LMFDB - Embedded newform 840.2.g.d.421.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(421,840)] 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([0, 1, 0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.421"); 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.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 2 x^{13} + x^{12} - 8 x^{10} + 24 x^{9} - 32 x^{8} + 48 x^{7} + \cdots + 256 $ x^16 - 2x^15 + 2x^14 - 2x^13 + x^12 - 8x^10 + 24x^9 - 32x^8 + 48x^7 - 32x^6 + 16x^4 - 64x^3 + 128x^2 - 256x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			421.1
Root			$-0.0395670 + 1.41366i$ of defining polynomial
Character	$\chi$	$=$	840.421
Dual form			840.2.g.d.421.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41366 - 0.0395670i) q^{2} +1.00000i q^{3} +(1.99687 + 0.111869i) q^{4} -1.00000i q^{5} +(0.0395670 - 1.41366i) q^{6} -1.00000 q^{7} +(-2.81847 - 0.237154i) q^{8} -1.00000 q^{9} +(-0.0395670 + 1.41366i) q^{10} -2.80961i q^{11} +(-0.111869 + 1.99687i) q^{12} +3.47943i q^{13} +(1.41366 + 0.0395670i) q^{14} +1.00000 q^{15} +(3.97497 + 0.446774i) q^{16} +0.863547 q^{17} +(1.41366 + 0.0395670i) q^{18} -0.553442i q^{19} +(0.111869 - 1.99687i) q^{20} -1.00000i q^{21} +(-0.111168 + 3.97184i) q^{22} +7.12393 q^{23} +(0.237154 - 2.81847i) q^{24} -1.00000 q^{25} +(0.137670 - 4.91872i) q^{26} -1.00000i q^{27} +(-1.99687 - 0.111869i) q^{28} -7.52924i q^{29} +(-1.41366 - 0.0395670i) q^{30} +9.48607 q^{31} +(-5.60158 - 0.788864i) q^{32} +2.80961 q^{33} +(-1.22076 - 0.0341680i) q^{34} +1.00000i q^{35} +(-1.99687 - 0.111869i) q^{36} -1.31102i q^{37} +(-0.0218981 + 0.782379i) q^{38} -3.47943 q^{39} +(-0.237154 + 2.81847i) q^{40} -2.72185 q^{41} +(-0.0395670 + 1.41366i) q^{42} +7.80458i q^{43} +(0.314308 - 5.61043i) q^{44} +1.00000i q^{45} +(-10.0708 - 0.281873i) q^{46} +8.67645 q^{47} +(-0.446774 + 3.97497i) q^{48} +1.00000 q^{49} +(1.41366 + 0.0395670i) q^{50} +0.863547i q^{51} +(-0.389238 + 6.94796i) q^{52} -8.75346i q^{53} +(-0.0395670 + 1.41366i) q^{54} -2.80961 q^{55} +(2.81847 + 0.237154i) q^{56} +0.553442 q^{57} +(-0.297909 + 10.6438i) q^{58} +3.04890i q^{59} +(1.99687 + 0.111869i) q^{60} -7.97671i q^{61} +(-13.4101 - 0.375335i) q^{62} +1.00000 q^{63} +(7.88752 + 1.33682i) q^{64} +3.47943 q^{65} +(-3.97184 - 0.111168i) q^{66} -1.95461i q^{67} +(1.72439 + 0.0966037i) q^{68} +7.12393i q^{69} +(0.0395670 - 1.41366i) q^{70} +5.56767 q^{71} +(2.81847 + 0.237154i) q^{72} +3.39782 q^{73} +(-0.0518732 + 1.85334i) q^{74} -1.00000i q^{75} +(0.0619128 - 1.10515i) q^{76} +2.80961i q^{77} +(4.91872 + 0.137670i) q^{78} +12.8403 q^{79} +(0.446774 - 3.97497i) q^{80} +1.00000 q^{81} +(3.84777 + 0.107695i) q^{82} +15.0988i q^{83} +(0.111869 - 1.99687i) q^{84} -0.863547i q^{85} +(0.308804 - 11.0330i) q^{86} +7.52924 q^{87} +(-0.666312 + 7.91881i) q^{88} +6.06670 q^{89} +(0.0395670 - 1.41366i) q^{90} -3.47943i q^{91} +(14.2256 + 0.796944i) q^{92} +9.48607i q^{93} +(-12.2656 - 0.343301i) q^{94} -0.553442 q^{95} +(0.788864 - 5.60158i) q^{96} -0.563842 q^{97} +(-1.41366 - 0.0395670i) q^{98} +2.80961i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{6} - 16 q^{7} - 2 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{14} + 16 q^{15} + 4 q^{16} + 2 q^{18} + 2 q^{24} - 16 q^{25} - 2 q^{30} - 2 q^{32} + 24 q^{34} - 28 q^{38} - 2 q^{40} + 2 q^{42}+ \cdots - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^6 - 16 * q^7 - 2 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^14 + 16 * q^15 + 4 * q^16 + 2 * q^18 + 2 * q^24 - 16 * q^25 - 2 * q^30 - 2 * q^32 + 24 * q^34 - 28 * q^38 - 2 * q^40 + 2 * q^42 + 8 * q^44 - 36 * q^46 + 32 * q^47 + 16 * q^49 + 2 * q^50 + 4 * q^52 + 2 * q^54 + 2 * q^56 + 32 * q^58 - 12 * q^62 + 16 * q^63 - 48 * q^64 + 28 * q^66 + 56 * q^68 - 2 * q^70 - 64 * q^71 + 2 * q^72 + 24 * q^74 + 8 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^81 + 4 * q^82 - 36 * q^86 - 16 * q^87 - 2 * q^90 + 80 * q^92 - 44 * q^94 - 2 * q^96 - 2 * 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 $

$2$	−1.41366	−	0.0395670i	−0.999609	−	0.0279781i
$2$	−1.41366	−	0.0395670i	−0.999609	−	0.0279781i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.99687	+	0.111869i	0.998434	+	0.0559343i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.0395670	−	1.41366i	0.0161532	−	0.577124i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.81847	−	0.237154i	−0.996479	−	0.0838467i
$9$	−1.00000			−0.333333
$10$	−0.0395670	+	1.41366i	−0.0125122	+	0.447039i
$11$		−	2.80961i		−	0.847131i	−0.905866	−	0.423565i	$-0.860778\pi$
$11$		−	2.80961i		−	0.847131i	0.905866	−	0.423565i	$-0.139222\pi$
$12$	−0.111869	+	1.99687i	−0.0322937	+	0.576446i
$13$			3.47943i			0.965019i	0.875891	+	0.482509i	$0.160275\pi$
$13$			3.47943i			0.965019i	−0.875891	+	0.482509i	$0.839725\pi$
$14$	1.41366	+	0.0395670i	0.377817	+	0.0105747i
$15$	1.00000			0.258199
$16$	3.97497	+	0.446774i	0.993743	+	0.111693i
$17$	0.863547			0.209441			0.104720	−	0.994502i	$-0.466605\pi$
$17$	0.863547			0.209441			0.104720	+	0.994502i	$0.466605\pi$
$18$	1.41366	+	0.0395670i	0.333203	+	0.00932603i
$19$		−	0.553442i		−	0.126968i	−0.997983	−	0.0634842i	$-0.979779\pi$
$19$		−	0.553442i		−	0.126968i	0.997983	−	0.0634842i	$-0.0202212\pi$
$20$	0.111869	−	1.99687i	0.0250146	−	0.446513i
$21$		−	1.00000i		−	0.218218i
$22$	−0.111168	+	3.97184i	−0.0237011	+	0.846799i
$23$	7.12393			1.48544			0.742721	−	0.669601i	$-0.233535\pi$
$23$	7.12393			1.48544			0.742721	+	0.669601i	$0.233535\pi$
$24$	0.237154	−	2.81847i	0.0484089	−	0.575317i
$25$	−1.00000			−0.200000
$26$	0.137670	−	4.91872i	0.0269994	−	0.964641i
$27$		−	1.00000i		−	0.192450i
$28$	−1.99687	−	0.111869i	−0.377373	−	0.0211412i
$29$		−	7.52924i		−	1.39814i	−0.715051	−	0.699072i	$-0.753597\pi$
$29$		−	7.52924i		−	1.39814i	0.715051	−	0.699072i	$-0.246403\pi$
$30$	−1.41366	−	0.0395670i	−0.258098	−	0.00722391i
$31$	9.48607			1.70375			0.851874	−	0.523747i	$-0.175466\pi$
$31$	9.48607			1.70375			0.851874	+	0.523747i	$0.175466\pi$
$32$	−5.60158	−	0.788864i	−0.990229	−	0.139453i
$33$	2.80961			0.489091
$34$	−1.22076	−	0.0341680i	−0.209359	−	0.00585976i
$35$			1.00000i			0.169031i
$36$	−1.99687	−	0.111869i	−0.332811	−	0.0186448i
$37$		−	1.31102i		−	0.215531i	−0.994176	−	0.107765i	$-0.965631\pi$
$37$		−	1.31102i		−	0.215531i	0.994176	−	0.107765i	$-0.0343695\pi$
$38$	−0.0218981	+	0.782379i	−0.00355233	+	0.126919i
$39$	−3.47943			−0.557154
$40$	−0.237154	+	2.81847i	−0.0374974	+	0.445639i
$41$	−2.72185			−0.425081			−0.212540	−	0.977152i	$-0.568174\pi$
$41$	−2.72185			−0.425081			−0.212540	+	0.977152i	$0.568174\pi$
$42$	−0.0395670	+	1.41366i	−0.00610532	+	0.218132i
$43$			7.80458i			1.19019i	0.803656	+	0.595094i	$0.202885\pi$
$43$			7.80458i			1.19019i	−0.803656	+	0.595094i	$0.797115\pi$
$44$	0.314308	−	5.61043i	0.0473837	−	0.845804i
$45$			1.00000i			0.149071i
$46$	−10.0708	−	0.281873i	−1.48486	−	0.0415598i
$47$	8.67645			1.26559			0.632795	−	0.774319i	$-0.281907\pi$
$47$	8.67645			1.26559			0.632795	+	0.774319i	$0.281907\pi$
$48$	−0.446774	+	3.97497i	−0.0644862	+	0.573738i
$49$	1.00000			0.142857
$50$	1.41366	+	0.0395670i	0.199922	+	0.00559562i
$51$			0.863547i			0.120921i
$52$	−0.389238	+	6.94796i	−0.0539776	+	0.963508i
$53$		−	8.75346i		−	1.20238i	−0.799106	−	0.601190i	$-0.794693\pi$
$53$		−	8.75346i		−	1.20238i	0.799106	−	0.601190i	$-0.205307\pi$
$54$	−0.0395670	+	1.41366i	−0.00538439	+	0.192375i
$55$	−2.80961			−0.378848
$56$	2.81847	+	0.237154i	0.376634	+	0.0316911i
$57$	0.553442			0.0733052
$58$	−0.297909	+	10.6438i	−0.0391174	+	1.39760i
$59$			3.04890i			0.396933i	0.980108	+	0.198466i	$0.0635960\pi$
$59$			3.04890i			0.396933i	−0.980108	+	0.198466i	$0.936404\pi$
$60$	1.99687	+	0.111869i	0.257795	+	0.0144422i
$61$		−	7.97671i		−	1.02131i	−0.859785	−	0.510657i	$-0.829402\pi$
$61$		−	7.97671i		−	1.02131i	0.859785	−	0.510657i	$-0.170598\pi$
$62$	−13.4101	−	0.375335i	−1.70308	−	0.0476676i
$63$	1.00000			0.125988
$64$	7.88752	+	1.33682i	0.985939	+	0.167103i
$65$	3.47943			0.431570
$66$	−3.97184	−	0.111168i	−0.488900	−	0.0136838i
$67$		−	1.95461i		−	0.238793i	−0.992847	−	0.119397i	$-0.961904\pi$
$67$		−	1.95461i		−	0.238793i	0.992847	−	0.119397i	$-0.0380960\pi$
$68$	1.72439	+	0.0966037i	0.209113	+	0.0117149i
$69$			7.12393i			0.857620i
$70$	0.0395670	−	1.41366i	0.00472916	−	0.168965i
$71$	5.56767			0.660761			0.330381	−	0.943848i	$-0.392823\pi$
$71$	5.56767			0.660761			0.330381	+	0.943848i	$0.392823\pi$
$72$	2.81847	+	0.237154i	0.332160	+	0.0279489i
$73$	3.39782			0.397685			0.198842	−	0.980031i	$-0.436282\pi$
$73$	3.39782			0.397685			0.198842	+	0.980031i	$0.436282\pi$
$74$	−0.0518732	+	1.85334i	−0.00603013	+	0.215446i
$75$		−	1.00000i		−	0.115470i
$76$	0.0619128	−	1.10515i	0.00710189	−	0.126770i
$77$			2.80961i			0.320185i
$78$	4.91872	+	0.137670i	0.556936	+	0.0155881i
$79$	12.8403			1.44464			0.722321	−	0.691558i	$-0.243075\pi$
$79$	12.8403			1.44464			0.722321	+	0.691558i	$0.243075\pi$
$80$	0.446774	−	3.97497i	0.0499508	−	0.444415i
$81$	1.00000			0.111111
$82$	3.84777	+	0.107695i	0.424915	+	0.0118930i
$83$			15.0988i			1.65731i	0.559760	+	0.828655i	$0.310893\pi$
$83$			15.0988i			1.65731i	−0.559760	+	0.828655i	$0.689107\pi$
$84$	0.111869	−	1.99687i	0.0122059	−	0.217876i
$85$		−	0.863547i		−	0.0936648i
$86$	0.308804	−	11.0330i	0.0332992	−	1.18972i
$87$	7.52924			0.807219
$88$	−0.666312	+	7.91881i	−0.0710291	+	0.844148i
$89$	6.06670			0.643069			0.321535	−	0.946898i	$-0.395801\pi$
$89$	6.06670			0.643069			0.321535	+	0.946898i	$0.395801\pi$
$90$	0.0395670	−	1.41366i	0.00417073	−	0.149013i
$91$		−	3.47943i		−	0.364743i
$92$	14.2256	+	0.796944i	1.48312	+	0.0830871i
$93$			9.48607i			0.983660i
$94$	−12.2656	−	0.343301i	−1.26510	−	0.0354088i
$95$	−0.553442			−0.0567820
$96$	0.788864	−	5.60158i	0.0805131	−	0.571709i
$97$	−0.563842			−0.0572495			−0.0286247	−	0.999590i	$-0.509113\pi$
$97$	−0.563842			−0.0572495			−0.0286247	+	0.999590i	$0.509113\pi$
$98$	−1.41366	−	0.0395670i	−0.142801	−	0.00399687i
$99$			2.80961i			0.282377i
$100$	−1.99687	−	0.111869i	−0.199687	−	0.0111869i
$101$		−	14.0321i		−	1.39625i	−0.715978	−	0.698123i	$-0.754019\pi$
$101$		−	14.0321i		−	1.39625i	0.715978	−	0.698123i	$-0.245981\pi$
$102$	0.0341680	−	1.22076i	0.00338313	−	0.120873i
$103$	14.2681			1.40588			0.702940	−	0.711249i	$-0.251870\pi$
$103$	14.2681			1.40588			0.702940	+	0.711249i	$0.251870\pi$
$104$	0.825160	−	9.80665i	0.0809136	−	0.961621i
$105$	−1.00000			−0.0975900
$106$	−0.346348	+	12.3744i	−0.0336403	+	1.20191i
$107$		−	11.9082i		−	1.15121i	−0.817728	−	0.575605i	$-0.804767\pi$
$107$		−	11.9082i		−	1.15121i	0.817728	−	0.575605i	$-0.195233\pi$
$108$	0.111869	−	1.99687i	0.0107646	−	0.192149i
$109$			15.7813i			1.51157i	0.654818	+	0.755787i	$0.272745\pi$
$109$			15.7813i			1.51157i	−0.654818	+	0.755787i	$0.727255\pi$
$110$	3.97184	+	0.111168i	0.378700	+	0.0105995i
$111$	1.31102			0.124437
$112$	−3.97497	−	0.446774i	−0.375599	−	0.0422162i
$113$	−5.91888			−0.556801			−0.278401	−	0.960465i	$-0.589804\pi$
$113$	−5.91888			−0.556801			−0.278401	+	0.960465i	$0.589804\pi$
$114$	−0.782379	−	0.0218981i	−0.0732765	−	0.00205094i
$115$		−	7.12393i		−	0.664310i
$116$	0.842285	−	15.0349i	0.0782042	−	1.39596i
$117$		−	3.47943i		−	0.321673i
$118$	0.120636	−	4.31010i	0.0111054	−	0.396777i
$119$	−0.863547			−0.0791612
$120$	−2.81847	−	0.237154i	−0.257290	−	0.0216491i
$121$	3.10607			0.282370
$122$	−0.315615	+	11.2764i	−0.0285744	+	1.02091i
$123$		−	2.72185i		−	0.245421i
$124$	18.9424	+	1.06119i	1.70108	+	0.0952979i
$125$			1.00000i			0.0894427i
$126$	−1.41366	−	0.0395670i	−0.125939	−	0.00352491i
$127$	−1.00101			−0.0888256			−0.0444128	−	0.999013i	$-0.514142\pi$
$127$	−1.00101			−0.0888256			−0.0444128	+	0.999013i	$0.514142\pi$
$128$	−11.0974	−	2.20190i	−0.980878	−	0.194622i
$129$	−7.80458			−0.687155
$130$	−4.91872	−	0.137670i	−0.431401	−	0.0120745i
$131$			4.36825i			0.381655i	0.981624	+	0.190828i	$0.0611172\pi$
$131$			4.36825i			0.381655i	−0.981624	+	0.190828i	$0.938883\pi$
$132$	5.61043	+	0.314308i	0.488325	+	0.0273570i
$133$			0.553442i			0.0479895i
$134$	−0.0773380	+	2.76315i	−0.00668098	+	0.238700i
$135$	−1.00000			−0.0860663
$136$	−2.43388	−	0.204794i	−0.208703	−	0.0175609i
$137$	−12.1165			−1.03518			−0.517592	−	0.855628i	$-0.673171\pi$
$137$	−12.1165			−1.03518			−0.517592	+	0.855628i	$0.673171\pi$
$138$	0.281873	−	10.0708i	0.0239946	−	0.857285i
$139$		−	9.43649i		−	0.800392i	−0.916429	−	0.400196i	$-0.868942\pi$
$139$		−	9.43649i		−	0.800392i	0.916429	−	0.400196i	$-0.131058\pi$
$140$	−0.111869	+	1.99687i	−0.00945462	+	0.168766i
$141$			8.67645i			0.730689i
$142$	−7.87080	−	0.220296i	−0.660503	−	0.0184868i
$143$	9.77584			0.817497
$144$	−3.97497	−	0.446774i	−0.331248	−	0.0372311i
$145$	−7.52924			−0.625269
$146$	−4.80336	−	0.134442i	−0.397529	−	0.0111265i
$147$			1.00000i			0.0824786i
$148$	0.146662	−	2.61794i	0.0120555	−	0.215193i
$149$			16.8619i			1.38138i	0.723152	+	0.690689i	$0.242693\pi$
$149$			16.8619i			1.38138i	−0.723152	+	0.690689i	$0.757307\pi$
$150$	−0.0395670	+	1.41366i	−0.00323063	+	0.115425i
$151$	−11.8374			−0.963318			−0.481659	−	0.876359i	$-0.659966\pi$
$151$	−11.8374			−0.963318			−0.481659	+	0.876359i	$0.659966\pi$
$152$	−0.131251	+	1.55986i	−0.0106459	+	0.126521i
$153$	−0.863547			−0.0698136
$154$	0.111168	−	3.97184i	0.00895817	−	0.320060i
$155$		−	9.48607i		−	0.761939i
$156$	−6.94796	−	0.389238i	−0.556282	−	0.0311640i
$157$		−	0.482238i		−	0.0384868i	−0.999815	−	0.0192434i	$-0.993874\pi$
$157$		−	0.482238i		−	0.0384868i	0.999815	−	0.0192434i	$-0.00612574\pi$
$158$	−18.1518	−	0.508051i	−1.44408	−	0.0404183i
$159$	8.75346			0.694195
$160$	−0.788864	+	5.60158i	−0.0623652	+	0.442844i
$161$	−7.12393			−0.561444
$162$	−1.41366	−	0.0395670i	−0.111068	−	0.00310868i
$163$		−	4.33358i		−	0.339432i	−0.985493	−	0.169716i	$-0.945715\pi$
$163$		−	4.33358i		−	0.339432i	0.985493	−	0.169716i	$-0.0542851\pi$
$164$	−5.43517	−	0.304489i	−0.424416	−	0.0237766i
$165$		−	2.80961i		−	0.218728i
$166$	0.597415	−	21.3446i	0.0463684	−	1.65666i
$167$	−7.80031			−0.603606			−0.301803	−	0.953370i	$-0.597589\pi$
$167$	−7.80031			−0.603606			−0.301803	+	0.953370i	$0.597589\pi$
$168$	−0.237154	+	2.81847i	−0.0182968	+	0.217449i
$169$	0.893602			0.0687386
$170$	−0.0341680	+	1.22076i	−0.00262056	+	0.0936281i
$171$			0.553442i			0.0423228i
$172$	−0.873087	+	15.5847i	−0.0665723	+	1.18832i
$173$			9.27539i			0.705195i	0.935775	+	0.352597i	$0.114701\pi$
$173$			9.27539i			0.705195i	−0.935775	+	0.352597i	$0.885299\pi$
$174$	−10.6438	−	0.297909i	−0.806903	−	0.0225845i
$175$	1.00000			0.0755929
$176$	1.25526	−	11.1681i	0.0946189	−	0.841830i
$177$	−3.04890			−0.229169
$178$	−8.57626	−	0.240041i	−0.642818	−	0.0179919i
$179$			6.53854i			0.488714i	0.969685	+	0.244357i	$0.0785768\pi$
$179$			6.53854i			0.488714i	−0.969685	+	0.244357i	$0.921423\pi$
$180$	−0.111869	+	1.99687i	−0.00833819	+	0.148838i
$181$		−	19.6396i		−	1.45980i	−0.683555	−	0.729899i	$-0.739567\pi$
$181$		−	19.6396i		−	1.45980i	0.683555	−	0.729899i	$-0.260433\pi$
$182$	−0.137670	+	4.91872i	−0.0102048	+	0.364600i
$183$	7.97671			0.589656
$184$	−20.0786	−	1.68947i	−1.48021	−	0.124549i
$185$	−1.31102			−0.0963882
$186$	0.375335	−	13.4101i	0.0275209	−	0.983274i
$187$		−	2.42623i		−	0.177424i
$188$	17.3257	+	0.970623i	1.26361	+	0.0707899i
$189$			1.00000i			0.0727393i
$190$	0.782379	+	0.0218981i	0.0567598	+	0.00158865i
$191$	−14.0209			−1.01452			−0.507258	−	0.861794i	$-0.669341\pi$
$191$	−14.0209			−1.01452			−0.507258	+	0.861794i	$0.669341\pi$
$192$	−1.33682	+	7.88752i	−0.0964769	+	0.569232i
$193$	−20.5477			−1.47906			−0.739529	−	0.673124i	$-0.764952\pi$
$193$	−20.5477			−1.47906			−0.739529	+	0.673124i	$0.764952\pi$
$194$	0.797081	+	0.0223095i	0.0572271	+	0.00160173i
$195$			3.47943i			0.249167i
$196$	1.99687	+	0.111869i	0.142633	+	0.00799061i
$197$		−	7.83824i		−	0.558451i	−0.960225	−	0.279226i	$-0.909922\pi$
$197$		−	7.83824i		−	0.558451i	0.960225	−	0.279226i	$-0.0900778\pi$
$198$	0.111168	−	3.97184i	0.00790037	−	0.282266i
$199$	−18.7178			−1.32687			−0.663436	−	0.748233i	$-0.730902\pi$
$199$	−18.7178			−1.32687			−0.663436	+	0.748233i	$0.730902\pi$
$200$	2.81847	+	0.237154i	0.199296	+	0.0167693i
$201$	1.95461			0.137867
$202$	−0.555208	+	19.8366i	−0.0390643	+	1.39570i
$203$			7.52924i			0.528449i
$204$	−0.0966037	+	1.72439i	−0.00676361	+	0.120731i
$205$			2.72185i			0.190102i
$206$	−20.1703	−	0.564547i	−1.40533	−	0.0393339i
$207$	−7.12393			−0.495147
$208$	−1.55452	+	13.8306i	−0.107786	+	0.958980i
$209$	−1.55496			−0.107559
$210$	1.41366	+	0.0395670i	0.0975518	+	0.00273038i
$211$		−	19.6301i		−	1.35139i	−0.737181	−	0.675695i	$-0.763843\pi$
$211$		−	19.6301i		−	1.35139i	0.737181	−	0.675695i	$-0.236157\pi$
$212$	0.979237	−	17.4795i	0.0672543	−	1.20050i
$213$			5.56767i			0.381491i
$214$	−0.471172	+	16.8342i	−0.0322087	+	1.15076i
$215$	7.80458			0.532268
$216$	−0.237154	+	2.81847i	−0.0161363	+	0.191772i
$217$	−9.48607			−0.643956
$218$	0.624418	−	22.3094i	0.0422910	−	1.51098i
$219$			3.39782i			0.229603i
$220$	−5.61043	−	0.314308i	−0.378255	−	0.0211906i
$221$			3.00465i			0.202114i
$222$	−1.85334	−	0.0518732i	−0.124388	−	0.00348150i
$223$	−16.8902			−1.13105			−0.565525	−	0.824731i	$-0.691326\pi$
$223$	−16.8902			−1.13105			−0.565525	+	0.824731i	$0.691326\pi$
$224$	5.60158	+	0.788864i	0.374271	+	0.0527082i
$225$	1.00000			0.0666667
$226$	8.36728	+	0.234192i	0.556583	+	0.0155782i
$227$			21.1593i			1.40439i	0.711985	+	0.702194i	$0.247796\pi$
$227$			21.1593i			1.40439i	−0.711985	+	0.702194i	$0.752204\pi$
$228$	1.10515	+	0.0619128i	0.0731905	+	0.00410028i
$229$			24.5393i			1.62160i	0.585323	+	0.810800i	$0.300968\pi$
$229$			24.5393i			1.62160i	−0.585323	+	0.810800i	$0.699032\pi$
$230$	−0.281873	+	10.0708i	−0.0185861	+	0.664050i
$231$	−2.80961			−0.184859
$232$	−1.78559	+	21.2209i	−0.117230	+	1.39322i
$233$	−21.3530			−1.39888			−0.699442	−	0.714690i	$-0.746568\pi$
$233$	−21.3530			−1.39888			−0.699442	+	0.714690i	$0.746568\pi$
$234$	−0.137670	+	4.91872i	−0.00899980	+	0.321547i
$235$		−	8.67645i		−	0.565989i
$236$	−0.341076	+	6.08825i	−0.0222021	+	0.396311i
$237$			12.8403i			0.834065i
$238$	1.22076	+	0.0341680i	0.0791302	+	0.00221478i
$239$	12.8637			0.832081			0.416041	−	0.909346i	$-0.363417\pi$
$239$	12.8637			0.832081			0.416041	+	0.909346i	$0.363417\pi$
$240$	3.97497	+	0.446774i	0.256583	+	0.0288391i
$241$	9.69675			0.624623			0.312311	−	0.949980i	$-0.398897\pi$
$241$	9.69675			0.624623			0.312311	+	0.949980i	$0.398897\pi$
$242$	−4.39092	−	0.122898i	−0.282259	−	0.00790016i
$243$			1.00000i			0.0641500i
$244$	0.892344	−	15.9285i	0.0571264	−	1.01971i
$245$		−	1.00000i		−	0.0638877i
$246$	−0.107695	+	3.84777i	−0.00686640	+	0.245325i
$247$	1.92566			0.122527
$248$	−26.7362	−	2.24966i	−1.69775	−	0.142854i
$249$	−15.0988			−0.956848
$250$	0.0395670	−	1.41366i	0.00250244	−	0.0894077i
$251$			2.53329i			0.159900i	0.996799	+	0.0799499i	$0.0254760\pi$
$251$			2.53329i			0.159900i	−0.996799	+	0.0799499i	$0.974524\pi$
$252$	1.99687	+	0.111869i	0.125791	+	0.00704706i
$253$		−	20.0155i		−	1.25836i
$254$	1.41509	+	0.0396071i	0.0887908	+	0.00248517i
$255$	0.863547			0.0540774
$256$	15.6008	+	3.55183i	0.975049	+	0.221989i
$257$	21.5413			1.34371			0.671853	−	0.740684i	$-0.265499\pi$
$257$	21.5413			1.34371			0.671853	+	0.740684i	$0.265499\pi$
$258$	11.0330	+	0.308804i	0.686886	+	0.0192253i
$259$			1.31102i			0.0814629i
$260$	6.94796	+	0.389238i	0.430894	+	0.0241395i
$261$			7.52924i			0.466048i
$262$	0.172838	−	6.17521i	0.0106780	−	0.381506i
$263$	4.25109			0.262133			0.131067	−	0.991374i	$-0.458160\pi$
$263$	4.25109			0.262133			0.131067	+	0.991374i	$0.458160\pi$
$264$	−7.91881	−	0.666312i	−0.487369	−	0.0410087i
$265$	−8.75346			−0.537721
$266$	0.0218981	−	0.782379i	0.00134266	−	0.0479708i
$267$			6.06670i			0.371276i
$268$	0.218659	−	3.90310i	0.0133567	−	0.238420i
$269$		−	8.65414i		−	0.527652i	−0.964570	−	0.263826i	$-0.915016\pi$
$269$		−	8.65414i		−	0.527652i	0.964570	−	0.263826i	$-0.0849845\pi$
$270$	1.41366	+	0.0395670i	0.0860326	+	0.00240797i
$271$	30.4146			1.84755			0.923777	−	0.382931i	$-0.125085\pi$
$271$	30.4146			1.84755			0.923777	+	0.382931i	$0.125085\pi$
$272$	3.43257	+	0.385810i	0.208130	+	0.0233932i
$273$	3.47943			0.210584
$274$	17.1286	+	0.479414i	1.03478	+	0.0289625i
$275$			2.80961i			0.169426i
$276$	−0.796944	+	14.2256i	−0.0479704	+	0.856278i
$277$		−	9.76898i		−	0.586961i	−0.955965	−	0.293481i	$-0.905186\pi$
$277$		−	9.76898i		−	0.586961i	0.955965	−	0.293481i	$-0.0948136\pi$
$278$	−0.373374	+	13.3400i	−0.0223935	+	0.800079i
$279$	−9.48607			−0.567916
$280$	0.237154	−	2.81847i	0.0141727	−	0.168436i
$281$	−28.0103			−1.67096			−0.835479	−	0.549523i	$-0.814809\pi$
$281$	−28.0103			−1.67096			−0.835479	+	0.549523i	$0.814809\pi$
$282$	0.343301	−	12.2656i	0.0204433	−	0.730403i
$283$		−	8.40448i		−	0.499594i	−0.968298	−	0.249797i	$-0.919636\pi$
$283$		−	8.40448i		−	0.499594i	0.968298	−	0.249797i	$-0.0803640\pi$
$284$	11.1179	+	0.622848i	0.659727	+	0.0369592i
$285$		−	0.553442i		−	0.0327831i
$286$	−13.8197	−	0.386801i	−0.817177	−	0.0228720i
$287$	2.72185			0.160666
$288$	5.60158	+	0.788864i	0.330076	+	0.0464842i
$289$	−16.2543			−0.956135
$290$	10.6438	+	0.297909i	0.625025	+	0.0174938i
$291$		−	0.563842i		−	0.0330530i
$292$	6.78500	+	0.380109i	0.397062	+	0.0222442i
$293$		−	13.1337i		−	0.767281i	−0.923482	−	0.383641i	$-0.874670\pi$
$293$		−	13.1337i		−	0.767281i	0.923482	−	0.383641i	$-0.125330\pi$
$294$	0.0395670	−	1.41366i	0.00230759	−	0.0824463i
$295$	3.04890			0.177514
$296$	−0.310914	+	3.69507i	−0.0180715	+	0.214772i
$297$	−2.80961			−0.163030
$298$	0.667174	−	23.8370i	0.0386483	−	1.38084i
$299$			24.7872i			1.43348i
$300$	0.111869	−	1.99687i	0.00645873	−	0.115289i
$301$		−	7.80458i		−	0.449849i
$302$	16.7341	+	0.468372i	0.962941	+	0.0269518i
$303$	14.0321			0.806123
$304$	0.247264	−	2.19992i	0.0141815	−	0.126174i
$305$	−7.97671			−0.456745
$306$	1.22076	+	0.0341680i	0.0697863	+	0.00195325i
$307$		−	21.2100i		−	1.21052i	−0.796029	−	0.605259i	$-0.793070\pi$
$307$		−	21.2100i		−	1.21052i	0.796029	−	0.605259i	$-0.206930\pi$
$308$	−0.314308	+	5.61043i	−0.0179093	+	0.319684i
$309$			14.2681i			0.811686i
$310$	−0.375335	+	13.4101i	−0.0213176	+	0.761641i
$311$	−28.7116			−1.62809			−0.814043	−	0.580805i	$-0.802738\pi$
$311$	−28.7116			−1.62809			−0.814043	+	0.580805i	$0.802738\pi$
$312$	9.80665	+	0.825160i	0.555192	+	0.0467155i
$313$	−2.95790			−0.167190			−0.0835952	−	0.996500i	$-0.526640\pi$
$313$	−2.95790			−0.167190			−0.0835952	+	0.996500i	$0.526640\pi$
$314$	−0.0190807	+	0.681720i	−0.00107679	+	0.0384717i
$315$		−	1.00000i		−	0.0563436i
$316$	25.6403	+	1.43642i	1.44238	+	0.0808050i
$317$		−	7.82017i		−	0.439225i	−0.975587	−	0.219612i	$-0.929521\pi$
$317$		−	7.82017i		−	0.439225i	0.975587	−	0.219612i	$-0.0704793\pi$
$318$	−12.3744	−	0.346348i	−0.693923	−	0.0194222i
$319$	−21.1543			−1.18441
$320$	1.33682	−	7.88752i	0.0747307	−	0.440926i
$321$	11.9082			0.664652
$322$	10.0708	+	0.281873i	0.561224	+	0.0157081i
$323$		−	0.477923i		−	0.0265924i
$324$	1.99687	+	0.111869i	0.110937	+	0.00621492i
$325$		−	3.47943i		−	0.193004i
$326$	−0.171467	+	6.12621i	−0.00949667	+	0.339299i
$327$	−15.7813			−0.872708
$328$	7.67144	+	0.645497i	0.423584	+	0.0356416i
$329$	−8.67645			−0.478348
$330$	−0.111168	+	3.97184i	−0.00611960	+	0.218643i
$331$		−	4.74076i		−	0.260576i	−0.991476	−	0.130288i	$-0.958410\pi$
$331$		−	4.74076i		−	0.260576i	0.991476	−	0.130288i	$-0.0415902\pi$
$332$	−1.68908	+	30.1503i	−0.0927004	+	1.65471i
$333$			1.31102i			0.0718435i
$334$	11.0270	+	0.308635i	0.603370	+	0.0168878i
$335$	−1.95461			−0.106792
$336$	0.446774	−	3.97497i	0.0243735	−	0.216852i
$337$	−3.31491			−0.180574			−0.0902872	−	0.995916i	$-0.528778\pi$
$337$	−3.31491			−0.180574			−0.0902872	+	0.995916i	$0.528778\pi$
$338$	−1.26325	−	0.0353571i	−0.0687117	−	0.00192317i
$339$		−	5.91888i		−	0.321469i
$340$	0.0966037	−	1.72439i	0.00523907	−	0.0935182i
$341$		−	26.6522i		−	1.44330i
$342$	0.0218981	−	0.782379i	0.00118411	−	0.0423062i
$343$	−1.00000			−0.0539949
$344$	1.85089	−	21.9970i	0.0997933	−	1.18600i
$345$	7.12393			0.383539
$346$	0.366999	−	13.1122i	0.0197300	−	0.704918i
$347$		−	14.6395i		−	0.785891i	−0.919562	−	0.392945i	$-0.871456\pi$
$347$		−	14.6395i		−	0.785891i	0.919562	−	0.392945i	$-0.128544\pi$
$348$	15.0349	+	0.842285i	0.805955	+	0.0451512i
$349$			15.0773i			0.807071i	0.914964	+	0.403535i	$0.132219\pi$
$349$			15.0773i			0.807071i	−0.914964	+	0.403535i	$0.867781\pi$
$350$	−1.41366	−	0.0395670i	−0.0755633	−	0.00211495i
$351$	3.47943			0.185718
$352$	−2.21640	+	15.7383i	−0.118135	+	0.838853i
$353$	10.9907			0.584975			0.292487	−	0.956269i	$-0.405517\pi$
$353$	10.9907			0.584975			0.292487	+	0.956269i	$0.405517\pi$
$354$	4.31010	+	0.120636i	0.229079	+	0.00641172i
$355$		−	5.56767i		−	0.295501i
$356$	12.1144	+	0.678673i	0.642063	+	0.0359696i
$357$		−	0.863547i		−	0.0457037i
$358$	0.258710	−	9.24327i	0.0136733	−	0.488522i
$359$	15.9728			0.843013			0.421506	−	0.906825i	$-0.361502\pi$
$359$	15.9728			0.843013			0.421506	+	0.906825i	$0.361502\pi$
$360$	0.237154	−	2.81847i	0.0124991	−	0.148546i
$361$	18.6937			0.983879
$362$	−0.777079	+	27.7637i	−0.0408424	+	1.45923i
$363$			3.10607i			0.163026i
$364$	0.389238	−	6.94796i	0.0204016	−	0.364172i
$365$		−	3.39782i		−	0.177850i
$366$	−11.2764	−	0.315615i	−0.589425	−	0.0164974i
$367$	30.3136			1.58236			0.791178	−	0.611586i	$-0.209468\pi$
$367$	30.3136			1.58236			0.791178	+	0.611586i	$0.209468\pi$
$368$	28.3174	+	3.18278i	1.47615	+	0.165914i
$369$	2.72185			0.141694
$370$	1.85334	+	0.0518732i	0.0963505	+	0.00269676i
$371$			8.75346i			0.454457i
$372$	−1.06119	+	18.9424i	−0.0550203	+	0.982120i
$373$		−	18.4520i		−	0.955408i	−0.878521	−	0.477704i	$-0.841469\pi$
$373$		−	18.4520i		−	0.955408i	0.878521	−	0.477704i	$-0.158531\pi$
$374$	−0.0959988	+	3.42987i	−0.00496398	+	0.177354i
$375$	−1.00000			−0.0516398
$376$	−24.4543	−	2.05766i	−1.26113	−	0.106116i
$377$	26.1974			1.34924
$378$	0.0395670	−	1.41366i	0.00203511	−	0.0727108i
$379$		−	24.6867i		−	1.26807i	−0.773304	−	0.634036i	$-0.781397\pi$
$379$		−	24.6867i		−	1.26807i	0.773304	−	0.634036i	$-0.218603\pi$
$380$	−1.10515	−	0.0619128i	−0.0566931	−	0.00317606i
$381$		−	1.00101i		−	0.0512835i
$382$	19.8208	+	0.554764i	1.01412	+	0.0283842i
$383$	−5.48907			−0.280478			−0.140239	−	0.990118i	$-0.544787\pi$
$383$	−5.48907			−0.280478			−0.140239	+	0.990118i	$0.544787\pi$
$384$	2.20190	−	11.0974i	0.112365	−	0.566310i
$385$	2.80961			0.143191
$386$	29.0475	+	0.813012i	1.47848	+	0.0413812i
$387$		−	7.80458i		−	0.396729i
$388$	−1.12592	−	0.0630762i	−0.0571599	−	0.00320221i
$389$			22.0112i			1.11601i	0.829836	+	0.558007i	$0.188434\pi$
$389$			22.0112i			1.11601i	−0.829836	+	0.558007i	$0.811566\pi$
$390$	0.137670	−	4.91872i	0.00697121	−	0.249069i
$391$	6.15185			0.311112
$392$	−2.81847	−	0.237154i	−0.142354	−	0.0119781i
$393$	−4.36825			−0.220349
$394$	−0.310136	+	11.0806i	−0.0156244	+	0.558233i
$395$		−	12.8403i		−	0.646064i
$396$	−0.314308	+	5.61043i	−0.0157946	+	0.281935i
$397$		−	13.0077i		−	0.652837i	−0.945225	−	0.326418i	$-0.894158\pi$
$397$		−	13.0077i		−	0.652837i	0.945225	−	0.326418i	$-0.105842\pi$
$398$	26.4606	+	0.740608i	1.32635	+	0.0371233i
$399$	−0.553442			−0.0277068
$400$	−3.97497	−	0.446774i	−0.198749	−	0.0223387i
$401$	−7.32422			−0.365754			−0.182877	−	0.983136i	$-0.558541\pi$
$401$	−7.32422			−0.365754			−0.182877	+	0.983136i	$0.558541\pi$
$402$	−2.76315	−	0.0773380i	−0.137813	−	0.00385727i
$403$			33.0061i			1.64415i
$404$	1.56975	−	28.0203i	0.0780980	−	1.39406i
$405$		−	1.00000i		−	0.0496904i
$406$	0.297909	−	10.6438i	0.0147850	−	0.528242i
$407$	−3.68346			−0.182583
$408$	0.204794	−	2.43388i	0.0101388	−	0.120495i
$409$	9.66468			0.477888			0.238944	−	0.971033i	$-0.423199\pi$
$409$	9.66468			0.477888			0.238944	+	0.971033i	$0.423199\pi$
$410$	0.107695	−	3.84777i	0.00531869	−	0.190028i
$411$		−	12.1165i		−	0.597664i
$412$	28.4916	+	1.59616i	1.40368	+	0.0786369i
$413$		−	3.04890i		−	0.150026i
$414$	10.0708	+	0.281873i	0.494953	+	0.0138533i
$415$	15.0988			0.741171
$416$	2.74479	−	19.4903i	0.134575	−	0.955589i
$417$	9.43649			0.462107
$418$	2.19818	+	0.0615251i	0.107517	+	0.00300929i
$419$			5.38879i			0.263260i	0.991299	+	0.131630i	$0.0420210\pi$
$419$			5.38879i			0.263260i	−0.991299	+	0.131630i	$0.957979\pi$
$420$	−1.99687	−	0.111869i	−0.0974372	−	0.00545863i
$421$			32.7820i			1.59770i	0.601533	+	0.798848i	$0.294557\pi$
$421$			32.7820i			1.59770i	−0.601533	+	0.798848i	$0.705443\pi$
$422$	−0.776704	+	27.7503i	−0.0378093	+	1.35086i
$423$	−8.67645			−0.421864
$424$	−2.07592	+	24.6713i	−0.100816	+	1.19815i
$425$	−0.863547			−0.0418882
$426$	0.220296	−	7.87080i	0.0106734	−	0.381341i
$427$			7.97671i			0.386020i
$428$	1.33215	−	23.7791i	0.0643921	−	1.14941i
$429$			9.77584i			0.471982i
$430$	−11.0330	−	0.308804i	−0.532060	−	0.0148918i
$431$	−32.4970			−1.56533			−0.782663	−	0.622445i	$-0.786139\pi$
$431$	−32.4970			−1.56533			−0.782663	+	0.622445i	$0.786139\pi$
$432$	0.446774	−	3.97497i	0.0214954	−	0.191246i
$433$	1.48523			0.0713754			0.0356877	−	0.999363i	$-0.488638\pi$
$433$	1.48523			0.0713754			0.0356877	+	0.999363i	$0.488638\pi$
$434$	13.4101	+	0.375335i	0.643704	+	0.0180167i
$435$		−	7.52924i		−	0.360999i
$436$	−1.76543	+	31.5132i	−0.0845488	+	1.50921i
$437$		−	3.94268i		−	0.188604i
$438$	0.134442	−	4.80336i	0.00642387	−	0.229514i
$439$	−3.99942			−0.190882			−0.0954409	−	0.995435i	$-0.530426\pi$
$439$	−3.99942			−0.190882			−0.0954409	+	0.995435i	$0.530426\pi$
$440$	7.91881	+	0.666312i	0.377514	+	0.0317652i
$441$	−1.00000			−0.0476190
$442$	0.118885	−	4.24755i	0.00565478	−	0.202035i
$443$			31.9373i			1.51739i	0.651447	+	0.758694i	$0.274162\pi$
$443$			31.9373i			1.51739i	−0.651447	+	0.758694i	$0.725838\pi$
$444$	2.61794	+	0.146662i	0.124242	+	0.00696027i
$445$		−	6.06670i		−	0.287589i
$446$	23.8770	+	0.668293i	1.13061	+	0.0316446i
$447$	−16.8619			−0.797539
$448$	−7.88752	−	1.33682i	−0.372650	−	0.0631589i
$449$	−10.3778			−0.489760			−0.244880	−	0.969553i	$-0.578749\pi$
$449$	−10.3778			−0.489760			−0.244880	+	0.969553i	$0.578749\pi$
$450$	−1.41366	−	0.0395670i	−0.0666406	−	0.00186521i
$451$			7.64734i			0.360099i
$452$	−11.8192	−	0.662136i	−0.555929	−	0.0311443i
$453$		−	11.8374i		−	0.556172i
$454$	0.837208	−	29.9120i	0.0392921	−	1.40384i
$455$	−3.47943			−0.163118
$456$	−1.55986	−	0.131251i	−0.0730471	−	0.00614640i
$457$	−18.0964			−0.846512			−0.423256	−	0.906010i	$-0.639113\pi$
$457$	−18.0964			−0.846512			−0.423256	+	0.906010i	$0.639113\pi$
$458$	0.970945	−	34.6902i	0.0453693	−	1.62097i
$459$		−	0.863547i		−	0.0403069i
$460$	0.796944	−	14.2256i	0.0371577	−	0.663270i
$461$			28.7960i			1.34116i	0.741836	+	0.670582i	$0.233955\pi$
$461$			28.7960i			1.34116i	−0.741836	+	0.670582i	$0.766045\pi$
$462$	3.97184	+	0.111168i	0.184787	+	0.00517200i
$463$	−16.8916			−0.785021			−0.392510	−	0.919748i	$-0.628393\pi$
$463$	−16.8916			−0.785021			−0.392510	+	0.919748i	$0.628393\pi$
$464$	3.36387	−	29.9285i	0.156164	−	1.38940i
$465$	9.48607			0.439906
$466$	30.1859	+	0.844875i	1.39834	+	0.0391381i
$467$		−	7.75973i		−	0.359077i	−0.983751	−	0.179539i	$-0.942539\pi$
$467$		−	7.75973i		−	0.359077i	0.983751	−	0.179539i	$-0.0574605\pi$
$468$	0.389238	−	6.94796i	0.0179925	−	0.321169i
$469$			1.95461i			0.0902554i
$470$	−0.343301	+	12.2656i	−0.0158353	+	0.565768i
$471$	0.482238			0.0222203
$472$	0.723059	−	8.59322i	0.0332815	−	0.395535i
$473$	21.9279			1.00824
$474$	0.508051	−	18.1518i	0.0233355	−	0.833738i
$475$			0.553442i			0.0253937i
$476$	−1.72439	−	0.0966037i	−0.0790373	−	0.00442783i
$477$			8.75346i			0.400793i
$478$	−18.1848	−	0.508977i	−0.831756	−	0.0232800i
$479$	42.8009			1.95562			0.977811	−	0.209488i	$-0.0671797\pi$
$479$	42.8009			1.95562			0.977811	+	0.209488i	$0.0671797\pi$
$480$	−5.60158	−	0.788864i	−0.255676	−	0.0360065i
$481$	4.56160			0.207991
$482$	−13.7079	−	0.383671i	−0.624378	−	0.0174758i
$483$		−	7.12393i		−	0.324150i
$484$	6.20241	+	0.347471i	0.281928	+	0.0157941i
$485$			0.563842i			0.0256028i
$486$	0.0395670	−	1.41366i	0.00179480	−	0.0641249i
$487$	−27.5656			−1.24912			−0.624559	−	0.780978i	$-0.714721\pi$
$487$	−27.5656			−1.24912			−0.624559	+	0.780978i	$0.714721\pi$
$488$	−1.89171	+	22.4821i	−0.0856338	+	1.01772i
$489$	4.33358			0.195971
$490$	−0.0395670	+	1.41366i	−0.00178745	+	0.0638626i
$491$			42.7380i			1.92874i	0.264560	+	0.964369i	$0.414773\pi$
$491$			42.7380i			1.92874i	−0.264560	+	0.964369i	$0.585227\pi$
$492$	0.304489	−	5.43517i	0.0137274	−	0.245036i
$493$		−	6.50185i		−	0.292829i
$494$	−2.72223	−	0.0761927i	−0.122479	−	0.00342807i
$495$	2.80961			0.126283
$496$	37.7068	+	4.23813i	1.69309	+	0.190298i
$497$	−5.56767			−0.249744
$498$	21.3446	+	0.597415i	0.956474	+	0.0267708i
$499$		−	38.3432i		−	1.71648i	−0.513250	−	0.858239i	$-0.671559\pi$
$499$		−	38.3432i		−	1.71648i	0.513250	−	0.858239i	$-0.328441\pi$
$500$	−0.111869	+	1.99687i	−0.00500291	+	0.0893027i
$501$		−	7.80031i		−	0.348492i
$502$	0.100235	−	3.58121i	0.00447369	−	0.159837i
$503$	−6.94672			−0.309739			−0.154869	−	0.987935i	$-0.549496\pi$
$503$	−6.94672			−0.309739			−0.154869	+	0.987935i	$0.549496\pi$
$504$	−2.81847	−	0.237154i	−0.125545	−	0.0105637i
$505$	−14.0321			−0.624420
$506$	−0.791953	+	28.2951i	−0.0352066	+	1.25787i
$507$			0.893602i			0.0396862i
$508$	−1.99889	−	0.111982i	−0.0886866	−	0.00496840i
$509$			35.7341i			1.58389i	0.610594	+	0.791944i	$0.290931\pi$
$509$			35.7341i			1.58389i	−0.610594	+	0.791944i	$0.709069\pi$
$510$	−1.22076	−	0.0341680i	−0.0540562	−	0.00151298i
$511$	−3.39782			−0.150311
$512$	−21.9137	−	5.63835i	−0.968457	−	0.249182i
$513$	−0.553442			−0.0244351
$514$	−30.4520	−	0.852323i	−1.34318	−	0.0375943i
$515$		−	14.2681i		−	0.628729i
$516$	−15.5847	−	0.873087i	−0.686079	−	0.0384355i
$517$		−	24.3775i		−	1.07212i
$518$	0.0518732	−	1.85334i	0.00227918	−	0.0814310i
$519$	−9.27539			−0.407144
$520$	−9.80665	−	0.825160i	−0.430050	−	0.0361857i
$521$	31.3294			1.37256			0.686282	−	0.727335i	$-0.259241\pi$
$521$	31.3294			1.37256			0.686282	+	0.727335i	$0.259241\pi$
$522$	0.297909	−	10.6438i	0.0130391	−	0.465866i
$523$			20.4455i			0.894019i	0.894529	+	0.447010i	$0.147511\pi$
$523$			20.4455i			0.894019i	−0.894529	+	0.447010i	$0.852489\pi$
$524$	−0.488669	+	8.72282i	−0.0213476	+	0.381058i
$525$			1.00000i			0.0436436i
$526$	−6.00959	−	0.168203i	−0.262031	−	0.00733399i
$527$	8.19166			0.356835
$528$	11.1681	+	1.25526i	0.486031	+	0.0546283i
$529$	27.7504			1.20654
$530$	12.3744	+	0.346348i	0.537510	+	0.0150444i
$531$		−	3.04890i		−	0.132311i
$532$	−0.0619128	+	1.10515i	−0.00268426	+	0.0479144i
$533$		−	9.47046i		−	0.410211i
$534$	0.240041	−	8.57626i	0.0103876	−	0.371131i
$535$	−11.9082			−0.514837
$536$	−0.463544	+	5.50900i	−0.0200220	+	0.237953i
$537$	−6.53854			−0.282159
$538$	−0.342418	+	12.2340i	−0.0147627	+	0.527445i
$539$		−	2.80961i		−	0.121019i
$540$	−1.99687	−	0.111869i	−0.0859316	−	0.00481406i
$541$			16.4956i			0.709200i	0.935018	+	0.354600i	$0.115383\pi$
$541$			16.4956i			0.709200i	−0.935018	+	0.354600i	$0.884617\pi$
$542$	−42.9959	−	1.20341i	−1.84683	−	0.0516910i
$543$	19.6396			0.842815
$544$	−4.83723	−	0.681221i	−0.207394	−	0.0292071i
$545$	15.7813			0.675996
$546$	−4.91872	−	0.137670i	−0.210502	−	0.00589175i
$547$			0.601699i			0.0257268i	0.999917	+	0.0128634i	$0.00409466\pi$
$547$			0.601699i			0.0257268i	−0.999917	+	0.0128634i	$0.995905\pi$
$548$	−24.1951	−	1.35546i	−1.03356	−	0.0579023i
$549$			7.97671i			0.340438i
$550$	0.111168	−	3.97184i	0.00474022	−	0.169360i
$551$	−4.16700			−0.177520
$552$	1.68947	−	20.0786i	0.0719086	−	0.854600i
$553$	−12.8403			−0.546023
$554$	−0.386529	+	13.8100i	−0.0164221	+	0.586731i
$555$		−	1.31102i		−	0.0556497i
$556$	1.05565	−	18.8434i	0.0447694	−	0.799139i
$557$		−	34.5932i		−	1.46576i	−0.680357	−	0.732881i	$-0.738175\pi$
$557$		−	34.5932i		−	1.46576i	0.680357	−	0.732881i	$-0.261825\pi$
$558$	13.4101	+	0.375335i	0.567694	+	0.0158892i
$559$	−27.1555			−1.14855
$560$	−0.446774	+	3.97497i	−0.0188796	+	0.167973i
$561$	2.42623			0.102436
$562$	39.5971	+	1.10829i	1.67030	+	0.0467502i
$563$			30.6398i			1.29131i	0.763629	+	0.645656i	$0.223416\pi$
$563$			30.6398i			1.29131i	−0.763629	+	0.645656i	$0.776584\pi$
$564$	−0.970623	+	17.3257i	−0.0408706	+	0.729545i
$565$			5.91888i			0.249009i
$566$	−0.332540	+	11.8811i	−0.0139777	+	0.499399i
$567$	−1.00000			−0.0419961
$568$	−15.6923	−	1.32040i	−0.658435	−	0.0554026i
$569$	30.5985			1.28276			0.641378	−	0.767225i	$-0.278363\pi$
$569$	30.5985			1.28276			0.641378	+	0.767225i	$0.278363\pi$
$570$	−0.0218981	+	0.782379i	−0.000917209	+	0.0327703i
$571$			35.9626i			1.50499i	0.658598	+	0.752495i	$0.271150\pi$
$571$			35.9626i			1.50499i	−0.658598	+	0.752495i	$0.728850\pi$
$572$	19.5211	+	1.09361i	0.816217	+	0.0457261i
$573$		−	14.0209i		−	0.585731i
$574$	−3.84777	−	0.107695i	−0.160603	−	0.00449512i
$575$	−7.12393			−0.297088
$576$	−7.88752	−	1.33682i	−0.328646	−	0.0557010i
$577$	0.504706			0.0210112			0.0105056	−	0.999945i	$-0.496656\pi$
$577$	0.504706			0.0210112			0.0105056	+	0.999945i	$0.496656\pi$
$578$	22.9780	+	0.643133i	0.955760	+	0.0267508i
$579$		−	20.5477i		−	0.853935i
$580$	−15.0349	−	0.842285i	−0.624290	−	0.0349740i
$581$		−	15.0988i		−	0.626404i
$582$	−0.0223095	+	0.797081i	−0.000924760	+	0.0330401i
$583$	−24.5939			−1.01857
$584$	−9.57665	−	0.805808i	−0.396284	−	0.0333446i
$585$	−3.47943			−0.143857
$586$	−0.519663	+	18.5666i	−0.0214671	+	0.766981i
$587$			41.6609i			1.71953i	0.510691	+	0.859764i	$0.329390\pi$
$587$			41.6609i			1.71953i	−0.510691	+	0.859764i	$0.670610\pi$
$588$	−0.111869	+	1.99687i	−0.00461338	+	0.0823495i
$589$		−	5.24999i		−	0.216322i
$590$	−4.31010	−	0.120636i	−0.177444	−	0.00496649i
$591$	7.83824			0.322422
$592$	0.585730	−	5.21127i	0.0240733	−	0.214182i
$593$	−35.3697			−1.45246			−0.726229	−	0.687452i	$-0.758729\pi$
$593$	−35.3697			−1.45246			−0.726229	+	0.687452i	$0.758729\pi$
$594$	3.97184	+	0.111168i	0.162967	+	0.00456128i
$595$			0.863547i			0.0354020i
$596$	−1.88631	+	33.6710i	−0.0772664	+	1.37922i
$597$		−	18.7178i		−	0.766070i
$598$	0.980754	−	35.0406i	0.0401060	−	1.43292i
$599$	−9.60460			−0.392433			−0.196217	−	0.980561i	$-0.562866\pi$
$599$	−9.60460			−0.392433			−0.196217	+	0.980561i	$0.562866\pi$
$600$	−0.237154	+	2.81847i	−0.00968178	+	0.115063i
$601$	24.0066			0.979249			0.489625	−	0.871933i	$-0.337134\pi$
$601$	24.0066			0.979249			0.489625	+	0.871933i	$0.337134\pi$
$602$	−0.308804	+	11.0330i	−0.0125859	+	0.449672i
$603$			1.95461i			0.0795978i
$604$	−23.6378	−	1.32424i	−0.961810	−	0.0538825i
$605$		−	3.10607i		−	0.126280i
$606$	−19.8366	−	0.555208i	−0.805807	−	0.0225538i
$607$	27.6599			1.12268			0.561340	−	0.827585i	$-0.310286\pi$
$607$	27.6599			1.12268			0.561340	+	0.827585i	$0.310286\pi$
$608$	−0.436591	+	3.10015i	−0.0177061	+	0.125728i
$609$	−7.52924			−0.305100
$610$	11.2764	+	0.315615i	0.456566	+	0.0127789i
$611$			30.1891i			1.22132i
$612$	−1.72439	−	0.0966037i	−0.0697043	−	0.00390497i
$613$			42.6747i			1.72361i	0.507237	+	0.861807i	$0.330667\pi$
$613$			42.6747i			1.72361i	−0.507237	+	0.861807i	$0.669333\pi$
$614$	−0.839215	+	29.9837i	−0.0338680	+	1.21004i
$615$	−2.72185			−0.109755
$616$	0.666312	−	7.91881i	0.0268465	−	0.319058i
$617$	3.74613			0.150813			0.0754067	−	0.997153i	$-0.475975\pi$
$617$	3.74613			0.150813			0.0754067	+	0.997153i	$0.475975\pi$
$618$	0.564547	−	20.1703i	0.0227094	−	0.811368i
$619$			12.8696i			0.517275i	0.965974	+	0.258637i	$0.0832735\pi$
$619$			12.8696i			0.517275i	−0.965974	+	0.258637i	$0.916727\pi$
$620$	1.06119	−	18.9424i	0.0426185	−	0.760747i
$621$		−	7.12393i		−	0.285873i
$622$	40.5884	+	1.13603i	1.62745	+	0.0455507i
$623$	−6.06670			−0.243057
$624$	−13.8306	−	1.55452i	−0.553668	−	0.0622304i
$625$	1.00000			0.0400000
$626$	4.18147	+	0.117035i	0.167125	+	0.00467767i
$627$		−	1.55496i		−	0.0620991i
$628$	0.0539472	−	0.962966i	0.00215273	−	0.0384265i
$629$		−	1.13213i		−	0.0451409i
$630$	−0.0395670	+	1.41366i	−0.00157639	+	0.0563216i
$631$	13.6593			0.543768			0.271884	−	0.962330i	$-0.412353\pi$
$631$	13.6593			0.543768			0.271884	+	0.962330i	$0.412353\pi$
$632$	−36.1899	−	3.04512i	−1.43956	−	0.121128i
$633$	19.6301			0.780226
$634$	−0.309421	+	11.0551i	−0.0122887	+	0.439053i
$635$			1.00101i			0.0397240i
$636$	17.4795	+	0.979237i	0.693108	+	0.0388293i
$637$			3.47943i			0.137860i
$638$	29.9049	+	0.837011i	1.18395	+	0.0331376i
$639$	−5.56767			−0.220254
$640$	−2.20190	+	11.0974i	−0.0870377	+	0.438662i
$641$	−27.6311			−1.09136			−0.545682	−	0.837993i	$-0.683729\pi$
$641$	−27.6311			−1.09136			−0.545682	+	0.837993i	$0.683729\pi$
$642$	−16.8342	−	0.471172i	−0.664391	−	0.0185957i
$643$		−	43.5088i		−	1.71582i	−0.513799	−	0.857911i	$-0.671762\pi$
$643$		−	43.5088i		−	1.71582i	0.513799	−	0.857911i	$-0.328238\pi$
$644$	−14.2256	−	0.796944i	−0.560565	−	0.0314040i
$645$			7.80458i			0.307305i
$646$	−0.0189100	+	0.675621i	−0.000744004	+	0.0265820i
$647$	−4.11243			−0.161676			−0.0808381	−	0.996727i	$-0.525760\pi$
$647$	−4.11243			−0.161676			−0.0808381	+	0.996727i	$0.525760\pi$
$648$	−2.81847	−	0.237154i	−0.110720	−	0.00931630i
$649$	8.56623			0.336254
$650$	−0.137670	+	4.91872i	−0.00539988	+	0.192928i
$651$		−	9.48607i		−	0.371788i
$652$	0.484791	−	8.65359i	0.0189859	−	0.338901i
$653$		−	20.3053i		−	0.794608i	−0.917687	−	0.397304i	$-0.869946\pi$
$653$		−	20.3053i		−	0.794608i	0.917687	−	0.397304i	$-0.130054\pi$
$654$	22.3094	+	0.624418i	0.872366	+	0.0244167i
$655$	4.36825			0.170682
$656$	−10.8193	−	1.21605i	−0.422421	−	0.0474788i
$657$	−3.39782			−0.132562
$658$	12.2656	+	0.343301i	0.478161	+	0.0133833i
$659$		−	29.4449i		−	1.14701i	−0.819201	−	0.573506i	$-0.805583\pi$
$659$		−	29.4449i		−	1.14701i	0.819201	−	0.573506i	$-0.194417\pi$
$660$	0.314308	−	5.61043i	0.0122344	−	0.218386i
$661$			4.38825i			0.170683i	0.996352	+	0.0853416i	$0.0271982\pi$
$661$			4.38825i			0.170683i	−0.996352	+	0.0853416i	$0.972802\pi$
$662$	−0.187578	+	6.70182i	−0.00729041	+	0.260474i
$663$	−3.00465			−0.116691
$664$	3.58075	−	42.5555i	0.138960	−	1.65147i
$665$	0.553442			0.0214616
$666$	0.0518732	−	1.85334i	0.00201004	−	0.0718154i
$667$		−	53.6378i		−	2.07686i
$668$	−15.5762	−	0.872610i	−0.602661	−	0.0337623i
$669$		−	16.8902i		−	0.653012i
$670$	2.76315	+	0.0773380i	0.106750	+	0.00298783i
$671$	−22.4115			−0.865186
$672$	−0.788864	+	5.60158i	−0.0304311	+	0.216086i
$673$	−26.9497			−1.03883			−0.519417	−	0.854521i	$-0.673851\pi$
$673$	−26.9497			−1.03883			−0.519417	+	0.854521i	$0.673851\pi$
$674$	4.68615	+	0.131161i	0.180504	+	0.00505213i
$675$			1.00000i			0.0384900i
$676$	1.78441	+	0.0999659i	0.0686310	+	0.00384484i
$677$		−	17.3231i		−	0.665781i	−0.942966	−	0.332890i	$-0.891976\pi$
$677$		−	17.3231i		−	0.665781i	0.942966	−	0.332890i	$-0.108024\pi$
$678$	−0.234192	+	8.36728i	−0.00899410	+	0.321343i
$679$	0.563842			0.0216383
$680$	−0.204794	+	2.43388i	−0.00785348	+	0.0933350i
$681$	−21.1593			−0.810824
$682$	−1.05455	+	37.6771i	−0.0403807	+	1.44273i
$683$			3.60974i			0.138123i	0.997612	+	0.0690614i	$0.0220005\pi$
$683$			3.60974i			0.138123i	−0.997612	+	0.0690614i	$0.978000\pi$
$684$	−0.0619128	+	1.10515i	−0.00236730	+	0.0422565i
$685$			12.1165i			0.462948i
$686$	1.41366	+	0.0395670i	0.0539738	+	0.00151068i
$687$	−24.5393			−0.936232
$688$	−3.48688	+	31.0230i	−0.132936	+	1.18274i
$689$	30.4570			1.16032
$690$	−10.0708	−	0.281873i	−0.383389	−	0.0107307i
$691$			10.7675i			0.409616i	0.978802	+	0.204808i	$0.0656570\pi$
$691$			10.7675i			0.409616i	−0.978802	+	0.204808i	$0.934343\pi$
$692$	−1.03762	+	18.5217i	−0.0394446	+	0.704091i
$693$		−	2.80961i		−	0.106728i
$694$	−0.579242	+	20.6953i	−0.0219877	+	0.785583i
$695$	−9.43649			−0.357946
$696$	−21.2209	−	1.78559i	−0.804377	−	0.0676827i
$697$	−2.35044			−0.0890293
$698$	0.596564	−	21.3142i	0.0225803	−	0.806755i
$699$		−	21.3530i		−	0.807646i
$700$	1.99687	+	0.111869i	0.0754746	+	0.00422823i
$701$		−	18.0315i		−	0.681041i	−0.940237	−	0.340520i	$-0.889397\pi$
$701$		−	18.0315i		−	0.681041i	0.940237	−	0.340520i	$-0.110603\pi$
$702$	−4.91872	−	0.137670i	−0.185645	−	0.00519603i
$703$	−0.725575			−0.0273656
$704$	3.75596	−	22.1609i	0.141558	−	0.835220i
$705$	8.67645			0.326774
$706$	−15.5371	−	0.434868i	−0.584746	−	0.0163665i
$707$			14.0321i			0.527731i
$708$	−6.08825	−	0.341076i	−0.228810	−	0.0128184i
$709$			3.58513i			0.134642i	0.997731	+	0.0673212i	$0.0214452\pi$
$709$			3.58513i			0.134642i	−0.997731	+	0.0673212i	$0.978555\pi$
$710$	−0.220296	+	7.87080i	−0.00826757	+	0.295386i
$711$	−12.8403			−0.481547
$712$	−17.0988	−	1.43874i	−0.640805	−	0.0539192i
$713$	67.5781			2.53082
$714$	−0.0341680	+	1.22076i	−0.00127870	+	0.0456859i
$715$		−	9.77584i		−	0.365596i
$716$	−0.731457	+	13.0566i	−0.0273358	+	0.487948i
$717$			12.8637i			0.480402i
$718$	−22.5801	−	0.631996i	−0.842683	−	0.0235859i
$719$	17.2843			0.644595			0.322297	−	0.946638i	$-0.395545\pi$
$719$	17.2843			0.644595			0.322297	+	0.946638i	$0.395545\pi$
$720$	−0.446774	+	3.97497i	−0.0166503	+	0.148138i
$721$	−14.2681			−0.531373
$722$	−26.4265	−	0.739654i	−0.983494	−	0.0275271i
$723$			9.69675i			0.360626i
$724$	2.19705	−	39.2177i	0.0816528	−	1.45751i
$725$			7.52924i			0.279629i
$726$	0.122898	−	4.39092i	0.00456116	−	0.162962i
$727$	−11.3098			−0.419458			−0.209729	−	0.977760i	$-0.567258\pi$
$727$	−11.3098			−0.419458			−0.209729	+	0.977760i	$0.567258\pi$
$728$	−0.825160	+	9.80665i	−0.0305825	+	0.363458i
$729$	−1.00000			−0.0370370
$730$	−0.134442	+	4.80336i	−0.00497591	+	0.177780i
$731$			6.73962i			0.249274i
$732$	15.9285	+	0.892344i	0.588732	+	0.0329820i
$733$			3.01616i			0.111404i	0.998447	+	0.0557022i	$0.0177397\pi$
$733$			3.01616i			0.111404i	−0.998447	+	0.0557022i	$0.982260\pi$
$734$	−42.8531	−	1.19942i	−1.58174	−	0.0442713i
$735$	1.00000			0.0368856
$736$	−39.9053	−	5.61981i	−1.47093	−	0.207149i
$737$	−5.49170			−0.202289
$738$	−3.84777	−	0.107695i	−0.141638	−	0.00396432i
$739$			38.9051i			1.43115i	0.698537	+	0.715574i	$0.253835\pi$
$739$			38.9051i			1.43115i	−0.698537	+	0.715574i	$0.746165\pi$
$740$	−2.61794	−	0.146662i	−0.0962373	−	0.00539140i
$741$			1.92566i			0.0707409i
$742$	0.346348	−	12.3744i	0.0127148	−	0.454279i
$743$	−40.1048			−1.47130			−0.735651	−	0.677361i	$-0.763124\pi$
$743$	−40.1048			−1.47130			−0.735651	+	0.677361i	$0.763124\pi$
$744$	2.24966	−	26.7362i	0.0824766	−	0.980196i
$745$	16.8619			0.617771
$746$	−0.730090	+	26.0848i	−0.0267305	+	0.955034i
$747$		−	15.0988i		−	0.552437i
$748$	0.271419	−	4.84487i	0.00992407	−	0.177146i
$749$			11.9082i			0.435117i
$750$	1.41366	+	0.0395670i	0.0516196	+	0.00144478i
$751$	10.5756			0.385909			0.192954	−	0.981208i	$-0.438193\pi$
$751$	10.5756			0.385909			0.192954	+	0.981208i	$0.438193\pi$
$752$	34.4887	+	3.87641i	1.25767	+	0.141358i
$753$	−2.53329			−0.0923182
$754$	−37.0342	−	1.03655i	−1.34871	−	0.0377491i
$755$			11.8374i			0.430809i
$756$	−0.111869	+	1.99687i	−0.00406862	+	0.0726254i
$757$			34.1819i			1.24236i	0.783667	+	0.621181i	$0.213347\pi$
$757$			34.1819i			1.24236i	−0.783667	+	0.621181i	$0.786653\pi$
$758$	−0.976780	+	34.8986i	−0.0354782	+	1.26758i
$759$	20.0155			0.726516
$760$	1.55986	+	0.131251i	0.0565821	+	0.00476098i
$761$	5.79177			0.209951			0.104976	−	0.994475i	$-0.466524\pi$
$761$	5.79177			0.209951			0.104976	+	0.994475i	$0.466524\pi$
$762$	−0.0396071	+	1.41509i	−0.00143481	+	0.0512634i
$763$		−	15.7813i		−	0.571321i
$764$	−27.9979	−	1.56850i	−1.01293	−	0.0567462i
$765$			0.863547i			0.0312216i
$766$	7.75968	+	0.217186i	0.280369	+	0.00784725i
$767$	−10.6084			−0.383047
$768$	−3.55183	+	15.6008i	−0.128165	+	0.562945i
$769$	40.6536			1.46601			0.733003	−	0.680225i	$-0.238118\pi$
$769$	40.6536			1.46601			0.733003	+	0.680225i	$0.238118\pi$
$770$	−3.97184	−	0.111168i	−0.143135	−	0.00400622i
$771$			21.5413i			0.775789i
$772$	−41.0311	−	2.29865i	−1.47674	−	0.0827301i
$773$		−	33.1380i		−	1.19189i	−0.803024	−	0.595946i	$-0.796777\pi$
$773$		−	33.1380i		−	1.19189i	0.803024	−	0.595946i	$-0.203223\pi$
$774$	−0.308804	+	11.0330i	−0.0110997	+	0.396574i
$775$	−9.48607			−0.340750
$776$	1.58917	+	0.133718i	0.0570479	+	0.00480018i
$777$	−1.31102			−0.0470326
$778$	0.870919	−	31.1164i	0.0312240	−	1.11558i
$779$			1.50639i			0.0539719i
$780$	−0.389238	+	6.94796i	−0.0139370	+	0.248777i
$781$		−	15.6430i		−	0.559751i
$782$	−8.69662	−	0.243410i	−0.310990	−	0.00870433i
$783$	−7.52924			−0.269073
$784$	3.97497	+	0.446774i	0.141963	+	0.0159562i
$785$	−0.482238			−0.0172118
$786$	6.17521	+	0.172838i	0.220263	+	0.00616494i
$787$			13.6518i			0.486635i	0.969947	+	0.243318i	$0.0782357\pi$
$787$			13.6518i			0.486635i	−0.969947	+	0.243318i	$0.921764\pi$
$788$	0.876853	−	15.6519i	0.0312366	−	0.557577i
$789$			4.25109i			0.151343i
$790$	−0.508051	+	18.1518i	−0.0180756	+	0.645811i
$791$	5.91888			0.210451
$792$	0.666312	−	7.91881i	0.0236764	−	0.281383i
$793$	27.7544			0.985587
$794$	−0.514675	+	18.3884i	−0.0182651	+	0.652581i
$795$		−	8.75346i		−	0.310453i
$796$	−37.3770	−	2.09394i	−1.32479	−	0.0742176i
$797$		−	16.7731i		−	0.594132i	−0.954857	−	0.297066i	$-0.903992\pi$
$797$		−	16.7731i		−	0.594132i	0.954857	−	0.297066i	$-0.0960082\pi$
$798$	0.782379	+	0.0218981i	0.0276959	+	0.000775183i
$799$	7.49252			0.265066
$800$	5.60158	+	0.788864i	0.198046	+	0.0278905i
$801$	−6.06670			−0.214356
$802$	10.3540	+	0.289797i	0.365611	+	0.0102331i
$803$		−	9.54657i		−	0.336891i
$804$	3.90310	+	0.218659i	0.137652	+	0.00771152i
$805$			7.12393i			0.251085i
$806$	1.30595	−	46.6594i	0.0460002	−	1.64351i
$807$	8.65414			0.304640
$808$	−3.32777	+	39.5490i	−0.117071	+	1.39133i
$809$	−11.8608			−0.417005			−0.208502	−	0.978022i	$-0.566859\pi$
$809$	−11.8608			−0.417005			−0.208502	+	0.978022i	$0.566859\pi$
$810$	−0.0395670	+	1.41366i	−0.00139024	+	0.0496709i
$811$		−	11.4122i		−	0.400736i	−0.979721	−	0.200368i	$-0.935786\pi$
$811$		−	11.4122i		−	0.400736i	0.979721	−	0.200368i	$-0.0642138\pi$
$812$	−0.842285	+	15.0349i	−0.0295584	+	0.527622i
$813$			30.4146i			1.06669i
$814$	5.20717	+	0.145744i	0.182511	+	0.00510831i
$815$	−4.33358			−0.151799
$816$	−0.385810	+	3.43257i	−0.0135061	+	0.120164i
$817$	4.31939			0.151116
$818$	−13.6626	−	0.382402i	−0.477701	−	0.0133704i
$819$			3.47943i			0.121581i
$820$	−0.304489	+	5.43517i	−0.0106332	+	0.189804i
$821$			38.7018i			1.35070i	0.737496	+	0.675351i	$0.236008\pi$
$821$			38.7018i			1.35070i	−0.737496	+	0.675351i	$0.763992\pi$
$822$	−0.479414	+	17.1286i	−0.0167215	+	0.597430i
$823$	−18.7529			−0.653686			−0.326843	−	0.945079i	$-0.605985\pi$
$823$	−18.7529			−0.653686			−0.326843	+	0.945079i	$0.605985\pi$
$824$	−40.2143	−	3.38375i	−1.40093	−	0.117878i
$825$	−2.80961			−0.0978182
$826$	−0.120636	+	4.31010i	−0.00419745	+	0.149968i
$827$		−	21.4894i		−	0.747261i	−0.927578	−	0.373630i	$-0.878113\pi$
$827$		−	21.4894i		−	0.747261i	0.927578	−	0.373630i	$-0.121887\pi$
$828$	−14.2256	−	0.796944i	−0.494372	−	0.0276957i
$829$			31.8149i			1.10498i	0.833521	+	0.552488i	$0.186322\pi$
$829$			31.8149i			1.10498i	−0.833521	+	0.552488i	$0.813678\pi$
$830$	−21.3446	−	0.597415i	−0.740881	−	0.0207366i
$831$	9.76898			0.338882
$832$	−4.65138	+	27.4440i	−0.161257	+	0.951450i
$833$	0.863547			0.0299201
$834$	−13.3400	−	0.373374i	−0.461926	−	0.0129289i
$835$			7.80031i			0.269941i
$836$	−3.10505	−	0.173951i	−0.107390	−	0.00601623i
$837$		−	9.48607i		−	0.327887i
$838$	0.213218	−	7.61792i	0.00736550	−	0.263157i
$839$	−45.6480			−1.57594			−0.787972	−	0.615711i	$-0.788869\pi$
$839$	−45.6480			−1.57594			−0.787972	+	0.615711i	$0.788869\pi$
$840$	2.81847	+	0.237154i	0.0972464	+	0.00818260i
$841$	−27.6894			−0.954808
$842$	1.29708	−	46.3426i	0.0447005	−	1.59707i
$843$		−	28.0103i		−	0.964728i
$844$	2.19599	−	39.1987i	0.0755891	−	1.34928i
$845$		−	0.893602i		−	0.0307408i
$846$	12.2656	+	0.343301i	0.421699	+	0.0118029i
$847$	−3.10607			−0.106726
$848$	3.91082	−	34.7948i	0.134298	−	1.19486i
$849$	8.40448			0.288441
$850$	1.22076	+	0.0341680i	0.0418718	+	0.00117195i
$851$		−	9.33962i		−	0.320158i
$852$	−0.622848	+	11.1179i	−0.0213384	+	0.380893i
$853$		−	28.2677i		−	0.967869i	−0.875104	−	0.483934i	$-0.839207\pi$
$853$		−	28.2677i		−	0.967869i	0.875104	−	0.483934i	$-0.160793\pi$
$854$	0.315615	−	11.2764i	0.0108001	−	0.385869i
$855$	0.553442			0.0189273
$856$	−2.82408	+	33.5629i	−0.0965252	+	1.14716i
$857$	15.9761			0.545732			0.272866	−	0.962052i	$-0.412028\pi$
$857$	15.9761			0.545732			0.272866	+	0.962052i	$0.412028\pi$
$858$	0.386801	−	13.8197i	0.0132052	−	0.471797i
$859$			12.6407i			0.431295i	0.976471	+	0.215648i	$0.0691862\pi$
$859$			12.6407i			0.431295i	−0.976471	+	0.215648i	$0.930814\pi$
$860$	15.5847	+	0.873087i	0.531435	+	0.0297720i
$861$			2.72185i			0.0927603i
$862$	45.9398	+	1.28581i	1.56471	+	0.0437949i
$863$	50.8623			1.73137			0.865687	−	0.500586i	$-0.166882\pi$
$863$	50.8623			1.73137			0.865687	+	0.500586i	$0.166882\pi$
$864$	−0.788864	+	5.60158i	−0.0268377	+	0.190570i
$865$	9.27539			0.315373
$866$	−2.09960	−	0.0587659i	−0.0713474	−	0.00199695i
$867$		−	16.2543i		−	0.552025i
$868$	−18.9424	−	1.06119i	−0.642948	−	0.0360192i
$869$		−	36.0762i		−	1.22380i
$870$	−0.297909	+	10.6438i	−0.0101001	+	0.360858i
$871$	6.80091			0.230440
$872$	3.74260	−	44.4791i	0.126740	−	1.50625i
$873$	0.563842			0.0190832
$874$	−0.156000	+	5.57362i	−0.00527679	+	0.188530i
$875$		−	1.00000i		−	0.0338062i
$876$	−0.380109	+	6.78500i	−0.0128427	+	0.229244i
$877$		−	43.1596i		−	1.45740i	−0.684835	−	0.728698i	$-0.740126\pi$
$877$		−	43.1596i		−	1.45740i	0.684835	−	0.728698i	$-0.259874\pi$
$878$	5.65382	+	0.158245i	0.190807	+	0.00534051i
$879$	13.1337			0.442990
$880$	−11.1681	−	1.25526i	−0.376478	−	0.0423149i
$881$	−38.4122			−1.29414			−0.647071	−	0.762430i	$-0.724006\pi$
$881$	−38.4122			−1.29414			−0.647071	+	0.762430i	$0.724006\pi$
$882$	1.41366	+	0.0395670i	0.0476004	+	0.00133229i
$883$			51.4057i			1.72994i	0.501824	+	0.864970i	$0.332663\pi$
$883$			51.4057i			1.72994i	−0.501824	+	0.864970i	$0.667337\pi$
$884$	−0.336125	+	5.99988i	−0.0113051	+	0.201798i
$885$			3.04890i			0.102488i
$886$	1.26366	−	45.1485i	0.0424536	−	1.51679i
$887$	−10.0880			−0.338722			−0.169361	−	0.985554i	$-0.554170\pi$
$887$	−10.0880			−0.338722			−0.169361	+	0.985554i	$0.554170\pi$
$888$	−3.69507	−	0.310914i	−0.123998	−	0.0104336i
$889$	1.00101			0.0335729
$890$	−0.240041	+	8.57626i	−0.00804620	+	0.287477i
$891$		−	2.80961i		−	0.0941256i
$892$	−33.7275	−	1.88948i	−1.12928	−	0.0632644i
$893$		−	4.80192i		−	0.160690i
$894$	23.8370	+	0.667174i	0.797227	+	0.0223136i
$895$	6.53854			0.218559
$896$	11.0974	+	2.20190i	0.370737	+	0.0735603i
$897$	−24.7872			−0.827620
$898$	14.6707	+	0.410620i	0.489568	+	0.0137026i
$899$		−	71.4229i		−	2.38209i
$900$	1.99687	+	0.111869i	0.0665623	+	0.00372895i
$901$		−	7.55902i		−	0.251828i
$902$	0.302582	−	10.8107i	0.0100749	−	0.359958i
$903$	7.80458			0.259720
$904$	16.6822	+	1.40369i	0.554840	+	0.0466859i
$905$	−19.6396			−0.652841
$906$	−0.468372	+	16.7341i	−0.0155606	+	0.555954i
$907$		−	17.8486i		−	0.592654i	−0.955086	−	0.296327i	$-0.904238\pi$
$907$		−	17.8486i		−	0.592654i	0.955086	−	0.296327i	$-0.0957619\pi$
$908$	−2.36706	+	42.2523i	−0.0785535	+	1.40219i
$909$			14.0321i			0.465415i
$910$	4.91872	+	0.137670i	0.163054	+	0.00456373i
$911$	34.9379			1.15755			0.578773	−	0.815489i	$-0.303532\pi$
$911$	34.9379			1.15755			0.578773	+	0.815489i	$0.303532\pi$
$912$	2.19992	+	0.247264i	0.0728466	+	0.00818771i
$913$	42.4218			1.40396
$914$	25.5821	+	0.716019i	0.846181	+	0.0236838i
$915$		−	7.97671i		−	0.263702i
$916$	−2.74517	+	49.0017i	−0.0907031	+	1.61906i
$917$		−	4.36825i		−	0.144252i
$918$	−0.0341680	+	1.22076i	−0.00112771	+	0.0402911i
$919$	−15.2529			−0.503146			−0.251573	−	0.967838i	$-0.580948\pi$
$919$	−15.2529			−0.503146			−0.251573	+	0.967838i	$0.580948\pi$
$920$	−1.68947	+	20.0786i	−0.0557002	+	0.661971i
$921$	21.2100			0.698892
$922$	1.13937	−	40.7077i	0.0375232	−	1.34064i
$923$			19.3723i			0.637647i
$924$	−5.61043	−	0.314308i	−0.184570	−	0.0103400i
$925$			1.31102i			0.0431061i
$926$	23.8790	+	0.668351i	0.784714	+	0.0219634i
$927$	−14.2681			−0.468627
$928$	−5.93954	+	42.1756i	−0.194975	+	1.38448i
$929$	1.95849			0.0642559			0.0321279	−	0.999484i	$-0.489772\pi$
$929$	1.95849			0.0642559			0.0321279	+	0.999484i	$0.489772\pi$
$930$	−13.4101	−	0.375335i	−0.439734	−	0.0123077i
$931$		−	0.553442i		−	0.0181383i
$932$	−42.6392	−	2.38873i	−1.39669	−	0.0782455i
$933$		−	28.7116i		−	0.939976i
$934$	−0.307029	+	10.9696i	−0.0100463	+	0.358937i
$935$	−2.42623			−0.0793463
$936$	−0.825160	+	9.80665i	−0.0269712	+	0.320540i
$937$	11.6735			0.381357			0.190679	−	0.981653i	$-0.438931\pi$
$937$	11.6735			0.381357			0.190679	+	0.981653i	$0.438931\pi$
$938$	0.0773380	−	2.76315i	0.00252517	−	0.0902201i
$939$		−	2.95790i		−	0.0965275i
$940$	0.970623	−	17.3257i	0.0316582	−	0.565103i
$941$		−	32.4009i		−	1.05624i	−0.849170	−	0.528119i	$-0.822897\pi$
$941$		−	32.4009i		−	1.05624i	0.849170	−	0.528119i	$-0.177103\pi$
$942$	−0.681720	−	0.0190807i	−0.0222116	−	0.000621683i
$943$	−19.3902			−0.631433
$944$	−1.36217	+	12.1193i	−0.0443348	+	0.394449i
$945$	1.00000			0.0325300
$946$	−30.9985	−	0.867620i	−1.00785	−	0.0282088i
$947$		−	15.7346i		−	0.511306i	−0.966769	−	0.255653i	$-0.917710\pi$
$947$		−	15.7346i		−	0.511306i	0.966769	−	0.255653i	$-0.0822905\pi$
$948$	−1.43642	+	25.6403i	−0.0466528	+	0.832759i
$949$			11.8225i			0.383773i
$950$	0.0218981	−	0.782379i	0.000710467	−	0.0253837i
$951$	7.82017			0.253587
$952$	2.43388	+	0.204794i	0.0788824	+	0.00663740i
$953$	−15.9340			−0.516153			−0.258076	−	0.966125i	$-0.583089\pi$
$953$	−15.9340			−0.516153			−0.258076	+	0.966125i	$0.583089\pi$
$954$	0.346348	−	12.3744i	0.0112134	−	0.400637i
$955$			14.0209i			0.453705i
$956$	25.6871	+	1.43904i	0.830779	+	0.0465419i
$957$		−	21.1543i		−	0.683820i
$958$	−60.5059	−	1.69350i	−1.95486	−	0.0547146i
$959$	12.1165			0.391263
$960$	7.88752	+	1.33682i	0.254568	+	0.0431458i
$961$	58.9855			1.90276
$962$	−6.44855	−	0.180489i	−0.207910	−	0.00581919i
$963$			11.9082i			0.383737i
$964$	19.3631	+	1.08476i	0.623645	+	0.0349378i
$965$			20.5477i			0.661455i
$966$	−0.281873	+	10.0708i	−0.00906910	+	0.324023i
$967$	12.0835			0.388579			0.194290	−	0.980944i	$-0.437760\pi$
$967$	12.0835			0.388579			0.194290	+	0.980944i	$0.437760\pi$
$968$	−8.75434	−	0.736617i	−0.281375	−	0.0236758i
$969$	0.477923			0.0153531
$970$	0.0223095	−	0.797081i	0.000716316	−	0.0255927i
$971$		−	24.5135i		−	0.786677i	−0.919394	−	0.393338i	$-0.871320\pi$
$971$		−	24.5135i		−	0.786677i	0.919394	−	0.393338i	$-0.128680\pi$
$972$	−0.111869	+	1.99687i	−0.00358819	+	0.0640496i
$973$			9.43649i			0.302520i
$974$	38.9684	+	1.09069i	1.24863	+	0.0349480i
$975$	3.47943			0.111431
$976$	3.56379	−	31.7072i	0.114074	−	1.01492i
$977$	53.2542			1.70375			0.851876	−	0.523743i	$-0.175465\pi$
$977$	53.2542			1.70375			0.851876	+	0.523743i	$0.175465\pi$
$978$	−6.12621	−	0.171467i	−0.195895	−	0.00548290i
$979$		−	17.0451i		−	0.544764i
$980$	0.111869	−	1.99687i	0.00357351	−	0.0637876i
$981$		−	15.7813i		−	0.503858i
$982$	1.69101	−	60.4170i	0.0539624	−	1.92798i
$983$	50.7409			1.61838			0.809191	−	0.587546i	$-0.199906\pi$
$983$	50.7409			1.61838			0.809191	+	0.587546i	$0.199906\pi$
$984$	−0.645497	+	7.67144i	−0.0205777	+	0.244556i
$985$	−7.83824			−0.249747
$986$	−0.257259	+	9.19141i	−0.00819279	+	0.292714i
$987$		−	8.67645i		−	0.276175i
$988$	3.84529	+	0.215421i	0.122335	+	0.00685346i
$989$			55.5993i			1.76795i
$990$	−3.97184	−	0.111168i	−0.126233	−	0.00353315i
$991$	26.4152			0.839105			0.419553	−	0.907731i	$-0.362187\pi$
$991$	26.4152			0.839105			0.419553	+	0.907731i	$0.362187\pi$
$992$	−53.1370	−	7.48322i	−1.68710	−	0.237592i
$993$	4.74076			0.150443
$994$	7.87080	+	0.220296i	0.249647	+	0.00698737i
$995$			18.7178i			0.593395i
$996$	−30.1503	−	1.68908i	−0.955350	−	0.0535206i
$997$			61.2231i			1.93896i	0.245179	+	0.969478i	$0.421153\pi$
$997$			61.2231i			1.93896i	−0.245179	+	0.969478i	$0.578847\pi$
$998$	−1.51713	+	54.2043i	−0.0480238	+	1.71581i
$999$	−1.31102			−0.0414789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.g.d.421.1	✓	16
4.3	odd	2		3360.2.g.d.1681.7		16
8.3	odd	2		3360.2.g.d.1681.10		16
8.5	even	2	inner	840.2.g.d.421.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.g.d.421.1	✓	16	1.1	even	1	trivial
840.2.g.d.421.2	yes	16	8.5	even	2	inner
3360.2.g.d.1681.7		16	4.3	odd	2
3360.2.g.d.1681.10		16	8.3	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41366 - 0.0395670i) q^{2} +1.00000i q^{3} +(1.99687 + 0.111869i) q^{4} -1.00000i q^{5} +(0.0395670 - 1.41366i) q^{6} -1.00000 q^{7} +(-2.81847 - 0.237154i) q^{8} -1.00000 q^{9} +(-0.0395670 + 1.41366i) q^{10} -2.80961i q^{11} +(-0.111869 + 1.99687i) q^{12} +3.47943i q^{13} +(1.41366 + 0.0395670i) q^{14} +1.00000 q^{15} +(3.97497 + 0.446774i) q^{16} +0.863547 q^{17} +(1.41366 + 0.0395670i) q^{18} -0.553442i q^{19} +(0.111869 - 1.99687i) q^{20} -1.00000i q^{21} +(-0.111168 + 3.97184i) q^{22} +7.12393 q^{23} +(0.237154 - 2.81847i) q^{24} -1.00000 q^{25} +(0.137670 - 4.91872i) q^{26} -1.00000i q^{27} +(-1.99687 - 0.111869i) q^{28} -7.52924i q^{29} +(-1.41366 - 0.0395670i) q^{30} +9.48607 q^{31} +(-5.60158 - 0.788864i) q^{32} +2.80961 q^{33} +(-1.22076 - 0.0341680i) q^{34} +1.00000i q^{35} +(-1.99687 - 0.111869i) q^{36} -1.31102i q^{37} +(-0.0218981 + 0.782379i) q^{38} -3.47943 q^{39} +(-0.237154 + 2.81847i) q^{40} -2.72185 q^{41} +(-0.0395670 + 1.41366i) q^{42} +7.80458i q^{43} +(0.314308 - 5.61043i) q^{44} +1.00000i q^{45} +(-10.0708 - 0.281873i) q^{46} +8.67645 q^{47} +(-0.446774 + 3.97497i) q^{48} +1.00000 q^{49} +(1.41366 + 0.0395670i) q^{50} +0.863547i q^{51} +(-0.389238 + 6.94796i) q^{52} -8.75346i q^{53} +(-0.0395670 + 1.41366i) q^{54} -2.80961 q^{55} +(2.81847 + 0.237154i) q^{56} +0.553442 q^{57} +(-0.297909 + 10.6438i) q^{58} +3.04890i q^{59} +(1.99687 + 0.111869i) q^{60} -7.97671i q^{61} +(-13.4101 - 0.375335i) q^{62} +1.00000 q^{63} +(7.88752 + 1.33682i) q^{64} +3.47943 q^{65} +(-3.97184 - 0.111168i) q^{66} -1.95461i q^{67} +(1.72439 + 0.0966037i) q^{68} +7.12393i q^{69} +(0.0395670 - 1.41366i) q^{70} +5.56767 q^{71} +(2.81847 + 0.237154i) q^{72} +3.39782 q^{73} +(-0.0518732 + 1.85334i) q^{74} -1.00000i q^{75} +(0.0619128 - 1.10515i) q^{76} +2.80961i q^{77} +(4.91872 + 0.137670i) q^{78} +12.8403 q^{79} +(0.446774 - 3.97497i) q^{80} +1.00000 q^{81} +(3.84777 + 0.107695i) q^{82} +15.0988i q^{83} +(0.111869 - 1.99687i) q^{84} -0.863547i q^{85} +(0.308804 - 11.0330i) q^{86} +7.52924 q^{87} +(-0.666312 + 7.91881i) q^{88} +6.06670 q^{89} +(0.0395670 - 1.41366i) q^{90} -3.47943i q^{91} +(14.2256 + 0.796944i) q^{92} +9.48607i q^{93} +(-12.2656 - 0.343301i) q^{94} -0.553442 q^{95} +(0.788864 - 5.60158i) q^{96} -0.563842 q^{97} +(-1.41366 - 0.0395670i) q^{98} +2.80961i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{6} - 16 q^{7} - 2 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{14} + 16 q^{15} + 4 q^{16} + 2 q^{18} + 2 q^{24} - 16 q^{25} - 2 q^{30} - 2 q^{32} + 24 q^{34} - 28 q^{38} - 2 q^{40} + 2 q^{42}+ \cdots - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^6 - 16 * q^7 - 2 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^14 + 16 * q^15 + 4 * q^16 + 2 * q^18 + 2 * q^24 - 16 * q^25 - 2 * q^30 - 2 * q^32 + 24 * q^34 - 28 * q^38 - 2 * q^40 + 2 * q^42 + 8 * q^44 - 36 * q^46 + 32 * q^47 + 16 * q^49 + 2 * q^50 + 4 * q^52 + 2 * q^54 + 2 * q^56 + 32 * q^58 - 12 * q^62 + 16 * q^63 - 48 * q^64 + 28 * q^66 + 56 * q^68 - 2 * q^70 - 64 * q^71 + 2 * q^72 + 24 * q^74 + 8 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^81 + 4 * q^82 - 36 * q^86 - 16 * q^87 - 2 * q^90 + 80 * q^92 - 44 * q^94 - 2 * q^96 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more