LMFDB - Embedded newform 84.2.b.a.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(55,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("84.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.b (of order $2$, degree $1$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.1
Root			$1.28078 + 0.599676i$ of defining polynomial
Character	$\chi$	$=$	84.55
Dual form			84.2.b.a.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +(-2.00000 + 4.27156i) q^{10} -0.936426i q^{11} +(-1.28078 - 1.53610i) q^{12} -1.87285i q^{13} +(0.719224 + 3.67188i) q^{14} +3.33513i q^{15} +(-0.719224 + 3.93481i) q^{16} +5.20798i q^{17} +(-1.28078 - 0.599676i) q^{18} +7.12311 q^{19} +(5.12311 - 4.27156i) q^{20} +(1.56155 + 2.13578i) q^{21} +(-0.561553 + 1.19935i) q^{22} +0.936426i q^{23} +(0.719224 + 2.73546i) q^{24} -6.12311 q^{25} +(-1.12311 + 2.39871i) q^{26} -1.00000 q^{27} +(1.28078 - 5.13416i) q^{28} -2.00000 q^{29} +(2.00000 - 4.27156i) q^{30} +(3.28078 - 4.60831i) q^{32} +0.936426i q^{33} +(3.12311 - 6.67026i) q^{34} +(-7.12311 + 5.20798i) q^{35} +(1.28078 + 1.53610i) q^{36} +1.12311 q^{37} +(-9.12311 - 4.27156i) q^{38} +1.87285i q^{39} +(-9.12311 + 2.39871i) q^{40} +1.46228i q^{41} +(-0.719224 - 3.67188i) q^{42} -9.06897i q^{43} +(1.43845 - 1.19935i) q^{44} -3.33513i q^{45} +(0.561553 - 1.19935i) q^{46} +6.24621 q^{47} +(0.719224 - 3.93481i) q^{48} +(-2.12311 + 6.67026i) q^{49} +(7.84233 + 3.67188i) q^{50} -5.20798i q^{51} +(2.87689 - 2.39871i) q^{52} +12.2462 q^{53} +(1.28078 + 0.599676i) q^{54} -3.12311 q^{55} +(-4.71922 + 5.80766i) q^{56} -7.12311 q^{57} +(2.56155 + 1.19935i) q^{58} +4.00000 q^{59} +(-5.12311 + 4.27156i) q^{60} -4.79741i q^{61} +(-1.56155 - 2.13578i) q^{63} +(-6.96543 + 3.93481i) q^{64} -6.24621 q^{65} +(0.561553 - 1.19935i) q^{66} +10.9418i q^{67} +(-8.00000 + 6.67026i) q^{68} -0.936426i q^{69} +(12.2462 - 2.39871i) q^{70} +3.86098i q^{71} +(-0.719224 - 2.73546i) q^{72} -6.67026i q^{73} +(-1.43845 - 0.673500i) q^{74} +6.12311 q^{75} +(9.12311 + 10.9418i) q^{76} +(-2.00000 + 1.46228i) q^{77} +(1.12311 - 2.39871i) q^{78} +2.39871i q^{79} +(13.1231 + 2.39871i) q^{80} +1.00000 q^{81} +(0.876894 - 1.87285i) q^{82} -10.2462 q^{83} +(-1.28078 + 5.13416i) q^{84} +17.3693 q^{85} +(-5.43845 + 11.6153i) q^{86} +2.00000 q^{87} +(-2.56155 + 0.673500i) q^{88} -1.46228i q^{89} +(-2.00000 + 4.27156i) q^{90} +(-4.00000 + 2.92456i) q^{91} +(-1.43845 + 1.19935i) q^{92} +(-8.00000 - 3.74571i) q^{94} -23.7565i q^{95} +(-3.28078 + 4.60831i) q^{96} +10.4160i q^{97} +(6.71922 - 7.26994i) q^{98} -0.936426i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 + q^4 + q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	$ 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{14} - 7 q^{16} - q^{18} + 12 q^{19} + 4 q^{20} - 2 q^{21} + 6 q^{22} + 7 q^{24} - 8 q^{25} + 12 q^{26} - 4 q^{27} + q^{28} - 8 q^{29} + 8 q^{30} + 9 q^{32} - 4 q^{34} - 12 q^{35} + q^{36} - 12 q^{37} - 20 q^{38} - 20 q^{40} - 7 q^{42} + 14 q^{44} - 6 q^{46} - 8 q^{47} + 7 q^{48} + 8 q^{49} + 19 q^{50} + 28 q^{52} + 16 q^{53} + q^{54} + 4 q^{55} - 23 q^{56} - 12 q^{57} + 2 q^{58} + 16 q^{59} - 4 q^{60} + 2 q^{63} + q^{64} + 8 q^{65} - 6 q^{66} - 32 q^{68} + 16 q^{70} - 7 q^{72} - 14 q^{74} + 8 q^{75} + 20 q^{76} - 8 q^{77} - 12 q^{78} + 36 q^{80} + 4 q^{81} + 20 q^{82} - 8 q^{83} - q^{84} + 20 q^{85} - 30 q^{86} + 8 q^{87} - 2 q^{88} - 8 q^{90} - 16 q^{91} - 14 q^{92} - 32 q^{94} - 9 q^{96} + 31 q^{98}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 + q^4 + q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 - 8 * q^10 - q^12 + 7 * q^14 - 7 * q^16 - q^18 + 12 * q^19 + 4 * q^20 - 2 * q^21 + 6 * q^22 + 7 * q^24 - 8 * q^25 + 12 * q^26 - 4 * q^27 + q^28 - 8 * q^29 + 8 * q^30 + 9 * q^32 - 4 * q^34 - 12 * q^35 + q^36 - 12 * q^37 - 20 * q^38 - 20 * q^40 - 7 * q^42 + 14 * q^44 - 6 * q^46 - 8 * q^47 + 7 * q^48 + 8 * q^49 + 19 * q^50 + 28 * q^52 + 16 * q^53 + q^54 + 4 * q^55 - 23 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^59 - 4 * q^60 + 2 * q^63 + q^64 + 8 * q^65 - 6 * q^66 - 32 * q^68 + 16 * q^70 - 7 * q^72 - 14 * q^74 + 8 * q^75 + 20 * q^76 - 8 * q^77 - 12 * q^78 + 36 * q^80 + 4 * q^81 + 20 * q^82 - 8 * q^83 - q^84 + 20 * q^85 - 30 * q^86 + 8 * q^87 - 2 * q^88 - 8 * q^90 - 16 * q^91 - 14 * q^92 - 32 * q^94 - 9 * q^96 + 31 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.28078	−	0.599676i	−0.905646	−	0.424035i
$2$	−1.28078	−	0.599676i	−0.905646	−	0.424035i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.28078	+	1.53610i	0.640388	+	0.768051i
$5$		−	3.33513i		−	1.49152i	−0.666217	−	0.745758i	$-0.732087\pi$
$5$		−	3.33513i		−	1.49152i	0.666217	−	0.745758i	$-0.267913\pi$
$6$	1.28078	+	0.599676i	0.522875	+	0.244817i
$7$	−1.56155	−	2.13578i	−0.590211	−	0.807249i
$7$	−1.56155	−	2.13578i	−0.590211	−	0.807249i
$8$	−0.719224	−	2.73546i	−0.254284	−	0.967130i
$9$	1.00000			0.333333
$10$	−2.00000	+	4.27156i	−0.632456	+	1.35079i
$11$		−	0.936426i		−	0.282343i	−0.989985	−	0.141172i	$-0.954913\pi$
$11$		−	0.936426i		−	0.282343i	0.989985	−	0.141172i	$-0.0450869\pi$
$12$	−1.28078	−	1.53610i	−0.369728	−	0.443435i
$13$		−	1.87285i		−	0.519436i	−0.965685	−	0.259718i	$-0.916370\pi$
$13$		−	1.87285i		−	0.519436i	0.965685	−	0.259718i	$-0.0836296\pi$
$14$	0.719224	+	3.67188i	0.192221	+	0.981352i
$15$			3.33513i			0.861127i
$16$	−0.719224	+	3.93481i	−0.179806	+	0.983702i
$17$			5.20798i			1.26312i	0.775326	+	0.631561i	$0.217585\pi$
$17$			5.20798i			1.26312i	−0.775326	+	0.631561i	$0.782415\pi$
$18$	−1.28078	−	0.599676i	−0.301882	−	0.141345i
$19$	7.12311			1.63415			0.817076	−	0.576530i	$-0.195593\pi$
$19$	7.12311			1.63415			0.817076	+	0.576530i	$0.195593\pi$
$20$	5.12311	−	4.27156i	1.14556	−	0.955149i
$21$	1.56155	+	2.13578i	0.340759	+	0.466065i
$22$	−0.561553	+	1.19935i	−0.119723	+	0.255703i
$23$			0.936426i			0.195258i	0.995223	+	0.0976292i	$0.0311259\pi$
$23$			0.936426i			0.195258i	−0.995223	+	0.0976292i	$0.968874\pi$
$24$	0.719224	+	2.73546i	0.146811	+	0.558373i
$25$	−6.12311			−1.22462
$26$	−1.12311	+	2.39871i	−0.220259	+	0.470425i
$27$	−1.00000			−0.192450
$28$	1.28078	−	5.13416i	0.242044	−	0.970265i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	2.00000	−	4.27156i	0.365148	−	0.779876i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	3.28078	−	4.60831i	0.579965	−	0.814642i
$33$			0.936426i			0.163011i
$34$	3.12311	−	6.67026i	0.535608	−	1.14394i
$35$	−7.12311	+	5.20798i	−1.20402	+	0.880310i
$36$	1.28078	+	1.53610i	0.213463	+	0.256017i
$37$	1.12311			0.184637			0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311			0.184637			0.0923187	+	0.995730i	$0.470572\pi$
$38$	−9.12311	−	4.27156i	−1.47996	−	0.692938i
$39$			1.87285i			0.299896i
$40$	−9.12311	+	2.39871i	−1.44249	+	0.379269i
$41$			1.46228i			0.228370i	0.993460	+	0.114185i	$0.0364256\pi$
$41$			1.46228i			0.228370i	−0.993460	+	0.114185i	$0.963574\pi$
$42$	−0.719224	−	3.67188i	−0.110979	−	0.566584i
$43$		−	9.06897i		−	1.38300i	−0.722374	−	0.691502i	$-0.756949\pi$
$43$		−	9.06897i		−	1.38300i	0.722374	−	0.691502i	$-0.243051\pi$
$44$	1.43845	−	1.19935i	0.216854	−	0.180809i
$45$		−	3.33513i		−	0.497172i
$46$	0.561553	−	1.19935i	0.0827964	−	0.176835i
$47$	6.24621			0.911104			0.455552	−	0.890209i	$-0.349442\pi$
$47$	6.24621			0.911104			0.455552	+	0.890209i	$0.349442\pi$
$48$	0.719224	−	3.93481i	0.103811	−	0.567941i
$49$	−2.12311	+	6.67026i	−0.303301	+	0.952895i
$50$	7.84233	+	3.67188i	1.10907	+	0.519283i
$51$		−	5.20798i		−	0.729264i
$52$	2.87689	−	2.39871i	0.398953	−	0.332641i
$53$	12.2462			1.68215			0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462			1.68215			0.841073	+	0.540921i	$0.181924\pi$
$54$	1.28078	+	0.599676i	0.174292	+	0.0816056i
$55$	−3.12311			−0.421119
$56$	−4.71922	+	5.80766i	−0.630633	+	0.776081i
$57$	−7.12311			−0.943478
$58$	2.56155	+	1.19935i	0.336348	+	0.157483i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$	−5.12311	+	4.27156i	−0.661390	+	0.551456i
$61$		−	4.79741i		−	0.614246i	−0.951670	−	0.307123i	$-0.900634\pi$
$61$		−	4.79741i		−	0.614246i	0.951670	−	0.307123i	$-0.0993662\pi$
$62$		0			0
$63$	−1.56155	−	2.13578i	−0.196737	−	0.269083i
$64$	−6.96543	+	3.93481i	−0.870679	+	0.491851i
$65$	−6.24621			−0.774747
$66$	0.561553	−	1.19935i	0.0691224	−	0.147630i
$67$			10.9418i			1.33676i	0.743822	+	0.668378i	$0.233011\pi$
$67$			10.9418i			1.33676i	−0.743822	+	0.668378i	$0.766989\pi$
$68$	−8.00000	+	6.67026i	−0.970143	+	0.808888i
$69$		−	0.936426i		−	0.112732i
$70$	12.2462	−	2.39871i	1.46370	−	0.286700i
$71$			3.86098i			0.458215i	0.973401	+	0.229107i	$0.0735807\pi$
$71$			3.86098i			0.458215i	−0.973401	+	0.229107i	$0.926419\pi$
$72$	−0.719224	−	2.73546i	−0.0847613	−	0.322377i
$73$		−	6.67026i		−	0.780695i	−0.920668	−	0.390348i	$-0.872355\pi$
$73$		−	6.67026i		−	0.780695i	0.920668	−	0.390348i	$-0.127645\pi$
$74$	−1.43845	−	0.673500i	−0.167216	−	0.0782928i
$75$	6.12311			0.707035
$76$	9.12311	+	10.9418i	1.04649	+	1.25511i
$77$	−2.00000	+	1.46228i	−0.227921	+	0.166642i
$78$	1.12311	−	2.39871i	0.127167	−	0.271600i
$79$			2.39871i			0.269875i	0.990854	+	0.134938i	$0.0430834\pi$
$79$			2.39871i			0.269875i	−0.990854	+	0.134938i	$0.956917\pi$
$80$	13.1231	+	2.39871i	1.46721	+	0.268183i
$81$	1.00000			0.111111
$82$	0.876894	−	1.87285i	0.0968368	−	0.206822i
$83$	−10.2462			−1.12467			−0.562334	−	0.826910i	$-0.690096\pi$
$83$	−10.2462			−1.12467			−0.562334	+	0.826910i	$0.690096\pi$
$84$	−1.28078	+	5.13416i	−0.139744	+	0.560183i
$85$	17.3693			1.88397
$86$	−5.43845	+	11.6153i	−0.586443	+	1.25251i
$87$	2.00000			0.214423
$88$	−2.56155	+	0.673500i	−0.273062	+	0.0717953i
$89$		−	1.46228i		−	0.155001i	−0.996992	−	0.0775006i	$-0.975306\pi$
$89$		−	1.46228i		−	0.155001i	0.996992	−	0.0775006i	$-0.0246940\pi$
$90$	−2.00000	+	4.27156i	−0.210819	+	0.450262i
$91$	−4.00000	+	2.92456i	−0.419314	+	0.306577i
$92$	−1.43845	+	1.19935i	−0.149968	+	0.125041i
$93$		0			0
$94$	−8.00000	−	3.74571i	−0.825137	−	0.386340i
$95$		−	23.7565i		−	2.43737i
$96$	−3.28078	+	4.60831i	−0.334843	+	0.470334i
$97$			10.4160i			1.05758i	0.848752	+	0.528791i	$0.177354\pi$
$97$			10.4160i			1.05758i	−0.848752	+	0.528791i	$0.822646\pi$
$98$	6.71922	−	7.26994i	0.678744	−	0.734375i
$99$		−	0.936426i		−	0.0941144i
$100$	−7.84233	−	9.40572i	−0.784233	−	0.940572i
$101$		−	13.7511i		−	1.36829i	−0.729348	−	0.684143i	$-0.760176\pi$
$101$		−	13.7511i		−	1.36829i	0.729348	−	0.684143i	$-0.239824\pi$
$102$	−3.12311	+	6.67026i	−0.309234	+	0.660455i
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−5.12311	+	1.34700i	−0.502362	+	0.132084i
$105$	7.12311	−	5.20798i	0.695144	−	0.508247i
$106$	−15.6847	−	7.34376i	−1.52343	−	0.713289i
$107$			9.47954i			0.916422i	0.888843	+	0.458211i	$0.151510\pi$
$107$			9.47954i			0.916422i	−0.888843	+	0.458211i	$0.848490\pi$
$108$	−1.28078	−	1.53610i	−0.123243	−	0.147812i
$109$	−8.24621			−0.789844			−0.394922	−	0.918715i	$-0.629228\pi$
$109$	−8.24621			−0.789844			−0.394922	+	0.918715i	$0.629228\pi$
$110$	4.00000	+	1.87285i	0.381385	+	0.178570i
$111$	−1.12311			−0.106600
$112$	9.52699	−	4.60831i	0.900216	−	0.435444i
$113$	−4.24621			−0.399450			−0.199725	−	0.979852i	$-0.564005\pi$
$113$	−4.24621			−0.399450			−0.199725	+	0.979852i	$0.564005\pi$
$114$	9.12311	+	4.27156i	0.854457	+	0.400068i
$115$	3.12311			0.291231
$116$	−2.56155	−	3.07221i	−0.237834	−	0.285247i
$117$		−	1.87285i		−	0.173145i
$118$	−5.12311	−	2.39871i	−0.471620	−	0.220819i
$119$	11.1231	−	8.13254i	1.01965	−	0.745509i
$120$	9.12311	−	2.39871i	0.832822	−	0.218971i
$121$	10.1231			0.920282
$122$	−2.87689	+	6.14441i	−0.260462	+	0.556289i
$123$		−	1.46228i		−	0.131849i
$124$		0			0
$125$			3.74571i			0.335026i
$126$	0.719224	+	3.67188i	0.0640735	+	0.327117i
$127$			9.89012i			0.877606i	0.898583	+	0.438803i	$0.144597\pi$
$127$			9.89012i			0.877606i	−0.898583	+	0.438803i	$0.855403\pi$
$128$	11.2808	−	0.862603i	0.997089	−	0.0762440i
$129$			9.06897i			0.798478i
$130$	8.00000	+	3.74571i	0.701646	+	0.328520i
$131$	5.75379			0.502711			0.251355	−	0.967895i	$-0.419124\pi$
$131$	5.75379			0.502711			0.251355	+	0.967895i	$0.419124\pi$
$132$	−1.43845	+	1.19935i	−0.125201	+	0.104390i
$133$	−11.1231	−	15.2134i	−0.964496	−	1.31917i
$134$	6.56155	−	14.0140i	0.566832	−	1.21063i
$135$			3.33513i			0.287042i
$136$	14.2462	−	3.74571i	1.22160	−	0.321192i
$137$	0.246211			0.0210352			0.0105176	−	0.999945i	$-0.496652\pi$
$137$	0.246211			0.0210352			0.0105176	+	0.999945i	$0.496652\pi$
$138$	−0.561553	+	1.19935i	−0.0478025	+	0.102096i
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	−17.1231	−	4.27156i	−1.44717	−	0.361013i
$141$	−6.24621			−0.526026
$142$	2.31534	−	4.94506i	0.194299	−	0.414980i
$143$	−1.75379			−0.146659
$144$	−0.719224	+	3.93481i	−0.0599353	+	0.327901i
$145$			6.67026i			0.553935i
$146$	−4.00000	+	8.54312i	−0.331042	+	0.707033i
$147$	2.12311	−	6.67026i	0.175111	−	0.550154i
$148$	1.43845	+	1.72521i	0.118240	+	0.141811i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	−7.84233	−	3.67188i	−0.640323	−	0.299808i
$151$			9.06897i			0.738022i	0.929425	+	0.369011i	$0.120304\pi$
$151$			9.06897i			0.738022i	−0.929425	+	0.369011i	$0.879696\pi$
$152$	−5.12311	−	19.4849i	−0.415539	−	1.58044i
$153$			5.20798i			0.421041i
$154$	3.43845	−	0.673500i	0.277078	−	0.0542722i
$155$		0			0
$156$	−2.87689	+	2.39871i	−0.230336	+	0.192050i
$157$			21.8836i			1.74650i	0.487268	+	0.873252i	$0.337993\pi$
$157$			21.8836i			1.74650i	−0.487268	+	0.873252i	$0.662007\pi$
$158$	1.43845	−	3.07221i	0.114437	−	0.244412i
$159$	−12.2462			−0.971188
$160$	−15.3693	−	10.9418i	−1.21505	−	0.865027i
$161$	2.00000	−	1.46228i	0.157622	−	0.115244i
$162$	−1.28078	−	0.599676i	−0.100627	−	0.0471150i
$163$		−	15.7392i		−	1.23279i	−0.787436	−	0.616396i	$-0.788592\pi$
$163$		−	15.7392i		−	1.23279i	0.787436	−	0.616396i	$-0.211408\pi$
$164$	−2.24621	+	1.87285i	−0.175400	+	0.146245i
$165$	3.12311			0.243133
$166$	13.1231	+	6.14441i	1.01855	+	0.476899i
$167$	14.2462			1.10240			0.551202	−	0.834372i	$-0.314169\pi$
$167$	14.2462			1.10240			0.551202	+	0.834372i	$0.314169\pi$
$168$	4.71922	−	5.80766i	0.364096	−	0.448071i
$169$	9.49242			0.730186
$170$	−22.2462	−	10.4160i	−1.70621	−	0.798868i
$171$	7.12311			0.544718
$172$	13.9309	−	11.6153i	1.06222	−	0.885660i
$173$			16.6757i			1.26783i	0.773404	+	0.633913i	$0.218552\pi$
$173$			16.6757i			1.26783i	−0.773404	+	0.633913i	$0.781448\pi$
$174$	−2.56155	−	1.19935i	−0.194191	−	0.0909227i
$175$	9.56155	+	13.0776i	0.722785	+	0.988574i
$176$	3.68466	+	0.673500i	0.277742	+	0.0507670i
$177$	−4.00000			−0.300658
$178$	−0.876894	+	1.87285i	−0.0657260	+	0.140376i
$179$			16.1498i			1.20709i	0.797328	+	0.603547i	$0.206246\pi$
$179$			16.1498i			1.20709i	−0.797328	+	0.603547i	$0.793754\pi$
$180$	5.12311	−	4.27156i	0.381854	−	0.318383i
$181$			1.87285i			0.139208i	0.997575	+	0.0696040i	$0.0221736\pi$
$181$			1.87285i			0.139208i	−0.997575	+	0.0696040i	$0.977826\pi$
$182$	6.87689	−	1.34700i	0.509749	−	0.0998463i
$183$			4.79741i			0.354635i
$184$	2.56155	−	0.673500i	0.188840	−	0.0496511i
$185$		−	3.74571i		−	0.275390i
$186$		0			0
$187$	4.87689			0.356634
$188$	8.00000	+	9.59482i	0.583460	+	0.699774i
$189$	1.56155	+	2.13578i	0.113586	+	0.155355i
$190$	−14.2462	+	30.4268i	−1.03353	+	2.20739i
$191$		−	2.80928i		−	0.203272i	−0.994822	−	0.101636i	$-0.967592\pi$
$191$		−	2.80928i		−	0.203272i	0.994822	−	0.101636i	$-0.0324078\pi$
$192$	6.96543	−	3.93481i	0.502687	−	0.283970i
$193$	−15.3693			−1.10631			−0.553154	−	0.833079i	$-0.686576\pi$
$193$	−15.3693			−1.10631			−0.553154	+	0.833079i	$0.686576\pi$
$194$	6.24621	−	13.3405i	0.448452	−	0.957794i
$195$	6.24621			0.447300
$196$	−12.9654	+	5.28181i	−0.926102	+	0.377272i
$197$	−16.2462			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$197$	−16.2462			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$198$	−0.561553	+	1.19935i	−0.0399078	+	0.0852343i
$199$	−3.12311			−0.221391			−0.110696	−	0.993854i	$-0.535308\pi$
$199$	−3.12311			−0.221391			−0.110696	+	0.993854i	$0.535308\pi$
$200$	4.40388	+	16.7495i	0.311401	+	1.18437i
$201$		−	10.9418i		−	0.771777i
$202$	−8.24621	+	17.6121i	−0.580201	+	1.23918i
$203$	3.12311	+	4.27156i	0.219199	+	0.299805i
$204$	8.00000	−	6.67026i	0.560112	−	0.467012i
$205$	4.87689			0.340617
$206$	10.2462	+	4.79741i	0.713887	+	0.334251i
$207$			0.936426i			0.0650861i
$208$	7.36932	+	1.34700i	0.510970	+	0.0933976i
$209$		−	6.67026i		−	0.461392i
$210$	−12.2462	+	2.39871i	−0.845069	+	0.165526i
$211$		−	12.8147i		−	0.882199i	−0.897458	−	0.441099i	$-0.854589\pi$
$211$		−	12.8147i		−	0.882199i	0.897458	−	0.441099i	$-0.145411\pi$
$212$	15.6847	+	18.8114i	1.07723	+	1.29197i
$213$		−	3.86098i		−	0.264550i
$214$	5.68466	−	12.1412i	0.388595	−	0.829954i
$215$	−30.2462			−2.06277
$216$	0.719224	+	2.73546i	0.0489370	+	0.186124i
$217$		0			0
$218$	10.5616	+	4.94506i	0.715319	+	0.334922i
$219$			6.67026i			0.450735i
$220$	−4.00000	−	4.79741i	−0.269680	−	0.323441i
$221$	9.75379			0.656111
$222$	1.43845	+	0.673500i	0.0965423	+	0.0452024i
$223$	27.1231			1.81630			0.908149	−	0.418648i	$-0.137496\pi$
$223$	27.1231			1.81630			0.908149	+	0.418648i	$0.137496\pi$
$224$	−14.9654	+	0.189103i	−0.999920	+	0.0126350i
$225$	−6.12311			−0.408207
$226$	5.43845	+	2.54635i	0.361760	+	0.169381i
$227$	−16.4924			−1.09464			−0.547320	−	0.836923i	$-0.684352\pi$
$227$	−16.4924			−1.09464			−0.547320	+	0.836923i	$0.684352\pi$
$228$	−9.12311	−	10.9418i	−0.604192	−	0.724640i
$229$		−	5.61856i		−	0.371285i	−0.982617	−	0.185642i	$-0.940563\pi$
$229$		−	5.61856i		−	0.371285i	0.982617	−	0.185642i	$-0.0594366\pi$
$230$	−4.00000	−	1.87285i	−0.263752	−	0.123492i
$231$	2.00000	−	1.46228i	0.131590	−	0.0962109i
$232$	1.43845	+	5.47091i	0.0944387	+	0.359183i
$233$	22.4924			1.47353			0.736764	−	0.676150i	$-0.236353\pi$
$233$	22.4924			1.47353			0.736764	+	0.676150i	$0.236353\pi$
$234$	−1.12311	+	2.39871i	−0.0734197	+	0.156808i
$235$		−	20.8319i		−	1.35893i
$236$	5.12311	+	6.14441i	0.333486	+	0.399967i
$237$		−	2.39871i		−	0.155813i
$238$	−19.1231	+	3.74571i	−1.23957	+	0.242798i
$239$		−	16.1498i		−	1.04464i	−0.852748	−	0.522322i	$-0.825066\pi$
$239$		−	16.1498i		−	1.04464i	0.852748	−	0.522322i	$-0.174934\pi$
$240$	−13.1231	−	2.39871i	−0.847093	−	0.154836i
$241$		−	23.7565i		−	1.53029i	−0.643858	−	0.765145i	$-0.722667\pi$
$241$		−	23.7565i		−	1.53029i	0.643858	−	0.765145i	$-0.277333\pi$
$242$	−12.9654	−	6.07059i	−0.833450	−	0.390232i
$243$	−1.00000			−0.0641500
$244$	7.36932	−	6.14441i	0.471772	−	0.393356i
$245$	22.2462	+	7.08084i	1.42126	+	0.452378i
$246$	−0.876894	+	1.87285i	−0.0559087	+	0.119409i
$247$		−	13.3405i		−	0.848837i
$248$		0			0
$249$	10.2462			0.649327
$250$	2.24621	−	4.79741i	0.142063	−	0.303415i
$251$	−5.75379			−0.363176			−0.181588	−	0.983375i	$-0.558124\pi$
$251$	−5.75379			−0.363176			−0.181588	+	0.983375i	$0.558124\pi$
$252$	1.28078	−	5.13416i	0.0806813	−	0.323422i
$253$	0.876894			0.0551299
$254$	5.93087	−	12.6670i	0.372136	−	0.794800i
$255$	−17.3693			−1.08771
$256$	−14.9654	−	5.66001i	−0.935340	−	0.353751i
$257$		−	2.28343i		−	0.142436i	−0.997461	−	0.0712181i	$-0.977311\pi$
$257$		−	2.28343i		−	0.142436i	0.997461	−	0.0712181i	$-0.0226886\pi$
$258$	5.43845	−	11.6153i	0.338583	−	0.723138i
$259$	−1.75379	−	2.39871i	−0.108975	−	0.149048i
$260$	−8.00000	−	9.59482i	−0.496139	−	0.595046i
$261$	−2.00000			−0.123797
$262$	−7.36932	−	3.45041i	−0.455278	−	0.213167i
$263$			24.6929i			1.52263i	0.648382	+	0.761315i	$0.275446\pi$
$263$			24.6929i			1.52263i	−0.648382	+	0.761315i	$0.724554\pi$
$264$	2.56155	−	0.673500i	0.157653	−	0.0414511i
$265$		−	40.8427i		−	2.50895i
$266$	5.12311	+	26.1552i	0.314118	+	1.60368i
$267$			1.46228i			0.0894900i
$268$	−16.8078	+	14.0140i	−1.02670	+	0.856043i
$269$			10.8265i			0.660106i	0.943962	+	0.330053i	$0.107067\pi$
$269$			10.8265i			0.660106i	−0.943962	+	0.330053i	$0.892933\pi$
$270$	2.00000	−	4.27156i	0.121716	−	0.259959i
$271$	−28.4924			−1.73079			−0.865396	−	0.501089i	$-0.832933\pi$
$271$	−28.4924			−1.73079			−0.865396	+	0.501089i	$0.832933\pi$
$272$	−20.4924	−	3.74571i	−1.24254	−	0.227117i
$273$	4.00000	−	2.92456i	0.242091	−	0.177002i
$274$	−0.315342	−	0.147647i	−0.0190505	−	0.00891969i
$275$			5.73384i			0.345763i
$276$	1.43845	−	1.19935i	0.0865843	−	0.0721926i
$277$	−5.12311			−0.307818			−0.153909	−	0.988085i	$-0.549186\pi$
$277$	−5.12311			−0.307818			−0.153909	+	0.988085i	$0.549186\pi$
$278$	15.3693	+	7.19612i	0.921790	+	0.431594i
$279$		0			0
$280$	19.3693	+	15.7392i	1.15754	+	0.940599i
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	8.00000	+	3.74571i	0.476393	+	0.223054i
$283$	8.87689			0.527677			0.263838	−	0.964567i	$-0.415011\pi$
$283$	8.87689			0.527677			0.263838	+	0.964567i	$0.415011\pi$
$284$	−5.93087	+	4.94506i	−0.351932	+	0.293435i
$285$			23.7565i			1.40721i
$286$	2.24621	+	1.05171i	0.132821	+	0.0621887i
$287$	3.12311	−	2.28343i	0.184351	−	0.134786i
$288$	3.28078	−	4.60831i	0.193322	−	0.271547i
$289$	−10.1231			−0.595477
$290$	4.00000	−	8.54312i	0.234888	−	0.501669i
$291$		−	10.4160i		−	0.610595i
$292$	10.2462	−	8.54312i	0.599614	−	0.499948i
$293$		−	13.7511i		−	0.803348i	−0.915783	−	0.401674i	$-0.868429\pi$
$293$		−	13.7511i		−	0.803348i	0.915783	−	0.401674i	$-0.131571\pi$
$294$	−6.71922	+	7.26994i	−0.391873	+	0.423992i
$295$		−	13.3405i		−	0.776716i
$296$	−0.807764	−	3.07221i	−0.0469503	−	0.178568i
$297$			0.936426i			0.0543370i
$298$	12.8078	+	5.99676i	0.741934	+	0.347383i
$299$	1.75379			0.101424
$300$	7.84233	+	9.40572i	0.452777	+	0.543039i
$301$	−19.3693	+	14.1617i	−1.11643	+	0.816265i
$302$	5.43845	−	11.6153i	0.312947	−	0.668387i
$303$			13.7511i			0.789980i
$304$	−5.12311	+	28.0281i	−0.293830	+	1.60752i
$305$	−16.0000			−0.916157
$306$	3.12311	−	6.67026i	0.178536	−	0.381314i
$307$	19.6155			1.11952			0.559759	−	0.828656i	$-0.310894\pi$
$307$	19.6155			1.11952			0.559759	+	0.828656i	$0.310894\pi$
$308$	−4.80776	−	1.19935i	−0.273948	−	0.0683395i
$309$	8.00000			0.455104
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$	5.12311	−	1.34700i	0.290039	−	0.0762589i
$313$			22.9354i			1.29638i	0.761478	+	0.648191i	$0.224474\pi$
$313$			22.9354i			1.29638i	−0.761478	+	0.648191i	$0.775526\pi$
$314$	13.1231	−	28.0281i	0.740580	−	1.58171i
$315$	−7.12311	+	5.20798i	−0.401342	+	0.293437i
$316$	−3.68466	+	3.07221i	−0.207278	+	0.172825i
$317$	−14.4924			−0.813976			−0.406988	−	0.913434i	$-0.633421\pi$
$317$	−14.4924			−0.813976			−0.406988	+	0.913434i	$0.633421\pi$
$318$	15.6847	+	7.34376i	0.879552	+	0.411818i
$319$			1.87285i			0.104860i
$320$	13.1231	+	23.2306i	0.733604	+	1.29863i
$321$		−	9.47954i		−	0.529097i
$322$	−3.43845	+	0.673500i	−0.191617	+	0.0375327i
$323$			37.0970i			2.06413i
$324$	1.28078	+	1.53610i	0.0711542	+	0.0853390i
$325$			11.4677i			0.636112i
$326$	−9.43845	+	20.1584i	−0.522747	+	1.11647i
$327$	8.24621			0.456017
$328$	4.00000	−	1.05171i	0.220863	−	0.0580707i
$329$	−9.75379	−	13.3405i	−0.537744	−	0.735487i
$330$	−4.00000	−	1.87285i	−0.220193	−	0.103097i
$331$			17.6121i			0.968048i	0.875055	+	0.484024i	$0.160825\pi$
$331$			17.6121i			0.968048i	−0.875055	+	0.484024i	$0.839175\pi$
$332$	−13.1231	−	15.7392i	−0.720224	−	0.863803i
$333$	1.12311			0.0615458
$334$	−18.2462	−	8.54312i	−0.998388	−	0.467459i
$335$	36.4924			1.99379
$336$	−9.52699	+	4.60831i	−0.519740	+	0.251404i
$337$	8.24621			0.449200			0.224600	−	0.974451i	$-0.427892\pi$
$337$	8.24621			0.449200			0.224600	+	0.974451i	$0.427892\pi$
$338$	−12.1577	−	5.69238i	−0.661290	−	0.309625i
$339$	4.24621			0.230623
$340$	22.2462	+	26.6811i	1.20647	+	1.44698i
$341$		0			0
$342$	−9.12311	−	4.27156i	−0.493321	−	0.230979i
$343$	17.5616	−	5.88148i	0.948235	−	0.317570i
$344$	−24.8078	+	6.52262i	−1.33754	+	0.351676i
$345$	−3.12311			−0.168142
$346$	10.0000	−	21.3578i	0.537603	−	1.14820i
$347$		−	20.1261i		−	1.08042i	−0.841529	−	0.540212i	$-0.818344\pi$
$347$		−	20.1261i		−	1.08042i	0.841529	−	0.540212i	$-0.181656\pi$
$348$	2.56155	+	3.07221i	0.137314	+	0.164688i
$349$			21.8836i			1.17140i	0.810526	+	0.585702i	$0.199181\pi$
$349$			21.8836i			1.17140i	−0.810526	+	0.585702i	$0.800819\pi$
$350$	−4.40388	−	22.4833i	−0.235397	−	1.20178i
$351$			1.87285i			0.0999655i
$352$	−4.31534	−	3.07221i	−0.230008	−	0.163749i
$353$			28.9645i			1.54162i	0.637063	+	0.770812i	$0.280149\pi$
$353$			28.9645i			1.54162i	−0.637063	+	0.770812i	$0.719851\pi$
$354$	5.12311	+	2.39871i	0.272290	+	0.127490i
$355$	12.8769			0.683435
$356$	2.24621	−	1.87285i	0.119049	−	0.0992610i
$357$	−11.1231	+	8.13254i	−0.588697	+	0.430420i
$358$	9.68466	−	20.6843i	0.511850	−	1.09320i
$359$		−	22.8201i		−	1.20440i	−0.798346	−	0.602199i	$-0.794292\pi$
$359$		−	22.8201i		−	1.20440i	0.798346	−	0.602199i	$-0.205708\pi$
$360$	−9.12311	+	2.39871i	−0.480830	+	0.126423i
$361$	31.7386			1.67045
$362$	1.12311	−	2.39871i	0.0590291	−	0.126073i
$363$	−10.1231			−0.531325
$364$	−9.61553	−	2.39871i	−0.503991	−	0.125726i
$365$	−22.2462			−1.16442
$366$	2.87689	−	6.14441i	0.150378	−	0.321174i
$367$	−33.3693			−1.74186			−0.870932	−	0.491403i	$-0.836484\pi$
$367$	−33.3693			−1.74186			−0.870932	+	0.491403i	$0.836484\pi$
$368$	−3.68466	−	0.673500i	−0.192076	−	0.0351086i
$369$			1.46228i			0.0761232i
$370$	−2.24621	+	4.79741i	−0.116775	+	0.249406i
$371$	−19.1231	−	26.1552i	−0.992822	−	1.35791i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	−6.24621	−	2.92456i	−0.322984	−	0.151225i
$375$		−	3.74571i		−	0.193427i
$376$	−4.49242	−	17.0862i	−0.231679	−	0.881155i
$377$			3.74571i			0.192914i
$378$	−0.719224	−	3.67188i	−0.0369929	−	0.188861i
$379$			25.1035i			1.28948i	0.764402	+	0.644740i	$0.223034\pi$
$379$			25.1035i			1.28948i	−0.764402	+	0.644740i	$0.776966\pi$
$380$	36.4924	−	30.4268i	1.87202	−	1.56086i
$381$		−	9.89012i		−	0.506686i
$382$	−1.68466	+	3.59806i	−0.0861946	+	0.184093i
$383$	−9.75379			−0.498395			−0.249198	−	0.968453i	$-0.580167\pi$
$383$	−9.75379			−0.498395			−0.249198	+	0.968453i	$0.580167\pi$
$384$	−11.2808	+	0.862603i	−0.575670	+	0.0440195i
$385$	4.87689	+	6.67026i	0.248550	+	0.339948i
$386$	19.6847	+	9.21662i	1.00192	+	0.469113i
$387$		−	9.06897i		−	0.461002i
$388$	−16.0000	+	13.3405i	−0.812277	+	0.677263i
$389$	−16.2462			−0.823716			−0.411858	−	0.911248i	$-0.635120\pi$
$389$	−16.2462			−0.823716			−0.411858	+	0.911248i	$0.635120\pi$
$390$	−8.00000	−	3.74571i	−0.405096	−	0.189671i
$391$	−4.87689			−0.246635
$392$	19.7732	+	1.01025i	0.998697	+	0.0510253i
$393$	−5.75379			−0.290240
$394$	20.8078	+	9.74247i	1.04828	+	0.490819i
$395$	8.00000			0.402524
$396$	1.43845	−	1.19935i	0.0722847	−	0.0602697i
$397$		−	18.1379i		−	0.910317i	−0.890410	−	0.455159i	$-0.849583\pi$
$397$		−	18.1379i		−	0.910317i	0.890410	−	0.455159i	$-0.150417\pi$
$398$	4.00000	+	1.87285i	0.200502	+	0.0938776i
$399$	11.1231	+	15.2134i	0.556852	+	0.761622i
$400$	4.40388	−	24.0932i	0.220194	−	1.20466i
$401$	8.24621			0.411796			0.205898	−	0.978573i	$-0.433988\pi$
$401$	8.24621			0.411796			0.205898	+	0.978573i	$0.433988\pi$
$402$	−6.56155	+	14.0140i	−0.327261	+	0.698956i
$403$		0			0
$404$	21.1231	−	17.6121i	1.05091	−	0.876234i
$405$		−	3.33513i		−	0.165724i
$406$	−1.43845	−	7.34376i	−0.0713889	−	0.364465i
$407$		−	1.05171i		−	0.0521311i
$408$	−14.2462	+	3.74571i	−0.705293	+	0.185440i
$409$			0.821147i			0.0406031i	0.999794	+	0.0203016i	$0.00646263\pi$
$409$			0.821147i			0.0406031i	−0.999794	+	0.0203016i	$0.993537\pi$
$410$	−6.24621	−	2.92456i	−0.308478	−	0.144434i
$411$	−0.246211			−0.0121447
$412$	−10.2462	−	12.2888i	−0.504795	−	0.605427i
$413$	−6.24621	−	8.54312i	−0.307356	−	0.420379i
$414$	0.561553	−	1.19935i	0.0275988	−	0.0589450i
$415$			34.1725i			1.67746i
$416$	−8.63068	−	6.14441i	−0.423154	−	0.301255i
$417$	12.0000			0.587643
$418$	−4.00000	+	8.54312i	−0.195646	+	0.417858i
$419$	−16.4924			−0.805708			−0.402854	−	0.915264i	$-0.631982\pi$
$419$	−16.4924			−0.805708			−0.402854	+	0.915264i	$0.631982\pi$
$420$	17.1231	+	4.27156i	0.835522	+	0.208431i
$421$	10.8769			0.530107			0.265054	−	0.964234i	$-0.414610\pi$
$421$	10.8769			0.530107			0.265054	+	0.964234i	$0.414610\pi$
$422$	−7.68466	+	16.4127i	−0.374083	+	0.798959i
$423$	6.24621			0.303701
$424$	−8.80776	−	33.4990i	−0.427743	−	1.62685i
$425$		−	31.8890i		−	1.54685i
$426$	−2.31534	+	4.94506i	−0.112179	+	0.239589i
$427$	−10.2462	+	7.49141i	−0.495849	+	0.362535i
$428$	−14.5616	+	12.1412i	−0.703859	+	0.586866i
$429$	1.75379			0.0846737
$430$	38.7386	+	18.1379i	1.86814	+	0.874689i
$431$			4.68213i			0.225530i	0.993622	+	0.112765i	$0.0359708\pi$
$431$			4.68213i			0.225530i	−0.993622	+	0.112765i	$0.964029\pi$
$432$	0.719224	−	3.93481i	0.0346037	−	0.189314i
$433$			13.3405i			0.641105i	0.947231	+	0.320552i	$0.103869\pi$
$433$			13.3405i			0.641105i	−0.947231	+	0.320552i	$0.896131\pi$
$434$		0			0
$435$		−	6.67026i		−	0.319815i
$436$	−10.5616	−	12.6670i	−0.505807	−	0.606641i
$437$			6.67026i			0.319082i
$438$	4.00000	−	8.54312i	0.191127	−	0.408206i
$439$	−6.63068			−0.316465			−0.158233	−	0.987402i	$-0.550580\pi$
$439$	−6.63068			−0.316465			−0.158233	+	0.987402i	$0.550580\pi$
$440$	2.24621	+	8.54312i	0.107084	+	0.407277i
$441$	−2.12311	+	6.67026i	−0.101100	+	0.317632i
$442$	−12.4924	−	5.84912i	−0.594204	−	0.278214i
$443$		−	18.8438i		−	0.895296i	−0.894210	−	0.447648i	$-0.852262\pi$
$443$		−	18.8438i		−	0.895296i	0.894210	−	0.447648i	$-0.147738\pi$
$444$	−1.43845	−	1.72521i	−0.0682657	−	0.0818746i
$445$	−4.87689			−0.231187
$446$	−34.7386	−	16.2651i	−1.64492	−	0.770174i
$447$	10.0000			0.472984
$448$	19.2808	+	8.73222i	0.910931	+	0.412559i
$449$	11.7538			0.554696			0.277348	−	0.960770i	$-0.410545\pi$
$449$	11.7538			0.554696			0.277348	+	0.960770i	$0.410545\pi$
$450$	7.84233	+	3.67188i	0.369691	+	0.173094i
$451$	1.36932			0.0644786
$452$	−5.43845	−	6.52262i	−0.255803	−	0.306798i
$453$		−	9.06897i		−	0.426097i
$454$	21.1231	+	9.89012i	0.991356	+	0.464166i
$455$	9.75379	+	13.3405i	0.457265	+	0.625414i
$456$	5.12311	+	19.4849i	0.239911	+	0.912466i
$457$	0.246211			0.0115173			0.00575864	−	0.999983i	$-0.498167\pi$
$457$	0.246211			0.0115173			0.00575864	+	0.999983i	$0.498167\pi$
$458$	−3.36932	+	7.19612i	−0.157438	+	0.336252i
$459$		−	5.20798i		−	0.243088i
$460$	4.00000	+	4.79741i	0.186501	+	0.223680i
$461$			6.25969i			0.291543i	0.989318	+	0.145771i	$0.0465664\pi$
$461$			6.25969i			0.291543i	−0.989318	+	0.145771i	$0.953434\pi$
$462$	−3.43845	+	0.673500i	−0.159971	+	0.0313341i
$463$		−	39.2652i		−	1.82481i	−0.409292	−	0.912404i	$-0.634224\pi$
$463$		−	39.2652i		−	1.82481i	0.409292	−	0.912404i	$-0.365776\pi$
$464$	1.43845	−	7.86962i	0.0667782	−	0.365338i
$465$		0			0
$466$	−28.8078	−	13.4882i	−1.33449	−	0.624828i
$467$	34.2462			1.58473			0.792363	−	0.610050i	$-0.208851\pi$
$467$	34.2462			1.58473			0.792363	+	0.610050i	$0.208851\pi$
$468$	2.87689	−	2.39871i	0.132984	−	0.110880i
$469$	23.3693	−	17.0862i	1.07909	−	0.788969i
$470$	−12.4924	+	26.6811i	−0.576232	+	1.23071i
$471$		−	21.8836i		−	1.00835i
$472$	−2.87689	−	10.9418i	−0.132420	−	0.503638i
$473$	−8.49242			−0.390482
$474$	−1.43845	+	3.07221i	−0.0660701	+	0.141111i
$475$	−43.6155			−2.00122
$476$	26.7386	+	6.67026i	1.22556	+	0.305731i
$477$	12.2462			0.560715
$478$	−9.68466	+	20.6843i	−0.442966	+	0.946077i
$479$	12.4924			0.570793			0.285397	−	0.958409i	$-0.407875\pi$
$479$	12.4924			0.570793			0.285397	+	0.958409i	$0.407875\pi$
$480$	15.3693	+	10.9418i	0.701510	+	0.499424i
$481$		−	2.10341i		−	0.0959073i
$482$	−14.2462	+	30.4268i	−0.648897	+	1.38590i
$483$	−2.00000	+	1.46228i	−0.0910032	+	0.0665360i
$484$	12.9654	+	15.5501i	0.589338	+	0.706824i
$485$	34.7386			1.57740
$486$	1.28078	+	0.599676i	0.0580972	+	0.0272019i
$487$			1.57756i			0.0714860i	0.999361	+	0.0357430i	$0.0113798\pi$
$487$			1.57756i			0.0714860i	−0.999361	+	0.0357430i	$0.988620\pi$
$488$	−13.1231	+	3.45041i	−0.594055	+	0.156193i
$489$			15.7392i			0.711753i
$490$	−24.2462	−	22.4095i	−1.09533	−	1.01236i
$491$		−	11.3524i		−	0.512326i	−0.966634	−	0.256163i	$-0.917542\pi$
$491$		−	11.3524i		−	0.512326i	0.966634	−	0.256163i	$-0.0824585\pi$
$492$	2.24621	−	1.87285i	0.101267	−	0.0844347i
$493$		−	10.4160i		−	0.469112i
$494$	−8.00000	+	17.0862i	−0.359937	+	0.768746i
$495$	−3.12311			−0.140373
$496$		0			0
$497$	8.24621	−	6.02913i	0.369893	−	0.270444i
$498$	−13.1231	−	6.14441i	−0.588060	−	0.275338i
$499$			13.8664i			0.620744i	0.950615	+	0.310372i	$0.100454\pi$
$499$			13.8664i			0.620744i	−0.950615	+	0.310372i	$0.899546\pi$
$500$	−5.75379	+	4.79741i	−0.257317	+	0.214547i
$501$	−14.2462			−0.636474
$502$	7.36932	+	3.45041i	0.328909	+	0.153999i
$503$	−26.7386			−1.19222			−0.596108	−	0.802904i	$-0.703287\pi$
$503$	−26.7386			−1.19222			−0.596108	+	0.802904i	$0.703287\pi$
$504$	−4.71922	+	5.80766i	−0.210211	+	0.258694i
$505$	−45.8617			−2.04082
$506$	−1.12311	−	0.525853i	−0.0499281	−	0.0233770i
$507$	−9.49242			−0.421573
$508$	−15.1922	+	12.6670i	−0.674046	+	0.562008i
$509$			3.33513i			0.147827i	0.997265	+	0.0739136i	$0.0235489\pi$
$509$			3.33513i			0.147827i	−0.997265	+	0.0739136i	$0.976451\pi$
$510$	22.2462	+	10.4160i	0.985079	+	0.461227i
$511$	−14.2462	+	10.4160i	−0.630215	+	0.460775i
$512$	15.7732	+	16.2236i	0.697083	+	0.716990i
$513$	−7.12311			−0.314493
$514$	−1.36932	+	2.92456i	−0.0603980	+	0.128997i
$515$			26.6811i			1.17571i
$516$	−13.9309	+	11.6153i	−0.613272	+	0.511336i
$517$		−	5.84912i		−	0.257244i
$518$	0.807764	+	4.12391i	0.0354911	+	0.181194i
$519$		−	16.6757i		−	0.731980i
$520$	4.49242	+	17.0862i	0.197006	+	0.749281i
$521$		−	29.7856i		−	1.30493i	−0.757818	−	0.652466i	$-0.773734\pi$
$521$		−	29.7856i		−	1.30493i	0.757818	−	0.652466i	$-0.226266\pi$
$522$	2.56155	+	1.19935i	0.112116	+	0.0524942i
$523$	32.4924			1.42079			0.710397	−	0.703801i	$-0.248515\pi$
$523$	32.4924			1.42079			0.710397	+	0.703801i	$0.248515\pi$
$524$	7.36932	+	8.83841i	0.321930	+	0.386108i
$525$	−9.56155	−	13.0776i	−0.417300	−	0.570753i
$526$	14.8078	−	31.6261i	0.645649	−	1.37896i
$527$		0			0
$528$	−3.68466	−	0.673500i	−0.160354	−	0.0293103i
$529$	22.1231			0.961874
$530$	−24.4924	+	52.3104i	−1.06388	+	2.27222i
$531$	4.00000			0.173585
$532$	9.12311	−	36.5712i	0.395537	−	1.58556i
$533$	2.73863			0.118623
$534$	0.876894	−	1.87285i	0.0379469	−	0.0810463i
$535$	31.6155			1.36686
$536$	29.9309	−	7.86962i	1.29282	−	0.339916i
$537$		−	16.1498i		−	0.696916i
$538$	6.49242	−	13.8664i	0.279908	−	0.597822i
$539$	6.24621	+	1.98813i	0.269043	+	0.0856349i
$540$	−5.12311	+	4.27156i	−0.220463	+	0.183819i
$541$	2.87689			0.123687			0.0618437	−	0.998086i	$-0.480302\pi$
$541$	2.87689			0.123687			0.0618437	+	0.998086i	$0.480302\pi$
$542$	36.4924	+	17.0862i	1.56748	+	0.733917i
$543$		−	1.87285i		−	0.0803718i
$544$	24.0000	+	17.0862i	1.02899	+	0.732566i
$545$			27.5022i			1.17806i
$546$	−6.87689	+	1.34700i	−0.294304	+	0.0576463i
$547$			16.7909i			0.717929i	0.933351	+	0.358964i	$0.116870\pi$
$547$			16.7909i			0.717929i	−0.933351	+	0.358964i	$0.883130\pi$
$548$	0.315342	+	0.378206i	0.0134707	+	0.0161562i
$549$		−	4.79741i		−	0.204749i
$550$	3.43845	−	7.34376i	0.146616	−	0.313139i
$551$	−14.2462			−0.606909
$552$	−2.56155	+	0.673500i	−0.109027	+	0.0286661i
$553$	5.12311	−	3.74571i	0.217857	−	0.159284i
$554$	6.56155	+	3.07221i	0.278774	+	0.130526i
$555$			3.74571i			0.158996i
$556$	−15.3693	−	18.4332i	−0.651804	−	0.781743i
$557$	14.0000			0.593199			0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000			0.593199			0.296600	+	0.955002i	$0.404147\pi$
$558$		0			0
$559$	−16.9848			−0.718382
$560$	−15.3693	−	31.7738i	−0.649472	−	1.34269i
$561$	−4.87689			−0.205903
$562$	−20.8078	−	9.74247i	−0.877723	−	0.410961i
$563$	2.24621			0.0946665			0.0473333	−	0.998879i	$-0.484928\pi$
$563$	2.24621			0.0946665			0.0473333	+	0.998879i	$0.484928\pi$
$564$	−8.00000	−	9.59482i	−0.336861	−	0.404015i
$565$			14.1617i			0.595786i
$566$	−11.3693	−	5.32326i	−0.477888	−	0.223753i
$567$	−1.56155	−	2.13578i	−0.0655791	−	0.0896943i
$568$	10.5616	−	2.77691i	0.443153	−	0.116517i
$569$	−30.9848			−1.29895			−0.649476	−	0.760382i	$-0.725012\pi$
$569$	−30.9848			−1.29895			−0.649476	+	0.760382i	$0.725012\pi$
$570$	14.2462	−	30.4268i	0.596708	−	1.27444i
$571$			8.83841i			0.369876i	0.982750	+	0.184938i	$0.0592084\pi$
$571$			8.83841i			0.369876i	−0.982750	+	0.184938i	$0.940792\pi$
$572$	−2.24621	−	2.69400i	−0.0939188	−	0.112642i
$573$			2.80928i			0.117359i
$574$	−5.36932	+	1.05171i	−0.224111	+	0.0438973i
$575$		−	5.73384i		−	0.239118i
$576$	−6.96543	+	3.93481i	−0.290226	+	0.163950i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	12.9654	+	6.07059i	0.539291	+	0.252503i
$579$	15.3693			0.638727
$580$	−10.2462	+	8.54312i	−0.425451	+	0.354734i
$581$	16.0000	+	21.8836i	0.663792	+	0.907887i
$582$	−6.24621	+	13.3405i	−0.258914	+	0.552983i
$583$		−	11.4677i		−	0.474943i
$584$	−18.2462	+	4.79741i	−0.755034	+	0.198518i
$585$	−6.24621			−0.258249
$586$	−8.24621	+	17.6121i	−0.340648	+	0.727549i
$587$	−21.7538			−0.897875			−0.448937	−	0.893563i	$-0.648197\pi$
$587$	−21.7538			−0.897875			−0.448937	+	0.893563i	$0.648197\pi$
$588$	12.9654	−	5.28181i	0.534686	−	0.217818i
$589$		0			0
$590$	−8.00000	+	17.0862i	−0.329355	+	0.703429i
$591$	16.2462			0.668280
$592$	−0.807764	+	4.41921i	−0.0331989	+	0.181628i
$593$			26.0399i			1.06933i	0.845064	+	0.534666i	$0.179562\pi$
$593$			26.0399i			1.06933i	−0.845064	+	0.534666i	$0.820438\pi$
$594$	0.561553	−	1.19935i	0.0230408	−	0.0492100i
$595$	−27.1231	−	37.0970i	−1.11194	−	1.52083i
$596$	−12.8078	−	15.3610i	−0.524626	−	0.629212i
$597$	3.12311			0.127820
$598$	−2.24621	−	1.05171i	−0.0918544	−	0.0430074i
$599$			17.2015i			0.702835i	0.936219	+	0.351417i	$0.114300\pi$
$599$			17.2015i			0.702835i	−0.936219	+	0.351417i	$0.885700\pi$
$600$	−4.40388	−	16.7495i	−0.179788	−	0.683795i
$601$			17.0862i			0.696962i	0.937316	+	0.348481i	$0.113302\pi$
$601$			17.0862i			0.696962i	−0.937316	+	0.348481i	$0.886698\pi$
$602$	33.3002	−	6.52262i	1.35721	−	0.265842i
$603$			10.9418i			0.445585i
$604$	−13.9309	+	11.6153i	−0.566839	+	0.472621i
$605$		−	33.7619i		−	1.37262i
$606$	8.24621	−	17.6121i	0.334979	−	0.715442i
$607$	7.61553			0.309105			0.154552	−	0.987985i	$-0.450606\pi$
$607$	7.61553			0.309105			0.154552	+	0.987985i	$0.450606\pi$
$608$	23.3693	−	32.8255i	0.947751	−	1.33125i
$609$	−3.12311	−	4.27156i	−0.126555	−	0.173092i
$610$	20.4924	+	9.59482i	0.829714	+	0.388483i
$611$		−	11.6982i		−	0.473260i
$612$	−8.00000	+	6.67026i	−0.323381	+	0.269629i
$613$	8.73863			0.352950			0.176475	−	0.984305i	$-0.443531\pi$
$613$	8.73863			0.352950			0.176475	+	0.984305i	$0.443531\pi$
$614$	−25.1231	−	11.7630i	−1.01389	−	0.474715i
$615$	−4.87689			−0.196655
$616$	5.43845	+	4.41921i	0.219121	+	0.178055i
$617$	32.2462			1.29818			0.649092	−	0.760710i	$-0.275149\pi$
$617$	32.2462			1.29818			0.649092	+	0.760710i	$0.275149\pi$
$618$	−10.2462	−	4.79741i	−0.412163	−	0.192980i
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$		0			0
$621$		−	0.936426i		−	0.0375775i
$622$	−10.2462	−	4.79741i	−0.410836	−	0.192359i
$623$	−3.12311	+	2.28343i	−0.125125	+	0.0914835i
$624$	−7.36932	−	1.34700i	−0.295009	−	0.0539232i
$625$	−18.1231			−0.724924
$626$	13.7538	−	29.3751i	0.549712	−	1.17406i
$627$			6.67026i			0.266385i
$628$	−33.6155	+	28.0281i	−1.34141	+	1.11844i
$629$			5.84912i			0.233220i
$630$	12.2462	−	2.39871i	0.487901	−	0.0955667i
$631$			40.3169i			1.60499i	0.596659	+	0.802495i	$0.296494\pi$
$631$			40.3169i			1.60499i	−0.596659	+	0.802495i	$0.703506\pi$
$632$	6.56155	−	1.72521i	0.261005	−	0.0686250i
$633$			12.8147i			0.509338i
$634$	18.5616	+	8.69076i	0.737173	+	0.345154i
$635$	32.9848			1.30896
$636$	−15.6847	−	18.8114i	−0.621937	−	0.745922i
$637$	12.4924	+	3.97626i	0.494968	+	0.157545i
$638$	1.12311	−	2.39871i	0.0444642	−	0.0949657i
$639$			3.86098i			0.152738i
$640$	−2.87689	−	37.6229i	−0.113719	−	1.48717i
$641$	−42.4924			−1.67835			−0.839175	−	0.543862i	$-0.816962\pi$
$641$	−42.4924			−1.67835			−0.839175	+	0.543862i	$0.816962\pi$
$642$	−5.68466	+	12.1412i	−0.224356	+	0.479174i
$643$	−11.6155			−0.458072			−0.229036	−	0.973418i	$-0.573557\pi$
$643$	−11.6155			−0.458072			−0.229036	+	0.973418i	$0.573557\pi$
$644$	4.80776	+	1.19935i	0.189452	+	0.0472611i
$645$	30.2462			1.19094
$646$	22.2462	−	47.5130i	0.875265	−	1.86937i
$647$	−32.9848			−1.29677			−0.648384	−	0.761313i	$-0.724555\pi$
$647$	−32.9848			−1.29677			−0.648384	+	0.761313i	$0.724555\pi$
$648$	−0.719224	−	2.73546i	−0.0282538	−	0.107459i
$649$		−	3.74571i		−	0.147032i
$650$	6.87689	−	14.6875i	0.269734	−	0.576092i
$651$		0			0
$652$	24.1771	−	20.1584i	0.946848	−	0.789465i
$653$	16.7386			0.655033			0.327517	−	0.944845i	$-0.393788\pi$
$653$	16.7386			0.655033			0.327517	+	0.944845i	$0.393788\pi$
$654$	−10.5616	−	4.94506i	−0.412989	−	0.193367i
$655$		−	19.1896i		−	0.749801i
$656$	−5.75379	−	1.05171i	−0.224648	−	0.0410622i
$657$		−	6.67026i		−	0.260232i
$658$	4.49242	+	22.9354i	0.175133	+	0.894113i
$659$		−	26.7963i		−	1.04384i	−0.852995	−	0.521919i	$-0.825217\pi$
$659$		−	26.7963i		−	1.04384i	0.852995	−	0.521919i	$-0.174783\pi$
$660$	4.00000	+	4.79741i	0.155700	+	0.186739i
$661$		−	8.54312i		−	0.332289i	−0.986101	−	0.166144i	$-0.946868\pi$
$661$		−	8.54312i		−	0.332289i	0.986101	−	0.166144i	$-0.0531318\pi$
$662$	10.5616	−	22.5571i	0.410486	−	0.876708i
$663$	−9.75379			−0.378806
$664$	7.36932	+	28.0281i	0.285985	+	1.08770i
$665$	−50.7386	+	37.0970i	−1.96756	+	1.43856i
$666$	−1.43845	−	0.673500i	−0.0557387	−	0.0260976i
$667$		−	1.87285i		−	0.0725171i
$668$	18.2462	+	21.8836i	0.705967	+	0.846704i
$669$	−27.1231			−1.04864
$670$	−46.7386	−	21.8836i	−1.80567	−	0.845439i
$671$	−4.49242			−0.173428
$672$	14.9654	−	0.189103i	0.577304	−	0.00729480i
$673$	−27.8617			−1.07399			−0.536996	−	0.843585i	$-0.680441\pi$
$673$	−27.8617			−1.07399			−0.536996	+	0.843585i	$0.680441\pi$
$674$	−10.5616	−	4.94506i	−0.406816	−	0.190477i
$675$	6.12311			0.235678
$676$	12.1577	+	14.5813i	0.467603	+	0.560821i
$677$		−	9.18425i		−	0.352979i	−0.984302	−	0.176490i	$-0.943526\pi$
$677$		−	9.18425i		−	0.352979i	0.984302	−	0.176490i	$-0.0564742\pi$
$678$	−5.43845	−	2.54635i	−0.208862	−	0.0977921i
$679$	22.2462	−	16.2651i	0.853731	−	0.624197i
$680$	−12.4924	−	47.5130i	−0.479063	−	1.82204i
$681$	16.4924			0.631991
$682$		0			0
$683$		−	32.1843i		−	1.23150i	−0.787942	−	0.615750i	$-0.788853\pi$
$683$		−	32.1843i		−	1.23150i	0.787942	−	0.615750i	$-0.211147\pi$
$684$	9.12311	+	10.9418i	0.348831	+	0.418371i
$685$		−	0.821147i		−	0.0313744i
$686$	−26.0194	−	2.99838i	−0.993426	−	0.114479i
$687$			5.61856i			0.214361i
$688$	35.6847	+	6.52262i	1.36046	+	0.248672i
$689$		−	22.9354i		−	0.873767i
$690$	4.00000	+	1.87285i	0.152277	+	0.0712983i
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	−25.6155	+	21.3578i	−0.973756	+	0.811901i
$693$	−2.00000	+	1.46228i	−0.0759737	+	0.0555474i
$694$	−12.0691	+	25.7770i	−0.458138	+	0.978481i
$695$			40.0216i			1.51811i
$696$	−1.43845	−	5.47091i	−0.0545242	−	0.207374i
$697$	−7.61553			−0.288459
$698$	13.1231	−	28.0281i	0.496717	−	1.06088i
$699$	−22.4924			−0.850742
$700$	−7.84233	+	31.4370i	−0.296412	+	1.18821i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	1.12311	−	2.39871i	0.0423889	−	0.0905333i
$703$	8.00000			0.301726
$704$	3.68466	+	6.52262i	0.138871	+	0.245830i
$705$			20.8319i			0.784576i
$706$	17.3693	−	37.0970i	0.653703	−	1.39616i
$707$	−29.3693	+	21.4731i	−1.10455	+	0.807578i
$708$	−5.12311	−	6.14441i	−0.192538	−	0.230921i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	−16.4924	−	7.72197i	−0.618950	−	0.289800i
$711$			2.39871i			0.0899585i
$712$	−4.00000	+	1.05171i	−0.149906	+	0.0394143i
$713$		0			0
$714$	19.1231	−	3.74571i	0.715664	−	0.140180i
$715$			5.84912i			0.218745i
$716$	−24.8078	+	20.6843i	−0.927110	+	0.773008i
$717$			16.1498i			0.603126i
$718$	−13.6847	+	29.2274i	−0.510707	+	1.09076i
$719$	28.4924			1.06259			0.531294	−	0.847187i	$-0.321706\pi$
$719$	28.4924			1.06259			0.531294	+	0.847187i	$0.321706\pi$
$720$	13.1231	+	2.39871i	0.489069	+	0.0893945i
$721$	12.4924	+	17.0862i	0.465242	+	0.636325i
$722$	−40.6501	−	19.0329i	−1.51284	−	0.708332i
$723$			23.7565i			0.883514i
$724$	−2.87689	+	2.39871i	−0.106919	+	0.0891472i
$725$	12.2462			0.454813
$726$	12.9654	+	6.07059i	0.481192	+	0.225301i
$727$	32.9848			1.22334			0.611670	−	0.791113i	$-0.290498\pi$
$727$	32.9848			1.22334			0.611670	+	0.791113i	$0.290498\pi$
$728$	10.8769	+	8.83841i	0.403125	+	0.327573i
$729$	1.00000			0.0370370
$730$	28.4924	+	13.3405i	1.05455	+	0.493755i
$731$	47.2311			1.74690
$732$	−7.36932	+	6.14441i	−0.272378	+	0.227104i
$733$		−	36.0453i		−	1.33136i	−0.746235	−	0.665682i	$-0.768141\pi$
$733$		−	36.0453i		−	1.33136i	0.746235	−	0.665682i	$-0.231859\pi$
$734$	42.7386	+	20.0108i	1.57751	+	0.738612i
$735$	−22.2462	−	7.08084i	−0.820564	−	0.261181i
$736$	4.31534	+	3.07221i	0.159066	+	0.113243i
$737$	10.2462			0.377424
$738$	0.876894	−	1.87285i	0.0322789	−	0.0689407i
$739$		−	36.5712i		−	1.34529i	−0.739964	−	0.672646i	$-0.765158\pi$
$739$		−	36.5712i		−	1.34529i	0.739964	−	0.672646i	$-0.234842\pi$
$740$	5.75379	−	4.79741i	0.211513	−	0.176356i
$741$			13.3405i			0.490077i
$742$	8.80776	+	44.9666i	0.323343	+	1.65078i
$743$			35.1089i			1.28802i	0.765017	+	0.644010i	$0.222731\pi$
$743$			35.1089i			1.28802i	−0.765017	+	0.644010i	$0.777269\pi$
$744$		0			0
$745$			33.3513i			1.22190i
$746$	12.8078	+	5.99676i	0.468926	+	0.219557i
$747$	−10.2462			−0.374889
$748$	6.24621	+	7.49141i	0.228384	+	0.273913i
$749$	20.2462	−	14.8028i	0.739780	−	0.540883i
$750$	−2.24621	+	4.79741i	−0.0820200	+	0.175177i
$751$		−	28.8492i		−	1.05272i	−0.850261	−	0.526361i	$-0.823556\pi$
$751$		−	28.8492i		−	1.05272i	0.850261	−	0.526361i	$-0.176444\pi$
$752$	−4.49242	+	24.5776i	−0.163822	+	0.896254i
$753$	5.75379			0.209680
$754$	2.24621	−	4.79741i	0.0818022	−	0.174711i
$755$	30.2462			1.10077
$756$	−1.28078	+	5.13416i	−0.0465814	+	0.186728i
$757$	−34.9848			−1.27155			−0.635773	−	0.771876i	$-0.719319\pi$
$757$	−34.9848			−1.27155			−0.635773	+	0.771876i	$0.719319\pi$
$758$	15.0540	−	32.1520i	0.546785	−	1.16781i
$759$	−0.876894			−0.0318292
$760$	−64.9848	+	17.0862i	−2.35725	+	0.619783i
$761$			29.7856i			1.07973i	0.841752	+	0.539864i	$0.181524\pi$
$761$			29.7856i			1.07973i	−0.841752	+	0.539864i	$0.818476\pi$
$762$	−5.93087	+	12.6670i	−0.214853	+	0.458878i
$763$	12.8769	+	17.6121i	0.466175	+	0.637600i
$764$	4.31534	−	3.59806i	0.156124	−	0.130173i
$765$	17.3693			0.627989
$766$	12.4924	+	5.84912i	0.451370	+	0.211337i
$767$		−	7.49141i		−	0.270499i
$768$	14.9654	+	5.66001i	0.540019	+	0.204238i
$769$			32.5302i			1.17307i	0.809925	+	0.586534i	$0.199508\pi$
$769$			32.5302i			1.17307i	−0.809925	+	0.586534i	$0.800492\pi$
$770$	−2.24621	−	11.4677i	−0.0809478	−	0.413266i
$771$			2.28343i			0.0822356i
$772$	−19.6847	−	23.6089i	−0.708466	−	0.849701i
$773$		−	3.33513i		−	0.119956i	−0.998200	−	0.0599782i	$-0.980897\pi$
$773$		−	3.33513i		−	0.119956i	0.998200	−	0.0599782i	$-0.0191031\pi$
$774$	−5.43845	+	11.6153i	−0.195481	+	0.417504i
$775$		0			0
$776$	28.4924	−	7.49141i	1.02282	−	0.268926i
$777$	1.75379	+	2.39871i	0.0629168	+	0.0860531i
$778$	20.8078	+	9.74247i	0.745994	+	0.349284i
$779$			10.4160i			0.373191i
$780$	8.00000	+	9.59482i	0.286446	+	0.343550i
$781$	3.61553			0.129374
$782$	6.24621	+	2.92456i	0.223364	+	0.104582i
$783$	2.00000			0.0714742
$784$	−24.7192	−	13.1514i	−0.882829	−	0.469694i
$785$	72.9848			2.60494
$786$	7.36932	+	3.45041i	0.262855	+	0.123072i
$787$	−44.9848			−1.60354			−0.801768	−	0.597635i	$-0.796107\pi$
$787$	−44.9848			−1.60354			−0.801768	+	0.597635i	$0.796107\pi$
$788$	−20.8078	−	24.9559i	−0.741246	−	0.889015i
$789$		−	24.6929i		−	0.879091i
$790$	−10.2462	−	4.79741i	−0.364544	−	0.170684i
$791$	6.63068	+	9.06897i	0.235760	+	0.322455i
$792$	−2.56155	+	0.673500i	−0.0910208	+	0.0239318i
$793$	−8.98485			−0.319061
$794$	−10.8769	+	23.2306i	−0.386007	+	0.824425i
$795$			40.8427i			1.44854i
$796$	−4.00000	−	4.79741i	−0.141776	−	0.170040i
$797$		−	39.6110i		−	1.40309i	−0.712623	−	0.701547i	$-0.752493\pi$
$797$		−	39.6110i		−	1.40309i	0.712623	−	0.701547i	$-0.247507\pi$
$798$	−5.12311	−	26.1552i	−0.181356	−	0.925884i
$799$			32.5302i			1.15083i
$800$	−20.0885	+	28.2172i	−0.710237	+	0.997627i
$801$		−	1.46228i		−	0.0516671i
$802$	−10.5616	−	4.94506i	−0.372941	−	0.174616i
$803$	−6.24621			−0.220424
$804$	16.8078	−	14.0140i	0.592764	−	0.494237i
$805$	−4.87689	−	6.67026i	−0.171888	−	0.235096i
$806$		0			0
$807$		−	10.8265i		−	0.381112i
$808$	−37.6155	+	9.89012i	−1.32331	+	0.347933i
$809$	22.4924			0.790791			0.395396	−	0.918511i	$-0.370607\pi$
$809$	22.4924			0.790791			0.395396	+	0.918511i	$0.370607\pi$
$810$	−2.00000	+	4.27156i	−0.0702728	+	0.150087i
$811$	0.492423			0.0172913			0.00864565	−	0.999963i	$-0.497248\pi$
$811$	0.492423			0.0172913			0.00864565	+	0.999963i	$0.497248\pi$
$812$	−2.56155	+	10.2683i	−0.0898929	+	0.360347i
$813$	28.4924			0.999273
$814$	−0.630683	+	1.34700i	−0.0221054	+	0.0472123i
$815$	−52.4924			−1.83873
$816$	20.4924	+	3.74571i	0.717378	+	0.131126i
$817$		−	64.5992i		−	2.26004i
$818$	0.492423	−	1.05171i	0.0172171	−	0.0367720i
$819$	−4.00000	+	2.92456i	−0.139771	+	0.102192i
$820$	6.24621	+	7.49141i	0.218127	+	0.261611i
$821$	−57.2311			−1.99738			−0.998689	−	0.0511922i	$-0.983698\pi$
$821$	−57.2311			−1.99738			−0.998689	+	0.0511922i	$0.983698\pi$
$822$	0.315342	+	0.147647i	0.0109988	+	0.00514978i
$823$		−	13.0452i		−	0.454728i	−0.973810	−	0.227364i	$-0.926989\pi$
$823$		−	13.0452i		−	0.454728i	0.973810	−	0.227364i	$-0.0730108\pi$
$824$	5.75379	+	21.8836i	0.200443	+	0.762353i
$825$		−	5.73384i		−	0.199627i
$826$	2.87689	+	14.6875i	0.100100	+	0.511044i
$827$		−	55.9408i		−	1.94525i	−0.232373	−	0.972627i	$-0.574649\pi$
$827$		−	55.9408i		−	1.94525i	0.232373	−	0.972627i	$-0.425351\pi$
$828$	−1.43845	+	1.19935i	−0.0499895	+	0.0416804i
$829$		−	21.0625i		−	0.731531i	−0.930707	−	0.365765i	$-0.880807\pi$
$829$		−	21.0625i		−	0.731531i	0.930707	−	0.365765i	$-0.119193\pi$
$830$	20.4924	−	43.7673i	0.711302	−	1.51918i
$831$	5.12311			0.177719
$832$	7.36932	+	13.0452i	0.255485	+	0.452262i
$833$	−34.7386	−	11.0571i	−1.20362	−	0.383106i
$834$	−15.3693	−	7.19612i	−0.532196	−	0.249181i
$835$		−	47.5130i		−	1.64426i
$836$	10.2462	−	8.54312i	0.354373	−	0.295470i
$837$		0			0
$838$	21.1231	+	9.89012i	0.729686	+	0.341648i
$839$	−42.7386			−1.47550			−0.737751	−	0.675073i	$-0.764112\pi$
$839$	−42.7386			−1.47550			−0.737751	+	0.675073i	$0.764112\pi$
$840$	−19.3693	−	15.7392i	−0.668305	−	0.543055i
$841$	−25.0000			−0.862069
$842$	−13.9309	−	6.52262i	−0.480089	−	0.224784i
$843$	−16.2462			−0.559549
$844$	19.6847	−	16.4127i	0.677574	−	0.564950i
$845$		−	31.6585i		−	1.08908i
$846$	−8.00000	−	3.74571i	−0.275046	−	0.128780i
$847$	−15.8078	−	21.6207i	−0.543161	−	0.742897i
$848$	−8.80776	+	48.1865i	−0.302460	+	1.65473i
$849$	−8.87689			−0.304654
$850$	−19.1231	+	40.8427i	−0.655917	+	1.40089i
$851$			1.05171i			0.0360520i
$852$	5.93087	−	4.94506i	0.203188	−	0.169415i
$853$		−	50.2070i		−	1.71905i	−0.511090	−	0.859527i	$-0.670758\pi$
$853$		−	50.2070i		−	1.71905i	0.511090	−	0.859527i	$-0.329242\pi$
$854$	17.6155	−	3.45041i	0.602791	−	0.118071i
$855$		−	23.7565i		−	0.812455i
$856$	25.9309	−	6.81791i	0.886299	−	0.233031i
$857$			56.4667i			1.92887i	0.264329	+	0.964433i	$0.414850\pi$
$857$			56.4667i			1.92887i	−0.264329	+	0.964433i	$0.585150\pi$
$858$	−2.24621	−	1.05171i	−0.0766844	−	0.0359046i
$859$	−25.8617			−0.882391			−0.441196	−	0.897411i	$-0.645445\pi$
$859$	−25.8617			−0.882391			−0.441196	+	0.897411i	$0.645445\pi$
$860$	−38.7386	−	46.4613i	−1.32098	−	1.58432i
$861$	−3.12311	+	2.28343i	−0.106435	+	0.0778190i
$862$	2.80776	−	5.99676i	0.0956328	−	0.204251i
$863$		−	8.65840i		−	0.294735i	−0.989082	−	0.147368i	$-0.952920\pi$
$863$		−	8.65840i		−	0.294735i	0.989082	−	0.147368i	$-0.0470800\pi$
$864$	−3.28078	+	4.60831i	−0.111614	+	0.156778i
$865$	55.6155			1.89098
$866$	8.00000	−	17.0862i	0.271851	−	0.580614i
$867$	10.1231			0.343799
$868$		0			0
$869$	2.24621			0.0761975
$870$	−4.00000	+	8.54312i	−0.135613	+	0.289639i
$871$	20.4924			0.694359
$872$	5.93087	+	22.5571i	0.200845	+	0.763881i
$873$			10.4160i			0.352527i
$874$	4.00000	−	8.54312i	0.135302	−	0.288975i
$875$	8.00000	−	5.84912i	0.270449	−	0.197736i
$876$	−10.2462	+	8.54312i	−0.346187	+	0.288645i
$877$	36.2462			1.22395			0.611974	−	0.790878i	$-0.290376\pi$
$877$	36.2462			1.22395			0.611974	+	0.790878i	$0.290376\pi$
$878$	8.49242	+	3.97626i	0.286605	+	0.134192i
$879$			13.7511i			0.463813i
$880$	2.24621	−	12.2888i	0.0757198	−	0.414256i
$881$		−	46.8719i		−	1.57915i	−0.613652	−	0.789577i	$-0.710300\pi$
$881$		−	46.8719i		−	1.57915i	0.613652	−	0.789577i	$-0.289700\pi$
$882$	6.71922	−	7.26994i	0.226248	−	0.244792i
$883$		−	18.6638i		−	0.628087i	−0.949409	−	0.314043i	$-0.898316\pi$
$883$		−	18.6638i		−	0.628087i	0.949409	−	0.314043i	$-0.101684\pi$
$884$	12.4924	+	14.9828i	0.420166	+	0.503927i
$885$			13.3405i			0.448437i
$886$	−11.3002	+	24.1347i	−0.379637	+	0.810821i
$887$	−26.7386			−0.897795			−0.448898	−	0.893583i	$-0.648183\pi$
$887$	−26.7386			−0.897795			−0.448898	+	0.893583i	$0.648183\pi$
$888$	0.807764	+	3.07221i	0.0271068	+	0.103096i
$889$	21.1231	−	15.4439i	0.708446	−	0.517973i
$890$	6.24621	+	2.92456i	0.209373	+	0.0980314i
$891$		−	0.936426i		−	0.0313715i
$892$	34.7386	+	41.6639i	1.16314	+	1.39501i
$893$	44.4924			1.48888
$894$	−12.8078	−	5.99676i	−0.428356	−	0.200562i
$895$	53.8617			1.80040
$896$	−19.4579	−	22.7462i	−0.650041	−	0.759899i
$897$	−1.75379			−0.0585573
$898$	−15.0540	−	7.04847i	−0.502358	−	0.235210i
$899$		0			0
$900$	−7.84233	−	9.40572i	−0.261411	−	0.313524i
$901$			63.7781i			2.12476i
$902$	−1.75379	−	0.821147i	−0.0583948	−	0.0273412i
$903$	19.3693	−	14.1617i	0.644571	−	0.471271i
$904$	3.05398	+	11.6153i	0.101574	+	0.386320i
$905$	6.24621			0.207631
$906$	−5.43845	+	11.6153i	−0.180680	+	0.385893i
$907$			38.4440i			1.27651i	0.769824	+	0.638256i	$0.220344\pi$
$907$			38.4440i			1.27651i	−0.769824	+	0.638256i	$0.779656\pi$
$908$	−21.1231	−	25.3341i	−0.700995	−	0.840740i
$909$		−	13.7511i		−	0.456095i
$910$	−4.49242	−	22.9354i	−0.148922	−	0.760299i
$911$		−	5.73384i		−	0.189971i	−0.995479	−	0.0949853i	$-0.969720\pi$
$911$		−	5.73384i		−	0.189971i	0.995479	−	0.0949853i	$-0.0302804\pi$
$912$	5.12311	−	28.0281i	0.169643	−	0.928102i
$913$			9.59482i			0.317542i
$914$	−0.315342	−	0.147647i	−0.0104306	−	0.00488373i
$915$	16.0000			0.528944
$916$	8.63068	−	7.19612i	0.285166	−	0.237766i
$917$	−8.98485	−	12.2888i	−0.296706	−	0.405813i
$918$	−3.12311	+	6.67026i	−0.103078	+	0.220152i
$919$			9.06897i			0.299158i	0.988750	+	0.149579i	$0.0477918\pi$
$919$			9.06897i			0.299158i	−0.988750	+	0.149579i	$0.952208\pi$
$920$	−2.24621	−	8.54312i	−0.0740554	−	0.281658i
$921$	−19.6155			−0.646354
$922$	3.75379	−	8.01726i	0.123624	−	0.264035i
$923$	7.23106			0.238013
$924$	4.80776	+	1.19935i	0.158164	+	0.0394558i
$925$	−6.87689			−0.226111
$926$	−23.5464	+	50.2899i	−0.773783	+	1.65263i
$927$	−8.00000			−0.262754
$928$	−6.56155	+	9.21662i	−0.215394	+	0.302550i
$929$			3.56569i			0.116987i	0.998288	+	0.0584933i	$0.0186296\pi$
$929$			3.56569i			0.116987i	−0.998288	+	0.0584933i	$0.981370\pi$
$930$		0			0
$931$	−15.1231	+	47.5130i	−0.495640	+	1.55718i
$932$	28.8078	+	34.5507i	0.943630	+	1.13174i
$933$	−8.00000			−0.261908
$934$	−43.8617	−	20.5366i	−1.43520	−	0.671980i
$935$		−	16.2651i		−	0.531925i
$936$	−5.12311	+	1.34700i	−0.167454	+	0.0440281i
$937$		−	28.7845i		−	0.940348i	−0.882574	−	0.470174i	$-0.844191\pi$
$937$		−	28.7845i		−	0.940348i	0.882574	−	0.470174i	$-0.155809\pi$
$938$	−40.1771	+	7.86962i	−1.31183	+	0.256952i
$939$		−	22.9354i		−	0.748467i
$940$	32.0000	−	26.6811i	1.04372	−	0.870240i
$941$			53.7727i			1.75294i	0.481457	+	0.876470i	$0.340108\pi$
$941$			53.7727i			1.75294i	−0.481457	+	0.876470i	$0.659892\pi$
$942$	−13.1231	+	28.0281i	−0.427574	+	0.913203i
$943$	−1.36932			−0.0445911
$944$	−2.87689	+	15.7392i	−0.0936349	+	0.512268i
$945$	7.12311	−	5.20798i	0.231715	−	0.169416i
$946$	10.8769	+	5.09271i	0.353638	+	0.165578i
$947$			48.6800i			1.58189i	0.611889	+	0.790943i	$0.290410\pi$
$947$			48.6800i			1.58189i	−0.611889	+	0.790943i	$0.709590\pi$
$948$	3.68466	−	3.07221i	0.119672	−	0.0997806i
$949$	−12.4924			−0.405521
$950$	55.8617	+	26.1552i	1.81239	+	0.848587i
$951$	14.4924			0.469949
$952$	−30.2462	−	24.5776i	−0.980285	−	0.796566i
$953$	−21.2311			−0.687741			−0.343871	−	0.939017i	$-0.611738\pi$
$953$	−21.2311			−0.687741			−0.343871	+	0.939017i	$0.611738\pi$
$954$	−15.6847	−	7.34376i	−0.507810	−	0.237763i
$955$	−9.36932			−0.303184
$956$	24.8078	−	20.6843i	0.802340	−	0.668978i
$957$		−	1.87285i		−	0.0605407i
$958$	−16.0000	−	7.49141i	−0.516937	−	0.242037i
$959$	−0.384472	−	0.525853i	−0.0124152	−	0.0169807i
$960$	−13.1231	−	23.2306i	−0.423546	−	0.749766i
$961$	−31.0000			−1.00000
$962$	−1.26137	+	2.69400i	−0.0406681	+	0.0868580i
$963$			9.47954i			0.305474i
$964$	36.4924	−	30.4268i	1.17534	−	0.979980i
$965$			51.2587i			1.65008i
$966$	3.43845	−	0.673500i	0.110630	−	0.0216695i
$967$		−	8.83841i		−	0.284224i	−0.989851	−	0.142112i	$-0.954611\pi$
$967$		−	8.83841i		−	0.284224i	0.989851	−	0.142112i	$-0.0453893\pi$
$968$	−7.28078	−	27.6913i	−0.234013	−	0.890032i
$969$		−	37.0970i		−	1.19173i
$970$	−44.4924	−	20.8319i	−1.42857	−	0.668873i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	−1.28078	−	1.53610i	−0.0410809	−	0.0492705i
$973$	18.7386	+	25.6294i	0.600733	+	0.821639i
$974$	0.946025	−	2.02050i	0.0303126	−	0.0647410i
$975$		−	11.4677i		−	0.367260i
$976$	18.8769	+	3.45041i	0.604235	+	0.110445i
$977$	−11.2614			−0.360283			−0.180142	−	0.983641i	$-0.557656\pi$
$977$	−11.2614			−0.360283			−0.180142	+	0.983641i	$0.557656\pi$
$978$	9.43845	−	20.1584i	0.301808	−	0.644596i
$979$	−1.36932			−0.0437636
$980$	17.6155	+	43.2414i	0.562707	+	1.38130i
$981$	−8.24621			−0.263281
$982$	−6.80776	+	14.5399i	−0.217244	+	0.463986i
$983$	5.26137			0.167812			0.0839058	−	0.996474i	$-0.473261\pi$
$983$	5.26137			0.167812			0.0839058	+	0.996474i	$0.473261\pi$
$984$	−4.00000	+	1.05171i	−0.127515	+	0.0335272i
$985$			54.1833i			1.72642i
$986$	−6.24621	+	13.3405i	−0.198920	+	0.424849i
$987$	9.75379	+	13.3405i	0.310467	+	0.424634i
$988$	20.4924	−	17.0862i	0.651951	−	0.543586i
$989$	8.49242			0.270043
$990$	4.00000	+	1.87285i	0.127128	+	0.0595232i
$991$		−	0.525853i		−	0.0167043i	−0.999965	−	0.00835213i	$-0.997341\pi$
$991$		−	0.525853i		−	0.0167043i	0.999965	−	0.00835213i	$-0.00265860\pi$
$992$		0			0
$993$		−	17.6121i		−	0.558903i
$994$	−14.1771	+	2.77691i	−0.449670	+	0.0880783i
$995$			10.4160i			0.330208i
$996$	13.1231	+	15.7392i	0.415822	+	0.498717i
$997$			19.7802i			0.626446i	0.949680	+	0.313223i	$0.101409\pi$
$997$			19.7802i			0.626446i	−0.949680	+	0.313223i	$0.898591\pi$
$998$	8.31534	−	17.7597i	0.263218	−	0.562175i
$999$	−1.12311			−0.0355335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.b.a.55.1	✓	4
3.2	odd	2		252.2.b.e.55.4		4
4.3	odd	2		84.2.b.b.55.2	yes	4
7.2	even	3		588.2.o.c.31.2		8
7.3	odd	6		588.2.o.a.19.4		8
7.4	even	3		588.2.o.c.19.4		8
7.5	odd	6		588.2.o.a.31.2		8
7.6	odd	2		84.2.b.b.55.1	yes	4
8.3	odd	2		1344.2.b.e.895.4		4
8.5	even	2		1344.2.b.f.895.4		4
12.11	even	2		252.2.b.d.55.3		4
21.20	even	2		252.2.b.d.55.4		4
24.5	odd	2		4032.2.b.n.3583.1		4
24.11	even	2		4032.2.b.j.3583.1		4
28.3	even	6		588.2.o.c.19.2		8
28.11	odd	6		588.2.o.a.19.2		8
28.19	even	6		588.2.o.c.31.4		8
28.23	odd	6		588.2.o.a.31.4		8
28.27	even	2	inner	84.2.b.a.55.2	yes	4
56.13	odd	2		1344.2.b.e.895.1		4
56.27	even	2		1344.2.b.f.895.1		4
84.83	odd	2		252.2.b.e.55.3		4
168.83	odd	2		4032.2.b.n.3583.4		4
168.125	even	2		4032.2.b.j.3583.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.1	✓	4	1.1	even	1	trivial
84.2.b.a.55.2	yes	4	28.27	even	2	inner
84.2.b.b.55.1	yes	4	7.6	odd	2
84.2.b.b.55.2	yes	4	4.3	odd	2
252.2.b.d.55.3		4	12.11	even	2
252.2.b.d.55.4		4	21.20	even	2
252.2.b.e.55.3		4	84.83	odd	2
252.2.b.e.55.4		4	3.2	odd	2
588.2.o.a.19.2		8	28.11	odd	6
588.2.o.a.19.4		8	7.3	odd	6
588.2.o.a.31.2		8	7.5	odd	6
588.2.o.a.31.4		8	28.23	odd	6
588.2.o.c.19.2		8	28.3	even	6
588.2.o.c.19.4		8	7.4	even	3
588.2.o.c.31.2		8	7.2	even	3
588.2.o.c.31.4		8	28.19	even	6
1344.2.b.e.895.1		4	56.13	odd	2
1344.2.b.e.895.4		4	8.3	odd	2
1344.2.b.f.895.1		4	56.27	even	2
1344.2.b.f.895.4		4	8.5	even	2
4032.2.b.j.3583.1		4	24.11	even	2
4032.2.b.j.3583.4		4	168.125	even	2
4032.2.b.n.3583.1		4	24.5	odd	2
4032.2.b.n.3583.4		4	168.83	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +(-2.00000 + 4.27156i) q^{10} -0.936426i q^{11} +(-1.28078 - 1.53610i) q^{12} -1.87285i q^{13} +(0.719224 + 3.67188i) q^{14} +3.33513i q^{15} +(-0.719224 + 3.93481i) q^{16} +5.20798i q^{17} +(-1.28078 - 0.599676i) q^{18} +7.12311 q^{19} +(5.12311 - 4.27156i) q^{20} +(1.56155 + 2.13578i) q^{21} +(-0.561553 + 1.19935i) q^{22} +0.936426i q^{23} +(0.719224 + 2.73546i) q^{24} -6.12311 q^{25} +(-1.12311 + 2.39871i) q^{26} -1.00000 q^{27} +(1.28078 - 5.13416i) q^{28} -2.00000 q^{29} +(2.00000 - 4.27156i) q^{30} +(3.28078 - 4.60831i) q^{32} +0.936426i q^{33} +(3.12311 - 6.67026i) q^{34} +(-7.12311 + 5.20798i) q^{35} +(1.28078 + 1.53610i) q^{36} +1.12311 q^{37} +(-9.12311 - 4.27156i) q^{38} +1.87285i q^{39} +(-9.12311 + 2.39871i) q^{40} +1.46228i q^{41} +(-0.719224 - 3.67188i) q^{42} -9.06897i q^{43} +(1.43845 - 1.19935i) q^{44} -3.33513i q^{45} +(0.561553 - 1.19935i) q^{46} +6.24621 q^{47} +(0.719224 - 3.93481i) q^{48} +(-2.12311 + 6.67026i) q^{49} +(7.84233 + 3.67188i) q^{50} -5.20798i q^{51} +(2.87689 - 2.39871i) q^{52} +12.2462 q^{53} +(1.28078 + 0.599676i) q^{54} -3.12311 q^{55} +(-4.71922 + 5.80766i) q^{56} -7.12311 q^{57} +(2.56155 + 1.19935i) q^{58} +4.00000 q^{59} +(-5.12311 + 4.27156i) q^{60} -4.79741i q^{61} +(-1.56155 - 2.13578i) q^{63} +(-6.96543 + 3.93481i) q^{64} -6.24621 q^{65} +(0.561553 - 1.19935i) q^{66} +10.9418i q^{67} +(-8.00000 + 6.67026i) q^{68} -0.936426i q^{69} +(12.2462 - 2.39871i) q^{70} +3.86098i q^{71} +(-0.719224 - 2.73546i) q^{72} -6.67026i q^{73} +(-1.43845 - 0.673500i) q^{74} +6.12311 q^{75} +(9.12311 + 10.9418i) q^{76} +(-2.00000 + 1.46228i) q^{77} +(1.12311 - 2.39871i) q^{78} +2.39871i q^{79} +(13.1231 + 2.39871i) q^{80} +1.00000 q^{81} +(0.876894 - 1.87285i) q^{82} -10.2462 q^{83} +(-1.28078 + 5.13416i) q^{84} +17.3693 q^{85} +(-5.43845 + 11.6153i) q^{86} +2.00000 q^{87} +(-2.56155 + 0.673500i) q^{88} -1.46228i q^{89} +(-2.00000 + 4.27156i) q^{90} +(-4.00000 + 2.92456i) q^{91} +(-1.43845 + 1.19935i) q^{92} +(-8.00000 - 3.74571i) q^{94} -23.7565i q^{95} +(-3.28078 + 4.60831i) q^{96} +10.4160i q^{97} +(6.71922 - 7.26994i) q^{98} -0.936426i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + q^4 + q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{14} - 7 q^{16} - q^{18} + 12 q^{19} + 4 q^{20} - 2 q^{21} + 6 q^{22} + 7 q^{24} - 8 q^{25} + 12 q^{26} - 4 q^{27} + q^{28} - 8 q^{29} + 8 q^{30} + 9 q^{32} - 4 q^{34} - 12 q^{35} + q^{36} - 12 q^{37} - 20 q^{38} - 20 q^{40} - 7 q^{42} + 14 q^{44} - 6 q^{46} - 8 q^{47} + 7 q^{48} + 8 q^{49} + 19 q^{50} + 28 q^{52} + 16 q^{53} + q^{54} + 4 q^{55} - 23 q^{56} - 12 q^{57} + 2 q^{58} + 16 q^{59} - 4 q^{60} + 2 q^{63} + q^{64} + 8 q^{65} - 6 q^{66} - 32 q^{68} + 16 q^{70} - 7 q^{72} - 14 q^{74} + 8 q^{75} + 20 q^{76} - 8 q^{77} - 12 q^{78} + 36 q^{80} + 4 q^{81} + 20 q^{82} - 8 q^{83} - q^{84} + 20 q^{85} - 30 q^{86} + 8 q^{87} - 2 q^{88} - 8 q^{90} - 16 q^{91} - 14 q^{92} - 32 q^{94} - 9 q^{96} + 31 q^{98}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + q^4 + q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 - 8 * q^10 - q^12 + 7 * q^14 - 7 * q^16 - q^18 + 12 * q^19 + 4 * q^20 - 2 * q^21 + 6 * q^22 + 7 * q^24 - 8 * q^25 + 12 * q^26 - 4 * q^27 + q^28 - 8 * q^29 + 8 * q^30 + 9 * q^32 - 4 * q^34 - 12 * q^35 + q^36 - 12 * q^37 - 20 * q^38 - 20 * q^40 - 7 * q^42 + 14 * q^44 - 6 * q^46 - 8 * q^47 + 7 * q^48 + 8 * q^49 + 19 * q^50 + 28 * q^52 + 16 * q^53 + q^54 + 4 * q^55 - 23 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^59 - 4 * q^60 + 2 * q^63 + q^64 + 8 * q^65 - 6 * q^66 - 32 * q^68 + 16 * q^70 - 7 * q^72 - 14 * q^74 + 8 * q^75 + 20 * q^76 - 8 * q^77 - 12 * q^78 + 36 * q^80 + 4 * q^81 + 20 * q^82 - 8 * q^83 - q^84 + 20 * q^85 - 30 * q^86 + 8 * q^87 - 2 * q^88 - 8 * q^90 - 16 * q^91 - 14 * q^92 - 32 * q^94 - 9 * q^96 + 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more