LMFDB - Embedded newform 572.2.b.c.571.5

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			571.5
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.8

$q$-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} +(2.05409 - 4.21672i) q^{22} -0.308907i q^{23} +(1.49301 - 0.579758i) q^{24} -5.85828 q^{25} +(-0.956723 - 5.00846i) 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} +(-4.99843 + 4.36070i) 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} +(-1.51300 + 7.05059i) 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} +(2.38775 + 1.16315i) 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} +(2.83608 - 0.541752i) 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} +(8.91276 - 2.92621i) 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	$0.0522670\pi$
$3$			0.566258i			0.326929i	−0.986549	+	0.163465i	$0.947733\pi$
$4$	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	$0.124843\pi$
$7$			2.02255i			0.764453i	−0.924069	+	0.382226i	$0.875157\pi$
$8$	−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	$-0.900167\pi$
$19$		−	2.68960i		−	0.617036i	0.951219	−	0.308518i	$-0.0998330\pi$
$20$	4.72888	−	4.59029i	1.05741	−	1.02642i
$21$	−1.14529			−0.249922
$22$	2.05409	−	4.21672i	0.437934	−	0.899007i
$23$		−	0.308907i		−	0.0644115i	−0.999481	−	0.0322057i	$-0.989747\pi$
$23$		−	0.308907i		−	0.0644115i	0.999481	−	0.0322057i	$-0.0102532\pi$
$24$	1.49301	−	0.579758i	0.304759	−	0.118343i
$25$	−5.85828			−1.17166
$26$	−0.956723	−	5.00846i	−0.187629	−	0.982240i
$27$			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	$-0.276064\pi$
$31$	7.20359			1.29380			0.646902	+	0.762573i	$0.276064\pi$
$32$	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	$-0.275123\pi$
$43$	8.51358			1.29831			0.649154	+	0.760657i	$0.275123\pi$
$44$	−4.99843	+	4.36070i	−0.753542	+	0.657400i
$45$		−	8.82897i		−	1.31615i
$46$	−0.170175	+	0.402352i	−0.0250910	+	0.0593235i
$47$	3.39367			0.495017			0.247509	−	0.968886i	$-0.420388\pi$
$47$	3.39367			0.495017			0.247509	+	0.968886i	$0.420388\pi$
$48$	−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
$52$	−1.51300	+	7.05059i	−0.209816	+	0.977741i
$53$	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	$-0.636299\pi$
$59$	−6.37888			−0.830460			−0.415230	+	0.909717i	$0.636299\pi$
$60$	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
$66$	2.38775	+	1.16315i	0.293912	+	0.143173i
$67$	−15.1432			−1.85003			−0.925015	−	0.379930i	$-0.875948\pi$
$67$	−15.1432			−1.85003			−0.925015	+	0.379930i	$0.875948\pi$
$68$	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	$-0.266644\pi$
$71$	11.2773			1.33836			0.669182	+	0.743098i	$0.266644\pi$
$72$	−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
$78$	2.83608	−	0.541752i	0.321123	−	0.0613414i
$79$	6.80153			0.765231			0.382616	−	0.923908i	$-0.375023\pi$
$79$	6.80153			0.765231			0.382616	+	0.923908i	$0.375023\pi$
$80$	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	$0.0702549\pi$
$83$			3.98900i			0.437850i	−0.975742	+	0.218925i	$0.929745\pi$
$84$	−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
$88$	8.91276	−	2.92621i	0.950104	−	0.311935i
$89$		−	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	$-0.720140\pi$
$103$		−	15.6340i		−	1.54046i	0.637764	−	0.770232i	$-0.279860\pi$
$104$	5.85483	−	8.34991i	0.574114	−	0.818776i
$105$			3.77394i			0.368299i
$106$	−7.71642	−	3.26367i	−0.749485	−	0.316996i
$107$	−1.68984			−0.163363			−0.0816814	−	0.996658i	$-0.526029\pi$
$107$	−1.68984			−0.163363			−0.0816814	+	0.996658i	$0.526029\pi$
$108$	−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	$0.361043\pi$
$110$	−13.8949	−	6.76862i	−1.32483	−	0.645363i
$111$	−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	$-0.587172\pi$
$127$	−6.09562			−0.540899			−0.270449	+	0.962734i	$0.587172\pi$
$128$	10.6636	−	3.77993i	0.942537	−	0.334102i
$129$			4.82088i			0.424455i
$130$	−16.5038	+	3.15259i	−1.44748	+	0.276500i
$131$	−16.2333			−1.41831			−0.709157	−	0.705051i	$-0.750924\pi$
$131$	−16.2333			−1.41831			−0.709157	+	0.705051i	$0.750924\pi$
$132$	−2.46928	−	2.83040i	−0.214923	−	0.246355i
$133$	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	$-0.593453\pi$
$139$	−6.82374			−0.578782			−0.289391	+	0.957211i	$0.593453\pi$
$140$	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	$-0.820973\pi$
$151$		−	13.1052i		−	1.06649i	0.845962	−	0.533244i	$-0.179027\pi$
$152$	−7.09144	+	2.75372i	−0.575192	+	0.223356i
$153$		−	5.30308i		−	0.428729i
$154$	8.52853	+	4.15451i	0.687249	+	0.334780i
$155$		−	23.7372i		−	1.90662i
$156$	−3.99245	−	0.856751i	−0.319652	−	0.0685950i
$157$	−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	$-0.774450\pi$
$163$	−19.3878			−1.51857			−0.759283	+	0.650761i	$0.774450\pi$
$164$	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	$0.135880\pi$
$167$			10.7009i			0.828063i	−0.910262	+	0.414032i	$0.864120\pi$
$168$	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
$176$	−13.2209	−	1.09861i	−0.996565	−	0.0828109i
$177$		−	3.61209i		−	0.271501i
$178$	−5.13393	+	12.1383i	−0.384804	+	0.909807i
$179$			22.7340i			1.69922i	0.527414	+	0.849609i	$0.323162\pi$
$179$			22.7340i			1.69922i	−0.527414	+	0.849609i	$0.676838\pi$
$180$	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	$0.570045\pi$
$182$	10.1299	−	1.93502i	0.750876	−	0.143433i
$183$	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	$0.175973\pi$
$191$			14.5141i			1.05020i	−0.851039	+	0.525102i	$0.824027\pi$
$192$	−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	$0.740278\pi$
$198$	5.50364	−	11.2981i	0.391126	−	0.802919i
$199$		−	3.92359i		−	0.278136i	−0.990283	−	0.139068i	$-0.955589\pi$
$199$		−	3.92359i		−	0.278136i	0.990283	−	0.139068i	$-0.0444107\pi$
$200$	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
$208$	−12.2259	+	7.65038i	−0.847711	+	0.530458i
$209$	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	$-0.641712\pi$
$211$	−12.5108			−0.861281			−0.430641	+	0.902523i	$0.641712\pi$
$212$	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
$220$	14.3693	+	16.4708i	0.968780	+	1.11046i
$221$	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	$-0.530587\pi$
$223$	−2.86548			−0.191887			−0.0959434	+	0.995387i	$0.530587\pi$
$224$	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	$-0.674564\pi$
$227$		−	25.7142i		−	1.70671i	0.521331	−	0.853355i	$-0.325436\pi$
$228$	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	$-0.140484\pi$
$234$	−2.56340	−	13.4194i	−0.167575	−	0.877256i
$235$		−	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	$0.115027\pi$
$239$			10.9316i			0.707106i	−0.935414	+	0.353553i	$0.884973\pi$
$240$	−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	$0.460736\pi$
$242$	13.6035	+	7.54620i	0.874465	+	0.485088i
$243$			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	$-0.755844\pi$
$251$		−	21.9902i		−	1.38801i	0.719969	−	0.694006i	$-0.244156\pi$
$252$	−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
$260$	23.2330	+	4.98564i	1.44085	+	0.309196i
$261$		−	13.0931i		−	0.810444i
$262$	21.1440	+	8.94288i	1.30628	+	0.552493i
$263$	−30.2037			−1.86244			−0.931219	−	0.364459i	$-0.881254\pi$
$263$	−30.2037			−1.86244			−0.931219	+	0.364459i	$0.881254\pi$
$264$	1.65699	+	5.04692i	0.101981	+	0.310617i
$265$		−	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	$0.101210\pi$
$271$			10.2931i			0.625262i	−0.949875	+	0.312631i	$0.898790\pi$
$272$	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	$-0.447310\pi$
$283$	5.54393			0.329553			0.164776	+	0.986331i	$0.447310\pi$
$284$	15.7095	+	16.1838i	0.932190	+	0.960335i
$285$		−	5.01860i		−	0.297276i
$286$	16.7563	−	2.28589i	0.990823	−	0.135168i
$287$			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	$0.159133\pi$
$307$			16.7983i			0.958732i	−0.877615	+	0.479366i	$0.840867\pi$
$308$	−8.81974	−	10.1096i	−0.502551	−	0.576047i
$309$	8.85288			0.503623
$310$	−13.0767	+	30.9178i	−0.742708	+	1.75601i
$311$			2.05498i			0.116527i	0.998301	+	0.0582637i	$0.0185564\pi$
$311$			2.05498i			0.116527i	−0.998301	+	0.0582637i	$0.981444\pi$
$312$	4.72820	+	3.31535i	0.267682	+	0.187694i
$313$	−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
$330$	3.83279	−	7.86809i	0.210988	−	0.433124i
$331$	−19.2651			−1.05891			−0.529453	−	0.848339i	$-0.677603\pi$
$331$	−19.2651			−1.05891			−0.529453	+	0.848339i	$0.677603\pi$
$332$	−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	$0.707442\pi$
$338$	13.1006	−	12.8986i	0.712579	−	0.701592i
$339$		−	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	$-0.851939\pi$
$347$	−33.2976			−1.78751			−0.893755	+	0.448555i	$0.851939\pi$
$348$	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
$352$	16.6151	+	8.71430i	0.885587	+	0.464474i
$353$		−	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	$-0.943722\pi$
$359$		−	6.66503i		−	0.351767i	0.984411	−	0.175884i	$-0.0562782\pi$
$360$	−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
$364$	−14.2602	−	3.06013i	−0.747437	−	0.160394i
$365$			20.7732i			1.08732i
$366$	−7.42814	−	3.14174i	−0.388275	−	0.164222i
$367$			20.5750i			1.07401i	0.843580	+	0.537003i	$0.180444\pi$
$367$			20.5750i			1.07401i	−0.843580	+	0.537003i	$0.819556\pi$
$368$	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	$-0.0388819\pi$
$374$	−8.34590	−	4.06554i	−0.431556	−	0.210224i
$375$	−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	$-0.492657\pi$
$379$	0.898174			0.0461361			0.0230680	+	0.999734i	$0.492657\pi$
$380$	−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	$-0.445876\pi$
$383$	6.62328			0.338434			0.169217	+	0.985579i	$0.445876\pi$
$384$	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	$0.723704\pi$
$390$	−1.78518	−	9.34543i	−0.0903959	−	0.473224i
$391$	−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
$396$	−13.3926	+	11.6838i	−0.673001	+	0.587135i
$397$		−	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
$416$	20.1388	−	3.22946i	0.987385	−	0.158337i
$417$		−	3.86400i		−	0.189221i
$418$	−11.3413	−	5.52468i	−0.554720	−	0.270221i
$419$		−	10.2084i		−	0.498715i	−0.968411	−	0.249358i	$-0.919781\pi$
$419$		−	10.2084i		−	0.498715i	0.968411	−	0.249358i	$-0.0802195\pi$
$420$	−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	$-0.810843\pi$
$431$		−	23.2473i		−	1.11978i	0.828566	−	0.559892i	$-0.189157\pi$
$432$	−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	$-0.387128\pi$
$439$	14.5498			0.694426			0.347213	+	0.937786i	$0.387128\pi$
$440$	−9.64240	−	29.3692i	−0.459684	−	1.40012i
$441$	7.79499			0.371190
$442$	−9.91295	+	1.89359i	−0.471511	+	0.0900687i
$443$		−	31.6516i		−	1.50381i	−0.659271	−	0.751905i	$-0.729135\pi$
$443$		−	31.6516i		−	1.50381i	0.659271	−	0.751905i	$-0.270865\pi$
$444$	−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	$0.738004\pi$
$462$	−2.35252	+	4.82935i	−0.109449	+	0.224682i
$463$	6.18860			0.287609			0.143804	−	0.989606i	$-0.454066\pi$
$463$	6.18860			0.287609			0.143804	+	0.989606i	$0.454066\pi$
$464$	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	$-0.685677\pi$
$467$		−	36.0734i		−	1.66928i	0.550798	−	0.834639i	$-0.314323\pi$
$468$	−4.05387	+	18.8910i	−0.187390	+	0.873237i
$469$		−	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	$-0.937482\pi$
$479$		−	8.54198i		−	0.390293i	0.980774	−	0.195146i	$-0.0625182\pi$
$480$	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
$484$	−13.5614	−	17.3231i	−0.616428	−	0.787411i
$485$	32.2475			1.46428
$486$	7.25439	−	17.1518i	0.329066	−	0.778022i
$487$	−34.2160			−1.55048			−0.775238	−	0.631669i	$-0.782370\pi$
$487$	−34.2160			−1.55048			−0.775238	+	0.631669i	$0.782370\pi$
$488$	−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	$-0.734893\pi$
$491$	−29.8149			−1.34553			−0.672764	+	0.739857i	$0.734893\pi$
$492$	−2.85289	+	2.76927i	−0.128618	+	0.124849i
$493$	−9.67191			−0.435601
$494$	−13.4707	+	2.57320i	−0.606077	+	0.115774i
$495$	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	$-0.551570\pi$
$499$	−7.20650			−0.322607			−0.161304	+	0.986905i	$0.551570\pi$
$500$	−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	$-0.256360\pi$
$503$	31.0775			1.38568			0.692839	+	0.721093i	$0.256360\pi$
$504$	14.2882	−	5.54832i	0.636446	−	0.247142i
$505$	39.9258			1.77667
$506$	−1.30257	−	0.634523i	−0.0579064	−	0.0282080i
$507$	−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
$520$	−27.5145	−	19.2928i	−1.20659	−	0.846045i
$521$	−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	$-0.191316\pi$
$523$	37.7227			1.64950			0.824749	+	0.565499i	$0.191316\pi$
$524$	−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
$528$	0.622097	−	7.48646i	0.0270733	−	0.325806i
$529$	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
$546$	1.09572	+	5.73612i	0.0468926	+	0.245483i
$547$	−7.67744			−0.328264			−0.164132	−	0.986438i	$-0.552482\pi$
$547$	−7.67744			−0.328264			−0.164132	+	0.986438i	$0.552482\pi$
$548$	−20.9387	+	20.3251i	−0.894458	+	0.868244i
$549$		−	26.9847i		−	1.15168i
$550$	−12.0334	+	24.7027i	−0.513108	+	1.05333i
$551$	−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	$-0.253460\pi$
$563$	33.1892			1.39876			0.699379	+	0.714751i	$0.253460\pi$
$564$	−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	$-0.588037\pi$
$571$	−13.0501			−0.546130			−0.273065	+	0.961996i	$0.588037\pi$
$572$	−23.0845	−	6.25361i	−0.965210	−	0.261476i
$573$	−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	$-0.356442\pi$
$587$	21.1204			0.871731			0.435865	+	0.900012i	$0.356442\pi$
$588$	−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	$0.441664\pi$
$594$	13.5609	+	6.60592i	0.556409	+	0.271044i
$595$		−	13.1910i		−	0.540780i
$596$	−3.23806	−	3.33582i	−0.132636	−	0.136641i
$597$	2.22176			0.0909308
$598$	−1.54715	+	0.295538i	−0.0632675	+	0.0120855i
$599$		−	29.4065i		−	1.20152i	−0.799430	−	0.600759i	$-0.794865\pi$
$599$		−	29.4065i		−	1.20152i	0.799430	−	0.600759i	$-0.205135\pi$
$600$	−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	$-0.416392\pi$
$607$	12.7943			0.519305			0.259652	+	0.965702i	$0.416392\pi$
$608$	−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
$616$	5.91840	+	18.0265i	0.238459	+	0.726309i
$617$		−	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	$-0.302304\pi$
$619$	28.9557			1.16383			0.581914	+	0.813250i	$0.302304\pi$
$620$	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
$624$	−4.33209	−	6.92299i	−0.173422	−	0.277142i
$625$	−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	$-0.447649\pi$
$631$	8.22541			0.327448			0.163724	+	0.986506i	$0.447649\pi$
$632$	−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
$638$	−20.6057	−	10.0377i	−0.815789	−	0.397396i
$639$	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	$-0.740352\pi$
$643$	−34.7576			−1.37071			−0.685353	+	0.728211i	$0.740352\pi$
$644$	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	$0.0394858\pi$
$647$			6.29445i			0.247461i	−0.992316	+	0.123730i	$0.960514\pi$
$648$	−6.36520	−	16.3918i	−0.250049	−	0.643931i
$649$	1.12424	−	21.1265i	0.0441305	−	0.829286i
$650$	5.60475	+	29.3410i	0.219836	+	1.15085i
$651$	−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	$-0.489092\pi$
$659$	1.75900			0.0685210			0.0342605	+	0.999413i	$0.489092\pi$
$660$	−9.32671	+	8.13674i	−0.363042	+	0.316722i
$661$		−	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
$676$	−24.1694	+	9.58342i	−0.929591	+	0.368593i
$677$			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
$682$	14.7968	−	30.3755i	0.566600	−	1.16314i
$683$	36.1620			1.38370			0.691850	−	0.722041i	$-0.256796\pi$
$683$	36.1620			1.38370			0.691850	+	0.722041i	$0.256796\pi$
$684$	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	$-0.625867\pi$
$691$	−20.2513			−0.770394			−0.385197	+	0.922834i	$0.625867\pi$
$692$	−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	$0.811582\pi$
$702$	16.1071	−	3.07680i	0.607923	−	0.116126i
$703$	18.4314			0.695153
$704$	−16.8405	−	20.5036i	−0.634701	−	0.772758i
$705$	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	$0.197142\pi$
$719$			31.1311i			1.16099i	−0.814262	+	0.580497i	$0.802858\pi$
$720$	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
$726$	−4.27310	+	7.70308i	−0.158590	+	0.285888i
$727$		−	43.4457i		−	1.61131i	−0.592385	−	0.805655i	$-0.701814\pi$
$727$		−	43.4457i		−	1.61131i	0.592385	−	0.805655i	$-0.298186\pi$
$728$	16.8881	+	11.8417i	0.625916	+	0.438883i
$729$	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	$0.0702747\pi$
$739$			11.9060i			0.437971i	−0.975728	+	0.218985i	$0.929725\pi$
$740$	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	$0.0862207\pi$
$743$			14.5869i			0.535140i	−0.963538	+	0.267570i	$0.913779\pi$
$744$	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
$748$	8.63087	+	9.89310i	0.315576	+	0.361728i
$749$		−	3.41779i		−	0.124883i
$750$	2.08594	+	0.882251i	0.0761677	+	0.0322153i
$751$			12.0462i			0.439570i	0.975548	+	0.219785i	$0.0705357\pi$
$751$			12.0462i			0.439570i	−0.975548	+	0.219785i	$0.929464\pi$
$752$	−0.403664	+	13.5687i	−0.0147201	+	0.494798i
$753$	12.4522			0.453782
$754$	−24.4747	+	4.67520i	−0.891317	+	0.170261i
$755$	−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	$0.532013\pi$
$770$	13.6899	−	28.1031i	0.493350	−	1.01277i
$771$		−	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
$780$	−2.82316	+	13.1559i	−0.101085	+	0.471056i
$781$	−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	$-0.814363\pi$
$787$		−	30.8979i		−	1.10139i	0.834706	−	0.550695i	$-0.185637\pi$
$788$	−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
$792$	23.8804	−	7.84033i	0.848554	−	0.278594i
$793$	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
$806$	−6.89185	−	36.0789i	−0.242755	−	1.27083i
$807$			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	$-0.915034\pi$
$811$		−	15.0233i		−	0.527538i	0.964586	−	0.263769i	$-0.0849657\pi$
$812$	13.7681	+	14.1838i	0.483165	+	0.497752i
$813$	−5.82855			−0.204416
$814$	28.8965	+	14.0764i	1.01282	+	0.493376i
$815$			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	$-0.587334\pi$
$823$		−	55.2299i		−	1.92519i	0.270940	−	0.962596i	$-0.412666\pi$
$824$	−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	$-0.873245\pi$
$827$		−	22.3027i		−	0.775542i	0.921756	−	0.387771i	$-0.126755\pi$
$828$	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
$832$	−28.0099	−	6.88798i	−0.971069	−	0.238798i
$833$		−	5.75817i		−	0.199509i
$834$	−2.12866	+	5.03287i	−0.0737094	+	0.174274i
$835$	35.2616			1.22028
$836$	11.7285	+	13.4438i	0.405639	+	0.464963i
$837$			23.1666i			0.800755i
$838$	−5.62379	+	13.2965i	−0.194271	+	0.459321i
$839$	17.6559			0.609548			0.304774	−	0.952425i	$-0.401419\pi$
$839$	17.6559			0.609548			0.304774	+	0.952425i	$0.401419\pi$
$840$	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	$0.939411\pi$
$858$	1.29441	+	9.48841i	0.0441903	+	0.323929i
$859$			47.0064i			1.60384i	0.597433	+	0.801919i	$0.296187\pi$
$859$			47.0064i			1.60384i	−0.597433	+	0.801919i	$0.703813\pi$
$860$	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	$-0.448802\pi$
$863$	9.40938			0.320299			0.160149	+	0.987093i	$0.448802\pi$
$864$	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
$880$	−3.62013	+	43.5655i	−0.122035	+	1.46859i
$881$	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	$0.0770418\pi$
$883$			14.2442i			0.479356i	−0.970852	+	0.239678i	$0.922958\pi$
$884$	13.9548	+	2.99460i	0.469351	+	0.100719i
$885$	−11.9025			−0.400099
$886$	−17.4367	+	41.2262i	−0.585798	+	1.38502i
$887$	−46.1304			−1.54891			−0.774453	−	0.632632i	$-0.781975\pi$
$887$	−46.1304			−1.54891			−0.774453	+	0.632632i	$0.781975\pi$
$888$	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
$902$	7.21127	−	14.8036i	0.240109	−	0.492905i
$903$	−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	$0.266907\pi$
$907$			44.7921i			1.48730i	−0.668570	+	0.743649i	$0.733093\pi$
$908$	36.9021	−	35.8206i	1.22464	−	1.18875i
$909$			32.4640i			1.07676i
$910$	−6.37627	−	33.3799i	−0.211371	−	1.10653i
$911$		−	2.41882i		−	0.0801390i	−0.999197	−	0.0400695i	$-0.987242\pi$
$911$		−	2.41882i		−	0.0801390i	0.999197	−	0.0400695i	$-0.0127579\pi$
$912$	−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	$-0.261894\pi$
$919$	41.2404			1.36039			0.680197	+	0.733029i	$0.261894\pi$
$920$	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
$924$	5.72464	−	4.99425i	0.188327	−	0.164299i
$925$		−	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
$936$	15.6872	−	22.3723i	0.512751	−	0.731263i
$937$		−	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
$946$	17.4877	−	35.8993i	0.568573	−	1.16719i
$947$	−39.8617			−1.29533			−0.647666	−	0.761924i	$-0.724255\pi$
$947$	−39.8617			−1.29533			−0.647666	+	0.761924i	$0.724255\pi$
$948$	−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
$962$	34.3222	−	6.55627i	1.10659	−	0.211383i
$963$	−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	$-0.966634\pi$
$967$		−	6.50738i		−	0.209263i	0.994511	−	0.104632i	$-0.0333664\pi$
$968$	8.12058	+	30.0342i	0.261005	+	0.965337i
$969$		−	3.01440i		−	0.0968364i
$970$	−42.0025	−	17.7650i	−1.34862	−	0.570400i
$971$			32.9668i			1.05795i	0.848636	+	0.528977i	$0.177424\pi$
$971$			32.9668i			1.05795i	−0.848636	+	0.528977i	$0.822576\pi$
$972$	−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	$-0.585948\pi$
$983$	−16.7264			−0.533490			−0.266745	+	0.963767i	$0.585948\pi$
$984$	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
$988$	18.9633	+	4.06937i	0.603301	+	0.129464i
$989$		−	2.62990i		−	0.0836260i
$990$	−37.2293	−	18.1355i	−1.18322	−	0.576385i
$991$		−	49.2134i		−	1.56332i	−0.623707	−	0.781658i	$-0.714374\pi$
$991$		−	49.2134i		−	1.56332i	0.623707	−	0.781658i	$-0.285626\pi$
$992$	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.571.5	✓	56
4.3	odd	2	inner	572.2.b.c.571.7	yes	56
11.10	odd	2	inner	572.2.b.c.571.51	yes	56
13.12	even	2	inner	572.2.b.c.571.52	yes	56
44.43	even	2	inner	572.2.b.c.571.49	yes	56
52.51	odd	2	inner	572.2.b.c.571.50	yes	56
143.142	odd	2	inner	572.2.b.c.571.6	yes	56
572.571	even	2	inner	572.2.b.c.571.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.5	✓	56	1.1	even	1	trivial
572.2.b.c.571.6	yes	56	143.142	odd	2	inner
572.2.b.c.571.7	yes	56	4.3	odd	2	inner
572.2.b.c.571.8	yes	56	572.571	even	2	inner
572.2.b.c.571.49	yes	56	44.43	even	2	inner
572.2.b.c.571.50	yes	56	52.51	odd	2	inner
572.2.b.c.571.51	yes	56	11.10	odd	2	inner
572.2.b.c.571.52	yes	56	13.12	even	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} +(2.05409 - 4.21672i) q^{22} -0.308907i q^{23} +(1.49301 - 0.579758i) q^{24} -5.85828 q^{25} +(-0.956723 - 5.00846i) 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} +(-4.99843 + 4.36070i) 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} +(-1.51300 + 7.05059i) 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} +(2.38775 + 1.16315i) 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} +(2.83608 - 0.541752i) 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} +(8.91276 - 2.92621i) 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

Modular forms

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Database

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