LMFDB - Embedded newform 1088.2.j.a.81.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(81,1088)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1088, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1088.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.j (of order $4$, degree $2$, not 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:	$8.68772373992$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 272)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.11
Character	$\chi$	$=$	1088.81
Dual form			1088.2.j.a.497.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68708i q^{3} +0.660632 q^{5} +(-0.710367 - 0.710367i) q^{7} +0.153763 q^{9} +O(q^{10})$	\(q-1.68708i q^{3} +0.660632 q^{5} +(-0.710367 - 0.710367i) q^{7} +0.153763 q^{9} +4.46078i q^{11} +(4.51933 + 4.51933i) q^{13} -1.11454i q^{15} +(0.869766 + 4.03032i) q^{17} +(1.70072 - 1.70072i) q^{19} +(-1.19845 + 1.19845i) q^{21} +(4.11170 + 4.11170i) q^{23} -4.56357 q^{25} -5.32065i q^{27} -5.37730i q^{29} +(6.53867 + 6.53867i) q^{31} +7.52570 q^{33} +(-0.469292 - 0.469292i) q^{35} -4.81250 q^{37} +(7.62446 - 7.62446i) q^{39} +(0.645043 + 0.645043i) q^{41} +(-7.23424 - 7.23424i) q^{43} +0.101581 q^{45} +10.3100 q^{47} -5.99076i q^{49} +(6.79948 - 1.46736i) q^{51} +(1.52379 + 1.52379i) q^{53} +2.94694i q^{55} +(-2.86925 - 2.86925i) q^{57} +(-5.13534 - 5.13534i) q^{59} -2.23831 q^{61} +(-0.109229 - 0.109229i) q^{63} +(2.98561 + 2.98561i) q^{65} +(-0.119907 - 0.119907i) q^{67} +(6.93677 - 6.93677i) q^{69} +(-5.41828 + 5.41828i) q^{71} +(-2.55202 + 2.55202i) q^{73} +7.69910i q^{75} +(3.16880 - 3.16880i) q^{77} +(2.79211 - 2.79211i) q^{79} -8.51507 q^{81} +(2.60652 - 2.60652i) q^{83} +(0.574596 + 2.66256i) q^{85} -9.07192 q^{87} +12.7100i q^{89} -6.42077i q^{91} +(11.0313 - 11.0313i) q^{93} +(1.12355 - 1.12355i) q^{95} +(4.43572 + 4.43572i) q^{97} +0.685906i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^5 - 60 * q^9	$ 68 q - 4 q^{5} - 60 q^{9} - 4 q^{13} - 4 q^{17} - 4 q^{21} + 52 q^{25} + 4 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} - 12 q^{39} - 12 q^{45} + 48 q^{47} - 32 q^{51} + 12 q^{57} - 32 q^{59} - 36 q^{61} + 32 q^{63} + 4 q^{65} + 4 q^{67} + 28 q^{69} - 8 q^{73} + 28 q^{77} - 12 q^{79} + 28 q^{81} - 28 q^{85} + 24 q^{87} + 12 q^{93} + 4 q^{95} - 4 q^{97}+O(q^{100}) $ 68 * q - 4 * q^5 - 60 * q^9 - 4 * q^13 - 4 * q^17 - 4 * q^21 + 52 * q^25 + 4 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 - 12 * q^39 - 12 * q^45 + 48 * q^47 - 32 * q^51 + 12 * q^57 - 32 * q^59 - 36 * q^61 + 32 * q^63 + 4 * q^65 + 4 * q^67 + 28 * q^69 - 8 * q^73 + 28 * q^77 - 12 * q^79 + 28 * q^81 - 28 * q^85 + 24 * q^87 + 12 * q^93 + 4 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$		−	1.68708i		−	0.974036i	−0.873392	−	0.487018i	$-0.838085\pi$
$3$		−	1.68708i		−	0.974036i	0.873392	−	0.487018i	$-0.161915\pi$
$4$		0			0
$5$	0.660632			0.295444			0.147722	−	0.989029i	$-0.452806\pi$
$5$	0.660632			0.295444			0.147722	+	0.989029i	$0.452806\pi$
$6$		0			0
$7$	−0.710367	−	0.710367i	−0.268494	−	0.268494i	0.559999	−	0.828493i	$-0.310801\pi$
$7$	−0.710367	−	0.710367i	−0.268494	−	0.268494i	−0.828493	+	0.559999i	$0.810801\pi$
$8$		0			0
$9$	0.153763			0.0512545
$10$		0			0
$11$			4.46078i			1.34498i	0.740108	+	0.672489i	$0.234775\pi$
$11$			4.46078i			1.34498i	−0.740108	+	0.672489i	$0.765225\pi$
$12$		0			0
$13$	4.51933	+	4.51933i	1.25344	+	1.25344i	0.954170	+	0.299266i	$0.0967420\pi$
$13$	4.51933	+	4.51933i	1.25344	+	1.25344i	0.299266	+	0.954170i	$0.403258\pi$
$14$		0			0
$15$		−	1.11454i		−	0.287773i
$16$		0			0
$17$	0.869766	+	4.03032i	0.210949	+	0.977497i
$17$	0.869766	+	4.03032i	0.210949	+	0.977497i
$18$		0			0
$19$	1.70072	−	1.70072i	0.390172	−	0.390172i	−0.484577	−	0.874749i	$-0.661026\pi$
$19$	1.70072	−	1.70072i	0.390172	−	0.390172i	0.874749	+	0.484577i	$0.161026\pi$
$20$		0			0
$21$	−1.19845	+	1.19845i	−0.261522	+	0.261522i
$22$		0			0
$23$	4.11170	+	4.11170i	0.857349	+	0.857349i	0.991025	−	0.133676i	$-0.0426782\pi$
$23$	4.11170	+	4.11170i	0.857349	+	0.857349i	−0.133676	+	0.991025i	$0.542678\pi$
$24$		0			0
$25$	−4.56357			−0.912713
$26$		0			0
$27$		−	5.32065i		−	1.02396i
$28$		0			0
$29$		−	5.37730i		−	0.998539i	−0.866447	−	0.499269i	$-0.833602\pi$
$29$		−	5.37730i		−	0.998539i	0.866447	−	0.499269i	$-0.166398\pi$
$30$		0			0
$31$	6.53867	+	6.53867i	1.17438	+	1.17438i	0.981154	+	0.193225i	$0.0618947\pi$
$31$	6.53867	+	6.53867i	1.17438	+	1.17438i	0.193225	+	0.981154i	$0.438105\pi$
$32$		0			0
$33$	7.52570			1.31006
$34$		0			0
$35$	−0.469292	−	0.469292i	−0.0793247	−	0.0793247i
$36$		0			0
$37$	−4.81250			−0.791169			−0.395585	−	0.918429i	$-0.629458\pi$
$37$	−4.81250			−0.791169			−0.395585	+	0.918429i	$0.629458\pi$
$38$		0			0
$39$	7.62446	−	7.62446i	1.22089	−	1.22089i
$40$		0			0
$41$	0.645043	+	0.645043i	0.100739	+	0.100739i	0.755680	−	0.654941i	$-0.227307\pi$
$41$	0.645043	+	0.645043i	0.100739	+	0.100739i	−0.654941	+	0.755680i	$0.727307\pi$
$42$		0			0
$43$	−7.23424	−	7.23424i	−1.10321	−	1.10321i	−0.994021	−	0.109191i	$-0.965174\pi$
$43$	−7.23424	−	7.23424i	−1.10321	−	1.10321i	−0.109191	−	0.994021i	$-0.534826\pi$
$44$		0			0
$45$	0.101581			0.0151428
$46$		0			0
$47$	10.3100			1.50386			0.751931	−	0.659242i	$-0.229123\pi$
$47$	10.3100			1.50386			0.751931	+	0.659242i	$0.229123\pi$
$48$		0			0
$49$		−	5.99076i		−	0.855822i
$50$		0			0
$51$	6.79948	−	1.46736i	0.952117	−	0.205472i
$52$		0			0
$53$	1.52379	+	1.52379i	0.209308	+	0.209308i	0.803973	−	0.594665i	$-0.202715\pi$
$53$	1.52379	+	1.52379i	0.209308	+	0.209308i	−0.594665	+	0.803973i	$0.702715\pi$
$54$		0			0
$55$			2.94694i			0.397365i
$56$		0			0
$57$	−2.86925	−	2.86925i	−0.380041	−	0.380041i
$58$		0			0
$59$	−5.13534	−	5.13534i	−0.668564	−	0.668564i	0.288820	−	0.957384i	$-0.406737\pi$
$59$	−5.13534	−	5.13534i	−0.668564	−	0.668564i	−0.957384	+	0.288820i	$0.906737\pi$
$60$		0			0
$61$	−2.23831			−0.286586			−0.143293	−	0.989680i	$-0.545769\pi$
$61$	−2.23831			−0.286586			−0.143293	+	0.989680i	$0.545769\pi$
$62$		0			0
$63$	−0.109229	−	0.109229i	−0.0137615	−	0.0137615i
$64$		0			0
$65$	2.98561	+	2.98561i	0.370320	+	0.370320i
$66$		0			0
$67$	−0.119907	−	0.119907i	−0.0146490	−	0.0146490i	0.699744	−	0.714393i	$-0.253297\pi$
$67$	−0.119907	−	0.119907i	−0.0146490	−	0.0146490i	−0.714393	+	0.699744i	$0.753297\pi$
$68$		0			0
$69$	6.93677	−	6.93677i	0.835089	−	0.835089i
$70$		0			0
$71$	−5.41828	+	5.41828i	−0.643031	+	0.643031i	−0.951299	−	0.308268i	$-0.900251\pi$
$71$	−5.41828	+	5.41828i	−0.643031	+	0.643031i	0.308268	+	0.951299i	$0.400251\pi$
$72$		0			0
$73$	−2.55202	+	2.55202i	−0.298691	+	0.298691i	−0.840501	−	0.541810i	$-0.817739\pi$
$73$	−2.55202	+	2.55202i	−0.298691	+	0.298691i	0.541810	+	0.840501i	$0.317739\pi$
$74$		0			0
$75$			7.69910i			0.889015i
$76$		0			0
$77$	3.16880	−	3.16880i	0.361118	−	0.361118i
$78$		0			0
$79$	2.79211	−	2.79211i	0.314137	−	0.314137i	−0.532373	−	0.846510i	$-0.678700\pi$
$79$	2.79211	−	2.79211i	0.314137	−	0.314137i	0.846510	+	0.532373i	$0.178700\pi$
$80$		0			0
$81$	−8.51507			−0.946118
$82$		0			0
$83$	2.60652	−	2.60652i	0.286103	−	0.286103i	−0.549434	−	0.835537i	$-0.685157\pi$
$83$	2.60652	−	2.60652i	0.286103	−	0.286103i	0.835537	+	0.549434i	$0.185157\pi$
$84$		0			0
$85$	0.574596	+	2.66256i	0.0623236	+	0.288795i
$86$		0			0
$87$	−9.07192			−0.972612
$88$		0			0
$89$			12.7100i			1.34725i	0.739072	+	0.673626i	$0.235264\pi$
$89$			12.7100i			1.34725i	−0.739072	+	0.673626i	$0.764736\pi$
$90$		0			0
$91$		−	6.42077i		−	0.673079i
$92$		0			0
$93$	11.0313	−	11.0313i	1.14389	−	1.14389i
$94$		0			0
$95$	1.12355	−	1.12355i	0.115274	−	0.115274i
$96$		0			0
$97$	4.43572	+	4.43572i	0.450379	+	0.450379i	0.895480	−	0.445101i	$-0.146832\pi$
$97$	4.43572	+	4.43572i	0.450379	+	0.450379i	−0.445101	+	0.895480i	$0.646832\pi$
$98$		0			0
$99$			0.685906i			0.0689361i
$100$		0			0
$101$	4.95673	−	4.95673i	0.493213	−	0.493213i	−0.416104	−	0.909317i	$-0.636605\pi$
$101$	4.95673	−	4.95673i	0.493213	−	0.493213i	0.909317	+	0.416104i	$0.136605\pi$
$102$		0			0
$103$		−	1.55328i		−	0.153049i	−0.997068	−	0.0765247i	$-0.975618\pi$
$103$		−	1.55328i		−	0.153049i	0.997068	−	0.0765247i	$-0.0243824\pi$
$104$		0			0
$105$	−0.791732	+	0.791732i	−0.0772651	+	0.0772651i
$106$		0			0
$107$	−10.3209			−0.997759			−0.498880	−	0.866671i	$-0.666255\pi$
$107$	−10.3209			−0.997759			−0.498880	+	0.866671i	$0.666255\pi$
$108$		0			0
$109$	10.1611			0.973261			0.486630	−	0.873608i	$-0.338226\pi$
$109$	10.1611			0.973261			0.486630	+	0.873608i	$0.338226\pi$
$110$		0			0
$111$			8.11906i			0.770627i
$112$		0			0
$113$	13.5524	−	13.5524i	1.27491	−	1.27491i	0.331425	−	0.943482i	$-0.392471\pi$
$113$	13.5524	−	13.5524i	1.27491	−	1.27491i	0.943482	−	0.331425i	$-0.107529\pi$
$114$		0			0
$115$	2.71632	+	2.71632i	0.253298	+	0.253298i
$116$		0			0
$117$	0.694907	+	0.694907i	0.0642442	+	0.0642442i
$118$		0			0
$119$	2.24516	−	3.48086i	0.205813	−	0.319090i
$120$		0			0
$121$	−8.89860			−0.808963
$122$		0			0
$123$	1.08824	−	1.08824i	0.0981232	−	0.0981232i
$124$		0			0
$125$	−6.31800			−0.565099
$126$		0			0
$127$			1.34918i			0.119720i	0.998207	+	0.0598600i	$0.0190654\pi$
$127$			1.34918i			0.119720i	−0.998207	+	0.0598600i	$0.980935\pi$
$128$		0			0
$129$	−12.2047	+	12.2047i	−1.07457	+	1.07457i
$130$		0			0
$131$			8.45298i			0.738540i	0.929322	+	0.369270i	$0.120392\pi$
$131$			8.45298i			0.738540i	−0.929322	+	0.369270i	$0.879608\pi$
$132$		0			0
$133$	−2.41627			−0.209517
$134$		0			0
$135$		−	3.51499i		−	0.302522i
$136$		0			0
$137$		−	14.1506i		−	1.20897i	−0.796616	−	0.604486i	$-0.793379\pi$
$137$		−	14.1506i		−	1.20897i	0.796616	−	0.604486i	$-0.206621\pi$
$138$		0			0
$139$	3.08931			0.262032			0.131016	−	0.991380i	$-0.458176\pi$
$139$	3.08931			0.262032			0.131016	+	0.991380i	$0.458176\pi$
$140$		0			0
$141$		−	17.3937i		−	1.46482i
$142$		0			0
$143$	−20.1597	+	20.1597i	−1.68584	+	1.68584i
$144$		0			0
$145$		−	3.55241i		−	0.295012i
$146$		0			0
$147$	−10.1069			−0.833601
$148$		0			0
$149$	8.68362	−	8.68362i	0.711390	−	0.711390i	−0.255436	−	0.966826i	$-0.582219\pi$
$149$	8.68362	−	8.68362i	0.711390	−	0.711390i	0.966826	+	0.255436i	$0.0822189\pi$
$150$		0			0
$151$	13.1040			1.06639			0.533196	−	0.845992i	$-0.320991\pi$
$151$	13.1040			1.06639			0.533196	+	0.845992i	$0.320991\pi$
$152$		0			0
$153$	0.133738	+	0.619716i	0.0108121	+	0.0501011i
$154$		0			0
$155$	4.31965	+	4.31965i	0.346963	+	0.346963i
$156$		0			0
$157$	−8.55811	−	8.55811i	−0.683012	−	0.683012i	0.277666	−	0.960678i	$-0.410439\pi$
$157$	−8.55811	−	8.55811i	−0.683012	−	0.683012i	−0.960678	+	0.277666i	$0.910439\pi$
$158$		0			0
$159$	2.57075	−	2.57075i	0.203874	−	0.203874i
$160$		0			0
$161$		−	5.84164i		−	0.460386i
$162$		0			0
$163$	−3.09968			−0.242785			−0.121393	−	0.992605i	$-0.538736\pi$
$163$	−3.09968			−0.242785			−0.121393	+	0.992605i	$0.538736\pi$
$164$		0			0
$165$	4.97172			0.387048
$166$		0			0
$167$	9.51730	−	9.51730i	0.736471	−	0.736471i	−0.235423	−	0.971893i	$-0.575647\pi$
$167$	9.51730	−	9.51730i	0.736471	−	0.736471i	0.971893	+	0.235423i	$0.0756474\pi$
$168$		0			0
$169$			27.8487i			2.14220i
$170$		0			0
$171$	0.261508	−	0.261508i	0.0199980	−	0.0199980i
$172$		0			0
$173$		−	10.4190i		−	0.792145i	−0.918219	−	0.396072i	$-0.870373\pi$
$173$		−	10.4190i		−	0.792145i	0.918219	−	0.396072i	$-0.129627\pi$
$174$		0			0
$175$	3.24181	+	3.24181i	0.245058	+	0.245058i
$176$		0			0
$177$	−8.66372	+	8.66372i	−0.651205	+	0.651205i
$178$		0			0
$179$	−8.85807	+	8.85807i	−0.662083	+	0.662083i	−0.955871	−	0.293787i	$-0.905084\pi$
$179$	−8.85807	+	8.85807i	−0.662083	+	0.662083i	0.293787	+	0.955871i	$0.405084\pi$
$180$		0			0
$181$			14.9928i			1.11441i	0.830375	+	0.557204i	$0.188126\pi$
$181$			14.9928i			1.11441i	−0.830375	+	0.557204i	$0.811874\pi$
$182$		0			0
$183$			3.77620i			0.279145i
$184$		0			0
$185$	−3.17929			−0.233746
$186$		0			0
$187$	−17.9784	+	3.87984i	−1.31471	+	0.283722i
$188$		0			0
$189$	−3.77962	+	3.77962i	−0.274927	+	0.274927i
$190$		0			0
$191$	−9.70819			−0.702460			−0.351230	−	0.936289i	$-0.614236\pi$
$191$	−9.70819			−0.702460			−0.351230	+	0.936289i	$0.614236\pi$
$192$		0			0
$193$	−16.0757	+	16.0757i	−1.15715	+	1.15715i	−0.172066	+	0.985085i	$0.555044\pi$
$193$	−16.0757	+	16.0757i	−1.15715	+	1.15715i	−0.985085	+	0.172066i	$0.944956\pi$
$194$		0			0
$195$	5.03697	−	5.03697i	0.360705	−	0.360705i
$196$		0			0
$197$			21.3989i			1.52461i	0.647218	+	0.762305i	$0.275932\pi$
$197$			21.3989i			1.52461i	−0.647218	+	0.762305i	$0.724068\pi$
$198$		0			0
$199$	−9.81760	+	9.81760i	−0.695951	+	0.695951i	−0.963535	−	0.267583i	$-0.913775\pi$
$199$	−9.81760	+	9.81760i	−0.695951	+	0.695951i	0.267583	+	0.963535i	$0.413775\pi$
$200$		0			0
$201$	−0.202293	+	0.202293i	−0.0142686	+	0.0142686i
$202$		0			0
$203$	−3.81986	+	3.81986i	−0.268101	+	0.268101i
$204$		0			0
$205$	0.426136	+	0.426136i	0.0297626	+	0.0297626i
$206$		0			0
$207$	0.632229	+	0.632229i	0.0439430	+	0.0439430i
$208$		0			0
$209$	7.58654	+	7.58654i	0.524772	+	0.524772i
$210$		0			0
$211$	−16.8728			−1.16157			−0.580785	−	0.814057i	$-0.697254\pi$
$211$	−16.8728			−1.16157			−0.580785	+	0.814057i	$0.697254\pi$
$212$		0			0
$213$	9.14106	+	9.14106i	0.626335	+	0.626335i
$214$		0			0
$215$	−4.77917	−	4.77917i	−0.325937	−	0.325937i
$216$		0			0
$217$		−	9.28971i		−	0.630627i
$218$		0			0
$219$	4.30545	+	4.30545i	0.290936	+	0.290936i
$220$		0			0
$221$	−14.2836	+	22.1451i	−0.960818	+	1.48964i
$222$		0			0
$223$		−	10.2389i		−	0.685646i	−0.939400	−	0.342823i	$-0.888617\pi$
$223$		−	10.2389i		−	0.685646i	0.939400	−	0.342823i	$-0.111383\pi$
$224$		0			0
$225$	−0.701709			−0.0467806
$226$		0			0
$227$	18.3970			1.22105			0.610525	−	0.791997i	$-0.290958\pi$
$227$	18.3970			1.22105			0.610525	+	0.791997i	$0.290958\pi$
$228$		0			0
$229$	−16.9747	−	16.9747i	−1.12172	−	1.12172i	−0.991483	−	0.130238i	$-0.958426\pi$
$229$	−16.9747	−	16.9747i	−1.12172	−	1.12172i	−0.130238	−	0.991483i	$-0.541574\pi$
$230$		0			0
$231$	−5.34601	−	5.34601i	−0.351742	−	0.351742i
$232$		0			0
$233$	4.70105	−	4.70105i	0.307976	−	0.307976i	−0.536148	−	0.844124i	$-0.680121\pi$
$233$	4.70105	−	4.70105i	0.307976	−	0.307976i	0.844124	+	0.536148i	$0.180121\pi$
$234$		0			0
$235$	6.81109			0.444307
$236$		0			0
$237$	−4.71051	−	4.71051i	−0.305980	−	0.305980i
$238$		0			0
$239$	−11.9132			−0.770598			−0.385299	−	0.922792i	$-0.625902\pi$
$239$	−11.9132			−0.770598			−0.385299	+	0.922792i	$0.625902\pi$
$240$		0			0
$241$	2.65347	+	2.65347i	0.170925	+	0.170925i	0.787386	−	0.616461i	$-0.211434\pi$
$241$	2.65347	+	2.65347i	0.170925	+	0.170925i	−0.616461	+	0.787386i	$0.711434\pi$
$242$		0			0
$243$		−	1.59635i		−	0.102406i
$244$		0			0
$245$		−	3.95769i		−	0.252847i
$246$		0			0
$247$	15.3722			0.978110
$248$		0			0
$249$	−4.39741	−	4.39741i	−0.278674	−	0.278674i
$250$		0			0
$251$	7.81420	−	7.81420i	0.493228	−	0.493228i	−0.416094	−	0.909322i	$-0.636601\pi$
$251$	7.81420	−	7.81420i	0.493228	−	0.493228i	0.909322	+	0.416094i	$0.136601\pi$
$252$		0			0
$253$	−18.3414	+	18.3414i	−1.15311	+	1.15311i
$254$		0			0
$255$	4.49195	−	0.969388i	0.281297	−	0.0607055i
$256$		0			0
$257$		−	22.1390i		−	1.38099i	−0.723335	−	0.690497i	$-0.757392\pi$
$257$		−	22.1390i		−	1.38099i	0.723335	−	0.690497i	$-0.242608\pi$
$258$		0			0
$259$	3.41864	+	3.41864i	0.212424	+	0.212424i
$260$		0			0
$261$		−	0.826831i		−	0.0511796i
$262$		0			0
$263$	−6.13241			−0.378141			−0.189070	−	0.981964i	$-0.560547\pi$
$263$	−6.13241			−0.378141			−0.189070	+	0.981964i	$0.560547\pi$
$264$		0			0
$265$	1.00666	+	1.00666i	0.0618387	+	0.0618387i
$266$		0			0
$267$	21.4427			1.31227
$268$		0			0
$269$			4.13108i			0.251877i	0.992038	+	0.125938i	$0.0401941\pi$
$269$			4.13108i			0.251877i	−0.992038	+	0.125938i	$0.959806\pi$
$270$		0			0
$271$	−26.4578			−1.60720			−0.803599	−	0.595171i	$-0.797084\pi$
$271$	−26.4578			−1.60720			−0.803599	+	0.595171i	$0.797084\pi$
$272$		0			0
$273$	−10.8323			−0.655603
$274$		0			0
$275$		−	20.3571i		−	1.22758i
$276$		0			0
$277$	2.98864			0.179570			0.0897849	−	0.995961i	$-0.471382\pi$
$277$	2.98864			0.179570			0.0897849	+	0.995961i	$0.471382\pi$
$278$		0			0
$279$	1.00541	+	1.00541i	0.0601922	+	0.0601922i
$280$		0			0
$281$	−12.7021			−0.757746			−0.378873	−	0.925449i	$-0.623688\pi$
$281$	−12.7021			−0.757746			−0.378873	+	0.925449i	$0.623688\pi$
$282$		0			0
$283$		−	8.27786i		−	0.492068i	−0.969261	−	0.246034i	$-0.920873\pi$
$283$		−	8.27786i		−	0.492068i	0.969261	−	0.246034i	$-0.0791274\pi$
$284$		0			0
$285$	−1.89552	−	1.89552i	−0.112281	−	0.112281i
$286$		0			0
$287$		−	0.916435i		−	0.0540955i
$288$		0			0
$289$	−15.4870	+	7.01088i	−0.911001	+	0.412405i
$290$		0			0
$291$	7.48341	−	7.48341i	0.438685	−	0.438685i
$292$		0			0
$293$	−3.98808	+	3.98808i	−0.232986	+	0.232986i	−0.813938	−	0.580952i	$-0.802680\pi$
$293$	−3.98808	+	3.98808i	−0.232986	+	0.232986i	0.580952	+	0.813938i	$0.302680\pi$
$294$		0			0
$295$	−3.39257	−	3.39257i	−0.197523	−	0.197523i
$296$		0			0
$297$	23.7343			1.37720
$298$		0			0
$299$			37.1643i			2.14926i
$300$		0			0
$301$			10.2779i			0.592411i
$302$		0			0
$303$	−8.36239	−	8.36239i	−0.480407	−	0.480407i
$304$		0			0
$305$	−1.47870			−0.0846700
$306$		0			0
$307$	−13.0855	−	13.0855i	−0.746831	−	0.746831i	0.227052	−	0.973883i	$-0.427091\pi$
$307$	−13.0855	−	13.0855i	−0.746831	−	0.746831i	−0.973883	+	0.227052i	$0.927091\pi$
$308$		0			0
$309$	−2.62051			−0.149076
$310$		0			0
$311$	−2.87815	+	2.87815i	−0.163205	+	0.163205i	−0.783985	−	0.620780i	$-0.786816\pi$
$311$	−2.87815	+	2.87815i	−0.163205	+	0.163205i	0.620780	+	0.783985i	$0.286816\pi$
$312$		0			0
$313$	−13.0365	−	13.0365i	−0.736869	−	0.736869i	0.235102	−	0.971971i	$-0.424458\pi$
$313$	−13.0365	−	13.0365i	−0.736869	−	0.736869i	−0.971971	+	0.235102i	$0.924458\pi$
$314$		0			0
$315$	−0.0721599	−	0.0721599i	−0.00406575	−	0.00406575i
$316$		0			0
$317$	23.1467			1.30005			0.650024	−	0.759913i	$-0.274759\pi$
$317$	23.1467			1.30005			0.650024	+	0.759913i	$0.274759\pi$
$318$		0			0
$319$	23.9870			1.34301
$320$		0			0
$321$			17.4122i			0.971853i
$322$		0			0
$323$	8.33367	+	5.37522i	0.463698	+	0.299085i
$324$		0			0
$325$	−20.6242	−	20.6242i	−1.14403	−	1.14403i
$326$		0			0
$327$		−	17.1427i		−	0.947991i
$328$		0			0
$329$	−7.32386	−	7.32386i	−0.403778	−	0.403778i
$330$		0			0
$331$	−23.0392	−	23.0392i	−1.26635	−	1.26635i	−0.947960	−	0.318390i	$-0.896858\pi$
$331$	−23.0392	−	23.0392i	−1.26635	−	1.26635i	−0.318390	−	0.947960i	$-0.603142\pi$
$332$		0			0
$333$	−0.739986			−0.0405510
$334$		0			0
$335$	−0.0792144	−	0.0792144i	−0.00432795	−	0.00432795i
$336$		0			0
$337$	−5.14335	−	5.14335i	−0.280176	−	0.280176i	0.553003	−	0.833179i	$-0.313482\pi$
$337$	−5.14335	−	5.14335i	−0.280176	−	0.280176i	−0.833179	+	0.553003i	$0.813482\pi$
$338$		0			0
$339$	−22.8640	−	22.8640i	−1.24180	−	1.24180i
$340$		0			0
$341$	−29.1676	+	29.1676i	−1.57951	+	1.57951i
$342$		0			0
$343$	−9.22821	+	9.22821i	−0.498277	+	0.498277i
$344$		0			0
$345$	4.58265	−	4.58265i	0.246722	−	0.246722i
$346$		0			0
$347$		−	5.49772i		−	0.295133i	−0.989052	−	0.147566i	$-0.952856\pi$
$347$		−	5.49772i		−	0.295133i	0.989052	−	0.147566i	$-0.0471440\pi$
$348$		0			0
$349$	4.24654	−	4.24654i	0.227312	−	0.227312i	−0.584257	−	0.811569i	$-0.698614\pi$
$349$	4.24654	−	4.24654i	0.227312	−	0.227312i	0.811569	+	0.584257i	$0.198614\pi$
$350$		0			0
$351$	24.0458	−	24.0458i	1.28347	−	1.28347i
$352$		0			0
$353$	33.2789			1.77126			0.885629	−	0.464394i	$-0.153728\pi$
$353$	33.2789			1.77126			0.885629	+	0.464394i	$0.153728\pi$
$354$		0			0
$355$	−3.57949	+	3.57949i	−0.189979	+	0.189979i
$356$		0			0
$357$	−5.87249	−	3.78776i	−0.310805	−	0.200469i
$358$		0			0
$359$	18.0559			0.952956			0.476478	−	0.879186i	$-0.341913\pi$
$359$	18.0559			0.952956			0.476478	+	0.879186i	$0.341913\pi$
$360$		0			0
$361$			13.2151i			0.695532i
$362$		0			0
$363$			15.0126i			0.787959i
$364$		0			0
$365$	−1.68594	+	1.68594i	−0.0882463	+	0.0882463i
$366$		0			0
$367$	0.532226	−	0.532226i	0.0277820	−	0.0277820i	−0.693079	−	0.720861i	$-0.743746\pi$
$367$	0.532226	−	0.532226i	0.0277820	−	0.0277820i	0.720861	+	0.693079i	$0.243746\pi$
$368$		0			0
$369$	0.0991841	+	0.0991841i	0.00516332	+	0.00516332i
$370$		0			0
$371$		−	2.16490i		−	0.112396i
$372$		0			0
$373$	19.9705	−	19.9705i	1.03404	−	1.03404i	0.0346355	−	0.999400i	$-0.488973\pi$
$373$	19.9705	−	19.9705i	1.03404	−	1.03404i	0.999400	−	0.0346355i	$-0.0110270\pi$
$374$		0			0
$375$			10.6590i			0.550427i
$376$		0			0
$377$	24.3018	−	24.3018i	1.25160	−	1.25160i
$378$		0			0
$379$	21.4630			1.10248			0.551239	−	0.834347i	$-0.314155\pi$
$379$	21.4630			1.10248			0.551239	+	0.834347i	$0.314155\pi$
$380$		0			0
$381$	2.27617			0.116612
$382$		0			0
$383$			5.67078i			0.289763i	0.989449	+	0.144882i	$0.0462801\pi$
$383$			5.67078i			0.289763i	−0.989449	+	0.144882i	$0.953720\pi$
$384$		0			0
$385$	2.09341	−	2.09341i	0.106690	−	0.106690i
$386$		0			0
$387$	−1.11236	−	1.11236i	−0.0565445	−	0.0565445i
$388$		0			0
$389$	4.86412	+	4.86412i	0.246621	+	0.246621i	0.819582	−	0.572961i	$-0.194206\pi$
$389$	4.86412	+	4.86412i	0.246621	+	0.246621i	−0.572961	+	0.819582i	$0.694206\pi$
$390$		0			0
$391$	−12.9953	+	20.1477i	−0.657199	+	1.01891i
$392$		0			0
$393$	14.2608			0.719365
$394$		0			0
$395$	1.84456	−	1.84456i	0.0928097	−	0.0928097i
$396$		0			0
$397$	−38.0559			−1.90997			−0.954985	−	0.296655i	$-0.904129\pi$
$397$	−38.0559			−1.90997			−0.954985	+	0.296655i	$0.904129\pi$
$398$		0			0
$399$			4.07644i			0.204077i
$400$		0			0
$401$	19.2352	−	19.2352i	0.960562	−	0.960562i	−0.0386895	−	0.999251i	$-0.512318\pi$
$401$	19.2352	−	19.2352i	0.960562	−	0.960562i	0.999251	+	0.0386895i	$0.0123183\pi$
$402$		0			0
$403$			59.1008i			2.94402i
$404$		0			0
$405$	−5.62533			−0.279525
$406$		0			0
$407$		−	21.4675i		−	1.06410i
$408$		0			0
$409$			25.5142i			1.26160i	0.775946	+	0.630799i	$0.217273\pi$
$409$			25.5142i			1.26160i	−0.775946	+	0.630799i	$0.782727\pi$
$410$		0			0
$411$	−23.8733			−1.17758
$412$		0			0
$413$			7.29595i			0.359010i
$414$		0			0
$415$	1.72195	−	1.72195i	0.0845272	−	0.0845272i
$416$		0			0
$417$		−	5.21191i		−	0.255229i
$418$		0			0
$419$	0.951368			0.0464774			0.0232387	−	0.999730i	$-0.492602\pi$
$419$	0.951368			0.0464774			0.0232387	+	0.999730i	$0.492602\pi$
$420$		0			0
$421$	−1.63456	+	1.63456i	−0.0796638	+	0.0796638i	−0.745816	−	0.666152i	$-0.767940\pi$
$421$	−1.63456	+	1.63456i	−0.0796638	+	0.0796638i	0.666152	+	0.745816i	$0.267940\pi$
$422$		0			0
$423$	1.58530			0.0770797
$424$		0			0
$425$	−3.96924	−	18.3926i	−0.192536	−	0.892174i
$426$		0			0
$427$	1.59002	+	1.59002i	0.0769465	+	0.0769465i
$428$		0			0
$429$	34.0111	+	34.0111i	1.64207	+	1.64207i
$430$		0			0
$431$	9.72576	−	9.72576i	0.468473	−	0.468473i	−0.432946	−	0.901420i	$-0.642526\pi$
$431$	9.72576	−	9.72576i	0.468473	−	0.468473i	0.901420	+	0.432946i	$0.142526\pi$
$432$		0			0
$433$		−	33.1400i		−	1.59260i	−0.604899	−	0.796302i	$-0.706786\pi$
$433$		−	33.1400i		−	1.59260i	0.604899	−	0.796302i	$-0.293214\pi$
$434$		0			0
$435$	−5.99320			−0.287352
$436$		0			0
$437$	13.9857			0.669027
$438$		0			0
$439$	−18.6911	+	18.6911i	−0.892077	+	0.892077i	−0.994718	−	0.102642i	$-0.967270\pi$
$439$	−18.6911	+	18.6911i	−0.892077	+	0.892077i	0.102642	+	0.994718i	$0.467270\pi$
$440$		0			0
$441$		−	0.921159i		−	0.0438647i
$442$		0			0
$443$	6.54839	−	6.54839i	0.311123	−	0.311123i	−0.534221	−	0.845345i	$-0.679395\pi$
$443$	6.54839	−	6.54839i	0.311123	−	0.311123i	0.845345	+	0.534221i	$0.179395\pi$
$444$		0			0
$445$			8.39661i			0.398037i
$446$		0			0
$447$	−14.6500	−	14.6500i	−0.692919	−	0.692919i
$448$		0			0
$449$	−14.1132	+	14.1132i	−0.666045	+	0.666045i	−0.956798	−	0.290753i	$-0.906094\pi$
$449$	−14.1132	+	14.1132i	−0.666045	+	0.666045i	0.290753	+	0.956798i	$0.406094\pi$
$450$		0			0
$451$	−2.87740	+	2.87740i	−0.135491	+	0.135491i
$452$		0			0
$453$		−	22.1076i		−	1.03870i
$454$		0			0
$455$		−	4.24176i		−	0.198857i
$456$		0			0
$457$	12.3725			0.578763			0.289382	−	0.957214i	$-0.406550\pi$
$457$	12.3725			0.578763			0.289382	+	0.957214i	$0.406550\pi$
$458$		0			0
$459$	21.4439	−	4.62772i	1.00092	−	0.216004i
$460$		0			0
$461$	−3.00912	+	3.00912i	−0.140149	+	0.140149i	−0.773700	−	0.633552i	$-0.781596\pi$
$461$	−3.00912	+	3.00912i	−0.140149	+	0.140149i	0.633552	+	0.773700i	$0.281596\pi$
$462$		0			0
$463$	−13.4812			−0.626526			−0.313263	−	0.949666i	$-0.601422\pi$
$463$	−13.4812			−0.626526			−0.313263	+	0.949666i	$0.601422\pi$
$464$		0			0
$465$	7.28760	−	7.28760i	0.337954	−	0.337954i
$466$		0			0
$467$	26.9533	−	26.9533i	1.24725	−	1.24725i	0.290318	−	0.956930i	$-0.406239\pi$
$467$	26.9533	−	26.9533i	1.24725	−	1.24725i	0.956930	−	0.290318i	$-0.0937611\pi$
$468$		0			0
$469$			0.170356i			0.00786632i
$470$		0			0
$471$	−14.4382	+	14.4382i	−0.665278	+	0.665278i
$472$		0			0
$473$	32.2704	−	32.2704i	1.48379	−	1.48379i
$474$		0			0
$475$	−7.76134	+	7.76134i	−0.356115	+	0.356115i
$476$		0			0
$477$	0.234303	+	0.234303i	0.0107280	+	0.0107280i
$478$		0			0
$479$	10.1712	+	10.1712i	0.464736	+	0.464736i	0.900204	−	0.435468i	$-0.143417\pi$
$479$	10.1712	+	10.1712i	0.464736	+	0.464736i	−0.435468	+	0.900204i	$0.643417\pi$
$480$		0			0
$481$	−21.7492	−	21.7492i	−0.991680	−	0.991680i
$482$		0			0
$483$	−9.85531			−0.448432
$484$		0			0
$485$	2.93038	+	2.93038i	0.133062	+	0.133062i
$486$		0			0
$487$	−2.70291	−	2.70291i	−0.122481	−	0.122481i	0.643210	−	0.765690i	$-0.277602\pi$
$487$	−2.70291	−	2.70291i	−0.122481	−	0.122481i	−0.765690	+	0.643210i	$0.777602\pi$
$488$		0			0
$489$			5.22940i			0.236482i
$490$		0			0
$491$	10.4721	+	10.4721i	0.472597	+	0.472597i	0.902754	−	0.430157i	$-0.141542\pi$
$491$	10.4721	+	10.4721i	0.472597	+	0.472597i	−0.430157	+	0.902754i	$0.641542\pi$
$492$		0			0
$493$	21.6722	−	4.67699i	0.976069	−	0.210641i
$494$		0			0
$495$			0.453131i			0.0203667i
$496$		0			0
$497$	7.69794			0.345300
$498$		0			0
$499$	−2.05944			−0.0921930			−0.0460965	−	0.998937i	$-0.514678\pi$
$499$	−2.05944			−0.0921930			−0.0460965	+	0.998937i	$0.514678\pi$
$500$		0			0
$501$	−16.0564	−	16.0564i	−0.717349	−	0.717349i
$502$		0			0
$503$	18.7589	+	18.7589i	0.836419	+	0.836419i	0.988386	−	0.151966i	$-0.0485606\pi$
$503$	18.7589	+	18.7589i	0.836419	+	0.836419i	−0.151966	+	0.988386i	$0.548561\pi$
$504$		0			0
$505$	3.27457	−	3.27457i	0.145717	−	0.145717i
$506$		0			0
$507$	46.9829			2.08658
$508$		0			0
$509$	−14.7964	−	14.7964i	−0.655838	−	0.655838i	0.298555	−	0.954392i	$-0.403495\pi$
$509$	−14.7964	−	14.7964i	−0.655838	−	0.655838i	−0.954392	+	0.298555i	$0.903495\pi$
$510$		0			0
$511$	3.62574			0.160393
$512$		0			0
$513$	−9.04893	−	9.04893i	−0.399520	−	0.399520i
$514$		0			0
$515$		−	1.02615i		−	0.0452175i
$516$		0			0
$517$			45.9905i			2.02266i
$518$		0			0
$519$	−17.5777			−0.771577
$520$		0			0
$521$	1.74504	+	1.74504i	0.0764518	+	0.0764518i	0.744299	−	0.667847i	$-0.232784\pi$
$521$	1.74504	+	1.74504i	0.0764518	+	0.0764518i	−0.667847	+	0.744299i	$0.732784\pi$
$522$		0			0
$523$	−13.8349	+	13.8349i	−0.604957	+	0.604957i	−0.941624	−	0.336667i	$-0.890700\pi$
$523$	−13.8349	+	13.8349i	−0.604957	+	0.604957i	0.336667	+	0.941624i	$0.390700\pi$
$524$		0			0
$525$	5.46919	−	5.46919i	0.238695	−	0.238695i
$526$		0			0
$527$	−20.6658	+	32.0401i	−0.900218	+	1.39569i
$528$		0			0
$529$			10.8122i			0.470095i
$530$		0			0
$531$	−0.789627	−	0.789627i	−0.0342669	−	0.0342669i
$532$		0			0
$533$			5.83032i			0.252539i
$534$		0			0
$535$	−6.81832			−0.294782
$536$		0			0
$537$	14.9443	+	14.9443i	0.644893	+	0.644893i
$538$		0			0
$539$	26.7235			1.15106
$540$		0			0
$541$			40.8382i			1.75577i	0.478871	+	0.877885i	$0.341046\pi$
$541$			40.8382i			1.75577i	−0.478871	+	0.877885i	$0.658954\pi$
$542$		0			0
$543$	25.2941			1.08547
$544$		0			0
$545$	6.71278			0.287544
$546$		0			0
$547$			13.1513i			0.562307i	0.959663	+	0.281153i	$0.0907170\pi$
$547$			13.1513i			0.562307i	−0.959663	+	0.281153i	$0.909283\pi$
$548$		0			0
$549$	−0.344170			−0.0146888
$550$		0			0
$551$	−9.14527	−	9.14527i	−0.389601	−	0.389601i
$552$		0			0
$553$	−3.96685			−0.168687
$554$		0			0
$555$			5.36371i			0.227677i
$556$		0			0
$557$	−6.65668	−	6.65668i	−0.282053	−	0.282053i	0.551875	−	0.833927i	$-0.313913\pi$
$557$	−6.65668	−	6.65668i	−0.282053	−	0.282053i	−0.833927	+	0.551875i	$0.813913\pi$
$558$		0			0
$559$		−	65.3878i		−	2.76561i
$560$		0			0
$561$	6.54560	+	30.3310i	0.276355	+	1.28058i
$562$		0			0
$563$	−25.0477	+	25.0477i	−1.05563	+	1.05563i	−0.0572764	+	0.998358i	$0.518242\pi$
$563$	−25.0477	+	25.0477i	−1.05563	+	1.05563i	−0.998358	+	0.0572764i	$0.981758\pi$
$564$		0			0
$565$	8.95318	−	8.95318i	0.376663	−	0.376663i
$566$		0			0
$567$	6.04883	+	6.04883i	0.254027	+	0.254027i
$568$		0			0
$569$	−3.58046			−0.150100			−0.0750502	−	0.997180i	$-0.523912\pi$
$569$	−3.58046			−0.150100			−0.0750502	+	0.997180i	$0.523912\pi$
$570$		0			0
$571$		−	14.2299i		−	0.595502i	−0.954644	−	0.297751i	$-0.903764\pi$
$571$		−	14.2299i		−	0.595502i	0.954644	−	0.297751i	$-0.0962365\pi$
$572$		0			0
$573$			16.3785i			0.684221i
$574$		0			0
$575$	−18.7640	−	18.7640i	−0.782514	−	0.782514i
$576$		0			0
$577$	−0.566677			−0.0235911			−0.0117955	−	0.999930i	$-0.503755\pi$
$577$	−0.566677			−0.0235911			−0.0117955	+	0.999930i	$0.503755\pi$
$578$		0			0
$579$	27.1209	+	27.1209i	1.12711	+	1.12711i
$580$		0			0
$581$	−3.70317			−0.153634
$582$		0			0
$583$	−6.79728	+	6.79728i	−0.281515	+	0.281515i
$584$		0			0
$585$	0.459078	+	0.459078i	0.0189805	+	0.0189805i
$586$		0			0
$587$	7.30229	+	7.30229i	0.301398	+	0.301398i	0.841560	−	0.540163i	$-0.181637\pi$
$587$	7.30229	+	7.30229i	0.301398	+	0.301398i	−0.540163	+	0.841560i	$0.681637\pi$
$588$		0			0
$589$	22.2409			0.916419
$590$		0			0
$591$	36.1017			1.48502
$592$		0			0
$593$		−	4.53761i		−	0.186337i	−0.995650	−	0.0931686i	$-0.970300\pi$
$593$		−	4.53761i		−	0.186337i	0.995650	−	0.0931686i	$-0.0296996\pi$
$594$		0			0
$595$	1.48322	−	2.29957i	0.0608062	−	0.0942732i
$596$		0			0
$597$	16.5631	+	16.5631i	0.677881	+	0.677881i
$598$		0			0
$599$		−	3.03305i		−	0.123927i	−0.998078	−	0.0619636i	$-0.980264\pi$
$599$		−	3.03305i		−	0.123927i	0.998078	−	0.0619636i	$-0.0197363\pi$
$600$		0			0
$601$	3.46382	+	3.46382i	0.141292	+	0.141292i	0.774215	−	0.632923i	$-0.218145\pi$
$601$	3.46382	+	3.46382i	0.141292	+	0.141292i	−0.632923	+	0.774215i	$0.718145\pi$
$602$		0			0
$603$	−0.0184373	−	0.0184373i	−0.000750826	−	0.000750826i
$604$		0			0
$605$	−5.87870			−0.239003
$606$		0			0
$607$	−1.57808	−	1.57808i	−0.0640523	−	0.0640523i	0.674355	−	0.738407i	$-0.264422\pi$
$607$	−1.57808	−	1.57808i	−0.0640523	−	0.0640523i	−0.738407	+	0.674355i	$0.764422\pi$
$608$		0			0
$609$	6.44440	+	6.44440i	0.261140	+	0.261140i
$610$		0			0
$611$	46.5941	+	46.5941i	1.88500	+	1.88500i
$612$		0			0
$613$	33.2321	−	33.2321i	1.34223	−	1.34223i	0.448400	−	0.893833i	$-0.351994\pi$
$613$	33.2321	−	33.2321i	1.34223	−	1.34223i	0.893833	−	0.448400i	$-0.148006\pi$
$614$		0			0
$615$	0.718926	−	0.718926i	0.0289899	−	0.0289899i
$616$		0			0
$617$	−6.47600	+	6.47600i	−0.260714	+	0.260714i	−0.825344	−	0.564630i	$-0.809019\pi$
$617$	−6.47600	+	6.47600i	−0.260714	+	0.260714i	0.564630	+	0.825344i	$0.309019\pi$
$618$		0			0
$619$		−	8.60581i		−	0.345897i	−0.984931	−	0.172948i	$-0.944671\pi$
$619$		−	8.60581i		−	0.345897i	0.984931	−	0.172948i	$-0.0553294\pi$
$620$		0			0
$621$	21.8769	−	21.8769i	0.877891	−	0.877891i
$622$		0			0
$623$	9.02874	−	9.02874i	0.361729	−	0.361729i
$624$		0			0
$625$	18.6440			0.745758
$626$		0			0
$627$	12.7991	−	12.7991i	0.511147	−	0.511147i
$628$		0			0
$629$	−4.18575	−	19.3959i	−0.166897	−	0.773366i
$630$		0			0
$631$	−2.17744			−0.0866824			−0.0433412	−	0.999060i	$-0.513800\pi$
$631$	−2.17744			−0.0866824			−0.0433412	+	0.999060i	$0.513800\pi$
$632$		0			0
$633$			28.4657i			1.13141i
$634$		0			0
$635$			0.891310i			0.0353705i
$636$		0			0
$637$	27.0742	−	27.0742i	1.07272	−	1.07272i
$638$		0			0
$639$	−0.833133	+	0.833133i	−0.0329582	+	0.0329582i
$640$		0			0
$641$	−17.4848	−	17.4848i	−0.690607	−	0.690607i	0.271759	−	0.962365i	$-0.412395\pi$
$641$	−17.4848	−	17.4848i	−0.690607	−	0.690607i	−0.962365	+	0.271759i	$0.912395\pi$
$642$		0			0
$643$		−	41.6732i		−	1.64343i	−0.569900	−	0.821714i	$-0.693018\pi$
$643$		−	41.6732i		−	1.64343i	0.569900	−	0.821714i	$-0.306982\pi$
$644$		0			0
$645$	−8.06284	+	8.06284i	−0.317474	+	0.317474i
$646$		0			0
$647$		−	45.4306i		−	1.78606i	−0.449997	−	0.893030i	$-0.648575\pi$
$647$		−	45.4306i		−	1.78606i	0.449997	−	0.893030i	$-0.351425\pi$
$648$		0			0
$649$	22.9076	−	22.9076i	0.899203	−	0.899203i
$650$		0			0
$651$	−15.6725			−0.614253
$652$		0			0
$653$	−46.2114			−1.80839			−0.904195	−	0.427120i	$-0.859528\pi$
$653$	−46.2114			−1.80839			−0.904195	+	0.427120i	$0.859528\pi$
$654$		0			0
$655$			5.58431i			0.218197i
$656$		0			0
$657$	−0.392407	+	0.392407i	−0.0153092	+	0.0153092i
$658$		0			0
$659$	20.2503	+	20.2503i	0.788841	+	0.788841i	0.981304	−	0.192463i	$-0.0616475\pi$
$659$	20.2503	+	20.2503i	0.788841	+	0.788841i	−0.192463	+	0.981304i	$0.561647\pi$
$660$		0			0
$661$	−26.8431	−	26.8431i	−1.04408	−	1.04408i	−0.998983	−	0.0450926i	$-0.985642\pi$
$661$	−26.8431	−	26.8431i	−1.04408	−	1.04408i	−0.0450926	−	0.998983i	$-0.514358\pi$
$662$		0			0
$663$	37.3606	+	24.0976i	1.45096	+	0.935871i
$664$		0			0
$665$	−1.59627			−0.0619005
$666$		0			0
$667$	22.1098	−	22.1098i	0.856096	−	0.856096i
$668$		0			0
$669$	−17.2738			−0.667844
$670$		0			0
$671$		−	9.98461i		−	0.385451i
$672$		0			0
$673$	7.78102	−	7.78102i	0.299936	−	0.299936i	−0.541053	−	0.840989i	$-0.681974\pi$
$673$	7.78102	−	7.78102i	0.299936	−	0.299936i	0.840989	+	0.541053i	$0.181974\pi$
$674$		0			0
$675$			24.2811i			0.934581i
$676$		0			0
$677$	1.36144			0.0523244			0.0261622	−	0.999658i	$-0.491671\pi$
$677$	1.36144			0.0523244			0.0261622	+	0.999658i	$0.491671\pi$
$678$		0			0
$679$		−	6.30198i		−	0.241848i
$680$		0			0
$681$		−	31.0372i		−	1.18935i
$682$		0			0
$683$	−20.1014			−0.769158			−0.384579	−	0.923092i	$-0.625653\pi$
$683$	−20.1014			−0.769158			−0.384579	+	0.923092i	$0.625653\pi$
$684$		0			0
$685$		−	9.34837i		−	0.357183i
$686$		0			0
$687$	−28.6377	+	28.6377i	−1.09260	+	1.09260i
$688$		0			0
$689$			13.7730i			0.524709i
$690$		0			0
$691$	−24.8161			−0.944048			−0.472024	−	0.881586i	$-0.656476\pi$
$691$	−24.8161			−0.944048			−0.472024	+	0.881586i	$0.656476\pi$
$692$		0			0
$693$	0.487245	−	0.487245i	0.0185089	−	0.0185089i
$694$		0			0
$695$	2.04090			0.0774157
$696$		0			0
$697$	−2.03870	+	3.16077i	−0.0772211	+	0.119723i
$698$		0			0
$699$	−7.93105	−	7.93105i	−0.299980	−	0.299980i
$700$		0			0
$701$	5.15361	+	5.15361i	0.194649	+	0.194649i	0.797702	−	0.603052i	$-0.206049\pi$
$701$	5.15361	+	5.15361i	0.194649	+	0.194649i	−0.603052	+	0.797702i	$0.706049\pi$
$702$		0			0
$703$	−8.18470	+	8.18470i	−0.308692	+	0.308692i
$704$		0			0
$705$		−	11.4909i		−	0.432770i
$706$		0			0
$707$	−7.04220			−0.264849
$708$		0			0
$709$	−0.233300			−0.00876175			−0.00438088	−	0.999990i	$-0.501394\pi$
$709$	−0.233300			−0.00876175			−0.00438088	+	0.999990i	$0.501394\pi$
$710$		0			0
$711$	0.429324	−	0.429324i	0.0161009	−	0.0161009i
$712$		0			0
$713$			53.7701i			2.01371i
$714$		0			0
$715$	−13.3182	+	13.3182i	−0.498072	+	0.498072i
$716$		0			0
$717$			20.0985i			0.750590i
$718$		0			0
$719$	2.05800	+	2.05800i	0.0767506	+	0.0767506i	0.744440	−	0.667689i	$-0.232717\pi$
$719$	2.05800	+	2.05800i	0.0767506	+	0.0767506i	−0.667689	+	0.744440i	$0.732717\pi$
$720$		0			0
$721$	−1.10340	+	1.10340i	−0.0410928	+	0.0410928i
$722$		0			0
$723$	4.47662	−	4.47662i	0.166487	−	0.166487i
$724$		0			0
$725$			24.5396i			0.911379i
$726$		0			0
$727$			5.59376i			0.207461i	0.994605	+	0.103730i	$0.0330779\pi$
$727$			5.59376i			0.207461i	−0.994605	+	0.103730i	$0.966922\pi$
$728$		0			0
$729$	−28.2384			−1.04587
$730$		0			0
$731$	22.8642	−	35.4484i	0.845664	−	1.31111i
$732$		0			0
$733$	−7.89935	+	7.89935i	−0.291769	+	0.291769i	−0.837779	−	0.546010i	$-0.816146\pi$
$733$	−7.89935	+	7.89935i	−0.291769	+	0.291769i	0.546010	+	0.837779i	$0.316146\pi$
$734$		0			0
$735$	−6.67693			−0.246282
$736$		0			0
$737$	0.534880	−	0.534880i	0.0197025	−	0.0197025i
$738$		0			0
$739$	26.5112	−	26.5112i	0.975230	−	0.975230i	−0.0244710	−	0.999701i	$-0.507790\pi$
$739$	26.5112	−	26.5112i	0.975230	−	0.975230i	0.999701	+	0.0244710i	$0.00779015\pi$
$740$		0			0
$741$		−	25.9341i		−	0.952714i
$742$		0			0
$743$	8.50256	−	8.50256i	0.311929	−	0.311929i	−0.533728	−	0.845656i	$-0.679209\pi$
$743$	8.50256	−	8.50256i	0.311929	−	0.311929i	0.845656	+	0.533728i	$0.179209\pi$
$744$		0			0
$745$	5.73668	−	5.73668i	0.210176	−	0.210176i
$746$		0			0
$747$	0.400787	−	0.400787i	0.0146640	−	0.0146640i
$748$		0			0
$749$	7.33163	+	7.33163i	0.267892	+	0.267892i
$750$		0			0
$751$	−17.8058	−	17.8058i	−0.649744	−	0.649744i	0.303187	−	0.952931i	$-0.401949\pi$
$751$	−17.8058	−	17.8058i	−0.649744	−	0.649744i	−0.952931	+	0.303187i	$0.901949\pi$
$752$		0			0
$753$	−13.1832	−	13.1832i	−0.480422	−	0.480422i
$754$		0			0
$755$	8.65695			0.315059
$756$		0			0
$757$	8.53855	+	8.53855i	0.310339	+	0.310339i	0.845041	−	0.534702i	$-0.179576\pi$
$757$	8.53855	+	8.53855i	0.310339	+	0.310339i	−0.534702	+	0.845041i	$0.679576\pi$
$758$		0			0
$759$	30.9434	+	30.9434i	1.12318	+	1.12318i
$760$		0			0
$761$			48.2997i			1.75086i	0.483343	+	0.875431i	$0.339423\pi$
$761$			48.2997i			1.75086i	−0.483343	+	0.875431i	$0.660577\pi$
$762$		0			0
$763$	−7.21815	−	7.21815i	−0.261314	−	0.261314i
$764$		0			0
$765$	0.0883518	+	0.409405i	0.00319437	+	0.0148021i
$766$		0			0
$767$		−	46.4165i		−	1.67600i
$768$		0			0
$769$	20.3258			0.732966			0.366483	−	0.930425i	$-0.380562\pi$
$769$	20.3258			0.732966			0.366483	+	0.930425i	$0.380562\pi$
$770$		0			0
$771$	−37.3503			−1.34514
$772$		0			0
$773$	2.54123	+	2.54123i	0.0914017	+	0.0914017i	0.751329	−	0.659928i	$-0.229413\pi$
$773$	2.54123	+	2.54123i	0.0914017	+	0.0914017i	−0.659928	+	0.751329i	$0.729413\pi$
$774$		0			0
$775$	−29.8396	−	29.8396i	−1.07187	−	1.07187i
$776$		0			0
$777$	5.76752	−	5.76752i	0.206909	−	0.206909i
$778$		0			0
$779$	2.19407			0.0786109
$780$		0			0
$781$	−24.1698	−	24.1698i	−0.864862	−	0.864862i
$782$		0			0
$783$	−28.6107			−1.02246
$784$		0			0
$785$	−5.65376	−	5.65376i	−0.201791	−	0.201791i
$786$		0			0
$787$			2.46137i			0.0877384i	0.999037	+	0.0438692i	$0.0139685\pi$
$787$			2.46137i			0.0877384i	−0.999037	+	0.0438692i	$0.986032\pi$
$788$		0			0
$789$			10.3459i			0.368323i
$790$		0			0
$791$	−19.2544			−0.684609
$792$		0			0
$793$	−10.1156	−	10.1156i	−0.359217	−	0.359217i
$794$		0			0
$795$	1.69832	−	1.69832i	0.0602331	−	0.0602331i
$796$		0			0
$797$	11.1955	−	11.1955i	0.396565	−	0.396565i	−0.480455	−	0.877019i	$-0.659528\pi$
$797$	11.1955	−	11.1955i	0.396565	−	0.396565i	0.877019	+	0.480455i	$0.159528\pi$
$798$		0			0
$799$	8.96726	+	41.5525i	0.317239	+	1.47002i
$800$		0			0
$801$			1.95433i			0.0690527i
$802$		0			0
$803$	−11.3840	−	11.3840i	−0.401732	−	0.401732i
$804$		0			0
$805$		−	3.85917i		−	0.136018i
$806$		0			0
$807$	6.96947			0.245337
$808$		0			0
$809$	−26.2205	−	26.2205i	−0.921863	−	0.921863i	0.0752979	−	0.997161i	$-0.476009\pi$
$809$	−26.2205	−	26.2205i	−0.921863	−	0.921863i	−0.997161	+	0.0752979i	$0.976009\pi$
$810$		0			0
$811$	2.01203			0.0706518			0.0353259	−	0.999376i	$-0.488753\pi$
$811$	2.01203			0.0706518			0.0353259	+	0.999376i	$0.488753\pi$
$812$		0			0
$813$			44.6364i			1.56547i
$814$		0			0
$815$	−2.04775			−0.0717294
$816$		0			0
$817$	−24.6068			−0.860884
$818$		0			0
$819$		−	0.987279i		−	0.0344983i
$820$		0			0
$821$	3.62789			0.126614			0.0633071	−	0.997994i	$-0.479835\pi$
$821$	3.62789			0.126614			0.0633071	+	0.997994i	$0.479835\pi$
$822$		0			0
$823$	31.0177	+	31.0177i	1.08121	+	1.08121i	0.996397	+	0.0848124i	$0.0270291\pi$
$823$	31.0177	+	31.0177i	1.08121	+	1.08121i	0.0848124	+	0.996397i	$0.472971\pi$
$824$		0			0
$825$	−34.3440			−1.19570
$826$		0			0
$827$			8.06566i			0.280470i	0.990118	+	0.140235i	$0.0447859\pi$
$827$			8.06566i			0.280470i	−0.990118	+	0.140235i	$0.955214\pi$
$828$		0			0
$829$	11.3489	+	11.3489i	0.394163	+	0.394163i	0.876168	−	0.482005i	$-0.160091\pi$
$829$	11.3489	+	11.3489i	0.394163	+	0.394163i	−0.482005	+	0.876168i	$0.660091\pi$
$830$		0			0
$831$		−	5.04207i		−	0.174907i
$832$		0			0
$833$	24.1447	−	5.21056i	0.836564	−	0.180535i
$834$		0			0
$835$	6.28743	−	6.28743i	0.217586	−	0.217586i
$836$		0			0
$837$	34.7900	−	34.7900i	1.20252	−	1.20252i
$838$		0			0
$839$	−36.1477	−	36.1477i	−1.24796	−	1.24796i	−0.956621	−	0.291334i	$-0.905901\pi$
$839$	−36.1477	−	36.1477i	−1.24796	−	1.24796i	−0.291334	−	0.956621i	$-0.594099\pi$
$840$		0			0
$841$	0.0846922			0.00292042
$842$		0			0
$843$			21.4295i			0.738071i
$844$		0			0
$845$			18.3977i			0.632901i
$846$		0			0
$847$	6.32127	+	6.32127i	0.217202	+	0.217202i
$848$		0			0
$849$	−13.9654			−0.479292
$850$		0			0
$851$	−19.7875	−	19.7875i	−0.678308	−	0.678308i
$852$		0			0
$853$	−32.4377			−1.11064			−0.555322	−	0.831635i	$-0.687405\pi$
$853$	−32.4377			−1.11064			−0.555322	+	0.831635i	$0.687405\pi$
$854$		0			0
$855$	0.172761	−	0.172761i	0.00590830	−	0.00590830i
$856$		0			0
$857$	−3.19873	−	3.19873i	−0.109267	−	0.109267i	0.650360	−	0.759626i	$-0.274618\pi$
$857$	−3.19873	−	3.19873i	−0.109267	−	0.109267i	−0.759626	+	0.650360i	$0.774618\pi$
$858$		0			0
$859$	−3.73081	−	3.73081i	−0.127294	−	0.127294i	0.640590	−	0.767883i	$-0.278690\pi$
$859$	−3.73081	−	3.73081i	−0.127294	−	0.127294i	−0.767883	+	0.640590i	$0.778690\pi$
$860$		0			0
$861$	−1.54610			−0.0526909
$862$		0			0
$863$	10.1542			0.345653			0.172827	−	0.984952i	$-0.444710\pi$
$863$	10.1542			0.345653			0.172827	+	0.984952i	$0.444710\pi$
$864$		0			0
$865$		−	6.88315i		−	0.234034i
$866$		0			0
$867$	11.8279	+	26.1278i	0.401697	+	0.887347i
$868$		0			0
$869$	12.4550	+	12.4550i	0.422507	+	0.422507i
$870$		0			0
$871$		−	1.08380i		−	0.0367231i
$872$		0			0
$873$	0.682051	+	0.682051i	0.0230839	+	0.0230839i
$874$		0			0
$875$	4.48810	+	4.48810i	0.151725	+	0.151725i
$876$		0			0
$877$	−23.4025			−0.790246			−0.395123	−	0.918628i	$-0.629298\pi$
$877$	−23.4025			−0.790246			−0.395123	+	0.918628i	$0.629298\pi$
$878$		0			0
$879$	6.72821	+	6.72821i	0.226937	+	0.226937i
$880$		0			0
$881$	−18.8306	−	18.8306i	−0.634418	−	0.634418i	0.314755	−	0.949173i	$-0.398078\pi$
$881$	−18.8306	−	18.8306i	−0.634418	−	0.634418i	−0.949173	+	0.314755i	$0.898078\pi$
$882$		0			0
$883$	−33.3118	−	33.3118i	−1.12103	−	1.12103i	−0.991587	−	0.129446i	$-0.958680\pi$
$883$	−33.3118	−	33.3118i	−1.12103	−	1.12103i	−0.129446	−	0.991587i	$-0.541320\pi$
$884$		0			0
$885$	−5.72353	+	5.72353i	−0.192394	+	0.192394i
$886$		0			0
$887$	19.8243	−	19.8243i	0.665634	−	0.665634i	−0.291068	−	0.956702i	$-0.594011\pi$
$887$	19.8243	−	19.8243i	0.665634	−	0.665634i	0.956702	+	0.291068i	$0.0940108\pi$
$888$		0			0
$889$	0.958411	−	0.958411i	0.0321441	−	0.0321441i
$890$		0			0
$891$		−	37.9839i		−	1.27251i
$892$		0			0
$893$	17.5343	−	17.5343i	0.586764	−	0.586764i
$894$		0			0
$895$	−5.85193	+	5.85193i	−0.195608	+	0.195608i
$896$		0			0
$897$	62.6990			2.09346
$898$		0			0
$899$	35.1604	−	35.1604i	1.17266	−	1.17266i
$900$		0			0
$901$	−4.81601	+	7.46669i	−0.160445	+	0.248751i
$902$		0			0
$903$	17.3397			0.577029
$904$		0			0
$905$			9.90475i			0.329245i
$906$		0			0
$907$			51.6850i			1.71617i	0.513505	+	0.858086i	$0.328347\pi$
$907$			51.6850i			1.71617i	−0.513505	+	0.858086i	$0.671653\pi$
$908$		0			0
$909$	0.762164	−	0.762164i	0.0252794	−	0.0252794i
$910$		0			0
$911$	15.5378	−	15.5378i	0.514790	−	0.514790i	−0.401200	−	0.915990i	$-0.631407\pi$
$911$	15.5378	−	15.5378i	0.514790	−	0.514790i	0.915990	+	0.401200i	$0.131407\pi$
$912$		0			0
$913$	11.6271	+	11.6271i	0.384802	+	0.384802i
$914$		0			0
$915$			2.49468i			0.0824716i
$916$		0			0
$917$	6.00472	−	6.00472i	0.198293	−	0.198293i
$918$		0			0
$919$			12.5941i			0.415442i	0.978188	+	0.207721i	$0.0666047\pi$
$919$			12.5941i			0.415442i	−0.978188	+	0.207721i	$0.933395\pi$
$920$		0			0
$921$	−22.0763	+	22.0763i	−0.727440	+	0.727440i
$922$		0			0
$923$	−48.9739			−1.61200
$924$		0			0
$925$	21.9621			0.722111
$926$		0			0
$927$		−	0.238838i		−	0.00784447i
$928$		0			0
$929$	−8.94445	+	8.94445i	−0.293458	+	0.293458i	−0.838445	−	0.544987i	$-0.816535\pi$
$929$	−8.94445	+	8.94445i	−0.293458	+	0.293458i	0.544987	+	0.838445i	$0.316535\pi$
$930$		0			0
$931$	−10.1886	−	10.1886i	−0.333918	−	0.333918i
$932$		0			0
$933$	4.85567	+	4.85567i	0.158968	+	0.158968i
$934$		0			0
$935$	−11.8771	+	2.56315i	−0.388423	+	0.0838239i
$936$		0			0
$937$	−52.1851			−1.70481			−0.852407	−	0.522879i	$-0.824858\pi$
$937$	−52.1851			−1.70481			−0.852407	+	0.522879i	$0.824858\pi$
$938$		0			0
$939$	−21.9937	+	21.9937i	−0.717736	+	0.717736i
$940$		0			0
$941$	−10.0824			−0.328678			−0.164339	−	0.986404i	$-0.552549\pi$
$941$	−10.0824			−0.328678			−0.164339	+	0.986404i	$0.552549\pi$
$942$		0			0
$943$			5.30445i			0.172737i
$944$		0			0
$945$	−2.49694	+	2.49694i	−0.0812253	+	0.0812253i
$946$		0			0
$947$		−	22.4277i		−	0.728804i	−0.931242	−	0.364402i	$-0.881273\pi$
$947$		−	22.4277i		−	0.728804i	0.931242	−	0.364402i	$-0.118727\pi$
$948$		0			0
$949$	−23.0668			−0.748780
$950$		0			0
$951$		−	39.0503i		−	1.26629i
$952$		0			0
$953$		−	13.1185i		−	0.424950i	−0.977166	−	0.212475i	$-0.931848\pi$
$953$		−	13.1185i		−	0.424950i	0.977166	−	0.212475i	$-0.0681524\pi$
$954$		0			0
$955$	−6.41354			−0.207537
$956$		0			0
$957$		−	40.4679i		−	1.30814i
$958$		0			0
$959$	−10.0522	+	10.0522i	−0.324601	+	0.324601i
$960$		0			0
$961$			54.5084i			1.75833i
$962$		0			0
$963$	−1.58698			−0.0511396
$964$		0			0
$965$	−10.6201	+	10.6201i	−0.341873	+	0.341873i
$966$		0			0
$967$	−1.46198			−0.0470141			−0.0235071	−	0.999724i	$-0.507483\pi$
$967$	−1.46198			−0.0470141			−0.0235071	+	0.999724i	$0.507483\pi$
$968$		0			0
$969$	9.06842	−	14.0596i	0.291320	−	0.451658i
$970$		0			0
$971$	0.458271	+	0.458271i	0.0147066	+	0.0147066i	0.714422	−	0.699715i	$-0.246690\pi$
$971$	0.458271	+	0.458271i	0.0147066	+	0.0147066i	−0.699715	+	0.714422i	$0.746690\pi$
$972$		0			0
$973$	−2.19455	−	2.19455i	−0.0703539	−	0.0703539i
$974$		0			0
$975$	−34.7947	+	34.7947i	−1.11432	+	1.11432i
$976$		0			0
$977$			43.2807i			1.38467i	0.721575	+	0.692336i	$0.243418\pi$
$977$			43.2807i			1.38467i	−0.721575	+	0.692336i	$0.756582\pi$
$978$		0			0
$979$	−56.6964			−1.81202
$980$		0			0
$981$	1.56241			0.0498840
$982$		0			0
$983$	−9.75627	+	9.75627i	−0.311177	+	0.311177i	−0.845365	−	0.534189i	$-0.820617\pi$
$983$	−9.75627	+	9.75627i	−0.311177	+	0.311177i	0.534189	+	0.845365i	$0.320617\pi$
$984$		0			0
$985$			14.1368i			0.450436i
$986$		0			0
$987$	−12.3559	+	12.3559i	−0.393294	+	0.393294i
$988$		0			0
$989$		−	59.4901i		−	1.89167i
$990$		0			0
$991$	9.27317	+	9.27317i	0.294572	+	0.294572i	0.838883	−	0.544311i	$-0.183209\pi$
$991$	9.27317	+	9.27317i	0.294572	+	0.294572i	−0.544311	+	0.838883i	$0.683209\pi$
$992$		0			0
$993$	−38.8690	+	38.8690i	−1.23347	+	1.23347i
$994$		0			0
$995$	−6.48582	+	6.48582i	−0.205614	+	0.205614i
$996$		0			0
$997$			21.1988i			0.671373i	0.941974	+	0.335686i	$0.108968\pi$
$997$			21.1988i			0.671373i	−0.941974	+	0.335686i	$0.891032\pi$
$998$		0			0
$999$			25.6056i			0.810125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.j.a.81.11		68
4.3	odd	2		272.2.j.a.13.26	✓	68
16.5	even	4		1088.2.s.a.625.11		68
16.11	odd	4		272.2.s.a.149.9	yes	68
17.4	even	4		1088.2.s.a.1041.11		68
68.55	odd	4		272.2.s.a.157.9	yes	68
272.21	even	4	inner	1088.2.j.a.497.24		68
272.123	odd	4		272.2.j.a.21.26	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.j.a.13.26	✓	68	4.3	odd	2
272.2.j.a.21.26	yes	68	272.123	odd	4
272.2.s.a.149.9	yes	68	16.11	odd	4
272.2.s.a.157.9	yes	68	68.55	odd	4
1088.2.j.a.81.11		68	1.1	even	1	trivial
1088.2.j.a.497.24		68	272.21	even	4	inner
1088.2.s.a.625.11		68	16.5	even	4
1088.2.s.a.1041.11		68	17.4	even	4

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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.68708i q^{3} +0.660632 q^{5} +(-0.710367 - 0.710367i) q^{7} +0.153763 q^{9} +O(q^{10})\)	\(q-1.68708i q^{3} +0.660632 q^{5} +(-0.710367 - 0.710367i) q^{7} +0.153763 q^{9} +4.46078i q^{11} +(4.51933 + 4.51933i) q^{13} -1.11454i q^{15} +(0.869766 + 4.03032i) q^{17} +(1.70072 - 1.70072i) q^{19} +(-1.19845 + 1.19845i) q^{21} +(4.11170 + 4.11170i) q^{23} -4.56357 q^{25} -5.32065i q^{27} -5.37730i q^{29} +(6.53867 + 6.53867i) q^{31} +7.52570 q^{33} +(-0.469292 - 0.469292i) q^{35} -4.81250 q^{37} +(7.62446 - 7.62446i) q^{39} +(0.645043 + 0.645043i) q^{41} +(-7.23424 - 7.23424i) q^{43} +0.101581 q^{45} +10.3100 q^{47} -5.99076i q^{49} +(6.79948 - 1.46736i) q^{51} +(1.52379 + 1.52379i) q^{53} +2.94694i q^{55} +(-2.86925 - 2.86925i) q^{57} +(-5.13534 - 5.13534i) q^{59} -2.23831 q^{61} +(-0.109229 - 0.109229i) q^{63} +(2.98561 + 2.98561i) q^{65} +(-0.119907 - 0.119907i) q^{67} +(6.93677 - 6.93677i) q^{69} +(-5.41828 + 5.41828i) q^{71} +(-2.55202 + 2.55202i) q^{73} +7.69910i q^{75} +(3.16880 - 3.16880i) q^{77} +(2.79211 - 2.79211i) q^{79} -8.51507 q^{81} +(2.60652 - 2.60652i) q^{83} +(0.574596 + 2.66256i) q^{85} -9.07192 q^{87} +12.7100i q^{89} -6.42077i q^{91} +(11.0313 - 11.0313i) q^{93} +(1.12355 - 1.12355i) q^{95} +(4.43572 + 4.43572i) q^{97} +0.685906i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^5 - 60 * q^9	\( 68 q - 4 q^{5} - 60 q^{9} - 4 q^{13} - 4 q^{17} - 4 q^{21} + 52 q^{25} + 4 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} - 12 q^{39} - 12 q^{45} + 48 q^{47} - 32 q^{51} + 12 q^{57} - 32 q^{59} - 36 q^{61} + 32 q^{63} + 4 q^{65} + 4 q^{67} + 28 q^{69} - 8 q^{73} + 28 q^{77} - 12 q^{79} + 28 q^{81} - 28 q^{85} + 24 q^{87} + 12 q^{93} + 4 q^{95} - 4 q^{97}+O(q^{100}) \) 68 * q - 4 * q^5 - 60 * q^9 - 4 * q^13 - 4 * q^17 - 4 * q^21 + 52 * q^25 + 4 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 - 12 * q^39 - 12 * q^45 + 48 * q^47 - 32 * q^51 + 12 * q^57 - 32 * q^59 - 36 * q^61 + 32 * q^63 + 4 * q^65 + 4 * q^67 + 28 * q^69 - 8 * q^73 + 28 * q^77 - 12 * q^79 + 28 * q^81 - 28 * q^85 + 24 * q^87 + 12 * q^93 + 4 * q^95 - 4 * q^97

Introduction

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