LMFDB - Embedded newform 572.2.e.b.131.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.13
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24299 - 0.674518i) q^{2} -2.42300i q^{3} +(1.09005 + 1.67684i) q^{4} -0.123164 q^{5} +(-1.63435 + 3.01176i) q^{6} -2.37508 q^{7} +(-0.223868 - 2.81955i) q^{8} -2.87092 q^{9} +O(q^{10})$	\(q+(-1.24299 - 0.674518i) q^{2} -2.42300i q^{3} +(1.09005 + 1.67684i) q^{4} -0.123164 q^{5} +(-1.63435 + 3.01176i) q^{6} -2.37508 q^{7} +(-0.223868 - 2.81955i) q^{8} -2.87092 q^{9} +(0.153091 + 0.0830761i) q^{10} +(-2.22776 + 2.45705i) q^{11} +(4.06297 - 2.64119i) q^{12} -1.00000i q^{13} +(2.95220 + 1.60203i) q^{14} +0.298425i q^{15} +(-1.62357 + 3.65568i) q^{16} +5.72225i q^{17} +(3.56852 + 1.93648i) q^{18} -3.87930 q^{19} +(-0.134255 - 0.206526i) q^{20} +5.75481i q^{21} +(4.42641 - 1.55143i) q^{22} -3.35974i q^{23} +(-6.83177 + 0.542431i) q^{24} -4.98483 q^{25} +(-0.674518 + 1.24299i) q^{26} -0.312771i q^{27} +(-2.58896 - 3.98262i) q^{28} +7.91062i q^{29} +(0.201293 - 0.370940i) q^{30} +2.43566i q^{31} +(4.48391 - 3.44885i) q^{32} +(5.95343 + 5.39785i) q^{33} +(3.85976 - 7.11271i) q^{34} +0.292524 q^{35} +(-3.12945 - 4.81406i) q^{36} -9.98686 q^{37} +(4.82194 + 2.61666i) q^{38} -2.42300 q^{39} +(0.0275724 + 0.347267i) q^{40} -11.6600i q^{41} +(3.88172 - 7.15318i) q^{42} +5.63323 q^{43} +(-6.54845 - 1.05728i) q^{44} +0.353593 q^{45} +(-2.26620 + 4.17613i) q^{46} +8.44267i q^{47} +(8.85771 + 3.93391i) q^{48} -1.35900 q^{49} +(6.19610 + 3.36236i) q^{50} +13.8650 q^{51} +(1.67684 - 1.09005i) q^{52} +14.4069 q^{53} +(-0.210969 + 0.388771i) q^{54} +(0.274379 - 0.302620i) q^{55} +(0.531703 + 6.69666i) q^{56} +9.39954i q^{57} +(5.33586 - 9.83283i) q^{58} +12.2130i q^{59} +(-0.500411 + 0.325299i) q^{60} +1.34026i q^{61} +(1.64290 - 3.02750i) q^{62} +6.81865 q^{63} +(-7.89977 + 1.26241i) q^{64} +0.123164i q^{65} +(-3.75911 - 10.7252i) q^{66} -4.01039i q^{67} +(-9.59530 + 6.23755i) q^{68} -8.14064 q^{69} +(-0.363604 - 0.197312i) q^{70} -3.53902i q^{71} +(0.642705 + 8.09470i) q^{72} -4.62922i q^{73} +(12.4136 + 6.73631i) q^{74} +12.0782i q^{75} +(-4.22864 - 6.50496i) q^{76} +(5.29110 - 5.83569i) q^{77} +(3.01176 + 1.63435i) q^{78} -6.73595 q^{79} +(0.199965 - 0.450247i) q^{80} -9.37059 q^{81} +(-7.86490 + 14.4933i) q^{82} -1.78490 q^{83} +(-9.64989 + 6.27304i) q^{84} -0.704774i q^{85} +(-7.00205 - 3.79971i) q^{86} +19.1674 q^{87} +(7.42651 + 5.73123i) q^{88} -3.09609 q^{89} +(-0.439513 - 0.238505i) q^{90} +2.37508i q^{91} +(5.63374 - 3.66229i) q^{92} +5.90160 q^{93} +(5.69473 - 10.4942i) q^{94} +0.477789 q^{95} +(-8.35655 - 10.8645i) q^{96} -15.4918 q^{97} +(1.68922 + 0.916667i) q^{98} +(6.39570 - 7.05398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.24299	−	0.674518i	−0.878927	−	0.476956i
$2$	−1.24299	−	0.674518i	−0.878927	−	0.476956i
$3$		−	2.42300i		−	1.39892i	−0.714673	−	0.699459i	$-0.753424\pi$
$3$		−	2.42300i		−	1.39892i	0.714673	−	0.699459i	$-0.246576\pi$
$4$	1.09005	+	1.67684i	0.545026	+	0.838419i
$5$	−0.123164			−0.0550805			−0.0275403	−	0.999621i	$-0.508767\pi$
$5$	−0.123164			−0.0550805			−0.0275403	+	0.999621i	$0.508767\pi$
$6$	−1.63435	+	3.01176i	−0.667222	+	1.22955i
$7$	−2.37508			−0.897696			−0.448848	−	0.893608i	$-0.648165\pi$
$7$	−2.37508			−0.897696			−0.448848	+	0.893608i	$0.648165\pi$
$8$	−0.223868	−	2.81955i	−0.0791491	−	0.996863i
$9$	−2.87092			−0.956972
$10$	0.153091	+	0.0830761i	0.0484118	+	0.0262710i
$11$	−2.22776	+	2.45705i	−0.671694	+	0.740829i
$11$	−2.22776	+	2.45705i	−0.671694	+	0.740829i
$12$	4.06297	−	2.64119i	1.17288	−	0.762447i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.95220	+	1.60203i	0.789009	+	0.428161i
$15$			0.298425i			0.0770531i
$16$	−1.62357	+	3.65568i	−0.405893	+	0.913920i
$17$			5.72225i			1.38785i	0.720047	+	0.693925i	$0.244120\pi$
$17$			5.72225i			1.38785i	−0.720047	+	0.693925i	$0.755880\pi$
$18$	3.56852	+	1.93648i	0.841109	+	0.456433i
$19$	−3.87930			−0.889973			−0.444986	−	0.895537i	$-0.646791\pi$
$19$	−3.87930			−0.889973			−0.444986	+	0.895537i	$0.646791\pi$
$20$	−0.134255	−	0.206526i	−0.0300203	−	0.0461805i
$21$			5.75481i			1.25580i
$22$	4.42641	−	1.55143i	0.943713	−	0.330766i
$23$		−	3.35974i		−	0.700554i	−0.936646	−	0.350277i	$-0.886087\pi$
$23$		−	3.35974i		−	0.700554i	0.936646	−	0.350277i	$-0.113913\pi$
$24$	−6.83177	+	0.542431i	−1.39453	+	0.110723i
$25$	−4.98483			−0.996966
$26$	−0.674518	+	1.24299i	−0.132284	+	0.243771i
$27$		−	0.312771i		−	0.0601928i
$28$	−2.58896	−	3.98262i	−0.489267	−	0.752645i
$29$			7.91062i			1.46897i	0.678627	+	0.734483i	$0.262575\pi$
$29$			7.91062i			1.46897i	−0.678627	+	0.734483i	$0.737425\pi$
$30$	0.201293	−	0.370940i	0.0367509	−	0.0677241i
$31$			2.43566i			0.437457i	0.975786	+	0.218729i	$0.0701910\pi$
$31$			2.43566i			0.437457i	−0.975786	+	0.218729i	$0.929809\pi$
$32$	4.48391	−	3.44885i	0.792651	−	0.609676i
$33$	5.95343	+	5.39785i	1.03636	+	0.939645i
$34$	3.85976	−	7.11271i	0.661944	−	1.21982i
$35$	0.292524			0.0494455
$36$	−3.12945	−	4.81406i	−0.521575	−	0.802344i
$37$	−9.98686			−1.64183			−0.820915	−	0.571051i	$-0.806536\pi$
$37$	−9.98686			−1.64183			−0.820915	+	0.571051i	$0.806536\pi$
$38$	4.82194	+	2.61666i	0.782221	+	0.424478i
$39$	−2.42300			−0.387990
$40$	0.0275724	+	0.347267i	0.00435957	+	0.0549077i
$41$		−	11.6600i		−	1.82099i	−0.413519	−	0.910496i	$-0.635700\pi$
$41$		−	11.6600i		−	1.82099i	0.413519	−	0.910496i	$-0.364300\pi$
$42$	3.88172	−	7.15318i	0.598963	−	1.10376i
$43$	5.63323			0.859060			0.429530	−	0.903053i	$-0.358679\pi$
$43$	5.63323			0.859060			0.429530	+	0.903053i	$0.358679\pi$
$44$	−6.54845	−	1.05728i	−0.987216	−	0.159390i
$45$	0.353593			0.0527105
$46$	−2.26620	+	4.17613i	−0.334134	+	0.615736i
$47$			8.44267i			1.23149i	0.787945	+	0.615745i	$0.211145\pi$
$47$			8.44267i			1.23149i	−0.787945	+	0.615745i	$0.788855\pi$
$48$	8.85771	+	3.93391i	1.27850	+	0.567812i
$49$	−1.35900			−0.194142
$50$	6.19610	+	3.36236i	0.876261	+	0.475509i
$51$	13.8650			1.94149
$52$	1.67684	−	1.09005i	0.232536	−	0.151163i
$53$	14.4069			1.97895			0.989473	−	0.144720i	$-0.0462282\pi$
$53$	14.4069			1.97895			0.989473	+	0.144720i	$0.0462282\pi$
$54$	−0.210969	+	0.388771i	−0.0287093	+	0.0529050i
$55$	0.274379	−	0.302620i	0.0369973	−	0.0408052i
$56$	0.531703	+	6.69666i	0.0710518	+	0.894879i
$57$			9.39954i			1.24500i
$58$	5.33586	−	9.83283i	0.700632	−	1.29111i
$59$			12.2130i			1.59000i	0.606613	+	0.794998i	$0.292528\pi$
$59$			12.2130i			1.59000i	−0.606613	+	0.794998i	$0.707472\pi$
$60$	−0.500411	+	0.325299i	−0.0646028	+	0.0419960i
$61$			1.34026i			0.171603i	0.996312	+	0.0858017i	$0.0273451\pi$
$61$			1.34026i			0.171603i	−0.996312	+	0.0858017i	$0.972655\pi$
$62$	1.64290	−	3.02750i	0.208648	−	0.384493i
$63$	6.81865			0.859070
$64$	−7.89977	+	1.26241i	−0.987471	+	0.157802i
$65$			0.123164i			0.0152766i
$66$	−3.75911	−	10.7252i	−0.462714	−	1.32018i
$67$		−	4.01039i		−	0.489947i	−0.969530	−	0.244974i	$-0.921221\pi$
$67$		−	4.01039i		−	0.489947i	0.969530	−	0.244974i	$-0.0787793\pi$
$68$	−9.59530	+	6.23755i	−1.16360	+	0.756415i
$69$	−8.14064			−0.980018
$70$	−0.363604	−	0.197312i	−0.0434590	−	0.0235833i
$71$		−	3.53902i		−	0.420004i	−0.977701	−	0.210002i	$-0.932653\pi$
$71$		−	3.53902i		−	0.420004i	0.977701	−	0.210002i	$-0.0673471\pi$
$72$	0.642705	+	8.09470i	0.0757435	+	0.953970i
$73$		−	4.62922i		−	0.541809i	−0.962606	−	0.270905i	$-0.912677\pi$
$73$		−	4.62922i		−	0.541809i	0.962606	−	0.270905i	$-0.0873228\pi$
$74$	12.4136	+	6.73631i	1.44305	+	0.783080i
$75$			12.0782i			1.39467i
$76$	−4.22864	−	6.50496i	−0.485058	−	0.746170i
$77$	5.29110	−	5.83569i	0.602977	−	0.665039i
$78$	3.01176	+	1.63435i	0.341015	+	0.185054i
$79$	−6.73595			−0.757854			−0.378927	−	0.925427i	$-0.623707\pi$
$79$	−6.73595			−0.757854			−0.378927	+	0.925427i	$0.623707\pi$
$80$	0.199965	−	0.450247i	0.0223568	−	0.0503392i
$81$	−9.37059			−1.04118
$82$	−7.86490	+	14.4933i	−0.868533	+	1.60052i
$83$	−1.78490			−0.195918			−0.0979589	−	0.995190i	$-0.531231\pi$
$83$	−1.78490			−0.195918			−0.0979589	+	0.995190i	$0.531231\pi$
$84$	−9.64989	+	6.27304i	−1.05289	+	0.684445i
$85$		−	0.704774i		−	0.0764435i
$86$	−7.00205	−	3.79971i	−0.755051	−	0.409734i
$87$	19.1674			2.05496
$88$	7.42651	+	5.73123i	0.791668	+	0.610951i
$89$	−3.09609			−0.328185			−0.164092	−	0.986445i	$-0.552470\pi$
$89$	−3.09609			−0.328185			−0.164092	+	0.986445i	$0.552470\pi$
$90$	−0.439513	−	0.238505i	−0.0463287	−	0.0251406i
$91$			2.37508i			0.248976i
$92$	5.63374	−	3.66229i	0.587358	−	0.381820i
$93$	5.90160			0.611967
$94$	5.69473	−	10.4942i	0.587367	−	1.08239i
$95$	0.477789			0.0490201
$96$	−8.35655	−	10.8645i	−0.852887	−	1.10885i
$97$	−15.4918			−1.57295			−0.786476	−	0.617621i	$-0.788096\pi$
$97$	−15.4918			−1.57295			−0.786476	+	0.617621i	$0.788096\pi$
$98$	1.68922	+	0.916667i	0.170637	+	0.0925974i
$99$	6.39570	−	7.05398i	0.642792	−	0.708952i
$100$	−5.43372	−	8.35875i	−0.543372	−	0.835875i
$101$			2.45807i			0.244588i	0.992494	+	0.122294i	$0.0390250\pi$
$101$			2.45807i			0.244588i	−0.992494	+	0.122294i	$0.960975\pi$
$102$	−17.2341	−	9.35219i	−1.70643	−	0.926005i
$103$		−	10.3831i		−	1.02308i	−0.859261	−	0.511538i	$-0.829076\pi$
$103$		−	10.3831i		−	1.02308i	0.859261	−	0.511538i	$-0.170924\pi$
$104$	−2.81955	+	0.223868i	−0.276480	+	0.0219520i
$105$		−	0.708784i		−	0.0691703i
$106$	−17.9077	−	9.71773i	−1.73935	−	0.943870i
$107$	5.37504			0.519625			0.259813	−	0.965659i	$-0.416339\pi$
$107$	5.37504			0.519625			0.259813	+	0.965659i	$0.416339\pi$
$108$	0.524466	−	0.340936i	0.0504668	−	0.0328066i
$109$			1.79803i			0.172220i	0.996286	+	0.0861099i	$0.0274436\pi$
$109$			1.79803i			0.172220i	−0.996286	+	0.0861099i	$0.972556\pi$
$110$	−0.545173	+	0.191080i	−0.0519802	+	0.0182187i
$111$			24.1981i			2.29679i
$112$	3.85612	−	8.68254i	0.364369	−	0.820422i
$113$	−12.7384			−1.19833			−0.599164	−	0.800626i	$-0.704500\pi$
$113$	−12.7384			−1.19833			−0.599164	+	0.800626i	$0.704500\pi$
$114$	6.34015	−	11.6835i	0.593810	−	1.09426i
$115$			0.413798i			0.0385869i
$116$	−13.2648	+	8.62299i	−1.23161	+	0.800625i
$117$			2.87092i			0.265416i
$118$	8.23787	−	15.1806i	0.758358	−	1.39749i
$119$		−	13.5908i		−	1.24587i
$120$	0.841427	−	0.0668078i	0.0768114	−	0.00609869i
$121$	−1.07419	−	10.9474i	−0.0976538	−	0.995220i
$122$	0.904032	−	1.66594i	0.0818472	−	0.150827i
$123$	−28.2522			−2.54742
$124$	−4.08421	+	2.65500i	−0.366773	+	0.238426i
$125$	1.22977			0.109994
$126$	−8.47552	−	4.59930i	−0.755060	−	0.409738i
$127$	7.85305			0.696846			0.348423	−	0.937337i	$-0.386717\pi$
$127$	7.85305			0.696846			0.348423	+	0.937337i	$0.386717\pi$
$128$	10.6709	+	3.75936i	0.943179	+	0.332284i
$129$		−	13.6493i		−	1.20175i
$130$	0.0830761	−	0.153091i	0.00728626	−	0.0134270i
$131$	−17.1207			−1.49585			−0.747923	−	0.663786i	$-0.768949\pi$
$131$	−17.1207			−1.49585			−0.747923	+	0.663786i	$0.768949\pi$
$132$	−2.56178	+	15.8669i	−0.222974	+	1.38103i
$133$	9.21365			0.798925
$134$	−2.70508	+	4.98488i	−0.233683	+	0.430628i
$135$			0.0385220i			0.00331545i
$136$	16.1342	−	1.28103i	1.38350	−	0.109847i
$137$	−11.8315			−1.01084			−0.505418	−	0.862875i	$-0.668662\pi$
$137$	−11.8315			−1.01084			−0.505418	+	0.862875i	$0.668662\pi$
$138$	10.1187	+	5.49101i	0.861365	+	0.467426i
$139$	−10.2699			−0.871080			−0.435540	−	0.900169i	$-0.643443\pi$
$139$	−10.2699			−0.871080			−0.435540	+	0.900169i	$0.643443\pi$
$140$	0.318866	+	0.490515i	0.0269491	+	0.0414561i
$141$	20.4566			1.72275
$142$	−2.38713	+	4.39897i	−0.200324	+	0.369153i
$143$	2.45705	+	2.22776i	0.205469	+	0.186294i
$144$	4.66114	−	10.4952i	0.388429	−	0.874596i
$145$		−	0.974302i		−	0.0809114i
$146$	−3.12249	+	5.75408i	−0.258419	+	0.476211i
$147$			3.29285i			0.271589i
$148$	−10.8862	−	16.7463i	−0.894840	−	1.37654i
$149$		−	12.4784i		−	1.02227i	−0.859501	−	0.511133i	$-0.829226\pi$
$149$		−	12.4784i		−	1.02227i	0.859501	−	0.511133i	$-0.170774\pi$
$150$	8.14698	−	15.0131i	0.665198	−	1.22582i
$151$	6.09748			0.496206			0.248103	−	0.968734i	$-0.420193\pi$
$151$	6.09748			0.496206			0.248103	+	0.968734i	$0.420193\pi$
$152$	0.868450	+	10.9379i	0.0704406	+	0.887181i
$153$		−	16.4281i		−	1.32813i
$154$	−10.5131	+	3.68477i	−0.847167	+	0.296927i
$155$		−	0.299985i		−	0.0240954i
$156$	−2.64119	−	4.06297i	−0.211465	−	0.325298i
$157$	−6.21999			−0.496409			−0.248205	−	0.968708i	$-0.579841\pi$
$157$	−6.21999			−0.496409			−0.248205	+	0.968708i	$0.579841\pi$
$158$	8.37273	+	4.54352i	0.666099	+	0.361463i
$159$		−	34.9080i		−	2.76838i
$160$	−0.552255	+	0.424773i	−0.0436596	+	0.0335813i
$161$			7.97965i			0.628885i
$162$	11.6476	+	6.32063i	0.915118	+	0.496595i
$163$		−	10.7050i		−	0.838479i	−0.907876	−	0.419240i	$-0.862297\pi$
$163$		−	10.7050i		−	0.838479i	0.907876	−	0.419240i	$-0.137703\pi$
$164$	19.5520	−	12.7100i	1.52675	−	0.992487i
$165$	−0.733246	−	0.664820i	−0.0570831	−	0.0517561i
$166$	2.21861	+	1.20394i	0.172198	+	0.0934442i
$167$	−2.63563			−0.203952			−0.101976	−	0.994787i	$-0.532516\pi$
$167$	−2.63563			−0.203952			−0.101976	+	0.994787i	$0.532516\pi$
$168$	16.2260	−	1.28832i	1.25186	−	0.0993957i
$169$	−1.00000			−0.0769231
$170$	−0.475383	+	0.876028i	−0.0364602	+	0.0671883i
$171$	11.1371			0.851679
$172$	6.14051	+	9.44602i	0.468210	+	0.720252i
$173$			11.2619i			0.856225i	0.903725	+	0.428113i	$0.140821\pi$
$173$			11.2619i			0.856225i	−0.903725	+	0.428113i	$0.859179\pi$
$174$	−23.8249	−	12.9288i	−1.80616	−	0.980127i
$175$	11.8394			0.894972
$176$	−5.36527	−	12.1332i	−0.404422	−	0.914572i
$177$	29.5920			2.22427
$178$	3.84841	+	2.08837i	0.288451	+	0.156530i
$179$			10.5250i			0.786672i	0.919395	+	0.393336i	$0.128679\pi$
$179$			10.5250i			0.786672i	−0.919395	+	0.393336i	$0.871321\pi$
$180$	0.385434	+	0.592918i	0.0287286	+	0.0441935i
$181$	−8.14357			−0.605307			−0.302654	−	0.953101i	$-0.597873\pi$
$181$	−8.14357			−0.605307			−0.302654	+	0.953101i	$0.597873\pi$
$182$	1.60203	−	2.95220i	0.118751	−	0.218832i
$183$	3.24746			0.240059
$184$	−9.47297	+	0.752137i	−0.698357	+	0.0554483i
$185$	1.23002			0.0904328
$186$	−7.33563	−	3.98073i	−0.537875	−	0.291881i
$187$	−14.0599	−	12.7478i	−1.02816	−	0.932211i
$188$	−14.1570	+	9.20295i	−1.03251	+	0.671194i
$189$			0.742855i			0.0540348i
$190$	−0.593888	−	0.322277i	−0.0430851	−	0.0233804i
$191$		−	17.9251i		−	1.29701i	−0.761209	−	0.648507i	$-0.775394\pi$
$191$		−	17.9251i		−	1.29701i	0.761209	−	0.648507i	$-0.224606\pi$
$192$	3.05882	+	19.1411i	0.220752	+	1.38139i
$193$			12.4688i			0.897521i	0.893652	+	0.448760i	$0.148134\pi$
$193$			12.4688i			0.897521i	−0.893652	+	0.448760i	$0.851866\pi$
$194$	19.2561	+	10.4495i	1.38251	+	0.750229i
$195$	0.298425			0.0213707
$196$	−1.48138	−	2.27882i	−0.105813	−	0.162773i
$197$			19.6209i			1.39793i	0.715156	+	0.698965i	$0.246356\pi$
$197$			19.6209i			1.39793i	−0.715156	+	0.698965i	$0.753644\pi$
$198$	−12.7078	+	4.45402i	−0.903107	+	0.316534i
$199$		−	2.15098i		−	0.152479i	−0.997090	−	0.0762395i	$-0.975709\pi$
$199$		−	2.15098i		−	0.152479i	0.997090	−	0.0762395i	$-0.0242914\pi$
$200$	1.11594	+	14.0550i	0.0789090	+	0.993838i
$201$	−9.71717			−0.685396
$202$	1.65801	−	3.05536i	0.116658	−	0.214975i
$203$		−	18.7884i		−	1.31868i
$204$	15.1136	+	23.2494i	1.05816	+	1.62778i
$205$			1.43609i			0.100301i
$206$	−7.00357	+	12.9061i	−0.487962	+	0.899209i
$207$			9.64553i			0.670411i
$208$	3.65568	+	1.62357i	0.253476	+	0.112575i
$209$	8.64214	−	9.53164i	0.597789	−	0.659317i
$210$	−0.478087	+	0.881012i	−0.0329912	+	0.0607956i
$211$	−1.05066			−0.0723305			−0.0361652	−	0.999346i	$-0.511514\pi$
$211$	−1.05066			−0.0723305			−0.0361652	+	0.999346i	$0.511514\pi$
$212$	15.7043	+	24.1581i	1.07858	+	1.65919i
$213$	−8.57503			−0.587551
$214$	−6.68113	−	3.62556i	−0.456713	−	0.247838i
$215$	−0.693810			−0.0473174
$216$	−0.881874	+	0.0700192i	−0.0600039	+	0.00476420i
$217$		−	5.78489i		−	0.392704i
$218$	1.21280	−	2.23493i	0.0821413	−	0.151369i
$219$	−11.2166			−0.757947
$220$	0.806531	+	0.130218i	0.0543763	+	0.00877931i
$221$	5.72225			0.384920
$222$	16.3221	−	30.0781i	1.09547	−	2.01871i
$223$		−	5.67581i		−	0.380081i	−0.981776	−	0.190040i	$-0.939138\pi$
$223$		−	5.67581i		−	0.380081i	0.981776	−	0.190040i	$-0.0608619\pi$
$224$	−10.6496	+	8.19129i	−0.711559	+	0.547304i
$225$	14.3110			0.954069
$226$	15.8337	+	8.59228i	1.05324	+	0.571550i
$227$	−23.0123			−1.52738			−0.763691	−	0.645582i	$-0.776615\pi$
$227$	−23.0123			−1.52738			−0.763691	+	0.645582i	$0.776615\pi$
$228$	−15.7615	+	10.2460i	−1.04383	+	0.678557i
$229$	2.46910			0.163163			0.0815814	−	0.996667i	$-0.474003\pi$
$229$	2.46910			0.163163			0.0815814	+	0.996667i	$0.474003\pi$
$230$	0.279114	−	0.514348i	0.0184042	−	0.0339151i
$231$	−14.1399	−	12.8203i	−0.930335	−	0.843515i
$232$	22.3044	−	1.77093i	1.46436	−	0.116267i
$233$		−	16.2972i		−	1.06766i	−0.845591	−	0.533831i	$-0.820752\pi$
$233$		−	16.2972i		−	1.06766i	0.845591	−	0.533831i	$-0.179248\pi$
$234$	1.93648	−	3.56852i	0.126592	−	0.233282i
$235$		−	1.03983i		−	0.0678311i
$236$	−20.4792	+	13.3128i	−1.33308	+	0.866589i
$237$			16.3212i			1.06018i
$238$	−9.16724	+	16.8933i	−0.594224	+	1.09503i
$239$	−25.6039			−1.65618			−0.828088	−	0.560597i	$-0.810572\pi$
$239$	−25.6039			−1.65618			−0.828088	+	0.560597i	$0.810572\pi$
$240$	−1.09095	−	0.484516i	−0.0704204	−	0.0312753i
$241$			1.89733i			0.122217i	0.998131	+	0.0611087i	$0.0194636\pi$
$241$			1.89733i			0.122217i	−0.998131	+	0.0611087i	$0.980536\pi$
$242$	−6.04902	+	14.3321i	−0.388846	+	0.921303i
$243$			21.7666i			1.39633i
$244$	−2.24741	+	1.46096i	−0.143876	+	0.0935283i
$245$	0.167379			0.0106935
$246$	35.1173	+	19.0566i	2.23899	+	1.21501i
$247$			3.87930i			0.246834i
$248$	6.86747	−	0.545265i	0.436085	−	0.0346244i
$249$			4.32480i			0.274073i
$250$	−1.52859	−	0.829501i	−0.0966766	−	0.0524622i
$251$			11.9038i			0.751362i	0.926749	+	0.375681i	$0.122591\pi$
$251$			11.9038i			0.751362i	−0.926749	+	0.375681i	$0.877409\pi$
$252$	7.43269	+	11.4338i	0.468215	+	0.720260i
$253$	8.25505	+	7.48469i	0.518991	+	0.470558i
$254$	−9.76127	−	5.29702i	−0.612477	−	0.332365i
$255$	−1.70767			−0.106938
$256$	−10.7280	−	11.8705i	−0.670501	−	0.741908i
$257$	−3.77178			−0.235277			−0.117638	−	0.993056i	$-0.537532\pi$
$257$	−3.77178			−0.235277			−0.117638	+	0.993056i	$0.537532\pi$
$258$	−9.20670	+	16.9660i	−0.573184	+	1.05625i
$259$	23.7196			1.47386
$260$	−0.206526	+	0.134255i	−0.0128082	+	0.00832613i
$261$		−	22.7107i		−	1.40576i
$262$	21.2809	+	11.5482i	1.31474	+	0.713453i
$263$	19.2919			1.18959			0.594794	−	0.803878i	$-0.297233\pi$
$263$	19.2919			1.18959			0.594794	+	0.803878i	$0.297233\pi$
$264$	13.8868	−	17.9944i	0.854670	−	1.10748i
$265$	−1.77441			−0.109001
$266$	−11.4525	−	6.21477i	−0.702197	−	0.381052i
$267$			7.50181i			0.459104i
$268$	6.72478	−	4.37153i	0.410781	−	0.267034i
$269$	31.2799			1.90717			0.953586	−	0.301122i	$-0.0973612\pi$
$269$	31.2799			1.90717			0.953586	+	0.301122i	$0.0973612\pi$
$270$	0.0259838	−	0.0478825i	0.00158132	−	0.00291404i
$271$	9.35876			0.568504			0.284252	−	0.958750i	$-0.408255\pi$
$271$	9.35876			0.568504			0.284252	+	0.958750i	$0.408255\pi$
$272$	−20.9187	−	9.29050i	−1.26839	−	0.563319i
$273$	5.75481			0.348297
$274$	14.7065	+	7.98058i	0.888452	+	0.482124i
$275$	11.1050	−	12.2480i	0.669656	−	0.738581i
$276$	−8.87373	−	13.6505i	−0.534135	−	0.821666i
$277$		−	18.6205i		−	1.11880i	−0.828899	−	0.559399i	$-0.811032\pi$
$277$		−	18.6205i		−	1.11880i	0.828899	−	0.559399i	$-0.188968\pi$
$278$	12.7654	+	6.92721i	0.765616	+	0.415467i
$279$		−	6.99258i		−	0.418635i
$280$	−0.0654866	−	0.824786i	−0.00391357	−	0.0492904i
$281$		−	3.22676i		−	0.192493i	−0.995358	−	0.0962463i	$-0.969316\pi$
$281$		−	3.22676i		−	0.192493i	0.995358	−	0.0962463i	$-0.0306836\pi$
$282$	−25.4273	−	13.7983i	−1.51418	−	0.821678i
$283$	−12.2271			−0.726828			−0.363414	−	0.931628i	$-0.618389\pi$
$283$	−12.2271			−0.726828			−0.363414	+	0.931628i	$0.618389\pi$
$284$	5.93436	−	3.85771i	0.352140	−	0.228913i
$285$		−	1.15768i		−	0.0685752i
$286$	−1.55143	−	4.42641i	−0.0917379	−	0.261739i
$287$			27.6935i			1.63470i
$288$	−12.8729	+	9.90136i	−0.758544	+	0.583443i
$289$	−15.7442			−0.926129
$290$	−0.657184	+	1.21105i	−0.0385912	+	0.0711152i
$291$			37.5365i			2.20043i
$292$	7.76245	−	5.04609i	0.454263	−	0.295300i
$293$		−	1.81964i		−	0.106305i	−0.998586	−	0.0531523i	$-0.983073\pi$
$293$		−	1.81964i		−	0.106305i	0.998586	−	0.0531523i	$-0.0169269\pi$
$294$	2.22108	−	4.09298i	0.129536	−	0.238707i
$295$		−	1.50420i		−	0.0875777i
$296$	2.23573	+	28.1585i	0.129949	+	1.63668i
$297$	0.768493	+	0.696777i	0.0445925	+	0.0404311i
$298$	−8.41687	+	15.5105i	−0.487576	+	0.898498i
$299$	−3.35974			−0.194299
$300$	−20.2532	+	13.1659i	−1.16932	+	0.760134i
$301$	−13.3794			−0.771174
$302$	−7.57912	−	4.11286i	−0.436129	−	0.236669i
$303$	5.95591			0.342158
$304$	6.29833	−	14.1815i	0.361234	−	0.813364i
$305$		−	0.165072i		−	0.00945200i
$306$	−11.0810	+	20.4200i	−0.633461	+	1.16733i
$307$	0.0752752			0.00429618			0.00214809	−	0.999998i	$-0.499316\pi$
$307$	0.0752752			0.00429618			0.00214809	+	0.999998i	$0.499316\pi$
$308$	15.5531	+	2.51112i	0.886219	+	0.143084i
$309$	−25.1582			−1.43120
$310$	−0.202345	+	0.372879i	−0.0114924	+	0.0211781i
$311$			8.45816i			0.479618i	0.970820	+	0.239809i	$0.0770849\pi$
$311$			8.45816i			0.479618i	−0.970820	+	0.239809i	$0.922915\pi$
$312$	0.542431	+	6.83177i	0.0307091	+	0.386773i
$313$	25.5086			1.44183			0.720917	−	0.693022i	$-0.243721\pi$
$313$	25.5086			1.44183			0.720917	+	0.693022i	$0.243721\pi$
$314$	7.73139	+	4.19549i	0.436307	+	0.236765i
$315$	−0.839811			−0.0473180
$316$	−7.34254	−	11.2951i	−0.413050	−	0.635399i
$317$	21.5943			1.21286			0.606429	−	0.795138i	$-0.292601\pi$
$317$	21.5943			1.21286			0.606429	+	0.795138i	$0.292601\pi$
$318$	−23.5460	+	43.3903i	−1.32040	+	2.43321i
$319$	−19.4368	−	17.6230i	−1.08825	−	0.986696i
$320$	0.972965	−	0.155484i	0.0543904	−	0.00869179i
$321$		−	13.0237i		−	0.726913i
$322$	5.38242	−	9.91863i	0.299950	−	0.552744i
$323$		−	22.1983i		−	1.23515i
$324$	−10.2144	−	15.7130i	−0.567468	−	0.872942i
$325$			4.98483i			0.276509i
$326$	−7.22070	+	13.3062i	−0.399918	+	0.736962i
$327$	4.35662			0.240921
$328$	−32.8761	+	2.61030i	−1.81528	+	0.144130i
$329$		−	20.0520i		−	1.10550i
$330$	0.462986	+	1.32095i	0.0254865	+	0.0727160i
$331$			35.1165i			1.93017i	0.261928	+	0.965087i	$0.415642\pi$
$331$			35.1165i			1.93017i	−0.261928	+	0.965087i	$0.584358\pi$
$332$	−1.94563	−	2.99298i	−0.106780	−	0.164261i
$333$	28.6714			1.57118
$334$	3.27607	+	1.77778i	0.179259	+	0.0972759i
$335$			0.493935i			0.0269865i
$336$	−21.0378	−	9.34336i	−1.14770	−	0.509722i
$337$		−	14.3386i		−	0.781076i	−0.920587	−	0.390538i	$-0.872289\pi$
$337$		−	14.3386i		−	0.781076i	0.920587	−	0.390538i	$-0.127711\pi$
$338$	1.24299	+	0.674518i	0.0676098	+	0.0366889i
$339$			30.8651i			1.67636i
$340$	1.18179	−	0.768241i	0.0640917	−	0.0416637i
$341$	−5.98454	−	5.42606i	−0.324081	−	0.293838i
$342$	−13.8434	−	7.51220i	−0.748564	−	0.406213i
$343$	19.8533			1.07198
$344$	−1.26110	−	15.8832i	−0.0679938	−	0.856365i
$345$	1.00263			0.0539799
$346$	7.59634	−	13.9984i	0.408382	−	0.752560i
$347$	6.53488			0.350811			0.175405	−	0.984496i	$-0.443876\pi$
$347$	6.53488			0.350811			0.175405	+	0.984496i	$0.443876\pi$
$348$	20.8935	+	32.1407i	1.12001	+	1.72292i
$349$			30.7300i			1.64494i	0.568810	+	0.822469i	$0.307404\pi$
$349$			30.7300i			1.64494i	−0.568810	+	0.822469i	$0.692596\pi$
$350$	−14.7162	−	7.98586i	−0.786615	−	0.426862i
$351$	−0.312771			−0.0166945
$352$	−1.51506	+	18.7004i	−0.0807532	+	0.996734i
$353$	33.7401			1.79580			0.897901	−	0.440197i	$-0.145091\pi$
$353$	33.7401			1.79580			0.897901	+	0.440197i	$0.145091\pi$
$354$	−36.7826	−	19.9603i	−1.95497	−	1.06088i
$355$			0.435879i			0.0231340i
$356$	−3.37490	−	5.19164i	−0.178869	−	0.275156i
$357$	−32.9305			−1.74287
$358$	7.09927	−	13.0824i	0.375208	−	0.691427i
$359$	10.4299			0.550472			0.275236	−	0.961377i	$-0.411244\pi$
$359$	10.4299			0.550472			0.275236	+	0.961377i	$0.411244\pi$
$360$	−0.0791580	−	0.996974i	−0.00417199	−	0.0525451i
$361$	−3.95102			−0.207949
$362$	10.1224	+	5.49298i	0.532021	+	0.288705i
$363$	−26.5256	+	2.60276i	−1.39223	+	0.136610i
$364$	−3.98262	+	2.58896i	−0.208746	+	0.135698i
$365$			0.570152i			0.0298431i
$366$	−4.03656	−	2.19047i	−0.210994	−	0.114498i
$367$		−	11.8143i		−	0.616701i	−0.951273	−	0.308350i	$-0.900223\pi$
$367$		−	11.8143i		−	0.616701i	0.951273	−	0.308350i	$-0.0997769\pi$
$368$	12.2821	+	5.45479i	0.640251	+	0.284350i
$369$			33.4750i			1.74264i
$370$	−1.52890	−	0.829670i	−0.0794839	−	0.0431325i
$371$	−34.2176			−1.77649
$372$	6.43305	+	9.89603i	0.333538	+	0.513085i
$373$			20.2689i			1.04949i	0.851261	+	0.524743i	$0.175839\pi$
$373$			20.2689i			1.04949i	−0.851261	+	0.524743i	$0.824161\pi$
$374$	8.87767	+	25.3290i	0.459053	+	1.30973i
$375$		−	2.97973i		−	0.153872i
$376$	23.8046	−	1.89004i	1.22763	−	0.0974714i
$377$	7.91062			0.407418
$378$	0.501069	−	0.923362i	0.0257722	−	0.0474926i
$379$		−	0.761826i		−	0.0391324i	−0.999809	−	0.0195662i	$-0.993771\pi$
$379$		−	0.761826i		−	0.0391324i	0.999809	−	0.0195662i	$-0.00622851\pi$
$380$	0.520815	+	0.801175i	0.0267173	+	0.0410994i
$381$		−	19.0279i		−	0.974830i
$382$	−12.0908	+	22.2807i	−0.618618	+	1.13998i
$383$		−	8.32548i		−	0.425412i	−0.977116	−	0.212706i	$-0.931772\pi$
$383$		−	8.32548i		−	0.425412i	0.977116	−	0.212706i	$-0.0682277\pi$
$384$	9.10893	−	25.8555i	0.464838	−	1.31943i
$385$	−0.651672	+	0.718745i	−0.0332123	+	0.0366307i
$386$	8.41039	−	15.4985i	0.428078	−	0.788855i
$387$	−16.1725			−0.822096
$388$	−16.8868	−	25.9772i	−0.857299	−	1.31879i
$389$	6.48008			0.328553			0.164277	−	0.986414i	$-0.447471\pi$
$389$	6.48008			0.328553			0.164277	+	0.986414i	$0.447471\pi$
$390$	−0.370940	−	0.201293i	−0.0187833	−	0.0101929i
$391$	19.2253			0.972265
$392$	0.304235	+	3.83176i	0.0153662	+	0.193533i
$393$			41.4835i			2.09257i
$394$	13.2346	−	24.3886i	0.666751	−	1.22868i
$395$	0.829625			0.0417430
$396$	18.8000	+	3.03535i	0.944738	+	0.152532i
$397$	8.22750			0.412926			0.206463	−	0.978454i	$-0.433805\pi$
$397$	8.22750			0.412926			0.206463	+	0.978454i	$0.433805\pi$
$398$	−1.45087	+	2.67365i	−0.0727258	+	0.134018i
$399$		−	22.3246i		−	1.11763i
$400$	8.09324	−	18.2230i	0.404662	−	0.911148i
$401$	18.6420			0.930936			0.465468	−	0.885065i	$-0.345886\pi$
$401$	18.6420			0.930936			0.465468	+	0.885065i	$0.345886\pi$
$402$	12.0783	+	6.55440i	0.602413	+	0.326904i
$403$	2.43566			0.121329
$404$	−4.12179	+	2.67943i	−0.205067	+	0.133307i
$405$	1.15412			0.0573485
$406$	−12.6731	+	23.3538i	−0.628954	+	1.15903i
$407$	22.2483	−	24.5382i	1.10281	−	1.21631i
$408$	−3.10393	−	39.0931i	−0.153667	−	1.93540i
$409$		−	18.2518i		−	0.902495i	−0.892399	−	0.451247i	$-0.850979\pi$
$409$		−	18.2518i		−	0.902495i	0.892399	−	0.451247i	$-0.149021\pi$
$410$	0.968670	−	1.78505i	0.0478392	−	0.0881574i
$411$			28.6678i			1.41408i
$412$	17.4107	−	11.3181i	0.857766	−	0.557603i
$413$		−	29.0068i		−	1.42733i
$414$	6.50608	−	11.9893i	0.319757	−	0.589242i
$415$	0.219835			0.0107913
$416$	−3.44885	−	4.48391i	−0.169094	−	0.219842i
$417$			24.8839i			1.21857i
$418$	−17.1714	+	6.01846i	−0.839879	+	0.294372i
$419$		−	15.5301i		−	0.758693i	−0.925255	−	0.379346i	$-0.876149\pi$
$419$		−	15.5301i		−	0.758693i	0.925255	−	0.379346i	$-0.123851\pi$
$420$	1.18852	−	0.772612i	0.0579937	−	0.0376996i
$421$	−9.24095			−0.450376			−0.225188	−	0.974315i	$-0.572300\pi$
$421$	−9.24095			−0.450376			−0.225188	+	0.974315i	$0.572300\pi$
$422$	1.30596	+	0.708689i	0.0635732	+	0.0344985i
$423$		−	24.2382i		−	1.17850i
$424$	−3.22525	−	40.6211i	−0.156632	−	1.97274i
$425$		−	28.5245i		−	1.38364i
$426$	10.6587	+	5.78401i	0.516415	+	0.280236i
$427$		−	3.18324i		−	0.154048i
$428$	5.85908	+	9.01308i	0.283209	+	0.435664i
$429$	5.39785	−	5.95343i	0.260611	−	0.287434i
$430$	0.862399	+	0.467987i	0.0415886	+	0.0225683i
$431$	25.8158			1.24350			0.621752	−	0.783214i	$-0.286421\pi$
$431$	25.8158			1.24350			0.621752	+	0.783214i	$0.286421\pi$
$432$	1.14339	+	0.507806i	0.0550114	+	0.0244318i
$433$	−3.38260			−0.162557			−0.0812787	−	0.996691i	$-0.525900\pi$
$433$	−3.38260			−0.162557			−0.0812787	+	0.996691i	$0.525900\pi$
$434$	−3.90201	+	7.19056i	−0.187302	+	0.345158i
$435$	−2.36073			−0.113188
$436$	−3.01500	+	1.95994i	−0.144392	+	0.0938643i
$437$			13.0334i			0.623474i
$438$	13.9421	+	7.56578i	0.666180	+	0.361507i
$439$	0.658736			0.0314398			0.0157199	−	0.999876i	$-0.494996\pi$
$439$	0.658736			0.0314398			0.0157199	+	0.999876i	$0.494996\pi$
$440$	−0.914677	−	0.705880i	−0.0436055	−	0.0336515i
$441$	3.90157			0.185789
$442$	−7.11271	−	3.85976i	−0.338317	−	0.183590i
$443$		−	12.7677i		−	0.606610i	−0.952893	−	0.303305i	$-0.901910\pi$
$443$		−	12.7677i		−	0.606610i	0.952893	−	0.303305i	$-0.0980902\pi$
$444$	−40.5764	+	26.3772i	−1.92567	+	1.25181i
$445$	0.381326			0.0180766
$446$	−3.82844	+	7.05498i	−0.181282	+	0.334063i
$447$	−30.2350			−1.43007
$448$	18.7626	−	2.99833i	0.886448	−	0.141658i
$449$	4.84675			0.228732			0.114366	−	0.993439i	$-0.463516\pi$
$449$	4.84675			0.228732			0.114366	+	0.993439i	$0.463516\pi$
$450$	−17.7885	−	9.65304i	−0.838557	−	0.455049i
$451$	28.6493	+	25.9757i	1.34904	+	1.22315i
$452$	−13.8855	−	21.3602i	−0.653120	−	1.00470i
$453$		−	14.7742i		−	0.694152i
$454$	28.6041	+	15.5222i	1.34246	+	0.728494i
$455$		−	0.292524i		−	0.0137137i
$456$	26.5025	−	2.10425i	1.24109	−	0.0985406i
$457$		−	4.27748i		−	0.200092i	−0.994983	−	0.100046i	$-0.968101\pi$
$457$		−	4.27748i		−	0.200092i	0.994983	−	0.100046i	$-0.0318990\pi$
$458$	−3.06907	−	1.66545i	−0.143408	−	0.0778214i
$459$	1.78975			0.0835385
$460$	−0.693873	+	0.451062i	−0.0323520	+	0.0210309i
$461$		−	11.0858i		−	0.516319i	−0.966102	−	0.258159i	$-0.916884\pi$
$461$		−	11.0858i		−	0.516319i	0.966102	−	0.258159i	$-0.0831160\pi$
$462$	8.92818	+	25.4731i	0.415377	+	1.18512i
$463$			4.01675i			0.186674i	0.995635	+	0.0933372i	$0.0297534\pi$
$463$			4.01675i			0.186674i	−0.995635	+	0.0933372i	$0.970247\pi$
$464$	−28.9187	−	12.8435i	−1.34252	−	0.596244i
$465$	−0.726863			−0.0337075
$466$	−10.9927	+	20.2572i	−0.509228	+	0.938397i
$467$		−	30.9031i		−	1.43003i	−0.699111	−	0.715013i	$-0.746421\pi$
$467$		−	30.9031i		−	1.43003i	0.699111	−	0.715013i	$-0.253579\pi$
$468$	−4.81406	+	3.12945i	−0.222530	+	0.144659i
$469$			9.52500i			0.439824i
$470$	−0.701385	+	1.29250i	−0.0323525	+	0.0596186i
$471$			15.0710i			0.694436i
$472$	34.4352	−	2.73409i	1.58501	−	0.125847i
$473$	−12.5495	+	13.8411i	−0.577025	+	0.636416i
$474$	11.0089	−	20.2871i	0.505657	−	0.931817i
$475$	19.3377			0.887273
$476$	22.7896	−	14.8147i	1.04456	−	0.679030i
$477$	−41.3611			−1.89380
$478$	31.8254	+	17.2703i	1.45566	+	0.789923i
$479$	5.69850			0.260371			0.130185	−	0.991490i	$-0.458443\pi$
$479$	5.69850			0.260371			0.130185	+	0.991490i	$0.458443\pi$
$480$	1.02922	+	1.33811i	0.0469775	+	0.0610762i
$481$			9.98686i			0.455362i
$482$	1.27978	−	2.35836i	0.0582924	−	0.107420i
$483$	19.3347			0.879758
$484$	17.1861	−	13.7345i	0.781188	−	0.624296i
$485$	1.90802			0.0866390
$486$	14.6820	−	27.0557i	0.665987	−	1.22727i
$487$			27.9762i			1.26772i	0.773446	+	0.633862i	$0.218531\pi$
$487$			27.9762i			1.26772i	−0.773446	+	0.633862i	$0.781469\pi$
$488$	3.77895	−	0.300042i	0.171065	−	0.0135823i
$489$	−25.9382			−1.17296
$490$	−0.208051	−	0.112900i	−0.00939877	−	0.00510031i
$491$	18.7779			0.847434			0.423717	−	0.905795i	$-0.360725\pi$
$491$	18.7779			0.847434			0.423717	+	0.905795i	$0.360725\pi$
$492$	−30.7964	−	47.3744i	−1.38841	−	2.13580i
$493$	−45.2666			−2.03871
$494$	2.61666	−	4.82194i	0.117729	−	0.216949i
$495$	−0.787719	+	0.868795i	−0.0354053	+	0.0390494i
$496$	−8.90400	−	3.95447i	−0.399801	−	0.177561i
$497$			8.40545i			0.377036i
$498$	2.91715	−	5.37569i	0.130721	−	0.240890i
$499$		−	25.3336i		−	1.13409i	−0.823687	−	0.567044i	$-0.808087\pi$
$499$		−	25.3336i		−	1.13409i	0.823687	−	0.567044i	$-0.191913\pi$
$500$	1.34051	+	2.06212i	0.0599495	+	0.0922210i
$501$			6.38613i			0.285311i
$502$	8.02933	−	14.7963i	0.358366	−	0.660392i
$503$	−38.7203			−1.72646			−0.863228	−	0.504815i	$-0.831561\pi$
$503$	−38.7203			−1.72646			−0.863228	+	0.504815i	$0.831561\pi$
$504$	−1.52648	−	19.2256i	−0.0679946	−	0.856375i
$505$		−	0.302746i		−	0.0134720i
$506$	−5.21240	−	14.8716i	−0.231719	−	0.661122i
$507$			2.42300i			0.107609i
$508$	8.56023	+	13.1683i	0.379799	+	0.584249i
$509$	5.13007			0.227386			0.113693	−	0.993516i	$-0.463732\pi$
$509$	5.13007			0.227386			0.113693	+	0.993516i	$0.463732\pi$
$510$	2.12261	+	1.15185i	0.0939909	+	0.0510048i
$511$			10.9948i			0.486380i
$512$	5.32794	+	21.9912i	0.235464	+	0.971883i
$513$			1.21333i			0.0535699i
$514$	4.68828	+	2.54413i	0.206791	+	0.112217i
$515$			1.27882i			0.0563515i
$516$	22.8877	−	14.8785i	1.00757	−	0.654987i
$517$	−20.7441	−	18.8082i	−0.912323	−	0.827185i
$518$	−29.4832	−	15.9993i	−1.29542	−	0.702968i
$519$	27.2875			1.19779
$520$	0.347267	−	0.0275724i	0.0152287	−	0.00120913i
$521$	−33.9046			−1.48539			−0.742693	−	0.669632i	$-0.766452\pi$
$521$	−33.9046			−1.48539			−0.742693	+	0.669632i	$0.766452\pi$
$522$	−15.3188	+	28.2292i	−0.670485	+	1.23556i
$523$	−15.0173			−0.656662			−0.328331	−	0.944563i	$-0.606486\pi$
$523$	−15.0173			−0.656662			−0.328331	+	0.944563i	$0.606486\pi$
$524$	−18.6625	−	28.7087i	−0.815275	−	1.25415i
$525$		−	28.6868i		−	1.25199i
$526$	−23.9796	−	13.0127i	−1.04556	−	0.567382i
$527$	−13.9375			−0.607126
$528$	−29.3986	+	13.0000i	−1.27941	+	0.565753i
$529$	11.7121			0.509223
$530$	2.20558	+	1.19687i	0.0958042	+	0.0519888i
$531$		−	35.0625i		−	1.52158i
$532$	10.0434	+	15.4498i	0.435435	+	0.669834i
$533$	−11.6600			−0.505052
$534$	5.06011	−	9.32469i	0.218972	−	0.403519i
$535$	−0.662010			−0.0286212
$536$	−11.3075	+	0.897797i	−0.488410	+	0.0387789i
$537$	25.5019			1.10049
$538$	−38.8807	−	21.0989i	−1.67626	−	0.909637i
$539$	3.02752	−	3.33912i	0.130404	−	0.143826i
$540$	−0.0645952	+	0.0419910i	−0.00277973	+	0.00180700i
$541$			17.9341i			0.771047i	0.922698	+	0.385523i	$0.125979\pi$
$541$			17.9341i			0.771047i	−0.922698	+	0.385523i	$0.874021\pi$
$542$	−11.6329	−	6.31265i	−0.499674	−	0.271152i
$543$			19.7319i			0.846775i
$544$	19.7352	+	25.6581i	0.846140	+	1.10008i
$545$		−	0.221452i		−	0.00948595i
$546$	−7.15318	−	3.88172i	−0.306128	−	0.166122i
$547$	17.7238			0.757816			0.378908	−	0.925434i	$-0.376300\pi$
$547$	17.7238			0.757816			0.378908	+	0.925434i	$0.376300\pi$
$548$	−12.8970	−	19.8396i	−0.550932	−	0.847505i
$549$		−	3.84779i		−	0.164220i
$550$	−22.0649	+	7.73361i	−0.940850	+	0.329762i
$551$		−	30.6877i		−	1.30734i
$552$	1.82243	+	22.9530i	0.0775676	+	0.976944i
$553$	15.9984			0.680322
$554$	−12.5599	+	23.1451i	−0.533617	+	0.983342i
$555$		−	2.98033i		−	0.126508i
$556$	−11.1947	−	17.2209i	−0.474761	−	0.730330i
$557$			17.3649i			0.735774i	0.929871	+	0.367887i	$0.119919\pi$
$557$			17.3649i			0.735774i	−0.929871	+	0.367887i	$0.880081\pi$
$558$	−4.71662	+	8.69171i	−0.199670	+	0.367949i
$559$		−	5.63323i		−	0.238260i
$560$	−0.474934	+	1.06937i	−0.0200696	+	0.0451893i
$561$	−30.8879	+	34.0670i	−1.30409	+	1.43831i
$562$	−2.17651	+	4.01084i	−0.0918105	+	0.169187i
$563$	−38.9605			−1.64199			−0.820994	−	0.570937i	$-0.806580\pi$
$563$	−38.9605			−1.64199			−0.820994	+	0.570937i	$0.806580\pi$
$564$	22.2987	+	34.3024i	0.938946	+	1.44439i
$565$	1.56891			0.0660045
$566$	15.1982	+	8.24742i	0.638829	+	0.346665i
$567$	22.2559			0.934660
$568$	−9.97845	+	0.792271i	−0.418687	+	0.0332430i
$569$			23.8432i			0.999559i	0.866153	+	0.499780i	$0.166586\pi$
$569$			23.8432i			0.999559i	−0.866153	+	0.499780i	$0.833414\pi$
$570$	−0.780877	+	1.43899i	−0.0327073	+	0.0602726i
$571$	−47.3837			−1.98295			−0.991473	−	0.130311i	$-0.958402\pi$
$571$	−47.3837			−1.98295			−0.991473	+	0.130311i	$0.958402\pi$
$572$	−1.05728	+	6.54845i	−0.0442070	+	0.273804i
$573$	−43.4324			−1.81442
$574$	18.6798	−	34.4228i	0.779678	−	1.43678i
$575$			16.7477i			0.698429i
$576$	22.6796	−	3.62428i	0.944982	−	0.151012i
$577$	−29.9490			−1.24679			−0.623397	−	0.781905i	$-0.714248\pi$
$577$	−29.9490			−1.24679			−0.623397	+	0.781905i	$0.714248\pi$
$578$	19.5699	+	10.6197i	0.814000	+	0.441723i
$579$	30.2118			1.25556
$580$	1.63375	−	1.06204i	0.0678377	−	0.0440988i
$581$	4.23927			0.175875
$582$	25.3190	−	46.6576i	1.04951	−	1.93402i
$583$	−32.0952	+	35.3986i	−1.32925	+	1.46606i
$584$	−13.0523	+	1.03633i	−0.540109	+	0.0428837i
$585$		−	0.353593i		−	0.0146193i
$586$	−1.22738	+	2.26180i	−0.0507026	+	0.0934340i
$587$		−	3.34200i		−	0.137939i	−0.997619	−	0.0689695i	$-0.978029\pi$
$587$		−	3.34200i		−	0.137939i	0.997619	−	0.0689695i	$-0.0219711\pi$
$588$	−5.52157	+	3.58937i	−0.227706	+	0.148023i
$589$		−	9.44866i		−	0.389325i
$590$	−1.01461	+	1.86970i	−0.0417707	+	0.0769745i
$591$	47.5414			1.95559
$592$	16.2144	−	36.5088i	0.666408	−	1.50050i
$593$		−	7.13514i		−	0.293005i	−0.989210	−	0.146502i	$-0.953198\pi$
$593$		−	7.13514i		−	0.293005i	0.989210	−	0.146502i	$-0.0468016\pi$
$594$	−0.485242	−	1.38445i	−0.0199097	−	0.0568047i
$595$			1.67390i			0.0686230i
$596$	20.9242	−	13.6021i	0.857088	−	0.557162i
$597$	−5.21182			−0.213306
$598$	4.17613	+	2.26620i	0.170775	+	0.0926720i
$599$			44.4128i			1.81466i	0.420422	+	0.907329i	$0.361882\pi$
$599$			44.4128i			1.81466i	−0.420422	+	0.907329i	$0.638118\pi$
$600$	34.0552	−	2.70392i	1.39030	−	0.110387i
$601$			23.8222i			0.971727i	0.874035	+	0.485863i	$0.161495\pi$
$601$			23.8222i			0.971727i	−0.874035	+	0.485863i	$0.838505\pi$
$602$	16.6304	+	9.02462i	0.677806	+	0.367816i
$603$			11.5135i			0.468866i
$604$	6.64658	+	10.2245i	0.270445	+	0.416029i
$605$	0.132302	+	1.34833i	0.00537882	+	0.0548172i
$606$	−7.40314	−	4.01737i	−0.300732	−	0.163194i
$607$	−30.6103			−1.24243			−0.621217	−	0.783639i	$-0.713361\pi$
$607$	−30.6103			−1.24243			−0.621217	+	0.783639i	$0.713361\pi$
$608$	−17.3944	+	13.3791i	−0.705437	+	0.542595i
$609$	−45.5242			−1.84473
$610$	−0.111344	+	0.205183i	−0.00450819	+	0.00830762i
$611$	8.44267			0.341554
$612$	27.5473	−	17.9075i	1.11353	−	0.723868i
$613$		−	24.2063i		−	0.977684i	−0.872372	−	0.488842i	$-0.837419\pi$
$613$		−	24.2063i		−	0.977684i	0.872372	−	0.488842i	$-0.162581\pi$
$614$	−0.0935664	−	0.0507745i	−0.00377603	−	0.00204909i
$615$	3.47965			0.140313
$616$	−17.6385	−	13.6121i	−0.710677	−	0.548448i
$617$	−39.5531			−1.59235			−0.796174	−	0.605068i	$-0.793146\pi$
$617$	−39.5531			−1.59235			−0.796174	+	0.605068i	$0.793146\pi$
$618$	31.2714	+	16.9696i	1.25792	+	0.682619i
$619$			29.6475i			1.19163i	0.803120	+	0.595817i	$0.203172\pi$
$619$			29.6475i			1.19163i	−0.803120	+	0.595817i	$0.796828\pi$
$620$	0.503026	−	0.326999i	0.0202020	−	0.0131326i
$621$	−1.05083			−0.0421683
$622$	5.70518	−	10.5134i	0.228757	−	0.421550i
$623$	7.35346			0.294610
$624$	3.93391	−	8.85771i	0.157483	−	0.354592i
$625$	24.7727			0.990908
$626$	−31.7070	−	17.2060i	−1.26727	−	0.687691i
$627$	−23.0951	−	20.9399i	−0.922331	−	0.836259i
$628$	−6.78011	−	10.4299i	−0.270556	−	0.416199i
$629$		−	57.1474i		−	2.27861i
$630$	1.04388	+	0.566467i	0.0415891	+	0.0225686i
$631$		−	32.5129i		−	1.29432i	−0.762355	−	0.647159i	$-0.775957\pi$
$631$		−	32.5129i		−	1.29432i	0.762355	−	0.647159i	$-0.224043\pi$
$632$	1.50796	+	18.9924i	0.0599835	+	0.755477i
$633$			2.54575i			0.101184i
$634$	−26.8415	−	14.5658i	−1.06601	−	0.578480i
$635$	−0.967211			−0.0383826
$636$	58.5350	−	38.0515i	2.32106	−	1.50884i
$637$			1.35900i			0.0538454i
$638$	12.2728	+	35.0156i	0.485884	+	1.38628i
$639$			10.1602i			0.401932i
$640$	−1.31426	−	0.463017i	−0.0519508	−	0.0183024i
$641$	37.9090			1.49732			0.748658	−	0.662956i	$-0.230698\pi$
$641$	37.9090			1.49732			0.748658	+	0.662956i	$0.230698\pi$
$642$	−8.78473	+	16.1884i	−0.346705	+	0.638904i
$643$		−	18.7758i		−	0.740447i	−0.928943	−	0.370223i	$-0.879281\pi$
$643$		−	18.7758i		−	0.740447i	0.928943	−	0.370223i	$-0.120719\pi$
$644$	−13.3806	+	8.69824i	−0.527269	+	0.342759i
$645$			1.68110i			0.0661932i
$646$	−14.9732	+	27.5923i	−0.589112	+	1.08561i
$647$			3.12450i			0.122837i	0.998112	+	0.0614183i	$0.0195624\pi$
$647$			3.12450i			0.122837i	−0.998112	+	0.0614183i	$0.980438\pi$
$648$	2.09777	+	26.4209i	0.0824082	+	1.03791i
$649$	−30.0079	−	27.2076i	−1.17791	−	1.06799i
$650$	3.36236	−	6.19610i	0.131882	−	0.243031i
$651$	−14.0168			−0.549360
$652$	17.9505	−	11.6690i	0.702997	−	0.456993i
$653$	30.8196			1.20606			0.603032	−	0.797717i	$-0.293959\pi$
$653$	30.8196			1.20606			0.603032	+	0.797717i	$0.293959\pi$
$654$	−5.41523	−	2.93861i	−0.211752	−	0.114909i
$655$	2.10865			0.0823919
$656$	42.6254	+	18.9309i	1.66424	+	0.739128i
$657$			13.2901i			0.518496i
$658$	−13.5254	+	24.9245i	−0.527277	+	0.971657i
$659$	−22.4295			−0.873728			−0.436864	−	0.899528i	$-0.643911\pi$
$659$	−22.4295			−0.873728			−0.436864	+	0.899528i	$0.643911\pi$
$660$	0.315518	−	1.95422i	0.0122815	−	0.0760680i
$661$	25.4609			0.990313			0.495157	−	0.868804i	$-0.335111\pi$
$661$	25.4609			0.990313			0.495157	+	0.868804i	$0.335111\pi$
$662$	23.6867	−	43.6494i	0.920608	−	1.69648i
$663$		−	13.8650i		−	0.538472i
$664$	0.399580	+	5.03261i	0.0155067	+	0.195303i
$665$	−1.13479			−0.0440052
$666$	−35.6383	−	19.3394i	−1.38096	−	0.749386i
$667$	26.5777			1.02909
$668$	−2.87298	−	4.41953i	−0.111159	−	0.170997i
$669$	−13.7525			−0.531702
$670$	0.333168	−	0.613956i	0.0128714	−	0.0237192i
$671$	−3.29310	−	2.98579i	−0.127129	−	0.115265i
$672$	19.8475	+	25.8040i	0.765633	+	0.995413i
$673$			14.5732i			0.561754i	0.959744	+	0.280877i	$0.0906254\pi$
$673$			14.5732i			0.561754i	−0.959744	+	0.280877i	$0.909375\pi$
$674$	−9.67167	+	17.8228i	−0.372539	+	0.686509i
$675$			1.55911i			0.0600101i
$676$	−1.09005	−	1.67684i	−0.0419251	−	0.0644938i
$677$			0.788336i			0.0302982i	0.999885	+	0.0151491i	$0.00482229\pi$
$677$			0.788336i			0.0302982i	−0.999885	+	0.0151491i	$0.995178\pi$
$678$	20.8191	−	38.3651i	0.799551	−	1.47340i
$679$	36.7942			1.41203
$680$	−1.98715	+	0.157776i	−0.0762037	+	0.00605044i
$681$			55.7588i			2.13668i
$682$	3.77875	+	10.7812i	0.144696	+	0.412834i
$683$			31.8924i			1.22033i	0.792274	+	0.610165i	$0.208897\pi$
$683$			31.8924i			1.22033i	−0.792274	+	0.610165i	$0.791103\pi$
$684$	12.1401	+	18.6752i	0.464187	+	0.714064i
$685$	1.45722			0.0556774
$686$	−24.6774	−	13.3914i	−0.942189	−	0.511286i
$687$		−	5.98262i		−	0.228251i
$688$	−9.14596	+	20.5933i	−0.348687	+	0.785112i
$689$		−	14.4069i		−	0.548861i
$690$	−1.24626	−	0.676293i	−0.0474444	−	0.0257460i
$691$			15.7575i			0.599443i	0.954027	+	0.299721i	$0.0968937\pi$
$691$			15.7575i			0.599443i	−0.954027	+	0.299721i	$0.903106\pi$
$692$	−18.8844	+	12.2760i	−0.717876	+	0.466665i
$693$	−15.1903	+	16.7538i	−0.577032	+	0.636423i
$694$	−8.12280	−	4.40789i	−0.308337	−	0.167321i
$695$	1.26488			0.0479795
$696$	−4.29096	−	54.0436i	−0.162649	−	2.04852i
$697$	66.7217			2.52726
$698$	20.7279	−	38.1971i	0.784563	−	1.44578i
$699$	−39.4880			−1.49357
$700$	12.9055	+	19.8527i	0.487783	+	0.750362i
$701$			24.4739i			0.924366i	0.886785	+	0.462183i	$0.152934\pi$
$701$			24.4739i			0.924366i	−0.886785	+	0.462183i	$0.847066\pi$
$702$	0.388771	+	0.210969i	0.0146732	+	0.00796252i
$703$	38.7420			1.46118
$704$	14.4970	−	22.2225i	0.546374	−	0.837541i
$705$	−2.51951			−0.0948902
$706$	−41.9386	−	22.7583i	−1.57838	−	0.856519i
$707$		−	5.83812i		−	0.219565i
$708$	32.2568	+	49.6210i	1.21229	+	1.86487i
$709$	−12.6066			−0.473450			−0.236725	−	0.971577i	$-0.576074\pi$
$709$	−12.6066			−0.473450			−0.236725	+	0.971577i	$0.576074\pi$
$710$	0.294008	−	0.541793i	0.0110339	−	0.0203331i
$711$	19.3384			0.725245
$712$	0.693114	+	8.72959i	0.0259755	+	0.327155i
$713$	8.18319			0.306463
$714$	40.9323	+	22.2122i	1.53185	+	0.831271i
$715$	−0.302620	−	0.274379i	−0.0113173	−	0.0102612i
$716$	−17.6486	+	11.4727i	−0.659561	+	0.428757i
$717$			62.0381i			2.31686i
$718$	−12.9643	−	7.03518i	−0.483824	−	0.262551i
$719$		−	45.9113i		−	1.71220i	−0.516809	−	0.856101i	$-0.672880\pi$
$719$		−	45.9113i		−	1.71220i	0.516809	−	0.856101i	$-0.327120\pi$
$720$	−0.574084	+	1.29262i	−0.0213948	+	0.0481732i
$721$			24.6606i			0.918410i
$722$	4.91109	+	2.66504i	0.182772	+	0.0991824i
$723$	4.59721			0.170972
$724$	−8.87692	−	13.6555i	−0.329908	−	0.507501i
$725$		−	39.4331i		−	1.46451i
$726$	34.7267	+	14.6568i	1.28883	+	0.543963i
$727$			15.7767i			0.585126i	0.956246	+	0.292563i	$0.0945082\pi$
$727$			15.7767i			0.585126i	−0.956246	+	0.292563i	$0.905492\pi$
$728$	6.69666	−	0.531703i	0.248195	−	0.0197062i
$729$	24.6286			0.912172
$730$	0.384578	−	0.708694i	0.0142339	−	0.0262299i
$731$			32.2348i			1.19225i
$732$	3.53990	+	5.44546i	0.130838	+	0.201270i
$733$			22.5361i			0.832391i	0.909275	+	0.416195i	$0.136637\pi$
$733$			22.5361i			0.832391i	−0.909275	+	0.416195i	$0.863363\pi$
$734$	−7.96895	+	14.6851i	−0.294139	+	0.542035i
$735$		−	0.405559i		−	0.0149593i
$736$	−11.5872	−	15.0648i	−0.427111	−	0.555295i
$737$	9.85373	+	8.93418i	0.362967	+	0.329095i
$738$	22.5795	−	41.6091i	0.831161	−	1.53165i
$739$	44.1755			1.62502			0.812512	−	0.582945i	$-0.198100\pi$
$739$	44.1755			1.62502			0.812512	+	0.582945i	$0.198100\pi$
$740$	1.34078	+	2.06254i	0.0492882	+	0.0758206i
$741$	9.39954			0.345301
$742$	42.5322	+	23.0804i	1.56141	+	0.847308i
$743$	3.20609			0.117620			0.0588099	−	0.998269i	$-0.481269\pi$
$743$	3.20609			0.117620			0.0588099	+	0.998269i	$0.481269\pi$
$744$	−1.32118	−	16.6399i	−0.0484367	−	0.610047i
$745$			1.53688i			0.0563070i
$746$	13.6718	−	25.1941i	0.500559	−	0.922422i
$747$	5.12429			0.187488
$748$	6.05001	−	37.4719i	0.221210	−	1.37011i
$749$	−12.7662			−0.466465
$750$	−2.00988	+	3.70377i	−0.0733904	+	0.135243i
$751$			11.0916i			0.404737i	0.979309	+	0.202369i	$0.0648639\pi$
$751$			11.0916i			0.404737i	−0.979309	+	0.202369i	$0.935136\pi$
$752$	−30.8637	−	13.7073i	−1.12548	−	0.499854i
$753$	28.8429			1.05109
$754$	−9.83283	−	5.33586i	−0.358091	−	0.194320i
$755$	−0.750989			−0.0273313
$756$	−1.24565	+	0.809751i	−0.0453038	+	0.0294504i
$757$	−4.45598			−0.161955			−0.0809777	−	0.996716i	$-0.525804\pi$
$757$	−4.45598			−0.161955			−0.0809777	+	0.996716i	$0.525804\pi$
$758$	−0.513865	+	0.946942i	−0.0186644	+	0.0343945i
$759$	18.1354	−	20.0020i	0.658273	−	0.726026i
$760$	−0.106962	−	1.34715i	−0.00387990	−	0.0488664i
$761$			14.9261i			0.541070i	0.962710	+	0.270535i	$0.0872005\pi$
$761$			14.9261i			0.541070i	−0.962710	+	0.270535i	$0.912799\pi$
$762$	−12.8347	+	23.6515i	−0.464951	+	0.856805i
$763$		−	4.27046i		−	0.154601i
$764$	30.0575	−	19.5393i	1.08744	−	0.706906i
$765$			2.02335i			0.0731543i
$766$	−5.61568	+	10.3485i	−0.202903	+	0.373906i
$767$	12.2130			0.440985
$768$	−28.7623	+	25.9940i	−1.03787	+	0.937976i
$769$			3.05197i			0.110057i	0.998485	+	0.0550283i	$0.0175249\pi$
$769$			3.05197i			0.110057i	−0.998485	+	0.0550283i	$0.982475\pi$
$770$	1.29483	−	0.453830i	0.0466624	−	0.0163549i
$771$			9.13900i			0.329133i
$772$	−20.9081	+	13.5916i	−0.752498	+	0.489172i
$773$	6.09930			0.219377			0.109688	−	0.993966i	$-0.465015\pi$
$773$	6.09930			0.219377			0.109688	+	0.993966i	$0.465015\pi$
$774$	20.1023	+	10.9087i	0.722563	+	0.392104i
$775$		−	12.1414i		−	0.436130i
$776$	3.46811	+	43.6799i	0.124498	+	1.56802i
$777$		−	57.4725i		−	2.06181i
$778$	−8.05468	−	4.37093i	−0.288774	−	0.156705i
$779$			45.2328i			1.62063i
$780$	0.325299	+	0.500411i	0.0116476	+	0.0179176i
$781$	8.69555	+	7.88407i	0.311151	+	0.282114i
$782$	−23.8969	−	12.9678i	−0.854550	−	0.463728i
$783$	2.47421			0.0884211
$784$	2.20643	−	4.96806i	0.0788011	−	0.177431i
$785$	0.766077			0.0273425
$786$	27.9814	−	51.5636i	0.998062	−	1.83921i
$787$	27.0725			0.965029			0.482515	−	0.875888i	$-0.339724\pi$
$787$	27.0725			0.965029			0.482515	+	0.875888i	$0.339724\pi$
$788$	−32.9011	+	21.3878i	−1.17205	+	0.761909i
$789$		−	46.7442i		−	1.66414i
$790$	−1.03122	−	0.559597i	−0.0366890	−	0.0199096i
$791$	30.2547			1.07573
$792$	−21.3209	−	16.4539i	−0.757604	−	0.584663i
$793$	1.34026			0.0475942
$794$	−10.2267	−	5.54959i	−0.362932	−	0.196948i
$795$			4.29940i			0.152484i
$796$	3.60685	−	2.34468i	0.127841	−	0.0831050i
$797$	−5.71759			−0.202527			−0.101264	−	0.994860i	$-0.532289\pi$
$797$	−5.71759			−0.202527			−0.101264	+	0.994860i	$0.532289\pi$
$798$	−15.0584	+	27.7493i	−0.533060	+	0.982316i
$799$	−48.3111			−1.70912
$800$	−22.3515	+	17.1919i	−0.790246	+	0.607827i
$801$	8.88861			0.314064
$802$	−23.1718	−	12.5743i	−0.818225	−	0.444015i
$803$	11.3742	+	10.3128i	0.401388	+	0.363930i
$804$	−10.5922	−	16.2941i	−0.373559	−	0.574649i
$805$		−	0.982804i		−	0.0346393i
$806$	−3.02750	−	1.64290i	−0.106639	−	0.0578685i
$807$		−	75.7912i		−	2.66798i
$808$	6.93067	−	0.550283i	0.243820	−	0.0193589i
$809$			43.0476i			1.51347i	0.653720	+	0.756736i	$0.273207\pi$
$809$			43.0476i			1.51347i	−0.653720	+	0.756736i	$0.726793\pi$
$810$	−1.43456	−	0.778472i	−0.0504052	−	0.0273527i
$811$	18.0663			0.634394			0.317197	−	0.948360i	$-0.397258\pi$
$811$	18.0663			0.634394			0.317197	+	0.948360i	$0.397258\pi$
$812$	31.5050	−	20.4803i	1.10561	−	0.718717i
$813$		−	22.6763i		−	0.795291i
$814$	−44.2059	+	15.4939i	−1.54942	+	0.543061i
$815$			1.31847i			0.0461839i
$816$	−22.5109	+	50.6861i	−0.788038	+	1.77437i
$817$	−21.8530			−0.764540
$818$	−12.3112	+	22.6869i	−0.430450	+	0.793227i
$819$		−	6.81865i		−	0.238263i
$820$	−2.40810	+	1.56542i	−0.0840944	+	0.0546667i
$821$			44.3842i			1.54902i	0.632563	+	0.774509i	$0.282003\pi$
$821$			44.3842i			1.54902i	−0.632563	+	0.774509i	$0.717997\pi$
$822$	19.3369	−	35.6338i	0.674453	−	1.24287i
$823$			23.5358i			0.820405i	0.911994	+	0.410203i	$0.134542\pi$
$823$			23.5358i			0.820405i	−0.911994	+	0.410203i	$0.865458\pi$
$824$	−29.2756	+	2.32443i	−1.01987	+	0.0809755i
$825$	−29.6768	−	26.9074i	−1.03321	−	0.936794i
$826$	−19.5656	+	36.0552i	−0.680774	+	1.25452i
$827$	−44.5610			−1.54954			−0.774768	−	0.632245i	$-0.782134\pi$
$827$	−44.5610			−1.54954			−0.774768	+	0.632245i	$0.782134\pi$
$828$	−16.1740	+	10.5141i	−0.562085	+	0.365391i
$829$	−26.4826			−0.919779			−0.459889	−	0.887976i	$-0.652111\pi$
$829$	−26.4826			−0.919779			−0.459889	+	0.887976i	$0.652111\pi$
$830$	−0.273252	−	0.148282i	−0.00948473	−	0.00514695i
$831$	−45.1174			−1.56511
$832$	1.26241	+	7.89977i	0.0437663	+	0.273875i
$833$		−	7.77653i		−	0.269441i
$834$	16.7846	−	30.9304i	0.581204	−	1.07103i
$835$	0.324615			0.0112338
$836$	25.4034	+	4.10149i	0.878595	+	0.141853i
$837$	0.761803			0.0263318
$838$	−10.4753	+	19.3037i	−0.361863	+	0.666836i
$839$		−	9.00011i		−	0.310718i	−0.987858	−	0.155359i	$-0.950347\pi$
$839$		−	9.00011i		−	0.310718i	0.987858	−	0.155359i	$-0.0496535\pi$
$840$	−1.99846	+	0.158674i	−0.0689532	+	0.00547477i
$841$	−33.5780			−1.15786
$842$	11.4864	+	6.23318i	0.395848	+	0.214810i
$843$	−7.81844			−0.269281
$844$	−1.14527	−	1.76179i	−0.0394220	−	0.0606433i
$845$	0.123164			0.00423696
$846$	−16.3491	+	30.1279i	−0.562093	+	1.03582i
$847$	2.55129	+	26.0010i	0.0876634	+	0.893405i
$848$	−23.3907	+	52.6672i	−0.803241	+	1.80860i
$849$			29.6263i			1.01677i
$850$	−19.2403	+	35.4557i	−0.659935	+	1.21612i
$851$			33.5533i			1.15019i
$852$	−9.34723	−	14.3789i	−0.320231	−	0.492614i
$853$		−	43.0231i		−	1.47308i	−0.676392	−	0.736542i	$-0.736457\pi$
$853$		−	43.0231i		−	1.47308i	0.676392	−	0.736542i	$-0.263543\pi$
$854$	−2.14715	+	3.95673i	−0.0734739	+	0.135397i
$855$	−1.37169			−0.0469109
$856$	−1.20330	−	15.1552i	−0.0411279	−	0.517995i
$857$		−	20.2819i		−	0.692817i	−0.938084	−	0.346409i	$-0.887401\pi$
$857$		−	20.2819i		−	0.692817i	0.938084	−	0.346409i	$-0.112599\pi$
$858$	−10.7252	+	3.75911i	−0.366151	+	0.128334i
$859$		−	17.4503i		−	0.595396i	−0.954660	−	0.297698i	$-0.903781\pi$
$859$		−	17.4503i		−	0.595396i	0.954660	−	0.297698i	$-0.0962188\pi$
$860$	−0.756289	−	1.16341i	−0.0257892	−	0.0396718i
$861$	67.1013			2.28681
$862$	−32.0888	−	17.4132i	−1.09295	−	0.593097i
$863$		−	26.3121i		−	0.895675i	−0.894115	−	0.447837i	$-0.852194\pi$
$863$		−	26.3121i		−	0.895675i	0.894115	−	0.447837i	$-0.147806\pi$
$864$	−1.07870	−	1.40244i	−0.0366981	−	0.0477118i
$865$		−	1.38706i		−	0.0471613i
$866$	4.20454	+	2.28162i	0.142876	+	0.0775327i
$867$			38.1481i			1.29558i
$868$	9.70032	−	6.30583i	0.329250	−	0.214034i
$869$	15.0061	−	16.5506i	0.509046	−	0.561440i
$870$	2.93437	+	1.59236i	0.0994844	+	0.0539859i
$871$	−4.01039			−0.135887
$872$	5.06964	−	0.402520i	0.171680	−	0.0136310i
$873$	44.4756			1.50527
$874$	8.79129	−	16.2005i	0.297370	−	0.547989i
$875$	−2.92080			−0.0987411
$876$	−12.2267	−	18.8084i	−0.413101	−	0.635477i
$877$		−	55.4423i		−	1.87215i	−0.351795	−	0.936077i	$-0.614429\pi$
$877$		−	55.4423i		−	1.87215i	0.351795	−	0.936077i	$-0.385571\pi$
$878$	−0.818803	−	0.444329i	−0.0276333	−	0.0149954i
$879$	−4.40898			−0.148711
$880$	0.660806	+	1.49437i	0.0222758	+	0.0503751i
$881$	22.9564			0.773420			0.386710	−	0.922201i	$-0.373611\pi$
$881$	22.9564			0.773420			0.386710	+	0.922201i	$0.373611\pi$
$882$	−4.84961	−	2.63167i	−0.163295	−	0.0886131i
$883$			31.0856i			1.04611i	0.852297	+	0.523057i	$0.175209\pi$
$883$			31.0856i			1.04611i	−0.852297	+	0.523057i	$0.824791\pi$
$884$	6.23755	+	9.59530i	0.209792	+	0.322725i
$885$	−3.64467			−0.122514
$886$	−8.61202	+	15.8701i	−0.289326	+	0.533166i
$887$	−48.3417			−1.62315			−0.811577	−	0.584245i	$-0.801391\pi$
$887$	−48.3417			−1.62315			−0.811577	+	0.584245i	$0.801391\pi$
$888$	68.2279	−	5.41718i	2.28958	−	0.181789i
$889$	−18.6516			−0.625555
$890$	−0.473985	−	0.257211i	−0.0158880	−	0.00862173i
$891$	20.8754	−	23.0240i	0.699352	−	0.771333i
$892$	9.51742	−	6.18693i	0.318667	−	0.207154i
$893$		−	32.7517i		−	1.09599i
$894$	37.5818	+	20.3941i	1.25692	+	0.682079i
$895$		−	1.29629i		−	0.0433303i
$896$	−25.3441	−	8.92879i	−0.846688	−	0.298290i
$897$			8.14064i			0.271808i
$898$	−6.02447	−	3.26922i	−0.201039	−	0.109095i
$899$	−19.2676			−0.642610
$900$	15.5998	+	23.9973i	0.519992	+	0.799909i
$901$			82.4402i			2.74648i
$902$	−18.0897	−	51.6120i	−0.602322	−	1.71849i
$903$			32.4182i			1.07881i
$904$	2.85172	+	35.9166i	0.0948467	+	1.19457i
$905$	1.00299			0.0333406
$906$	−9.96545	+	18.3642i	−0.331080	+	0.610109i
$907$		−	0.523117i		−	0.0173698i	−0.999962	−	0.00868490i	$-0.997235\pi$
$907$		−	0.523117i		−	0.0173698i	0.999962	−	0.00868490i	$-0.00276453\pi$
$908$	−25.0846	−	38.5879i	−0.832463	−	1.28059i
$909$		−	7.05693i		−	0.234063i
$910$	−0.197312	+	0.363604i	−0.00654084	+	0.0120534i
$911$		−	11.8577i		−	0.392862i	−0.980518	−	0.196431i	$-0.937065\pi$
$911$		−	11.8577i		−	0.392862i	0.980518	−	0.196431i	$-0.0629352\pi$
$912$	−34.3617	−	15.2608i	−1.13783	−	0.505337i
$913$	3.97632	−	4.38558i	0.131597	−	0.145142i
$914$	−2.88524	+	5.31687i	−0.0954352	+	0.175867i
$915$	−0.399969			−0.0132226
$916$	2.69145	+	4.14028i	0.0889279	+	0.136799i
$917$	40.6631			1.34281
$918$	−2.22465	−	1.20722i	−0.0734243	−	0.0398442i
$919$	−50.1553			−1.65447			−0.827235	−	0.561857i	$-0.810087\pi$
$919$	−50.1553			−1.65447			−0.827235	+	0.561857i	$0.810087\pi$
$920$	1.16673	−	0.0926360i	0.0384658	−	0.00305412i
$921$		−	0.182392i		−	0.00601001i
$922$	−7.47759	+	13.7796i	−0.246261	+	0.453807i
$923$	−3.53902			−0.116488
$924$	6.08443	−	37.6851i	0.200163	−	1.23975i
$925$	49.7828			1.63685
$926$	2.70937	−	4.99279i	0.0890354	−	0.164073i
$927$			29.8089i			0.979054i
$928$	27.2826	+	35.4705i	0.895594	+	1.16438i
$929$	−54.9688			−1.80347			−0.901734	−	0.432291i	$-0.857705\pi$
$929$	−54.9688			−1.80347			−0.901734	+	0.432291i	$0.857705\pi$
$930$	0.903484	+	0.490282i	0.0296264	+	0.0160770i
$931$	5.27196			0.172781
$932$	27.3277	−	17.7647i	0.895149	−	0.581904i
$933$	20.4941			0.670947
$934$	−20.8447	+	38.4123i	−0.682059	+	1.25689i
$935$	1.73167	+	1.57007i	0.0566315	+	0.0513467i
$936$	8.09470	−	0.642705i	0.264584	−	0.0210075i
$937$		−	32.2149i		−	1.05241i	−0.850357	−	0.526207i	$-0.823614\pi$
$937$		−	32.2149i		−	1.05241i	0.850357	−	0.526207i	$-0.176386\pi$
$938$	6.42478	−	11.8395i	0.209776	−	0.386573i
$939$		−	61.8074i		−	2.01701i
$940$	1.74363	−	1.13347i	0.0568709	−	0.0369697i
$941$		−	23.4885i		−	0.765703i	−0.923810	−	0.382852i	$-0.874942\pi$
$941$		−	23.4885i		−	0.765703i	0.923810	−	0.382852i	$-0.125058\pi$
$942$	10.1657	−	18.7331i	0.331215	−	0.610358i
$943$	−39.1747			−1.27570
$944$	−44.6468	−	19.8287i	−1.45313	−	0.645368i
$945$		−	0.0914928i		−	0.00297626i
$946$	24.9350	−	8.73956i	0.810706	−	0.284148i
$947$			20.6893i			0.672313i	0.941806	+	0.336156i	$0.109127\pi$
$947$			20.6893i			0.672313i	−0.941806	+	0.336156i	$0.890873\pi$
$948$	−27.3680	+	17.7910i	−0.888872	+	0.577823i
$949$	−4.62922			−0.150271
$950$	−24.0365	−	13.0436i	−0.779848	−	0.423190i
$951$		−	52.3230i		−	1.69669i
$952$	−38.3200	+	3.04254i	−1.24196	+	0.0986093i
$953$			6.22452i			0.201632i	0.994905	+	0.100816i	$0.0321453\pi$
$953$			6.22452i			0.201632i	−0.994905	+	0.100816i	$0.967855\pi$
$954$	51.4115	+	27.8988i	1.66451	+	0.903257i
$955$			2.20772i			0.0714402i
$956$	−27.9096	−	42.9336i	−0.902659	−	1.38857i
$957$	−42.7004	+	47.0953i	−1.38031	+	1.52238i
$958$	−7.08318	−	3.84374i	−0.228847	−	0.124185i
$959$	28.1008			0.907424
$960$	−0.376736	−	2.35749i	−0.0121591	−	0.0760877i
$961$	25.0676			0.808631
$962$	6.73631	−	12.4136i	0.217187	−	0.400230i
$963$	−15.4313			−0.497267
$964$	−3.18151	+	2.06818i	−0.102469	+	0.0666117i
$965$		−	1.53570i		−	0.0494359i
$966$	−24.0328	−	13.0416i	−0.773243	−	0.419606i
$967$	51.2785			1.64900			0.824502	−	0.565859i	$-0.191455\pi$
$967$	51.2785			1.64900			0.824502	+	0.565859i	$0.191455\pi$
$968$	−30.6264	+	5.47952i	−0.984369	+	0.176118i
$969$	−53.7865			−1.72787
$970$	−2.37166	−	1.28700i	−0.0761493	−	0.0413230i
$971$			1.61997i			0.0519872i	0.999662	+	0.0259936i	$0.00827495\pi$
$971$			1.61997i			0.0519872i	−0.999662	+	0.0259936i	$0.991725\pi$
$972$	−36.4991	+	23.7267i	−1.17071	+	0.761035i
$973$	24.3918			0.781965
$974$	18.8705	−	34.7742i	0.604648	−	1.11424i
$975$	12.0782			0.386813
$976$	−4.89958	−	2.17602i	−0.156832	−	0.0696527i
$977$	12.5194			0.400531			0.200265	−	0.979742i	$-0.435820\pi$
$977$	12.5194			0.400531			0.200265	+	0.979742i	$0.435820\pi$
$978$	32.2409	+	17.4957i	1.03095	+	0.559452i
$979$	6.89734	−	7.60725i	0.220440	−	0.243129i
$980$	0.182452	+	0.280668i	0.00582821	+	0.00896560i
$981$		−	5.16199i		−	0.164810i
$982$	−23.3407	−	12.6660i	−0.744833	−	0.404189i
$983$		−	14.9564i		−	0.477034i	−0.971138	−	0.238517i	$-0.923339\pi$
$983$		−	14.9564i		−	0.477034i	0.971138	−	0.238517i	$-0.0766613\pi$
$984$	6.32476	+	79.6587i	0.201626	+	2.53943i
$985$		−	2.41658i		−	0.0769987i
$986$	56.2660	+	30.5331i	1.79187	+	0.972373i
$987$	−48.5860			−1.54651
$988$	−6.50496	+	4.22864i	−0.206950	+	0.134531i
$989$		−	18.9262i		−	0.601818i
$990$	1.56515	−	0.548574i	0.0497436	−	0.0174348i
$991$			44.3993i			1.41039i	0.709014	+	0.705195i	$0.249140\pi$
$991$			44.3993i			1.41039i	−0.709014	+	0.705195i	$0.750860\pi$
$992$	8.40023	+	10.9213i	0.266707	+	0.346751i
$993$	85.0871			2.70016
$994$	5.66962	−	10.4479i	0.179830	−	0.331387i
$995$			0.264923i			0.00839862i
$996$	−7.25199	+	4.71426i	−0.229788	+	0.149377i
$997$			39.1807i			1.24087i	0.784259	+	0.620433i	$0.213043\pi$
$997$			39.1807i			1.24087i	−0.784259	+	0.620433i	$0.786957\pi$
$998$	−17.0880	+	31.4895i	−0.540910	+	0.996781i
$999$			3.12360i			0.0988262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.13	✓	64
4.3	odd	2	inner	572.2.e.b.131.51	yes	64
11.10	odd	2	inner	572.2.e.b.131.52	yes	64
44.43	even	2	inner	572.2.e.b.131.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.13	✓	64	1.1	even	1	trivial
572.2.e.b.131.14	yes	64	44.43	even	2	inner
572.2.e.b.131.51	yes	64	4.3	odd	2	inner
572.2.e.b.131.52	yes	64	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24299 - 0.674518i) q^{2} -2.42300i q^{3} +(1.09005 + 1.67684i) q^{4} -0.123164 q^{5} +(-1.63435 + 3.01176i) q^{6} -2.37508 q^{7} +(-0.223868 - 2.81955i) q^{8} -2.87092 q^{9} +O(q^{10})\)	\(q+(-1.24299 - 0.674518i) q^{2} -2.42300i q^{3} +(1.09005 + 1.67684i) q^{4} -0.123164 q^{5} +(-1.63435 + 3.01176i) q^{6} -2.37508 q^{7} +(-0.223868 - 2.81955i) q^{8} -2.87092 q^{9} +(0.153091 + 0.0830761i) q^{10} +(-2.22776 + 2.45705i) q^{11} +(4.06297 - 2.64119i) q^{12} -1.00000i q^{13} +(2.95220 + 1.60203i) q^{14} +0.298425i q^{15} +(-1.62357 + 3.65568i) q^{16} +5.72225i q^{17} +(3.56852 + 1.93648i) q^{18} -3.87930 q^{19} +(-0.134255 - 0.206526i) q^{20} +5.75481i q^{21} +(4.42641 - 1.55143i) q^{22} -3.35974i q^{23} +(-6.83177 + 0.542431i) q^{24} -4.98483 q^{25} +(-0.674518 + 1.24299i) q^{26} -0.312771i q^{27} +(-2.58896 - 3.98262i) q^{28} +7.91062i q^{29} +(0.201293 - 0.370940i) q^{30} +2.43566i q^{31} +(4.48391 - 3.44885i) q^{32} +(5.95343 + 5.39785i) q^{33} +(3.85976 - 7.11271i) q^{34} +0.292524 q^{35} +(-3.12945 - 4.81406i) q^{36} -9.98686 q^{37} +(4.82194 + 2.61666i) q^{38} -2.42300 q^{39} +(0.0275724 + 0.347267i) q^{40} -11.6600i q^{41} +(3.88172 - 7.15318i) q^{42} +5.63323 q^{43} +(-6.54845 - 1.05728i) q^{44} +0.353593 q^{45} +(-2.26620 + 4.17613i) q^{46} +8.44267i q^{47} +(8.85771 + 3.93391i) q^{48} -1.35900 q^{49} +(6.19610 + 3.36236i) q^{50} +13.8650 q^{51} +(1.67684 - 1.09005i) q^{52} +14.4069 q^{53} +(-0.210969 + 0.388771i) q^{54} +(0.274379 - 0.302620i) q^{55} +(0.531703 + 6.69666i) q^{56} +9.39954i q^{57} +(5.33586 - 9.83283i) q^{58} +12.2130i q^{59} +(-0.500411 + 0.325299i) q^{60} +1.34026i q^{61} +(1.64290 - 3.02750i) q^{62} +6.81865 q^{63} +(-7.89977 + 1.26241i) q^{64} +0.123164i q^{65} +(-3.75911 - 10.7252i) q^{66} -4.01039i q^{67} +(-9.59530 + 6.23755i) q^{68} -8.14064 q^{69} +(-0.363604 - 0.197312i) q^{70} -3.53902i q^{71} +(0.642705 + 8.09470i) q^{72} -4.62922i q^{73} +(12.4136 + 6.73631i) q^{74} +12.0782i q^{75} +(-4.22864 - 6.50496i) q^{76} +(5.29110 - 5.83569i) q^{77} +(3.01176 + 1.63435i) q^{78} -6.73595 q^{79} +(0.199965 - 0.450247i) q^{80} -9.37059 q^{81} +(-7.86490 + 14.4933i) q^{82} -1.78490 q^{83} +(-9.64989 + 6.27304i) q^{84} -0.704774i q^{85} +(-7.00205 - 3.79971i) q^{86} +19.1674 q^{87} +(7.42651 + 5.73123i) q^{88} -3.09609 q^{89} +(-0.439513 - 0.238505i) q^{90} +2.37508i q^{91} +(5.63374 - 3.66229i) q^{92} +5.90160 q^{93} +(5.69473 - 10.4942i) q^{94} +0.477789 q^{95} +(-8.35655 - 10.8645i) q^{96} -15.4918 q^{97} +(1.68922 + 0.916667i) q^{98} +(6.39570 - 7.05398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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