LMFDB - Embedded newform 1088.2.s.a.625.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(625,1088)]

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, 1, 1]))

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

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

chi := DirichletCharacter("1088.625");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.s (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			625.10
Character	$\chi$	$=$	1088.625
Dual form			1088.2.s.a.1041.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70026 q^{3} +2.90401i q^{5} +(-0.453147 - 0.453147i) q^{7} -0.109126 q^{9} +O(q^{10})$	\(q-1.70026 q^{3} +2.90401i q^{5} +(-0.453147 - 0.453147i) q^{7} -0.109126 q^{9} -2.30130 q^{11} +(-2.83013 + 2.83013i) q^{13} -4.93756i q^{15} +(2.55560 - 3.23557i) q^{17} +(-2.28566 - 2.28566i) q^{19} +(0.770467 + 0.770467i) q^{21} +(-2.63418 - 2.63418i) q^{23} -3.43327 q^{25} +5.28631 q^{27} +3.29992 q^{29} +(3.92140 + 3.92140i) q^{31} +3.91280 q^{33} +(1.31594 - 1.31594i) q^{35} +1.27321i q^{37} +(4.81195 - 4.81195i) q^{39} +(-4.47191 - 4.47191i) q^{41} +(4.30802 - 4.30802i) q^{43} -0.316902i q^{45} -5.63952 q^{47} -6.58931i q^{49} +(-4.34517 + 5.50130i) q^{51} +(4.23584 - 4.23584i) q^{53} -6.68299i q^{55} +(3.88622 + 3.88622i) q^{57} +(-3.50296 + 3.50296i) q^{59} -10.8401i q^{61} +(0.0494500 + 0.0494500i) q^{63} +(-8.21873 - 8.21873i) q^{65} +(-8.74835 + 8.74835i) q^{67} +(4.47878 + 4.47878i) q^{69} +(0.687850 - 0.687850i) q^{71} +(11.8374 - 11.8374i) q^{73} +5.83745 q^{75} +(1.04283 + 1.04283i) q^{77} +(7.30349 - 7.30349i) q^{79} -8.66071 q^{81} +(-4.42323 - 4.42323i) q^{83} +(9.39613 + 7.42148i) q^{85} -5.61071 q^{87} -0.595133i q^{89} +2.56493 q^{91} +(-6.66740 - 6.66740i) q^{93} +(6.63759 - 6.63759i) q^{95} +(-9.56777 - 9.56777i) q^{97} +0.251131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 60 q^{9}+O(q^{10}) $ 68 * q + 4 * q^3 + 60 * q^9	$ 68 q + 4 q^{3} + 60 q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{17} - 4 q^{21} - 52 q^{25} + 16 q^{27} - 4 q^{29} + 4 q^{31} - 8 q^{33} + 4 q^{35} + 12 q^{39} + 48 q^{47} - 4 q^{51} - 12 q^{57} + 32 q^{59} + 32 q^{63} + 4 q^{65} + 4 q^{67} + 28 q^{69} + 8 q^{73} - 4 q^{75} - 28 q^{77} - 12 q^{79} + 28 q^{81} + 24 q^{85} - 24 q^{87} - 40 q^{91} - 12 q^{93} + 4 q^{95} - 4 q^{97} + 52 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 60 * q^9 + 4 * q^11 - 4 * q^13 - 4 * q^17 - 4 * q^21 - 52 * q^25 + 16 * q^27 - 4 * q^29 + 4 * q^31 - 8 * q^33 + 4 * q^35 + 12 * q^39 + 48 * q^47 - 4 * q^51 - 12 * q^57 + 32 * q^59 + 32 * q^63 + 4 * q^65 + 4 * q^67 + 28 * q^69 + 8 * q^73 - 4 * q^75 - 28 * q^77 - 12 * q^79 + 28 * q^81 + 24 * q^85 - 24 * q^87 - 40 * q^91 - 12 * q^93 + 4 * q^95 - 4 * q^97 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.70026			−0.981644			−0.490822	−	0.871260i	$-0.663303\pi$
$3$	−1.70026			−0.981644			−0.490822	+	0.871260i	$0.663303\pi$
$4$		0			0
$5$			2.90401i			1.29871i	0.760484	+	0.649356i	$0.224962\pi$
$5$			2.90401i			1.29871i	−0.760484	+	0.649356i	$0.775038\pi$
$6$		0			0
$7$	−0.453147	−	0.453147i	−0.171274	−	0.171274i	0.616265	−	0.787539i	$-0.288645\pi$
$7$	−0.453147	−	0.453147i	−0.171274	−	0.171274i	−0.787539	+	0.616265i	$0.788645\pi$
$8$		0			0
$9$	−0.109126			−0.0363752
$10$		0			0
$11$	−2.30130			−0.693867			−0.346934	−	0.937890i	$-0.612777\pi$
$11$	−2.30130			−0.693867			−0.346934	+	0.937890i	$0.612777\pi$
$12$		0			0
$13$	−2.83013	+	2.83013i	−0.784937	+	0.784937i	−0.980659	−	0.195722i	$-0.937295\pi$
$13$	−2.83013	+	2.83013i	−0.784937	+	0.784937i	0.195722	+	0.980659i	$0.437295\pi$
$14$		0			0
$15$		−	4.93756i		−	1.27487i
$16$		0			0
$17$	2.55560	−	3.23557i	0.619823	−	0.784741i
$17$	2.55560	−	3.23557i	0.619823	−	0.784741i
$18$		0			0
$19$	−2.28566	−	2.28566i	−0.524367	−	0.524367i	0.394520	−	0.918887i	$-0.370911\pi$
$19$	−2.28566	−	2.28566i	−0.524367	−	0.524367i	−0.918887	+	0.394520i	$0.870911\pi$
$20$		0			0
$21$	0.770467	+	0.770467i	0.168130	+	0.168130i
$22$		0			0
$23$	−2.63418	−	2.63418i	−0.549264	−	0.549264i	0.376964	−	0.926228i	$-0.376968\pi$
$23$	−2.63418	−	2.63418i	−0.549264	−	0.549264i	−0.926228	+	0.376964i	$0.876968\pi$
$24$		0			0
$25$	−3.43327			−0.686655
$26$		0			0
$27$	5.28631			1.01735
$28$		0			0
$29$	3.29992			0.612779			0.306390	−	0.951906i	$-0.400879\pi$
$29$	3.29992			0.612779			0.306390	+	0.951906i	$0.400879\pi$
$30$		0			0
$31$	3.92140	+	3.92140i	0.704305	+	0.704305i	0.965332	−	0.261027i	$-0.0840610\pi$
$31$	3.92140	+	3.92140i	0.704305	+	0.704305i	−0.261027	+	0.965332i	$0.584061\pi$
$32$		0			0
$33$	3.91280			0.681131
$34$		0			0
$35$	1.31594	−	1.31594i	0.222435	−	0.222435i
$36$		0			0
$37$			1.27321i			0.209314i	0.994508	+	0.104657i	$0.0333745\pi$
$37$			1.27321i			0.209314i	−0.994508	+	0.104657i	$0.966625\pi$
$38$		0			0
$39$	4.81195	−	4.81195i	0.770528	−	0.770528i
$40$		0			0
$41$	−4.47191	−	4.47191i	−0.698395	−	0.698395i	0.265669	−	0.964064i	$-0.414407\pi$
$41$	−4.47191	−	4.47191i	−0.698395	−	0.698395i	−0.964064	+	0.265669i	$0.914407\pi$
$42$		0			0
$43$	4.30802	−	4.30802i	0.656967	−	0.656967i	−0.297694	−	0.954661i	$-0.596218\pi$
$43$	4.30802	−	4.30802i	0.656967	−	0.656967i	0.954661	+	0.297694i	$0.0962176\pi$
$44$		0			0
$45$		−	0.316902i		−	0.0472410i
$46$		0			0
$47$	−5.63952			−0.822609			−0.411305	−	0.911498i	$-0.634927\pi$
$47$	−5.63952			−0.822609			−0.411305	+	0.911498i	$0.634927\pi$
$48$		0			0
$49$		−	6.58931i		−	0.941331i
$50$		0			0
$51$	−4.34517	+	5.50130i	−0.608446	+	0.770337i
$52$		0			0
$53$	4.23584	−	4.23584i	0.581838	−	0.581838i	−0.353570	−	0.935408i	$-0.615032\pi$
$53$	4.23584	−	4.23584i	0.581838	−	0.581838i	0.935408	+	0.353570i	$0.115032\pi$
$54$		0			0
$55$		−	6.68299i		−	0.901134i
$56$		0			0
$57$	3.88622	+	3.88622i	0.514742	+	0.514742i
$58$		0			0
$59$	−3.50296	+	3.50296i	−0.456046	+	0.456046i	−0.897355	−	0.441309i	$-0.854514\pi$
$59$	−3.50296	+	3.50296i	−0.456046	+	0.456046i	0.441309	+	0.897355i	$0.354514\pi$
$60$		0			0
$61$		−	10.8401i		−	1.38793i	−0.720009	−	0.693964i	$-0.755863\pi$
$61$		−	10.8401i		−	1.38793i	0.720009	−	0.693964i	$-0.244137\pi$
$62$		0			0
$63$	0.0494500	+	0.0494500i	0.00623012	+	0.00623012i
$64$		0			0
$65$	−8.21873	−	8.21873i	−1.01941	−	1.01941i
$66$		0			0
$67$	−8.74835	+	8.74835i	−1.06878	+	1.06878i	−0.0713278	+	0.997453i	$0.522724\pi$
$67$	−8.74835	+	8.74835i	−1.06878	+	1.06878i	−0.997453	+	0.0713278i	$0.977276\pi$
$68$		0			0
$69$	4.47878	+	4.47878i	0.539181	+	0.539181i
$70$		0			0
$71$	0.687850	−	0.687850i	0.0816327	−	0.0816327i	−0.665111	−	0.746744i	$-0.731616\pi$
$71$	0.687850	−	0.687850i	0.0816327	−	0.0816327i	0.746744	+	0.665111i	$0.231616\pi$
$72$		0			0
$73$	11.8374	−	11.8374i	1.38547	−	1.38547i	0.550886	−	0.834581i	$-0.314290\pi$
$73$	11.8374	−	11.8374i	1.38547	−	1.38547i	0.834581	−	0.550886i	$-0.185710\pi$
$74$		0			0
$75$	5.83745			0.674050
$76$		0			0
$77$	1.04283	+	1.04283i	0.118841	+	0.118841i
$78$		0			0
$79$	7.30349	−	7.30349i	0.821707	−	0.821707i	−0.164646	−	0.986353i	$-0.552648\pi$
$79$	7.30349	−	7.30349i	0.821707	−	0.821707i	0.986353	+	0.164646i	$0.0526481\pi$
$80$		0			0
$81$	−8.66071			−0.962302
$82$		0			0
$83$	−4.42323	−	4.42323i	−0.485513	−	0.485513i	0.421374	−	0.906887i	$-0.361548\pi$
$83$	−4.42323	−	4.42323i	−0.485513	−	0.485513i	−0.906887	+	0.421374i	$0.861548\pi$
$84$		0			0
$85$	9.39613	+	7.42148i	1.01915	+	0.804972i
$86$		0			0
$87$	−5.61071			−0.601531
$88$		0			0
$89$		−	0.595133i		−	0.0630840i	−0.999502	−	0.0315420i	$-0.989958\pi$
$89$		−	0.595133i		−	0.0630840i	0.999502	−	0.0315420i	$-0.0100418\pi$
$90$		0			0
$91$	2.56493			0.268878
$92$		0			0
$93$	−6.66740	−	6.66740i	−0.691377	−	0.691377i
$94$		0			0
$95$	6.63759	−	6.63759i	0.681002	−	0.681002i
$96$		0			0
$97$	−9.56777	−	9.56777i	−0.971460	−	0.971460i	0.0281440	−	0.999604i	$-0.491040\pi$
$97$	−9.56777	−	9.56777i	−0.971460	−	0.971460i	−0.999604	+	0.0281440i	$0.991040\pi$
$98$		0			0
$99$	0.251131			0.0252396
$100$		0			0
$101$	−1.96630	−	1.96630i	−0.195654	−	0.195654i	0.602480	−	0.798134i	$-0.294179\pi$
$101$	−1.96630	−	1.96630i	−0.195654	−	0.195654i	−0.798134	+	0.602480i	$0.794179\pi$
$102$		0			0
$103$		−	15.6956i		−	1.54653i	−0.634083	−	0.773265i	$-0.718622\pi$
$103$		−	15.6956i		−	1.54653i	0.634083	−	0.773265i	$-0.281378\pi$
$104$		0			0
$105$	−2.23744	+	2.23744i	−0.218352	+	0.218352i
$106$		0			0
$107$			9.13741i			0.883347i	0.897176	+	0.441673i	$0.145615\pi$
$107$			9.13741i			0.883347i	−0.897176	+	0.441673i	$0.854385\pi$
$108$		0			0
$109$		−	6.62557i		−	0.634614i	−0.948323	−	0.317307i	$-0.897221\pi$
$109$		−	6.62557i		−	0.634614i	0.948323	−	0.317307i	$-0.102779\pi$
$110$		0			0
$111$		−	2.16478i		−	0.205472i
$112$		0			0
$113$	−14.5533	+	14.5533i	−1.36906	+	1.36906i	−0.507271	+	0.861787i	$0.669346\pi$
$113$	−14.5533	+	14.5533i	−1.36906	+	1.36906i	−0.861787	+	0.507271i	$0.830654\pi$
$114$		0			0
$115$	7.64967	−	7.64967i	0.713336	−	0.713336i
$116$		0			0
$117$	0.308840	−	0.308840i	0.0285523	−	0.0285523i
$118$		0			0
$119$	−2.62425	+	0.308129i	−0.240565	+	0.0282461i
$120$		0			0
$121$	−5.70403			−0.518548
$122$		0			0
$123$	7.60340	+	7.60340i	0.685575	+	0.685575i
$124$		0			0
$125$			4.54979i			0.406946i
$126$		0			0
$127$			17.4654i			1.54980i	0.632082	+	0.774902i	$0.282201\pi$
$127$			17.4654i			1.54980i	−0.632082	+	0.774902i	$0.717799\pi$
$128$		0			0
$129$	−7.32474	+	7.32474i	−0.644908	+	0.644908i
$130$		0			0
$131$	−16.9527			−1.48116			−0.740582	−	0.671966i	$-0.765450\pi$
$131$	−16.9527			−1.48116			−0.740582	+	0.671966i	$0.765450\pi$
$132$		0			0
$133$			2.07149i			0.179621i
$134$		0			0
$135$			15.3515i			1.32125i
$136$		0			0
$137$			5.65049i			0.482754i	0.970431	+	0.241377i	$0.0775990\pi$
$137$			5.65049i			0.482754i	−0.970431	+	0.241377i	$0.922401\pi$
$138$		0			0
$139$		−	17.4550i		−	1.48052i	−0.672323	−	0.740258i	$-0.734703\pi$
$139$		−	17.4550i		−	1.48052i	0.672323	−	0.740258i	$-0.265297\pi$
$140$		0			0
$141$	9.58864			0.807509
$142$		0			0
$143$	6.51297	−	6.51297i	0.544642	−	0.544642i
$144$		0			0
$145$			9.58299i			0.795824i
$146$		0			0
$147$			11.2035i			0.924052i
$148$		0			0
$149$	−5.02131	−	5.02131i	−0.411362	−	0.411362i	0.470851	−	0.882213i	$-0.343947\pi$
$149$	−5.02131	−	5.02131i	−0.411362	−	0.411362i	−0.882213	+	0.470851i	$0.843947\pi$
$150$		0			0
$151$	7.45484			0.606667			0.303333	−	0.952885i	$-0.401900\pi$
$151$	7.45484			0.606667			0.303333	+	0.952885i	$0.401900\pi$
$152$		0			0
$153$	−0.278881	+	0.353084i	−0.0225462	+	0.0285451i
$154$		0			0
$155$	−11.3878	+	11.3878i	−0.914690	+	0.914690i
$156$		0			0
$157$	−8.31618	+	8.31618i	−0.663703	+	0.663703i	−0.956251	−	0.292548i	$-0.905497\pi$
$157$	−8.31618	+	8.31618i	−0.663703	+	0.663703i	0.292548	+	0.956251i	$0.405497\pi$
$158$		0			0
$159$	−7.20202	+	7.20202i	−0.571157	+	0.571157i
$160$		0			0
$161$			2.38734i			0.188149i
$162$		0			0
$163$		−	8.04352i		−	0.630017i	−0.949089	−	0.315009i	$-0.897993\pi$
$163$		−	8.04352i		−	0.630017i	0.949089	−	0.315009i	$-0.102007\pi$
$164$		0			0
$165$			11.3628i			0.884593i
$166$		0			0
$167$	1.92440	−	1.92440i	0.148915	−	0.148915i	−0.628718	−	0.777633i	$-0.716420\pi$
$167$	1.92440	−	1.92440i	0.148915	−	0.148915i	0.777633	+	0.628718i	$0.216420\pi$
$168$		0			0
$169$		−	3.01927i		−	0.232252i
$170$		0			0
$171$	0.249425	+	0.249425i	0.0190740	+	0.0190740i
$172$		0			0
$173$	23.0699			1.75398			0.876988	−	0.480513i	$-0.159549\pi$
$173$	23.0699			1.75398			0.876988	+	0.480513i	$0.159549\pi$
$174$		0			0
$175$	1.55578	+	1.55578i	0.117606	+	0.117606i
$176$		0			0
$177$	5.95593	−	5.95593i	0.447675	−	0.447675i
$178$		0			0
$179$	4.53693	+	4.53693i	0.339106	+	0.339106i	0.856031	−	0.516925i	$-0.172923\pi$
$179$	4.53693	+	4.53693i	0.339106	+	0.339106i	−0.516925	+	0.856031i	$0.672923\pi$
$180$		0			0
$181$	−7.30229			−0.542775			−0.271387	−	0.962470i	$-0.587482\pi$
$181$	−7.30229			−0.542775			−0.271387	+	0.962470i	$0.587482\pi$
$182$		0			0
$183$			18.4309i			1.36245i
$184$		0			0
$185$	−3.69741			−0.271839
$186$		0			0
$187$	−5.88119	+	7.44601i	−0.430075	+	0.544506i
$188$		0			0
$189$	−2.39548	−	2.39548i	−0.174245	−	0.174245i
$190$		0			0
$191$	14.1529			1.02406			0.512032	−	0.858966i	$-0.328893\pi$
$191$	14.1529			1.02406			0.512032	+	0.858966i	$0.328893\pi$
$192$		0			0
$193$	−2.01748	+	2.01748i	−0.145221	+	0.145221i	−0.775979	−	0.630758i	$-0.782744\pi$
$193$	−2.01748	+	2.01748i	−0.145221	+	0.145221i	0.630758	+	0.775979i	$0.282744\pi$
$194$		0			0
$195$	13.9739	+	13.9739i	1.00070	+	1.00070i
$196$		0			0
$197$	6.52444			0.464847			0.232424	−	0.972615i	$-0.425334\pi$
$197$	6.52444			0.464847			0.232424	+	0.972615i	$0.425334\pi$
$198$		0			0
$199$	14.7184	−	14.7184i	1.04336	−	1.04336i	0.0443456	−	0.999016i	$-0.485880\pi$
$199$	14.7184	−	14.7184i	1.04336	−	1.04336i	0.999016	−	0.0443456i	$-0.0141203\pi$
$200$		0			0
$201$	14.8744	−	14.8744i	1.04916	−	1.04916i
$202$		0			0
$203$	−1.49535	−	1.49535i	−0.104953	−	0.104953i
$204$		0			0
$205$	12.9865	−	12.9865i	0.907014	−	0.907014i
$206$		0			0
$207$	0.287456	+	0.287456i	0.0199796	+	0.0199796i
$208$		0			0
$209$	5.25999	+	5.25999i	0.363841	+	0.363841i
$210$		0			0
$211$		−	7.42372i		−	0.511070i	−0.966800	−	0.255535i	$-0.917748\pi$
$211$		−	7.42372i		−	0.511070i	0.966800	−	0.255535i	$-0.0822516\pi$
$212$		0			0
$213$	−1.16952	+	1.16952i	−0.0801343	+	0.0801343i
$214$		0			0
$215$	12.5105	+	12.5105i	0.853211	+	0.853211i
$216$		0			0
$217$		−	3.55395i		−	0.241258i
$218$		0			0
$219$	−20.1267	+	20.1267i	−1.36003	+	1.36003i
$220$		0			0
$221$	1.92442	+	16.3898i	0.129450	+	1.10249i
$222$		0			0
$223$			29.8095i			1.99619i	0.0616829	+	0.998096i	$0.480353\pi$
$223$			29.8095i			1.99619i	−0.0616829	+	0.998096i	$0.519647\pi$
$224$		0			0
$225$	0.374658			0.0249772
$226$		0			0
$227$			1.47706i			0.0980357i	0.998798	+	0.0490178i	$0.0156091\pi$
$227$			1.47706i			0.0980357i	−0.998798	+	0.0490178i	$0.984391\pi$
$228$		0			0
$229$	−18.7066	+	18.7066i	−1.23617	+	1.23617i	−0.274613	+	0.961555i	$0.588550\pi$
$229$	−18.7066	+	18.7066i	−1.23617	+	1.23617i	−0.961555	+	0.274613i	$0.911450\pi$
$230$		0			0
$231$	−1.77307	−	1.77307i	−0.116660	−	0.116660i
$232$		0			0
$233$	−10.1492	+	10.1492i	−0.664894	+	0.664894i	−0.956530	−	0.291635i	$-0.905801\pi$
$233$	−10.1492	+	10.1492i	−0.664894	+	0.664894i	0.291635	+	0.956530i	$0.405801\pi$
$234$		0			0
$235$		−	16.3772i		−	1.06833i
$236$		0			0
$237$	−12.4178	+	12.4178i	−0.806624	+	0.806624i
$238$		0			0
$239$	4.78383			0.309440			0.154720	−	0.987958i	$-0.450552\pi$
$239$	4.78383			0.309440			0.154720	+	0.987958i	$0.450552\pi$
$240$		0			0
$241$	18.5466	+	18.5466i	1.19469	+	1.19469i	0.975735	+	0.218954i	$0.0702643\pi$
$241$	18.5466	+	18.5466i	1.19469	+	1.19469i	0.218954	+	0.975735i	$0.429736\pi$
$242$		0			0
$243$	−1.13350			−0.0727139
$244$		0			0
$245$	19.1354			1.22252
$246$		0			0
$247$	12.9374			0.823190
$248$		0			0
$249$	7.52063	+	7.52063i	0.476601	+	0.476601i
$250$		0			0
$251$	−21.5723	−	21.5723i	−1.36163	−	1.36163i	−0.871841	−	0.489789i	$-0.837074\pi$
$251$	−21.5723	−	21.5723i	−1.36163	−	1.36163i	−0.489789	−	0.871841i	$-0.662926\pi$
$252$		0			0
$253$	6.06202	+	6.06202i	0.381116	+	0.381116i
$254$		0			0
$255$	−15.9758	−	12.6184i	−1.00045	−	0.790196i
$256$		0			0
$257$			5.33373i			0.332709i	0.986066	+	0.166355i	$0.0531996\pi$
$257$			5.33373i			0.332709i	−0.986066	+	0.166355i	$0.946800\pi$
$258$		0			0
$259$	0.576952	−	0.576952i	0.0358500	−	0.0358500i
$260$		0			0
$261$	−0.360106			−0.0222900
$262$		0			0
$263$	−26.7881			−1.65183			−0.825914	−	0.563797i	$-0.809340\pi$
$263$	−26.7881			−1.65183			−0.825914	+	0.563797i	$0.809340\pi$
$264$		0			0
$265$	12.3009	+	12.3009i	0.755640	+	0.755640i
$266$		0			0
$267$			1.01188i			0.0619260i
$268$		0			0
$269$	−12.0097			−0.732245			−0.366123	−	0.930567i	$-0.619315\pi$
$269$	−12.0097			−0.732245			−0.366123	+	0.930567i	$0.619315\pi$
$270$		0			0
$271$	−15.1708			−0.921563			−0.460781	−	0.887514i	$-0.652431\pi$
$271$	−15.1708			−0.921563			−0.460781	+	0.887514i	$0.652431\pi$
$272$		0			0
$273$	−4.36104			−0.263942
$274$		0			0
$275$	7.90098			0.476447
$276$		0			0
$277$		−	18.6570i		−	1.12099i	−0.828158	−	0.560495i	$-0.810611\pi$
$277$		−	18.6570i		−	1.12099i	0.828158	−	0.560495i	$-0.189389\pi$
$278$		0			0
$279$	−0.427926	−	0.427926i	−0.0256193	−	0.0256193i
$280$		0			0
$281$	−1.39844			−0.0834240			−0.0417120	−	0.999130i	$-0.513281\pi$
$281$	−1.39844			−0.0834240			−0.0417120	+	0.999130i	$0.513281\pi$
$282$		0			0
$283$	−10.9791			−0.652638			−0.326319	−	0.945260i	$-0.605808\pi$
$283$	−10.9791			−0.652638			−0.326319	+	0.945260i	$0.605808\pi$
$284$		0			0
$285$	−11.2856	+	11.2856i	−0.668502	+	0.668502i
$286$		0			0
$287$			4.05287i			0.239233i
$288$		0			0
$289$	−3.93785	−	16.5376i	−0.231638	−	0.972802i
$290$		0			0
$291$	16.2677	+	16.2677i	0.953628	+	0.953628i
$292$		0			0
$293$	−4.64879	−	4.64879i	−0.271585	−	0.271585i	0.558153	−	0.829738i	$-0.311510\pi$
$293$	−4.64879	−	4.64879i	−0.271585	−	0.271585i	−0.829738	+	0.558153i	$0.811510\pi$
$294$		0			0
$295$	−10.1726	−	10.1726i	−0.592273	−	0.592273i
$296$		0			0
$297$	−12.1654			−0.705907
$298$		0			0
$299$	14.9101			0.862274
$300$		0			0
$301$	−3.90434			−0.225042
$302$		0			0
$303$	3.34322	+	3.34322i	0.192063	+	0.192063i
$304$		0			0
$305$	31.4797			1.80252
$306$		0			0
$307$	−6.75740	+	6.75740i	−0.385665	+	0.385665i	−0.873138	−	0.487473i	$-0.837919\pi$
$307$	−6.75740	+	6.75740i	−0.385665	+	0.385665i	0.487473	+	0.873138i	$0.337919\pi$
$308$		0			0
$309$			26.6865i			1.51814i
$310$		0			0
$311$	7.32752	−	7.32752i	0.415506	−	0.415506i	−0.468146	−	0.883651i	$-0.655078\pi$
$311$	7.32752	−	7.32752i	0.415506	−	0.415506i	0.883651	+	0.468146i	$0.155078\pi$
$312$		0			0
$313$	−6.51145	−	6.51145i	−0.368049	−	0.368049i	0.498716	−	0.866765i	$-0.333805\pi$
$313$	−6.51145	−	6.51145i	−0.368049	−	0.368049i	−0.866765	+	0.498716i	$0.833805\pi$
$314$		0			0
$315$	−0.143603	+	0.143603i	−0.00809113	+	0.00809113i
$316$		0			0
$317$			5.72102i			0.321325i	0.987009	+	0.160662i	$0.0513630\pi$
$317$			5.72102i			0.321325i	−0.987009	+	0.160662i	$0.948637\pi$
$318$		0			0
$319$	−7.59409			−0.425187
$320$		0			0
$321$		−	15.5359i		−	0.867132i
$322$		0			0
$323$	−13.2367	+	1.55419i	−0.736508	+	0.0864776i
$324$		0			0
$325$	9.71661	−	9.71661i	0.538980	−	0.538980i
$326$		0			0
$327$			11.2652i			0.622965i
$328$		0			0
$329$	2.55554	+	2.55554i	0.140891	+	0.140891i
$330$		0			0
$331$	13.7414	−	13.7414i	0.755293	−	0.755293i	−0.220169	−	0.975462i	$-0.570661\pi$
$331$	13.7414	−	13.7414i	0.755293	−	0.755293i	0.975462	+	0.220169i	$0.0706608\pi$
$332$		0			0
$333$		−	0.138940i		−	0.00761386i
$334$		0			0
$335$	−25.4053	−	25.4053i	−1.38804	−	1.38804i
$336$		0			0
$337$	−12.9768	−	12.9768i	−0.706889	−	0.706889i	0.258991	−	0.965880i	$-0.416610\pi$
$337$	−12.9768	−	12.9768i	−0.706889	−	0.706889i	−0.965880	+	0.258991i	$0.916610\pi$
$338$		0			0
$339$	24.7443	−	24.7443i	1.34393	−	1.34393i
$340$		0			0
$341$	−9.02432	−	9.02432i	−0.488694	−	0.488694i
$342$		0			0
$343$	−6.15796	+	6.15796i	−0.332499	+	0.332499i
$344$		0			0
$345$	−13.0064	+	13.0064i	−0.700241	+	0.700241i
$346$		0			0
$347$	16.4162			0.881267			0.440634	−	0.897687i	$-0.354754\pi$
$347$	16.4162			0.881267			0.440634	+	0.897687i	$0.354754\pi$
$348$		0			0
$349$	−17.9170	−	17.9170i	−0.959074	−	0.959074i	0.0401206	−	0.999195i	$-0.487226\pi$
$349$	−17.9170	−	17.9170i	−0.959074	−	0.959074i	−0.999195	+	0.0401206i	$0.987226\pi$
$350$		0			0
$351$	−14.9610	+	14.9610i	−0.798557	+	0.798557i
$352$		0			0
$353$	21.9140			1.16637			0.583183	−	0.812341i	$-0.301807\pi$
$353$	21.9140			1.16637			0.583183	+	0.812341i	$0.301807\pi$
$354$		0			0
$355$	1.99752	+	1.99752i	0.106017	+	0.106017i
$356$		0			0
$357$	4.46191	−	0.523898i	0.236149	−	0.0277276i
$358$		0			0
$359$	−9.33467			−0.492665			−0.246332	−	0.969185i	$-0.579226\pi$
$359$	−9.33467			−0.492665			−0.246332	+	0.969185i	$0.579226\pi$
$360$		0			0
$361$		−	8.55148i		−	0.450078i
$362$		0			0
$363$	9.69831			0.509030
$364$		0			0
$365$	34.3760	+	34.3760i	1.79932	+	1.79932i
$366$		0			0
$367$	−3.61520	+	3.61520i	−0.188712	+	0.188712i	−0.795139	−	0.606427i	$-0.792602\pi$
$367$	−3.61520	+	3.61520i	−0.188712	+	0.188712i	0.606427	+	0.795139i	$0.292602\pi$
$368$		0			0
$369$	0.488000	+	0.488000i	0.0254043	+	0.0254043i
$370$		0			0
$371$	−3.83892			−0.199307
$372$		0			0
$373$	−25.2600	−	25.2600i	−1.30791	−	1.30791i	−0.922921	−	0.384990i	$-0.874205\pi$
$373$	−25.2600	−	25.2600i	−1.30791	−	1.30791i	−0.384990	−	0.922921i	$-0.625795\pi$
$374$		0			0
$375$		−	7.73582i		−	0.399476i
$376$		0			0
$377$	−9.33919	+	9.33919i	−0.480993	+	0.480993i
$378$		0			0
$379$		−	6.47597i		−	0.332648i	−0.986071	−	0.166324i	$-0.946810\pi$
$379$		−	6.47597i		−	0.332648i	0.986071	−	0.166324i	$-0.0531898\pi$
$380$		0			0
$381$		−	29.6957i		−	1.52135i
$382$		0			0
$383$		−	8.02155i		−	0.409882i	−0.978774	−	0.204941i	$-0.934300\pi$
$383$		−	8.02155i		−	0.409882i	0.978774	−	0.204941i	$-0.0657003\pi$
$384$		0			0
$385$	−3.02838	+	3.02838i	−0.154341	+	0.154341i
$386$		0			0
$387$	−0.470116	+	0.470116i	−0.0238973	+	0.0238973i
$388$		0			0
$389$	−7.97607	+	7.97607i	−0.404403	+	0.404403i	−0.879781	−	0.475379i	$-0.842311\pi$
$389$	−7.97607	+	7.97607i	−0.404403	+	0.404403i	0.475379	+	0.879781i	$0.342311\pi$
$390$		0			0
$391$	−15.2550	+	1.79117i	−0.771476	+	0.0905835i
$392$		0			0
$393$	28.8239			1.45397
$394$		0			0
$395$	21.2094	+	21.2094i	1.06716	+	1.06716i
$396$		0			0
$397$		−	3.13526i		−	0.157354i	−0.996900	−	0.0786772i	$-0.974930\pi$
$397$		−	3.13526i		−	0.157354i	0.996900	−	0.0786772i	$-0.0250696\pi$
$398$		0			0
$399$		−	3.52206i		−	0.176323i
$400$		0			0
$401$	−4.62232	+	4.62232i	−0.230828	+	0.230828i	−0.813038	−	0.582211i	$-0.802188\pi$
$401$	−4.62232	+	4.62232i	−0.230828	+	0.230828i	0.582211	+	0.813038i	$0.302188\pi$
$402$		0			0
$403$	−22.1962			−1.10567
$404$		0			0
$405$		−	25.1508i		−	1.24975i
$406$		0			0
$407$		−	2.93004i		−	0.145236i
$408$		0			0
$409$		−	17.9564i		−	0.887889i	−0.896054	−	0.443944i	$-0.853579\pi$
$409$		−	17.9564i		−	0.887889i	0.896054	−	0.443944i	$-0.146421\pi$
$410$		0			0
$411$		−	9.60728i		−	0.473892i
$412$		0			0
$413$	3.17471			0.156217
$414$		0			0
$415$	12.8451	−	12.8451i	0.630542	−	0.630542i
$416$		0			0
$417$			29.6780i			1.45334i
$418$		0			0
$419$		−	10.9256i		−	0.533750i	−0.963731	−	0.266875i	$-0.914009\pi$
$419$		−	10.9256i		−	0.533750i	0.963731	−	0.266875i	$-0.0859910\pi$
$420$		0			0
$421$	−18.9448	−	18.9448i	−0.923314	−	0.923314i	0.0739483	−	0.997262i	$-0.476440\pi$
$421$	−18.9448	−	18.9448i	−0.923314	−	0.923314i	−0.997262	+	0.0739483i	$0.976440\pi$
$422$		0			0
$423$	0.615417			0.0299226
$424$		0			0
$425$	−8.77406	+	11.1086i	−0.425604	+	0.538846i
$426$		0			0
$427$	−4.91215	+	4.91215i	−0.237716	+	0.237716i
$428$		0			0
$429$	−11.0737	+	11.0737i	−0.534645	+	0.534645i
$430$		0			0
$431$	10.5663	−	10.5663i	0.508961	−	0.508961i	−0.405246	−	0.914208i	$-0.632814\pi$
$431$	10.5663	−	10.5663i	0.508961	−	0.508961i	0.914208	+	0.405246i	$0.132814\pi$
$432$		0			0
$433$			33.8764i			1.62799i	0.580868	+	0.813997i	$0.302713\pi$
$433$			33.8764i			1.62799i	−0.580868	+	0.813997i	$0.697287\pi$
$434$		0			0
$435$		−	16.2935i		−	0.781216i
$436$		0			0
$437$			12.0417i			0.576032i
$438$		0			0
$439$	−4.75800	+	4.75800i	−0.227087	+	0.227087i	−0.811475	−	0.584388i	$-0.801335\pi$
$439$	−4.75800	+	4.75800i	−0.227087	+	0.227087i	0.584388	+	0.811475i	$0.301335\pi$
$440$		0			0
$441$			0.719063i			0.0342411i
$442$		0			0
$443$	7.75885	+	7.75885i	0.368634	+	0.368634i	0.866979	−	0.498345i	$-0.166059\pi$
$443$	7.75885	+	7.75885i	0.368634	+	0.368634i	−0.498345	+	0.866979i	$0.666059\pi$
$444$		0			0
$445$	1.72827			0.0819280
$446$		0			0
$447$	8.53752	+	8.53752i	0.403811	+	0.403811i
$448$		0			0
$449$	7.94202	−	7.94202i	0.374807	−	0.374807i	−0.494417	−	0.869225i	$-0.664619\pi$
$449$	7.94202	−	7.94202i	0.374807	−	0.374807i	0.869225	+	0.494417i	$0.164619\pi$
$450$		0			0
$451$	10.2912	+	10.2912i	0.484593	+	0.484593i
$452$		0			0
$453$	−12.6752			−0.595531
$454$		0			0
$455$			7.44859i			0.349195i
$456$		0			0
$457$	14.9110			0.697509			0.348755	−	0.937214i	$-0.386605\pi$
$457$	14.9110			0.697509			0.348755	+	0.937214i	$0.386605\pi$
$458$		0			0
$459$	13.5097	−	17.1042i	0.630578	−	0.798358i
$460$		0			0
$461$	−20.3523	−	20.3523i	−0.947903	−	0.947903i	0.0508059	−	0.998709i	$-0.483821\pi$
$461$	−20.3523	−	20.3523i	−0.947903	−	0.947903i	−0.998709	+	0.0508059i	$0.983821\pi$
$462$		0			0
$463$	5.33676			0.248020			0.124010	−	0.992281i	$-0.460424\pi$
$463$	5.33676			0.248020			0.124010	+	0.992281i	$0.460424\pi$
$464$		0			0
$465$	19.3622	−	19.3622i	0.897900	−	0.897900i
$466$		0			0
$467$	12.7977	+	12.7977i	0.592209	+	0.592209i	0.938228	−	0.346019i	$-0.112467\pi$
$467$	12.7977	+	12.7977i	0.592209	+	0.592209i	−0.346019	+	0.938228i	$0.612467\pi$
$468$		0			0
$469$	7.92858			0.366108
$470$		0			0
$471$	14.1396	−	14.1396i	0.651520	−	0.651520i
$472$		0			0
$473$	−9.91404	+	9.91404i	−0.455848	+	0.455848i
$474$		0			0
$475$	7.84731	+	7.84731i	0.360059	+	0.360059i
$476$		0			0
$477$	−0.462239	+	0.462239i	−0.0211645	+	0.0211645i
$478$		0			0
$479$	−4.79918	−	4.79918i	−0.219280	−	0.219280i	0.588915	−	0.808195i	$-0.299555\pi$
$479$	−4.79918	−	4.79918i	−0.219280	−	0.219280i	−0.808195	+	0.588915i	$0.799555\pi$
$480$		0			0
$481$	−3.60335	−	3.60335i	−0.164299	−	0.164299i
$482$		0			0
$483$		−	4.05909i		−	0.184695i
$484$		0			0
$485$	27.7849	−	27.7849i	1.26165	−	1.26165i
$486$		0			0
$487$	17.6181	+	17.6181i	0.798351	+	0.798351i	0.982835	−	0.184484i	$-0.0590614\pi$
$487$	17.6181	+	17.6181i	0.798351	+	0.798351i	−0.184484	+	0.982835i	$0.559061\pi$
$488$		0			0
$489$			13.6761i			0.618453i
$490$		0			0
$491$	−6.22500	+	6.22500i	−0.280930	+	0.280930i	−0.833480	−	0.552550i	$-0.813655\pi$
$491$	−6.22500	+	6.22500i	−0.280930	+	0.280930i	0.552550	+	0.833480i	$0.313655\pi$
$492$		0			0
$493$	8.43326	−	10.6771i	0.379815	−	0.480873i
$494$		0			0
$495$			0.729286i			0.0327790i
$496$		0			0
$497$	−0.623395			−0.0279631
$498$		0			0
$499$		−	20.6000i		−	0.922183i	−0.887353	−	0.461091i	$-0.847458\pi$
$499$		−	20.6000i		−	0.922183i	0.887353	−	0.461091i	$-0.152542\pi$
$500$		0			0
$501$	−3.27198	+	3.27198i	−0.146181	+	0.146181i
$502$		0			0
$503$	17.7747	+	17.7747i	0.792536	+	0.792536i	0.981906	−	0.189370i	$-0.0606445\pi$
$503$	17.7747	+	17.7747i	0.792536	+	0.792536i	−0.189370	+	0.981906i	$0.560644\pi$
$504$		0			0
$505$	5.71015	−	5.71015i	0.254099	−	0.254099i
$506$		0			0
$507$			5.13354i			0.227988i
$508$		0			0
$509$	−21.5098	+	21.5098i	−0.953405	+	0.953405i	−0.998962	−	0.0455569i	$-0.985494\pi$
$509$	−21.5098	+	21.5098i	−0.953405	+	0.953405i	0.0455569	+	0.998962i	$0.485494\pi$
$510$		0			0
$511$	−10.7282			−0.474588
$512$		0			0
$513$	−12.0827	−	12.0827i	−0.533466	−	0.533466i
$514$		0			0
$515$	45.5801			2.00850
$516$		0			0
$517$	12.9782			0.570782
$518$		0			0
$519$	−39.2248			−1.72178
$520$		0			0
$521$	−17.5475	−	17.5475i	−0.768772	−	0.768772i	0.209118	−	0.977890i	$-0.432941\pi$
$521$	−17.5475	−	17.5475i	−0.768772	−	0.768772i	−0.977890	+	0.209118i	$0.932941\pi$
$522$		0			0
$523$	−21.9175	−	21.9175i	−0.958387	−	0.958387i	0.0407809	−	0.999168i	$-0.487015\pi$
$523$	−21.9175	−	21.9175i	−0.958387	−	0.958387i	−0.999168	+	0.0407809i	$0.987015\pi$
$524$		0			0
$525$	−2.64522	−	2.64522i	−0.115447	−	0.115447i
$526$		0			0
$527$	22.7095	−	2.66646i	0.989242	−	0.116153i
$528$		0			0
$529$		−	9.12224i		−	0.396619i
$530$		0			0
$531$	0.382263	−	0.382263i	0.0165888	−	0.0165888i
$532$		0			0
$533$	25.3122			1.09639
$534$		0			0
$535$	−26.5351			−1.14721
$536$		0			0
$537$	−7.71394	−	7.71394i	−0.332881	−	0.332881i
$538$		0			0
$539$			15.1640i			0.653159i
$540$		0			0
$541$	27.4283			1.17923			0.589617	−	0.807683i	$-0.299279\pi$
$541$	27.4283			1.17923			0.589617	+	0.807683i	$0.299279\pi$
$542$		0			0
$543$	12.4158			0.532812
$544$		0			0
$545$	19.2407			0.824182
$546$		0			0
$547$	12.3612			0.528526			0.264263	−	0.964451i	$-0.414871\pi$
$547$	12.3612			0.528526			0.264263	+	0.964451i	$0.414871\pi$
$548$		0			0
$549$			1.18293i			0.0504862i
$550$		0			0
$551$	−7.54250	−	7.54250i	−0.321321	−	0.321321i
$552$		0			0
$553$	−6.61912			−0.281474
$554$		0			0
$555$	6.28656			0.266849
$556$		0			0
$557$	−14.3843	+	14.3843i	−0.609481	+	0.609481i	−0.942811	−	0.333329i	$-0.891828\pi$
$557$	−14.3843	+	14.3843i	−0.609481	+	0.609481i	0.333329	+	0.942811i	$0.391828\pi$
$558$		0			0
$559$			24.3845i			1.03136i
$560$		0			0
$561$	9.99954	−	12.6601i	0.422181	−	0.534511i
$562$		0			0
$563$	−29.6349	−	29.6349i	−1.24896	−	1.24896i	−0.956179	−	0.292782i	$-0.905419\pi$
$563$	−29.6349	−	29.6349i	−1.24896	−	1.24896i	−0.292782	−	0.956179i	$-0.594581\pi$
$564$		0			0
$565$	−42.2629	−	42.2629i	−1.77801	−	1.77801i
$566$		0			0
$567$	3.92458	+	3.92458i	0.164817	+	0.164817i
$568$		0			0
$569$	13.9146			0.583331			0.291665	−	0.956520i	$-0.405791\pi$
$569$	13.9146			0.583331			0.291665	+	0.956520i	$0.405791\pi$
$570$		0			0
$571$	9.40703			0.393672			0.196836	−	0.980436i	$-0.436933\pi$
$571$	9.40703			0.393672			0.196836	+	0.980436i	$0.436933\pi$
$572$		0			0
$573$	−24.0635			−1.00527
$574$		0			0
$575$	9.04384	+	9.04384i	0.377154	+	0.377154i
$576$		0			0
$577$	40.7743			1.69746			0.848729	−	0.528828i	$-0.177368\pi$
$577$	40.7743			1.69746			0.848729	+	0.528828i	$0.177368\pi$
$578$		0			0
$579$	3.43023	−	3.43023i	0.142555	−	0.142555i
$580$		0			0
$581$			4.00875i			0.166311i
$582$		0			0
$583$	−9.74793	+	9.74793i	−0.403718	+	0.403718i
$584$		0			0
$585$	0.896874	+	0.896874i	0.0370812	+	0.0370812i
$586$		0			0
$587$	−14.2585	+	14.2585i	−0.588510	+	0.588510i	−0.937228	−	0.348717i	$-0.886617\pi$
$587$	−14.2585	+	14.2585i	−0.588510	+	0.588510i	0.348717	+	0.937228i	$0.386617\pi$
$588$		0			0
$589$		−	17.9260i		−	0.738629i
$590$		0			0
$591$	−11.0932			−0.456315
$592$		0			0
$593$		−	34.5234i		−	1.41771i	−0.705357	−	0.708853i	$-0.749213\pi$
$593$		−	34.5234i		−	1.41771i	0.705357	−	0.708853i	$-0.250787\pi$
$594$		0			0
$595$	−0.894809	−	7.62086i	−0.0366836	−	0.312425i
$596$		0			0
$597$	−25.0251	+	25.0251i	−1.02421	+	1.02421i
$598$		0			0
$599$			38.8784i			1.58853i	0.607571	+	0.794265i	$0.292144\pi$
$599$			38.8784i			1.58853i	−0.607571	+	0.794265i	$0.707856\pi$
$600$		0			0
$601$	3.04984	+	3.04984i	0.124406	+	0.124406i	0.766568	−	0.642163i	$-0.221963\pi$
$601$	3.04984	+	3.04984i	0.124406	+	0.124406i	−0.642163	+	0.766568i	$0.721963\pi$
$602$		0			0
$603$	0.954669	−	0.954669i	0.0388771	−	0.0388771i
$604$		0			0
$605$		−	16.5646i		−	0.673445i
$606$		0			0
$607$	−22.7358	−	22.7358i	−0.922816	−	0.922816i	0.0744119	−	0.997228i	$-0.476292\pi$
$607$	−22.7358	−	22.7358i	−0.922816	−	0.922816i	−0.997228	+	0.0744119i	$0.976292\pi$
$608$		0			0
$609$	2.54248	+	2.54248i	0.103026	+	0.103026i
$610$		0			0
$611$	15.9606	−	15.9606i	0.645696	−	0.645696i
$612$		0			0
$613$	14.2821	+	14.2821i	0.576847	+	0.576847i	0.934033	−	0.357186i	$-0.116264\pi$
$613$	14.2821	+	14.2821i	0.576847	+	0.576847i	−0.357186	+	0.934033i	$0.616264\pi$
$614$		0			0
$615$	−22.0803	+	22.0803i	−0.890365	+	0.890365i
$616$		0			0
$617$	−28.5056	+	28.5056i	−1.14759	+	1.14759i	−0.160569	+	0.987025i	$0.551333\pi$
$617$	−28.5056	+	28.5056i	−1.14759	+	1.14759i	−0.987025	+	0.160569i	$0.948667\pi$
$618$		0			0
$619$	−14.7720			−0.593736			−0.296868	−	0.954918i	$-0.595942\pi$
$619$	−14.7720			−0.593736			−0.296868	+	0.954918i	$0.595942\pi$
$620$		0			0
$621$	−13.9251	−	13.9251i	−0.558794	−	0.558794i
$622$		0			0
$623$	−0.269683	+	0.269683i	−0.0108046	+	0.0108046i
$624$		0			0
$625$	−30.3790			−1.21516
$626$		0			0
$627$	−8.94334	−	8.94334i	−0.357163	−	0.357163i
$628$		0			0
$629$	4.11956	+	3.25381i	0.164258	+	0.129738i
$630$		0			0
$631$	39.3665			1.56716			0.783579	−	0.621292i	$-0.213392\pi$
$631$	39.3665			1.56716			0.783579	+	0.621292i	$0.213392\pi$
$632$		0			0
$633$			12.6222i			0.501689i
$634$		0			0
$635$	−50.7197			−2.01275
$636$		0			0
$637$	18.6486	+	18.6486i	0.738885	+	0.738885i
$638$		0			0
$639$	−0.0750620	+	0.0750620i	−0.00296941	+	0.00296941i
$640$		0			0
$641$	−23.1295	−	23.1295i	−0.913562	−	0.913562i	0.0829885	−	0.996551i	$-0.473554\pi$
$641$	−23.1295	−	23.1295i	−0.913562	−	0.913562i	−0.996551	+	0.0829885i	$0.973554\pi$
$642$		0			0
$643$	16.3300			0.643991			0.321996	−	0.946741i	$-0.395646\pi$
$643$	16.3300			0.643991			0.321996	+	0.946741i	$0.395646\pi$
$644$		0			0
$645$	−21.2711	−	21.2711i	−0.837550	−	0.837550i
$646$		0			0
$647$			36.7870i			1.44625i	0.690719	+	0.723123i	$0.257294\pi$
$647$			36.7870i			1.44625i	−0.690719	+	0.723123i	$0.742706\pi$
$648$		0			0
$649$	8.06135	−	8.06135i	0.316436	−	0.316436i
$650$		0			0
$651$			6.04263i			0.236829i
$652$		0			0
$653$			11.3812i			0.445381i	0.974889	+	0.222690i	$0.0714839\pi$
$653$			11.3812i			0.445381i	−0.974889	+	0.222690i	$0.928516\pi$
$654$		0			0
$655$		−	49.2308i		−	1.92361i
$656$		0			0
$657$	−1.29177	+	1.29177i	−0.0503966	+	0.0503966i
$658$		0			0
$659$	−16.2184	+	16.2184i	−0.631778	+	0.631778i	−0.948514	−	0.316736i	$-0.897413\pi$
$659$	−16.2184	+	16.2184i	−0.631778	+	0.631778i	0.316736	+	0.948514i	$0.397413\pi$
$660$		0			0
$661$	30.4626	−	30.4626i	1.18486	−	1.18486i	0.206390	−	0.978470i	$-0.433829\pi$
$661$	30.4626	−	30.4626i	1.18486	−	1.18486i	0.978470	−	0.206390i	$-0.0661714\pi$
$662$		0			0
$663$	−3.27200	−	27.8668i	−0.127074	−	1.08226i
$664$		0			0
$665$	−6.01561			−0.233275
$666$		0			0
$667$	−8.69256	−	8.69256i	−0.336577	−	0.336577i
$668$		0			0
$669$		−	50.6838i		−	1.95955i
$670$		0			0
$671$			24.9462i			0.963038i
$672$		0			0
$673$	7.92507	−	7.92507i	0.305489	−	0.305489i	−0.537668	−	0.843157i	$-0.680695\pi$
$673$	7.92507	−	7.92507i	0.305489	−	0.305489i	0.843157	+	0.537668i	$0.180695\pi$
$674$		0			0
$675$	−18.1494			−0.698569
$676$		0			0
$677$			34.6387i			1.33127i	0.746276	+	0.665636i	$0.231840\pi$
$677$			34.6387i			1.33127i	−0.746276	+	0.665636i	$0.768160\pi$
$678$		0			0
$679$			8.67122i			0.332771i
$680$		0			0
$681$		−	2.51138i		−	0.0962361i
$682$		0			0
$683$		−	25.8929i		−	0.990763i	−0.868675	−	0.495382i	$-0.835028\pi$
$683$		−	25.8929i		−	0.990763i	0.868675	−	0.495382i	$-0.164972\pi$
$684$		0			0
$685$	−16.4091			−0.626958
$686$		0			0
$687$	31.8061	−	31.8061i	1.21348	−	1.21348i
$688$		0			0
$689$			23.9760i			0.913412i
$690$		0			0
$691$		−	34.7341i		−	1.32135i	−0.750673	−	0.660673i	$-0.770271\pi$
$691$		−	34.7341i		−	1.32135i	0.750673	−	0.660673i	$-0.229729\pi$
$692$		0			0
$693$	−0.113799	−	0.113799i	−0.00432287	−	0.00432287i
$694$		0			0
$695$	50.6896			1.92276
$696$		0			0
$697$	−25.8976	+	3.04078i	−0.980941	+	0.115178i
$698$		0			0
$699$	17.2562	−	17.2562i	0.652689	−	0.652689i
$700$		0			0
$701$	−0.958097	+	0.958097i	−0.0361868	+	0.0361868i	−0.724969	−	0.688782i	$-0.758146\pi$
$701$	−0.958097	+	0.958097i	−0.0361868	+	0.0361868i	0.688782	+	0.724969i	$0.258146\pi$
$702$		0			0
$703$	2.91013	−	2.91013i	0.109758	−	0.109758i
$704$		0			0
$705$			27.8455i			1.04872i
$706$		0			0
$707$			1.78205i			0.0670208i
$708$		0			0
$709$			7.17134i			0.269325i	0.990892	+	0.134663i	$0.0429951\pi$
$709$			7.17134i			0.269325i	−0.990892	+	0.134663i	$0.957005\pi$
$710$		0			0
$711$	−0.796998	+	0.796998i	−0.0298898	+	0.0298898i
$712$		0			0
$713$		−	20.6593i		−	0.773698i
$714$		0			0
$715$	18.9137	+	18.9137i	0.707334	+	0.707334i
$716$		0			0
$717$	−8.13374			−0.303760
$718$		0			0
$719$	−27.6410	−	27.6410i	−1.03084	−	1.03084i	−0.999509	−	0.0313267i	$-0.990027\pi$
$719$	−27.6410	−	27.6410i	−1.03084	−	1.03084i	−0.0313267	−	0.999509i	$-0.509973\pi$
$720$		0			0
$721$	−7.11241	+	7.11241i	−0.264880	+	0.264880i
$722$		0			0
$723$	−31.5339	−	31.5339i	−1.17276	−	1.17276i
$724$		0			0
$725$	−11.3295			−0.420768
$726$		0			0
$727$			43.2566i			1.60430i	0.597124	+	0.802149i	$0.296310\pi$
$727$			43.2566i			1.60430i	−0.597124	+	0.802149i	$0.703690\pi$
$728$		0			0
$729$	27.9094			1.03368
$730$		0			0
$731$	−2.92934	−	24.9485i	−0.108346	−	0.922753i
$732$		0			0
$733$	−5.70127	−	5.70127i	−0.210581	−	0.210581i	0.593933	−	0.804514i	$-0.297574\pi$
$733$	−5.70127	−	5.70127i	−0.210581	−	0.210581i	−0.804514	+	0.593933i	$0.797574\pi$
$734$		0			0
$735$	−32.5352			−1.20008
$736$		0			0
$737$	20.1326	−	20.1326i	0.741592	−	0.741592i
$738$		0			0
$739$	32.8899	+	32.8899i	1.20988	+	1.20988i	0.971067	+	0.238809i	$0.0767569\pi$
$739$	32.8899	+	32.8899i	1.20988	+	1.20988i	0.238809	+	0.971067i	$0.423243\pi$
$740$		0			0
$741$	−21.9970			−0.808080
$742$		0			0
$743$	18.0698	−	18.0698i	0.662916	−	0.662916i	−0.293151	−	0.956066i	$-0.594704\pi$
$743$	18.0698	−	18.0698i	0.662916	−	0.662916i	0.956066	+	0.293151i	$0.0947037\pi$
$744$		0			0
$745$	14.5819	−	14.5819i	0.534241	−	0.534241i
$746$		0			0
$747$	0.482688	+	0.482688i	0.0176606	+	0.0176606i
$748$		0			0
$749$	4.14059	−	4.14059i	0.151294	−	0.151294i
$750$		0			0
$751$	14.7068	+	14.7068i	0.536658	+	0.536658i	0.922546	−	0.385888i	$-0.126105\pi$
$751$	14.7068	+	14.7068i	0.536658	+	0.536658i	−0.385888	+	0.922546i	$0.626105\pi$
$752$		0			0
$753$	36.6784	+	36.6784i	1.33664	+	1.33664i
$754$		0			0
$755$			21.6489i			0.787886i
$756$		0			0
$757$	−0.821243	+	0.821243i	−0.0298486	+	0.0298486i	−0.721874	−	0.692025i	$-0.756719\pi$
$757$	−0.821243	+	0.821243i	−0.0298486	+	0.0298486i	0.692025	+	0.721874i	$0.256719\pi$
$758$		0			0
$759$	−10.3070	−	10.3070i	−0.374120	−	0.374120i
$760$		0			0
$761$			3.47539i			0.125983i	0.998014	+	0.0629914i	$0.0200641\pi$
$761$			3.47539i			0.125983i	−0.998014	+	0.0629914i	$0.979936\pi$
$762$		0			0
$763$	−3.00236	+	3.00236i	−0.108693	+	0.108693i
$764$		0			0
$765$	−1.02536	−	0.809874i	−0.0370719	−	0.0292810i
$766$		0			0
$767$		−	19.8277i		−	0.715935i
$768$		0			0
$769$	−9.10087			−0.328186			−0.164093	−	0.986445i	$-0.552470\pi$
$769$	−9.10087			−0.328186			−0.164093	+	0.986445i	$0.552470\pi$
$770$		0			0
$771$		−	9.06872i		−	0.326602i
$772$		0			0
$773$	31.0432	−	31.0432i	1.11655	−	1.11655i	0.124304	−	0.992244i	$-0.460330\pi$
$773$	31.0432	−	31.0432i	1.11655	−	1.11655i	0.992244	−	0.124304i	$-0.0396698\pi$
$774$		0			0
$775$	−13.4633	−	13.4633i	−0.483614	−	0.483614i
$776$		0			0
$777$	−0.980967	+	0.980967i	−0.0351920	+	0.0351920i
$778$		0			0
$779$			20.4426i			0.732431i
$780$		0			0
$781$	−1.58295	+	1.58295i	−0.0566423	+	0.0566423i
$782$		0			0
$783$	17.4444			0.623412
$784$		0			0
$785$	−24.1503	−	24.1503i	−0.861960	−	0.861960i
$786$		0			0
$787$	0.846755			0.0301836			0.0150918	−	0.999886i	$-0.495196\pi$
$787$	0.846755			0.0301836			0.0150918	+	0.999886i	$0.495196\pi$
$788$		0			0
$789$	45.5467			1.62151
$790$		0			0
$791$	13.1896			0.468967
$792$		0			0
$793$	30.6788	+	30.6788i	1.08944	+	1.08944i
$794$		0			0
$795$	−20.9147	−	20.9147i	−0.741769	−	0.741769i
$796$		0			0
$797$	37.3001	+	37.3001i	1.32124	+	1.32124i	0.912777	+	0.408459i	$0.133934\pi$
$797$	37.3001	+	37.3001i	1.32124	+	1.32124i	0.408459	+	0.912777i	$0.366066\pi$
$798$		0			0
$799$	−14.4124	+	18.2471i	−0.509872	+	0.645535i
$800$		0			0
$801$			0.0649443i			0.00229469i
$802$		0			0
$803$	−27.2415	+	27.2415i	−0.961330	+	0.961330i
$804$		0			0
$805$	−6.93286			−0.244351
$806$		0			0
$807$	20.4196			0.718804
$808$		0			0
$809$	7.72963	+	7.72963i	0.271759	+	0.271759i	0.829808	−	0.558049i	$-0.188450\pi$
$809$	7.72963	+	7.72963i	0.271759	+	0.271759i	−0.558049	+	0.829808i	$0.688450\pi$
$810$		0			0
$811$		−	36.4279i		−	1.27916i	−0.768726	−	0.639579i	$-0.779109\pi$
$811$		−	36.4279i		−	1.27916i	0.768726	−	0.639579i	$-0.220891\pi$
$812$		0			0
$813$	25.7943			0.904647
$814$		0			0
$815$	23.3585			0.818211
$816$		0			0
$817$	−19.6934			−0.688984
$818$		0			0
$819$	−0.279900			−0.00978050
$820$		0			0
$821$			19.1033i			0.666709i	0.942801	+	0.333355i	$0.108181\pi$
$821$			19.1033i			0.666709i	−0.942801	+	0.333355i	$0.891819\pi$
$822$		0			0
$823$	−18.6920	−	18.6920i	−0.651561	−	0.651561i	0.301808	−	0.953369i	$-0.402410\pi$
$823$	−18.6920	−	18.6920i	−0.651561	−	0.651561i	−0.953369	+	0.301808i	$0.902410\pi$
$824$		0			0
$825$	−13.4337			−0.467701
$826$		0			0
$827$	−42.9348			−1.49299			−0.746495	−	0.665391i	$-0.768265\pi$
$827$	−42.9348			−1.49299			−0.746495	+	0.665391i	$0.768265\pi$
$828$		0			0
$829$	1.32065	−	1.32065i	0.0458681	−	0.0458681i	−0.683801	−	0.729669i	$-0.739674\pi$
$829$	1.32065	−	1.32065i	0.0458681	−	0.0458681i	0.729669	+	0.683801i	$0.239674\pi$
$830$		0			0
$831$			31.7217i			1.10041i
$832$		0			0
$833$	−21.3202	−	16.8396i	−0.738701	−	0.583459i
$834$		0			0
$835$	5.58849	+	5.58849i	0.193398	+	0.193398i
$836$		0			0
$837$	20.7298	+	20.7298i	0.716526	+	0.716526i
$838$		0			0
$839$	−20.9488	−	20.9488i	−0.723232	−	0.723232i	0.246030	−	0.969262i	$-0.420874\pi$
$839$	−20.9488	−	20.9488i	−0.723232	−	0.723232i	−0.969262	+	0.246030i	$0.920874\pi$
$840$		0			0
$841$	−18.1106			−0.624502
$842$		0			0
$843$	2.37771			0.0818927
$844$		0			0
$845$	8.76800			0.301628
$846$		0			0
$847$	2.58477	+	2.58477i	0.0888136	+	0.0888136i
$848$		0			0
$849$	18.6672			0.640658
$850$		0			0
$851$	3.35386	−	3.35386i	0.114969	−	0.114969i
$852$		0			0
$853$			11.0116i			0.377030i	0.982070	+	0.188515i	$0.0603674\pi$
$853$			11.0116i			0.377030i	−0.982070	+	0.188515i	$0.939633\pi$
$854$		0			0
$855$	−0.724331	+	0.724331i	−0.0247716	+	0.0247716i
$856$		0			0
$857$	−0.460268	−	0.460268i	−0.0157225	−	0.0157225i	0.699202	−	0.714924i	$-0.253539\pi$
$857$	−0.460268	−	0.460268i	−0.0157225	−	0.0157225i	−0.714924	+	0.699202i	$0.753539\pi$
$858$		0			0
$859$	26.3736	−	26.3736i	0.899856	−	0.899856i	−0.0955668	−	0.995423i	$-0.530466\pi$
$859$	26.3736	−	26.3736i	0.899856	−	0.899856i	0.995423	+	0.0955668i	$0.0304663\pi$
$860$		0			0
$861$		−	6.89092i		−	0.234842i
$862$		0			0
$863$	−16.7048			−0.568637			−0.284319	−	0.958730i	$-0.591767\pi$
$863$	−16.7048			−0.568637			−0.284319	+	0.958730i	$0.591767\pi$
$864$		0			0
$865$			66.9953i			2.27791i
$866$		0			0
$867$	6.69535	+	28.1182i	0.227386	+	0.954945i
$868$		0			0
$869$	−16.8075	+	16.8075i	−0.570156	+	0.570156i
$870$		0			0
$871$		−	49.5179i		−	1.67785i
$872$		0			0
$873$	1.04409	+	1.04409i	0.0353371	+	0.0353371i
$874$		0			0
$875$	2.06173	−	2.06173i	0.0696991	−	0.0696991i
$876$		0			0
$877$			15.0180i			0.507123i	0.967319	+	0.253562i	$0.0816021\pi$
$877$			15.0180i			0.507123i	−0.967319	+	0.253562i	$0.918398\pi$
$878$		0			0
$879$	7.90415	+	7.90415i	0.266600	+	0.266600i
$880$		0			0
$881$	−21.0314	−	21.0314i	−0.708565	−	0.708565i	0.257669	−	0.966233i	$-0.417046\pi$
$881$	−21.0314	−	21.0314i	−0.708565	−	0.708565i	−0.966233	+	0.257669i	$0.917046\pi$
$882$		0			0
$883$	26.3009	−	26.3009i	0.885094	−	0.885094i	−0.108953	−	0.994047i	$-0.534750\pi$
$883$	26.3009	−	26.3009i	0.885094	−	0.885094i	0.994047	+	0.108953i	$0.0347496\pi$
$884$		0			0
$885$	17.2961	+	17.2961i	0.581402	+	0.581402i
$886$		0			0
$887$	26.2983	−	26.2983i	0.883011	−	0.883011i	−0.110829	−	0.993840i	$-0.535350\pi$
$887$	26.2983	−	26.2983i	0.883011	−	0.883011i	0.993840	+	0.110829i	$0.0353505\pi$
$888$		0			0
$889$	7.91440	−	7.91440i	0.265440	−	0.265440i
$890$		0			0
$891$	19.9309			0.667710
$892$		0			0
$893$	12.8901	+	12.8901i	0.431349	+	0.431349i
$894$		0			0
$895$	−13.1753	+	13.1753i	−0.440401	+	0.440401i
$896$		0			0
$897$	−25.3510			−0.846446
$898$		0			0
$899$	12.9403	+	12.9403i	0.431583	+	0.431583i
$900$		0			0
$901$	−2.88027	−	24.5305i	−0.0959555	−	0.817229i
$902$		0			0
$903$	6.63838			0.220911
$904$		0			0
$905$		−	21.2059i		−	0.704908i
$906$		0			0
$907$	44.8042			1.48770			0.743849	−	0.668347i	$-0.232998\pi$
$907$	44.8042			1.48770			0.743849	+	0.668347i	$0.232998\pi$
$908$		0			0
$909$	0.214574	+	0.214574i	0.00711696	+	0.00711696i
$910$		0			0
$911$	−4.59278	+	4.59278i	−0.152166	+	0.152166i	−0.779085	−	0.626919i	$-0.784316\pi$
$911$	−4.59278	+	4.59278i	−0.152166	+	0.152166i	0.626919	+	0.779085i	$0.284316\pi$
$912$		0			0
$913$	10.1792	+	10.1792i	0.336882	+	0.336882i
$914$		0			0
$915$	−53.5235			−1.76943
$916$		0			0
$917$	7.68207	+	7.68207i	0.253684	+	0.253684i
$918$		0			0
$919$		−	49.5374i		−	1.63409i	−0.576575	−	0.817044i	$-0.695611\pi$
$919$		−	49.5374i		−	1.63409i	0.576575	−	0.817044i	$-0.304389\pi$
$920$		0			0
$921$	11.4893	−	11.4893i	0.378586	−	0.378586i
$922$		0			0
$923$			3.89341i			0.128153i
$924$		0			0
$925$		−	4.37128i		−	0.143727i
$926$		0			0
$927$			1.71279i			0.0562554i
$928$		0			0
$929$	−37.1359	+	37.1359i	−1.21839	+	1.21839i	−0.250193	+	0.968196i	$0.580494\pi$
$929$	−37.1359	+	37.1359i	−1.21839	+	1.21839i	−0.968196	+	0.250193i	$0.919506\pi$
$930$		0			0
$931$	−15.0610	+	15.0610i	−0.493603	+	0.493603i
$932$		0			0
$933$	−12.4587	+	12.4587i	−0.407879	+	0.407879i
$934$		0			0
$935$	−21.6233	−	17.0790i	−0.707157	−	0.558544i
$936$		0			0
$937$	−9.63338			−0.314709			−0.157354	−	0.987542i	$-0.550296\pi$
$937$	−9.63338			−0.314709			−0.157354	+	0.987542i	$0.550296\pi$
$938$		0			0
$939$	11.0711	+	11.0711i	0.361293	+	0.361293i
$940$		0			0
$941$		−	16.4065i		−	0.534836i	−0.963581	−	0.267418i	$-0.913830\pi$
$941$		−	16.4065i		−	0.534836i	0.963581	−	0.267418i	$-0.0861704\pi$
$942$		0			0
$943$			23.5596i			0.767206i
$944$		0			0
$945$	6.95650	−	6.95650i	0.226295	−	0.226295i
$946$		0			0
$947$	−40.6424			−1.32070			−0.660351	−	0.750957i	$-0.729592\pi$
$947$	−40.6424			−1.32070			−0.660351	+	0.750957i	$0.729592\pi$
$948$		0			0
$949$			67.0029i			2.17501i
$950$		0			0
$951$		−	9.72721i		−	0.315426i
$952$		0			0
$953$		−	11.9230i		−	0.386225i	−0.981177	−	0.193113i	$-0.938142\pi$
$953$		−	11.9230i		−	0.386225i	0.981177	−	0.193113i	$-0.0618583\pi$
$954$		0			0
$955$			41.1000i			1.32997i
$956$		0			0
$957$	12.9119			0.417383
$958$		0			0
$959$	2.56050	−	2.56050i	0.0826830	−	0.0826830i
$960$		0			0
$961$		−	0.245174i		−	0.00790885i
$962$		0			0
$963$		−	0.997126i		−	0.0321319i
$964$		0			0
$965$	−5.85877	−	5.85877i	−0.188601	−	0.188601i
$966$		0			0
$967$	−22.9488			−0.737985			−0.368992	−	0.929432i	$-0.620297\pi$
$967$	−22.9488			−0.737985			−0.368992	+	0.929432i	$0.620297\pi$
$968$		0			0
$969$	22.5057	−	2.64253i	0.722988	−	0.0848902i
$970$		0			0
$971$	−24.1016	+	24.1016i	−0.773458	+	0.773458i	−0.978709	−	0.205252i	$-0.934199\pi$
$971$	−24.1016	+	24.1016i	−0.773458	+	0.773458i	0.205252	+	0.978709i	$0.434199\pi$
$972$		0			0
$973$	−7.90970	+	7.90970i	−0.253573	+	0.253573i
$974$		0			0
$975$	−16.5207	+	16.5207i	−0.529087	+	0.529087i
$976$		0			0
$977$		−	13.4414i		−	0.430027i	−0.976611	−	0.215014i	$-0.931020\pi$
$977$		−	13.4414i		−	0.430027i	0.976611	−	0.215014i	$-0.0689796\pi$
$978$		0			0
$979$			1.36958i			0.0437719i
$980$		0			0
$981$			0.723019i			0.0230842i
$982$		0			0
$983$	1.22871	−	1.22871i	0.0391897	−	0.0391897i	−0.687240	−	0.726430i	$-0.741178\pi$
$983$	1.22871	−	1.22871i	0.0391897	−	0.0391897i	0.726430	+	0.687240i	$0.241178\pi$
$984$		0			0
$985$			18.9471i			0.603703i
$986$		0			0
$987$	−4.34507	−	4.34507i	−0.138305	−	0.138305i
$988$		0			0
$989$	−22.6962			−0.721696
$990$		0			0
$991$	2.36115	+	2.36115i	0.0750043	+	0.0750043i	0.743614	−	0.668609i	$-0.233110\pi$
$991$	2.36115	+	2.36115i	0.0750043	+	0.0750043i	−0.668609	+	0.743614i	$0.733110\pi$
$992$		0			0
$993$	−23.3638	+	23.3638i	−0.741429	+	0.741429i
$994$		0			0
$995$	42.7425	+	42.7425i	1.35503	+	1.35503i
$996$		0			0
$997$	30.2281			0.957333			0.478667	−	0.877997i	$-0.341120\pi$
$997$	30.2281			0.957333			0.478667	+	0.877997i	$0.341120\pi$
$998$		0			0
$999$			6.73059i			0.212946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.s.a.625.10		68
4.3	odd	2		272.2.s.a.149.10	yes	68
16.3	odd	4		272.2.j.a.13.25	✓	68
16.13	even	4		1088.2.j.a.81.10		68
17.4	even	4		1088.2.j.a.497.25		68
68.55	odd	4		272.2.j.a.21.25	yes	68
272.157	even	4	inner	1088.2.s.a.1041.10		68
272.259	odd	4		272.2.s.a.157.10	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.j.a.13.25	✓	68	16.3	odd	4
272.2.j.a.21.25	yes	68	68.55	odd	4
272.2.s.a.149.10	yes	68	4.3	odd	2
272.2.s.a.157.10	yes	68	272.259	odd	4
1088.2.j.a.81.10		68	16.13	even	4
1088.2.j.a.497.25		68	17.4	even	4
1088.2.s.a.625.10		68	1.1	even	1	trivial
1088.2.s.a.1041.10		68	272.157	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.70026 q^{3} +2.90401i q^{5} +(-0.453147 - 0.453147i) q^{7} -0.109126 q^{9} +O(q^{10})\)	\(q-1.70026 q^{3} +2.90401i q^{5} +(-0.453147 - 0.453147i) q^{7} -0.109126 q^{9} -2.30130 q^{11} +(-2.83013 + 2.83013i) q^{13} -4.93756i q^{15} +(2.55560 - 3.23557i) q^{17} +(-2.28566 - 2.28566i) q^{19} +(0.770467 + 0.770467i) q^{21} +(-2.63418 - 2.63418i) q^{23} -3.43327 q^{25} +5.28631 q^{27} +3.29992 q^{29} +(3.92140 + 3.92140i) q^{31} +3.91280 q^{33} +(1.31594 - 1.31594i) q^{35} +1.27321i q^{37} +(4.81195 - 4.81195i) q^{39} +(-4.47191 - 4.47191i) q^{41} +(4.30802 - 4.30802i) q^{43} -0.316902i q^{45} -5.63952 q^{47} -6.58931i q^{49} +(-4.34517 + 5.50130i) q^{51} +(4.23584 - 4.23584i) q^{53} -6.68299i q^{55} +(3.88622 + 3.88622i) q^{57} +(-3.50296 + 3.50296i) q^{59} -10.8401i q^{61} +(0.0494500 + 0.0494500i) q^{63} +(-8.21873 - 8.21873i) q^{65} +(-8.74835 + 8.74835i) q^{67} +(4.47878 + 4.47878i) q^{69} +(0.687850 - 0.687850i) q^{71} +(11.8374 - 11.8374i) q^{73} +5.83745 q^{75} +(1.04283 + 1.04283i) q^{77} +(7.30349 - 7.30349i) q^{79} -8.66071 q^{81} +(-4.42323 - 4.42323i) q^{83} +(9.39613 + 7.42148i) q^{85} -5.61071 q^{87} -0.595133i q^{89} +2.56493 q^{91} +(-6.66740 - 6.66740i) q^{93} +(6.63759 - 6.63759i) q^{95} +(-9.56777 - 9.56777i) q^{97} +0.251131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 60 q^{9}+O(q^{10}) \) 68 * q + 4 * q^3 + 60 * q^9	\( 68 q + 4 q^{3} + 60 q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{17} - 4 q^{21} - 52 q^{25} + 16 q^{27} - 4 q^{29} + 4 q^{31} - 8 q^{33} + 4 q^{35} + 12 q^{39} + 48 q^{47} - 4 q^{51} - 12 q^{57} + 32 q^{59} + 32 q^{63} + 4 q^{65} + 4 q^{67} + 28 q^{69} + 8 q^{73} - 4 q^{75} - 28 q^{77} - 12 q^{79} + 28 q^{81} + 24 q^{85} - 24 q^{87} - 40 q^{91} - 12 q^{93} + 4 q^{95} - 4 q^{97} + 52 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 60 * q^9 + 4 * q^11 - 4 * q^13 - 4 * q^17 - 4 * q^21 - 52 * q^25 + 16 * q^27 - 4 * q^29 + 4 * q^31 - 8 * q^33 + 4 * q^35 + 12 * q^39 + 48 * q^47 - 4 * q^51 - 12 * q^57 + 32 * q^59 + 32 * q^63 + 4 * q^65 + 4 * q^67 + 28 * q^69 + 8 * q^73 - 4 * q^75 - 28 * q^77 - 12 * q^79 + 28 * q^81 + 24 * q^85 - 24 * q^87 - 40 * q^91 - 12 * q^93 + 4 * q^95 - 4 * q^97 + 52 * q^99

Introduction

L-functions

Modular forms

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