LMFDB - Embedded newform 572.2.e.b.131.6

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			131.6
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39939 + 0.204204i) q^{2} +3.30990i q^{3} +(1.91660 - 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 - 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 + 1.19116i) q^{8} -7.95546 q^{9} +O(q^{10})$	\(q+(-1.39939 + 0.204204i) q^{2} +3.30990i q^{3} +(1.91660 - 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 - 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 + 1.19116i) q^{8} -7.95546 q^{9} +(-4.74137 + 0.691875i) q^{10} +(-3.04826 + 1.30695i) q^{11} +(1.89168 + 6.34377i) q^{12} -1.00000i q^{13} +(-5.10568 + 0.745036i) q^{14} +11.2145i q^{15} +(3.34672 - 2.19076i) q^{16} +2.46031i q^{17} +(11.1328 - 1.62454i) q^{18} +2.27167 q^{19} +(6.49376 - 1.93641i) q^{20} +12.0762i q^{21} +(3.99883 - 2.45141i) q^{22} -3.66413i q^{23} +(-3.94263 - 8.49114i) q^{24} +6.47965 q^{25} +(0.204204 + 1.39939i) q^{26} -16.4021i q^{27} +(6.99271 - 2.08520i) q^{28} +5.42789i q^{29} +(-2.29004 - 15.6935i) q^{30} +8.06247i q^{31} +(-4.23602 + 3.74915i) q^{32} +(-4.32589 - 10.0894i) q^{33} +(-0.502404 - 3.44294i) q^{34} +12.3617 q^{35} +(-15.2475 + 4.54673i) q^{36} -1.66138 q^{37} +(-3.17896 + 0.463884i) q^{38} +3.30990 q^{39} +(-8.69190 + 4.03585i) q^{40} +4.13884i q^{41} +(-2.46600 - 16.8993i) q^{42} +0.268482 q^{43} +(-5.09534 + 4.24706i) q^{44} -26.9544 q^{45} +(0.748229 + 5.12756i) q^{46} +1.47252i q^{47} +(7.25121 + 11.0773i) q^{48} +6.31152 q^{49} +(-9.06758 + 1.32317i) q^{50} -8.14339 q^{51} +(-0.571522 - 1.91660i) q^{52} +0.462704 q^{53} +(3.34937 + 22.9530i) q^{54} +(-10.3280 + 4.42817i) q^{55} +(-9.35975 + 4.34595i) q^{56} +7.51902i q^{57} +(-1.10840 - 7.59576i) q^{58} -12.1193i q^{59} +(6.40933 + 21.4937i) q^{60} -13.0200i q^{61} +(-1.64639 - 11.2826i) q^{62} -29.0255 q^{63} +(5.16227 - 6.11155i) q^{64} -3.38816i q^{65} +(8.11392 + 13.2357i) q^{66} -3.80684i q^{67} +(1.40612 + 4.71543i) q^{68} +12.1279 q^{69} +(-17.2989 + 2.52430i) q^{70} -3.16290i q^{71} +(20.4087 - 9.47624i) q^{72} -4.95698i q^{73} +(2.32493 - 0.339261i) q^{74} +21.4470i q^{75} +(4.35389 - 1.29831i) q^{76} +(-11.1216 + 4.76841i) q^{77} +(-4.63186 + 0.675895i) q^{78} +8.18019 q^{79} +(11.3392 - 7.42266i) q^{80} +30.4230 q^{81} +(-0.845166 - 5.79186i) q^{82} -7.49670 q^{83} +(6.90180 + 23.1452i) q^{84} +8.33593i q^{85} +(-0.375712 + 0.0548250i) q^{86} -17.9658 q^{87} +(6.26312 - 6.98379i) q^{88} +11.1692 q^{89} +(37.7198 - 5.50419i) q^{90} -3.64850i q^{91} +(-2.09413 - 7.02268i) q^{92} -26.6860 q^{93} +(-0.300694 - 2.06063i) q^{94} +7.69680 q^{95} +(-12.4093 - 14.0208i) q^{96} -2.07823 q^{97} +(-8.83229 + 1.28883i) q^{98} +(24.2503 - 10.3974i) 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 $

$2$	−1.39939	+	0.204204i	−0.989520	+	0.144394i
$2$	−1.39939	+	0.204204i	−0.989520	+	0.144394i
$3$			3.30990i			1.91097i	0.295033	+	0.955487i	$0.404669\pi$
$3$			3.30990i			1.91097i	−0.295033	+	0.955487i	$0.595331\pi$
$4$	1.91660	−	0.571522i	0.958301	−	0.285761i
$5$	3.38816			1.51523			0.757616	−	0.652700i	$-0.226364\pi$
$5$	3.38816			1.51523			0.757616	+	0.652700i	$0.226364\pi$
$6$	−0.675895	−	4.63186i	−0.275933	−	1.89095i
$7$	3.64850			1.37900			0.689501	−	0.724285i	$-0.257830\pi$
$7$	3.64850			1.37900			0.689501	+	0.724285i	$0.257830\pi$
$8$	−2.56537	+	1.19116i	−0.906996	+	0.421139i
$9$	−7.95546			−2.65182
$10$	−4.74137	+	0.691875i	−1.49935	+	0.218790i
$11$	−3.04826	+	1.30695i	−0.919084	+	0.394061i
$11$	−3.04826	+	1.30695i	−0.919084	+	0.394061i
$12$	1.89168	+	6.34377i	0.546082	+	1.83129i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−5.10568	+	0.745036i	−1.36455	+	0.199119i
$15$			11.2145i			2.89557i
$16$	3.34672	−	2.19076i	0.836681	−	0.547690i
$17$			2.46031i			0.596713i	0.954455	+	0.298356i	$0.0964384\pi$
$17$			2.46031i			0.596713i	−0.954455	+	0.298356i	$0.903562\pi$
$18$	11.1328	−	1.62454i	2.62403	−	0.382907i
$19$	2.27167			0.521158			0.260579	−	0.965453i	$-0.416087\pi$
$19$	2.27167			0.521158			0.260579	+	0.965453i	$0.416087\pi$
$20$	6.49376	−	1.93641i	1.45205	−	0.432995i
$21$			12.0762i			2.63524i
$22$	3.99883	−	2.45141i	0.852552	−	0.522642i
$23$		−	3.66413i		−	0.764024i	−0.924157	−	0.382012i	$-0.875231\pi$
$23$		−	3.66413i		−	0.764024i	0.924157	−	0.382012i	$-0.124769\pi$
$24$	−3.94263	−	8.49114i	−0.804786	−	1.73325i
$25$	6.47965			1.29593
$26$	0.204204	+	1.39939i	0.0400476	+	0.274444i
$27$		−	16.4021i		−	3.15659i
$28$	6.99271	−	2.08520i	1.32150	−	0.394065i
$29$			5.42789i			1.00793i	0.863723	+	0.503967i	$0.168127\pi$
$29$			5.42789i			1.00793i	−0.863723	+	0.503967i	$0.831873\pi$
$30$	−2.29004	−	15.6935i	−0.418102	−	2.86523i
$31$			8.06247i			1.44806i	0.689767	+	0.724031i	$0.257713\pi$
$31$			8.06247i			1.44806i	−0.689767	+	0.724031i	$0.742287\pi$
$32$	−4.23602	+	3.74915i	−0.748830	+	0.662762i
$33$	−4.32589	−	10.0894i	−0.753041	−	1.75635i
$34$	−0.502404	−	3.44294i	−0.0861616	−	0.590459i
$35$	12.3617			2.08951
$36$	−15.2475	+	4.54673i	−2.54124	+	0.757788i
$37$	−1.66138			−0.273130			−0.136565	−	0.990631i	$-0.543606\pi$
$37$	−1.66138			−0.273130			−0.136565	+	0.990631i	$0.543606\pi$
$38$	−3.17896	+	0.463884i	−0.515696	+	0.0752519i
$39$	3.30990			0.530009
$40$	−8.69190	+	4.03585i	−1.37431	+	0.638124i
$41$			4.13884i			0.646378i	0.946334	+	0.323189i	$0.104755\pi$
$41$			4.13884i			0.646378i	−0.946334	+	0.323189i	$0.895245\pi$
$42$	−2.46600	−	16.8993i	−0.380512	−	2.60762i
$43$	0.268482			0.0409431			0.0204716	−	0.999790i	$-0.493483\pi$
$43$	0.268482			0.0409431			0.0204716	+	0.999790i	$0.493483\pi$
$44$	−5.09534	+	4.24706i	−0.768152	+	0.640268i
$45$	−26.9544			−4.01813
$46$	0.748229	+	5.12756i	0.110320	+	0.756018i
$47$			1.47252i			0.214789i	0.994216	+	0.107395i	$0.0342508\pi$
$47$			1.47252i			0.214789i	−0.994216	+	0.107395i	$0.965749\pi$
$48$	7.25121	+	11.0773i	1.04662	+	1.59888i
$49$	6.31152			0.901645
$50$	−9.06758	+	1.32317i	−1.28235	+	0.187124i
$51$	−8.14339			−1.14030
$52$	−0.571522	−	1.91660i	−0.0792559	−	0.265785i
$53$	0.462704			0.0635573			0.0317786	−	0.999495i	$-0.489883\pi$
$53$	0.462704			0.0635573			0.0317786	+	0.999495i	$0.489883\pi$
$54$	3.34937	+	22.9530i	0.455792	+	3.12351i
$55$	−10.3280	+	4.42817i	−1.39263	+	0.597094i
$56$	−9.35975	+	4.34595i	−1.25075	+	0.580752i
$57$			7.51902i			0.995919i
$58$	−1.10840	−	7.59576i	−0.145539	−	0.997371i
$59$		−	12.1193i		−	1.57780i	−0.614523	−	0.788899i	$-0.710651\pi$
$59$		−	12.1193i		−	1.57780i	0.614523	−	0.788899i	$-0.289349\pi$
$60$	6.40933	+	21.4937i	0.827442	+	2.77483i
$61$		−	13.0200i		−	1.66705i	−0.552484	−	0.833523i	$-0.686320\pi$
$61$		−	13.0200i		−	1.66705i	0.552484	−	0.833523i	$-0.313680\pi$
$62$	−1.64639	−	11.2826i	−0.209091	−	1.43289i
$63$	−29.0255			−3.65687
$64$	5.16227	−	6.11155i	0.645284	−	0.763943i
$65$		−	3.38816i		−	0.420250i
$66$	8.11392	+	13.2357i	0.998755	+	1.62921i
$67$		−	3.80684i		−	0.465079i	−0.972587	−	0.232539i	$-0.925297\pi$
$67$		−	3.80684i		−	0.465079i	0.972587	−	0.232539i	$-0.0747035\pi$
$68$	1.40612	+	4.71543i	0.170517	+	0.571830i
$69$	12.1279			1.46003
$70$	−17.2989	+	2.52430i	−2.06761	+	0.301712i
$71$		−	3.16290i		−	0.375367i	−0.982230	−	0.187683i	$-0.939902\pi$
$71$		−	3.16290i		−	0.375367i	0.982230	−	0.187683i	$-0.0600979\pi$
$72$	20.4087	−	9.47624i	2.40519	−	1.11679i
$73$		−	4.95698i		−	0.580171i	−0.957001	−	0.290086i	$-0.906316\pi$
$73$		−	4.95698i		−	0.580171i	0.957001	−	0.290086i	$-0.0936838\pi$
$74$	2.32493	−	0.339261i	0.270268	−	0.0394383i
$75$			21.4470i			2.47649i
$76$	4.35389	−	1.29831i	0.499426	−	0.148927i
$77$	−11.1216	+	4.76841i	−1.26742	+	0.543411i
$78$	−4.63186	+	0.675895i	−0.524454	+	0.0765300i
$79$	8.18019			0.920343			0.460171	−	0.887830i	$-0.347788\pi$
$79$	8.18019			0.920343			0.460171	+	0.887830i	$0.347788\pi$
$80$	11.3392	−	7.42266i	1.26777	−	0.829878i
$81$	30.4230			3.38034
$82$	−0.845166	−	5.79186i	−0.0933329	−	0.639604i
$83$	−7.49670			−0.822869			−0.411435	−	0.911439i	$-0.634972\pi$
$83$	−7.49670			−0.822869			−0.411435	+	0.911439i	$0.634972\pi$
$84$	6.90180	+	23.1452i	0.753048	+	2.52535i
$85$			8.33593i			0.904159i
$86$	−0.375712	+	0.0548250i	−0.0405140	+	0.00591193i
$87$	−17.9658			−1.92614
$88$	6.26312	−	6.98379i	0.667651	−	0.744474i
$89$	11.1692			1.18394			0.591968	−	0.805961i	$-0.298351\pi$
$89$	11.1692			1.18394			0.591968	+	0.805961i	$0.298351\pi$
$90$	37.7198	−	5.50419i	3.97602	−	0.580193i
$91$		−	3.64850i		−	0.382466i
$92$	−2.09413	−	7.02268i	−0.218329	−	0.732165i
$93$	−26.6860			−2.76721
$94$	−0.300694	−	2.06063i	−0.0310142	−	0.212538i
$95$	7.69680			0.789675
$96$	−12.4093	−	14.0208i	−1.26652	−	1.43099i
$97$	−2.07823			−0.211012			−0.105506	−	0.994419i	$-0.533646\pi$
$97$	−2.07823			−0.211012			−0.105506	+	0.994419i	$0.533646\pi$
$98$	−8.83229	+	1.28883i	−0.892196	+	0.130192i
$99$	24.2503	−	10.3974i	2.43725	−	1.04498i
$100$	12.4189	−	3.70327i	1.24189	−	0.370327i
$101$			3.48082i			0.346354i	0.984891	+	0.173177i	$0.0554033\pi$
$101$			3.48082i			0.346354i	−0.984891	+	0.173177i	$0.944597\pi$
$102$	11.3958	−	1.66291i	1.12835	−	0.164653i
$103$			0.786469i			0.0774931i	0.999249	+	0.0387465i	$0.0123365\pi$
$103$			0.786469i			0.0774931i	−0.999249	+	0.0387465i	$0.987664\pi$
$104$	1.19116	+	2.56537i	0.116803	+	0.251555i
$105$			40.9160i			3.99300i
$106$	−0.647504	+	0.0944858i	−0.0628912	+	0.00917727i
$107$	5.01242			0.484569			0.242285	−	0.970205i	$-0.422103\pi$
$107$	5.01242			0.484569			0.242285	+	0.970205i	$0.422103\pi$
$108$	−9.37417	−	31.4363i	−0.902030	−	3.02496i
$109$		−	4.68963i		−	0.449185i	−0.974453	−	0.224593i	$-0.927895\pi$
$109$		−	4.68963i		−	0.449185i	0.974453	−	0.224593i	$-0.0721051\pi$
$110$	13.5487	−	8.30577i	1.29182	−	0.791924i
$111$		−	5.49902i		−	0.521944i
$112$	12.2105	−	7.99298i	1.15378	−	0.755266i
$113$	−0.503468			−0.0473623			−0.0236811	−	0.999720i	$-0.507539\pi$
$113$	−0.503468			−0.0473623			−0.0236811	+	0.999720i	$0.507539\pi$
$114$	−1.53541	−	10.5221i	−0.143805	−	0.985482i
$115$		−	12.4147i		−	1.15767i
$116$	3.10216	+	10.4031i	0.288029	+	0.965904i
$117$			7.95546i			0.735483i
$118$	2.47480	+	16.9597i	0.227824	+	1.56126i
$119$			8.97643i			0.822868i
$120$	−13.3583	−	28.7694i	−1.21944	−	2.62627i
$121$	7.58375	−	7.96786i	0.689431	−	0.724351i
$122$	2.65874	+	18.2202i	0.240711	+	1.64958i
$123$	−13.6992			−1.23521
$124$	4.60788	+	15.4526i	0.413800	+	1.38768i
$125$	5.01330			0.448403
$126$	40.6180	−	5.92711i	3.61854	−	0.528029i
$127$	15.7562			1.39814			0.699070	−	0.715053i	$-0.253597\pi$
$127$	15.7562			1.39814			0.699070	+	0.715053i	$0.253597\pi$
$128$	−5.97604	+	9.60661i	−0.528213	+	0.849112i
$129$			0.888649i			0.0782412i
$130$	0.691875	+	4.74137i	0.0606815	+	0.415846i
$131$	−18.4648			−1.61328			−0.806640	−	0.591044i	$-0.798716\pi$
$131$	−18.4648			−1.61328			−0.806640	+	0.591044i	$0.798716\pi$
$132$	−14.0573	−	16.8651i	−1.22354	−	1.46792i
$133$	8.28819			0.718677
$134$	0.777370	+	5.32726i	0.0671545	+	0.460205i
$135$		−	55.5730i		−	4.78297i
$136$	−2.93063	−	6.31161i	−0.251299	−	0.541216i
$137$	−10.6968			−0.913893			−0.456947	−	0.889494i	$-0.651057\pi$
$137$	−10.6968			−0.913893			−0.456947	+	0.889494i	$0.651057\pi$
$138$	−16.9717	+	2.47657i	−1.44473	+	0.210819i
$139$	4.88465			0.414311			0.207155	−	0.978308i	$-0.433579\pi$
$139$	4.88465			0.414311			0.207155	+	0.978308i	$0.433579\pi$
$140$	23.6924	−	7.06499i	2.00238	−	0.597100i
$141$	−4.87390			−0.410456
$142$	0.645875	+	4.42613i	0.0542006	+	0.371433i
$143$	1.30695	+	3.04826i	0.109293	+	0.254908i
$144$	−26.6247	+	17.4285i	−2.21873	+	1.45238i
$145$			18.3906i			1.52726i
$146$	1.01223	+	6.93677i	0.0837731	+	0.574091i
$147$			20.8905i			1.72302i
$148$	−3.18421	+	0.949518i	−0.261741	+	0.0780499i
$149$			6.42574i			0.526417i	0.964739	+	0.263209i	$0.0847807\pi$
$149$			6.42574i			0.526417i	−0.964739	+	0.263209i	$0.915219\pi$
$150$	−4.37956	−	30.0128i	−0.357590	−	2.45054i
$151$	−1.34645			−0.109572			−0.0547862	−	0.998498i	$-0.517448\pi$
$151$	−1.34645			−0.109572			−0.0547862	+	0.998498i	$0.517448\pi$
$152$	−5.82769	+	2.70593i	−0.472688	+	0.219480i
$153$		−	19.5729i		−	1.58238i
$154$	14.5897	−	8.94394i	1.17567	−	0.720724i
$155$			27.3170i			2.19415i
$156$	6.34377	−	1.89168i	0.507908	−	0.151456i
$157$	−0.284135			−0.0226765			−0.0113382	−	0.999936i	$-0.503609\pi$
$157$	−0.284135			−0.0226765			−0.0113382	+	0.999936i	$0.503609\pi$
$158$	−11.4473	+	1.67042i	−0.910698	+	0.132892i
$159$			1.53151i			0.121456i
$160$	−14.3523	+	12.7027i	−1.13465	+	1.00424i
$161$		−	13.3686i		−	1.05359i
$162$	−42.5738	+	6.21249i	−3.34491	+	0.488100i
$163$		−	22.6394i		−	1.77326i	−0.462482	−	0.886629i	$-0.653041\pi$
$163$		−	22.6394i		−	1.77326i	0.462482	−	0.886629i	$-0.346959\pi$
$164$	2.36544	+	7.93250i	0.184710	+	0.619424i
$165$	−14.6568	−	34.1847i	−1.14103	−	2.66127i
$166$	10.4908	−	1.53085i	0.814246	−	0.118817i
$167$	22.6967			1.75633			0.878163	−	0.478361i	$-0.158769\pi$
$167$	22.6967			1.75633			0.878163	+	0.478361i	$0.158769\pi$
$168$	−14.3847	−	30.9799i	−1.10980	−	2.39015i
$169$	−1.00000			−0.0769231
$170$	−1.70223	−	11.6652i	−0.130555	−	0.894683i
$171$	−18.0722			−1.38202
$172$	0.514573	−	0.153443i	0.0392358	−	0.0117000i
$173$		−	13.4534i		−	1.02284i	−0.859331	−	0.511421i	$-0.829119\pi$
$173$		−	13.4534i		−	1.02284i	0.859331	−	0.511421i	$-0.170881\pi$
$174$	25.1412	−	3.66868i	1.90595	−	0.278122i
$175$	23.6410			1.78709
$176$	−7.33845	+	11.0520i	−0.553157	+	0.833077i
$177$	40.1137			3.01513
$178$	−15.6302	+	2.28080i	−1.17153	+	0.170953i
$179$		−	0.860764i		−	0.0643365i	−0.999482	−	0.0321682i	$-0.989759\pi$
$179$		−	0.860764i		−	0.0643365i	0.999482	−	0.0321682i	$-0.0102412\pi$
$180$	−51.6609	+	15.4051i	−3.85057	+	1.14822i
$181$	0.970978			0.0721722			0.0360861	−	0.999349i	$-0.488511\pi$
$181$	0.970978			0.0721722			0.0360861	+	0.999349i	$0.488511\pi$
$182$	0.745036	+	5.10568i	0.0552257	+	0.378458i
$183$	43.0951			3.18568
$184$	4.36457	+	9.39986i	0.321761	+	0.692967i
$185$	−5.62904			−0.413855
$186$	37.3442	−	5.44938i	2.73821	−	0.399568i
$187$	−3.21551	−	7.49966i	−0.235141	−	0.548429i
$188$	0.841578	+	2.82223i	0.0613784	+	0.205833i
$189$		−	59.8430i		−	4.35294i
$190$	−10.7709	+	1.57172i	−0.781400	+	0.114024i
$191$		−	4.91996i		−	0.355996i	−0.984031	−	0.177998i	$-0.943038\pi$
$191$		−	4.91996i		−	0.355996i	0.984031	−	0.177998i	$-0.0569620\pi$
$192$	20.2286	+	17.0866i	1.45988	+	1.23312i
$193$		−	18.3240i		−	1.31899i	−0.751709	−	0.659495i	$-0.770770\pi$
$193$		−	18.3240i		−	1.31899i	0.751709	−	0.659495i	$-0.229230\pi$
$194$	2.90826	−	0.424382i	0.208801	−	0.0304688i
$195$	11.2145			0.803087
$196$	12.0967	−	3.60717i	0.864047	−	0.257655i
$197$		−	8.55064i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$197$		−	8.55064i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$198$	−31.8125	+	19.5021i	−2.26082	+	1.38595i
$199$			10.0993i			0.715921i	0.933737	+	0.357960i	$0.116528\pi$
$199$			10.0993i			0.715921i	−0.933737	+	0.357960i	$0.883472\pi$
$200$	−16.6227	+	7.71831i	−1.17540	+	0.545767i
$201$	12.6003			0.888754
$202$	−0.710796	−	4.87103i	−0.0500114	−	0.342725i
$203$			19.8036i			1.38994i
$204$	−15.6076	+	4.65413i	−1.09275	+	0.325854i
$205$			14.0231i			0.979413i
$206$	−0.160600	−	1.10058i	−0.0111895	−	0.0766810i
$207$			29.1499i			2.02606i
$208$	−2.19076	−	3.34672i	−0.151902	−	0.232054i
$209$	−6.92465	+	2.96897i	−0.478988	+	0.205368i
$210$	−8.35520	−	57.2576i	−0.576564	−	3.95115i
$211$	13.2949			0.915260			0.457630	−	0.889143i	$-0.348698\pi$
$211$	13.2949			0.915260			0.457630	+	0.889143i	$0.348698\pi$
$212$	0.886819	−	0.264446i	0.0609070	−	0.0181622i
$213$	10.4689			0.717316
$214$	−7.01435	+	1.02356i	−0.479491	+	0.0699688i
$215$	0.909661			0.0620383
$216$	19.5376	+	42.0775i	1.32936	+	2.86301i
$217$			29.4159i			1.99688i
$218$	0.957640	+	6.56264i	0.0648595	+	0.444478i
$219$	16.4071			1.10869
$220$	−17.2639	+	14.3897i	−1.16393	+	0.970155i
$221$	2.46031			0.165498
$222$	1.12292	+	7.69529i	0.0753655	+	0.516474i
$223$			13.9178i			0.932005i	0.884783	+	0.466002i	$0.154306\pi$
$223$			13.9178i			0.932005i	−0.884783	+	0.466002i	$0.845694\pi$
$224$	−15.4551	+	13.6788i	−1.03264	+	0.913950i
$225$	−51.5486			−3.43658
$226$	0.704550	−	0.102810i	0.0468659	−	0.00683882i
$227$	−18.3127			−1.21546			−0.607728	−	0.794145i	$-0.707919\pi$
$227$	−18.3127			−1.21546			−0.607728	+	0.794145i	$0.707919\pi$
$228$	4.29729	+	14.4110i	0.284595	+	0.954390i
$229$	−17.5457			−1.15946			−0.579728	−	0.814810i	$-0.696841\pi$
$229$	−17.5457			−1.15946			−0.579728	+	0.814810i	$0.696841\pi$
$230$	2.53512	+	17.3730i	0.167161	+	1.14554i
$231$	−15.7830	−	36.8113i	−1.03844	−	2.42200i
$232$	−6.46550	−	13.9246i	−0.424481	−	0.914192i
$233$		−	21.7862i		−	1.42726i	−0.700521	−	0.713632i	$-0.747049\pi$
$233$		−	21.7862i		−	1.42726i	0.700521	−	0.713632i	$-0.252951\pi$
$234$	−1.62454	−	11.1328i	−0.106199	−	0.727775i
$235$			4.98914i			0.325456i
$236$	−6.92645	−	23.2279i	−0.450873	−	1.51201i
$237$			27.0756i			1.75875i
$238$	−1.83302	−	12.5616i	−0.118817	−	0.814244i
$239$	2.91796			0.188747			0.0943737	−	0.995537i	$-0.469915\pi$
$239$	2.91796			0.188747			0.0943737	+	0.995537i	$0.469915\pi$
$240$	24.5683	+	37.5318i	1.58588	+	2.42267i
$241$			24.7077i			1.59156i	0.605585	+	0.795780i	$0.292939\pi$
$241$			24.7077i			1.59156i	−0.605585	+	0.795780i	$0.707061\pi$
$242$	−8.98558	+	12.6988i	−0.577615	+	0.816310i
$243$			51.4910i			3.30315i
$244$	−7.44125	−	24.9542i	−0.476377	−	1.59753i
$245$	21.3844			1.36620
$246$	19.1705	−	2.79742i	1.22227	−	0.178357i
$247$		−	2.27167i		−	0.144543i
$248$	−9.60371	−	20.6832i	−0.609836	−	1.31339i
$249$		−	24.8133i		−	1.57248i
$250$	−7.01557	+	1.02373i	−0.443704	+	0.0647466i
$251$			25.9522i			1.63809i	0.573732	+	0.819043i	$0.305495\pi$
$251$			25.9522i			1.63809i	−0.573732	+	0.819043i	$0.694505\pi$
$252$	−55.6303	+	16.5887i	−3.50438	+	1.04499i
$253$	4.78885	+	11.1692i	0.301072	+	0.702203i
$254$	−22.0492	+	3.21748i	−1.38349	+	0.201883i
$255$	−27.5911			−1.72782
$256$	6.40113	−	14.6637i	0.400071	−	0.916484i
$257$	−1.66514			−0.103868			−0.0519342	−	0.998651i	$-0.516539\pi$
$257$	−1.66514			−0.103868			−0.0519342	+	0.998651i	$0.516539\pi$
$258$	−0.181465	−	1.24357i	−0.0112975	−	0.0774213i
$259$	−6.06155			−0.376646
$260$	−1.93641	−	6.49376i	−0.120091	−	0.402726i
$261$		−	43.1814i		−	2.67286i
$262$	25.8395	−	3.77058i	1.59637	−	0.232947i
$263$	6.26154			0.386103			0.193051	−	0.981189i	$-0.438162\pi$
$263$	6.26154			0.386103			0.193051	+	0.981189i	$0.438162\pi$
$264$	23.1157	+	20.7303i	1.42267	+	1.27586i
$265$	1.56772			0.0963040
$266$	−11.5984	+	1.69248i	−0.711146	+	0.103773i
$267$			36.9691i			2.26247i
$268$	−2.17569	−	7.29619i	−0.132902	−	0.445686i
$269$	30.9237			1.88545			0.942725	−	0.333572i	$-0.108254\pi$
$269$	30.9237			1.88545			0.942725	+	0.333572i	$0.108254\pi$
$270$	11.3482	+	77.7685i	0.690631	+	4.73284i
$271$	4.30761			0.261669			0.130834	−	0.991404i	$-0.458234\pi$
$271$	4.30761			0.261669			0.130834	+	0.991404i	$0.458234\pi$
$272$	5.38995	+	8.23398i	0.326814	+	0.499258i
$273$	12.0762			0.730883
$274$	14.9691	−	2.18434i	0.904316	−	0.131961i
$275$	−19.7516	+	8.46860i	−1.19107	+	0.510676i
$276$	23.2444	−	6.93138i	1.39915	−	0.417220i
$277$		−	16.8748i		−	1.01391i	−0.861973	−	0.506954i	$-0.830772\pi$
$277$		−	16.8748i		−	1.01391i	0.861973	−	0.506954i	$-0.169228\pi$
$278$	−6.83555	+	0.997464i	−0.409969	+	0.0598239i
$279$		−	64.1407i		−	3.84000i
$280$	−31.7124	+	14.7248i	−1.89518	+	0.879974i
$281$			21.3762i			1.27520i	0.770369	+	0.637598i	$0.220072\pi$
$281$			21.3762i			1.27520i	−0.770369	+	0.637598i	$0.779928\pi$
$282$	6.82050	−	0.995268i	0.406155	−	0.0592674i
$283$	15.8967			0.944961			0.472481	−	0.881341i	$-0.343359\pi$
$283$	15.8967			0.944961			0.472481	+	0.881341i	$0.343359\pi$
$284$	−1.80767	−	6.06201i	−0.107265	−	0.359714i
$285$			25.4757i			1.50905i
$286$	−2.45141	−	3.99883i	−0.144955	−	0.236456i
$287$			15.1005i			0.891356i
$288$	33.6995	−	29.8262i	1.98576	−	1.75753i
$289$	10.9469			0.643934
$290$	−3.75542	−	25.7357i	−0.220526	−	1.51125i
$291$		−	6.87873i		−	0.403238i
$292$	−2.83303	−	9.50056i	−0.165790	−	0.555979i
$293$			24.3974i			1.42531i	0.701513	+	0.712657i	$0.252508\pi$
$293$			24.3974i			1.42531i	−0.701513	+	0.712657i	$0.747492\pi$
$294$	−4.26592	−	29.2340i	−0.248793	−	1.70496i
$295$		−	41.0622i		−	2.39073i
$296$	4.26207	−	1.97898i	0.247728	−	0.115026i
$297$	21.4368	+	49.9979i	1.24389	+	2.90117i
$298$	−1.31216	−	8.99214i	−0.0760114	−	0.520900i
$299$	−3.66413			−0.211902
$300$	12.2575	+	41.1054i	0.707684	+	2.37322i
$301$	0.979555			0.0564606
$302$	1.88421	−	0.274950i	0.108424	−	0.0158216i
$303$	−11.5212			−0.661874
$304$	7.60267	−	4.97670i	0.436043	−	0.285433i
$305$		−	44.1141i		−	2.52596i
$306$	3.99686	+	27.3902i	0.228485	+	1.56579i
$307$	−4.97498			−0.283937			−0.141969	−	0.989871i	$-0.545343\pi$
$307$	−4.97498			−0.283937			−0.141969	+	0.989871i	$0.545343\pi$
$308$	−18.5903	+	15.4954i	−1.05928	+	0.882930i
$309$	−2.60314			−0.148087
$310$	−5.57823	−	38.2272i	−0.316822	−	2.17116i
$311$		−	20.9744i		−	1.18935i	−0.803966	−	0.594675i	$-0.797281\pi$
$311$		−	20.9744i		−	1.18935i	0.803966	−	0.594675i	$-0.202719\pi$
$312$	−8.49114	+	3.94263i	−0.480716	+	0.223207i
$313$	−13.9454			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$313$	−13.9454			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$314$	0.397617	−	0.0580215i	0.0224388	−	0.00327434i
$315$	−98.3430			−5.54100
$316$	15.6782	−	4.67516i	0.881965	−	0.262998i
$317$	−30.2567			−1.69939			−0.849694	−	0.527277i	$-0.823213\pi$
$317$	−30.2567			−1.69939			−0.849694	+	0.527277i	$0.823213\pi$
$318$	−0.312739	−	2.14318i	−0.0175375	−	0.120183i
$319$	−7.09400	−	16.5456i	−0.397188	−	0.926377i
$320$	17.4906	−	20.7069i	0.977755	−	1.15755i
$321$			16.5906i			0.925999i
$322$	2.72991	+	18.7079i	0.152132	+	1.04255i
$323$			5.58902i			0.310981i
$324$	58.3088	−	17.3874i	3.23938	−	0.965969i
$325$		−	6.47965i		−	0.359426i
$326$	4.62306	+	31.6815i	0.256047	+	1.75467i
$327$	15.5222			0.858381
$328$	−4.93002	−	10.6177i	−0.272215	−	0.586262i
$329$			5.37248i			0.296195i
$330$	27.4913	+	44.8448i	1.51335	+	2.46863i
$331$			13.7221i			0.754232i	0.926166	+	0.377116i	$0.123084\pi$
$331$			13.7221i			0.754232i	−0.926166	+	0.377116i	$0.876916\pi$
$332$	−14.3682	+	4.28453i	−0.788556	+	0.235144i
$333$	13.2171			0.724292
$334$	−31.7617	+	4.63476i	−1.73792	+	0.253603i
$335$		−	12.8982i		−	0.704703i
$336$	26.4560	+	40.4156i	1.44329	+	2.20485i
$337$		−	22.8260i		−	1.24341i	−0.783252	−	0.621705i	$-0.786440\pi$
$337$		−	22.8260i		−	1.24341i	0.783252	−	0.621705i	$-0.213560\pi$
$338$	1.39939	−	0.204204i	0.0761169	−	0.0111072i
$339$		−	1.66643i		−	0.0905081i
$340$	4.76417	+	15.9767i	0.258373	+	0.866456i
$341$	−10.5373	−	24.5765i	−0.570625	−	1.33089i
$342$	25.2901	−	3.69041i	1.36753	−	0.199555i
$343$	−2.51193			−0.135632
$344$	−0.688756	+	0.319805i	−0.0371352	+	0.0172427i
$345$	41.0914			2.21229
$346$	2.74723	+	18.8266i	0.147692	+	1.01212i
$347$	26.5720			1.42646			0.713230	−	0.700930i	$-0.247231\pi$
$347$	26.5720			1.42646			0.713230	+	0.700930i	$0.247231\pi$
$348$	−34.4333	+	10.2679i	−1.84582	+	0.550415i
$349$			7.59546i			0.406575i	0.979119	+	0.203288i	$0.0651627\pi$
$349$			7.59546i			0.406575i	−0.979119	+	0.203288i	$0.934837\pi$
$350$	−33.0830	+	4.82757i	−1.76836	+	0.258045i
$351$	−16.4021			−0.875480
$352$	8.01252	−	16.9647i	0.427069	−	0.904219i
$353$	−18.8949			−1.00567			−0.502836	−	0.864382i	$-0.667710\pi$
$353$	−18.8949			−1.00567			−0.502836	+	0.864382i	$0.667710\pi$
$354$	−56.1348	+	8.19137i	−2.98353	+	0.435366i
$355$		−	10.7164i		−	0.568768i
$356$	21.4070	−	6.38347i	1.13457	−	0.338323i
$357$	−29.7111			−1.57248
$358$	0.175771	+	1.20455i	0.00928979	+	0.0636623i
$359$	26.7350			1.41102			0.705510	−	0.708700i	$-0.250718\pi$
$359$	26.7350			1.41102			0.705510	+	0.708700i	$0.250718\pi$
$360$	69.1481	−	32.1071i	3.64443	−	1.69219i
$361$	−13.8395			−0.728395
$362$	−1.35878	+	0.198277i	−0.0714159	+	0.0104212i
$363$	26.3729	+	25.1015i	1.38422	+	1.31749i
$364$	−2.08520	−	6.99271i	−0.109294	−	0.366518i
$365$		−	16.7951i		−	0.879094i
$366$	−60.3070	+	8.80018i	−3.15230	+	0.459993i
$367$			21.4052i			1.11734i	0.829389	+	0.558672i	$0.188689\pi$
$367$			21.4052i			1.11734i	−0.829389	+	0.558672i	$0.811311\pi$
$368$	−8.02724	−	12.2628i	−0.418449	−	0.639245i
$369$		−	32.9264i		−	1.71408i
$370$	7.87724	−	1.14947i	0.409518	−	0.0597581i
$371$	1.68817			0.0876456
$372$	−51.1465	+	15.2517i	−2.65182	+	0.790761i
$373$			1.40274i			0.0726311i	0.999340	+	0.0363155i	$0.0115621\pi$
$373$			1.40274i			0.0726311i	−0.999340	+	0.0363155i	$0.988438\pi$
$374$	6.03122	+	9.83835i	0.311867	+	0.508729i
$375$			16.5935i			0.856886i
$376$	−1.75401	−	3.77756i	−0.0904561	−	0.194813i
$377$	5.42789			0.279551
$378$	12.2202	+	83.7439i	0.628537	+	4.30732i
$379$			28.5798i			1.46804i	0.679125	+	0.734022i	$0.262359\pi$
$379$			28.5798i			1.46804i	−0.679125	+	0.734022i	$0.737641\pi$
$380$	14.7517	−	4.39889i	0.756746	−	0.225659i
$381$			52.1517i			2.67181i
$382$	1.00467	+	6.88495i	0.0514035	+	0.352265i
$383$			4.13836i			0.211460i	0.994395	+	0.105730i	$0.0337180\pi$
$383$			4.13836i			0.211460i	−0.994395	+	0.105730i	$0.966282\pi$
$384$	−31.7969	−	19.7801i	−1.62263	−	1.00940i
$385$	−37.6816	+	16.1562i	−1.92043	+	0.823394i
$386$	3.74183	+	25.6425i	0.190454	+	1.30517i
$387$	−2.13590			−0.108574
$388$	−3.98313	+	1.18775i	−0.202213	+	0.0602990i
$389$	8.97124			0.454860			0.227430	−	0.973794i	$-0.426968\pi$
$389$	8.97124			0.454860			0.227430	+	0.973794i	$0.426968\pi$
$390$	−15.6935	+	2.29004i	−0.794671	+	0.115961i
$391$	9.01490			0.455903
$392$	−16.1914	+	7.51803i	−0.817789	+	0.379718i
$393$		−	61.1168i		−	3.08293i
$394$	1.74607	+	11.9657i	0.0879659	+	0.602824i
$395$	27.7158			1.39453
$396$	40.5358	−	33.7873i	2.03700	−	1.69788i
$397$	−32.2239			−1.61727			−0.808636	−	0.588309i	$-0.799794\pi$
$397$	−32.2239			−1.61727			−0.808636	+	0.588309i	$0.799794\pi$
$398$	−2.06231	−	14.1329i	−0.103375	−	0.708418i
$399$			27.4331i			1.37337i
$400$	21.6856	−	14.1954i	1.08428	−	0.709768i
$401$	11.9891			0.598706			0.299353	−	0.954142i	$-0.403229\pi$
$401$	11.9891			0.598706			0.299353	+	0.954142i	$0.403229\pi$
$402$	−17.6327	+	2.57302i	−0.879440	+	0.128331i
$403$	8.06247			0.401620
$404$	1.98936	+	6.67134i	0.0989746	+	0.331912i
$405$	103.078			5.12200
$406$	−4.04398	−	27.7131i	−0.200699	−	1.37538i
$407$	5.06433	−	2.17135i	0.251029	−	0.107630i
$408$	20.8908	−	9.70009i	1.03425	−	0.480226i
$409$			7.91270i			0.391258i	0.980678	+	0.195629i	$0.0626748\pi$
$409$			7.91270i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$410$	−2.86356	−	19.6238i	−0.141421	−	0.969149i
$411$		−	35.4055i		−	1.74643i
$412$	0.449485	+	1.50735i	0.0221445	+	0.0742617i
$413$		−	44.2172i		−	2.17579i
$414$	−5.95251	−	40.7921i	−0.292550	−	2.00482i
$415$	−25.4000			−1.24684
$416$	3.74915	+	4.23602i	0.183817	+	0.207688i
$417$			16.1677i			0.791737i
$418$	9.08403	−	5.56880i	0.444314	−	0.272379i
$419$		−	8.99176i		−	0.439276i	−0.975581	−	0.219638i	$-0.929512\pi$
$419$		−	8.99176i		−	0.439276i	0.975581	−	0.219638i	$-0.0704876\pi$
$420$	23.3844	+	78.4197i	1.14104	+	3.82649i
$421$	0.804120			0.0391904			0.0195952	−	0.999808i	$-0.493762\pi$
$421$	0.804120			0.0391904			0.0195952	+	0.999808i	$0.493762\pi$
$422$	−18.6048	+	2.71487i	−0.905668	+	0.132158i
$423$		−	11.7146i		−	0.569583i
$424$	−1.18701	+	0.551155i	−0.0576462	+	0.0267665i
$425$			15.9419i			0.773298i
$426$	−14.6501	+	2.13778i	−0.709799	+	0.103576i
$427$		−	47.5036i		−	2.29886i
$428$	9.60682	−	2.86471i	0.464363	−	0.138471i
$429$	−10.0894	+	4.32589i	−0.487123	+	0.208856i
$430$	−1.27297	+	0.185756i	−0.0613882	+	0.00895795i
$431$	−33.8112			−1.62863			−0.814314	−	0.580424i	$-0.802887\pi$
$431$	−33.8112			−1.62863			−0.814314	+	0.580424i	$0.802887\pi$
$432$	−35.9331	−	54.8934i	−1.72883	−	2.64106i
$433$	−30.1294			−1.44793			−0.723964	−	0.689838i	$-0.757682\pi$
$433$	−30.1294			−1.44793			−0.723964	+	0.689838i	$0.757682\pi$
$434$	−6.00683	−	41.1644i	−0.288337	−	1.97595i
$435$	−60.8711			−2.91854
$436$	−2.68023	−	8.98815i	−0.128360	−	0.430454i
$437$		−	8.32371i		−	0.398177i
$438$	−22.9600	+	3.35040i	−1.09707	+	0.160088i
$439$	−26.3144			−1.25592			−0.627960	−	0.778246i	$-0.716110\pi$
$439$	−26.3144			−1.25592			−0.627960	+	0.778246i	$0.716110\pi$
$440$	21.2205	−	23.6622i	1.01165	−	1.12805i
$441$	−50.2110			−2.39100
$442$	−3.44294	+	0.502404i	−0.163764	+	0.0238969i
$443$		−	14.9454i		−	0.710080i	−0.934851	−	0.355040i	$-0.884467\pi$
$443$		−	14.9454i		−	0.710080i	0.934851	−	0.355040i	$-0.115533\pi$
$444$	−3.14281	−	10.5394i	−0.149151	−	0.500179i
$445$	37.8432			1.79394
$446$	−2.84207	−	19.4765i	−0.134576	−	0.922238i
$447$	−21.2686			−1.00597
$448$	18.8345	−	22.2979i	0.889847	−	1.05348i
$449$	−10.3204			−0.487052			−0.243526	−	0.969894i	$-0.578304\pi$
$449$	−10.3204			−0.487052			−0.243526	+	0.969894i	$0.578304\pi$
$450$	72.1368	−	10.5264i	3.40056	−	0.496220i
$451$	−5.40927	−	12.6162i	−0.254712	−	0.594076i
$452$	−0.964948	+	0.287743i	−0.0453873	+	0.0135343i
$453$		−	4.45661i		−	0.209390i
$454$	25.6267	−	3.73952i	1.20272	−	0.175504i
$455$		−	12.3617i		−	0.579525i
$456$	−8.95637	−	19.2891i	−0.419420	−	0.903294i
$457$			14.7674i			0.690788i	0.938458	+	0.345394i	$0.112255\pi$
$457$			14.7674i			0.690788i	−0.938458	+	0.345394i	$0.887745\pi$
$458$	24.5534	−	3.58291i	1.14730	−	0.167418i
$459$	40.3543			1.88358
$460$	−7.09527	−	23.7940i	−0.330818	−	1.10940i
$461$		−	21.2808i		−	0.991148i	−0.868566	−	0.495574i	$-0.834958\pi$
$461$		−	21.2808i		−	0.991148i	0.868566	−	0.495574i	$-0.165042\pi$
$462$	29.6036	+	48.2905i	1.37728	+	2.24668i
$463$		−	16.7667i		−	0.779217i	−0.920981	−	0.389608i	$-0.872610\pi$
$463$		−	16.7667i		−	0.779217i	0.920981	−	0.389608i	$-0.127390\pi$
$464$	11.8912	+	18.1657i	0.552036	+	0.843320i
$465$	−90.4166			−4.19297
$466$	4.44883	+	30.4875i	0.206088	+	1.41231i
$467$			19.2629i			0.891383i	0.895187	+	0.445691i	$0.147042\pi$
$467$			19.2629i			0.891383i	−0.895187	+	0.445691i	$0.852958\pi$
$468$	4.54673	+	15.2475i	0.210172	+	0.704814i
$469$		−	13.8892i		−	0.641345i
$470$	−1.01880	−	6.98177i	−0.0469938	−	0.322045i
$471$		−	0.940460i		−	0.0433341i
$472$	14.4360	+	31.0905i	0.664473	+	1.43106i
$473$	−0.818402	+	0.350893i	−0.0376302	+	0.0161341i
$474$	−5.52894	−	37.8895i	−0.253953	−	1.74032i
$475$	14.7197			0.675384
$476$	5.13023	+	17.2042i	0.235144	+	0.788555i
$477$	−3.68102			−0.168543
$478$	−4.08338	+	0.595859i	−0.186769	+	0.0272539i
$479$	−25.7851			−1.17815			−0.589077	−	0.808077i	$-0.700508\pi$
$479$	−25.7851			−1.17815			−0.589077	+	0.808077i	$0.700508\pi$
$480$	−42.0448	−	47.5048i	−1.91907	−	2.16829i
$481$			1.66138i			0.0757526i
$482$	−5.04540	−	34.5757i	−0.229812	−	1.57488i
$483$	44.2487			2.01338
$484$	9.98121	−	19.6055i	0.453691	−	0.891159i
$485$	−7.04137			−0.319732
$486$	−10.5146	−	72.0561i	−0.476954	−	3.26853i
$487$			39.7733i			1.80230i	0.433505	+	0.901151i	$0.357277\pi$
$487$			39.7733i			1.80230i	−0.433505	+	0.901151i	$0.642723\pi$
$488$	15.5090	+	33.4013i	0.702059	+	1.51200i
$489$	74.9344			3.38865
$490$	−29.9252	+	4.36678i	−1.35188	+	0.197271i
$491$	−20.7840			−0.937969			−0.468984	−	0.883206i	$-0.655380\pi$
$491$	−20.7840			−0.937969			−0.468984	+	0.883206i	$0.655380\pi$
$492$	−26.2558	+	7.82937i	−1.18370	+	0.352975i
$493$	−13.3543			−0.601447
$494$	0.463884	+	3.17896i	0.0208711	+	0.143028i
$495$	82.1640	−	35.2282i	3.69300	−	1.58339i
$496$	17.6630	+	26.9829i	0.793090	+	1.21157i
$497$		−	11.5398i		−	0.517631i
$498$	5.06698	+	34.7236i	0.227057	+	1.55600i
$499$		−	8.26104i		−	0.369815i	−0.982756	−	0.184907i	$-0.940801\pi$
$499$		−	8.26104i		−	0.369815i	0.982756	−	0.184907i	$-0.0591985\pi$
$500$	9.60850	−	2.86521i	0.429705	−	0.128136i
$501$			75.1241i			3.35630i
$502$	−5.29953	−	36.3173i	−0.236529	−	1.62092i
$503$	11.5844			0.516525			0.258262	−	0.966075i	$-0.416850\pi$
$503$	11.5844			0.516525			0.258262	+	0.966075i	$0.416850\pi$
$504$	74.4611	−	34.5740i	3.31676	−	1.54005i
$505$			11.7936i			0.524807i
$506$	−8.98228	−	14.6522i	−0.399311	−	0.651371i
$507$		−	3.30990i		−	0.146998i
$508$	30.1985	−	9.00505i	1.33984	−	0.399534i
$509$	27.8518			1.23451			0.617255	−	0.786763i	$-0.288245\pi$
$509$	27.8518			1.23451			0.617255	+	0.786763i	$0.288245\pi$
$510$	38.6108	−	5.63421i	1.70972	−	0.249487i
$511$		−	18.0855i		−	0.800057i
$512$	−5.96330	+	21.8275i	−0.263543	+	0.964648i
$513$		−	37.2603i		−	1.64508i
$514$	2.33018	−	0.340027i	0.102780	−	0.0149980i
$515$			2.66469i			0.117420i
$516$	0.507883	+	1.70319i	0.0223583	+	0.0749786i
$517$	−1.92452	−	4.48862i	−0.0846401	−	0.197409i
$518$	8.48249	−	1.23779i	0.372699	−	0.0543854i
$519$	44.5294			1.95462
$520$	4.03585	+	8.69190i	0.176984	+	0.381165i
$521$	33.9509			1.48742			0.743708	−	0.668505i	$-0.233065\pi$
$521$	33.9509			1.48742			0.743708	+	0.668505i	$0.233065\pi$
$522$	8.81780	+	60.4278i	0.385945	+	2.64485i
$523$	−26.6616			−1.16583			−0.582916	−	0.812533i	$-0.698088\pi$
$523$	−26.6616			−1.16583			−0.582916	+	0.812533i	$0.698088\pi$
$524$	−35.3897	+	10.5531i	−1.54601	+	0.461013i
$525$			78.2494i			3.41508i
$526$	−8.76235	+	1.27863i	−0.382057	+	0.0557509i
$527$	−19.8362			−0.864078
$528$	−36.5811	−	24.2896i	−1.59199	−	1.05707i
$529$	9.57413			0.416267
$530$	−2.19385	+	0.320133i	−0.0952948	+	0.0139057i
$531$			96.4146i			4.18404i
$532$	15.8852	−	4.73689i	0.688709	−	0.205370i
$533$	4.13884			0.179273
$534$	−7.54923	−	51.7343i	−0.326687	−	2.23876i
$535$	16.9829			0.734235
$536$	4.53456	+	9.76595i	0.195863	+	0.421825i
$537$	2.84905			0.122945
$538$	−43.2744	+	6.31473i	−1.86569	+	0.272247i
$539$	−19.2391	+	8.24886i	−0.828688	+	0.355303i
$540$	−31.7612	−	106.511i	−1.36679	−	4.58352i
$541$			2.26817i			0.0975161i	0.998811	+	0.0487580i	$0.0155263\pi$
$541$			2.26817i			0.0975161i	−0.998811	+	0.0487580i	$0.984474\pi$
$542$	−6.02804	+	0.879630i	−0.258927	+	0.0377833i
$543$			3.21384i			0.137919i
$544$	−9.22407	−	10.4219i	−0.395479	−	0.446836i
$545$		−	15.8892i		−	0.680620i
$546$	−16.8993	+	2.46600i	−0.723224	+	0.105535i
$547$	6.31707			0.270098			0.135049	−	0.990839i	$-0.456881\pi$
$547$	6.31707			0.270098			0.135049	+	0.990839i	$0.456881\pi$
$548$	−20.5016	+	6.11349i	−0.875785	+	0.261155i
$549$			103.581i			4.42071i
$550$	25.9110	−	15.8843i	1.10485	−	0.677307i
$551$			12.3304i			0.525293i
$552$	−31.1126	+	14.4463i	−1.32424	+	0.614876i
$553$	29.8454			1.26915
$554$	3.44589	+	23.6144i	0.146402	+	1.00328i
$555$		−	18.6316i		−	0.790867i
$556$	9.36193	−	2.79169i	0.397034	−	0.118394i
$557$		−	27.1008i		−	1.14830i	−0.818752	−	0.574148i	$-0.805333\pi$
$557$		−	27.1008i		−	1.14830i	0.818752	−	0.574148i	$-0.194667\pi$
$558$	13.0978	+	89.7581i	0.554473	+	3.79976i
$559$		−	0.268482i		−	0.0113556i
$560$	41.3712	−	27.0815i	1.74825	−	1.14440i
$561$	24.8231	−	10.6430i	1.04803	−	0.449349i
$562$	−4.36509	−	29.9137i	−0.184130	−	1.26183i
$563$	−17.6243			−0.742777			−0.371389	−	0.928477i	$-0.621118\pi$
$563$	−17.6243			−0.742777			−0.371389	+	0.928477i	$0.621118\pi$
$564$	−9.34133	+	2.78554i	−0.393341	+	0.117293i
$565$	−1.70583			−0.0717649
$566$	−22.2457	+	3.24617i	−0.935058	+	0.136447i
$567$	110.998			4.66149
$568$	3.76752	+	8.11400i	0.158082	+	0.340456i
$569$		−	12.6178i		−	0.528966i	−0.964390	−	0.264483i	$-0.914799\pi$
$569$		−	12.6178i		−	0.528966i	0.964390	−	0.264483i	$-0.0852013\pi$
$570$	−5.20223	−	35.6505i	−0.217897	−	1.49323i
$571$	−22.1407			−0.926560			−0.463280	−	0.886212i	$-0.653328\pi$
$571$	−22.1407			−0.926560			−0.463280	+	0.886212i	$0.653328\pi$
$572$	4.24706	+	5.09534i	0.177578	+	0.213047i
$573$	16.2846			0.680298
$574$	−3.08358	−	21.1316i	−0.128706	−	0.882015i
$575$		−	23.7423i		−	0.990122i
$576$	−41.0682	+	48.6202i	−1.71118	+	2.02584i
$577$	11.8129			0.491779			0.245889	−	0.969298i	$-0.420920\pi$
$577$	11.8129			0.491779			0.245889	+	0.969298i	$0.420920\pi$
$578$	−15.3190	+	2.23539i	−0.637186	+	0.0929800i
$579$	60.6506			2.52055
$580$	10.5106	+	35.2474i	0.436430	+	1.46357i
$581$	−27.3517			−1.13474
$582$	1.40466	+	9.62605i	0.0582251	+	0.399013i
$583$	−1.41044	+	0.604732i	−0.0584145	+	0.0250455i
$584$	5.90457	+	12.7165i	0.244333	+	0.526213i
$585$			26.9544i			1.11443i
$586$	−4.98205	−	34.1416i	−0.205806	−	1.41038i
$587$		−	27.8673i		−	1.15021i	−0.818081	−	0.575103i	$-0.804962\pi$
$587$		−	27.8673i		−	1.15021i	0.818081	−	0.575103i	$-0.195038\pi$
$588$	11.9394	+	40.0388i	0.492372	+	1.65117i
$589$			18.3153i			0.754669i
$590$	8.38504	+	57.4621i	0.345207	+	2.36568i
$591$	28.3018			1.16418
$592$	−5.56019	+	3.63970i	−0.228523	+	0.149591i
$593$		−	18.2908i		−	0.751113i	−0.926799	−	0.375557i	$-0.877452\pi$
$593$		−	18.2908i		−	0.751113i	0.926799	−	0.375557i	$-0.122548\pi$
$594$	−40.2082	−	65.5892i	−1.64976	−	2.69116i
$595$			30.4136i			1.24684i
$596$	3.67245	+	12.3156i	0.150430	+	0.504466i
$597$	−33.4277			−1.36811
$598$	5.12756	−	0.748229i	0.209682	−	0.0305974i
$599$		−	21.6501i		−	0.884601i	−0.896867	−	0.442300i	$-0.854163\pi$
$599$		−	21.6501i		−	0.884601i	0.896867	−	0.442300i	$-0.145837\pi$
$600$	−25.5469	−	55.0196i	−1.04295	−	2.24617i
$601$			5.66018i			0.230884i	0.993314	+	0.115442i	$0.0368284\pi$
$601$			5.66018i			0.230884i	−0.993314	+	0.115442i	$0.963172\pi$
$602$	−1.37078	+	0.200029i	−0.0558689	+	0.00815256i
$603$			30.2851i			1.23331i
$604$	−2.58061	+	0.769525i	−0.105003	+	0.0313115i
$605$	25.6950	−	26.9964i	1.04465	−	1.09756i
$606$	16.1226	−	2.35267i	0.654938	−	0.0955705i
$607$	−33.0850			−1.34288			−0.671439	−	0.741059i	$-0.734324\pi$
$607$	−33.0850			−1.34288			−0.671439	+	0.741059i	$0.734324\pi$
$608$	−9.62286	+	8.51685i	−0.390258	+	0.345404i
$609$	−65.5481			−2.65614
$610$	9.00825	+	61.7329i	0.364733	+	2.49949i
$611$	1.47252			0.0595718
$612$	−11.1864	−	37.5135i	−0.452182	−	1.51639i
$613$			47.3563i			1.91270i	0.292221	+	0.956351i	$0.405606\pi$
$613$			47.3563i			1.91270i	−0.292221	+	0.956351i	$0.594394\pi$
$614$	6.96195	−	1.01591i	0.280962	−	0.0409988i
$615$	−46.4150			−1.87163
$616$	22.8510	−	25.4803i	0.920692	−	1.02663i
$617$	−3.03586			−0.122219			−0.0611095	−	0.998131i	$-0.519464\pi$
$617$	−3.03586			−0.122219			−0.0611095	+	0.998131i	$0.519464\pi$
$618$	3.64281	−	0.531570i	0.146535	−	0.0213829i
$619$			8.34589i			0.335449i	0.985834	+	0.167725i	$0.0536420\pi$
$619$			8.34589i			0.335449i	−0.985834	+	0.167725i	$0.946358\pi$
$620$	15.6123	+	52.3558i	0.627004	+	2.10266i
$621$	−60.0995			−2.41171
$622$	4.28305	+	29.3514i	0.171735	+	1.17689i
$623$	40.7509			1.63265
$624$	11.0773	−	7.25121i	0.443448	−	0.290281i
$625$	−15.4124			−0.616495
$626$	19.5151	−	2.84770i	0.779978	−	0.113817i
$627$	−9.82701	−	22.9199i	−0.392453	−	0.915333i
$628$	−0.544574	+	0.162390i	−0.0217309	+	0.00648005i
$629$		−	4.08752i		−	0.162980i
$630$	137.621	−	20.0820i	5.48293	−	0.800086i
$631$		−	5.91858i		−	0.235615i	−0.993036	−	0.117808i	$-0.962413\pi$
$631$		−	5.91858i		−	0.235615i	0.993036	−	0.117808i	$-0.0375866\pi$
$632$	−20.9852	+	9.74392i	−0.834747	+	0.387592i
$633$			44.0049i			1.74904i
$634$	42.3411	−	6.17854i	1.68158	−	0.245381i
$635$	53.3847			2.11851
$636$	0.875289	+	2.93529i	0.0347075	+	0.116392i
$637$		−	6.31152i		−	0.250071i
$638$	13.3060	+	21.7052i	0.526788	+	0.859317i
$639$			25.1623i			0.995405i
$640$	−20.2478	+	32.5488i	−0.800365	+	1.28660i
$641$	31.0384			1.22594			0.612972	−	0.790105i	$-0.289974\pi$
$641$	31.0384			1.22594			0.612972	+	0.790105i	$0.289974\pi$
$642$	−3.38787	−	23.2168i	−0.133709	−	0.916295i
$643$		−	21.3963i		−	0.843786i	−0.906646	−	0.421893i	$-0.861366\pi$
$643$		−	21.3963i		−	0.843786i	0.906646	−	0.421893i	$-0.138634\pi$
$644$	−7.64044	−	25.6222i	−0.301075	−	1.00966i
$645$			3.01089i			0.118554i
$646$	−1.14130	−	7.82124i	−0.0449038	−	0.307723i
$647$		−	10.1571i		−	0.399317i	−0.979866	−	0.199658i	$-0.936017\pi$
$647$		−	10.1571i		−	0.399317i	0.979866	−	0.199658i	$-0.0639832\pi$
$648$	−78.0464	+	36.2387i	−3.06595	+	1.42359i
$649$	15.8394	+	36.9427i	0.621749	+	1.45013i
$650$	1.32317	+	9.06758i	0.0518989	+	0.355660i
$651$	−97.3638			−3.81599
$652$	−12.9389	−	43.3908i	−0.506728	−	1.69931i
$653$	−13.1760			−0.515617			−0.257809	−	0.966196i	$-0.583000\pi$
$653$	−13.1760			−0.515617			−0.257809	+	0.966196i	$0.583000\pi$
$654$	−21.7217	+	3.16969i	−0.849385	+	0.123945i
$655$	−62.5618			−2.44449
$656$	9.06721	+	13.8515i	0.354015	+	0.540812i
$657$			39.4351i			1.53851i
$658$	−1.09708	−	7.51822i	−0.0427687	−	0.293091i
$659$	−1.29334			−0.0503815			−0.0251907	−	0.999683i	$-0.508019\pi$
$659$	−1.29334			−0.0503815			−0.0251907	+	0.999683i	$0.508019\pi$
$660$	−47.6286	−	57.1417i	−1.85394	−	2.22424i
$661$	2.67377			0.103997			0.0519987	−	0.998647i	$-0.483441\pi$
$661$	2.67377			0.103997			0.0519987	+	0.998647i	$0.483441\pi$
$662$	−2.80209	−	19.2025i	−0.108906	−	0.746328i
$663$			8.14339i			0.316263i
$664$	19.2318	−	8.92978i	0.746339	−	0.346542i
$665$	28.0817			1.08896
$666$	−18.4959	+	2.69898i	−0.716701	+	0.104583i
$667$	19.8885			0.770086
$668$	43.5006	−	12.9717i	1.68309	−	0.501890i
$669$	−46.0666			−1.78104
$670$	2.63386	+	18.0496i	0.101755	+	0.697318i
$671$	17.0166	+	39.6885i	0.656918	+	1.53216i
$672$	−45.2754	−	51.1549i	−1.74654	−	1.97334i
$673$			46.4120i			1.78905i	0.447016	+	0.894526i	$0.352487\pi$
$673$			46.4120i			1.78905i	−0.447016	+	0.894526i	$0.647513\pi$
$674$	4.66114	+	31.9425i	0.179541	+	1.23038i
$675$		−	106.280i		−	4.09072i
$676$	−1.91660	+	0.571522i	−0.0737155	+	0.0219816i
$677$		−	33.1432i		−	1.27380i	−0.770948	−	0.636898i	$-0.780217\pi$
$677$		−	33.1432i		−	1.27380i	0.770948	−	0.636898i	$-0.219783\pi$
$678$	0.340291	+	2.33199i	0.0130688	+	0.0895596i
$679$	−7.58240			−0.290986
$680$	−9.92944	−	21.3848i	−0.380777	−	0.820068i
$681$		−	60.6132i		−	2.32270i
$682$	19.7644	+	32.2404i	0.756818	+	1.23455i
$683$		−	11.2715i		−	0.431293i	−0.976471	−	0.215647i	$-0.930814\pi$
$683$		−	11.2715i		−	0.431293i	0.976471	−	0.215647i	$-0.0691859\pi$
$684$	−34.6373	+	10.3287i	−1.32439	+	0.394927i
$685$	−36.2427			−1.38476
$686$	3.51518	−	0.512945i	0.134210	−	0.0195843i
$687$		−	58.0747i		−	2.21569i
$688$	0.898535	−	0.588180i	0.0342563	−	0.0224241i
$689$		−	0.462704i		−	0.0176276i
$690$	−57.5030	+	8.39101i	−2.18910	+	0.319440i
$691$			12.0248i			0.457446i	0.973492	+	0.228723i	$0.0734550\pi$
$691$			12.0248i			0.457446i	−0.973492	+	0.228723i	$0.926545\pi$
$692$	−7.68890	−	25.7848i	−0.292288	−	0.980189i
$693$	88.4771	−	37.9349i	3.36097	−	1.44103i
$694$	−37.1847	+	5.42610i	−1.41151	+	0.205972i
$695$	16.5500			0.627777
$696$	46.0890	−	21.4002i	1.74700	−	0.811171i
$697$	−10.1828			−0.385702
$698$	−1.55102	−	10.6290i	−0.0587070	−	0.402315i
$699$	72.1103			2.72746
$700$	45.3103	−	13.5113i	1.71257	−	0.510681i
$701$		−	4.98845i		−	0.188411i	−0.995553	−	0.0942056i	$-0.969969\pi$
$701$		−	4.98845i		−	0.188411i	0.995553	−	0.0942056i	$-0.0300311\pi$
$702$	22.9530	−	3.34937i	0.866305	−	0.126414i
$703$	−3.77412			−0.142344
$704$	−7.74842	+	25.3764i	−0.292030	+	0.956409i
$705$	−16.5136			−0.621937
$706$	26.4414	−	3.85840i	0.995134	−	0.145213i
$707$			12.6997i			0.477623i
$708$	76.8820	−	22.9259i	2.88940	−	0.861607i
$709$	4.82025			0.181028			0.0905141	−	0.995895i	$-0.471149\pi$
$709$	4.82025			0.181028			0.0905141	+	0.995895i	$0.471149\pi$
$710$	2.18833	+	14.9965i	0.0821265	+	0.562807i
$711$	−65.0772			−2.44059
$712$	−28.6533	+	13.3044i	−1.07383	+	0.498602i
$713$	29.5420			1.10636
$714$	41.5775	−	6.06712i	1.55600	−	0.227056i
$715$	4.42817	+	10.3280i	0.165604	+	0.386245i
$716$	−0.491946	−	1.64974i	−0.0183849	−	0.0616537i
$717$			9.65818i			0.360691i
$718$	−37.4128	+	5.45939i	−1.39623	+	0.203743i
$719$		−	47.2849i		−	1.76343i	−0.471784	−	0.881714i	$-0.656390\pi$
$719$		−	47.2849i		−	1.76343i	0.471784	−	0.881714i	$-0.343610\pi$
$720$	−90.2090	+	59.0507i	−3.36189	+	2.20069i
$721$			2.86943i			0.106863i
$722$	19.3669	−	2.82608i	0.720761	−	0.105176i
$723$	−81.7800			−3.04143
$724$	1.86098	−	0.554936i	0.0691627	−	0.0206240i
$725$			35.1708i			1.30621i
$726$	−42.0318	−	29.7414i	−1.55995	−	1.10381i
$727$		−	22.9216i		−	0.850117i	−0.905166	−	0.425058i	$-0.860254\pi$
$727$		−	22.9216i		−	0.850117i	0.905166	−	0.425058i	$-0.139746\pi$
$728$	4.34595	+	9.35975i	0.161072	+	0.346895i
$729$	−79.1611			−2.93189
$730$	3.42962	+	23.5029i	0.126936	+	0.869882i
$731$			0.660549i			0.0244313i
$732$	82.5962	−	24.6298i	3.05284	−	0.910344i
$733$			32.5604i			1.20265i	0.799006	+	0.601323i	$0.205360\pi$
$733$			32.5604i			1.20265i	−0.799006	+	0.601323i	$0.794640\pi$
$734$	−4.37102	−	29.9543i	−0.161337	−	1.10563i
$735$			70.7805i			2.61078i
$736$	13.7374	+	15.5213i	0.506367	+	0.572124i
$737$	4.97536	+	11.6042i	0.183270	+	0.427447i
$738$	6.72369	+	46.0769i	0.247502	+	1.69612i
$739$	−38.4469			−1.41429			−0.707146	−	0.707068i	$-0.750018\pi$
$739$	−38.4469			−1.41429			−0.707146	+	0.707068i	$0.750018\pi$
$740$	−10.7886	+	3.21712i	−0.396598	+	0.118264i
$741$	7.51902			0.276218
$742$	−2.36242	+	0.344731i	−0.0867271	+	0.0126555i
$743$	−38.2393			−1.40286			−0.701432	−	0.712737i	$-0.747455\pi$
$743$	−38.2393			−1.40286			−0.701432	+	0.712737i	$0.747455\pi$
$744$	68.4596	−	31.7874i	2.50985	−	1.16538i
$745$			21.7715i			0.797644i
$746$	−0.286444	−	1.96298i	−0.0104875	−	0.0718699i
$747$	59.6397			2.18210
$748$	−10.4491	−	12.5361i	−0.382056	−	0.458366i
$749$	18.2878			0.668222
$750$	−3.38846	−	23.2209i	−0.123729	−	0.847907i
$751$			17.9107i			0.653571i	0.945098	+	0.326786i	$0.105966\pi$
$751$			17.9107i			0.653571i	−0.945098	+	0.326786i	$0.894034\pi$
$752$	3.22594	+	4.92812i	0.117638	+	0.179710i
$753$	−85.8992			−3.13034
$754$	−7.59576	+	1.10840i	−0.276621	+	0.0403654i
$755$	−4.56199			−0.166028
$756$	−34.2016	−	114.695i	−1.24390	−	4.17143i
$757$	25.8674			0.940168			0.470084	−	0.882622i	$-0.344224\pi$
$757$	25.8674			0.940168			0.470084	+	0.882622i	$0.344224\pi$
$758$	−5.83610	−	39.9943i	−0.211977	−	1.45266i
$759$	−36.9690	+	15.8506i	−1.34189	+	0.575342i
$760$	−19.7452	+	9.16813i	−0.716232	+	0.332563i
$761$		−	22.3556i		−	0.810392i	−0.914230	−	0.405196i	$-0.867203\pi$
$761$		−	22.3556i		−	0.810392i	0.914230	−	0.405196i	$-0.132797\pi$
$762$	−10.6496	−	72.9807i	−0.385793	−	2.64381i
$763$		−	17.1101i		−	0.619427i
$764$	−2.81186	−	9.42960i	−0.101730	−	0.341151i
$765$		−	66.3162i		−	2.39767i
$766$	−0.845068	−	5.79119i	−0.0305336	−	0.209244i
$767$	−12.1193			−0.437602
$768$	48.5356	+	21.1871i	1.75138	+	0.764524i
$769$		−	33.3904i		−	1.20409i	−0.798463	−	0.602044i	$-0.794353\pi$
$769$		−	33.3904i		−	1.20409i	0.798463	−	0.602044i	$-0.205647\pi$
$770$	49.4323	−	30.3035i	1.78142	−	1.09206i
$771$		−	5.51145i		−	0.198490i
$772$	−10.4726	−	35.1198i	−0.376916	−	1.26399i
$773$	−28.6201			−1.02939			−0.514696	−	0.857373i	$-0.672095\pi$
$773$	−28.6201			−1.02939			−0.514696	+	0.857373i	$0.672095\pi$
$774$	2.98896	−	0.436158i	0.107436	−	0.0156774i
$775$			52.2420i			1.87659i
$776$	5.33143	−	2.47550i	0.191387	−	0.0888654i
$777$		−	20.0632i		−	0.719762i
$778$	−12.5543	+	1.83196i	−0.450093	+	0.0656789i
$779$			9.40209i			0.336865i
$780$	21.4937	−	6.40933i	0.769599	−	0.229491i
$781$	4.13376	+	9.64132i	0.147917	+	0.344994i
$782$	−12.6154	+	1.84088i	−0.451125	+	0.0658296i
$783$	89.0289			3.18163
$784$	21.1229	−	13.8270i	0.754389	−	0.493822i
$785$	−0.962697			−0.0343601
$786$	12.4803	+	85.5264i	0.445157	+	3.05063i
$787$	−33.4844			−1.19359			−0.596795	−	0.802394i	$-0.703559\pi$
$787$	−33.4844			−1.19359			−0.596795	+	0.802394i	$0.703559\pi$
$788$	−4.88688	−	16.3882i	−0.174088	−	0.583805i
$789$			20.7251i			0.737833i
$790$	−38.7853	+	5.65967i	−1.37992	+	0.201362i
$791$	−1.83690			−0.0653127
$792$	−49.8260	+	55.5593i	−1.77049	+	1.97421i
$793$	−13.0200			−0.462355
$794$	45.0939	−	6.58024i	1.60032	−	0.233524i
$795$			5.18899i			0.184035i
$796$	5.77198	+	19.3563i	0.204582	+	0.686067i
$797$	14.4788			0.512867			0.256433	−	0.966562i	$-0.417453\pi$
$797$	14.4788			0.512867			0.256433	+	0.966562i	$0.417453\pi$
$798$	−5.60194	−	38.3897i	−0.198307	−	1.35898i
$799$	−3.62286			−0.128167
$800$	−27.4479	+	24.2932i	−0.970431	+	0.858894i
$801$	−88.8565			−3.13959
$802$	−16.7774	+	2.44821i	−0.592431	+	0.0864494i
$803$	6.47855	+	15.1102i	0.228623	+	0.533226i
$804$	24.1497	−	7.20133i	0.851694	−	0.253971i
$805$		−	45.2949i		−	1.59644i
$806$	−11.2826	+	1.64639i	−0.397412	+	0.0579915i
$807$			102.354i			3.60304i
$808$	−4.14622	−	8.92959i	−0.145863	−	0.314142i
$809$			5.77857i			0.203164i	0.994827	+	0.101582i	$0.0323904\pi$
$809$			5.77857i			0.203164i	−0.994827	+	0.101582i	$0.967610\pi$
$810$	−144.247	+	21.0489i	−5.06832	+	0.739584i
$811$	−24.0975			−0.846178			−0.423089	−	0.906088i	$-0.639054\pi$
$811$	−24.0975			−0.846178			−0.423089	+	0.906088i	$0.639054\pi$
$812$	11.3182	+	37.9557i	0.397192	+	1.33198i
$813$			14.2578i			0.500042i
$814$	−6.64359	+	4.07273i	−0.232858	+	0.142749i
$815$		−	76.7061i		−	2.68690i
$816$	−27.2537	+	17.8402i	−0.954070	+	0.624533i
$817$	0.609903			0.0213378
$818$	−1.61580	−	11.0730i	−0.0564952	−	0.387158i
$819$			29.0255i			1.01423i
$820$	8.01449	+	26.8766i	0.279878	+	0.938572i
$821$			40.1363i			1.40077i	0.713767	+	0.700383i	$0.246987\pi$
$821$			40.1363i			1.40077i	−0.713767	+	0.700383i	$0.753013\pi$
$822$	7.22994	+	49.5463i	0.252173	+	1.72812i
$823$			38.6066i			1.34574i	0.739759	+	0.672871i	$0.234939\pi$
$823$			38.6066i			1.34574i	−0.739759	+	0.672871i	$0.765061\pi$
$824$	−0.936812	−	2.01759i	−0.0326354	−	0.0702859i
$825$	−28.0303	−	65.3760i	−0.975888	−	2.27610i
$826$	9.02931	+	61.8772i	0.314170	+	2.15298i
$827$	−2.93825			−0.102173			−0.0510865	−	0.998694i	$-0.516268\pi$
$827$	−2.93825			−0.102173			−0.0510865	+	0.998694i	$0.516268\pi$
$828$	16.6598	+	55.8687i	0.578968	+	1.94157i
$829$	−3.99161			−0.138634			−0.0693172	−	0.997595i	$-0.522082\pi$
$829$	−3.99161			−0.138634			−0.0693172	+	0.997595i	$0.522082\pi$
$830$	35.5446	−	5.18678i	1.23377	−	0.180036i
$831$	55.8539			1.93755
$832$	−6.11155	−	5.16227i	−0.211880	−	0.178969i
$833$			15.5283i			0.538023i
$834$	−3.30151	−	22.6250i	−0.114322	−	0.783440i
$835$	76.9003			2.66124
$836$	−11.5750	+	9.64793i	−0.400328	+	0.333681i
$837$	132.242			4.57094
$838$	1.83615	+	12.5830i	0.0634287	+	0.434673i
$839$		−	51.7240i		−	1.78571i	−0.450345	−	0.892855i	$-0.648699\pi$
$839$		−	51.7240i		−	1.78571i	0.450345	−	0.892855i	$-0.351301\pi$
$840$	−48.7376	−	104.965i	−1.68161	−	3.62163i
$841$	−0.462017			−0.0159316
$842$	−1.12528	+	0.164204i	−0.0387797	+	0.00565885i
$843$	−70.7531			−2.43687
$844$	25.4811	−	7.59834i	0.877094	−	0.261546i
$845$	−3.38816			−0.116556
$846$	2.39216	+	16.3933i	0.0822442	+	0.563613i
$847$	27.6693	−	29.0707i	0.950727	−	0.998881i
$848$	1.54854	−	1.01367i	0.0531772	−	0.0348097i
$849$			52.6166i			1.80580i
$850$	−3.25540	−	22.3091i	−0.111659	−	0.765194i
$851$			6.08753i			0.208678i
$852$	20.0647	−	5.98320i	0.687404	−	0.204981i
$853$		−	10.3548i		−	0.354542i	−0.984162	−	0.177271i	$-0.943273\pi$
$853$		−	10.3548i		−	0.354542i	0.984162	−	0.177271i	$-0.0567269\pi$
$854$	9.70041	+	66.4762i	0.331941	+	2.27477i
$855$	−61.2316			−2.09408
$856$	−12.8587	+	5.97061i	−0.439502	+	0.204071i
$857$			19.2916i			0.658988i	0.944158	+	0.329494i	$0.106878\pi$
$857$			19.2916i			0.658988i	−0.944158	+	0.329494i	$0.893122\pi$
$858$	13.2357	−	8.11392i	0.451860	−	0.277005i
$859$			6.88893i			0.235047i	0.993070	+	0.117524i	$0.0374956\pi$
$859$			6.88893i			0.235047i	−0.993070	+	0.117524i	$0.962504\pi$
$860$	1.74346	−	0.519891i	0.0594514	−	0.0177281i
$861$	−49.9813			−1.70336
$862$	47.3152	−	6.90437i	1.61156	−	0.235164i
$863$			48.8191i			1.66182i	0.556405	+	0.830911i	$0.312180\pi$
$863$			48.8191i			1.66182i	−0.556405	+	0.830911i	$0.687820\pi$
$864$	61.4940	+	69.4797i	2.09207	+	2.36375i
$865$		−	45.5822i		−	1.54984i
$866$	42.1629	−	6.15254i	1.43275	−	0.209072i
$867$			36.2331i			1.23054i
$868$	16.8118	+	56.3786i	0.570631	+	1.91361i
$869$	−24.9353	+	10.6911i	−0.845873	+	0.362671i
$870$	85.1826	−	12.4301i	2.88796	−	0.421420i
$871$	−3.80684			−0.128990
$872$	5.58611	+	12.0306i	0.189169	+	0.407409i
$873$	16.5333			0.559566
$874$	1.69973	+	11.6481i	0.0574943	+	0.394004i
$875$	18.2910			0.618348
$876$	31.4460	−	9.37705i	1.06246	−	0.316821i
$877$		−	18.5633i		−	0.626838i	−0.949615	−	0.313419i	$-0.898525\pi$
$877$		−	18.5633i		−	0.626838i	0.949615	−	0.313419i	$-0.101475\pi$
$878$	36.8242	−	5.37350i	1.24276	−	0.181347i
$879$	−80.7532			−2.72374
$880$	−24.8639	+	37.4460i	−0.838161	+	1.26231i
$881$	11.4335			0.385204			0.192602	−	0.981277i	$-0.438307\pi$
$881$	11.4335			0.385204			0.192602	+	0.981277i	$0.438307\pi$
$882$	70.2650	−	10.2533i	2.36595	−	0.345246i
$883$		−	11.9040i		−	0.400601i	−0.979734	−	0.200301i	$-0.935808\pi$
$883$		−	11.9040i		−	0.400601i	0.979734	−	0.200301i	$-0.0641919\pi$
$884$	4.71543	−	1.40612i	0.158597	−	0.0472930i
$885$	135.912			4.56863
$886$	3.05191	+	20.9146i	0.102531	+	0.702638i
$887$	−25.6648			−0.861740			−0.430870	−	0.902414i	$-0.641793\pi$
$887$	−25.6648			−0.861740			−0.430870	+	0.902414i	$0.641793\pi$
$888$	6.55022	+	14.1070i	0.219811	+	0.473401i
$889$	57.4866			1.92804
$890$	−52.9575	+	7.72772i	−1.77514	+	0.259034i
$891$	−92.7372	+	39.7615i	−3.10681	+	1.33206i
$892$	7.95433	+	26.6749i	0.266331	+	0.893141i
$893$			3.34509i			0.111939i
$894$	29.7631	−	4.34312i	0.995427	−	0.145256i
$895$		−	2.91641i		−	0.0974848i
$896$	−21.8036	+	35.0497i	−0.728406	+	1.17093i
$897$		−	12.1279i		−	0.404940i
$898$	14.4424	−	2.10747i	0.481948	−	0.0703272i
$899$	−43.7622			−1.45955
$900$	−98.7982	+	29.4612i	−3.29327	+	0.982040i
$901$			1.13839i			0.0379254i
$902$	10.1460	+	16.5505i	0.337824	+	0.551071i
$903$			3.24223i			0.107895i
$904$	1.29158	−	0.599712i	0.0429574	−	0.0199461i
$905$	3.28983			0.109358
$906$	0.910057	+	6.23656i	0.0302346	+	0.207196i
$907$		−	51.3966i		−	1.70660i	−0.521424	−	0.853298i	$-0.674599\pi$
$907$		−	51.3966i		−	1.70660i	0.521424	−	0.853298i	$-0.325401\pi$
$908$	−35.0981	+	10.4661i	−1.16477	+	0.347330i
$909$		−	27.6915i		−	0.918470i
$910$	2.52430	+	17.2989i	0.0836799	+	0.573452i
$911$			16.2748i			0.539208i	0.962971	+	0.269604i	$0.0868928\pi$
$911$			16.2748i			0.539208i	−0.962971	+	0.269604i	$0.913107\pi$
$912$	16.4724	+	25.1641i	0.545455	+	0.833267i
$913$	22.8519	−	9.79783i	0.756286	−	0.324261i
$914$	−3.01555	−	20.6653i	−0.0997455	−	0.683549i
$915$	146.013			4.82705
$916$	−33.6282	+	10.0278i	−1.11111	+	0.331327i
$917$	−67.3688			−2.22471
$918$	−56.4715	+	8.24049i	−1.86384	+	0.271977i
$919$	−19.9121			−0.656840			−0.328420	−	0.944532i	$-0.606516\pi$
$919$	−19.9121			−0.656840			−0.328420	+	0.944532i	$0.606516\pi$
$920$	14.7879	+	31.8483i	0.487542	+	1.05001i
$921$		−	16.4667i		−	0.542596i
$922$	4.34563	+	29.7803i	0.143116	+	0.980761i
$923$	−3.16290			−0.104108
$924$	−51.2882	−	61.5322i	−1.68726	−	2.02426i
$925$	−10.7652			−0.353957
$926$	3.42383	+	23.4633i	0.112514	+	0.771051i
$927$		−	6.25673i		−	0.205498i
$928$	−20.3500	−	22.9927i	−0.668021	−	0.754771i
$929$	20.6217			0.676577			0.338288	−	0.941043i	$-0.390152\pi$
$929$	20.6217			0.676577			0.338288	+	0.941043i	$0.390152\pi$
$930$	126.528	−	18.4634i	4.14903	−	0.605439i
$931$	14.3377			0.469899
$932$	−12.4513	−	41.7555i	−0.407856	−	1.36775i
$933$	69.4233			2.27282
$934$	−3.93356	−	26.9564i	−0.128710	−	0.882041i
$935$	−10.8947	−	25.4101i	−0.356294	−	0.830998i
$936$	−9.47624	−	20.4087i	−0.309741	−	0.667080i
$937$		−	38.4363i		−	1.25566i	−0.778351	−	0.627829i	$-0.783944\pi$
$937$		−	38.4363i		−	1.25566i	0.778351	−	0.627829i	$-0.216056\pi$
$938$	2.83623	+	19.4365i	0.0926062	+	0.634623i
$939$		−	46.1578i		−	1.50630i
$940$	2.85140	+	9.56219i	0.0930026	+	0.311884i
$941$			35.4911i			1.15698i	0.815690	+	0.578489i	$0.196357\pi$
$941$			35.4911i			1.15698i	−0.815690	+	0.578489i	$0.803643\pi$
$942$	0.192045	+	1.31607i	0.00625718	+	0.0428800i
$943$	15.1652			0.493848
$944$	−26.5505	−	40.5599i	−0.864145	−	1.32011i
$945$		−	202.758i		−	6.59572i
$946$	1.07361	−	0.658158i	0.0349061	−	0.0213986i
$947$			7.04671i			0.228987i	0.993424	+	0.114494i	$0.0365246\pi$
$947$			7.04671i			0.228987i	−0.993424	+	0.114494i	$0.963475\pi$
$948$	15.4743	+	51.8932i	0.502583	+	1.68541i
$949$	−4.95698			−0.160911
$950$	−20.5986	+	3.00581i	−0.668306	+	0.0975213i
$951$		−	100.147i		−	3.24749i
$952$	−10.6924	−	23.0279i	−0.346542	−	0.746338i
$953$		−	36.6850i		−	1.18834i	−0.804338	−	0.594171i	$-0.797480\pi$
$953$		−	36.6850i		−	1.18834i	0.804338	−	0.594171i	$-0.202520\pi$
$954$	5.15120	−	0.751679i	0.166776	−	0.0243365i
$955$		−	16.6696i		−	0.539416i
$956$	5.59257	−	1.66768i	0.180877	−	0.0539367i
$957$	54.7644	−	23.4805i	1.77028	−	0.759016i
$958$	36.0835	−	5.26542i	1.16581	−	0.170118i
$959$	−39.0274			−1.26026
$960$	68.5379	+	57.8922i	2.21205	+	1.86846i
$961$	−34.0035			−1.09689
$962$	−0.339261	−	2.32493i	−0.0109382	−	0.0749587i
$963$	−39.8762			−1.28499
$964$	14.1210	+	47.3548i	0.454806	+	1.52519i
$965$		−	62.0847i		−	1.99858i
$966$	−61.9213	+	9.03574i	−1.99228	+	0.290720i
$967$	0.191793			0.00616763			0.00308382	−	0.999995i	$-0.499018\pi$
$967$	0.191793			0.00616763			0.00308382	+	0.999995i	$0.499018\pi$
$968$	−9.96412	+	29.4740i	−0.320259	+	0.947330i
$969$	−18.4991			−0.594278
$970$	9.85365	−	1.43787i	0.316382	−	0.0461674i
$971$			52.6104i			1.68835i	0.536069	+	0.844174i	$0.319909\pi$
$971$			52.6104i			1.68835i	−0.536069	+	0.844174i	$0.680091\pi$
$972$	29.4282	+	98.6877i	0.943911	+	3.16541i
$973$	17.8216			0.571335
$974$	−8.12186	−	55.6585i	−0.260241	−	1.78341i
$975$	21.4470			0.686854
$976$	−28.5238	−	43.5745i	−0.913025	−	1.39479i
$977$	37.7870			1.20891			0.604456	−	0.796639i	$-0.293391\pi$
$977$	37.7870			1.20891			0.604456	+	0.796639i	$0.293391\pi$
$978$	−104.863	+	15.3019i	−3.35314	+	0.489300i
$979$	−34.0467	+	14.5977i	−1.08814	+	0.466544i
$980$	40.9855	−	12.2217i	1.30923	−	0.390408i
$981$			37.3082i			1.19116i
$982$	29.0850	−	4.24417i	0.928139	−	0.135437i
$983$		−	23.2609i		−	0.741907i	−0.928651	−	0.370953i	$-0.879031\pi$
$983$		−	23.2609i		−	0.741907i	0.928651	−	0.370953i	$-0.120969\pi$
$984$	35.1434	−	16.3179i	1.12033	−	0.520196i
$985$		−	28.9710i		−	0.923092i
$986$	18.6879	−	2.72700i	0.595144	−	0.0868453i
$987$	−17.7824			−0.566020
$988$	−1.29831	−	4.35389i	−0.0413048	−	0.138516i
$989$		−	0.983753i		−	0.0312815i
$990$	−107.786	+	66.0762i	−3.42566	+	2.10004i
$991$		−	4.40605i		−	0.139963i	−0.997548	−	0.0699815i	$-0.977706\pi$
$991$		−	4.40605i		−	0.139963i	0.997548	−	0.0699815i	$-0.0222940\pi$
$992$	−30.2274	−	34.1528i	−0.959722	−	1.08435i
$993$	−45.4187			−1.44132
$994$	2.35647	+	16.1487i	0.0747427	+	0.512206i
$995$			34.2181i			1.08479i
$996$	−14.1814	−	47.5573i	−0.449354	−	1.50691i
$997$		−	36.5300i		−	1.15692i	−0.815712	−	0.578458i	$-0.803655\pi$
$997$		−	36.5300i		−	1.15692i	0.815712	−	0.578458i	$-0.196345\pi$
$998$	1.68693	+	11.5604i	0.0533990	+	0.365939i
$999$			27.2502i			0.862159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.6	yes	64
4.3	odd	2	inner	572.2.e.b.131.60	yes	64
11.10	odd	2	inner	572.2.e.b.131.59	yes	64
44.43	even	2	inner	572.2.e.b.131.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.5	✓	64	44.43	even	2	inner
572.2.e.b.131.6	yes	64	1.1	even	1	trivial
572.2.e.b.131.59	yes	64	11.10	odd	2	inner
572.2.e.b.131.60	yes	64	4.3	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)

\(f(q)\)	\(=\)	\(q+(-1.39939 + 0.204204i) q^{2} +3.30990i q^{3} +(1.91660 - 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 - 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 + 1.19116i) q^{8} -7.95546 q^{9} +O(q^{10})\)	\(q+(-1.39939 + 0.204204i) q^{2} +3.30990i q^{3} +(1.91660 - 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 - 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 + 1.19116i) q^{8} -7.95546 q^{9} +(-4.74137 + 0.691875i) q^{10} +(-3.04826 + 1.30695i) q^{11} +(1.89168 + 6.34377i) q^{12} -1.00000i q^{13} +(-5.10568 + 0.745036i) q^{14} +11.2145i q^{15} +(3.34672 - 2.19076i) q^{16} +2.46031i q^{17} +(11.1328 - 1.62454i) q^{18} +2.27167 q^{19} +(6.49376 - 1.93641i) q^{20} +12.0762i q^{21} +(3.99883 - 2.45141i) q^{22} -3.66413i q^{23} +(-3.94263 - 8.49114i) q^{24} +6.47965 q^{25} +(0.204204 + 1.39939i) q^{26} -16.4021i q^{27} +(6.99271 - 2.08520i) q^{28} +5.42789i q^{29} +(-2.29004 - 15.6935i) q^{30} +8.06247i q^{31} +(-4.23602 + 3.74915i) q^{32} +(-4.32589 - 10.0894i) q^{33} +(-0.502404 - 3.44294i) q^{34} +12.3617 q^{35} +(-15.2475 + 4.54673i) q^{36} -1.66138 q^{37} +(-3.17896 + 0.463884i) q^{38} +3.30990 q^{39} +(-8.69190 + 4.03585i) q^{40} +4.13884i q^{41} +(-2.46600 - 16.8993i) q^{42} +0.268482 q^{43} +(-5.09534 + 4.24706i) q^{44} -26.9544 q^{45} +(0.748229 + 5.12756i) q^{46} +1.47252i q^{47} +(7.25121 + 11.0773i) q^{48} +6.31152 q^{49} +(-9.06758 + 1.32317i) q^{50} -8.14339 q^{51} +(-0.571522 - 1.91660i) q^{52} +0.462704 q^{53} +(3.34937 + 22.9530i) q^{54} +(-10.3280 + 4.42817i) q^{55} +(-9.35975 + 4.34595i) q^{56} +7.51902i q^{57} +(-1.10840 - 7.59576i) q^{58} -12.1193i q^{59} +(6.40933 + 21.4937i) q^{60} -13.0200i q^{61} +(-1.64639 - 11.2826i) q^{62} -29.0255 q^{63} +(5.16227 - 6.11155i) q^{64} -3.38816i q^{65} +(8.11392 + 13.2357i) q^{66} -3.80684i q^{67} +(1.40612 + 4.71543i) q^{68} +12.1279 q^{69} +(-17.2989 + 2.52430i) q^{70} -3.16290i q^{71} +(20.4087 - 9.47624i) q^{72} -4.95698i q^{73} +(2.32493 - 0.339261i) q^{74} +21.4470i q^{75} +(4.35389 - 1.29831i) q^{76} +(-11.1216 + 4.76841i) q^{77} +(-4.63186 + 0.675895i) q^{78} +8.18019 q^{79} +(11.3392 - 7.42266i) q^{80} +30.4230 q^{81} +(-0.845166 - 5.79186i) q^{82} -7.49670 q^{83} +(6.90180 + 23.1452i) q^{84} +8.33593i q^{85} +(-0.375712 + 0.0548250i) q^{86} -17.9658 q^{87} +(6.26312 - 6.98379i) q^{88} +11.1692 q^{89} +(37.7198 - 5.50419i) q^{90} -3.64850i q^{91} +(-2.09413 - 7.02268i) q^{92} -26.6860 q^{93} +(-0.300694 - 2.06063i) q^{94} +7.69680 q^{95} +(-12.4093 - 14.0208i) q^{96} -2.07823 q^{97} +(-8.83229 + 1.28883i) q^{98} +(24.2503 - 10.3974i) 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

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