LMFDB - Embedded newform 210.2.u.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.3
Root			$0.117630 + 0.893490i$ of defining polynomial
Character	$\chi$	$=$	210.103
Dual form			210.2.u.a.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.04129 + 1.97882i) q^{5} +1.00000i q^{6} +(-2.55046 + 0.703686i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.04129 + 1.97882i) q^{5} +1.00000i q^{6} +(-2.55046 + 0.703686i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.64189 + 1.51796i) q^{10} +(0.989376 + 1.71365i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(2.19222 - 2.19222i) q^{13} +(-1.33981 - 2.28142i) q^{14} +(0.493652 + 2.18090i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.19130 - 4.44599i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-2.10939 + 3.65357i) q^{19} +(-1.89119 - 1.19306i) q^{20} +(-2.64568 + 0.0196015i) q^{21} +(-1.39919 + 1.39919i) q^{22} +(5.68202 - 1.52249i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.83144 + 4.12104i) q^{25} +(2.68491 + 1.55013i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.85692 - 1.88464i) q^{28} -8.94996i q^{29} +(-1.97882 + 1.04129i) q^{30} +(-1.50157 + 0.866930i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.512139 + 1.91133i) q^{33} +4.60282 q^{34} +(-4.04823 - 4.31415i) q^{35} -1.00000 q^{36} +(-0.717425 - 2.67747i) q^{37} +(-4.07503 - 1.09190i) q^{38} +(2.68491 - 1.55013i) q^{39} +(0.662933 - 2.13554i) q^{40} +6.55691i q^{41} +(-0.703686 - 2.55046i) q^{42} +(-6.33724 - 6.33724i) q^{43} +(-1.71365 - 0.989376i) q^{44} +(-0.0876265 + 2.23435i) q^{45} +(2.94123 + 5.09436i) q^{46} +(5.87298 - 1.57366i) q^{47} +(0.707107 - 0.707107i) q^{48} +(6.00965 - 3.58944i) q^{49} +(-4.71345 - 1.66835i) q^{50} +(2.30141 - 3.98616i) q^{51} +(-0.802407 + 2.99462i) q^{52} +(2.95926 - 11.0441i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.36077 + 3.74220i) q^{55} +(2.30103 + 1.30586i) q^{56} +(-2.98313 + 2.98313i) q^{57} +(8.64500 - 2.31642i) q^{58} +(2.10351 + 3.64339i) q^{59} +(-1.51796 - 1.64189i) q^{60} +(9.63018 + 5.55999i) q^{61} +(-1.22602 - 1.22602i) q^{62} +(-2.56060 - 0.665818i) q^{63} +1.00000i q^{64} +(6.62073 + 2.05527i) q^{65} +(-1.71365 + 0.989376i) q^{66} +(-5.32434 - 1.42665i) q^{67} +(1.19130 + 4.44599i) q^{68} +5.88246 q^{69} +(3.11939 - 5.02687i) q^{70} -3.86002 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-14.7013 - 3.93920i) q^{73} +(2.40055 - 1.38596i) q^{74} +(-3.80156 + 3.24779i) q^{75} -4.21878i q^{76} +(-3.72923 - 3.67438i) q^{77} +(2.19222 + 2.19222i) q^{78} +(-2.21282 - 1.27757i) q^{79} +(2.23435 + 0.0876265i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-6.33349 + 1.69705i) q^{82} +(-9.52969 + 9.52969i) q^{83} +(2.28142 - 1.33981i) q^{84} +(10.0383 - 2.27219i) q^{85} +(4.48111 - 7.76151i) q^{86} +(2.31642 - 8.64500i) q^{87} +(0.512139 - 1.91133i) q^{88} +(-3.09593 + 5.36231i) q^{89} +(-2.18090 + 0.493652i) q^{90} +(-4.04852 + 7.13378i) q^{91} +(-4.15953 + 4.15953i) q^{92} +(-1.67478 + 0.448756i) q^{93} +(3.04008 + 5.26557i) q^{94} +(-9.42624 - 0.369678i) q^{95} +(0.866025 + 0.500000i) q^{96} +(1.48031 + 1.48031i) q^{97} +(5.02254 + 4.87586i) q^{98} +1.97875i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 8 * q^7	$ 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.04129	+	1.97882i	0.465678	+	0.884954i
$5$	1.04129	+	1.97882i	0.465678	+	0.884954i
$6$			1.00000i			0.408248i
$7$	−2.55046	+	0.703686i	−0.963982	+	0.265968i
$7$	−2.55046	+	0.703686i	−0.963982	+	0.265968i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−1.64189	+	1.51796i	−0.519210	+	0.480022i
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	0.975749	−	0.218892i	$-0.0702443\pi$
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	−0.677441	+	0.735577i	$0.736911\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	2.19222	−	2.19222i	0.608011	−	0.608011i	−0.334415	−	0.942426i	$-0.608539\pi$
$13$	2.19222	−	2.19222i	0.608011	−	0.608011i	0.942426	+	0.334415i	$0.108539\pi$
$14$	−1.33981	−	2.28142i	−0.358081	−	0.609736i
$15$	0.493652	+	2.18090i	0.127460	+	0.563105i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.19130	−	4.44599i	0.288932	−	1.07831i	−0.656985	−	0.753903i	$-0.728169\pi$
$17$	1.19130	−	4.44599i	0.288932	−	1.07831i	0.945918	−	0.324407i	$-0.105165\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	−2.10939	+	3.65357i	−0.483928	+	0.838188i	−0.999830	−	0.0184602i	$-0.994124\pi$
$19$	−2.10939	+	3.65357i	−0.483928	+	0.838188i	0.515902	+	0.856648i	$0.327457\pi$
$20$	−1.89119	−	1.19306i	−0.422883	−	0.266777i
$21$	−2.64568	+	0.0196015i	−0.577334	+	0.00427740i
$22$	−1.39919	+	1.39919i	−0.298308	+	0.298308i
$23$	5.68202	−	1.52249i	1.18478	−	0.317462i	0.387961	−	0.921676i	$-0.373179\pi$
$23$	5.68202	−	1.52249i	1.18478	−	0.317462i	0.796822	+	0.604214i	$0.206513\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−2.83144	+	4.12104i	−0.566287	+	0.824208i
$26$	2.68491	+	1.55013i	0.526553	+	0.304006i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.85692	−	1.88464i	0.350924	−	0.356163i
$29$		−	8.94996i		−	1.66197i	−0.556298	−	0.830983i	$-0.687779\pi$
$29$		−	8.94996i		−	1.66197i	0.556298	−	0.830983i	$-0.312221\pi$
$30$	−1.97882	+	1.04129i	−0.361281	+	0.190112i
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	−0.628747	−	0.777610i	$-0.716432\pi$
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	0.359057	+	0.933316i	$0.383098\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.512139	+	1.91133i	0.0891519	+	0.332720i
$34$	4.60282			0.789378
$35$	−4.04823	−	4.31415i	−0.684275	−	0.729224i
$36$	−1.00000			−0.166667
$37$	−0.717425	−	2.67747i	−0.117944	−	0.440173i	0.881546	−	0.472097i	$-0.156503\pi$
$37$	−0.717425	−	2.67747i	−0.117944	−	0.440173i	−0.999490	+	0.0319248i	$0.989836\pi$
$38$	−4.07503	−	1.09190i	−0.661058	−	0.177130i
$39$	2.68491	−	1.55013i	0.429929	−	0.248220i
$40$	0.662933	−	2.13554i	0.104819	−	0.337658i
$41$			6.55691i			1.02402i	0.858980	+	0.512008i	$0.171098\pi$
$41$			6.55691i			1.02402i	−0.858980	+	0.512008i	$0.828902\pi$
$42$	−0.703686	−	2.55046i	−0.108581	−	0.393544i
$43$	−6.33724	−	6.33724i	−0.966421	−	0.966421i	0.0330335	−	0.999454i	$-0.489483\pi$
$43$	−6.33724	−	6.33724i	−0.966421	−	0.966421i	−0.999454	+	0.0330335i	$0.989483\pi$
$44$	−1.71365	−	0.989376i	−0.258342	−	0.149154i
$45$	−0.0876265	+	2.23435i	−0.0130626	+	0.333077i
$46$	2.94123	+	5.09436i	0.433661	+	0.751122i
$47$	5.87298	−	1.57366i	0.856663	−	0.229542i	0.196351	−	0.980534i	$-0.437091\pi$
$47$	5.87298	−	1.57366i	0.856663	−	0.229542i	0.660312	+	0.750992i	$0.270424\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	6.00965	−	3.58944i	0.858522	−	0.512777i
$50$	−4.71345	−	1.66835i	−0.666582	−	0.235941i
$51$	2.30141	−	3.98616i	0.322262	−	0.558174i
$52$	−0.802407	+	2.99462i	−0.111274	+	0.415280i
$53$	2.95926	−	11.0441i	0.406485	−	1.51702i	−0.394814	−	0.918761i	$-0.629191\pi$
$53$	2.95926	−	11.0441i	0.406485	−	1.51702i	0.801300	−	0.598263i	$-0.204142\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.36077	+	3.74220i	−0.318327	+	0.504598i
$56$	2.30103	+	1.30586i	0.307487	+	0.174503i
$57$	−2.98313	+	2.98313i	−0.395125	+	0.395125i
$58$	8.64500	−	2.31642i	1.13514	−	0.304161i
$59$	2.10351	+	3.64339i	0.273854	+	0.474329i	0.969845	−	0.243721i	$-0.0783682\pi$
$59$	2.10351	+	3.64339i	0.273854	+	0.474329i	−0.695991	+	0.718050i	$0.745035\pi$
$60$	−1.51796	−	1.64189i	−0.195968	−	0.211967i
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.967658	−	0.252266i	$-0.0811759\pi$
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.265360	+	0.964149i	$0.414509\pi$
$62$	−1.22602	−	1.22602i	−0.155705	−	0.155705i
$63$	−2.56060	−	0.665818i	−0.322606	−	0.0838852i
$64$			1.00000i			0.125000i
$65$	6.62073	+	2.05527i	0.821200	+	0.254924i
$66$	−1.71365	+	0.989376i	−0.210936	+	0.121784i
$67$	−5.32434	−	1.42665i	−0.650472	−	0.174294i	−0.0815298	−	0.996671i	$-0.525981\pi$
$67$	−5.32434	−	1.42665i	−0.650472	−	0.174294i	−0.568942	+	0.822377i	$0.692647\pi$
$68$	1.19130	+	4.44599i	0.144466	+	0.539155i
$69$	5.88246			0.708165
$70$	3.11939	−	5.02687i	0.372838	−	0.600826i
$71$	−3.86002			−0.458100			−0.229050	−	0.973415i	$-0.573562\pi$
$71$	−3.86002			−0.458100			−0.229050	+	0.973415i	$0.573562\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	−14.7013	−	3.93920i	−1.72066	−	0.461048i	−0.742660	−	0.669669i	$-0.766436\pi$
$73$	−14.7013	−	3.93920i	−1.72066	−	0.461048i	−0.977997	+	0.208621i	$0.933103\pi$
$74$	2.40055	−	1.38596i	0.279058	−	0.161114i
$75$	−3.80156	+	3.24779i	−0.438967	+	0.375022i
$76$		−	4.21878i		−	0.483928i
$77$	−3.72923	−	3.67438i	−0.424985	−	0.418734i
$78$	2.19222	+	2.19222i	0.248220	+	0.248220i
$79$	−2.21282	−	1.27757i	−0.248962	−	0.143738i	0.370327	−	0.928901i	$-0.379246\pi$
$79$	−2.21282	−	1.27757i	−0.248962	−	0.143738i	−0.619289	+	0.785163i	$0.712579\pi$
$80$	2.23435	+	0.0876265i	0.249808	+	0.00979695i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−6.33349	+	1.69705i	−0.699416	+	0.187408i
$83$	−9.52969	+	9.52969i	−1.04602	+	1.04602i	−0.0471311	+	0.998889i	$0.515008\pi$
$83$	−9.52969	+	9.52969i	−1.04602	+	1.04602i	−0.998889	+	0.0471311i	$0.984992\pi$
$84$	2.28142	−	1.33981i	0.248924	−	0.146186i
$85$	10.0383	−	2.27219i	1.08880	−	0.246454i
$86$	4.48111	−	7.76151i	0.483210	−	0.836945i
$87$	2.31642	−	8.64500i	0.248346	−	0.926841i
$88$	0.512139	−	1.91133i	0.0545942	−	0.203748i
$89$	−3.09593	+	5.36231i	−0.328168	+	0.568404i	−0.982148	−	0.188108i	$-0.939765\pi$
$89$	−3.09593	+	5.36231i	−0.328168	+	0.568404i	0.653980	+	0.756512i	$0.273098\pi$
$90$	−2.18090	+	0.493652i	−0.229887	+	0.0520355i
$91$	−4.04852	+	7.13378i	−0.424400	+	0.747824i
$92$	−4.15953	+	4.15953i	−0.433661	+	0.433661i
$93$	−1.67478	+	0.448756i	−0.173667	+	0.0465339i
$94$	3.04008	+	5.26557i	0.313560	+	0.543102i
$95$	−9.42624	−	0.369678i	−0.967112	−	0.0379281i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	1.48031	+	1.48031i	0.150303	+	0.150303i	0.778253	−	0.627951i	$-0.216106\pi$
$97$	1.48031	+	1.48031i	0.150303	+	0.150303i	−0.627951	+	0.778253i	$0.716106\pi$
$98$	5.02254	+	4.87586i	0.507354	+	0.492537i
$99$			1.97875i			0.198872i
$100$	0.391577	−	4.98464i	0.0391577	−	0.498464i
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	−0.865948	−	0.500134i	$-0.833284\pi$
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	0.000154194		1.00000i	$0.499951\pi$
$102$	4.44599	+	1.19130i	0.440218	+	0.117956i
$103$	1.29095	+	4.81790i	0.127201	+	0.474722i	0.999909	−	0.0135219i	$-0.00430427\pi$
$103$	1.29095	+	4.81790i	0.127201	+	0.474722i	−0.872707	+	0.488244i	$0.837638\pi$
$104$	−3.10026			−0.304006
$105$	−2.79370	−	5.21490i	−0.272637	−	0.508923i
$106$	11.4337			1.11054
$107$	1.56576	+	5.84351i	0.151368	+	0.564913i	0.999389	+	0.0349507i	$0.0111274\pi$
$107$	1.56576	+	5.84351i	0.151368	+	0.564913i	−0.848021	+	0.529963i	$0.822206\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−8.44287	+	4.87449i	−0.808680	+	0.466892i	−0.846497	−	0.532393i	$-0.821293\pi$
$109$	−8.44287	+	4.87449i	−0.808680	+	0.466892i	0.0378171	+	0.999285i	$0.487960\pi$
$110$	−4.22570	−	1.31178i	−0.402905	−	0.125073i
$111$		−	2.77192i		−	0.263099i
$112$	−0.665818	+	2.56060i	−0.0629139	+	0.241954i
$113$	6.02504	+	6.02504i	0.566788	+	0.566788i	0.931227	−	0.364439i	$-0.118739\pi$
$113$	6.02504	+	6.02504i	0.566788	+	0.566788i	−0.364439	+	0.931227i	$0.618739\pi$
$114$	−3.65357	−	2.10939i	−0.342189	−	0.197563i
$115$	8.92936	+	9.65833i	0.832667	+	0.900644i
$116$	4.47498	+	7.75089i	0.415491	+	0.719652i
$117$	2.99462	−	0.802407i	0.276853	−	0.0741826i
$118$	−2.97481	+	2.97481i	−0.273854	+	0.273854i
$119$	0.0902224	+	12.1776i	0.00827067	+	1.11632i
$120$	1.19306	−	1.89119i	0.108911	−	0.172641i
$121$	3.54227	−	6.13539i	0.322024	−	0.557763i
$122$	−2.87806	+	10.7411i	−0.260567	+	0.972451i
$123$	−1.69705	+	6.33349i	−0.153018	+	0.571071i
$124$	0.866930	−	1.50157i	0.0778527	−	0.134845i
$125$	−11.1031	−	1.31171i	−0.993094	−	0.117323i
$126$	−0.0196015	−	2.64568i	−0.00174624	−	0.235696i
$127$	−8.92770	+	8.92770i	−0.792205	+	0.792205i	−0.981852	−	0.189647i	$-0.939266\pi$
$127$	−8.92770	+	8.92770i	−0.792205	+	0.792205i	0.189647	+	0.981852i	$0.439266\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.48111	−	7.76151i	−0.394540	−	0.683363i
$130$	−0.271665	+	6.92707i	−0.0238266	+	0.607544i
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	0.293562	−	0.955940i	$-0.405159\pi$
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	−0.681087	+	0.732202i	$0.738493\pi$
$132$	−1.39919	−	1.39919i	−0.121784	−	0.121784i
$133$	2.80894	−	10.8026i	0.243566	−	0.936707i
$134$		−	5.51217i		−	0.476179i
$135$	−0.662933	+	2.13554i	−0.0570562	+	0.183798i
$136$	−3.98616	+	2.30141i	−0.341811	+	0.197344i
$137$	11.1877	+	2.99773i	0.955829	+	0.256114i	0.702834	−	0.711354i	$-0.251918\pi$
$137$	11.1877	+	2.99773i	0.955829	+	0.256114i	0.252995	+	0.967468i	$0.418584\pi$
$138$	1.52249	+	5.68202i	0.129603	+	0.483686i
$139$	−2.87054			−0.243476			−0.121738	−	0.992562i	$-0.538847\pi$
$139$	−2.87054			−0.243476			−0.121738	+	0.992562i	$0.538847\pi$
$140$	5.66294	+	1.71205i	0.478606	+	0.144694i
$141$	6.08016			0.512042
$142$	−0.999046	−	3.72849i	−0.0838381	−	0.312888i
$143$	5.92562	+	1.58776i	0.495525	+	0.132776i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	17.7103	−	9.31949i	1.47076	−	0.773941i
$146$		−	15.2199i		−	1.25961i
$147$	6.73389	−	1.91172i	0.555402	−	0.157676i
$148$	1.96004	+	1.96004i	0.161114	+	0.161114i
$149$	13.4924	+	7.78982i	1.10534	+	0.638167i	0.937618	−	0.347668i	$-0.113026\pi$
$149$	13.4924	+	7.78982i	1.10534	+	0.638167i	0.167720	+	0.985835i	$0.446360\pi$
$150$	−4.12104	−	2.83144i	−0.336481	−	0.231186i
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	−0.869769	−	0.493459i	$-0.835732\pi$
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	0.00753703	−	0.999972i	$-0.497601\pi$
$152$	4.07503	−	1.09190i	0.330529	−	0.0885649i
$153$	3.25469	−	3.25469i	0.263126	−	0.263126i
$154$	2.58398	−	4.55316i	0.208223	−	0.366904i
$155$	−3.27906	−	2.06860i	−0.263381	−	0.166154i
$156$	−1.55013	+	2.68491i	−0.124110	+	0.214965i
$157$	3.92974	−	14.6660i	0.313627	−	1.17047i	−0.611633	−	0.791141i	$-0.709487\pi$
$157$	3.92974	−	14.6660i	0.313627	−	1.17047i	0.925261	−	0.379332i	$-0.123846\pi$
$158$	0.661320	−	2.46808i	0.0526118	−	0.196350i
$159$	5.71685	−	9.90187i	0.453375	−	0.785269i
$160$	0.493652	+	2.18090i	0.0390266	+	0.172415i
$161$	−13.4204	+	7.88141i	−1.05767	+	0.621142i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−21.5624	+	5.77762i	−1.68890	+	0.452538i	−0.970105	−	0.242687i	$-0.921971\pi$
$163$	−21.5624	+	5.77762i	−1.68890	+	0.452538i	−0.718792	+	0.695225i	$0.755305\pi$
$164$	−3.27845	−	5.67845i	−0.256004	−	0.443412i
$165$	−3.24889	+	3.00367i	−0.252925	+	0.233836i
$166$	−11.6714	−	6.73851i	−0.905880	−	0.523010i
$167$	6.91224	+	6.91224i	0.534885	+	0.534885i	0.922022	−	0.387137i	$-0.126536\pi$
$167$	6.91224	+	6.91224i	0.534885	+	0.534885i	−0.387137	+	0.922022i	$0.626536\pi$
$168$	1.88464	+	1.85692i	0.145403	+	0.143264i
$169$			3.38837i			0.260644i
$170$	4.79287	+	9.10815i	0.367596	+	0.698563i
$171$	−3.65357	+	2.10939i	−0.279396	+	0.161309i
$172$	8.65684	+	2.31959i	0.660078	+	0.176867i
$173$	−1.17183	−	4.37334i	−0.0890928	−	0.332499i	0.906965	−	0.421206i	$-0.138393\pi$
$173$	−1.17183	−	4.37334i	−0.0890928	−	0.332499i	−0.996058	+	0.0887072i	$0.971726\pi$
$174$	8.94996			0.678495
$175$	4.32154	−	12.5030i	0.326678	−	0.945136i
$176$	1.97875			0.149154
$177$	1.08886	+	4.06367i	0.0818436	+	0.305444i
$178$	−5.98088	−	1.60257i	−0.448286	−	0.120118i
$179$	−1.79084	+	1.03394i	−0.133853	+	0.0772803i	−0.565431	−	0.824795i	$-0.691290\pi$
$179$	−1.79084	+	1.03394i	−0.133853	+	0.0772803i	0.431578	+	0.902076i	$0.357957\pi$
$180$	−1.04129	−	1.97882i	−0.0776131	−	0.147492i
$181$			6.13199i			0.455787i	0.973686	+	0.227894i	$0.0731839\pi$
$181$			6.13199i			0.455787i	−0.973686	+	0.227894i	$0.926816\pi$
$182$	−7.93854	−	2.06421i	−0.588444	−	0.153010i
$183$	7.86301	+	7.86301i	0.581250	+	0.581250i
$184$	−5.09436	−	2.94123i	−0.375561	−	0.216830i
$185$	4.55117	−	4.20767i	0.334609	−	0.309354i
$186$	−0.866930	−	1.50157i	−0.0635664	−	0.110100i
$187$	8.79751	−	2.35728i	0.643337	−	0.172382i
$188$	−4.29932	+	4.29932i	−0.313560	+	0.313560i
$189$	−2.30103	−	1.30586i	−0.167375	−	0.0949876i
$190$	−2.08261	−	9.20073i	−0.151088	−	0.667491i
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	−0.410022	−	0.912075i	$-0.634479\pi$
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	0.994892	−	0.100948i	$-0.0321876\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	5.63991	−	21.0484i	0.405969	−	1.51510i	−0.396292	−	0.918125i	$-0.629703\pi$
$193$	5.63991	−	21.0484i	0.405969	−	1.51510i	0.802261	−	0.596973i	$-0.203630\pi$
$194$	−1.04674	+	1.81300i	−0.0751514	+	0.130166i
$195$	5.86319	+	3.69881i	0.419872	+	0.264877i
$196$	−3.40979	+	6.11337i	−0.243557	+	0.436669i
$197$	−0.628120	+	0.628120i	−0.0447517	+	0.0447517i	−0.729129	−	0.684377i	$-0.760074\pi$
$197$	−0.628120	+	0.628120i	−0.0447517	+	0.0447517i	0.684377	+	0.729129i	$0.260074\pi$
$198$	−1.91133	+	0.512139i	−0.135832	+	0.0363961i
$199$	4.81248	+	8.33546i	0.341147	+	0.590885i	0.984646	−	0.174563i	$-0.0558511\pi$
$199$	4.81248	+	8.33546i	0.341147	+	0.590885i	−0.643499	+	0.765447i	$0.722518\pi$
$200$	4.91614	−	0.911886i	0.347624	−	0.0644801i
$201$	−4.77368	−	2.75608i	−0.336709	−	0.194399i
$202$	−7.10444	−	7.10444i	−0.499866	−	0.499866i
$203$	6.29796	+	22.8265i	0.442030	+	1.60210i
$204$			4.60282i			0.322262i
$205$	−12.9749	+	6.82763i	−0.906208	+	0.476862i
$206$	−4.31961	+	2.49393i	−0.300962	+	0.173760i
$207$	5.68202	+	1.52249i	0.394928	+	0.105821i
$208$	−0.802407	−	2.99462i	−0.0556369	−	0.207640i
$209$	−8.34793			−0.577439
$210$	4.31415	−	4.04823i	0.297704	−	0.279354i
$211$	11.2669			0.775648			0.387824	−	0.921733i	$-0.373227\pi$
$211$	11.2669			0.775648			0.387824	+	0.921733i	$0.373227\pi$
$212$	2.95926	+	11.0441i	0.203243	+	0.758512i
$213$	−3.72849	−	0.999046i	−0.255472	−	0.0684535i
$214$	−5.23915	+	3.02482i	−0.358141	+	0.206773i
$215$	5.94135	−	19.1391i	0.405197	−	1.30528i
$216$		−	1.00000i		−	0.0680414i
$217$	3.21964	−	3.26770i	0.218563	−	0.221826i
$218$	−6.89357	−	6.89357i	−0.466892	−	0.466892i
$219$	−13.1808	−	7.60995i	−0.890677	−	0.514233i
$220$	0.173391	−	4.42123i	0.0116900	−	0.298079i
$221$	−7.13498	−	12.3581i	−0.479951	−	0.831299i
$222$	2.67747	−	0.717425i	0.179700	−	0.0481504i
$223$	13.1718	−	13.1718i	0.882048	−	0.882048i	−0.111694	−	0.993743i	$-0.535628\pi$
$223$	13.1718	−	13.1718i	0.882048	−	0.882048i	0.993743	+	0.111694i	$0.0356277\pi$
$224$	−2.64568	+	0.0196015i	−0.176772	+	0.00130968i
$225$	−4.51262	+	2.15321i	−0.300841	+	0.143547i
$226$	−4.26035	+	7.37914i	−0.283394	+	0.490853i
$227$	6.96589	−	25.9971i	0.462343	−	1.72549i	−0.203210	−	0.979135i	$-0.565137\pi$
$227$	6.96589	−	25.9971i	0.462343	−	1.72549i	0.665552	−	0.746351i	$-0.268196\pi$
$228$	1.09190	−	4.07503i	0.0723130	−	0.269876i
$229$	−13.4452	+	23.2878i	−0.888486	+	1.53890i	−0.0468199	+	0.998903i	$0.514909\pi$
$229$	−13.4452	+	23.2878i	−0.888486	+	1.53890i	−0.841666	+	0.539999i	$0.818425\pi$
$230$	−7.01814	+	11.1249i	−0.462762	+	0.733551i
$231$	−2.65116	−	4.51437i	−0.174434	−	0.297024i
$232$	−6.32858	+	6.32858i	−0.415491	+	0.415491i
$233$	0.889853	−	0.238436i	0.0582962	−	0.0156204i	−0.229553	−	0.973296i	$-0.573726\pi$
$233$	0.889853	−	0.238436i	0.0582962	−	0.0156204i	0.287849	+	0.957676i	$0.407060\pi$
$234$	1.55013	+	2.68491i	0.101335	+	0.175518i
$235$	9.22946	+	9.98293i	0.602063	+	0.651214i
$236$	−3.64339	−	2.10351i	−0.237164	−	0.136927i
$237$	−1.80676	−	1.80676i	−0.117362	−	0.117362i
$238$	−11.7393	+	3.23894i	−0.760946	+	0.209949i
$239$		−	25.3432i		−	1.63931i	−0.572856	−	0.819656i	$-0.694164\pi$
$239$		−	25.3432i		−	1.63931i	0.572856	−	0.819656i	$-0.305836\pi$
$240$	2.13554	+	0.662933i	0.137848	+	0.0427922i
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.222597	−	0.974911i	$-0.428547\pi$
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.955596	+	0.294681i	$0.0952134\pi$
$242$	6.84314	+	1.83361i	0.439894	+	0.117869i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−11.1200			−0.711883
$245$	13.3606	+	8.15437i	0.853579	+	0.520963i
$246$	−6.55691			−0.418053
$247$	3.38518	+	12.6337i	0.215394	+	0.803861i
$248$	1.67478	+	0.448756i	0.106349	+	0.0284960i
$249$	−11.6714	+	6.73851i	−0.739648	+	0.427036i
$250$	−1.60669	−	11.0643i	−0.101616	−	0.699767i
$251$			2.70623i			0.170816i	0.996346	+	0.0854078i	$0.0272193\pi$
$251$			2.70623i			0.170816i	−0.996346	+	0.0854078i	$0.972781\pi$
$252$	2.55046	−	0.703686i	0.160664	−	0.0443280i
$253$	8.23068	+	8.23068i	0.517458	+	0.517458i
$254$	−10.9342	−	6.31283i	−0.686070	−	0.396102i
$255$	10.2843	+	0.403330i	0.644029	+	0.0252575i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.2035	+	6.21737i	−1.44740	+	0.387829i	−0.895117	−	0.445831i	$-0.852908\pi$
$257$	−23.2035	+	6.21737i	−1.44740	+	0.387829i	−0.552279	+	0.833660i	$0.686242\pi$
$258$	6.33724	−	6.33724i	0.394540	−	0.394540i
$259$	3.71385	+	6.32392i	0.230768	+	0.392949i
$260$	−6.76135	+	1.53045i	−0.419321	+	0.0949145i
$261$	4.47498	−	7.75089i	0.276994	−	0.479768i
$262$	1.32557	−	4.94708i	0.0818938	−	0.305632i
$263$	0.220080	−	0.821351i	0.0135707	−	0.0506467i	−0.958808	−	0.284053i	$-0.908321\pi$
$263$	0.220080	−	0.821351i	0.0135707	−	0.0506467i	0.972379	+	0.233407i	$0.0749874\pi$
$264$	0.989376	−	1.71365i	0.0608919	−	0.105468i
$265$	24.9357	−	5.64426i	1.53179	−	0.346724i
$266$	11.1615	−	0.0826946i	0.684359	−	0.00507033i
$267$	−4.37831	+	4.37831i	−0.267948	+	0.267948i
$268$	5.32434	−	1.42665i	0.325236	−	0.0871468i
$269$	5.82171	+	10.0835i	0.354956	+	0.614802i	0.987110	−	0.160041i	$-0.0511625\pi$
$269$	5.82171	+	10.0835i	0.354956	+	0.614802i	−0.632154	+	0.774842i	$0.717829\pi$
$270$	−2.23435	−	0.0876265i	−0.135978	−	0.00533278i
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.261471	−	0.965211i	$-0.584208\pi$
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.966633	+	0.256165i	$0.917541\pi$
$272$	−3.25469	−	3.25469i	−0.197344	−	0.197344i
$273$	−5.75693	+	5.84287i	−0.348425	+	0.353627i
$274$			11.5824i			0.699715i
$275$	−9.86338	−	0.774834i	−0.594784	−	0.0467242i
$276$	−5.09436	+	2.94123i	−0.306644	+	0.177041i
$277$	−9.12775	−	2.44577i	−0.548433	−	0.146952i	−0.0260462	−	0.999661i	$-0.508292\pi$
$277$	−9.12775	−	2.44577i	−0.548433	−	0.146952i	−0.522387	+	0.852708i	$0.674958\pi$
$278$	−0.742949	−	2.77273i	−0.0445591	−	0.166297i
$279$	−1.73386			−0.103804
$280$	−0.188035	+	5.91309i	−0.0112372	+	0.353375i
$281$	−11.7320			−0.699871			−0.349935	−	0.936774i	$-0.613796\pi$
$281$	−11.7320			−0.699871			−0.349935	+	0.936774i	$0.613796\pi$
$282$	1.57366	+	5.87298i	0.0937101	+	0.349731i
$283$	3.52349	+	0.944117i	0.209450	+	0.0561219i	0.362018	−	0.932171i	$-0.382088\pi$
$283$	3.52349	+	0.944117i	0.209450	+	0.0561219i	−0.152568	+	0.988293i	$0.548754\pi$
$284$	3.34287	−	1.93001i	0.198363	−	0.114525i
$285$	−9.00937	−	2.79677i	−0.533669	−	0.165667i
$286$			6.13465i			0.362750i
$287$	−4.61400	−	16.7231i	−0.272356	−	0.987133i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−3.62517	−	2.09299i	−0.213245	−	0.123117i
$290$	13.5857	+	14.6948i	0.797780	+	0.862909i
$291$	1.04674	+	1.81300i	0.0613609	+	0.106280i
$292$	14.7013	−	3.93920i	0.860328	−	0.230524i
$293$	−8.62354	+	8.62354i	−0.503793	+	0.503793i	−0.912614	−	0.408822i	$-0.865940\pi$
$293$	−8.62354	+	8.62354i	−0.503793	+	0.503793i	0.408822	+	0.912614i	$0.365940\pi$
$294$	3.58944	+	6.00965i	0.209340	+	0.350490i
$295$	−5.01924	+	7.95628i	−0.292231	+	0.463233i
$296$	−1.38596	+	2.40055i	−0.0805572	+	0.139529i
$297$	−0.512139	+	1.91133i	−0.0297173	+	0.110907i
$298$	−4.03231	+	15.0488i	−0.233585	+	0.871752i
$299$	9.11859	−	15.7939i	0.527341	−	0.913382i
$300$	1.66835	−	4.71345i	0.0963225	−	0.272131i
$301$	20.6223	+	11.7034i	1.18865	+	0.674575i
$302$	14.9840	−	14.9840i	0.862232	−	0.862232i
$303$	−9.70484	+	2.60040i	−0.557529	+	0.149389i
$304$	2.10939	+	3.65357i	0.120982	+	0.209547i
$305$	−0.974405	+	24.8459i	−0.0557942	+	1.42267i
$306$	3.98616	+	2.30141i	0.227874	+	0.131563i
$307$	15.9933	+	15.9933i	0.912785	+	0.912785i	0.996490	−	0.0837060i	$-0.0266757\pi$
$307$	15.9933	+	15.9933i	0.912785	+	0.912785i	−0.0837060	+	0.996490i	$0.526676\pi$
$308$	5.06680	+	1.31749i	0.288708	+	0.0750710i
$309$			4.98786i			0.283750i
$310$	1.14943	−	3.70272i	0.0652835	−	0.210301i
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	−0.297695	−	0.954661i	$-0.596218\pi$
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	0.677913	+	0.735142i	$0.262885\pi$
$312$	−2.99462	−	0.802407i	−0.169537	−	0.0454273i
$313$	5.18810	+	19.3623i	0.293249	+	1.09442i	0.942598	+	0.333929i	$0.108375\pi$
$313$	5.18810	+	19.3623i	0.293249	+	1.09442i	−0.649349	+	0.760490i	$0.724959\pi$
$314$	15.1833			0.856846
$315$	−1.34879	−	5.76027i	−0.0759959	−	0.324555i
$316$	2.55514			0.143738
$317$	−0.771364	−	2.87877i	−0.0433241	−	0.161688i	0.940875	−	0.338755i	$-0.110006\pi$
$317$	−0.771364	−	2.87877i	−0.0433241	−	0.161688i	−0.984199	+	0.177067i	$0.943339\pi$
$318$	11.0441	+	2.95926i	0.619322	+	0.165947i
$319$	15.3371	−	8.85488i	0.858713	−	0.495778i
$320$	−1.97882	+	1.04129i	−0.110619	+	0.0582098i
$321$			6.04965i			0.337658i
$322$	−11.0863	−	10.9232i	−0.617816	−	0.608728i
$323$	13.7308	+	13.7308i	0.764004	+	0.764004i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	2.82709	+	15.2413i	0.156819	+	0.845437i
$326$	−11.1615	−	19.3323i	−0.618179	−	1.07072i
$327$	−9.41680	+	2.52322i	−0.520750	+	0.139535i
$328$	4.63643	−	4.63643i	0.256004	−	0.256004i
$329$	−13.8714	+	8.14629i	−0.764756	+	0.449119i
$330$	−3.74220	−	2.36077i	−0.206001	−	0.129956i
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	0.175194	+	0.984534i	$0.443945\pi$
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	−0.940228	+	0.340545i	$0.889388\pi$
$332$	3.48811	−	13.0178i	0.191435	−	0.714445i
$333$	0.717425	−	2.67747i	0.0393146	−	0.146724i
$334$	−4.88769	+	8.46573i	−0.267442	+	0.463224i
$335$	−2.72109	−	12.0215i	−0.148669	−	0.656803i
$336$	−1.30586	+	2.30103i	−0.0712407	+	0.125531i
$337$	−17.1567	+	17.1567i	−0.934583	+	0.934583i	−0.997988	−	0.0634051i	$-0.979804\pi$
$337$	−17.1567	+	17.1567i	−0.934583	+	0.934583i	0.0634051	+	0.997988i	$0.479804\pi$
$338$	−3.27292	+	0.876975i	−0.178023	+	0.0477012i
$339$	4.26035	+	7.37914i	0.231390	+	0.400780i
$340$	−7.55731	+	6.98692i	−0.409853	+	0.378919i
$341$	−2.97123	−	1.71544i	−0.160901	−	0.0928963i
$342$	−2.98313	−	2.98313i	−0.161309	−	0.161309i
$343$	−12.8015	+	13.3836i	−0.691217	+	0.722647i
$344$			8.96222i			0.483210i
$345$	6.12534	+	11.6403i	0.329777	+	0.626694i
$346$	3.92103	−	2.26381i	0.210796	−	0.121703i
$347$	24.1895	+	6.48156i	1.29856	+	0.347948i	0.840906	−	0.541181i	$-0.182023\pi$
$347$	24.1895	+	6.48156i	1.29856	+	0.347948i	0.457655	+	0.889130i	$0.348689\pi$
$348$	2.31642	+	8.64500i	0.124173	+	0.463421i
$349$	−18.0130			−0.964212			−0.482106	−	0.876113i	$-0.660128\pi$
$349$	−18.0130			−0.964212			−0.482106	+	0.876113i	$0.660128\pi$
$350$	13.1954	+	0.938280i	0.705326	+	0.0501532i
$351$	3.10026			0.165480
$352$	0.512139	+	1.91133i	0.0272971	+	0.101874i
$353$	7.33911	+	1.96651i	0.390621	+	0.104667i	0.448784	−	0.893641i	$-0.351857\pi$
$353$	7.33911	+	1.96651i	0.390621	+	0.104667i	−0.0581623	+	0.998307i	$0.518524\pi$
$354$	−3.64339	+	2.10351i	−0.193644	+	0.111800i
$355$	−4.01939	−	7.63827i	−0.213327	−	0.405397i
$356$		−	6.19187i		−	0.328168i
$357$	−3.06464	+	11.7860i	−0.162198	+	0.623781i
$358$	−1.46221	−	1.46221i	−0.0772803	−	0.0772803i
$359$	−2.84638	−	1.64336i	−0.150226	−	0.0867332i	0.423003	−	0.906128i	$-0.360976\pi$
$359$	−2.84638	−	1.64336i	−0.150226	−	0.0867332i	−0.573229	+	0.819395i	$0.694309\pi$
$360$	1.64189	−	1.51796i	0.0865350	−	0.0800037i
$361$	0.600927	+	1.04084i	0.0316277	+	0.0547808i
$362$	−5.92305	+	1.58708i	−0.311309	+	0.0834149i
$363$	5.00952	−	5.00952i	0.262932	−	0.262932i
$364$	−0.0607699	−	8.20230i	−0.00318521	−	0.429917i
$365$	−7.51333	−	33.1930i	−0.393266	−	1.73740i
$366$	−5.55999	+	9.63018i	−0.290625	+	0.503377i
$367$	−0.840538	+	3.13693i	−0.0438757	+	0.163746i	−0.984388	−	0.176014i	$-0.943679\pi$
$367$	−0.840538	+	3.13693i	−0.0438757	+	0.163746i	0.940512	+	0.339761i	$0.110346\pi$
$368$	1.52249	−	5.68202i	0.0793654	−	0.296196i
$369$	−3.27845	+	5.67845i	−0.170669	+	0.295608i
$370$	5.24222	+	3.30707i	0.272530	+	0.171926i
$371$	0.224118	+	30.2499i	0.0116356	+	1.57050i
$372$	1.22602	−	1.22602i	0.0635664	−	0.0635664i
$373$	15.2290	−	4.08060i	0.788529	−	0.211286i	0.157987	−	0.987441i	$-0.449500\pi$
$373$	15.2290	−	4.08060i	0.788529	−	0.211286i	0.630542	+	0.776156i	$0.282833\pi$
$374$	4.55392	+	7.88763i	0.235478	+	0.407860i
$375$	−10.3853	−	4.14071i	−0.536295	−	0.213825i
$376$	−5.26557	−	3.04008i	−0.271551	−	0.156780i
$377$	−19.6203	−	19.6203i	−1.01049	−	1.01049i
$378$	0.665818	−	2.56060i	0.0342460	−	0.131703i
$379$		−	21.7428i		−	1.11685i	−0.829555	−	0.558426i	$-0.811406\pi$
$379$		−	21.7428i		−	1.11685i	0.829555	−	0.558426i	$-0.188594\pi$
$380$	8.34821	−	4.39297i	0.428254	−	0.225355i
$381$	−10.9342	+	6.31283i	−0.560174	+	0.323416i
$382$	15.6153	+	4.18410i	0.798946	+	0.214077i
$383$	−4.62973	−	17.2784i	−0.236568	−	0.882883i	−0.977436	−	0.211233i	$-0.932252\pi$
$383$	−4.62973	−	17.2784i	−0.236568	−	0.882883i	0.740868	−	0.671651i	$-0.234414\pi$
$384$	−1.00000			−0.0510310
$385$	3.38772	−	11.2056i	0.172654	−	0.571088i
$386$	21.7909			1.10913
$387$	−2.31959	−	8.65684i	−0.117912	−	0.440052i
$388$	−2.02214	−	0.541831i	−0.102659	−	0.0275073i
$389$	4.36130	−	2.51800i	0.221127	−	0.127667i	−0.385345	−	0.922772i	$-0.625918\pi$
$389$	4.36130	−	2.51800i	0.221127	−	0.127667i	0.606472	+	0.795105i	$0.292584\pi$
$390$	−2.05527	+	6.62073i	−0.104072	+	0.335254i
$391$		−	27.0759i		−	1.36929i
$392$	−6.78758	−	1.71135i	−0.342825	−	0.0864362i
$393$	−3.62152	−	3.62152i	−0.182681	−	0.182681i
$394$	−0.769287	−	0.444148i	−0.0387561	−	0.0223759i
$395$	0.223898	−	5.70908i	0.0112655	−	0.287255i
$396$	−0.989376	−	1.71365i	−0.0497180	−	0.0861142i
$397$	−14.2520	+	3.81880i	−0.715285	+	0.191660i	−0.598067	−	0.801446i	$-0.704064\pi$
$397$	−14.2520	+	3.81880i	−0.715285	+	0.191660i	−0.117218	+	0.993106i	$0.537398\pi$
$398$	−6.80587	+	6.80587i	−0.341147	+	0.341147i
$399$	5.50916	−	9.70753i	0.275803	−	0.485984i
$400$	2.15321	+	4.51262i	0.107660	+	0.225631i
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	−0.736840	−	0.676067i	$-0.763683\pi$
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	0.953911	+	0.300088i	$0.0970162\pi$
$402$	1.42665	−	5.32434i	0.0711550	−	0.265554i
$403$	−1.39126	+	5.19226i	−0.0693037	+	0.258645i
$404$	5.02360	−	8.70112i	0.249933	−	0.432897i
$405$	−1.19306	+	1.89119i	−0.0592837	+	0.0939740i
$406$	−20.4187	+	11.9913i	−1.01336	+	0.595118i
$407$	3.87844	−	3.87844i	0.192247	−	0.192247i
$408$	−4.44599	+	1.19130i	−0.220109	+	0.0589781i
$409$	−9.49095	−	16.4388i	−0.469297	−	0.812847i	0.530087	−	0.847944i	$-0.322159\pi$
$409$	−9.49095	−	16.4388i	−0.469297	−	0.812847i	−0.999384	+	0.0350966i	$0.988826\pi$
$410$	−9.95314	−	10.7657i	−0.491551	−	0.531680i
$411$	10.0306	+	5.79118i	0.494774	+	0.285658i
$412$	−3.52695	−	3.52695i	−0.173760	−	0.173760i
$413$	−7.92871	−	7.81209i	−0.390147	−	0.384408i
$414$			5.88246i			0.289107i
$415$	−28.7807	−	8.93437i	−1.41279	−	0.438571i
$416$	2.68491	−	1.55013i	0.131638	−	0.0760014i
$417$	−2.77273	−	0.742949i	−0.135781	−	0.0363824i
$418$	−2.16060	−	8.06348i	−0.105679	−	0.394398i
$419$	11.9171			0.582188			0.291094	−	0.956695i	$-0.405981\pi$
$419$	11.9171			0.582188			0.291094	+	0.956695i	$0.405981\pi$
$420$	5.02687	+	3.11939i	0.245286	+	0.152211i
$421$	6.95263			0.338850			0.169425	−	0.985543i	$-0.445809\pi$
$421$	6.95263			0.338850			0.169425	+	0.985543i	$0.445809\pi$
$422$	2.91610	+	10.8830i	0.141953	+	0.529778i
$423$	5.87298	+	1.57366i	0.285554	+	0.0765140i
$424$	−9.90187	+	5.71685i	−0.480877	+	0.277635i
$425$	14.9490	+	17.4979i	0.725133	+	0.848774i
$426$		−	3.86002i		−	0.187018i
$427$	−28.4738	−	7.40388i	−1.37795	−	0.358299i
$428$	−4.27775	−	4.27775i	−0.206773	−	0.206773i
$429$	5.31277	+	3.06733i	0.256503	+	0.148092i
$430$	20.0247	+	0.785328i	0.965678	+	0.0378719i
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	0.780928	−	0.624621i	$-0.214747\pi$
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	−0.931402	+	0.363993i	$0.881413\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	15.1544	−	15.1544i	0.728274	−	0.728274i	−0.242002	−	0.970276i	$-0.577804\pi$
$433$	15.1544	−	15.1544i	0.728274	−	0.728274i	0.970276	+	0.242002i	$0.0778040\pi$
$434$	3.98966	+	2.26419i	0.191510	+	0.108684i
$435$	19.5189	−	4.41816i	0.935861	−	0.211835i
$436$	4.87449	−	8.44287i	0.233446	−	0.404340i
$437$	−6.42307	+	23.9712i	−0.307257	+	1.14670i
$438$	3.93920	−	14.7013i	0.188222	−	0.702455i
$439$	16.3729	−	28.3588i	0.781438	−	1.35349i	−0.149666	−	0.988737i	$-0.547820\pi$
$439$	16.3729	−	28.3588i	0.781438	−	1.35349i	0.931104	−	0.364753i	$-0.118847\pi$
$440$	4.31545	−	0.976815i	0.205731	−	0.0465678i
$441$	6.99923	−	0.103719i	0.333297	−	0.00493899i
$442$	10.0904	−	10.0904i	0.479951	−	0.479951i
$443$	−29.7032	+	7.95895i	−1.41124	+	0.378141i	−0.882368	−	0.470559i	$-0.844052\pi$
$443$	−29.7032	+	7.95895i	−1.41124	+	0.378141i	−0.528874	+	0.848701i	$0.677385\pi$
$444$	1.38596	+	2.40055i	0.0657747	+	0.113925i
$445$	−13.8348	−	0.542572i	−0.655832	−	0.0257204i
$446$	16.1321	+	9.31386i	0.763876	+	0.441024i
$447$	11.0165	+	11.0165i	0.521061	+	0.521061i
$448$	−0.703686	−	2.55046i	−0.0332460	−	0.120498i
$449$		−	16.8713i		−	0.796207i	−0.917341	−	0.398103i	$-0.869669\pi$
$449$		−	16.8713i		−	0.796207i	0.917341	−	0.398103i	$-0.130331\pi$
$450$	−3.24779	−	3.80156i	−0.153102	−	0.179207i
$451$	−11.2362	+	6.48725i	−0.529094	+	0.305473i
$452$	−8.23036	−	2.20532i	−0.387123	−	0.103729i
$453$	−5.48452	−	20.4685i	−0.257685	−	0.961695i
$454$	26.9142			1.26314
$455$	−18.3321	−	0.582958i	−0.859424	−	0.0273295i
$456$	4.21878			0.197563
$457$	5.13696	+	19.1714i	0.240297	+	0.896800i	0.975689	+	0.219158i	$0.0703311\pi$
$457$	5.13696	+	19.1714i	0.240297	+	0.896800i	−0.735393	+	0.677641i	$0.763002\pi$
$458$	−25.9742	−	6.95976i	−1.21369	−	0.325208i
$459$	3.98616	−	2.30141i	0.186058	−	0.107421i
$460$	−12.5622	−	3.89968i	−0.585716	−	0.181823i
$461$			15.7775i			0.734830i	0.930057	+	0.367415i	$0.119757\pi$
$461$			15.7775i			0.734830i	−0.930057	+	0.367415i	$0.880243\pi$
$462$	3.67438	−	3.72923i	0.170948	−	0.173500i
$463$	4.48617	+	4.48617i	0.208490	+	0.208490i	0.803625	−	0.595135i	$-0.202902\pi$
$463$	4.48617	+	4.48617i	0.208490	+	0.208490i	−0.595135	+	0.803625i	$0.702902\pi$
$464$	−7.75089	−	4.47498i	−0.359826	−	0.207746i
$465$	−2.63194	−	2.84680i	−0.122053	−	0.132017i
$466$	0.460622	+	0.797821i	0.0213379	+	0.0369583i
$467$	−16.8554	+	4.51639i	−0.779975	+	0.208994i	−0.626774	−	0.779201i	$-0.715625\pi$
$467$	−16.8554	+	4.51639i	−0.779975	+	0.208994i	−0.153201	+	0.988195i	$0.548958\pi$
$468$	−2.19222	+	2.19222i	−0.101335	+	0.101335i
$469$	14.5834	−	0.108047i	0.673400	−	0.00498914i
$470$	−7.25401	+	11.4987i	−0.334602	+	0.530397i
$471$	7.59167	−	13.1492i	0.349806	−	0.605881i
$472$	1.08886	−	4.06367i	0.0501187	−	0.187046i
$473$	4.58990	−	17.1297i	0.211044	−	0.787626i
$474$	1.27757	−	2.21282i	0.0586808	−	0.101638i
$475$	−9.08391	−	19.0378i	−0.416799	−	0.873512i
$476$	−6.16693	−	10.5010i	−0.282661	−	0.481312i
$477$	8.08484	−	8.08484i	0.370180	−	0.370180i
$478$	24.4796	−	6.55929i	1.11967	−	0.300015i
$479$	15.8748	+	27.4960i	0.725339	+	1.25632i	0.958834	+	0.283966i	$0.0916503\pi$
$479$	15.8748	+	27.4960i	0.725339	+	1.25632i	−0.233495	+	0.972358i	$0.575016\pi$
$480$	−0.0876265	+	2.23435i	−0.00399959	+	0.101984i
$481$	−7.44233	−	4.29683i	−0.339341	−	0.195919i
$482$	14.9341	+	14.9341i	0.680230	+	0.680230i
$483$	−15.0030	+	4.13940i	−0.682658	+	0.188349i
$484$			7.08454i			0.322024i
$485$	−1.38783	+	4.47069i	−0.0630183	+	0.203004i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	28.8890	+	7.74077i	1.30908	+	0.350768i	0.844878	−	0.534960i	$-0.179673\pi$
$487$	28.8890	+	7.74077i	1.30908	+	0.350768i	0.464206	+	0.885727i	$0.346340\pi$
$488$	−2.87806	−	10.7411i	−0.130284	−	0.486225i
$489$	−22.3230			−1.00948
$490$	−4.41853	+	15.0159i	−0.199609	+	0.678348i
$491$	1.57179			0.0709340			0.0354670	−	0.999371i	$-0.488708\pi$
$491$	1.57179			0.0709340			0.0354670	+	0.999371i	$0.488708\pi$
$492$	−1.69705	−	6.33349i	−0.0765090	−	0.285536i
$493$	−39.7914	−	10.6621i	−1.79211	−	0.480196i
$494$	−11.3270	+	6.53967i	−0.509628	+	0.294234i
$495$	−3.91559	+	2.06045i	−0.175993	+	0.0926104i
$496$			1.73386i			0.0778527i
$497$	9.84480	−	2.71624i	0.441600	−	0.121840i
$498$	−9.52969	−	9.52969i	−0.427036	−	0.427036i
$499$	12.3491	+	7.12977i	0.552823	+	0.319172i	0.750260	−	0.661143i	$-0.229928\pi$
$499$	12.3491	+	7.12977i	0.552823	+	0.319172i	−0.197437	+	0.980316i	$0.563262\pi$
$500$	10.2714	−	4.41559i	0.459353	−	0.197471i
$501$	4.88769	+	8.46573i	0.218366	+	0.378221i
$502$	−2.61401	+	0.700423i	−0.116669	+	0.0312614i
$503$	28.7896	−	28.7896i	1.28367	−	1.28367i	0.345100	−	0.938566i	$-0.387845\pi$
$503$	28.7896	−	28.7896i	1.28367	−	1.28367i	0.938566	−	0.345100i	$-0.112155\pi$
$504$	1.33981	+	2.28142i	0.0596801	+	0.101623i
$505$	−19.0012	−	11.9869i	−0.845540	−	0.533411i
$506$	−5.81997	+	10.0805i	−0.258729	+	0.448132i
$507$	−0.876975	+	3.27292i	−0.0389478	+	0.145355i
$508$	3.26776	−	12.1955i	0.144984	−	0.541086i
$509$	7.30942	−	12.6603i	0.323984	−	0.561157i	−0.657322	−	0.753610i	$-0.728311\pi$
$509$	7.30942	−	12.6603i	0.323984	−	0.561157i	0.981306	+	0.192453i	$0.0616442\pi$
$510$	2.27219	+	10.0383i	0.100614	+	0.444502i
$511$	40.2670	−	0.298333i	1.78131	−	0.0131975i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.07503	+	1.09190i	−0.179917	+	0.0482086i
$514$	−12.0110	−	20.8037i	−0.529784	−	0.917612i
$515$	−8.18950	+	7.57139i	−0.360872	+	0.333635i
$516$	7.76151	+	4.48111i	0.341681	+	0.197270i
$517$	8.50729	+	8.50729i	0.374150	+	0.374150i
$518$	−5.14722	+	5.22406i	−0.226156	+	0.229532i
$519$		−	4.52762i		−	0.198740i
$520$	−3.22827	−	6.13485i	−0.141569	−	0.269031i
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	−0.762464	−	0.647030i	$-0.776011\pi$
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	0.179112	+	0.983829i	$0.442677\pi$
$522$	8.64500	+	2.31642i	0.378381	+	0.101387i
$523$	6.06041	+	22.6178i	0.265003	+	0.989006i	0.962248	+	0.272173i	$0.0877423\pi$
$523$	6.06041	+	22.6178i	0.265003	+	0.989006i	−0.697245	+	0.716833i	$0.745591\pi$
$524$	5.12160			0.223738
$525$	7.41029	−	10.9584i	0.323412	−	0.478266i
$526$	0.850325			0.0370759
$527$	2.06555	+	7.70872i	0.0899766	+	0.335797i
$528$	1.91133	+	0.512139i	0.0831799	+	0.0222880i
$529$	10.0488	−	5.80167i	0.436904	−	0.252247i
$530$	11.9058	+	22.6252i	0.517154	+	0.982776i
$531$			4.20702i			0.182569i
$532$	2.96870	+	10.7598i	0.128709	+	0.466498i
$533$	14.3742	+	14.3742i	0.622614	+	0.622614i
$534$	−5.36231	−	3.09593i	−0.232050	−	0.133974i
$535$	−9.93283	+	9.18314i	−0.429434	+	0.397022i
$536$	2.75608	+	4.77368i	0.119045	+	0.206191i
$537$	−1.99742	+	0.535206i	−0.0861949	+	0.0230959i
$538$	−8.23314	+	8.23314i	−0.354956	+	0.354956i
$539$	12.0969	+	6.74714i	0.521048	+	0.290620i
$540$	−0.493652	−	2.18090i	−0.0212434	−	0.0938508i
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	−0.938875	−	0.344258i	$-0.888131\pi$
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	0.767574	+	0.640961i	$0.221464\pi$
$542$	6.04206	−	22.5493i	0.259529	−	0.968575i
$543$	−1.58708	+	5.92305i	−0.0681080	+	0.254182i
$544$	2.30141	−	3.98616i	0.0986722	−	0.170905i
$545$	−18.4372	−	11.6311i	−0.789763	−	0.498224i
$546$	−7.13378	−	4.04852i	−0.305298	−	0.173261i
$547$	−5.88082	+	5.88082i	−0.251446	+	0.251446i	−0.821563	−	0.570117i	$-0.806898\pi$
$547$	−5.88082	+	5.88082i	−0.251446	+	0.251446i	0.570117	+	0.821563i	$0.306898\pi$
$548$	−11.1877	+	2.99773i	−0.477915	+	0.128057i
$549$	5.55999	+	9.63018i	0.237294	+	0.411006i
$550$	−1.80440	−	9.72783i	−0.0769398	−	0.414796i
$551$	32.6994	+	18.8790i	1.39304	+	0.804272i
$552$	−4.15953	−	4.15953i	−0.177041	−	0.177041i
$553$	6.54271	+	1.70126i	0.278224	+	0.0723450i
$554$		−	9.44974i		−	0.401481i
$555$	5.48512	−	2.88636i	0.232830	−	0.122519i
$556$	2.48596	−	1.43527i	0.105428	−	0.0608689i
$557$	−25.3198	−	6.78443i	−1.07284	−	0.287466i	−0.321178	−	0.947019i	$-0.604079\pi$
$557$	−25.3198	−	6.78443i	−1.07284	−	0.287466i	−0.751658	+	0.659553i	$0.770746\pi$
$558$	−0.448756	−	1.67478i	−0.0189974	−	0.0708991i
$559$	−27.7852			−1.17519
$560$	−5.76027	+	1.34879i	−0.243416	+	0.0569969i
$561$	9.10785			0.384534
$562$	−3.03646	−	11.3322i	−0.128085	−	0.478020i
$563$	0.844624	+	0.226316i	0.0355967	+	0.00953810i	0.276573	−	0.960993i	$-0.410801\pi$
$563$	0.844624	+	0.226316i	0.0355967	+	0.00953810i	−0.240977	+	0.970531i	$0.577468\pi$
$564$	−5.26557	+	3.04008i	−0.221721	+	0.128010i
$565$	−5.64865	+	18.1963i	−0.237640	+	0.765522i
$566$			3.64779i			0.153328i
$567$	−1.88464	−	1.85692i	−0.0791473	−	0.0779832i
$568$	2.72944	+	2.72944i	0.114525	+	0.114525i
$569$	28.5877	+	16.5051i	1.19846	+	0.691929i	0.960211	−	0.279275i	$-0.0900943\pi$
$569$	28.5877	+	16.5051i	1.19846	+	0.691929i	0.238246	+	0.971205i	$0.423428\pi$
$570$	0.369678	−	9.42624i	0.0154841	−	0.394822i
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	0.811528	−	0.584314i	$-0.198636\pi$
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	−0.911795	+	0.410646i	$0.865303\pi$
$572$	−5.92562	+	1.58776i	−0.247763	+	0.0663878i
$573$	11.4312	−	11.4312i	0.477544	−	0.477544i
$574$	14.9591	−	8.78504i	0.624380	−	0.366680i
$575$	−9.81403	+	27.7267i	−0.409273	+	1.15628i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	8.45046	−	31.5375i	0.351797	−	1.31293i	−0.532670	−	0.846323i	$-0.678811\pi$
$577$	8.45046	−	31.5375i	0.351797	−	1.31293i	0.884467	−	0.466602i	$-0.154522\pi$
$578$	1.08341	−	4.04335i	0.0450640	−	0.168181i
$579$	10.8955	−	18.8715i	0.452800	−	0.784272i
$580$	−10.6779	+	16.9261i	−0.443374	+	0.702817i
$581$	17.5992	−	31.0110i	0.730136	−	1.28655i
$582$	−1.48031	+	1.48031i	−0.0613609	+	0.0613609i
$583$	21.8535	−	5.85564i	0.905081	−	0.242516i
$584$	7.60995	+	13.1808i	0.314902	+	0.545426i
$585$	4.70608	+	5.09028i	0.194573	+	0.210457i
$586$	−10.5616	−	6.09777i	−0.436297	−	0.251896i
$587$	6.03856	+	6.03856i	0.249238	+	0.249238i	0.820658	−	0.571420i	$-0.193607\pi$
$587$	6.03856	+	6.03856i	0.249238	+	0.249238i	−0.571420	+	0.820658i	$0.693607\pi$
$588$	−4.87586	+	5.02254i	−0.201077	+	0.207126i
$589$		−	7.31479i		−	0.301401i
$590$	−8.98425	−	2.78898i	−0.369876	−	0.114820i
$591$	−0.769287	+	0.444148i	−0.0316442	+	0.0182698i
$592$	−2.67747	−	0.717425i	−0.110043	−	0.0294860i
$593$	1.05350	+	3.93171i	0.0432620	+	0.161456i	0.984177	−	0.177186i	$-0.0566993\pi$
$593$	1.05350	+	3.93171i	0.0432620	+	0.161456i	−0.940915	+	0.338642i	$0.890033\pi$
$594$	−1.97875			−0.0811892
$595$	−24.0033	+	12.8589i	−0.984039	+	0.527164i
$596$	−15.5796			−0.638167
$597$	2.49112	+	9.29699i	0.101955	+	0.380501i
$598$	17.6158	+	4.72013i	0.720362	+	0.193020i
$599$	−29.5547	+	17.0634i	−1.20757	+	0.697193i	−0.962229	−	0.272243i	$-0.912235\pi$
$599$	−29.5547	+	17.0634i	−1.20757	+	0.697193i	−0.245345	+	0.969436i	$0.578901\pi$
$600$	4.98464	+	0.391577i	0.203497	+	0.0159861i
$601$			9.99405i			0.407666i	0.979006	+	0.203833i	$0.0653399\pi$
$601$			9.99405i			0.407666i	−0.979006	+	0.203833i	$0.934660\pi$
$602$	−5.96721	+	22.9487i	−0.243205	+	0.935318i
$603$	−3.89769	−	3.89769i	−0.158726	−	0.158726i
$604$	18.3516	+	10.5953i	0.746715	+	0.431116i
$605$	15.8293	+	0.620794i	0.643554	+	0.0252388i
$606$	−5.02360	−	8.70112i	−0.204070	−	0.353459i
$607$	17.6567	−	4.73109i	0.716662	−	0.192029i	0.117980	−	0.993016i	$-0.462358\pi$
$607$	17.6567	−	4.73109i	0.716662	−	0.192029i	0.598682	+	0.800987i	$0.295691\pi$
$608$	−2.98313	+	2.98313i	−0.120982	+	0.120982i
$609$	0.175433	+	23.6787i	0.00710890	+	0.959510i
$610$	−24.2515	+	5.48939i	−0.981915	+	0.222259i
$611$	9.42504	−	16.3247i	0.381296	−	0.660425i
$612$	−1.19130	+	4.44599i	−0.0481554	+	0.179718i
$613$	−7.72109	+	28.8155i	−0.311852	+	1.16385i	0.615033	+	0.788501i	$0.289143\pi$
$613$	−7.72109	+	28.8155i	−0.311852	+	1.16385i	−0.926885	+	0.375346i	$0.877524\pi$
$614$	−11.3090	+	19.5877i	−0.456392	+	0.790495i
$615$	−14.2999	+	3.23683i	−0.576629	+	0.130521i
$616$	0.0387866	+	5.23514i	0.00156276	+	0.210930i
$617$	−35.0246	+	35.0246i	−1.41004	+	1.41004i	−0.650721	+	0.759317i	$0.725533\pi$
$617$	−35.0246	+	35.0246i	−1.41004	+	1.41004i	−0.759317	+	0.650721i	$0.774467\pi$
$618$	−4.81790	+	1.29095i	−0.193805	+	0.0519298i
$619$	−5.75770	−	9.97263i	−0.231422	−	0.400834i	0.726805	−	0.686844i	$-0.241004\pi$
$619$	−5.75770	−	9.97263i	−0.231422	−	0.400834i	−0.958227	+	0.286010i	$0.907671\pi$
$620$	3.87405	+	0.151932i	0.155586	+	0.00610175i
$621$	5.09436	+	2.94123i	0.204430	+	0.118028i
$622$	5.47479	+	5.47479i	0.219519	+	0.219519i
$623$	4.12266	−	15.8549i	0.165171	−	0.635214i
$624$		−	3.10026i		−	0.124110i
$625$	−8.96593	−	23.3369i	−0.358637	−	0.933477i
$626$	−17.3597	+	10.0226i	−0.693834	+	0.400585i
$627$	−8.06348	−	2.16060i	−0.322024	−	0.0862862i
$628$	3.92974	+	14.6660i	0.156814	+	0.585237i
$629$	−12.7586			−0.508720
$630$	5.21490	−	2.79370i	0.207767	−	0.111304i
$631$	18.4477			0.734390			0.367195	−	0.930144i	$-0.380318\pi$
$631$	18.4477			0.734390			0.367195	+	0.930144i	$0.380318\pi$
$632$	0.661320	+	2.46808i	0.0263059	+	0.0981749i
$633$	10.8830	+	2.91610i	0.432562	+	0.115905i
$634$	2.58104	−	1.49016i	0.102506	−	0.0591819i
$635$	−26.9626	−	8.36998i	−1.06998	−	0.332152i
$636$			11.4337i			0.453375i
$637$	5.30563	−	21.0433i	0.210217	−	0.833765i
$638$	12.5227	+	12.5227i	0.495778	+	0.495778i
$639$	−3.34287	−	1.93001i	−0.132242	−	0.0763499i
$640$	−1.51796	−	1.64189i	−0.0600028	−	0.0649012i
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	0.991741	−	0.128256i	$-0.0409380\pi$
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	−0.606944	+	0.794745i	$0.707605\pi$
$642$	−5.84351	+	1.56576i	−0.230625	+	0.0617958i
$643$	−28.2707	+	28.2707i	−1.11489	+	1.11489i	−0.122408	+	0.992480i	$0.539062\pi$
$643$	−28.2707	+	28.2707i	−1.11489	+	1.11489i	−0.992480	+	0.122408i	$0.960938\pi$
$644$	7.68169	−	13.5357i	0.302701	−	0.533381i
$645$	10.6925	−	16.9493i	0.421016	−	0.667377i
$646$	−9.70916	+	16.8168i	−0.382002	+	0.661647i
$647$	−6.45214	+	24.0797i	−0.253660	+	0.946672i	0.715171	+	0.698949i	$0.246349\pi$
$647$	−6.45214	+	24.0797i	−0.253660	+	0.946672i	−0.968831	+	0.247722i	$0.920318\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−4.16233	+	7.20937i	−0.163386	+	0.282992i
$650$	−13.9903	+	6.67550i	−0.548744	+	0.261835i
$651$	3.95567	−	2.32305i	0.155035	−	0.0910476i
$652$	15.7848	−	15.7848i	0.618179	−	0.618179i
$653$	48.0477	−	12.8743i	1.88025	−	0.503812i	0.880705	−	0.473666i	$-0.157070\pi$
$653$	48.0477	−	12.8743i	1.88025	−	0.503812i	0.999546	−	0.0301458i	$-0.00959716\pi$
$654$	−4.87449	−	8.44287i	−0.190608	−	0.330142i
$655$	0.448788	−	11.4434i	0.0175356	−	0.447132i
$656$	5.67845	+	3.27845i	0.221706	+	0.128002i
$657$	−10.7621	−	10.7621i	−0.419869	−	0.419869i
$658$	−11.4589	−	11.2903i	−0.446714	−	0.440144i
$659$			39.5644i			1.54121i	0.637312	+	0.770606i	$0.280046\pi$
$659$			39.5644i			1.54121i	−0.637312	+	0.770606i	$0.719954\pi$
$660$	1.31178	−	4.22570i	0.0510610	−	0.164485i
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	−0.533646	−	0.845708i	$-0.679179\pi$
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	0.465581	+	0.885005i	$0.345845\pi$
$662$	−26.8886	−	7.20479i	−1.04506	−	0.280022i
$663$	−3.69334	−	13.7837i	−0.143437	−	0.535315i
$664$	13.4770			0.523010
$665$	24.3014	−	5.69027i	0.942366	−	0.220659i
$666$	2.77192			0.107410
$667$	−13.6263	−	50.8539i	−0.527611	−	1.96907i
$668$	−9.44229	−	2.53005i	−0.365333	−	0.0978907i
$669$	16.1321	−	9.31386i	0.623702	−	0.360095i
$670$	10.9076	−	5.73976i	0.421396	−	0.221746i
$671$			22.0037i			0.849442i
$672$	−2.56060	−	0.665818i	−0.0987774	−	0.0256845i
$673$	−19.7775	−	19.7775i	−0.762366	−	0.762366i	0.214383	−	0.976750i	$-0.431226\pi$
$673$	−19.7775	−	19.7775i	−0.762366	−	0.762366i	−0.976750	+	0.214383i	$0.931226\pi$
$674$	−21.0125	−	12.1316i	−0.809372	−	0.467291i
$675$	−4.91614	+	0.911886i	−0.189222	+	0.0350985i
$676$	−1.69419	−	2.93442i	−0.0651610	−	0.112862i
$677$	−16.5748	+	4.44120i	−0.637021	+	0.170689i	−0.562854	−	0.826557i	$-0.690297\pi$
$677$	−16.5748	+	4.44120i	−0.637021	+	0.170689i	−0.0741672	+	0.997246i	$0.523630\pi$
$678$	−6.02504	+	6.02504i	−0.231390	+	0.231390i
$679$	−4.81714	−	2.73379i	−0.184865	−	0.104913i
$680$	−8.70482	−	5.49145i	−0.333815	−	0.210588i
$681$	13.4571	−	23.3083i	0.515676	−	0.893177i
$682$	0.887978	−	3.31398i	0.0340024	−	0.126899i
$683$	0.130540	−	0.487181i	0.00499496	−	0.0186414i	−0.963383	−	0.268128i	$-0.913595\pi$
$683$	0.130540	−	0.487181i	0.00499496	−	0.0186414i	0.968378	+	0.249486i	$0.0802617\pi$
$684$	2.10939	−	3.65357i	0.0806546	−	0.139698i
$685$	5.71765	+	25.2599i	0.218460	+	0.965131i
$686$	−16.2409	−	8.90138i	−0.620079	−	0.339856i
$687$	−19.0144	+	19.0144i	−0.725445	+	0.725445i
$688$	−8.65684	+	2.31959i	−0.330039	+	0.0884336i
$689$	−17.7237	−	30.6984i	−0.675220	−	1.16952i
$690$	−9.65833	+	8.92936i	−0.367686	+	0.339935i
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	0.734916	−	0.678158i	$-0.237222\pi$
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	−0.219845	+	0.975535i	$0.570555\pi$
$692$	3.20151	+	3.20151i	0.121703	+	0.121703i
$693$	−1.39242	−	5.04672i	−0.0528937	−	0.191709i
$694$			25.0428i			0.950613i
$695$	−2.98906	−	5.68027i	−0.113381	−	0.215465i
$696$	−7.75089	+	4.47498i	−0.293797	+	0.169624i
$697$	29.1519	+	7.81123i	1.10421	+	0.295871i
$698$	−4.66210	−	17.3992i	−0.176463	−	0.658569i
$699$	0.921244			0.0348447
$700$	2.50892	+	12.9887i	0.0948284	+	0.490925i
$701$	8.02724			0.303185			0.151592	−	0.988443i	$-0.451560\pi$
$701$	8.02724			0.303185			0.151592	+	0.988443i	$0.451560\pi$
$702$	0.802407	+	2.99462i	0.0302849	+	0.113025i
$703$	11.2956	+	3.02666i	0.426023	+	0.114153i
$704$	−1.71365	+	0.989376i	−0.0645856	+	0.0372885i
$705$	6.33120	+	12.0315i	0.238447	+	0.453133i
$706$			7.59800i			0.285955i
$707$	18.6568	−	18.9353i	0.701661	−	0.712136i
$708$	−2.97481	−	2.97481i	−0.111800	−	0.111800i
$709$	11.8457	+	6.83914i	0.444876	+	0.256849i	0.705664	−	0.708547i	$-0.250649\pi$
$709$	11.8457	+	6.83914i	0.444876	+	0.256849i	−0.260788	+	0.965396i	$0.583982\pi$
$710$	6.33770	−	5.85936i	0.237850	−	0.219898i
$711$	−1.27757	−	2.21282i	−0.0479127	−	0.0829872i
$712$	5.98088	−	1.60257i	0.224143	−	0.0600590i
$713$	−7.21204	+	7.21204i	−0.270093	+	0.270093i
$714$	−12.1776	+	0.0902224i	−0.455735	+	0.00337649i
$715$	3.02838	+	13.3790i	0.113255	+	0.500348i
$716$	1.03394	−	1.79084i	0.0386401	−	0.0669267i
$717$	6.55929	−	24.4796i	0.244961	−	0.914208i
$718$	0.850665	−	3.17473i	0.0317465	−	0.118480i
$719$	−10.5235	+	18.2273i	−0.392462	+	0.679764i	−0.992774	−	0.120002i	$-0.961710\pi$
$719$	−10.5235	+	18.2273i	−0.392462	+	0.679764i	0.600312	+	0.799766i	$0.295043\pi$
$720$	1.89119	+	1.19306i	0.0704805	+	0.0444628i
$721$	−6.68281	−	11.3794i	−0.248881	−	0.423792i
$722$	−0.849839	+	0.849839i	−0.0316277	+	0.0316277i
$723$	20.4004	−	5.46626i	0.758698	−	0.203292i
$724$	−3.06600	−	5.31046i	−0.113947	−	0.197362i
$725$	36.8831	+	25.3412i	1.36981	+	0.941150i
$726$	6.13539	+	3.54227i	0.227706	+	0.131466i
$727$	−11.2251	−	11.2251i	−0.416317	−	0.416317i	0.467615	−	0.883932i	$-0.345113\pi$
$727$	−11.2251	−	11.2251i	−0.416317	−	0.416317i	−0.883932	+	0.467615i	$0.845113\pi$
$728$	7.90708	−	2.18161i	0.293056	−	0.0808559i
$729$			1.00000i			0.0370370i
$730$	30.1174	−	15.8483i	1.11470	−	0.586572i
$731$	−35.7248	+	20.6258i	−1.32133	+	0.762871i
$732$	−10.7411	−	2.87806i	−0.397001	−	0.106376i
$733$	7.44145	+	27.7719i	0.274856	+	1.02578i	0.955938	+	0.293570i	$0.0948434\pi$
$733$	7.44145	+	27.7719i	0.274856	+	1.02578i	−0.681081	+	0.732208i	$0.738490\pi$
$734$	−3.24759			−0.119871
$735$	10.7949	+	11.3345i	0.398175	+	0.418079i
$736$	5.88246			0.216830
$737$	−2.82300	−	10.5356i	−0.103986	−	0.388082i
$738$	−6.33349	−	1.69705i	−0.233139	−	0.0624694i
$739$	36.3593	−	20.9921i	1.33750	−	0.772205i	0.351063	−	0.936352i	$-0.385820\pi$
$739$	36.3593	−	20.9921i	1.33750	−	0.772205i	0.986436	+	0.164147i	$0.0524871\pi$
$740$	−1.83760	+	5.91953i	−0.0675513	+	0.217606i
$741$			13.0793i			0.480482i
$742$	−29.1611	+	8.04573i	−1.07054	+	0.295368i
$743$	8.63799	+	8.63799i	0.316897	+	0.316897i	0.847574	−	0.530677i	$-0.178062\pi$
$743$	8.63799	+	8.63799i	0.316897	+	0.316897i	−0.530677	+	0.847574i	$0.678062\pi$
$744$	1.50157	+	0.866930i	0.0550501	+	0.0317832i
$745$	−1.36519	+	34.8104i	−0.0500167	+	1.27535i
$746$	7.88312	+	13.6540i	0.288622	+	0.499907i
$747$	−13.0178	+	3.48811i	−0.476297	+	0.127623i
$748$	−6.44022	+	6.44022i	−0.235478	+	0.235478i
$749$	−8.10541	−	13.8018i	−0.296165	−	0.504307i
$750$	1.31171	−	11.1031i	0.0478968	−	0.405429i
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	0.416384	+	0.909189i	$0.363297\pi$
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	−0.995573	+	0.0939948i	$0.970036\pi$
$752$	1.57366	−	5.87298i	0.0573855	−	0.214166i
$753$	−0.700423	+	2.61401i	−0.0255248	+	0.0952600i
$754$	13.8736	−	24.0298i	0.505247	−	0.875114i
$755$	25.2817	−	40.0754i	0.920094	−	1.45849i
$756$	2.64568	−	0.0196015i	0.0962224	−	0.000712901i
$757$	−9.81959	+	9.81959i	−0.356899	+	0.356899i	−0.862669	−	0.505770i	$-0.831209\pi$
$757$	−9.81959	+	9.81959i	−0.356899	+	0.356899i	0.505770	+	0.862669i	$0.331209\pi$
$758$	21.0019	−	5.62744i	0.762824	−	0.204398i
$759$	5.81997	+	10.0805i	0.211251	+	0.365898i
$760$	6.40396	+	6.92676i	0.232296	+	0.251260i
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.909077	−	0.416628i	$-0.136788\pi$
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.0937278	+	0.995598i	$0.470122\pi$
$762$	−8.92770	−	8.92770i	−0.323416	−	0.323416i
$763$	18.1031	−	18.3733i	0.655375	−	0.665158i
$764$			16.1661i			0.584869i
$765$	9.82950	+	3.05136i	0.355386	+	0.110322i
$766$	15.4914	−	8.94394i	0.559726	−	0.323158i
$767$	12.5985	+	3.37574i	0.454904	+	0.121891i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	−26.3715			−0.950981			−0.475490	−	0.879721i	$-0.657729\pi$
$769$	−26.3715			−0.950981			−0.475490	+	0.879721i	$0.657729\pi$
$770$	11.7005	+	0.372075i	0.421658	+	0.0134086i
$771$	−24.0221			−0.865133
$772$	5.63991	+	21.0484i	0.202985	+	0.757549i
$773$	−44.4561	−	11.9120i	−1.59898	−	0.428444i	−0.654242	−	0.756285i	$-0.727012\pi$
$773$	−44.4561	−	11.9120i	−1.59898	−	0.428444i	−0.944733	+	0.327841i	$0.893679\pi$
$774$	7.76151	−	4.48111i	0.278982	−	0.161070i
$775$	0.678940	−	8.64268i	0.0243882	−	0.310454i
$776$		−	2.09348i		−	0.0751514i
$777$	1.95056	+	7.06965i	0.0699759	+	0.253622i
$778$	3.56098	+	3.56098i	0.127667	+	0.127667i
$779$	−23.9561	−	13.8311i	−0.858318	−	0.495550i
$780$	−6.92707	−	0.271665i	−0.248029	−	0.00972718i
$781$	−3.81901	−	6.61472i	−0.136655	−	0.236693i
$782$	26.1533	−	7.00777i	0.935241	−	0.250597i
$783$	6.32858	−	6.32858i	0.226165	−	0.226165i
$784$	−0.103719	−	6.99923i	−0.00370424	−	0.249973i
$785$	33.1133	−	7.49528i	1.18186	−	0.267518i
$786$	2.56080	−	4.43543i	0.0913407	−	0.158207i
$787$	−2.93226	+	10.9433i	−0.104524	+	0.390088i	−0.998291	−	0.0584437i	$-0.981386\pi$
$787$	−2.93226	+	10.9433i	−0.104524	+	0.390088i	0.893767	+	0.448532i	$0.148053\pi$
$788$	0.229908	−	0.858028i	0.00819013	−	0.0305660i
$789$	0.425163	−	0.736403i	0.0151362	−	0.0262167i
$790$	5.57250	−	1.26135i	0.198261	−	0.0448768i
$791$	−19.6063	−	11.1269i	−0.697121	−	0.395626i
$792$	1.39919	−	1.39919i	0.0497180	−	0.0497180i
$793$	33.3001	−	8.92274i	1.18252	−	0.316856i
$794$	−7.37735	−	12.7780i	−0.261813	−	0.453473i
$795$	25.5469	+	1.00190i	0.906054	+	0.0355336i
$796$	−8.33546	−	4.81248i	−0.295442	−	0.170574i
$797$	24.7239	+	24.7239i	0.875767	+	0.875767i	0.993093	−	0.117327i	$-0.0374325\pi$
$797$	24.7239	+	24.7239i	0.875767	+	0.875767i	−0.117327	+	0.993093i	$0.537432\pi$
$798$	10.8026	+	2.80894i	0.382409	+	0.0994356i
$799$		−	27.9859i		−	0.990070i
$800$	−3.80156	+	3.24779i	−0.134405	+	0.114827i
$801$	−5.36231	+	3.09593i	−0.189468	+	0.109389i
$802$	8.39748	+	2.25010i	0.296525	+	0.0794537i
$803$	−7.79470	−	29.0902i	−0.275069	−	1.02657i
$804$	5.51217			0.194399
$805$	−29.5704	−	18.3497i	−1.04222	−	0.646741i
$806$	−5.37542			−0.189341
$807$	3.01354	+	11.2467i	0.106082	+	0.395902i
$808$	9.70484	+	2.60040i	0.341415	+	0.0914819i
$809$	5.02215	−	2.89954i	0.176569	−	0.101942i	−0.409110	−	0.912485i	$-0.634161\pi$
$809$	5.02215	−	2.89954i	0.176569	−	0.101942i	0.585680	+	0.810542i	$0.300828\pi$
$810$	−2.13554	−	0.662933i	−0.0750351	−	0.0232931i
$811$		−	28.8064i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$811$		−	28.8064i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$812$	−16.8674	−	16.6193i	−0.591931	−	0.583224i
$813$	−16.5072	−	16.5072i	−0.578934	−	0.578934i
$814$	4.75009	+	2.74247i	0.166491	+	0.0961235i
$815$	−33.8855	−	36.6519i	−1.18696	−	1.28386i
$816$	−2.30141	−	3.98616i	−0.0805655	−	0.139544i
$817$	36.5213	−	9.78586i	1.27772	−	0.342364i
$818$	13.4222	−	13.4222i	0.469297	−	0.469297i
$819$	−7.07301	+	4.15378i	−0.247151	+	0.145145i
$820$	7.82280	−	12.4004i	0.273184	−	0.433039i
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	−0.902749	−	0.430167i	$-0.858455\pi$
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	0.823910	+	0.566721i	$0.191788\pi$
$822$	−2.99773	+	11.1877i	−0.104558	+	0.390216i
$823$	−5.79271	+	21.6187i	−0.201921	+	0.753580i	0.788445	+	0.615105i	$0.210887\pi$
$823$	−5.79271	+	21.6187i	−0.201921	+	0.753580i	−0.990366	+	0.138474i	$0.955780\pi$
$824$	2.49393	−	4.31961i	0.0868802	−	0.150481i
$825$	−9.32675	−	3.30126i	−0.324716	−	0.114935i
$826$	5.49380	−	9.68047i	0.191154	−	0.336827i
$827$	22.5410	−	22.5410i	0.783826	−	0.783826i	−0.196648	−	0.980474i	$-0.563006\pi$
$827$	22.5410	−	22.5410i	0.783826	−	0.783826i	0.980474	+	0.196648i	$0.0630057\pi$
$828$	−5.68202	+	1.52249i	−0.197464	+	0.0529103i
$829$	3.61347	+	6.25871i	0.125501	+	0.217374i	0.921929	−	0.387360i	$-0.126613\pi$
$829$	3.61347	+	6.25871i	0.125501	+	0.217374i	−0.796428	+	0.604734i	$0.793280\pi$
$830$	1.18094	−	30.1124i	0.0409912	−	1.04522i
$831$	−8.18372	−	4.72487i	−0.283890	−	0.163904i
$832$	2.19222	+	2.19222i	0.0760014	+	0.0760014i
$833$	−8.79930	−	30.9949i	−0.304878	−	1.07391i
$834$		−	2.87054i		−	0.0993985i
$835$	−6.48042	+	20.8757i	−0.224264	+	0.722433i
$836$	7.22952	−	4.17397i	0.250038	−	0.144360i
$837$	−1.67478	−	0.448756i	−0.0578889	−	0.0155113i
$838$	3.08437	+	11.5110i	0.106548	+	0.397642i
$839$	5.52622			0.190786			0.0953932	−	0.995440i	$-0.469589\pi$
$839$	5.52622			0.190786			0.0953932	+	0.995440i	$0.469589\pi$
$840$	−1.71205	+	5.66294i	−0.0590713	+	0.195390i
$841$	−51.1018			−1.76213
$842$	1.79947	+	6.71572i	0.0620139	+	0.231439i
$843$	−11.3322	−	3.03646i	−0.390302	−	0.104581i
$844$	−9.75746	+	5.63347i	−0.335866	+	0.193912i
$845$	−6.70497	+	3.52827i	−0.230658	+	0.121376i
$846$			6.08016i			0.209040i
$847$	−4.71702	+	18.1407i	−0.162079	+	0.623321i
$848$	−8.08484	−	8.08484i	−0.277635	−	0.277635i
$849$	3.15908	+	1.82389i	0.108419	+	0.0625959i
$850$	−13.0326	+	18.9684i	−0.447015	+	0.650611i
$851$	−8.15284	−	14.1211i	−0.279476	−	0.484066i
$852$	3.72849	−	0.999046i	0.127736	−	0.0342267i
$853$	−10.4649	+	10.4649i	−0.358313	+	0.358313i	−0.863191	−	0.504878i	$-0.831538\pi$
$853$	−10.4649	+	10.4649i	−0.358313	+	0.358313i	0.504878	+	0.863191i	$0.331538\pi$
$854$	−0.217968	−	29.4199i	−0.00745873	−	1.00673i
$855$	−7.97853	−	5.03327i	−0.272860	−	0.172134i
$856$	3.02482	−	5.23915i	0.103386	−	0.179070i
$857$	0.556370	−	2.07640i	0.0190053	−	0.0709286i	−0.955772	−	0.294109i	$-0.904977\pi$
$857$	0.556370	−	2.07640i	0.0190053	−	0.0709286i	0.974777	+	0.223180i	$0.0716439\pi$
$858$	−1.58776	+	5.92562i	−0.0542054	+	0.202297i
$859$	−3.59455	+	6.22594i	−0.122644	+	0.212426i	−0.920810	−	0.390012i	$-0.872471\pi$
$859$	−3.59455	+	6.22594i	−0.122644	+	0.212426i	0.798165	+	0.602439i	$0.205804\pi$
$860$	4.42421	+	19.5457i	0.150864	+	0.666502i
$861$	−0.128525	−	17.3475i	−0.00438013	−	0.591200i
$862$	4.41788	−	4.41788i	0.150474	−	0.150474i
$863$	−39.1589	+	10.4926i	−1.33298	+	0.357172i	−0.853827	−	0.520557i	$-0.825724\pi$
$863$	−39.1589	+	10.4926i	−1.33298	+	0.357172i	−0.479157	+	0.877729i	$0.659057\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	7.43383	−	6.87275i	0.252758	−	0.233681i
$866$	18.5603	+	10.7158i	0.630704	+	0.364137i
$867$	−2.95994	−	2.95994i	−0.100525	−	0.100525i
$868$	−1.15444	+	4.43973i	−0.0391841	+	0.150694i
$869$		−	5.05600i		−	0.171513i
$870$	9.31949	+	17.7103i	0.315960	+	0.600437i
$871$	−14.7997	+	8.54458i	−0.501467	+	0.289522i
$872$	9.41680	+	2.52322i	0.318893	+	0.0854471i
$873$	0.541831	+	2.02214i	0.0183382	+	0.0684391i
$874$	−24.8168			−0.839442
$875$	29.2411	−	4.46766i	0.988528	−	0.151034i
$876$	15.2199			0.514233
$877$	−13.2237	−	49.3516i	−0.446533	−	1.66648i	−0.711857	−	0.702325i	$-0.752145\pi$
$877$	−13.2237	−	49.3516i	−0.446533	−	1.66648i	0.265324	−	0.964159i	$-0.414521\pi$
$878$	31.6301	+	8.47526i	1.06746	+	0.286026i
$879$	−10.5616	+	6.09777i	−0.356235	+	0.205673i
$880$	2.06045	+	3.91559i	0.0694578	+	0.131995i
$881$		−	27.9972i		−	0.943251i	−0.881799	−	0.471625i	$-0.843667\pi$
$881$		−	27.9972i		−	0.943251i	0.881799	−	0.471625i	$-0.156333\pi$
$882$	1.91172	+	6.73389i	0.0643709	+	0.226742i
$883$	4.66131	+	4.66131i	0.156865	+	0.156865i	0.781176	−	0.624311i	$-0.214620\pi$
$883$	4.66131	+	4.66131i	0.156865	+	0.156865i	−0.624311	+	0.781176i	$0.714620\pi$
$884$	12.3581	+	7.13498i	0.415650	+	0.239975i
$885$	−6.90745	+	6.38610i	−0.232191	+	0.214667i
$886$	−15.3755	−	26.6312i	−0.516550	−	0.894692i
$887$	−13.4547	+	3.60517i	−0.451763	+	0.121050i	−0.477524	−	0.878619i	$-0.658466\pi$
$887$	−13.4547	+	3.60517i	−0.451763	+	0.121050i	0.0257610	+	0.999668i	$0.491799\pi$
$888$	−1.96004	+	1.96004i	−0.0657747	+	0.0657747i
$889$	16.4874	−	29.0520i	0.552970	−	0.974372i
$890$	−3.05663	−	13.5038i	−0.102458	−	0.452649i
$891$	−0.989376	+	1.71365i	−0.0331454	+	0.0574094i
$892$	−4.82121	+	17.9930i	−0.161426	+	0.602450i
$893$	−6.63894	+	24.7768i	−0.222164	+	0.829126i
$894$	−7.78982	+	13.4924i	−0.260531	+	0.451252i
$895$	−3.91075	−	2.46711i	−0.130722	−	0.0824663i
$896$	2.28142	−	1.33981i	0.0762170	−	0.0447601i
$897$	12.8956	−	12.8956i	0.430573	−	0.430573i
$898$	16.2964	−	4.36662i	0.543819	−	0.145716i
$899$	7.75899	+	13.4390i	0.258777	+	0.448215i
$900$	2.83144	−	4.12104i	0.0943812	−	0.137368i
$901$	−45.5766	−	26.3136i	−1.51838	−	0.876634i
$902$	−9.17435	−	9.17435i	−0.305473	−	0.305473i
$903$	16.8905	+	16.6421i	0.562082	+	0.553814i
$904$		−	8.52069i		−	0.283394i
$905$	−12.1341	+	6.38517i	−0.403351	+	0.212250i
$906$	18.3516	−	10.5953i	0.609690	−	0.352005i
$907$	−26.0691	−	6.98519i	−0.865610	−	0.231939i	−0.201421	−	0.979505i	$-0.564556\pi$
$907$	−26.0691	−	6.98519i	−0.865610	−	0.231939i	−0.664188	+	0.747565i	$0.731223\pi$
$908$	6.96589	+	25.9971i	0.231171	+	0.862743i
$909$	−10.0472			−0.333244
$910$	−4.18161	−	17.8584i	−0.138619	−	0.591999i
$911$	−15.5364			−0.514744			−0.257372	−	0.966312i	$-0.582857\pi$
$911$	−15.5364			−0.514744			−0.257372	+	0.966312i	$0.582857\pi$
$912$	1.09190	+	4.07503i	0.0361565	+	0.134938i
$913$	−25.7590	−	6.90211i	−0.852499	−	0.228426i
$914$	−17.1886	+	9.92384i	−0.568548	+	0.328251i
$915$	−7.37180	+	23.7471i	−0.243704	+	0.785055i
$916$		−	26.8905i		−	0.888486i
$917$	13.1144	+	3.41005i	0.433075	+	0.112610i
$918$	3.25469	+	3.25469i	0.107421	+	0.107421i
$919$	32.7915	+	18.9322i	1.08169	+	0.624515i	0.931352	−	0.364120i	$-0.118630\pi$
$919$	32.7915	+	18.9322i	1.08169	+	0.624515i	0.150339	+	0.988634i	$0.451963\pi$
$920$	0.515460	−	13.1435i	0.0169942	−	0.433328i
$921$	11.3090	+	19.5877i	0.372643	+	0.645436i
$922$	−15.2399	+	4.08351i	−0.501898	+	0.134483i
$923$	−8.46199	+	8.46199i	−0.278530	+	0.278530i
$924$	4.55316	+	2.58398i	0.149788	+	0.0850068i
$925$	13.0653	+	4.62454i	0.429584	+	0.152054i
$926$	−3.17220	+	5.49441i	−0.104245	+	0.180558i
$927$	−1.29095	+	4.81790i	−0.0424005	+	0.158241i
$928$	2.31642	−	8.64500i	0.0760402	−	0.283786i
$929$	8.75685	−	15.1673i	0.287303	−	0.497624i	−0.685862	−	0.727732i	$-0.740575\pi$
$929$	8.75685	−	15.1673i	0.287303	−	0.497624i	0.973165	+	0.230108i	$0.0739080\pi$
$930$	2.06860	−	3.27906i	0.0678322	−	0.107525i
$931$	0.437567	+	29.5283i	0.0143407	+	0.967749i
$932$	−0.651418	+	0.651418i	−0.0213379	+	0.0213379i
$933$	7.47870	−	2.00391i	0.244842	−	0.0656051i
$934$	−8.72500	−	15.1121i	−0.285491	−	0.494484i
$935$	13.8254	+	14.9540i	0.452138	+	0.489050i
$936$	−2.68491	−	1.55013i	−0.0877589	−	0.0506676i
$937$	2.68964	+	2.68964i	0.0878666	+	0.0878666i	0.749674	−	0.661807i	$-0.230210\pi$
$937$	2.68964	+	2.68964i	0.0878666	+	0.0878666i	−0.661807	+	0.749674i	$0.730210\pi$
$938$	3.87883	+	14.0585i	0.126648	+	0.459028i
$939$			20.0453i			0.654153i
$940$	−12.9844	−	4.03074i	−0.423505	−	0.131468i
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.0328543	−	0.999460i	$-0.489540\pi$
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.881985	+	0.471277i	$0.156207\pi$
$942$	14.6660	+	3.92974i	0.477844	+	0.128038i
$943$	9.98284	+	37.2565i	0.325086	+	1.21324i
$944$	4.20702			0.136927
$945$	0.188035	−	5.91309i	0.00611678	−	0.192353i
$946$	17.7340			0.576582
$947$	−9.93164	−	37.0654i	−0.322735	−	1.20446i	−0.916569	−	0.399876i	$-0.869053\pi$
$947$	−9.93164	−	37.0654i	−0.322735	−	1.20446i	0.593834	−	0.804587i	$-0.297614\pi$
$948$	2.46808	+	0.661320i	0.0801595	+	0.0214787i
$949$	−40.8640	+	23.5928i	−1.32650	+	0.765856i
$950$	16.0380	−	13.7017i	0.520340	−	0.444543i
$951$		−	2.98032i		−	0.0966436i
$952$	8.54706	−	8.67465i	0.277012	−	0.281147i
$953$	12.2232	+	12.2232i	0.395949	+	0.395949i	0.876801	−	0.480853i	$-0.159673\pi$
$953$	12.2232	+	12.2232i	0.395949	+	0.395949i	−0.480853	+	0.876801i	$0.659673\pi$
$954$	9.90187	+	5.71685i	0.320585	+	0.185090i
$955$	36.1208	+	1.41658i	1.16884	+	0.0458395i
$956$	12.6716	+	21.9478i	0.409828	+	0.709843i
$957$	17.1063	−	4.58362i	0.552969	−	0.148167i
$958$	−22.4504	+	22.4504i	−0.725339	+	0.725339i
$959$	−30.6432	+	0.227032i	−0.989520	+	0.00733124i
$960$	−2.18090	+	0.493652i	−0.0703881	+	0.0159325i
$961$	−13.9969	+	24.2433i	−0.451512	+	0.782041i
$962$	2.22420	−	8.30084i	0.0717112	−	0.267630i
$963$	−1.56576	+	5.84351i	−0.0504560	+	0.188304i
$964$	−10.5600	+	18.2905i	−0.340115	+	0.589096i
$965$	47.5237	−	10.7571i	1.52984	−	0.346284i
$966$	−7.88141	−	13.4204i	−0.253580	−	0.431794i
$967$	24.7551	−	24.7551i	0.796071	−	0.796071i	−0.186402	−	0.982474i	$-0.559683\pi$
$967$	24.7551	−	24.7551i	0.796071	−	0.796071i	0.982474	+	0.186402i	$0.0596827\pi$
$968$	−6.84314	+	1.83361i	−0.219947	+	0.0589346i
$969$	9.70916	+	16.8168i	0.311903	+	0.540232i
$970$	−4.67756	−	0.183444i	−0.150187	−	0.00589003i
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	0.635152	−	0.772387i	$-0.280937\pi$
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	−0.351331	+	0.936251i	$0.614271\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	7.32118	−	2.01996i	0.234706	−	0.0647568i
$974$			29.9080i			0.958316i
$975$	−1.21399	+	15.4537i	−0.0388788	+	0.494915i
$976$	9.63018	−	5.55999i	0.308254	−	0.177971i
$977$	15.4715	+	4.14558i	0.494977	+	0.132629i	0.497668	−	0.867368i	$-0.334190\pi$
$977$	15.4715	+	4.14558i	0.494977	+	0.132629i	−0.00269080	+	0.999996i	$0.500857\pi$
$978$	−5.77762	−	21.5624i	−0.184748	−	0.689489i
$979$	−12.2522			−0.391581
$980$	−15.6478	−	0.381575i	−0.499851	−	0.0121890i
$981$	−9.74899			−0.311261
$982$	0.406810	+	1.51824i	0.0129818	+	0.0484488i
$983$	7.36683	+	1.97394i	0.234965	+	0.0629588i	0.374380	−	0.927275i	$-0.377855\pi$
$983$	7.36683	+	1.97394i	0.234965	+	0.0629588i	−0.139415	+	0.990234i	$0.544522\pi$
$984$	5.67845	−	3.27845i	0.181022	−	0.104513i
$985$	−1.89699	−	0.588881i	−0.0604431	−	0.0187633i
$986$		−	41.1951i		−	1.31192i
$987$	−15.5072	+	4.27852i	−0.493599	+	0.136187i
$988$	−9.24849	−	9.24849i	−0.294234	−	0.294234i
$989$	−45.6568	−	26.3599i	−1.45180	−	0.838198i
$990$	−3.00367	−	3.24889i	−0.0954630	−	0.103256i
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	−0.914206	−	0.405251i	$-0.867184\pi$
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	0.106145	−	0.994351i	$-0.466149\pi$
$992$	−1.67478	+	0.448756i	−0.0531743	+	0.0142480i
$993$	−19.6839	+	19.6839i	−0.624648	+	0.624648i
$994$	5.17171	+	8.80633i	0.164037	+	0.279320i
$995$	−11.4832	+	18.2026i	−0.364041	+	0.577062i
$996$	6.73851	−	11.6714i	0.213518	−	0.369824i
$997$	−10.5401	+	39.3361i	−0.333808	+	1.24579i	0.571348	+	0.820708i	$0.306421\pi$
$997$	−10.5401	+	39.3361i	−0.333808	+	1.24579i	−0.905156	+	0.425080i	$0.860246\pi$
$998$	−3.69064	+	13.7737i	−0.116825	+	0.435997i
$999$	1.38596	−	2.40055i	0.0438498	−	0.0759500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.a.103.3	✓	16
3.2	odd	2		630.2.bv.a.523.2		16
5.2	odd	4		210.2.u.b.187.2	yes	16
5.3	odd	4		1050.2.bc.g.607.4		16
5.4	even	2		1050.2.bc.h.943.2		16
7.2	even	3		1470.2.m.d.1273.7		16
7.3	odd	6		210.2.u.b.73.2	yes	16
7.5	odd	6		1470.2.m.e.1273.6		16
15.2	even	4		630.2.bv.b.397.3		16
21.17	even	6		630.2.bv.b.73.3		16
35.2	odd	12		1470.2.m.e.97.6		16
35.3	even	12		1050.2.bc.h.157.2		16
35.12	even	12		1470.2.m.d.97.7		16
35.17	even	12	inner	210.2.u.a.157.3	yes	16
35.24	odd	6		1050.2.bc.g.493.4		16
105.17	odd	12		630.2.bv.a.577.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.3	✓	16	1.1	even	1	trivial
210.2.u.a.157.3	yes	16	35.17	even	12	inner
210.2.u.b.73.2	yes	16	7.3	odd	6
210.2.u.b.187.2	yes	16	5.2	odd	4
630.2.bv.a.523.2		16	3.2	odd	2
630.2.bv.a.577.2		16	105.17	odd	12
630.2.bv.b.73.3		16	21.17	even	6
630.2.bv.b.397.3		16	15.2	even	4
1050.2.bc.g.493.4		16	35.24	odd	6
1050.2.bc.g.607.4		16	5.3	odd	4
1050.2.bc.h.157.2		16	35.3	even	12
1050.2.bc.h.943.2		16	5.4	even	2
1470.2.m.d.97.7		16	35.12	even	12
1470.2.m.d.1273.7		16	7.2	even	3
1470.2.m.e.97.6		16	35.2	odd	12
1470.2.m.e.1273.6		16	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.04129 + 1.97882i) q^{5} +1.00000i q^{6} +(-2.55046 + 0.703686i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.04129 + 1.97882i) q^{5} +1.00000i q^{6} +(-2.55046 + 0.703686i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.64189 + 1.51796i) q^{10} +(0.989376 + 1.71365i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(2.19222 - 2.19222i) q^{13} +(-1.33981 - 2.28142i) q^{14} +(0.493652 + 2.18090i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.19130 - 4.44599i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-2.10939 + 3.65357i) q^{19} +(-1.89119 - 1.19306i) q^{20} +(-2.64568 + 0.0196015i) q^{21} +(-1.39919 + 1.39919i) q^{22} +(5.68202 - 1.52249i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.83144 + 4.12104i) q^{25} +(2.68491 + 1.55013i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.85692 - 1.88464i) q^{28} -8.94996i q^{29} +(-1.97882 + 1.04129i) q^{30} +(-1.50157 + 0.866930i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.512139 + 1.91133i) q^{33} +4.60282 q^{34} +(-4.04823 - 4.31415i) q^{35} -1.00000 q^{36} +(-0.717425 - 2.67747i) q^{37} +(-4.07503 - 1.09190i) q^{38} +(2.68491 - 1.55013i) q^{39} +(0.662933 - 2.13554i) q^{40} +6.55691i q^{41} +(-0.703686 - 2.55046i) q^{42} +(-6.33724 - 6.33724i) q^{43} +(-1.71365 - 0.989376i) q^{44} +(-0.0876265 + 2.23435i) q^{45} +(2.94123 + 5.09436i) q^{46} +(5.87298 - 1.57366i) q^{47} +(0.707107 - 0.707107i) q^{48} +(6.00965 - 3.58944i) q^{49} +(-4.71345 - 1.66835i) q^{50} +(2.30141 - 3.98616i) q^{51} +(-0.802407 + 2.99462i) q^{52} +(2.95926 - 11.0441i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.36077 + 3.74220i) q^{55} +(2.30103 + 1.30586i) q^{56} +(-2.98313 + 2.98313i) q^{57} +(8.64500 - 2.31642i) q^{58} +(2.10351 + 3.64339i) q^{59} +(-1.51796 - 1.64189i) q^{60} +(9.63018 + 5.55999i) q^{61} +(-1.22602 - 1.22602i) q^{62} +(-2.56060 - 0.665818i) q^{63} +1.00000i q^{64} +(6.62073 + 2.05527i) q^{65} +(-1.71365 + 0.989376i) q^{66} +(-5.32434 - 1.42665i) q^{67} +(1.19130 + 4.44599i) q^{68} +5.88246 q^{69} +(3.11939 - 5.02687i) q^{70} -3.86002 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-14.7013 - 3.93920i) q^{73} +(2.40055 - 1.38596i) q^{74} +(-3.80156 + 3.24779i) q^{75} -4.21878i q^{76} +(-3.72923 - 3.67438i) q^{77} +(2.19222 + 2.19222i) q^{78} +(-2.21282 - 1.27757i) q^{79} +(2.23435 + 0.0876265i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-6.33349 + 1.69705i) q^{82} +(-9.52969 + 9.52969i) q^{83} +(2.28142 - 1.33981i) q^{84} +(10.0383 - 2.27219i) q^{85} +(4.48111 - 7.76151i) q^{86} +(2.31642 - 8.64500i) q^{87} +(0.512139 - 1.91133i) q^{88} +(-3.09593 + 5.36231i) q^{89} +(-2.18090 + 0.493652i) q^{90} +(-4.04852 + 7.13378i) q^{91} +(-4.15953 + 4.15953i) q^{92} +(-1.67478 + 0.448756i) q^{93} +(3.04008 + 5.26557i) q^{94} +(-9.42624 - 0.369678i) q^{95} +(0.866025 + 0.500000i) q^{96} +(1.48031 + 1.48031i) q^{97} +(5.02254 + 4.87586i) q^{98} +1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 8 * q^7	\( 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more