LMFDB - Embedded newform 1088.2.o.w.897.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(769,1088)]

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, 0, 3]))

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

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

chi := DirichletCharacter("1088.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.o (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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 544)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			897.2
Root			$1.35164 + 0.416001i$ of defining polynomial
Character	$\chi$	$=$	1088.897
Dual form			1088.2.o.w.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57184 - 1.57184i) q^{3} +(2.77846 + 2.77846i) q^{5} +(-2.70329 + 2.70329i) q^{7} +1.94137i q^{9} +O(q^{10})$	\(q+(-1.57184 - 1.57184i) q^{3} +(2.77846 + 2.77846i) q^{5} +(-2.70329 + 2.70329i) q^{7} +1.94137i q^{9} +(3.23584 - 3.23584i) q^{11} +0.941367 q^{13} -8.73458i q^{15} +(-3.71982 + 1.77846i) q^{17} +0.880784i q^{19} +8.49828 q^{21} +(-2.10439 + 2.10439i) q^{23} +10.4396i q^{25} +(-1.66400 + 1.66400i) q^{27} +(1.71982 + 1.71982i) q^{29} +(4.36729 + 4.36729i) q^{31} -10.1725 q^{33} -15.0219 q^{35} +(-4.77846 - 4.77846i) q^{37} +(-1.47968 - 1.47968i) q^{39} +(1.00000 - 1.00000i) q^{41} +7.66948i q^{43} +(-5.39400 + 5.39400i) q^{45} -10.8132 q^{47} -7.61555i q^{49} +(8.64242 + 3.05152i) q^{51} +7.55691i q^{53} +17.9813 q^{55} +(1.38445 - 1.38445i) q^{57} +6.47169i q^{59} +(-0.778457 + 0.778457i) q^{61} +(-5.24808 - 5.24808i) q^{63} +(2.61555 + 2.61555i) q^{65} +7.35247 q^{67} +6.61555 q^{69} +(11.2535 + 11.2535i) q^{71} +(10.4396 + 10.4396i) q^{73} +(16.4095 - 16.4095i) q^{75} +17.4948i q^{77} +(1.22361 - 1.22361i) q^{79} +11.0552 q^{81} -12.7591i q^{83} +(-15.2767 - 5.39400i) q^{85} -5.40658i q^{87} -14.6155 q^{89} +(-2.54479 + 2.54479i) q^{91} -13.7294i q^{93} +(-2.44722 + 2.44722i) q^{95} +(-5.49828 - 5.49828i) q^{97} +(6.28196 + 6.28196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) $ 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.57184	−	1.57184i	−0.907503	−	0.907503i	0.0885675	−	0.996070i	$-0.471771\pi$
$3$	−1.57184	−	1.57184i	−0.907503	−	0.907503i	−0.996070	+	0.0885675i	$0.971771\pi$
$4$		0			0
$5$	2.77846	+	2.77846i	1.24256	+	1.24256i	0.958934	+	0.283630i	$0.0915387\pi$
$5$	2.77846	+	2.77846i	1.24256	+	1.24256i	0.283630	+	0.958934i	$0.408461\pi$
$6$		0			0
$7$	−2.70329	+	2.70329i	−1.02175	+	1.02175i	−0.0219892	+	0.999758i	$0.507000\pi$
$7$	−2.70329	+	2.70329i	−1.02175	+	1.02175i	−0.999758	+	0.0219892i	$0.993000\pi$
$8$		0			0
$9$			1.94137i			0.647122i
$10$		0			0
$11$	3.23584	−	3.23584i	0.975644	−	0.975644i	−0.0240668	−	0.999710i	$-0.507661\pi$
$11$	3.23584	−	3.23584i	0.975644	−	0.975644i	0.999710	+	0.0240668i	$0.00766145\pi$
$12$		0			0
$13$	0.941367			0.261088			0.130544	−	0.991443i	$-0.458328\pi$
$13$	0.941367			0.261088			0.130544	+	0.991443i	$0.458328\pi$
$14$		0			0
$15$		−	8.73458i		−	2.25526i
$16$		0			0
$17$	−3.71982	+	1.77846i	−0.902190	+	0.431339i
$17$	−3.71982	+	1.77846i	−0.902190	+	0.431339i
$18$		0			0
$19$			0.880784i			0.202066i	0.994883	+	0.101033i	$0.0322147\pi$
$19$			0.880784i			0.202066i	−0.994883	+	0.101033i	$0.967785\pi$
$20$		0			0
$21$	8.49828			1.85448
$22$		0			0
$23$	−2.10439	+	2.10439i	−0.438797	+	0.438797i	−0.891607	−	0.452810i	$-0.850422\pi$
$23$	−2.10439	+	2.10439i	−0.438797	+	0.438797i	0.452810	+	0.891607i	$0.350422\pi$
$24$		0			0
$25$			10.4396i			2.08793i
$26$		0			0
$27$	−1.66400	+	1.66400i	−0.320237	+	0.320237i
$28$		0			0
$29$	1.71982	+	1.71982i	0.319363	+	0.319363i	0.848523	−	0.529159i	$-0.177493\pi$
$29$	1.71982	+	1.71982i	0.319363	+	0.319363i	−0.529159	+	0.848523i	$0.677493\pi$
$30$		0			0
$31$	4.36729	+	4.36729i	0.784389	+	0.784389i	0.980568	−	0.196179i	$-0.0628534\pi$
$31$	4.36729	+	4.36729i	0.784389	+	0.784389i	−0.196179	+	0.980568i	$0.562853\pi$
$32$		0			0
$33$	−10.1725			−1.77080
$34$		0			0
$35$	−15.0219			−2.53917
$36$		0			0
$37$	−4.77846	−	4.77846i	−0.785574	−	0.785574i	0.195192	−	0.980765i	$-0.437467\pi$
$37$	−4.77846	−	4.77846i	−0.785574	−	0.785574i	−0.980765	+	0.195192i	$0.937467\pi$
$38$		0			0
$39$	−1.47968	−	1.47968i	−0.236938	−	0.236938i
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$			7.66948i			1.16958i	0.811183	+	0.584792i	$0.198824\pi$
$43$			7.66948i			1.16958i	−0.811183	+	0.584792i	$0.801176\pi$
$44$		0			0
$45$	−5.39400	+	5.39400i	−0.804091	+	0.804091i
$46$		0			0
$47$	−10.8132			−1.57726			−0.788631	−	0.614867i	$-0.789210\pi$
$47$	−10.8132			−1.57726			−0.788631	+	0.614867i	$0.789210\pi$
$48$		0			0
$49$		−	7.61555i		−	1.08794i
$50$		0			0
$51$	8.64242	+	3.05152i	1.21018	+	0.427298i
$52$		0			0
$53$			7.55691i			1.03802i	0.854768	+	0.519011i	$0.173700\pi$
$53$			7.55691i			1.03802i	−0.854768	+	0.519011i	$0.826300\pi$
$54$		0			0
$55$	17.9813			2.42460
$56$		0			0
$57$	1.38445	−	1.38445i	0.183375	−	0.183375i
$58$		0			0
$59$			6.47169i			0.842542i	0.906935	+	0.421271i	$0.138416\pi$
$59$			6.47169i			0.842542i	−0.906935	+	0.421271i	$0.861584\pi$
$60$		0			0
$61$	−0.778457	+	0.778457i	−0.0996712	+	0.0996712i	−0.755184	−	0.655513i	$-0.772453\pi$
$61$	−0.778457	+	0.778457i	−0.0996712	+	0.0996712i	0.655513	+	0.755184i	$0.272453\pi$
$62$		0			0
$63$	−5.24808	−	5.24808i	−0.661195	−	0.661195i
$64$		0			0
$65$	2.61555	+	2.61555i	0.324419	+	0.324419i
$66$		0			0
$67$	7.35247			0.898247			0.449124	−	0.893470i	$-0.351736\pi$
$67$	7.35247			0.898247			0.449124	+	0.893470i	$0.351736\pi$
$68$		0			0
$69$	6.61555			0.796418
$70$		0			0
$71$	11.2535	+	11.2535i	1.33555	+	1.33555i	0.900318	+	0.435233i	$0.143334\pi$
$71$	11.2535	+	11.2535i	1.33555	+	1.33555i	0.435233	+	0.900318i	$0.356666\pi$
$72$		0			0
$73$	10.4396	+	10.4396i	1.22187	+	1.22187i	0.966967	+	0.254901i	$0.0820430\pi$
$73$	10.4396	+	10.4396i	1.22187	+	1.22187i	0.254901	+	0.966967i	$0.417957\pi$
$74$		0			0
$75$	16.4095	−	16.4095i	1.89480	−	1.89480i
$76$		0			0
$77$			17.4948i			1.99372i
$78$		0			0
$79$	1.22361	−	1.22361i	0.137667	−	0.137667i	−0.634915	−	0.772582i	$-0.718965\pi$
$79$	1.22361	−	1.22361i	0.137667	−	0.137667i	0.772582	+	0.634915i	$0.218965\pi$
$80$		0			0
$81$	11.0552			1.22836
$82$		0			0
$83$		−	12.7591i		−	1.40049i	−0.713904	−	0.700244i	$-0.753075\pi$
$83$		−	12.7591i		−	1.40049i	0.713904	−	0.700244i	$-0.246925\pi$
$84$		0			0
$85$	−15.2767	−	5.39400i	−1.65699	−	0.585062i
$86$		0			0
$87$		−	5.40658i		−	0.579646i
$88$		0			0
$89$	−14.6155			−1.54924			−0.774622	−	0.632424i	$-0.782060\pi$
$89$	−14.6155			−1.54924			−0.774622	+	0.632424i	$0.782060\pi$
$90$		0			0
$91$	−2.54479	+	2.54479i	−0.266766	+	0.266766i
$92$		0			0
$93$		−	13.7294i		−	1.42367i
$94$		0			0
$95$	−2.44722	+	2.44722i	−0.251080	+	0.251080i
$96$		0			0
$97$	−5.49828	−	5.49828i	−0.558266	−	0.558266i	0.370548	−	0.928813i	$-0.379170\pi$
$97$	−5.49828	−	5.49828i	−0.558266	−	0.558266i	−0.928813	+	0.370548i	$0.879170\pi$
$98$		0			0
$99$	6.28196	+	6.28196i	0.631361	+	0.631361i
$100$		0			0
$101$	8.94137			0.889699			0.444850	−	0.895605i	$-0.353257\pi$
$101$	8.94137			0.889699			0.444850	+	0.895605i	$0.353257\pi$
$102$		0			0
$103$	−7.85380			−0.773858			−0.386929	−	0.922110i	$-0.626464\pi$
$103$	−7.85380			−0.773858			−0.386929	+	0.922110i	$0.626464\pi$
$104$		0			0
$105$	23.6121	+	23.6121i	2.30431	+	2.30431i
$106$		0			0
$107$	4.71552	+	4.71552i	0.455867	+	0.455867i	0.897296	−	0.441429i	$-0.145528\pi$
$107$	4.71552	+	4.71552i	0.455867	+	0.455867i	−0.441429	+	0.897296i	$0.645528\pi$
$108$		0			0
$109$	4.89572	−	4.89572i	0.468925	−	0.468925i	−0.432641	−	0.901566i	$-0.642418\pi$
$109$	4.89572	−	4.89572i	0.468925	−	0.468925i	0.901566	+	0.432641i	$0.142418\pi$
$110$		0			0
$111$			15.0219i			1.42582i
$112$		0			0
$113$	−0.501719	+	0.501719i	−0.0471977	+	0.0471977i	−0.730312	−	0.683114i	$-0.760625\pi$
$113$	−0.501719	+	0.501719i	−0.0471977	+	0.0471977i	0.683114	+	0.730312i	$0.260625\pi$
$114$		0			0
$115$	−11.6939			−1.09047
$116$		0			0
$117$			1.82754i			0.168956i
$118$		0			0
$119$	5.24808	−	14.8634i	0.481090	−	1.36253i
$120$		0			0
$121$		−	9.94137i		−	0.903761i
$122$		0			0
$123$	−3.14368			−0.283456
$124$		0			0
$125$	−15.1138	+	15.1138i	−1.35182	+	1.35182i
$126$		0			0
$127$			16.7835i			1.48930i	0.667457	+	0.744648i	$0.267383\pi$
$127$			16.7835i			1.48930i	−0.667457	+	0.744648i	$0.732617\pi$
$128$		0			0
$129$	12.0552	−	12.0552i	1.06140	−	1.06140i
$130$		0			0
$131$	−7.16274	−	7.16274i	−0.625812	−	0.625812i	0.321200	−	0.947011i	$-0.395914\pi$
$131$	−7.16274	−	7.16274i	−0.625812	−	0.625812i	−0.947011	+	0.321200i	$0.895914\pi$
$132$		0			0
$133$	−2.38101	−	2.38101i	−0.206460	−	0.206460i
$134$		0			0
$135$	−9.24672			−0.795831
$136$		0			0
$137$	10.1725			0.869092			0.434546	−	0.900650i	$-0.356909\pi$
$137$	10.1725			0.869092			0.434546	+	0.900650i	$0.356909\pi$
$138$		0			0
$139$	−5.49874	−	5.49874i	−0.466397	−	0.466397i	0.434348	−	0.900745i	$-0.356979\pi$
$139$	−5.49874	−	5.49874i	−0.466397	−	0.466397i	−0.900745	+	0.434348i	$0.856979\pi$
$140$		0			0
$141$	16.9966	+	16.9966i	1.43137	+	1.43137i
$142$		0			0
$143$	3.04612	−	3.04612i	0.254729	−	0.254729i
$144$		0			0
$145$			9.55691i			0.793659i
$146$		0			0
$147$	−11.9704	+	11.9704i	−0.987304	+	0.987304i
$148$		0			0
$149$	−21.1138			−1.72971			−0.864856	−	0.502020i	$-0.832590\pi$
$149$	−21.1138			−1.72971			−0.864856	+	0.502020i	$0.832590\pi$
$150$		0			0
$151$			12.0626i			0.981640i	0.871261	+	0.490820i	$0.163303\pi$
$151$			12.0626i			0.981640i	−0.871261	+	0.490820i	$0.836697\pi$
$152$		0			0
$153$	−3.45264	−	7.22154i	−0.279129	−	0.583827i
$154$		0			0
$155$			24.2687i			1.94931i
$156$		0			0
$157$	8.11727			0.647828			0.323914	−	0.946086i	$-0.395001\pi$
$157$	8.11727			0.647828			0.323914	+	0.946086i	$0.395001\pi$
$158$		0			0
$159$	11.8783	−	11.8783i	0.942008	−	0.942008i
$160$		0			0
$161$		−	11.3776i		−	0.896679i
$162$		0			0
$163$	11.7861	−	11.7861i	0.923159	−	0.923159i	−0.0740925	−	0.997251i	$-0.523606\pi$
$163$	11.7861	−	11.7861i	0.923159	−	0.923159i	0.997251	+	0.0740925i	$0.0236060\pi$
$164$		0			0
$165$	−28.2637	−	28.2637i	−2.20033	−	2.20033i
$166$		0			0
$167$	−6.91208	−	6.91208i	−0.534873	−	0.534873i	0.387146	−	0.922019i	$-0.373461\pi$
$167$	−6.91208	−	6.91208i	−0.534873	−	0.534873i	−0.922019	+	0.387146i	$0.873461\pi$
$168$		0			0
$169$	−12.1138			−0.931833
$170$		0			0
$171$	−1.70993			−0.130761
$172$		0			0
$173$	1.71982	+	1.71982i	0.130756	+	0.130756i	0.769456	−	0.638700i	$-0.220528\pi$
$173$	1.71982	+	1.71982i	0.130756	+	0.130756i	−0.638700	+	0.769456i	$0.720528\pi$
$174$		0			0
$175$	−28.2214	−	28.2214i	−2.13334	−	2.13334i
$176$		0			0
$177$	10.1725	−	10.1725i	0.764609	−	0.764609i
$178$		0			0
$179$			4.20879i			0.314580i	0.987552	+	0.157290i	$0.0502757\pi$
$179$			4.20879i			0.314580i	−0.987552	+	0.157290i	$0.949724\pi$
$180$		0			0
$181$	−6.66119	+	6.66119i	−0.495122	+	0.495122i	−0.909916	−	0.414793i	$-0.863854\pi$
$181$	−6.66119	+	6.66119i	−0.495122	+	0.495122i	0.414793	+	0.909916i	$0.363854\pi$
$182$		0			0
$183$	2.44722			0.180904
$184$		0			0
$185$		−	26.5535i		−	1.95225i
$186$		0			0
$187$	−6.28196	+	17.7916i	−0.459382	+	1.30105i
$188$		0			0
$189$		−	8.99656i		−	0.654404i
$190$		0			0
$191$	22.1901			1.60562			0.802809	−	0.596236i	$-0.203338\pi$
$191$	22.1901			1.60562			0.802809	+	0.596236i	$0.203338\pi$
$192$		0			0
$193$	−3.99656	+	3.99656i	−0.287679	+	0.287679i	−0.836162	−	0.548483i	$-0.815206\pi$
$193$	−3.99656	+	3.99656i	−0.287679	+	0.287679i	0.548483	+	0.836162i	$0.315206\pi$
$194$		0			0
$195$		−	8.22245i		−	0.588822i
$196$		0			0
$197$	13.2767	−	13.2767i	0.945928	−	0.945928i	−0.0526829	−	0.998611i	$-0.516777\pi$
$197$	13.2767	−	13.2767i	0.945928	−	0.945928i	0.998611	+	0.0526829i	$0.0167772\pi$
$198$		0			0
$199$	−8.70876	−	8.70876i	−0.617348	−	0.617348i	0.327502	−	0.944850i	$-0.393793\pi$
$199$	−8.70876	−	8.70876i	−0.617348	−	0.617348i	−0.944850	+	0.327502i	$0.893793\pi$
$200$		0			0
$201$	−11.5569	−	11.5569i	−0.815162	−	0.815162i
$202$		0			0
$203$	−9.29836			−0.652617
$204$		0			0
$205$	5.55691			0.388112
$206$		0			0
$207$	−4.08540	−	4.08540i	−0.283955	−	0.283955i
$208$		0			0
$209$	2.85008	+	2.85008i	0.197144	+	0.197144i
$210$		0			0
$211$	−0.691057	+	0.691057i	−0.0475743	+	0.0475743i	−0.730494	−	0.682919i	$-0.760710\pi$
$211$	−0.691057	+	0.691057i	−0.0475743	+	0.0475743i	0.682919	+	0.730494i	$0.260710\pi$
$212$		0			0
$213$		−	35.3776i		−	2.42403i
$214$		0			0
$215$	−21.3093	+	21.3093i	−1.45328	+	1.45328i
$216$		0			0
$217$	−23.6121			−1.60289
$218$		0			0
$219$		−	32.8189i		−	2.21770i
$220$		0			0
$221$	−3.50172	+	1.67418i	−0.235551	+	0.112618i
$222$		0			0
$223$			3.64501i			0.244088i	0.992525	+	0.122044i	$0.0389449\pi$
$223$			3.64501i			0.244088i	−0.992525	+	0.122044i	$0.961055\pi$
$224$		0			0
$225$	−20.2672			−1.35115
$226$		0			0
$227$	9.52321	−	9.52321i	0.632077	−	0.632077i	−0.316511	−	0.948589i	$-0.602512\pi$
$227$	9.52321	−	9.52321i	0.632077	−	0.632077i	0.948589	+	0.316511i	$0.102512\pi$
$228$		0			0
$229$		−	9.61211i		−	0.635186i	−0.948227	−	0.317593i	$-0.897125\pi$
$229$		−	9.61211i		−	0.635186i	0.948227	−	0.317593i	$-0.102875\pi$
$230$		0			0
$231$	27.4991	−	27.4991i	1.80931	−	1.80931i
$232$		0			0
$233$	7.94137	+	7.94137i	0.520256	+	0.520256i	0.917649	−	0.397392i	$-0.130085\pi$
$233$	7.94137	+	7.94137i	0.520256	+	0.520256i	−0.397392	+	0.917649i	$0.630085\pi$
$234$		0			0
$235$	−30.0439	−	30.0439i	−1.95985	−	1.95985i
$236$		0			0
$237$	−3.84664			−0.249866
$238$		0			0
$239$	−2.95936			−0.191425			−0.0957125	−	0.995409i	$-0.530513\pi$
$239$	−2.95936			−0.191425			−0.0957125	+	0.995409i	$0.530513\pi$
$240$		0			0
$241$	−7.55348	−	7.55348i	−0.486562	−	0.486562i	0.420657	−	0.907220i	$-0.361799\pi$
$241$	−7.55348	−	7.55348i	−0.486562	−	0.486562i	−0.907220	+	0.420657i	$0.861799\pi$
$242$		0			0
$243$	−12.3850	−	12.3850i	−0.794498	−	0.794498i
$244$		0			0
$245$	21.1595	−	21.1595i	1.35183	−	1.35183i
$246$		0			0
$247$			0.829141i			0.0527570i
$248$		0			0
$249$	−20.0552	+	20.0552i	−1.27095	+	1.27095i
$250$		0			0
$251$	−1.89425			−0.119564			−0.0597820	−	0.998211i	$-0.519041\pi$
$251$	−1.89425			−0.119564			−0.0597820	+	0.998211i	$0.519041\pi$
$252$		0			0
$253$			13.6190i			0.856218i
$254$		0			0
$255$	15.5341	+	32.4911i	0.972782	+	2.03467i
$256$		0			0
$257$		−	23.2863i		−	1.45256i	−0.687400	−	0.726279i	$-0.741248\pi$
$257$		−	23.2863i		−	1.45256i	0.687400	−	0.726279i	$-0.258752\pi$
$258$		0			0
$259$	25.8351			1.60532
$260$		0			0
$261$	−3.33881	+	3.33881i	−0.206667	+	0.206667i
$262$		0			0
$263$		−	5.77523i		−	0.356116i	−0.984020	−	0.178058i	$-0.943019\pi$
$263$		−	5.77523i		−	0.356116i	0.984020	−	0.178058i	$-0.0569814\pi$
$264$		0			0
$265$	−20.9966	+	20.9966i	−1.28981	+	1.28981i
$266$		0			0
$267$	22.9733	+	22.9733i	1.40594	+	1.40594i
$268$		0			0
$269$	10.5439	+	10.5439i	0.642874	+	0.642874i	0.951261	−	0.308387i	$-0.0997891\pi$
$269$	10.5439	+	10.5439i	0.642874	+	0.642874i	−0.308387	+	0.951261i	$0.599789\pi$
$270$		0			0
$271$	2.95936			0.179768			0.0898841	−	0.995952i	$-0.471350\pi$
$271$	2.95936			0.179768			0.0898841	+	0.995952i	$0.471350\pi$
$272$		0			0
$273$	8.00000			0.484182
$274$		0			0
$275$	33.7811	+	33.7811i	2.03708	+	2.03708i
$276$		0			0
$277$	1.95436	+	1.95436i	0.117426	+	0.117426i	0.763378	−	0.645952i	$-0.223539\pi$
$277$	1.95436	+	1.95436i	0.117426	+	0.117426i	−0.645952	+	0.763378i	$0.723539\pi$
$278$		0			0
$279$	−8.47852	+	8.47852i	−0.507595	+	0.507595i
$280$		0			0
$281$			2.56035i			0.152738i	0.997080	+	0.0763689i	$0.0243327\pi$
$281$			2.56035i			0.152738i	−0.997080	+	0.0763689i	$0.975667\pi$
$282$		0			0
$283$	7.76164	−	7.76164i	0.461381	−	0.461381i	−0.437727	−	0.899108i	$-0.644216\pi$
$283$	7.76164	−	7.76164i	0.461381	−	0.461381i	0.899108	+	0.437727i	$0.144216\pi$
$284$		0			0
$285$	7.69328			0.455711
$286$		0			0
$287$			5.40658i			0.319140i
$288$		0			0
$289$	10.6742	−	13.2311i	0.627893	−	0.778300i
$290$		0			0
$291$			17.2848i			1.01326i
$292$		0			0
$293$	11.2311			0.656128			0.328064	−	0.944656i	$-0.393604\pi$
$293$	11.2311			0.656128			0.328064	+	0.944656i	$0.393604\pi$
$294$		0			0
$295$	−17.9813	+	17.9813i	−1.04691	+	1.04691i
$296$		0			0
$297$			10.7689i			0.624875i
$298$		0			0
$299$	−1.98101	+	1.98101i	−0.114565	+	0.114565i
$300$		0			0
$301$	−20.7328	−	20.7328i	−1.19502	−	1.19502i
$302$		0			0
$303$	−14.0544	−	14.0544i	−0.807404	−	0.807404i
$304$		0			0
$305$	−4.32582			−0.247696
$306$		0			0
$307$	−11.7456			−0.670356			−0.335178	−	0.942155i	$-0.608796\pi$
$307$	−11.7456			−0.670356			−0.335178	+	0.942155i	$0.608796\pi$
$308$		0			0
$309$	12.3449	+	12.3449i	0.702278	+	0.702278i
$310$		0			0
$311$	1.50550	+	1.50550i	0.0853691	+	0.0853691i	0.748502	−	0.663133i	$-0.230774\pi$
$311$	1.50550	+	1.50550i	0.0853691	+	0.0853691i	−0.663133	+	0.748502i	$0.730774\pi$
$312$		0			0
$313$	3.56035	−	3.56035i	0.201243	−	0.201243i	−0.599289	−	0.800532i	$-0.704550\pi$
$313$	3.56035	−	3.56035i	0.201243	−	0.201243i	0.800532	+	0.599289i	$0.204550\pi$
$314$		0			0
$315$		−	29.1631i		−	1.64316i
$316$		0			0
$317$	17.2767	−	17.2767i	0.970358	−	0.970358i	−0.0292149	−	0.999573i	$-0.509301\pi$
$317$	17.2767	−	17.2767i	0.970358	−	0.970358i	0.999573	+	0.0292149i	$0.00930070\pi$
$318$		0			0
$319$	11.1302			0.623169
$320$		0			0
$321$		−	14.8241i		−	0.827401i
$322$		0			0
$323$	−1.56644	−	3.27636i	−0.0871589	−	0.182302i
$324$		0			0
$325$			9.82754i			0.545134i
$326$		0			0
$327$	−15.3906			−0.851102
$328$		0			0
$329$	29.2311	−	29.2311i	1.61156	−	1.61156i
$330$		0			0
$331$			9.79969i			0.538640i	0.963051	+	0.269320i	$0.0867989\pi$
$331$			9.79969i			0.538640i	−0.963051	+	0.269320i	$0.913201\pi$
$332$		0			0
$333$	9.27674	−	9.27674i	0.508362	−	0.508362i
$334$		0			0
$335$	20.4285	+	20.4285i	1.11613	+	1.11613i
$336$		0			0
$337$	−17.6707	−	17.6707i	−0.962587	−	0.962587i	0.0367382	−	0.999325i	$-0.488303\pi$
$337$	−17.6707	−	17.6707i	−0.962587	−	0.962587i	−0.999325	+	0.0367382i	$0.988303\pi$
$338$		0			0
$339$	1.57724			0.0856642
$340$		0			0
$341$	28.2637			1.53057
$342$		0			0
$343$	1.66400	+	1.66400i	0.0898477	+	0.0898477i
$344$		0			0
$345$	18.3810	+	18.3810i	0.989601	+	0.989601i
$346$		0			0
$347$	3.23584	−	3.23584i	0.173709	−	0.173709i	−0.614898	−	0.788607i	$-0.710803\pi$
$347$	3.23584	−	3.23584i	0.173709	−	0.173709i	0.788607	+	0.614898i	$0.210803\pi$
$348$		0			0
$349$		−	0.443086i		−	0.0237178i	−0.999930	−	0.0118589i	$-0.996225\pi$
$349$		−	0.443086i		−	0.0237178i	0.999930	−	0.0118589i	$-0.00377490\pi$
$350$		0			0
$351$	−1.56644	+	1.56644i	−0.0836102	+	0.0836102i
$352$		0			0
$353$	8.67074			0.461497			0.230749	−	0.973013i	$-0.425883\pi$
$353$	8.67074			0.461497			0.230749	+	0.973013i	$0.425883\pi$
$354$		0			0
$355$			62.5350i			3.31901i
$356$		0			0
$357$	−31.6121	+	15.1138i	−1.67309	+	0.799909i
$358$		0			0
$359$			9.29836i			0.490749i	0.969428	+	0.245374i	$0.0789109\pi$
$359$			9.29836i			0.490749i	−0.969428	+	0.245374i	$0.921089\pi$
$360$		0			0
$361$	18.2242			0.959169
$362$		0			0
$363$	−15.6262	+	15.6262i	−0.820165	+	0.820165i
$364$		0			0
$365$			58.0122i			3.03650i
$366$		0			0
$367$	4.64918	−	4.64918i	0.242685	−	0.242685i	−0.575275	−	0.817960i	$-0.695105\pi$
$367$	4.64918	−	4.64918i	0.242685	−	0.242685i	0.817960	+	0.575275i	$0.195105\pi$
$368$		0			0
$369$	1.94137	+	1.94137i	0.101064	+	0.101064i
$370$		0			0
$371$	−20.4285	−	20.4285i	−1.06060	−	1.06060i
$372$		0			0
$373$	−13.7034			−0.709535			−0.354767	−	0.934955i	$-0.615440\pi$
$373$	−13.7034			−0.709535			−0.354767	+	0.934955i	$0.615440\pi$
$374$		0			0
$375$	47.5131			2.45356
$376$		0			0
$377$	1.61899	+	1.61899i	0.0833820	+	0.0833820i
$378$		0			0
$379$	5.91331	+	5.91331i	0.303746	+	0.303746i	0.842478	−	0.538731i	$-0.181096\pi$
$379$	5.91331	+	5.91331i	0.303746	+	0.303746i	−0.538731	+	0.842478i	$0.681096\pi$
$380$		0			0
$381$	26.3810	−	26.3810i	1.35154	−	1.35154i
$382$		0			0
$383$		−	9.56373i		−	0.488684i	−0.969689	−	0.244342i	$-0.921428\pi$
$383$		−	9.56373i		−	0.488684i	0.969689	−	0.244342i	$-0.0785719\pi$
$384$		0			0
$385$	−48.6087	+	48.6087i	−2.47733	+	2.47733i
$386$		0			0
$387$	−14.8893			−0.756864
$388$		0			0
$389$		−	16.7259i		−	0.848039i	−0.905653	−	0.424019i	$-0.860619\pi$
$389$		−	16.7259i		−	0.848039i	0.905653	−	0.424019i	$-0.139381\pi$
$390$		0			0
$391$	4.08540	−	11.5706i	0.206608	−	0.585148i
$392$		0			0
$393$			22.5174i			1.13585i
$394$		0			0
$395$	6.79950			0.342120
$396$		0			0
$397$	−4.54392	+	4.54392i	−0.228053	+	0.228053i	−0.811879	−	0.583826i	$-0.801555\pi$
$397$	−4.54392	+	4.54392i	−0.228053	+	0.228053i	0.583826	+	0.811879i	$0.301555\pi$
$398$		0			0
$399$			7.48515i			0.374726i
$400$		0			0
$401$	−4.67418	+	4.67418i	−0.233417	+	0.233417i	−0.814118	−	0.580700i	$-0.802779\pi$
$401$	−4.67418	+	4.67418i	−0.233417	+	0.233417i	0.580700	+	0.814118i	$0.302779\pi$
$402$		0			0
$403$	4.11122	+	4.11122i	0.204795	+	0.204795i
$404$		0			0
$405$	30.7164	+	30.7164i	1.52631	+	1.52631i
$406$		0			0
$407$	−30.9247			−1.53288
$408$		0			0
$409$	4.32582			0.213898			0.106949	−	0.994265i	$-0.465892\pi$
$409$	4.32582			0.213898			0.106949	+	0.994265i	$0.465892\pi$
$410$		0			0
$411$	−15.9895	−	15.9895i	−0.788703	−	0.788703i
$412$		0			0
$413$	−17.4948	−	17.4948i	−0.860865	−	0.860865i
$414$		0			0
$415$	35.4505	−	35.4505i	1.74020	−	1.74020i
$416$		0			0
$417$			17.2863i			0.846513i
$418$		0			0
$419$	14.5152	−	14.5152i	0.709115	−	0.709115i	−0.257234	−	0.966349i	$-0.582811\pi$
$419$	14.5152	−	14.5152i	0.709115	−	0.709115i	0.966349	+	0.257234i	$0.0828112\pi$
$420$		0			0
$421$	−18.4070			−0.897102			−0.448551	−	0.893757i	$-0.648060\pi$
$421$	−18.4070			−0.897102			−0.448551	+	0.893757i	$0.648060\pi$
$422$		0			0
$423$		−	20.9923i		−	1.02068i
$424$		0			0
$425$	−18.5665	−	38.8337i	−0.900606	−	1.88371i
$426$		0			0
$427$		−	4.20879i		−	0.203678i
$428$		0			0
$429$	−9.57602			−0.462335
$430$		0			0
$431$	2.98518	−	2.98518i	0.143791	−	0.143791i	−0.631547	−	0.775338i	$-0.717580\pi$
$431$	2.98518	−	2.98518i	0.143791	−	0.143791i	0.775338	+	0.631547i	$0.217580\pi$
$432$		0			0
$433$			13.2672i			0.637580i	0.947825	+	0.318790i	$0.103277\pi$
$433$			13.2672i			0.637580i	−0.947825	+	0.318790i	$0.896723\pi$
$434$		0			0
$435$	15.0219	−	15.0219i	0.720247	−	0.720247i
$436$		0			0
$437$	−1.85352	−	1.85352i	−0.0886658	−	0.0886658i
$438$		0			0
$439$	−9.17498	−	9.17498i	−0.437898	−	0.437898i	0.453406	−	0.891304i	$-0.350209\pi$
$439$	−9.17498	−	9.17498i	−0.437898	−	0.437898i	−0.891304	+	0.453406i	$0.850209\pi$
$440$		0			0
$441$	14.7846			0.704027
$442$		0			0
$443$	37.0277			1.75924			0.879620	−	0.475677i	$-0.157797\pi$
$443$	37.0277			1.75924			0.879620	+	0.475677i	$0.157797\pi$
$444$		0			0
$445$	−40.6087	−	40.6087i	−1.92504	−	1.92504i
$446$		0			0
$447$	33.1876	+	33.1876i	1.56972	+	1.56972i
$448$		0			0
$449$	15.2637	−	15.2637i	0.720341	−	0.720341i	−0.248334	−	0.968675i	$-0.579883\pi$
$449$	15.2637	−	15.2637i	0.720341	−	0.720341i	0.968675	+	0.248334i	$0.0798830\pi$
$450$		0			0
$451$		−	6.47169i		−	0.304740i
$452$		0			0
$453$	18.9605	−	18.9605i	0.890841	−	0.890841i
$454$		0			0
$455$	−14.1412			−0.662948
$456$		0			0
$457$			12.3810i			0.579159i	0.957154	+	0.289580i	$0.0935155\pi$
$457$			12.3810i			0.579159i	−0.957154	+	0.289580i	$0.906484\pi$
$458$		0			0
$459$	3.23044	−	9.14915i	0.150784	−	0.427046i
$460$		0			0
$461$			18.4362i			0.858660i	0.903148	+	0.429330i	$0.141250\pi$
$461$			18.4362i			0.858660i	−0.903148	+	0.429330i	$0.858750\pi$
$462$		0			0
$463$	−18.2983			−0.850395			−0.425197	−	0.905101i	$-0.639795\pi$
$463$	−18.2983			−0.850395			−0.425197	+	0.905101i	$0.639795\pi$
$464$		0			0
$465$	38.1465	−	38.1465i	1.76900	−	1.76900i
$466$		0			0
$467$			38.4098i			1.77740i	0.458494	+	0.888698i	$0.348389\pi$
$467$			38.4098i			1.77740i	−0.458494	+	0.888698i	$0.651611\pi$
$468$		0			0
$469$	−19.8759	+	19.8759i	−0.917782	+	0.917782i
$470$		0			0
$471$	−12.7591	−	12.7591i	−0.587906	−	0.587906i
$472$		0			0
$473$	24.8172	+	24.8172i	1.14110	+	1.14110i
$474$		0			0
$475$	−9.19508			−0.421899
$476$		0			0
$477$	−14.6707			−0.671727
$478$		0			0
$479$	−15.5599	−	15.5599i	−0.710950	−	0.710950i	0.255784	−	0.966734i	$-0.417666\pi$
$479$	−15.5599	−	15.5599i	−0.710950	−	0.710950i	−0.966734	+	0.255784i	$0.917666\pi$
$480$		0			0
$481$	−4.49828	−	4.49828i	−0.205104	−	0.205104i
$482$		0			0
$483$	−17.8837	+	17.8837i	−0.813738	+	0.813738i
$484$		0			0
$485$		−	30.5535i		−	1.38736i
$486$		0			0
$487$	6.21562	−	6.21562i	0.281657	−	0.281657i	−0.552113	−	0.833769i	$-0.686178\pi$
$487$	6.21562	−	6.21562i	0.281657	−	0.281657i	0.833769	+	0.552113i	$0.186178\pi$
$488$		0			0
$489$	−37.0518			−1.67554
$490$		0			0
$491$		−	20.7455i		−	0.936233i	−0.883667	−	0.468116i	$-0.844933\pi$
$491$		−	20.7455i		−	0.936233i	0.883667	−	0.468116i	$-0.155067\pi$
$492$		0			0
$493$	−9.45608	−	3.33881i	−0.425880	−	0.150372i
$494$		0			0
$495$			34.9083i			1.56901i
$496$		0			0
$497$	−60.8432			−2.72919
$498$		0			0
$499$	17.8432	−	17.8432i	0.798772	−	0.798772i	−0.184130	−	0.982902i	$-0.558947\pi$
$499$	17.8432	−	17.8432i	0.798772	−	0.798772i	0.982902	+	0.184130i	$0.0589466\pi$
$500$		0			0
$501$			21.7294i			0.970797i
$502$		0			0
$503$	7.60854	−	7.60854i	0.339248	−	0.339248i	−0.516836	−	0.856084i	$-0.672890\pi$
$503$	7.60854	−	7.60854i	0.339248	−	0.339248i	0.856084	+	0.516836i	$0.172890\pi$
$504$		0			0
$505$	24.8432	+	24.8432i	1.10551	+	1.10551i
$506$		0			0
$507$	19.0410	+	19.0410i	0.845641	+	0.845641i
$508$		0			0
$509$	−21.8759			−0.969630			−0.484815	−	0.874617i	$-0.661113\pi$
$509$	−21.8759			−0.969630			−0.484815	+	0.874617i	$0.661113\pi$
$510$		0			0
$511$	−56.4428			−2.49688
$512$		0			0
$513$	−1.46563	−	1.46563i	−0.0647090	−	0.0647090i
$514$		0			0
$515$	−21.8214	−	21.8214i	−0.961568	−	0.961568i
$516$		0			0
$517$	−34.9897	+	34.9897i	−1.53884	+	1.53884i
$518$		0			0
$519$		−	5.40658i		−	0.237322i
$520$		0			0
$521$	30.5500	−	30.5500i	1.33842	−	1.33842i	0.440832	−	0.897590i	$-0.354684\pi$
$521$	30.5500	−	30.5500i	1.33842	−	1.33842i	0.897590	−	0.440832i	$-0.145316\pi$
$522$		0			0
$523$	−10.6805			−0.467025			−0.233512	−	0.972354i	$-0.575022\pi$
$523$	−10.6805			−0.467025			−0.233512	+	0.972354i	$0.575022\pi$
$524$		0			0
$525$			88.7191i			3.87202i
$526$		0			0
$527$	−24.0126	−	8.47852i	−1.04601	−	0.369330i
$528$		0			0
$529$			14.1430i			0.614915i
$530$		0			0
$531$	−12.5639			−0.545228
$532$		0			0
$533$	0.941367	−	0.941367i	0.0407751	−	0.0407751i
$534$		0			0
$535$			26.2038i			1.13289i
$536$		0			0
$537$	6.61555	−	6.61555i	0.285482	−	0.285482i
$538$		0			0
$539$	−24.6427	−	24.6427i	−1.06144	−	1.06144i
$540$		0			0
$541$	22.3354	+	22.3354i	0.960273	+	0.960273i	0.999240	−	0.0389678i	$-0.0124070\pi$
$541$	22.3354	+	22.3354i	0.960273	+	0.960273i	−0.0389678	+	0.999240i	$0.512407\pi$
$542$		0			0
$543$	20.9407			0.898650
$544$		0			0
$545$	27.2051			1.16534
$546$		0			0
$547$	−32.1171	−	32.1171i	−1.37323	−	1.37323i	−0.855617	−	0.517610i	$-0.826822\pi$
$547$	−32.1171	−	32.1171i	−1.37323	−	1.37323i	−0.517610	−	0.855617i	$-0.673178\pi$
$548$		0			0
$549$	−1.51127	−	1.51127i	−0.0644995	−	0.0644995i
$550$		0			0
$551$	−1.51479	+	1.51479i	−0.0645324	+	0.0645324i
$552$		0			0
$553$			6.61555i			0.281322i
$554$		0			0
$555$	−41.7378	+	41.7378i	−1.77167	+	1.77167i
$556$		0			0
$557$	−7.05863			−0.299084			−0.149542	−	0.988755i	$-0.547780\pi$
$557$	−7.05863			−0.299084			−0.149542	+	0.988755i	$0.547780\pi$
$558$		0			0
$559$			7.21979i			0.305365i
$560$		0			0
$561$	37.8398	−	18.0913i	1.59760	−	0.763815i
$562$		0			0
$563$		−	42.2392i		−	1.78017i	−0.455796	−	0.890084i	$-0.650645\pi$
$563$		−	42.2392i		−	1.78017i	0.455796	−	0.890084i	$-0.349355\pi$
$564$		0			0
$565$	−2.78801			−0.117292
$566$		0			0
$567$	−29.8854	+	29.8854i	−1.25507	+	1.25507i
$568$		0			0
$569$			22.1173i			0.927204i	0.886044	+	0.463602i	$0.153443\pi$
$569$			22.1173i			0.927204i	−0.886044	+	0.463602i	$0.846557\pi$
$570$		0			0
$571$	19.8702	−	19.8702i	0.831540	−	0.831540i	−0.156188	−	0.987727i	$-0.549920\pi$
$571$	19.8702	−	19.8702i	0.831540	−	0.831540i	0.987727	+	0.156188i	$0.0499204\pi$
$572$		0			0
$573$	−34.8793	−	34.8793i	−1.45710	−	1.45710i
$574$		0			0
$575$	−21.9691	−	21.9691i	−0.916177	−	0.916177i
$576$		0			0
$577$	41.2863			1.71877			0.859385	−	0.511328i	$-0.170846\pi$
$577$	41.2863			1.71877			0.859385	+	0.511328i	$0.170846\pi$
$578$		0			0
$579$	12.5639			0.522139
$580$		0			0
$581$	34.4914	+	34.4914i	1.43094	+	1.43094i
$582$		0			0
$583$	24.4530	+	24.4530i	1.01274	+	1.01274i
$584$		0			0
$585$	−5.07774	+	5.07774i	−0.209939	+	0.209939i
$586$		0			0
$587$			16.7835i			0.692730i	0.938100	+	0.346365i	$0.112584\pi$
$587$			16.7835i			0.692730i	−0.938100	+	0.346365i	$0.887416\pi$
$588$		0			0
$589$	−3.84664	+	3.84664i	−0.158498	+	0.158498i
$590$		0			0
$591$	−41.7378			−1.71687
$592$		0			0
$593$			41.2173i			1.69259i	0.532712	+	0.846297i	$0.321173\pi$
$593$			41.2173i			1.69259i	−0.532712	+	0.846297i	$0.678827\pi$
$594$		0			0
$595$	55.8790	−	26.7159i	2.29082	−	1.09524i
$596$		0			0
$597$			27.3776i			1.12049i
$598$		0			0
$599$	31.6103			1.29156			0.645782	−	0.763522i	$-0.276532\pi$
$599$	31.6103			1.29156			0.645782	+	0.763522i	$0.276532\pi$
$600$		0			0
$601$	6.67418	−	6.67418i	0.272246	−	0.272246i	−0.557758	−	0.830004i	$-0.688338\pi$
$601$	6.67418	−	6.67418i	0.272246	−	0.272246i	0.830004	+	0.557758i	$0.188338\pi$
$602$		0			0
$603$			14.2738i			0.581276i
$604$		0			0
$605$	27.6217	−	27.6217i	1.12298	−	1.12298i
$606$		0			0
$607$	20.2700	+	20.2700i	0.822735	+	0.822735i	0.986499	−	0.163765i	$-0.0523637\pi$
$607$	20.2700	+	20.2700i	0.822735	+	0.822735i	−0.163765	+	0.986499i	$0.552364\pi$
$608$		0			0
$609$	14.6155	+	14.6155i	0.592252	+	0.592252i
$610$		0			0
$611$	−10.1791			−0.411804
$612$		0			0
$613$	−12.6448			−0.510717			−0.255359	−	0.966846i	$-0.582194\pi$
$613$	−12.6448			−0.510717			−0.255359	+	0.966846i	$0.582194\pi$
$614$		0			0
$615$	−8.73458	−	8.73458i	−0.352212	−	0.352212i
$616$		0			0
$617$	4.38445	+	4.38445i	0.176511	+	0.176511i	0.789833	−	0.613322i	$-0.210167\pi$
$617$	4.38445	+	4.38445i	0.176511	+	0.176511i	−0.613322	+	0.789833i	$0.710167\pi$
$618$		0			0
$619$	−9.20620	+	9.20620i	−0.370028	+	0.370028i	−0.867487	−	0.497459i	$-0.834266\pi$
$619$	−9.20620	+	9.20620i	−0.370028	+	0.370028i	0.497459	+	0.867487i	$0.334266\pi$
$620$		0			0
$621$		−	7.00344i		−	0.281038i
$622$		0			0
$623$	39.5101	−	39.5101i	1.58294	−	1.58294i
$624$		0			0
$625$	−31.7880			−1.27152
$626$		0			0
$627$		−	8.95974i		−	0.357818i
$628$		0			0
$629$	26.2733	+	9.27674i	1.04759	+	0.369888i
$630$		0			0
$631$		−	23.4395i		−	0.933113i	−0.884491	−	0.466556i	$-0.845494\pi$
$631$		−	23.4395i		−	0.933113i	0.884491	−	0.466556i	$-0.154506\pi$
$632$		0			0
$633$	2.17246			0.0863476
$634$		0			0
$635$	−46.6323	+	46.6323i	−1.85055	+	1.85055i
$636$		0			0
$637$		−	7.16902i		−	0.284047i
$638$		0			0
$639$	−21.8473	+	21.8473i	−0.864265	+	0.864265i
$640$		0			0
$641$	1.82410	+	1.82410i	0.0720476	+	0.0720476i	0.742212	−	0.670165i	$-0.233777\pi$
$641$	1.82410	+	1.82410i	0.0720476	+	0.0720476i	−0.670165	+	0.742212i	$0.733777\pi$
$642$		0			0
$643$	15.3960	+	15.3960i	0.607159	+	0.607159i	0.942203	−	0.335044i	$-0.108751\pi$
$643$	15.3960	+	15.3960i	0.607159	+	0.607159i	−0.335044	+	0.942203i	$0.608751\pi$
$644$		0			0
$645$	66.9897			2.63772
$646$		0			0
$647$	5.35494			0.210524			0.105262	−	0.994445i	$-0.466432\pi$
$647$	5.35494			0.210524			0.105262	+	0.994445i	$0.466432\pi$
$648$		0			0
$649$	20.9414	+	20.9414i	0.822021	+	0.822021i
$650$		0			0
$651$	37.1145	+	37.1145i	1.45463	+	1.45463i
$652$		0			0
$653$	30.9509	−	30.9509i	1.21120	−	1.21120i	0.240572	−	0.970631i	$-0.422665\pi$
$653$	30.9509	−	30.9509i	1.21120	−	1.21120i	0.970631	−	0.240572i	$-0.0773349\pi$
$654$		0			0
$655$		−	39.8028i		−	1.55522i
$656$		0			0
$657$	−20.2672	+	20.2672i	−0.790698	+	0.790698i
$658$		0			0
$659$	23.3879			0.911063			0.455531	−	0.890220i	$-0.349449\pi$
$659$	23.3879			0.911063			0.455531	+	0.890220i	$0.349449\pi$
$660$		0			0
$661$			23.6673i			0.920551i	0.887776	+	0.460276i	$0.152249\pi$
$661$			23.6673i			0.920551i	−0.887776	+	0.460276i	$0.847751\pi$
$662$		0			0
$663$	8.13569	+	2.87260i	0.315964	+	0.111563i
$664$		0			0
$665$		−	13.2311i		−	0.513080i
$666$		0			0
$667$	−7.23838			−0.280271
$668$		0			0
$669$	5.72938	−	5.72938i	0.221510	−	0.221510i
$670$		0			0
$671$			5.03793i			0.194487i
$672$		0			0
$673$	−3.82410	+	3.82410i	−0.147408	+	0.147408i	−0.776959	−	0.629551i	$-0.783239\pi$
$673$	−3.82410	+	3.82410i	−0.147408	+	0.147408i	0.629551	+	0.776959i	$0.283239\pi$
$674$		0			0
$675$	−17.3716	−	17.3716i	−0.668633	−	0.668633i
$676$		0			0
$677$	−27.8302	−	27.8302i	−1.06960	−	1.06960i	−0.997389	−	0.0722128i	$-0.976994\pi$
$677$	−27.8302	−	27.8302i	−1.06960	−	1.06960i	−0.0722128	−	0.997389i	$-0.523006\pi$
$678$		0			0
$679$	29.7269			1.14081
$680$		0			0
$681$	−29.9379			−1.14722
$682$		0			0
$683$	5.78063	+	5.78063i	0.221190	+	0.221190i	0.808999	−	0.587810i	$-0.200010\pi$
$683$	5.78063	+	5.78063i	0.221190	+	0.221190i	−0.587810	+	0.808999i	$0.700010\pi$
$684$		0			0
$685$	28.2637	+	28.2637i	1.07990	+	1.07990i
$686$		0			0
$687$	−15.1087	+	15.1087i	−0.576433	+	0.576433i
$688$		0			0
$689$			7.11383i			0.271015i
$690$		0			0
$691$	9.52321	−	9.52321i	0.362280	−	0.362280i	−0.502372	−	0.864652i	$-0.667539\pi$
$691$	9.52321	−	9.52321i	0.362280	−	0.362280i	0.864652	+	0.502372i	$0.167539\pi$
$692$		0			0
$693$	−33.9639			−1.29018
$694$		0			0
$695$		−	30.5560i		−	1.15906i
$696$		0			0
$697$	−1.94137	+	5.49828i	−0.0735345	+	0.208262i
$698$		0			0
$699$		−	24.9651i		−	0.944268i
$700$		0			0
$701$	7.16902			0.270770			0.135385	−	0.990793i	$-0.456773\pi$
$701$	7.16902			0.270770			0.135385	+	0.990793i	$0.456773\pi$
$702$		0			0
$703$	4.20879	−	4.20879i	0.158738	−	0.158738i
$704$		0			0
$705$			94.4484i			3.55713i
$706$		0			0
$707$	−24.1711	+	24.1711i	−0.909048	+	0.909048i
$708$		0			0
$709$	11.9475	+	11.9475i	0.448697	+	0.448697i	0.894921	−	0.446224i	$-0.147232\pi$
$709$	11.9475	+	11.9475i	0.448697	+	0.448697i	−0.446224	+	0.894921i	$0.647232\pi$
$710$		0			0
$711$	2.37548	+	2.37548i	0.0890874	+	0.0890874i
$712$		0			0
$713$	−18.3810			−0.688374
$714$		0			0
$715$	16.9270			0.633034
$716$		0			0
$717$	4.65164	+	4.65164i	0.173719	+	0.173719i
$718$		0			0
$719$	1.44305	+	1.44305i	0.0538167	+	0.0538167i	0.733503	−	0.679686i	$-0.237884\pi$
$719$	1.44305	+	1.44305i	0.0538167	+	0.0538167i	−0.679686	+	0.733503i	$0.737884\pi$
$720$		0			0
$721$	21.2311	−	21.2311i	0.790687	−	0.790687i
$722$		0			0
$723$			23.7457i			0.883113i
$724$		0			0
$725$	−17.9544	+	17.9544i	−0.666808	+	0.666808i
$726$		0			0
$727$	42.6186			1.58064			0.790319	−	0.612696i	$-0.209915\pi$
$727$	42.6186			1.58064			0.790319	+	0.612696i	$0.209915\pi$
$728$		0			0
$729$			5.76891i			0.213663i
$730$		0			0
$731$	−13.6398	−	28.5291i	−0.504488	−	1.05519i
$732$		0			0
$733$		−	4.31894i		−	0.159524i	−0.996814	−	0.0797619i	$-0.974584\pi$
$733$		−	4.31894i		−	0.159524i	0.996814	−	0.0797619i	$-0.0254160\pi$
$734$		0			0
$735$	−66.5186			−2.45358
$736$		0			0
$737$	23.7914	−	23.7914i	0.876369	−	0.876369i
$738$		0			0
$739$			4.20879i			0.154823i	0.996999	+	0.0774114i	$0.0246655\pi$
$739$			4.20879i			0.154823i	−0.996999	+	0.0774114i	$0.975335\pi$
$740$		0			0
$741$	1.30328	−	1.30328i	0.0478771	−	0.0478771i
$742$		0			0
$743$	28.9530	+	28.9530i	1.06218	+	1.06218i	0.997934	+	0.0642473i	$0.0204646\pi$
$743$	28.9530	+	28.9530i	1.06218	+	1.06218i	0.0642473	+	0.997934i	$0.479535\pi$
$744$		0			0
$745$	−58.6639	−	58.6639i	−2.14928	−	2.14928i
$746$		0			0
$747$	24.7700			0.906287
$748$		0			0
$749$	−25.4948			−0.931561
$750$		0			0
$751$	6.72776	+	6.72776i	0.245499	+	0.245499i	0.819121	−	0.573621i	$-0.194462\pi$
$751$	6.72776	+	6.72776i	0.245499	+	0.245499i	−0.573621	+	0.819121i	$0.694462\pi$
$752$		0			0
$753$	2.97746	+	2.97746i	0.108505	+	0.108505i
$754$		0			0
$755$	−33.5154	+	33.5154i	−1.21975	+	1.21975i
$756$		0			0
$757$		−	7.20188i		−	0.261757i	−0.991398	−	0.130878i	$-0.958220\pi$
$757$		−	7.20188i		−	0.261757i	0.991398	−	0.130878i	$-0.0417797\pi$
$758$		0			0
$759$	21.4069	−	21.4069i	0.777020	−	0.777020i
$760$		0			0
$761$	17.2863			0.626628			0.313314	−	0.949650i	$-0.398561\pi$
$761$	17.2863			0.626628			0.313314	+	0.949650i	$0.398561\pi$
$762$		0			0
$763$			26.4691i			0.958246i
$764$		0			0
$765$	10.4717	−	29.6578i	0.378607	−	1.07228i
$766$		0			0
$767$			6.09223i			0.219978i
$768$		0			0
$769$	−43.1690			−1.55671			−0.778357	−	0.627821i	$-0.783947\pi$
$769$	−43.1690			−1.55671			−0.778357	+	0.627821i	$0.783947\pi$
$770$		0			0
$771$	−36.6023	+	36.6023i	−1.31820	+	1.31820i
$772$		0			0
$773$			18.0812i			0.650335i	0.945656	+	0.325167i	$0.105421\pi$
$773$			18.0812i			0.650335i	−0.945656	+	0.325167i	$0.894579\pi$
$774$		0			0
$775$	−45.5930	+	45.5930i	−1.63775	+	1.63775i
$776$		0			0
$777$	−40.6087	−	40.6087i	−1.45683	−	1.45683i
$778$		0			0
$779$	0.880784	+	0.880784i	0.0315574	+	0.0315574i
$780$		0			0
$781$	72.8295			2.60604
$782$		0			0
$783$	−5.72358			−0.204544
$784$		0			0
$785$	22.5535	+	22.5535i	0.804968	+	0.804968i
$786$		0			0
$787$	−33.4749	−	33.4749i	−1.19325	−	1.19325i	−0.976149	−	0.217101i	$-0.930340\pi$
$787$	−33.4749	−	33.4749i	−1.19325	−	1.19325i	−0.217101	−	0.976149i	$-0.569660\pi$
$788$		0			0
$789$	−9.07774	+	9.07774i	−0.323176	+	0.323176i
$790$		0			0
$791$		−	2.71258i		−	0.0964483i
$792$		0			0
$793$	−0.732814	+	0.732814i	−0.0260230	+	0.0260230i
$794$		0			0
$795$	66.0065			2.34101
$796$		0			0
$797$			29.6742i			1.05111i	0.850759	+	0.525557i	$0.176143\pi$
$797$			29.6742i			1.05111i	−0.850759	+	0.525557i	$0.823857\pi$
$798$		0			0
$799$	40.2230	−	19.2307i	1.42299	−	0.680335i
$800$		0			0
$801$		−	28.3741i		−	1.00255i
$802$		0			0
$803$	67.5621			2.38422
$804$		0			0
$805$	31.6121	−	31.6121i	1.11418	−	1.11418i
$806$		0			0
$807$		−	33.1467i		−	1.16682i
$808$		0			0
$809$	−31.7259	+	31.7259i	−1.11542	+	1.11542i	−0.123020	+	0.992404i	$0.539258\pi$
$809$	−31.7259	+	31.7259i	−1.11542	+	1.11542i	−0.992404	+	0.123020i	$0.960742\pi$
$810$		0			0
$811$	6.88085	+	6.88085i	0.241619	+	0.241619i	0.817520	−	0.575900i	$-0.195348\pi$
$811$	6.88085	+	6.88085i	0.241619	+	0.241619i	−0.575900	+	0.817520i	$0.695348\pi$
$812$		0			0
$813$	−4.65164	−	4.65164i	−0.163140	−	0.163140i
$814$		0			0
$815$	65.4944			2.29417
$816$		0			0
$817$	−6.75515			−0.236333
$818$		0			0
$819$	−4.94037	−	4.94037i	−0.172630	−	0.172630i
$820$		0			0
$821$	−20.7164	−	20.7164i	−0.723007	−	0.723007i	0.246210	−	0.969217i	$-0.420815\pi$
$821$	−20.7164	−	20.7164i	−0.723007	−	0.723007i	−0.969217	+	0.246210i	$0.920815\pi$
$822$		0			0
$823$	−13.8500	+	13.8500i	−0.482780	+	0.482780i	−0.906018	−	0.423238i	$-0.860893\pi$
$823$	−13.8500	+	13.8500i	−0.482780	+	0.482780i	0.423238	+	0.906018i	$0.360893\pi$
$824$		0			0
$825$		−	106.197i		−	3.69730i
$826$		0			0
$827$	29.9868	−	29.9868i	1.04274	−	1.04274i	0.0437002	−	0.999045i	$-0.486085\pi$
$827$	29.9868	−	29.9868i	1.04274	−	1.04274i	0.999045	−	0.0437002i	$-0.0139146\pi$
$828$		0			0
$829$	−34.7620			−1.20734			−0.603668	−	0.797236i	$-0.706295\pi$
$829$	−34.7620			−1.20734			−0.603668	+	0.797236i	$0.706295\pi$
$830$		0			0
$831$		−	6.14387i		−	0.213129i
$832$		0			0
$833$	13.5439	+	28.3285i	0.469269	+	0.981524i
$834$		0			0
$835$		−	38.4098i		−	1.32923i
$836$		0			0
$837$	−14.5344			−0.502381
$838$		0			0
$839$	6.91208	−	6.91208i	0.238631	−	0.238631i	−0.577652	−	0.816283i	$-0.696031\pi$
$839$	6.91208	−	6.91208i	0.238631	−	0.238631i	0.816283	+	0.577652i	$0.196031\pi$
$840$		0			0
$841$		−	23.0844i		−	0.796014i
$842$		0			0
$843$	4.02447	−	4.02447i	0.138610	−	0.138610i
$844$		0			0
$845$	−33.6578	−	33.6578i	−1.15786	−	1.15786i
$846$		0			0
$847$	26.8744	+	26.8744i	0.923415	+	0.923415i
$848$		0			0
$849$	−24.4001			−0.837410
$850$		0			0
$851$	20.1115			0.689414
$852$		0			0
$853$	−33.5665	−	33.5665i	−1.14929	−	1.14929i	−0.986692	−	0.162602i	$-0.948011\pi$
$853$	−33.5665	−	33.5665i	−1.14929	−	1.14929i	−0.162602	−	0.986692i	$-0.551989\pi$
$854$		0			0
$855$	−4.75095	−	4.75095i	−0.162479	−	0.162479i
$856$		0			0
$857$	−26.8759	+	26.8759i	−0.918062	+	0.918062i	−0.996888	−	0.0788265i	$-0.974883\pi$
$857$	−26.8759	+	26.8759i	−0.918062	+	0.918062i	0.0788265	+	0.996888i	$0.474883\pi$
$858$		0			0
$859$			35.1443i			1.19911i	0.800335	+	0.599554i	$0.204655\pi$
$859$			35.1443i			1.19911i	−0.800335	+	0.599554i	$0.795345\pi$
$860$		0			0
$861$	8.49828	−	8.49828i	0.289621	−	0.289621i
$862$		0			0
$863$	−5.72358			−0.194833			−0.0974165	−	0.995244i	$-0.531058\pi$
$863$	−5.72358			−0.194833			−0.0974165	+	0.995244i	$0.531058\pi$
$864$		0			0
$865$			9.55691i			0.324945i
$866$		0			0
$867$	−37.5753	+	4.01906i	−1.27612	+	0.136495i
$868$		0			0
$869$		−	7.91883i		−	0.268628i
$870$		0			0
$871$	6.92137			0.234522
$872$		0			0
$873$	10.6742	−	10.6742i	0.361266	−	0.361266i
$874$		0			0
$875$		−	81.7141i		−	2.76244i
$876$		0			0
$877$	−28.6803	+	28.6803i	−0.968465	+	0.968465i	−0.999518	−	0.0310530i	$-0.990114\pi$
$877$	−28.6803	+	28.6803i	−0.968465	+	0.968465i	0.0310530	+	0.999518i	$0.490114\pi$
$878$		0			0
$879$	−17.6535	−	17.6535i	−0.595438	−	0.595438i
$880$		0			0
$881$	36.4588	+	36.4588i	1.22833	+	1.22833i	0.964597	+	0.263730i	$0.0849528\pi$
$881$	36.4588	+	36.4588i	1.22833	+	1.22833i	0.263730	+	0.964597i	$0.415047\pi$
$882$		0			0
$883$	−53.9331			−1.81499			−0.907497	−	0.420059i	$-0.862009\pi$
$883$	−53.9331			−1.81499			−0.907497	+	0.420059i	$0.862009\pi$
$884$		0			0
$885$	56.5275			1.90015
$886$		0			0
$887$	19.2049	+	19.2049i	0.644838	+	0.644838i	0.951741	−	0.306903i	$-0.0992927\pi$
$887$	19.2049	+	19.2049i	0.644838	+	0.644838i	−0.306903	+	0.951741i	$0.599293\pi$
$888$		0			0
$889$	−45.3707	−	45.3707i	−1.52168	−	1.52168i
$890$		0			0
$891$	35.7729	−	35.7729i	1.19844	−	1.19844i
$892$		0			0
$893$		−	9.52406i		−	0.318710i
$894$		0			0
$895$	−11.6939	+	11.6939i	−0.390885	+	0.390885i
$896$		0			0
$897$	6.22766			0.207935
$898$		0			0
$899$			15.0219i			0.501010i
$900$		0			0
$901$	−13.4396	−	28.1104i	−0.447740	−	0.936493i
$902$		0			0
$903$			65.1774i			2.16897i
$904$		0			0
$905$	−37.0157			−1.23044
$906$		0			0
$907$	33.2797	−	33.2797i	1.10504	−	1.10504i	0.111242	−	0.993793i	$-0.464517\pi$
$907$	33.2797	−	33.2797i	1.10504	−	1.10504i	0.993793	−	0.111242i	$-0.0354830\pi$
$908$		0			0
$909$			17.3585i			0.575744i
$910$		0			0
$911$	3.38894	−	3.38894i	0.112281	−	0.112281i	−0.648734	−	0.761015i	$-0.724701\pi$
$911$	3.38894	−	3.38894i	0.112281	−	0.112281i	0.761015	+	0.648734i	$0.224701\pi$
$912$		0			0
$913$	−41.2863	−	41.2863i	−1.36638	−	1.36638i
$914$		0			0
$915$	6.79950	+	6.79950i	0.224785	+	0.224785i
$916$		0			0
$917$	38.7259			1.27884
$918$		0			0
$919$	4.89444			0.161453			0.0807264	−	0.996736i	$-0.474276\pi$
$919$	4.89444			0.161453			0.0807264	+	0.996736i	$0.474276\pi$
$920$		0			0
$921$	18.4622	+	18.4622i	0.608350	+	0.608350i
$922$		0			0
$923$	10.5937	+	10.5937i	0.348696	+	0.348696i
$924$		0			0
$925$	49.8854	−	49.8854i	1.64022	−	1.64022i
$926$		0			0
$927$		−	15.2471i		−	0.500781i
$928$		0			0
$929$	−3.88617	+	3.88617i	−0.127501	+	0.127501i	−0.767978	−	0.640477i	$-0.778737\pi$
$929$	−3.88617	+	3.88617i	−0.127501	+	0.127501i	0.640477	+	0.767978i	$0.278737\pi$
$930$		0			0
$931$	6.70765			0.219834
$932$		0			0
$933$		−	4.73281i		−	0.154945i
$934$		0			0
$935$	−66.8873	+	31.9790i	−2.18745	+	1.04582i
$936$		0			0
$937$		−	11.9740i		−	0.391174i	−0.980686	−	0.195587i	$-0.937339\pi$
$937$		−	11.9740i		−	0.391174i	0.980686	−	0.195587i	$-0.0626612\pi$
$938$		0			0
$939$	−11.1926			−0.365257
$940$		0			0
$941$	27.1595	−	27.1595i	0.885373	−	0.885373i	−0.108701	−	0.994074i	$-0.534669\pi$
$941$	27.1595	−	27.1595i	0.885373	−	0.885373i	0.994074	+	0.108701i	$0.0346691\pi$
$942$		0			0
$943$			4.20879i			0.137057i
$944$		0			0
$945$	24.9966	−	24.9966i	0.813138	−	0.813138i
$946$		0			0
$947$	17.5613	+	17.5613i	0.570667	+	0.570667i	0.932315	−	0.361648i	$-0.117786\pi$
$947$	17.5613	+	17.5613i	0.570667	+	0.570667i	−0.361648	+	0.932315i	$0.617786\pi$
$948$		0			0
$949$	9.82754	+	9.82754i	0.319015	+	0.319015i
$950$		0			0
$951$	−54.3126			−1.76121
$952$		0			0
$953$	−37.2603			−1.20698			−0.603490	−	0.797371i	$-0.706224\pi$
$953$	−37.2603			−1.20698			−0.603490	+	0.797371i	$0.706224\pi$
$954$		0			0
$955$	61.6542	+	61.6542i	1.99508	+	1.99508i
$956$		0			0
$957$	−17.4948	−	17.4948i	−0.565528	−	0.565528i
$958$		0			0
$959$	−27.4991	+	27.4991i	−0.887993	+	0.887993i
$960$		0			0
$961$			7.14648i			0.230532i
$962$		0			0
$963$	−9.15456	+	9.15456i	−0.295002	+	0.295002i
$964$		0			0
$965$	−22.2086			−0.714919
$966$		0			0
$967$		−	36.0143i		−	1.15814i	−0.815278	−	0.579070i	$-0.803416\pi$
$967$		−	36.0143i		−	1.15814i	0.815278	−	0.579070i	$-0.196584\pi$
$968$		0			0
$969$	−2.68773	+	7.61211i	−0.0863423	+	0.244536i
$970$		0			0
$971$			49.5292i			1.58947i	0.606958	+	0.794734i	$0.292389\pi$
$971$			49.5292i			1.58947i	−0.606958	+	0.794734i	$0.707611\pi$
$972$		0			0
$973$	29.7294			0.953080
$974$		0			0
$975$	15.4473	−	15.4473i	0.494710	−	0.494710i
$976$		0			0
$977$			40.1104i			1.28325i	0.767021	+	0.641623i	$0.221738\pi$
$977$			40.1104i			1.28325i	−0.767021	+	0.641623i	$0.778262\pi$
$978$		0			0
$979$	−47.2936	+	47.2936i	−1.51151	+	1.51151i
$980$		0			0
$981$	9.50440	+	9.50440i	0.303452	+	0.303452i
$982$		0			0
$983$	22.6305	+	22.6305i	0.721800	+	0.721800i	0.968972	−	0.247171i	$-0.0795011\pi$
$983$	22.6305	+	22.6305i	0.721800	+	0.721800i	−0.247171	+	0.968972i	$0.579501\pi$
$984$		0			0
$985$	73.7777			2.35075
$986$		0			0
$987$	−91.8933			−2.92499
$988$		0			0
$989$	−16.1396	−	16.1396i	−0.513210	−	0.513210i
$990$		0			0
$991$	−37.0887	−	37.0887i	−1.17816	−	1.17816i	−0.980213	−	0.197947i	$-0.936573\pi$
$991$	−37.0887	−	37.0887i	−1.17816	−	1.17816i	−0.197947	−	0.980213i	$-0.563427\pi$
$992$		0			0
$993$	15.4036	−	15.4036i	0.488817	−	0.488817i
$994$		0			0
$995$		−	48.3938i		−	1.53419i
$996$		0			0
$997$	−33.9475	+	33.9475i	−1.07513	+	1.07513i	−0.0781889	+	0.996939i	$0.524914\pi$
$997$	−33.9475	+	33.9475i	−1.07513	+	1.07513i	−0.996939	+	0.0781889i	$0.975086\pi$
$998$		0			0
$999$	15.9027			0.503140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.o.w.897.2		12
4.3	odd	2	inner	1088.2.o.w.897.5		12
8.3	odd	2		544.2.o.i.353.2	yes	12
8.5	even	2		544.2.o.i.353.5	yes	12
17.4	even	4	inner	1088.2.o.w.769.2		12
68.55	odd	4	inner	1088.2.o.w.769.5		12
136.19	odd	8		9248.2.a.bv.1.4		12
136.21	even	4		544.2.o.i.225.5	yes	12
136.53	even	8		9248.2.a.bv.1.10		12
136.83	odd	8		9248.2.a.bv.1.9		12
136.117	even	8		9248.2.a.bv.1.3		12
136.123	odd	4		544.2.o.i.225.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.o.i.225.2	✓	12	136.123	odd	4
544.2.o.i.225.5	yes	12	136.21	even	4
544.2.o.i.353.2	yes	12	8.3	odd	2
544.2.o.i.353.5	yes	12	8.5	even	2
1088.2.o.w.769.2		12	17.4	even	4	inner
1088.2.o.w.769.5		12	68.55	odd	4	inner
1088.2.o.w.897.2		12	1.1	even	1	trivial
1088.2.o.w.897.5		12	4.3	odd	2	inner
9248.2.a.bv.1.3		12	136.117	even	8
9248.2.a.bv.1.4		12	136.19	odd	8
9248.2.a.bv.1.9		12	136.83	odd	8
9248.2.a.bv.1.10		12	136.53	even	8

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.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57184 - 1.57184i) q^{3} +(2.77846 + 2.77846i) q^{5} +(-2.70329 + 2.70329i) q^{7} +1.94137i q^{9} +O(q^{10})\)	\(q+(-1.57184 - 1.57184i) q^{3} +(2.77846 + 2.77846i) q^{5} +(-2.70329 + 2.70329i) q^{7} +1.94137i q^{9} +(3.23584 - 3.23584i) q^{11} +0.941367 q^{13} -8.73458i q^{15} +(-3.71982 + 1.77846i) q^{17} +0.880784i q^{19} +8.49828 q^{21} +(-2.10439 + 2.10439i) q^{23} +10.4396i q^{25} +(-1.66400 + 1.66400i) q^{27} +(1.71982 + 1.71982i) q^{29} +(4.36729 + 4.36729i) q^{31} -10.1725 q^{33} -15.0219 q^{35} +(-4.77846 - 4.77846i) q^{37} +(-1.47968 - 1.47968i) q^{39} +(1.00000 - 1.00000i) q^{41} +7.66948i q^{43} +(-5.39400 + 5.39400i) q^{45} -10.8132 q^{47} -7.61555i q^{49} +(8.64242 + 3.05152i) q^{51} +7.55691i q^{53} +17.9813 q^{55} +(1.38445 - 1.38445i) q^{57} +6.47169i q^{59} +(-0.778457 + 0.778457i) q^{61} +(-5.24808 - 5.24808i) q^{63} +(2.61555 + 2.61555i) q^{65} +7.35247 q^{67} +6.61555 q^{69} +(11.2535 + 11.2535i) q^{71} +(10.4396 + 10.4396i) q^{73} +(16.4095 - 16.4095i) q^{75} +17.4948i q^{77} +(1.22361 - 1.22361i) q^{79} +11.0552 q^{81} -12.7591i q^{83} +(-15.2767 - 5.39400i) q^{85} -5.40658i q^{87} -14.6155 q^{89} +(-2.54479 + 2.54479i) q^{91} -13.7294i q^{93} +(-2.44722 + 2.44722i) q^{95} +(-5.49828 - 5.49828i) q^{97} +(6.28196 + 6.28196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) \) 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Introduction

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