LMFDB - Embedded newform 840.2.g.b.421.10

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)

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);

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")

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 = [12,-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:	$12$
Coefficient field:	12.0.3058043990573056.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{7} - 16x^{5} + 16x^{2} + 64 $ x^12 + x^10 - 8x^7 - 16x^5 + 16*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			421.10
Root			$-1.11568 - 0.869059i$ of defining polynomial
Character	$\chi$	$=$	840.421
Dual form			840.2.g.b.421.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.869059 + 1.11568i) q^{2} +1.00000i q^{3} +(-0.489471 + 1.93918i) q^{4} +1.00000i q^{5} +(-1.11568 + 0.869059i) q^{6} -1.00000 q^{7} +(-2.58888 + 1.13917i) q^{8} -1.00000 q^{9} +(-1.11568 + 0.869059i) q^{10} +0.759176i q^{11} +(-1.93918 - 0.489471i) q^{12} +0.759176i q^{13} +(-0.869059 - 1.11568i) q^{14} -1.00000 q^{15} +(-3.52084 - 1.89835i) q^{16} -5.26887 q^{17} +(-0.869059 - 1.11568i) q^{18} +1.64700i q^{19} +(-1.93918 - 0.489471i) q^{20} -1.00000i q^{21} +(-0.846995 + 0.659769i) q^{22} +2.20737 q^{23} +(-1.13917 - 2.58888i) q^{24} -1.00000 q^{25} +(-0.846995 + 0.659769i) q^{26} -1.00000i q^{27} +(0.489471 - 1.93918i) q^{28} +1.39265i q^{29} +(-0.869059 - 1.11568i) q^{30} +3.52322 q^{31} +(-0.941874 - 5.57789i) q^{32} -0.759176 q^{33} +(-4.57896 - 5.87836i) q^{34} -1.00000i q^{35} +(0.489471 - 1.93918i) q^{36} +11.4133i q^{37} +(-1.83753 + 1.43135i) q^{38} -0.759176 q^{39} +(-1.13917 - 2.58888i) q^{40} -1.60002 q^{41} +(1.11568 - 0.869059i) q^{42} -9.22676i q^{43} +(-1.47218 - 0.371595i) q^{44} -1.00000i q^{45} +(1.91833 + 2.46271i) q^{46} -2.62393 q^{47} +(1.89835 - 3.52084i) q^{48} +1.00000 q^{49} +(-0.869059 - 1.11568i) q^{50} -5.26887i q^{51} +(-1.47218 - 0.371595i) q^{52} -2.62309i q^{53} +(1.11568 - 0.869059i) q^{54} -0.759176 q^{55} +(2.58888 - 1.13917i) q^{56} -1.64700 q^{57} +(-1.55375 + 1.21030i) q^{58} +8.77025i q^{59} +(0.489471 - 1.93918i) q^{60} +2.97609i q^{61} +(3.06189 + 3.93078i) q^{62} +1.00000 q^{63} +(5.40458 - 5.89835i) q^{64} -0.759176 q^{65} +(-0.659769 - 0.846995i) q^{66} +6.36407i q^{67} +(2.57896 - 10.2173i) q^{68} +2.20737i q^{69} +(1.11568 - 0.869059i) q^{70} +8.77979 q^{71} +(2.58888 - 1.13917i) q^{72} +4.59136 q^{73} +(-12.7335 + 9.91881i) q^{74} -1.00000i q^{75} +(-3.19384 - 0.806162i) q^{76} -0.759176i q^{77} +(-0.659769 - 0.846995i) q^{78} +15.8524 q^{79} +(1.89835 - 3.52084i) q^{80} +1.00000 q^{81} +(-1.39051 - 1.78510i) q^{82} +2.86269i q^{83} +(1.93918 + 0.489471i) q^{84} -5.26887i q^{85} +(10.2941 - 8.01860i) q^{86} -1.39265 q^{87} +(-0.864831 - 1.96541i) q^{88} -15.0005 q^{89} +(1.11568 - 0.869059i) q^{90} -0.759176i q^{91} +(-1.08044 + 4.28048i) q^{92} +3.52322i q^{93} +(-2.28035 - 2.92746i) q^{94} -1.64700 q^{95} +(5.57789 - 0.941874i) q^{96} -6.10971 q^{97} +(0.869059 + 1.11568i) q^{98} -0.759176i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 12 q^{7} - 2 q^{8} - 12 q^{9} + 2 q^{14} - 12 q^{15} + 2 q^{16} + 2 q^{18} + 40 q^{23} - 12 q^{25} - 2 q^{28} + 2 q^{30} - 8 q^{31} - 2 q^{32} - 20 q^{34} - 2 q^{36} + 24 q^{38}+ \cdots - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 12 * q^7 - 2 * q^8 - 12 * q^9 + 2 * q^14 - 12 * q^15 + 2 * q^16 + 2 * q^18 + 40 * q^23 - 12 * q^25 - 2 * q^28 + 2 * q^30 - 8 * q^31 - 2 * q^32 - 20 * q^34 - 2 * q^36 + 24 * q^38 + 24 * q^46 - 32 * q^47 + 12 * q^49 + 2 * q^50 + 2 * q^56 - 20 * q^58 - 2 * q^60 + 52 * q^62 + 12 * q^63 + 2 * q^64 - 20 * q^66 - 4 * q^68 - 8 * q^71 + 2 * q^72 - 60 * q^74 - 48 * q^76 - 20 * q^78 - 80 * q^79 + 12 * q^81 + 24 * q^86 + 16 * q^87 + 40 * q^88 - 8 * q^92 + 36 * q^94 + 40 * 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 $

$2$	0.869059	+	1.11568i	0.614518	+	0.788903i
$2$	0.869059	+	1.11568i	0.614518	+	0.788903i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.489471	+	1.93918i	−0.244736	+	0.969590i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.11568	+	0.869059i	−0.455473	+	0.354792i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.58888	+	1.13917i	−0.915307	+	0.402757i
$9$	−1.00000			−0.333333
$10$	−1.11568	+	0.869059i	−0.352808	+	0.274821i
$11$			0.759176i			0.228900i	0.993429	+	0.114450i	$0.0365106\pi$
$11$			0.759176i			0.228900i	−0.993429	+	0.114450i	$0.963489\pi$
$12$	−1.93918	−	0.489471i	−0.559793	−	0.141298i
$13$			0.759176i			0.210558i	0.994443	+	0.105279i	$0.0335735\pi$
$13$			0.759176i			0.210558i	−0.994443	+	0.105279i	$0.966427\pi$
$14$	−0.869059	−	1.11568i	−0.232266	−	0.298177i
$15$	−1.00000			−0.258199
$16$	−3.52084	−	1.89835i	−0.880209	−	0.474587i
$17$	−5.26887			−1.27789			−0.638944	−	0.769253i	$-0.720629\pi$
$17$	−5.26887			−1.27789			−0.638944	+	0.769253i	$0.720629\pi$
$18$	−0.869059	−	1.11568i	−0.204839	−	0.262968i
$19$			1.64700i			0.377849i	0.981992	+	0.188924i	$0.0605001\pi$
$19$			1.64700i			0.377849i	−0.981992	+	0.188924i	$0.939500\pi$
$20$	−1.93918	−	0.489471i	−0.433614	−	0.109449i
$21$		−	1.00000i		−	0.218218i
$22$	−0.846995	+	0.659769i	−0.180580	+	0.140663i
$23$	2.20737			0.460268			0.230134	−	0.973159i	$-0.426084\pi$
$23$	2.20737			0.460268			0.230134	+	0.973159i	$0.426084\pi$
$24$	−1.13917	−	2.58888i	−0.232532	−	0.528453i
$25$	−1.00000			−0.200000
$26$	−0.846995	+	0.659769i	−0.166109	+	0.129391i
$27$		−	1.00000i		−	0.192450i
$28$	0.489471	−	1.93918i	0.0925014	−	0.366471i
$29$			1.39265i			0.258609i	0.991605	+	0.129304i	$0.0412745\pi$
$29$			1.39265i			0.258609i	−0.991605	+	0.129304i	$0.958726\pi$
$30$	−0.869059	−	1.11568i	−0.158668	−	0.203694i
$31$	3.52322			0.632790			0.316395	−	0.948628i	$-0.397528\pi$
$31$	3.52322			0.632790			0.316395	+	0.948628i	$0.397528\pi$
$32$	−0.941874	−	5.57789i	−0.166501	−	0.986041i
$33$	−0.759176			−0.132156
$34$	−4.57896	−	5.87836i	−0.785285	−	1.00813i
$35$		−	1.00000i		−	0.169031i
$36$	0.489471	−	1.93918i	0.0815786	−	0.323197i
$37$			11.4133i			1.87633i	0.346189	+	0.938165i	$0.387475\pi$
$37$			11.4133i			1.87633i	−0.346189	+	0.938165i	$0.612525\pi$
$38$	−1.83753	+	1.43135i	−0.298086	+	0.232195i
$39$	−0.759176			−0.121565
$40$	−1.13917	−	2.58888i	−0.180119	−	0.409338i
$41$	−1.60002			−0.249881			−0.124940	−	0.992164i	$-0.539874\pi$
$41$	−1.60002			−0.249881			−0.124940	+	0.992164i	$0.539874\pi$
$42$	1.11568	−	0.869059i	0.172153	−	0.134099i
$43$		−	9.22676i		−	1.40707i	−0.710662	−	0.703534i	$-0.751604\pi$
$43$		−	9.22676i		−	1.40707i	0.710662	−	0.703534i	$-0.248396\pi$
$44$	−1.47218	−	0.371595i	−0.221939	−	0.0560200i
$45$		−	1.00000i		−	0.149071i
$46$	1.91833	+	2.46271i	0.282843	+	0.363107i
$47$	−2.62393			−0.382740			−0.191370	−	0.981518i	$-0.561293\pi$
$47$	−2.62393			−0.382740			−0.191370	+	0.981518i	$0.561293\pi$
$48$	1.89835	−	3.52084i	0.274003	−	0.508189i
$49$	1.00000			0.142857
$50$	−0.869059	−	1.11568i	−0.122904	−	0.157781i
$51$		−	5.26887i		−	0.737789i
$52$	−1.47218	−	0.371595i	−0.204154	−	0.0515309i
$53$		−	2.62309i		−	0.360309i	−0.983638	−	0.180155i	$-0.942340\pi$
$53$		−	2.62309i		−	0.360309i	0.983638	−	0.180155i	$-0.0576598\pi$
$54$	1.11568	−	0.869059i	0.151824	−	0.118264i
$55$	−0.759176			−0.102367
$56$	2.58888	−	1.13917i	0.345953	−	0.152228i
$57$	−1.64700			−0.218151
$58$	−1.55375	+	1.21030i	−0.204017	+	0.158920i
$59$			8.77025i			1.14179i	0.821023	+	0.570894i	$0.193403\pi$
$59$			8.77025i			1.14179i	−0.821023	+	0.570894i	$0.806597\pi$
$60$	0.489471	−	1.93918i	0.0631905	−	0.250347i
$61$			2.97609i			0.381049i	0.981682	+	0.190524i	$0.0610188\pi$
$61$			2.97609i			0.381049i	−0.981682	+	0.190524i	$0.938981\pi$
$62$	3.06189	+	3.93078i	0.388860	+	0.499210i
$63$	1.00000			0.125988
$64$	5.40458	−	5.89835i	0.675573	−	0.737293i
$65$	−0.759176			−0.0941642
$66$	−0.659769	−	0.846995i	−0.0812120	−	0.104258i
$67$			6.36407i			0.777494i	0.921344	+	0.388747i	$0.127092\pi$
$67$			6.36407i			0.777494i	−0.921344	+	0.388747i	$0.872908\pi$
$68$	2.57896	−	10.2173i	0.312745	−	1.23903i
$69$			2.20737i			0.265736i
$70$	1.11568	−	0.869059i	0.133349	−	0.103872i
$71$	8.77979			1.04197			0.520985	−	0.853566i	$-0.325565\pi$
$71$	8.77979			1.04197			0.520985	+	0.853566i	$0.325565\pi$
$72$	2.58888	−	1.13917i	0.305102	−	0.134252i
$73$	4.59136			0.537378			0.268689	−	0.963227i	$-0.413410\pi$
$73$	4.59136			0.537378			0.268689	+	0.963227i	$0.413410\pi$
$74$	−12.7335	+	9.91881i	−1.48024	+	1.15304i
$75$		−	1.00000i		−	0.115470i
$76$	−3.19384	−	0.806162i	−0.366358	−	0.0924731i
$77$		−	0.759176i		−	0.0865161i
$78$	−0.659769	−	0.846995i	−0.0747041	−	0.0959033i
$79$	15.8524			1.78353			0.891765	−	0.452498i	$-0.149467\pi$
$79$	15.8524			1.78353			0.891765	+	0.452498i	$0.149467\pi$
$80$	1.89835	−	3.52084i	0.212242	−	0.393641i
$81$	1.00000			0.111111
$82$	−1.39051	−	1.78510i	−0.153556	−	0.197132i
$83$			2.86269i			0.314221i	0.987581	+	0.157111i	$0.0502179\pi$
$83$			2.86269i			0.314221i	−0.987581	+	0.157111i	$0.949782\pi$
$84$	1.93918	+	0.489471i	0.211582	+	0.0534057i
$85$		−	5.26887i		−	0.571489i
$86$	10.2941	−	8.01860i	1.11004	−	0.864668i
$87$	−1.39265			−0.149308
$88$	−0.864831	−	1.96541i	−0.0921913	−	0.209514i
$89$	−15.0005			−1.59004			−0.795022	−	0.606580i	$-0.792541\pi$
$89$	−15.0005			−1.59004			−0.795022	+	0.606580i	$0.792541\pi$
$90$	1.11568	−	0.869059i	0.117603	−	0.0916069i
$91$		−	0.759176i		−	0.0795833i
$92$	−1.08044	+	4.28048i	−0.112644	+	0.446271i
$93$			3.52322i			0.365341i
$94$	−2.28035	−	2.92746i	−0.235201	−	0.301945i
$95$	−1.64700			−0.168979
$96$	5.57789	−	0.941874i	0.569291	−	0.0961296i
$97$	−6.10971			−0.620347			−0.310174	−	0.950680i	$-0.600387\pi$
$97$	−6.10971			−0.620347			−0.310174	+	0.950680i	$0.600387\pi$
$98$	0.869059	+	1.11568i	0.0877883	+	0.112700i
$99$		−	0.759176i		−	0.0763001i
$100$	0.489471	−	1.93918i	0.0489471	−	0.193918i
$101$			18.7638i			1.86707i	0.358489	+	0.933534i	$0.383292\pi$
$101$			18.7638i			1.86707i	−0.358489	+	0.933534i	$0.616708\pi$
$102$	5.87836	−	4.57896i	0.582044	−	0.453385i
$103$	−2.87928			−0.283703			−0.141852	−	0.989888i	$-0.545306\pi$
$103$	−2.87928			−0.283703			−0.141852	+	0.989888i	$0.545306\pi$
$104$	−0.864831	−	1.96541i	−0.0848036	−	0.192725i
$105$	1.00000			0.0975900
$106$	2.92652	−	2.27962i	0.284249	−	0.221416i
$107$			6.05806i			0.585654i	0.956165	+	0.292827i	$0.0945961\pi$
$107$			6.05806i			0.585654i	−0.956165	+	0.292827i	$0.905404\pi$
$108$	1.93918	+	0.489471i	0.186598	+	0.0470994i
$109$			5.64799i			0.540980i	0.962723	+	0.270490i	$0.0871857\pi$
$109$			5.64799i			0.540980i	−0.962723	+	0.270490i	$0.912814\pi$
$110$	−0.659769	−	0.846995i	−0.0629065	−	0.0807578i
$111$	−11.4133			−1.08330
$112$	3.52084	+	1.89835i	0.332688	+	0.179377i
$113$	−5.92320			−0.557208			−0.278604	−	0.960406i	$-0.589872\pi$
$113$	−5.92320			−0.557208			−0.278604	+	0.960406i	$0.589872\pi$
$114$	−1.43135	−	1.83753i	−0.134058	−	0.172100i
$115$			2.20737i			0.205838i
$116$	−2.70060	−	0.681663i	−0.250745	−	0.0632909i
$117$		−	0.759176i		−	0.0701858i
$118$	−9.78477	+	7.62187i	−0.900761	+	0.701650i
$119$	5.26887			0.482997
$120$	2.58888	−	1.13917i	0.236331	−	0.103992i
$121$	10.4237			0.947605
$122$	−3.32035	+	2.58639i	−0.300610	+	0.234161i
$123$		−	1.60002i		−	0.144269i
$124$	−1.72452	+	6.83216i	−0.154866	+	0.613546i
$125$		−	1.00000i		−	0.0894427i
$126$	0.869059	+	1.11568i	0.0774220	+	0.0993924i
$127$	8.08979			0.717852			0.358926	−	0.933366i	$-0.383143\pi$
$127$	8.08979			0.717852			0.358926	+	0.933366i	$0.383143\pi$
$128$	11.2776	+	0.903757i	0.996804	+	0.0798815i
$129$	9.22676			0.812371
$130$	−0.659769	−	0.846995i	−0.0578656	−	0.0742864i
$131$		−	7.28585i		−	0.636567i	−0.947996	−	0.318284i	$-0.896894\pi$
$131$		−	7.28585i		−	0.636567i	0.947996	−	0.318284i	$-0.103106\pi$
$132$	0.371595	−	1.47218i	0.0323432	−	0.128137i
$133$		−	1.64700i		−	0.142813i
$134$	−7.10024	+	5.53075i	−0.613368	+	0.477784i
$135$	1.00000			0.0860663
$136$	13.6405	−	6.00214i	1.16966	−	0.514679i
$137$	−8.53031			−0.728793			−0.364397	−	0.931244i	$-0.618725\pi$
$137$	−8.53031			−0.728793			−0.364397	+	0.931244i	$0.618725\pi$
$138$	−2.46271	+	1.91833i	−0.209640	+	0.163299i
$139$		−	6.26877i		−	0.531710i	−0.964013	−	0.265855i	$-0.914346\pi$
$139$		−	6.26877i		−	0.531710i	0.964013	−	0.265855i	$-0.0856542\pi$
$140$	1.93918	+	0.489471i	0.163891	+	0.0413679i
$141$		−	2.62393i		−	0.220975i
$142$	7.63016	+	9.79541i	0.640309	+	0.822013i
$143$	−0.576348			−0.0481967
$144$	3.52084	+	1.89835i	0.293403	+	0.158196i
$145$	−1.39265			−0.115653
$146$	3.99017	+	5.12248i	0.330229	+	0.423939i
$147$			1.00000i			0.0824786i
$148$	−22.1324	−	5.58647i	−1.81927	−	0.459205i
$149$			14.4120i			1.18068i	0.807155	+	0.590340i	$0.201006\pi$
$149$			14.4120i			1.18068i	−0.807155	+	0.590340i	$0.798994\pi$
$150$	1.11568	−	0.869059i	0.0910947	−	0.0709584i
$151$	20.0306			1.63006			0.815032	−	0.579416i	$-0.196719\pi$
$151$	20.0306			1.63006			0.815032	+	0.579416i	$0.196719\pi$
$152$	−1.87622	−	4.26390i	−0.152181	−	0.345848i
$153$	5.26887			0.425963
$154$	0.846995	−	0.659769i	0.0682528	−	0.0531657i
$155$			3.52322i			0.282992i
$156$	0.371595	−	1.47218i	0.0297514	−	0.117869i
$157$			14.6849i			1.17198i	0.810317	+	0.585991i	$0.199295\pi$
$157$			14.6849i			1.17198i	−0.810317	+	0.585991i	$0.800705\pi$
$158$	13.7766	+	17.6861i	1.09601	+	1.40703i
$159$	2.62309			0.208025
$160$	5.57789	−	0.941874i	0.440971	−	0.0744616i
$161$	−2.20737			−0.173965
$162$	0.869059	+	1.11568i	0.0682798	+	0.0876559i
$163$		−	10.5669i		−	0.827664i	−0.910353	−	0.413832i	$-0.864190\pi$
$163$		−	10.5669i		−	0.827664i	0.910353	−	0.413832i	$-0.135810\pi$
$164$	0.783164	−	3.10272i	0.0611548	−	0.242282i
$165$		−	0.759176i		−	0.0591018i
$166$	−3.19384	+	2.48785i	−0.247890	+	0.193094i
$167$	−8.60243			−0.665676			−0.332838	−	0.942984i	$-0.608006\pi$
$167$	−8.60243			−0.665676			−0.332838	+	0.942984i	$0.608006\pi$
$168$	1.13917	+	2.58888i	0.0878889	+	0.199736i
$169$	12.4237			0.955666
$170$	5.87836	−	4.57896i	0.450850	−	0.351190i
$171$		−	1.64700i		−	0.125950i
$172$	17.8923	+	4.51623i	1.36428	+	0.344360i
$173$		−	0.318314i		−	0.0242010i	−0.999927	−	0.0121005i	$-0.996148\pi$
$173$		−	0.318314i		−	0.0242010i	0.999927	−	0.0121005i	$-0.00385180\pi$
$174$	−1.21030	−	1.55375i	−0.0917524	−	0.117789i
$175$	1.00000			0.0755929
$176$	1.44118	−	2.67293i	0.108633	−	0.201480i
$177$	−8.77025			−0.659212
$178$	−13.0363	−	16.7357i	−0.977111	−	1.25439i
$179$			12.9092i			0.964882i	0.875928	+	0.482441i	$0.160250\pi$
$179$			12.9092i			0.964882i	−0.875928	+	0.482441i	$0.839750\pi$
$180$	1.93918	+	0.489471i	0.144538	+	0.0364830i
$181$		−	10.0187i		−	0.744684i	−0.928096	−	0.372342i	$-0.878555\pi$
$181$		−	10.0187i		−	0.744684i	0.928096	−	0.372342i	$-0.121445\pi$
$182$	0.846995	−	0.659769i	0.0627835	−	0.0489053i
$183$	−2.97609			−0.219999
$184$	−5.71460	+	2.51457i	−0.421286	+	0.185376i
$185$	−11.4133			−0.839120
$186$	−3.93078	+	3.06189i	−0.288219	+	0.224509i
$187$		−	4.00000i		−	0.292509i
$188$	1.28434	−	5.08828i	0.0936702	−	0.371101i
$189$			1.00000i			0.0727393i
$190$	−1.43135	−	1.83753i	−0.103841	−	0.133308i
$191$	2.08846			0.151115			0.0755577	−	0.997141i	$-0.475926\pi$
$191$	2.08846			0.151115			0.0755577	+	0.997141i	$0.475926\pi$
$192$	5.89835	+	5.40458i	0.425676	+	0.390042i
$193$	2.39763			0.172585			0.0862925	−	0.996270i	$-0.472498\pi$
$193$	2.39763			0.172585			0.0862925	+	0.996270i	$0.472498\pi$
$194$	−5.30970	−	6.81647i	−0.381215	−	0.489394i
$195$		−	0.759176i		−	0.0543657i
$196$	−0.489471	+	1.93918i	−0.0349622	+	0.138513i
$197$			7.00832i			0.499322i	0.968333	+	0.249661i	$0.0803192\pi$
$197$			7.00832i			0.499322i	−0.968333	+	0.249661i	$0.919681\pi$
$198$	0.846995	−	0.659769i	0.0601933	−	0.0468877i
$199$	22.6390			1.60484			0.802419	−	0.596761i	$-0.203546\pi$
$199$	22.6390			1.60484			0.802419	+	0.596761i	$0.203546\pi$
$200$	2.58888	−	1.13917i	0.183061	−	0.0805515i
$201$	−6.36407			−0.448887
$202$	−20.9343	+	16.3069i	−1.47294	+	1.14735i
$203$		−	1.39265i		−	0.0977450i
$204$	10.2173	+	2.57896i	0.715353	+	0.180563i
$205$		−	1.60002i		−	0.111750i
$206$	−2.50226	−	3.21234i	−0.174341	−	0.223815i
$207$	−2.20737			−0.153423
$208$	1.44118	−	2.67293i	0.0999278	−	0.185335i
$209$	−1.25037			−0.0864897
$210$	0.869059	+	1.11568i	0.0599708	+	0.0769890i
$211$		−	27.5670i		−	1.89779i	−0.315594	−	0.948894i	$-0.602204\pi$
$211$		−	27.5670i		−	1.89779i	0.315594	−	0.948894i	$-0.397796\pi$
$212$	5.08664	+	1.28393i	0.349352	+	0.0881805i
$213$			8.77979i			0.601581i
$214$	−6.75884	+	5.26481i	−0.462025	+	0.359895i
$215$	9.22676			0.629260
$216$	1.13917	+	2.58888i	0.0775107	+	0.176151i
$217$	−3.52322			−0.239172
$218$	−6.30134	+	4.90844i	−0.426781	+	0.332442i
$219$			4.59136i			0.310255i
$220$	0.371595	−	1.47218i	0.0250529	−	0.0992543i
$221$		−	4.00000i		−	0.269069i
$222$	−9.91881	−	12.7335i	−0.665707	−	0.854618i
$223$	−16.5839			−1.11054			−0.555269	−	0.831670i	$-0.687385\pi$
$223$	−16.5839			−1.11054			−0.555269	+	0.831670i	$0.687385\pi$
$224$	0.941874	+	5.57789i	0.0629316	+	0.372689i
$225$	1.00000			0.0666667
$226$	−5.14762	−	6.60838i	−0.342414	−	0.439583i
$227$			15.9885i			1.06119i	0.847625	+	0.530595i	$0.178032\pi$
$227$			15.9885i			1.06119i	−0.847625	+	0.530595i	$0.821968\pi$
$228$	0.806162	−	3.19384i	0.0533894	−	0.211517i
$229$			7.71525i			0.509838i	0.966962	+	0.254919i	$0.0820488\pi$
$229$			7.71525i			0.509838i	−0.966962	+	0.254919i	$0.917951\pi$
$230$	−2.46271	+	1.91833i	−0.162386	+	0.126491i
$231$	0.759176			0.0499501
$232$	−1.58647	−	3.60541i	−0.104157	−	0.236707i
$233$	22.7547			1.49071			0.745353	−	0.666670i	$-0.232281\pi$
$233$	22.7547			1.49071			0.745353	+	0.666670i	$0.232281\pi$
$234$	0.846995	−	0.659769i	0.0553698	−	0.0431304i
$235$		−	2.62393i		−	0.171167i
$236$	−17.0071	−	4.29279i	−1.10707	−	0.279437i
$237$			15.8524i			1.02972i
$238$	4.57896	+	5.87836i	0.296810	+	0.381037i
$239$	−1.92129			−0.124278			−0.0621388	−	0.998068i	$-0.519792\pi$
$239$	−1.92129			−0.124278			−0.0621388	+	0.998068i	$0.519792\pi$
$240$	3.52084	+	1.89835i	0.227269	+	0.122538i
$241$	13.8987			0.895292			0.447646	−	0.894211i	$-0.352263\pi$
$241$	13.8987			0.895292			0.447646	+	0.894211i	$0.352263\pi$
$242$	9.05877	+	11.6294i	0.582320	+	0.747568i
$243$			1.00000i			0.0641500i
$244$	−5.77116	−	1.45671i	−0.369461	−	0.0932562i
$245$			1.00000i			0.0638877i
$246$	1.78510	−	1.39051i	0.113814	−	0.0886558i
$247$	−1.25037			−0.0795589
$248$	−9.12120	+	4.01355i	−0.579197	+	0.254861i
$249$	−2.86269			−0.181416
$250$	1.11568	−	0.869059i	0.0705616	−	0.0549641i
$251$		−	8.35551i		−	0.527395i	−0.964605	−	0.263698i	$-0.915058\pi$
$251$		−	8.35551i		−	0.527395i	0.964605	−	0.263698i	$-0.0849421\pi$
$252$	−0.489471	+	1.93918i	−0.0308338	+	0.122157i
$253$			1.67578i			0.105355i
$254$	7.03050	+	9.02559i	0.441133	+	0.566316i
$255$	5.26887			0.329949
$256$	8.79256	+	13.3675i	0.549535	+	0.835471i
$257$	−22.7154			−1.41695			−0.708474	−	0.705737i	$-0.750616\pi$
$257$	−22.7154			−1.41695			−0.708474	+	0.705737i	$0.750616\pi$
$258$	8.01860	+	10.2941i	0.499216	+	0.640882i
$259$		−	11.4133i		−	0.709186i
$260$	0.371595	−	1.47218i	0.0230453	−	0.0913006i
$261$		−	1.39265i		−	0.0862030i
$262$	8.12865	−	6.33183i	0.502190	−	0.391182i
$263$	6.68922			0.412475			0.206238	−	0.978502i	$-0.433878\pi$
$263$	6.68922			0.412475			0.206238	+	0.978502i	$0.433878\pi$
$264$	1.96541	−	0.864831i	0.120963	−	0.0532266i
$265$	2.62309			0.161135
$266$	1.83753	−	1.43135i	0.112666	−	0.0877614i
$267$		−	15.0005i		−	0.918013i
$268$	−12.3411	−	3.11503i	−0.753851	−	0.190281i
$269$		−	22.9310i		−	1.39813i	−0.715060	−	0.699063i	$-0.753601\pi$
$269$		−	22.9310i		−	1.39813i	0.715060	−	0.699063i	$-0.246399\pi$
$270$	0.869059	+	1.11568i	0.0528893	+	0.0678980i
$271$	−13.9109			−0.845027			−0.422513	−	0.906357i	$-0.638852\pi$
$271$	−13.9109			−0.845027			−0.422513	+	0.906357i	$0.638852\pi$
$272$	18.5508	+	10.0021i	1.12481	+	0.606469i
$273$	0.759176			0.0459474
$274$	−7.41335	−	9.51707i	−0.447857	−	0.574947i
$275$		−	0.759176i		−	0.0457800i
$276$	−4.28048	−	1.08044i	−0.257655	−	0.0650350i
$277$		−	6.88548i		−	0.413708i	−0.978372	−	0.206854i	$-0.933677\pi$
$277$		−	6.88548i		−	0.413708i	0.978372	−	0.206854i	$-0.0663225\pi$
$278$	6.99392	−	5.44793i	0.419467	−	0.326745i
$279$	−3.52322			−0.210930
$280$	1.13917	+	2.58888i	0.0680784	+	0.154715i
$281$	−4.53774			−0.270699			−0.135349	−	0.990798i	$-0.543216\pi$
$281$	−4.53774			−0.270699			−0.135349	+	0.990798i	$0.543216\pi$
$282$	2.92746	−	2.28035i	0.174328	−	0.135793i
$283$		−	8.07320i		−	0.479902i	−0.970785	−	0.239951i	$-0.922869\pi$
$283$		−	8.07320i		−	0.479902i	0.970785	−	0.239951i	$-0.0771314\pi$
$284$	−4.29746	+	17.0256i	−0.255007	+	1.01028i
$285$		−	1.64700i		−	0.0975601i
$286$	−0.500881	−	0.643018i	−0.0296177	−	0.0380225i
$287$	1.60002			0.0944461
$288$	0.941874	+	5.57789i	0.0555004	+	0.328680i
$289$	10.7610			0.633000
$290$	−1.21030	−	1.55375i	−0.0710711	−	0.0912394i
$291$		−	6.10971i		−	0.358158i
$292$	−2.24734	+	8.90348i	−0.131516	+	0.521036i
$293$		−	8.07931i		−	0.471999i	−0.971753	−	0.235999i	$-0.924164\pi$
$293$		−	8.07931i		−	0.471999i	0.971753	−	0.235999i	$-0.0758363\pi$
$294$	−1.11568	+	0.869059i	−0.0650676	+	0.0506846i
$295$	−8.77025			−0.510624
$296$	−13.0017	−	29.5476i	−0.755706	−	1.71742i
$297$	0.759176			0.0440519
$298$	−16.0792	+	12.5249i	−0.931442	+	0.725549i
$299$			1.67578i			0.0969129i
$300$	1.93918	+	0.489471i	0.111959	+	0.0282596i
$301$			9.22676i			0.531821i
$302$	17.4078	+	22.3476i	1.00170	+	1.28596i
$303$	−18.7638			−1.07795
$304$	3.12659	−	5.79883i	0.179322	−	0.332586i
$305$	−2.97609			−0.170410
$306$	4.57896	+	5.87836i	0.261762	+	0.336043i
$307$			14.0669i			0.802841i	0.915894	+	0.401421i	$0.131483\pi$
$307$			14.0669i			0.802841i	−0.915894	+	0.401421i	$0.868517\pi$
$308$	1.47218	+	0.371595i	0.0838852	+	0.0211736i
$309$		−	2.87928i		−	0.163796i
$310$	−3.93078	+	3.06189i	−0.223253	+	0.173904i
$311$	17.0926			0.969232			0.484616	−	0.874727i	$-0.338959\pi$
$311$	17.0926			0.969232			0.484616	+	0.874727i	$0.338959\pi$
$312$	1.96541	−	0.864831i	0.111270	−	0.0489614i
$313$	−10.6013			−0.599222			−0.299611	−	0.954062i	$-0.596857\pi$
$313$	−10.6013			−0.599222			−0.299611	+	0.954062i	$0.596857\pi$
$314$	−16.3836	+	12.7620i	−0.924580	+	0.720204i
$315$			1.00000i			0.0563436i
$316$	−7.75928	+	30.7406i	−0.436494	+	1.72929i
$317$		−	0.755148i		−	0.0424133i	−0.999775	−	0.0212067i	$-0.993249\pi$
$317$		−	0.755148i		−	0.0424133i	0.999775	−	0.0212067i	$-0.00675080\pi$
$318$	2.27962	+	2.92652i	0.127835	+	0.164111i
$319$	−1.05727			−0.0591956
$320$	5.89835	+	5.40458i	0.329728	+	0.302125i
$321$	−6.05806			−0.338128
$322$	−1.91833	−	2.46271i	−0.106905	−	0.137241i
$323$		−	8.67786i		−	0.482849i
$324$	−0.489471	+	1.93918i	−0.0271929	+	0.107732i
$325$		−	0.759176i		−	0.0421115i
$326$	11.7893	−	9.18327i	0.652947	−	0.508614i
$327$	−5.64799			−0.312335
$328$	4.14225	−	1.82269i	0.228718	−	0.100641i
$329$	2.62393			0.144662
$330$	0.846995	−	0.659769i	0.0466256	−	0.0363191i
$331$		−	19.8656i		−	1.09191i	−0.837814	−	0.545956i	$-0.816167\pi$
$331$		−	19.8656i		−	1.09191i	0.837814	−	0.545956i	$-0.183833\pi$
$332$	−5.55127	−	1.40121i	−0.304666	−	0.0769011i
$333$		−	11.4133i		−	0.625443i
$334$	−7.47603	−	9.59754i	−0.409070	−	0.525154i
$335$	−6.36407			−0.347706
$336$	−1.89835	+	3.52084i	−0.103563	+	0.192077i
$337$	−0.827020			−0.0450506			−0.0225253	−	0.999746i	$-0.507171\pi$
$337$	−0.827020			−0.0450506			−0.0225253	+	0.999746i	$0.507171\pi$
$338$	10.7969	+	13.8608i	0.587273	+	0.753927i
$339$		−	5.92320i		−	0.321704i
$340$	10.2173	+	2.57896i	0.554110	+	0.139864i
$341$			2.67475i			0.144846i
$342$	1.83753	−	1.43135i	0.0993620	−	0.0773983i
$343$	−1.00000			−0.0539949
$344$	10.5108	+	23.8870i	0.566707	+	1.28790i
$345$	−2.20737			−0.118841
$346$	0.355136	−	0.276634i	0.0190922	−	0.0148719i
$347$		−	33.6178i		−	1.80470i	−0.431004	−	0.902350i	$-0.641840\pi$
$347$		−	33.6178i		−	1.80470i	0.431004	−	0.902350i	$-0.358160\pi$
$348$	0.681663	−	2.70060i	0.0365410	−	0.144767i
$349$		−	22.3359i		−	1.19562i	−0.801640	−	0.597808i	$-0.796039\pi$
$349$		−	22.3359i		−	1.19562i	0.801640	−	0.597808i	$-0.203961\pi$
$350$	0.869059	+	1.11568i	0.0464532	+	0.0596355i
$351$	0.759176			0.0405218
$352$	4.23460	−	0.715048i	0.225705	−	0.0381122i
$353$	17.0337			0.906613			0.453306	−	0.891355i	$-0.350244\pi$
$353$	17.0337			0.906613			0.453306	+	0.891355i	$0.350244\pi$
$354$	−7.62187	−	9.78477i	−0.405098	−	0.520054i
$355$			8.77979i			0.465983i
$356$	7.34229	−	29.0886i	0.389141	−	1.54169i
$357$			5.26887i			0.278858i
$358$	−14.4025	+	11.2189i	−0.761198	+	0.592937i
$359$	28.5845			1.50863			0.754316	−	0.656512i	$-0.227969\pi$
$359$	28.5845			1.50863			0.754316	+	0.656512i	$0.227969\pi$
$360$	1.13917	+	2.58888i	0.0600395	+	0.136446i
$361$	16.2874			0.857230
$362$	11.1776	−	8.70684i	0.587483	−	0.457621i
$363$			10.4237i			0.547100i
$364$	1.47218	+	0.371595i	0.0771631	+	0.0194769i
$365$			4.59136i			0.240323i
$366$	−2.58639	−	3.32035i	−0.135193	−	0.173558i
$367$	−30.3026			−1.58178			−0.790891	−	0.611957i	$-0.790382\pi$
$367$	−30.3026			−1.58178			−0.790891	+	0.611957i	$0.790382\pi$
$368$	−7.77178	−	4.19035i	−0.405132	−	0.218437i
$369$	1.60002			0.0832937
$370$	−9.91881	−	12.7335i	−0.515654	−	0.661984i
$371$			2.62309i			0.136184i
$372$	−6.83216	−	1.72452i	−0.354231	−	0.0894121i
$373$			18.9208i			0.979682i	0.871812	+	0.489841i	$0.162945\pi$
$373$			18.9208i			0.979682i	−0.871812	+	0.489841i	$0.837055\pi$
$374$	4.46271	−	3.47624i	0.230761	−	0.179752i
$375$	1.00000			0.0516398
$376$	6.79305	−	2.98911i	0.350325	−	0.154151i
$377$	−1.05727			−0.0544521
$378$	−1.11568	+	0.869059i	−0.0573842	+	0.0446996i
$379$		−	26.1328i		−	1.34235i	−0.741297	−	0.671177i	$-0.765789\pi$
$379$		−	26.1328i		−	1.34235i	0.741297	−	0.671177i	$-0.234211\pi$
$380$	0.806162	−	3.19384i	0.0413552	−	0.163840i
$381$			8.08979i			0.414452i
$382$	1.81499	+	2.33004i	0.0928631	+	0.119215i
$383$	2.42915			0.124124			0.0620618	−	0.998072i	$-0.480232\pi$
$383$	2.42915			0.124124			0.0620618	+	0.998072i	$0.480232\pi$
$384$	−0.903757	+	11.2776i	−0.0461196	+	0.575505i
$385$	0.759176			0.0386912
$386$	2.08368	+	2.67498i	0.106057	+	0.136153i
$387$			9.22676i			0.469022i
$388$	2.99053	−	11.8478i	0.151821	−	0.601483i
$389$		−	11.9716i		−	0.606985i	−0.952834	−	0.303493i	$-0.901847\pi$
$389$		−	11.9716i		−	0.606985i	0.952834	−	0.303493i	$-0.0981528\pi$
$390$	0.846995	−	0.659769i	0.0428893	−	0.0334087i
$391$	−11.6303			−0.588171
$392$	−2.58888	+	1.13917i	−0.130758	+	0.0575368i
$393$	7.28585			0.367522
$394$	−7.81902	+	6.09065i	−0.393917	+	0.306842i
$395$			15.8524i			0.797619i
$396$	1.47218	+	0.371595i	0.0739798	+	0.0186733i
$397$		−	9.76882i		−	0.490283i	−0.969487	−	0.245142i	$-0.921166\pi$
$397$		−	9.76882i		−	0.490283i	0.969487	−	0.245142i	$-0.0788344\pi$
$398$	19.6747	+	25.2579i	0.986202	+	1.26606i
$399$	1.64700			0.0824534
$400$	3.52084	+	1.89835i	0.176042	+	0.0949173i
$401$	−36.6062			−1.82803			−0.914014	−	0.405683i	$-0.867034\pi$
$401$	−36.6062			−1.82803			−0.914014	+	0.405683i	$0.867034\pi$
$402$	−5.53075	−	7.10024i	−0.275849	−	0.354128i
$403$			2.67475i			0.133239i
$404$	−36.3864	−	9.18435i	−1.81029	−	0.456938i
$405$			1.00000i			0.0496904i
$406$	1.55375	−	1.21030i	0.0771113	−	0.0600661i
$407$	−8.66468			−0.429492
$408$	6.00214	+	13.6405i	0.297150	+	0.675304i
$409$	−28.8414			−1.42612			−0.713058	−	0.701105i	$-0.752690\pi$
$409$	−28.8414			−1.42612			−0.713058	+	0.701105i	$0.752690\pi$
$410$	1.78510	−	1.39051i	0.0881600	−	0.0686725i
$411$		−	8.53031i		−	0.420769i
$412$	1.40932	−	5.58343i	0.0694324	−	0.275076i
$413$		−	8.77025i		−	0.431556i
$414$	−1.91833	−	2.46271i	−0.0942809	−	0.121036i
$415$	−2.86269			−0.140524
$416$	4.23460	−	0.715048i	0.207618	−	0.0350581i
$417$	6.26877			0.306983
$418$	−1.08664	−	1.39501i	−0.0531494	−	0.0682319i
$419$			3.79286i			0.185294i	0.995699	+	0.0926468i	$0.0295327\pi$
$419$			3.79286i			0.185294i	−0.995699	+	0.0926468i	$0.970467\pi$
$420$	−0.489471	+	1.93918i	−0.0238838	+	0.0946223i
$421$		−	26.4659i		−	1.28987i	−0.764238	−	0.644935i	$-0.776885\pi$
$421$		−	26.4659i		−	1.28987i	0.764238	−	0.644935i	$-0.223115\pi$
$422$	30.7558	−	23.9573i	1.49717	−	1.16622i
$423$	2.62393			0.127580
$424$	2.98815	+	6.79086i	0.145117	+	0.329793i
$425$	5.26887			0.255578
$426$	−9.79541	+	7.63016i	−0.474589	+	0.369682i
$427$		−	2.97609i		−	0.144023i
$428$	−11.7477	−	2.96525i	−0.567845	−	0.143331i
$429$		−	0.576348i		−	0.0278263i
$430$	8.01860	+	10.2941i	0.386691	+	0.496425i
$431$	−14.2288			−0.685376			−0.342688	−	0.939449i	$-0.611337\pi$
$431$	−14.2288			−0.685376			−0.342688	+	0.939449i	$0.611337\pi$
$432$	−1.89835	+	3.52084i	−0.0913342	+	0.169396i
$433$	38.8923			1.86904			0.934521	−	0.355907i	$-0.115828\pi$
$433$	38.8923			1.86904			0.934521	+	0.355907i	$0.115828\pi$
$434$	−3.06189	−	3.93078i	−0.146975	−	0.188683i
$435$		−	1.39265i		−	0.0667726i
$436$	−10.9525	−	2.76453i	−0.524528	−	0.132397i
$437$			3.63554i			0.173912i
$438$	−5.12248	+	3.99017i	−0.244761	+	0.190658i
$439$	31.0557			1.48221			0.741105	−	0.671389i	$-0.234302\pi$
$439$	31.0557			1.48221			0.741105	+	0.671389i	$0.234302\pi$
$440$	1.96541	−	0.864831i	0.0936974	−	0.0412292i
$441$	−1.00000			−0.0476190
$442$	4.46271	−	3.47624i	0.212269	−	0.165348i
$443$		−	14.7071i		−	0.698755i	−0.936982	−	0.349377i	$-0.886393\pi$
$443$		−	14.7071i		−	0.698755i	0.936982	−	0.349377i	$-0.113607\pi$
$444$	5.58647	−	22.1324i	0.265122	−	1.05036i
$445$		−	15.0005i		−	0.711090i
$446$	−14.4124	−	18.5023i	−0.682446	−	0.876107i
$447$	−14.4120			−0.681666
$448$	−5.40458	+	5.89835i	−0.255343	+	0.278671i
$449$	−37.7617			−1.78208			−0.891042	−	0.453920i	$-0.850025\pi$
$449$	−37.7617			−1.78208			−0.891042	+	0.453920i	$0.850025\pi$
$450$	0.869059	+	1.11568i	0.0409679	+	0.0525935i
$451$		−	1.21470i		−	0.0571978i
$452$	2.89924	−	11.4862i	0.136369	−	0.540263i
$453$			20.0306i			0.941118i
$454$	−17.8380	+	13.8949i	−0.837177	+	0.652121i
$455$	0.759176			0.0355907
$456$	4.26390	−	1.87622i	0.199675	−	0.0878620i
$457$	21.8085			1.02016			0.510080	−	0.860127i	$-0.329616\pi$
$457$	21.8085			1.02016			0.510080	+	0.860127i	$0.329616\pi$
$458$	−8.60773	+	6.70501i	−0.402213	+	0.313304i
$459$			5.26887i			0.245930i
$460$	−4.28048	−	1.08044i	−0.199578	−	0.0503759i
$461$		−	29.4253i		−	1.37047i	−0.728321	−	0.685236i	$-0.759699\pi$
$461$		−	29.4253i		−	1.37047i	0.728321	−	0.685236i	$-0.240301\pi$
$462$	0.659769	+	0.846995i	0.0306952	+	0.0394058i
$463$	−16.5881			−0.770913			−0.385457	−	0.922726i	$-0.625956\pi$
$463$	−16.5881			−0.770913			−0.385457	+	0.922726i	$0.625956\pi$
$464$	2.64374	−	4.90330i	0.122732	−	0.227630i
$465$	−3.52322			−0.163386
$466$	19.7751	+	25.3868i	0.916066	+	1.17602i
$467$		−	29.4748i		−	1.36393i	−0.731384	−	0.681966i	$-0.761125\pi$
$467$		−	29.4748i		−	1.36393i	0.731384	−	0.681966i	$-0.238875\pi$
$468$	1.47218	+	0.371595i	0.0680515	+	0.0171770i
$469$		−	6.36407i		−	0.293865i
$470$	2.92746	−	2.28035i	0.135034	−	0.105185i
$471$	−14.6849			−0.676644
$472$	−9.99080	−	22.7051i	−0.459864	−	1.04509i
$473$	7.00473			0.322078
$474$	−17.6861	+	13.7766i	−0.812351	+	0.632782i
$475$		−	1.64700i		−	0.0755698i
$476$	−2.57896	+	10.2173i	−0.118207	+	0.468309i
$477$			2.62309i			0.120103i
$478$	−1.66971	−	2.14354i	−0.0763708	−	0.0980430i
$479$	6.48363			0.296244			0.148122	−	0.988969i	$-0.452677\pi$
$479$	6.48363			0.296244			0.148122	+	0.988969i	$0.452677\pi$
$480$	0.941874	+	5.57789i	0.0429905	+	0.254595i
$481$	−8.66468			−0.395075
$482$	12.0788	+	15.5064i	0.550173	+	0.706298i
$483$		−	2.20737i		−	0.100439i
$484$	−5.10208	+	20.2133i	−0.231913	+	0.918788i
$485$		−	6.10971i		−	0.277428i
$486$	−1.11568	+	0.869059i	−0.0506081	+	0.0394213i
$487$	4.21121			0.190828			0.0954142	−	0.995438i	$-0.469582\pi$
$487$	4.21121			0.190828			0.0954142	+	0.995438i	$0.469582\pi$
$488$	−3.39027	−	7.70472i	−0.153470	−	0.348776i
$489$	10.5669			0.477852
$490$	−1.11568	+	0.869059i	−0.0504012	+	0.0392601i
$491$			21.1287i			0.953523i	0.879033	+	0.476762i	$0.158190\pi$
$491$			21.1287i			0.953523i	−0.879033	+	0.476762i	$0.841810\pi$
$492$	3.10272	+	0.783164i	0.139882	+	0.0353077i
$493$		−	7.33770i		−	0.330474i
$494$	−1.08664	−	1.39501i	−0.0488904	−	0.0627643i
$495$	0.759176			0.0341224
$496$	−12.4047	−	6.68830i	−0.556987	−	0.300313i
$497$	−8.77979			−0.393827
$498$	−2.48785	−	3.19384i	−0.111483	−	0.143119i
$499$			31.4442i			1.40763i	0.710381	+	0.703817i	$0.248523\pi$
$499$			31.4442i			1.40763i	−0.710381	+	0.703817i	$0.751477\pi$
$500$	1.93918	+	0.489471i	0.0867228	+	0.0218898i
$501$		−	8.60243i		−	0.384328i
$502$	9.32206	−	7.26144i	0.416064	−	0.324094i
$503$	3.33411			0.148661			0.0743303	−	0.997234i	$-0.476318\pi$
$503$	3.33411			0.148661			0.0743303	+	0.997234i	$0.476318\pi$
$504$	−2.58888	+	1.13917i	−0.115318	+	0.0507427i
$505$	−18.7638			−0.834978
$506$	−1.86963	+	1.45635i	−0.0831152	+	0.0647428i
$507$			12.4237i			0.551754i
$508$	−3.95972	+	15.6875i	−0.175684	+	0.696022i
$509$		−	41.0835i		−	1.82099i	−0.413516	−	0.910497i	$-0.635699\pi$
$509$		−	41.0835i		−	1.82099i	0.413516	−	0.910497i	$-0.364301\pi$
$510$	4.57896	+	5.87836i	0.202760	+	0.260298i
$511$	−4.59136			−0.203110
$512$	−7.27259	+	21.4268i	−0.321406	+	0.946941i
$513$	1.64700			0.0727170
$514$	−19.7410	−	25.3430i	−0.870739	−	1.11783i
$515$		−	2.87928i		−	0.126876i
$516$	−4.51623	+	17.8923i	−0.198816	+	0.787666i
$517$		−	1.99203i		−	0.0876093i
$518$	12.7335	−	9.91881i	0.559479	−	0.435807i
$519$	0.318314			0.0139724
$520$	1.96541	−	0.864831i	0.0861891	−	0.0379253i
$521$	18.4073			0.806437			0.403218	−	0.915104i	$-0.367892\pi$
$521$	18.4073			0.806437			0.403218	+	0.915104i	$0.367892\pi$
$522$	1.55375	−	1.21030i	0.0680058	−	0.0529733i
$523$			18.0585i			0.789645i	0.918757	+	0.394822i	$0.129194\pi$
$523$			18.0585i			0.789645i	−0.918757	+	0.394822i	$0.870806\pi$
$524$	14.1286	+	3.56621i	0.617209	+	0.155791i
$525$			1.00000i			0.0436436i
$526$	5.81333	+	7.46301i	0.253473	+	0.325403i
$527$	−18.5634			−0.808635
$528$	2.67293	+	1.44118i	0.116325	+	0.0627193i
$529$	−18.1275			−0.788154
$530$	2.27962	+	2.92652i	0.0990204	+	0.127120i
$531$		−	8.77025i		−	0.380596i
$532$	3.19384	+	0.806162i	0.138470	+	0.0349515i
$533$		−	1.21470i		−	0.0526143i
$534$	16.7357	−	13.0363i	0.724223	−	0.564135i
$535$	−6.05806			−0.261913
$536$	−7.24975	−	16.4758i	−0.313142	−	0.711646i
$537$	−12.9092			−0.557075
$538$	25.5836	−	19.9284i	1.10299	−	0.859173i
$539$			0.759176i			0.0327000i
$540$	−0.489471	+	1.93918i	−0.0210635	+	0.0834490i
$541$			22.9354i			0.986069i	0.870010	+	0.493034i	$0.164112\pi$
$541$			22.9354i			0.986069i	−0.870010	+	0.493034i	$0.835888\pi$
$542$	−12.0894	−	15.5201i	−0.519284	−	0.666644i
$543$	10.0187			0.429943
$544$	4.96261	+	29.3892i	0.212770	+	1.26005i
$545$	−5.64799			−0.241933
$546$	0.659769	+	0.846995i	0.0282355	+	0.0362481i
$547$			13.0149i			0.556475i	0.960512	+	0.278238i	$0.0897503\pi$
$547$			13.0149i			0.556475i	−0.960512	+	0.278238i	$0.910250\pi$
$548$	4.17534	−	16.5418i	0.178362	−	0.706631i
$549$		−	2.97609i		−	0.127016i
$550$	0.846995	−	0.659769i	0.0361160	−	0.0281326i
$551$	−2.29370			−0.0977151
$552$	−2.51457	−	5.71460i	−0.107027	−	0.243230i
$553$	−15.8524			−0.674111
$554$	7.68197	−	5.98389i	0.326376	−	0.254231i
$555$		−	11.4133i		−	0.484466i
$556$	12.1563	+	3.06838i	0.515540	+	0.130128i
$557$		−	38.6281i		−	1.63673i	−0.574701	−	0.818363i	$-0.694882\pi$
$557$		−	38.6281i		−	1.63673i	0.574701	−	0.818363i	$-0.305118\pi$
$558$	−3.06189	−	3.93078i	−0.129620	−	0.166403i
$559$	7.00473			0.296269
$560$	−1.89835	+	3.52084i	−0.0802198	+	0.148782i
$561$	4.00000			0.168880
$562$	−3.94357	−	5.06266i	−0.166349	−	0.213555i
$563$			32.4427i			1.36730i	0.729812	+	0.683648i	$0.239608\pi$
$563$			32.4427i			1.36730i	−0.729812	+	0.683648i	$0.760392\pi$
$564$	5.08828	+	1.28434i	0.214255	+	0.0540805i
$565$		−	5.92320i		−	0.249191i
$566$	9.00709	−	7.01609i	0.378596	−	0.294908i
$567$	−1.00000			−0.0419961
$568$	−22.7298	+	10.0017i	−0.953722	+	0.419661i
$569$	−12.0215			−0.503969			−0.251984	−	0.967731i	$-0.581083\pi$
$569$	−12.0215			−0.503969			−0.251984	+	0.967731i	$0.581083\pi$
$570$	1.83753	−	1.43135i	0.0769655	−	0.0599524i
$571$			35.0459i			1.46662i	0.679892	+	0.733312i	$0.262026\pi$
$571$			35.0459i			1.46662i	−0.679892	+	0.733312i	$0.737974\pi$
$572$	0.282106	−	1.11764i	0.0117954	−	0.0467310i
$573$			2.08846i			0.0872466i
$574$	1.39051	+	1.78510i	0.0580388	+	0.0745088i
$575$	−2.20737			−0.0920536
$576$	−5.40458	+	5.89835i	−0.225191	+	0.245764i
$577$	22.7204			0.945865			0.472932	−	0.881099i	$-0.343196\pi$
$577$	22.7204			0.945865			0.472932	+	0.881099i	$0.343196\pi$
$578$	9.35195	+	12.0058i	0.388990	+	0.499376i
$579$			2.39763i			0.0996420i
$580$	0.681663	−	2.70060i	0.0283045	−	0.112136i
$581$		−	2.86269i		−	0.118764i
$582$	6.81647	−	5.30970i	0.282552	−	0.220094i
$583$	1.99139			0.0824748
$584$	−11.8865	+	5.23034i	−0.491866	+	0.216433i
$585$	0.759176			0.0313881
$586$	9.01391	−	7.02140i	0.372361	−	0.290052i
$587$			6.79336i			0.280392i	0.990124	+	0.140196i	$0.0447733\pi$
$587$			6.79336i			0.280392i	−0.990124	+	0.140196i	$0.955227\pi$
$588$	−1.93918	−	0.489471i	−0.0799704	−	0.0201855i
$589$			5.80277i			0.239099i
$590$	−7.62187	−	9.78477i	−0.313787	−	0.402832i
$591$	−7.00832			−0.288284
$592$	21.6663	−	40.1842i	0.890481	−	1.65156i
$593$	10.3483			0.424953			0.212476	−	0.977166i	$-0.431847\pi$
$593$	10.3483			0.424953			0.212476	+	0.977166i	$0.431847\pi$
$594$	0.659769	+	0.846995i	0.0270707	+	0.0347526i
$595$			5.26887i			0.216003i
$596$	−27.9475	−	7.05428i	−1.14478	−	0.288955i
$597$			22.6390i			0.926554i
$598$	−1.86963	+	1.45635i	−0.0764548	+	0.0595547i
$599$	−15.4656			−0.631908			−0.315954	−	0.948775i	$-0.602325\pi$
$599$	−15.4656			−0.631908			−0.315954	+	0.948775i	$0.602325\pi$
$600$	1.13917	+	2.58888i	0.0465064	+	0.105691i
$601$	9.98426			0.407267			0.203633	−	0.979047i	$-0.434725\pi$
$601$	9.98426			0.407267			0.203633	+	0.979047i	$0.434725\pi$
$602$	−10.2941	+	8.01860i	−0.419555	+	0.326814i
$603$		−	6.36407i		−	0.259165i
$604$	−9.80439	+	38.8429i	−0.398935	+	1.58049i
$605$			10.4237i			0.423782i
$606$	−16.3069	−	20.9343i	−0.662421	−	0.850400i
$607$	−40.7315			−1.65324			−0.826620	−	0.562761i	$-0.809739\pi$
$607$	−40.7315			−1.65324			−0.826620	+	0.562761i	$0.809739\pi$
$608$	9.18681	−	1.55127i	0.372575	−	0.0629123i
$609$	1.39265			0.0564331
$610$	−2.58639	−	3.32035i	−0.104720	−	0.134437i
$611$		−	1.99203i		−	0.0805888i
$612$	−2.57896	+	10.2173i	−0.104248	+	0.413009i
$613$			3.70254i			0.149544i	0.997201	+	0.0747722i	$0.0238230\pi$
$613$			3.70254i			0.149544i	−0.997201	+	0.0747722i	$0.976177\pi$
$614$	−15.6941	+	12.2250i	−0.633364	+	0.493360i
$615$	1.60002			0.0645190
$616$	0.864831	+	1.96541i	0.0348450	+	0.0791888i
$617$	−39.8374			−1.60379			−0.801897	−	0.597462i	$-0.796176\pi$
$617$	−39.8374			−1.60379			−0.801897	+	0.597462i	$0.796176\pi$
$618$	3.21234	−	2.50226i	0.129219	−	0.100656i
$619$			39.2895i			1.57918i	0.613635	+	0.789590i	$0.289707\pi$
$619$			39.2895i			1.57918i	−0.613635	+	0.789590i	$0.710293\pi$
$620$	−6.83216	−	1.72452i	−0.274386	−	0.0692583i
$621$		−	2.20737i		−	0.0885786i
$622$	14.8545	+	19.0698i	0.595610	+	0.764630i
$623$	15.0005			0.600980
$624$	2.67293	+	1.44118i	0.107003	+	0.0576933i
$625$	1.00000			0.0400000
$626$	−9.21317	−	11.8276i	−0.368232	−	0.472728i
$627$		−	1.25037i		−	0.0499348i
$628$	−28.4767	−	7.18784i	−1.13634	−	0.286826i
$629$		−	60.1350i		−	2.39774i
$630$	−1.11568	+	0.869059i	−0.0444496	+	0.0346242i
$631$	0.347978			0.0138528			0.00692639	−	0.999976i	$-0.497795\pi$
$631$	0.347978			0.0138528			0.00692639	+	0.999976i	$0.497795\pi$
$632$	−41.0398	+	18.0585i	−1.63248	+	0.718330i
$633$	27.5670			1.09569
$634$	0.842501	−	0.656269i	0.0334600	−	0.0260638i
$635$			8.08979i			0.321033i
$636$	−1.28393	+	5.08664i	−0.0509110	+	0.201699i
$637$			0.759176i			0.0300796i
$638$	−0.918829	−	1.17957i	−0.0363768	−	0.0466996i
$639$	−8.77979			−0.347323
$640$	−0.903757	+	11.2776i	−0.0357241	+	0.445784i
$641$	39.9083			1.57628			0.788142	−	0.615494i	$-0.211043\pi$
$641$	39.9083			1.57628			0.788142	+	0.615494i	$0.211043\pi$
$642$	−5.26481	−	6.75884i	−0.207786	−	0.266750i
$643$		−	9.88587i		−	0.389860i	−0.980817	−	0.194930i	$-0.937552\pi$
$643$		−	9.88587i		−	0.389860i	0.980817	−	0.194930i	$-0.0624480\pi$
$644$	1.08044	−	4.28048i	0.0425754	−	0.168675i
$645$			9.22676i			0.363303i
$646$	9.68169	−	7.54157i	0.380921	−	0.296719i
$647$	21.3778			0.840447			0.420224	−	0.907421i	$-0.361952\pi$
$647$	21.3778			0.840447			0.420224	+	0.907421i	$0.361952\pi$
$648$	−2.58888	+	1.13917i	−0.101701	+	0.0447508i
$649$	−6.65816			−0.261356
$650$	0.846995	−	0.659769i	0.0332219	−	0.0258783i
$651$		−	3.52322i		−	0.138086i
$652$	20.4911	+	5.17220i	0.802495	+	0.202559i
$653$			28.7011i			1.12316i	0.827422	+	0.561581i	$0.189807\pi$
$653$			28.7011i			1.12316i	−0.827422	+	0.561581i	$0.810193\pi$
$654$	−4.90844	−	6.30134i	−0.191935	−	0.246402i
$655$	7.28585			0.284682
$656$	5.63340	+	3.03739i	0.219947	+	0.118590i
$657$	−4.59136			−0.179126
$658$	2.28035	+	2.92746i	0.0888975	+	0.114124i
$659$			2.45444i			0.0956115i	0.998857	+	0.0478058i	$0.0152228\pi$
$659$			2.45444i			0.0956115i	−0.998857	+	0.0478058i	$0.984777\pi$
$660$	1.47218	+	0.371595i	0.0573045	+	0.0144643i
$661$			25.9433i			1.00908i	0.863389	+	0.504539i	$0.168338\pi$
$661$			25.9433i			1.00908i	−0.863389	+	0.504539i	$0.831662\pi$
$662$	22.1636	−	17.2644i	0.861412	−	0.670999i
$663$	4.00000			0.155347
$664$	−3.26109	−	7.41116i	−0.126555	−	0.287609i
$665$	1.64700			0.0638681
$666$	12.7335	−	9.91881i	0.493414	−	0.384346i
$667$			3.07409i			0.119029i
$668$	4.21065	−	16.6817i	0.162915	−	0.645433i
$669$		−	16.5839i		−	0.641170i
$670$	−5.53075	−	7.10024i	−0.213672	−	0.274306i
$671$	−2.25937			−0.0872221
$672$	−5.57789	+	0.941874i	−0.215172	+	0.0363336i
$673$	4.38031			0.168849			0.0844243	−	0.996430i	$-0.473095\pi$
$673$	4.38031			0.168849			0.0844243	+	0.996430i	$0.473095\pi$
$674$	−0.718729	−	0.922687i	−0.0276844	−	0.0355406i
$675$			1.00000i			0.0384900i
$676$	−6.08102	+	24.0917i	−0.233885	+	0.926604i
$677$			1.75980i			0.0676346i	0.999428	+	0.0338173i	$0.0107664\pi$
$677$			1.75980i			0.0676346i	−0.999428	+	0.0338173i	$0.989234\pi$
$678$	6.60838	−	5.14762i	0.253793	−	0.197693i
$679$	6.10971			0.234469
$680$	6.00214	+	13.6405i	0.230172	+	0.523088i
$681$	−15.9885			−0.612679
$682$	−2.98415	+	2.32451i	−0.114269	+	0.0890102i
$683$			2.63083i			0.100666i	0.998732	+	0.0503329i	$0.0160282\pi$
$683$			2.63083i			0.100666i	−0.998732	+	0.0503329i	$0.983972\pi$
$684$	3.19384	+	0.806162i	0.122119	+	0.0308244i
$685$		−	8.53031i		−	0.325926i
$686$	−0.869059	−	1.11568i	−0.0331808	−	0.0425968i
$687$	−7.71525			−0.294355
$688$	−17.5156	+	32.4859i	−0.667775	+	1.23851i
$689$	1.99139			0.0758658
$690$	−1.91833	−	2.46271i	−0.0730297	−	0.0937537i
$691$			5.14804i			0.195841i	0.995194	+	0.0979204i	$0.0312191\pi$
$691$			5.14804i			0.195841i	−0.995194	+	0.0979204i	$0.968781\pi$
$692$	0.617268	+	0.155806i	0.0234650	+	0.00592284i
$693$			0.759176i			0.0288387i
$694$	37.5067	−	29.2159i	1.42373	−	1.10902i
$695$	6.26877			0.237788
$696$	3.60541	−	1.58647i	0.136663	−	0.0601349i
$697$	8.43029			0.319320
$698$	24.9197	−	19.4113i	0.943224	−	0.734727i
$699$			22.7547i			0.860660i
$700$	−0.489471	+	1.93918i	−0.0185003	+	0.0732941i
$701$			10.2199i			0.386000i	0.981199	+	0.193000i	$0.0618217\pi$
$701$			10.2199i			0.386000i	−0.981199	+	0.193000i	$0.938178\pi$
$702$	0.659769	+	0.846995i	0.0249014	+	0.0319678i
$703$	−18.7977			−0.708969
$704$	4.47788	+	4.10303i	0.168767	+	0.154639i
$705$	2.62393			0.0988231
$706$	14.8033	+	19.0041i	0.557130	+	0.715229i
$707$		−	18.7638i		−	0.705685i
$708$	4.29279	−	17.0071i	0.161333	−	0.639165i
$709$			4.28151i			0.160796i	0.996763	+	0.0803978i	$0.0256191\pi$
$709$			4.28151i			0.160796i	−0.996763	+	0.0803978i	$0.974381\pi$
$710$	−9.79541	+	7.63016i	−0.367615	+	0.286355i
$711$	−15.8524			−0.594510
$712$	38.8343	−	17.0881i	1.45538	−	0.640402i
$713$	7.77705			0.291253
$714$	−5.87836	+	4.57896i	−0.219992	+	0.171363i
$715$		−	0.576348i		−	0.0215542i
$716$	−25.0333	−	6.31870i	−0.935540	−	0.236141i
$717$		−	1.92129i		−	0.0717517i
$718$	24.8416	+	31.8911i	0.927081	+	1.19016i
$719$	25.3452			0.945216			0.472608	−	0.881273i	$-0.343313\pi$
$719$	25.3452			0.945216			0.472608	+	0.881273i	$0.343313\pi$
$720$	−1.89835	+	3.52084i	−0.0707472	+	0.131214i
$721$	2.87928			0.107230
$722$	14.1547	+	18.1715i	0.526783	+	0.676271i
$723$			13.8987i			0.516897i
$724$	19.4280	+	4.90387i	0.722038	+	0.182251i
$725$		−	1.39265i		−	0.0517218i
$726$	−11.6294	+	9.05877i	−0.431609	+	0.336203i
$727$	−16.9514			−0.628693			−0.314346	−	0.949308i	$-0.601785\pi$
$727$	−16.9514			−0.628693			−0.314346	+	0.949308i	$0.601785\pi$
$728$	0.864831	+	1.96541i	0.0320528	+	0.0728431i
$729$	−1.00000			−0.0370370
$730$	−5.12248	+	3.99017i	−0.189591	+	0.147683i
$731$			48.6146i			1.79808i
$732$	1.45671	−	5.77116i	0.0538415	−	0.213308i
$733$			32.0871i			1.18516i	0.805511	+	0.592581i	$0.201891\pi$
$733$			32.0871i			1.18516i	−0.805511	+	0.592581i	$0.798109\pi$
$734$	−26.3347	−	33.8079i	−0.972033	−	1.24787i
$735$	−1.00000			−0.0368856
$736$	−2.07906	−	12.3125i	−0.0766352	−	0.453843i
$737$	−4.83145			−0.177969
$738$	1.39051	+	1.78510i	0.0511854	+	0.0657106i
$739$		−	20.2790i		−	0.745973i	−0.927837	−	0.372987i	$-0.878334\pi$
$739$		−	20.2790i		−	0.745973i	0.927837	−	0.372987i	$-0.121666\pi$
$740$	5.58647	−	22.1324i	0.205363	−	0.813602i
$741$		−	1.25037i		−	0.0459334i
$742$	−2.92652	+	2.27962i	−0.107436	+	0.0836875i
$743$	25.7769			0.945663			0.472831	−	0.881153i	$-0.343232\pi$
$743$	25.7769			0.945663			0.472831	+	0.881153i	$0.343232\pi$
$744$	−4.01355	−	9.12120i	−0.147144	−	0.334399i
$745$	−14.4120			−0.528016
$746$	−21.1095	+	16.4433i	−0.772874	+	0.602032i
$747$		−	2.86269i		−	0.104740i
$748$	7.75672	+	1.95789i	0.283614	+	0.0715874i
$749$		−	6.05806i		−	0.221357i
$750$	0.869059	+	1.11568i	0.0317336	+	0.0407388i
$751$	40.8693			1.49134			0.745671	−	0.666315i	$-0.232129\pi$
$751$	40.8693			1.49134			0.745671	+	0.666315i	$0.232129\pi$
$752$	9.23844	+	4.98113i	0.336891	+	0.181643i
$753$	8.35551			0.304492
$754$	−0.918829	−	1.17957i	−0.0334618	−	0.0429574i
$755$			20.0306i			0.728987i
$756$	−1.93918	−	0.489471i	−0.0705273	−	0.0178019i
$757$			11.8206i			0.429628i	0.976655	+	0.214814i	$0.0689146\pi$
$757$			11.8206i			0.429628i	−0.976655	+	0.214814i	$0.931085\pi$
$758$	29.1558	−	22.7110i	1.05899	−	0.824901i
$759$	−1.67578			−0.0608270
$760$	4.26390	−	1.87622i	0.154668	−	0.0680576i
$761$	9.26267			0.335772			0.167886	−	0.985806i	$-0.446306\pi$
$761$	9.26267			0.335772			0.167886	+	0.985806i	$0.446306\pi$
$762$	−9.02559	+	7.03050i	−0.326963	+	0.254688i
$763$		−	5.64799i		−	0.204471i
$764$	−1.02224	+	4.04989i	−0.0369834	+	0.146520i
$765$			5.26887i			0.190496i
$766$	2.11107	+	2.71014i	0.0762762	+	0.0979215i
$767$	−6.65816			−0.240412
$768$	−13.3675	+	8.79256i	−0.482359	+	0.317274i
$769$	41.1208			1.48286			0.741428	−	0.671033i	$-0.234149\pi$
$769$	41.1208			1.48286			0.741428	+	0.671033i	$0.234149\pi$
$770$	0.659769	+	0.846995i	0.0237764	+	0.0305236i
$771$		−	22.7154i		−	0.818075i
$772$	−1.17357	+	4.64943i	−0.0422377	+	0.167337i
$773$		−	9.81275i		−	0.352940i	−0.984306	−	0.176470i	$-0.943532\pi$
$773$		−	9.81275i		−	0.352940i	0.984306	−	0.176470i	$-0.0564679\pi$
$774$	−10.2941	+	8.01860i	−0.370013	+	0.288223i
$775$	−3.52322			−0.126558
$776$	15.8173	−	6.96000i	0.567808	−	0.249850i
$777$	11.4133			0.409449
$778$	13.3565	−	10.4041i	0.478852	−	0.373003i
$779$		−	2.63524i		−	0.0944172i
$780$	1.47218	+	0.371595i	0.0527124	+	0.0133052i
$781$			6.66541i			0.238507i
$782$	−10.1074	−	12.9757i	−0.361442	−	0.464010i
$783$	1.39265			0.0497693
$784$	−3.52084	−	1.89835i	−0.125744	−	0.0677981i
$785$	−14.6849			−0.524127
$786$	6.33183	+	8.12865i	0.225849	+	0.289939i
$787$			40.6459i			1.44887i	0.689343	+	0.724435i	$0.257899\pi$
$787$			40.6459i			1.44887i	−0.689343	+	0.724435i	$0.742101\pi$
$788$	−13.5904	−	3.43037i	−0.484138	−	0.122202i
$789$			6.68922i			0.238143i
$790$	−17.6861	+	13.7766i	−0.629244	+	0.490151i
$791$	5.92320			0.210605
$792$	0.864831	+	1.96541i	0.0307304	+	0.0698380i
$793$	−2.25937			−0.0802327
$794$	10.8989	−	8.48969i	0.386786	−	0.301288i
$795$			2.62309i			0.0930314i
$796$	−11.0812	+	43.9012i	−0.392761	+	1.55604i
$797$		−	37.9464i		−	1.34413i	−0.740492	−	0.672065i	$-0.765408\pi$
$797$		−	37.9464i		−	1.34413i	0.740492	−	0.672065i	$-0.234592\pi$
$798$	1.43135	+	1.83753i	0.0506691	+	0.0650477i
$799$	13.8252			0.489099
$800$	0.941874	+	5.57789i	0.0333003	+	0.197208i
$801$	15.0005			0.530015
$802$	−31.8130	−	40.8407i	−1.12336	−	1.44214i
$803$			3.48565i			0.123006i
$804$	3.11503	−	12.3411i	0.109859	−	0.435236i
$805$		−	2.20737i		−	0.0777995i
$806$	−2.98415	+	2.32451i	−0.105112	+	0.0818775i
$807$	22.9310			0.807209
$808$	−21.3752	−	48.5772i	−0.751976	−	1.70894i
$809$	9.34260			0.328468			0.164234	−	0.986421i	$-0.447485\pi$
$809$	9.34260			0.328468			0.164234	+	0.986421i	$0.447485\pi$
$810$	−1.11568	+	0.869059i	−0.0392009	+	0.0305356i
$811$			15.4683i			0.543167i	0.962415	+	0.271583i	$0.0875473\pi$
$811$			15.4683i			0.543167i	−0.962415	+	0.271583i	$0.912453\pi$
$812$	2.70060	+	0.681663i	0.0947726	+	0.0239217i
$813$		−	13.9109i		−	0.487877i
$814$	−7.53012	−	9.66698i	−0.263931	−	0.338828i
$815$	10.5669			0.370143
$816$	−10.0021	+	18.5508i	−0.350145	+	0.649409i
$817$	15.1965			0.531659
$818$	−25.0649	−	32.1777i	−0.876373	−	1.12507i
$819$			0.759176i			0.0265278i
$820$	3.10272	+	0.783164i	0.108352	+	0.0273493i
$821$			19.8793i			0.693794i	0.937903	+	0.346897i	$0.112765\pi$
$821$			19.8793i			0.693794i	−0.937903	+	0.346897i	$0.887235\pi$
$822$	9.51707	−	7.41335i	0.331946	−	0.258570i
$823$	−32.6029			−1.13646			−0.568232	−	0.822868i	$-0.692372\pi$
$823$	−32.6029			−1.13646			−0.568232	+	0.822868i	$0.692372\pi$
$824$	7.45410	−	3.27999i	0.259676	−	0.114264i
$825$	0.759176			0.0264311
$826$	9.78477	−	7.62187i	0.340456	−	0.265199i
$827$		−	8.21342i		−	0.285609i	−0.989751	−	0.142804i	$-0.954388\pi$
$827$		−	8.21342i		−	0.285609i	0.989751	−	0.142804i	$-0.0456119\pi$
$828$	1.08044	−	4.28048i	0.0375480	−	0.148757i
$829$			21.6603i			0.752294i	0.926560	+	0.376147i	$0.122751\pi$
$829$			21.6603i			0.752294i	−0.926560	+	0.376147i	$0.877249\pi$
$830$	−2.48785	−	3.19384i	−0.0863545	−	0.110860i
$831$	6.88548			0.238854
$832$	4.47788	+	4.10303i	0.155243	+	0.142247i
$833$	−5.26887			−0.182556
$834$	5.44793	+	6.99392i	0.188646	+	0.242180i
$835$		−	8.60243i		−	0.297699i
$836$	0.612019	−	2.42469i	0.0211671	−	0.0838595i
$837$		−	3.52322i		−	0.121780i
$838$	−4.23161	+	3.29622i	−0.146179	+	0.113866i
$839$	40.4787			1.39748			0.698740	−	0.715376i	$-0.253744\pi$
$839$	40.4787			1.39748			0.698740	+	0.715376i	$0.253744\pi$
$840$	−2.58888	+	1.13917i	−0.0893248	+	0.0393051i
$841$	27.0605			0.933121
$842$	29.5274	−	23.0005i	1.01758	−	0.792648i
$843$		−	4.53774i		−	0.156288i
$844$	53.4573	+	13.4932i	1.84008	+	0.464457i
$845$			12.4237i			0.427387i
$846$	2.28035	+	2.92746i	0.0784002	+	0.100648i
$847$	−10.4237			−0.358161
$848$	−4.97953	+	9.23547i	−0.170998	+	0.317147i
$849$	8.07320			0.277071
$850$	4.57896	+	5.87836i	0.157057	+	0.201626i
$851$			25.1933i			0.863614i
$852$	−17.0256	−	4.29746i	−0.583287	−	0.147228i
$853$		−	13.2477i		−	0.453593i	−0.973942	−	0.226797i	$-0.927175\pi$
$853$		−	13.2477i		−	0.453593i	0.973942	−	0.226797i	$-0.0728253\pi$
$854$	3.32035	−	2.58639i	0.113620	−	0.0885046i
$855$	1.64700			0.0563264
$856$	−6.90116	−	15.6836i	−0.235877	−	0.536054i
$857$	−23.4200			−0.800012			−0.400006	−	0.916512i	$-0.630992\pi$
$857$	−23.4200			−0.800012			−0.400006	+	0.916512i	$0.630992\pi$
$858$	0.643018	−	0.500881i	0.0219523	−	0.0170998i
$859$			34.2044i			1.16704i	0.812099	+	0.583520i	$0.198325\pi$
$859$			34.2044i			1.16704i	−0.812099	+	0.583520i	$0.801675\pi$
$860$	−4.51623	+	17.8923i	−0.154002	+	0.610124i
$861$			1.60002i			0.0545285i
$862$	−12.3657	−	15.8747i	−0.421176	−	0.540695i
$863$	−40.9143			−1.39274			−0.696369	−	0.717684i	$-0.745202\pi$
$863$	−40.9143			−1.39274			−0.696369	+	0.717684i	$0.745202\pi$
$864$	−5.57789	+	0.941874i	−0.189764	+	0.0320432i
$865$	0.318314			0.0108230
$866$	33.7997	+	43.3912i	1.14856	+	1.47449i
$867$			10.7610i			0.365463i
$868$	1.72452	−	6.83216i	0.0585339	−	0.231899i
$869$			12.0347i			0.408250i
$870$	1.55375	−	1.21030i	0.0526771	−	0.0410329i
$871$	−4.83145			−0.163707
$872$	−6.43403	−	14.6220i	−0.217884	−	0.495162i
$873$	6.10971			0.206782
$874$	−4.05609	+	3.15950i	−0.137199	+	0.106872i
$875$			1.00000i			0.0338062i
$876$	−8.90348	−	2.24734i	−0.300821	−	0.0759306i
$877$			12.3099i			0.415674i	0.978163	+	0.207837i	$0.0666424\pi$
$877$			12.3099i			0.415674i	−0.978163	+	0.207837i	$0.933358\pi$
$878$	26.9893	+	34.6482i	0.910844	+	1.16932i
$879$	8.07931			0.272508
$880$	2.67293	+	1.44118i	0.0901046	+	0.0485821i
$881$	26.0861			0.878865			0.439432	−	0.898276i	$-0.355180\pi$
$881$	26.0861			0.878865			0.439432	+	0.898276i	$0.355180\pi$
$882$	−0.869059	−	1.11568i	−0.0292628	−	0.0375668i
$883$		−	21.7051i		−	0.730435i	−0.930922	−	0.365218i	$-0.880995\pi$
$883$		−	21.7051i		−	0.730435i	0.930922	−	0.365218i	$-0.119005\pi$
$884$	7.75672	+	1.95789i	0.260887	+	0.0658508i
$885$		−	8.77025i		−	0.294809i
$886$	16.4084	−	12.7813i	0.551250	−	0.429397i
$887$	23.3521			0.784086			0.392043	−	0.919947i	$-0.371768\pi$
$887$	23.3521			0.784086			0.392043	+	0.919947i	$0.371768\pi$
$888$	29.5476	−	13.0017i	0.991551	−	0.436307i
$889$	−8.08979			−0.271323
$890$	16.7357	−	13.0363i	0.560981	−	0.436977i
$891$			0.759176i			0.0254334i
$892$	8.11734	−	32.1591i	0.271789	−	1.07677i
$893$		−	4.32163i		−	0.144618i
$894$	−12.5249	−	16.0792i	−0.418896	−	0.537768i
$895$	−12.9092			−0.431508
$896$	−11.2776	−	0.903757i	−0.376757	−	0.0301924i
$897$	−1.67578			−0.0559527
$898$	−32.8172	−	42.1299i	−1.09512	−	1.40589i
$899$			4.90662i			0.163645i
$900$	−0.489471	+	1.93918i	−0.0163157	+	0.0646393i
$901$			13.8207i			0.460435i
$902$	1.35521	−	1.05564i	0.0451235	−	0.0351491i
$903$	−9.22676			−0.307047
$904$	15.3345	−	6.74754i	0.510016	−	0.224420i
$905$	10.0187			0.333033
$906$	−22.3476	+	17.4078i	−0.742451	+	0.578334i
$907$		−	6.78247i		−	0.225208i	−0.993640	−	0.112604i	$-0.964081\pi$
$907$		−	6.78247i		−	0.225208i	0.993640	−	0.112604i	$-0.0359192\pi$
$908$	−31.0045	−	7.82589i	−1.02892	−	0.259711i
$909$		−	18.7638i		−	0.622356i
$910$	0.659769	+	0.846995i	0.0218711	+	0.0280776i
$911$	−24.9299			−0.825963			−0.412981	−	0.910739i	$-0.635513\pi$
$911$	−24.9299			−0.825963			−0.412981	+	0.910739i	$0.635513\pi$
$912$	5.79883	+	3.12659i	0.192019	+	0.103532i
$913$	−2.17329			−0.0719253
$914$	18.9529	+	24.3313i	0.626907	+	0.804807i
$915$		−	2.97609i		−	0.0983863i
$916$	−14.9613	−	3.77639i	−0.494334	−	0.124776i
$917$			7.28585i			0.240600i
$918$	−5.87836	+	4.57896i	−0.194015	+	0.151128i
$919$	26.2942			0.867364			0.433682	−	0.901066i	$-0.357214\pi$
$919$	26.2942			0.867364			0.433682	+	0.901066i	$0.357214\pi$
$920$	−2.51457	−	5.71460i	−0.0829028	−	0.188405i
$921$	−14.0669			−0.463521
$922$	32.8291	−	25.5723i	1.08117	−	0.842179i
$923$			6.66541i			0.219394i
$924$	−0.371595	+	1.47218i	−0.0122246	+	0.0484311i
$925$		−	11.4133i		−	0.375266i
$926$	−14.4160	−	18.5069i	−0.473740	−	0.608176i
$927$	2.87928			0.0945678
$928$	7.76806	−	1.31170i	0.254999	−	0.0430587i
$929$	55.6150			1.82467			0.912335	−	0.409444i	$-0.134277\pi$
$929$	55.6150			1.82467			0.912335	+	0.409444i	$0.134277\pi$
$930$	−3.06189	−	3.93078i	−0.100403	−	0.128895i
$931$			1.64700i			0.0539784i
$932$	−11.1378	+	44.1254i	−0.364829	+	1.44537i
$933$			17.0926i			0.559586i
$934$	32.8844	−	25.6154i	1.07601	−	0.838161i
$935$	4.00000			0.130814
$936$	0.864831	+	1.96541i	0.0282679	+	0.0642416i
$937$	45.8876			1.49908			0.749542	−	0.661957i	$-0.230274\pi$
$937$	45.8876			1.49908			0.749542	+	0.661957i	$0.230274\pi$
$938$	7.10024	−	5.53075i	0.231831	−	0.180585i
$939$		−	10.6013i		−	0.345961i
$940$	5.08828	+	1.28434i	0.165961	+	0.0418906i
$941$			32.9890i			1.07541i	0.843133	+	0.537705i	$0.180709\pi$
$941$			32.9890i			1.07541i	−0.843133	+	0.537705i	$0.819291\pi$
$942$	−12.7620	−	16.3836i	−0.415810	−	0.533807i
$943$	−3.53183			−0.115012
$944$	16.6490	−	30.8786i	0.541878	−	1.00501i
$945$	−1.00000			−0.0325300
$946$	6.08753	+	7.81502i	0.197923	+	0.254088i
$947$			26.7187i			0.868240i	0.900855	+	0.434120i	$0.142941\pi$
$947$			26.7187i			0.868240i	−0.900855	+	0.434120i	$0.857059\pi$
$948$	−30.7406	−	7.75928i	−0.998408	−	0.252010i
$949$			3.48565i			0.113149i
$950$	1.83753	−	1.43135i	0.0596172	−	0.0464390i
$951$	0.755148			0.0244874
$952$	−13.6405	+	6.00214i	−0.442090	+	0.194530i
$953$	57.3519			1.85781			0.928906	−	0.370317i	$-0.120751\pi$
$953$	57.3519			1.85781			0.928906	+	0.370317i	$0.120751\pi$
$954$	−2.92652	+	2.27962i	−0.0947496	+	0.0738055i
$955$			2.08846i			0.0675809i
$956$	0.940415	−	3.72572i	0.0304152	−	0.120498i
$957$		−	1.05727i		−	0.0341766i
$958$	5.63466	+	7.23363i	0.182048	+	0.233708i
$959$	8.53031			0.275458
$960$	−5.40458	+	5.89835i	−0.174432	+	0.190368i
$961$	−18.5869			−0.599577
$962$	−7.53012	−	9.66698i	−0.242781	−	0.311676i
$963$		−	6.05806i		−	0.195218i
$964$	−6.80300	+	26.9520i	−0.219110	+	0.868066i
$965$			2.39763i			0.0771824i
$966$	2.46271	−	1.91833i	0.0792364	−	0.0617214i
$967$	23.2866			0.748848			0.374424	−	0.927258i	$-0.377840\pi$
$967$	23.2866			0.748848			0.374424	+	0.927258i	$0.377840\pi$
$968$	−26.9856	+	11.8743i	−0.867349	+	0.381655i
$969$	8.67786			0.278773
$970$	6.81647	−	5.30970i	0.218864	−	0.170484i
$971$			11.6103i			0.372591i	0.982494	+	0.186296i	$0.0596483\pi$
$971$			11.6103i			0.372591i	−0.982494	+	0.186296i	$0.940352\pi$
$972$	−1.93918	−	0.489471i	−0.0621992	−	0.0156998i
$973$			6.26877i			0.200967i
$974$	3.65980	+	4.69836i	0.117267	+	0.150545i
$975$	0.759176			0.0243131
$976$	5.64964	−	10.4783i	0.180841	−	0.335402i
$977$	36.1908			1.15784			0.578922	−	0.815383i	$-0.303473\pi$
$977$	36.1908			1.15784			0.578922	+	0.815383i	$0.303473\pi$
$978$	9.18327	+	11.7893i	0.293649	+	0.376979i
$979$		−	11.3880i		−	0.363961i
$980$	−1.93918	−	0.489471i	−0.0619448	−	0.0156356i
$981$		−	5.64799i		−	0.180327i
$982$	−23.5728	+	18.3621i	−0.752237	+	0.585957i
$983$	15.7506			0.502365			0.251182	−	0.967940i	$-0.419181\pi$
$983$	15.7506			0.502365			0.251182	+	0.967940i	$0.419181\pi$
$984$	1.82269	+	4.14225i	0.0581054	+	0.132050i
$985$	−7.00832			−0.223304
$986$	8.18651	−	6.37690i	0.260712	−	0.203082i
$987$			2.62393i			0.0835207i
$988$	0.612019	−	2.42469i	0.0194709	−	0.0771395i
$989$		−	20.3668i		−	0.647628i
$990$	0.659769	+	0.846995i	0.0209688	+	0.0269193i
$991$	−56.8361			−1.80546			−0.902729	−	0.430209i	$-0.858440\pi$
$991$	−56.8361			−1.80546			−0.902729	+	0.430209i	$0.858440\pi$
$992$	−3.31843	−	19.6522i	−0.105360	−	0.623957i
$993$	19.8656			0.630415
$994$	−7.63016	−	9.79541i	−0.242014	−	0.310692i
$995$			22.6390i			0.717706i
$996$	1.40121	−	5.55127i	0.0443989	−	0.175899i
$997$		−	56.6951i		−	1.79555i	−0.440451	−	0.897777i	$-0.645182\pi$
$997$		−	56.6951i		−	1.79555i	0.440451	−	0.897777i	$-0.354818\pi$
$998$	−35.0815	+	27.3269i	−1.11049	+	0.865016i
$999$	11.4133			0.361100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.g.b.421.10	yes	12
4.3	odd	2		3360.2.g.c.1681.3		12
8.3	odd	2		3360.2.g.c.1681.10		12
8.5	even	2	inner	840.2.g.b.421.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.g.b.421.9	✓	12	8.5	even	2	inner
840.2.g.b.421.10	yes	12	1.1	even	1	trivial
3360.2.g.c.1681.3		12	4.3	odd	2
3360.2.g.c.1681.10		12	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+(0.869059 + 1.11568i) q^{2} +1.00000i q^{3} +(-0.489471 + 1.93918i) q^{4} +1.00000i q^{5} +(-1.11568 + 0.869059i) q^{6} -1.00000 q^{7} +(-2.58888 + 1.13917i) q^{8} -1.00000 q^{9} +(-1.11568 + 0.869059i) q^{10} +0.759176i q^{11} +(-1.93918 - 0.489471i) q^{12} +0.759176i q^{13} +(-0.869059 - 1.11568i) q^{14} -1.00000 q^{15} +(-3.52084 - 1.89835i) q^{16} -5.26887 q^{17} +(-0.869059 - 1.11568i) q^{18} +1.64700i q^{19} +(-1.93918 - 0.489471i) q^{20} -1.00000i q^{21} +(-0.846995 + 0.659769i) q^{22} +2.20737 q^{23} +(-1.13917 - 2.58888i) q^{24} -1.00000 q^{25} +(-0.846995 + 0.659769i) q^{26} -1.00000i q^{27} +(0.489471 - 1.93918i) q^{28} +1.39265i q^{29} +(-0.869059 - 1.11568i) q^{30} +3.52322 q^{31} +(-0.941874 - 5.57789i) q^{32} -0.759176 q^{33} +(-4.57896 - 5.87836i) q^{34} -1.00000i q^{35} +(0.489471 - 1.93918i) q^{36} +11.4133i q^{37} +(-1.83753 + 1.43135i) q^{38} -0.759176 q^{39} +(-1.13917 - 2.58888i) q^{40} -1.60002 q^{41} +(1.11568 - 0.869059i) q^{42} -9.22676i q^{43} +(-1.47218 - 0.371595i) q^{44} -1.00000i q^{45} +(1.91833 + 2.46271i) q^{46} -2.62393 q^{47} +(1.89835 - 3.52084i) q^{48} +1.00000 q^{49} +(-0.869059 - 1.11568i) q^{50} -5.26887i q^{51} +(-1.47218 - 0.371595i) q^{52} -2.62309i q^{53} +(1.11568 - 0.869059i) q^{54} -0.759176 q^{55} +(2.58888 - 1.13917i) q^{56} -1.64700 q^{57} +(-1.55375 + 1.21030i) q^{58} +8.77025i q^{59} +(0.489471 - 1.93918i) q^{60} +2.97609i q^{61} +(3.06189 + 3.93078i) q^{62} +1.00000 q^{63} +(5.40458 - 5.89835i) q^{64} -0.759176 q^{65} +(-0.659769 - 0.846995i) q^{66} +6.36407i q^{67} +(2.57896 - 10.2173i) q^{68} +2.20737i q^{69} +(1.11568 - 0.869059i) q^{70} +8.77979 q^{71} +(2.58888 - 1.13917i) q^{72} +4.59136 q^{73} +(-12.7335 + 9.91881i) q^{74} -1.00000i q^{75} +(-3.19384 - 0.806162i) q^{76} -0.759176i q^{77} +(-0.659769 - 0.846995i) q^{78} +15.8524 q^{79} +(1.89835 - 3.52084i) q^{80} +1.00000 q^{81} +(-1.39051 - 1.78510i) q^{82} +2.86269i q^{83} +(1.93918 + 0.489471i) q^{84} -5.26887i q^{85} +(10.2941 - 8.01860i) q^{86} -1.39265 q^{87} +(-0.864831 - 1.96541i) q^{88} -15.0005 q^{89} +(1.11568 - 0.869059i) q^{90} -0.759176i q^{91} +(-1.08044 + 4.28048i) q^{92} +3.52322i q^{93} +(-2.28035 - 2.92746i) q^{94} -1.64700 q^{95} +(5.57789 - 0.941874i) q^{96} -6.10971 q^{97} +(0.869059 + 1.11568i) q^{98} -0.759176i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 12 q^{7} - 2 q^{8} - 12 q^{9} + 2 q^{14} - 12 q^{15} + 2 q^{16} + 2 q^{18} + 40 q^{23} - 12 q^{25} - 2 q^{28} + 2 q^{30} - 8 q^{31} - 2 q^{32} - 20 q^{34} - 2 q^{36} + 24 q^{38}+ \cdots - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 12 * q^7 - 2 * q^8 - 12 * q^9 + 2 * q^14 - 12 * q^15 + 2 * q^16 + 2 * q^18 + 40 * q^23 - 12 * q^25 - 2 * q^28 + 2 * q^30 - 8 * q^31 - 2 * q^32 - 20 * q^34 - 2 * q^36 + 24 * q^38 + 24 * q^46 - 32 * q^47 + 12 * q^49 + 2 * q^50 + 2 * q^56 - 20 * q^58 - 2 * q^60 + 52 * q^62 + 12 * q^63 + 2 * q^64 - 20 * q^66 - 4 * q^68 - 8 * q^71 + 2 * q^72 - 60 * q^74 - 48 * q^76 - 20 * q^78 - 80 * q^79 + 12 * q^81 + 24 * q^86 + 16 * q^87 + 40 * q^88 - 8 * q^92 + 36 * q^94 + 40 * q^96 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more