LMFDB - Embedded newform 76.2.d.a.75.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.d (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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14453810176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 6x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.6
Root			$0.331077 + 1.37491i$ of defining polynomial
Character	$\chi$	$=$	76.75
Dual form			76.2.d.a.75.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.331077 + 1.37491i) q^{2} +2.35829 q^{3} +(-1.78078 + 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 + 3.24245i) q^{6} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +O(q^{10})$	\(q+(0.331077 + 1.37491i) q^{2} +2.35829 q^{3} +(-1.78078 + 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 + 3.24245i) q^{6} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +(-0.848071 - 3.52191i) q^{10} +2.33205i q^{11} +(-4.19960 + 2.14700i) q^{12} +4.29400i q^{13} +(5.70982 - 1.37491i) q^{14} -6.04090 q^{15} +(2.34233 - 3.24245i) q^{16} -1.00000 q^{17} +(0.848071 + 3.52191i) q^{18} +(3.68260 - 2.33205i) q^{19} +(4.56155 - 2.33205i) q^{20} -9.79366i q^{21} +(-3.20636 + 0.772087i) q^{22} +1.82081i q^{23} +(-4.34233 - 5.06326i) q^{24} +1.56155 q^{25} +(-5.90388 + 1.42164i) q^{26} -1.03399 q^{27} +(3.78078 + 7.39531i) q^{28} +1.20565i q^{29} +(-2.00000 - 8.30571i) q^{30} -1.32431 q^{31} +(5.23358 + 2.14700i) q^{32} +5.49966i q^{33} +(-0.331077 - 1.37491i) q^{34} +10.6378i q^{35} +(-4.56155 + 2.33205i) q^{36} -5.49966i q^{37} +(4.42559 + 4.29117i) q^{38} +10.1265i q^{39} +(4.71659 + 5.49966i) q^{40} +5.49966i q^{41} +(13.4654 - 3.24245i) q^{42} -1.30957i q^{43} +(-2.12311 - 4.15286i) q^{44} -6.56155 q^{45} +(-2.50345 + 0.602827i) q^{46} -6.99614i q^{47} +(5.52390 - 7.64666i) q^{48} -10.2462 q^{49} +(0.516994 + 2.14700i) q^{50} -2.35829 q^{51} +(-3.90928 - 7.64666i) q^{52} +9.79366i q^{53} +(-0.342329 - 1.42164i) q^{54} -5.97366i q^{55} +(-8.91618 + 7.64666i) q^{56} +(8.68466 - 5.49966i) q^{57} +(-1.65767 + 0.399164i) q^{58} +6.33122 q^{59} +(10.7575 - 5.49966i) q^{60} +11.6847 q^{61} +(-0.438447 - 1.82081i) q^{62} -10.6378i q^{63} +(-1.21922 + 7.90655i) q^{64} -10.9993i q^{65} +(-7.56155 + 1.82081i) q^{66} -0.290319 q^{67} +(1.78078 - 0.910404i) q^{68} +4.29400i q^{69} +(-14.6260 + 3.52191i) q^{70} +2.06798 q^{71} +(-4.71659 - 5.49966i) q^{72} -0.123106 q^{73} +(7.56155 - 1.82081i) q^{74} +3.68260 q^{75} +(-4.43478 + 7.50551i) q^{76} +9.68466 q^{77} +(-13.9231 + 3.35265i) q^{78} -13.4061 q^{79} +(-6.00000 + 8.30571i) q^{80} -10.1231 q^{81} +(-7.56155 + 1.82081i) q^{82} -11.9473i q^{83} +(8.91618 + 17.4403i) q^{84} +2.56155 q^{85} +(1.80054 - 0.433567i) q^{86} +2.84329i q^{87} +(5.00691 - 4.29400i) q^{88} -14.0877i q^{89} +(-2.17238 - 9.02157i) q^{90} +17.8324 q^{91} +(-1.65767 - 3.24245i) q^{92} -3.12311 q^{93} +(9.61909 - 2.31626i) q^{94} +(-9.43318 + 5.97366i) q^{95} +(12.3423 + 5.06326i) q^{96} -2.41131i q^{97} +(-3.39228 - 14.0877i) q^{98} +5.97366i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9	$ 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} - 6 q^{16} - 8 q^{17} + 20 q^{20} - 10 q^{24} - 4 q^{25} - 6 q^{26} + 22 q^{28} - 16 q^{30} - 20 q^{36} + 18 q^{38} + 50 q^{42} + 16 q^{44} - 36 q^{45} - 16 q^{49} + 22 q^{54} + 20 q^{57} - 38 q^{58} + 44 q^{61} - 20 q^{62} - 18 q^{64} - 44 q^{66} + 6 q^{68} + 32 q^{73} + 44 q^{74} - 16 q^{76} + 28 q^{77} - 48 q^{80} - 48 q^{81} - 44 q^{82} + 4 q^{85} - 38 q^{92} + 8 q^{93} + 74 q^{96}+O(q^{100}) $ 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9 - 6 * q^16 - 8 * q^17 + 20 * q^20 - 10 * q^24 - 4 * q^25 - 6 * q^26 + 22 * q^28 - 16 * q^30 - 20 * q^36 + 18 * q^38 + 50 * q^42 + 16 * q^44 - 36 * q^45 - 16 * q^49 + 22 * q^54 + 20 * q^57 - 38 * q^58 + 44 * q^61 - 20 * q^62 - 18 * q^64 - 44 * q^66 + 6 * q^68 + 32 * q^73 + 44 * q^74 - 16 * q^76 + 28 * q^77 - 48 * q^80 - 48 * q^81 - 44 * q^82 + 4 * q^85 - 38 * q^92 + 8 * q^93 + 74 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.331077	+	1.37491i	0.234107	+	0.972211i
$2$	0.331077	+	1.37491i	0.234107	+	0.972211i
$3$	2.35829			1.36156			0.680781	−	0.732487i	$-0.261641\pi$
$3$	2.35829			1.36156			0.680781	+	0.732487i	$0.261641\pi$
$4$	−1.78078	+	0.910404i	−0.890388	+	0.455202i
$5$	−2.56155			−1.14556			−0.572781	−	0.819709i	$-0.694135\pi$
$5$	−2.56155			−1.14556			−0.572781	+	0.819709i	$0.694135\pi$
$6$	0.780776	+	3.24245i	0.318751	+	1.32373i
$7$		−	4.15286i		−	1.56963i	−0.619729	−	0.784816i	$-0.712757\pi$
$7$		−	4.15286i		−	1.56963i	0.619729	−	0.784816i	$-0.287243\pi$
$8$	−1.84130	−	2.14700i	−0.650998	−	0.759079i
$9$	2.56155			0.853851
$10$	−0.848071	−	3.52191i	−0.268183	−	1.11373i
$11$			2.33205i			0.703139i	0.936162	+	0.351569i	$0.114352\pi$
$11$			2.33205i			0.703139i	−0.936162	+	0.351569i	$0.885648\pi$
$12$	−4.19960	+	2.14700i	−1.21232	+	0.619786i
$13$			4.29400i			1.19094i	0.803377	+	0.595471i	$0.203034\pi$
$13$			4.29400i			1.19094i	−0.803377	+	0.595471i	$0.796966\pi$
$14$	5.70982	−	1.37491i	1.52601	−	0.367461i
$15$	−6.04090			−1.55975
$16$	2.34233	−	3.24245i	0.585582	−	0.810613i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$	0.848071	+	3.52191i	0.199892	+	0.830123i
$19$	3.68260	−	2.33205i	0.844847	−	0.535008i
$19$	3.68260	−	2.33205i	0.844847	−	0.535008i
$20$	4.56155	−	2.33205i	1.01999	−	0.521462i
$21$		−	9.79366i		−	2.13715i
$22$	−3.20636	+	0.772087i	−0.683599	+	0.164609i
$23$			1.82081i			0.379665i	0.981817	+	0.189832i	$0.0607944\pi$
$23$			1.82081i			0.379665i	−0.981817	+	0.189832i	$0.939206\pi$
$24$	−4.34233	−	5.06326i	−0.886374	−	1.03353i
$25$	1.56155			0.312311
$26$	−5.90388	+	1.42164i	−1.15785	+	0.278807i
$27$	−1.03399			−0.198991
$28$	3.78078	+	7.39531i	0.714500	+	1.39758i
$29$			1.20565i			0.223884i	0.993715	+	0.111942i	$0.0357071\pi$
$29$			1.20565i			0.223884i	−0.993715	+	0.111942i	$0.964293\pi$
$30$	−2.00000	−	8.30571i	−0.365148	−	1.51641i
$31$	−1.32431			−0.237853			−0.118926	−	0.992903i	$-0.537945\pi$
$31$	−1.32431			−0.237853			−0.118926	+	0.992903i	$0.537945\pi$
$32$	5.23358	+	2.14700i	0.925175	+	0.379540i
$33$			5.49966i			0.957367i
$34$	−0.331077	−	1.37491i	−0.0567792	−	0.235796i
$35$			10.6378i			1.79811i
$36$	−4.56155	+	2.33205i	−0.760259	+	0.388675i
$37$		−	5.49966i		−	0.904138i	−0.891983	−	0.452069i	$-0.850686\pi$
$37$		−	5.49966i		−	0.904138i	0.891983	−	0.452069i	$-0.149314\pi$
$38$	4.42559	+	4.29117i	0.717925	+	0.696120i
$39$			10.1265i			1.62154i
$40$	4.71659	+	5.49966i	0.745758	+	0.869572i
$41$			5.49966i			0.858902i	0.903090	+	0.429451i	$0.141293\pi$
$41$			5.49966i			0.858902i	−0.903090	+	0.429451i	$0.858707\pi$
$42$	13.4654	−	3.24245i	2.07776	−	0.500321i
$43$		−	1.30957i		−	0.199707i	−0.995002	−	0.0998536i	$-0.968163\pi$
$43$		−	1.30957i		−	0.199707i	0.995002	−	0.0998536i	$-0.0318375\pi$
$44$	−2.12311	−	4.15286i	−0.320070	−	0.626067i
$45$	−6.56155			−0.978139
$46$	−2.50345	+	0.602827i	−0.369114	+	0.0888820i
$47$		−	6.99614i		−	1.02049i	−0.860028	−	0.510246i	$-0.829554\pi$
$47$		−	6.99614i		−	1.02049i	0.860028	−	0.510246i	$-0.170446\pi$
$48$	5.52390	−	7.64666i	0.797307	−	1.10370i
$49$	−10.2462			−1.46374
$50$	0.516994	+	2.14700i	0.0731140	+	0.303632i
$51$	−2.35829			−0.330227
$52$	−3.90928	−	7.64666i	−0.542119	−	1.06040i
$53$			9.79366i			1.34526i	0.739978	+	0.672631i	$0.234836\pi$
$53$			9.79366i			1.34526i	−0.739978	+	0.672631i	$0.765164\pi$
$54$	−0.342329	−	1.42164i	−0.0465851	−	0.193461i
$55$		−	5.97366i		−	0.805489i
$56$	−8.91618	+	7.64666i	−1.19148	+	1.02183i
$57$	8.68466	−	5.49966i	1.15031	−	0.728447i
$58$	−1.65767	+	0.399164i	−0.217663	+	0.0524128i
$59$	6.33122			0.824254			0.412127	−	0.911126i	$-0.364786\pi$
$59$	6.33122			0.824254			0.412127	+	0.911126i	$0.364786\pi$
$60$	10.7575	−	5.49966i	1.38879	−	0.710002i
$61$	11.6847			1.49607			0.748034	−	0.663661i	$-0.230998\pi$
$61$	11.6847			1.49607			0.748034	+	0.663661i	$0.230998\pi$
$62$	−0.438447	−	1.82081i	−0.0556828	−	0.231243i
$63$		−	10.6378i		−	1.34023i
$64$	−1.21922	+	7.90655i	−0.152403	+	0.988318i
$65$		−	10.9993i		−	1.36430i
$66$	−7.56155	+	1.82081i	−0.930763	+	0.224126i
$67$	−0.290319			−0.0354681			−0.0177341	−	0.999843i	$-0.505645\pi$
$67$	−0.290319			−0.0354681			−0.0177341	+	0.999843i	$0.505645\pi$
$68$	1.78078	−	0.910404i	0.215951	−	0.110403i
$69$			4.29400i			0.516937i
$70$	−14.6260	+	3.52191i	−1.74814	+	0.420949i
$71$	2.06798			0.245423			0.122712	−	0.992442i	$-0.460841\pi$
$71$	2.06798			0.245423			0.122712	+	0.992442i	$0.460841\pi$
$72$	−4.71659	−	5.49966i	−0.555855	−	0.648141i
$73$	−0.123106			−0.0144084			−0.00720421	−	0.999974i	$-0.502293\pi$
$73$	−0.123106			−0.0144084			−0.00720421	+	0.999974i	$0.502293\pi$
$74$	7.56155	−	1.82081i	0.879013	−	0.211665i
$75$	3.68260			0.425230
$76$	−4.43478	+	7.50551i	−0.508705	+	0.860941i
$77$	9.68466			1.10367
$78$	−13.9231	+	3.35265i	−1.57648	+	0.379613i
$79$	−13.4061			−1.50830			−0.754152	−	0.656700i	$-0.771952\pi$
$79$	−13.4061			−1.50830			−0.754152	+	0.656700i	$0.771952\pi$
$80$	−6.00000	+	8.30571i	−0.670820	+	0.928607i
$81$	−10.1231			−1.12479
$82$	−7.56155	+	1.82081i	−0.835034	+	0.201075i
$83$		−	11.9473i		−	1.31139i	−0.755026	−	0.655695i	$-0.772376\pi$
$83$		−	11.9473i		−	1.31139i	0.755026	−	0.655695i	$-0.227624\pi$
$84$	8.91618	+	17.4403i	0.972835	+	1.90289i
$85$	2.56155			0.277839
$86$	1.80054	−	0.433567i	0.194158	−	0.0467528i
$87$			2.84329i			0.304832i
$88$	5.00691	−	4.29400i	0.533738	−	0.457742i
$89$		−	14.0877i		−	1.49329i	−0.665223	−	0.746644i	$-0.731664\pi$
$89$		−	14.0877i		−	1.49329i	0.665223	−	0.746644i	$-0.268336\pi$
$90$	−2.17238	−	9.02157i	−0.228989	−	0.950957i
$91$	17.8324			1.86934
$92$	−1.65767	−	3.24245i	−0.172824	−	0.338049i
$93$	−3.12311			−0.323851
$94$	9.61909	−	2.31626i	0.992134	−	0.238904i
$95$	−9.43318	+	5.97366i	−0.967824	+	0.612885i
$96$	12.3423	+	5.06326i	1.25968	+	0.516767i
$97$		−	2.41131i		−	0.244831i	−0.992479	−	0.122416i	$-0.960936\pi$
$97$		−	2.41131i		−	0.244831i	0.992479	−	0.122416i	$-0.0390641\pi$
$98$	−3.39228	−	14.0877i	−0.342672	−	1.42307i
$99$			5.97366i			0.600376i
$100$	−2.78078	+	1.42164i	−0.278078	+	0.142164i
$101$	−8.24621			−0.820529			−0.410264	−	0.911967i	$-0.634564\pi$
$101$	−8.24621			−0.820529			−0.410264	+	0.911967i	$0.634564\pi$
$102$	−0.780776	−	3.24245i	−0.0773084	−	0.321051i
$103$	12.0818			1.19045			0.595227	−	0.803557i	$-0.297062\pi$
$103$	12.0818			1.19045			0.595227	+	0.803557i	$0.297062\pi$
$104$	9.21922	−	7.90655i	0.904019	−	0.775301i
$105$			25.0870i			2.44824i
$106$	−13.4654	+	3.24245i	−1.30788	+	0.314935i
$107$	−5.75058			−0.555929			−0.277965	−	0.960591i	$-0.589660\pi$
$107$	−5.75058			−0.555929			−0.277965	+	0.960591i	$0.589660\pi$
$108$	1.84130	−	0.941346i	0.177179	−	0.0905811i
$109$			12.2050i			1.16902i	0.811385	+	0.584512i	$0.198714\pi$
$109$			12.2050i			1.16902i	−0.811385	+	0.584512i	$0.801286\pi$
$110$	8.21327	−	1.97774i	0.783105	−	0.188570i
$111$		−	12.9698i		−	1.23104i
$112$	−13.4654	−	9.72736i	−1.27236	−	0.919149i
$113$		−	5.49966i		−	0.517364i	−0.965963	−	0.258682i	$-0.916712\pi$
$113$		−	5.49966i		−	0.517364i	0.965963	−	0.258682i	$-0.0832882\pi$
$114$	10.4368	+	10.1198i	0.977500	+	0.947811i
$115$		−	4.66410i		−	0.434929i
$116$	−1.09763	−	2.14700i	−0.101913	−	0.199344i
$117$			10.9993i			1.01689i
$118$	2.09612	+	8.70488i	0.192963	+	0.801349i
$119$			4.15286i			0.380692i
$120$	11.1231	+	12.9698i	1.01540	+	1.18398i
$121$	5.56155			0.505596
$122$	3.86852	+	16.0654i	0.350239	+	1.45449i
$123$			12.9698i			1.16945i
$124$	2.35829	−	1.20565i	0.211781	−	0.108271i
$125$	8.80776			0.787790
$126$	14.6260	−	3.52191i	1.30299	−	0.313757i
$127$	6.04090			0.536043			0.268021	−	0.963413i	$-0.413630\pi$
$127$	6.04090			0.536043			0.268021	+	0.963413i	$0.413630\pi$
$128$	−11.2745	+	0.941346i	−0.996533	+	0.0832041i
$129$		−	3.08835i		−	0.271914i
$130$	15.1231	−	3.64162i	1.32638	−	0.319391i
$131$			5.97366i			0.521921i	0.965349	+	0.260961i	$0.0840393\pi$
$131$			5.97366i			0.521921i	−0.965349	+	0.260961i	$0.915961\pi$
$132$	−5.00691	−	9.79366i	−0.435795	−	0.852428i
$133$	−9.68466	−	15.2933i	−0.839766	−	1.32610i
$134$	−0.0961180	−	0.399164i	−0.00830333	−	0.0344825i
$135$	2.64861			0.227956
$136$	1.84130	+	2.14700i	0.157890	+	0.184104i
$137$	−12.1231			−1.03575			−0.517873	−	0.855457i	$-0.673276\pi$
$137$	−12.1231			−1.03575			−0.517873	+	0.855457i	$0.673276\pi$
$138$	−5.90388	+	1.42164i	−0.502572	+	0.121018i
$139$			18.9435i			1.60676i	0.595464	+	0.803382i	$0.296968\pi$
$139$			18.9435i			1.60676i	−0.595464	+	0.803382i	$0.703032\pi$
$140$	−9.68466	−	18.9435i	−0.818503	−	1.60102i
$141$		−	16.4990i		−	1.38946i
$142$	0.684658	+	2.84329i	0.0574553	+	0.238603i
$143$	−10.0138			−0.837397
$144$	6.00000	−	8.30571i	0.500000	−	0.692143i
$145$		−	3.08835i		−	0.256473i
$146$	−0.0407574	−	0.169260i	−0.00337311	−	0.0140080i
$147$	−24.1636			−1.99298
$148$	5.00691	+	9.79366i	0.411565	+	0.805034i
$149$	2.80776			0.230021			0.115010	−	0.993364i	$-0.463310\pi$
$149$	2.80776			0.230021			0.115010	+	0.993364i	$0.463310\pi$
$150$	1.21922	+	5.06326i	0.0995492	+	0.413413i
$151$	−8.85254			−0.720409			−0.360205	−	0.932873i	$-0.617293\pi$
$151$	−8.85254			−0.720409			−0.360205	+	0.932873i	$0.617293\pi$
$152$	−11.7877	−	3.61255i	−0.956107	−	0.293016i
$153$	−2.56155			−0.207089
$154$	3.20636	+	13.3156i	0.258376	+	1.07300i
$155$	3.39228			0.272475
$156$	−9.21922	−	18.0331i	−0.738129	−	1.44380i
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	−4.43845	−	18.4322i	−0.353104	−	1.46639i
$159$			23.0963i			1.83166i
$160$	−13.4061	−	5.49966i	−1.05985	−	0.434786i
$161$	7.56155			0.595934
$162$	−3.35152	−	13.9184i	−0.263321	−	1.09353i
$163$		−	17.6339i		−	1.38119i	−0.723240	−	0.690597i	$-0.757348\pi$
$163$		−	17.6339i		−	1.38119i	0.723240	−	0.690597i	$-0.242652\pi$
$164$	−5.00691	−	9.79366i	−0.390974	−	0.764756i
$165$		−	14.0877i		−	1.09672i
$166$	16.4265	−	3.95548i	1.27495	−	0.307005i
$167$	−10.7575			−0.832439			−0.416220	−	0.909264i	$-0.636645\pi$
$167$	−10.7575			−0.832439			−0.416220	+	0.909264i	$0.636645\pi$
$168$	−21.0270	+	18.0331i	−1.62227	+	1.39128i
$169$	−5.43845			−0.418342
$170$	0.848071	+	3.52191i	0.0650440	+	0.270119i
$171$	9.43318	−	5.97366i	0.721373	−	0.456817i
$172$	1.19224	+	2.33205i	0.0909071	+	0.177817i
$173$		−	2.41131i		−	0.183328i	−0.995790	−	0.0916642i	$-0.970781\pi$
$173$		−	2.41131i		−	0.183328i	0.995790	−	0.0916642i	$-0.0292186\pi$
$174$	−3.90928	+	0.941346i	−0.296361	+	0.0713633i
$175$		−	6.48490i		−	0.490213i
$176$	7.56155	+	5.46242i	0.569973	+	0.411746i
$177$	14.9309			1.12227
$178$	19.3693	−	4.66410i	1.45179	−	0.349589i
$179$	−8.10887			−0.606085			−0.303043	−	0.952977i	$-0.598002\pi$
$179$	−8.10887			−0.606085			−0.303043	+	0.952977i	$0.598002\pi$
$180$	11.6847	−	5.97366i	0.870923	−	0.445251i
$181$			19.5873i			1.45591i	0.685623	+	0.727957i	$0.259530\pi$
$181$			19.5873i			1.45591i	−0.685623	+	0.727957i	$0.740470\pi$
$182$	5.90388	+	24.5180i	0.437625	+	1.81739i
$183$	27.5559			2.03699
$184$	3.90928	−	3.35265i	0.288196	−	0.247161i
$185$			14.0877i			1.03575i
$186$	−1.03399	−	4.29400i	−0.0758156	−	0.314851i
$187$		−	2.33205i		−	0.170536i
$188$	6.36932	+	12.4586i	0.464530	+	0.908634i
$189$			4.29400i			0.312343i
$190$	−11.3364	−	10.9921i	−0.822427	−	0.797448i
$191$		−	7.79447i		−	0.563988i	−0.959416	−	0.281994i	$-0.909004\pi$
$191$		−	7.79447i		−	0.563988i	0.959416	−	0.281994i	$-0.0909959\pi$
$192$	−2.87529	+	18.6460i	−0.207506	+	1.34566i
$193$			5.49966i			0.395874i	0.980215	+	0.197937i	$0.0634241\pi$
$193$			5.49966i			0.395874i	−0.980215	+	0.197937i	$0.936576\pi$
$194$	3.31534	−	0.798328i	0.238028	−	0.0573166i
$195$		−	25.9396i		−	1.85757i
$196$	18.2462	−	9.32819i	1.30330	−	0.666299i
$197$	−22.4924			−1.60252			−0.801259	−	0.598317i	$-0.795836\pi$
$197$	−22.4924			−1.60252			−0.801259	+	0.598317i	$0.795836\pi$
$198$	−8.21327	+	1.97774i	−0.583692	+	0.140552i
$199$			5.17534i			0.366870i	0.983032	+	0.183435i	$0.0587217\pi$
$199$			5.17534i			0.366870i	−0.983032	+	0.183435i	$0.941278\pi$
$200$	−2.87529	−	3.35265i	−0.203314	−	0.237069i
$201$	−0.684658			−0.0482921
$202$	−2.73013	−	11.3378i	−0.192091	−	0.797727i
$203$	5.00691			0.351416
$204$	4.19960	−	2.14700i	0.294030	−	0.150320i
$205$		−	14.0877i		−	0.983925i
$206$	4.00000	+	16.6114i	0.278693	+	1.15737i
$207$			4.66410i			0.324177i
$208$	13.9231	+	10.0580i	0.965393	+	0.697394i
$209$	5.43845	+	8.58800i	0.376185	+	0.594045i
$210$	−34.4924	+	8.30571i	−2.38020	+	0.573149i
$211$	−25.1976			−1.73467			−0.867336	−	0.497723i	$-0.834170\pi$
$211$	−25.1976			−1.73467			−0.867336	+	0.497723i	$0.834170\pi$
$212$	−8.91618	−	17.4403i	−0.612366	−	1.19781i
$213$	4.87689			0.334159
$214$	−1.90388	−	7.90655i	−0.130147	−	0.540480i
$215$			3.35453i			0.228777i
$216$	1.90388	+	2.21997i	0.129543	+	0.151050i
$217$			5.49966i			0.373341i
$218$	−16.7808	+	4.04078i	−1.13654	+	0.273676i
$219$	−0.290319			−0.0196180
$220$	5.43845	+	10.6378i	0.366660	+	0.717198i
$221$		−	4.29400i		−	0.288846i
$222$	17.8324	−	4.29400i	1.19683	−	0.288194i
$223$	22.2586			1.49055			0.745274	−	0.666758i	$-0.232319\pi$
$223$	22.2586			1.49055			0.745274	+	0.666758i	$0.232319\pi$
$224$	8.91618	−	21.7343i	0.595738	−	1.45218i
$225$	4.00000			0.266667
$226$	7.56155	−	1.82081i	0.502987	−	0.121118i
$227$	24.6169			1.63388			0.816942	−	0.576720i	$-0.195668\pi$
$227$	24.6169			1.63388			0.816942	+	0.576720i	$0.195668\pi$
$228$	−10.4585	+	17.7002i	−0.692633	+	1.17222i
$229$	−6.56155			−0.433600			−0.216800	−	0.976216i	$-0.569562\pi$
$229$	−6.56155			−0.433600			−0.216800	+	0.976216i	$0.569562\pi$
$230$	6.41273	−	1.54417i	0.422843	−	0.101820i
$231$	22.8393			1.50271
$232$	2.58854	−	2.21997i	0.169946	−	0.145748i
$233$	10.8078			0.708040			0.354020	−	0.935238i	$-0.384814\pi$
$233$	10.8078			0.708040			0.354020	+	0.935238i	$0.384814\pi$
$234$	−15.1231	+	3.64162i	−0.988628	+	0.238060i
$235$			17.9210i			1.16904i
$236$	−11.2745	+	5.76396i	−0.733906	+	0.375202i
$237$	−31.6155			−2.05365
$238$	−5.70982	+	1.37491i	−0.370113	+	0.0891224i
$239$		−	9.83943i		−	0.636460i	−0.948014	−	0.318230i	$-0.896912\pi$
$239$		−	9.83943i		−	0.636460i	0.948014	−	0.318230i	$-0.103088\pi$
$240$	−14.1498	+	19.5873i	−0.913364	+	1.26436i
$241$			22.6757i			1.46067i	0.683090	+	0.730334i	$0.260635\pi$
$241$			22.6757i			1.46067i	−0.683090	+	0.730334i	$0.739365\pi$
$242$	1.84130	+	7.64666i	0.118363	+	0.491546i
$243$	−20.7713			−1.33248
$244$	−20.8078	+	10.6378i	−1.33208	+	0.681013i
$245$	26.2462			1.67681
$246$	−17.8324	+	4.29400i	−1.13695	+	0.273776i
$247$	10.0138	+	15.8131i	0.637164	+	1.00616i
$248$	2.43845	+	2.84329i	0.154842	+	0.180549i
$249$		−	28.1753i		−	1.78554i
$250$	2.91605	+	12.1099i	0.184427	+	0.765898i
$251$		−	21.5626i		−	1.36102i	−0.732739	−	0.680510i	$-0.761758\pi$
$251$		−	21.5626i		−	1.36102i	0.732739	−	0.680510i	$-0.238242\pi$
$252$	9.68466	+	18.9435i	0.610076	+	1.19333i
$253$	−4.24621			−0.266957
$254$	2.00000	+	8.30571i	0.125491	+	0.521147i
$255$	6.04090			0.378296
$256$	−5.02699	−	15.1898i	−0.314187	−	0.949361i
$257$		−	17.1760i		−	1.07141i	−0.844405	−	0.535705i	$-0.820046\pi$
$257$		−	17.1760i		−	1.07141i	0.844405	−	0.535705i	$-0.179954\pi$
$258$	4.24621	−	1.02248i	0.264358	−	0.0636568i
$259$	−22.8393			−1.41916
$260$	10.0138	+	19.5873i	0.621031	+	1.21475i
$261$			3.08835i			0.191164i
$262$	−8.21327	+	1.97774i	−0.507418	+	0.122185i
$263$		−	14.2794i		−	0.880504i	−0.897874	−	0.440252i	$-0.854889\pi$
$263$		−	14.2794i		−	0.880504i	0.897874	−	0.440252i	$-0.145111\pi$
$264$	11.8078	−	10.1265i	0.726718	−	0.623244i
$265$		−	25.0870i		−	1.54108i
$266$	17.8206	−	18.3788i	1.09265	−	1.12688i
$267$		−	33.2228i		−	2.03321i
$268$	0.516994	−	0.264308i	0.0315804	−	0.0161452i
$269$			5.49966i			0.335320i	0.985845	+	0.167660i	$0.0536211\pi$
$269$			5.49966i			0.335320i	−0.985845	+	0.167660i	$0.946379\pi$
$270$	0.876894	+	3.64162i	0.0533661	+	0.221622i
$271$			22.0738i			1.34089i	0.741959	+	0.670445i	$0.233897\pi$
$271$			22.0738i			1.34089i	−0.741959	+	0.670445i	$0.766103\pi$
$272$	−2.34233	+	3.24245i	−0.142025	+	0.196603i
$273$	42.0540			2.54522
$274$	−4.01368	−	16.6682i	−0.242475	−	1.00696i
$275$			3.64162i			0.219598i
$276$	−3.90928	−	7.64666i	−0.235311	−	0.460275i
$277$	13.0540			0.784337			0.392169	−	0.919893i	$-0.371725\pi$
$277$	13.0540			0.784337			0.392169	+	0.919893i	$0.371725\pi$
$278$	−26.0456	+	6.27174i	−1.56211	+	0.376154i
$279$	−3.39228			−0.203091
$280$	22.8393	−	19.5873i	1.36491	−	1.17057i
$281$			28.1753i			1.68080i	0.541968	+	0.840399i	$0.317679\pi$
$281$			28.1753i			1.68080i	−0.541968	+	0.840399i	$0.682321\pi$
$282$	22.6847	−	5.46242i	1.35085	−	0.325283i
$283$			5.97366i			0.355097i	0.984112	+	0.177549i	$0.0568167\pi$
$283$			5.97366i			0.355097i	−0.984112	+	0.177549i	$0.943183\pi$
$284$	−3.68260	+	1.88269i	−0.218522	+	0.111717i
$285$	−22.2462	+	14.0877i	−1.31775	+	0.834481i
$286$	−3.31534	−	13.7681i	−0.196040	−	0.814127i
$287$	22.8393			1.34816
$288$	13.4061	+	5.49966i	0.789962	+	0.324070i
$289$	−16.0000			−0.941176
$290$	4.24621	−	1.02248i	0.249346	−	0.0600421i
$291$		−	5.68658i		−	0.333353i
$292$	0.219224	−	0.112076i	0.0128291	−	0.00655874i
$293$		−	4.29400i		−	0.250858i	−0.992103	−	0.125429i	$-0.959969\pi$
$293$		−	4.29400i		−	0.250858i	0.992103	−	0.125429i	$-0.0400308\pi$
$294$	−8.00000	−	33.2228i	−0.466569	−	1.93760i
$295$	−16.2177			−0.944233
$296$	−11.8078	+	10.1265i	−0.686312	+	0.588592i
$297$		−	2.41131i		−	0.139918i
$298$	0.929585	+	3.86043i	0.0538494	+	0.223629i
$299$	−7.81855			−0.452159
$300$	−6.55789	+	3.35265i	−0.378620	+	0.193566i
$301$	−5.43845			−0.313467
$302$	−2.93087	−	12.1715i	−0.168653	−	0.700390i
$303$	−19.4470			−1.11720
$304$	1.06431	−	17.4031i	0.0610425	−	0.998135i
$305$	−29.9309			−1.71384
$306$	−0.848071	−	3.52191i	−0.0484810	−	0.201334i
$307$	−13.4061			−0.765126			−0.382563	−	0.923929i	$-0.624959\pi$
$307$	−13.4061			−0.765126			−0.382563	+	0.923929i	$0.624959\pi$
$308$	−17.2462	+	8.81695i	−0.982694	+	0.502392i
$309$	28.4924			1.62088
$310$	1.12311	+	4.66410i	0.0637881	+	0.264903i
$311$		−	4.15286i		−	0.235487i	−0.993044	−	0.117743i	$-0.962434\pi$
$311$		−	4.15286i		−	0.235487i	0.993044	−	0.117743i	$-0.0375660\pi$
$312$	21.7416	−	18.6460i	1.23088	−	1.05562i
$313$	−0.438447			−0.0247825			−0.0123913	−	0.999923i	$-0.503944\pi$
$313$	−0.438447			−0.0247825			−0.0123913	+	0.999923i	$0.503944\pi$
$314$	1.98646	+	8.24948i	0.112102	+	0.465545i
$315$			27.2492i			1.53532i
$316$	23.8733	−	12.2050i	1.34298	−	0.686583i
$317$			4.29400i			0.241175i	0.992703	+	0.120588i	$0.0384779\pi$
$317$			4.29400i			0.241175i	−0.992703	+	0.120588i	$0.961522\pi$
$318$	−31.7555	+	7.64666i	−1.78076	+	0.428803i
$319$	−2.81164			−0.157422
$320$	3.12311	−	20.2530i	0.174587	−	1.13218i
$321$	−13.5616			−0.756932
$322$	2.50345	+	10.3965i	0.139512	+	0.579373i
$323$	−3.68260	+	2.33205i	−0.204905	+	0.129759i
$324$	18.0270	−	9.21612i	1.00150	−	0.512006i
$325$			6.70531i			0.371944i
$326$	24.2451	−	5.83817i	1.34281	−	0.323347i
$327$			28.7829i			1.59170i
$328$	11.8078	−	10.1265i	0.651975	−	0.559144i
$329$	−29.0540			−1.60180
$330$	19.3693	−	4.66410i	1.06625	−	0.256750i
$331$	−23.8733			−1.31219			−0.656097	−	0.754677i	$-0.727794\pi$
$331$	−23.8733			−1.31219			−0.656097	+	0.754677i	$0.727794\pi$
$332$	10.8769	+	21.2755i	0.596947	+	1.16765i
$333$		−	14.0877i		−	0.771999i
$334$	−3.56155	−	14.7906i	−0.194879	−	0.809306i
$335$	0.743668			0.0406309
$336$	−31.7555	−	22.9400i	−1.73240	−	1.25148i
$337$		−	6.17669i		−	0.336466i	−0.985747	−	0.168233i	$-0.946194\pi$
$337$		−	6.17669i		−	0.336466i	0.985747	−	0.168233i	$-0.0538061\pi$
$338$	−1.80054	−	7.47740i	−0.0979366	−	0.406717i
$339$		−	12.9698i		−	0.704423i
$340$	−4.56155	+	2.33205i	−0.247385	+	0.126473i
$341$		−	3.08835i		−	0.167243i
$342$	11.3364	+	10.9921i	0.613001	+	0.594383i
$343$			13.4810i			0.727908i
$344$	−2.81164	+	2.41131i	−0.151594	+	0.130009i
$345$		−	10.9993i		−	0.592183i
$346$	3.31534	−	0.798328i	0.178234	−	0.0429184i
$347$			29.8683i			1.60342i	0.597716	+	0.801708i	$0.296075\pi$
$347$			29.8683i			1.60342i	−0.597716	+	0.801708i	$0.703925\pi$
$348$	−2.58854	−	5.06326i	−0.138760	−	0.271419i
$349$	9.05398			0.484648			0.242324	−	0.970195i	$-0.422090\pi$
$349$	9.05398			0.484648			0.242324	+	0.970195i	$0.422090\pi$
$350$	8.91618	−	2.14700i	0.476590	−	0.114762i
$351$		−	4.43994i		−	0.236987i
$352$	−5.00691	+	12.2050i	−0.266869	+	0.650527i
$353$	18.6847			0.994484			0.497242	−	0.867612i	$-0.334346\pi$
$353$	18.6847			0.994484			0.497242	+	0.867612i	$0.334346\pi$
$354$	4.94326	+	20.5287i	0.262731	+	1.09109i
$355$	−5.29723			−0.281148
$356$	12.8255	+	25.0870i	0.679748	+	1.32961i
$357$			9.79366i			0.518335i
$358$	−2.68466	−	11.1490i	−0.141889	−	0.589243i
$359$		−	6.19782i		−	0.327108i	−0.986534	−	0.163554i	$-0.947704\pi$
$359$		−	6.19782i		−	0.327108i	0.986534	−	0.163554i	$-0.0522958\pi$
$360$	12.0818	+	14.0877i	0.636766	+	0.742485i
$361$	8.12311	−	17.1760i	0.427532	−	0.904000i
$362$	−26.9309	+	6.48490i	−1.41546	+	0.340839i
$363$	13.1158			0.688400
$364$	−31.7555	+	16.2347i	−1.66444	+	0.850927i
$365$	0.315342			0.0165057
$366$	9.12311	+	37.8869i	0.476872	+	1.98038i
$367$		−	1.02248i		−	0.0533730i	−0.999644	−	0.0266865i	$-0.991504\pi$
$367$		−	1.02248i		−	0.0533730i	0.999644	−	0.0266865i	$-0.00849559\pi$
$368$	5.90388	+	4.26493i	0.307761	+	0.222325i
$369$			14.0877i			0.733374i
$370$	−19.3693	+	4.66410i	−1.00696	+	0.242475i
$371$	40.6716			2.11157
$372$	5.56155	−	2.84329i	0.288353	−	0.147418i
$373$			6.70531i			0.347188i	0.984817	+	0.173594i	$0.0555380\pi$
$373$			6.70531i			0.347188i	−0.984817	+	0.173594i	$0.944462\pi$
$374$	3.20636	−	0.772087i	0.165797	−	0.0399237i
$375$	20.7713			1.07263
$376$	−15.0207	+	12.8820i	−0.774635	+	0.664339i
$377$	−5.17708			−0.266633
$378$	−5.90388	+	1.42164i	−0.303663	+	0.0731215i
$379$	15.7644			0.809762			0.404881	−	0.914369i	$-0.367313\pi$
$379$	15.7644			0.809762			0.404881	+	0.914369i	$0.367313\pi$
$380$	11.3599	−	19.2258i	0.582752	−	0.986261i
$381$	14.2462			0.729856
$382$	10.7167	−	2.58057i	0.548315	−	0.132033i
$383$	−22.2586			−1.13736			−0.568682	−	0.822558i	$-0.692546\pi$
$383$	−22.2586			−1.13736			−0.568682	+	0.822558i	$0.692546\pi$
$384$	−26.5885	+	2.21997i	−1.35684	+	0.113287i
$385$	−24.8078			−1.26432
$386$	−7.56155	+	1.82081i	−0.384873	+	0.0926767i
$387$		−	3.35453i		−	0.170520i
$388$	2.19526	+	4.29400i	0.111448	+	0.217995i
$389$	14.8078			0.750783			0.375392	−	0.926866i	$-0.377508\pi$
$389$	14.8078			0.750783			0.375392	+	0.926866i	$0.377508\pi$
$390$	35.6647	−	8.58800i	1.80595	−	0.434870i
$391$		−	1.82081i		−	0.0920822i
$392$	18.8664	+	21.9986i	0.952895	+	1.11110i
$393$			14.0877i			0.710628i
$394$	−7.44672	−	30.9251i	−0.375160	−	1.55799i
$395$	34.3404			1.72785
$396$	−5.43845	−	10.6378i	−0.273292	−	0.534568i
$397$	−3.93087			−0.197285			−0.0986423	−	0.995123i	$-0.531450\pi$
$397$	−3.93087			−0.197285			−0.0986423	+	0.995123i	$0.531450\pi$
$398$	−7.11564	+	1.71343i	−0.356675	+	0.0858866i
$399$	−22.8393	−	36.0661i	−1.14339	−	1.80557i
$400$	3.65767	−	5.06326i	0.182884	−	0.253163i
$401$			7.91096i			0.395055i	0.980297	+	0.197527i	$0.0632911\pi$
$401$			7.91096i			0.395055i	−0.980297	+	0.197527i	$0.936709\pi$
$402$	−0.226674	−	0.941346i	−0.0113055	−	0.0469501i
$403$		−	5.68658i		−	0.283269i
$404$	14.6847	−	7.50738i	0.730589	−	0.373506i
$405$	25.9309			1.28852
$406$	1.65767	+	6.88407i	0.0822688	+	0.341651i
$407$	12.8255			0.635734
$408$	4.34233	+	5.06326i	0.214977	+	0.250669i
$409$		−	27.4983i		−	1.35970i	−0.733350	−	0.679851i	$-0.762044\pi$
$409$		−	27.4983i		−	1.35970i	0.733350	−	0.679851i	$-0.237956\pi$
$410$	19.3693	−	4.66410i	0.956582	−	0.230343i
$411$	−28.5899			−1.41023
$412$	−21.5150	+	10.9993i	−1.05997	+	0.541897i
$413$		−	26.2926i		−	1.29378i
$414$	−6.41273	+	1.54417i	−0.315168	+	0.0758920i
$415$			30.6037i			1.50228i
$416$	−9.21922	+	22.4730i	−0.452010	+	1.10183i
$417$			44.6743i			2.18771i
$418$	−10.0072	+	10.3207i	−0.489469	+	0.504801i
$419$			39.9319i			1.95080i	0.220440	+	0.975401i	$0.429251\pi$
$419$			39.9319i			1.95080i	−0.220440	+	0.975401i	$0.570749\pi$
$420$	−22.8393	−	44.6743i	−1.11444	−	2.17988i
$421$		−	23.2043i		−	1.13091i	−0.824780	−	0.565454i	$-0.808701\pi$
$421$		−	23.2043i		−	1.13091i	0.824780	−	0.565454i	$-0.191299\pi$
$422$	−8.34233	−	34.6445i	−0.406098	−	1.68647i
$423$		−	17.9210i		−	0.871348i
$424$	21.0270	−	18.0331i	1.02116	−	0.875763i
$425$	−1.56155			−0.0757464
$426$	1.61463	+	6.70531i	0.0782289	+	0.324873i
$427$		−	48.5247i		−	2.34827i
$428$	10.2405	−	5.23535i	0.494993	−	0.253060i
$429$	−23.6155			−1.14017
$430$	−4.61219	+	1.11061i	−0.222419	+	0.0535582i
$431$	−5.29723			−0.255158			−0.127579	−	0.991828i	$-0.540721\pi$
$431$	−5.29723			−0.255158			−0.127579	+	0.991828i	$0.540721\pi$
$432$	−2.42194	+	3.35265i	−0.116526	+	0.161305i
$433$		−	18.9103i		−	0.908770i	−0.890805	−	0.454385i	$-0.849859\pi$
$433$		−	18.9103i		−	0.908770i	0.890805	−	0.454385i	$-0.150141\pi$
$434$	−7.56155	+	1.82081i	−0.362966	+	0.0874016i
$435$		−	7.28323i		−	0.349204i
$436$	−11.1114	−	21.7343i	−0.532142	−	1.04088i
$437$	4.24621	+	6.70531i	0.203124	+	0.320758i
$438$	−0.0961180	−	0.399164i	−0.00459269	−	0.0190728i
$439$	19.6100			0.935935			0.467968	−	0.883746i	$-0.344986\pi$
$439$	19.6100			0.935935			0.467968	+	0.883746i	$0.344986\pi$
$440$	−12.8255	+	10.9993i	−0.611430	+	0.524372i
$441$	−26.2462			−1.24982
$442$	5.90388	−	1.42164i	0.280819	−	0.0676207i
$443$		−	12.2344i		−	0.581275i	−0.956833	−	0.290637i	$-0.906133\pi$
$443$		−	12.2344i		−	0.581275i	0.956833	−	0.290637i	$-0.0938673\pi$
$444$	11.8078	+	23.0963i	0.560372	+	1.09610i
$445$			36.0863i			1.71065i
$446$	7.36932	+	30.6037i	0.348947	+	1.44913i
$447$	6.62153			0.313188
$448$	32.8348	+	5.06326i	1.55130	+	0.239217i
$449$			14.7647i			0.696789i	0.937348	+	0.348395i	$0.113273\pi$
$449$			14.7647i			0.696789i	−0.937348	+	0.348395i	$0.886727\pi$
$450$	1.32431	+	5.49966i	0.0624284	+	0.259256i
$451$	−12.8255			−0.603927
$452$	5.00691	+	9.79366i	0.235505	+	0.460655i
$453$	−20.8769			−0.980882
$454$	8.15009	+	33.8462i	0.382503	+	1.58848i
$455$	−45.6786			−2.14144
$456$	−27.7988	−	8.51945i	−1.30180	−	0.398960i
$457$	3.87689			0.181353			0.0906767	−	0.995880i	$-0.471097\pi$
$457$	3.87689			0.181353			0.0906767	+	0.995880i	$0.471097\pi$
$458$	−2.17238	−	9.02157i	−0.101509	−	0.421550i
$459$	1.03399			0.0482624
$460$	4.24621	+	8.30571i	0.197981	+	0.387256i
$461$	31.6847			1.47570			0.737851	−	0.674964i	$-0.235841\pi$
$461$	31.6847			1.47570			0.737851	+	0.674964i	$0.235841\pi$
$462$	7.56155	+	31.4020i	0.351795	+	1.46096i
$463$		−	16.3243i		−	0.758656i	−0.925262	−	0.379328i	$-0.876155\pi$
$463$		−	16.3243i		−	0.758656i	0.925262	−	0.379328i	$-0.123845\pi$
$464$	3.90928	+	2.82404i	0.181484	+	0.131103i
$465$	8.00000			0.370991
$466$	3.57820	+	14.8597i	0.165757	+	0.688364i
$467$			2.33205i			0.107914i	0.998543	+	0.0539572i	$0.0171834\pi$
$467$			2.33205i			0.107914i	−0.998543	+	0.0539572i	$0.982817\pi$
$468$	−10.0138	−	19.5873i	−0.462889	−	0.905424i
$469$			1.20565i			0.0556719i
$470$	−24.6398	+	5.93322i	−1.13655	+	0.273679i
$471$	14.1498			0.651987
$472$	−11.6577	−	13.5931i	−0.536588	−	0.625674i
$473$	3.05398			0.140422
$474$	−10.4672	−	43.4686i	−0.480773	−	1.99658i
$475$	5.75058	−	3.64162i	0.263855	−	0.167089i
$476$	−3.78078	−	7.39531i	−0.173292	−	0.338963i
$477$			25.0870i			1.14865i
$478$	13.5284	−	3.25761i	0.618773	−	0.148999i
$479$		−	41.5286i		−	1.89749i	−0.316045	−	0.948744i	$-0.602355\pi$
$479$		−	41.5286i		−	1.89749i	0.316045	−	0.948744i	$-0.397645\pi$
$480$	−31.6155	−	12.9698i	−1.44304	−	0.591988i
$481$	23.6155			1.07678
$482$	−31.1771	+	7.50738i	−1.42008	+	0.341952i
$483$	17.8324			0.811401
$484$	−9.90388	+	5.06326i	−0.450176	+	0.230148i
$485$			6.17669i			0.280469i
$486$	−6.87689	−	28.5588i	−0.311942	−	1.29545i
$487$	18.8664			0.854916			0.427458	−	0.904035i	$-0.359409\pi$
$487$	18.8664			0.854916			0.427458	+	0.904035i	$0.359409\pi$
$488$	−21.5150	−	25.0870i	−0.973937	−	1.13563i
$489$		−	41.5859i		−	1.88058i
$490$	8.68951	+	36.0863i	0.392552	+	1.63021i
$491$			21.2755i			0.960151i	0.877227	+	0.480075i	$0.159391\pi$
$491$			21.2755i			0.960151i	−0.877227	+	0.480075i	$0.840609\pi$
$492$	−11.8078	−	23.0963i	−0.532335	−	1.04126i
$493$		−	1.20565i		−	0.0542999i
$494$	−18.4263	+	19.0035i	−0.829039	+	0.855007i
$495$		−	15.3019i		−	0.687767i
$496$	−3.10196	+	4.29400i	−0.139282	+	0.192806i
$497$		−	8.58800i		−	0.385225i
$498$	38.7386	−	9.32819i	1.73592	−	0.418006i
$499$		−	1.30957i		−	0.0586243i	−0.999570	−	0.0293122i	$-0.990668\pi$
$499$		−	1.30957i		−	0.0586243i	0.999570	−	0.0293122i	$-0.00933169\pi$
$500$	−15.6847	+	8.01862i	−0.701439	+	0.358604i
$501$	−25.3693			−1.13342
$502$	29.6467	−	7.13888i	1.32320	−	0.318624i
$503$			16.3873i			0.730672i	0.930876	+	0.365336i	$0.119046\pi$
$503$			16.3873i			0.730672i	−0.930876	+	0.365336i	$0.880954\pi$
$504$	−22.8393	+	19.5873i	−1.01734	+	0.872488i
$505$	21.1231			0.939966
$506$	−1.40582	−	5.83817i	−0.0624964	−	0.259539i
$507$	−12.8255			−0.569599
$508$	−10.7575	+	5.49966i	−0.477286	+	0.244008i
$509$		−	8.58800i		−	0.380657i	−0.981721	−	0.190328i	$-0.939045\pi$
$509$		−	8.58800i		−	0.380657i	0.981721	−	0.190328i	$-0.0609552\pi$
$510$	2.00000	+	8.30571i	0.0885615	+	0.367783i
$511$			0.511240i			0.0226159i
$512$	19.2203	−	11.9407i	0.849426	−	0.527707i
$513$	−3.80776	+	2.41131i	−0.168117	+	0.106462i
$514$	23.6155	−	5.68658i	1.04164	−	0.250824i
$515$	−30.9481			−1.36374
$516$	2.81164	+	5.49966i	0.123776	+	0.242109i
$517$	16.3153			0.717548
$518$	−7.56155	−	31.4020i	−0.332236	−	1.37973i
$519$		−	5.68658i		−	0.249613i
$520$	−23.6155	+	20.2530i	−1.03561	+	0.888155i
$521$		−	22.6757i		−	0.993439i	−0.867911	−	0.496719i	$-0.834538\pi$
$521$		−	22.6757i		−	0.993439i	0.867911	−	0.496719i	$-0.165462\pi$
$522$	−4.24621	+	1.02248i	−0.185852	+	0.0447527i
$523$	2.19526			0.0959922			0.0479961	−	0.998848i	$-0.484716\pi$
$523$	2.19526			0.0959922			0.0479961	+	0.998848i	$0.484716\pi$
$524$	−5.43845	−	10.6378i	−0.237580	−	0.464713i
$525$		−	15.2933i		−	0.667455i
$526$	19.6329	−	4.72757i	0.856036	−	0.206132i
$527$	1.32431			0.0576877
$528$	17.8324	+	12.8820i	0.776054	+	0.560617i
$529$	19.6847			0.855855
$530$	34.4924	−	8.30571i	1.49826	−	0.360777i
$531$	16.2177			0.703790
$532$	31.1693	+	18.4170i	1.35136	+	0.798479i
$533$	−23.6155			−1.02290
$534$	45.6786	−	10.9993i	1.97670	−	0.475987i
$535$	14.7304			0.636851
$536$	0.534565	+	0.623316i	0.0230897	+	0.0269231i
$537$	−19.1231			−0.825223
$538$	−7.56155	+	1.82081i	−0.326002	+	0.0785006i
$539$		−	23.8947i		−	1.02922i
$540$	−4.71659	+	2.41131i	−0.202970	+	0.103766i
$541$	−32.8078			−1.41052			−0.705258	−	0.708951i	$-0.749169\pi$
$541$	−32.8078			−1.41052			−0.705258	+	0.708951i	$0.749169\pi$
$542$	−30.3496	+	7.30814i	−1.30363	+	0.313911i
$543$			46.1927i			1.98232i
$544$	−5.23358	−	2.14700i	−0.224388	−	0.0920519i
$545$		−	31.2637i		−	1.33919i
$546$	13.9231	+	57.8206i	0.595853	+	2.47449i
$547$	0.580639			0.0248263			0.0124132	−	0.999923i	$-0.496049\pi$
$547$	0.580639			0.0248263			0.0124132	+	0.999923i	$0.496049\pi$
$548$	21.5885	−	11.0369i	0.922217	−	0.471474i
$549$	29.9309			1.27742
$550$	−5.00691	+	1.20565i	−0.213495	+	0.0514093i
$551$	2.81164	+	4.43994i	0.119780	+	0.189148i
$552$	9.21922	−	7.90655i	0.392396	−	0.336525i
$553$			55.6736i			2.36748i
$554$	4.32187	+	17.9481i	0.183619	+	0.762541i
$555$			33.2228i			1.41023i
$556$	−17.2462	−	33.7341i	−0.731402	−	1.43064i
$557$	9.93087			0.420784			0.210392	−	0.977617i	$-0.432526\pi$
$557$	9.93087			0.420784			0.210392	+	0.977617i	$0.432526\pi$
$558$	−1.12311	−	4.66410i	−0.0475449	−	0.197447i
$559$	5.62329			0.237840
$560$	34.4924	+	24.9171i	1.45757	+	1.05294i
$561$		−	5.49966i		−	0.232196i
$562$	−38.7386	+	9.32819i	−1.63409	+	0.393486i
$563$	21.3519			0.899877			0.449938	−	0.893060i	$-0.351446\pi$
$563$	21.3519			0.899877			0.449938	+	0.893060i	$0.351446\pi$
$564$	15.0207	+	29.3810i	0.632487	+	1.23716i
$565$			14.0877i			0.592672i
$566$	−8.21327	+	1.97774i	−0.345230	+	0.0831307i
$567$			42.0398i			1.76551i
$568$	−3.80776	−	4.43994i	−0.159770	−	0.186296i
$569$			41.5859i			1.74337i	0.490064	+	0.871687i	$0.336973\pi$
$569$			41.5859i			1.74337i	−0.490064	+	0.871687i	$0.663027\pi$
$570$	−26.7345	−	25.9225i	−1.11979	−	1.08578i
$571$			15.5889i			0.652377i	0.945305	+	0.326188i	$0.105764\pi$
$571$			15.5889i			0.652377i	−0.945305	+	0.326188i	$0.894236\pi$
$572$	17.8324	−	9.11662i	0.745609	−	0.381185i
$573$		−	18.3817i		−	0.767905i
$574$	7.56155	+	31.4020i	0.315613	+	1.31070i
$575$			2.84329i			0.118573i
$576$	−3.12311	+	20.2530i	−0.130129	+	0.843877i
$577$	27.0000			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$578$	−5.29723	−	21.9986i	−0.220336	−	0.915022i
$579$			12.9698i			0.539007i
$580$	2.81164	+	5.49966i	0.116747	+	0.228361i
$581$	−49.6155			−2.05840
$582$	7.81855	−	1.88269i	0.324089	−	0.0780401i
$583$	−22.8393			−0.945906
$584$	0.226674	+	0.264308i	0.00937986	+	0.0109371i
$585$		−	28.1753i		−	1.16491i
$586$	5.90388	−	1.42164i	0.243887	−	0.0587276i
$587$			5.97366i			0.246559i	0.992372	+	0.123280i	$0.0393412\pi$
$587$			5.97366i			0.246559i	−0.992372	+	0.123280i	$0.960659\pi$
$588$	43.0299	−	21.9986i	1.77452	−	0.907208i
$589$	−4.87689	+	3.08835i	−0.200949	+	0.127253i
$590$	−5.36932	−	22.2980i	−0.221051	−	0.917994i
$591$	−53.0438			−2.18193
$592$	−17.8324	−	12.8820i	−0.732906	−	0.529447i
$593$	12.7386			0.523113			0.261556	−	0.965188i	$-0.415764\pi$
$593$	12.7386			0.523113			0.261556	+	0.965188i	$0.415764\pi$
$594$	3.31534	−	0.798328i	0.136030	−	0.0327558i
$595$		−	10.6378i		−	0.436106i
$596$	−5.00000	+	2.55620i	−0.204808	+	0.104706i
$597$			12.2050i			0.499516i
$598$	−2.58854	−	10.7498i	−0.105853	−	0.439593i
$599$	−24.9073			−1.01768			−0.508841	−	0.860860i	$-0.669926\pi$
$599$	−24.9073			−1.01768			−0.508841	+	0.860860i	$0.669926\pi$
$600$	−6.78078	−	7.90655i	−0.276824	−	0.322783i
$601$			35.4092i			1.44437i	0.691698	+	0.722187i	$0.256863\pi$
$601$			35.4092i			1.44437i	−0.691698	+	0.722187i	$0.743137\pi$
$602$	−1.80054	−	7.47740i	−0.0733847	−	0.304756i
$603$	−0.743668			−0.0302845
$604$	15.7644	−	8.05939i	0.641444	−	0.327932i
$605$	−14.2462			−0.579191
$606$	−6.43845	−	26.7379i	−0.261544	−	1.08615i
$607$	31.5288			1.27971			0.639857	−	0.768494i	$-0.278994\pi$
$607$	31.5288			1.27971			0.639857	+	0.768494i	$0.278994\pi$
$608$	24.2801	−	4.29842i	0.984688	−	0.174324i
$609$	11.8078			0.478475
$610$	−9.90941	−	41.1524i	−0.401220	−	1.66621i
$611$	30.0414			1.21535
$612$	4.56155	−	2.33205i	0.184390	−	0.0942674i
$613$	−29.3002			−1.18342			−0.591712	−	0.806150i	$-0.701548\pi$
$613$	−29.3002			−1.18342			−0.591712	+	0.806150i	$0.701548\pi$
$614$	−4.43845	−	18.4322i	−0.179121	−	0.743864i
$615$		−	33.2228i		−	1.33967i
$616$	−17.8324	−	20.7930i	−0.718487	−	0.837773i
$617$	41.5464			1.67259			0.836297	−	0.548276i	$-0.184716\pi$
$617$	41.5464			1.67259			0.836297	+	0.548276i	$0.184716\pi$
$618$	9.43318	+	39.1746i	0.379458	+	1.57583i
$619$			6.70906i			0.269660i	0.990869	+	0.134830i	$0.0430488\pi$
$619$			6.70906i			0.269660i	−0.990869	+	0.134830i	$0.956951\pi$
$620$	−6.04090	+	3.08835i	−0.242608	+	0.124031i
$621$		−	1.88269i		−	0.0755499i
$622$	5.70982	−	1.37491i	0.228943	−	0.0551290i
$623$	−58.5040			−2.34391
$624$	32.8348	+	23.7196i	1.31444	+	0.949546i
$625$	−30.3693			−1.21477
$626$	−0.145160	−	0.602827i	−0.00580175	−	0.0240938i
$627$	12.8255	+	20.2530i	0.512200	+	0.808828i
$628$	−10.6847	+	5.46242i	−0.426364	+	0.217974i
$629$			5.49966i			0.219286i
$630$	−37.4653	+	9.02157i	−1.49265	+	0.359428i
$631$			9.61528i			0.382778i	0.981514	+	0.191389i	$0.0612992\pi$
$631$			9.61528i			0.382778i	−0.981514	+	0.191389i	$0.938701\pi$
$632$	24.6847	+	28.7829i	0.981903	+	1.14492i
$633$	−59.4233			−2.36186
$634$	−5.90388	+	1.42164i	−0.234473	+	0.0564607i
$635$	−15.4741			−0.614070
$636$	−21.0270	−	41.1294i	−0.833774	−	1.63089i
$637$		−	43.9972i		−	1.74323i
$638$	−0.930870	−	3.86577i	−0.0368535	−	0.153047i
$639$	5.29723			0.209555
$640$	28.8802	−	2.41131i	1.14159	−	0.0953153i
$641$		−	26.8212i		−	1.05938i	−0.848193	−	0.529688i	$-0.822309\pi$
$641$		−	26.8212i		−	1.05938i	0.848193	−	0.529688i	$-0.177691\pi$
$642$	−4.48991	−	18.6460i	−0.177203	−	0.735898i
$643$		−	14.2794i		−	0.563124i	−0.959543	−	0.281562i	$-0.909148\pi$
$643$		−	14.2794i		−	0.563124i	0.959543	−	0.281562i	$-0.0908524\pi$
$644$	−13.4654	+	6.88407i	−0.530612	+	0.271270i
$645$			7.91096i			0.311494i
$646$	−4.42559	−	4.29117i	−0.174122	−	0.168834i
$647$		−	32.1374i		−	1.26345i	−0.775191	−	0.631726i	$-0.782347\pi$
$647$		−	32.1374i		−	1.26345i	0.775191	−	0.631726i	$-0.217653\pi$
$648$	18.6397	+	21.7343i	0.732236	+	0.853805i
$649$			14.7647i			0.579565i
$650$	−9.21922	+	2.21997i	−0.361608	+	0.0870745i
$651$			12.9698i			0.508327i
$652$	16.0540	+	31.4020i	0.628722	+	1.22980i
$653$	−25.1922			−0.985848			−0.492924	−	0.870072i	$-0.664072\pi$
$653$	−25.1922			−0.985848			−0.492924	+	0.870072i	$0.664072\pi$
$654$	−39.5740	+	9.52935i	−1.54747	+	0.372627i
$655$		−	15.3019i		−	0.597893i
$656$	17.8324	+	12.8820i	0.696237	+	0.502958i
$657$	−0.315342			−0.0123026
$658$	−9.61909	−	39.9467i	−0.374991	−	1.55729i
$659$	41.9960			1.63593			0.817965	−	0.575268i	$-0.195102\pi$
$659$	41.9960			1.63593			0.817965	+	0.575268i	$0.195102\pi$
$660$	12.8255	+	25.0870i	0.499230	+	0.976509i
$661$		−	37.2919i		−	1.45049i	−0.688492	−	0.725244i	$-0.741727\pi$
$661$		−	37.2919i		−	1.45049i	0.688492	−	0.725244i	$-0.258273\pi$
$662$	−7.90388	−	32.8237i	−0.307193	−	1.27573i
$663$		−	10.1265i		−	0.393281i
$664$	−25.6509	+	21.9986i	−0.995449	+	0.853712i
$665$	24.8078	+	39.1746i	0.962004	+	1.51913i
$666$	19.3693	−	4.66410i	0.750546	−	0.180730i
$667$	−2.19526			−0.0850010
$668$	19.1567	−	9.79366i	0.741194	−	0.378928i
$669$	52.4924			2.02947
$670$	0.246211	+	1.02248i	0.00951197	+	0.0395018i
$671$			27.2492i			1.05194i
$672$	21.0270	−	51.2559i	0.811134	−	1.97724i
$673$			24.4099i			0.940934i	0.882418	+	0.470467i	$0.155914\pi$
$673$			24.4099i			0.940934i	−0.882418	+	0.470467i	$0.844086\pi$
$674$	8.49242	−	2.04496i	0.327116	−	0.0787689i
$675$	−1.61463			−0.0621470
$676$	9.68466	−	4.95118i	0.372487	−	0.190430i
$677$		−	40.3803i		−	1.55194i	−0.630770	−	0.775970i	$-0.717261\pi$
$677$		−	40.3803i		−	1.55194i	0.630770	−	0.775970i	$-0.282739\pi$
$678$	17.8324	−	4.29400i	0.684848	−	0.164910i
$679$	−10.0138			−0.384295
$680$	−4.71659	−	5.49966i	−0.180873	−	0.210902i
$681$	58.0540			2.22463
$682$	4.24621	−	1.02248i	0.162596	−	0.0391528i
$683$	−31.5288			−1.20642			−0.603208	−	0.797584i	$-0.706111\pi$
$683$	−31.5288			−1.20642			−0.603208	+	0.797584i	$0.706111\pi$
$684$	−11.3599	+	19.2258i	−0.434358	+	0.735115i
$685$	31.0540			1.18651
$686$	−18.5353	+	4.46326i	−0.707680	+	0.170408i
$687$	−15.4741			−0.590373
$688$	−4.24621	−	3.06744i	−0.161885	−	0.116945i
$689$	−42.0540			−1.60213
$690$	15.1231	−	3.64162i	0.575727	−	0.138634i
$691$			8.01862i			0.305043i	0.988300	+	0.152521i	$0.0487393\pi$
$691$			8.01862i			0.305043i	−0.988300	+	0.152521i	$0.951261\pi$
$692$	2.19526	+	4.29400i	0.0834514	+	0.163233i
$693$	24.8078			0.942369
$694$	−41.0664	+	9.88871i	−1.55886	+	0.375370i
$695$		−	48.5247i		−	1.84065i
$696$	6.10454	−	5.23535i	0.231392	−	0.198445i
$697$		−	5.49966i		−	0.208314i
$698$	2.99756	+	12.4484i	0.113459	+	0.471180i
$699$	25.4879			0.964041
$700$	5.90388	+	11.5482i	0.223146	+	0.436480i
$701$	4.63068			0.174898			0.0874492	−	0.996169i	$-0.472128\pi$
$701$	4.63068			0.174898			0.0874492	+	0.996169i	$0.472128\pi$
$702$	6.10454	−	1.46996i	0.230401	−	0.0554801i
$703$	−12.8255	−	20.2530i	−0.483721	−	0.763858i
$704$	−18.4384	−	2.84329i	−0.694925	−	0.107160i
$705$			42.2630i			1.59172i
$706$	6.18606	+	25.6898i	0.232815	+	0.966848i
$707$			34.2453i			1.28793i
$708$	−26.5885	+	13.5931i	−0.999259	+	0.510861i
$709$	12.6307			0.474355			0.237178	−	0.971466i	$-0.423778\pi$
$709$	12.6307			0.474355			0.237178	+	0.971466i	$0.423778\pi$
$710$	−1.75379	−	7.28323i	−0.0658185	−	0.273335i
$711$	−34.3404			−1.28787
$712$	−30.2462	+	25.9396i	−1.13352	+	0.972128i
$713$		−	2.41131i		−	0.0903042i
$714$	−13.4654	+	3.24245i	−0.503931	+	0.121346i
$715$	25.6509			0.959290
$716$	14.4401	−	7.38235i	0.539651	−	0.275891i
$717$		−	23.2043i		−	0.866580i
$718$	8.52146	−	2.05195i	0.318018	−	0.0765782i
$719$		−	26.4509i		−	0.986450i	−0.869902	−	0.493225i	$-0.835818\pi$
$719$		−	26.4509i		−	0.986450i	0.869902	−	0.493225i	$-0.164182\pi$
$720$	−15.3693	+	21.2755i	−0.572781	+	0.792892i
$721$		−	50.1739i		−	1.86858i
$722$	26.3049	+	5.48200i	0.978967	+	0.204019i
$723$			53.4759i			1.98879i
$724$	−17.8324	−	34.8806i	−0.662735	−	1.29633i
$725$			1.88269i			0.0699215i
$726$	4.34233	+	18.0331i	0.161159	+	0.669270i
$727$		−	44.6589i		−	1.65631i	−0.560500	−	0.828154i	$-0.689391\pi$
$727$		−	44.6589i		−	1.65631i	0.560500	−	0.828154i	$-0.310609\pi$
$728$	−32.8348	−	38.2861i	−1.21694	−	1.41898i
$729$	−18.6155			−0.689464
$730$	0.104402	+	0.433567i	0.00386410	+	0.0160471i
$731$			1.30957i			0.0484361i
$732$	−49.0708	+	25.0870i	−1.81371	+	0.927241i
$733$	−5.12311			−0.189226			−0.0946131	−	0.995514i	$-0.530161\pi$
$733$	−5.12311			−0.189226			−0.0946131	+	0.995514i	$0.530161\pi$
$734$	1.40582	−	0.338519i	0.0518898	−	0.0124950i
$735$	61.8963			2.28308
$736$	−3.90928	+	9.52935i	−0.144098	+	0.351256i
$737$		−	0.677039i		−	0.0249390i
$738$	−19.3693	+	4.66410i	−0.712994	+	0.171688i
$739$		−	25.2042i		−	0.927152i	−0.886057	−	0.463576i	$-0.846566\pi$
$739$		−	25.2042i		−	0.927152i	0.886057	−	0.463576i	$-0.153434\pi$
$740$	−12.8255	−	25.0870i	−0.471473	−	0.922215i
$741$	23.6155	+	37.2919i	0.867538	+	1.36995i
$742$	13.4654	+	55.9200i	0.494332	+	2.05289i
$743$	−11.9188			−0.437257			−0.218628	−	0.975808i	$-0.570158\pi$
$743$	−11.9188			−0.437257			−0.218628	+	0.975808i	$0.570158\pi$
$744$	5.75058	+	6.70531i	0.210826	+	0.245829i
$745$	−7.19224			−0.263503
$746$	−9.21922	+	2.21997i	−0.337540	+	0.0812789i
$747$		−	30.6037i		−	1.11973i
$748$	2.12311	+	4.15286i	0.0776284	+	0.151843i
$749$			23.8813i			0.872604i
$750$	6.87689	+	28.5588i	0.251109	+	1.04282i
$751$	35.6647			1.30142			0.650712	−	0.759324i	$-0.274470\pi$
$751$	35.6647			1.30142			0.650712	+	0.759324i	$0.274470\pi$
$752$	−22.6847	−	16.3873i	−0.827224	−	0.597582i
$753$		−	50.8510i		−	1.85311i
$754$	−1.71401	−	7.11804i	−0.0624206	−	0.259224i
$755$	22.6762			0.825273
$756$	−3.90928	−	7.64666i	−0.142179	−	0.278106i
$757$	−44.8078			−1.62857			−0.814283	−	0.580468i	$-0.802870\pi$
$757$	−44.8078			−1.62857			−0.814283	+	0.580468i	$0.802870\pi$
$758$	5.21922	+	21.6747i	0.189571	+	0.787260i
$759$	−10.0138			−0.363479
$760$	30.1948	+	9.25373i	1.09528	+	0.335668i
$761$	30.6155			1.10981			0.554906	−	0.831913i	$-0.312754\pi$
$761$	30.6155			1.10981			0.554906	+	0.831913i	$0.312754\pi$
$762$	4.71659	+	19.5873i	0.170864	+	0.709574i
$763$	50.6855			1.83494
$764$	7.09612	+	13.8802i	0.256729	+	0.502168i
$765$	6.56155			0.237233
$766$	−7.36932	−	30.6037i	−0.266264	−	1.10576i
$767$			27.1862i			0.981638i
$768$	−11.8551	−	35.8220i	−0.427785	−	1.29261i
$769$	−28.2311			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$769$	−28.2311			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$770$	−8.21327	−	34.1085i	−0.295986	−	1.22919i
$771$		−	40.5061i		−	1.45879i
$772$	−5.00691	−	9.79366i	−0.180203	−	0.352481i
$773$			41.0573i			1.47673i	0.674402	+	0.738365i	$0.264402\pi$
$773$			41.0573i			1.47673i	−0.674402	+	0.738365i	$0.735598\pi$
$774$	4.61219	−	1.11061i	0.165782	−	0.0399199i
$775$	−2.06798			−0.0742839
$776$	−5.17708	+	4.43994i	−0.185846	+	0.159385i
$777$	−53.8617			−1.93228
$778$	4.90251	+	20.3594i	0.175763	+	0.729920i
$779$	12.8255	+	20.2530i	0.459520	+	0.725640i
$780$	23.6155	+	46.1927i	0.845572	+	1.65396i
$781$			4.82262i			0.172567i
$782$	2.50345	−	0.602827i	0.0895233	−	0.0215571i
$783$		−	1.24663i		−	0.0445510i
$784$	−24.0000	+	33.2228i	−0.857143	+	1.18653i
$785$	−15.3693			−0.548554
$786$	−19.3693	+	4.66410i	−0.690881	+	0.166363i
$787$	−26.3588			−0.939591			−0.469796	−	0.882775i	$-0.655672\pi$
$787$	−26.3588			−0.939591			−0.469796	+	0.882775i	$0.655672\pi$
$788$	40.0540	−	20.4772i	1.42686	−	0.729470i
$789$		−	33.6750i		−	1.19886i
$790$	11.3693	+	47.2151i	0.404502	+	1.67984i
$791$	−22.8393			−0.812071
$792$	12.8255	−	10.9993i	0.455733	−	0.390844i
$793$			50.1739i			1.78173i
$794$	−1.30142	−	5.40461i	−0.0461856	−	0.191802i
$795$		−	59.1625i		−	2.09828i
$796$	−4.71165	−	9.21612i	−0.167000	−	0.326657i
$797$			23.2043i			0.821938i	0.911649	+	0.410969i	$0.134809\pi$
$797$			23.2043i			0.821938i	−0.911649	+	0.410969i	$0.865191\pi$
$798$	42.0263	−	43.3427i	1.48771	−	1.53431i
$799$			6.99614i			0.247506i
$800$	8.17252	+	3.35265i	0.288942	+	0.118534i
$801$		−	36.0863i		−	1.27505i
$802$	−10.8769	+	2.61914i	−0.384076	+	0.0924849i
$803$		−	0.287088i		−	0.0101311i
$804$	1.21922	−	0.623316i	0.0429987	−	0.0219827i
$805$	−19.3693			−0.682679
$806$	7.81855	−	1.88269i	0.275397	−	0.0663150i
$807$			12.9698i			0.456559i
$808$	15.1838	+	17.7046i	0.534163	+	0.622846i
$809$	44.3693			1.55994			0.779971	−	0.625816i	$-0.215234\pi$
$809$	44.3693			1.55994			0.779971	+	0.625816i	$0.215234\pi$
$810$	8.58511	+	35.6527i	0.301650	+	1.25271i
$811$	−29.9142			−1.05043			−0.525214	−	0.850970i	$-0.676015\pi$
$811$	−29.9142			−1.05043			−0.525214	+	0.850970i	$0.676015\pi$
$812$	−8.91618	+	4.55831i	−0.312897	+	0.159965i
$813$			52.0566i			1.82571i
$814$	4.24621	+	17.6339i	0.148830	+	0.618068i
$815$			45.1702i			1.58224i
$816$	−5.52390	+	7.64666i	−0.193375	+	0.267687i
$817$	−3.05398	−	4.82262i	−0.106845	−	0.168722i
$818$	37.8078	−	9.10404i	1.32192	−	0.318315i
$819$	45.6786			1.59614
$820$	12.8255	+	25.0870i	0.447884	+	0.876075i
$821$	−28.4233			−0.991980			−0.495990	−	0.868328i	$-0.665195\pi$
$821$	−28.4233			−0.991980			−0.495990	+	0.868328i	$0.665195\pi$
$822$	−9.46543	−	39.3086i	−0.330145	−	1.37104i
$823$			31.1150i			1.08460i	0.840185	+	0.542299i	$0.182446\pi$
$823$			31.1150i			1.08460i	−0.840185	+	0.542299i	$0.817554\pi$
$824$	−22.2462	−	25.9396i	−0.774983	−	0.903649i
$825$			8.58800i			0.298996i
$826$	36.1501	−	8.70488i	1.25782	−	0.302881i
$827$	−49.5242			−1.72212			−0.861062	−	0.508499i	$-0.830200\pi$
$827$	−49.5242			−1.72212			−0.861062	+	0.508499i	$0.830200\pi$
$828$	−4.24621	−	8.30571i	−0.147566	−	0.288643i
$829$			43.4686i			1.50973i	0.655881	+	0.754864i	$0.272297\pi$
$829$			43.4686i			1.50973i	−0.655881	+	0.754864i	$0.727703\pi$
$830$	−42.0775	+	10.1322i	−1.46053	+	0.351693i
$831$	30.7851			1.06792
$832$	−33.9507	−	5.23535i	−1.17703	−	0.181503i
$833$	10.2462			0.355010
$834$	−61.4233	+	14.7906i	−2.12691	+	0.512157i
$835$	27.5559			0.953610
$836$	−17.5032	−	10.3421i	−0.605361	−	0.357690i
$837$	1.36932			0.0473305
$838$	−54.9029	+	13.2205i	−1.89659	+	0.456695i
$839$	−15.8917			−0.548642			−0.274321	−	0.961638i	$-0.588453\pi$
$839$	−15.8917			−0.548642			−0.274321	+	0.961638i	$0.588453\pi$
$840$	53.8617	−	46.1927i	1.85841	−	1.59380i
$841$	27.5464			0.949876
$842$	31.9039	−	7.68240i	1.09948	−	0.264753i
$843$			66.4457i			2.28851i
$844$	44.8712	−	22.9400i	1.54453	−	0.789626i
$845$	13.9309			0.479236
$846$	24.6398	−	5.93322i	0.847134	−	0.203988i
$847$		−	23.0963i		−	0.793599i
$848$	31.7555	+	22.9400i	1.09049	+	0.787762i
$849$			14.0877i			0.483487i
$850$	−0.516994	−	2.14700i	−0.0177327	−	0.0736415i
$851$	10.0138			0.343269
$852$	−8.68466	+	4.43994i	−0.297531	+	0.152110i
$853$	31.3693			1.07406			0.537032	−	0.843562i	$-0.319545\pi$
$853$	31.3693			1.07406			0.537032	+	0.843562i	$0.319545\pi$
$854$	66.7173	−	16.0654i	2.28302	−	0.549747i
$855$	−24.1636	+	15.3019i	−0.826377	+	0.523312i
$856$	10.5885	+	12.3465i	0.361909	+	0.421994i
$857$		−	39.1746i		−	1.33818i	−0.743181	−	0.669090i	$-0.766684\pi$
$857$		−	39.1746i		−	1.33818i	0.743181	−	0.669090i	$-0.233316\pi$
$858$	−7.81855	−	32.4693i	−0.266921	−	1.10848i
$859$		−	45.9056i		−	1.56628i	−0.621847	−	0.783139i	$-0.713617\pi$
$859$		−	45.9056i		−	1.56628i	0.621847	−	0.783139i	$-0.286383\pi$
$860$	−3.05398	−	5.97366i	−0.104140	−	0.203700i
$861$	53.8617			1.83560
$862$	−1.75379	−	7.28323i	−0.0597343	−	0.248068i
$863$	23.4199			0.797223			0.398612	−	0.917120i	$-0.369492\pi$
$863$	23.4199			0.797223			0.398612	+	0.917120i	$0.369492\pi$
$864$	−5.41146	−	2.21997i	−0.184102	−	0.0755250i
$865$			6.17669i			0.210014i
$866$	26.0000	−	6.26075i	0.883516	−	0.212749i
$867$	−37.7327			−1.28147
$868$	−5.00691	−	9.79366i	−0.169946	−	0.332418i
$869$		−	31.2637i		−	1.06055i
$870$	10.0138	−	2.41131i	0.339500	−	0.0817510i
$871$		−	1.24663i		−	0.0422405i
$872$	26.2041	−	22.4730i	0.887382	−	0.761032i
$873$		−	6.17669i		−	0.209049i
$874$	−7.81340	+	8.05815i	−0.264292	+	0.272571i
$875$		−	36.5774i		−	1.23654i
$876$	0.516994	−	0.264308i	0.0174676	−	0.00893013i
$877$		−	12.8820i		−	0.434994i	−0.976061	−	0.217497i	$-0.930211\pi$
$877$		−	12.8820i		−	0.434994i	0.976061	−	0.217497i	$-0.0697893\pi$
$878$	6.49242	+	26.9621i	0.219109	+	0.909927i
$879$		−	10.1265i		−	0.341559i
$880$	−19.3693	−	13.9923i	−0.652940	−	0.471680i
$881$	−10.1771			−0.342875			−0.171437	−	0.985195i	$-0.554841\pi$
$881$	−10.1771			−0.342875			−0.171437	+	0.985195i	$0.554841\pi$
$882$	−8.68951	−	36.0863i	−0.292591	−	1.21509i
$883$			48.5247i			1.63299i	0.577355	+	0.816493i	$0.304085\pi$
$883$			48.5247i			1.63299i	−0.577355	+	0.816493i	$0.695915\pi$
$884$	3.90928	+	7.64666i	0.131483	+	0.257185i
$885$	−38.2462			−1.28563
$886$	16.8213	−	4.05053i	0.565122	−	0.136080i
$887$	−23.0023			−0.772342			−0.386171	−	0.922427i	$-0.626203\pi$
$887$	−23.0023			−0.772342			−0.386171	+	0.922427i	$0.626203\pi$
$888$	−27.8462	+	23.8813i	−0.934457	+	0.801404i
$889$		−	25.0870i		−	0.841390i
$890$	−49.6155	+	11.9473i	−1.66312	+	0.400475i
$891$		−	23.6076i		−	0.790883i
$892$	−39.6377	+	20.2644i	−1.32717	+	0.678501i
$893$	−16.3153	−	25.7640i	−0.545972	−	0.862160i
$894$	2.19224	+	9.10404i	0.0733193	+	0.304485i
$895$	20.7713			0.694308
$896$	3.90928	+	46.8213i	0.130600	+	1.56419i
$897$	−18.4384			−0.615642
$898$	−20.3002	+	4.88825i	−0.677426	+	0.163123i
$899$		−	1.59666i		−	0.0532515i
$900$	−7.12311	+	3.64162i	−0.237437	+	0.121387i
$901$		−	9.79366i		−	0.326274i
$902$	−4.24621	−	17.6339i	−0.141383	−	0.587145i
$903$	−12.8255			−0.426805
$904$	−11.8078	+	10.1265i	−0.392720	+	0.336803i
$905$		−	50.1739i		−	1.66784i
$906$	−6.91185	−	28.7039i	−0.229631	−	0.953624i
$907$	−25.0345			−0.831258			−0.415629	−	0.909534i	$-0.636439\pi$
$907$	−25.0345			−0.831258			−0.415629	+	0.909534i	$0.636439\pi$
$908$	−43.8373	+	22.4114i	−1.45479	+	0.743747i
$909$	−21.1231			−0.700609
$910$	−15.1231	−	62.8041i	−0.501326	−	2.08193i
$911$	40.3813			1.33789			0.668946	−	0.743311i	$-0.266746\pi$
$911$	40.3813			1.33789			0.668946	+	0.743311i	$0.266746\pi$
$912$	2.50996	−	41.0416i	0.0831131	−	1.35902i
$913$	27.8617			0.922089
$914$	1.28355	+	5.33040i	0.0424560	+	0.176314i
$915$	−70.5858			−2.33349
$916$	11.6847	−	5.97366i	0.386072	−	0.197375i
$917$	24.8078			0.819225
$918$	0.342329	+	1.42164i	0.0112985	+	0.0469212i
$919$		−	24.1188i		−	0.795606i	−0.917471	−	0.397803i	$-0.869773\pi$
$919$		−	24.1188i		−	0.795606i	0.917471	−	0.397803i	$-0.130227\pi$
$920$	−10.0138	+	8.58800i	−0.330146	+	0.283138i
$921$	−31.6155			−1.04177
$922$	10.4901	+	43.5637i	0.345471	+	1.43469i
$923$			8.87989i			0.292285i
$924$	−40.6716	+	20.7930i	−1.33800	+	0.684038i
$925$		−	8.58800i		−	0.282372i
$926$	22.4446	−	5.40461i	0.737574	−	0.177606i
$927$	30.9481			1.01647
$928$	−2.58854	+	6.30989i	−0.0849730	+	0.207132i
$929$	−13.3153			−0.436862			−0.218431	−	0.975852i	$-0.570094\pi$
$929$	−13.3153			−0.436862			−0.218431	+	0.975852i	$0.570094\pi$
$930$	2.64861	+	10.9993i	0.0868515	+	0.360682i
$931$	−37.7327	+	23.8947i	−1.23664	+	0.783116i
$932$	−19.2462	+	9.83943i	−0.630431	+	0.322301i
$933$		−	9.79366i		−	0.320630i
$934$	−3.20636	+	0.772087i	−0.104915	+	0.0252635i
$935$			5.97366i			0.195360i
$936$	23.6155	−	20.2530i	0.771898	−	0.661991i
$937$	−13.8769			−0.453338			−0.226669	−	0.973972i	$-0.572784\pi$
$937$	−13.8769			−0.453338			−0.226669	+	0.973972i	$0.572784\pi$
$938$	−1.65767	+	0.399164i	−0.0541249	+	0.0130332i
$939$	−1.03399			−0.0337429
$940$	−16.3153	−	31.9133i	−0.532148	−	1.04090i
$941$			48.2912i			1.57425i	0.616794	+	0.787125i	$0.288431\pi$
$941$			48.2912i			1.57425i	−0.616794	+	0.787125i	$0.711569\pi$
$942$	4.68466	+	19.4547i	0.152634	+	0.633869i
$943$	−10.0138			−0.326095
$944$	14.8298	−	20.5287i	0.482669	−	0.668151i
$945$		−	10.9993i		−	0.357808i
$946$	1.01110	+	4.19895i	0.0328737	+	0.136520i
$947$			21.2755i			0.691361i	0.938352	+	0.345681i	$0.112352\pi$
$947$			21.2755i			0.691361i	−0.938352	+	0.345681i	$0.887648\pi$
$948$	56.3002	−	28.7829i	1.82855	−	0.934825i
$949$		−	0.528616i		−	0.0171596i
$950$	6.91079	+	6.70089i	0.224216	+	0.217406i
$951$			10.1265i			0.328375i
$952$	8.91618	−	7.64666i	0.288975	−	0.247830i
$953$		−	31.2637i		−	1.01273i	−0.862319	−	0.506365i	$-0.830989\pi$
$953$		−	31.2637i		−	1.01273i	0.862319	−	0.506365i	$-0.169011\pi$
$954$	−34.4924	+	8.30571i	−1.11673	+	0.268907i
$955$			19.9660i			0.646083i
$956$	8.95786	+	17.5218i	0.289718	+	0.566696i
$957$	−6.63068			−0.214340
$958$	57.0982	−	13.7491i	1.84476	−	0.444215i
$959$			50.3455i			1.62574i
$960$	7.36520	−	47.7626i	0.237711	−	1.54153i
$961$	−29.2462			−0.943426
$962$	7.81855	+	32.4693i	0.252080	+	1.04685i
$963$	−14.7304			−0.474681
$964$	−20.6440	−	40.3803i	−0.664899	−	1.30056i
$965$		−	14.0877i		−	0.453498i
$966$	5.90388	+	24.5180i	0.189954	+	0.788853i
$967$			10.3507i			0.332855i	0.986054	+	0.166428i	$0.0532232\pi$
$967$			10.3507i			0.332855i	−0.986054	+	0.166428i	$0.946777\pi$
$968$	−10.2405	−	11.9407i	−0.329142	−	0.383787i
$969$	−8.68466	+	5.49966i	−0.278991	+	0.176674i
$970$	−8.49242	+	2.04496i	−0.272675	+	0.0656597i
$971$	−0.580639			−0.0186336			−0.00931679	−	0.999957i	$-0.502966\pi$
$971$	−0.580639			−0.0186336			−0.00931679	+	0.999957i	$0.502966\pi$
$972$	36.9890	−	18.9103i	1.18642	−	0.606547i
$973$	78.6695			2.52203
$974$	6.24621	+	25.9396i	0.200142	+	0.831159i
$975$			15.8131i			0.506424i
$976$	27.3693	−	37.8869i	0.876070	−	1.21273i
$977$			50.8510i			1.62687i	0.581658	+	0.813433i	$0.302404\pi$
$977$			50.8510i			1.62687i	−0.581658	+	0.813433i	$0.697596\pi$
$978$	57.1771	−	13.7681i	1.82832	−	0.440256i
$979$	32.8531			1.04999
$980$	−46.7386	+	23.8947i	−1.49301	+	0.763287i
$981$			31.2637i			0.998172i
$982$	−29.2520	+	7.04383i	−0.933469	+	0.224778i
$983$	−6.78456			−0.216394			−0.108197	−	0.994129i	$-0.534508\pi$
$983$	−6.78456			−0.216394			−0.108197	+	0.994129i	$0.534508\pi$
$984$	27.8462	−	23.8813i	0.887704	−	0.761309i
$985$	57.6155			1.83578
$986$	1.65767	−	0.399164i	0.0527910	−	0.0127120i
$987$	−68.5178			−2.18095
$988$	−32.2287	−	19.0430i	−1.02533	−	0.605838i
$989$	2.38447			0.0758218
$990$	21.0387	−	5.06609i	0.668655	−	0.161011i
$991$	0.417609			0.0132658			0.00663289	−	0.999978i	$-0.497889\pi$
$991$	0.417609			0.0132658			0.00663289	+	0.999978i	$0.497889\pi$
$992$	−6.93087	−	2.84329i	−0.220055	−	0.0902745i
$993$	−56.3002			−1.78663
$994$	11.8078	−	2.84329i	0.374520	−	0.0901836i
$995$		−	13.2569i		−	0.420272i
$996$	25.6509	+	50.1739i	0.812780	+	1.58982i
$997$	41.5464			1.31579			0.657894	−	0.753111i	$-0.271448\pi$
$997$	41.5464			1.31579			0.657894	+	0.753111i	$0.271448\pi$
$998$	1.80054	−	0.433567i	0.0569952	−	0.0137243i
$999$			5.68658i			0.179915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.d.a.75.6	yes	8
3.2	odd	2		684.2.f.b.379.3		8
4.3	odd	2	inner	76.2.d.a.75.4	yes	8
8.3	odd	2		1216.2.h.d.1215.8		8
8.5	even	2		1216.2.h.d.1215.1		8
12.11	even	2		684.2.f.b.379.5		8
19.18	odd	2	inner	76.2.d.a.75.3	✓	8
57.56	even	2		684.2.f.b.379.6		8
76.75	even	2	inner	76.2.d.a.75.5	yes	8
152.37	odd	2		1216.2.h.d.1215.7		8
152.75	even	2		1216.2.h.d.1215.2		8
228.227	odd	2		684.2.f.b.379.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.d.a.75.3	✓	8	19.18	odd	2	inner
76.2.d.a.75.4	yes	8	4.3	odd	2	inner
76.2.d.a.75.5	yes	8	76.75	even	2	inner
76.2.d.a.75.6	yes	8	1.1	even	1	trivial
684.2.f.b.379.3		8	3.2	odd	2
684.2.f.b.379.4		8	228.227	odd	2
684.2.f.b.379.5		8	12.11	even	2
684.2.f.b.379.6		8	57.56	even	2
1216.2.h.d.1215.1		8	8.5	even	2
1216.2.h.d.1215.2		8	152.75	even	2
1216.2.h.d.1215.7		8	152.37	odd	2
1216.2.h.d.1215.8		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.331077 + 1.37491i) q^{2} +2.35829 q^{3} +(-1.78078 + 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 + 3.24245i) q^{6} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +O(q^{10})\)	\(q+(0.331077 + 1.37491i) q^{2} +2.35829 q^{3} +(-1.78078 + 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 + 3.24245i) q^{6} -4.15286i q^{7} +(-1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +(-0.848071 - 3.52191i) q^{10} +2.33205i q^{11} +(-4.19960 + 2.14700i) q^{12} +4.29400i q^{13} +(5.70982 - 1.37491i) q^{14} -6.04090 q^{15} +(2.34233 - 3.24245i) q^{16} -1.00000 q^{17} +(0.848071 + 3.52191i) q^{18} +(3.68260 - 2.33205i) q^{19} +(4.56155 - 2.33205i) q^{20} -9.79366i q^{21} +(-3.20636 + 0.772087i) q^{22} +1.82081i q^{23} +(-4.34233 - 5.06326i) q^{24} +1.56155 q^{25} +(-5.90388 + 1.42164i) q^{26} -1.03399 q^{27} +(3.78078 + 7.39531i) q^{28} +1.20565i q^{29} +(-2.00000 - 8.30571i) q^{30} -1.32431 q^{31} +(5.23358 + 2.14700i) q^{32} +5.49966i q^{33} +(-0.331077 - 1.37491i) q^{34} +10.6378i q^{35} +(-4.56155 + 2.33205i) q^{36} -5.49966i q^{37} +(4.42559 + 4.29117i) q^{38} +10.1265i q^{39} +(4.71659 + 5.49966i) q^{40} +5.49966i q^{41} +(13.4654 - 3.24245i) q^{42} -1.30957i q^{43} +(-2.12311 - 4.15286i) q^{44} -6.56155 q^{45} +(-2.50345 + 0.602827i) q^{46} -6.99614i q^{47} +(5.52390 - 7.64666i) q^{48} -10.2462 q^{49} +(0.516994 + 2.14700i) q^{50} -2.35829 q^{51} +(-3.90928 - 7.64666i) q^{52} +9.79366i q^{53} +(-0.342329 - 1.42164i) q^{54} -5.97366i q^{55} +(-8.91618 + 7.64666i) q^{56} +(8.68466 - 5.49966i) q^{57} +(-1.65767 + 0.399164i) q^{58} +6.33122 q^{59} +(10.7575 - 5.49966i) q^{60} +11.6847 q^{61} +(-0.438447 - 1.82081i) q^{62} -10.6378i q^{63} +(-1.21922 + 7.90655i) q^{64} -10.9993i q^{65} +(-7.56155 + 1.82081i) q^{66} -0.290319 q^{67} +(1.78078 - 0.910404i) q^{68} +4.29400i q^{69} +(-14.6260 + 3.52191i) q^{70} +2.06798 q^{71} +(-4.71659 - 5.49966i) q^{72} -0.123106 q^{73} +(7.56155 - 1.82081i) q^{74} +3.68260 q^{75} +(-4.43478 + 7.50551i) q^{76} +9.68466 q^{77} +(-13.9231 + 3.35265i) q^{78} -13.4061 q^{79} +(-6.00000 + 8.30571i) q^{80} -10.1231 q^{81} +(-7.56155 + 1.82081i) q^{82} -11.9473i q^{83} +(8.91618 + 17.4403i) q^{84} +2.56155 q^{85} +(1.80054 - 0.433567i) q^{86} +2.84329i q^{87} +(5.00691 - 4.29400i) q^{88} -14.0877i q^{89} +(-2.17238 - 9.02157i) q^{90} +17.8324 q^{91} +(-1.65767 - 3.24245i) q^{92} -3.12311 q^{93} +(9.61909 - 2.31626i) q^{94} +(-9.43318 + 5.97366i) q^{95} +(12.3423 + 5.06326i) q^{96} -2.41131i q^{97} +(-3.39228 - 14.0877i) q^{98} +5.97366i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9	\( 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} - 6 q^{16} - 8 q^{17} + 20 q^{20} - 10 q^{24} - 4 q^{25} - 6 q^{26} + 22 q^{28} - 16 q^{30} - 20 q^{36} + 18 q^{38} + 50 q^{42} + 16 q^{44} - 36 q^{45} - 16 q^{49} + 22 q^{54} + 20 q^{57} - 38 q^{58} + 44 q^{61} - 20 q^{62} - 18 q^{64} - 44 q^{66} + 6 q^{68} + 32 q^{73} + 44 q^{74} - 16 q^{76} + 28 q^{77} - 48 q^{80} - 48 q^{81} - 44 q^{82} + 4 q^{85} - 38 q^{92} + 8 q^{93} + 74 q^{96}+O(q^{100}) \) 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9 - 6 * q^16 - 8 * q^17 + 20 * q^20 - 10 * q^24 - 4 * q^25 - 6 * q^26 + 22 * q^28 - 16 * q^30 - 20 * q^36 + 18 * q^38 + 50 * q^42 + 16 * q^44 - 36 * q^45 - 16 * q^49 + 22 * q^54 + 20 * q^57 - 38 * q^58 + 44 * q^61 - 20 * q^62 - 18 * q^64 - 44 * q^66 + 6 * q^68 + 32 * q^73 + 44 * q^74 - 16 * q^76 + 28 * q^77 - 48 * q^80 - 48 * q^81 - 44 * q^82 + 4 * q^85 - 38 * q^92 + 8 * q^93 + 74 * q^96

Introduction

L-functions

Modular forms

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