LMFDB - Embedded newform 1512.2.c.f.757.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.15
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671239 - 1.24476i) q^{2} +(-1.09888 - 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(-2.81770 + 0.246156i) q^{8} +O(q^{10})$	\(q+(0.671239 - 1.24476i) q^{2} +(-1.09888 - 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(-2.81770 + 0.246156i) q^{8} +(4.56453 + 2.46142i) q^{10} +4.45794i q^{11} -1.51546i q^{13} +(0.671239 - 1.24476i) q^{14} +(-1.58494 + 3.67260i) q^{16} -3.45516 q^{17} -2.29933i q^{19} +(6.12778 - 4.02956i) q^{20} +(5.54908 + 2.99234i) q^{22} -8.76326 q^{23} -8.44677 q^{25} +(-1.88640 - 1.01724i) q^{26} +(-1.09888 - 1.67107i) q^{28} -1.62037i q^{29} -9.26498 q^{31} +(3.50764 + 4.43807i) q^{32} +(-2.31924 + 4.30086i) q^{34} +3.66698i q^{35} +5.69381i q^{37} +(-2.86213 - 1.54340i) q^{38} +(-0.902651 - 10.3324i) q^{40} -6.86926 q^{41} -0.880042i q^{43} +(7.44952 - 4.89872i) q^{44} +(-5.88224 + 10.9082i) q^{46} +10.5955 q^{47} +1.00000 q^{49} +(-5.66980 + 10.5142i) q^{50} +(-2.53244 + 1.66531i) q^{52} +11.5036i q^{53} -16.3472 q^{55} +(-2.81770 + 0.246156i) q^{56} +(-2.01698 - 1.08766i) q^{58} -2.99426i q^{59} +8.51202i q^{61} +(-6.21902 + 11.5327i) q^{62} +(7.87881 - 1.38719i) q^{64} +5.55718 q^{65} -10.6629i q^{67} +(3.79680 + 5.77381i) q^{68} +(4.56453 + 2.46142i) q^{70} +10.6172 q^{71} +7.85523 q^{73} +(7.08745 + 3.82191i) q^{74} +(-3.84235 + 2.52668i) q^{76} +4.45794i q^{77} +4.57730 q^{79} +(-13.4674 - 5.81195i) q^{80} +(-4.61091 + 8.55061i) q^{82} +2.60500i q^{83} -12.6700i q^{85} +(-1.09545 - 0.590719i) q^{86} +(-1.09735 - 12.5611i) q^{88} -2.14381 q^{89} -1.51546i q^{91} +(9.62974 + 14.6440i) q^{92} +(7.11208 - 13.1888i) q^{94} +8.43162 q^{95} -13.8317 q^{97} +(0.671239 - 1.24476i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.671239	−	1.24476i	0.474638	−	0.880181i
$2$	0.671239	−	1.24476i	0.474638	−	0.880181i
$3$		0			0
$3$		0			0
$4$	−1.09888	−	1.67107i	−0.549438	−	0.835534i
$5$			3.66698i			1.63993i	0.572417	+	0.819963i	$0.306006\pi$
$5$			3.66698i			1.63993i	−0.572417	+	0.819963i	$0.693994\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.81770	+	0.246156i	−0.996206	+	0.0870294i
$9$		0			0
$10$	4.56453	+	2.46142i	1.44343	+	0.778370i
$11$			4.45794i			1.34412i	0.740498	+	0.672059i	$0.234590\pi$
$11$			4.45794i			1.34412i	−0.740498	+	0.672059i	$0.765410\pi$
$12$		0			0
$13$		−	1.51546i		−	0.420314i	−0.977668	−	0.210157i	$-0.932602\pi$
$13$		−	1.51546i		−	0.420314i	0.977668	−	0.210157i	$-0.0673975\pi$
$14$	0.671239	−	1.24476i	0.179396	−	0.332677i
$15$		0			0
$16$	−1.58494	+	3.67260i	−0.396235	+	0.918149i
$17$	−3.45516			−0.838000			−0.419000	−	0.907986i	$-0.637619\pi$
$17$	−3.45516			−0.838000			−0.419000	+	0.907986i	$0.637619\pi$
$18$		0			0
$19$		−	2.29933i		−	0.527503i	−0.964591	−	0.263752i	$-0.915040\pi$
$19$		−	2.29933i		−	0.527503i	0.964591	−	0.263752i	$-0.0849600\pi$
$20$	6.12778	−	4.02956i	1.37021	−	0.901038i
$21$		0			0
$22$	5.54908	+	2.99234i	1.18307	+	0.637969i
$23$	−8.76326			−1.82727			−0.913633	−	0.406539i	$-0.866735\pi$
$23$	−8.76326			−1.82727			−0.913633	+	0.406539i	$0.866735\pi$
$24$		0			0
$25$	−8.44677			−1.68935
$26$	−1.88640	−	1.01724i	−0.369953	−	0.199497i
$27$		0			0
$28$	−1.09888	−	1.67107i	−0.207668	−	0.315802i
$29$		−	1.62037i		−	0.300895i	−0.988618	−	0.150448i	$-0.951928\pi$
$29$		−	1.62037i		−	0.300895i	0.988618	−	0.150448i	$-0.0480715\pi$
$30$		0			0
$31$	−9.26498			−1.66404			−0.832020	−	0.554746i	$-0.812816\pi$
$31$	−9.26498			−1.66404			−0.832020	+	0.554746i	$0.812816\pi$
$32$	3.50764	+	4.43807i	0.620070	+	0.784547i
$33$		0			0
$34$	−2.31924	+	4.30086i	−0.397746	+	0.737592i
$35$			3.66698i			0.619833i
$36$		0			0
$37$			5.69381i			0.936056i	0.883714	+	0.468028i	$0.155035\pi$
$37$			5.69381i			0.936056i	−0.883714	+	0.468028i	$0.844965\pi$
$38$	−2.86213	−	1.54340i	−0.464299	−	0.250373i
$39$		0			0
$40$	−0.902651	−	10.3324i	−0.142722	−	1.63370i
$41$	−6.86926			−1.07280			−0.536399	−	0.843965i	$-0.680216\pi$
$41$	−6.86926			−1.07280			−0.536399	+	0.843965i	$0.680216\pi$
$42$		0			0
$43$		−	0.880042i		−	0.134205i	−0.997746	−	0.0671026i	$-0.978625\pi$
$43$		−	0.880042i		−	0.134205i	0.997746	−	0.0671026i	$-0.0213755\pi$
$44$	7.44952	−	4.89872i	1.12306	−	0.738510i
$45$		0			0
$46$	−5.88224	+	10.9082i	−0.867289	+	1.60833i
$47$	10.5955			1.54551			0.772753	−	0.634707i	$-0.218879\pi$
$47$	10.5955			1.54551			0.772753	+	0.634707i	$0.218879\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−5.66980	+	10.5142i	−0.801831	+	1.48694i
$51$		0			0
$52$	−2.53244	+	1.66531i	−0.351187	+	0.230937i
$53$			11.5036i			1.58014i	0.613014	+	0.790072i	$0.289957\pi$
$53$			11.5036i			1.58014i	−0.613014	+	0.790072i	$0.710043\pi$
$54$		0			0
$55$	−16.3472			−2.20425
$56$	−2.81770	+	0.246156i	−0.376530	+	0.0328940i
$57$		0			0
$58$	−2.01698	−	1.08766i	−0.264843	−	0.142816i
$59$		−	2.99426i		−	0.389819i	−0.980821	−	0.194909i	$-0.937559\pi$
$59$		−	2.99426i		−	0.389819i	0.980821	−	0.194909i	$-0.0624413\pi$
$60$		0			0
$61$			8.51202i			1.08985i	0.838484	+	0.544926i	$0.183442\pi$
$61$			8.51202i			1.08985i	−0.838484	+	0.544926i	$0.816558\pi$
$62$	−6.21902	+	11.5327i	−0.789816	+	1.46466i
$63$		0			0
$64$	7.87881	−	1.38719i	0.984852	−	0.173398i
$65$	5.55718			0.689284
$66$		0			0
$67$		−	10.6629i		−	1.30268i	−0.758786	−	0.651341i	$-0.774207\pi$
$67$		−	10.6629i		−	1.30268i	0.758786	−	0.651341i	$-0.225793\pi$
$68$	3.79680	+	5.77381i	0.460429	+	0.700178i
$69$		0			0
$70$	4.56453	+	2.46142i	0.545566	+	0.294196i
$71$	10.6172			1.26003			0.630015	−	0.776583i	$-0.283049\pi$
$71$	10.6172			1.26003			0.630015	+	0.776583i	$0.283049\pi$
$72$		0			0
$73$	7.85523			0.919385			0.459692	−	0.888078i	$-0.347960\pi$
$73$	7.85523			0.919385			0.459692	+	0.888078i	$0.347960\pi$
$74$	7.08745	+	3.82191i	0.823899	+	0.444288i
$75$		0			0
$76$	−3.84235	+	2.52668i	−0.440747	+	0.289831i
$77$			4.45794i			0.508029i
$78$		0			0
$79$	4.57730			0.514986			0.257493	−	0.966280i	$-0.417104\pi$
$79$	4.57730			0.514986			0.257493	+	0.966280i	$0.417104\pi$
$80$	−13.4674	−	5.81195i	−1.50570	−	0.649796i
$81$		0			0
$82$	−4.61091	+	8.55061i	−0.509190	+	0.944257i
$83$			2.60500i			0.285936i	0.989727	+	0.142968i	$0.0456645\pi$
$83$			2.60500i			0.285936i	−0.989727	+	0.142968i	$0.954335\pi$
$84$		0			0
$85$		−	12.6700i		−	1.37426i
$86$	−1.09545	−	0.590719i	−0.118125	−	0.0636988i
$87$		0			0
$88$	−1.09735	−	12.5611i	−0.116978	−	1.33902i
$89$	−2.14381			−0.227244			−0.113622	−	0.993524i	$-0.536245\pi$
$89$	−2.14381			−0.227244			−0.113622	+	0.993524i	$0.536245\pi$
$90$		0			0
$91$		−	1.51546i		−	0.158864i
$92$	9.62974	+	14.6440i	1.00397	+	1.52674i
$93$		0			0
$94$	7.11208	−	13.1888i	0.733555	−	1.36033i
$95$	8.43162			0.865066
$96$		0			0
$97$	−13.8317			−1.40440			−0.702199	−	0.711981i	$-0.747798\pi$
$97$	−13.8317			−1.40440			−0.702199	+	0.711981i	$0.747798\pi$
$98$	0.671239	−	1.24476i	0.0678054	−	0.125740i
$99$		0			0
$100$	9.28196	+	14.1151i	0.928196	+	1.41151i
$101$			10.2333i			1.01826i	0.860691	+	0.509128i	$0.170032\pi$
$101$			10.2333i			1.01826i	−0.860691	+	0.509128i	$0.829968\pi$
$102$		0			0
$103$	−12.7223			−1.25357			−0.626784	−	0.779193i	$-0.715629\pi$
$103$	−12.7223			−1.25357			−0.626784	+	0.779193i	$0.715629\pi$
$104$	0.373041	+	4.27012i	0.0365797	+	0.418719i
$105$		0			0
$106$	14.3193	+	7.72168i	1.39081	+	0.749996i
$107$			6.40575i			0.619268i	0.950856	+	0.309634i	$0.100206\pi$
$107$			6.40575i			0.619268i	−0.950856	+	0.309634i	$0.899794\pi$
$108$		0			0
$109$			3.38839i			0.324549i	0.986746	+	0.162274i	$0.0518829\pi$
$109$			3.38839i			0.324549i	−0.986746	+	0.162274i	$0.948117\pi$
$110$	−10.9729	+	20.3484i	−1.04622	+	1.94014i
$111$		0			0
$112$	−1.58494	+	3.67260i	−0.149763	+	0.347028i
$113$	−1.40668			−0.132329			−0.0661644	−	0.997809i	$-0.521076\pi$
$113$	−1.40668			−0.132329			−0.0661644	+	0.997809i	$0.521076\pi$
$114$		0			0
$115$		−	32.1347i		−	2.99658i
$116$	−2.70775	+	1.78059i	−0.251408	+	0.165323i
$117$		0			0
$118$	−3.72714	−	2.00986i	−0.343111	−	0.185023i
$119$	−3.45516			−0.316734
$120$		0			0
$121$	−8.87319			−0.806653
$122$	10.5955	+	5.71360i	0.959268	+	0.517285i
$123$		0			0
$124$	10.1811	+	15.4824i	0.914287	+	1.39036i
$125$		−	12.6393i		−	1.13049i
$126$		0			0
$127$	10.4597			0.928152			0.464076	−	0.885795i	$-0.346386\pi$
$127$	10.4597			0.928152			0.464076	+	0.885795i	$0.346386\pi$
$128$	3.56185	−	10.7384i	0.314826	−	0.949150i
$129$		0			0
$130$	3.73020	−	6.91738i	0.327160	−	0.606695i
$131$		−	12.6638i		−	1.10644i	−0.833034	−	0.553221i	$-0.813398\pi$
$131$		−	12.6638i		−	1.10644i	0.833034	−	0.553221i	$-0.186602\pi$
$132$		0			0
$133$		−	2.29933i		−	0.199378i
$134$	−13.2728	−	7.15736i	−1.14660	−	0.618301i
$135$		0			0
$136$	9.73559	−	0.850510i	0.834820	−	0.0729306i
$137$	−6.87026			−0.586966			−0.293483	−	0.955964i	$-0.594814\pi$
$137$	−6.87026			−0.586966			−0.293483	+	0.955964i	$0.594814\pi$
$138$		0			0
$139$			13.4362i			1.13964i	0.821768	+	0.569822i	$0.192988\pi$
$139$			13.4362i			1.13964i	−0.821768	+	0.569822i	$0.807012\pi$
$140$	6.12778	−	4.02956i	0.517892	−	0.340560i
$141$		0			0
$142$	7.12668	−	13.2159i	0.598058	−	1.10905i
$143$	6.75584			0.564952
$144$		0			0
$145$	5.94188			0.493446
$146$	5.27273	−	9.77790i	0.436374	−	0.809225i
$147$		0			0
$148$	9.51475	−	6.25679i	0.782107	−	0.514305i
$149$			6.35294i			0.520453i	0.965548	+	0.260227i	$0.0837973\pi$
$149$			6.35294i			0.520453i	−0.965548	+	0.260227i	$0.916203\pi$
$150$		0			0
$151$	19.5918			1.59436			0.797179	−	0.603743i	$-0.206325\pi$
$151$	19.5918			1.59436			0.797179	+	0.603743i	$0.206325\pi$
$152$	0.565996	+	6.47882i	0.0459083	+	0.525502i
$153$		0			0
$154$	5.54908	+	2.99234i	0.447158	+	0.241130i
$155$		−	33.9745i		−	2.72890i
$156$		0			0
$157$			22.6978i			1.81148i	0.423834	+	0.905740i	$0.360684\pi$
$157$			22.6978i			1.81148i	−0.423834	+	0.905740i	$0.639316\pi$
$158$	3.07246	−	5.69766i	0.244432	−	0.453281i
$159$		0			0
$160$	−16.2743	+	12.8625i	−1.28660	+	1.01687i
$161$	−8.76326			−0.690642
$162$		0			0
$163$			3.60107i			0.282058i	0.990005	+	0.141029i	$0.0450410\pi$
$163$			3.60107i			0.282058i	−0.990005	+	0.141029i	$0.954959\pi$
$164$	7.54847	+	11.4790i	0.589436	+	0.896359i
$165$		0			0
$166$	3.24261	+	1.74857i	0.251675	+	0.135716i
$167$	−5.46351			−0.422779			−0.211390	−	0.977402i	$-0.567799\pi$
$167$	−5.46351			−0.422779			−0.211390	+	0.977402i	$0.567799\pi$
$168$		0			0
$169$	10.7034			0.823336
$170$	−15.7712	−	8.50461i	−1.20960	−	0.652274i
$171$		0			0
$172$	−1.47061	+	0.967058i	−0.112133	+	0.0737375i
$173$			1.71944i			0.130727i	0.997862	+	0.0653634i	$0.0208207\pi$
$173$			1.71944i			0.130727i	−0.997862	+	0.0653634i	$0.979179\pi$
$174$		0			0
$175$	−8.44677			−0.638516
$176$	−16.3722	−	7.06556i	−1.23410	−	0.532587i
$177$		0			0
$178$	−1.43901	+	2.66854i	−0.107858	+	0.200016i
$179$			10.9956i			0.821846i	0.911670	+	0.410923i	$0.134794\pi$
$179$			10.9956i			0.821846i	−0.911670	+	0.410923i	$0.865206\pi$
$180$		0			0
$181$		−	26.6227i		−	1.97885i	−0.145040	−	0.989426i	$-0.546331\pi$
$181$		−	26.6227i		−	1.97885i	0.145040	−	0.989426i	$-0.453669\pi$
$182$	−1.88640	−	1.01724i	−0.139829	−	0.0754027i
$183$		0			0
$184$	24.6922	−	2.15713i	1.82033	−	0.159026i
$185$	−20.8791			−1.53506
$186$		0			0
$187$		−	15.4029i		−	1.12637i
$188$	−11.6431	−	17.7057i	−0.849160	−	1.29132i
$189$		0			0
$190$	5.65963	−	10.4954i	0.410593	−	0.761415i
$191$	22.1581			1.60330			0.801652	−	0.597791i	$-0.203955\pi$
$191$	22.1581			1.60330			0.801652	+	0.597791i	$0.203955\pi$
$192$		0			0
$193$	11.5599			0.832098			0.416049	−	0.909342i	$-0.363414\pi$
$193$	11.5599			0.832098			0.416049	+	0.909342i	$0.363414\pi$
$194$	−9.28438	+	17.2172i	−0.666580	+	1.23612i
$195$		0			0
$196$	−1.09888	−	1.67107i	−0.0784912	−	0.119362i
$197$		−	13.1740i		−	0.938611i	−0.883036	−	0.469305i	$-0.844504\pi$
$197$		−	13.1740i		−	0.938611i	0.883036	−	0.469305i	$-0.155496\pi$
$198$		0			0
$199$	−12.1012			−0.857828			−0.428914	−	0.903345i	$-0.641104\pi$
$199$	−12.1012			−0.857828			−0.428914	+	0.903345i	$0.641104\pi$
$200$	23.8004	−	2.07923i	1.68294	−	0.147024i
$201$		0			0
$202$	12.7381	+	6.86902i	0.896250	+	0.483302i
$203$		−	1.62037i		−	0.113728i
$204$		0			0
$205$		−	25.1895i		−	1.75931i
$206$	−8.53972	+	15.8363i	−0.594990	+	1.10337i
$207$		0			0
$208$	5.56569	+	2.40192i	0.385911	+	0.166543i
$209$	10.2503			0.709027
$210$		0			0
$211$			21.7501i			1.49734i	0.662944	+	0.748669i	$0.269307\pi$
$211$			21.7501i			1.49734i	−0.662944	+	0.748669i	$0.730693\pi$
$212$	19.2233	−	12.6411i	1.32027	−	0.868192i
$213$		0			0
$214$	7.97365	+	4.29979i	0.545068	+	0.293928i
$215$	3.22710			0.220086
$216$		0			0
$217$	−9.26498			−0.628948
$218$	4.21774	+	2.27442i	0.285662	+	0.154043i
$219$		0			0
$220$	17.9635	+	27.3173i	1.21110	+	1.84173i
$221$			5.23617i			0.352223i
$222$		0			0
$223$	−3.00739			−0.201390			−0.100695	−	0.994917i	$-0.532107\pi$
$223$	−3.00739			−0.201390			−0.100695	+	0.994917i	$0.532107\pi$
$224$	3.50764	+	4.43807i	0.234364	+	0.296531i
$225$		0			0
$226$	−0.944215	+	1.75098i	−0.0628083	+	0.116473i
$227$			11.1508i			0.740102i	0.929011	+	0.370051i	$0.120660\pi$
$227$			11.1508i			0.740102i	−0.929011	+	0.370051i	$0.879340\pi$
$228$		0			0
$229$		−	2.46317i		−	0.162771i	−0.996683	−	0.0813853i	$-0.974066\pi$
$229$		−	2.46317i		−	0.162771i	0.996683	−	0.0813853i	$-0.0259344\pi$
$230$	−40.0002	−	21.5701i	−2.63753	−	1.42229i
$231$		0			0
$232$	0.398865	+	4.56571i	0.0261867	+	0.299754i
$233$	−26.1143			−1.71080			−0.855401	−	0.517966i	$-0.826689\pi$
$233$	−26.1143			−1.71080			−0.855401	+	0.517966i	$0.826689\pi$
$234$		0			0
$235$			38.8534i			2.53451i
$236$	−5.00361	+	3.29032i	−0.325707	+	0.214181i
$237$		0			0
$238$	−2.31924	+	4.30086i	−0.150334	+	0.278783i
$239$	24.4496			1.58151			0.790757	−	0.612130i	$-0.209687\pi$
$239$	24.4496			1.58151			0.790757	+	0.612130i	$0.209687\pi$
$240$		0			0
$241$	−9.01348			−0.580609			−0.290305	−	0.956934i	$-0.593757\pi$
$241$	−9.01348			−0.580609			−0.290305	+	0.956934i	$0.593757\pi$
$242$	−5.95603	+	11.0450i	−0.382868	+	0.710001i
$243$		0			0
$244$	14.2242	−	9.35366i	0.910609	−	0.598807i
$245$			3.66698i			0.234275i
$246$		0			0
$247$	−3.48456			−0.221717
$248$	26.1059	−	2.28063i	1.65773	−	0.144820i
$249$		0			0
$250$	−15.7329	−	8.48397i	−0.995036	−	0.536573i
$251$		−	24.7649i		−	1.56315i	−0.623814	−	0.781573i	$-0.714418\pi$
$251$		−	24.7649i		−	1.56315i	0.623814	−	0.781573i	$-0.285582\pi$
$252$		0			0
$253$		−	39.0661i		−	2.45606i
$254$	7.02099	−	13.0199i	0.440536	−	0.816942i
$255$		0			0
$256$	−10.9759	−	11.6417i	−0.685996	−	0.727606i
$257$	17.1618			1.07052			0.535262	−	0.844686i	$-0.320213\pi$
$257$	17.1618			1.07052			0.535262	+	0.844686i	$0.320213\pi$
$258$		0			0
$259$			5.69381i			0.353796i
$260$	−6.10666	−	9.28644i	−0.378719	−	0.575920i
$261$		0			0
$262$	−15.7635	−	8.50045i	−0.973870	−	0.525159i
$263$	4.02861			0.248415			0.124207	−	0.992256i	$-0.460361\pi$
$263$	4.02861			0.248415			0.124207	+	0.992256i	$0.460361\pi$
$264$		0			0
$265$	−42.1836			−2.59132
$266$	−2.86213	−	1.54340i	−0.175488	−	0.0946321i
$267$		0			0
$268$	−17.8184	+	11.7172i	−1.08843	+	0.715743i
$269$			24.4193i			1.48887i	0.667693	+	0.744436i	$0.267282\pi$
$269$			24.4193i			1.48887i	−0.667693	+	0.744436i	$0.732718\pi$
$270$		0			0
$271$	−1.21510			−0.0738120			−0.0369060	−	0.999319i	$-0.511750\pi$
$271$	−1.21510			−0.0738120			−0.0369060	+	0.999319i	$0.511750\pi$
$272$	5.47622	−	12.6894i	0.332045	−	0.769409i
$273$		0			0
$274$	−4.61159	+	8.55185i	−0.278596	+	0.516636i
$275$		−	37.6552i		−	2.27069i
$276$		0			0
$277$		−	11.1239i		−	0.668371i	−0.942507	−	0.334185i	$-0.891539\pi$
$277$		−	11.1239i		−	0.668371i	0.942507	−	0.334185i	$-0.108461\pi$
$278$	16.7249	+	9.01890i	1.00309	+	0.540918i
$279$		0			0
$280$	−0.902651	−	10.3324i	−0.0539437	−	0.617482i
$281$	−29.4678			−1.75790			−0.878952	−	0.476910i	$-0.841757\pi$
$281$	−29.4678			−1.75790			−0.878952	+	0.476910i	$0.841757\pi$
$282$		0			0
$283$		−	13.0312i		−	0.774624i	−0.921949	−	0.387312i	$-0.873404\pi$
$283$		−	13.0312i		−	0.774624i	0.921949	−	0.387312i	$-0.126596\pi$
$284$	−11.6670	−	17.7421i	−0.692309	−	1.05280i
$285$		0			0
$286$	4.53478	−	8.40943i	0.268147	−	0.497260i
$287$	−6.86926			−0.405479
$288$		0			0
$289$	−5.06186			−0.297756
$290$	3.98842	−	7.39624i	0.234208	−	0.434322i
$291$		0			0
$292$	−8.63192	−	13.1266i	−0.505145	−	0.768177i
$293$		−	4.86503i		−	0.284218i	−0.989851	−	0.142109i	$-0.954612\pi$
$293$		−	4.86503i		−	0.284218i	0.989851	−	0.142109i	$-0.0453883\pi$
$294$		0			0
$295$	10.9799			0.639274
$296$	−1.40157	−	16.0434i	−0.0814644	−	0.932505i
$297$		0			0
$298$	7.90792	+	4.26434i	0.458093	+	0.247027i
$299$			13.2804i			0.768026i
$300$		0			0
$301$		−	0.880042i		−	0.0507248i
$302$	13.1508	−	24.3872i	0.756742	−	1.40332i
$303$		0			0
$304$	8.44453	+	3.64431i	0.484327	+	0.209015i
$305$	−31.2134			−1.78728
$306$		0			0
$307$		−	9.07611i		−	0.518001i	−0.965877	−	0.259000i	$-0.916607\pi$
$307$		−	9.07611i		−	0.518001i	0.965877	−	0.259000i	$-0.0833931\pi$
$308$	7.44952	−	4.89872i	0.424476	−	0.279131i
$309$		0			0
$310$	−42.2903	−	22.8050i	−2.40193	−	1.29524i
$311$	1.21020			0.0686240			0.0343120	−	0.999411i	$-0.489076\pi$
$311$	1.21020			0.0686240			0.0343120	+	0.999411i	$0.489076\pi$
$312$		0			0
$313$	−3.15697			−0.178443			−0.0892214	−	0.996012i	$-0.528438\pi$
$313$	−3.15697			−0.178443			−0.0892214	+	0.996012i	$0.528438\pi$
$314$	28.2534	+	15.2356i	1.59443	+	0.859796i
$315$		0			0
$316$	−5.02989	−	7.64898i	−0.282953	−	0.430289i
$317$		−	7.08197i		−	0.397763i	−0.980024	−	0.198882i	$-0.936269\pi$
$317$		−	7.08197i		−	0.397763i	0.980024	−	0.198882i	$-0.0637309\pi$
$318$		0			0
$319$	7.22351			0.404439
$320$	5.08679	+	28.8915i	0.284360	+	1.61508i
$321$		0			0
$322$	−5.88224	+	10.9082i	−0.327805	+	0.607890i
$323$			7.94457i			0.442048i
$324$		0			0
$325$			12.8008i			0.710060i
$326$	4.48248	+	2.41718i	0.248262	+	0.133875i
$327$		0			0
$328$	19.3555	−	1.69091i	1.06873	−	0.0933649i
$329$	10.5955			0.584146
$330$		0			0
$331$			7.34765i			0.403863i	0.979400	+	0.201932i	$0.0647219\pi$
$331$			7.34765i			0.403863i	−0.979400	+	0.201932i	$0.935278\pi$
$332$	4.35313	−	2.86257i	0.238909	−	0.157104i
$333$		0			0
$334$	−3.66732	+	6.80078i	−0.200667	+	0.372122i
$335$	39.1007			2.13630
$336$		0			0
$337$	−26.9873			−1.47009			−0.735046	−	0.678017i	$-0.762840\pi$
$337$	−26.9873			−1.47009			−0.735046	+	0.678017i	$0.762840\pi$
$338$	7.18452	−	13.3232i	0.390786	−	0.724685i
$339$		0			0
$340$	−21.1725	+	13.9228i	−1.14824	+	0.755069i
$341$		−	41.3027i		−	2.23667i
$342$		0			0
$343$	1.00000			0.0539949
$344$	0.216628	+	2.47969i	0.0116798	+	0.133696i
$345$		0			0
$346$	2.14030	+	1.15416i	0.115063	+	0.0620479i
$347$			9.06776i			0.486783i	0.969928	+	0.243391i	$0.0782599\pi$
$347$			9.06776i			0.486783i	−0.969928	+	0.243391i	$0.921740\pi$
$348$		0			0
$349$		−	13.6784i		−	0.732191i	−0.930577	−	0.366095i	$-0.880694\pi$
$349$		−	13.6784i		−	0.732191i	0.930577	−	0.366095i	$-0.119306\pi$
$350$	−5.66980	+	10.5142i	−0.303064	+	0.562010i
$351$		0			0
$352$	−19.7846	+	15.6368i	−1.05452	+	0.833447i
$353$	−0.949067			−0.0505138			−0.0252569	−	0.999681i	$-0.508040\pi$
$353$	−0.949067			−0.0505138			−0.0252569	+	0.999681i	$0.508040\pi$
$354$		0			0
$355$			38.9331i			2.06636i
$356$	2.35578	+	3.58246i	0.124856	+	0.189870i
$357$		0			0
$358$	13.6869	+	7.38064i	0.723374	+	0.390079i
$359$	−15.0508			−0.794351			−0.397175	−	0.917743i	$-0.630009\pi$
$359$	−15.0508			−0.794351			−0.397175	+	0.917743i	$0.630009\pi$
$360$		0			0
$361$	13.7131			0.721740
$362$	−33.1390	−	17.8702i	−1.74175	−	0.939237i
$363$		0			0
$364$	−2.53244	+	1.66531i	−0.132736	+	0.0872859i
$365$			28.8050i			1.50772i
$366$		0			0
$367$	−3.70674			−0.193490			−0.0967451	−	0.995309i	$-0.530843\pi$
$367$	−3.70674			−0.193490			−0.0967451	+	0.995309i	$0.530843\pi$
$368$	13.8892	−	32.1839i	0.724027	−	1.67770i
$369$		0			0
$370$	−14.0149	+	25.9896i	−0.728598	+	1.35113i
$371$			11.5036i			0.597239i
$372$		0			0
$373$			31.3688i			1.62421i	0.583508	+	0.812107i	$0.301680\pi$
$373$			31.3688i			1.62421i	−0.583508	+	0.812107i	$0.698320\pi$
$374$	−19.1730	−	10.3390i	−0.991410	−	0.534618i
$375$		0			0
$376$	−29.8548	+	2.60814i	−1.53964	+	0.134504i
$377$	−2.45562			−0.126471
$378$		0			0
$379$		−	17.6560i		−	0.906930i	−0.891274	−	0.453465i	$-0.850188\pi$
$379$		−	17.6560i		−	0.906930i	0.891274	−	0.453465i	$-0.149812\pi$
$380$	−9.26531	−	14.0898i	−0.475301	−	0.722792i
$381$		0			0
$382$	14.8734	−	27.5816i	0.760989	−	1.41120i
$383$	−17.7974			−0.909402			−0.454701	−	0.890644i	$-0.650254\pi$
$383$	−17.7974			−0.909402			−0.454701	+	0.890644i	$0.650254\pi$
$384$		0			0
$385$	−16.3472			−0.833129
$386$	7.75944	−	14.3893i	0.394945	−	0.732397i
$387$		0			0
$388$	15.1993	+	23.1137i	0.771630	+	1.17342i
$389$			25.1886i			1.27711i	0.769574	+	0.638557i	$0.220468\pi$
$389$			25.1886i			1.27711i	−0.769574	+	0.638557i	$0.779532\pi$
$390$		0			0
$391$	30.2785			1.53125
$392$	−2.81770	+	0.246156i	−0.142315	+	0.0124328i
$393$		0			0
$394$	−16.3986	−	8.84292i	−0.826148	−	0.445500i
$395$			16.7849i			0.844539i
$396$		0			0
$397$			34.3710i			1.72503i	0.506032	+	0.862515i	$0.331112\pi$
$397$			34.3710i			1.72503i	−0.506032	+	0.862515i	$0.668888\pi$
$398$	−8.12276	+	15.0631i	−0.407157	+	0.755044i
$399$		0			0
$400$	13.3876	−	31.0216i	0.669382	−	1.55108i
$401$	9.65560			0.482178			0.241089	−	0.970503i	$-0.422495\pi$
$401$	9.65560			0.482178			0.241089	+	0.970503i	$0.422495\pi$
$402$		0			0
$403$			14.0408i			0.699420i
$404$	17.1006	−	11.2452i	0.850788	−	0.559469i
$405$		0			0
$406$	−2.01698	−	1.08766i	−0.100101	−	0.0539795i
$407$	−25.3826			−1.25817
$408$		0			0
$409$	28.4161			1.40509			0.702543	−	0.711642i	$-0.252048\pi$
$409$	28.4161			1.40509			0.702543	+	0.711642i	$0.252048\pi$
$410$	−31.3549	−	16.9081i	−1.54851	−	0.835034i
$411$		0			0
$412$	13.9803	+	21.2599i	0.688758	+	1.04740i
$413$		−	2.99426i		−	0.147338i
$414$		0			0
$415$	−9.55248			−0.468913
$416$	6.72573	−	5.31571i	0.329756	−	0.260624i
$417$		0			0
$418$	6.88039	−	12.7592i	0.336531	−	0.624072i
$419$		−	11.5381i		−	0.563673i	−0.959462	−	0.281837i	$-0.909056\pi$
$419$		−	11.5381i		−	0.563673i	0.959462	−	0.281837i	$-0.0909436\pi$
$420$		0			0
$421$			6.84814i			0.333758i	0.985977	+	0.166879i	$0.0533689\pi$
$421$			6.84814i			0.333758i	−0.985977	+	0.166879i	$0.946631\pi$
$422$	27.0737	+	14.5995i	1.31793	+	0.710692i
$423$		0			0
$424$	−2.83169	−	32.4137i	−0.137519	−	1.57415i
$425$	29.1850			1.41568
$426$		0			0
$427$			8.51202i			0.411925i
$428$	10.7045	−	7.03913i	0.517419	−	0.340249i
$429$		0			0
$430$	2.16616	−	4.01698i	0.104461	−	0.193716i
$431$	10.4500			0.503357			0.251679	−	0.967811i	$-0.419017\pi$
$431$	10.4500			0.503357			0.251679	+	0.967811i	$0.419017\pi$
$432$		0			0
$433$	18.1818			0.873763			0.436882	−	0.899519i	$-0.356083\pi$
$433$	18.1818			0.873763			0.436882	+	0.899519i	$0.356083\pi$
$434$	−6.21902	+	11.5327i	−0.298522	+	0.553588i
$435$		0			0
$436$	5.66223	−	3.72342i	0.271171	−	0.178319i
$437$			20.1497i			0.963889i
$438$		0			0
$439$	7.91836			0.377923			0.188961	−	0.981985i	$-0.439488\pi$
$439$	7.91836			0.377923			0.188961	+	0.981985i	$0.439488\pi$
$440$	46.0614	−	4.02396i	2.19589	−	0.191835i
$441$		0			0
$442$	6.51780	+	3.51472i	0.310020	+	0.167178i
$443$		−	18.2916i		−	0.869062i	−0.900657	−	0.434531i	$-0.856914\pi$
$443$		−	18.2916i		−	0.869062i	0.900657	−	0.434531i	$-0.143086\pi$
$444$		0			0
$445$		−	7.86132i		−	0.372662i
$446$	−2.01868	+	3.74350i	−0.0955873	+	0.177260i
$447$		0			0
$448$	7.87881	−	1.38719i	0.372239	−	0.0655384i
$449$	−15.2172			−0.718144			−0.359072	−	0.933310i	$-0.616907\pi$
$449$	−15.2172			−0.718144			−0.359072	+	0.933310i	$0.616907\pi$
$450$		0			0
$451$		−	30.6227i		−	1.44197i
$452$	1.54576	+	2.35065i	0.0727066	+	0.110565i
$453$		0			0
$454$	13.8801	+	7.48482i	0.651424	+	0.351280i
$455$	5.55718			0.260525
$456$		0			0
$457$	38.6658			1.80871			0.904354	−	0.426783i	$-0.140353\pi$
$457$	38.6658			1.80871			0.904354	+	0.426783i	$0.140353\pi$
$458$	−3.06606	−	1.65337i	−0.143268	−	0.0772570i
$459$		0			0
$460$	−53.6994	+	35.3121i	−2.50375	+	1.64644i
$461$		−	5.18888i		−	0.241670i	−0.992673	−	0.120835i	$-0.961443\pi$
$461$		−	5.18888i		−	0.241670i	0.992673	−	0.120835i	$-0.0385572\pi$
$462$		0			0
$463$	−3.81583			−0.177337			−0.0886683	−	0.996061i	$-0.528261\pi$
$463$	−3.81583			−0.177337			−0.0886683	+	0.996061i	$0.528261\pi$
$464$	5.95097	+	2.56819i	0.276267	+	0.119225i
$465$		0			0
$466$	−17.5289	+	32.5061i	−0.812011	+	1.50582i
$467$		−	7.29246i		−	0.337455i	−0.985663	−	0.168727i	$-0.946034\pi$
$467$		−	7.29246i		−	0.337455i	0.985663	−	0.168727i	$-0.0539657\pi$
$468$		0			0
$469$		−	10.6629i		−	0.492367i
$470$	48.3633	+	26.0799i	2.23083	+	1.20298i
$471$		0			0
$472$	0.737055	+	8.43690i	0.0339257	+	0.388340i
$473$	3.92317			0.180388
$474$		0			0
$475$			19.4220i			0.891140i
$476$	3.79680	+	5.77381i	0.174026	+	0.264642i
$477$		0			0
$478$	16.4115	−	30.4340i	0.750646	−	1.39202i
$479$	16.2695			0.743371			0.371686	−	0.928359i	$-0.378780\pi$
$479$	16.2695			0.743371			0.371686	+	0.928359i	$0.378780\pi$
$480$		0			0
$481$	8.62876			0.393438
$482$	−6.05020	+	11.2197i	−0.275579	+	0.511042i
$483$		0			0
$484$	9.75054	+	14.8277i	0.443206	+	0.673986i
$485$		−	50.7207i		−	2.30311i
$486$		0			0
$487$	7.16667			0.324753			0.162376	−	0.986729i	$-0.448084\pi$
$487$	7.16667			0.324753			0.162376	+	0.986729i	$0.448084\pi$
$488$	−2.09529	−	23.9843i	−0.0948492	−	1.08572i
$489$		0			0
$490$	4.56453	+	2.46142i	0.206205	+	0.111196i
$491$		−	17.8247i		−	0.804418i	−0.915548	−	0.402209i	$-0.868243\pi$
$491$		−	17.8247i		−	0.804418i	0.915548	−	0.402209i	$-0.131757\pi$
$492$		0			0
$493$			5.59864i			0.252150i
$494$	−2.33897	+	4.33746i	−0.105235	+	0.195151i
$495$		0			0
$496$	14.6844	−	34.0265i	0.659351	−	1.52784i
$497$	10.6172			0.476247
$498$		0			0
$499$		−	37.6121i		−	1.68375i	−0.539673	−	0.841875i	$-0.681452\pi$
$499$		−	37.6121i		−	1.68375i	0.539673	−	0.841875i	$-0.318548\pi$
$500$	−21.1211	+	13.8890i	−0.944563	+	0.621135i
$501$		0			0
$502$	−30.8265	−	16.6232i	−1.37585	−	0.741928i
$503$	−20.3707			−0.908286			−0.454143	−	0.890929i	$-0.650055\pi$
$503$	−20.3707			−0.908286			−0.454143	+	0.890929i	$0.650055\pi$
$504$		0			0
$505$	−37.5255			−1.66986
$506$	−48.6280	−	26.2227i	−2.16178	−	1.16574i
$507$		0			0
$508$	−11.4940	−	17.4789i	−0.509962	−	0.775503i
$509$			26.6481i			1.18116i	0.806980	+	0.590578i	$0.201100\pi$
$509$			26.6481i			1.18116i	−0.806980	+	0.590578i	$0.798900\pi$
$510$		0			0
$511$	7.85523			0.347495
$512$	−21.8586	+	5.84809i	−0.966024	+	0.258451i
$513$		0			0
$514$	11.5197	−	21.3624i	0.508111	−	0.942256i
$515$		−	46.6526i		−	2.05576i
$516$		0			0
$517$			47.2339i			2.07734i
$518$	7.08745	+	3.82191i	0.311405	+	0.167925i
$519$		0			0
$520$	−15.6585	+	1.36794i	−0.686669	+	0.0599880i
$521$	−13.2614			−0.580992			−0.290496	−	0.956876i	$-0.593820\pi$
$521$	−13.2614			−0.580992			−0.290496	+	0.956876i	$0.593820\pi$
$522$		0			0
$523$		−	21.3786i		−	0.934821i	−0.884040	−	0.467411i	$-0.845187\pi$
$523$		−	21.3786i		−	0.934821i	0.884040	−	0.467411i	$-0.154813\pi$
$524$	−21.1621	+	13.9160i	−0.924471	+	0.607922i
$525$		0			0
$526$	2.70416	−	5.01467i	0.117907	−	0.218650i
$527$	32.0120			1.39447
$528$		0			0
$529$	53.7948			2.33890
$530$	−28.3153	+	52.5087i	−1.22994	+	2.28083i
$531$		0			0
$532$	−3.84235	+	2.52668i	−0.166587	+	0.109546i
$533$			10.4101i			0.450912i
$534$		0			0
$535$	−23.4898			−1.01555
$536$	2.62474	+	30.0448i	0.113372	+	1.29774i
$537$		0			0
$538$	30.3963	+	16.3912i	1.31048	+	0.706675i
$539$			4.45794i			0.192017i
$540$		0			0
$541$			31.4969i			1.35416i	0.735910	+	0.677080i	$0.236755\pi$
$541$			31.4969i			1.35416i	−0.735910	+	0.677080i	$0.763245\pi$
$542$	−0.815621	+	1.51251i	−0.0350339	+	0.0649679i
$543$		0			0
$544$	−12.1195	−	15.3342i	−0.519618	−	0.657450i
$545$	−12.4252			−0.532235
$546$		0			0
$547$		−	1.38840i		−	0.0593637i	−0.999559	−	0.0296819i	$-0.990551\pi$
$547$		−	1.38840i		−	0.0593637i	0.999559	−	0.0296819i	$-0.00944942\pi$
$548$	7.54957	+	11.4807i	0.322502	+	0.490430i
$549$		0			0
$550$	−46.8718	−	25.2756i	−1.99862	−	1.07776i
$551$	−3.72578			−0.158723
$552$		0			0
$553$	4.57730			0.194647
$554$	−13.8466	−	7.46680i	−0.588287	−	0.317234i
$555$		0			0
$556$	22.4528	−	14.7647i	0.952212	−	0.626164i
$557$		−	10.8246i		−	0.458654i	−0.973349	−	0.229327i	$-0.926347\pi$
$557$		−	10.8246i		−	0.458654i	0.973349	−	0.229327i	$-0.0736525\pi$
$558$		0			0
$559$	−1.33367			−0.0564083
$560$	−13.4674	−	5.81195i	−0.569100	−	0.245600i
$561$		0			0
$562$	−19.7800	+	36.6805i	−0.834367	+	1.54727i
$563$		−	7.56473i		−	0.318816i	−0.987213	−	0.159408i	$-0.949042\pi$
$563$		−	7.56473i		−	0.318816i	0.987213	−	0.159408i	$-0.0509585\pi$
$564$		0			0
$565$		−	5.15826i		−	0.217009i
$566$	−16.2208	−	8.74704i	−0.681810	−	0.367666i
$567$		0			0
$568$	−29.9160	+	2.61349i	−1.25525	+	0.109660i
$569$	−21.9063			−0.918360			−0.459180	−	0.888343i	$-0.651857\pi$
$569$	−21.9063			−0.918360			−0.459180	+	0.888343i	$0.651857\pi$
$570$		0			0
$571$			43.6061i			1.82486i	0.409235	+	0.912429i	$0.365796\pi$
$571$			43.6061i			1.82486i	−0.409235	+	0.912429i	$0.634204\pi$
$572$	−7.42384	−	11.2895i	−0.310406	−	0.472037i
$573$		0			0
$574$	−4.61091	+	8.55061i	−0.192456	+	0.356895i
$575$	74.0213			3.08690
$576$		0			0
$577$	12.6116			0.525028			0.262514	−	0.964928i	$-0.415448\pi$
$577$	12.6116			0.525028			0.262514	+	0.964928i	$0.415448\pi$
$578$	−3.39772	+	6.30082i	−0.141326	+	0.262080i
$579$		0			0
$580$	−6.52939	−	9.92928i	−0.271118	−	0.412291i
$581$			2.60500i			0.108073i
$582$		0			0
$583$	−51.2824			−2.12390
$584$	−22.1336	+	1.93361i	−0.915896	+	0.0800135i
$585$		0			0
$586$	−6.05581	−	3.26560i	−0.250163	−	0.134901i
$587$		−	10.5118i		−	0.433866i	−0.976186	−	0.216933i	$-0.930395\pi$
$587$		−	10.5118i		−	0.433866i	0.976186	−	0.216933i	$-0.0696054\pi$
$588$		0			0
$589$			21.3033i			0.877787i
$590$	7.37013	−	13.6674i	0.303423	−	0.562677i
$591$		0			0
$592$	−20.9111	−	9.02435i	−0.859439	−	0.370898i
$593$	−23.9765			−0.984598			−0.492299	−	0.870426i	$-0.663843\pi$
$593$	−23.9765			−0.984598			−0.492299	+	0.870426i	$0.663843\pi$
$594$		0			0
$595$		−	12.6700i		−	0.519420i
$596$	10.6162	−	6.98110i	0.434857	−	0.285957i
$597$		0			0
$598$	16.5310	+	8.91433i	0.676002	+	0.364534i
$599$	−32.2302			−1.31689			−0.658446	−	0.752628i	$-0.728786\pi$
$599$	−32.2302			−1.31689			−0.658446	+	0.752628i	$0.728786\pi$
$600$		0			0
$601$	43.3405			1.76790			0.883949	−	0.467584i	$-0.154875\pi$
$601$	43.3405			1.76790			0.883949	+	0.467584i	$0.154875\pi$
$602$	−1.09545	−	0.590719i	−0.0446470	−	0.0240759i
$603$		0			0
$604$	−21.5290	−	32.7392i	−0.876001	−	1.33214i
$605$		−	32.5378i		−	1.32285i
$606$		0			0
$607$	−13.2372			−0.537283			−0.268642	−	0.963240i	$-0.586575\pi$
$607$	−13.2372			−0.537283			−0.268642	+	0.963240i	$0.586575\pi$
$608$	10.2046	−	8.06525i	0.413851	−	0.327089i
$609$		0			0
$610$	−20.9517	+	38.8534i	−0.848308	+	1.57313i
$611$		−	16.0570i		−	0.649598i
$612$		0			0
$613$			6.23612i			0.251874i	0.992038	+	0.125937i	$0.0401938\pi$
$613$			6.23612i			0.251874i	−0.992038	+	0.125937i	$0.959806\pi$
$614$	−11.2976	−	6.09224i	−0.455935	−	0.245863i
$615$		0			0
$616$	−1.09735	−	12.5611i	−0.0442134	−	0.506101i
$617$	7.66713			0.308667			0.154334	−	0.988019i	$-0.450677\pi$
$617$	7.66713			0.308667			0.154334	+	0.988019i	$0.450677\pi$
$618$		0			0
$619$		−	27.9974i		−	1.12531i	−0.826692	−	0.562655i	$-0.809780\pi$
$619$		−	27.9974i		−	1.12531i	0.826692	−	0.562655i	$-0.190220\pi$
$620$	−56.7738	+	37.3338i	−2.28009	+	1.49936i
$621$		0			0
$622$	0.812332	−	1.50641i	0.0325715	−	0.0604016i
$623$	−2.14381			−0.0858900
$624$		0			0
$625$	4.11412			0.164565
$626$	−2.11908	+	3.92969i	−0.0846956	+	0.157062i
$627$		0			0
$628$	37.9295	−	24.9421i	1.51355	−	0.995297i
$629$		−	19.6730i		−	0.784415i
$630$		0			0
$631$	18.2806			0.727739			0.363869	−	0.931450i	$-0.381455\pi$
$631$	18.2806			0.727739			0.363869	+	0.931450i	$0.381455\pi$
$632$	−12.8974	+	1.12673i	−0.513032	+	0.0448189i
$633$		0			0
$634$	−8.81539	−	4.75370i	−0.350104	−	0.188793i
$635$			38.3557i			1.52210i
$636$		0			0
$637$		−	1.51546i		−	0.0600449i
$638$	4.84870	−	8.99157i	0.191962	−	0.355980i
$639$		0			0
$640$	39.3775	+	13.0612i	1.55653	+	0.516291i
$641$	5.99361			0.236733			0.118367	−	0.992970i	$-0.462234\pi$
$641$	5.99361			0.236733			0.118367	+	0.992970i	$0.462234\pi$
$642$		0			0
$643$		−	29.0547i		−	1.14581i	−0.819623	−	0.572903i	$-0.805817\pi$
$643$		−	29.0547i		−	1.14581i	0.819623	−	0.572903i	$-0.194183\pi$
$644$	9.62974	+	14.6440i	0.379465	+	0.577055i
$645$		0			0
$646$	9.88912	+	5.33271i	0.389082	+	0.209812i
$647$	26.7288			1.05082			0.525408	−	0.850850i	$-0.323913\pi$
$647$	26.7288			1.05082			0.525408	+	0.850850i	$0.323913\pi$
$648$		0			0
$649$	13.3482			0.523963
$650$	15.9340	+	8.59238i	0.624981	+	0.337021i
$651$		0			0
$652$	6.01763	−	3.95713i	0.235669	−	0.154973i
$653$		−	41.0011i		−	1.60450i	−0.596991	−	0.802248i	$-0.703637\pi$
$653$		−	41.0011i		−	1.60450i	0.596991	−	0.802248i	$-0.296363\pi$
$654$		0			0
$655$	46.4380			1.81448
$656$	10.8874	−	25.2280i	0.425080	−	0.984988i
$657$		0			0
$658$	7.11208	−	13.1888i	0.277258	−	0.514155i
$659$			1.91818i			0.0747219i	0.999302	+	0.0373609i	$0.0118951\pi$
$659$			1.91818i			0.0747219i	−0.999302	+	0.0373609i	$0.988105\pi$
$660$		0			0
$661$		−	10.9347i		−	0.425312i	−0.977127	−	0.212656i	$-0.931789\pi$
$661$		−	10.9347i		−	0.425312i	0.977127	−	0.212656i	$-0.0682114\pi$
$662$	9.14609	+	4.93203i	0.355473	+	0.191689i
$663$		0			0
$664$	−0.641236	−	7.34009i	−0.0248848	−	0.284851i
$665$	8.43162			0.326964
$666$		0			0
$667$			14.1997i			0.549816i
$668$	6.00373	+	9.12990i	0.232291	+	0.353247i
$669$		0			0
$670$	26.2459	−	48.6712i	1.01397	−	1.88033i
$671$	−37.9460			−1.46489
$672$		0			0
$673$	10.0071			0.385745			0.192872	−	0.981224i	$-0.438220\pi$
$673$	10.0071			0.385745			0.192872	+	0.981224i	$0.438220\pi$
$674$	−18.1149	+	33.5928i	−0.697761	+	1.29395i
$675$		0			0
$676$	−11.7617	−	17.8861i	−0.452372	−	0.687925i
$677$			35.4441i			1.36223i	0.732178	+	0.681113i	$0.238504\pi$
$677$			35.4441i			1.36223i	−0.732178	+	0.681113i	$0.761496\pi$
$678$		0			0
$679$	−13.8317			−0.530812
$680$	3.11881	+	35.7003i	0.119601	+	1.36904i
$681$		0			0
$682$	−51.4121	−	27.7240i	−1.96867	−	1.06161i
$683$			34.8397i			1.33310i	0.745459	+	0.666551i	$0.232230\pi$
$683$			34.8397i			1.33310i	−0.745459	+	0.666551i	$0.767770\pi$
$684$		0			0
$685$		−	25.1931i		−	0.962580i
$686$	0.671239	−	1.24476i	0.0256280	−	0.0475253i
$687$		0			0
$688$	3.23204	+	1.39481i	0.123220	+	0.0531768i
$689$	17.4333			0.664157
$690$		0			0
$691$		−	16.2381i		−	0.617727i	−0.951106	−	0.308864i	$-0.900051\pi$
$691$		−	16.2381i		−	0.617727i	0.951106	−	0.308864i	$-0.0999486\pi$
$692$	2.87331	−	1.88946i	0.109227	−	0.0718263i
$693$		0			0
$694$	11.2872	+	6.08663i	0.428457	+	0.231045i
$695$	−49.2704			−1.86893
$696$		0			0
$697$	23.7344			0.899004
$698$	−17.0264	−	9.18151i	−0.644461	−	0.347525i
$699$		0			0
$700$	9.28196	+	14.1151i	0.350825	+	0.533502i
$701$			28.8081i			1.08807i	0.839064	+	0.544033i	$0.183103\pi$
$701$			28.8081i			1.08807i	−0.839064	+	0.544033i	$0.816897\pi$
$702$		0			0
$703$	13.0920			0.493773
$704$	6.18399	+	35.1232i	0.233068	+	1.32376i
$705$		0			0
$706$	−0.637051	+	1.18137i	−0.0239757	+	0.0444613i
$707$			10.2333i			0.384864i
$708$		0			0
$709$			18.1039i			0.679906i	0.940442	+	0.339953i	$0.110411\pi$
$709$			18.1039i			0.679906i	−0.940442	+	0.339953i	$0.889589\pi$
$710$	48.4626	+	26.1334i	1.81877	+	0.980770i
$711$		0			0
$712$	6.04061	−	0.527713i	0.226381	−	0.0197769i
$713$	81.1915			3.04064
$714$		0			0
$715$			24.7736i			0.926479i
$716$	18.3743	−	12.0828i	0.686681	−	0.451554i
$717$		0			0
$718$	−10.1027	+	18.7347i	−0.377029	+	0.699173i
$719$	−12.7731			−0.476357			−0.238179	−	0.971221i	$-0.576550\pi$
$719$	−12.7731			−0.476357			−0.238179	+	0.971221i	$0.576550\pi$
$720$		0			0
$721$	−12.7223			−0.473804
$722$	9.20474	−	17.0695i	0.342565	−	0.635262i
$723$		0			0
$724$	−44.4884	+	29.2551i	−1.65340	+	1.08726i
$725$			13.6869i			0.508319i
$726$		0			0
$727$	−10.1654			−0.377012			−0.188506	−	0.982072i	$-0.560365\pi$
$727$	−10.1654			−0.377012			−0.188506	+	0.982072i	$0.560365\pi$
$728$	0.373041	+	4.27012i	0.0138258	+	0.158261i
$729$		0			0
$730$	35.8554	+	19.3350i	1.32707	+	0.715621i
$731$			3.04069i			0.112464i
$732$		0			0
$733$			26.1041i			0.964178i	0.876122	+	0.482089i	$0.160122\pi$
$733$			26.1041i			0.964178i	−0.876122	+	0.482089i	$0.839878\pi$
$734$	−2.48811	+	4.61402i	−0.0918377	+	0.170307i
$735$		0			0
$736$	−30.7384	−	38.8919i	−1.13303	−	1.43358i
$737$	47.5345			1.75096
$738$		0			0
$739$		−	9.90517i		−	0.364368i	−0.983264	−	0.182184i	$-0.941683\pi$
$739$		−	9.90517i		−	0.364368i	0.983264	−	0.182184i	$-0.0583166\pi$
$740$	22.9436	+	34.8904i	0.843422	+	1.28260i
$741$		0			0
$742$	14.3193	+	7.72168i	0.525678	+	0.283472i
$743$	33.5353			1.23029			0.615146	−	0.788413i	$-0.289097\pi$
$743$	33.5353			1.23029			0.615146	+	0.788413i	$0.289097\pi$
$744$		0			0
$745$	−23.2961			−0.853504
$746$	39.0468	+	21.0560i	1.42960	+	0.770913i
$747$		0			0
$748$	−25.7393	+	16.9259i	−0.941121	+	0.618871i
$749$			6.40575i			0.234061i
$750$		0			0
$751$	53.8436			1.96478			0.982391	−	0.186839i	$-0.0598243\pi$
$751$	53.8436			1.96478			0.982391	+	0.186839i	$0.0598243\pi$
$752$	−16.7932	+	38.9128i	−0.612384	+	1.41901i
$753$		0			0
$754$	−1.64830	+	3.05666i	−0.0600277	+	0.111317i
$755$			71.8428i			2.61463i
$756$		0			0
$757$		−	1.18921i		−	0.0432225i	−0.999766	−	0.0216113i	$-0.993120\pi$
$757$		−	1.18921i		−	0.0432225i	0.999766	−	0.0216113i	$-0.00687962\pi$
$758$	−21.9776	−	11.8514i	−0.798262	−	0.430463i
$759$		0			0
$760$	−23.7577	+	2.07550i	−0.861784	+	0.0752862i
$761$	−38.0810			−1.38043			−0.690217	−	0.723602i	$-0.742485\pi$
$761$	−38.0810			−1.38043			−0.690217	+	0.723602i	$0.742485\pi$
$762$		0			0
$763$			3.38839i			0.122668i
$764$	−24.3490	−	37.0277i	−0.880917	−	1.33962i
$765$		0			0
$766$	−11.9463	+	22.1535i	−0.431637	+	0.800439i
$767$	−4.53769			−0.163846
$768$		0			0
$769$	−38.6053			−1.39214			−0.696071	−	0.717973i	$-0.745070\pi$
$769$	−38.6053			−1.39214			−0.696071	+	0.717973i	$0.745070\pi$
$770$	−10.9729	+	20.3484i	−0.395434	+	0.733305i
$771$		0			0
$772$	−12.7029	−	19.3173i	−0.457187	−	0.695246i
$773$			18.5902i			0.668642i	0.942459	+	0.334321i	$0.108507\pi$
$773$			18.5902i			0.668642i	−0.942459	+	0.334321i	$0.891493\pi$
$774$		0			0
$775$	78.2592			2.81115
$776$	38.9736	−	3.40476i	1.39907	−	0.122224i
$777$		0			0
$778$	31.3539	+	16.9076i	1.12409	+	0.606166i
$779$			15.7947i			0.565905i
$780$		0			0
$781$			47.3308i			1.69363i
$782$	20.3241	−	37.6896i	0.726788	−	1.34778i
$783$		0			0
$784$	−1.58494	+	3.67260i	−0.0566050	+	0.131164i
$785$	−83.2324			−2.97069
$786$		0			0
$787$			17.3947i			0.620056i	0.950727	+	0.310028i	$0.100338\pi$
$787$			17.3947i			0.620056i	−0.950727	+	0.310028i	$0.899662\pi$
$788$	−22.0147	+	14.4766i	−0.784241	+	0.515709i
$789$		0			0
$790$	20.8932	+	11.2667i	0.743347	+	0.400850i
$791$	−1.40668			−0.0500156
$792$		0			0
$793$	12.8997			0.458080
$794$	42.7838	+	23.0711i	1.51834	+	0.818764i
$795$		0			0
$796$	13.2977	+	20.2219i	0.471324	+	0.716745i
$797$			15.3683i			0.544374i	0.962244	+	0.272187i	$0.0877470\pi$
$797$			15.3683i			0.544374i	−0.962244	+	0.272187i	$0.912253\pi$
$798$		0			0
$799$	−36.6090			−1.29513
$800$	−29.6283	−	37.4873i	−1.04752	−	1.32538i
$801$		0			0
$802$	6.48122	−	12.0190i	0.228860	−	0.424404i
$803$			35.0181i			1.23576i
$804$		0			0
$805$		−	32.1347i		−	1.13260i
$806$	17.4774	+	9.42470i	0.615616	+	0.331971i
$807$		0			0
$808$	−2.51900	−	28.8344i	−0.0886182	−	1.01439i
$809$	29.7888			1.04732			0.523659	−	0.851928i	$-0.324567\pi$
$809$	29.7888			1.04732			0.523659	+	0.851928i	$0.324567\pi$
$810$		0			0
$811$		−	6.50515i		−	0.228427i	−0.993456	−	0.114213i	$-0.963565\pi$
$811$		−	6.50515i		−	0.228427i	0.993456	−	0.114213i	$-0.0364347\pi$
$812$	−2.70775	+	1.78059i	−0.0950235	+	0.0624864i
$813$		0			0
$814$	−17.0378	+	31.5954i	−0.597175	+	1.10742i
$815$	−13.2051			−0.462553
$816$		0			0
$817$	−2.02351			−0.0707937
$818$	19.0740	−	35.3713i	0.666906	−	1.23673i
$819$		0			0
$820$	−42.0933	+	27.6801i	−1.46996	+	0.966631i
$821$			3.89581i			0.135965i	0.997687	+	0.0679823i	$0.0216562\pi$
$821$			3.89581i			0.135965i	−0.997687	+	0.0679823i	$0.978344\pi$
$822$		0			0
$823$	47.1577			1.64381			0.821907	−	0.569621i	$-0.192910\pi$
$823$	47.1577			1.64381			0.821907	+	0.569621i	$0.192910\pi$
$824$	35.8476	−	3.13168i	1.24881	−	0.109097i
$825$		0			0
$826$	−3.72714	−	2.00986i	−0.129684	−	0.0699320i
$827$			30.9915i			1.07768i	0.842408	+	0.538841i	$0.181138\pi$
$827$			30.9915i			1.07768i	−0.842408	+	0.538841i	$0.818862\pi$
$828$		0			0
$829$			34.2090i			1.18813i	0.804417	+	0.594065i	$0.202478\pi$
$829$			34.2090i			1.18813i	−0.804417	+	0.594065i	$0.797522\pi$
$830$	−6.41200	+	11.8906i	−0.222564	+	0.412728i
$831$		0			0
$832$	−2.10223	−	11.9401i	−0.0728818	−	0.413947i
$833$	−3.45516			−0.119714
$834$		0			0
$835$		−	20.0346i		−	0.693326i
$836$	−11.2638	−	17.1289i	−0.389567	−	0.592416i
$837$		0			0
$838$	−14.3622	−	7.74483i	−0.496135	−	0.267541i
$839$	−40.9980			−1.41541			−0.707704	−	0.706509i	$-0.750269\pi$
$839$	−40.9980			−1.41541			−0.707704	+	0.706509i	$0.750269\pi$
$840$		0			0
$841$	26.3744			0.909462
$842$	8.52432	+	4.59674i	0.293768	+	0.158414i
$843$		0			0
$844$	36.3459	−	23.9007i	1.25108	−	0.822694i
$845$			39.2491i			1.35021i
$846$		0			0
$847$	−8.87319			−0.304886
$848$	−42.2482	−	18.2326i	−1.45081	−	0.626109i
$849$		0			0
$850$	19.5901	−	36.3284i	0.671934	−	1.24605i
$851$		−	49.8963i		−	1.71042i
$852$		0			0
$853$		−	26.3408i		−	0.901891i	−0.892551	−	0.450946i	$-0.851087\pi$
$853$		−	26.3408i		−	0.901891i	0.892551	−	0.450946i	$-0.148913\pi$
$854$	10.5955	+	5.71360i	0.362569	+	0.195515i
$855$		0			0
$856$	−1.57682	−	18.0495i	−0.0538945	−	0.616918i
$857$	−56.4187			−1.92723			−0.963613	−	0.267300i	$-0.913868\pi$
$857$	−56.4187			−1.92723			−0.963613	+	0.267300i	$0.913868\pi$
$858$		0			0
$859$			34.5693i			1.17949i	0.807589	+	0.589745i	$0.200772\pi$
$859$			34.5693i			1.17949i	−0.807589	+	0.589745i	$0.799228\pi$
$860$	−3.54619	−	5.39271i	−0.120924	−	0.183890i
$861$		0			0
$862$	7.01443	−	13.0078i	0.238912	−	0.443046i
$863$	1.52709			0.0519826			0.0259913	−	0.999662i	$-0.491726\pi$
$863$	1.52709			0.0519826			0.0259913	+	0.999662i	$0.491726\pi$
$864$		0			0
$865$	−6.30517			−0.214382
$866$	12.2044	−	22.6321i	0.414721	−	0.769070i
$867$		0			0
$868$	10.1811	+	15.4824i	0.345568	+	0.525508i
$869$			20.4053i			0.692202i
$870$		0			0
$871$	−16.1593			−0.547535
$872$	−0.834073	−	9.54744i	−0.0282453	−	0.323317i
$873$		0			0
$874$	25.0816	+	13.5252i	0.848397	+	0.457498i
$875$		−	12.6393i		−	0.427285i
$876$		0			0
$877$			20.5638i			0.694389i	0.937793	+	0.347195i	$0.112866\pi$
$877$			20.5638i			0.694389i	−0.937793	+	0.347195i	$0.887134\pi$
$878$	5.31511	−	9.85650i	0.179376	−	0.332641i
$879$		0			0
$880$	25.9093	−	60.0366i	0.873402	−	2.02383i
$881$	−16.8073			−0.566252			−0.283126	−	0.959083i	$-0.591371\pi$
$881$	−16.8073			−0.566252			−0.283126	+	0.959083i	$0.591371\pi$
$882$		0			0
$883$		−	13.7849i		−	0.463900i	−0.972728	−	0.231950i	$-0.925489\pi$
$883$		−	13.7849i		−	0.463900i	0.972728	−	0.231950i	$-0.0745105\pi$
$884$	8.75001	−	5.75391i	0.294295	−	0.193525i
$885$		0			0
$886$	−22.7688	−	12.2781i	−0.764932	−	0.412490i
$887$	−25.0037			−0.839541			−0.419771	−	0.907630i	$-0.637889\pi$
$887$	−25.0037			−0.839541			−0.419771	+	0.907630i	$0.637889\pi$
$888$		0			0
$889$	10.4597			0.350808
$890$	−9.78550	−	5.27683i	−0.328011	−	0.176880i
$891$		0			0
$892$	3.30475	+	5.02556i	0.110651	+	0.168268i
$893$		−	24.3625i		−	0.815260i
$894$		0			0
$895$	−40.3205			−1.34777
$896$	3.56185	−	10.7384i	0.118993	−	0.358745i
$897$		0			0
$898$	−10.2144	+	18.9418i	−0.340858	+	0.632097i
$899$			15.0127i			0.500702i
$900$		0			0
$901$		−	39.7469i		−	1.32416i
$902$	−38.1181	−	20.5551i	−1.26919	−	0.684412i
$903$		0			0
$904$	3.96358	−	0.346262i	0.131827	−	0.0115165i
$905$	97.6251			3.24517
$906$		0			0
$907$			23.5827i			0.783052i	0.920167	+	0.391526i	$0.128053\pi$
$907$			23.5827i			0.783052i	−0.920167	+	0.391526i	$0.871947\pi$
$908$	18.6337	−	12.2533i	0.618380	−	0.406640i
$909$		0			0
$910$	3.73020	−	6.91738i	0.123655	−	0.229309i
$911$	−29.1770			−0.966677			−0.483338	−	0.875434i	$-0.660576\pi$
$911$	−29.1770			−0.966677			−0.483338	+	0.875434i	$0.660576\pi$
$912$		0			0
$913$	−11.6129			−0.384331
$914$	25.9540	−	48.1298i	0.858481	−	1.59199i
$915$		0			0
$916$	−4.11612	+	2.70671i	−0.136000	+	0.0894324i
$917$		−	12.6638i		−	0.418196i
$918$		0			0
$919$	51.6854			1.70494			0.852472	−	0.522772i	$-0.175102\pi$
$919$	51.6854			1.70494			0.852472	+	0.522772i	$0.175102\pi$
$920$	7.91017	+	90.5459i	0.260791	+	2.98521i
$921$		0			0
$922$	−6.45893	−	3.48298i	−0.212713	−	0.114706i
$923$		−	16.0900i		−	0.529609i
$924$		0			0
$925$		−	48.0943i		−	1.58133i
$926$	−2.56133	+	4.74981i	−0.0841707	+	0.156088i
$927$		0			0
$928$	7.19132	−	5.68369i	0.236067	−	0.186576i
$929$	−20.0819			−0.658865			−0.329432	−	0.944179i	$-0.606857\pi$
$929$	−20.0819			−0.658865			−0.329432	+	0.944179i	$0.606857\pi$
$930$		0			0
$931$		−	2.29933i		−	0.0753576i
$932$	28.6964	+	43.6387i	0.939980	+	1.42943i
$933$		0			0
$934$	−9.07739	−	4.89498i	−0.297021	−	0.160169i
$935$	56.4821			1.84716
$936$		0			0
$937$	−19.1583			−0.625875			−0.312937	−	0.949774i	$-0.601313\pi$
$937$	−19.1583			−0.625875			−0.312937	+	0.949774i	$0.601313\pi$
$938$	−13.2728	−	7.15736i	−0.433372	−	0.233696i
$939$		0			0
$940$	64.9266	−	42.6951i	2.11767	−	1.39256i
$941$			54.2409i			1.76820i	0.467296	+	0.884101i	$0.345228\pi$
$941$			54.2409i			1.76820i	−0.467296	+	0.884101i	$0.654772\pi$
$942$		0			0
$943$	60.1971			1.96029
$944$	10.9967	+	4.74572i	0.357912	+	0.154460i
$945$		0			0
$946$	2.63339	−	4.88342i	0.0856187	−	0.158774i
$947$			47.7355i			1.55120i	0.631228	+	0.775598i	$0.282551\pi$
$947$			47.7355i			1.55120i	−0.631228	+	0.775598i	$0.717449\pi$
$948$		0			0
$949$		−	11.9043i		−	0.386430i
$950$	24.1758	+	13.0368i	0.784365	+	0.422969i
$951$		0			0
$952$	9.73559	−	0.850510i	0.315532	−	0.0275652i
$953$	11.2075			0.363046			0.181523	−	0.983387i	$-0.441897\pi$
$953$	11.2075			0.363046			0.181523	+	0.983387i	$0.441897\pi$
$954$		0			0
$955$			81.2534i			2.62930i
$956$	−26.8671	−	40.8570i	−0.868945	−	1.32141i
$957$		0			0
$958$	10.9207	−	20.2517i	0.352832	−	0.654301i
$959$	−6.87026			−0.221852
$960$		0			0
$961$	54.8399			1.76903
$962$	5.79196	−	10.7408i	0.186740	−	0.346297i
$963$		0			0
$964$	9.90470	+	15.0621i	0.319009	+	0.485119i
$965$			42.3899i			1.36458i
$966$		0			0
$967$	−22.5979			−0.726701			−0.363350	−	0.931653i	$-0.618367\pi$
$967$	−22.5979			−0.726701			−0.363350	+	0.931653i	$0.618367\pi$
$968$	25.0019	−	2.18419i	0.803593	−	0.0702025i
$969$		0			0
$970$	−63.1353	−	34.0457i	−2.02715	−	1.09314i
$971$			46.5586i			1.49414i	0.664747	+	0.747068i	$0.268539\pi$
$971$			46.5586i			1.49414i	−0.664747	+	0.747068i	$0.731461\pi$
$972$		0			0
$973$			13.4362i			0.430745i
$974$	4.81055	−	8.92081i	0.154140	−	0.285841i
$975$		0			0
$976$	−31.2612	−	13.4910i	−1.00065	−	0.431838i
$977$	−43.5968			−1.39479			−0.697393	−	0.716689i	$-0.745657\pi$
$977$	−43.5968			−1.39479			−0.697393	+	0.716689i	$0.745657\pi$
$978$		0			0
$979$		−	9.55697i		−	0.305442i
$980$	6.12778	−	4.02956i	0.195745	−	0.128720i
$981$		0			0
$982$	−22.1876	−	11.9646i	−0.708034	−	0.381807i
$983$	22.5407			0.718937			0.359469	−	0.933157i	$-0.382958\pi$
$983$	22.5407			0.718937			0.359469	+	0.933157i	$0.382958\pi$
$984$		0			0
$985$	48.3090			1.53925
$986$	6.96899	+	3.75803i	0.221938	+	0.119680i
$987$		0			0
$988$	3.82910	+	5.82294i	0.121820	+	0.185252i
$989$			7.71204i			0.245229i
$990$		0			0
$991$	24.2444			0.770148			0.385074	−	0.922886i	$-0.374176\pi$
$991$	24.2444			0.770148			0.385074	+	0.922886i	$0.374176\pi$
$992$	−32.4983	−	41.1186i	−1.03182	−	1.30552i
$993$		0			0
$994$	7.12668	−	13.2159i	0.226045	−	0.419183i
$995$		−	44.3747i		−	1.40677i
$996$		0			0
$997$		−	49.3412i		−	1.56265i	−0.624124	−	0.781325i	$-0.714544\pi$
$997$		−	49.3412i		−	1.56265i	0.624124	−	0.781325i	$-0.285456\pi$
$998$	−46.8182	−	25.2467i	−1.48201	−	0.799171i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.f.757.15	yes	24
3.2	odd	2	inner	1512.2.c.f.757.10	yes	24
4.3	odd	2		6048.2.c.g.3025.23		24
8.3	odd	2		6048.2.c.g.3025.2		24
8.5	even	2	inner	1512.2.c.f.757.16	yes	24
12.11	even	2		6048.2.c.g.3025.1		24
24.5	odd	2	inner	1512.2.c.f.757.9	✓	24
24.11	even	2		6048.2.c.g.3025.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.f.757.9	✓	24	24.5	odd	2	inner
1512.2.c.f.757.10	yes	24	3.2	odd	2	inner
1512.2.c.f.757.15	yes	24	1.1	even	1	trivial
1512.2.c.f.757.16	yes	24	8.5	even	2	inner
6048.2.c.g.3025.1		24	12.11	even	2
6048.2.c.g.3025.2		24	8.3	odd	2
6048.2.c.g.3025.23		24	4.3	odd	2
6048.2.c.g.3025.24		24	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.671239 - 1.24476i) q^{2} +(-1.09888 - 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(-2.81770 + 0.246156i) q^{8} +O(q^{10})\)	\(q+(0.671239 - 1.24476i) q^{2} +(-1.09888 - 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(-2.81770 + 0.246156i) q^{8} +(4.56453 + 2.46142i) q^{10} +4.45794i q^{11} -1.51546i q^{13} +(0.671239 - 1.24476i) q^{14} +(-1.58494 + 3.67260i) q^{16} -3.45516 q^{17} -2.29933i q^{19} +(6.12778 - 4.02956i) q^{20} +(5.54908 + 2.99234i) q^{22} -8.76326 q^{23} -8.44677 q^{25} +(-1.88640 - 1.01724i) q^{26} +(-1.09888 - 1.67107i) q^{28} -1.62037i q^{29} -9.26498 q^{31} +(3.50764 + 4.43807i) q^{32} +(-2.31924 + 4.30086i) q^{34} +3.66698i q^{35} +5.69381i q^{37} +(-2.86213 - 1.54340i) q^{38} +(-0.902651 - 10.3324i) q^{40} -6.86926 q^{41} -0.880042i q^{43} +(7.44952 - 4.89872i) q^{44} +(-5.88224 + 10.9082i) q^{46} +10.5955 q^{47} +1.00000 q^{49} +(-5.66980 + 10.5142i) q^{50} +(-2.53244 + 1.66531i) q^{52} +11.5036i q^{53} -16.3472 q^{55} +(-2.81770 + 0.246156i) q^{56} +(-2.01698 - 1.08766i) q^{58} -2.99426i q^{59} +8.51202i q^{61} +(-6.21902 + 11.5327i) q^{62} +(7.87881 - 1.38719i) q^{64} +5.55718 q^{65} -10.6629i q^{67} +(3.79680 + 5.77381i) q^{68} +(4.56453 + 2.46142i) q^{70} +10.6172 q^{71} +7.85523 q^{73} +(7.08745 + 3.82191i) q^{74} +(-3.84235 + 2.52668i) q^{76} +4.45794i q^{77} +4.57730 q^{79} +(-13.4674 - 5.81195i) q^{80} +(-4.61091 + 8.55061i) q^{82} +2.60500i q^{83} -12.6700i q^{85} +(-1.09545 - 0.590719i) q^{86} +(-1.09735 - 12.5611i) q^{88} -2.14381 q^{89} -1.51546i q^{91} +(9.62974 + 14.6440i) q^{92} +(7.11208 - 13.1888i) q^{94} +8.43162 q^{95} -13.8317 q^{97} +(0.671239 - 1.24476i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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