even	1	trivial
840.2.z.d.811.6	yes	28	56.27	even	2	inner
3360.2.z.c.1231.17		28	28.27	even	2
3360.2.z.c.1231.18		28	8.5	even	2
3360.2.z.d.1231.11		28	56.13	odd	2
3360.2.z.d.1231.12		28	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.z (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22597 - 0.704981i) q^{2} -1.00000i q^{3} +(1.00600 + 1.72857i) q^{4} +1.00000 q^{5} +(-0.704981 + 1.22597i) q^{6} +(2.37591 - 1.16407i) q^{7} +(-0.0147234 - 2.82839i) q^{8} -1.00000 q^{9} +(-1.22597 - 0.704981i) q^{10} -2.29742 q^{11} +(1.72857 - 1.00600i) q^{12} -6.22162 q^{13} +(-3.73344 - 0.247852i) q^{14} -1.00000i q^{15} +(-1.97591 + 3.47790i) q^{16} -2.99183i q^{17} +(1.22597 + 0.704981i) q^{18} +0.901647i q^{19} +(1.00600 + 1.72857i) q^{20} +(-1.16407 - 2.37591i) q^{21} +(2.81657 + 1.61964i) q^{22} -8.15215i q^{23} +(-2.82839 + 0.0147234i) q^{24} +1.00000 q^{25} +(7.62752 + 4.38612i) q^{26} +1.00000i q^{27} +(4.40235 + 2.93586i) q^{28} -1.15423i q^{29} +(-0.704981 + 1.22597i) q^{30} -1.82156 q^{31} +(4.87426 - 2.87082i) q^{32} +2.29742i q^{33} +(-2.10918 + 3.66790i) q^{34} +(2.37591 - 1.16407i) q^{35} +(-1.00600 - 1.72857i) q^{36} -1.80548i q^{37} +(0.635644 - 1.10539i) q^{38} +6.22162i q^{39} +(-0.0147234 - 2.82839i) q^{40} -11.3040i q^{41} +(-0.247852 + 3.73344i) q^{42} +11.5218 q^{43} +(-2.31121 - 3.97125i) q^{44} -1.00000 q^{45} +(-5.74710 + 9.99429i) q^{46} -9.48888 q^{47} +(3.47790 + 1.97591i) q^{48} +(4.28987 - 5.53145i) q^{49} +(-1.22597 - 0.704981i) q^{50} -2.99183 q^{51} +(-6.25898 - 10.7545i) q^{52} -4.44952i q^{53} +(0.704981 - 1.22597i) q^{54} -2.29742 q^{55} +(-3.32743 - 6.70285i) q^{56} +0.901647 q^{57} +(-0.813710 + 1.41505i) q^{58} +5.71571i q^{59} +(1.72857 - 1.00600i) q^{60} -11.0303 q^{61} +(2.23318 + 1.28417i) q^{62} +(-2.37591 + 1.16407i) q^{63} +(-7.99957 + 0.0832869i) q^{64} -6.22162 q^{65} +(1.61964 - 2.81657i) q^{66} +6.42834 q^{67} +(5.17159 - 3.00980i) q^{68} -8.15215 q^{69} +(-3.73344 - 0.247852i) q^{70} -7.96854i q^{71} +(0.0147234 + 2.82839i) q^{72} +4.10159i q^{73} +(-1.27282 + 2.21346i) q^{74} -1.00000i q^{75} +(-1.55856 + 0.907061i) q^{76} +(-5.45846 + 2.67436i) q^{77} +(4.38612 - 7.62752i) q^{78} +14.9684i q^{79} +(-1.97591 + 3.47790i) q^{80} +1.00000 q^{81} +(-7.96912 + 13.8584i) q^{82} +10.3637i q^{83} +(2.93586 - 4.40235i) q^{84} -2.99183i q^{85} +(-14.1254 - 8.12264i) q^{86} -1.15423 q^{87} +(0.0338258 + 6.49800i) q^{88} -1.36087i q^{89} +(1.22597 + 0.704981i) q^{90} +(-14.7820 + 7.24242i) q^{91} +(14.0916 - 8.20110i) q^{92} +1.82156i q^{93} +(11.6331 + 6.68948i) q^{94} +0.901647i q^{95} +(-2.87082 - 4.87426i) q^{96} -8.12945i q^{97} +(-9.15882 + 3.75712i) q^{98} +2.29742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 2 q^{4} + 28 q^{5} + 4 q^{6} + 4 q^{7} - 10 q^{8} - 28 q^{9} + 2 q^{10} - 8 q^{12} - 8 q^{13} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 - 2 * q^4 + 28 * q^5 + 4 * q^6 + 4 * q^7 - 10 * q^8 - 28 * q^9 + 2 * q^10 - 8 * q^12 - 8 * q^13 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * q^28 + 4 * q^30 + 24 * q^31 + 2 * q^32 + 8 * q^34 + 4 * q^35 + 2 * q^36 + 36 * q^38 - 10 * q^40 + 24 * q^43 - 4 * q^44 - 28 * q^45 - 44 * q^46 - 24 * q^47 + 16 * q^48 + 28 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^54 - 22 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 - 16 * q^61 - 28 * q^62 - 4 * q^63 + 22 * q^64 - 8 * q^65 - 20 * q^66 - 8 * q^67 - 12 * q^68 - 24 * q^69 + 2 * q^70 + 10 * q^72 - 8 * q^74 - 16 * q^76 + 16 * q^77 + 20 * q^78 + 6 * q^80 + 28 * q^81 + 24 * q^82 - 12 * q^84 - 4 * q^86 + 16 * q^87 + 40 * q^88 - 2 * q^90 + 48 * q^91 + 40 * q^92 + 52 * q^94 - 16 * q^96 - 30 * q^98

Introduction

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