LMFDB - Embedded newform 640.2.x.a.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (of order $8$, degree $4$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.5
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36989 - 0.567426i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.427148 - 0.427148i) q^{7} +(-0.566703 - 0.566703i) q^{9} +O(q^{10})$	\(q+(-1.36989 - 0.567426i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.427148 - 0.427148i) q^{7} +(-0.566703 - 0.566703i) q^{9} +(-3.45736 + 1.43209i) q^{11} +(-0.333465 + 0.805056i) q^{13} -1.48275i q^{15} +0.0153095i q^{17} +(-0.855154 + 2.06452i) q^{19} +(-0.827520 + 0.342770i) q^{21} +(-1.86931 - 1.86931i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(2.15703 + 5.20754i) q^{27} +(-7.97042 - 3.30145i) q^{29} -3.77517 q^{31} +5.54879 q^{33} +(0.558096 + 0.231171i) q^{35} +(2.37256 + 5.72787i) q^{37} +(0.913619 - 0.913619i) q^{39} +(-4.52394 - 4.52394i) q^{41} +(-10.6328 + 4.40426i) q^{43} +(0.306698 - 0.740434i) q^{45} +2.09456i q^{47} +6.63509i q^{49} +(0.00868701 - 0.0209723i) q^{51} +(-7.81478 + 3.23699i) q^{53} +(-2.64615 - 2.64615i) q^{55} +(2.34293 - 2.34293i) q^{57} +(2.58580 + 6.24268i) q^{59} +(-12.3059 - 5.09729i) q^{61} -0.484133 q^{63} -0.871387 q^{65} +(9.93846 + 4.11664i) q^{67} +(1.50004 + 3.62143i) q^{69} +(2.84472 - 2.84472i) q^{71} +(7.30183 + 7.30183i) q^{73} +(1.36989 - 0.567426i) q^{75} +(-0.865093 + 2.08852i) q^{77} -10.8716i q^{79} -5.95338i q^{81} +(6.12342 - 14.7832i) q^{83} +(-0.0141441 + 0.00585870i) q^{85} +(9.04524 + 9.04524i) q^{87} +(-8.49306 + 8.49306i) q^{89} +(0.201439 + 0.486318i) q^{91} +(5.17156 + 2.14213i) q^{93} -2.23462 q^{95} +13.4111 q^{97} +(2.77087 + 1.14773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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			0
$2$		0			0
$3$	−1.36989	−	0.567426i	−0.790904	−	0.327603i	−0.0495972	−	0.998769i	$-0.515794\pi$
$3$	−1.36989	−	0.567426i	−0.790904	−	0.327603i	−0.741307	+	0.671166i	$0.765794\pi$
$4$		0			0
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$		0			0
$7$	0.427148	−	0.427148i	0.161447	−	0.161447i	−0.621760	−	0.783207i	$-0.713582\pi$
$7$	0.427148	−	0.427148i	0.161447	−	0.161447i	0.783207	+	0.621760i	$0.213582\pi$
$8$		0			0
$9$	−0.566703	−	0.566703i	−0.188901	−	0.188901i
$10$		0			0
$11$	−3.45736	+	1.43209i	−1.04243	+	0.431790i	−0.837185	−	0.546920i	$-0.815800\pi$
$11$	−3.45736	+	1.43209i	−1.04243	+	0.431790i	−0.205249	+	0.978710i	$0.565800\pi$
$12$		0			0
$13$	−0.333465	+	0.805056i	−0.0924866	+	0.223282i	−0.963353	−	0.268238i	$-0.913559\pi$
$13$	−0.333465	+	0.805056i	−0.0924866	+	0.223282i	0.870866	+	0.491520i	$0.163559\pi$
$14$		0			0
$15$		−	1.48275i		−	0.382846i
$16$		0			0
$17$			0.0153095i			0.00371310i	0.999998	+	0.00185655i	$0.000590959\pi$
$17$			0.0153095i			0.00371310i	−0.999998	+	0.00185655i	$0.999409\pi$
$18$		0			0
$19$	−0.855154	+	2.06452i	−0.196186	+	0.473634i	−0.991105	−	0.133081i	$-0.957513\pi$
$19$	−0.855154	+	2.06452i	−0.196186	+	0.473634i	0.794920	+	0.606715i	$0.207513\pi$
$20$		0			0
$21$	−0.827520	+	0.342770i	−0.180580	+	0.0747985i
$22$		0			0
$23$	−1.86931	−	1.86931i	−0.389777	−	0.389777i	0.484831	−	0.874608i	$-0.338881\pi$
$23$	−1.86931	−	1.86931i	−0.389777	−	0.389777i	−0.874608	+	0.484831i	$0.838881\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	2.15703	+	5.20754i	0.415121	+	1.00219i
$28$		0			0
$29$	−7.97042	−	3.30145i	−1.48007	−	0.613065i	−0.510940	−	0.859617i	$-0.670702\pi$
$29$	−7.97042	−	3.30145i	−1.48007	−	0.613065i	−0.969130	+	0.246552i	$0.920702\pi$
$30$		0			0
$31$	−3.77517			−0.678041			−0.339021	−	0.940779i	$-0.610096\pi$
$31$	−3.77517			−0.678041			−0.339021	+	0.940779i	$0.610096\pi$
$32$		0			0
$33$	5.54879			0.965921
$34$		0			0
$35$	0.558096	+	0.231171i	0.0943355	+	0.0390750i
$36$		0			0
$37$	2.37256	+	5.72787i	0.390047	+	0.941656i	0.989929	+	0.141568i	$0.0452142\pi$
$37$	2.37256	+	5.72787i	0.390047	+	0.941656i	−0.599882	+	0.800089i	$0.704786\pi$
$38$		0			0
$39$	0.913619	−	0.913619i	0.146296	−	0.146296i
$40$		0			0
$41$	−4.52394	−	4.52394i	−0.706521	−	0.706521i	0.259281	−	0.965802i	$-0.416514\pi$
$41$	−4.52394	−	4.52394i	−0.706521	−	0.706521i	−0.965802	+	0.259281i	$0.916514\pi$
$42$		0			0
$43$	−10.6328	+	4.40426i	−1.62149	+	0.671643i	−0.994240	−	0.107174i	$-0.965820\pi$
$43$	−10.6328	+	4.40426i	−1.62149	+	0.671643i	−0.627250	+	0.778818i	$0.715820\pi$
$44$		0			0
$45$	0.306698	−	0.740434i	0.0457198	−	0.110377i
$46$		0			0
$47$			2.09456i			0.305524i	0.988263	+	0.152762i	$0.0488167\pi$
$47$			2.09456i			0.305524i	−0.988263	+	0.152762i	$0.951183\pi$
$48$		0			0
$49$			6.63509i			0.947870i
$50$		0			0
$51$	0.00868701	−	0.0209723i	0.00121642	−	0.00293671i
$52$		0			0
$53$	−7.81478	+	3.23699i	−1.07344	+	0.444634i	−0.848204	−	0.529669i	$-0.822316\pi$
$53$	−7.81478	+	3.23699i	−1.07344	+	0.444634i	−0.225238	+	0.974304i	$0.572316\pi$
$54$		0			0
$55$	−2.64615	−	2.64615i	−0.356807	−	0.356807i
$56$		0			0
$57$	2.34293	−	2.34293i	0.310328	−	0.310328i
$58$		0			0
$59$	2.58580	+	6.24268i	0.336643	+	0.812727i	0.998033	+	0.0626856i	$0.0199665\pi$
$59$	2.58580	+	6.24268i	0.336643	+	0.812727i	−0.661391	+	0.750042i	$0.730033\pi$
$60$		0			0
$61$	−12.3059	−	5.09729i	−1.57562	−	0.652641i	−0.587904	−	0.808931i	$-0.700047\pi$
$61$	−12.3059	−	5.09729i	−1.57562	−	0.652641i	−0.987711	+	0.156290i	$0.950047\pi$
$62$		0			0
$63$	−0.484133			−0.0609950
$64$		0			0
$65$	−0.871387			−0.108082
$66$		0			0
$67$	9.93846	+	4.11664i	1.21418	+	0.502928i	0.895554	−	0.444954i	$-0.146780\pi$
$67$	9.93846	+	4.11664i	1.21418	+	0.502928i	0.318622	+	0.947882i	$0.396780\pi$
$68$		0			0
$69$	1.50004	+	3.62143i	0.180584	+	0.435969i
$70$		0			0
$71$	2.84472	−	2.84472i	0.337606	−	0.337606i	−0.517859	−	0.855466i	$-0.673271\pi$
$71$	2.84472	−	2.84472i	0.337606	−	0.337606i	0.855466	+	0.517859i	$0.173271\pi$
$72$		0			0
$73$	7.30183	+	7.30183i	0.854614	+	0.854614i	0.990697	−	0.136083i	$-0.0434515\pi$
$73$	7.30183	+	7.30183i	0.854614	+	0.854614i	−0.136083	+	0.990697i	$0.543451\pi$
$74$		0			0
$75$	1.36989	−	0.567426i	0.158181	−	0.0655207i
$76$		0			0
$77$	−0.865093	+	2.08852i	−0.0985865	+	0.238009i
$78$		0			0
$79$		−	10.8716i		−	1.22315i	−0.791187	−	0.611574i	$-0.790536\pi$
$79$		−	10.8716i		−	1.22315i	0.791187	−	0.611574i	$-0.209464\pi$
$80$		0			0
$81$		−	5.95338i		−	0.661486i
$82$		0			0
$83$	6.12342	−	14.7832i	0.672133	−	1.62267i	−0.105847	−	0.994382i	$-0.533755\pi$
$83$	6.12342	−	14.7832i	0.672133	−	1.62267i	0.777980	−	0.628289i	$-0.216245\pi$
$84$		0			0
$85$	−0.0141441	+	0.00585870i	−0.00153415	+	0.000635465i
$86$		0			0
$87$	9.04524	+	9.04524i	0.969751	+	0.969751i
$88$		0			0
$89$	−8.49306	+	8.49306i	−0.900263	+	0.900263i	−0.995459	−	0.0951955i	$-0.969652\pi$
$89$	−8.49306	+	8.49306i	−0.900263	+	0.900263i	0.0951955	+	0.995459i	$0.469652\pi$
$90$		0			0
$91$	0.201439	+	0.486318i	0.0211166	+	0.0509799i
$92$		0			0
$93$	5.17156	+	2.14213i	0.536266	+	0.222128i
$94$		0			0
$95$	−2.23462			−0.229268
$96$		0			0
$97$	13.4111			1.36169			0.680847	−	0.732426i	$-0.261612\pi$
$97$	13.4111			1.36169			0.680847	+	0.732426i	$0.261612\pi$
$98$		0			0
$99$	2.77087	+	1.14773i	0.278483	+	0.115351i
$100$		0			0
$101$	−3.48141	−	8.40487i	−0.346413	−	0.836315i	−0.997038	−	0.0769157i	$-0.975493\pi$
$101$	−3.48141	−	8.40487i	−0.346413	−	0.836315i	0.650624	−	0.759400i	$-0.274507\pi$
$102$		0			0
$103$	6.96753	−	6.96753i	0.686532	−	0.686532i	−0.274932	−	0.961464i	$-0.588655\pi$
$103$	6.96753	−	6.96753i	0.686532	−	0.686532i	0.961464	+	0.274932i	$0.0886554\pi$
$104$		0			0
$105$	−0.633356	−	0.633356i	−0.0618092	−	0.0618092i
$106$		0			0
$107$	7.64935	−	3.16847i	0.739491	−	0.306307i	0.0190453	−	0.999819i	$-0.493937\pi$
$107$	7.64935	−	3.16847i	0.739491	−	0.306307i	0.720446	+	0.693511i	$0.243937\pi$
$108$		0			0
$109$	6.38851	−	15.4232i	0.611908	−	1.47728i	−0.248993	−	0.968505i	$-0.580100\pi$
$109$	6.38851	−	15.4232i	0.611908	−	1.47728i	0.860901	−	0.508772i	$-0.169900\pi$
$110$		0			0
$111$		−	9.19278i		−	0.872540i
$112$		0			0
$113$		−	1.19651i		−	0.112558i	−0.998415	−	0.0562789i	$-0.982076\pi$
$113$		−	1.19651i		−	0.112558i	0.998415	−	0.0562789i	$-0.0179236\pi$
$114$		0			0
$115$	1.01166	−	2.44237i	0.0943379	−	0.227752i
$116$		0			0
$117$	0.645204	−	0.267252i	0.0596491	−	0.0247075i
$118$		0			0
$119$	0.00653944	+	0.00653944i	0.000599469	+	0.000599469i
$120$		0			0
$121$	2.12430	−	2.12430i	0.193119	−	0.193119i
$122$		0			0
$123$	3.63029	+	8.76428i	0.327332	+	0.790249i
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$		0			0
$127$	−15.1676			−1.34591			−0.672953	−	0.739685i	$-0.734975\pi$
$127$	−15.1676			−1.34591			−0.672953	+	0.739685i	$0.734975\pi$
$128$		0			0
$129$	17.0649			1.50248
$130$		0			0
$131$	−6.67305	−	2.76407i	−0.583027	−	0.241498i	0.0716207	−	0.997432i	$-0.477183\pi$
$131$	−6.67305	−	2.76407i	−0.583027	−	0.241498i	−0.654647	+	0.755934i	$0.727183\pi$
$132$		0			0
$133$	0.516580	+	1.24714i	0.0447932	+	0.108140i
$134$		0			0
$135$	−3.98568	+	3.98568i	−0.343033	+	0.343033i
$136$		0			0
$137$	−4.09945	−	4.09945i	−0.350240	−	0.350240i	0.509959	−	0.860199i	$-0.329661\pi$
$137$	−4.09945	−	4.09945i	−0.350240	−	0.350240i	−0.860199	+	0.509959i	$0.829661\pi$
$138$		0			0
$139$	−5.82792	+	2.41401i	−0.494318	+	0.204753i	−0.615894	−	0.787829i	$-0.711205\pi$
$139$	−5.82792	+	2.41401i	−0.494318	+	0.204753i	0.121576	+	0.992582i	$0.461205\pi$
$140$		0			0
$141$	1.18851	−	2.86932i	0.100091	−	0.241640i
$142$		0			0
$143$		−	3.26092i		−	0.272692i
$144$		0			0
$145$		−	8.62712i		−	0.716443i
$146$		0			0
$147$	3.76492	−	9.08932i	0.310525	−	0.749674i
$148$		0			0
$149$	14.5575	−	6.02993i	1.19260	−	0.493991i	0.304000	−	0.952672i	$-0.401678\pi$
$149$	14.5575	−	6.02993i	1.19260	−	0.493991i	0.888601	+	0.458681i	$0.151678\pi$
$150$		0			0
$151$	11.4571	+	11.4571i	0.932368	+	0.932368i	0.997853	−	0.0654858i	$-0.0208597\pi$
$151$	11.4571	+	11.4571i	0.932368	+	0.932368i	−0.0654858	+	0.997853i	$0.520860\pi$
$152$		0			0
$153$	0.00867595	−	0.00867595i	0.000701409	−	0.000701409i
$154$		0			0
$155$	−1.44470	−	3.48780i	−0.116041	−	0.280147i
$156$		0			0
$157$	10.4646	+	4.33459i	0.835169	+	0.345938i	0.758947	−	0.651153i	$-0.225714\pi$
$157$	10.4646	+	4.33459i	0.835169	+	0.345938i	0.0762220	+	0.997091i	$0.475714\pi$
$158$		0			0
$159$	12.5421			0.994654
$160$		0			0
$161$	−1.59694			−0.125857
$162$		0			0
$163$	−6.60440	−	2.73563i	−0.517297	−	0.214271i	0.108732	−	0.994071i	$-0.465321\pi$
$163$	−6.60440	−	2.73563i	−0.517297	−	0.214271i	−0.626029	+	0.779800i	$0.715321\pi$
$164$		0			0
$165$	2.12343	+	5.12642i	0.165309	+	0.399091i
$166$		0			0
$167$	−3.73167	+	3.73167i	−0.288765	+	0.288765i	−0.836592	−	0.547827i	$-0.815455\pi$
$167$	−3.73167	+	3.73167i	−0.288765	+	0.288765i	0.547827	+	0.836592i	$0.315455\pi$
$168$		0			0
$169$	8.65547	+	8.65547i	0.665806	+	0.665806i
$170$		0			0
$171$	1.65459	−	0.685354i	0.126530	−	0.0524103i
$172$		0			0
$173$	2.64349	−	6.38195i	0.200981	−	0.485210i	−0.790967	−	0.611859i	$-0.790422\pi$
$173$	2.64349	−	6.38195i	0.200981	−	0.485210i	0.991948	+	0.126649i	$0.0404220\pi$
$174$		0			0
$175$			0.604079i			0.0456641i
$176$		0			0
$177$		−	10.0190i		−	0.753075i
$178$		0			0
$179$	−7.71999	+	18.6377i	−0.577019	+	1.39305i	0.318457	+	0.947937i	$0.396835\pi$
$179$	−7.71999	+	18.6377i	−0.577019	+	1.39305i	−0.895476	+	0.445110i	$0.853165\pi$
$180$		0			0
$181$	−1.41333	+	0.585421i	−0.105052	+	0.0435140i	−0.434590	−	0.900628i	$-0.643107\pi$
$181$	−1.41333	+	0.585421i	−0.105052	+	0.0435140i	0.329538	+	0.944142i	$0.393107\pi$
$182$		0			0
$183$	13.9654	+	13.9654i	1.03235	+	1.03235i
$184$		0			0
$185$	−4.38392	+	4.38392i	−0.322312	+	0.322312i
$186$		0			0
$187$	−0.0219245	−	0.0529305i	−0.00160328	−	0.00387066i
$188$		0			0
$189$	3.14577	+	1.30302i	0.228821	+	0.0947807i
$190$		0			0
$191$	−20.3604			−1.47323			−0.736615	−	0.676312i	$-0.763577\pi$
$191$	−20.3604			−1.47323			−0.736615	+	0.676312i	$0.763577\pi$
$192$		0			0
$193$	−6.97481			−0.502058			−0.251029	−	0.967980i	$-0.580769\pi$
$193$	−6.97481			−0.502058			−0.251029	+	0.967980i	$0.580769\pi$
$194$		0			0
$195$	1.19370	+	0.494447i	0.0854827	+	0.0354081i
$196$		0			0
$197$	8.42271	+	20.3342i	0.600093	+	1.44875i	0.873486	+	0.486850i	$0.161854\pi$
$197$	8.42271	+	20.3342i	0.600093	+	1.44875i	−0.273393	+	0.961903i	$0.588146\pi$
$198$		0			0
$199$	3.69237	−	3.69237i	0.261745	−	0.261745i	−0.564018	−	0.825763i	$-0.690745\pi$
$199$	3.69237	−	3.69237i	0.261745	−	0.261745i	0.825763	+	0.564018i	$0.190745\pi$
$200$		0			0
$201$	−11.2787	−	11.2787i	−0.795536	−	0.795536i
$202$		0			0
$203$	−4.81476	+	1.99434i	−0.337930	+	0.139975i
$204$		0			0
$205$	2.44834	−	5.91081i	0.170999	−	0.412829i
$206$		0			0
$207$			2.11868i			0.147259i
$208$		0			0
$209$		−	8.36246i		−	0.578443i
$210$		0			0
$211$	2.94819	−	7.11756i	0.202962	−	0.489993i	−0.789322	−	0.613979i	$-0.789568\pi$
$211$	2.94819	−	7.11756i	0.202962	−	0.489993i	0.992284	+	0.123986i	$0.0395679\pi$
$212$		0			0
$213$	−5.51111	+	2.28278i	−0.377615	+	0.156413i
$214$		0			0
$215$	−8.13801	−	8.13801i	−0.555008	−	0.555008i
$216$		0			0
$217$	−1.61256	+	1.61256i	−0.109468	+	0.109468i
$218$		0			0
$219$	−5.85943	−	14.1459i	−0.395944	−	0.955892i
$220$		0			0
$221$	−0.0123250	−	0.00510519i	−0.000829071	−	0.000343412i
$222$		0			0
$223$	6.40937			0.429203			0.214602	−	0.976702i	$-0.431155\pi$
$223$	6.40937			0.429203			0.214602	+	0.976702i	$0.431155\pi$
$224$		0			0
$225$	0.801440			0.0534293
$226$		0			0
$227$	0.266022	+	0.110190i	0.0176565	+	0.00731356i	0.391494	−	0.920181i	$-0.371958\pi$
$227$	0.266022	+	0.110190i	0.0176565	+	0.00731356i	−0.373838	+	0.927494i	$0.621958\pi$
$228$		0			0
$229$	2.22745	+	5.37754i	0.147194	+	0.355358i	0.980230	−	0.197861i	$-0.0633995\pi$
$229$	2.22745	+	5.37754i	0.147194	+	0.355358i	−0.833036	+	0.553219i	$0.813399\pi$
$230$		0			0
$231$	2.37016	−	2.37016i	0.155945	−	0.155945i
$232$		0			0
$233$	−0.710691	−	0.710691i	−0.0465589	−	0.0465589i	0.683444	−	0.730003i	$-0.260481\pi$
$233$	−0.710691	−	0.710691i	−0.0465589	−	0.0465589i	−0.730003	+	0.683444i	$0.760481\pi$
$234$		0			0
$235$	−1.93513	+	0.801555i	−0.126234	+	0.0522877i
$236$		0			0
$237$	−6.16882	+	14.8928i	−0.400708	+	0.967394i
$238$		0			0
$239$			19.4309i			1.25688i	0.777858	+	0.628440i	$0.216306\pi$
$239$			19.4309i			1.25688i	−0.777858	+	0.628440i	$0.783694\pi$
$240$		0			0
$241$			20.9777i			1.35129i	0.737225	+	0.675647i	$0.236136\pi$
$241$			20.9777i			1.35129i	−0.737225	+	0.675647i	$0.763864\pi$
$242$		0			0
$243$	3.09300	−	7.46717i	0.198416	−	0.479019i
$244$		0			0
$245$	−6.13002	+	2.53914i	−0.391633	+	0.162220i
$246$		0			0
$247$	−1.37689	−	1.37689i	−0.0876096	−	0.0876096i
$248$		0			0
$249$	−16.7768	+	16.7768i	−1.06319	+	1.06319i
$250$		0			0
$251$	−6.59019	−	15.9101i	−0.415969	−	1.00424i	−0.983504	−	0.180889i	$-0.942103\pi$
$251$	−6.59019	−	15.9101i	−0.415969	−	1.00424i	0.567534	−	0.823350i	$-0.307897\pi$
$252$		0			0
$253$	9.13987	+	3.78586i	0.574619	+	0.238015i
$254$		0			0
$255$	0.0227003			0.00142154
$256$		0			0
$257$	−30.9499			−1.93060			−0.965302	−	0.261137i	$-0.915903\pi$
$257$	−30.9499			−1.93060			−0.965302	+	0.261137i	$0.915903\pi$
$258$		0			0
$259$	3.46009	+	1.43322i	0.214999	+	0.0890556i
$260$		0			0
$261$	2.64592	+	6.38781i	0.163778	+	0.395395i
$262$		0			0
$263$	−0.786099	+	0.786099i	−0.0484730	+	0.0484730i	−0.730928	−	0.682455i	$-0.760912\pi$
$263$	−0.786099	+	0.786099i	−0.0484730	+	0.0484730i	0.682455	+	0.730928i	$0.260912\pi$
$264$		0			0
$265$	−5.98117	−	5.98117i	−0.367421	−	0.367421i
$266$		0			0
$267$	16.4537	−	6.81535i	1.00695	−	0.417093i
$268$		0			0
$269$	2.42905	−	5.86426i	0.148102	−	0.357550i	−0.832367	−	0.554225i	$-0.813015\pi$
$269$	2.42905	−	5.86426i	0.148102	−	0.357550i	0.980469	+	0.196675i	$0.0630145\pi$
$270$		0			0
$271$		−	11.7409i		−	0.713210i	−0.934255	−	0.356605i	$-0.883934\pi$
$271$		−	11.7409i		−	0.713210i	0.934255	−	0.356605i	$-0.116066\pi$
$272$		0			0
$273$		−	0.780502i		−	0.0472381i
$274$		0			0
$275$	1.43209	−	3.45736i	0.0863580	−	0.208487i
$276$		0			0
$277$	7.45143	−	3.08648i	0.447713	−	0.185449i	−0.147423	−	0.989073i	$-0.547098\pi$
$277$	7.45143	−	3.08648i	0.447713	−	0.185449i	0.595137	+	0.803625i	$0.297098\pi$
$278$		0			0
$279$	2.13940	+	2.13940i	0.128083	+	0.128083i
$280$		0			0
$281$	2.88925	−	2.88925i	0.172358	−	0.172358i	−0.615656	−	0.788015i	$-0.711109\pi$
$281$	2.88925	−	2.88925i	0.172358	−	0.172358i	0.788015	+	0.615656i	$0.211109\pi$
$282$		0			0
$283$	6.72469	+	16.2348i	0.399741	+	0.965061i	0.987727	+	0.156190i	$0.0499211\pi$
$283$	6.72469	+	16.2348i	0.399741	+	0.965061i	−0.587986	+	0.808871i	$0.700079\pi$
$284$		0			0
$285$	3.06118	+	1.26798i	0.181329	+	0.0751088i
$286$		0			0
$287$	−3.86479			−0.228131
$288$		0			0
$289$	16.9998			0.999986
$290$		0			0
$291$	−18.3717	−	7.60981i	−1.07697	−	0.446095i
$292$		0			0
$293$	−10.7316	−	25.9085i	−0.626949	−	1.51359i	−0.843395	−	0.537295i	$-0.819446\pi$
$293$	−10.7316	−	25.9085i	−0.626949	−	1.51359i	0.216445	−	0.976295i	$-0.430554\pi$
$294$		0			0
$295$	−4.77794	+	4.77794i	−0.278182	+	0.278182i
$296$		0			0
$297$	−14.9153	−	14.9153i	−0.865473	−	0.865473i
$298$		0			0
$299$	2.12824	−	0.881548i	0.123080	−	0.0509812i
$300$		0			0
$301$	−2.66052	+	6.42307i	−0.153350	+	0.370219i
$302$		0			0
$303$			13.4892i			0.774931i
$304$		0			0
$305$		−	13.3199i		−	0.762693i
$306$		0			0
$307$	−0.855856	+	2.06622i	−0.0488463	+	0.117925i	−0.946419	−	0.322941i	$-0.895329\pi$
$307$	−0.855856	+	2.06622i	−0.0488463	+	0.117925i	0.897573	+	0.440866i	$0.145329\pi$
$308$		0			0
$309$	−13.4983	+	5.59117i	−0.767891	+	0.318071i
$310$		0			0
$311$	−4.13010	−	4.13010i	−0.234197	−	0.234197i	0.580245	−	0.814442i	$-0.302957\pi$
$311$	−4.13010	−	4.13010i	−0.234197	−	0.234197i	−0.814442	+	0.580245i	$0.802957\pi$
$312$		0			0
$313$	1.09825	−	1.09825i	0.0620765	−	0.0620765i	−0.675387	−	0.737463i	$-0.736023\pi$
$313$	1.09825	−	1.09825i	0.0620765	−	0.0620765i	0.737463	+	0.675387i	$0.236023\pi$
$314$		0			0
$315$	−0.185270	−	0.447280i	−0.0104388	−	0.0252014i
$316$		0			0
$317$	6.78494	+	2.81041i	0.381080	+	0.157849i	0.564996	−	0.825093i	$-0.308878\pi$
$317$	6.78494	+	2.81041i	0.381080	+	0.157849i	−0.183916	+	0.982942i	$0.558878\pi$
$318$		0			0
$319$	32.2846			1.80759
$320$		0			0
$321$	−12.2766			−0.685214
$322$		0			0
$323$	−0.0316069	−	0.0130920i	−0.00175865	−	0.000728458i
$324$		0			0
$325$	−0.333465	−	0.805056i	−0.0184973	−	0.0446565i
$326$		0			0
$327$	−17.5031	+	17.5031i	−0.967922	+	0.967922i
$328$		0			0
$329$	0.894690	+	0.894690i	0.0493259	+	0.0493259i
$330$		0			0
$331$	−1.85529	+	0.768485i	−0.101976	+	0.0422398i	−0.433088	−	0.901352i	$-0.642576\pi$
$331$	−1.85529	+	0.768485i	−0.101976	+	0.0422398i	0.331112	+	0.943591i	$0.392576\pi$
$332$		0			0
$333$	1.90146	−	4.59054i	0.104200	−	0.251560i
$334$		0			0
$335$			10.7573i			0.587735i
$336$		0			0
$337$			3.65265i			0.198972i	0.995039	+	0.0994862i	$0.0317199\pi$
$337$			3.65265i			0.198972i	−0.995039	+	0.0994862i	$0.968280\pi$
$338$		0			0
$339$	−0.678928	+	1.63908i	−0.0368743	+	0.0890224i
$340$		0			0
$341$	13.0521	−	5.40637i	0.706813	−	0.292771i
$342$		0			0
$343$	5.82421	+	5.82421i	0.314478	+	0.314478i
$344$		0			0
$345$	−2.77172	+	2.77172i	−0.149224	+	0.149224i
$346$		0			0
$347$	−0.846773	−	2.04429i	−0.0454571	−	0.109743i	0.899520	−	0.436880i	$-0.143916\pi$
$347$	−0.846773	−	2.04429i	−0.0454571	−	0.109743i	−0.944977	+	0.327136i	$0.893916\pi$
$348$		0			0
$349$	−30.2452	−	12.5280i	−1.61899	−	0.670607i	−0.625054	−	0.780581i	$-0.714923\pi$
$349$	−30.2452	−	12.5280i	−1.61899	−	0.670607i	−0.993934	+	0.109974i	$0.964923\pi$
$350$		0			0
$351$	−4.91166			−0.262165
$352$		0			0
$353$	−30.9821			−1.64901			−0.824506	−	0.565853i	$-0.808547\pi$
$353$	−30.9821			−1.64901			−0.824506	+	0.565853i	$0.808547\pi$
$354$		0			0
$355$	3.71681	+	1.53955i	0.197268	+	0.0817109i
$356$		0			0
$357$	−0.00524764	−	0.0126689i	−0.000277735	−	0.000670511i
$358$		0			0
$359$	−7.35498	+	7.35498i	−0.388181	+	0.388181i	−0.874038	−	0.485857i	$-0.838507\pi$
$359$	−7.35498	+	7.35498i	−0.388181	+	0.388181i	0.485857	+	0.874038i	$0.338507\pi$
$360$		0			0
$361$	9.90406	+	9.90406i	0.521266	+	0.521266i
$362$		0			0
$363$	−4.11544	+	1.70467i	−0.216005	+	0.0894720i
$364$		0			0
$365$	−3.95172	+	9.54030i	−0.206842	+	0.499362i
$366$		0			0
$367$			7.08695i			0.369936i	0.982745	+	0.184968i	$0.0592181\pi$
$367$			7.08695i			0.369936i	−0.982745	+	0.184968i	$0.940782\pi$
$368$		0			0
$369$			5.12746i			0.266925i
$370$		0			0
$371$	−1.95540	+	4.72075i	−0.101519	+	0.245089i
$372$		0			0
$373$	2.57518	−	1.06668i	0.133338	−	0.0552304i	−0.315017	−	0.949086i	$-0.602010\pi$
$373$	2.57518	−	1.06668i	0.133338	−	0.0552304i	0.448355	+	0.893856i	$0.352010\pi$
$374$		0			0
$375$	1.04847	+	1.04847i	0.0541425	+	0.0541425i
$376$		0			0
$377$	5.31571	−	5.31571i	0.273773	−	0.273773i
$378$		0			0
$379$	−11.8931	−	28.7124i	−0.610906	−	1.47486i	−0.862007	−	0.506896i	$-0.830793\pi$
$379$	−11.8931	−	28.7124i	−0.610906	−	1.47486i	0.251101	−	0.967961i	$-0.419207\pi$
$380$		0			0
$381$	20.7779	+	8.60648i	1.06448	+	0.440923i
$382$		0			0
$383$	−21.0040			−1.07326			−0.536628	−	0.843819i	$-0.680302\pi$
$383$	−21.0040			−1.07326			−0.536628	+	0.843819i	$0.680302\pi$
$384$		0			0
$385$	−2.26060			−0.115211
$386$		0			0
$387$	8.52157	+	3.52975i	0.433176	+	0.179427i
$388$		0			0
$389$	1.45291	+	3.50763i	0.0736654	+	0.177844i	0.956423	−	0.291985i	$-0.0943157\pi$
$389$	1.45291	+	3.50763i	0.0736654	+	0.177844i	−0.882758	+	0.469829i	$0.844316\pi$
$390$		0			0
$391$	0.0286182	−	0.0286182i	0.00144728	−	0.00144728i
$392$		0			0
$393$	7.57291	+	7.57291i	0.382003	+	0.382003i
$394$		0			0
$395$	10.0440	−	4.16038i	0.505370	−	0.209331i
$396$		0			0
$397$	0.460353	−	1.11139i	0.0231045	−	0.0557791i	−0.911906	−	0.410399i	$-0.865390\pi$
$397$	0.460353	−	1.11139i	0.0231045	−	0.0557791i	0.935011	+	0.354619i	$0.115390\pi$
$398$		0			0
$399$		−	2.00155i		−	0.100203i
$400$		0			0
$401$			13.6454i			0.681418i	0.940169	+	0.340709i	$0.110667\pi$
$401$			13.6454i			0.681418i	−0.940169	+	0.340709i	$0.889333\pi$
$402$		0			0
$403$	1.25889	−	3.03923i	0.0627097	−	0.151395i
$404$		0			0
$405$	5.50020	−	2.27826i	0.273307	−	0.113208i
$406$		0			0
$407$	−16.4056	−	16.4056i	−0.813196	−	0.813196i
$408$		0			0
$409$	−9.81584	+	9.81584i	−0.485362	+	0.485362i	−0.906839	−	0.421477i	$-0.861512\pi$
$409$	−9.81584	+	9.81584i	−0.485362	+	0.485362i	0.421477	+	0.906839i	$0.361512\pi$
$410$		0			0
$411$	3.28965	+	7.94192i	0.162267	+	0.391746i
$412$		0			0
$413$	3.77107	+	1.56203i	0.185562	+	0.0768624i
$414$		0			0
$415$	16.0013			0.785471
$416$		0			0
$417$	9.35336			0.458036
$418$		0			0
$419$	−22.4982	−	9.31905i	−1.09911	−	0.455265i	−0.241934	−	0.970293i	$-0.577782\pi$
$419$	−22.4982	−	9.31905i	−1.09911	−	0.455265i	−0.857174	+	0.515027i	$0.827782\pi$
$420$		0			0
$421$	−6.37434	−	15.3890i	−0.310666	−	0.750015i	−0.999681	−	0.0252671i	$-0.991956\pi$
$421$	−6.37434	−	15.3890i	−0.310666	−	0.750015i	0.689014	−	0.724748i	$-0.258044\pi$
$422$		0			0
$423$	1.18700	−	1.18700i	0.0577138	−	0.0577138i
$424$		0			0
$425$	−0.0108255	−	0.0108255i	−0.000525112	−	0.000525112i
$426$		0			0
$427$	−7.43377	+	3.07917i	−0.359745	+	0.149011i
$428$		0			0
$429$	−1.85033	+	4.46709i	−0.0893348	+	0.215673i
$430$		0			0
$431$			33.5430i			1.61571i	0.589382	+	0.807855i	$0.299371\pi$
$431$			33.5430i			1.61571i	−0.589382	+	0.807855i	$0.700629\pi$
$432$		0			0
$433$			37.4886i			1.80159i	0.434248	+	0.900793i	$0.357014\pi$
$433$			37.4886i			1.80159i	−0.434248	+	0.900793i	$0.642986\pi$
$434$		0			0
$435$	−4.89525	+	11.8182i	−0.234709	+	0.566638i
$436$		0			0
$437$	5.45777	−	2.26068i	0.261081	−	0.108143i
$438$		0			0
$439$	−17.0314	−	17.0314i	−0.812862	−	0.812862i	0.172200	−	0.985062i	$-0.444912\pi$
$439$	−17.0314	−	17.0314i	−0.812862	−	0.812862i	−0.985062	+	0.172200i	$0.944912\pi$
$440$		0			0
$441$	3.76013	−	3.76013i	0.179054	−	0.179054i
$442$		0			0
$443$	7.47579	+	18.0482i	0.355185	+	0.857494i	0.995963	+	0.0897668i	$0.0286122\pi$
$443$	7.47579	+	18.0482i	0.355185	+	0.857494i	−0.640777	+	0.767727i	$0.721388\pi$
$444$		0			0
$445$	−11.0967	−	4.59641i	−0.526035	−	0.217891i
$446$		0			0
$447$	−23.3637			−1.10507
$448$		0			0
$449$	−8.81595			−0.416051			−0.208025	−	0.978123i	$-0.566704\pi$
$449$	−8.81595			−0.416051			−0.208025	+	0.978123i	$0.566704\pi$
$450$		0			0
$451$	22.1196	+	9.16223i	1.04157	+	0.431432i
$452$		0			0
$453$	−9.19389	−	22.1960i	−0.431967	−	1.04286i
$454$		0			0
$455$	−0.372211	+	0.372211i	−0.0174495	+	0.0174495i
$456$		0			0
$457$	−0.833036	−	0.833036i	−0.0389678	−	0.0389678i	0.687354	−	0.726322i	$-0.258772\pi$
$457$	−0.833036	−	0.833036i	−0.0389678	−	0.0389678i	−0.726322	+	0.687354i	$0.758772\pi$
$458$		0			0
$459$	−0.0797249	+	0.0330231i	−0.00372124	+	0.00154139i
$460$		0			0
$461$	−7.51373	+	18.1398i	−0.349949	+	0.844853i	0.646676	+	0.762765i	$0.276159\pi$
$461$	−7.51373	+	18.1398i	−0.349949	+	0.844853i	−0.996625	+	0.0820876i	$0.973841\pi$
$462$		0			0
$463$		−	11.0030i		−	0.511352i	−0.966762	−	0.255676i	$-0.917702\pi$
$463$		−	11.0030i		−	0.511352i	0.966762	−	0.255676i	$-0.0822981\pi$
$464$		0			0
$465$			5.59765i			0.259585i
$466$		0			0
$467$	9.58426	−	23.1385i	0.443507	−	1.07072i	−0.531203	−	0.847245i	$-0.678260\pi$
$467$	9.58426	−	23.1385i	0.443507	−	1.07072i	0.974710	−	0.223475i	$-0.0717403\pi$
$468$		0			0
$469$	6.00362	−	2.48678i	0.277221	−	0.114829i
$470$		0			0
$471$	−11.8758	−	11.8758i	−0.547208	−	0.547208i
$472$		0			0
$473$	30.4542	−	30.4542i	1.40029	−	1.40029i
$474$		0			0
$475$	−0.855154	−	2.06452i	−0.0392371	−	0.0947268i
$476$		0			0
$477$	6.26307	+	2.59425i	0.286766	+	0.118783i
$478$		0			0
$479$	36.4379			1.66489			0.832446	−	0.554107i	$-0.186940\pi$
$479$	36.4379			1.66489			0.832446	+	0.554107i	$0.186940\pi$
$480$		0			0
$481$	−5.40242			−0.246329
$482$		0			0
$483$	2.18763	+	0.906146i	0.0995406	+	0.0412311i
$484$		0			0
$485$	5.13221	+	12.3903i	0.233042	+	0.562613i
$486$		0			0
$487$	0.972321	−	0.972321i	0.0440601	−	0.0440601i	−0.684733	−	0.728794i	$-0.740081\pi$
$487$	0.972321	−	0.972321i	0.0440601	−	0.0440601i	0.728794	+	0.684733i	$0.240081\pi$
$488$		0			0
$489$	7.49501	+	7.49501i	0.338936	+	0.338936i
$490$		0			0
$491$	2.77382	−	1.14895i	0.125181	−	0.0518515i	−0.319214	−	0.947683i	$-0.603419\pi$
$491$	2.77382	−	1.14895i	0.125181	−	0.0518515i	0.444395	+	0.895831i	$0.353419\pi$
$492$		0			0
$493$	0.0505437	−	0.122023i	0.00227637	−	0.00549565i
$494$		0			0
$495$			2.99916i			0.134802i
$496$		0			0
$497$		−	2.43024i		−	0.109011i
$498$		0			0
$499$	−13.1249	+	31.6863i	−0.587551	+	1.41847i	0.298286	+	0.954477i	$0.403585\pi$
$499$	−13.1249	+	31.6863i	−0.587551	+	1.41847i	−0.885837	+	0.463997i	$0.846415\pi$
$500$		0			0
$501$	7.22941	−	2.99452i	0.322986	−	0.133785i
$502$		0			0
$503$	−18.7300	−	18.7300i	−0.835132	−	0.835132i	0.153082	−	0.988213i	$-0.451080\pi$
$503$	−18.7300	−	18.7300i	−0.835132	−	0.835132i	−0.988213	+	0.153082i	$0.951080\pi$
$504$		0			0
$505$	6.43281	−	6.43281i	0.286256	−	0.286256i
$506$		0			0
$507$	−6.94568	−	16.7683i	−0.308468	−	0.744709i
$508$		0			0
$509$	−24.5496	−	10.1688i	−1.08814	−	0.450724i	−0.234785	−	0.972047i	$-0.575438\pi$
$509$	−24.5496	−	10.1688i	−1.08814	−	0.450724i	−0.853359	+	0.521324i	$0.825438\pi$
$510$		0			0
$511$	6.23793			0.275950
$512$		0			0
$513$	−12.5957			−0.556113
$514$		0			0
$515$	9.10352	+	3.77080i	0.401149	+	0.166161i
$516$		0			0
$517$	−2.99960	−	7.24167i	−0.131922	−	0.318488i
$518$		0			0
$519$	−7.24256	+	7.24256i	−0.317913	+	0.317913i
$520$		0			0
$521$	18.5736	+	18.5736i	0.813726	+	0.813726i	0.985190	−	0.171464i	$-0.0548498\pi$
$521$	18.5736	+	18.5736i	0.813726	+	0.813726i	−0.171464	+	0.985190i	$0.554850\pi$
$522$		0			0
$523$	−27.2189	+	11.2744i	−1.19020	+	0.492997i	−0.887820	−	0.460191i	$-0.847781\pi$
$523$	−27.2189	+	11.2744i	−1.19020	+	0.492997i	−0.302380	+	0.953188i	$0.597781\pi$
$524$		0			0
$525$	0.342770	−	0.827520i	0.0149597	−	0.0361159i
$526$		0			0
$527$		−	0.0577961i		−	0.00251764i
$528$		0			0
$529$		−	16.0114i		−	0.696147i
$530$		0			0
$531$	2.07236	−	5.00313i	0.0899329	−	0.217117i
$532$		0			0
$533$	5.15060	−	2.13345i	0.223097	−	0.0924100i
$534$		0			0
$535$	5.85456	+	5.85456i	0.253115	+	0.253115i
$536$		0			0
$537$	21.1510	−	21.1510i	0.912733	−	0.912733i
$538$		0			0
$539$	−9.50202	−	22.9399i	−0.409281	−	0.988091i
$540$		0			0
$541$	14.4095	+	5.96861i	0.619512	+	0.256610i	0.670290	−	0.742100i	$-0.266170\pi$
$541$	14.4095	+	5.96861i	0.619512	+	0.256610i	−0.0507773	+	0.998710i	$0.516170\pi$
$542$		0			0
$543$	2.26829			0.0973414
$544$		0			0
$545$	16.6940			0.715092
$546$		0			0
$547$	−4.37081	−	1.81045i	−0.186882	−	0.0774092i	0.287280	−	0.957847i	$-0.407249\pi$
$547$	−4.37081	−	1.81045i	−0.186882	−	0.0774092i	−0.474162	+	0.880437i	$0.657249\pi$
$548$		0			0
$549$	4.08517	+	9.86247i	0.174351	+	0.420920i
$550$		0			0
$551$	13.6319	−	13.6319i	0.580737	−	0.580737i
$552$		0			0
$553$	−4.64378	−	4.64378i	−0.197474	−	0.197474i
$554$		0			0
$555$	8.49303	−	3.51793i	0.360509	−	0.149328i
$556$		0			0
$557$	−13.1484	+	31.7432i	−0.557118	+	1.34500i	0.354921	+	0.934896i	$0.384508\pi$
$557$	−13.1484	+	31.7432i	−0.557118	+	1.34500i	−0.912039	+	0.410105i	$0.865492\pi$
$558$		0			0
$559$		−	10.0287i		−	0.424168i
$560$		0			0
$561$			0.0849494i			0.00358656i
$562$		0			0
$563$	−7.93601	+	19.1592i	−0.334463	+	0.807465i	0.663764	+	0.747942i	$0.268958\pi$
$563$	−7.93601	+	19.1592i	−0.334463	+	0.807465i	−0.998227	+	0.0595228i	$0.981042\pi$
$564$		0			0
$565$	1.10543	−	0.457883i	0.0465057	−	0.0192633i
$566$		0			0
$567$	−2.54298	−	2.54298i	−0.106795	−	0.106795i
$568$		0			0
$569$	25.7783	−	25.7783i	1.08068	−	1.08068i	0.0842382	−	0.996446i	$-0.473154\pi$
$569$	25.7783	−	25.7783i	1.08068	−	1.08068i	0.996446	−	0.0842382i	$-0.0268457\pi$
$570$		0			0
$571$	16.8658	+	40.7177i	0.705812	+	1.70398i	0.710209	+	0.703991i	$0.248600\pi$
$571$	16.8658	+	40.7177i	0.705812	+	1.70398i	−0.00439689	+	0.999990i	$0.501400\pi$
$572$		0			0
$573$	27.8915	+	11.5530i	1.16518	+	0.482635i
$574$		0			0
$575$	2.64360			0.110246
$576$		0			0
$577$	5.40896			0.225178			0.112589	−	0.993642i	$-0.464086\pi$
$577$	5.40896			0.225178			0.112589	+	0.993642i	$0.464086\pi$
$578$		0			0
$579$	9.55470	+	3.95769i	0.397080	+	0.164476i
$580$		0			0
$581$	−3.69903	−	8.93025i	−0.153462	−	0.370489i
$582$		0			0
$583$	22.3829	−	22.3829i	0.927004	−	0.927004i
$584$		0			0
$585$	0.493818	+	0.493818i	0.0204168	+	0.0204168i
$586$		0			0
$587$	21.6654	−	8.97412i	0.894228	−	0.370402i	0.112230	−	0.993682i	$-0.464201\pi$
$587$	21.6654	−	8.97412i	0.894228	−	0.370402i	0.781998	+	0.623281i	$0.214201\pi$
$588$		0			0
$589$	3.22835	−	7.79393i	0.133022	−	0.321143i
$590$		0			0
$591$		−	32.6348i		−	1.34242i
$592$		0			0
$593$		−	17.2718i		−	0.709268i	−0.935005	−	0.354634i	$-0.884606\pi$
$593$		−	17.2718i		−	0.709268i	0.935005	−	0.354634i	$-0.115394\pi$
$594$		0			0
$595$	−0.00353912	+	0.00854418i	−0.000145090	+	0.000350277i
$596$		0			0
$597$	−7.15328	+	2.96298i	−0.292764	+	0.121267i
$598$		0			0
$599$	−11.6233	−	11.6233i	−0.474917	−	0.474917i	0.428585	−	0.903502i	$-0.359012\pi$
$599$	−11.6233	−	11.6233i	−0.474917	−	0.474917i	−0.903502	+	0.428585i	$0.859012\pi$
$600$		0			0
$601$	20.8792	−	20.8792i	0.851682	−	0.851682i	−0.138659	−	0.990340i	$-0.544279\pi$
$601$	20.8792	−	20.8792i	0.851682	−	0.851682i	0.990340	+	0.138659i	$0.0442791\pi$
$602$		0			0
$603$	−3.29924	−	7.96507i	−0.134356	−	0.324363i
$604$		0			0
$605$	2.77554	+	1.14967i	0.112842	+	0.0467405i
$606$		0			0
$607$	36.0408			1.46285			0.731426	−	0.681921i	$-0.238855\pi$
$607$	36.0408			1.46285			0.731426	+	0.681921i	$0.238855\pi$
$608$		0			0
$609$	7.72732			0.313127
$610$		0			0
$611$	−1.68624	−	0.698464i	−0.0682181	−	0.0282568i
$612$		0			0
$613$	−13.6351	−	32.9181i	−0.550718	−	1.32955i	−0.916941	−	0.399024i	$-0.869349\pi$
$613$	−13.6351	−	32.9181i	−0.550718	−	1.32955i	0.366222	−	0.930527i	$-0.380651\pi$
$614$		0			0
$615$	−6.70789	+	6.70789i	−0.270488	+	0.270488i
$616$		0			0
$617$	16.9582	+	16.9582i	0.682712	+	0.682712i	0.960611	−	0.277898i	$-0.0896378\pi$
$617$	16.9582	+	16.9582i	0.682712	+	0.682712i	−0.277898	+	0.960611i	$0.589638\pi$
$618$		0			0
$619$	17.3994	−	7.20706i	0.699340	−	0.289676i	−0.00454535	−	0.999990i	$-0.501447\pi$
$619$	17.3994	−	7.20706i	0.699340	−	0.289676i	0.703885	+	0.710314i	$0.251447\pi$
$620$		0			0
$621$	5.70233	−	13.7666i	0.228827	−	0.552436i
$622$		0			0
$623$			7.25560i			0.290689i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−4.74507	+	11.4556i	−0.189500	+	0.457493i
$628$		0			0
$629$	−0.0876909	+	0.0363228i	−0.00349647	+	0.00144828i
$630$		0			0
$631$	20.6664	+	20.6664i	0.822717	+	0.822717i	0.986497	−	0.163780i	$-0.0523687\pi$
$631$	20.6664	+	20.6664i	0.822717	+	0.822717i	−0.163780	+	0.986497i	$0.552369\pi$
$632$		0			0
$633$	−8.07737	+	8.07737i	−0.321047	+	0.321047i
$634$		0			0
$635$	−5.80439	−	14.0130i	−0.230340	−	0.556090i
$636$		0			0
$637$	−5.34162	−	2.21257i	−0.211643	−	0.0876653i
$638$		0			0
$639$	−3.22422			−0.127548
$640$		0			0
$641$	4.54436			0.179491			0.0897456	−	0.995965i	$-0.471395\pi$
$641$	4.54436			0.179491			0.0897456	+	0.995965i	$0.471395\pi$
$642$		0			0
$643$	11.4862	+	4.75774i	0.452972	+	0.187627i	0.597492	−	0.801875i	$-0.296164\pi$
$643$	11.4862	+	4.75774i	0.452972	+	0.187627i	−0.144520	+	0.989502i	$0.546164\pi$
$644$		0			0
$645$	6.53044	+	15.7659i	0.257136	+	0.620780i
$646$		0			0
$647$	19.6034	−	19.6034i	0.770690	−	0.770690i	−0.207537	−	0.978227i	$-0.566545\pi$
$647$	19.6034	−	19.6034i	0.770690	−	0.770690i	0.978227	+	0.207537i	$0.0665447\pi$
$648$		0			0
$649$	−17.8801	−	17.8801i	−0.701855	−	0.701855i
$650$		0			0
$651$	3.12403	−	1.29402i	0.122440	−	0.0507165i
$652$		0			0
$653$	−16.0457	+	38.7377i	−0.627917	+	1.51592i	0.214290	+	0.976770i	$0.431256\pi$
$653$	−16.0457	+	38.7377i	−0.627917	+	1.51592i	−0.842207	+	0.539155i	$0.818744\pi$
$654$		0			0
$655$		−	7.22285i		−	0.282220i
$656$		0			0
$657$		−	8.27594i		−	0.322875i
$658$		0			0
$659$	−17.3133	+	41.7979i	−0.674429	+	1.62822i	0.0995705	+	0.995031i	$0.468253\pi$
$659$	−17.3133	+	41.7979i	−0.674429	+	1.62822i	−0.774000	+	0.633186i	$0.781747\pi$
$660$		0			0
$661$	−30.5817	+	12.6674i	−1.18949	+	0.492704i	−0.887590	−	0.460635i	$-0.847622\pi$
$661$	−30.5817	+	12.6674i	−1.18949	+	0.492704i	−0.301902	+	0.953339i	$0.597622\pi$
$662$		0			0
$663$	0.0139871	+	0.0139871i	0.000543212	+	0.000543212i
$664$		0			0
$665$	−0.954516	+	0.954516i	−0.0370146	+	0.0370146i
$666$		0			0
$667$	8.72772	+	21.0706i	0.337939	+	0.815856i
$668$		0			0
$669$	−8.78011	−	3.63684i	−0.339459	−	0.140608i
$670$		0			0
$671$	49.8459			1.92428
$672$		0			0
$673$	3.25654			0.125530			0.0627652	−	0.998028i	$-0.480008\pi$
$673$	3.25654			0.125530			0.0627652	+	0.998028i	$0.480008\pi$
$674$		0			0
$675$	−5.20754	−	2.15703i	−0.200438	−	0.0830243i
$676$		0			0
$677$	−14.5065	−	35.0217i	−0.557528	−	1.34599i	−0.911717	−	0.410818i	$-0.865243\pi$
$677$	−14.5065	−	35.0217i	−0.557528	−	1.34599i	0.354189	−	0.935174i	$-0.384757\pi$
$678$		0			0
$679$	5.72854	−	5.72854i	0.219841	−	0.219841i
$680$		0			0
$681$	−0.301895	−	0.301895i	−0.0115687	−	0.0115687i
$682$		0			0
$683$	41.9152	−	17.3618i	1.60384	−	0.664332i	0.611887	−	0.790945i	$-0.290411\pi$
$683$	41.9152	−	17.3618i	1.60384	−	0.664332i	0.991952	+	0.126613i	$0.0404105\pi$
$684$		0			0
$685$	2.21861	−	5.35619i	0.0847687	−	0.204650i
$686$		0			0
$687$		−	8.63052i		−	0.329275i
$688$		0			0
$689$		−	7.37076i		−	0.280804i
$690$		0			0
$691$	−6.67763	+	16.1212i	−0.254029	+	0.613280i	−0.998522	−	0.0543500i	$-0.982691\pi$
$691$	−6.67763	+	16.1212i	−0.254029	+	0.613280i	0.744493	+	0.667630i	$0.232691\pi$
$692$		0			0
$693$	1.67382	−	0.693320i	0.0635833	−	0.0263370i
$694$		0			0
$695$	−4.46050	−	4.46050i	−0.169196	−	0.169196i
$696$		0			0
$697$	0.0692593	−	0.0692593i	0.00262338	−	0.00262338i
$698$		0			0
$699$	0.570302	+	1.37683i	0.0215708	+	0.0520765i
$700$		0			0
$701$	15.6519	+	6.48321i	0.591163	+	0.244868i	0.658151	−	0.752886i	$-0.271339\pi$
$701$	15.6519	+	6.48321i	0.591163	+	0.244868i	−0.0669880	+	0.997754i	$0.521339\pi$
$702$		0			0
$703$	−13.8542			−0.522522
$704$		0			0
$705$	3.10573			0.116968
$706$		0			0
$707$	−5.07720	−	2.10305i	−0.190948	−	0.0790932i
$708$		0			0
$709$	−4.65105	−	11.2286i	−0.174674	−	0.421700i	0.812161	−	0.583434i	$-0.198291\pi$
$709$	−4.65105	−	11.2286i	−0.174674	−	0.421700i	−0.986834	+	0.161734i	$0.948291\pi$
$710$		0			0
$711$	−6.16096	+	6.16096i	−0.231054	+	0.231054i
$712$		0			0
$713$	7.05695	+	7.05695i	0.264285	+	0.264285i
$714$		0			0
$715$	3.01270	−	1.24790i	0.112669	−	0.0466688i
$716$		0			0
$717$	11.0256	−	26.6181i	0.411758	−	0.994072i
$718$		0			0
$719$		−	14.8144i		−	0.552483i	−0.961088	−	0.276241i	$-0.910911\pi$
$719$		−	14.8144i		−	0.552483i	0.961088	−	0.276241i	$-0.0890889\pi$
$720$		0			0
$721$		−	5.95234i		−	0.221677i
$722$		0			0
$723$	11.9033	−	28.7371i	0.442688	−	1.06874i
$724$		0			0
$725$	7.97042	−	3.30145i	0.296014	−	0.122613i
$726$		0			0
$727$	−17.7788	−	17.7788i	−0.659380	−	0.659380i	0.295854	−	0.955233i	$-0.404396\pi$
$727$	−17.7788	−	17.7788i	−0.659380	−	0.659380i	−0.955233	+	0.295854i	$0.904396\pi$
$728$		0			0
$729$	−21.1031	+	21.1031i	−0.781598	+	0.781598i
$730$		0			0
$731$	−0.0674271	−	0.162783i	−0.00249388	−	0.00602076i
$732$		0			0
$733$	−4.02249	−	1.66617i	−0.148574	−	0.0615414i	0.307157	−	0.951659i	$-0.400622\pi$
$733$	−4.02249	−	1.66617i	−0.148574	−	0.0615414i	−0.455731	+	0.890117i	$0.650622\pi$
$734$		0			0
$735$	9.83821			0.362888
$736$		0			0
$737$	−40.2562			−1.48286
$738$		0			0
$739$	−23.8733	−	9.88864i	−0.878193	−	0.363760i	−0.102397	−	0.994744i	$-0.532651\pi$
$739$	−23.8733	−	9.88864i	−0.878193	−	0.363760i	−0.775796	+	0.630984i	$0.782651\pi$
$740$		0			0
$741$	1.10490	+	2.66747i	0.0405896	+	0.0979920i
$742$		0			0
$743$	7.72863	−	7.72863i	0.283536	−	0.283536i	−0.550982	−	0.834517i	$-0.685747\pi$
$743$	7.72863	−	7.72863i	0.283536	−	0.283536i	0.834517	+	0.550982i	$0.185747\pi$
$744$		0			0
$745$	11.1419	+	11.1419i	0.408206	+	0.408206i
$746$		0			0
$747$	−11.8479	+	4.90755i	−0.433491	+	0.179558i
$748$		0			0
$749$	1.91400	−	4.62081i	0.0699362	−	0.168841i
$750$		0			0
$751$			21.6135i			0.788687i	0.918963	+	0.394343i	$0.129028\pi$
$751$			21.6135i			0.788687i	−0.918963	+	0.394343i	$0.870972\pi$
$752$		0			0
$753$			25.5345i			0.930529i
$754$		0			0
$755$	−6.20055	+	14.9695i	−0.225661	+	0.544794i
$756$		0			0
$757$	−35.8533	+	14.8509i	−1.30311	+	0.539766i	−0.922866	−	0.385121i	$-0.874160\pi$
$757$	−35.8533	+	14.8509i	−1.30311	+	0.539766i	−0.380244	+	0.924886i	$0.624160\pi$
$758$		0			0
$759$	−10.3724	−	10.3724i	−0.376494	−	0.376494i
$760$		0			0
$761$	−14.1289	+	14.1289i	−0.512173	+	0.512173i	−0.915192	−	0.403019i	$-0.867961\pi$
$761$	−14.1289	+	14.1289i	−0.512173	+	0.512173i	0.403019	+	0.915192i	$0.367961\pi$
$762$		0			0
$763$	−3.85917	−	9.31685i	−0.139711	−	0.337293i
$764$		0			0
$765$	0.0113357	+	0.00469539i	0.000409842	+	0.000169762i
$766$		0			0
$767$	−5.88798			−0.212603
$768$		0			0
$769$	32.2019			1.16123			0.580615	−	0.814178i	$-0.302812\pi$
$769$	32.2019			1.16123			0.580615	+	0.814178i	$0.302812\pi$
$770$		0			0
$771$	42.3979	+	17.5618i	1.52692	+	0.632472i
$772$		0			0
$773$	3.97329	+	9.59238i	0.142909	+	0.345014i	0.979086	−	0.203446i	$-0.0652142\pi$
$773$	3.97329	+	9.59238i	0.142909	+	0.345014i	−0.836177	+	0.548460i	$0.815214\pi$
$774$		0			0
$775$	2.66945	−	2.66945i	0.0958895	−	0.0958895i
$776$		0			0
$777$	−3.92668	−	3.92668i	−0.140869	−	0.140869i
$778$		0			0
$779$	13.2084	−	5.47112i	0.473242	−	0.196023i
$780$		0			0
$781$	−5.76134	+	13.9091i	−0.206157	+	0.497707i
$782$		0			0
$783$		−	48.6276i		−	1.73781i
$784$		0			0
$785$			11.3268i			0.404272i
$786$		0			0
$787$	−11.2062	+	27.0542i	−0.399459	+	0.964379i	0.588336	+	0.808617i	$0.299783\pi$
$787$	−11.2062	+	27.0542i	−0.399459	+	0.964379i	−0.987795	+	0.155762i	$0.950217\pi$
$788$		0			0
$789$	1.52292	−	0.630814i	0.0542174	−	0.0224576i
$790$		0			0
$791$	−0.511085	−	0.511085i	−0.0181721	−	0.0181721i
$792$		0			0
$793$	8.20721	−	8.20721i	0.291447	−	0.291447i
$794$		0			0
$795$	4.79966	+	11.5874i	0.170226	+	0.410963i
$796$		0			0
$797$	8.07977	+	3.34675i	0.286200	+	0.118548i	0.521165	−	0.853456i	$-0.325498\pi$
$797$	8.07977	+	3.34675i	0.286200	+	0.118548i	−0.234965	+	0.972004i	$0.575498\pi$
$798$		0			0
$799$	−0.0320668			−0.00113444
$800$		0			0
$801$	9.62610			0.340121
$802$		0			0
$803$	−35.7019	−	14.7882i	−1.25989	−	0.521865i
$804$		0			0
$805$	−0.611123	−	1.47538i	−0.0215393	−	0.0520004i
$806$		0			0
$807$	−6.65506	+	6.65506i	−0.234269	+	0.234269i
$808$		0			0
$809$	9.78942	+	9.78942i	0.344178	+	0.344178i	0.857935	−	0.513758i	$-0.171747\pi$
$809$	9.78942	+	9.78942i	0.344178	+	0.344178i	−0.513758	+	0.857935i	$0.671747\pi$
$810$		0			0
$811$	−15.4195	+	6.38698i	−0.541453	+	0.224277i	−0.636611	−	0.771185i	$-0.719664\pi$
$811$	−15.4195	+	6.38698i	−0.541453	+	0.224277i	0.0951581	+	0.995462i	$0.469664\pi$
$812$		0			0
$813$	−6.66210	+	16.0837i	−0.233650	+	0.564081i
$814$		0			0
$815$		−	7.14856i		−	0.250403i
$816$		0			0
$817$		−	25.7180i		−	0.899760i
$818$		0			0
$819$	0.161441	−	0.389754i	0.00564122	−	0.0136191i
$820$		0			0
$821$	−0.451900	+	0.187183i	−0.0157714	+	0.00653273i	−0.390555	−	0.920580i	$-0.627717\pi$
$821$	−0.451900	+	0.187183i	−0.0157714	+	0.00653273i	0.374784	+	0.927112i	$0.377717\pi$
$822$		0			0
$823$	30.9346	+	30.9346i	1.07831	+	1.07831i	0.996661	+	0.0816524i	$0.0260197\pi$
$823$	30.9346	+	30.9346i	1.07831	+	1.07831i	0.0816524	+	0.996661i	$0.473980\pi$
$824$		0			0
$825$	−3.92359	+	3.92359i	−0.136602	+	0.136602i
$826$		0			0
$827$	−1.65221	−	3.98878i	−0.0574528	−	0.138703i	0.892546	−	0.450955i	$-0.148917\pi$
$827$	−1.65221	−	3.98878i	−0.0574528	−	0.138703i	−0.949999	+	0.312252i	$0.898917\pi$
$828$		0			0
$829$	−13.8592	−	5.74068i	−0.481350	−	0.199382i	0.128795	−	0.991671i	$-0.458889\pi$
$829$	−13.8592	−	5.74068i	−0.481350	−	0.199382i	−0.610146	+	0.792289i	$0.708889\pi$
$830$		0			0
$831$	−11.9590			−0.414852
$832$		0			0
$833$	−0.101580			−0.00351954
$834$		0			0
$835$	−4.87566	−	2.01957i	−0.168729	−	0.0698899i
$836$		0			0
$837$	−8.14318	−	19.6594i	−0.281469	−	0.679527i
$838$		0			0
$839$	−27.3865	+	27.3865i	−0.945487	+	0.945487i	−0.998589	−	0.0531021i	$-0.983089\pi$
$839$	−27.3865	+	27.3865i	−0.945487	+	0.945487i	0.0531021	+	0.998589i	$0.483089\pi$
$840$		0			0
$841$	32.1218	+	32.1218i	1.10765	+	1.10765i
$842$		0			0
$843$	−5.59738	+	2.31851i	−0.192784	+	0.0798538i
$844$		0			0
$845$	−4.68431	+	11.3089i	−0.161145	+	0.389039i
$846$		0			0
$847$		−	1.81479i		−	0.0623568i
$848$		0			0
$849$		−	26.0556i		−	0.894227i
$850$		0			0
$851$	6.27210	−	15.1422i	0.215005	−	0.519067i
$852$		0			0
$853$	−33.9630	+	14.0679i	−1.16287	+	0.481677i	−0.878830	−	0.477135i	$-0.841675\pi$
$853$	−33.9630	+	14.0679i	−1.16287	+	0.481677i	−0.284041	+	0.958812i	$0.591675\pi$
$854$		0			0
$855$	1.26637	+	1.26637i	0.0433089	+	0.0433089i
$856$		0			0
$857$	−21.4996	+	21.4996i	−0.734411	+	0.734411i	−0.971490	−	0.237079i	$-0.923810\pi$
$857$	−21.4996	+	21.4996i	−0.734411	+	0.734411i	0.237079	+	0.971490i	$0.423810\pi$
$858$		0			0
$859$	−9.98497	−	24.1059i	−0.340683	−	0.822481i	−0.997647	−	0.0685594i	$-0.978160\pi$
$859$	−9.98497	−	24.1059i	−0.340683	−	0.822481i	0.656964	−	0.753922i	$-0.271840\pi$
$860$		0			0
$861$	5.29432	+	2.19298i	0.180430	+	0.0747365i
$862$		0			0
$863$	−52.3559			−1.78222			−0.891108	−	0.453791i	$-0.850071\pi$
$863$	−52.3559			−1.78222			−0.891108	+	0.453791i	$0.850071\pi$
$864$		0			0
$865$	6.90777			0.234871
$866$		0			0
$867$	−23.2877	−	9.64610i	−0.790893	−	0.327599i
$868$		0			0
$869$	15.5690	+	37.5870i	0.528144	+	1.27505i
$870$		0			0
$871$	−6.62826	+	6.62826i	−0.224590	+	0.224590i
$872$		0			0
$873$	−7.60013	−	7.60013i	−0.257225	−	0.257225i
$874$		0			0
$875$	−0.558096	+	0.231171i	−0.0188671	+	0.00781501i
$876$		0			0
$877$	14.0543	−	33.9300i	0.474579	−	1.14574i	−0.487538	−	0.873102i	$-0.662105\pi$
$877$	14.0543	−	33.9300i	0.474579	−	1.14574i	0.962118	−	0.272635i	$-0.0878950\pi$
$878$		0			0
$879$			41.5811i			1.40250i
$880$		0			0
$881$		−	16.5899i		−	0.558928i	−0.960156	−	0.279464i	$-0.909843\pi$
$881$		−	16.5899i		−	0.558928i	0.960156	−	0.279464i	$-0.0901568\pi$
$882$		0			0
$883$	−5.08672	+	12.2804i	−0.171182	+	0.413270i	−0.986066	−	0.166354i	$-0.946800\pi$
$883$	−5.08672	+	12.2804i	−0.171182	+	0.413270i	0.814884	+	0.579624i	$0.196800\pi$
$884$		0			0
$885$	9.25635	−	3.83411i	0.311149	−	0.128882i
$886$		0			0
$887$	−0.492076	−	0.492076i	−0.0165223	−	0.0165223i	0.698797	−	0.715320i	$-0.253719\pi$
$887$	−0.492076	−	0.492076i	−0.0165223	−	0.0165223i	−0.715320	+	0.698797i	$0.753719\pi$
$888$		0			0
$889$	−6.47882	+	6.47882i	−0.217293	+	0.217293i
$890$		0			0
$891$	8.52575	+	20.5830i	0.285623	+	0.689556i
$892$		0			0
$893$	−4.32428	−	1.79117i	−0.144706	−	0.0599394i
$894$		0			0
$895$	−20.1733			−0.674319
$896$		0			0
$897$	−3.41567			−0.114046
$898$		0			0
$899$	30.0897	+	12.4636i	1.00355	+	0.415683i
$900$		0			0
$901$	−0.0495567	−	0.119641i	−0.00165097	−	0.00398580i
$902$		0			0
$903$	7.28922	−	7.28922i	0.242570	−	0.242570i
$904$		0			0
$905$	−1.08172	−	1.08172i	−0.0359575	−	0.0359575i
$906$		0			0
$907$	−32.4785	+	13.4530i	−1.07843	+	0.446701i	−0.849959	−	0.526850i	$-0.823373\pi$
$907$	−32.4785	+	13.4530i	−1.07843	+	0.446701i	−0.228473	+	0.973550i	$0.573373\pi$
$908$		0			0
$909$	−2.79014	+	6.73599i	−0.0925431	+	0.223419i
$910$		0			0
$911$			49.7306i			1.64765i	0.566845	+	0.823825i	$0.308164\pi$
$911$			49.7306i			1.64765i	−0.566845	+	0.823825i	$0.691836\pi$
$912$		0			0
$913$			59.8803i			1.98175i
$914$		0			0
$915$	−7.55803	+	18.2467i	−0.249861	+	0.603217i
$916$		0			0
$917$	−4.03105	+	1.66971i	−0.133117	+	0.0551388i
$918$		0			0
$919$	−27.1925	−	27.1925i	−0.896999	−	0.896999i	0.0981708	−	0.995170i	$-0.468701\pi$
$919$	−27.1925	−	27.1925i	−0.896999	−	0.896999i	−0.995170	+	0.0981708i	$0.968701\pi$
$920$		0			0
$921$	2.34485	−	2.34485i	0.0772655	−	0.0772655i
$922$		0			0
$923$	1.34154	+	3.23877i	0.0441575	+	0.106606i
$924$		0			0
$925$	−5.72787	−	2.37256i	−0.188331	−	0.0780094i
$926$		0			0
$927$	−7.89705			−0.259373
$928$		0			0
$929$	−12.2287			−0.401212			−0.200606	−	0.979672i	$-0.564291\pi$
$929$	−12.2287			−0.401212			−0.200606	+	0.979672i	$0.564291\pi$
$930$		0			0
$931$	−13.6983	−	5.67402i	−0.448944	−	0.185958i
$932$		0			0
$933$	3.31425	+	8.00130i	0.108504	+	0.261951i
$934$		0			0
$935$	0.0405113	−	0.0405113i	0.00132486	−	0.00132486i
$936$		0			0
$937$	−28.8548	−	28.8548i	−0.942644	−	0.942644i	0.0557978	−	0.998442i	$-0.482230\pi$
$937$	−28.8548	−	28.8548i	−0.942644	−	0.942644i	−0.998442	+	0.0557978i	$0.982230\pi$
$938$		0			0
$939$	−2.12764	+	0.881299i	−0.0694330	+	0.0287601i
$940$		0			0
$941$	3.15168	−	7.60882i	0.102742	−	0.248040i	−0.864147	−	0.503240i	$-0.832141\pi$
$941$	3.15168	−	7.60882i	0.102742	−	0.248040i	0.966888	+	0.255200i	$0.0821412\pi$
$942$		0			0
$943$			16.9133i			0.550771i
$944$		0			0
$945$			3.40495i			0.110763i
$946$		0			0
$947$	0.144481	−	0.348809i	0.00469501	−	0.0113348i	−0.921515	−	0.388344i	$-0.873047\pi$
$947$	0.144481	−	0.348809i	0.00469501	−	0.0113348i	0.926210	+	0.377009i	$0.123047\pi$
$948$		0			0
$949$	−8.31329	+	3.44348i	−0.269861	+	0.111780i
$950$		0			0
$951$	−7.69989	−	7.69989i	−0.249686	−	0.249686i
$952$		0			0
$953$	30.3920	−	30.3920i	0.984492	−	0.984492i	−0.0153897	−	0.999882i	$-0.504899\pi$
$953$	30.3920	−	30.3920i	0.984492	−	0.984492i	0.999882	+	0.0153897i	$0.00489890\pi$
$954$		0			0
$955$	−7.79161	−	18.8106i	−0.252130	−	0.608697i
$956$		0			0
$957$	−44.2262	−	18.3191i	−1.42963	−	0.592172i
$958$		0			0
$959$	−3.50215			−0.113090
$960$		0			0
$961$	−16.7481			−0.540260
$962$		0			0
$963$	−6.13049	−	2.53933i	−0.197552	−	0.0818289i
$964$		0			0
$965$	−2.66914	−	6.44388i	−0.0859228	−	0.207436i
$966$		0			0
$967$	1.78616	−	1.78616i	0.0574391	−	0.0574391i	−0.677804	−	0.735243i	$-0.737068\pi$
$967$	1.78616	−	1.78616i	0.0574391	−	0.0574391i	0.735243	+	0.677804i	$0.237068\pi$
$968$		0			0
$969$	0.0358691	+	0.0358691i	0.00115228	+	0.00115228i
$970$		0			0
$971$	16.5432	−	6.85242i	0.530897	−	0.219905i	−0.101099	−	0.994876i	$-0.532236\pi$
$971$	16.5432	−	6.85242i	0.530897	−	0.219905i	0.631996	+	0.774972i	$0.282236\pi$
$972$		0			0
$973$	−1.45825	+	3.52053i	−0.0467494	+	0.112863i
$974$		0			0
$975$			1.29205i			0.0413788i
$976$		0			0
$977$			13.5673i			0.434057i	0.976165	+	0.217029i	$0.0696365\pi$
$977$			13.5673i			0.434057i	−0.976165	+	0.217029i	$0.930364\pi$
$978$		0			0
$979$	17.2008	−	41.5264i	0.549740	−	1.32719i
$980$		0			0
$981$	−12.3608	+	5.12000i	−0.394649	+	0.163469i
$982$		0			0
$983$	16.2299	+	16.2299i	0.517655	+	0.517655i	0.916861	−	0.399206i	$-0.130714\pi$
$983$	16.2299	+	16.2299i	0.517655	+	0.517655i	−0.399206	+	0.916861i	$0.630714\pi$
$984$		0			0
$985$	−15.5631	+	15.5631i	−0.495883	+	0.495883i
$986$		0			0
$987$	−0.717954	−	1.73329i	−0.0228527	−	0.0551714i
$988$		0			0
$989$	28.1089	+	11.6431i	0.893811	+	0.370229i
$990$		0			0
$991$	−13.7716			−0.437470			−0.218735	−	0.975784i	$-0.570193\pi$
$991$	−13.7716			−0.437470			−0.218735	+	0.975784i	$0.570193\pi$
$992$		0			0
$993$	2.97759			0.0944910
$994$		0			0
$995$	4.82432	+	1.99830i	0.152941	+	0.0633503i
$996$		0			0
$997$	2.07494	+	5.00936i	0.0657141	+	0.158648i	0.953325	−	0.301946i	$-0.0976363\pi$
$997$	2.07494	+	5.00936i	0.0657141	+	0.158648i	−0.887611	+	0.460594i	$0.847636\pi$
$998$		0			0
$999$	−24.7104	+	24.7104i	−0.781803	+	0.781803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.5		64
4.3	odd	2		160.2.x.a.61.11	yes	64
20.3	even	4		800.2.ba.e.349.15		64
20.7	even	4		800.2.ba.g.349.2		64
20.19	odd	2		800.2.y.c.701.6		64
32.11	odd	8		160.2.x.a.21.11	✓	64
32.21	even	8	inner	640.2.x.a.561.5		64
160.43	even	8		800.2.ba.g.149.2		64
160.107	even	8		800.2.ba.e.149.15		64
160.139	odd	8		800.2.y.c.501.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.11	✓	64	32.11	odd	8
160.2.x.a.61.11	yes	64	4.3	odd	2
640.2.x.a.81.5		64	1.1	even	1	trivial
640.2.x.a.561.5		64	32.21	even	8	inner
800.2.y.c.501.6		64	160.139	odd	8
800.2.y.c.701.6		64	20.19	odd	2
800.2.ba.e.149.15		64	160.107	even	8
800.2.ba.e.349.15		64	20.3	even	4
800.2.ba.g.149.2		64	160.43	even	8
800.2.ba.g.349.2		64	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36989 - 0.567426i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.427148 - 0.427148i) q^{7} +(-0.566703 - 0.566703i) q^{9} +O(q^{10})\)	\(q+(-1.36989 - 0.567426i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.427148 - 0.427148i) q^{7} +(-0.566703 - 0.566703i) q^{9} +(-3.45736 + 1.43209i) q^{11} +(-0.333465 + 0.805056i) q^{13} -1.48275i q^{15} +0.0153095i q^{17} +(-0.855154 + 2.06452i) q^{19} +(-0.827520 + 0.342770i) q^{21} +(-1.86931 - 1.86931i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(2.15703 + 5.20754i) q^{27} +(-7.97042 - 3.30145i) q^{29} -3.77517 q^{31} +5.54879 q^{33} +(0.558096 + 0.231171i) q^{35} +(2.37256 + 5.72787i) q^{37} +(0.913619 - 0.913619i) q^{39} +(-4.52394 - 4.52394i) q^{41} +(-10.6328 + 4.40426i) q^{43} +(0.306698 - 0.740434i) q^{45} +2.09456i q^{47} +6.63509i q^{49} +(0.00868701 - 0.0209723i) q^{51} +(-7.81478 + 3.23699i) q^{53} +(-2.64615 - 2.64615i) q^{55} +(2.34293 - 2.34293i) q^{57} +(2.58580 + 6.24268i) q^{59} +(-12.3059 - 5.09729i) q^{61} -0.484133 q^{63} -0.871387 q^{65} +(9.93846 + 4.11664i) q^{67} +(1.50004 + 3.62143i) q^{69} +(2.84472 - 2.84472i) q^{71} +(7.30183 + 7.30183i) q^{73} +(1.36989 - 0.567426i) q^{75} +(-0.865093 + 2.08852i) q^{77} -10.8716i q^{79} -5.95338i q^{81} +(6.12342 - 14.7832i) q^{83} +(-0.0141441 + 0.00585870i) q^{85} +(9.04524 + 9.04524i) q^{87} +(-8.49306 + 8.49306i) q^{89} +(0.201439 + 0.486318i) q^{91} +(5.17156 + 2.14213i) q^{93} -2.23462 q^{95} +13.4111 q^{97} +(2.77087 + 1.14773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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