LMFDB - Embedded newform 572.2.bh.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	572.73
Dual form			572.2.bh.a.525.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.776972 + 2.39127i) q^{3} +(3.56342 + 0.564390i) q^{5} +(-0.372910 + 0.731878i) q^{7} +(-2.68746 - 1.95255i) q^{9} +O(q^{10})$	\(q+(-0.776972 + 2.39127i) q^{3} +(3.56342 + 0.564390i) q^{5} +(-0.372910 + 0.731878i) q^{7} +(-2.68746 - 1.95255i) q^{9} +(1.80041 + 2.78541i) q^{11} +(-0.795917 + 3.51661i) q^{13} +(-4.11829 + 8.08260i) q^{15} +(6.08841 - 4.42349i) q^{17} +(-2.48759 - 4.88217i) q^{19} +(-1.46038 - 1.46038i) q^{21} -2.25606i q^{23} +(7.62414 + 2.47723i) q^{25} +(0.654746 - 0.475701i) q^{27} +(-1.58095 + 0.513680i) q^{29} +(1.32405 + 8.35969i) q^{31} +(-8.05955 + 2.14109i) q^{33} +(-1.74190 + 2.39752i) q^{35} +(-6.81348 - 3.47164i) q^{37} +(-7.79076 - 4.63556i) q^{39} +(-1.56934 - 3.08001i) q^{41} -8.50352 q^{43} +(-8.47453 - 8.47453i) q^{45} +(0.815146 + 1.59981i) q^{47} +(3.71791 + 5.11727i) q^{49} +(5.84725 + 17.9960i) q^{51} +(-5.99489 - 4.35554i) q^{53} +(4.84356 + 10.9417i) q^{55} +(13.6074 - 2.15520i) q^{57} +(4.35736 + 2.22018i) q^{59} +(1.16051 + 1.59730i) q^{61} +(2.43121 - 1.23876i) q^{63} +(-4.82092 + 12.0819i) q^{65} +(-10.1682 - 10.1682i) q^{67} +(5.39486 + 1.75290i) q^{69} +(8.68606 + 1.37574i) q^{71} +(5.96570 - 11.7084i) q^{73} +(-11.8475 + 16.3067i) q^{75} +(-2.70997 + 0.278972i) q^{77} +(3.38958 - 4.66536i) q^{79} +(-2.45074 - 7.54260i) q^{81} +(0.133472 - 0.842707i) q^{83} +(24.1921 - 12.3265i) q^{85} -4.17959i q^{87} +(4.28915 - 4.28915i) q^{89} +(-2.27692 - 1.89389i) q^{91} +(-21.0191 - 3.32909i) q^{93} +(-6.10888 - 18.8012i) q^{95} +(2.43994 + 15.4052i) q^{97} +(0.600133 - 11.0011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.776972	+	2.39127i	−0.448585	+	1.38060i	0.429919	+	0.902868i	$0.358542\pi$
$3$	−0.776972	+	2.39127i	−0.448585	+	1.38060i	−0.878504	+	0.477735i	$0.841458\pi$
$4$		0			0
$5$	3.56342	+	0.564390i	1.59361	+	0.252403i	0.889244	−	0.457434i	$-0.151231\pi$
$5$	3.56342	+	0.564390i	1.59361	+	0.252403i	0.704366	+	0.709837i	$0.251231\pi$
$6$		0			0
$7$	−0.372910	+	0.731878i	−0.140947	+	0.276624i	−0.950679	−	0.310175i	$-0.899612\pi$
$7$	−0.372910	+	0.731878i	−0.140947	+	0.276624i	0.809732	+	0.586799i	$0.199612\pi$
$8$		0			0
$9$	−2.68746	−	1.95255i	−0.895819	−	0.650850i
$10$		0			0
$11$	1.80041	+	2.78541i	0.542844	+	0.839833i
$11$	1.80041	+	2.78541i	0.542844	+	0.839833i
$12$		0			0
$13$	−0.795917	+	3.51661i	−0.220748	+	0.975331i
$13$	−0.795917	+	3.51661i	−0.220748	+	0.975331i
$14$		0			0
$15$	−4.11829	+	8.08260i	−1.06334	+	2.08692i
$16$		0			0
$17$	6.08841	−	4.42349i	1.47666	−	1.07285i	0.498041	−	0.867154i	$-0.334053\pi$
$17$	6.08841	−	4.42349i	1.47666	−	1.07285i	0.978615	−	0.205699i	$-0.0659469\pi$
$18$		0			0
$19$	−2.48759	−	4.88217i	−0.570693	−	1.12005i	−0.978359	−	0.206916i	$-0.933657\pi$
$19$	−2.48759	−	4.88217i	−0.570693	−	1.12005i	0.407666	−	0.913131i	$-0.366343\pi$
$20$		0			0
$21$	−1.46038	−	1.46038i	−0.318681	−	0.318681i
$22$		0			0
$23$		−	2.25606i		−	0.470421i	−0.971944	−	0.235211i	$-0.924422\pi$
$23$		−	2.25606i		−	0.470421i	0.971944	−	0.235211i	$-0.0755780\pi$
$24$		0			0
$25$	7.62414	+	2.47723i	1.52483	+	0.495446i
$26$		0			0
$27$	0.654746	−	0.475701i	0.126006	−	0.0915486i
$28$		0			0
$29$	−1.58095	+	0.513680i	−0.293574	+	0.0953880i	−0.452101	−	0.891967i	$-0.649325\pi$
$29$	−1.58095	+	0.513680i	−0.293574	+	0.0953880i	0.158527	+	0.987355i	$0.449325\pi$
$30$		0			0
$31$	1.32405	+	8.35969i	0.237806	+	1.50144i	0.760731	+	0.649067i	$0.224840\pi$
$31$	1.32405	+	8.35969i	0.237806	+	1.50144i	−0.522926	+	0.852378i	$0.675160\pi$
$32$		0			0
$33$	−8.05955	+	2.14109i	−1.40299	+	0.372716i
$34$		0			0
$35$	−1.74190	+	2.39752i	−0.294435	+	0.405255i
$36$		0			0
$37$	−6.81348	−	3.47164i	−1.12013	−	0.570734i	−0.206974	−	0.978347i	$-0.566361\pi$
$37$	−6.81348	−	3.47164i	−1.12013	−	0.570734i	−0.913155	+	0.407612i	$0.866361\pi$
$38$		0			0
$39$	−7.79076	−	4.63556i	−1.24752	−	0.742284i
$40$		0			0
$41$	−1.56934	−	3.08001i	−0.245090	−	0.481016i	0.735388	−	0.677647i	$-0.237000\pi$
$41$	−1.56934	−	3.08001i	−0.245090	−	0.481016i	−0.980478	+	0.196630i	$0.937000\pi$
$42$		0			0
$43$	−8.50352			−1.29677			−0.648387	−	0.761311i	$-0.724556\pi$
$43$	−8.50352			−1.29677			−0.648387	+	0.761311i	$0.724556\pi$
$44$		0			0
$45$	−8.47453	−	8.47453i	−1.26331	−	1.26331i
$46$		0			0
$47$	0.815146	+	1.59981i	0.118901	+	0.233357i	0.942785	−	0.333403i	$-0.108197\pi$
$47$	0.815146	+	1.59981i	0.118901	+	0.233357i	−0.823883	+	0.566760i	$0.808197\pi$
$48$		0			0
$49$	3.71791	+	5.11727i	0.531131	+	0.731038i
$50$		0			0
$51$	5.84725	+	17.9960i	0.818779	+	2.51994i
$52$		0			0
$53$	−5.99489	−	4.35554i	−0.823462	−	0.598280i	0.0942402	−	0.995549i	$-0.469958\pi$
$53$	−5.99489	−	4.35554i	−0.823462	−	0.598280i	−0.917702	+	0.397269i	$0.869958\pi$
$54$		0			0
$55$	4.84356	+	10.9417i	0.653106	+	1.47538i
$56$		0			0
$57$	13.6074	−	2.15520i	1.80234	−	0.285463i
$58$		0			0
$59$	4.35736	+	2.22018i	0.567280	+	0.289043i	0.714013	−	0.700133i	$-0.246876\pi$
$59$	4.35736	+	2.22018i	0.567280	+	0.289043i	−0.146733	+	0.989176i	$0.546876\pi$
$60$		0			0
$61$	1.16051	+	1.59730i	0.148588	+	0.204513i	0.876822	−	0.480814i	$-0.159659\pi$
$61$	1.16051	+	1.59730i	0.148588	+	0.204513i	−0.728235	+	0.685328i	$0.759659\pi$
$62$		0			0
$63$	2.43121	−	1.23876i	0.306304	−	0.156070i
$64$		0			0
$65$	−4.82092	+	12.0819i	−0.597962	+	1.49858i
$66$		0			0
$67$	−10.1682	−	10.1682i	−1.24224	−	1.24224i	−0.959070	−	0.283169i	$-0.908614\pi$
$67$	−10.1682	−	10.1682i	−1.24224	−	1.24224i	−0.283169	−	0.959070i	$-0.591386\pi$
$68$		0			0
$69$	5.39486	+	1.75290i	0.649465	+	0.211024i
$70$		0			0
$71$	8.68606	+	1.37574i	1.03085	+	0.163270i	0.648868	−	0.760901i	$-0.275243\pi$
$71$	8.68606	+	1.37574i	1.03085	+	0.163270i	0.381978	+	0.924171i	$0.375243\pi$
$72$		0			0
$73$	5.96570	−	11.7084i	0.698233	−	1.37036i	−0.220464	−	0.975395i	$-0.570757\pi$
$73$	5.96570	−	11.7084i	0.698233	−	1.37036i	0.918697	−	0.394964i	$-0.129243\pi$
$74$		0			0
$75$	−11.8475	+	16.3067i	−1.36803	+	1.88293i
$76$		0			0
$77$	−2.70997	+	0.278972i	−0.308830	+	0.0317918i
$78$		0			0
$79$	3.38958	−	4.66536i	0.381358	−	0.524894i	−0.574586	−	0.818444i	$-0.694837\pi$
$79$	3.38958	−	4.66536i	0.381358	−	0.524894i	0.955944	+	0.293550i	$0.0948368\pi$
$80$		0			0
$81$	−2.45074	−	7.54260i	−0.272304	−	0.838067i
$82$		0			0
$83$	0.133472	−	0.842707i	0.0146504	−	0.0924991i	−0.979280	−	0.202512i	$-0.935089\pi$
$83$	0.133472	−	0.842707i	0.0146504	−	0.0924991i	0.993930	+	0.110013i	$0.0350894\pi$
$84$		0			0
$85$	24.1921	−	12.3265i	2.62400	−	1.33700i
$86$		0			0
$87$		−	4.17959i		−	0.448099i
$88$		0			0
$89$	4.28915	−	4.28915i	0.454649	−	0.454649i	−0.442245	−	0.896894i	$-0.645818\pi$
$89$	4.28915	−	4.28915i	0.454649	−	0.454649i	0.896894	+	0.442245i	$0.145818\pi$
$90$		0			0
$91$	−2.27692	−	1.89389i	−0.238686	−	0.198534i
$92$		0			0
$93$	−21.0191	−	3.32909i	−2.17958	−	0.345211i
$94$		0			0
$95$	−6.10888	−	18.8012i	−0.626758	−	1.92896i
$96$		0			0
$97$	2.43994	+	15.4052i	0.247739	+	1.56416i	0.727093	+	0.686539i	$0.240871\pi$
$97$	2.43994	+	15.4052i	0.247739	+	1.56416i	−0.479355	+	0.877621i	$0.659129\pi$
$98$		0			0
$99$	0.600133	−	11.0011i	0.0603156	−	1.10565i
$100$		0			0
$101$	3.06581	+	2.22744i	0.305060	+	0.221639i	0.729774	−	0.683689i	$-0.239625\pi$
$101$	3.06581	+	2.22744i	0.305060	+	0.221639i	−0.424714	+	0.905328i	$0.639625\pi$
$102$		0			0
$103$	16.4555	−	5.34672i	1.62141	−	0.526828i	0.649137	−	0.760672i	$-0.275130\pi$
$103$	16.4555	−	5.34672i	1.62141	−	0.526828i	0.972274	+	0.233843i	$0.0751302\pi$
$104$		0			0
$105$	−4.37972	−	6.02817i	−0.427417	−	0.588289i
$106$		0			0
$107$	0.149952	+	0.0487223i	0.0144964	+	0.00471016i	0.316256	−	0.948674i	$-0.397574\pi$
$107$	0.149952	+	0.0487223i	0.0144964	+	0.00471016i	−0.301760	+	0.953384i	$0.597574\pi$
$108$		0			0
$109$	7.62923	−	7.62923i	0.730748	−	0.730748i	−0.240020	−	0.970768i	$-0.577154\pi$
$109$	7.62923	−	7.62923i	0.730748	−	0.730748i	0.970768	+	0.240020i	$0.0771541\pi$
$110$		0			0
$111$	13.5955	−	13.5955i	1.29043	−	1.29043i
$112$		0			0
$113$	−3.51273	+	10.8111i	−0.330450	+	1.01702i	0.638471	+	0.769646i	$0.279567\pi$
$113$	−3.51273	+	10.8111i	−0.330450	+	1.01702i	−0.968920	+	0.247373i	$0.920433\pi$
$114$		0			0
$115$	1.27330	−	8.03929i	0.118736	−	0.749668i
$116$		0			0
$117$	9.00534	−	7.89666i	0.832544	−	0.730046i
$118$		0			0
$119$	0.967022	+	6.10554i	0.0886468	+	0.559694i
$120$		0			0
$121$	−4.51704	+	10.0298i	−0.410640	+	0.911798i
$122$		0			0
$123$	8.58448	−	1.35965i	0.774036	−	0.122595i
$124$		0			0
$125$	9.69683	+	4.94078i	0.867311	+	0.441917i
$126$		0			0
$127$	9.45356	−	6.86841i	0.838867	−	0.609473i	−0.0831867	−	0.996534i	$-0.526510\pi$
$127$	9.45356	−	6.86841i	0.838867	−	0.609473i	0.922054	+	0.387061i	$0.126510\pi$
$128$		0			0
$129$	6.60700	−	20.3342i	0.581714	−	1.79033i
$130$		0			0
$131$		−	13.8778i		−	1.21251i	−0.795269	−	0.606256i	$-0.792671\pi$
$131$		−	13.8778i		−	1.21251i	0.795269	−	0.606256i	$-0.207329\pi$
$132$		0			0
$133$	4.50080			0.390269
$134$		0			0
$135$	2.60161	−	1.32559i	0.223911	−	0.114089i
$136$		0			0
$137$	−0.701397	+	4.42845i	−0.0599244	+	0.378348i	0.939440	+	0.342712i	$0.111346\pi$
$137$	−0.701397	+	4.42845i	−0.0599244	+	0.378348i	−0.999365	+	0.0356356i	$0.988654\pi$
$138$		0			0
$139$	−6.56621	+	2.13349i	−0.556939	+	0.180960i	−0.573943	−	0.818895i	$-0.694587\pi$
$139$	−6.56621	+	2.13349i	−0.556939	+	0.180960i	0.0170045	+	0.999855i	$0.494587\pi$
$140$		0			0
$141$	−4.45894	+	0.706227i	−0.375511	+	0.0594750i
$142$		0			0
$143$	−11.2282	+	4.11438i	−0.938947	+	0.344062i
$144$		0			0
$145$	−5.92349	+	0.938188i	−0.491919	+	0.0779123i
$146$		0			0
$147$	−15.1255	+	4.91458i	−1.24753	+	0.405347i
$148$		0			0
$149$	−0.938892	+	5.92793i	−0.0769170	+	0.485635i	0.918917	+	0.394451i	$0.129065\pi$
$149$	−0.938892	+	5.92793i	−0.0769170	+	0.485635i	−0.995834	+	0.0911840i	$0.970935\pi$
$150$		0			0
$151$	7.92980	−	4.04044i	0.645318	−	0.328806i	−0.100518	−	0.994935i	$-0.532050\pi$
$151$	7.92980	−	4.04044i	0.645318	−	0.328806i	0.745836	+	0.666129i	$0.232050\pi$
$152$		0			0
$153$	−24.9994			−2.02108
$154$		0			0
$155$			30.5364i			2.45274i
$156$		0			0
$157$	1.22675	−	3.77554i	0.0979050	−	0.301321i	−0.890095	−	0.455775i	$-0.849362\pi$
$157$	1.22675	−	3.77554i	0.0979050	−	0.301321i	0.988000	+	0.154455i	$0.0493621\pi$
$158$		0			0
$159$	15.0732	−	10.9513i	1.19538	−	0.868494i
$160$		0			0
$161$	1.65116	+	0.841309i	0.130130	+	0.0663044i
$162$		0			0
$163$	−2.36668	+	0.374845i	−0.185373	+	0.0293602i	−0.248431	−	0.968650i	$-0.579915\pi$
$163$	−2.36668	+	0.374845i	−0.185373	+	0.0293602i	0.0630578	+	0.998010i	$0.479915\pi$
$164$		0			0
$165$	−29.9280	+	3.08087i	−2.32989	+	0.239845i
$166$		0			0
$167$	0.350811	+	2.21493i	0.0271466	+	0.171397i	0.997537	−	0.0701462i	$-0.0223466\pi$
$167$	0.350811	+	2.21493i	0.0271466	+	0.171397i	−0.970390	+	0.241543i	$0.922347\pi$
$168$		0			0
$169$	−11.7330	−	5.59785i	−0.902541	−	0.430604i
$170$		0			0
$171$	−2.84740	+	17.9778i	−0.217746	+	1.37479i
$172$		0			0
$173$	−0.0887153	+	0.273038i	−0.00674490	+	0.0207587i	−0.954372	−	0.298619i	$-0.903474\pi$
$173$	−0.0887153	+	0.273038i	−0.00674490	+	0.0207587i	0.947627	+	0.319378i	$0.103474\pi$
$174$		0			0
$175$	−4.65615	+	4.65615i	−0.351972	+	0.351972i
$176$		0			0
$177$	−8.69462	+	8.69462i	−0.653527	+	0.653527i
$178$		0			0
$179$	15.2860	+	4.96671i	1.14253	+	0.371230i	0.818324	−	0.574758i	$-0.194904\pi$
$179$	15.2860	+	4.96671i	1.14253	+	0.371230i	0.324204	+	0.945987i	$0.394904\pi$
$180$		0			0
$181$	−2.31444	−	3.18556i	−0.172031	−	0.236781i	0.714292	−	0.699848i	$-0.246749\pi$
$181$	−2.31444	−	3.18556i	−0.172031	−	0.236781i	−0.886323	+	0.463067i	$0.846749\pi$
$182$		0			0
$183$	−4.72126	+	1.53403i	−0.349006	+	0.113399i
$184$		0			0
$185$	−22.3199	−	16.2164i	−1.64099	−	1.19225i
$186$		0			0
$187$	23.2829	+	8.99463i	1.70261	+	0.657752i
$188$		0			0
$189$	0.103993	+	0.656588i	0.00756440	+	0.0477597i
$190$		0			0
$191$	0.148730	+	0.457744i	0.0107617	+	0.0331212i	0.956293	−	0.292410i	$-0.0944570\pi$
$191$	0.148730	+	0.457744i	0.0107617	+	0.0331212i	−0.945531	+	0.325531i	$0.894457\pi$
$192$		0			0
$193$	16.7993	+	2.66075i	1.20924	+	0.191525i	0.728319	−	0.685238i	$-0.240302\pi$
$193$	16.7993	+	2.66075i	1.20924	+	0.191525i	0.480923	+	0.876763i	$0.340302\pi$
$194$		0			0
$195$	−25.1455	−	20.9155i	−1.80071	−	1.49779i
$196$		0			0
$197$	8.04857	−	8.04857i	0.573437	−	0.573437i	−0.359651	−	0.933087i	$-0.617104\pi$
$197$	8.04857	−	8.04857i	0.573437	−	0.573437i	0.933087	+	0.359651i	$0.117104\pi$
$198$		0			0
$199$		−	4.13096i		−	0.292836i	−0.989223	−	0.146418i	$-0.953226\pi$
$199$		−	4.13096i		−	0.292836i	0.989223	−	0.146418i	$-0.0467745\pi$
$200$		0			0
$201$	32.2152	−	16.4145i	2.27229	−	1.15779i
$202$		0			0
$203$	0.213600	−	1.34862i	0.0149918	−	0.0946543i
$204$		0			0
$205$	−3.85390	−	11.8611i	−0.269168	−	0.828414i
$206$		0			0
$207$	−4.40508	+	6.06307i	−0.306174	+	0.421412i
$208$		0			0
$209$	9.12018	−	15.7189i	0.630856	−	1.08730i
$210$		0			0
$211$	−4.79877	+	6.60495i	−0.330361	+	0.454703i	−0.941595	−	0.336747i	$-0.890673\pi$
$211$	−4.79877	+	6.60495i	−0.330361	+	0.454703i	0.611234	+	0.791450i	$0.290673\pi$
$212$		0			0
$213$	−10.0386	+	19.7018i	−0.687833	+	1.34995i
$214$		0			0
$215$	−30.3016	−	4.79930i	−2.06655	−	0.327310i
$216$		0			0
$217$	−6.61202	−	2.14838i	−0.448853	−	0.145841i
$218$		0			0
$219$	23.3627	+	23.3627i	1.57871	+	1.57871i
$220$		0			0
$221$	10.7098	+	24.9313i	0.720419	+	1.67706i
$222$		0			0
$223$	−14.2656	+	7.26868i	−0.955294	+	0.486747i	−0.860892	−	0.508787i	$-0.830094\pi$
$223$	−14.2656	+	7.26868i	−0.955294	+	0.486747i	−0.0944022	+	0.995534i	$0.530094\pi$
$224$		0			0
$225$	−15.6526	−	21.5440i	−1.04351	−	1.43626i
$226$		0			0
$227$	−22.9009	−	11.6686i	−1.51998	−	0.774471i	−0.523020	−	0.852321i	$-0.675195\pi$
$227$	−22.9009	−	11.6686i	−1.51998	−	0.774471i	−0.996965	+	0.0778498i	$0.975195\pi$
$228$		0			0
$229$	19.3197	−	3.05994i	1.27668	−	0.202206i	0.518968	−	0.854794i	$-0.326317\pi$
$229$	19.3197	−	3.05994i	1.27668	−	0.202206i	0.757713	+	0.652587i	$0.226317\pi$
$230$		0			0
$231$	1.43848	−	6.69704i	0.0946447	−	0.440633i
$232$		0			0
$233$	−20.8385	−	15.1401i	−1.36518	−	0.991859i	−0.998097	−	0.0616699i	$-0.980357\pi$
$233$	−20.8385	−	15.1401i	−1.36518	−	0.991859i	−0.367080	−	0.930189i	$-0.619643\pi$
$234$		0			0
$235$	2.00179	+	6.16087i	0.130582	+	0.401891i
$236$		0			0
$237$	8.52255	+	11.7303i	0.553599	+	0.761964i
$238$		0			0
$239$	1.60963	+	3.15907i	0.104118	+	0.204343i	0.937188	−	0.348824i	$-0.113419\pi$
$239$	1.60963	+	3.15907i	0.104118	+	0.204343i	−0.833070	+	0.553168i	$0.813419\pi$
$240$		0			0
$241$	−3.44958	−	3.44958i	−0.222207	−	0.222207i	0.587220	−	0.809427i	$-0.300222\pi$
$241$	−3.44958	−	3.44958i	−0.222207	−	0.222207i	−0.809427	+	0.587220i	$0.800222\pi$
$242$		0			0
$243$	22.3685			1.43494
$244$		0			0
$245$	10.3603	+	20.3333i	0.661898	+	1.29905i
$246$		0			0
$247$	19.1486	−	4.86207i	1.21840	−	0.309366i
$248$		0			0
$249$	1.91144	+	0.973927i	0.121133	+	0.0617201i
$250$		0			0
$251$	2.32807	−	3.20432i	0.146947	−	0.202255i	−0.729198	−	0.684302i	$-0.760107\pi$
$251$	2.32807	−	3.20432i	0.146947	−	0.202255i	0.876145	+	0.482048i	$0.160107\pi$
$252$		0			0
$253$	6.28406	−	4.06184i	0.395075	−	0.255366i
$254$		0			0
$255$	10.6794	+	67.4273i	0.668773	+	4.22246i
$256$		0			0
$257$	−18.7852	+	6.10368i	−1.17179	+	0.380737i	−0.829310	−	0.558789i	$-0.811266\pi$
$257$	−18.7852	+	6.10368i	−1.17179	+	0.380737i	−0.342478	+	0.939526i	$0.611266\pi$
$258$		0			0
$259$	5.08163	−	3.69202i	0.315757	−	0.229411i
$260$		0			0
$261$	5.25171	+	1.70638i	0.325073	+	0.105623i
$262$		0			0
$263$			1.48206i			0.0913877i	0.998955	+	0.0456938i	$0.0145499\pi$
$263$			1.48206i			0.0913877i	−0.998955	+	0.0456938i	$0.985450\pi$
$264$		0			0
$265$	−18.9041	−	18.9041i	−1.16127	−	1.16127i
$266$		0			0
$267$	6.92398	+	13.5891i	0.423741	+	0.831638i
$268$		0			0
$269$	−22.8646	+	16.6121i	−1.39408	+	1.01286i	−0.398673	+	0.917093i	$0.630529\pi$
$269$	−22.8646	+	16.6121i	−1.39408	+	1.01286i	−0.995404	+	0.0957628i	$0.969471\pi$
$270$		0			0
$271$	9.28253	−	18.2180i	0.563874	−	1.10666i	−0.416430	−	0.909168i	$-0.636719\pi$
$271$	9.28253	−	18.2180i	0.563874	−	1.10666i	0.980304	−	0.197496i	$-0.0632811\pi$
$272$		0			0
$273$	6.29792	−	3.97324i	0.381168	−	0.240471i
$274$		0			0
$275$	6.82647	+	25.6964i	0.411652	+	1.54955i
$276$		0			0
$277$	−6.58420	−	4.78370i	−0.395606	−	0.287425i	0.372143	−	0.928176i	$-0.378623\pi$
$277$	−6.58420	−	4.78370i	−0.395606	−	0.287425i	−0.767749	+	0.640751i	$0.778623\pi$
$278$		0			0
$279$	12.7644	−	25.0516i	0.764185	−	1.49980i
$280$		0			0
$281$	4.74403	+	0.751380i	0.283005	+	0.0448236i	0.296323	−	0.955088i	$-0.404239\pi$
$281$	4.74403	+	0.751380i	0.283005	+	0.0448236i	−0.0133182	+	0.999911i	$0.504239\pi$
$282$		0			0
$283$	9.89177	−	30.4437i	0.588005	−	1.80969i	0.00115163	−	0.999999i	$-0.499633\pi$
$283$	9.89177	−	30.4437i	0.588005	−	1.80969i	0.586853	−	0.809693i	$-0.300367\pi$
$284$		0			0
$285$	49.7053			2.94429
$286$		0			0
$287$	2.83941			0.167605
$288$		0			0
$289$	12.2482	−	37.6960i	0.720481	−	2.21741i
$290$		0			0
$291$	−38.7338	−	6.13483i	−2.27062	−	0.359630i
$292$		0			0
$293$	−13.4517	+	26.4004i	−0.785854	+	1.54233i	0.0533914	+	0.998574i	$0.482997\pi$
$293$	−13.4517	+	26.4004i	−0.785854	+	1.54233i	−0.839246	+	0.543752i	$0.817003\pi$
$294$		0			0
$295$	14.2740	+	10.3707i	0.831067	+	0.603805i
$296$		0			0
$297$	2.50383	+	0.967280i	0.145287	+	0.0561273i
$298$		0			0
$299$	7.93368	+	1.79564i	0.458816	+	0.103844i
$300$		0			0
$301$	3.17105	−	6.22354i	0.182776	−	0.358719i
$302$		0			0
$303$	−7.70847	+	5.60053i	−0.442840	+	0.321742i
$304$		0			0
$305$	3.23387	+	6.34683i	0.185171	+	0.363418i
$306$		0			0
$307$	5.83186	+	5.83186i	0.332842	+	0.332842i	0.853665	−	0.520823i	$-0.174375\pi$
$307$	5.83186	+	5.83186i	0.332842	+	0.332842i	−0.520823	+	0.853665i	$0.674375\pi$
$308$		0			0
$309$			43.5039i			2.47485i
$310$		0			0
$311$	−1.47652	−	0.479751i	−0.0837259	−	0.0272042i	0.266855	−	0.963737i	$-0.414016\pi$
$311$	−1.47652	−	0.479751i	−0.0837259	−	0.0272042i	−0.350580	+	0.936533i	$0.614016\pi$
$312$		0			0
$313$	−4.73924	+	3.44326i	−0.267877	+	0.194624i	−0.713613	−	0.700541i	$-0.752942\pi$
$313$	−4.73924	+	3.44326i	−0.267877	+	0.194624i	0.445735	+	0.895165i	$0.352942\pi$
$314$		0			0
$315$	9.36256	−	3.04208i	0.527521	−	0.171402i
$316$		0			0
$317$	0.0292328	+	0.184569i	0.00164188	+	0.0103664i	0.988496	−	0.151249i	$-0.0483296\pi$
$317$	0.0292328	+	0.184569i	0.00164188	+	0.0103664i	−0.986854	+	0.161616i	$0.948330\pi$
$318$		0			0
$319$	−4.27716	−	3.47875i	−0.239475	−	0.194773i
$320$		0			0
$321$	−0.233017	+	0.320720i	−0.0130057	+	0.0179008i
$322$		0			0
$323$	−36.7417	−	18.7208i	−2.04436	−	1.04166i
$324$		0			0
$325$	−14.7796	+	24.8394i	−0.819826	+	1.37784i
$326$		0			0
$327$	12.3159	+	24.1713i	0.681070	+	1.33667i
$328$		0			0
$329$	−1.47485			−0.0813109
$330$		0			0
$331$	5.70022	+	5.70022i	0.313312	+	0.313312i	0.846191	−	0.532879i	$-0.178890\pi$
$331$	5.70022	+	5.70022i	0.313312	+	0.313312i	−0.532879	+	0.846191i	$0.678890\pi$
$332$		0			0
$333$	11.5324	+	22.6335i	0.631970	+	1.24031i
$334$		0			0
$335$	−30.4946	−	41.9722i	−1.66610	−	2.29319i
$336$		0			0
$337$	6.31722	+	19.4424i	0.344121	+	1.05909i	0.962053	+	0.272863i	$0.0879706\pi$
$337$	6.31722	+	19.4424i	0.344121	+	1.05909i	−0.617932	+	0.786231i	$0.712029\pi$
$338$		0			0
$339$	−23.1229	−	16.7998i	−1.25587	−	0.912439i
$340$		0			0
$341$	−20.9014	+	18.7389i	−1.13187	+	1.01477i
$342$		0			0
$343$	−10.8107	+	1.71225i	−0.583724	+	0.0924528i
$344$		0			0
$345$	18.2348	+	9.29111i	0.981731	+	0.500217i
$346$		0			0
$347$	2.81505	+	3.87459i	0.151120	+	0.207999i	0.877865	−	0.478909i	$-0.158968\pi$
$347$	2.81505	+	3.87459i	0.151120	+	0.207999i	−0.726745	+	0.686908i	$0.758968\pi$
$348$		0			0
$349$	−18.7488	+	9.55298i	−1.00360	+	0.511359i	−0.876947	−	0.480588i	$-0.840423\pi$
$349$	−18.7488	+	9.55298i	−1.00360	+	0.511359i	−0.126653	+	0.991947i	$0.540423\pi$
$350$		0			0
$351$	1.15173	+	2.68110i	0.0614747	+	0.143107i
$352$		0			0
$353$	1.36291	+	1.36291i	0.0725404	+	0.0725404i	0.742446	−	0.669906i	$-0.233666\pi$
$353$	1.36291	+	1.36291i	0.0725404	+	0.0725404i	−0.669906	+	0.742446i	$0.733666\pi$
$354$		0			0
$355$	30.1756	+	9.80465i	1.60156	+	0.520377i
$356$		0			0
$357$	−15.3514	−	2.43142i	−0.812480	−	0.128684i
$358$		0			0
$359$	−15.4405	+	30.3036i	−0.814917	+	1.59936i	−0.0145198	+	0.999895i	$0.504622\pi$
$359$	−15.4405	+	30.3036i	−0.814917	+	1.59936i	−0.800397	+	0.599470i	$0.795378\pi$
$360$		0			0
$361$	−6.47959	+	8.91838i	−0.341031	+	0.469389i
$362$		0			0
$363$	−20.4743	−	18.5943i	−1.07462	−	0.975949i
$364$		0			0
$365$	27.8664	−	38.3548i	1.45859	−	2.00758i
$366$		0			0
$367$	−3.84578	−	11.8361i	−0.200748	−	0.617839i	−0.999861	−	0.0166582i	$-0.994697\pi$
$367$	−3.84578	−	11.8361i	−0.200748	−	0.617839i	0.799113	−	0.601180i	$-0.205303\pi$
$368$		0			0
$369$	−1.79633	+	11.3416i	−0.0935134	+	0.590421i
$370$		0			0
$371$	5.42329	−	2.76330i	0.281563	−	0.143463i
$372$		0			0
$373$			25.4647i			1.31851i	0.751919	+	0.659255i	$0.229128\pi$
$373$			25.4647i			1.31851i	−0.751919	+	0.659255i	$0.770872\pi$
$374$		0			0
$375$	−19.3489	+	19.3489i	−0.999175	+	0.999175i
$376$		0			0
$377$	−0.548110	−	5.96841i	−0.0282291	−	0.307389i
$378$		0			0
$379$	−3.19050	−	0.505325i	−0.163885	−	0.0259568i	0.0739527	−	0.997262i	$-0.476439\pi$
$379$	−3.19050	−	0.505325i	−0.163885	−	0.0259568i	−0.237838	+	0.971305i	$0.576439\pi$
$380$		0			0
$381$	9.07910	+	27.9426i	0.465137	+	1.43154i
$382$		0			0
$383$	−0.0665171	−	0.419973i	−0.00339887	−	0.0214596i	0.985931	−	0.167155i	$-0.0534580\pi$
$383$	−0.0665171	−	0.419973i	−0.00339887	−	0.0214596i	−0.989329	+	0.145695i	$0.953458\pi$
$384$		0			0
$385$	−9.81422	−	0.535388i	−0.500179	−	0.0272859i
$386$		0			0
$387$	22.8528	+	16.6036i	1.16168	+	0.844006i
$388$		0			0
$389$	16.5688	−	5.38352i	0.840070	−	0.272955i	0.142789	−	0.989753i	$-0.454393\pi$
$389$	16.5688	−	5.38352i	0.840070	−	0.272955i	0.697281	+	0.716798i	$0.254393\pi$
$390$		0			0
$391$	−9.97966	−	13.7358i	−0.504693	−	0.694650i
$392$		0			0
$393$	33.1857	+	10.7827i	1.67400	+	0.543915i
$394$		0			0
$395$	14.7116	−	14.7116i	0.740221	−	0.740221i
$396$		0			0
$397$	10.8634	−	10.8634i	0.545218	−	0.545218i	−0.379836	−	0.925054i	$-0.624020\pi$
$397$	10.8634	−	10.8634i	0.545218	−	0.545218i	0.925054	+	0.379836i	$0.124020\pi$
$398$		0			0
$399$	−3.49700	+	10.7627i	−0.175069	+	0.538807i
$400$		0			0
$401$	−1.87475	+	11.8367i	−0.0936203	+	0.591095i	0.895623	+	0.444814i	$0.146730\pi$
$401$	−1.87475	+	11.8367i	−0.0936203	+	0.591095i	−0.989243	+	0.146281i	$0.953270\pi$
$402$		0			0
$403$	−30.4516	−	1.99748i	−1.51690	−	0.0995013i
$404$		0			0
$405$	−4.47604	−	28.2606i	−0.222416	−	1.40428i
$406$		0			0
$407$	−2.59711	−	25.2287i	−0.128734	−	1.25054i
$408$		0			0
$409$	14.3640	−	2.27503i	0.710253	−	0.112493i	0.209154	−	0.977883i	$-0.432929\pi$
$409$	14.3640	−	2.27503i	0.710253	−	0.112493i	0.501100	+	0.865390i	$0.332929\pi$
$410$		0			0
$411$	−10.0447	−	5.11801i	−0.495467	−	0.252453i
$412$		0			0
$413$	−3.24981	+	2.36112i	−0.159913	+	0.116183i
$414$		0			0
$415$	0.951231	−	2.92759i	0.0466941	−	0.143710i
$416$		0			0
$417$		−	17.3593i		−	0.850087i
$418$		0			0
$419$	−26.7053			−1.30464			−0.652319	−	0.757944i	$-0.726204\pi$
$419$	−26.7053			−1.30464			−0.652319	+	0.757944i	$0.726204\pi$
$420$		0			0
$421$	−20.9167	+	10.6576i	−1.01942	+	0.519418i	−0.882077	−	0.471106i	$-0.843855\pi$
$421$	−20.9167	+	10.6576i	−1.01942	+	0.519418i	−0.137339	+	0.990524i	$0.543855\pi$
$422$		0			0
$423$	0.933050	−	5.89105i	0.0453664	−	0.286432i
$424$		0			0
$425$	57.3769	−	18.6429i	2.78319	−	0.904312i
$426$		0			0
$427$	−1.60179	+	0.253699i	−0.0775162	+	0.0122774i
$428$		0			0
$429$	−1.11463	−	30.0464i	−0.0538151	−	1.45065i
$430$		0			0
$431$	3.63192	−	0.575240i	0.174944	−	0.0277084i	−0.0683479	−	0.997662i	$-0.521773\pi$
$431$	3.63192	−	0.575240i	0.174944	−	0.0277084i	0.243292	+	0.969953i	$0.421773\pi$
$432$		0			0
$433$	−36.4386	+	11.8396i	−1.75113	+	0.568975i	−0.996221	−	0.0868590i	$-0.972317\pi$
$433$	−36.4386	+	11.8396i	−1.75113	+	0.568975i	−0.754905	+	0.655834i	$0.772317\pi$
$434$		0			0
$435$	2.35892	−	14.8936i	0.113102	−	0.714095i
$436$		0			0
$437$	−11.0145	+	5.61216i	−0.526894	+	0.268466i
$438$		0			0
$439$	−19.7529			−0.942755			−0.471378	−	0.881932i	$-0.656243\pi$
$439$	−19.7529			−0.942755			−0.471378	+	0.881932i	$0.656243\pi$
$440$		0			0
$441$		−	21.0119i		−	1.00056i
$442$		0			0
$443$	−5.46701	+	16.8257i	−0.259745	+	0.799414i	0.733112	+	0.680108i	$0.238067\pi$
$443$	−5.46701	+	16.8257i	−0.259745	+	0.799414i	−0.992858	+	0.119306i	$0.961933\pi$
$444$		0			0
$445$	17.7048	−	12.8633i	0.839287	−	0.609778i
$446$		0			0
$447$	−13.4458	−	6.85098i	−0.635965	−	0.324040i
$448$		0			0
$449$	8.97254	−	1.42111i	0.423440	−	0.0670663i	0.0589219	−	0.998263i	$-0.481234\pi$
$449$	8.97254	−	1.42111i	0.423440	−	0.0670663i	0.364518	+	0.931196i	$0.381234\pi$
$450$		0			0
$451$	5.75363	−	9.91655i	0.270928	−	0.466952i
$452$		0			0
$453$	3.50056	+	22.1016i	0.164470	+	1.03843i
$454$		0			0
$455$	−7.04473	−	8.03381i	−0.330262	−	0.376631i
$456$		0			0
$457$	−0.975788	+	6.16088i	−0.0456454	+	0.288194i	−0.999943	−	0.0106638i	$-0.996606\pi$
$457$	−0.975788	+	6.16088i	−0.0456454	+	0.288194i	0.954298	+	0.298858i	$0.0966056\pi$
$458$		0			0
$459$	1.88210	−	5.79252i	0.0878491	−	0.270372i
$460$		0			0
$461$	22.5445	−	22.5445i	1.05000	−	1.05000i	0.0513193	−	0.998682i	$-0.483657\pi$
$461$	22.5445	−	22.5445i	1.05000	−	1.05000i	0.998682	−	0.0513193i	$-0.0163426\pi$
$462$		0			0
$463$	−12.1259	+	12.1259i	−0.563540	+	0.563540i	−0.930311	−	0.366771i	$-0.880463\pi$
$463$	−12.1259	+	12.1259i	−0.563540	+	0.563540i	0.366771	+	0.930311i	$0.380463\pi$
$464$		0			0
$465$	−73.0208	−	23.7259i	−3.38626	−	1.10026i
$466$		0			0
$467$	−22.9557	−	31.5958i	−1.06226	−	1.46208i	−0.877671	−	0.479263i	$-0.840904\pi$
$467$	−22.9557	−	31.5958i	−1.06226	−	1.46208i	−0.184591	−	0.982815i	$-0.559096\pi$
$468$		0			0
$469$	11.2337	−	3.65004i	0.518723	−	0.168543i
$470$		0			0
$471$	8.07519	+	5.86697i	0.372085	+	0.270336i
$472$		0			0
$473$	−15.3098	−	23.6858i	−0.703947	−	1.08907i
$474$		0			0
$475$	−6.87146	−	43.3847i	−0.315284	−	1.99063i
$476$		0			0
$477$	7.60659	+	23.4107i	0.348282	+	1.07190i
$478$		0			0
$479$	3.26761	+	0.517538i	0.149301	+	0.0236469i	0.230637	−	0.973040i	$-0.425919\pi$
$479$	3.26761	+	0.517538i	0.149301	+	0.0236469i	−0.0813367	+	0.996687i	$0.525919\pi$
$480$		0			0
$481$	17.6313	−	21.1972i	0.803920	−	0.966508i
$482$		0			0
$483$	−3.29471	+	3.29471i	−0.149914	+	0.149914i
$484$		0			0
$485$			56.2722i			2.55519i
$486$		0			0
$487$	25.6486	−	13.0686i	1.16225	−	0.592196i	0.236984	−	0.971514i	$-0.423841\pi$
$487$	25.6486	−	13.0686i	1.16225	−	0.592196i	0.925267	+	0.379317i	$0.123841\pi$
$488$		0			0
$489$	0.942487	−	5.95063i	0.0426207	−	0.269097i
$490$		0			0
$491$	3.25786	+	10.0267i	0.147025	+	0.452497i	0.997266	−	0.0738970i	$-0.0235436\pi$
$491$	3.25786	+	10.0267i	0.147025	+	0.452497i	−0.850241	+	0.526394i	$0.823544\pi$
$492$		0			0
$493$	−7.35318	+	10.1208i	−0.331171	+	0.455817i
$494$		0			0
$495$	8.34742	−	38.8627i	0.375189	−	1.74675i
$496$		0			0
$497$	−4.24599	+	5.84411i	−0.190459	+	0.262144i
$498$		0			0
$499$	3.75218	−	7.36407i	0.167971	−	0.329661i	−0.791642	−	0.610985i	$-0.790774\pi$
$499$	3.75218	−	7.36407i	0.167971	−	0.329661i	0.959613	+	0.281324i	$0.0907736\pi$
$500$		0			0
$501$	−5.56908	−	0.882056i	−0.248808	−	0.0394074i
$502$		0			0
$503$	−19.2095	−	6.24154i	−0.856508	−	0.278296i	−0.152339	−	0.988328i	$-0.548680\pi$
$503$	−19.2095	−	6.24154i	−0.856508	−	0.278296i	−0.704169	+	0.710032i	$0.748680\pi$
$504$		0			0
$505$	9.66762	+	9.66762i	0.430204	+	0.430204i
$506$		0			0
$507$	22.5022	−	23.7075i	0.999360	−	1.05289i
$508$		0			0
$509$	22.8333	−	11.6342i	1.01207	−	0.515675i	0.132367	−	0.991201i	$-0.457742\pi$
$509$	22.8333	−	11.6342i	1.01207	−	0.515675i	0.879702	+	0.475526i	$0.157742\pi$
$510$		0			0
$511$	6.34441	+	8.73234i	0.280660	+	0.386296i
$512$		0			0
$513$	−3.95119	−	2.01323i	−0.174449	−	0.0888864i
$514$		0			0
$515$	61.6556	−	9.76528i	2.71687	−	0.430310i
$516$		0			0
$517$	−2.98854	+	5.15084i	−0.131436	+	0.226534i
$518$		0			0
$519$	−0.583979	−	0.424285i	−0.0256338	−	0.0186241i
$520$		0			0
$521$	8.09010	+	24.8988i	0.354434	+	1.09083i	0.956337	+	0.292266i	$0.0944091\pi$
$521$	8.09010	+	24.8988i	0.354434	+	1.09083i	−0.601904	+	0.798569i	$0.705591\pi$
$522$		0			0
$523$	3.99774	+	5.50242i	0.174809	+	0.240604i	0.887427	−	0.460948i	$-0.152491\pi$
$523$	3.99774	+	5.50242i	0.174809	+	0.240604i	−0.712618	+	0.701552i	$0.752491\pi$
$524$		0			0
$525$	−7.51644	−	14.7518i	−0.328044	−	0.643823i
$526$		0			0
$527$	45.0403	+	45.0403i	1.96199	+	1.96199i
$528$		0			0
$529$	17.9102			0.778704
$530$		0			0
$531$	−7.37518	−	14.4746i	−0.320056	−	0.628145i
$532$		0			0
$533$	12.0802	−	3.06733i	0.523253	−	0.132861i
$534$		0			0
$535$	0.506842	+	0.258249i	0.0219127	+	0.0111651i
$536$		0			0
$537$	−23.7535	+	32.6940i	−1.02504	+	1.41085i
$538$		0			0
$539$	−7.55993	+	19.5691i	−0.325629	+	0.842901i
$540$		0			0
$541$	3.51520	+	22.1941i	0.151130	+	0.954199i	0.940380	+	0.340126i	$0.110470\pi$
$541$	3.51520	+	22.1941i	0.151130	+	0.954199i	−0.789249	+	0.614073i	$0.789530\pi$
$542$		0			0
$543$	9.41580	−	3.05938i	0.404071	−	0.131291i
$544$		0			0
$545$	31.4920	−	22.8803i	1.34897	−	0.980083i
$546$		0			0
$547$	−38.2397	−	12.4248i	−1.63501	−	0.531247i	−0.659596	−	0.751620i	$-0.729273\pi$
$547$	−38.2397	−	12.4248i	−1.63501	−	0.531247i	−0.975416	+	0.220373i	$0.929273\pi$
$548$		0			0
$549$		−	6.55862i		−	0.279915i
$550$		0			0
$551$	6.44062	+	6.44062i	0.274380	+	0.274380i
$552$		0			0
$553$	2.15046	+	4.22053i	0.0914471	+	0.179475i
$554$		0			0
$555$	56.1197	−	40.7734i	2.38215	−	1.73073i
$556$		0			0
$557$	11.4346	−	22.4417i	0.484500	−	0.950885i	−0.511306	−	0.859399i	$-0.670838\pi$
$557$	11.4346	−	22.4417i	0.484500	−	0.950885i	0.995806	−	0.0914863i	$-0.0291618\pi$
$558$		0			0
$559$	6.76810	−	29.9035i	0.286260	−	1.26478i
$560$		0			0
$561$	−39.5988	+	48.6872i	−1.67186	+	2.05557i
$562$		0			0
$563$	−16.3790	−	11.9000i	−0.690293	−	0.501527i	0.186464	−	0.982462i	$-0.440297\pi$
$563$	−16.3790	−	11.9000i	−0.690293	−	0.501527i	−0.876756	+	0.480935i	$0.840297\pi$
$564$		0			0
$565$	−18.6190	+	36.5418i	−0.783306	+	1.53733i
$566$		0			0
$567$	6.43417	+	1.01907i	0.270210	+	0.0427970i
$568$		0			0
$569$	9.48954	−	29.2058i	0.397822	−	1.22437i	−0.528920	−	0.848672i	$-0.677403\pi$
$569$	9.48954	−	29.2058i	0.397822	−	1.22437i	0.926742	−	0.375699i	$-0.122597\pi$
$570$		0			0
$571$	−3.50535			−0.146694			−0.0733471	−	0.997306i	$-0.523368\pi$
$571$	−3.50535			−0.146694			−0.0733471	+	0.997306i	$0.523368\pi$
$572$		0			0
$573$	−1.21015			−0.0505547
$574$		0			0
$575$	5.58879	−	17.2005i	0.233069	−	0.717311i
$576$		0			0
$577$	8.61980	+	1.36524i	0.358847	+	0.0568358i	0.333255	−	0.942837i	$-0.391853\pi$
$577$	8.61980	+	1.36524i	0.358847	+	0.0568358i	0.0255919	+	0.999672i	$0.491853\pi$
$578$		0			0
$579$	−19.4152	+	38.1045i	−0.806868	+	1.58357i
$580$		0			0
$581$	0.566986	+	0.411939i	0.0235225	+	0.0170901i
$582$		0			0
$583$	1.33871	−	24.5400i	0.0554438	−	1.01634i
$584$		0			0
$585$	36.5466	−	23.0566i	1.51102	−	0.953272i
$586$		0			0
$587$	−10.6371	+	20.8765i	−0.439040	+	0.861665i	0.560400	+	0.828222i	$0.310647\pi$
$587$	−10.6371	+	20.8765i	−0.439040	+	0.861665i	−0.999441	+	0.0334433i	$0.989353\pi$
$588$		0			0
$589$	37.5198	−	27.2597i	1.54598	−	1.12322i
$590$		0			0
$591$	12.9928	+	25.4998i	0.534453	+	1.04892i
$592$		0			0
$593$	−17.3077	−	17.3077i	−0.710744	−	0.710744i	0.255947	−	0.966691i	$-0.417613\pi$
$593$	−17.3077	−	17.3077i	−0.710744	−	0.710744i	−0.966691	+	0.255947i	$0.917613\pi$
$594$		0			0
$595$			22.3024i			0.914308i
$596$		0			0
$597$	9.87826	+	3.20964i	0.404290	+	0.131362i
$598$		0			0
$599$	18.2135	−	13.2329i	0.744182	−	0.540680i	−0.149836	−	0.988711i	$-0.547875\pi$
$599$	18.2135	−	13.2329i	0.744182	−	0.540680i	0.894018	+	0.448031i	$0.147875\pi$
$600$		0			0
$601$	−38.2012	+	12.4123i	−1.55826	+	0.506309i	−0.956342	−	0.292250i	$-0.905596\pi$
$601$	−38.2012	+	12.4123i	−1.55826	+	0.506309i	−0.601917	+	0.798559i	$0.705596\pi$
$602$		0			0
$603$	7.47263	+	47.1803i	0.304309	+	1.92133i
$604$		0			0
$605$	−21.7568	+	33.1909i	−0.884540	+	1.34940i
$606$		0			0
$607$	−4.44092	+	6.11240i	−0.180251	+	0.248095i	−0.889576	−	0.456787i	$-0.849000\pi$
$607$	−4.44092	+	6.11240i	−0.180251	+	0.248095i	0.709325	+	0.704882i	$0.249000\pi$
$608$		0			0
$609$	3.05895	+	1.55861i	0.123955	+	0.0631582i
$610$		0			0
$611$	−6.27470	+	1.59323i	−0.253847	+	0.0644551i
$612$		0			0
$613$	14.0160	+	27.5080i	0.566101	+	1.11104i	0.979680	+	0.200568i	$0.0642787\pi$
$613$	14.0160	+	27.5080i	0.566101	+	1.11104i	−0.413579	+	0.910468i	$0.635721\pi$
$614$		0			0
$615$	31.3575			1.26446
$616$		0			0
$617$	−17.2219	−	17.2219i	−0.693328	−	0.693328i	0.269635	−	0.962963i	$-0.413097\pi$
$617$	−17.2219	−	17.2219i	−0.693328	−	0.693328i	−0.962963	+	0.269635i	$0.913097\pi$
$618$		0			0
$619$	−8.31943	−	16.3278i	−0.334386	−	0.656270i	0.661191	−	0.750218i	$-0.270051\pi$
$619$	−8.31943	−	16.3278i	−0.334386	−	0.656270i	−0.995577	+	0.0939477i	$0.970051\pi$
$620$		0			0
$621$	−1.07321	−	1.47715i	−0.0430664	−	0.0592759i
$622$		0			0
$623$	1.53966	+	4.73860i	0.0616854	+	0.189848i
$624$		0			0
$625$	−0.662040	−	0.481000i	−0.0264816	−	0.0192400i
$626$		0			0
$627$	30.5020	+	34.0220i	1.21813	+	1.35871i
$628$		0			0
$629$	−56.8400	+	9.00257i	−2.26636	+	0.358956i
$630$		0			0
$631$	−13.8605	−	7.06227i	−0.551777	−	0.281144i	0.155791	−	0.987790i	$-0.450207\pi$
$631$	−13.8605	−	7.06227i	−0.551777	−	0.281144i	−0.707568	+	0.706646i	$0.750207\pi$
$632$		0			0
$633$	−12.0657	−	16.6070i	−0.479569	−	0.660071i
$634$		0			0
$635$	37.5634	−	19.1395i	1.49066	−	0.759529i
$636$		0			0
$637$	−20.9546	+	9.00152i	−0.830250	+	0.356653i
$638$		0			0
$639$	−20.6572	−	20.6572i	−0.817187	−	0.817187i
$640$		0			0
$641$	−19.3488	−	6.28680i	−0.764231	−	0.248314i	−0.0991376	−	0.995074i	$-0.531608\pi$
$641$	−19.3488	−	6.28680i	−0.764231	−	0.248314i	−0.665094	+	0.746760i	$0.731608\pi$
$642$		0			0
$643$	39.6885	+	6.28604i	1.56516	+	0.247897i	0.878019	−	0.478626i	$-0.158865\pi$
$643$	39.6885	+	6.28604i	1.56516	+	0.247897i	0.687142	+	0.726523i	$0.258865\pi$
$644$		0			0
$645$	35.0200	−	68.7305i	1.37891	−	2.70626i
$646$		0			0
$647$	17.0922	−	23.5254i	0.671964	−	0.924879i	−0.327839	−	0.944734i	$-0.606320\pi$
$647$	17.0922	−	23.5254i	0.671964	−	0.924879i	0.999803	+	0.0198549i	$0.00632044\pi$
$648$		0			0
$649$	1.66091	+	16.1343i	0.0651963	+	0.633326i
$650$		0			0
$651$	10.2747	−	14.1419i	0.402698	−	0.554266i
$652$		0			0
$653$	−3.59134	−	11.0530i	−0.140540	−	0.432538i	0.855870	−	0.517190i	$-0.173022\pi$
$653$	−3.59134	−	11.0530i	−0.140540	−	0.432538i	−0.996411	+	0.0846524i	$0.973022\pi$
$654$		0			0
$655$	7.83251	−	49.4525i	0.306042	−	1.93227i
$656$		0			0
$657$	−38.8937	+	19.8173i	−1.51739	+	0.773148i
$658$		0			0
$659$		−	43.8342i		−	1.70754i	−0.520652	−	0.853769i	$-0.674311\pi$
$659$		−	43.8342i		−	1.70754i	0.520652	−	0.853769i	$-0.325689\pi$
$660$		0			0
$661$	19.2496	−	19.2496i	0.748724	−	0.748724i	−0.225516	−	0.974239i	$-0.572407\pi$
$661$	19.2496	−	19.2496i	0.748724	−	0.748724i	0.974239	+	0.225516i	$0.0724068\pi$
$662$		0			0
$663$	−67.9387	+	6.23916i	−2.63852	+	0.242309i
$664$		0			0
$665$	16.0383	+	2.54021i	0.621937	+	0.0985051i
$666$		0			0
$667$	1.15889	+	3.56671i	0.0448726	+	0.138104i
$668$		0			0
$669$	−6.29744	−	39.7605i	−0.243473	−	1.53723i
$670$		0			0
$671$	−2.35975	+	6.10829i	−0.0910971	+	0.235808i
$672$		0			0
$673$	5.70258	+	4.14317i	0.219818	+	0.159707i	0.692245	−	0.721663i	$-0.256622\pi$
$673$	5.70258	+	4.14317i	0.219818	+	0.159707i	−0.472427	+	0.881370i	$0.656622\pi$
$674$		0			0
$675$	6.17029	−	2.00485i	0.237495	−	0.0771667i
$676$		0			0
$677$	−4.08432	−	5.62159i	−0.156973	−	0.216055i	0.723285	−	0.690549i	$-0.242631\pi$
$677$	−4.08432	−	5.62159i	−0.156973	−	0.216055i	−0.880259	+	0.474494i	$0.842631\pi$
$678$		0			0
$679$	−12.1846	−	3.95902i	−0.467602	−	0.151933i
$680$		0			0
$681$	45.6961	−	45.6961i	1.75108	−	1.75108i
$682$		0			0
$683$	−17.6078	+	17.6078i	−0.673744	+	0.673744i	−0.958577	−	0.284833i	$-0.908062\pi$
$683$	−17.6078	+	17.6078i	−0.673744	+	0.673744i	0.284833	+	0.958577i	$0.408062\pi$
$684$		0			0
$685$	−4.99874	+	15.3845i	−0.190992	+	0.587813i
$686$		0			0
$687$	−7.69371	+	48.5762i	−0.293533	+	1.85330i
$688$		0			0
$689$	20.0882	−	17.6150i	0.765298	−	0.671079i
$690$		0			0
$691$	−1.77650	−	11.2164i	−0.0675812	−	0.426691i	−0.998162	−	0.0606041i	$-0.980697\pi$
$691$	−1.77650	−	11.2164i	−0.0675812	−	0.426691i	0.930581	−	0.366087i	$-0.119303\pi$
$692$		0			0
$693$	7.82764	+	4.54164i	0.297348	+	0.172523i
$694$		0			0
$695$	−24.6023	+	3.89662i	−0.933218	+	0.147807i
$696$		0			0
$697$	−23.1792	−	11.8104i	−0.877974	−	0.447350i
$698$		0			0
$699$	52.3950	−	38.0672i	1.98176	−	1.43983i
$700$		0			0
$701$	−6.58370	+	20.2625i	−0.248663	+	0.765306i	0.746349	+	0.665554i	$0.231805\pi$
$701$	−6.58370	+	20.2625i	−0.248663	+	0.765306i	−0.995012	+	0.0997515i	$0.968195\pi$
$702$		0			0
$703$			41.9006i			1.58031i
$704$		0			0
$705$	−16.2877			−0.613429
$706$		0			0
$707$	−2.77349	+	1.41316i	−0.104308	+	0.0531475i
$708$		0			0
$709$	3.43258	−	21.6724i	0.128913	−	0.813925i	−0.835493	−	0.549501i	$-0.814818\pi$
$709$	3.43258	−	21.6724i	0.128913	−	0.813925i	0.964406	−	0.264425i	$-0.0851820\pi$
$710$		0			0
$711$	−18.2187	+	5.91962i	−0.683255	+	0.222003i
$712$		0			0
$713$	18.8600	−	2.98713i	0.706312	−	0.111869i
$714$		0			0
$715$	−42.3328	+	8.32419i	−1.58316	+	0.311307i
$716$		0			0
$717$	−8.80485	+	1.39455i	−0.328823	+	0.0520804i
$718$		0			0
$719$	22.4766	−	7.30310i	0.838237	−	0.272360i	0.141726	−	0.989906i	$-0.454735\pi$
$719$	22.4766	−	7.30310i	0.838237	−	0.272360i	0.696511	+	0.717546i	$0.254735\pi$
$720$		0			0
$721$	−2.22329	+	14.0373i	−0.0827996	+	0.522776i
$722$		0			0
$723$	10.9291	−	5.56866i	0.406458	−	0.207101i
$724$		0			0
$725$	−13.3258			−0.494910
$726$		0			0
$727$		−	20.7626i		−	0.770042i	−0.922908	−	0.385021i	$-0.874194\pi$
$727$		−	20.7626i		−	0.770042i	0.922908	−	0.385021i	$-0.125806\pi$
$728$		0			0
$729$	−10.0275	+	30.8614i	−0.371389	+	1.14302i
$730$		0			0
$731$	−51.7729	+	37.6152i	−1.91489	+	1.39125i
$732$		0			0
$733$	37.6445	+	19.1808i	1.39043	+	0.708461i	0.979167	−	0.203055i	$-0.0650871\pi$
$733$	37.6445	+	19.1808i	1.39043	+	0.708461i	0.411265	+	0.911516i	$0.365087\pi$
$734$		0			0
$735$	−56.6723	+	8.97600i	−2.09039	+	0.331085i
$736$		0			0
$737$	10.0156	−	46.6294i	0.368931	−	1.71762i
$738$		0			0
$739$	−0.352312	−	2.22441i	−0.0129600	−	0.0818263i	0.980361	−	0.197213i	$-0.0631892\pi$
$739$	−0.352312	−	2.22441i	−0.0129600	−	0.0818263i	−0.993321	+	0.115387i	$0.963189\pi$
$740$		0			0
$741$	−3.25137	+	49.5672i	−0.119442	+	1.82090i
$742$		0			0
$743$	−7.87523	+	49.7223i	−0.288914	+	1.82413i	0.234572	+	0.972099i	$0.424631\pi$
$743$	−7.87523	+	49.7223i	−0.288914	+	1.82413i	−0.523487	+	0.852034i	$0.675369\pi$
$744$		0			0
$745$	−6.69133	+	20.5938i	−0.245151	+	0.754498i
$746$		0			0
$747$	−2.00413	+	2.00413i	−0.0733272	+	0.0733272i
$748$		0			0
$749$	−0.0915773	+	0.0915773i	−0.00334616	+	0.00334616i
$750$		0			0
$751$	−9.46276	−	3.07464i	−0.345301	−	0.112195i	0.131232	−	0.991352i	$-0.458107\pi$
$751$	−9.46276	−	3.07464i	−0.345301	−	0.112195i	−0.476533	+	0.879157i	$0.658107\pi$
$752$		0			0
$753$	5.85355	+	8.05672i	0.213315	+	0.293603i
$754$		0			0
$755$	30.5376	−	9.92226i	1.11138	−	0.361108i
$756$		0			0
$757$	−13.7901	−	10.0191i	−0.501211	−	0.364151i	0.308268	−	0.951300i	$-0.400251\pi$
$757$	−13.7901	−	10.0191i	−0.501211	−	0.364151i	−0.809480	+	0.587148i	$0.800251\pi$
$758$		0			0
$759$	4.83043	+	18.1828i	0.175334	+	0.659996i
$760$		0			0
$761$	3.36684	+	21.2574i	0.122048	+	0.770579i	0.970463	+	0.241248i	$0.0775569\pi$
$761$	3.36684	+	21.2574i	0.122048	+	0.770579i	−0.848416	+	0.529331i	$0.822443\pi$
$762$		0			0
$763$	2.73865	+	8.42868i	0.0991456	+	0.305139i
$764$		0			0
$765$	−89.0834	−	14.1094i	−3.22082	−	0.510127i
$766$		0			0
$767$	−11.2756	+	13.5560i	−0.407139	+	0.489480i
$768$		0			0
$769$	−34.9013	+	34.9013i	−1.25857	+	1.25857i	−0.306801	+	0.951774i	$0.599259\pi$
$769$	−34.9013	+	34.9013i	−1.25857	+	1.25857i	−0.951774	+	0.306801i	$0.900741\pi$
$770$		0			0
$771$		−	49.6629i		−	1.78857i
$772$		0			0
$773$	−4.68269	+	2.38595i	−0.168425	+	0.0858166i	−0.536171	−	0.844110i	$-0.680130\pi$
$773$	−4.68269	+	2.38595i	−0.168425	+	0.0858166i	0.367746	+	0.929926i	$0.380130\pi$
$774$		0			0
$775$	−10.6142	+	67.0154i	−0.381273	+	2.40726i
$776$		0			0
$777$	4.88035	+	15.0202i	0.175082	+	0.538846i
$778$		0			0
$779$	−11.1332	+	15.3236i	−0.398890	+	0.549025i
$780$		0			0
$781$	11.8065	+	26.6712i	0.422469	+	0.954369i
$782$		0			0
$783$	−0.790759	+	1.08839i	−0.0282594	+	0.0388958i
$784$		0			0
$785$	6.50228	−	12.7615i	0.232076	−	0.455476i
$786$		0			0
$787$	7.70458	+	1.22029i	0.274639	+	0.0434985i	0.292234	−	0.956347i	$-0.405601\pi$
$787$	7.70458	+	1.22029i	0.274639	+	0.0434985i	−0.0175959	+	0.999845i	$0.505601\pi$
$788$		0			0
$789$	−3.54401	−	1.15152i	−0.126170	−	0.0409951i
$790$		0			0
$791$	−6.60245	−	6.60245i	−0.234756	−	0.234756i
$792$		0			0
$793$	−6.54074	+	2.80973i	−0.232269	+	0.0997763i
$794$		0			0
$795$	59.8928	−	30.5169i	2.12418	−	1.08232i
$796$		0			0
$797$	−12.5440	−	17.2653i	−0.444331	−	0.611570i	0.526836	−	0.849967i	$-0.323378\pi$
$797$	−12.5440	−	17.2653i	−0.444331	−	0.611570i	−0.971168	+	0.238397i	$0.923378\pi$
$798$		0			0
$799$	12.0397	+	6.13453i	0.425934	+	0.217024i
$800$		0			0
$801$	−19.9017	+	3.15212i	−0.703191	+	0.111375i
$802$		0			0
$803$	43.3533	−	4.46291i	1.52991	−	0.157493i
$804$		0			0
$805$	5.40895	+	3.92984i	0.190641	+	0.138509i
$806$		0			0
$807$	−21.9589	−	67.5826i	−0.772990	−	2.37902i
$808$		0			0
$809$	−17.0329	−	23.4438i	−0.598845	−	0.824240i	0.396757	−	0.917924i	$-0.370136\pi$
$809$	−17.0329	−	23.4438i	−0.598845	−	0.824240i	−0.995602	+	0.0936839i	$0.970136\pi$
$810$		0			0
$811$	−14.3117	−	28.0883i	−0.502552	−	0.986315i	−0.993360	−	0.115047i	$-0.963298\pi$
$811$	−14.3117	−	28.0883i	−0.502552	−	0.986315i	0.490808	−	0.871268i	$-0.336702\pi$
$812$		0			0
$813$	36.3520	+	36.3520i	1.27492	+	1.27492i
$814$		0			0
$815$	−8.64503			−0.302822
$816$		0			0
$817$	21.1533	+	41.5157i	0.740060	+	1.45245i
$818$		0			0
$819$	2.42120	+	9.53556i	0.0846036	+	0.333199i
$820$		0			0
$821$	−2.96815	−	1.51235i	−0.103589	−	0.0527813i	0.401428	−	0.915891i	$-0.368514\pi$
$821$	−2.96815	−	1.51235i	−0.103589	−	0.0527813i	−0.505017	+	0.863109i	$0.668514\pi$
$822$		0			0
$823$	−24.5845	+	33.8376i	−0.856960	+	1.17950i	0.125325	+	0.992116i	$0.460003\pi$
$823$	−24.5845	+	33.8376i	−0.856960	+	1.17950i	−0.982286	+	0.187389i	$0.939997\pi$
$824$		0			0
$825$	−66.7511	−	3.64142i	−2.32398	−	0.126778i
$826$		0			0
$827$	−0.540060	−	3.40980i	−0.0187797	−	0.118570i	0.976518	−	0.215438i	$-0.0691178\pi$
$827$	−0.540060	−	3.40980i	−0.0187797	−	0.118570i	−0.995297	+	0.0968672i	$0.969118\pi$
$828$		0			0
$829$	8.40269	−	2.73020i	0.291837	−	0.0948237i	−0.159439	−	0.987208i	$-0.550969\pi$
$829$	8.40269	−	2.73020i	0.291837	−	0.0948237i	0.451277	+	0.892384i	$0.350969\pi$
$830$		0			0
$831$	16.5549	−	12.0278i	0.574282	−	0.417241i
$832$		0			0
$833$	45.2723	+	14.7099i	1.56859	+	0.509667i
$834$		0			0
$835$			8.09073i			0.279991i
$836$		0			0
$837$	4.84362	+	4.84362i	0.167420	+	0.167420i
$838$		0			0
$839$	1.99887	+	3.92300i	0.0690086	+	0.135437i	0.922934	−	0.384959i	$-0.125784\pi$
$839$	1.99887	+	3.92300i	0.0690086	+	0.135437i	−0.853925	+	0.520396i	$0.825784\pi$
$840$		0			0
$841$	−21.2260	+	15.4216i	−0.731930	+	0.531778i
$842$		0			0
$843$	−5.48273	+	10.7605i	−0.188835	+	0.370610i
$844$		0			0
$845$	−38.6503	−	26.5695i	−1.32961	−	0.914019i
$846$		0			0
$847$	−5.65612	−	7.04613i	−0.194347	−	0.242108i
$848$		0			0
$849$	65.1137	+	47.3079i	2.23470	+	1.62360i
$850$		0			0
$851$	−7.83223	+	15.3716i	−0.268485	+	0.526932i
$852$		0			0
$853$	6.65108	+	1.05343i	0.227729	+	0.0360687i	0.269256	−	0.963069i	$-0.413222\pi$
$853$	6.65108	+	1.05343i	0.227729	+	0.0360687i	−0.0415271	+	0.999137i	$0.513222\pi$
$854$		0			0
$855$	−20.2930	+	62.4553i	−0.694005	+	2.13593i
$856$		0			0
$857$	−3.59093			−0.122664			−0.0613319	−	0.998117i	$-0.519535\pi$
$857$	−3.59093			−0.122664			−0.0613319	+	0.998117i	$0.519535\pi$
$858$		0			0
$859$	−3.29492			−0.112421			−0.0562105	−	0.998419i	$-0.517902\pi$
$859$	−3.29492			−0.112421			−0.0562105	+	0.998419i	$0.517902\pi$
$860$		0			0
$861$	−2.20615	+	6.78982i	−0.0751852	+	0.231396i
$862$		0			0
$863$	37.1283	+	5.88055i	1.26386	+	0.200176i	0.752157	−	0.658984i	$-0.229014\pi$
$863$	37.1283	+	5.88055i	1.26386	+	0.200176i	0.511706	+	0.859161i	$0.329014\pi$
$864$		0			0
$865$	−0.470230	+	0.922877i	−0.0159883	+	0.0313788i
$866$		0			0
$867$	80.6250	+	58.5775i	2.73817	+	1.98940i
$868$		0			0
$869$	19.0976	+	1.04182i	0.647842	+	0.0353412i
$870$		0			0
$871$	43.8504	−	27.6644i	1.48582	−	0.937373i
$872$		0			0
$873$	23.5222	−	46.1649i	0.796105	−	1.56244i
$874$		0			0
$875$	−7.23210	+	5.25443i	−0.244490	+	0.177632i
$876$		0			0
$877$	−13.3382	−	26.1776i	−0.450398	−	0.883956i	−0.998858	−	0.0477793i	$-0.984786\pi$
$877$	−13.3382	−	26.1776i	−0.450398	−	0.883956i	0.548460	−	0.836177i	$-0.315214\pi$
$878$		0			0
$879$	−52.6790	−	52.6790i	−1.77682	−	1.77682i
$880$		0			0
$881$			20.4628i			0.689408i	0.938711	+	0.344704i	$0.112021\pi$
$881$			20.4628i			0.689408i	−0.938711	+	0.344704i	$0.887979\pi$
$882$		0			0
$883$	21.3807	+	6.94701i	0.719518	+	0.233786i	0.645814	−	0.763495i	$-0.276518\pi$
$883$	21.3807	+	6.94701i	0.719518	+	0.233786i	0.0737037	+	0.997280i	$0.476518\pi$
$884$		0			0
$885$	−35.8897	+	26.0754i	−1.20642	+	0.876515i
$886$		0			0
$887$	−56.2779	+	18.2858i	−1.88963	+	0.613977i	−0.909467	+	0.415777i	$0.863510\pi$
$887$	−56.2779	+	18.2858i	−1.88963	+	0.613977i	−0.980162	+	0.198200i	$0.936490\pi$
$888$		0			0
$889$	1.50151	+	9.48015i	0.0503590	+	0.317954i
$890$		0			0
$891$	16.5969	−	20.4061i	0.556017	−	0.683630i
$892$		0			0
$893$	5.78282	−	7.95937i	0.193515	−	0.266350i
$894$		0			0
$895$	51.6672	+	26.3257i	1.72704	+	0.879972i
$896$		0			0
$897$	−10.4581	+	17.5764i	−0.349186	+	0.586860i
$898$		0			0
$899$	−6.38745	−	12.5361i	−0.213033	−	0.418102i
$900$		0			0
$901$	−55.7660			−1.85784
$902$		0			0
$903$	12.4184	+	12.4184i	0.413258	+	0.413258i
$904$		0			0
$905$	−6.44944	−	12.6577i	−0.214386	−	0.420757i
$906$		0			0
$907$	4.74010	+	6.52419i	0.157392	+	0.216632i	0.880429	−	0.474177i	$-0.157254\pi$
$907$	4.74010	+	6.52419i	0.157392	+	0.216632i	−0.723037	+	0.690809i	$0.757254\pi$
$908$		0			0
$909$	−3.89004	−	11.9723i	−0.129024	−	0.397096i
$910$		0			0
$911$	32.5725	+	23.6653i	1.07918	+	0.784067i	0.977539	−	0.210755i	$-0.0675922\pi$
$911$	32.5725	+	23.6653i	1.07918	+	0.784067i	0.101636	+	0.994822i	$0.467592\pi$
$912$		0			0
$913$	2.58759	−	1.14545i	0.0856367	−	0.0379087i
$914$		0			0
$915$	−17.6896	+	2.80176i	−0.584801	+	0.0926234i
$916$		0			0
$917$	10.1569	+	5.17519i	0.335410	+	0.170900i
$918$		0			0
$919$	9.37751	+	12.9070i	0.309336	+	0.425764i	0.935174	−	0.354189i	$-0.115243\pi$
$919$	9.37751	+	12.9070i	0.309336	+	0.425764i	−0.625838	+	0.779953i	$0.715243\pi$
$920$		0			0
$921$	−18.4768	+	9.41438i	−0.608830	+	0.310215i
$922$		0			0
$923$	−11.7513	+	29.4505i	−0.386799	+	0.969374i
$924$		0			0
$925$	−43.3468	−	43.3468i	−1.42523	−	1.42523i
$926$		0			0
$927$	−54.6633	−	17.7612i	−1.79538	−	0.583353i
$928$		0			0
$929$	15.3726	+	2.43478i	0.504358	+	0.0798825i	0.403429	−	0.915011i	$-0.367818\pi$
$929$	15.3726	+	2.43478i	0.504358	+	0.0798825i	0.100930	+	0.994894i	$0.467818\pi$
$930$		0			0
$931$	15.7347	−	30.8812i	0.515685	−	1.01209i
$932$		0			0
$933$	2.29443	−	3.15802i	0.0751164	−	0.103389i
$934$		0			0
$935$	77.8901	+	45.1922i	2.54728	+	1.47794i
$936$		0			0
$937$	−13.8090	+	19.0064i	−0.451119	+	0.620913i	−0.972638	−	0.232328i	$-0.925366\pi$
$937$	−13.8090	+	19.0064i	−0.451119	+	0.620913i	0.521518	+	0.853240i	$0.325366\pi$
$938$		0			0
$939$	−4.55152	−	14.0081i	−0.148533	−	0.457138i
$940$		0			0
$941$	−8.70551	+	54.9644i	−0.283792	+	1.79179i	0.273918	+	0.961753i	$0.411680\pi$
$941$	−8.70551	+	54.9644i	−0.283792	+	1.79179i	−0.557710	+	0.830036i	$0.688320\pi$
$942$		0			0
$943$	−6.94869	+	3.54053i	−0.226280	+	0.115296i
$944$		0			0
$945$			2.39839i			0.0780196i
$946$		0			0
$947$	4.03451	−	4.03451i	0.131104	−	0.131104i	−0.638510	−	0.769614i	$-0.720449\pi$
$947$	4.03451	−	4.03451i	0.131104	−	0.131104i	0.769614	+	0.638510i	$0.220449\pi$
$948$		0			0
$949$	36.4255	+	30.2979i	1.18242	+	0.983512i
$950$		0			0
$951$	−0.464068	−	0.0735011i	−0.0150484	−	0.00238344i
$952$		0			0
$953$	8.85741	+	27.2603i	0.286920	+	0.883048i	0.985817	+	0.167826i	$0.0536745\pi$
$953$	8.85741	+	27.2603i	0.286920	+	0.883048i	−0.698897	+	0.715222i	$0.746325\pi$
$954$		0			0
$955$	0.271641	+	1.71507i	0.00879010	+	0.0554985i
$956$		0			0
$957$	11.6419	−	7.52498i	0.376329	−	0.243248i
$958$		0			0
$959$	−2.97952	−	2.16475i	−0.0962139	−	0.0699035i
$960$		0			0
$961$	−38.6486	+	12.5577i	−1.24673	+	0.405087i
$962$		0			0
$963$	−0.307856	−	0.423727i	−0.00992052	−	0.0136544i
$964$		0			0
$965$	58.3613	+	18.9627i	1.87872	+	0.610432i
$966$		0			0
$967$	−10.2261	+	10.2261i	−0.328850	+	0.328850i	−0.852149	−	0.523299i	$-0.824701\pi$
$967$	−10.2261	+	10.2261i	−0.328850	+	0.328850i	0.523299	+	0.852149i	$0.324701\pi$
$968$		0			0
$969$	73.3139	−	73.3139i	2.35518	−	2.35518i
$970$		0			0
$971$	−1.56691	+	4.82246i	−0.0502846	+	0.154760i	−0.973046	−	0.230612i	$-0.925927\pi$
$971$	−1.56691	+	4.82246i	−0.0502846	+	0.154760i	0.922761	+	0.385373i	$0.125927\pi$
$972$		0			0
$973$	0.887154	−	5.60127i	0.0284408	−	0.179568i
$974$		0			0
$975$	−47.9145	−	54.6417i	−1.53449	−	1.74993i
$976$		0			0
$977$	−8.68014	−	54.8042i	−0.277702	−	1.75334i	−0.593797	−	0.804615i	$-0.702372\pi$
$977$	−8.68014	−	54.8042i	−0.277702	−	1.75334i	0.316094	−	0.948728i	$-0.397628\pi$
$978$		0			0
$979$	19.6693	+	4.22481i	0.628633	+	0.135026i
$980$		0			0
$981$	−35.3997	+	5.60676i	−1.13022	+	0.179010i
$982$		0			0
$983$	20.2369	+	10.3112i	0.645458	+	0.328877i	0.745892	−	0.666066i	$-0.232023\pi$
$983$	20.2369	+	10.3112i	0.645458	+	0.328877i	−0.100434	+	0.994944i	$0.532023\pi$
$984$		0			0
$985$	33.2229	−	24.1379i	1.05857	−	0.769097i
$986$		0			0
$987$	1.14591	−	3.52676i	0.0364748	−	0.112258i
$988$		0			0
$989$			19.1845i			0.610030i
$990$		0			0
$991$	−38.4693			−1.22202			−0.611008	−	0.791624i	$-0.709236\pi$
$991$	−38.4693			−1.22202			−0.611008	+	0.791624i	$0.709236\pi$
$992$		0			0
$993$	−18.0597	+	9.20188i	−0.573107	+	0.292013i
$994$		0			0
$995$	2.33147	−	14.7203i	0.0739127	−	0.466666i
$996$		0			0
$997$	−50.2325	+	16.3215i	−1.59088	+	0.516908i	−0.964830	−	0.262874i	$-0.915330\pi$
$997$	−50.2325	+	16.3215i	−1.59088	+	0.516908i	−0.626050	+	0.779783i	$0.715330\pi$
$998$		0			0
$999$	−6.11256	+	0.968134i	−0.193393	+	0.0306304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.73.2	✓	112
11.8	odd	10	inner	572.2.bh.a.437.2	yes	112
13.5	odd	4	inner	572.2.bh.a.161.2	yes	112
143.96	even	20	inner	572.2.bh.a.525.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.73.2	✓	112	1.1	even	1	trivial
572.2.bh.a.161.2	yes	112	13.5	odd	4	inner
572.2.bh.a.437.2	yes	112	11.8	odd	10	inner
572.2.bh.a.525.2	yes	112	143.96	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.776972 + 2.39127i) q^{3} +(3.56342 + 0.564390i) q^{5} +(-0.372910 + 0.731878i) q^{7} +(-2.68746 - 1.95255i) q^{9} +O(q^{10})\)	\(q+(-0.776972 + 2.39127i) q^{3} +(3.56342 + 0.564390i) q^{5} +(-0.372910 + 0.731878i) q^{7} +(-2.68746 - 1.95255i) q^{9} +(1.80041 + 2.78541i) q^{11} +(-0.795917 + 3.51661i) q^{13} +(-4.11829 + 8.08260i) q^{15} +(6.08841 - 4.42349i) q^{17} +(-2.48759 - 4.88217i) q^{19} +(-1.46038 - 1.46038i) q^{21} -2.25606i q^{23} +(7.62414 + 2.47723i) q^{25} +(0.654746 - 0.475701i) q^{27} +(-1.58095 + 0.513680i) q^{29} +(1.32405 + 8.35969i) q^{31} +(-8.05955 + 2.14109i) q^{33} +(-1.74190 + 2.39752i) q^{35} +(-6.81348 - 3.47164i) q^{37} +(-7.79076 - 4.63556i) q^{39} +(-1.56934 - 3.08001i) q^{41} -8.50352 q^{43} +(-8.47453 - 8.47453i) q^{45} +(0.815146 + 1.59981i) q^{47} +(3.71791 + 5.11727i) q^{49} +(5.84725 + 17.9960i) q^{51} +(-5.99489 - 4.35554i) q^{53} +(4.84356 + 10.9417i) q^{55} +(13.6074 - 2.15520i) q^{57} +(4.35736 + 2.22018i) q^{59} +(1.16051 + 1.59730i) q^{61} +(2.43121 - 1.23876i) q^{63} +(-4.82092 + 12.0819i) q^{65} +(-10.1682 - 10.1682i) q^{67} +(5.39486 + 1.75290i) q^{69} +(8.68606 + 1.37574i) q^{71} +(5.96570 - 11.7084i) q^{73} +(-11.8475 + 16.3067i) q^{75} +(-2.70997 + 0.278972i) q^{77} +(3.38958 - 4.66536i) q^{79} +(-2.45074 - 7.54260i) q^{81} +(0.133472 - 0.842707i) q^{83} +(24.1921 - 12.3265i) q^{85} -4.17959i q^{87} +(4.28915 - 4.28915i) q^{89} +(-2.27692 - 1.89389i) q^{91} +(-21.0191 - 3.32909i) q^{93} +(-6.10888 - 18.8012i) q^{95} +(2.43994 + 15.4052i) q^{97} +(0.600133 - 11.0011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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