LMFDB - Embedded newform 572.2.b.c.571.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(571,572)]

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, 1]))

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

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

chi := DirichletCharacter("572.571");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			571.7
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30250 + 0.550896i) q^{2} -0.566258i q^{3} +(1.39303 - 1.43509i) q^{4} -3.29519i q^{5} +(0.311949 + 0.737553i) q^{6} -2.02255i q^{7} +(-1.02384 + 2.63662i) q^{8} +2.67935 q^{9} +O(q^{10})$	\(q+(-1.30250 + 0.550896i) q^{2} -0.566258i q^{3} +(1.39303 - 1.43509i) q^{4} -3.29519i q^{5} +(0.311949 + 0.737553i) q^{6} -2.02255i q^{7} +(-1.02384 + 2.63662i) q^{8} +2.67935 q^{9} +(1.81531 + 4.29199i) q^{10} +(0.176245 - 3.31194i) q^{11} +(-0.812629 - 0.788813i) q^{12} +(2.00264 + 2.99824i) q^{13} +(1.11422 + 2.63438i) q^{14} -1.86593 q^{15} +(-0.118946 - 3.99823i) q^{16} -1.97924i q^{17} +(-3.48986 + 1.47604i) q^{18} +2.68960i q^{19} +(-4.72888 - 4.59029i) q^{20} -1.14529 q^{21} +(1.59497 + 4.41090i) q^{22} +0.308907i q^{23} +(1.49301 + 0.579758i) q^{24} -5.85828 q^{25} +(-4.26016 - 2.80197i) q^{26} -3.21598i q^{27} +(-2.90254 - 2.81747i) q^{28} -4.88668i q^{29} +(2.43038 - 1.02793i) q^{30} -7.20359 q^{31} +(2.35754 + 5.14218i) q^{32} +(-1.87541 - 0.0998000i) q^{33} +(1.09036 + 2.57797i) q^{34} -6.66469 q^{35} +(3.73241 - 3.84510i) q^{36} +6.85284i q^{37} +(-1.48169 - 3.50321i) q^{38} +(1.69778 - 1.13401i) q^{39} +(8.68816 + 3.37375i) q^{40} +3.51069 q^{41} +(1.49174 - 0.630933i) q^{42} -8.51358 q^{43} +(-4.50740 - 4.86655i) q^{44} -8.82897i q^{45} +(-0.170175 - 0.402352i) q^{46} -3.39367 q^{47} +(-2.26403 + 0.0673543i) q^{48} +2.90928 q^{49} +(7.63043 - 3.22730i) q^{50} -1.12076 q^{51} +(7.09246 + 1.30267i) q^{52} +5.92430 q^{53} +(1.77167 + 4.18882i) q^{54} +(-10.9135 - 0.580760i) q^{55} +(5.33270 + 2.07077i) q^{56} +1.52301 q^{57} +(2.69205 + 6.36491i) q^{58} +6.37888 q^{59} +(-2.59929 + 2.67777i) q^{60} -10.0713i q^{61} +(9.38270 - 3.96843i) q^{62} -5.41913i q^{63} +(-5.90350 - 5.39895i) q^{64} +(9.87977 - 6.59907i) q^{65} +(2.49771 - 0.903166i) q^{66} +15.1432 q^{67} +(-2.84038 - 2.75714i) q^{68} +0.174921 q^{69} +(8.68078 - 3.67155i) q^{70} -11.2773 q^{71} +(-2.74323 + 7.06443i) q^{72} -6.30410 q^{73} +(-3.77520 - 8.92584i) q^{74} +3.31730i q^{75} +(3.85981 + 3.74668i) q^{76} +(-6.69857 - 0.356464i) q^{77} +(-1.58664 + 2.41235i) q^{78} -6.80153 q^{79} +(-13.1749 + 0.391951i) q^{80} +6.21698 q^{81} +(-4.57268 + 1.93402i) q^{82} -3.98900i q^{83} +(-1.59542 + 1.64359i) q^{84} -6.52198 q^{85} +(11.0890 - 4.69009i) q^{86} -2.76712 q^{87} +(8.55187 + 3.85559i) q^{88} -9.31924i q^{89} +(4.86384 + 11.4998i) q^{90} +(6.06410 - 4.05044i) q^{91} +(0.443308 + 0.430316i) q^{92} +4.07909i q^{93} +(4.42026 - 1.86956i) q^{94} +8.86274 q^{95} +(2.91180 - 1.33497i) q^{96} +9.78624i q^{97} +(-3.78935 + 1.60271i) q^{98} +(0.472222 - 8.87385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^4 - 32 * q^9	$ 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) $ 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

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 $

$2$	−1.30250	+	0.550896i	−0.921009	+	0.389542i
$2$	−1.30250	+	0.550896i	−0.921009	+	0.389542i
$3$		−	0.566258i		−	0.326929i	−0.986549	−	0.163465i	$-0.947733\pi$
$3$		−	0.566258i		−	0.326929i	0.986549	−	0.163465i	$-0.0522670\pi$
$4$	1.39303	−	1.43509i	0.696514	−	0.717543i
$5$		−	3.29519i		−	1.47365i	−0.676081	−	0.736827i	$-0.736323\pi$
$5$		−	3.29519i		−	1.47365i	0.676081	−	0.736827i	$-0.263677\pi$
$6$	0.311949	+	0.737553i	0.127353	+	0.301105i
$7$		−	2.02255i		−	0.764453i	−0.924069	−	0.382226i	$-0.875157\pi$
$7$		−	2.02255i		−	0.764453i	0.924069	−	0.382226i	$-0.124843\pi$
$8$	−1.02384	+	2.63662i	−0.361982	+	0.932185i
$9$	2.67935			0.893117
$10$	1.81531	+	4.29199i	0.574050	+	1.35725i
$11$	0.176245	−	3.31194i	0.0531398	−	0.998587i
$11$	0.176245	−	3.31194i	0.0531398	−	0.998587i
$12$	−0.812629	−	0.788813i	−0.234586	−	0.227711i
$13$	2.00264	+	2.99824i	0.555432	+	0.831562i
$13$	2.00264	+	2.99824i	0.555432	+	0.831562i
$14$	1.11422	+	2.63438i	0.297787	+	0.704068i
$15$	−1.86593			−0.481780
$16$	−0.118946	−	3.99823i	−0.0297366	−	0.999558i
$17$		−	1.97924i		−	0.480037i	−0.970768	−	0.240018i	$-0.922847\pi$
$17$		−	1.97924i		−	0.480037i	0.970768	−	0.240018i	$-0.0771534\pi$
$18$	−3.48986	+	1.47604i	−0.822569	+	0.347907i
$19$			2.68960i			0.617036i	0.951219	+	0.308518i	$0.0998330\pi$
$19$			2.68960i			0.617036i	−0.951219	+	0.308518i	$0.900167\pi$
$20$	−4.72888	−	4.59029i	−1.05741	−	1.02642i
$21$	−1.14529			−0.249922
$22$	1.59497	+	4.41090i	0.340049	+	0.940408i
$23$			0.308907i			0.0644115i	0.999481	+	0.0322057i	$0.0102532\pi$
$23$			0.308907i			0.0644115i	−0.999481	+	0.0322057i	$0.989747\pi$
$24$	1.49301	+	0.579758i	0.304759	+	0.118343i
$25$	−5.85828			−1.17166
$26$	−4.26016	−	2.80197i	−0.835486	−	0.549512i
$27$		−	3.21598i		−	0.618915i
$28$	−2.90254	−	2.81747i	−0.548528	−	0.532452i
$29$		−	4.88668i		−	0.907433i	−0.891146	−	0.453716i	$-0.850098\pi$
$29$		−	4.88668i		−	0.907433i	0.891146	−	0.453716i	$-0.149902\pi$
$30$	2.43038	−	1.02793i	0.443724	−	0.187674i
$31$	−7.20359			−1.29380			−0.646902	−	0.762573i	$-0.723936\pi$
$31$	−7.20359			−1.29380			−0.646902	+	0.762573i	$0.723936\pi$
$32$	2.35754	+	5.14218i	0.416757	+	0.909018i
$33$	−1.87541	−	0.0998000i	−0.326467	−	0.0173730i
$34$	1.09036	+	2.57797i	0.186994	+	0.442118i
$35$	−6.66469			−1.12654
$36$	3.73241	−	3.84510i	0.622069	−	0.640850i
$37$			6.85284i			1.12660i	0.826253	+	0.563300i	$0.190468\pi$
$37$			6.85284i			1.12660i	−0.826253	+	0.563300i	$0.809532\pi$
$38$	−1.48169	−	3.50321i	−0.240361	−	0.568296i
$39$	1.69778	−	1.13401i	0.271862	−	0.181587i
$40$	8.68816	+	3.37375i	1.37372	+	0.533436i
$41$	3.51069			0.548277			0.274138	−	0.961690i	$-0.411607\pi$
$41$	3.51069			0.548277			0.274138	+	0.961690i	$0.411607\pi$
$42$	1.49174	−	0.630933i	0.230180	−	0.0973551i
$43$	−8.51358			−1.29831			−0.649154	−	0.760657i	$-0.724877\pi$
$43$	−8.51358			−1.29831			−0.649154	+	0.760657i	$0.724877\pi$
$44$	−4.50740	−	4.86655i	−0.679517	−	0.733660i
$45$		−	8.82897i		−	1.31615i
$46$	−0.170175	−	0.402352i	−0.0250910	−	0.0593235i
$47$	−3.39367			−0.495017			−0.247509	−	0.968886i	$-0.579612\pi$
$47$	−3.39367			−0.495017			−0.247509	+	0.968886i	$0.579612\pi$
$48$	−2.26403	+	0.0673543i	−0.326785	+	0.00972176i
$49$	2.90928			0.415612
$50$	7.63043	−	3.22730i	1.07911	−	0.456409i
$51$	−1.12076			−0.156938
$52$	7.09246	+	1.30267i	0.983548	+	0.180648i
$53$	5.92430			0.813766			0.406883	−	0.913480i	$-0.366616\pi$
$53$	5.92430			0.813766			0.406883	+	0.913480i	$0.366616\pi$
$54$	1.77167	+	4.18882i	0.241094	+	0.570026i
$55$	−10.9135	−	0.580760i	−1.47157	−	0.0783097i
$56$	5.33270	+	2.07077i	0.712612	+	0.276718i
$57$	1.52301			0.201727
$58$	2.69205	+	6.36491i	0.353483	+	0.835753i
$59$	6.37888			0.830460			0.415230	−	0.909717i	$-0.363701\pi$
$59$	6.37888			0.830460			0.415230	+	0.909717i	$0.363701\pi$
$60$	−2.59929	+	2.67777i	−0.335567	+	0.345698i
$61$		−	10.0713i		−	1.28950i	−0.764392	−	0.644751i	$-0.776961\pi$
$61$		−	10.0713i		−	1.28950i	0.764392	−	0.644751i	$-0.223039\pi$
$62$	9.38270	−	3.96843i	1.19160	−	0.503991i
$63$		−	5.41913i		−	0.682746i
$64$	−5.90350	−	5.39895i	−0.737938	−	0.674869i
$65$	9.87977	−	6.59907i	1.22543	−	0.818514i
$66$	2.49771	−	0.903166i	0.307447	−	0.111172i
$67$	15.1432			1.85003			0.925015	−	0.379930i	$-0.124052\pi$
$67$	15.1432			1.85003			0.925015	+	0.379930i	$0.124052\pi$
$68$	−2.84038	−	2.75714i	−0.344447	−	0.334352i
$69$	0.174921			0.0210580
$70$	8.68078	−	3.67155i	1.03755	−	0.438834i
$71$	−11.2773			−1.33836			−0.669182	−	0.743098i	$-0.733356\pi$
$71$	−11.2773			−1.33836			−0.669182	+	0.743098i	$0.733356\pi$
$72$	−2.74323	+	7.06443i	−0.323293	+	0.832551i
$73$	−6.30410			−0.737839			−0.368920	−	0.929461i	$-0.620272\pi$
$73$	−6.30410			−0.737839			−0.368920	+	0.929461i	$0.620272\pi$
$74$	−3.77520	−	8.92584i	−0.438858	−	1.03761i
$75$			3.31730i			0.383048i
$76$	3.85981	+	3.74668i	0.442750	+	0.429774i
$77$	−6.69857	−	0.356464i	−0.763373	−	0.0406229i
$78$	−1.58664	+	2.41235i	−0.179652	+	0.273145i
$79$	−6.80153			−0.765231			−0.382616	−	0.923908i	$-0.624977\pi$
$79$	−6.80153			−0.765231			−0.382616	+	0.923908i	$0.624977\pi$
$80$	−13.1749	+	0.391951i	−1.47300	+	0.0438214i
$81$	6.21698			0.690776
$82$	−4.57268	+	1.93402i	−0.504968	+	0.213577i
$83$		−	3.98900i		−	0.437850i	−0.975742	−	0.218925i	$-0.929745\pi$
$83$		−	3.98900i		−	0.437850i	0.975742	−	0.218925i	$-0.0702549\pi$
$84$	−1.59542	+	1.64359i	−0.174074	+	0.179330i
$85$	−6.52198			−0.707408
$86$	11.0890	−	4.69009i	1.19575	−	0.505746i
$87$	−2.76712			−0.296666
$88$	8.55187	+	3.85559i	0.911632	+	0.411007i
$89$		−	9.31924i		−	0.987837i	−0.869508	−	0.493919i	$-0.835564\pi$
$89$		−	9.31924i		−	0.987837i	0.869508	−	0.493919i	$-0.164436\pi$
$90$	4.86384	+	11.4998i	0.512694	+	1.21218i
$91$	6.06410	−	4.05044i	0.635690	−	0.424601i
$92$	0.443308	+	0.430316i	0.0462180	+	0.0448635i
$93$			4.07909i			0.422982i
$94$	4.42026	−	1.86956i	0.455915	−	0.192830i
$95$	8.86274			0.909298
$96$	2.91180	−	1.33497i	0.297184	−	0.136250i
$97$			9.78624i			0.993642i	0.867853	+	0.496821i	$0.165499\pi$
$97$			9.78624i			0.993642i	−0.867853	+	0.496821i	$0.834501\pi$
$98$	−3.78935	+	1.60271i	−0.382782	+	0.161898i
$99$	0.472222	−	8.87385i	0.0474601	−	0.891855i
$100$	−8.16075	+	8.40714i	−0.816075	+	0.840714i
$101$			12.1164i			1.20562i	0.797883	+	0.602812i	$0.205953\pi$
$101$			12.1164i			1.20562i	−0.797883	+	0.602812i	$0.794047\pi$
$102$	1.45979	−	0.617422i	0.144541	−	0.0611339i
$103$			15.6340i			1.54046i	0.637764	+	0.770232i	$0.279860\pi$
$103$			15.6340i			1.54046i	−0.637764	+	0.770232i	$0.720140\pi$
$104$	−9.95559	+	2.21047i	−0.976226	+	0.216754i
$105$			3.77394i			0.368299i
$106$	−7.71642	+	3.26367i	−0.749485	+	0.316996i
$107$	1.68984			0.163363			0.0816814	−	0.996658i	$-0.473971\pi$
$107$	1.68984			0.163363			0.0816814	+	0.996658i	$0.473971\pi$
$108$	−4.61521	−	4.47995i	−0.444099	−	0.431083i
$109$	8.82859			0.845626			0.422813	−	0.906217i	$-0.361043\pi$
$109$	8.82859			0.845626			0.422813	+	0.906217i	$0.361043\pi$
$110$	14.5348	−	5.25574i	1.38584	−	0.501115i
$111$	3.88048			0.368318
$112$	−8.08663	+	0.240575i	−0.764115	+	0.0227322i
$113$	−13.7534			−1.29381			−0.646905	−	0.762571i	$-0.723937\pi$
$113$	−13.7534			−1.29381			−0.646905	+	0.762571i	$0.723937\pi$
$114$	−1.98372	+	0.839017i	−0.185792	+	0.0785812i
$115$	1.01791			0.0949202
$116$	−7.01280	−	6.80727i	−0.651122	−	0.632040i
$117$	5.36577	+	8.03334i	0.496066	+	0.742683i
$118$	−8.30851	+	3.51410i	−0.764860	+	0.323499i
$119$	−4.00312			−0.366965
$120$	1.91041	−	4.91974i	0.174396	−	0.449109i
$121$	−10.9379	−	1.16742i	−0.994352	−	0.106129i
$122$	5.54826	+	13.1179i	0.502316	+	1.18764i
$123$		−	1.98795i		−	0.179248i
$124$	−10.0348	+	10.3378i	−0.901152	+	0.928360i
$125$			2.82819i			0.252961i
$126$	2.98537	+	7.05843i	0.265958	+	0.628815i
$127$	6.09562			0.540899			0.270449	−	0.962734i	$-0.412828\pi$
$127$	6.09562			0.540899			0.270449	+	0.962734i	$0.412828\pi$
$128$	10.6636	+	3.77993i	0.942537	+	0.334102i
$129$			4.82088i			0.424455i
$130$	−9.23303	+	14.0380i	−0.809791	+	1.23122i
$131$	16.2333			1.41831			0.709157	−	0.705051i	$-0.249076\pi$
$131$	16.2333			1.41831			0.709157	+	0.705051i	$0.249076\pi$
$132$	−2.75572	+	2.55235i	−0.239855	+	0.222154i
$133$	5.43985			0.471695
$134$	−19.7240	+	8.34230i	−1.70389	+	0.720665i
$135$	−10.5973			−0.912067
$136$	5.21850	+	2.02643i	0.447483	+	0.173765i
$137$			14.5906i			1.24656i	0.782000	+	0.623278i	$0.214199\pi$
$137$			14.5906i			1.24656i	−0.782000	+	0.623278i	$0.785801\pi$
$138$	−0.227835	+	0.0963631i	−0.0193946	+	0.00820298i
$139$	6.82374			0.578782			0.289391	−	0.957211i	$-0.406547\pi$
$139$	6.82374			0.578782			0.289391	+	0.957211i	$0.406547\pi$
$140$	−9.28411	+	9.56441i	−0.784650	+	0.808340i
$141$			1.92169i			0.161836i
$142$	14.6887	−	6.21259i	1.23265	−	0.521349i
$143$	10.2829	−	6.10419i	0.859903	−	0.510458i
$144$	−0.318699	−	10.7127i	−0.0265583	−	0.892722i
$145$	−16.1025			−1.33724
$146$	8.21111	−	3.47290i	0.679556	−	0.287419i
$147$		−	1.64740i		−	0.135876i
$148$	9.83442	+	9.54620i	0.808384	+	0.784693i
$149$	−2.32447			−0.190428			−0.0952142	−	0.995457i	$-0.530354\pi$
$149$	−2.32447			−0.190428			−0.0952142	+	0.995457i	$0.530354\pi$
$150$	−1.82748	−	4.32079i	−0.149213	−	0.352791i
$151$			13.1052i			1.06649i	0.845962	+	0.533244i	$0.179027\pi$
$151$			13.1052i			1.06649i	−0.845962	+	0.533244i	$0.820973\pi$
$152$	−7.09144	−	2.75372i	−0.575192	−	0.223356i
$153$		−	5.30308i		−	0.428729i
$154$	8.92128	−	3.22592i	0.718897	−	0.259952i
$155$			23.7372i			1.90662i
$156$	0.737650	−	4.01616i	0.0590593	−	0.321550i
$157$	−0.476003			−0.0379891			−0.0189946	−	0.999820i	$-0.506047\pi$
$157$	−0.476003			−0.0379891			−0.0189946	+	0.999820i	$0.506047\pi$
$158$	8.85901	−	3.74693i	0.704785	−	0.298090i
$159$		−	3.35468i		−	0.266044i
$160$	16.9445	−	7.76853i	1.33958	−	0.614156i
$161$	0.624780			0.0492395
$162$	−8.09764	+	3.42491i	−0.636211	+	0.269086i
$163$	19.3878			1.51857			0.759283	−	0.650761i	$-0.225550\pi$
$163$	19.3878			1.51857			0.759283	+	0.650761i	$0.225550\pi$
$164$	4.89048	−	5.03814i	0.381883	−	0.393412i
$165$	−0.328860	+	6.17984i	−0.0256017	+	0.481100i
$166$	2.19752	+	5.19568i	0.170561	+	0.403263i
$167$		−	10.7009i		−	0.828063i	−0.910262	−	0.414032i	$-0.864120\pi$
$167$		−	10.7009i		−	0.828063i	0.910262	−	0.414032i	$-0.135880\pi$
$168$	1.17259	−	3.01968i	0.0904673	−	0.232974i
$169$	−4.97889	+	12.0088i	−0.382991	+	0.923752i
$170$	8.49489	−	3.59293i	0.651529	−	0.275565i
$171$			7.20638i			0.551086i
$172$	−11.8596	+	12.2177i	−0.904290	+	0.931592i
$173$			2.43341i			0.185008i	0.995712	+	0.0925042i	$0.0294872\pi$
$173$			2.43341i			0.185008i	−0.995712	+	0.0925042i	$0.970513\pi$
$174$	3.60418	−	1.52439i	0.273232	−	0.115564i
$175$			11.8487i			0.895676i
$176$	−13.2629	−	0.310725i	−0.999726	−	0.0234217i
$177$		−	3.61209i		−	0.271501i
$178$	5.13393	+	12.1383i	0.384804	+	0.909807i
$179$		−	22.7340i		−	1.69922i	−0.527414	−	0.849609i	$-0.676838\pi$
$179$		−	22.7340i		−	1.69922i	0.527414	−	0.849609i	$-0.323162\pi$
$180$	−12.6703	−	12.2990i	−0.944391	−	0.916714i
$181$	−5.87335			−0.436563			−0.218281	−	0.975886i	$-0.570045\pi$
$181$	−5.87335			−0.436563			−0.218281	+	0.975886i	$0.570045\pi$
$182$	−5.66714	+	8.61639i	−0.420076	+	0.638690i
$183$	−5.70298			−0.421576
$184$	−0.814469	−	0.316271i	−0.0600434	−	0.0233158i
$185$	22.5814			1.66022
$186$	−2.24715	−	5.31303i	−0.164769	−	0.389570i
$187$	−6.55513	−	0.348831i	−0.479358	−	0.0255091i
$188$	−4.72747	+	4.87021i	−0.344786	+	0.355196i
$189$	−6.50448			−0.473132
$190$	−11.5437	+	4.88244i	−0.837471	+	0.354210i
$191$		−	14.5141i		−	1.05020i	−0.851039	−	0.525102i	$-0.824027\pi$
$191$		−	14.5141i		−	1.05020i	0.851039	−	0.525102i	$-0.175973\pi$
$192$	−3.05720	+	3.34291i	−0.220634	+	0.241253i
$193$	17.5788			1.26535			0.632673	−	0.774419i	$-0.281958\pi$
$193$	17.5788			1.26535			0.632673	+	0.774419i	$0.281958\pi$
$194$	−5.39120	−	12.7466i	−0.387065	−	0.915153i
$195$	−3.73678	−	5.59450i	−0.267596	−	0.400630i
$196$	4.05271	−	4.17507i	0.289479	−	0.298219i
$197$	−19.2340			−1.37037			−0.685183	−	0.728371i	$-0.740278\pi$
$197$	−19.2340			−1.37037			−0.685183	+	0.728371i	$0.740278\pi$
$198$	4.27349	+	11.8184i	0.303704	+	0.839894i
$199$			3.92359i			0.278136i	0.990283	+	0.139068i	$0.0444107\pi$
$199$			3.92359i			0.278136i	−0.990283	+	0.139068i	$0.955589\pi$
$200$	5.99794	−	15.4460i	0.424118	−	1.09220i
$201$		−	8.57493i		−	0.604829i
$202$	−6.67486	−	15.7816i	−0.469641	−	1.11039i
$203$	−9.88356			−0.693690
$204$	−1.56125	+	1.60839i	−0.109309	+	0.112610i
$205$		−	11.5684i		−	0.807970i
$206$	−8.61271	−	20.3633i	−0.600076	−	1.41878i
$207$			0.827670i			0.0575270i
$208$	11.7495	−	8.36364i	0.814678	−	0.579914i
$209$	8.90778	+	0.474028i	0.616164	+	0.0327892i
$210$	−2.07905	−	4.91556i	−0.143468	−	0.339206i
$211$	12.5108			0.861281			0.430641	−	0.902523i	$-0.358288\pi$
$211$	12.5108			0.861281			0.430641	+	0.902523i	$0.358288\pi$
$212$	8.25272	−	8.50189i	0.566799	−	0.583912i
$213$			6.38584i			0.437551i
$214$	−2.20102	+	0.930925i	−0.150459	+	0.0636367i
$215$			28.0539i			1.91326i
$216$	8.47930	+	3.29265i	0.576944	+	0.224036i
$217$			14.5696i			0.989052i
$218$	−11.4993	+	4.86363i	−0.778829	+	0.329407i
$219$			3.56975i			0.241221i
$220$	−16.0362	+	14.8528i	−1.08116	+	1.00137i
$221$	5.93424	−	3.96370i	0.399180	−	0.266627i
$222$	−5.05433	+	2.13774i	−0.339224	+	0.143476i
$223$	2.86548			0.191887			0.0959434	−	0.995387i	$-0.469413\pi$
$223$	2.86548			0.191887			0.0959434	+	0.995387i	$0.469413\pi$
$224$	10.4003	−	4.76824i	0.694901	−	0.318591i
$225$	−15.6964			−1.04643
$226$	17.9138	−	7.57668i	1.19161	−	0.503993i
$227$			25.7142i			1.70671i	0.521331	+	0.853355i	$0.325436\pi$
$227$			25.7142i			1.70671i	−0.521331	+	0.853355i	$0.674564\pi$
$228$	2.12159	−	2.18565i	0.140506	−	0.144748i
$229$		−	21.1894i		−	1.40023i	−0.714029	−	0.700116i	$-0.753132\pi$
$229$		−	21.1894i		−	1.40023i	0.714029	−	0.700116i	$-0.246868\pi$
$230$	−1.32583	+	0.560760i	−0.0874224	+	0.0369754i
$231$	−0.201851	+	3.79312i	−0.0132808	+	0.249569i
$232$	12.8843	+	5.00317i	0.845895	+	0.328474i
$233$		−	13.0405i		−	0.854311i	−0.904178	−	0.427156i	$-0.859516\pi$
$233$		−	13.0405i		−	0.854311i	0.904178	−	0.427156i	$-0.140484\pi$
$234$	−11.4145	−	7.50747i	−0.746187	−	0.490779i
$235$			11.1828i			0.729484i
$236$	8.88596	−	9.15425i	0.578427	−	0.595891i
$237$			3.85142i			0.250177i
$238$	5.21407	−	2.20530i	0.337978	−	0.142948i
$239$		−	10.9316i		−	0.707106i	−0.935414	−	0.353553i	$-0.884973\pi$
$239$		−	10.9316i		−	0.707106i	0.935414	−	0.353553i	$-0.115027\pi$
$240$	0.221945	+	7.46041i	0.0143265	+	0.481567i
$241$	3.82015			0.246078			0.123039	−	0.992402i	$-0.460736\pi$
$241$	3.82015			0.246078			0.123039	+	0.992402i	$0.460736\pi$
$242$	14.8897	−	4.50505i	0.957149	−	0.289596i
$243$		−	13.1684i		−	0.844750i
$244$	−14.4532	−	14.0297i	−0.925274	−	0.898157i
$245$		−	9.58664i		−	0.612468i
$246$	1.09516	+	2.58932i	0.0698245	+	0.165089i
$247$	−8.06406	+	5.38629i	−0.513104	+	0.342721i
$248$	7.37533	−	18.9931i	0.468334	−	1.20606i
$249$	−2.25880			−0.143146
$250$	−1.55804	−	3.68373i	−0.0985390	−	0.232979i
$251$			21.9902i			1.38801i	0.719969	+	0.694006i	$0.244156\pi$
$251$			21.9902i			1.38801i	−0.719969	+	0.694006i	$0.755844\pi$
$252$	−7.77692	−	7.54900i	−0.489900	−	0.475542i
$253$	1.02308	+	0.0544432i	0.0643205	+	0.00342281i
$254$	−7.93956	+	3.35805i	−0.498172	+	0.210703i
$255$			3.69312i			0.231272i
$256$	−15.9717	+	0.951150i	−0.998231	+	0.0594469i
$257$	−7.77431			−0.484948			−0.242474	−	0.970158i	$-0.577959\pi$
$257$	−7.77431			−0.484948			−0.242474	+	0.970158i	$0.577959\pi$
$258$	−2.65580	−	6.27921i	−0.165343	−	0.390927i
$259$	13.8602			0.861233
$260$	4.29256	−	23.3710i	0.266213	−	1.44941i
$261$		−	13.0931i		−	0.810444i
$262$	−21.1440	+	8.94288i	−1.30628	+	0.552493i
$263$	30.2037			1.86244			0.931219	−	0.364459i	$-0.118746\pi$
$263$	30.2037			1.86244			0.931219	+	0.364459i	$0.118746\pi$
$264$	2.18326	−	4.84256i	0.134370	−	0.298039i
$265$		−	19.5217i		−	1.19921i
$266$	−7.08542	+	2.99679i	−0.434435	+	0.183745i
$267$	−5.27709			−0.322953
$268$	21.0948	−	21.7317i	1.28857	−	1.32748i
$269$	10.1042			0.616063			0.308031	−	0.951376i	$-0.400330\pi$
$269$	10.1042			0.616063			0.308031	+	0.951376i	$0.400330\pi$
$270$	13.8030	−	5.83798i	0.840022	−	0.355288i
$271$		−	10.2931i		−	0.625262i	−0.949875	−	0.312631i	$-0.898790\pi$
$271$		−	10.2931i		−	0.625262i	0.949875	−	0.312631i	$-0.101210\pi$
$272$	−7.91346	+	0.235424i	−0.479824	+	0.0142746i
$273$	−2.29359	−	3.43384i	−0.138815	−	0.207826i
$274$	−8.03788	−	19.0043i	−0.485586	−	1.14809i
$275$	−1.03249	+	19.4023i	−0.0622616	+	1.17000i
$276$	0.243670	−	0.251027i	0.0146672	−	0.0151100i
$277$			7.47366i			0.449048i	0.974469	+	0.224524i	$0.0720828\pi$
$277$			7.47366i			0.449048i	−0.974469	+	0.224524i	$0.927917\pi$
$278$	−8.88794	+	3.75917i	−0.533063	+	0.225460i
$279$	−19.3010			−1.15552
$280$	6.82358	−	17.5723i	0.407787	−	1.05014i
$281$	15.6582			0.934092			0.467046	−	0.884233i	$-0.345318\pi$
$281$	15.6582			0.934092			0.467046	+	0.884233i	$0.345318\pi$
$282$	−1.05865	−	2.50301i	−0.0630418	−	0.149052i
$283$	−5.54393			−0.329553			−0.164776	−	0.986331i	$-0.552690\pi$
$283$	−5.54393			−0.329553			−0.164776	+	0.986331i	$0.552690\pi$
$284$	−15.7095	+	16.1838i	−0.932190	+	0.960335i
$285$		−	5.01860i		−	0.297276i
$286$	−10.0308	+	13.6156i	−0.593133	+	0.805104i
$287$		−	7.10055i		−	0.419132i
$288$	6.31667	+	13.7777i	0.372213	+	0.811859i
$289$	13.0826			0.769565
$290$	20.9736	−	8.87081i	1.23161	−	0.520912i
$291$	5.54154			0.324851
$292$	−8.78179	+	9.04693i	−0.513915	+	0.529432i
$293$	15.9521			0.931933			0.465966	−	0.884802i	$-0.345707\pi$
$293$	15.9521			0.931933			0.465966	+	0.884802i	$0.345707\pi$
$294$	0.907548	+	2.14575i	0.0529293	+	0.125143i
$295$		−	21.0196i		−	1.22381i
$296$	−18.0683	−	7.01621i	−1.05020	−	0.407809i
$297$	−10.6511	−	0.566800i	−0.618041	−	0.0328890i
$298$	3.02764	−	1.28054i	0.175386	−	0.0741799i
$299$	−0.926176	+	0.618628i	−0.0535622	+	0.0357762i
$300$	4.76061	+	4.62109i	0.274854	+	0.266799i
$301$			17.2192i			0.992495i
$302$	−7.21961	−	17.0696i	−0.415442	−	0.982244i
$303$	6.86099			0.394154
$304$	10.7536	−	0.319918i	0.616763	−	0.0183485i
$305$	−33.1870			−1.90028
$306$	2.92145	+	6.90728i	0.167008	+	0.394863i
$307$		−	16.7983i		−	0.958732i	−0.877615	−	0.479366i	$-0.840867\pi$
$307$		−	16.7983i		−	0.958732i	0.877615	−	0.479366i	$-0.159133\pi$
$308$	−9.84285	+	9.11646i	−0.560849	+	0.519459i
$309$	8.85288			0.503623
$310$	−13.0767	−	30.9178i	−0.742708	−	1.75601i
$311$		−	2.05498i		−	0.116527i	−0.998301	−	0.0582637i	$-0.981444\pi$
$311$		−	2.05498i		−	0.116527i	0.998301	−	0.0582637i	$-0.0185564\pi$
$312$	1.25170	+	5.63743i	0.0708633	+	0.319157i
$313$	−0.656102			−0.0370851			−0.0185425	−	0.999828i	$-0.505903\pi$
$313$	−0.656102			−0.0370851			−0.0185425	+	0.999828i	$0.505903\pi$
$314$	0.619995	−	0.262228i	0.0349883	−	0.0147984i
$315$	−17.8571			−1.00613
$316$	−9.47472	+	9.76078i	−0.532994	+	0.549087i
$317$		−	12.6773i		−	0.712027i	−0.934481	−	0.356014i	$-0.884136\pi$
$317$		−	12.6773i		−	0.712027i	0.934481	−	0.356014i	$-0.115864\pi$
$318$	1.84808	+	4.36949i	0.103635	+	0.245029i
$319$	−16.1844	−	0.861251i	−0.906151	−	0.0482208i
$320$	−17.7906	+	19.4532i	−0.994523	+	1.08746i
$321$		−	0.956885i		−	0.0534081i
$322$	−0.813778	+	0.344189i	−0.0453501	+	0.0191809i
$323$	5.32336			0.296200
$324$	8.66043	−	8.92191i	0.481135	−	0.495662i
$325$	−11.7320	−	17.5645i	−0.650775	−	0.974305i
$326$	−25.2526	+	10.6806i	−1.39861	+	0.591545i
$327$		−	4.99926i		−	0.276460i
$328$	−3.59438	+	9.25633i	−0.198466	+	0.511096i
$329$			6.86387i			0.378417i
$330$	−2.97610	−	8.23043i	−0.163829	−	0.453070i
$331$	19.2651			1.05891			0.529453	−	0.848339i	$-0.322397\pi$
$331$	19.2651			1.05891			0.529453	+	0.848339i	$0.322397\pi$
$332$	−5.72456	−	5.55679i	−0.314176	−	0.304968i
$333$			18.3612i			1.00619i
$334$	5.89510	+	13.9380i	0.322566	+	0.762654i
$335$		−	49.8996i		−	2.72630i
$336$	0.136228	+	4.57912i	0.00743183	+	0.249811i
$337$			29.1905i			1.59011i	0.606538	+	0.795054i	$0.292558\pi$
$337$			29.1905i			1.59011i	−0.606538	+	0.795054i	$0.707442\pi$
$338$	−0.130565	−	18.3843i	−0.00710179	−	0.999975i
$339$			7.78796i			0.422984i
$340$	−9.08530	+	9.35960i	−0.492719	+	0.507596i
$341$	−1.26960	+	23.8579i	−0.0687525	+	1.29198i
$342$	−3.96996	−	9.38633i	−0.214671	−	0.507555i
$343$		−	20.0420i		−	1.08217i
$344$	8.71654	−	22.4470i	0.469964	−	1.21026i
$345$		−	0.576397i		−	0.0310322i
$346$	−1.34055	−	3.16952i	−0.0720686	−	0.170394i
$347$	33.2976			1.78751			0.893755	−	0.448555i	$-0.148061\pi$
$347$	33.2976			1.78751			0.893755	+	0.448555i	$0.148061\pi$
$348$	−3.85467	+	3.97105i	−0.206632	+	0.212871i
$349$	33.9879			1.81933			0.909666	−	0.415340i	$-0.136337\pi$
$349$	33.9879			1.81933			0.909666	+	0.415340i	$0.136337\pi$
$350$	−6.52738	−	15.4329i	−0.348903	−	0.824925i
$351$	9.64228	−	6.44044i	0.514667	−	0.343765i
$352$	17.4461	−	6.90173i	0.929880	−	0.367864i
$353$		−	2.40079i		−	0.127781i	−0.997957	−	0.0638905i	$-0.979649\pi$
$353$		−	2.40079i		−	0.127781i	0.997957	−	0.0638905i	$-0.0203508\pi$
$354$	1.98989	+	4.70476i	0.105761	+	0.250055i
$355$			37.1607i			1.97229i
$356$	−13.3739	−	12.9820i	−0.708816	−	0.688042i
$357$			2.26680i			0.119972i
$358$	12.5241	+	29.6111i	0.661917	+	1.56499i
$359$			6.66503i			0.351767i	0.984411	+	0.175884i	$0.0562782\pi$
$359$			6.66503i			0.351767i	−0.984411	+	0.175884i	$0.943722\pi$
$360$	23.2786	+	9.03946i	1.22689	+	0.476421i
$361$	11.7661			0.619267
$362$	7.65005	−	3.23560i	0.402078	−	0.170059i
$363$	−0.661063	+	6.19366i	−0.0346968	+	0.325083i
$364$	2.63473	−	14.3449i	0.138097	−	0.751876i
$365$			20.7732i			1.08732i
$366$	7.42814	−	3.14174i	0.388275	−	0.164222i
$367$		−	20.5750i		−	1.07401i	−0.843580	−	0.537003i	$-0.819556\pi$
$367$		−	20.5750i		−	1.07401i	0.843580	−	0.537003i	$-0.180444\pi$
$368$	1.23508	−	0.0367433i	0.0643830	−	0.00191538i
$369$	9.40636			0.489676
$370$	−29.4124	+	12.4400i	−1.52908	+	0.646725i
$371$		−	11.9822i		−	0.622086i
$372$	5.85385	+	5.68229i	0.303508	+	0.294613i
$373$		−	4.70653i		−	0.243695i	−0.992549	−	0.121847i	$-0.961118\pi$
$373$		−	4.70653i		−	0.243695i	0.992549	−	0.121847i	$-0.0388819\pi$
$374$	8.73024	−	3.15684i	0.451430	−	0.163236i
$375$	1.60149			0.0827004
$376$	3.47457	−	8.94780i	0.179187	−	0.461448i
$377$	14.6514	−	9.78624i	0.754587	−	0.504017i
$378$	8.47211	−	3.58329i	0.435758	−	0.184305i
$379$	−0.898174			−0.0461361			−0.0230680	−	0.999734i	$-0.507343\pi$
$379$	−0.898174			−0.0461361			−0.0230680	+	0.999734i	$0.507343\pi$
$380$	12.3460	−	12.7188i	0.633338	−	0.652460i
$381$		−	3.45169i		−	0.176836i
$382$	7.99576	+	18.9047i	0.409099	+	0.967247i
$383$	−6.62328			−0.338434			−0.169217	−	0.985579i	$-0.554124\pi$
$383$	−6.62328			−0.338434			−0.169217	+	0.985579i	$0.554124\pi$
$384$	2.14042	−	6.03834i	0.109228	−	0.308143i
$385$	−1.17462	+	22.0731i	−0.0598641	+	1.12495i
$386$	−22.8964	+	9.68406i	−1.16539	+	0.492906i
$387$	−22.8109			−1.15954
$388$	14.0441	+	13.6325i	0.712981	+	0.692085i
$389$	−25.4959			−1.29269			−0.646346	−	0.763044i	$-0.723704\pi$
$389$	−25.4959			−1.29269			−0.646346	+	0.763044i	$0.723704\pi$
$390$	7.94915	+	5.22828i	0.402521	+	0.264744i
$391$	0.611401			0.0309199
$392$	−2.97864	+	7.67066i	−0.150444	+	0.387427i
$393$		−	9.19226i		−	0.463688i
$394$	25.0523	−	10.5959i	1.26212	−	0.533815i
$395$			22.4123i			1.12769i
$396$	−12.0769	−	13.0392i	−0.606888	−	0.655244i
$397$		−	7.89497i		−	0.396237i	−0.980178	−	0.198119i	$-0.936517\pi$
$397$		−	7.89497i		−	0.396237i	0.980178	−	0.198119i	$-0.0634832\pi$
$398$	−2.16149	−	5.11049i	−0.108346	−	0.256166i
$399$		−	3.08036i		−	0.154211i
$400$	0.696821	+	23.4228i	0.0348410	+	1.17114i
$401$			22.6985i			1.13351i	0.823887	+	0.566754i	$0.191801\pi$
$401$			22.6985i			1.13351i	−0.823887	+	0.566754i	$0.808199\pi$
$402$	4.72389	+	11.1689i	0.235606	+	0.557053i
$403$	−14.4262	−	21.5981i	−0.718619	−	1.07588i
$404$	17.3880	+	16.8784i	0.865088	+	0.839734i
$405$		−	20.4861i		−	1.01796i
$406$	12.8734	−	5.44481i	0.638894	−	0.270221i
$407$	22.6962	+	1.20778i	1.12501	+	0.0598673i
$408$	1.14748	−	2.95502i	0.0568087	−	0.146295i
$409$	−26.1421			−1.29264			−0.646321	−	0.763065i	$-0.723693\pi$
$409$	−26.1421			−1.29264			−0.646321	+	0.763065i	$0.723693\pi$
$410$	6.37297	+	15.0678i	0.314738	+	0.744148i
$411$	8.26202			0.407536
$412$	22.4362	+	21.7786i	1.10535	+	1.07295i
$413$		−	12.9016i		−	0.634847i
$414$	−0.455960	−	1.07804i	−0.0224092	−	0.0529829i
$415$	−13.1445			−0.645239
$416$	−10.6962	+	17.3664i	−0.524425	+	0.851457i
$417$		−	3.86400i		−	0.189221i
$418$	−11.8636	+	4.28984i	−0.580265	+	0.209823i
$419$			10.2084i			0.498715i	0.968411	+	0.249358i	$0.0802195\pi$
$419$			10.2084i			0.498715i	−0.968411	+	0.249358i	$0.919781\pi$
$420$	5.41593	+	5.25720i	0.264270	+	0.256525i
$421$			12.0697i			0.588242i	0.955768	+	0.294121i	$0.0950269\pi$
$421$			12.0697i			0.588242i	−0.955768	+	0.294121i	$0.904973\pi$
$422$	−16.2954	+	6.89217i	−0.793248	+	0.335505i
$423$	−9.09283			−0.442109
$424$	−6.06554	+	15.6201i	−0.294569	+	0.758580i
$425$			11.5949i			0.562438i
$426$	−3.51793	−	8.31758i	−0.170444	−	0.402988i
$427$	−20.3698			−0.985764
$428$	2.35399	−	2.42506i	0.113785	−	0.117220i
$429$	−3.45654	−	5.82280i	−0.166884	−	0.281127i
$430$	−15.4547	−	36.5402i	−0.745294	−	1.76213i
$431$			23.2473i			1.11978i	0.828566	+	0.559892i	$0.189157\pi$
$431$			23.2473i			1.11978i	−0.828566	+	0.559892i	$0.810843\pi$
$432$	−12.8582	+	0.382529i	−0.618642	+	0.0184044i
$433$	−24.0625			−1.15637			−0.578186	−	0.815905i	$-0.696239\pi$
$433$	−24.0625			−1.15637			−0.578186	+	0.815905i	$0.696239\pi$
$434$	−8.02635	−	18.9770i	−0.385277	−	0.910925i
$435$			9.11818i			0.437183i
$436$	12.2985	−	12.6698i	0.588990	−	0.606773i
$437$	−0.830835			−0.0397442
$438$	−1.96656	−	4.64961i	−0.0939658	−	0.222167i
$439$	−14.5498			−0.694426			−0.347213	−	0.937786i	$-0.612872\pi$
$439$	−14.5498			−0.694426			−0.347213	+	0.937786i	$0.612872\pi$
$440$	12.7049	−	28.1800i	0.605682	−	1.34343i
$441$	7.79499			0.371190
$442$	−5.54578	+	8.43188i	−0.263786	+	0.401064i
$443$			31.6516i			1.50381i	0.659271	+	0.751905i	$0.270865\pi$
$443$			31.6516i			1.50381i	−0.659271	+	0.751905i	$0.729135\pi$
$444$	5.40561	−	5.56882i	0.256539	−	0.264284i
$445$	−30.7087			−1.45573
$446$	−3.73230	+	1.57858i	−0.176729	+	0.0747480i
$447$			1.31625i			0.0622566i
$448$	−10.9197	+	11.9401i	−0.515905	+	0.564119i
$449$		−	40.9503i		−	1.93256i	−0.257489	−	0.966281i	$-0.582895\pi$
$449$		−	40.9503i		−	1.93256i	0.257489	−	0.966281i	$-0.417105\pi$
$450$	20.4446	−	8.64707i	0.963767	−	0.407627i
$451$	0.618740	−	11.6272i	0.0291353	−	0.547502i
$452$	−19.1588	+	19.7373i	−0.901156	+	0.928364i
$453$	7.42093			0.348666
$454$	−14.1658	−	33.4928i	−0.664835	−	1.57189i
$455$	−13.3470	−	19.9824i	−0.625715	−	0.936787i
$456$	−1.55931	+	4.01558i	−0.0730216	+	0.188047i
$457$	−1.93438			−0.0904867			−0.0452434	−	0.998976i	$-0.514406\pi$
$457$	−1.93438			−0.0904867			−0.0452434	+	0.998976i	$0.514406\pi$
$458$	11.6731	+	27.5992i	0.545449	+	1.28963i
$459$	−6.36520			−0.297102
$460$	1.41797	−	1.46078i	0.0661133	−	0.0681094i
$461$	−29.1988			−1.35992			−0.679962	−	0.733247i	$-0.738004\pi$
$461$	−29.1988			−1.35992			−0.679962	+	0.733247i	$0.738004\pi$
$462$	−1.82670	−	5.05175i	−0.0849858	−	0.235029i
$463$	−6.18860			−0.287609			−0.143804	−	0.989606i	$-0.545934\pi$
$463$	−6.18860			−0.287609			−0.143804	+	0.989606i	$0.545934\pi$
$464$	−19.5381	+	0.581252i	−0.907031	+	0.0269840i
$465$	13.4414			0.623329
$466$	7.18395	+	16.9853i	0.332790	+	0.786828i
$467$			36.0734i			1.66928i	0.550798	+	0.834639i	$0.314323\pi$
$467$			36.0734i			1.66928i	−0.550798	+	0.834639i	$0.685677\pi$
$468$	19.0032	+	3.49032i	0.878423	+	0.161340i
$469$		−	30.6278i		−	1.41426i
$470$	−6.16055	−	14.5656i	−0.284165	−	0.671861i
$471$			0.269540i			0.0124198i
$472$	−6.53095	+	16.8187i	−0.300612	+	0.774142i
$473$	−1.50047	+	28.1964i	−0.0689919	+	1.29647i
$474$	−2.12173	−	5.01648i	−0.0974543	−	0.230415i
$475$		−	15.7564i		−	0.722954i
$476$	−5.57646	+	5.74482i	−0.255596	+	0.263313i
$477$	15.8733			0.726788
$478$	6.02217	+	14.2384i	0.275448	+	0.651251i
$479$			8.54198i			0.390293i	0.980774	+	0.195146i	$0.0625182\pi$
$479$			8.54198i			0.390293i	−0.980774	+	0.195146i	$0.937482\pi$
$480$	−4.39899	−	9.59494i	−0.200786	−	0.437947i
$481$	−20.5465	+	13.7238i	−0.936838	+	0.625749i
$482$	−4.97576	+	2.10450i	−0.226640	+	0.0958575i
$483$		−	0.353787i		−	0.0160978i
$484$	−16.9121	+	14.0705i	−0.768733	+	0.639570i
$485$	32.2475			1.46428
$486$	7.25439	+	17.1518i	0.329066	+	0.778022i
$487$	34.2160			1.55048			0.775238	−	0.631669i	$-0.217630\pi$
$487$	34.2160			1.55048			0.775238	+	0.631669i	$0.217630\pi$
$488$	26.5543	+	10.3114i	1.20206	+	0.466777i
$489$		−	10.9785i		−	0.496464i
$490$	5.28124	+	12.4866i	0.238582	+	0.564088i
$491$	29.8149			1.34553			0.672764	−	0.739857i	$-0.265107\pi$
$491$	29.8149			1.34553			0.672764	+	0.739857i	$0.265107\pi$
$492$	−2.85289	−	2.76927i	−0.128618	−	0.124849i
$493$	−9.67191			−0.435601
$494$	7.53618	−	11.4581i	0.339069	−	0.515525i
$495$	−29.2410	−	1.55606i	−1.31429	−	0.0699397i
$496$	0.856841	+	28.8016i	0.0384733	+	1.29323i
$497$			22.8089i			1.02312i
$498$	2.94210	−	1.24436i	0.131839	−	0.0557613i
$499$	7.20650			0.322607			0.161304	−	0.986905i	$-0.448430\pi$
$499$	7.20650			0.322607			0.161304	+	0.986905i	$0.448430\pi$
$500$	4.05870	+	3.93975i	0.181510	+	0.176191i
$501$	−6.05949			−0.270718
$502$	−12.1143	−	28.6424i	−0.540689	−	1.27837i
$503$	−31.0775			−1.38568			−0.692839	−	0.721093i	$-0.743640\pi$
$503$	−31.0775			−1.38568			−0.692839	+	0.721093i	$0.743640\pi$
$504$	14.2882	+	5.54832i	0.636446	+	0.247142i
$505$	39.9258			1.77667
$506$	−1.36256	+	0.492698i	−0.0605730	+	0.0219031i
$507$	6.80006	+	2.81934i	0.302001	+	0.125211i
$508$	8.49136	−	8.74774i	0.376743	−	0.388118i
$509$		−	3.26699i		−	0.144807i	−0.997375	−	0.0724033i	$-0.976933\pi$
$509$		−	3.26699i		−	0.144807i	0.997375	−	0.0724033i	$-0.0230669\pi$
$510$	−2.03452	−	4.81030i	−0.0900903	−	0.213004i
$511$			12.7504i			0.564043i
$512$	20.2792	−	10.0376i	0.896223	−	0.443604i
$513$	8.64969			0.381893
$514$	10.1261	−	4.28283i	0.446641	−	0.188908i
$515$	51.5170			2.27011
$516$	6.91838	+	6.71562i	0.304565	+	0.295639i
$517$	−0.598116	+	11.2396i	−0.0263051	+	0.494318i
$518$	−18.0530	+	7.63554i	−0.793203	+	0.335486i
$519$	1.37794			0.0604847
$520$	7.28392	+	32.8056i	0.319421	+	1.43862i
$521$	−35.9580			−1.57535			−0.787675	−	0.616091i	$-0.788715\pi$
$521$	−35.9580			−1.57535			−0.787675	+	0.616091i	$0.788715\pi$
$522$	7.21294	+	17.0538i	0.315702	+	0.746426i
$523$	−37.7227			−1.64950			−0.824749	−	0.565499i	$-0.808684\pi$
$523$	−37.7227			−1.64950			−0.824749	+	0.565499i	$0.808684\pi$
$524$	22.6135	−	23.2962i	0.987875	−	1.01770i
$525$	6.70941			0.292823
$526$	−39.3404	+	16.6391i	−1.71532	+	0.725498i
$527$			14.2576i			0.621073i
$528$	−0.175950	+	7.51020i	−0.00765725	+	0.326840i
$529$	22.9046			0.995851
$530$	10.7544	+	25.4271i	0.467142	+	1.10448i
$531$	17.0913			0.741698
$532$	7.57787	−	7.80666i	0.328542	−	0.338462i
$533$	7.03063	+	10.5259i	0.304530	+	0.455926i
$534$	6.87343	−	2.90713i	0.297442	−	0.125804i
$535$		−	5.56834i		−	0.240740i
$536$	−15.5042	+	39.9267i	−0.669678	+	1.72457i
$537$	−12.8733			−0.555524
$538$	−13.1607	+	5.56635i	−0.567399	+	0.239982i
$539$	0.512746	−	9.63536i	0.0220855	−	0.415024i
$540$	−14.7623	+	15.2080i	−0.635267	+	0.654447i
$541$	23.5890			1.01417			0.507085	−	0.861896i	$-0.330723\pi$
$541$	23.5890			1.01417			0.507085	+	0.861896i	$0.330723\pi$
$542$	5.67043	+	13.4068i	0.243566	+	0.575871i
$543$			3.32583i			0.142725i
$544$	10.1776	−	4.66613i	0.436362	−	0.200059i
$545$		−	29.0919i		−	1.24616i
$546$	4.87910	+	3.20906i	0.208806	+	0.137335i
$547$	7.67744			0.328264			0.164132	−	0.986438i	$-0.447518\pi$
$547$	7.67744			0.328264			0.164132	+	0.986438i	$0.447518\pi$
$548$	20.9387	+	20.3251i	0.894458	+	0.868244i
$549$		−	26.9847i		−	1.15168i
$550$	−9.34380	−	25.8403i	−0.398421	−	1.10183i
$551$	13.1432			0.559919
$552$	−0.179091	+	0.461199i	−0.00762262	+	0.0196299i
$553$			13.7564i			0.584983i
$554$	−4.11720	−	9.73446i	−0.174923	−	0.413577i
$555$		−	12.7869i		−	0.542774i
$556$	9.50566	−	9.79265i	0.403130	−	0.415301i
$557$	−32.6865			−1.38497			−0.692487	−	0.721431i	$-0.743485\pi$
$557$	−32.6865			−1.38497			−0.692487	+	0.721431i	$0.743485\pi$
$558$	25.1396	−	10.6328i	1.06424	−	0.450123i
$559$	−17.0496	−	25.5257i	−0.721121	−	1.07962i
$560$	0.792741	+	26.6470i	0.0334994	+	1.12604i
$561$	−0.197528	+	3.71189i	−0.00833965	+	0.156716i
$562$	−20.3949	+	8.62605i	−0.860307	+	0.363868i
$563$	−33.1892			−1.39876			−0.699379	−	0.714751i	$-0.746540\pi$
$563$	−33.1892			−1.39876			−0.699379	+	0.714751i	$0.746540\pi$
$564$	2.75779	+	2.67697i	0.116124	+	0.112721i
$565$			45.3200i			1.90663i
$566$	7.22099	−	3.05413i	0.303521	−	0.128375i
$567$		−	12.5742i		−	0.528066i
$568$	11.5461	−	29.7338i	0.484464	−	1.24760i
$569$			0.0743011i			0.00311487i	0.999999	+	0.00155743i	$0.000495746\pi$
$569$			0.0743011i			0.00311487i	−0.999999	+	0.00155743i	$0.999504\pi$
$570$	2.76472	+	6.53673i	0.115801	+	0.273794i
$571$	13.0501			0.546130			0.273065	−	0.961996i	$-0.411963\pi$
$571$	13.0501			0.546130			0.273065	+	0.961996i	$0.411963\pi$
$572$	5.56439	−	23.2602i	0.232659	−	0.972558i
$573$	−8.21873			−0.343342
$574$	3.91166	+	9.24848i	0.163270	+	0.386024i
$575$		−	1.80966i		−	0.0754681i
$576$	−15.8176	−	14.4657i	−0.659065	−	0.602737i
$577$			10.3102i			0.429220i	0.976700	+	0.214610i	$0.0688481\pi$
$577$			10.3102i			0.429220i	−0.976700	+	0.214610i	$0.931152\pi$
$578$	−17.0401	+	7.20715i	−0.708776	+	0.299778i
$579$		−	9.95411i		−	0.413679i
$580$	−22.4313	+	23.1085i	−0.931408	+	0.959529i
$581$	−8.06796			−0.334715
$582$	−7.21787	+	3.05281i	−0.299190	+	0.126543i
$583$	1.04413	−	19.6209i	0.0432434	−	0.812616i
$584$	6.45439	−	16.6215i	0.267085	−	0.687803i
$585$	26.4714	−	17.6812i	1.09446	−	0.731029i
$586$	−20.7777	+	8.78795i	−0.858318	+	0.363027i
$587$	−21.1204			−0.871731			−0.435865	−	0.900012i	$-0.643558\pi$
$587$	−21.1204			−0.871731			−0.435865	+	0.900012i	$0.643558\pi$
$588$	−2.36417	−	2.29488i	−0.0974966	−	0.0946393i
$589$		−	19.3748i		−	0.798323i
$590$	11.5796	+	27.3781i	0.476725	+	1.12714i
$591$			10.8914i			0.448013i
$592$	27.3992	−	0.815120i	1.12610	−	0.0335012i
$593$	8.87584			0.364487			0.182243	−	0.983253i	$-0.441664\pi$
$593$	8.87584			0.364487			0.182243	+	0.983253i	$0.441664\pi$
$594$	14.1854	−	5.12940i	0.582033	−	0.210462i
$595$			13.1910i			0.540780i
$596$	−3.23806	+	3.33582i	−0.132636	+	0.136641i
$597$	2.22176			0.0909308
$598$	0.865548	−	1.31599i	0.0353949	−	0.0538149i
$599$			29.4065i			1.20152i	0.799430	+	0.600759i	$0.205135\pi$
$599$			29.4065i			1.20152i	−0.799430	+	0.600759i	$0.794865\pi$
$600$	−8.74644	−	3.39638i	−0.357072	−	0.138657i
$601$		−	43.4130i		−	1.77085i	−0.464780	−	0.885426i	$-0.653867\pi$
$601$		−	43.4130i		−	1.77085i	0.464780	−	0.885426i	$-0.346133\pi$
$602$	−9.48596	−	22.4280i	−0.386619	−	0.914097i
$603$	40.5738			1.65229
$604$	18.8071	+	18.2559i	0.765251	+	0.742823i
$605$	−3.84688	+	36.0424i	−0.156398	+	1.46533i
$606$	−8.93646	+	3.77969i	−0.363019	+	0.153539i
$607$	−12.7943			−0.519305			−0.259652	−	0.965702i	$-0.583608\pi$
$607$	−12.7943			−0.519305			−0.259652	+	0.965702i	$0.583608\pi$
$608$	−13.8304	+	6.34082i	−0.560897	+	0.257154i
$609$			5.59664i			0.226787i
$610$	43.2261	−	18.2826i	1.75017	−	0.740239i
$611$	−6.79629	−	10.1750i	−0.274948	−	0.411638i
$612$	−7.61038	−	7.38734i	−0.307632	−	0.298616i
$613$	31.6996			1.28033			0.640167	−	0.768236i	$-0.278865\pi$
$613$	31.6996			1.28033			0.640167	+	0.768236i	$0.278865\pi$
$614$	9.25413	+	21.8799i	0.373466	+	0.883000i
$615$	−6.55069			−0.264149
$616$	7.79812	−	17.2966i	0.314195	−	0.696900i
$617$		−	18.5466i		−	0.746659i	−0.927699	−	0.373329i	$-0.878216\pi$
$617$		−	18.5466i		−	0.746659i	0.927699	−	0.373329i	$-0.121784\pi$
$618$	−11.5309	+	4.87701i	−0.463841	+	0.196182i
$619$	−28.9557			−1.16383			−0.581914	−	0.813250i	$-0.697696\pi$
$619$	−28.9557			−1.16383			−0.581914	+	0.813250i	$0.697696\pi$
$620$	34.0649	+	33.0666i	1.36808	+	1.32799i
$621$	0.993437			0.0398653
$622$	1.13208	+	2.67662i	0.0453923	+	0.107323i
$623$	−18.8486			−0.755155
$624$	−4.73598	−	6.65322i	−0.189591	−	0.266342i
$625$	−19.9720			−0.798879
$626$	0.854574	−	0.361444i	0.0341557	−	0.0144462i
$627$	0.268422	−	5.04410i	0.0107197	−	0.201442i
$628$	−0.663085	+	0.683105i	−0.0264600	+	0.0272588i
$629$	13.5634			0.540809
$630$	23.2589	−	9.83738i	0.926656	−	0.391931i
$631$	−8.22541			−0.327448			−0.163724	−	0.986506i	$-0.552351\pi$
$631$	−8.22541			−0.327448			−0.163724	+	0.986506i	$0.552351\pi$
$632$	6.96368	−	17.9330i	0.277000	−	0.713337i
$633$		−	7.08436i		−	0.281578i
$634$	6.98386	+	16.5122i	0.277365	+	0.655783i
$635$		−	20.0862i		−	0.797097i
$636$	−4.81426	−	4.67317i	−0.190898	−	0.185303i
$637$	5.82624	+	8.72273i	0.230844	+	0.345607i
$638$	21.5546	−	7.79412i	0.853357	−	0.308572i
$639$	−30.2158			−1.19532
$640$	12.4556	−	35.1385i	0.492351	−	1.38897i
$641$	−9.12648			−0.360474			−0.180237	−	0.983623i	$-0.557687\pi$
$641$	−9.12648			−0.360474			−0.180237	+	0.983623i	$0.557687\pi$
$642$	0.527144	+	1.24635i	0.0208047	+	0.0491893i
$643$	34.7576			1.37071			0.685353	−	0.728211i	$-0.259648\pi$
$643$	34.7576			1.37071			0.685353	+	0.728211i	$0.259648\pi$
$644$	0.870336	−	0.896613i	0.0342960	−	0.0353315i
$645$	15.8857			0.625500
$646$	−6.93370	+	2.93262i	−0.272803	+	0.115382i
$647$		−	6.29445i		−	0.247461i	−0.992316	−	0.123730i	$-0.960514\pi$
$647$		−	6.29445i		−	0.247461i	0.992316	−	0.123730i	$-0.0394858\pi$
$648$	−6.36520	+	16.3918i	−0.250049	+	0.643931i
$649$	1.12424	−	21.1265i	0.0441305	−	0.829286i
$650$	24.9572	+	16.4147i	0.978902	+	0.643839i
$651$	8.25018			0.323350
$652$	27.0077	−	27.8231i	1.05770	−	1.08964i
$653$	−32.3299			−1.26517			−0.632584	−	0.774492i	$-0.718005\pi$
$653$	−32.3299			−1.26517			−0.632584	+	0.774492i	$0.718005\pi$
$654$	2.75407	+	6.51155i	0.107693	+	0.254622i
$655$		−	53.4919i		−	2.09010i
$656$	−0.417583	−	14.0365i	−0.0163039	−	0.548034i
$657$	−16.8909			−0.658977
$658$	−3.78128	−	8.94021i	−0.147410	−	0.348526i
$659$	−1.75900			−0.0685210			−0.0342605	−	0.999413i	$-0.510908\pi$
$659$	−1.75900			−0.0685210			−0.0342605	+	0.999413i	$0.510908\pi$
$660$	8.41049	+	9.08063i	0.327378	+	0.353463i
$661$		−	28.7803i		−	1.11942i	−0.828688	−	0.559712i	$-0.810912\pi$
$661$		−	28.7803i		−	1.11942i	0.828688	−	0.559712i	$-0.189088\pi$
$662$	−25.0929	+	10.6131i	−0.975262	+	0.412488i
$663$	−2.24448	−	3.36031i	−0.0871683	−	0.130504i
$664$	10.5175	+	4.08410i	0.408157	+	0.158494i
$665$		−	17.9253i		−	0.695115i
$666$	−10.1151	−	23.9155i	−0.391952	−	0.926706i
$667$	1.50953			0.0584491
$668$	−15.3568	−	14.9067i	−0.594171	−	0.576758i
$669$		−	1.62260i		−	0.0627334i
$670$	27.4895	+	64.9943i	1.06201	+	2.51095i
$671$	−33.3557	−	1.77502i	−1.28768	−	0.0685239i
$672$	−2.70005	−	5.88927i	−0.104157	−	0.227184i
$673$		−	12.9869i		−	0.500610i	−0.968167	−	0.250305i	$-0.919469\pi$
$673$		−	12.9869i		−	0.500610i	0.968167	−	0.250305i	$-0.0805309\pi$
$674$	−16.0809	−	38.0207i	−0.619414	−	1.46450i
$675$			18.8401i			0.725156i
$676$	10.2979	+	23.8737i	0.396073	+	0.918219i
$677$			28.3135i			1.08818i	0.839028	+	0.544088i	$0.183124\pi$
$677$			28.3135i			1.08818i	−0.839028	+	0.544088i	$0.816876\pi$
$678$	−4.29036	−	10.1438i	−0.164770	−	0.389572i
$679$	19.7932			0.759592
$680$	6.67746	−	17.1960i	0.256069	−	0.659435i
$681$	14.5609			0.557973
$682$	−11.4895	−	31.7743i	−0.439957	−	1.21670i
$683$	−36.1620			−1.38370			−0.691850	−	0.722041i	$-0.743204\pi$
$683$	−36.1620			−1.38370			−0.691850	+	0.722041i	$0.743204\pi$
$684$	10.3418	+	10.0387i	0.395428	+	0.383839i
$685$	48.0787			1.83699
$686$	11.0411	+	26.1048i	0.421550	+	0.996687i
$687$	−11.9986			−0.457777
$688$	1.01266	+	34.0392i	0.0386073	+	1.29773i
$689$	11.8642	+	17.7625i	0.451991	+	0.676697i
$690$	0.317535	+	0.750759i	0.0120883	+	0.0285809i
$691$	20.2513			0.770394			0.385197	−	0.922834i	$-0.374133\pi$
$691$	20.2513			0.770394			0.385197	+	0.922834i	$0.374133\pi$
$692$	3.49215	+	3.38980i	0.132752	+	0.128861i
$693$	−17.9478	−	0.955094i	−0.681781	−	0.0362810i
$694$	−43.3703	+	18.3435i	−1.64631	+	0.696311i
$695$		−	22.4855i		−	0.852924i
$696$	2.83309	−	7.29583i	0.107388	−	0.276548i
$697$		−	6.94849i		−	0.263193i
$698$	−44.2694	+	18.7238i	−1.67562	+	0.708707i
$699$	−7.38429			−0.279299
$700$	17.0039	+	16.5055i	0.642686	+	0.623851i
$701$			29.5458i			1.11593i	0.829865	+	0.557965i	$0.188418\pi$
$701$			29.5458i			1.11593i	−0.829865	+	0.557965i	$0.811582\pi$
$702$	−9.01108	+	13.7006i	−0.340101	+	0.517095i
$703$	−18.4314			−0.695153
$704$	−18.9215	+	18.6005i	−0.713129	+	0.701033i
$705$	6.33234			0.238490
$706$	1.32258	+	3.12703i	0.0497761	+	0.117687i
$707$	24.5060			0.921643
$708$	−5.18366	−	5.03175i	−0.194814	−	0.189105i
$709$		−	17.9628i		−	0.674605i	−0.941396	−	0.337303i	$-0.890485\pi$
$709$		−	17.9628i		−	0.674605i	0.941396	−	0.337303i	$-0.109515\pi$
$710$	−20.4717	−	48.4020i	−0.768289	−	1.81649i
$711$	−18.2237			−0.683441
$712$	24.5713	+	9.54141i	0.920847	+	0.357579i
$713$		−	2.22524i		−	0.0833358i
$714$	−1.24877	−	2.95251i	−0.0467340	−	0.110495i
$715$	−20.1145	−	33.8843i	−0.752238	−	1.26720i
$716$	−32.6252	−	31.6691i	−1.21926	−	1.18353i
$717$	−6.19011			−0.231174
$718$	−3.67174	−	8.68123i	−0.137028	−	0.323981i
$719$		−	31.1311i		−	1.16099i	−0.814262	−	0.580497i	$-0.802858\pi$
$719$		−	31.1311i		−	1.16099i	0.814262	−	0.580497i	$-0.197142\pi$
$720$	−35.3003	+	1.05017i	−1.31556	+	0.0391377i
$721$	31.6206			1.17761
$722$	−15.3253	+	6.48187i	−0.570350	+	0.241230i
$723$		−	2.16319i		−	0.0804499i
$724$	−8.18174	+	8.42876i	−0.304072	+	0.313253i
$725$			28.6275i			1.06320i
$726$	−2.55102	−	8.43144i	−0.0946774	−	0.312920i
$727$			43.4457i			1.61131i	0.592385	+	0.805655i	$0.298186\pi$
$727$			43.4457i			1.61131i	−0.592385	+	0.805655i	$0.701814\pi$
$728$	4.47079	+	20.1357i	0.165699	+	0.746279i
$729$	11.1943			0.414602
$730$	−11.4439	−	27.0572i	−0.423557	−	1.00143i
$731$			16.8504i			0.623235i
$732$	−7.94440	+	8.18426i	−0.293634	+	0.302499i
$733$	−34.3465			−1.26862			−0.634308	−	0.773081i	$-0.718715\pi$
$733$	−34.3465			−1.26862			−0.634308	+	0.773081i	$0.718715\pi$
$734$	11.3347	+	26.7990i	0.418370	+	0.989169i
$735$	−5.42851			−0.200234
$736$	−1.58845	+	0.728259i	−0.0585512	+	0.0268440i
$737$	2.66890	−	50.1532i	0.0983103	−	1.84742i
$738$	−12.2518	+	5.18192i	−0.450995	+	0.190749i
$739$		−	11.9060i		−	0.437971i	−0.975728	−	0.218985i	$-0.929725\pi$
$739$		−	11.9060i		−	0.437971i	0.975728	−	0.218985i	$-0.0702747\pi$
$740$	31.4565	−	32.4063i	1.15637	−	1.19128i
$741$	3.05003	+	4.56634i	0.112046	+	0.167749i
$742$	6.60095	+	15.6069i	0.242329	+	0.572946i
$743$		−	14.5869i		−	0.535140i	−0.963538	−	0.267570i	$-0.913779\pi$
$743$		−	14.5869i		−	0.535140i	0.963538	−	0.267570i	$-0.0862207\pi$
$744$	−10.7550	−	4.17634i	−0.394298	−	0.153112i
$745$			7.65959i			0.280626i
$746$	2.59281	+	6.13027i	0.0949294	+	0.224445i
$747$		−	10.6879i		−	0.391051i
$748$	−9.63208	+	8.92124i	−0.352184	+	0.326193i
$749$		−	3.41779i		−	0.124883i
$750$	−2.08594	+	0.882251i	−0.0761677	+	0.0322153i
$751$		−	12.0462i		−	0.439570i	−0.975548	−	0.219785i	$-0.929464\pi$
$751$		−	12.0462i		−	0.439570i	0.975548	−	0.219785i	$-0.0705357\pi$
$752$	0.403664	+	13.5687i	0.0147201	+	0.494798i
$753$	12.4522			0.453782
$754$	−13.6923	+	20.8180i	−0.498645	+	0.758147i
$755$	43.1842			1.57163
$756$	−9.06093	+	9.33450i	−0.329543	+	0.339492i
$757$	−5.92237			−0.215252			−0.107626	−	0.994191i	$-0.534325\pi$
$757$	−5.92237			−0.215252			−0.107626	+	0.994191i	$0.534325\pi$
$758$	1.16987	−	0.494800i	0.0424917	−	0.0179719i
$759$	0.0308289	−	0.579327i	0.00111902	−	0.0210282i
$760$	−9.07402	+	23.3676i	−0.329149	+	0.847634i
$761$	−36.3042			−1.31603			−0.658013	−	0.753007i	$-0.728603\pi$
$761$	−36.3042			−1.31603			−0.658013	+	0.753007i	$0.728603\pi$
$762$	1.90152	+	4.49584i	0.0688849	+	0.162867i
$763$		−	17.8563i		−	0.646441i
$764$	−20.8290	−	20.2186i	−0.753567	−	0.731482i
$765$	−17.4747			−0.631798
$766$	8.62684	−	3.64873i	0.311700	−	0.131834i
$767$	12.7746	+	19.1254i	0.461264	+	0.690579i
$768$	0.538596	+	9.04410i	0.0194349	+	0.326351i
$769$	−5.56848			−0.200805			−0.100402	−	0.994947i	$-0.532013\pi$
$769$	−5.56848			−0.200805			−0.100402	+	0.994947i	$0.532013\pi$
$770$	−10.6300	−	29.3973i	−0.383079	−	1.05941i
$771$			4.40226i			0.158544i
$772$	24.4877	−	25.2270i	0.881331	−	0.907941i
$773$		−	21.0272i		−	0.756295i	−0.925745	−	0.378147i	$-0.876561\pi$
$773$		−	21.0272i		−	0.756295i	0.925745	−	0.378147i	$-0.123439\pi$
$774$	29.7112	−	12.5664i	1.06795	−	0.451690i
$775$	42.2007			1.51589
$776$	−25.8026	−	10.0195i	−0.926258	−	0.359681i
$777$		−	7.84846i		−	0.281562i
$778$	33.2085	−	14.0456i	1.19058	−	0.503558i
$779$			9.44233i			0.338307i
$780$	−13.2340	−	2.43070i	−0.473854	−	0.0870329i
$781$	−1.98756	+	37.3496i	−0.0711205	+	1.33647i
$782$	−0.796351	+	0.336818i	−0.0284775	+	0.0120446i
$783$	−15.7154			−0.561624
$784$	−0.346048	−	11.6320i	−0.0123589	−	0.415428i
$785$			1.56852i			0.0559828i
$786$	5.06398	+	11.9729i	0.180626	+	0.427061i
$787$			30.8979i			1.10139i	0.834706	+	0.550695i	$0.185637\pi$
$787$			30.8979i			1.10139i	−0.834706	+	0.550695i	$0.814363\pi$
$788$	−26.7935	+	27.6025i	−0.954479	+	0.983297i
$789$		−	17.1031i		−	0.608886i
$790$	−12.3469	−	29.1921i	−0.439281	−	1.03861i
$791$			27.8169i			0.989057i
$792$	22.9135	+	10.3305i	0.814195	+	0.367077i
$793$	30.1963	−	20.1692i	1.07230	−	0.716231i
$794$	4.34931	+	10.2832i	0.154351	+	0.364938i
$795$	−11.0543			−0.392056
$796$	5.63069	+	5.46567i	0.199575	+	0.193726i
$797$	9.20602			0.326094			0.163047	−	0.986618i	$-0.447868\pi$
$797$	9.20602			0.326094			0.163047	+	0.986618i	$0.447868\pi$
$798$	1.69696	+	4.01218i	0.0600716	+	0.142030i
$799$			6.71689i			0.237626i
$800$	−13.8111	−	30.1243i	−0.488296	−	1.06506i
$801$		−	24.9695i		−	0.882255i
$802$	−12.5045	−	29.5649i	−0.441549	−	1.04397i
$803$	−1.11107	+	20.8788i	−0.0392086	+	0.736797i
$804$	−12.3058	−	11.9451i	−0.433991	−	0.421272i
$805$		−	2.05877i		−	0.0725621i
$806$	30.6884	+	20.1843i	1.08095	+	0.710961i
$807$		−	5.72157i		−	0.201409i
$808$	−31.9462	−	12.4052i	−1.12386	−	0.436414i
$809$			55.5715i			1.95379i	0.213719	+	0.976895i	$0.431442\pi$
$809$			55.5715i			1.95379i	−0.213719	+	0.976895i	$0.568558\pi$
$810$	11.2857	+	26.6833i	0.396540	+	0.937554i
$811$			15.0233i			0.527538i	0.964586	+	0.263769i	$0.0849657\pi$
$811$			15.0233i			0.527538i	−0.964586	+	0.263769i	$0.915034\pi$
$812$	−13.7681	+	14.1838i	−0.483165	+	0.497752i
$813$	−5.82855			−0.204416
$814$	−30.2272	+	10.9301i	−1.05946	+	0.383100i
$815$		−	63.8863i		−	2.23784i
$816$	0.133310	+	4.48106i	0.00466680	+	0.156869i
$817$		−	22.8981i		−	0.801103i
$818$	34.0501	−	14.4016i	1.19054	−	0.503539i
$819$	16.2479	−	10.8526i	0.567746	−	0.379219i
$820$	−16.6016	−	16.1151i	−0.579754	−	0.562763i
$821$	−8.14200			−0.284158			−0.142079	−	0.989855i	$-0.545379\pi$
$821$	−8.14200			−0.284158			−0.142079	+	0.989855i	$0.545379\pi$
$822$	−10.7613	+	4.55151i	−0.375344	+	0.158752i
$823$			55.2299i			1.92519i	0.270940	+	0.962596i	$0.412666\pi$
$823$			55.2299i			1.92519i	−0.270940	+	0.962596i	$0.587334\pi$
$824$	−41.2209	−	16.0067i	−1.43600	−	0.557621i
$825$	10.9867	+	0.584656i	0.382507	+	0.0203551i
$826$	7.10745	+	16.8044i	0.247300	+	0.584700i
$827$			22.3027i			0.775542i	0.921756	+	0.387771i	$0.126755\pi$
$827$			22.3027i			0.775542i	−0.921756	+	0.387771i	$0.873245\pi$
$828$	1.18778	+	1.15297i	0.0412781	+	0.0400684i
$829$	−11.0651			−0.384308			−0.192154	−	0.981365i	$-0.561547\pi$
$829$	−11.0651			−0.384308			−0.192154	+	0.981365i	$0.561547\pi$
$830$	17.1208	−	7.24125i	0.594270	−	0.251348i
$831$	4.23202			0.146807
$832$	4.36477	−	28.5123i	0.151321	−	0.988485i
$833$		−	5.75817i		−	0.199509i
$834$	2.12866	+	5.03287i	0.0737094	+	0.174274i
$835$	−35.2616			−1.22028
$836$	13.0891	−	12.1231i	0.452695	−	0.419286i
$837$			23.1666i			0.800755i
$838$	−5.62379	−	13.2965i	−0.194271	−	0.459321i
$839$	−17.6559			−0.609548			−0.304774	−	0.952425i	$-0.598581\pi$
$839$	−17.6559			−0.609548			−0.304774	+	0.952425i	$0.598581\pi$
$840$	−9.95043	−	3.86391i	−0.343322	−	0.133317i
$841$	5.12041			0.176566
$842$	−6.64916	−	15.7208i	−0.229145	−	0.541776i
$843$		−	8.86660i		−	0.305382i
$844$	17.4279	−	17.9541i	0.599895	−	0.618007i
$845$	39.5712	+	16.4064i	1.36129	+	0.564397i
$846$	11.8434	−	5.00920i	0.407186	−	0.172220i
$847$	−2.36118	+	22.1224i	−0.0811310	+	0.760136i
$848$	−0.704674	−	23.6867i	−0.0241986	−	0.813406i
$849$			3.13930i			0.107740i
$850$	−6.38761	−	15.1025i	−0.219093	−	0.518010i
$851$	−2.11689			−0.0725660
$852$	9.16423	+	8.89565i	0.313961	+	0.304760i
$853$	−52.2246			−1.78814			−0.894069	−	0.447929i	$-0.852162\pi$
$853$	−52.2246			−1.78814			−0.894069	+	0.447929i	$0.852162\pi$
$854$	26.5317	−	11.2216i	0.907897	−	0.383997i
$855$	23.7464			0.812109
$856$	−1.73012	+	4.45546i	−0.0591344	+	0.152284i
$857$			11.0774i			0.378397i	0.981939	+	0.189199i	$0.0605890\pi$
$857$			11.0774i			0.378397i	−0.981939	+	0.189199i	$0.939411\pi$
$858$	7.70991	+	5.68002i	0.263212	+	0.193913i
$859$		−	47.0064i		−	1.60384i	−0.597433	−	0.801919i	$-0.703813\pi$
$859$		−	47.0064i		−	1.60384i	0.597433	−	0.801919i	$-0.296187\pi$
$860$	40.2597	+	39.0798i	1.37284	+	1.33261i
$861$	−4.02074			−0.137026
$862$	−12.8068	−	30.2797i	−0.436203	−	1.03133i
$863$	−9.40938			−0.320299			−0.160149	−	0.987093i	$-0.551198\pi$
$863$	−9.40938			−0.320299			−0.160149	+	0.987093i	$0.551198\pi$
$864$	16.5371	−	7.58179i	0.562605	−	0.257938i
$865$	8.01854			0.272638
$866$	31.3415	−	13.2559i	1.06503	−	0.450455i
$867$		−	7.40813i		−	0.251593i
$868$	20.9087	+	20.2959i	0.709687	+	0.688888i
$869$	−1.19873	+	22.5262i	−0.0406643	+	0.764150i
$870$	−5.02317	−	11.8765i	−0.170301	−	0.402650i
$871$	30.3262	+	45.4028i	1.02757	+	1.53842i
$872$	−9.03907	+	23.2776i	−0.306101	+	0.788280i
$873$			26.2208i			0.887439i
$874$	1.08216	−	0.457703i	0.0366048	−	0.0154820i
$875$	5.72016			0.193377
$876$	5.12290	+	4.97276i	0.173087	+	0.168014i
$877$	8.80058			0.297174			0.148587	−	0.988899i	$-0.452527\pi$
$877$	8.80058			0.297174			0.148587	+	0.988899i	$0.452527\pi$
$878$	18.9512	−	8.01544i	0.639572	−	0.270508i
$879$		−	9.03302i		−	0.304676i
$880$	−1.02390	+	43.7036i	−0.0345155	+	1.47325i
$881$	9.21479			0.310454			0.155227	−	0.987879i	$-0.450389\pi$
$881$	9.21479			0.310454			0.155227	+	0.987879i	$0.450389\pi$
$882$	−10.1530	+	4.29423i	−0.341869	+	0.144594i
$883$		−	14.2442i		−	0.479356i	−0.970852	−	0.239678i	$-0.922958\pi$
$883$		−	14.2442i		−	0.479356i	0.970852	−	0.239678i	$-0.0770418\pi$
$884$	2.57831	−	14.0377i	0.0867179	−	0.472139i
$885$	−11.9025			−0.400099
$886$	−17.4367	−	41.2262i	−0.585798	−	1.38502i
$887$	46.1304			1.54891			0.774453	−	0.632632i	$-0.218025\pi$
$887$	46.1304			1.54891			0.774453	+	0.632632i	$0.218025\pi$
$888$	−3.97299	+	10.2313i	−0.133325	+	0.343341i
$889$		−	12.3287i		−	0.413491i
$890$	39.9981	−	16.9173i	1.34074	−	0.567068i
$891$	1.09571	−	20.5903i	0.0367077	−	0.689800i
$892$	3.99169	−	4.11221i	0.133652	−	0.137687i
$893$		−	9.12760i		−	0.305444i
$894$	−0.725118	−	1.71442i	−0.0242516	−	0.0573389i
$895$	−74.9128			−2.50406
$896$	7.64511	−	21.5677i	0.255405	−	0.720525i
$897$	0.350303	+	0.524455i	0.0116963	+	0.0175110i
$898$	22.5593	+	53.3378i	0.752814	+	1.77991i
$899$			35.2016i			1.17404i
$900$	−21.8655	+	22.5257i	−0.728850	+	0.750856i
$901$		−	11.7256i		−	0.390637i
$902$	5.59945	+	15.4853i	0.186441	+	0.515604i
$903$	9.75048			0.324476
$904$	14.0813	−	36.2624i	0.468336	−	1.20607i
$905$			19.3538i			0.643342i
$906$	−9.66579	+	4.08816i	−0.321124	+	0.135820i
$907$		−	44.7921i		−	1.48730i	−0.668570	−	0.743649i	$-0.733093\pi$
$907$		−	44.7921i		−	1.48730i	0.668570	−	0.743649i	$-0.266907\pi$
$908$	36.9021	+	35.8206i	1.22464	+	1.18875i
$909$			32.4640i			1.07676i
$910$	28.3927	+	18.6743i	0.941207	+	0.619047i
$911$			2.41882i			0.0801390i	0.999197	+	0.0400695i	$0.0127579\pi$
$911$			2.41882i			0.0801390i	−0.999197	+	0.0400695i	$0.987242\pi$
$912$	−0.181156	−	6.08933i	−0.00599868	−	0.201638i
$913$	−13.2113	−	0.703041i	−0.437231	−	0.0232672i
$914$	2.51954	−	1.06564i	0.0833390	−	0.0352484i
$915$			18.7924i			0.621257i
$916$	−30.4086	−	29.5174i	−1.00473	−	0.975281i
$917$		−	32.8328i		−	1.08423i
$918$	8.29069	−	3.50656i	0.273633	−	0.115734i
$919$	−41.2404			−1.36039			−0.680197	−	0.733029i	$-0.738106\pi$
$919$	−41.2404			−1.36039			−0.680197	+	0.733029i	$0.738106\pi$
$920$	−1.04217	+	2.68383i	−0.0343594	+	0.0884832i
$921$	−9.51219			−0.313437
$922$	38.0316	−	16.0855i	1.25250	−	0.529748i
$923$	−22.5843	−	33.8119i	−0.743370	−	1.11293i
$924$	5.16227	+	5.57359i	0.169826	+	0.183358i
$925$		−	40.1458i		−	1.31999i
$926$	8.06067	−	3.40927i	0.264890	−	0.112036i
$927$			41.8890i			1.37582i
$928$	25.1282	−	11.5205i	0.824872	−	0.378179i
$929$			32.8823i			1.07883i	0.842039	+	0.539416i	$0.181355\pi$
$929$			32.8823i			1.07883i	−0.842039	+	0.539416i	$0.818645\pi$
$930$	−17.5074	+	7.40480i	−0.574092	+	0.242813i
$931$			7.82480i			0.256447i
$932$	−18.7142	−	18.1658i	−0.613005	−	0.595040i
$933$	−1.16365			−0.0380962
$934$	−19.8727	−	46.9857i	−0.650254	−	1.53742i
$935$	−1.14946	+	21.6004i	−0.0375915	+	0.706408i
$936$	−26.6745	+	5.92263i	−0.871884	+	0.193587i
$937$		−	24.7005i		−	0.806929i	−0.914995	−	0.403465i	$-0.867806\pi$
$937$		−	24.7005i		−	0.806929i	0.914995	−	0.403465i	$-0.132194\pi$
$938$	16.8727	+	39.8928i	0.550914	+	1.30255i
$939$			0.371523i			0.0121242i
$940$	16.0483	+	15.5779i	0.523436	+	0.508096i
$941$	−2.48844			−0.0811210			−0.0405605	−	0.999177i	$-0.512914\pi$
$941$	−2.48844			−0.0811210			−0.0405605	+	0.999177i	$0.512914\pi$
$942$	−0.148489	−	0.351077i	−0.00483802	−	0.0114387i
$943$			1.08447i			0.0353153i
$944$	−0.758745	−	25.5042i	−0.0246950	−	0.830092i
$945$			21.4335i			0.697232i
$946$	−13.5789	−	37.5526i	−0.441489	−	1.22094i
$947$	39.8617			1.29533			0.647666	−	0.761924i	$-0.275745\pi$
$947$	39.8617			1.29533			0.647666	+	0.761924i	$0.275745\pi$
$948$	5.52712	+	5.36513i	0.179512	+	0.174251i
$949$	−12.6248	−	18.9012i	−0.409819	−	0.613559i
$950$	8.68014	+	20.5228i	0.281621	+	0.665847i
$951$	−7.17861			−0.232783
$952$	4.09855	−	10.5547i	0.132835	−	0.342080i
$953$		−	2.43748i		−	0.0789576i	−0.999220	−	0.0394788i	$-0.987430\pi$
$953$		−	2.43748i		−	0.0789576i	0.999220	−	0.0394788i	$-0.0125698\pi$
$954$	−20.6750	+	8.74453i	−0.669378	+	0.283115i
$955$	−47.8268			−1.54764
$956$	−15.6878	−	15.2280i	−0.507379	−	0.492509i
$957$	−0.487690	+	9.16453i	−0.0157648	+	0.296247i
$958$	−4.70574	−	11.1260i	−0.152036	−	0.359463i
$959$	29.5102			0.952933
$960$	11.0155	+	10.0740i	0.355524	+	0.325139i
$961$	20.8917			0.673927
$962$	19.2015	−	29.1942i	0.619080	−	0.941258i
$963$	4.52767			0.145902
$964$	5.32158	−	5.48225i	0.171396	−	0.176571i
$965$		−	57.9253i		−	1.86468i
$966$	0.194899	+	0.460808i	0.00627079	+	0.0148263i
$967$			6.50738i			0.209263i	0.994511	+	0.104632i	$0.0333664\pi$
$967$			6.50738i			0.209263i	−0.994511	+	0.104632i	$0.966634\pi$
$968$	14.2767	−	27.6437i	0.458870	−	0.888503i
$969$		−	3.01440i		−	0.0968364i
$970$	−42.0025	+	17.7650i	−1.34862	+	0.570400i
$971$		−	32.9668i		−	1.05795i	−0.848636	−	0.528977i	$-0.822576\pi$
$971$		−	32.9668i		−	1.05795i	0.848636	−	0.528977i	$-0.177424\pi$
$972$	−18.8977	−	18.3439i	−0.606145	−	0.588380i
$973$		−	13.8014i		−	0.442451i
$974$	−44.5665	+	18.8495i	−1.42800	+	0.603976i
$975$	−9.94605	+	6.64334i	−0.318529	+	0.212757i
$976$	−40.2675	+	1.19795i	−1.28893	+	0.0383454i
$977$			14.4762i			0.463136i	0.972819	+	0.231568i	$0.0743855\pi$
$977$			14.4762i			0.463136i	−0.972819	+	0.231568i	$0.925614\pi$
$978$	6.04799	+	14.2995i	0.193393	+	0.457247i
$979$	−30.8647	−	1.64247i	−0.986441	−	0.0524935i
$980$	−13.7577	−	13.3545i	−0.439472	−	0.426592i
$981$	23.6549			0.755243
$982$	−38.8340	+	16.4249i	−1.23924	+	0.524140i
$983$	16.7264			0.533490			0.266745	−	0.963767i	$-0.414052\pi$
$983$	16.7264			0.533490			0.266745	+	0.963767i	$0.414052\pi$
$984$	5.24147	+	2.03535i	0.167092	+	0.0648845i
$985$			63.3797i			2.01945i
$986$	12.5977	−	5.32821i	0.401192	−	0.169685i
$987$	3.88672			0.123716
$988$	−3.50367	+	19.0759i	−0.111467	+	0.606884i
$989$		−	2.62990i		−	0.0836260i
$990$	38.9437	−	14.0820i	1.23771	−	0.447555i
$991$			49.2134i			1.56332i	0.623707	+	0.781658i	$0.285626\pi$
$991$			49.2134i			1.56332i	−0.623707	+	0.781658i	$0.714374\pi$
$992$	−16.9827	−	37.0422i	−0.539202	−	1.17609i
$993$		−	10.9090i		−	0.346187i
$994$	−12.5653	−	29.7086i	−0.398547	−	0.942300i
$995$	12.9290			0.409876
$996$	−3.14658	+	3.24158i	−0.0997031	+	0.102713i
$997$			43.9297i			1.39127i	0.718397	+	0.695634i	$0.244876\pi$
$997$			43.9297i			1.39127i	−0.718397	+	0.695634i	$0.755124\pi$
$998$	−9.38649	+	3.97003i	−0.297124	+	0.125669i
$999$	22.0386			0.697270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.b.c.571.7	yes	56
4.3	odd	2	inner	572.2.b.c.571.5	✓	56
11.10	odd	2	inner	572.2.b.c.571.49	yes	56
13.12	even	2	inner	572.2.b.c.571.50	yes	56
44.43	even	2	inner	572.2.b.c.571.51	yes	56
52.51	odd	2	inner	572.2.b.c.571.52	yes	56
143.142	odd	2	inner	572.2.b.c.571.8	yes	56
572.571	even	2	inner	572.2.b.c.571.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.5	✓	56	4.3	odd	2	inner
572.2.b.c.571.6	yes	56	572.571	even	2	inner
572.2.b.c.571.7	yes	56	1.1	even	1	trivial
572.2.b.c.571.8	yes	56	143.142	odd	2	inner
572.2.b.c.571.49	yes	56	11.10	odd	2	inner
572.2.b.c.571.50	yes	56	13.12	even	2	inner
572.2.b.c.571.51	yes	56	44.43	even	2	inner
572.2.b.c.571.52	yes	56	52.51	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30250 + 0.550896i) q^{2} -0.566258i q^{3} +(1.39303 - 1.43509i) q^{4} -3.29519i q^{5} +(0.311949 + 0.737553i) q^{6} -2.02255i q^{7} +(-1.02384 + 2.63662i) q^{8} +2.67935 q^{9} +O(q^{10})\)	\(q+(-1.30250 + 0.550896i) q^{2} -0.566258i q^{3} +(1.39303 - 1.43509i) q^{4} -3.29519i q^{5} +(0.311949 + 0.737553i) q^{6} -2.02255i q^{7} +(-1.02384 + 2.63662i) q^{8} +2.67935 q^{9} +(1.81531 + 4.29199i) q^{10} +(0.176245 - 3.31194i) q^{11} +(-0.812629 - 0.788813i) q^{12} +(2.00264 + 2.99824i) q^{13} +(1.11422 + 2.63438i) q^{14} -1.86593 q^{15} +(-0.118946 - 3.99823i) q^{16} -1.97924i q^{17} +(-3.48986 + 1.47604i) q^{18} +2.68960i q^{19} +(-4.72888 - 4.59029i) q^{20} -1.14529 q^{21} +(1.59497 + 4.41090i) q^{22} +0.308907i q^{23} +(1.49301 + 0.579758i) q^{24} -5.85828 q^{25} +(-4.26016 - 2.80197i) q^{26} -3.21598i q^{27} +(-2.90254 - 2.81747i) q^{28} -4.88668i q^{29} +(2.43038 - 1.02793i) q^{30} -7.20359 q^{31} +(2.35754 + 5.14218i) q^{32} +(-1.87541 - 0.0998000i) q^{33} +(1.09036 + 2.57797i) q^{34} -6.66469 q^{35} +(3.73241 - 3.84510i) q^{36} +6.85284i q^{37} +(-1.48169 - 3.50321i) q^{38} +(1.69778 - 1.13401i) q^{39} +(8.68816 + 3.37375i) q^{40} +3.51069 q^{41} +(1.49174 - 0.630933i) q^{42} -8.51358 q^{43} +(-4.50740 - 4.86655i) q^{44} -8.82897i q^{45} +(-0.170175 - 0.402352i) q^{46} -3.39367 q^{47} +(-2.26403 + 0.0673543i) q^{48} +2.90928 q^{49} +(7.63043 - 3.22730i) q^{50} -1.12076 q^{51} +(7.09246 + 1.30267i) q^{52} +5.92430 q^{53} +(1.77167 + 4.18882i) q^{54} +(-10.9135 - 0.580760i) q^{55} +(5.33270 + 2.07077i) q^{56} +1.52301 q^{57} +(2.69205 + 6.36491i) q^{58} +6.37888 q^{59} +(-2.59929 + 2.67777i) q^{60} -10.0713i q^{61} +(9.38270 - 3.96843i) q^{62} -5.41913i q^{63} +(-5.90350 - 5.39895i) q^{64} +(9.87977 - 6.59907i) q^{65} +(2.49771 - 0.903166i) q^{66} +15.1432 q^{67} +(-2.84038 - 2.75714i) q^{68} +0.174921 q^{69} +(8.68078 - 3.67155i) q^{70} -11.2773 q^{71} +(-2.74323 + 7.06443i) q^{72} -6.30410 q^{73} +(-3.77520 - 8.92584i) q^{74} +3.31730i q^{75} +(3.85981 + 3.74668i) q^{76} +(-6.69857 - 0.356464i) q^{77} +(-1.58664 + 2.41235i) q^{78} -6.80153 q^{79} +(-13.1749 + 0.391951i) q^{80} +6.21698 q^{81} +(-4.57268 + 1.93402i) q^{82} -3.98900i q^{83} +(-1.59542 + 1.64359i) q^{84} -6.52198 q^{85} +(11.0890 - 4.69009i) q^{86} -2.76712 q^{87} +(8.55187 + 3.85559i) q^{88} -9.31924i q^{89} +(4.86384 + 11.4998i) q^{90} +(6.06410 - 4.05044i) q^{91} +(0.443308 + 0.430316i) q^{92} +4.07909i q^{93} +(4.42026 - 1.86956i) q^{94} +8.86274 q^{95} +(2.91180 - 1.33497i) q^{96} +9.78624i q^{97} +(-3.78935 + 1.60271i) q^{98} +(0.472222 - 8.87385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^4 - 32 * q^9	\( 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) \) 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Introduction

L-functions

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