LMFDB - Embedded newform 1512.2.c.e.757.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 $ x^20 + x^18 + 4x^16 + 8x^12 + 4x^10 + 32x^8 + 256x^4 + 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.12
Root			$0.328272 + 1.37559i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.e.757.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.328272 + 1.37559i) q^{2} +(-1.78447 + 0.903134i) q^{4} +0.512447i q^{5} -1.00000 q^{7} +(-1.82813 - 2.15822i) q^{8} +O(q^{10})$	\(q+(0.328272 + 1.37559i) q^{2} +(-1.78447 + 0.903134i) q^{4} +0.512447i q^{5} -1.00000 q^{7} +(-1.82813 - 2.15822i) q^{8} +(-0.704915 + 0.168222i) q^{10} -1.82890i q^{11} -1.80627i q^{13} +(-0.328272 - 1.37559i) q^{14} +(2.36870 - 3.22324i) q^{16} +8.11456 q^{17} -3.43946i q^{19} +(-0.462808 - 0.914448i) q^{20} +(2.51580 - 0.600376i) q^{22} -3.65626 q^{23} +4.73740 q^{25} +(2.48468 - 0.592948i) q^{26} +(1.78447 - 0.903134i) q^{28} -7.98990i q^{29} -1.56895 q^{31} +(5.21142 + 2.20025i) q^{32} +(2.66378 + 11.1623i) q^{34} -0.512447i q^{35} +8.44370i q^{37} +(4.73127 - 1.12908i) q^{38} +(1.10598 - 0.936820i) q^{40} -2.30828 q^{41} +10.7778i q^{43} +(1.65174 + 3.26362i) q^{44} +(-1.20025 - 5.02951i) q^{46} +11.3833 q^{47} +1.00000 q^{49} +(1.55516 + 6.51670i) q^{50} +(1.63130 + 3.22324i) q^{52} -8.87795i q^{53} +0.937212 q^{55} +(1.82813 + 2.15822i) q^{56} +(10.9908 - 2.62286i) q^{58} -2.50234i q^{59} +5.31310i q^{61} +(-0.515043 - 2.15822i) q^{62} +(-1.31587 + 7.89104i) q^{64} +0.925616 q^{65} -6.44648i q^{67} +(-14.4802 + 7.32853i) q^{68} +(0.704915 - 0.168222i) q^{70} +9.10975 q^{71} +9.24419 q^{73} +(-11.6150 + 2.77183i) q^{74} +(3.10629 + 6.13762i) q^{76} +1.82890i q^{77} +3.64300 q^{79} +(1.65174 + 1.21383i) q^{80} +(-0.757745 - 3.17524i) q^{82} -4.53105i q^{83} +4.15828i q^{85} +(-14.8258 + 3.53806i) q^{86} +(-3.94717 + 3.34346i) q^{88} -11.7359 q^{89} +1.80627i q^{91} +(6.52451 - 3.30209i) q^{92} +(3.73684 + 15.6588i) q^{94} +1.76254 q^{95} +15.2323 q^{97} +(0.328272 + 1.37559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} - 20 q^{7}+O(q^{10}) $ 20 * q - 2 * q^4 - 20 * q^7	$ 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70} + 12 q^{76} + 64 q^{79} - 92 q^{88} - 24 q^{94} + 56 q^{97}+O(q^{100}) $ 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	0.328272	+	1.37559i	0.232124	+	0.972686i
$2$	0.328272	+	1.37559i	0.232124	+	0.972686i
$3$		0			0
$3$		0			0
$4$	−1.78447	+	0.903134i	−0.892237	+	0.451567i
$5$			0.512447i			0.229173i	0.993413	+	0.114587i	$0.0365543\pi$
$5$			0.512447i			0.229173i	−0.993413	+	0.114587i	$0.963446\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.82813	−	2.15822i	−0.646342	−	0.763048i
$9$		0			0
$10$	−0.704915	+	0.168222i	−0.222914	+	0.0531965i
$11$		−	1.82890i		−	0.551433i	−0.961239	−	0.275716i	$-0.911085\pi$
$11$		−	1.82890i		−	0.551433i	0.961239	−	0.275716i	$-0.0889151\pi$
$12$		0			0
$13$		−	1.80627i		−	0.500968i	−0.968121	−	0.250484i	$-0.919410\pi$
$13$		−	1.80627i		−	0.500968i	0.968121	−	0.250484i	$-0.0805898\pi$
$14$	−0.328272	−	1.37559i	−0.0877345	−	0.367641i
$15$		0			0
$16$	2.36870	−	3.22324i	0.592175	−	0.805810i
$17$	8.11456			1.96807			0.984035	−	0.177977i	$-0.0569552\pi$
$17$	8.11456			1.96807			0.984035	+	0.177977i	$0.0569552\pi$
$18$		0			0
$19$		−	3.43946i		−	0.789066i	−0.918882	−	0.394533i	$-0.870906\pi$
$19$		−	3.43946i		−	0.789066i	0.918882	−	0.394533i	$-0.129094\pi$
$20$	−0.462808	−	0.914448i	−0.103487	−	0.204477i
$21$		0			0
$22$	2.51580	−	0.600376i	0.536371	−	0.128001i
$23$	−3.65626			−0.762384			−0.381192	−	0.924496i	$-0.624486\pi$
$23$	−3.65626			−0.762384			−0.381192	+	0.924496i	$0.624486\pi$
$24$		0			0
$25$	4.73740			0.947480
$26$	2.48468	−	0.592948i	0.487285	−	0.116287i
$27$		0			0
$28$	1.78447	−	0.903134i	0.337234	−	0.170676i
$29$		−	7.98990i		−	1.48369i	−0.670573	−	0.741843i	$-0.733952\pi$
$29$		−	7.98990i		−	1.48369i	0.670573	−	0.741843i	$-0.266048\pi$
$30$		0			0
$31$	−1.56895			−0.281792			−0.140896	−	0.990024i	$-0.544998\pi$
$31$	−1.56895			−0.281792			−0.140896	+	0.990024i	$0.544998\pi$
$32$	5.21142	+	2.20025i	0.921258	+	0.388953i
$33$		0			0
$34$	2.66378	+	11.1623i	0.456835	+	1.91431i
$35$		−	0.512447i		−	0.0866193i
$36$		0			0
$37$			8.44370i			1.38814i	0.719909	+	0.694068i	$0.244183\pi$
$37$			8.44370i			1.38814i	−0.719909	+	0.694068i	$0.755817\pi$
$38$	4.73127	−	1.12908i	0.767513	−	0.183161i
$39$		0			0
$40$	1.10598	−	0.936820i	0.174870	−	0.148124i
$41$	−2.30828			−0.360493			−0.180247	−	0.983621i	$-0.557690\pi$
$41$	−2.30828			−0.360493			−0.180247	+	0.983621i	$0.557690\pi$
$42$		0			0
$43$			10.7778i			1.64360i	0.569773	+	0.821802i	$0.307031\pi$
$43$			10.7778i			1.64360i	−0.569773	+	0.821802i	$0.692969\pi$
$44$	1.65174	+	3.26362i	0.249009	+	0.492009i
$45$		0			0
$46$	−1.20025	−	5.02951i	−0.176967	−	0.741560i
$47$	11.3833			1.66043			0.830216	−	0.557442i	$-0.188217\pi$
$47$	11.3833			1.66043			0.830216	+	0.557442i	$0.188217\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.55516	+	6.51670i	0.219932	+	0.921600i
$51$		0			0
$52$	1.63130	+	3.22324i	0.226221	+	0.446983i
$53$		−	8.87795i		−	1.21948i	−0.792601	−	0.609740i	$-0.791274\pi$
$53$		−	8.87795i		−	1.21948i	0.792601	−	0.609740i	$-0.208726\pi$
$54$		0			0
$55$	0.937212			0.126374
$56$	1.82813	+	2.15822i	0.244294	+	0.288405i
$57$		0			0
$58$	10.9908	−	2.62286i	1.44316	−	0.344399i
$59$		−	2.50234i		−	0.325778i	−0.986644	−	0.162889i	$-0.947919\pi$
$59$		−	2.50234i		−	0.325778i	0.986644	−	0.162889i	$-0.0520812\pi$
$60$		0			0
$61$			5.31310i			0.680272i	0.940376	+	0.340136i	$0.110473\pi$
$61$			5.31310i			0.680272i	−0.940376	+	0.340136i	$0.889527\pi$
$62$	−0.515043	−	2.15822i	−0.0654105	−	0.274095i
$63$		0			0
$64$	−1.31587	+	7.89104i	−0.164484	+	0.986380i
$65$	0.925616			0.114809
$66$		0			0
$67$		−	6.44648i		−	0.787562i	−0.919204	−	0.393781i	$-0.871167\pi$
$67$		−	6.44648i		−	0.787562i	0.919204	−	0.393781i	$-0.128833\pi$
$68$	−14.4802	+	7.32853i	−1.75598	+	0.888715i
$69$		0			0
$70$	0.704915	−	0.168222i	0.0842534	−	0.0201064i
$71$	9.10975			1.08113			0.540564	−	0.841303i	$-0.318211\pi$
$71$	9.10975			1.08113			0.540564	+	0.841303i	$0.318211\pi$
$72$		0			0
$73$	9.24419			1.08195			0.540975	−	0.841039i	$-0.318055\pi$
$73$	9.24419			1.08195			0.540975	+	0.841039i	$0.318055\pi$
$74$	−11.6150	+	2.77183i	−1.35022	+	0.322219i
$75$		0			0
$76$	3.10629	+	6.13762i	0.356316	+	0.704034i
$77$			1.82890i			0.208422i
$78$		0			0
$79$	3.64300			0.409870			0.204935	−	0.978776i	$-0.434302\pi$
$79$	3.64300			0.409870			0.204935	+	0.978776i	$0.434302\pi$
$80$	1.65174	+	1.21383i	0.184670	+	0.135711i
$81$		0			0
$82$	−0.757745	−	3.17524i	−0.0836790	−	0.350647i
$83$		−	4.53105i		−	0.497348i	−0.968587	−	0.248674i	$-0.920005\pi$
$83$		−	4.53105i		−	0.497348i	0.968587	−	0.248674i	$-0.0799948\pi$
$84$		0			0
$85$			4.15828i			0.451029i
$86$	−14.8258	+	3.53806i	−1.59871	+	0.381519i
$87$		0			0
$88$	−3.94717	+	3.34346i	−0.420770	+	0.356414i
$89$	−11.7359			−1.24401			−0.622003	−	0.783015i	$-0.713681\pi$
$89$	−11.7359			−1.24401			−0.622003	+	0.783015i	$0.713681\pi$
$90$		0			0
$91$			1.80627i			0.189348i
$92$	6.52451	−	3.30209i	0.680227	−	0.344267i
$93$		0			0
$94$	3.73684	+	15.6588i	0.385425	+	1.61508i
$95$	1.76254			0.180833
$96$		0			0
$97$	15.2323			1.54661			0.773303	−	0.634037i	$-0.218603\pi$
$97$	15.2323			1.54661			0.773303	+	0.634037i	$0.218603\pi$
$98$	0.328272	+	1.37559i	0.0331605	+	0.138955i
$99$		0			0
$100$	−8.45377	+	4.27850i	−0.845377	+	0.427850i
$101$		−	8.13524i		−	0.809487i	−0.914430	−	0.404744i	$-0.867361\pi$
$101$		−	8.13524i		−	0.809487i	0.914430	−	0.404744i	$-0.132639\pi$
$102$		0			0
$103$	−15.9816			−1.57471			−0.787356	−	0.616498i	$-0.788551\pi$
$103$	−15.9816			−1.57471			−0.787356	+	0.616498i	$0.788551\pi$
$104$	−3.89833	+	3.30209i	−0.382263	+	0.323797i
$105$		0			0
$106$	12.2124	−	2.91439i	1.18617	−	0.283070i
$107$		−	12.1695i		−	1.17647i	−0.808690	−	0.588235i	$-0.799823\pi$
$107$		−	12.1695i		−	1.17647i	0.808690	−	0.588235i	$-0.200177\pi$
$108$		0			0
$109$		−	10.8452i		−	1.03878i	−0.854537	−	0.519391i	$-0.826159\pi$
$109$		−	10.8452i		−	1.03878i	0.854537	−	0.519391i	$-0.173841\pi$
$110$	0.307661	+	1.28922i	0.0293343	+	0.122922i
$111$		0			0
$112$	−2.36870	+	3.22324i	−0.223821	+	0.304567i
$113$	3.07563			0.289331			0.144665	−	0.989481i	$-0.453789\pi$
$113$	3.07563			0.289331			0.144665	+	0.989481i	$0.453789\pi$
$114$		0			0
$115$		−	1.87364i		−	0.174718i
$116$	7.21595	+	14.2578i	0.669984	+	1.32380i
$117$		0			0
$118$	3.44219	−	0.821450i	0.316879	−	0.0756206i
$119$	−8.11456			−0.743860
$120$		0			0
$121$	7.65514			0.695922
$122$	−7.30862	+	1.74414i	−0.661692	+	0.157907i
$123$		0			0
$124$	2.79975	−	1.41697i	0.251425	−	0.127248i
$125$			4.98990i			0.446310i
$126$		0			0
$127$	6.67524			0.592332			0.296166	−	0.955137i	$-0.404292\pi$
$127$	6.67524			0.592332			0.296166	+	0.955137i	$0.404292\pi$
$128$	−11.2868	+	0.780319i	−0.997619	+	0.0689711i
$129$		0			0
$130$	0.303854	+	1.27326i	0.0266498	+	0.111673i
$131$		−	1.26995i		−	0.110956i	−0.998460	−	0.0554778i	$-0.982332\pi$
$131$		−	1.26995i		−	0.110956i	0.998460	−	0.0554778i	$-0.0176682\pi$
$132$		0			0
$133$			3.43946i			0.298239i
$134$	8.86768	−	2.11620i	0.766051	−	0.182812i
$135$		0			0
$136$	−14.8345	−	17.5130i	−1.27205	−	1.50173i
$137$	19.8507			1.69596			0.847980	−	0.530029i	$-0.177819\pi$
$137$	19.8507			1.69596			0.847980	+	0.530029i	$0.177819\pi$
$138$		0			0
$139$			13.9758i			1.18541i	0.805419	+	0.592706i	$0.201941\pi$
$139$			13.9758i			1.18541i	−0.805419	+	0.592706i	$0.798059\pi$
$140$	0.462808	+	0.914448i	0.0391144	+	0.0772850i
$141$		0			0
$142$	2.99048	+	12.5312i	0.250955	+	1.05160i
$143$	−3.30348			−0.276251
$144$		0			0
$145$	4.09440			0.340021
$146$	3.03461	+	12.7162i	0.251146	+	1.05240i
$147$		0			0
$148$	−7.62579	−	15.0676i	−0.626836	−	1.23855i
$149$			11.8561i			0.971286i	0.874157	+	0.485643i	$0.161415\pi$
$149$			11.8561i			0.971286i	−0.874157	+	0.485643i	$0.838585\pi$
$150$		0			0
$151$	−13.4949			−1.09820			−0.549100	−	0.835757i	$-0.685029\pi$
$151$	−13.4949			−1.09820			−0.549100	+	0.835757i	$0.685029\pi$
$152$	−7.42312	+	6.28778i	−0.602095	+	0.510006i
$153$		0			0
$154$	−2.51580	+	0.600376i	−0.202729	+	0.0483797i
$155$		−	0.804003i		−	0.0645791i
$156$		0			0
$157$			9.88593i			0.788983i	0.918900	+	0.394492i	$0.129079\pi$
$157$			9.88593i			0.788983i	−0.918900	+	0.394492i	$0.870921\pi$
$158$	1.19590	+	5.01126i	0.0951404	+	0.398675i
$159$		0			0
$160$	−1.12751	+	2.67058i	−0.0891376	+	0.211128i
$161$	3.65626			0.288154
$162$		0			0
$163$			4.43706i			0.347537i	0.984786	+	0.173769i	$0.0555945\pi$
$163$			4.43706i			0.347537i	−0.984786	+	0.173769i	$0.944405\pi$
$164$	4.11907	−	2.08469i	0.321645	−	0.162787i
$165$		0			0
$166$	6.23286	−	1.48742i	0.483763	−	0.115446i
$167$	−5.38391			−0.416619			−0.208310	−	0.978063i	$-0.566796\pi$
$167$	−5.38391			−0.416619			−0.208310	+	0.978063i	$0.566796\pi$
$168$		0			0
$169$	9.73740			0.749031
$170$	−5.72007	+	1.36505i	−0.438709	+	0.104694i
$171$		0			0
$172$	−9.73382	−	19.2328i	−0.742197	−	1.46648i
$173$		−	17.9611i		−	1.36556i	−0.730624	−	0.682780i	$-0.760771\pi$
$173$		−	17.9611i		−	1.36556i	0.730624	−	0.682780i	$-0.239229\pi$
$174$		0			0
$175$	−4.73740			−0.358114
$176$	−5.89497	−	4.33211i	−0.444350	−	0.326545i
$177$		0			0
$178$	−3.85258	−	16.1438i	−0.288763	−	1.21003i
$179$		−	16.0482i		−	1.19950i	−0.800188	−	0.599749i	$-0.795267\pi$
$179$		−	16.0482i		−	1.19950i	0.800188	−	0.599749i	$-0.204733\pi$
$180$		0			0
$181$			5.91861i			0.439927i	0.975508	+	0.219964i	$0.0705938\pi$
$181$			5.91861i			0.439927i	−0.975508	+	0.219964i	$0.929406\pi$
$182$	−2.48468	+	0.592948i	−0.184176	+	0.0439522i
$183$		0			0
$184$	6.68413	+	7.89104i	0.492761	+	0.581735i
$185$	−4.32695			−0.318123
$186$		0			0
$187$		−	14.8407i		−	1.08526i
$188$	−20.3133	+	10.2807i	−1.48150	+	0.749796i
$189$		0			0
$190$	0.578593	+	2.42452i	0.0419755	+	0.175893i
$191$	0.0697837			0.00504937			0.00252469	−	0.999997i	$-0.499196\pi$
$191$	0.0697837			0.00504937			0.00252469	+	0.999997i	$0.499196\pi$
$192$		0			0
$193$	−8.24356			−0.593384			−0.296692	−	0.954973i	$-0.595884\pi$
$193$	−8.24356			−0.593384			−0.296692	+	0.954973i	$0.595884\pi$
$194$	5.00034	+	20.9533i	0.359004	+	1.50436i
$195$		0			0
$196$	−1.78447	+	0.903134i	−0.127462	+	0.0645095i
$197$			1.91295i			0.136292i	0.997675	+	0.0681459i	$0.0217083\pi$
$197$			1.91295i			0.136292i	−0.997675	+	0.0681459i	$0.978292\pi$
$198$		0			0
$199$	−3.70579			−0.262696			−0.131348	−	0.991336i	$-0.541931\pi$
$199$	−3.70579			−0.262696			−0.131348	+	0.991336i	$0.541931\pi$
$200$	−8.66059	−	10.2244i	−0.612396	−	0.722972i
$201$		0			0
$202$	11.1907	−	2.67058i	0.787377	−	0.187901i
$203$			7.98990i			0.560781i
$204$		0			0
$205$		−	1.18287i		−	0.0826153i
$206$	−5.24631	−	21.9840i	−0.365528	−	1.53170i
$207$		0			0
$208$	−5.82203	−	4.27850i	−0.403685	−	0.296661i
$209$	−6.29041			−0.435117
$210$		0			0
$211$		−	25.6006i		−	1.76242i	−0.472724	−	0.881210i	$-0.656729\pi$
$211$		−	25.6006i		−	1.76242i	0.472724	−	0.881210i	$-0.343271\pi$
$212$	8.01798	+	15.8425i	0.550677	+	1.08807i
$213$		0			0
$214$	16.7402	−	3.99491i	1.14434	−	0.273087i
$215$	−5.52307			−0.376670
$216$		0			0
$217$	1.56895			0.106507
$218$	14.9185	−	3.56018i	1.01041	−	0.241126i
$219$		0			0
$220$	−1.67243	+	0.846428i	−0.112755	+	0.0570661i
$221$		−	14.6571i		−	0.985941i
$222$		0			0
$223$	−14.2639			−0.955182			−0.477591	−	0.878582i	$-0.658490\pi$
$223$	−14.2639			−0.955182			−0.477591	+	0.878582i	$0.658490\pi$
$224$	−5.21142	−	2.20025i	−0.348203	−	0.147010i
$225$		0			0
$226$	1.00964	+	4.23079i	0.0671605	+	0.281428i
$227$			2.58553i			0.171608i	0.996312	+	0.0858039i	$0.0273458\pi$
$227$			2.58553i			0.171608i	−0.996312	+	0.0858039i	$0.972654\pi$
$228$		0			0
$229$		−	27.5800i		−	1.82254i	−0.411813	−	0.911268i	$-0.635104\pi$
$229$		−	27.5800i		−	1.82254i	0.411813	−	0.911268i	$-0.364896\pi$
$230$	2.57735	−	0.615064i	0.169946	−	0.0405561i
$231$		0			0
$232$	−17.2440	+	14.6066i	−1.13212	+	0.958969i
$233$	5.61196			0.367652			0.183826	−	0.982959i	$-0.441152\pi$
$233$	5.61196			0.367652			0.183826	+	0.982959i	$0.441152\pi$
$234$		0			0
$235$			5.83336i			0.380526i
$236$	2.25995	+	4.46537i	0.147110	+	0.290671i
$237$		0			0
$238$	−2.66378	−	11.1623i	−0.172668	−	0.723543i
$239$	1.69275			0.109495			0.0547476	−	0.998500i	$-0.482565\pi$
$239$	1.69275			0.109495			0.0547476	+	0.998500i	$0.482565\pi$
$240$		0			0
$241$	−22.6246			−1.45738			−0.728689	−	0.684845i	$-0.759870\pi$
$241$	−22.6246			−1.45738			−0.728689	+	0.684845i	$0.759870\pi$
$242$	2.51297	+	10.5303i	0.161540	+	0.676913i
$243$		0			0
$244$	−4.79844	−	9.48109i	−0.307188	−	0.606964i
$245$			0.512447i			0.0327390i
$246$		0			0
$247$	−6.21258			−0.395297
$248$	2.86825	+	3.38615i	0.182134	+	0.215020i
$249$		0			0
$250$	−6.86403	+	1.63805i	−0.434120	+	0.103599i
$251$			18.1391i			1.14493i	0.819930	+	0.572464i	$0.194012\pi$
$251$			18.1391i			1.14493i	−0.819930	+	0.572464i	$0.805988\pi$
$252$		0			0
$253$			6.68693i			0.420403i
$254$	2.19130	+	9.18237i	0.137494	+	0.576153i
$255$		0			0
$256$	−4.77853	−	15.2698i	−0.298658	−	0.954360i
$257$	−8.62562			−0.538051			−0.269026	−	0.963133i	$-0.586702\pi$
$257$	−8.62562			−0.538051			−0.269026	+	0.963133i	$0.586702\pi$
$258$		0			0
$259$		−	8.44370i		−	0.524666i
$260$	−1.65174	+	0.835955i	−0.102436	+	0.0518437i
$261$		0			0
$262$	1.74692	−	0.416888i	0.107925	−	0.0257554i
$263$	2.79262			0.172201			0.0861003	−	0.996286i	$-0.472559\pi$
$263$	2.79262			0.172201			0.0861003	+	0.996286i	$0.472559\pi$
$264$		0			0
$265$	4.54948			0.279472
$266$	−4.73127	+	1.12908i	−0.290093	+	0.0692282i
$267$		0			0
$268$	5.82203	+	11.5036i	0.355637	+	0.702693i
$269$			17.8391i			1.08767i	0.839192	+	0.543836i	$0.183029\pi$
$269$			17.8391i			1.08767i	−0.839192	+	0.543836i	$0.816971\pi$
$270$		0			0
$271$	−22.5304			−1.36863			−0.684313	−	0.729188i	$-0.739898\pi$
$271$	−22.5304			−1.36863			−0.684313	+	0.729188i	$0.739898\pi$
$272$	19.2209	−	26.1552i	1.16544	−	1.58589i
$273$		0			0
$274$	6.51643	+	27.3063i	0.393672	+	1.64964i
$275$		−	8.66421i		−	0.522472i
$276$		0			0
$277$			2.18249i			0.131133i	0.997848	+	0.0655666i	$0.0208855\pi$
$277$			2.18249i			0.131133i	−0.997848	+	0.0655666i	$0.979115\pi$
$278$	−19.2249	+	4.58787i	−1.15303	+	0.275162i
$279$		0			0
$280$	−1.10598	+	0.936820i	−0.0660947	+	0.0559857i
$281$	7.54152			0.449890			0.224945	−	0.974372i	$-0.427780\pi$
$281$	7.54152			0.449890			0.224945	+	0.974372i	$0.427780\pi$
$282$		0			0
$283$		−	11.5743i		−	0.688021i	−0.938966	−	0.344011i	$-0.888214\pi$
$283$		−	11.5743i		−	0.688021i	0.938966	−	0.344011i	$-0.111786\pi$
$284$	−16.2561	+	8.22732i	−0.964623	+	0.488202i
$285$		0			0
$286$	−1.08444	−	4.54422i	−0.0641243	−	0.268705i
$287$	2.30828			0.136254
$288$		0			0
$289$	48.8460			2.87330
$290$	1.34408	+	5.63220i	0.0789269	+	0.330734i
$291$		0			0
$292$	−16.4960	+	8.34874i	−0.965356	+	0.488573i
$293$			8.12045i			0.474402i	0.971461	+	0.237201i	$0.0762300\pi$
$293$			8.12045i			0.474402i	−0.971461	+	0.237201i	$0.923770\pi$
$294$		0			0
$295$	1.28232			0.0746595
$296$	18.2234	−	15.4362i	1.05921	−	0.897211i
$297$		0			0
$298$	−16.3090	+	3.89202i	−0.944757	+	0.225458i
$299$			6.60419i			0.381930i
$300$		0			0
$301$		−	10.7778i		−	0.621224i
$302$	−4.43000	−	18.5634i	−0.254918	−	1.06820i
$303$		0			0
$304$	−11.0862	−	8.14704i	−0.635837	−	0.467265i
$305$	−2.72268			−0.155900
$306$		0			0
$307$		−	2.73852i		−	0.156295i	−0.996942	−	0.0781477i	$-0.975099\pi$
$307$		−	2.73852i		−	0.156295i	0.996942	−	0.0781477i	$-0.0249006\pi$
$308$	−1.65174	−	3.26362i	−0.0941165	−	0.185962i
$309$		0			0
$310$	1.10598	−	0.263932i	0.0628152	−	0.0149903i
$311$	17.9488			1.01778			0.508891	−	0.860831i	$-0.330055\pi$
$311$	17.9488			1.01778			0.508891	+	0.860831i	$0.330055\pi$
$312$		0			0
$313$	5.95819			0.336777			0.168388	−	0.985721i	$-0.446144\pi$
$313$	5.95819			0.336777			0.168388	+	0.985721i	$0.446144\pi$
$314$	−13.5990	+	3.24528i	−0.767433	+	0.183142i
$315$		0			0
$316$	−6.50084	+	3.29012i	−0.365701	+	0.185084i
$317$		−	21.6033i		−	1.21336i	−0.794945	−	0.606682i	$-0.792500\pi$
$317$		−	21.6033i		−	1.21336i	0.794945	−	0.606682i	$-0.207500\pi$
$318$		0			0
$319$	−14.6127			−0.818154
$320$	−4.04374	−	0.674313i	−0.226052	−	0.0376952i
$321$		0			0
$322$	1.20025	+	5.02951i	0.0668873	+	0.280283i
$323$		−	27.9097i		−	1.55294i
$324$		0			0
$325$		−	8.55701i		−	0.474657i
$326$	−6.10356	+	1.45656i	−0.338045	+	0.0806716i
$327$		0			0
$328$	4.21984	+	4.98179i	0.233002	+	0.275073i
$329$	−11.3833			−0.627584
$330$		0			0
$331$		−	12.6066i		−	0.692920i	−0.938065	−	0.346460i	$-0.887384\pi$
$331$		−	12.6066i		−	0.692920i	0.938065	−	0.346460i	$-0.112616\pi$
$332$	4.09215	+	8.08555i	0.224586	+	0.443752i
$333$		0			0
$334$	−1.76739	−	7.40603i	−0.0967072	−	0.405240i
$335$	3.30348			0.180488
$336$		0			0
$337$	−28.9818			−1.57874			−0.789370	−	0.613917i	$-0.789593\pi$
$337$	−28.9818			−1.57874			−0.789370	+	0.613917i	$0.789593\pi$
$338$	3.19652	+	13.3946i	0.173868	+	0.728572i
$339$		0			0
$340$	−3.75548	−	7.42034i	−0.203670	−	0.402425i
$341$			2.86945i			0.155389i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	23.2610	−	19.7033i	1.25415	−	1.06233i
$345$		0			0
$346$	24.7071	−	5.89614i	1.32826	−	0.316979i
$347$		−	12.2675i		−	0.658553i	−0.944234	−	0.329277i	$-0.893195\pi$
$347$		−	12.2675i		−	0.658553i	0.944234	−	0.329277i	$-0.106805\pi$
$348$		0			0
$349$			28.3289i			1.51641i	0.652016	+	0.758205i	$0.273923\pi$
$349$			28.3289i			1.51641i	−0.652016	+	0.758205i	$0.726077\pi$
$350$	−1.55516	−	6.51670i	−0.0831266	−	0.348332i
$351$		0			0
$352$	4.02403	−	9.53115i	0.214481	−	0.508012i
$353$	−1.40996			−0.0750444			−0.0375222	−	0.999296i	$-0.511946\pi$
$353$	−1.40996			−0.0750444			−0.0375222	+	0.999296i	$0.511946\pi$
$354$		0			0
$355$			4.66826i			0.247766i
$356$	20.9425	−	10.5991i	1.10995	−	0.561752i
$357$		0			0
$358$	22.0757	−	5.26818i	1.16674	−	0.278432i
$359$	17.0581			0.900290			0.450145	−	0.892955i	$-0.351372\pi$
$359$	17.0581			0.900290			0.450145	+	0.892955i	$0.351372\pi$
$360$		0			0
$361$	7.17014			0.377376
$362$	−8.14156	+	1.94292i	−0.427911	+	0.102117i
$363$		0			0
$364$	−1.63130	−	3.22324i	−0.0855034	−	0.168944i
$365$			4.73715i			0.247954i
$366$		0			0
$367$	−25.4558			−1.32878			−0.664390	−	0.747386i	$-0.731308\pi$
$367$	−25.4558			−1.32878			−0.664390	+	0.747386i	$0.731308\pi$
$368$	−8.66059	+	11.7850i	−0.451464	+	0.614336i
$369$		0			0
$370$	−1.42042	−	5.95209i	−0.0738440	−	0.309434i
$371$			8.87795i			0.460920i
$372$		0			0
$373$			20.3176i			1.05201i	0.850483	+	0.526003i	$0.176310\pi$
$373$			20.3176i			1.05201i	−0.850483	+	0.526003i	$0.823690\pi$
$374$	20.4146	−	4.87179i	1.05562	−	0.251914i
$375$		0			0
$376$	−20.8103	−	24.5678i	−1.07321	−	1.26699i
$377$	−14.4319			−0.743280
$378$		0			0
$379$			11.8832i			0.610397i	0.952289	+	0.305198i	$0.0987228\pi$
$379$			11.8832i			0.610397i	−0.952289	+	0.305198i	$0.901277\pi$
$380$	−3.14521	+	1.59181i	−0.161346	+	0.0816580i
$381$		0			0
$382$	0.0229081	+	0.0959935i	0.00117208	+	0.00491146i
$383$	−18.6261			−0.951749			−0.475874	−	0.879513i	$-0.657868\pi$
$383$	−18.6261			−0.951749			−0.475874	+	0.879513i	$0.657868\pi$
$384$		0			0
$385$	−0.937212			−0.0477647
$386$	−2.70613	−	11.3397i	−0.137739	−	0.577177i
$387$		0			0
$388$	−27.1816	+	13.7568i	−1.37994	+	0.698396i
$389$		−	20.7636i		−	1.05276i	−0.850251	−	0.526378i	$-0.823550\pi$
$389$		−	20.7636i		−	1.05276i	0.850251	−	0.526378i	$-0.176450\pi$
$390$		0			0
$391$	−29.6690			−1.50042
$392$	−1.82813	−	2.15822i	−0.0923346	−	0.109007i
$393$		0			0
$394$	−2.63142	+	0.627967i	−0.132569	+	0.0316365i
$395$			1.86684i			0.0939311i
$396$		0			0
$397$			20.9726i			1.05259i	0.850303	+	0.526293i	$0.176418\pi$
$397$			20.9726i			1.05259i	−0.850303	+	0.526293i	$0.823582\pi$
$398$	−1.21651	−	5.09763i	−0.0609780	−	0.255521i
$399$		0			0
$400$	11.2215	−	15.2698i	0.561074	−	0.763488i
$401$	−0.476166			−0.0237786			−0.0118893	−	0.999929i	$-0.503785\pi$
$401$	−0.476166			−0.0237786			−0.0118893	+	0.999929i	$0.503785\pi$
$402$		0			0
$403$			2.83394i			0.141169i
$404$	7.34721	+	14.5171i	0.365537	+	0.722255i
$405$		0			0
$406$	−10.9908	+	2.62286i	−0.545464	+	0.130170i
$407$	15.4427			0.765464
$408$		0			0
$409$	−2.08700			−0.103196			−0.0515978	−	0.998668i	$-0.516431\pi$
$409$	−2.08700			−0.103196			−0.0515978	+	0.998668i	$0.516431\pi$
$410$	1.62714	−	0.388304i	0.0803588	−	0.0191770i
$411$		0			0
$412$	28.5187	−	14.4335i	1.40502	−	0.711088i
$413$			2.50234i			0.123132i
$414$		0			0
$415$	2.32192			0.113979
$416$	3.97424	−	9.41322i	0.194853	−	0.461521i
$417$		0			0
$418$	−2.06497	−	8.65300i	−0.101001	−	0.423232i
$419$			15.8104i			0.772388i	0.922418	+	0.386194i	$0.126210\pi$
$419$			15.8104i			0.772388i	−0.922418	+	0.386194i	$0.873790\pi$
$420$		0			0
$421$		−	21.8824i		−	1.06648i	−0.845963	−	0.533241i	$-0.820974\pi$
$421$		−	21.8824i		−	1.06648i	0.845963	−	0.533241i	$-0.179026\pi$
$422$	35.2159	−	8.40398i	1.71428	−	0.409099i
$423$		0			0
$424$	−19.1606	+	16.2301i	−0.930522	+	0.788202i
$425$	38.4419			1.86471
$426$		0			0
$427$		−	5.31310i		−	0.257119i
$428$	10.9907	+	21.7162i	0.531255	+	1.04969i
$429$		0			0
$430$	−1.81307	−	7.59745i	−0.0874340	−	0.366382i
$431$	25.3231			1.21977			0.609885	−	0.792490i	$-0.291216\pi$
$431$	25.3231			1.21977			0.609885	+	0.792490i	$0.291216\pi$
$432$		0			0
$433$	30.9197			1.48590			0.742952	−	0.669344i	$-0.233425\pi$
$433$	30.9197			1.48590			0.742952	+	0.669344i	$0.233425\pi$
$434$	0.515043	+	2.15822i	0.0247228	+	0.103598i
$435$		0			0
$436$	9.79467	+	19.3530i	0.469080	+	0.926840i
$437$			12.5756i			0.601571i
$438$		0			0
$439$	−8.75669			−0.417934			−0.208967	−	0.977923i	$-0.567010\pi$
$439$	−8.75669			−0.417934			−0.208967	+	0.977923i	$0.567010\pi$
$440$	−1.71335	−	2.02271i	−0.0816806	−	0.0964291i
$441$		0			0
$442$	20.1620	−	4.81151i	0.959011	−	0.228860i
$443$			27.6190i			1.31222i	0.754666	+	0.656109i	$0.227799\pi$
$443$			27.6190i			1.31222i	−0.754666	+	0.656109i	$0.772201\pi$
$444$		0			0
$445$		−	6.01404i		−	0.285093i
$446$	−4.68244	−	19.6212i	−0.221720	−	0.929092i
$447$		0			0
$448$	1.31587	−	7.89104i	0.0621689	−	0.372817i
$449$	13.6994			0.646516			0.323258	−	0.946311i	$-0.395222\pi$
$449$	13.6994			0.646516			0.323258	+	0.946311i	$0.395222\pi$
$450$		0			0
$451$			4.22161i			0.198788i
$452$	−5.48838	+	2.77770i	−0.258152	+	0.130652i
$453$		0			0
$454$	−3.55662	+	0.848758i	−0.166920	+	0.0398342i
$455$	−0.925616			−0.0433935
$456$		0			0
$457$	5.85452			0.273863			0.136931	−	0.990581i	$-0.456276\pi$
$457$	5.85452			0.273863			0.136931	+	0.990581i	$0.456276\pi$
$458$	37.9386	−	9.05374i	1.77276	−	0.423054i
$459$		0			0
$460$	1.69215	+	3.34346i	0.0788968	+	0.155890i
$461$		−	2.42544i		−	0.112964i	−0.998404	−	0.0564821i	$-0.982012\pi$
$461$		−	2.42544i		−	0.112964i	0.998404	−	0.0564821i	$-0.0179884\pi$
$462$		0			0
$463$	−1.26366			−0.0587273			−0.0293636	−	0.999569i	$-0.509348\pi$
$463$	−1.26366			−0.0587273			−0.0293636	+	0.999569i	$0.509348\pi$
$464$	−25.7533	−	18.9257i	−1.19557	−	0.878602i
$465$		0			0
$466$	1.84225	+	7.71974i	0.0853407	+	0.357610i
$467$		−	27.2456i		−	1.26078i	−0.776280	−	0.630388i	$-0.782896\pi$
$467$		−	27.2456i		−	1.26078i	0.776280	−	0.630388i	$-0.217104\pi$
$468$		0			0
$469$			6.44648i			0.297671i
$470$	−8.02429	+	1.91493i	−0.370133	+	0.0883291i
$471$		0			0
$472$	−5.40062	+	4.57462i	−0.248584	+	0.210564i
$473$	19.7115			0.906338
$474$		0			0
$475$		−	16.2941i		−	0.747624i
$476$	14.4802	−	7.32853i	0.663700	−	0.335903i
$477$		0			0
$478$	0.555684	+	2.32853i	0.0254164	+	0.106504i
$479$	−27.4035			−1.25210			−0.626050	−	0.779783i	$-0.715329\pi$
$479$	−27.4035			−1.25210			−0.626050	+	0.779783i	$0.715329\pi$
$480$		0			0
$481$	15.2516			0.695412
$482$	−7.42703	−	31.1221i	−0.338292	−	1.41757i
$483$		0			0
$484$	−13.6604	+	6.91361i	−0.620927	+	0.314255i
$485$			7.80574i			0.354440i
$486$		0			0
$487$	27.0530			1.22589			0.612944	−	0.790126i	$-0.289985\pi$
$487$	27.0530			1.22589			0.612944	+	0.790126i	$0.289985\pi$
$488$	11.4669	−	9.71304i	0.519080	−	0.439689i
$489$		0			0
$490$	−0.704915	+	0.168222i	−0.0318448	+	0.00759950i
$491$			29.2739i			1.32111i	0.750776	+	0.660556i	$0.229680\pi$
$491$			29.2739i			1.32111i	−0.750776	+	0.660556i	$0.770320\pi$
$492$		0			0
$493$		−	64.8345i		−	2.92000i
$494$	−2.03942	−	8.54594i	−0.0917577	−	0.384500i
$495$		0			0
$496$	−3.71637	+	5.05710i	−0.166870	+	0.227070i
$497$	−9.10975			−0.408628
$498$		0			0
$499$			39.8348i			1.78325i	0.452775	+	0.891625i	$0.350434\pi$
$499$			39.8348i			1.78325i	−0.452775	+	0.891625i	$0.649566\pi$
$500$	−4.50654	−	8.90435i	−0.201539	−	0.398214i
$501$		0			0
$502$	−24.9518	+	5.95455i	−1.11366	+	0.265765i
$503$	−36.3079			−1.61889			−0.809444	−	0.587197i	$-0.800231\pi$
$503$	−36.3079			−1.61889			−0.809444	+	0.587197i	$0.800231\pi$
$504$		0			0
$505$	4.16888			0.185513
$506$	−9.19844	+	2.19513i	−0.408921	+	0.0975856i
$507$		0			0
$508$	−11.9118	+	6.02863i	−0.528500	+	0.267477i
$509$			22.2853i			0.987778i	0.869525	+	0.493889i	$0.164425\pi$
$509$			22.2853i			0.987778i	−0.869525	+	0.493889i	$0.835575\pi$
$510$		0			0
$511$	−9.24419			−0.408939
$512$	19.4362	−	11.5859i	0.858968	−	0.512030i
$513$		0			0
$514$	−2.83155	−	11.8653i	−0.124894	−	0.523355i
$515$		−	8.18971i		−	0.360882i
$516$		0			0
$517$		−	20.8190i		−	0.915617i
$518$	11.6150	−	2.77183i	0.510336	−	0.121787i
$519$		0			0
$520$	−1.69215	−	1.99769i	−0.0742056	−	0.0876044i
$521$	−28.8909			−1.26573			−0.632866	−	0.774261i	$-0.718122\pi$
$521$	−28.8909			−1.26573			−0.632866	+	0.774261i	$0.718122\pi$
$522$		0			0
$523$		−	22.7284i		−	0.993842i	−0.867796	−	0.496921i	$-0.834464\pi$
$523$		−	22.7284i		−	0.993842i	0.867796	−	0.496921i	$-0.165536\pi$
$524$	1.14693	+	2.26619i	0.0501039	+	0.0989988i
$525$		0			0
$526$	0.916741	+	3.84149i	0.0399718	+	0.167497i
$527$	−12.7313			−0.554585
$528$		0			0
$529$	−9.63174			−0.418771
$530$	1.49347	+	6.25820i	0.0648721	+	0.271839i
$531$		0			0
$532$	−3.10629	−	6.13762i	−0.134675	−	0.266100i
$533$			4.16938i			0.180596i
$534$		0			0
$535$	6.23622			0.269615
$536$	−13.9129	+	11.7850i	−0.600948	+	0.509035i
$537$		0			0
$538$	−24.5393	+	5.85610i	−1.05796	+	0.252474i
$539$		−	1.82890i		−	0.0787761i
$540$		0			0
$541$			12.7291i			0.547268i	0.961834	+	0.273634i	$0.0882257\pi$
$541$			12.7291i			0.547268i	−0.961834	+	0.273634i	$0.911774\pi$
$542$	−7.39612	−	30.9926i	−0.317690	−	1.33124i
$543$		0			0
$544$	42.2884	+	17.8541i	1.81310	+	0.765486i
$545$	5.55759			0.238061
$546$		0			0
$547$			28.7154i			1.22778i	0.789391	+	0.613890i	$0.210396\pi$
$547$			28.7154i			1.22778i	−0.789391	+	0.613890i	$0.789604\pi$
$548$	−35.4231	+	17.9278i	−1.51320	+	0.765839i
$549$		0			0
$550$	11.9184	−	2.84422i	0.508201	−	0.121278i
$551$	−27.4809			−1.17073
$552$		0			0
$553$	−3.64300			−0.154916
$554$	−3.00221	+	0.716452i	−0.127552	+	0.0304391i
$555$		0			0
$556$	−12.6220	−	24.9395i	−0.535293	−	1.05767i
$557$			7.36295i			0.311978i	0.987759	+	0.155989i	$0.0498565\pi$
$557$			7.36295i			0.311978i	−0.987759	+	0.155989i	$0.950143\pi$
$558$		0			0
$559$	19.4676			0.823394
$560$	−1.65174	−	1.21383i	−0.0697987	−	0.0512938i
$561$		0			0
$562$	2.47567	+	10.3740i	0.104430	+	0.437601i
$563$		−	15.9713i		−	0.673110i	−0.941664	−	0.336555i	$-0.890738\pi$
$563$		−	15.9713i		−	0.673110i	0.941664	−	0.336555i	$-0.109262\pi$
$564$		0			0
$565$			1.57610i			0.0663068i
$566$	15.9215	−	3.79952i	0.669229	−	0.159706i
$567$		0			0
$568$	−16.6538	−	19.6609i	−0.698779	−	0.824953i
$569$	−26.9769			−1.13093			−0.565465	−	0.824772i	$-0.691303\pi$
$569$	−26.9769			−1.13093			−0.565465	+	0.824772i	$0.691303\pi$
$570$		0			0
$571$		−	35.5632i		−	1.48827i	−0.668027	−	0.744137i	$-0.732861\pi$
$571$		−	35.5632i		−	1.48827i	0.668027	−	0.744137i	$-0.267139\pi$
$572$	5.89497	−	2.98348i	0.246481	−	0.124746i
$573$		0			0
$574$	0.757745	+	3.17524i	0.0316277	+	0.132532i
$575$	−17.3212			−0.722343
$576$		0			0
$577$	−23.4330			−0.975528			−0.487764	−	0.872976i	$-0.662187\pi$
$577$	−23.4330			−0.975528			−0.487764	+	0.872976i	$0.662187\pi$
$578$	16.0348	+	67.1919i	0.666960	+	2.79482i
$579$		0			0
$580$	−7.30635	+	3.69779i	−0.303380	+	0.153542i
$581$			4.53105i			0.187980i
$582$		0			0
$583$	−16.2369			−0.672462
$584$	−16.8996	−	19.9510i	−0.699310	−	0.825580i
$585$		0			0
$586$	−11.1704	+	2.66572i	−0.461444	+	0.110120i
$587$			37.1113i			1.53175i	0.642991	+	0.765874i	$0.277693\pi$
$587$			37.1113i			1.53175i	−0.642991	+	0.765874i	$0.722307\pi$
$588$		0			0
$589$			5.39633i			0.222352i
$590$	0.420950	+	1.76394i	0.0173302	+	0.0726202i
$591$		0			0
$592$	27.2161	+	20.0006i	1.11857	+	0.822019i
$593$	23.8317			0.978650			0.489325	−	0.872102i	$-0.337243\pi$
$593$	23.8317			0.978650			0.489325	+	0.872102i	$0.337243\pi$
$594$		0			0
$595$		−	4.15828i		−	0.170473i
$596$	−10.7076	−	21.1568i	−0.438601	−	0.866618i
$597$		0			0
$598$	−9.08463	+	2.16797i	−0.371498	+	0.0886550i
$599$	12.0955			0.494210			0.247105	−	0.968989i	$-0.420521\pi$
$599$	12.0955			0.494210			0.247105	+	0.968989i	$0.420521\pi$
$600$		0			0
$601$	20.4752			0.835202			0.417601	−	0.908631i	$-0.362871\pi$
$601$	20.4752			0.835202			0.417601	+	0.908631i	$0.362871\pi$
$602$	14.8258	−	3.53806i	0.604256	−	0.144201i
$603$		0			0
$604$	24.0813	−	12.1877i	0.979854	−	0.495910i
$605$			3.92285i			0.159487i
$606$		0			0
$607$	−24.0329			−0.975466			−0.487733	−	0.872993i	$-0.662176\pi$
$607$	−24.0329			−0.975466			−0.487733	+	0.872993i	$0.662176\pi$
$608$	7.56767	−	17.9245i	0.306909	−	0.726933i
$609$		0			0
$610$	−0.893780	−	3.74528i	−0.0361881	−	0.151642i
$611$		−	20.5614i		−	0.831824i
$612$		0			0
$613$			45.2862i			1.82909i	0.404480	+	0.914547i	$0.367452\pi$
$613$			45.2862i			1.82909i	−0.404480	+	0.914547i	$0.632548\pi$
$614$	3.76706	−	0.898979i	0.152026	−	0.0362798i
$615$		0			0
$616$	3.94717	−	3.34346i	0.159036	−	0.134712i
$617$	−20.4393			−0.822855			−0.411428	−	0.911442i	$-0.634970\pi$
$617$	−20.4393			−0.822855			−0.411428	+	0.911442i	$0.634970\pi$
$618$		0			0
$619$		−	15.3328i		−	0.616277i	−0.951342	−	0.308138i	$-0.900294\pi$
$619$		−	15.3328i		−	0.616277i	0.951342	−	0.308138i	$-0.0997060\pi$
$620$	0.726122	+	1.43472i	0.0291618	+	0.0576199i
$621$		0			0
$622$	5.89209	+	24.6901i	0.236251	+	0.989983i
$623$	11.7359			0.470190
$624$		0			0
$625$	21.1299			0.845197
$626$	1.95591	+	8.19600i	0.0781738	+	0.327578i
$627$		0			0
$628$	−8.92832	−	17.6412i	−0.356279	−	0.703960i
$629$			68.5169i			2.73195i
$630$		0			0
$631$	20.4869			0.815572			0.407786	−	0.913078i	$-0.366301\pi$
$631$	20.4869			0.815572			0.407786	+	0.913078i	$0.366301\pi$
$632$	−6.65989	−	7.86242i	−0.264916	−	0.312750i
$633$		0			0
$634$	29.7172	−	7.09177i	1.18022	−	0.281650i
$635$			3.42070i			0.135747i
$636$		0			0
$637$		−	1.80627i		−	0.0715669i
$638$	−4.79694	−	20.1010i	−0.189913	−	0.795807i
$639$		0			0
$640$	−0.399872	−	5.78387i	−0.0158063	−	0.228627i
$641$	−42.6868			−1.68603			−0.843013	−	0.537893i	$-0.819220\pi$
$641$	−42.6868			−1.68603			−0.843013	+	0.537893i	$0.819220\pi$
$642$		0			0
$643$		−	29.7804i		−	1.17442i	−0.809434	−	0.587211i	$-0.800226\pi$
$643$		−	29.7804i		−	1.17442i	0.809434	−	0.587211i	$-0.199774\pi$
$644$	−6.52451	+	3.30209i	−0.257102	+	0.130121i
$645$		0			0
$646$	38.3922	−	9.16197i	1.51052	−	0.360473i
$647$	6.63482			0.260842			0.130421	−	0.991459i	$-0.458367\pi$
$647$	6.63482			0.260842			0.130421	+	0.991459i	$0.458367\pi$
$648$		0			0
$649$	−4.57653			−0.179644
$650$	11.7709	−	2.80903i	0.461693	−	0.110179i
$651$		0			0
$652$	−4.00726	−	7.91782i	−0.156936	−	0.310086i
$653$			4.48147i			0.175373i	0.996148	+	0.0876867i	$0.0279474\pi$
$653$			4.48147i			0.175373i	−0.996148	+	0.0876867i	$0.972053\pi$
$654$		0			0
$655$	0.650779			0.0254281
$656$	−5.46763	+	7.44014i	−0.213475	+	0.290489i
$657$		0			0
$658$	−3.73684	−	15.6588i	−0.145677	−	0.610443i
$659$			49.4245i			1.92530i	0.270741	+	0.962652i	$0.412731\pi$
$659$			49.4245i			1.92530i	−0.270741	+	0.962652i	$0.587269\pi$
$660$		0			0
$661$			12.5279i			0.487278i	0.969866	+	0.243639i	$0.0783413\pi$
$661$			12.5279i			0.487278i	−0.969866	+	0.243639i	$0.921659\pi$
$662$	17.3414	−	4.13839i	0.673993	−	0.160843i
$663$		0			0
$664$	−9.77903	+	8.28336i	−0.379500	+	0.321457i
$665$	−1.76254			−0.0683483
$666$		0			0
$667$			29.2132i			1.13114i
$668$	9.60745	−	4.86239i	0.371723	−	0.188132i
$669$		0			0
$670$	1.08444	+	4.54422i	0.0418956	+	0.175558i
$671$	9.71710			0.375125
$672$		0			0
$673$	−26.3343			−1.01511			−0.507556	−	0.861619i	$-0.669451\pi$
$673$	−26.3343			−1.01511			−0.507556	+	0.861619i	$0.669451\pi$
$674$	−9.51393	−	39.8670i	−0.366463	−	1.53562i
$675$		0			0
$676$	−17.3761	+	8.79417i	−0.668313	+	0.338237i
$677$		−	14.4868i		−	0.556774i	−0.960469	−	0.278387i	$-0.910200\pi$
$677$		−	14.4868i		−	0.556774i	0.960469	−	0.278387i	$-0.0897998\pi$
$678$		0			0
$679$	−15.2323			−0.584562
$680$	8.97450	−	7.60188i	0.344156	−	0.291519i
$681$		0			0
$682$	−3.94717	+	0.941959i	−0.151145	+	0.0360695i
$683$			0.0232069i			0.000887989i	1.00000		0.000443994i	$0.000141328\pi$
$683$			0.0232069i			0.000887989i	−1.00000		0.000443994i	$0.999859\pi$
$684$		0			0
$685$			10.1724i			0.388668i
$686$	−0.328272	−	1.37559i	−0.0125335	−	0.0525201i
$687$		0			0
$688$	34.7395	+	25.5294i	1.32443	+	0.973301i
$689$	−16.0360			−0.610921
$690$		0			0
$691$			17.2719i			0.657054i	0.944495	+	0.328527i	$0.106552\pi$
$691$			17.2719i			0.657054i	−0.944495	+	0.328527i	$0.893448\pi$
$692$	16.2213	+	32.0512i	0.616642	+	1.21840i
$693$		0			0
$694$	16.8750	−	4.02708i	0.640566	−	0.152866i
$695$	−7.16186			−0.271665
$696$		0			0
$697$	−18.7307			−0.709476
$698$	−38.9688	+	9.29958i	−1.47499	+	0.351994i
$699$		0			0
$700$	8.45377	−	4.27850i	0.319522	−	0.161712i
$701$			23.9519i			0.904651i	0.891853	+	0.452326i	$0.149405\pi$
$701$			23.9519i			0.904651i	−0.891853	+	0.452326i	$0.850595\pi$
$702$		0			0
$703$	29.0417			1.09533
$704$	14.4319	+	2.40659i	0.543922	+	0.0907017i
$705$		0			0
$706$	−0.462850	−	1.93952i	−0.0174196	−	0.0729947i
$707$			8.13524i			0.305957i
$708$		0			0
$709$			32.1099i			1.20591i	0.797774	+	0.602956i	$0.206011\pi$
$709$			32.1099i			1.20591i	−0.797774	+	0.602956i	$0.793989\pi$
$710$	−6.42160	+	1.53246i	−0.240998	+	0.0575122i
$711$		0			0
$712$	21.4548	+	25.3288i	0.804054	+	0.949236i
$713$	5.73649			0.214833
$714$		0			0
$715$		−	1.69286i		−	0.0633092i
$716$	14.4937	+	28.6376i	0.541654	+	1.07024i
$717$		0			0
$718$	5.59969	+	23.4648i	0.208979	+	0.875700i
$719$	19.4708			0.726139			0.363070	−	0.931762i	$-0.381729\pi$
$719$	19.4708			0.726139			0.363070	+	0.931762i	$0.381729\pi$
$720$		0			0
$721$	15.9816			0.595185
$722$	2.35376	+	9.86314i	0.0875978	+	0.367068i
$723$		0			0
$724$	−5.34530	−	10.5616i	−0.198656	−	0.392519i
$725$		−	37.8513i		−	1.40576i
$726$		0			0
$727$	18.3066			0.678954			0.339477	−	0.940614i	$-0.389750\pi$
$727$	18.3066			0.678954			0.339477	+	0.940614i	$0.389750\pi$
$728$	3.89833	−	3.30209i	0.144482	−	0.122384i
$729$		0			0
$730$	−6.51636	+	1.55508i	−0.241181	+	0.0575560i
$731$			87.4573i			3.23473i
$732$		0			0
$733$			36.3167i			1.34139i	0.741735	+	0.670693i	$0.234003\pi$
$733$			36.3167i			1.34139i	−0.741735	+	0.670693i	$0.765997\pi$
$734$	−8.35642	−	35.0166i	−0.308441	−	1.29249i
$735$		0			0
$736$	−19.0543	−	8.04469i	−0.702352	−	0.296531i
$737$	−11.7899			−0.434288
$738$		0			0
$739$			15.6764i			0.576665i	0.957530	+	0.288332i	$0.0931008\pi$
$739$			15.6764i			0.576665i	−0.957530	+	0.288332i	$0.906899\pi$
$740$	7.72133	−	3.90781i	0.283842	−	0.143654i
$741$		0			0
$742$	−12.2124	+	2.91439i	−0.448331	+	0.106990i
$743$	−49.3578			−1.81076			−0.905381	−	0.424599i	$-0.860415\pi$
$743$	−49.3578			−1.81076			−0.905381	+	0.424599i	$0.860415\pi$
$744$		0			0
$745$	−6.07560			−0.222593
$746$	−27.9486	+	6.66971i	−1.02327	+	0.244195i
$747$		0			0
$748$	13.4031	+	26.4828i	0.490067	+	0.968308i
$749$			12.1695i			0.444664i
$750$		0			0
$751$	29.7930			1.08716			0.543582	−	0.839356i	$-0.317068\pi$
$751$	29.7930			1.08716			0.543582	+	0.839356i	$0.317068\pi$
$752$	26.9637	−	36.6912i	0.983266	−	1.33799i
$753$		0			0
$754$	−4.73759	−	19.8523i	−0.172533	−	0.722979i
$755$		−	6.91542i		−	0.251678i
$756$		0			0
$757$		−	13.6736i		−	0.496974i	−0.968635	−	0.248487i	$-0.920067\pi$
$757$		−	13.6736i		−	0.496974i	0.968635	−	0.248487i	$-0.0799333\pi$
$758$	−16.3463	+	3.90091i	−0.593725	+	0.141687i
$759$		0			0
$760$	−3.22215	−	3.80395i	−0.116880	−	0.137984i
$761$	3.34618			0.121299			0.0606494	−	0.998159i	$-0.480683\pi$
$761$	3.34618			0.121299			0.0606494	+	0.998159i	$0.480683\pi$
$762$		0			0
$763$			10.8452i			0.392623i
$764$	−0.124527	+	0.0630240i	−0.00450524	+	0.00228013i
$765$		0			0
$766$	−6.11443	−	25.6218i	−0.220923	−	0.925753i
$767$	−4.51990			−0.163204
$768$		0			0
$769$	10.2544			0.369783			0.184891	−	0.982759i	$-0.440807\pi$
$769$	10.2544			0.369783			0.184891	+	0.982759i	$0.440807\pi$
$770$	−0.307661	−	1.28922i	−0.0110873	−	0.0464601i
$771$		0			0
$772$	14.7104	−	7.44504i	0.529440	−	0.267953i
$773$			27.9261i			1.00443i	0.864742	+	0.502217i	$0.167482\pi$
$773$			27.9261i			1.00443i	−0.864742	+	0.502217i	$0.832518\pi$
$774$		0			0
$775$	−7.43274			−0.266992
$776$	−27.8466	−	32.8747i	−0.999636	−	1.18013i
$777$		0			0
$778$	28.5621	−	6.81611i	1.02400	−	0.244369i
$779$			7.93924i			0.284453i
$780$		0			0
$781$		−	16.6608i		−	0.596170i
$782$	−9.73950	−	40.8122i	−0.348284	−	1.45944i
$783$		0			0
$784$	2.36870	−	3.22324i	0.0845964	−	0.115116i
$785$	−5.06601			−0.180814
$786$		0			0
$787$			19.9536i			0.711268i	0.934625	+	0.355634i	$0.115735\pi$
$787$			19.9536i			0.711268i	−0.934625	+	0.355634i	$0.884265\pi$
$788$	−1.72765	−	3.41360i	−0.0615449	−	0.121605i
$789$		0			0
$790$	−2.56800	+	0.612833i	−0.0913655	+	0.0218036i
$791$	−3.07563			−0.109357
$792$		0			0
$793$	9.59687			0.340795
$794$	−28.8496	+	6.88473i	−1.02384	+	0.244330i
$795$		0			0
$796$	6.61289	−	3.34682i	0.234388	−	0.118625i
$797$		−	22.3652i		−	0.792217i	−0.918204	−	0.396108i	$-0.870360\pi$
$797$		−	22.3652i		−	0.792217i	0.918204	−	0.396108i	$-0.129640\pi$
$798$		0			0
$799$	92.3708			3.26785
$800$	24.6886	+	10.4235i	0.872873	+	0.368525i
$801$		0			0
$802$	−0.156312	−	0.655008i	−0.00551958	−	0.0231291i
$803$		−	16.9067i		−	0.596623i
$804$		0			0
$805$			1.87364i			0.0660371i
$806$	−3.89833	+	0.930305i	−0.137313	+	0.0327686i
$807$		0			0
$808$	−17.5577	+	14.8723i	−0.617677	+	0.523206i
$809$	8.28121			0.291152			0.145576	−	0.989347i	$-0.453496\pi$
$809$	8.28121			0.291152			0.145576	+	0.989347i	$0.453496\pi$
$810$		0			0
$811$			20.5177i			0.720474i	0.932861	+	0.360237i	$0.117304\pi$
$811$			20.5177i			0.720474i	−0.932861	+	0.360237i	$0.882696\pi$
$812$	−7.21595	−	14.2578i	−0.253230	−	0.500350i
$813$		0			0
$814$	5.06940	+	21.2427i	0.177682	+	0.744556i
$815$	−2.27376			−0.0796462
$816$		0			0
$817$	37.0699			1.29691
$818$	−0.685105	−	2.87085i	−0.0239541	−	0.100377i
$819$		0			0
$820$	1.06829	+	2.11080i	0.0373064	+	0.0737125i
$821$		−	6.88906i		−	0.240430i	−0.992748	−	0.120215i	$-0.961642\pi$
$821$		−	6.88906i		−	0.240430i	0.992748	−	0.120215i	$-0.0383584\pi$
$822$		0			0
$823$	−6.14442			−0.214181			−0.107091	−	0.994249i	$-0.534153\pi$
$823$	−6.14442			−0.214181			−0.107091	+	0.994249i	$0.534153\pi$
$824$	29.2164	+	34.4919i	1.01780	+	1.20158i
$825$		0			0
$826$	−3.44219	+	0.821450i	−0.119769	+	0.0285819i
$827$			29.6562i			1.03125i	0.856815	+	0.515623i	$0.172440\pi$
$827$			29.6562i			1.03125i	−0.856815	+	0.515623i	$0.827560\pi$
$828$		0			0
$829$			7.16328i			0.248791i	0.992233	+	0.124396i	$0.0396992\pi$
$829$			7.16328i			0.248791i	−0.992233	+	0.124396i	$0.960301\pi$
$830$	0.762223	+	3.19401i	0.0264572	+	0.110866i
$831$		0			0
$832$	14.2533	+	2.37681i	0.494145	+	0.0824011i
$833$	8.11456			0.281153
$834$		0			0
$835$		−	2.75897i		−	0.0954780i
$836$	11.2251	−	5.68108i	0.388227	−	0.196484i
$837$		0			0
$838$	−21.7485	+	5.19011i	−0.751291	+	0.179289i
$839$	−15.6136			−0.539041			−0.269520	−	0.962995i	$-0.586865\pi$
$839$	−15.6136			−0.539041			−0.269520	+	0.962995i	$0.586865\pi$
$840$		0			0
$841$	−34.8385			−1.20133
$842$	30.1011	−	7.18339i	1.03735	−	0.247556i
$843$		0			0
$844$	23.1208	+	45.6837i	0.795851	+	1.57250i
$845$			4.98990i			0.171658i
$846$		0			0
$847$	−7.65514			−0.263034
$848$	−28.6158	−	21.0292i	−0.982669	−	0.722146i
$849$		0			0
$850$	12.6194	+	52.8801i	0.432842	+	1.81377i
$851$		−	30.8724i		−	1.05829i
$852$		0			0
$853$		−	0.960301i		−	0.0328801i	−0.999865	−	0.0164400i	$-0.994767\pi$
$853$		−	0.960301i		−	0.0328801i	0.999865	−	0.0164400i	$-0.00523327\pi$
$854$	7.30862	−	1.74414i	0.250096	−	0.0596833i
$855$		0			0
$856$	−26.2645	+	22.2475i	−0.897703	+	0.760403i
$857$	17.3062			0.591168			0.295584	−	0.955317i	$-0.404486\pi$
$857$	17.3062			0.591168			0.295584	+	0.955317i	$0.404486\pi$
$858$		0			0
$859$			15.5416i			0.530273i	0.964211	+	0.265137i	$0.0854171\pi$
$859$			15.5416i			0.530273i	−0.964211	+	0.265137i	$0.914583\pi$
$860$	9.85577	−	4.98807i	0.336079	−	0.170092i
$861$		0			0
$862$	8.31287	+	34.8341i	0.283137	+	1.18645i
$863$	30.9082			1.05213			0.526063	−	0.850445i	$-0.323667\pi$
$863$	30.9082			1.05213			0.526063	+	0.850445i	$0.323667\pi$
$864$		0			0
$865$	9.20413			0.312950
$866$	10.1501	+	42.5327i	0.344913	+	1.44532i
$867$		0			0
$868$	−2.79975	+	1.41697i	−0.0950297	+	0.0480951i
$869$		−	6.66267i		−	0.226016i
$870$		0			0
$871$	−11.6441			−0.394544
$872$	−23.4064	+	19.8265i	−0.792640	+	0.671409i
$873$		0			0
$874$	−17.2988	+	4.12821i	−0.585140	+	0.139639i
$875$		−	4.98990i		−	0.168689i
$876$		0			0
$877$		−	30.0443i		−	1.01452i	−0.861792	−	0.507262i	$-0.830658\pi$
$877$		−	30.0443i		−	1.01452i	0.861792	−	0.507262i	$-0.169342\pi$
$878$	−2.87458	−	12.0456i	−0.0970123	−	0.406518i
$879$		0			0
$880$	2.21997	−	3.02086i	0.0748353	−	0.101833i
$881$	−43.7362			−1.47351			−0.736754	−	0.676160i	$-0.763643\pi$
$881$	−43.7362			−1.47351			−0.736754	+	0.676160i	$0.763643\pi$
$882$		0			0
$883$			11.9694i			0.402804i	0.979509	+	0.201402i	$0.0645497\pi$
$883$			11.9694i			0.402804i	−0.979509	+	0.201402i	$0.935450\pi$
$884$	13.2373	+	26.1552i	0.445218	+	0.879693i
$885$		0			0
$886$	−37.9923	+	9.06655i	−1.27638	+	0.304597i
$887$	50.6980			1.70227			0.851136	−	0.524945i	$-0.175914\pi$
$887$	50.6980			1.70227			0.851136	+	0.524945i	$0.175914\pi$
$888$		0			0
$889$	−6.67524			−0.223880
$890$	8.27283	−	1.97424i	0.277306	−	0.0661768i
$891$		0			0
$892$	25.4536	−	12.8822i	0.852249	−	0.431328i
$893$		−	39.1525i		−	1.31019i
$894$		0			0
$895$	8.22384			0.274893
$896$	11.2868	−	0.780319i	0.377064	−	0.0260686i
$897$		0			0
$898$	4.49715	+	18.8448i	0.150072	+	0.628858i
$899$			12.5357i			0.418090i
$900$		0			0
$901$		−	72.0406i		−	2.40002i
$902$	−5.80719	+	1.38584i	−0.193358	+	0.0461433i
$903$		0			0
$904$	−5.62265	−	6.63790i	−0.187007	−	0.220773i
$905$	−3.03297			−0.100819
$906$		0			0
$907$			5.94868i			0.197523i	0.995111	+	0.0987614i	$0.0314881\pi$
$907$			5.94868i			0.197523i	−0.995111	+	0.0987614i	$0.968512\pi$
$908$	−2.33508	−	4.61381i	−0.0774923	−	0.153115i
$909$		0			0
$910$	−0.303854	−	1.27326i	−0.0100727	−	0.0422083i
$911$	−49.6827			−1.64606			−0.823031	−	0.567996i	$-0.807719\pi$
$911$	−49.6827			−1.64606			−0.823031	+	0.567996i	$0.807719\pi$
$912$		0			0
$913$	−8.28683			−0.274254
$914$	1.92188	+	8.05340i	0.0635701	+	0.266383i
$915$		0			0
$916$	24.9084	+	49.2158i	0.822997	+	1.62614i
$917$			1.26995i			0.0419373i
$918$		0			0
$919$	16.5497			0.545923			0.272961	−	0.962025i	$-0.411997\pi$
$919$	16.5497			0.545923			0.272961	+	0.962025i	$0.411997\pi$
$920$	−4.04374	+	3.42526i	−0.133318	+	0.112928i
$921$		0			0
$922$	3.33641	−	0.796206i	0.109879	−	0.0262217i
$923$		−	16.4546i		−	0.541611i
$924$		0			0
$925$			40.0012i			1.31523i
$926$	−0.414825	−	1.73827i	−0.0136320	−	0.0571232i
$927$		0			0
$928$	17.5798	−	41.6387i	0.577084	−	1.36686i
$929$	−15.8292			−0.519339			−0.259669	−	0.965698i	$-0.583614\pi$
$929$	−15.8292			−0.519339			−0.259669	+	0.965698i	$0.583614\pi$
$930$		0			0
$931$		−	3.43946i		−	0.112724i
$932$	−10.0144	+	5.06835i	−0.328033	+	0.166019i
$933$		0			0
$934$	37.4787	−	8.94397i	1.22634	−	0.292656i
$935$	7.60506			0.248712
$936$		0			0
$937$	−14.1814			−0.463286			−0.231643	−	0.972801i	$-0.574410\pi$
$937$	−14.1814			−0.463286			−0.231643	+	0.972801i	$0.574410\pi$
$938$	−8.86768	+	2.11620i	−0.289540	+	0.0690964i
$939$		0			0
$940$	−5.26830	−	10.4095i	−0.171833	−	0.339520i
$941$			59.4006i			1.93641i	0.250166	+	0.968203i	$0.419515\pi$
$941$			59.4006i			1.93641i	−0.250166	+	0.968203i	$0.580485\pi$
$942$		0			0
$943$	8.43969			0.274834
$944$	−8.06565	−	5.92730i	−0.262515	−	0.192917i
$945$		0			0
$946$	6.47075	+	27.1149i	0.210382	+	0.881582i
$947$			6.81038i			0.221308i	0.993859	+	0.110654i	$0.0352945\pi$
$947$			6.81038i			0.221308i	−0.993859	+	0.110654i	$0.964706\pi$
$948$		0			0
$949$		−	16.6975i		−	0.542023i
$950$	22.4139	−	5.34889i	0.727203	−	0.173541i
$951$		0			0
$952$	14.8345	+	17.5130i	0.480788	+	0.567601i
$953$	−25.4827			−0.825466			−0.412733	−	0.910852i	$-0.635426\pi$
$953$	−25.4827			−0.825466			−0.412733	+	0.910852i	$0.635426\pi$
$954$		0			0
$955$			0.0357604i			0.00115718i
$956$	−3.02068	+	1.52878i	−0.0976957	+	0.0494444i
$957$		0			0
$958$	−8.99582	−	37.6959i	−0.290642	−	1.21790i
$959$	−19.8507			−0.641012
$960$		0			0
$961$	−28.5384			−0.920593
$962$	5.00667	+	20.9799i	0.161422	+	0.676418i
$963$		0			0
$964$	40.3730	−	20.4330i	1.30033	−	0.658103i
$965$		−	4.22439i		−	0.135988i
$966$		0			0
$967$	44.8473			1.44219			0.721096	−	0.692835i	$-0.243639\pi$
$967$	44.8473			1.44219			0.721096	+	0.692835i	$0.243639\pi$
$968$	−13.9946	−	16.5215i	−0.449804	−	0.531021i
$969$		0			0
$970$	−10.7375	+	2.56241i	−0.344759	+	0.0822740i
$971$		−	23.4868i		−	0.753728i	−0.926269	−	0.376864i	$-0.877002\pi$
$971$		−	23.4868i		−	0.753728i	0.926269	−	0.376864i	$-0.122998\pi$
$972$		0			0
$973$		−	13.9758i		−	0.448044i
$974$	8.88075	+	37.2137i	0.284558	+	1.19241i
$975$		0			0
$976$	17.1254	+	12.5851i	0.548170	+	0.402840i
$977$	54.0970			1.73072			0.865359	−	0.501153i	$-0.167091\pi$
$977$	54.0970			1.73072			0.865359	+	0.501153i	$0.167091\pi$
$978$		0			0
$979$			21.4638i			0.685986i
$980$	−0.462808	−	0.914448i	−0.0147839	−	0.0292110i
$981$		0			0
$982$	−40.2688	+	9.60981i	−1.28503	+	0.306661i
$983$	15.0476			0.479943			0.239972	−	0.970780i	$-0.422862\pi$
$983$	15.0476			0.479943			0.239972	+	0.970780i	$0.422862\pi$
$984$		0			0
$985$	−0.980283			−0.0312344
$986$	89.1854	−	21.2834i	2.84024	−	0.677800i
$987$		0			0
$988$	11.0862	−	5.61079i	0.352699	−	0.178503i
$989$		−	39.4066i		−	1.25306i
$990$		0			0
$991$	24.0651			0.764455			0.382227	−	0.924068i	$-0.375157\pi$
$991$	24.0651			0.764455			0.382227	+	0.924068i	$0.375157\pi$
$992$	−8.17645	−	3.45208i	−0.259603	−	0.109604i
$993$		0			0
$994$	−2.99048	−	12.5312i	−0.0948522	−	0.397467i
$995$		−	1.89902i		−	0.0602030i
$996$		0			0
$997$			46.1183i			1.46058i	0.683136	+	0.730291i	$0.260616\pi$
$997$			46.1183i			1.46058i	−0.683136	+	0.730291i	$0.739384\pi$
$998$	−54.7962	+	13.0767i	−1.73454	+	0.413934i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.e.757.12	yes	20
3.2	odd	2	inner	1512.2.c.e.757.9	✓	20
4.3	odd	2		6048.2.c.e.3025.13		20
8.3	odd	2		6048.2.c.e.3025.8		20
8.5	even	2	inner	1512.2.c.e.757.11	yes	20
12.11	even	2		6048.2.c.e.3025.7		20
24.5	odd	2	inner	1512.2.c.e.757.10	yes	20
24.11	even	2		6048.2.c.e.3025.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.e.757.9	✓	20	3.2	odd	2	inner
1512.2.c.e.757.10	yes	20	24.5	odd	2	inner
1512.2.c.e.757.11	yes	20	8.5	even	2	inner
1512.2.c.e.757.12	yes	20	1.1	even	1	trivial
6048.2.c.e.3025.7		20	12.11	even	2
6048.2.c.e.3025.8		20	8.3	odd	2
6048.2.c.e.3025.13		20	4.3	odd	2
6048.2.c.e.3025.14		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.328272 + 1.37559i) q^{2} +(-1.78447 + 0.903134i) q^{4} +0.512447i q^{5} -1.00000 q^{7} +(-1.82813 - 2.15822i) q^{8} +O(q^{10})\)	\(q+(0.328272 + 1.37559i) q^{2} +(-1.78447 + 0.903134i) q^{4} +0.512447i q^{5} -1.00000 q^{7} +(-1.82813 - 2.15822i) q^{8} +(-0.704915 + 0.168222i) q^{10} -1.82890i q^{11} -1.80627i q^{13} +(-0.328272 - 1.37559i) q^{14} +(2.36870 - 3.22324i) q^{16} +8.11456 q^{17} -3.43946i q^{19} +(-0.462808 - 0.914448i) q^{20} +(2.51580 - 0.600376i) q^{22} -3.65626 q^{23} +4.73740 q^{25} +(2.48468 - 0.592948i) q^{26} +(1.78447 - 0.903134i) q^{28} -7.98990i q^{29} -1.56895 q^{31} +(5.21142 + 2.20025i) q^{32} +(2.66378 + 11.1623i) q^{34} -0.512447i q^{35} +8.44370i q^{37} +(4.73127 - 1.12908i) q^{38} +(1.10598 - 0.936820i) q^{40} -2.30828 q^{41} +10.7778i q^{43} +(1.65174 + 3.26362i) q^{44} +(-1.20025 - 5.02951i) q^{46} +11.3833 q^{47} +1.00000 q^{49} +(1.55516 + 6.51670i) q^{50} +(1.63130 + 3.22324i) q^{52} -8.87795i q^{53} +0.937212 q^{55} +(1.82813 + 2.15822i) q^{56} +(10.9908 - 2.62286i) q^{58} -2.50234i q^{59} +5.31310i q^{61} +(-0.515043 - 2.15822i) q^{62} +(-1.31587 + 7.89104i) q^{64} +0.925616 q^{65} -6.44648i q^{67} +(-14.4802 + 7.32853i) q^{68} +(0.704915 - 0.168222i) q^{70} +9.10975 q^{71} +9.24419 q^{73} +(-11.6150 + 2.77183i) q^{74} +(3.10629 + 6.13762i) q^{76} +1.82890i q^{77} +3.64300 q^{79} +(1.65174 + 1.21383i) q^{80} +(-0.757745 - 3.17524i) q^{82} -4.53105i q^{83} +4.15828i q^{85} +(-14.8258 + 3.53806i) q^{86} +(-3.94717 + 3.34346i) q^{88} -11.7359 q^{89} +1.80627i q^{91} +(6.52451 - 3.30209i) q^{92} +(3.73684 + 15.6588i) q^{94} +1.76254 q^{95} +15.2323 q^{97} +(0.328272 + 1.37559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 20 q^{7}+O(q^{10}) \) 20 * q - 2 * q^4 - 20 * q^7	\( 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70} + 12 q^{76} + 64 q^{79} - 92 q^{88} - 24 q^{94} + 56 q^{97}+O(q^{100}) \) 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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