LMFDB - Embedded newform 840.2.z.d.811.18

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			811.18
Character	$\chi$	$=$	840.811
Dual form			840.2.z.d.811.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.531410 + 1.31057i) q^{2} +1.00000i q^{3} +(-1.43521 + 1.39290i) q^{4} +1.00000 q^{5} +(-1.31057 + 0.531410i) q^{6} +(-2.64060 + 0.165018i) q^{7} +(-2.58819 - 1.14074i) q^{8} -1.00000 q^{9} +(0.531410 + 1.31057i) q^{10} +0.264307 q^{11} +(-1.39290 - 1.43521i) q^{12} -6.07875 q^{13} +(-1.61951 - 3.37301i) q^{14} +1.00000i q^{15} +(0.119639 - 3.99821i) q^{16} +1.85661i q^{17} +(-0.531410 - 1.31057i) q^{18} -3.89210i q^{19} +(-1.43521 + 1.39290i) q^{20} +(-0.165018 - 2.64060i) q^{21} +(0.140455 + 0.346393i) q^{22} -2.09615i q^{23} +(1.14074 - 2.58819i) q^{24} +1.00000 q^{25} +(-3.23031 - 7.96665i) q^{26} -1.00000i q^{27} +(3.55995 - 3.91494i) q^{28} +7.65773i q^{29} +(-1.31057 + 0.531410i) q^{30} -7.19786 q^{31} +(5.30353 - 1.96789i) q^{32} +0.264307i q^{33} +(-2.43322 + 0.986621i) q^{34} +(-2.64060 + 0.165018i) q^{35} +(1.43521 - 1.39290i) q^{36} +8.95826i q^{37} +(5.10089 - 2.06830i) q^{38} -6.07875i q^{39} +(-2.58819 - 1.14074i) q^{40} -2.28921i q^{41} +(3.37301 - 1.61951i) q^{42} -1.71132 q^{43} +(-0.379335 + 0.368154i) q^{44} -1.00000 q^{45} +(2.74716 - 1.11392i) q^{46} -11.7259 q^{47} +(3.99821 + 0.119639i) q^{48} +(6.94554 - 0.871493i) q^{49} +(0.531410 + 1.31057i) q^{50} -1.85661 q^{51} +(8.72426 - 8.46711i) q^{52} -4.04788i q^{53} +(1.31057 - 0.531410i) q^{54} +0.264307 q^{55} +(7.02261 + 2.58515i) q^{56} +3.89210 q^{57} +(-10.0360 + 4.06939i) q^{58} +4.59290i q^{59} +(-1.39290 - 1.43521i) q^{60} +9.96739 q^{61} +(-3.82502 - 9.43333i) q^{62} +(2.64060 - 0.165018i) q^{63} +(5.39742 + 5.90491i) q^{64} -6.07875 q^{65} +(-0.346393 + 0.140455i) q^{66} +2.89202 q^{67} +(-2.58608 - 2.66462i) q^{68} +2.09615 q^{69} +(-1.61951 - 3.37301i) q^{70} -8.61213i q^{71} +(2.58819 + 1.14074i) q^{72} +4.16846i q^{73} +(-11.7405 + 4.76051i) q^{74} +1.00000i q^{75} +(5.42133 + 5.58597i) q^{76} +(-0.697928 + 0.0436153i) q^{77} +(7.96665 - 3.23031i) q^{78} +10.3007i q^{79} +(0.119639 - 3.99821i) q^{80} +1.00000 q^{81} +(3.00018 - 1.21651i) q^{82} -5.71691i q^{83} +(3.91494 + 3.55995i) q^{84} +1.85661i q^{85} +(-0.909415 - 2.24282i) q^{86} -7.65773 q^{87} +(-0.684075 - 0.301506i) q^{88} +13.3494i q^{89} +(-0.531410 - 1.31057i) q^{90} +(16.0515 - 1.00310i) q^{91} +(2.91974 + 3.00841i) q^{92} -7.19786i q^{93} +(-6.23127 - 15.3677i) q^{94} -3.89210i q^{95} +(1.96789 + 5.30353i) q^{96} +11.1183i q^{97} +(4.83308 + 8.63952i) q^{98} -0.264307 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 $

$2$	0.531410	+	1.31057i	0.375764	+	0.926716i
$2$	0.531410	+	1.31057i	0.375764	+	0.926716i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.43521	+	1.39290i	−0.717604	+	0.696452i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.31057	+	0.531410i	−0.535039	+	0.216947i
$7$	−2.64060	+	0.165018i	−0.998053	+	0.0623709i
$7$	−2.64060	+	0.165018i	−0.998053	+	0.0623709i
$8$	−2.58819	−	1.14074i	−0.915062	−	0.403313i
$9$	−1.00000			−0.333333
$10$	0.531410	+	1.31057i	0.168047	+	0.414440i
$11$	0.264307			0.0796915			0.0398457	−	0.999206i	$-0.487313\pi$
$11$	0.264307			0.0796915			0.0398457	+	0.999206i	$0.487313\pi$
$12$	−1.39290	−	1.43521i	−0.402097	−	0.414309i
$13$	−6.07875			−1.68594			−0.842971	−	0.537959i	$-0.819195\pi$
$13$	−6.07875			−1.68594			−0.842971	+	0.537959i	$0.819195\pi$
$14$	−1.61951	−	3.37301i	−0.432832	−	0.901475i
$15$			1.00000i			0.258199i
$16$	0.119639	−	3.99821i	0.0299097	−	0.999553i
$17$			1.85661i			0.450294i	0.974325	+	0.225147i	$0.0722863\pi$
$17$			1.85661i			0.450294i	−0.974325	+	0.225147i	$0.927714\pi$
$18$	−0.531410	−	1.31057i	−0.125255	−	0.308905i
$19$		−	3.89210i		−	0.892910i	−0.894806	−	0.446455i	$-0.852686\pi$
$19$		−	3.89210i		−	0.892910i	0.894806	−	0.446455i	$-0.147314\pi$
$20$	−1.43521	+	1.39290i	−0.320922	+	0.311463i
$21$	−0.165018	−	2.64060i	−0.0360099	−	0.576226i
$22$	0.140455	+	0.346393i	0.0299451	+	0.0738513i
$23$		−	2.09615i		−	0.437078i	−0.975828	−	0.218539i	$-0.929871\pi$
$23$		−	2.09615i		−	0.437078i	0.975828	−	0.218539i	$-0.0701291\pi$
$24$	1.14074	−	2.58819i	0.232853	−	0.528311i
$25$	1.00000			0.200000
$26$	−3.23031	−	7.96665i	−0.633515	−	1.56239i
$27$		−	1.00000i		−	0.192450i
$28$	3.55995	−	3.91494i	0.672768	−	0.739853i
$29$			7.65773i			1.42200i	0.703190	+	0.711002i	$0.251758\pi$
$29$			7.65773i			1.42200i	−0.703190	+	0.711002i	$0.748242\pi$
$30$	−1.31057	+	0.531410i	−0.239277	+	0.0970217i
$31$	−7.19786			−1.29277			−0.646387	−	0.763009i	$-0.723721\pi$
$31$	−7.19786			−1.29277			−0.646387	+	0.763009i	$0.723721\pi$
$32$	5.30353	−	1.96789i	0.937540	−	0.347878i
$33$			0.264307i			0.0460099i
$34$	−2.43322	+	0.986621i	−0.417295	+	0.169204i
$35$	−2.64060	+	0.165018i	−0.446343	+	0.0278931i
$36$	1.43521	−	1.39290i	0.239201	−	0.232151i
$37$			8.95826i			1.47273i	0.676585	+	0.736365i	$0.263459\pi$
$37$			8.95826i			1.47273i	−0.676585	+	0.736365i	$0.736541\pi$
$38$	5.10089	−	2.06830i	0.827473	−	0.335523i
$39$		−	6.07875i		−	0.973379i
$40$	−2.58819	−	1.14074i	−0.409228	−	0.180367i
$41$		−	2.28921i		−	0.357514i	−0.983893	−	0.178757i	$-0.942792\pi$
$41$		−	2.28921i		−	0.357514i	0.983893	−	0.178757i	$-0.0572076\pi$
$42$	3.37301	−	1.61951i	0.520467	−	0.249896i
$43$	−1.71132			−0.260974			−0.130487	−	0.991450i	$-0.541654\pi$
$43$	−1.71132			−0.260974			−0.130487	+	0.991450i	$0.541654\pi$
$44$	−0.379335	+	0.368154i	−0.0571869	+	0.0555013i
$45$	−1.00000			−0.149071
$46$	2.74716	−	1.11392i	0.405047	−	0.164238i
$47$	−11.7259			−1.71040			−0.855201	−	0.518297i	$-0.826566\pi$
$47$	−11.7259			−1.71040			−0.855201	+	0.518297i	$0.826566\pi$
$48$	3.99821	+	0.119639i	0.577092	+	0.0172684i
$49$	6.94554	−	0.871493i	0.992220	−	0.124499i
$50$	0.531410	+	1.31057i	0.0751527	+	0.185343i
$51$	−1.85661			−0.259977
$52$	8.72426	−	8.46711i	1.20984	−	1.17418i
$53$		−	4.04788i		−	0.556019i	−0.960578	−	0.278009i	$-0.910325\pi$
$53$		−	4.04788i		−	0.556019i	0.960578	−	0.278009i	$-0.0896746\pi$
$54$	1.31057	−	0.531410i	0.178346	−	0.0723157i
$55$	0.264307			0.0356391
$56$	7.02261	+	2.58515i	0.938435	+	0.345455i
$57$	3.89210			0.515522
$58$	−10.0360	+	4.06939i	−1.31779	+	0.534337i
$59$			4.59290i			0.597945i	0.954262	+	0.298973i	$0.0966439\pi$
$59$			4.59290i			0.597945i	−0.954262	+	0.298973i	$0.903356\pi$
$60$	−1.39290	−	1.43521i	−0.179823	−	0.185284i
$61$	9.96739			1.27619			0.638097	−	0.769956i	$-0.279722\pi$
$61$	9.96739			1.27619			0.638097	+	0.769956i	$0.279722\pi$
$62$	−3.82502	−	9.43333i	−0.485778	−	1.19803i
$63$	2.64060	−	0.165018i	0.332684	−	0.0207903i
$64$	5.39742	+	5.90491i	0.674677	+	0.738113i
$65$	−6.07875			−0.753976
$66$	−0.346393	+	0.140455i	−0.0426381	+	0.0172888i
$67$	2.89202			0.353317			0.176658	−	0.984272i	$-0.443471\pi$
$67$	2.89202			0.353317			0.176658	+	0.984272i	$0.443471\pi$
$68$	−2.58608	−	2.66462i	−0.313608	−	0.323133i
$69$	2.09615			0.252347
$70$	−1.61951	−	3.37301i	−0.193568	−	0.403152i
$71$		−	8.61213i		−	1.02207i	−0.859559	−	0.511036i	$-0.829262\pi$
$71$		−	8.61213i		−	1.02207i	0.859559	−	0.511036i	$-0.170738\pi$
$72$	2.58819	+	1.14074i	0.305021	+	0.134438i
$73$			4.16846i			0.487881i	0.969790	+	0.243940i	$0.0784401\pi$
$73$			4.16846i			0.487881i	−0.969790	+	0.243940i	$0.921560\pi$
$74$	−11.7405	+	4.76051i	−1.36480	+	0.553398i
$75$			1.00000i			0.115470i
$76$	5.42133	+	5.58597i	0.621869	+	0.640755i
$77$	−0.697928	+	0.0436153i	−0.0795363	+	0.00497043i
$78$	7.96665	−	3.23031i	0.902045	−	0.365760i
$79$			10.3007i			1.15891i	0.815003	+	0.579457i	$0.196735\pi$
$79$			10.3007i			1.15891i	−0.815003	+	0.579457i	$0.803265\pi$
$80$	0.119639	−	3.99821i	0.0133760	−	0.447014i
$81$	1.00000			0.111111
$82$	3.00018	−	1.21651i	0.331314	−	0.134341i
$83$		−	5.71691i		−	0.627512i	−0.949504	−	0.313756i	$-0.898413\pi$
$83$		−	5.71691i		−	0.627512i	0.949504	−	0.313756i	$-0.101587\pi$
$84$	3.91494	+	3.55995i	0.427155	+	0.388423i
$85$			1.85661i			0.201378i
$86$	−0.909415	−	2.24282i	−0.0980647	−	0.241849i
$87$	−7.65773			−0.820994
$88$	−0.684075	−	0.301506i	−0.0729226	−	0.0321406i
$89$			13.3494i			1.41503i	0.706696	+	0.707517i	$0.250185\pi$
$89$			13.3494i			1.41503i	−0.706696	+	0.707517i	$0.749815\pi$
$90$	−0.531410	−	1.31057i	−0.0560155	−	0.138147i
$91$	16.0515	−	1.00310i	1.68266	−	0.105154i
$92$	2.91974	+	3.00841i	0.304404	+	0.313649i
$93$		−	7.19786i		−	0.746384i
$94$	−6.23127	−	15.3677i	−0.642706	−	1.58506i
$95$		−	3.89210i		−	0.399321i
$96$	1.96789	+	5.30353i	0.200847	+	0.541289i
$97$			11.1183i			1.12889i	0.825470	+	0.564446i	$0.190910\pi$
$97$			11.1183i			1.12889i	−0.825470	+	0.564446i	$0.809090\pi$
$98$	4.83308	+	8.63952i	0.488215	+	0.872723i
$99$	−0.264307			−0.0265638
$100$	−1.43521	+	1.39290i	−0.143521	+	0.139290i
$101$	4.37247			0.435077			0.217539	−	0.976052i	$-0.430197\pi$
$101$	4.37247			0.435077			0.217539	+	0.976052i	$0.430197\pi$
$102$	−0.986621	−	2.43322i	−0.0976900	−	0.240925i
$103$	−4.82084			−0.475012			−0.237506	−	0.971386i	$-0.576330\pi$
$103$	−4.82084			−0.475012			−0.237506	+	0.971386i	$0.576330\pi$
$104$	15.7329	+	6.93429i	1.54274	+	0.679963i
$105$	−0.165018	−	2.64060i	−0.0161041	−	0.257696i
$106$	5.30504	−	2.15108i	0.515271	−	0.208932i
$107$	−6.14307			−0.593873			−0.296937	−	0.954897i	$-0.595965\pi$
$107$	−6.14307			−0.593873			−0.296937	+	0.954897i	$0.595965\pi$
$108$	1.39290	+	1.43521i	0.134032	+	0.138103i
$109$		−	15.4612i		−	1.48091i	−0.672105	−	0.740456i	$-0.734610\pi$
$109$		−	15.4612i		−	1.48091i	0.672105	−	0.740456i	$-0.265390\pi$
$110$	0.140455	+	0.346393i	0.0133919	+	0.0330273i
$111$	−8.95826			−0.850281
$112$	0.343858	+	10.5774i	0.0324915	+	0.999472i
$113$	−16.7857			−1.57907			−0.789534	−	0.613707i	$-0.789678\pi$
$113$	−16.7857			−1.57907			−0.789534	+	0.613707i	$0.789678\pi$
$114$	2.06830	+	5.10089i	0.193714	+	0.477742i
$115$		−	2.09615i		−	0.195467i
$116$	−10.6665	−	10.9904i	−0.990357	−	1.02044i
$117$	6.07875			0.561981
$118$	−6.01934	+	2.44071i	−0.554125	+	0.224686i
$119$	−0.306374	−	4.90257i	−0.0280853	−	0.449417i
$120$	1.14074	−	2.58819i	0.104135	−	0.236268i
$121$	−10.9301			−0.993649
$122$	5.29677	+	13.0630i	0.479547	+	1.18267i
$123$	2.28921			0.206411
$124$	10.3304	−	10.0259i	0.927700	−	0.900355i
$125$	1.00000			0.0894427
$126$	1.61951	+	3.37301i	0.144277	+	0.300492i
$127$			17.0682i			1.51456i	0.653089	+	0.757281i	$0.273473\pi$
$127$			17.0682i			1.51456i	−0.653089	+	0.757281i	$0.726527\pi$
$128$	−4.87057	+	10.2116i	−0.430502	+	0.902590i
$129$		−	1.71132i		−	0.150674i
$130$	−3.23031	−	7.96665i	−0.283317	−	0.698721i
$131$		−	1.99977i		−	0.174721i	−0.996177	−	0.0873605i	$-0.972157\pi$
$131$		−	1.99977i		−	0.174721i	0.996177	−	0.0873605i	$-0.0278432\pi$
$132$	−0.368154	−	0.379335i	−0.0320437	−	0.0330169i
$133$	0.642267	+	10.2775i	0.0556916	+	0.891171i
$134$	1.53685	+	3.79021i	0.132763	+	0.327424i
$135$		−	1.00000i		−	0.0860663i
$136$	2.11791	−	4.80525i	0.181610	−	0.412047i
$137$	−16.9556			−1.44862			−0.724308	−	0.689476i	$-0.757841\pi$
$137$	−16.9556			−1.44862			−0.724308	+	0.689476i	$0.757841\pi$
$138$	1.11392	+	2.74716i	0.0948228	+	0.233854i
$139$			19.9469i			1.69188i	0.533280	+	0.845939i	$0.320959\pi$
$139$			19.9469i			1.69188i	−0.533280	+	0.845939i	$0.679041\pi$
$140$	3.55995	−	3.91494i	0.300871	−	0.330873i
$141$		−	11.7259i		−	0.987501i
$142$	11.2868	−	4.57657i	0.947169	−	0.384057i
$143$	−1.60665			−0.134355
$144$	−0.119639	+	3.99821i	−0.00996990	+	0.333184i
$145$			7.65773i			0.635939i
$146$	−5.46307	+	2.21516i	−0.452127	+	0.183328i
$147$	0.871493	+	6.94554i	0.0718795	+	0.572858i
$148$	−12.4780	−	12.8570i	−1.02569	−	1.05684i
$149$			3.68761i			0.302101i	0.988526	+	0.151050i	$0.0482656\pi$
$149$			3.68761i			0.302101i	−0.988526	+	0.151050i	$0.951734\pi$
$150$	−1.31057	+	0.531410i	−0.107008	+	0.0433894i
$151$		−	14.4831i		−	1.17862i	−0.807907	−	0.589309i	$-0.799400\pi$
$151$		−	14.4831i		−	1.17862i	0.807907	−	0.589309i	$-0.200600\pi$
$152$	−4.43989	+	10.0735i	−0.360122	+	0.817068i
$153$		−	1.85661i		−	0.150098i
$154$	−0.428047	−	0.891509i	−0.0344930	−	0.0718398i
$155$	−7.19786			−0.578146
$156$	8.46711	+	8.72426i	0.677912	+	0.698500i
$157$	23.1101			1.84439			0.922193	−	0.386730i	$-0.126396\pi$
$157$	23.1101			1.84439			0.922193	+	0.386730i	$0.126396\pi$
$158$	−13.4998	+	5.47387i	−1.07398	+	0.435478i
$159$	4.04788			0.321018
$160$	5.30353	−	1.96789i	0.419281	−	0.155576i
$161$	0.345903	+	5.53510i	0.0272609	+	0.436227i
$162$	0.531410	+	1.31057i	0.0417515	+	0.102968i
$163$	13.9465			1.09238			0.546188	−	0.837663i	$-0.316078\pi$
$163$	13.9465			1.09238			0.546188	+	0.837663i	$0.316078\pi$
$164$	3.18865	+	3.28549i	0.248991	+	0.256553i
$165$			0.264307i			0.0205762i
$166$	7.49243	−	3.03802i	0.581525	−	0.235796i
$167$	−5.00401			−0.387222			−0.193611	−	0.981078i	$-0.562020\pi$
$167$	−5.00401			−0.387222			−0.193611	+	0.981078i	$0.562020\pi$
$168$	−2.58515	+	7.02261i	−0.199448	+	0.541806i
$169$	23.9512			1.84240
$170$	−2.43322	+	0.986621i	−0.186620	+	0.0756704i
$171$			3.89210i			0.297637i
$172$	2.45610	−	2.38371i	0.187276	−	0.181756i
$173$	−0.0398406			−0.00302903			−0.00151451	−	0.999999i	$-0.500482\pi$
$173$	−0.0398406			−0.00302903			−0.00151451	+	0.999999i	$0.500482\pi$
$174$	−4.06939	−	10.0360i	−0.308500	−	0.760828i
$175$	−2.64060	+	0.165018i	−0.199611	+	0.0124742i
$176$	0.0316213	−	1.05675i	0.00238355	−	0.0796558i
$177$	−4.59290			−0.345224
$178$	−17.4954	+	7.09401i	−1.31133	+	0.531718i
$179$	0.662470			0.0495153			0.0247577	−	0.999693i	$-0.492119\pi$
$179$	0.662470			0.0495153			0.0247577	+	0.999693i	$0.492119\pi$
$180$	1.43521	−	1.39290i	0.106974	−	0.103821i
$181$	−8.47656			−0.630058			−0.315029	−	0.949082i	$-0.602014\pi$
$181$	−8.47656			−0.630058			−0.315029	+	0.949082i	$0.602014\pi$
$182$	9.84459	+	20.5037i	0.729730	+	1.51983i
$183$			9.96739i			0.736810i
$184$	−2.39117	+	5.42523i	−0.176279	+	0.399953i
$185$			8.95826i			0.658625i
$186$	9.43333	−	3.82502i	0.691685	−	0.280464i
$187$			0.490714i			0.0358846i
$188$	16.8291	−	16.3331i	1.22739	−	1.19121i
$189$	0.165018	+	2.64060i	0.0120033	+	0.192075i
$190$	5.10089	−	2.06830i	0.370057	−	0.150050i
$191$			11.6714i			0.844513i	0.906476	+	0.422257i	$0.138762\pi$
$191$			11.6714i			0.844513i	−0.906476	+	0.422257i	$0.861238\pi$
$192$	−5.90491	+	5.39742i	−0.426150	+	0.389525i
$193$	2.29670			0.165320			0.0826600	−	0.996578i	$-0.473658\pi$
$193$	2.29670			0.165320			0.0826600	+	0.996578i	$0.473658\pi$
$194$	−14.5713	+	5.90837i	−1.04616	+	0.424196i
$195$		−	6.07875i		−	0.435308i
$196$	−8.75438	+	10.9252i	−0.625313	+	0.780374i
$197$			23.3822i			1.66591i	0.553339	+	0.832956i	$0.313354\pi$
$197$			23.3822i			1.66591i	−0.553339	+	0.832956i	$0.686646\pi$
$198$	−0.140455	−	0.346393i	−0.00998171	−	0.0246171i
$199$	−9.36275			−0.663708			−0.331854	−	0.943331i	$-0.607674\pi$
$199$	−9.36275			−0.663708			−0.331854	+	0.943331i	$0.607674\pi$
$200$	−2.58819	−	1.14074i	−0.183012	−	0.0806626i
$201$			2.89202i			0.203987i
$202$	2.32357	+	5.73045i	0.163486	+	0.403193i
$203$	−1.26366	−	20.2210i	−0.0886917	−	1.41924i
$204$	2.66462	−	2.58608i	0.186561	−	0.181062i
$205$		−	2.28921i		−	0.159885i
$206$	−2.56184	−	6.31807i	−0.178492	−	0.440201i
$207$			2.09615i			0.145693i
$208$	−0.727255	+	24.3041i	−0.0504260	+	1.68519i
$209$		−	1.02871i		−	0.0711573i
$210$	3.37301	−	1.61951i	0.232760	−	0.111757i
$211$	−15.8913			−1.09400			−0.547002	−	0.837132i	$-0.684231\pi$
$211$	−15.8913			−1.09400			−0.547002	+	0.837132i	$0.684231\pi$
$212$	5.63830	+	5.80954i	0.387240	+	0.399001i
$213$	8.61213			0.590093
$214$	−3.26449	−	8.05095i	−0.223156	−	0.550352i
$215$	−1.71132			−0.116711
$216$	−1.14074	+	2.58819i	−0.0776177	+	0.176104i
$217$	19.0067	−	1.18778i	1.29026	−	0.0806316i
$218$	20.2630	−	8.21622i	1.37238	−	0.556472i
$219$	−4.16846			−0.281678
$220$	−0.379335	+	0.368154i	−0.0255747	+	0.0248209i
$221$		−	11.2859i		−	0.759170i
$222$	−4.76051	−	11.7405i	−0.319504	−	0.787968i
$223$	−11.3286			−0.758619			−0.379309	−	0.925270i	$-0.623838\pi$
$223$	−11.3286			−0.758619			−0.379309	+	0.925270i	$0.623838\pi$
$224$	−13.6798	+	6.07160i	−0.914017	+	0.405676i
$225$	−1.00000			−0.0666667
$226$	−8.92010	−	21.9989i	−0.593356	−	1.46335i
$227$		−	4.60858i		−	0.305882i	−0.988235	−	0.152941i	$-0.951126\pi$
$227$		−	4.60858i		−	0.305882i	0.988235	−	0.152941i	$-0.0488745\pi$
$228$	−5.58597	+	5.42133i	−0.369940	+	0.359036i
$229$	−1.54270			−0.101945			−0.0509723	−	0.998700i	$-0.516232\pi$
$229$	−1.54270			−0.101945			−0.0509723	+	0.998700i	$0.516232\pi$
$230$	2.74716	−	1.11392i	0.181142	−	0.0734494i
$231$	−0.0436153	−	0.697928i	−0.00286968	−	0.0459203i
$232$	8.73549	−	19.8196i	0.573513	−	1.30122i
$233$	−3.72016			−0.243716			−0.121858	−	0.992548i	$-0.538885\pi$
$233$	−3.72016			−0.243716			−0.121858	+	0.992548i	$0.538885\pi$
$234$	3.23031	+	7.96665i	0.211172	+	0.520796i
$235$	−11.7259			−0.764915
$236$	−6.39747	−	6.59177i	−0.416440	−	0.429088i
$237$	−10.3007			−0.669100
$238$	6.26236	−	3.00680i	0.405929	−	0.194902i
$239$		−	28.0309i		−	1.81317i	−0.422027	−	0.906583i	$-0.638681\pi$
$239$		−	28.0309i		−	1.81317i	0.422027	−	0.906583i	$-0.361319\pi$
$240$	3.99821	+	0.119639i	0.258083	+	0.00772265i
$241$		−	8.95756i		−	0.577007i	−0.957479	−	0.288504i	$-0.906842\pi$
$241$		−	8.95756i		−	0.577007i	0.957479	−	0.288504i	$-0.0931577\pi$
$242$	−5.80839	−	14.3248i	−0.373377	−	0.920830i
$243$			1.00000i			0.0641500i
$244$	−14.3053	+	13.8836i	−0.915801	+	0.888807i
$245$	6.94554	−	0.871493i	0.443734	−	0.0556776i
$246$	1.21651	+	3.00018i	0.0775617	+	0.191284i
$247$			23.6591i			1.50539i
$248$	18.6294	+	8.21091i	1.18297	+	0.521393i
$249$	5.71691			0.362294
$250$	0.531410	+	1.31057i	0.0336093	+	0.0828880i
$251$			14.7968i			0.933965i	0.884266	+	0.466983i	$0.154659\pi$
$251$			14.7968i			0.933965i	−0.884266	+	0.466983i	$0.845341\pi$
$252$	−3.55995	+	3.91494i	−0.224256	+	0.246618i
$253$		−	0.554027i		−	0.0348314i
$254$	−22.3692	+	9.07023i	−1.40357	+	0.569117i
$255$	−1.85661			−0.116265
$256$	−15.9714	−	0.956682i	−0.998211	−	0.0597927i
$257$		−	12.8851i		−	0.803754i	−0.915694	−	0.401877i	$-0.868358\pi$
$257$		−	12.8851i		−	0.803754i	0.915694	−	0.401877i	$-0.131642\pi$
$258$	2.24282	−	0.909415i	0.139632	−	0.0566177i
$259$	−1.47827	−	23.6552i	−0.0918555	−	1.46986i
$260$	8.72426	−	8.46711i	0.541056	−	0.525108i
$261$		−	7.65773i		−	0.474001i
$262$	2.62085	−	1.06270i	0.161917	−	0.0656538i
$263$		−	7.26011i		−	0.447677i	−0.974626	−	0.223839i	$-0.928141\pi$
$263$		−	7.26011i		−	0.447677i	0.974626	−	0.223839i	$-0.0718589\pi$
$264$	0.301506	−	0.684075i	0.0185564	−	0.0421019i
$265$		−	4.04788i		−	0.248659i
$266$	−13.1281	+	6.30330i	−0.804935	+	0.386480i
$267$	−13.3494			−0.816971
$268$	−4.15065	+	4.02831i	−0.253541	+	0.246068i
$269$	12.0068			0.732067			0.366034	−	0.930602i	$-0.380715\pi$
$269$	12.0068			0.732067			0.366034	+	0.930602i	$0.380715\pi$
$270$	1.31057	−	0.531410i	0.0797590	−	0.0323406i
$271$	18.8132			1.14282			0.571411	−	0.820664i	$-0.306396\pi$
$271$	18.8132			1.14282			0.571411	+	0.820664i	$0.306396\pi$
$272$	7.42312	+	0.222123i	0.450093	+	0.0134682i
$273$	1.00310	+	16.0515i	0.0607105	+	0.971484i
$274$	−9.01038	−	22.2216i	−0.544337	−	1.34246i
$275$	0.264307			0.0159383
$276$	−3.00841	+	2.91974i	−0.181085	+	0.175748i
$277$		−	9.57593i		−	0.575362i	−0.957726	−	0.287681i	$-0.907116\pi$
$277$		−	9.57593i		−	0.575362i	0.957726	−	0.287681i	$-0.0928842\pi$
$278$	−26.1419	+	10.6000i	−1.56789	+	0.635746i
$279$	7.19786			0.430925
$280$	7.02261	+	2.58515i	0.419681	+	0.154492i
$281$	6.08335			0.362902			0.181451	−	0.983400i	$-0.441921\pi$
$281$	6.08335			0.362902			0.181451	+	0.983400i	$0.441921\pi$
$282$	15.3677	−	6.23127i	0.915132	−	0.371067i
$283$			8.00209i			0.475675i	0.971305	+	0.237838i	$0.0764386\pi$
$283$			8.00209i			0.475675i	−0.971305	+	0.237838i	$0.923561\pi$
$284$	11.9959	+	12.3602i	0.711823	+	0.733442i
$285$	3.89210			0.230548
$286$	−0.853792	−	2.10564i	−0.0504858	−	0.124509i
$287$	0.377760	+	6.04488i	0.0222985	+	0.356818i
$288$	−5.30353	+	1.96789i	−0.312513	+	0.115959i
$289$	13.5530			0.797235
$290$	−10.0360	+	4.06939i	−0.589335	+	0.238963i
$291$	−11.1183			−0.651766
$292$	−5.80626	−	5.98260i	−0.339785	−	0.350105i
$293$	14.1818			0.828509			0.414255	−	0.910161i	$-0.364042\pi$
$293$	14.1818			0.828509			0.414255	+	0.910161i	$0.364042\pi$
$294$	−8.63952	+	4.83308i	−0.503867	+	0.281871i
$295$			4.59290i			0.267409i
$296$	10.2191	−	23.1857i	0.593971	−	1.34764i
$297$		−	0.264307i		−	0.0153366i
$298$	−4.83289	+	1.95963i	−0.279962	+	0.113518i
$299$			12.7420i			0.736888i
$300$	−1.39290	−	1.43521i	−0.0804193	−	0.0828617i
$301$	4.51892	−	0.282399i	0.260466	−	0.0162772i
$302$	18.9812	−	7.69647i	1.09224	−	0.442882i
$303$			4.37247i			0.251192i
$304$	−15.5614	−	0.465647i	−0.892510	−	0.0267067i
$305$	9.96739			0.570731
$306$	2.43322	−	0.986621i	0.139098	−	0.0564014i
$307$		−	20.0654i		−	1.14519i	−0.819837	−	0.572597i	$-0.805936\pi$
$307$		−	20.0654i		−	1.14519i	0.819837	−	0.572597i	$-0.194064\pi$
$308$	0.940919	−	1.03474i	0.0536139	−	0.0589600i
$309$		−	4.82084i		−	0.274248i
$310$	−3.82502	−	9.43333i	−0.217246	−	0.535777i
$311$	−15.0389			−0.852777			−0.426389	−	0.904540i	$-0.640214\pi$
$311$	−15.0389			−0.852777			−0.426389	+	0.904540i	$0.640214\pi$
$312$	−6.93429	+	15.7329i	−0.392577	+	0.890702i
$313$			22.2502i			1.25766i	0.777545	+	0.628828i	$0.216465\pi$
$313$			22.2502i			1.25766i	−0.777545	+	0.628828i	$0.783535\pi$
$314$	12.2809	+	30.2875i	0.693053	+	1.70922i
$315$	2.64060	−	0.165018i	0.148781	−	0.00929771i
$316$	−14.3478	−	14.7836i	−0.807128	−	0.831641i
$317$			33.4862i			1.88077i	0.340112	+	0.940385i	$0.389535\pi$
$317$			33.4862i			1.88077i	−0.340112	+	0.940385i	$0.610465\pi$
$318$	2.15108	+	5.30504i	0.120627	+	0.297492i
$319$			2.02399i			0.113322i
$320$	5.39742	+	5.90491i	0.301725	+	0.330094i
$321$		−	6.14307i		−	0.342873i
$322$	−7.07034	+	3.39474i	−0.394015	+	0.189181i
$323$	7.22612			0.402072
$324$	−1.43521	+	1.39290i	−0.0797337	+	0.0773835i
$325$	−6.07875			−0.337188
$326$	7.41132	+	18.2780i	0.410475	+	1.01232i
$327$	15.4612			0.855004
$328$	−2.61140	+	5.92490i	−0.144190	+	0.327148i
$329$	30.9635	−	1.93499i	1.70707	−	0.106679i
$330$	−0.346393	+	0.140455i	−0.0190683	+	0.00773180i
$331$	23.5161			1.29256			0.646280	−	0.763100i	$-0.276324\pi$
$331$	23.5161			1.29256			0.646280	+	0.763100i	$0.276324\pi$
$332$	7.96310	+	8.20495i	0.437032	+	0.450305i
$333$		−	8.95826i		−	0.490910i
$334$	−2.65918	−	6.55812i	−0.145504	−	0.358844i
$335$	2.89202			0.158008
$336$	−10.5774	+	0.343858i	−0.577045	+	0.0187590i
$337$	−18.0622			−0.983911			−0.491955	−	0.870620i	$-0.663718\pi$
$337$	−18.0622			−0.983911			−0.491955	+	0.870620i	$0.663718\pi$
$338$	12.7279	+	31.3898i	0.692307	+	1.70738i
$339$		−	16.7857i		−	0.911675i
$340$	−2.58608	−	2.66462i	−0.140250	−	0.144509i
$341$	−1.90244			−0.103023
$342$	−5.10089	+	2.06830i	−0.275824	+	0.111841i
$343$	−18.1966	+	3.44740i	−0.982523	+	0.186142i
$344$	4.42923	+	1.95218i	0.238808	+	0.105254i
$345$	2.09615			0.112853
$346$	−0.0211717	−	0.0522141i	−0.00113820	−	0.00280705i
$347$	14.1722			0.760803			0.380401	−	0.924822i	$-0.375786\pi$
$347$	14.1722			0.760803			0.380401	+	0.924822i	$0.375786\pi$
$348$	10.9904	−	10.6665i	0.589148	−	0.571783i
$349$	29.8810			1.59949			0.799746	−	0.600339i	$-0.204968\pi$
$349$	29.8810			1.59949			0.799746	+	0.600339i	$0.204968\pi$
$350$	−1.61951	−	3.37301i	−0.0865664	−	0.180295i
$351$			6.07875i			0.324460i
$352$	1.40176	−	0.520127i	0.0747139	−	0.0277229i
$353$		−	17.7999i		−	0.947392i	−0.880688	−	0.473696i	$-0.842920\pi$
$353$		−	17.7999i		−	0.947392i	0.880688	−	0.473696i	$-0.157080\pi$
$354$	−2.44071	−	6.01934i	−0.129722	−	0.319924i
$355$		−	8.61213i		−	0.457084i
$356$	−18.5944	−	19.1592i	−0.985504	−	1.01543i
$357$	4.90257	−	0.306374i	0.259471	−	0.0162150i
$358$	0.352043	+	0.868215i	0.0186060	+	0.0458866i
$359$		−	16.1540i		−	0.852576i	−0.904588	−	0.426288i	$-0.859821\pi$
$359$		−	16.1540i		−	0.852576i	0.904588	−	0.426288i	$-0.140179\pi$
$360$	2.58819	+	1.14074i	0.136409	+	0.0601224i
$361$	3.85153			0.202712
$362$	−4.50453	−	11.1092i	−0.236753	−	0.583885i
$363$		−	10.9301i		−	0.573684i
$364$	−21.6401	+	23.7979i	−1.13425	+	1.24735i
$365$			4.16846i			0.218187i
$366$	−13.0630	+	5.29677i	−0.682814	+	0.276866i
$367$	33.5356			1.75054			0.875272	−	0.483631i	$-0.160682\pi$
$367$	33.5356			1.75054			0.875272	+	0.483631i	$0.160682\pi$
$368$	−8.38085	−	0.250781i	−0.436882	−	0.0130729i
$369$			2.28921i			0.119171i
$370$	−11.7405	+	4.76051i	−0.610358	+	0.247487i
$371$	0.667973	+	10.6888i	0.0346794	+	0.554936i
$372$	10.0259	+	10.3304i	0.519820	+	0.535608i
$373$		−	20.3929i		−	1.05590i	−0.849275	−	0.527951i	$-0.822960\pi$
$373$		−	20.3929i		−	1.05590i	0.849275	−	0.527951i	$-0.177040\pi$
$374$	−0.643117	+	0.260770i	−0.0332548	+	0.0134841i
$375$			1.00000i			0.0516398i
$376$	30.3489	+	13.3763i	1.56512	+	0.689827i
$377$		−	46.5494i		−	2.39742i
$378$	−3.37301	+	1.61951i	−0.173489	+	0.0832986i
$379$	−11.2350			−0.577101			−0.288550	−	0.957465i	$-0.593173\pi$
$379$	−11.2350			−0.577101			−0.288550	+	0.957465i	$0.593173\pi$
$380$	5.42133	+	5.58597i	0.278108	+	0.286554i
$381$	−17.0682			−0.874433
$382$	−15.2962	+	6.20230i	−0.782623	+	0.317337i
$383$	8.65284			0.442140			0.221070	−	0.975258i	$-0.429045\pi$
$383$	8.65284			0.442140			0.221070	+	0.975258i	$0.429045\pi$
$384$	−10.2116	−	4.87057i	−0.521110	−	0.248550i
$385$	−0.697928	+	0.0436153i	−0.0355697	+	0.00222284i
$386$	1.22049	+	3.00999i	0.0621212	+	0.153205i
$387$	1.71132			0.0869915
$388$	−15.4867	−	15.9571i	−0.786219	−	0.810097i
$389$			5.18569i			0.262925i	0.991321	+	0.131462i	$0.0419673\pi$
$389$			5.18569i			0.262925i	−0.991321	+	0.131462i	$0.958033\pi$
$390$	7.96665	−	3.23031i	0.403407	−	0.163573i
$391$	3.89174			0.196814
$392$	−18.9705	−	5.66748i	−0.958155	−	0.286251i
$393$	1.99977			0.100875
$394$	−30.6441	+	12.4255i	−1.54383	+	0.625989i
$395$			10.3007i			0.518282i
$396$	0.379335	−	0.368154i	0.0190623	−	0.0185004i
$397$	−6.42434			−0.322428			−0.161214	−	0.986919i	$-0.551541\pi$
$397$	−6.42434			−0.322428			−0.161214	+	0.986919i	$0.551541\pi$
$398$	−4.97546	−	12.2706i	−0.249397	−	0.615068i
$399$	−10.2775	+	0.642267i	−0.514518	+	0.0321536i
$400$	0.119639	−	3.99821i	0.00598194	−	0.199911i
$401$	−36.9183			−1.84361			−0.921806	−	0.387651i	$-0.873286\pi$
$401$	−36.9183			−1.84361			−0.921806	+	0.387651i	$0.873286\pi$
$402$	−3.79021	+	1.53685i	−0.189038	+	0.0766510i
$403$	43.7540			2.17954
$404$	−6.27540	+	6.09043i	−0.312213	+	0.303010i
$405$	1.00000			0.0496904
$406$	25.8296	−	12.4018i	1.28190	−	0.615489i
$407$			2.36773i			0.117364i
$408$	4.80525	+	2.11791i	0.237895	+	0.104852i
$409$		−	31.5872i		−	1.56189i	−0.624602	−	0.780943i	$-0.714739\pi$
$409$		−	31.5872i		−	1.56189i	0.624602	−	0.780943i	$-0.285261\pi$
$410$	3.00018	−	1.21651i	0.148168	−	0.0600790i
$411$		−	16.9556i		−	0.836359i
$412$	6.91891	−	6.71497i	0.340870	−	0.330823i
$413$	−0.757912	−	12.1280i	−0.0372944	−	0.596781i
$414$	−2.74716	+	1.11392i	−0.135016	+	0.0547460i
$415$		−	5.71691i		−	0.280632i
$416$	−32.2388	+	11.9623i	−1.58064	+	0.586501i
$417$	−19.9469			−0.976806
$418$	1.34820	−	0.546666i	0.0659426	−	0.0267383i
$419$		−	25.7821i		−	1.25954i	−0.776782	−	0.629770i	$-0.783149\pi$
$419$		−	25.7821i		−	1.25954i	0.776782	−	0.629770i	$-0.216851\pi$
$420$	3.91494	+	3.55995i	0.191029	+	0.173708i
$421$			1.53513i			0.0748174i	0.999300	+	0.0374087i	$0.0119103\pi$
$421$			1.53513i			0.0748174i	−0.999300	+	0.0374087i	$0.988090\pi$
$422$	−8.44480	−	20.8267i	−0.411086	−	1.01383i
$423$	11.7259			0.570134
$424$	−4.61758	+	10.4767i	−0.224250	+	0.508792i
$425$			1.85661i			0.0900588i
$426$	4.57657	+	11.2868i	0.221735	+	0.546849i
$427$	−26.3199	+	1.64480i	−1.27371	+	0.0795973i
$428$	8.81658	−	8.55671i	0.426166	−	0.413604i
$429$		−	1.60665i		−	0.0775700i
$430$	−0.909415	−	2.24282i	−0.0438559	−	0.108158i
$431$		−	31.2356i		−	1.50457i	−0.658840	−	0.752283i	$-0.728953\pi$
$431$		−	31.2356i		−	1.50457i	0.658840	−	0.752283i	$-0.271047\pi$
$432$	−3.99821	−	0.119639i	−0.192364	−	0.00575613i
$433$			6.85246i			0.329308i	0.986351	+	0.164654i	$0.0526508\pi$
$433$			6.85246i			0.329308i	−0.986351	+	0.164654i	$0.947349\pi$
$434$	11.6570	+	24.2785i	0.559554	+	1.16540i
$435$	−7.65773			−0.367160
$436$	21.5359	+	22.1900i	1.03138	+	1.06271i
$437$	−8.15844			−0.390271
$438$	−2.21516	−	5.46307i	−0.105844	−	0.261035i
$439$	0.157801			0.00753144			0.00376572	−	0.999993i	$-0.498801\pi$
$439$	0.157801			0.00753144			0.00376572	+	0.999993i	$0.498801\pi$
$440$	−0.684075	−	0.301506i	−0.0326120	−	0.0143737i
$441$	−6.94554	+	0.871493i	−0.330740	+	0.0414997i
$442$	14.7910	−	5.99742i	0.703534	−	0.285268i
$443$	39.7323			1.88774			0.943868	−	0.330323i	$-0.107158\pi$
$443$	39.7323			1.88774			0.943868	+	0.330323i	$0.107158\pi$
$444$	12.8570	−	12.4780i	0.610164	−	0.592180i
$445$			13.3494i			0.632823i
$446$	−6.02012	−	14.8470i	−0.285061	−	0.703024i
$447$	−3.68761			−0.174418
$448$	−15.2268	−	14.7018i	−0.719400	−	0.694596i
$449$	−9.45801			−0.446351			−0.223176	−	0.974778i	$-0.571642\pi$
$449$	−9.45801			−0.446351			−0.223176	+	0.974778i	$0.571642\pi$
$450$	−0.531410	−	1.31057i	−0.0250509	−	0.0617810i
$451$		−	0.605053i		−	0.0284908i
$452$	24.0910	−	23.3809i	1.13314	−	1.09974i
$453$	14.4831			0.680476
$454$	6.03988	−	2.44904i	0.283466	−	0.114939i
$455$	16.0515	−	1.00310i	0.752508	−	0.0470262i
$456$	−10.0735	−	4.43989i	−0.471734	−	0.207917i
$457$	−25.6849			−1.20149			−0.600745	−	0.799441i	$-0.705129\pi$
$457$	−25.6849			−1.20149			−0.600745	+	0.799441i	$0.705129\pi$
$458$	−0.819806	−	2.02182i	−0.0383070	−	0.0944736i
$459$	1.85661			0.0866591
$460$	2.91974	+	3.00841i	0.136133	+	0.140268i
$461$	27.4268			1.27739			0.638697	−	0.769459i	$-0.279474\pi$
$461$	27.4268			1.27739			0.638697	+	0.769459i	$0.279474\pi$
$462$	0.891509	−	0.428047i	0.0414767	−	0.0199146i
$463$			16.9982i			0.789972i	0.918687	+	0.394986i	$0.129251\pi$
$463$			16.9982i			0.789972i	−0.918687	+	0.394986i	$0.870749\pi$
$464$	30.6172	+	0.916161i	1.42137	+	0.0425317i
$465$		−	7.19786i		−	0.333793i
$466$	−1.97693	−	4.87555i	−0.0915796	−	0.225855i
$467$		−	8.95474i		−	0.414376i	−0.978301	−	0.207188i	$-0.933569\pi$
$467$		−	8.95474i		−	0.414376i	0.978301	−	0.207188i	$-0.0664312\pi$
$468$	−8.72426	+	8.46711i	−0.403279	+	0.391392i
$469$	−7.63667	+	0.477235i	−0.352629	+	0.0220367i
$470$	−6.23127	−	15.3677i	−0.287427	−	0.708858i
$471$			23.1101i			1.06486i
$472$	5.23932	−	11.8873i	0.241159	−	0.547157i
$473$	−0.452314			−0.0207974
$474$	−5.47387	−	13.4998i	−0.251423	−	0.620065i
$475$		−	3.89210i		−	0.178582i
$476$	7.26851	+	6.60945i	0.333152	+	0.302944i
$477$			4.04788i			0.185340i
$478$	36.7365	−	14.8959i	1.68029	−	0.681322i
$479$	4.76512			0.217724			0.108862	−	0.994057i	$-0.465279\pi$
$479$	4.76512			0.217724			0.108862	+	0.994057i	$0.465279\pi$
$480$	1.96789	+	5.30353i	0.0898216	+	0.242072i
$481$		−	54.4550i		−	2.48294i
$482$	11.7395	−	4.76014i	0.534722	−	0.216818i
$483$	−5.53510	+	0.345903i	−0.251856	+	0.0157391i
$484$	15.6870	−	15.2246i	0.713046	−	0.692029i
$485$			11.1183i			0.504856i
$486$	−1.31057	+	0.531410i	−0.0594488	+	0.0241052i
$487$			22.2240i			1.00707i	0.863975	+	0.503534i	$0.167967\pi$
$487$			22.2240i			1.00707i	−0.863975	+	0.503534i	$0.832033\pi$
$488$	−25.7975	−	11.3702i	−1.16780	−	0.514705i
$489$			13.9465i			0.630684i
$490$	4.83308	+	8.63952i	0.218336	+	0.390294i
$491$	−29.6305			−1.33721			−0.668604	−	0.743619i	$-0.733108\pi$
$491$	−29.6305			−1.33721			−0.668604	+	0.743619i	$0.733108\pi$
$492$	−3.28549	+	3.18865i	−0.148121	+	0.143755i
$493$	−14.2174			−0.640320
$494$	−31.0070	+	12.5727i	−1.39507	+	0.565672i
$495$	−0.264307			−0.0118797
$496$	−0.861144	+	28.7786i	−0.0386665	+	1.29220i
$497$	1.42116	+	22.7412i	0.0637475	+	1.02008i
$498$	3.03802	+	7.49243i	0.136137	+	0.335744i
$499$	−17.4850			−0.782738			−0.391369	−	0.920234i	$-0.627998\pi$
$499$	−17.4850			−0.782738			−0.391369	+	0.920234i	$0.627998\pi$
$500$	−1.43521	+	1.39290i	−0.0641844	+	0.0622925i
$501$		−	5.00401i		−	0.223562i
$502$	−19.3923	+	7.86316i	−0.865520	+	0.350950i
$503$	26.5951			1.18582			0.592908	−	0.805270i	$-0.297980\pi$
$503$	26.5951			1.18582			0.592908	+	0.805270i	$0.297980\pi$
$504$	−7.02261	−	2.58515i	−0.312812	−	0.115152i
$505$	4.37247			0.194572
$506$	0.726093	−	0.294415i	0.0322788	−	0.0130884i
$507$			23.9512i			1.06371i
$508$	−23.7744	−	24.4965i	−1.05482	−	1.08685i
$509$	−41.2008			−1.82620			−0.913098	−	0.407741i	$-0.866317\pi$
$509$	−41.2008			−1.82620			−0.913098	+	0.407741i	$0.866317\pi$
$510$	−0.986621	−	2.43322i	−0.0436883	−	0.107745i
$511$	−0.687870	−	11.0072i	−0.0304296	−	0.486931i
$512$	−7.23354	−	21.4401i	−0.319680	−	0.947525i
$513$	−3.89210			−0.171841
$514$	16.8869	−	6.84730i	0.744851	−	0.302021i
$515$	−4.82084			−0.212432
$516$	2.38371	+	2.45610i	0.104937	+	0.108124i
$517$	−3.09924			−0.136304
$518$	30.2163	−	14.5080i	1.32763	−	0.637444i
$519$		−	0.0398406i		−	0.00174881i
$520$	15.7329	+	6.93429i	0.689935	+	0.304089i
$521$			4.12574i			0.180752i	0.995908	+	0.0903761i	$0.0288069\pi$
$521$			4.12574i			0.180752i	−0.995908	+	0.0903761i	$0.971193\pi$
$522$	10.0360	−	4.06939i	0.439264	−	0.178112i
$523$		−	14.9470i		−	0.653586i	−0.945096	−	0.326793i	$-0.894032\pi$
$523$		−	14.9470i		−	0.653586i	0.945096	−	0.326793i	$-0.105968\pi$
$524$	2.78549	+	2.87009i	0.121685	+	0.125380i
$525$	−0.165018	−	2.64060i	−0.00720197	−	0.115245i
$526$	9.51490	−	3.85809i	0.414870	−	0.168221i
$527$		−	13.3636i		−	0.582129i
$528$	1.05675	+	0.0316213i	0.0459893	+	0.00137614i
$529$	18.6061			0.808963
$530$	5.30504	−	2.15108i	0.230436	−	0.0934370i
$531$		−	4.59290i		−	0.199315i
$532$	−15.2373	−	13.8557i	−0.660622	−	0.600721i
$533$			13.9155i			0.602748i
$534$	−7.09401	−	17.4954i	−0.306988	−	0.757099i
$535$	−6.14307			−0.265588
$536$	−7.48509	−	3.29905i	−0.323307	−	0.142497i
$537$			0.662470i			0.0285877i
$538$	6.38053	+	15.7358i	0.275084	+	0.678418i
$539$	1.83575	−	0.230341i	0.0790714	−	0.00992151i
$540$	1.39290	+	1.43521i	0.0599410	+	0.0617615i
$541$			8.25685i			0.354990i	0.984122	+	0.177495i	$0.0567993\pi$
$541$			8.25685i			0.354990i	−0.984122	+	0.177495i	$0.943201\pi$
$542$	9.99754	+	24.6561i	0.429431	+	1.05907i
$543$		−	8.47656i		−	0.363764i
$544$	3.65361	+	9.84658i	0.156647	+	0.422169i
$545$		−	15.4612i		−	0.662284i
$546$	−20.5037	+	9.84459i	−0.877476	+	0.421310i
$547$	−23.1912			−0.991586			−0.495793	−	0.868441i	$-0.665123\pi$
$547$	−23.1912			−0.991586			−0.495793	+	0.868441i	$0.665123\pi$
$548$	24.3348	−	23.6175i	1.03953	−	1.00889i
$549$	−9.96739			−0.425398
$550$	0.140455	+	0.346393i	0.00598903	+	0.0147703i
$551$	29.8047			1.26972
$552$	−5.42523	−	2.39117i	−0.230913	−	0.101775i
$553$	−1.69979	−	27.1999i	−0.0722826	−	1.15666i
$554$	12.5500	−	5.08874i	0.533197	−	0.216200i
$555$	−8.95826			−0.380257
$556$	−27.7842	−	28.6280i	−1.17831	−	1.21410i
$557$		−	24.5841i		−	1.04166i	−0.853660	−	0.520830i	$-0.825622\pi$
$557$		−	24.5841i		−	1.04166i	0.853660	−	0.520830i	$-0.174378\pi$
$558$	3.82502	+	9.43333i	0.161926	+	0.399345i
$559$	10.4027			0.439988
$560$	0.343858	+	10.5774i	0.0145307	+	0.446977i
$561$	−0.490714			−0.0207180
$562$	3.23275	+	7.97268i	0.136366	+	0.336307i
$563$		−	11.9197i		−	0.502354i	−0.967941	−	0.251177i	$-0.919182\pi$
$563$		−	11.9197i		−	0.502354i	0.967941	−	0.251177i	$-0.0808175\pi$
$564$	16.3331	+	16.8291i	0.687747	+	0.708634i
$565$	−16.7857			−0.706180
$566$	−10.4873	+	4.25239i	−0.440816	+	0.178741i
$567$	−2.64060	+	0.165018i	−0.110895	+	0.00693010i
$568$	−9.82421	+	22.2898i	−0.412215	+	0.935259i
$569$	17.2754			0.724221			0.362111	−	0.932135i	$-0.382056\pi$
$569$	17.2754			0.724221			0.362111	+	0.932135i	$0.382056\pi$
$570$	2.06830	+	5.10089i	0.0866316	+	0.213653i
$571$	−15.3607			−0.642823			−0.321412	−	0.946940i	$-0.604157\pi$
$571$	−15.3607			−0.642823			−0.321412	+	0.946940i	$0.604157\pi$
$572$	2.30588	−	2.23791i	0.0964137	−	0.0935719i
$573$	−11.6714			−0.487580
$574$	−7.72152	+	3.70739i	−0.322290	+	0.154744i
$575$		−	2.09615i		−	0.0874156i
$576$	−5.39742	−	5.90491i	−0.224892	−	0.246038i
$577$			18.5279i			0.771326i	0.922640	+	0.385663i	$0.126027\pi$
$577$			18.5279i			0.771326i	−0.922640	+	0.385663i	$0.873973\pi$
$578$	7.20220	+	17.7622i	0.299572	+	0.738810i
$579$			2.29670i			0.0954475i
$580$	−10.6665	−	10.9904i	−0.442901	−	0.456352i
$581$	0.943392	+	15.0961i	0.0391385	+	0.626290i
$582$	−5.90837	−	14.5713i	−0.244910	−	0.604002i
$583$		−	1.06988i		−	0.0443099i
$584$	4.75513	−	10.7887i	0.196769	−	0.446441i
$585$	6.07875			0.251325
$586$	7.53635	+	18.5863i	0.311324	+	0.767792i
$587$			20.7809i			0.857720i	0.903371	+	0.428860i	$0.141085\pi$
$587$			20.7809i			0.857720i	−0.903371	+	0.428860i	$0.858915\pi$
$588$	−10.9252	−	8.75438i	−0.450549	−	0.361025i
$589$			28.0148i			1.15433i
$590$	−6.01934	+	2.44071i	−0.247812	+	0.100483i
$591$	−23.3822			−0.961815
$592$	35.8170	+	1.07176i	1.47207	+	0.0440489i
$593$		−	1.59413i		−	0.0654632i	−0.999464	−	0.0327316i	$-0.989579\pi$
$593$		−	1.59413i		−	0.0654632i	0.999464	−	0.0327316i	$-0.0104206\pi$
$594$	0.346393	−	0.140455i	0.0142127	−	0.00576295i
$595$	−0.306374	−	4.90257i	−0.0125601	−	0.200986i
$596$	−5.13649	−	5.29248i	−0.210399	−	0.216789i
$597$		−	9.36275i		−	0.383192i
$598$	−16.6993	+	6.77121i	−0.682885	+	0.276896i
$599$		−	23.8540i		−	0.974650i	−0.873221	−	0.487325i	$-0.837973\pi$
$599$		−	23.8540i		−	0.974650i	0.873221	−	0.487325i	$-0.162027\pi$
$600$	1.14074	−	2.58819i	0.0465706	−	0.105662i
$601$			28.1413i			1.14791i	0.818887	+	0.573954i	$0.194591\pi$
$601$			28.1413i			1.14791i	−0.818887	+	0.573954i	$0.805409\pi$
$602$	2.77151	+	5.77231i	0.112958	+	0.235262i
$603$	−2.89202			−0.117772
$604$	20.1736	+	20.7863i	0.820851	+	0.845781i
$605$	−10.9301			−0.444373
$606$	−5.73045	+	2.32357i	−0.232783	+	0.0943888i
$607$	−9.91696			−0.402517			−0.201258	−	0.979538i	$-0.564503\pi$
$607$	−9.91696			−0.402517			−0.201258	+	0.979538i	$0.564503\pi$
$608$	−7.65924	−	20.6419i	−0.310623	−	0.837139i
$609$	20.2210	−	1.26366i	0.819396	−	0.0512062i
$610$	5.29677	+	13.0630i	0.214460	+	0.528905i
$611$	71.2789			2.88364
$612$	2.58608	+	2.66462i	0.104536	+	0.107711i
$613$		−	36.6198i		−	1.47906i	−0.673123	−	0.739531i	$-0.735047\pi$
$613$		−	36.6198i		−	1.47906i	0.673123	−	0.739531i	$-0.264953\pi$
$614$	26.2972	−	10.6630i	1.06127	−	0.430322i
$615$	2.28921			0.0923098
$616$	1.85612	+	0.683271i	0.0747853	+	0.0275298i
$617$	−21.8103			−0.878050			−0.439025	−	0.898475i	$-0.644676\pi$
$617$	−21.8103			−0.878050			−0.439025	+	0.898475i	$0.644676\pi$
$618$	6.31807	−	2.56184i	0.254150	−	0.103052i
$619$			31.3205i			1.25888i	0.777050	+	0.629439i	$0.216715\pi$
$619$			31.3205i			1.25888i	−0.777050	+	0.629439i	$0.783285\pi$
$620$	10.3304	−	10.0259i	0.414880	−	0.402651i
$621$	−2.09615			−0.0841157
$622$	−7.99181	−	19.7096i	−0.320443	−	0.790282i
$623$	−2.20289	−	35.2505i	−0.0882570	−	1.41228i
$624$	−24.3041	−	0.727255i	−0.972943	−	0.0291135i
$625$	1.00000			0.0400000
$626$	−29.1605	+	11.8240i	−1.16549	+	0.472581i
$627$	1.02871			0.0410827
$628$	−33.1678	+	32.1901i	−1.32354	+	1.28453i
$629$	−16.6320			−0.663161
$630$	1.61951	+	3.37301i	0.0645228	+	0.134384i
$631$			28.9853i			1.15389i	0.816785	+	0.576943i	$0.195754\pi$
$631$			28.9853i			1.15389i	−0.816785	+	0.576943i	$0.804246\pi$
$632$	11.7504	−	26.6600i	0.467406	−	1.06048i
$633$		−	15.8913i		−	0.631623i
$634$	−43.8861	+	17.7949i	−1.74294	+	0.706725i
$635$			17.0682i			0.677333i
$636$	−5.80954	+	5.63830i	−0.230363	+	0.223573i
$637$	−42.2202	+	5.29759i	−1.67282	+	0.209898i
$638$	−2.65259	+	1.07557i	−0.105017	+	0.0425821i
$639$			8.61213i			0.340690i
$640$	−4.87057	+	10.2116i	−0.192526	+	0.403650i
$641$	−5.84700			−0.230943			−0.115471	−	0.993311i	$-0.536838\pi$
$641$	−5.84700			−0.230943			−0.115471	+	0.993311i	$0.536838\pi$
$642$	8.05095	−	3.26449i	0.317746	−	0.128839i
$643$			47.7829i			1.88437i	0.335087	+	0.942187i	$0.391234\pi$
$643$			47.7829i			1.88437i	−0.335087	+	0.942187i	$0.608766\pi$
$644$	−8.20630	−	7.46220i	−0.323374	−	0.294052i
$645$		−	1.71132i		−	0.0673833i
$646$	3.84003	+	9.47036i	0.151084	+	0.372606i
$647$	−1.20494			−0.0473713			−0.0236856	−	0.999719i	$-0.507540\pi$
$647$	−1.20494			−0.0473713			−0.0236856	+	0.999719i	$0.507540\pi$
$648$	−2.58819	−	1.14074i	−0.101674	−	0.0448126i
$649$			1.21393i			0.0476511i
$650$	−3.23031	−	7.96665i	−0.126703	−	0.312478i
$651$	1.18778	+	19.0067i	0.0465526	+	0.744931i
$652$	−20.0162	+	19.4262i	−0.783893	+	0.760787i
$653$		−	2.29865i		−	0.0899531i	−0.998988	−	0.0449765i	$-0.985679\pi$
$653$		−	2.29865i		−	0.0899531i	0.998988	−	0.0449765i	$-0.0143213\pi$
$654$	8.21622	+	20.2630i	0.321279	+	0.792346i
$655$		−	1.99977i		−	0.0781376i
$656$	−9.15273	−	0.273878i	−0.357354	−	0.0106931i
$657$		−	4.16846i		−	0.162627i
$658$	18.9902	+	39.5516i	0.740316	+	1.54188i
$659$	−31.7367			−1.23629			−0.618143	−	0.786066i	$-0.712115\pi$
$659$	−31.7367			−1.23629			−0.618143	+	0.786066i	$0.712115\pi$
$660$	−0.368154	−	0.379335i	−0.0143304	−	0.0147656i
$661$	29.3254			1.14063			0.570313	−	0.821427i	$-0.306822\pi$
$661$	29.3254			1.14063			0.570313	+	0.821427i	$0.306822\pi$
$662$	12.4967	+	30.8195i	0.485697	+	1.19784i
$663$	11.2859			0.438307
$664$	−6.52152	+	14.7964i	−0.253084	+	0.574212i
$665$	0.642267	+	10.2775i	0.0249060	+	0.398544i
$666$	11.7405	−	4.76051i	0.454934	−	0.184466i
$667$	16.0518			0.621526
$668$	7.18178	−	6.97010i	0.277872	−	0.269681i
$669$		−	11.3286i		−	0.437989i
$670$	1.53685	+	3.79021i	0.0593736	+	0.146428i
$671$	2.63445			0.101702
$672$	−6.07160	−	13.6798i	−0.234217	−	0.527708i
$673$	−5.35156			−0.206287			−0.103144	−	0.994666i	$-0.532890\pi$
$673$	−5.35156			−0.206287			−0.103144	+	0.994666i	$0.532890\pi$
$674$	−9.59843	−	23.6718i	−0.369718	−	0.911806i
$675$		−	1.00000i		−	0.0384900i
$676$	−34.3749	+	33.3617i	−1.32211	+	1.28314i
$677$	−38.3482			−1.47384			−0.736921	−	0.675979i	$-0.763721\pi$
$677$	−38.3482			−1.47384			−0.736921	+	0.675979i	$0.763721\pi$
$678$	21.9989	−	8.92010i	0.844863	−	0.342574i
$679$	−1.83472	−	29.3590i	−0.0704100	−	1.12669i
$680$	2.11791	−	4.80525i	0.0812183	−	0.184273i
$681$	4.60858			0.176601
$682$	−1.01098	−	2.49329i	−0.0387123	−	0.0954731i
$683$	40.9876			1.56835			0.784174	−	0.620541i	$-0.213087\pi$
$683$	40.9876			1.56835			0.784174	+	0.620541i	$0.213087\pi$
$684$	−5.42133	−	5.58597i	−0.207290	−	0.213585i
$685$	−16.9556			−0.647841
$686$	−14.1879	−	22.0160i	−0.541697	−	0.840574i
$687$		−	1.54270i		−	0.0588577i
$688$	−0.204741	+	6.84223i	−0.00780567	+	0.260858i
$689$			24.6060i			0.937415i
$690$	1.11392	+	2.74716i	0.0424060	+	0.104583i
$691$		−	12.3363i		−	0.469297i	−0.972080	−	0.234648i	$-0.924606\pi$
$691$		−	12.3363i		−	0.469297i	0.972080	−	0.234648i	$-0.0753938\pi$
$692$	0.0571795	−	0.0554941i	0.00217364	−	0.00210957i
$693$	0.697928	−	0.0436153i	0.0265121	−	0.00165681i
$694$	7.53124	+	18.5737i	0.285882	+	0.705048i
$695$			19.9469i			0.756631i
$696$	19.8196	+	8.73549i	0.751261	+	0.331118i
$697$	4.25017			0.160987
$698$	15.8790	+	39.1612i	0.601030	+	1.48227i
$699$		−	3.72016i		−	0.140710i
$700$	3.55995	−	3.91494i	0.134554	−	0.147971i
$701$			30.1199i			1.13761i	0.822472	+	0.568806i	$0.192594\pi$
$701$			30.1199i			1.13761i	−0.822472	+	0.568806i	$0.807406\pi$
$702$	−7.96665	+	3.23031i	−0.300682	+	0.121920i
$703$	34.8665			1.31501
$704$	1.42657	+	1.56071i	0.0537660	+	0.0588213i
$705$		−	11.7259i		−	0.441624i
$706$	23.3280	−	9.45903i	0.877963	−	0.355995i
$707$	−11.5459	+	0.721536i	−0.434230	+	0.0271362i
$708$	6.59177	−	6.39747i	0.247734	−	0.240432i
$709$		−	1.69009i		−	0.0634728i	−0.999496	−	0.0317364i	$-0.989896\pi$
$709$		−	1.69009i		−	0.0634728i	0.999496	−	0.0317364i	$-0.0101037\pi$
$710$	11.2868	−	4.57657i	0.423587	−	0.171756i
$711$		−	10.3007i		−	0.386305i
$712$	15.2282	−	34.5508i	0.570702	−	1.29484i
$713$			15.0878i			0.565043i
$714$	3.00680	+	6.26236i	0.112527	+	0.234363i
$715$	−1.60665			−0.0600855
$716$	−0.950781	+	0.922756i	−0.0355324	+	0.0344850i
$717$	28.0309			1.04683
$718$	21.1710	−	8.58440i	0.790095	−	0.320367i
$719$	−43.0068			−1.60388			−0.801942	−	0.597402i	$-0.796200\pi$
$719$	−43.0068			−1.60388			−0.801942	+	0.597402i	$0.796200\pi$
$720$	−0.119639	+	3.99821i	−0.00445868	+	0.149005i
$721$	12.7299	−	0.795526i	0.474087	−	0.0296269i
$722$	2.04674	+	5.04771i	0.0761718	+	0.187856i
$723$	8.95756			0.333135
$724$	12.1656	−	11.8070i	0.452132	−	0.438805i
$725$			7.65773i			0.284401i
$726$	14.3248	−	5.80839i	0.531642	−	0.215569i
$727$	13.9472			0.517273			0.258636	−	0.965975i	$-0.416727\pi$
$727$	13.9472			0.517273			0.258636	+	0.965975i	$0.416727\pi$
$728$	−42.6887	−	15.7145i	−1.58215	−	0.582417i
$729$	−1.00000			−0.0370370
$730$	−5.46307	+	2.21516i	−0.202197	+	0.0819867i
$731$		−	3.17726i		−	0.117515i
$732$	−13.8836	−	14.3053i	−0.513153	−	0.528738i
$733$	−13.6799			−0.505280			−0.252640	−	0.967560i	$-0.581299\pi$
$733$	−13.6799			−0.505280			−0.252640	+	0.967560i	$0.581299\pi$
$734$	17.8211	+	43.9509i	0.657791	+	1.62226i
$735$	0.871493	+	6.94554i	0.0321455	+	0.256190i
$736$	−4.12500	−	11.1170i	−0.152050	−	0.409778i
$737$	0.764380			0.0281563
$738$	−3.00018	+	1.21651i	−0.110438	+	0.0447803i
$739$	−7.98250			−0.293641			−0.146820	−	0.989163i	$-0.546904\pi$
$739$	−7.98250			−0.293641			−0.146820	+	0.989163i	$0.546904\pi$
$740$	−12.4780	−	12.8570i	−0.458700	−	0.472631i
$741$	−23.6591			−0.869140
$742$	−13.6535	+	6.55558i	−0.501237	+	0.240663i
$743$		−	16.4647i		−	0.604030i	−0.953303	−	0.302015i	$-0.902341\pi$
$743$		−	16.4647i		−	0.604030i	0.953303	−	0.302015i	$-0.0976593\pi$
$744$	−8.21091	+	18.6294i	−0.301026	+	0.682987i
$745$			3.68761i			0.135104i
$746$	26.7263	−	10.8370i	0.978521	−	0.396769i
$747$			5.71691i			0.209171i
$748$	−0.683518	−	0.704277i	−0.0249919	−	0.0257509i
$749$	16.2214	−	1.01372i	0.592717	−	0.0370404i
$750$	−1.31057	+	0.531410i	−0.0478554	+	0.0194043i
$751$			25.8761i			0.944234i	0.881536	+	0.472117i	$0.156510\pi$
$751$			25.8761i			0.944234i	−0.881536	+	0.472117i	$0.843490\pi$
$752$	−1.40288	+	46.8827i	−0.0511576	+	1.70964i
$753$	−14.7968			−0.539225
$754$	61.0064	−	24.7368i	2.22172	−	0.900861i
$755$		−	14.4831i		−	0.527094i
$756$	−3.91494	−	3.55995i	−0.142385	−	0.129474i
$757$		−	0.192056i		−	0.00698040i	−0.999994	−	0.00349020i	$-0.998889\pi$
$757$		−	0.192056i		−	0.00698040i	0.999994	−	0.00349020i	$-0.00111097\pi$
$758$	−5.97037	−	14.7242i	−0.216853	−	0.534808i
$759$	0.554027			0.0201099
$760$	−4.43989	+	10.0735i	−0.161052	+	0.365404i
$761$			50.4508i			1.82884i	0.404766	+	0.914420i	$0.367353\pi$
$761$			50.4508i			1.82884i	−0.404766	+	0.914420i	$0.632647\pi$
$762$	−9.07023	−	22.3692i	−0.328580	−	0.810350i
$763$	2.55137	+	40.8268i	0.0923658	+	1.47803i
$764$	−16.2571	−	16.7509i	−0.588163	−	0.606026i
$765$		−	1.85661i		−	0.0671259i
$766$	4.59821	+	11.3402i	0.166140	+	0.409738i
$767$		−	27.9191i		−	1.00810i
$768$	0.956682	−	15.9714i	0.0345213	−	0.576317i
$769$			26.3495i			0.950186i	0.879936	+	0.475093i	$0.157586\pi$
$769$			26.3495i			0.950186i	−0.879936	+	0.475093i	$0.842414\pi$
$770$	−0.428047	−	0.891509i	−0.0154257	−	0.0321277i
$771$	12.8851			0.464047
$772$	−3.29624	+	3.19908i	−0.118634	+	0.115137i
$773$	−45.1896			−1.62536			−0.812678	−	0.582712i	$-0.801991\pi$
$773$	−45.1896			−1.62536			−0.812678	+	0.582712i	$0.801991\pi$
$774$	0.909415	+	2.24282i	0.0326882	+	0.0806164i
$775$	−7.19786			−0.258555
$776$	12.6831	−	28.7762i	0.455297	−	1.03301i
$777$	23.6552	−	1.47827i	0.848625	−	0.0530328i
$778$	−6.79623	+	2.75573i	−0.243657	+	0.0987976i
$779$	−8.90983			−0.319228
$780$	8.46711	+	8.72426i	0.303171	+	0.312379i
$781$		−	2.27624i		−	0.0814504i
$782$	2.06811	+	5.10041i	0.0739554	+	0.182390i
$783$	7.65773			0.273665
$784$	−2.65346	−	27.8740i	−0.0947663	−	0.995500i
$785$	23.1101			0.824834
$786$	1.06270	+	2.62085i	0.0379052	+	0.0934826i
$787$			19.9506i			0.711161i	0.934646	+	0.355580i	$0.115717\pi$
$787$			19.9506i			0.711161i	−0.934646	+	0.355580i	$0.884283\pi$
$788$	−32.5692	−	33.5583i	−1.16023	−	1.19546i
$789$	7.26011			0.258467
$790$	−13.4998	+	5.47387i	−0.480300	+	0.194752i
$791$	44.3244	−	2.76994i	1.57599	−	0.0984879i
$792$	0.684075	+	0.301506i	0.0243075	+	0.0107135i
$793$	−60.5892			−2.15159
$794$	−3.41396	−	8.41957i	−0.121157	−	0.298799i
$795$	4.04788			0.143563
$796$	13.4375	−	13.0414i	0.476279	−	0.462240i
$797$	−18.4653			−0.654075			−0.327037	−	0.945011i	$-0.606050\pi$
$797$	−18.4653			−0.654075			−0.327037	+	0.945011i	$0.606050\pi$
$798$	−6.30330	−	13.1281i	−0.223134	−	0.464730i
$799$		−	21.7705i		−	0.770184i
$800$	5.30353	−	1.96789i	0.187508	−	0.0695755i
$801$		−	13.3494i		−	0.471678i
$802$	−19.6188	−	48.3842i	−0.692762	−	1.70850i
$803$			1.10175i			0.0388799i
$804$	−4.02831	−	4.15065i	−0.142067	−	0.146382i
$805$	0.345903	+	5.53510i	0.0121915	+	0.195087i
$806$	23.2513	+	57.3429i	0.818993	+	2.01982i
$807$			12.0068i			0.422659i
$808$	−11.3168	−	4.98786i	−0.398123	−	0.175472i
$809$	38.2137			1.34352			0.671762	−	0.740767i	$-0.265538\pi$
$809$	38.2137			1.34352			0.671762	+	0.740767i	$0.265538\pi$
$810$	0.531410	+	1.31057i	0.0186718	+	0.0460489i
$811$			2.49948i			0.0877686i	0.999037	+	0.0438843i	$0.0139733\pi$
$811$			2.49948i			0.0877686i	−0.999037	+	0.0438843i	$0.986027\pi$
$812$	29.9795	+	27.2611i	1.05207	+	0.956679i
$813$			18.8132i			0.659809i
$814$	−3.10308	+	1.25823i	−0.108763	+	0.0441011i
$815$	13.9465			0.488525
$816$	−0.222123	+	7.42312i	−0.00777585	+	0.259861i
$817$			6.66065i			0.233027i
$818$	41.3974	−	16.7858i	1.44742	−	0.586900i
$819$	−16.0515	+	1.00310i	−0.560886	+	0.0350513i
$820$	3.18865	+	3.28549i	0.111352	+	0.114734i
$821$		−	45.2255i		−	1.57838i	−0.614149	−	0.789190i	$-0.710501\pi$
$821$		−	45.2255i		−	1.57838i	0.614149	−	0.789190i	$-0.289499\pi$
$822$	22.2216	−	9.01038i	0.775067	−	0.314273i
$823$			29.9944i			1.04554i	0.852474	+	0.522770i	$0.175101\pi$
$823$			29.9944i			1.04554i	−0.852474	+	0.522770i	$0.824899\pi$
$824$	12.4772	+	5.49934i	0.434665	+	0.191579i
$825$			0.264307i			0.00920198i
$826$	15.4919	−	7.43825i	0.539032	−	0.258810i
$827$	−12.7955			−0.444944			−0.222472	−	0.974939i	$-0.571413\pi$
$827$	−12.7955			−0.444944			−0.222472	+	0.974939i	$0.571413\pi$
$828$	−2.91974	−	3.00841i	−0.101468	−	0.104550i
$829$	15.8675			0.551103			0.275551	−	0.961286i	$-0.411140\pi$
$829$	15.8675			0.551103			0.275551	+	0.961286i	$0.411140\pi$
$830$	7.49243	−	3.03802i	0.260066	−	0.105451i
$831$	9.57593			0.332185
$832$	−32.8095	−	35.8944i	−1.13747	−	1.24442i
$833$	1.61802	+	12.8952i	0.0560612	+	0.446791i
$834$	−10.6000	−	26.1419i	−0.367048	−	0.905222i
$835$	−5.00401			−0.173171
$836$	1.43289	+	1.47641i	0.0495576	+	0.0510627i
$837$			7.19786i			0.248795i
$838$	33.7894	−	13.7009i	1.16723	−	0.473289i
$839$	7.71085			0.266208			0.133104	−	0.991102i	$-0.457506\pi$
$839$	7.71085			0.266208			0.133104	+	0.991102i	$0.457506\pi$
$840$	−2.58515	+	7.02261i	−0.0891960	+	0.242303i
$841$	−29.6408			−1.02210
$842$	−2.01189	+	0.815781i	−0.0693345	+	0.0281137i
$843$			6.08335i			0.209522i
$844$	22.8073	−	22.1351i	0.785060	−	0.761920i
$845$	23.9512			0.823946
$846$	6.23127	+	15.3677i	0.214235	+	0.528352i
$847$	28.8621	−	1.80367i	0.991715	−	0.0619748i
$848$	−16.1843	−	0.484283i	−0.555770	−	0.0166304i
$849$	−8.00209			−0.274631
$850$	−2.43322	+	0.986621i	−0.0834589	+	0.0338408i
$851$	18.7779			0.643697
$852$	−12.3602	+	11.9959i	−0.423453	+	0.410971i
$853$	−3.27559			−0.112154			−0.0560771	−	0.998426i	$-0.517859\pi$
$853$	−3.27559			−0.112154			−0.0560771	+	0.998426i	$0.517859\pi$
$854$	−16.1423	−	33.6201i	−0.552377	−	1.15046i
$855$			3.89210i			0.133107i
$856$	15.8994	+	7.00766i	0.543431	+	0.239517i
$857$		−	14.2127i		−	0.485497i	−0.970089	−	0.242749i	$-0.921951\pi$
$857$		−	14.2127i		−	0.485497i	0.970089	−	0.242749i	$-0.0780490\pi$
$858$	2.10564	−	0.853792i	0.0718853	−	0.0291480i
$859$			48.8464i			1.66662i	0.552807	+	0.833309i	$0.313557\pi$
$859$			48.8464i			1.66662i	−0.552807	+	0.833309i	$0.686443\pi$
$860$	2.45610	−	2.38371i	0.0837525	−	0.0812838i
$861$	−6.04488	+	0.377760i	−0.206009	+	0.0128740i
$862$	40.9365	−	16.5989i	1.39430	−	0.565361i
$863$			46.2121i			1.57308i	0.617540	+	0.786539i	$0.288129\pi$
$863$			46.2121i			1.57308i	−0.617540	+	0.786539i	$0.711871\pi$
$864$	−1.96789	−	5.30353i	−0.0669491	−	0.180430i
$865$	−0.0398406			−0.00135462
$866$	−8.98065	+	3.64146i	−0.305175	+	0.123742i
$867$			13.5530i			0.460284i
$868$	−25.6241	+	28.1792i	−0.869737	+	0.956464i
$869$			2.72253i			0.0923556i
$870$	−4.06939	−	10.0360i	−0.137965	−	0.340253i
$871$	−17.5799			−0.595671
$872$	−17.6372	+	40.0164i	−0.597271	+	1.35513i
$873$		−	11.1183i		−	0.376297i
$874$	−4.33547	−	10.6922i	−0.146650	−	0.361670i
$875$	−2.64060	+	0.165018i	−0.0892686	+	0.00557863i
$876$	5.98260	−	5.80626i	0.202133	−	0.196175i
$877$		−	19.3145i		−	0.652205i	−0.945334	−	0.326103i	$-0.894265\pi$
$877$		−	19.3145i		−	0.652205i	0.945334	−	0.326103i	$-0.105735\pi$
$878$	0.0838571	+	0.206810i	0.00283004	+	0.00697950i
$879$			14.1818i			0.478340i
$880$	0.0316213	−	1.05675i	0.00106596	−	0.0356232i
$881$			5.01092i			0.168822i	0.996431	+	0.0844110i	$0.0269009\pi$
$881$			5.01092i			0.168822i	−0.996431	+	0.0844110i	$0.973099\pi$
$882$	−4.83308	−	8.63952i	−0.162738	−	0.290908i
$883$	−46.2754			−1.55729			−0.778646	−	0.627463i	$-0.784093\pi$
$883$	−46.2754			−1.55729			−0.778646	+	0.627463i	$0.784093\pi$
$884$	15.7201	+	16.1976i	0.528725	+	0.544783i
$885$	−4.59290			−0.154389
$886$	21.1141	+	52.0720i	0.709342	+	1.74939i
$887$	−29.4098			−0.987484			−0.493742	−	0.869608i	$-0.664371\pi$
$887$	−29.4098			−0.987484			−0.493742	+	0.869608i	$0.664371\pi$
$888$	23.1857	+	10.2191i	0.778060	+	0.342929i
$889$	−2.81657	−	45.0704i	−0.0944646	−	1.51161i
$890$	−17.4954	+	7.09401i	−0.586447	+	0.237792i
$891$	0.264307			0.00885461
$892$	16.2589	−	15.7796i	0.544387	−	0.528341i
$893$			45.6385i			1.52723i
$894$	−1.95963	−	4.83289i	−0.0655399	−	0.161636i
$895$	0.662470			0.0221439
$896$	11.1761	−	27.7686i	0.373368	−	0.927683i
$897$	−12.7420			−0.425442
$898$	−5.02608	−	12.3954i	−0.167723	−	0.413641i
$899$		−	55.1193i		−	1.83833i
$900$	1.43521	−	1.39290i	0.0478402	−	0.0464301i
$901$	7.51533			0.250372
$902$	0.792966	−	0.321531i	0.0264029	−	0.0107058i
$903$	0.282399	+	4.51892i	0.00939766	+	0.150380i
$904$	43.4446	+	19.1482i	1.44494	+	0.636859i
$905$	−8.47656			−0.281770
$906$	7.69647	+	18.9812i	0.255698	+	0.630608i
$907$	12.0290			0.399417			0.199709	−	0.979855i	$-0.436000\pi$
$907$	12.0290			0.399417			0.199709	+	0.979855i	$0.436000\pi$
$908$	6.41931	+	6.61427i	0.213032	+	0.219502i
$909$	−4.37247			−0.145026
$910$	9.84459	+	20.5037i	0.326345	+	0.679690i
$911$			57.5846i			1.90786i	0.300023	+	0.953932i	$0.403006\pi$
$911$			57.5846i			1.90786i	−0.300023	+	0.953932i	$0.596994\pi$
$912$	0.465647	−	15.5614i	0.0154191	−	0.515291i
$913$		−	1.51102i		−	0.0500073i
$914$	−13.6492	−	33.6620i	−0.451476	−	1.11344i
$915$			9.96739i			0.329512i
$916$	2.21409	−	2.14883i	0.0731558	−	0.0709994i
$917$	0.329998	+	5.28060i	0.0108975	+	0.174381i
$918$	0.986621	+	2.43322i	0.0325633	+	0.0803084i
$919$		−	21.4808i		−	0.708585i	−0.935135	−	0.354293i	$-0.884722\pi$
$919$		−	21.4808i		−	0.708585i	0.935135	−	0.354293i	$-0.115278\pi$
$920$	−2.39117	+	5.42523i	−0.0788345	+	0.178865i
$921$	20.0654			0.661178
$922$	14.5749	+	35.9448i	0.479998	+	1.18378i
$923$			52.3510i			1.72315i
$924$	1.03474	+	0.940919i	0.0340406	+	0.0309540i
$925$			8.95826i			0.294546i
$926$	−22.2773	+	9.03299i	−0.732079	+	0.296843i
$927$	4.82084			0.158337
$928$	15.0696	+	40.6130i	0.494683	+	1.33319i
$929$		−	11.2995i		−	0.370723i	−0.982670	−	0.185362i	$-0.940654\pi$
$929$		−	11.2995i		−	0.370723i	0.982670	−	0.185362i	$-0.0593457\pi$
$930$	9.43333	−	3.82502i	0.309331	−	0.125427i
$931$	−3.39194	−	27.0328i	−0.111166	−	0.885963i
$932$	5.33921	−	5.18183i	0.174892	−	0.169736i
$933$		−	15.0389i		−	0.492351i
$934$	11.7358	−	4.75864i	0.384009	−	0.155707i
$935$			0.490714i			0.0160481i
$936$	−15.7329	−	6.93429i	−0.514247	−	0.226654i
$937$			24.5392i			0.801660i	0.916152	+	0.400830i	$0.131278\pi$
$937$			24.5392i			0.801660i	−0.916152	+	0.400830i	$0.868722\pi$
$938$	−4.68365	−	9.75481i	−0.152927	−	0.318506i
$939$	−22.2502			−0.726108
$940$	16.8291	−	16.3331i	0.548906	−	0.532726i
$941$	−51.5447			−1.68031			−0.840154	−	0.542348i	$-0.817536\pi$
$941$	−51.5447			−1.68031			−0.840154	+	0.542348i	$0.817536\pi$
$942$	−30.2875	+	12.2809i	−0.986819	+	0.400134i
$943$	−4.79853			−0.156262
$944$	18.3634	+	0.549490i	0.597678	+	0.0178844i
$945$	0.165018	+	2.64060i	0.00536803	+	0.0858987i
$946$	−0.240364	−	0.592791i	−0.00781492	−	0.0192733i
$947$	16.0492			0.521530			0.260765	−	0.965402i	$-0.416025\pi$
$947$	16.0492			0.521530			0.260765	+	0.965402i	$0.416025\pi$
$948$	14.7836	−	14.3478i	0.480148	−	0.465996i
$949$		−	25.3390i		−	0.822539i
$950$	5.10089	−	2.06830i	0.165495	−	0.0671046i
$951$	−33.4862			−1.08586
$952$	−4.79961	+	13.0382i	−0.155556	+	0.422572i
$953$	14.3868			0.466035			0.233018	−	0.972472i	$-0.425140\pi$
$953$	14.3868			0.466035			0.233018	+	0.972472i	$0.425140\pi$
$954$	−5.30504	+	2.15108i	−0.171757	+	0.0696439i
$955$			11.6714i			0.377678i
$956$	39.0443	+	40.2301i	1.26278	+	1.30114i
$957$	−2.02399			−0.0654262
$958$	2.53223	+	6.24505i	0.0818128	+	0.201768i
$959$	44.7730	−	2.79798i	1.44580	−	0.0903515i
$960$	−5.90491	+	5.39742i	−0.190580	+	0.174201i
$961$	20.8093			0.671266
$962$	71.3673	−	28.9379i	2.30098	−	0.932997i
$963$	6.14307			0.197958
$964$	12.4770	+	12.8560i	0.401858	+	0.414062i
$965$	2.29670			0.0739333
$966$	−3.39474	−	7.07034i	−0.109224	−	0.227484i
$967$		−	37.2171i		−	1.19682i	−0.801189	−	0.598411i	$-0.795799\pi$
$967$		−	37.2171i		−	1.19682i	0.801189	−	0.598411i	$-0.204201\pi$
$968$	28.2892	+	12.4685i	0.909251	+	0.400752i
$969$			7.22612i			0.232136i
$970$	−14.5713	+	5.90837i	−0.467858	+	0.189706i
$971$			43.0613i			1.38190i	0.722902	+	0.690951i	$0.242808\pi$
$971$			43.0613i			1.38190i	−0.722902	+	0.690951i	$0.757192\pi$
$972$	−1.39290	−	1.43521i	−0.0446774	−	0.0460343i
$973$	−3.29160	−	52.6719i	−0.105524	−	1.68858i
$974$	−29.1263	+	11.8101i	−0.933265	+	0.378419i
$975$		−	6.07875i		−	0.194676i
$976$	1.19249	−	39.8517i	0.0381706	−	1.27562i
$977$	−5.91287			−0.189169			−0.0945847	−	0.995517i	$-0.530152\pi$
$977$	−5.91287			−0.189169			−0.0945847	+	0.995517i	$0.530152\pi$
$978$	−18.2780	+	7.41132i	−0.584464	+	0.236988i
$979$			3.52834i			0.112766i
$980$	−8.75438	+	10.9252i	−0.279648	+	0.348994i
$981$			15.4612i			0.493637i
$982$	−15.7460	−	38.8330i	−0.502474	−	1.23921i
$983$	−1.42530			−0.0454599			−0.0227300	−	0.999742i	$-0.507236\pi$
$983$	−1.42530			−0.0454599			−0.0227300	+	0.999742i	$0.507236\pi$
$984$	−5.92490	−	2.61140i	−0.188879	−	0.0832482i
$985$			23.3822i			0.745019i
$986$	−7.55527	−	18.6330i	−0.240609	−	0.593395i
$987$	1.93499	+	30.9635i	0.0615913	+	0.985578i
$988$	−32.9549	−	33.9557i	−1.04843	−	1.08028i
$989$			3.58719i			0.114066i
$990$	−0.140455	−	0.346393i	−0.00446396	−	0.0110091i
$991$			25.8732i			0.821889i	0.911660	+	0.410945i	$0.134801\pi$
$991$			25.8732i			0.821889i	−0.911660	+	0.410945i	$0.865199\pi$
$992$	−38.1741	+	14.1646i	−1.21203	+	0.449727i
$993$			23.5161i			0.746260i
$994$	−29.0488	+	13.9474i	−0.921371	+	0.442385i
$995$	−9.36275			−0.296819
$996$	−8.20495	+	7.96310i	−0.259984	+	0.252320i
$997$	24.4403			0.774031			0.387015	−	0.922073i	$-0.373506\pi$
$997$	24.4403			0.774031			0.387015	+	0.922073i	$0.373506\pi$
$998$	−9.29173	−	22.9154i	−0.294125	−	0.725376i
$999$	8.95826			0.283427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.d.811.18	yes	28
4.3	odd	2		3360.2.z.d.1231.3		28
7.6	odd	2		840.2.z.c.811.18	yes	28
8.3	odd	2		840.2.z.c.811.17	✓	28
8.5	even	2		3360.2.z.c.1231.25		28
28.27	even	2		3360.2.z.c.1231.26		28
56.13	odd	2		3360.2.z.d.1231.4		28
56.27	even	2	inner	840.2.z.d.811.17	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.c.811.17	✓	28	8.3	odd	2
840.2.z.c.811.18	yes	28	7.6	odd	2
840.2.z.d.811.17	yes	28	56.27	even	2	inner
840.2.z.d.811.18	yes	28	1.1	even	1	trivial
3360.2.z.c.1231.25		28	8.5	even	2
3360.2.z.c.1231.26		28	28.27	even	2
3360.2.z.d.1231.3		28	4.3	odd	2
3360.2.z.d.1231.4		28	56.13	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+(0.531410 + 1.31057i) q^{2} +1.00000i q^{3} +(-1.43521 + 1.39290i) q^{4} +1.00000 q^{5} +(-1.31057 + 0.531410i) q^{6} +(-2.64060 + 0.165018i) q^{7} +(-2.58819 - 1.14074i) q^{8} -1.00000 q^{9} +(0.531410 + 1.31057i) q^{10} +0.264307 q^{11} +(-1.39290 - 1.43521i) q^{12} -6.07875 q^{13} +(-1.61951 - 3.37301i) q^{14} +1.00000i q^{15} +(0.119639 - 3.99821i) q^{16} +1.85661i q^{17} +(-0.531410 - 1.31057i) q^{18} -3.89210i q^{19} +(-1.43521 + 1.39290i) q^{20} +(-0.165018 - 2.64060i) q^{21} +(0.140455 + 0.346393i) q^{22} -2.09615i q^{23} +(1.14074 - 2.58819i) q^{24} +1.00000 q^{25} +(-3.23031 - 7.96665i) q^{26} -1.00000i q^{27} +(3.55995 - 3.91494i) q^{28} +7.65773i q^{29} +(-1.31057 + 0.531410i) q^{30} -7.19786 q^{31} +(5.30353 - 1.96789i) q^{32} +0.264307i q^{33} +(-2.43322 + 0.986621i) q^{34} +(-2.64060 + 0.165018i) q^{35} +(1.43521 - 1.39290i) q^{36} +8.95826i q^{37} +(5.10089 - 2.06830i) q^{38} -6.07875i q^{39} +(-2.58819 - 1.14074i) q^{40} -2.28921i q^{41} +(3.37301 - 1.61951i) q^{42} -1.71132 q^{43} +(-0.379335 + 0.368154i) q^{44} -1.00000 q^{45} +(2.74716 - 1.11392i) q^{46} -11.7259 q^{47} +(3.99821 + 0.119639i) q^{48} +(6.94554 - 0.871493i) q^{49} +(0.531410 + 1.31057i) q^{50} -1.85661 q^{51} +(8.72426 - 8.46711i) q^{52} -4.04788i q^{53} +(1.31057 - 0.531410i) q^{54} +0.264307 q^{55} +(7.02261 + 2.58515i) q^{56} +3.89210 q^{57} +(-10.0360 + 4.06939i) q^{58} +4.59290i q^{59} +(-1.39290 - 1.43521i) q^{60} +9.96739 q^{61} +(-3.82502 - 9.43333i) q^{62} +(2.64060 - 0.165018i) q^{63} +(5.39742 + 5.90491i) q^{64} -6.07875 q^{65} +(-0.346393 + 0.140455i) q^{66} +2.89202 q^{67} +(-2.58608 - 2.66462i) q^{68} +2.09615 q^{69} +(-1.61951 - 3.37301i) q^{70} -8.61213i q^{71} +(2.58819 + 1.14074i) q^{72} +4.16846i q^{73} +(-11.7405 + 4.76051i) q^{74} +1.00000i q^{75} +(5.42133 + 5.58597i) q^{76} +(-0.697928 + 0.0436153i) q^{77} +(7.96665 - 3.23031i) q^{78} +10.3007i q^{79} +(0.119639 - 3.99821i) q^{80} +1.00000 q^{81} +(3.00018 - 1.21651i) q^{82} -5.71691i q^{83} +(3.91494 + 3.55995i) q^{84} +1.85661i q^{85} +(-0.909415 - 2.24282i) q^{86} -7.65773 q^{87} +(-0.684075 - 0.301506i) q^{88} +13.3494i q^{89} +(-0.531410 - 1.31057i) q^{90} +(16.0515 - 1.00310i) q^{91} +(2.91974 + 3.00841i) q^{92} -7.19786i q^{93} +(-6.23127 - 15.3677i) q^{94} -3.89210i q^{95} +(1.96789 + 5.30353i) q^{96} +11.1183i q^{97} +(4.83308 + 8.63952i) q^{98} -0.264307 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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